Properties

Label 8002.2.a.e.1.20
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.59889 q^{3} +1.00000 q^{4} -0.0810696 q^{5} +1.59889 q^{6} +5.11538 q^{7} -1.00000 q^{8} -0.443564 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.59889 q^{3} +1.00000 q^{4} -0.0810696 q^{5} +1.59889 q^{6} +5.11538 q^{7} -1.00000 q^{8} -0.443564 q^{9} +0.0810696 q^{10} +4.94702 q^{11} -1.59889 q^{12} -3.53828 q^{13} -5.11538 q^{14} +0.129621 q^{15} +1.00000 q^{16} +5.73321 q^{17} +0.443564 q^{18} +1.42100 q^{19} -0.0810696 q^{20} -8.17891 q^{21} -4.94702 q^{22} -2.13818 q^{23} +1.59889 q^{24} -4.99343 q^{25} +3.53828 q^{26} +5.50587 q^{27} +5.11538 q^{28} +6.74732 q^{29} -0.129621 q^{30} +5.77357 q^{31} -1.00000 q^{32} -7.90971 q^{33} -5.73321 q^{34} -0.414702 q^{35} -0.443564 q^{36} +2.01340 q^{37} -1.42100 q^{38} +5.65730 q^{39} +0.0810696 q^{40} -7.93357 q^{41} +8.17891 q^{42} +6.63296 q^{43} +4.94702 q^{44} +0.0359595 q^{45} +2.13818 q^{46} -11.4823 q^{47} -1.59889 q^{48} +19.1671 q^{49} +4.99343 q^{50} -9.16675 q^{51} -3.53828 q^{52} +12.6709 q^{53} -5.50587 q^{54} -0.401053 q^{55} -5.11538 q^{56} -2.27201 q^{57} -6.74732 q^{58} -9.53989 q^{59} +0.129621 q^{60} -1.60736 q^{61} -5.77357 q^{62} -2.26900 q^{63} +1.00000 q^{64} +0.286847 q^{65} +7.90971 q^{66} -7.66131 q^{67} +5.73321 q^{68} +3.41871 q^{69} +0.414702 q^{70} +2.18583 q^{71} +0.443564 q^{72} +10.2130 q^{73} -2.01340 q^{74} +7.98392 q^{75} +1.42100 q^{76} +25.3059 q^{77} -5.65730 q^{78} +5.27760 q^{79} -0.0810696 q^{80} -7.47256 q^{81} +7.93357 q^{82} +9.28936 q^{83} -8.17891 q^{84} -0.464789 q^{85} -6.63296 q^{86} -10.7882 q^{87} -4.94702 q^{88} +10.9623 q^{89} -0.0359595 q^{90} -18.0996 q^{91} -2.13818 q^{92} -9.23129 q^{93} +11.4823 q^{94} -0.115200 q^{95} +1.59889 q^{96} -3.18214 q^{97} -19.1671 q^{98} -2.19432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.59889 −0.923117 −0.461559 0.887110i \(-0.652710\pi\)
−0.461559 + 0.887110i \(0.652710\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0810696 −0.0362554 −0.0181277 0.999836i \(-0.505771\pi\)
−0.0181277 + 0.999836i \(0.505771\pi\)
\(6\) 1.59889 0.652742
\(7\) 5.11538 1.93343 0.966716 0.255852i \(-0.0823560\pi\)
0.966716 + 0.255852i \(0.0823560\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.443564 −0.147855
\(10\) 0.0810696 0.0256365
\(11\) 4.94702 1.49158 0.745791 0.666180i \(-0.232072\pi\)
0.745791 + 0.666180i \(0.232072\pi\)
\(12\) −1.59889 −0.461559
\(13\) −3.53828 −0.981342 −0.490671 0.871345i \(-0.663248\pi\)
−0.490671 + 0.871345i \(0.663248\pi\)
\(14\) −5.11538 −1.36714
\(15\) 0.129621 0.0334680
\(16\) 1.00000 0.250000
\(17\) 5.73321 1.39051 0.695254 0.718764i \(-0.255292\pi\)
0.695254 + 0.718764i \(0.255292\pi\)
\(18\) 0.443564 0.104549
\(19\) 1.42100 0.325999 0.163000 0.986626i \(-0.447883\pi\)
0.163000 + 0.986626i \(0.447883\pi\)
\(20\) −0.0810696 −0.0181277
\(21\) −8.17891 −1.78478
\(22\) −4.94702 −1.05471
\(23\) −2.13818 −0.445842 −0.222921 0.974837i \(-0.571559\pi\)
−0.222921 + 0.974837i \(0.571559\pi\)
\(24\) 1.59889 0.326371
\(25\) −4.99343 −0.998686
\(26\) 3.53828 0.693913
\(27\) 5.50587 1.05960
\(28\) 5.11538 0.966716
\(29\) 6.74732 1.25295 0.626473 0.779443i \(-0.284498\pi\)
0.626473 + 0.779443i \(0.284498\pi\)
\(30\) −0.129621 −0.0236655
\(31\) 5.77357 1.03696 0.518482 0.855088i \(-0.326497\pi\)
0.518482 + 0.855088i \(0.326497\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.90971 −1.37690
\(34\) −5.73321 −0.983238
\(35\) −0.414702 −0.0700974
\(36\) −0.443564 −0.0739273
\(37\) 2.01340 0.331001 0.165501 0.986210i \(-0.447076\pi\)
0.165501 + 0.986210i \(0.447076\pi\)
\(38\) −1.42100 −0.230516
\(39\) 5.65730 0.905893
\(40\) 0.0810696 0.0128182
\(41\) −7.93357 −1.23902 −0.619508 0.784991i \(-0.712668\pi\)
−0.619508 + 0.784991i \(0.712668\pi\)
\(42\) 8.17891 1.26203
\(43\) 6.63296 1.01152 0.505758 0.862675i \(-0.331213\pi\)
0.505758 + 0.862675i \(0.331213\pi\)
\(44\) 4.94702 0.745791
\(45\) 0.0359595 0.00536053
\(46\) 2.13818 0.315258
\(47\) −11.4823 −1.67487 −0.837433 0.546540i \(-0.815945\pi\)
−0.837433 + 0.546540i \(0.815945\pi\)
\(48\) −1.59889 −0.230779
\(49\) 19.1671 2.73816
\(50\) 4.99343 0.706177
\(51\) −9.16675 −1.28360
\(52\) −3.53828 −0.490671
\(53\) 12.6709 1.74048 0.870241 0.492626i \(-0.163963\pi\)
0.870241 + 0.492626i \(0.163963\pi\)
\(54\) −5.50587 −0.749253
\(55\) −0.401053 −0.0540779
\(56\) −5.11538 −0.683571
\(57\) −2.27201 −0.300936
\(58\) −6.74732 −0.885967
\(59\) −9.53989 −1.24199 −0.620994 0.783815i \(-0.713271\pi\)
−0.620994 + 0.783815i \(0.713271\pi\)
\(60\) 0.129621 0.0167340
\(61\) −1.60736 −0.205801 −0.102900 0.994692i \(-0.532812\pi\)
−0.102900 + 0.994692i \(0.532812\pi\)
\(62\) −5.77357 −0.733245
\(63\) −2.26900 −0.285867
\(64\) 1.00000 0.125000
\(65\) 0.286847 0.0355790
\(66\) 7.90971 0.973619
\(67\) −7.66131 −0.935978 −0.467989 0.883734i \(-0.655021\pi\)
−0.467989 + 0.883734i \(0.655021\pi\)
\(68\) 5.73321 0.695254
\(69\) 3.41871 0.411564
\(70\) 0.414702 0.0495664
\(71\) 2.18583 0.259410 0.129705 0.991553i \(-0.458597\pi\)
0.129705 + 0.991553i \(0.458597\pi\)
\(72\) 0.443564 0.0522745
\(73\) 10.2130 1.19534 0.597671 0.801742i \(-0.296093\pi\)
0.597671 + 0.801742i \(0.296093\pi\)
\(74\) −2.01340 −0.234053
\(75\) 7.98392 0.921904
\(76\) 1.42100 0.163000
\(77\) 25.3059 2.88387
\(78\) −5.65730 −0.640563
\(79\) 5.27760 0.593777 0.296888 0.954912i \(-0.404051\pi\)
0.296888 + 0.954912i \(0.404051\pi\)
\(80\) −0.0810696 −0.00906386
\(81\) −7.47256 −0.830285
\(82\) 7.93357 0.876116
\(83\) 9.28936 1.01964 0.509820 0.860281i \(-0.329712\pi\)
0.509820 + 0.860281i \(0.329712\pi\)
\(84\) −8.17891 −0.892392
\(85\) −0.464789 −0.0504135
\(86\) −6.63296 −0.715250
\(87\) −10.7882 −1.15662
\(88\) −4.94702 −0.527354
\(89\) 10.9623 1.16200 0.581002 0.813902i \(-0.302661\pi\)
0.581002 + 0.813902i \(0.302661\pi\)
\(90\) −0.0359595 −0.00379047
\(91\) −18.0996 −1.89736
\(92\) −2.13818 −0.222921
\(93\) −9.23129 −0.957240
\(94\) 11.4823 1.18431
\(95\) −0.115200 −0.0118193
\(96\) 1.59889 0.163186
\(97\) −3.18214 −0.323098 −0.161549 0.986865i \(-0.551649\pi\)
−0.161549 + 0.986865i \(0.551649\pi\)
\(98\) −19.1671 −1.93617
\(99\) −2.19432 −0.220537
\(100\) −4.99343 −0.499343
\(101\) 7.96263 0.792311 0.396156 0.918183i \(-0.370344\pi\)
0.396156 + 0.918183i \(0.370344\pi\)
\(102\) 9.16675 0.907644
\(103\) 6.91916 0.681765 0.340883 0.940106i \(-0.389274\pi\)
0.340883 + 0.940106i \(0.389274\pi\)
\(104\) 3.53828 0.346957
\(105\) 0.663061 0.0647081
\(106\) −12.6709 −1.23071
\(107\) 3.67855 0.355619 0.177810 0.984065i \(-0.443099\pi\)
0.177810 + 0.984065i \(0.443099\pi\)
\(108\) 5.50587 0.529802
\(109\) −10.0586 −0.963435 −0.481717 0.876327i \(-0.659987\pi\)
−0.481717 + 0.876327i \(0.659987\pi\)
\(110\) 0.401053 0.0382389
\(111\) −3.21920 −0.305553
\(112\) 5.11538 0.483358
\(113\) 9.08743 0.854873 0.427437 0.904045i \(-0.359417\pi\)
0.427437 + 0.904045i \(0.359417\pi\)
\(114\) 2.27201 0.212794
\(115\) 0.173342 0.0161642
\(116\) 6.74732 0.626473
\(117\) 1.56945 0.145096
\(118\) 9.53989 0.878218
\(119\) 29.3276 2.68845
\(120\) −0.129621 −0.0118327
\(121\) 13.4730 1.22482
\(122\) 1.60736 0.145523
\(123\) 12.6849 1.14376
\(124\) 5.77357 0.518482
\(125\) 0.810164 0.0724632
\(126\) 2.26900 0.202138
\(127\) 0.538264 0.0477632 0.0238816 0.999715i \(-0.492398\pi\)
0.0238816 + 0.999715i \(0.492398\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.6053 −0.933748
\(130\) −0.286847 −0.0251581
\(131\) 20.0788 1.75430 0.877148 0.480220i \(-0.159443\pi\)
0.877148 + 0.480220i \(0.159443\pi\)
\(132\) −7.90971 −0.688452
\(133\) 7.26895 0.630298
\(134\) 7.66131 0.661837
\(135\) −0.446358 −0.0384164
\(136\) −5.73321 −0.491619
\(137\) −15.8971 −1.35818 −0.679090 0.734055i \(-0.737626\pi\)
−0.679090 + 0.734055i \(0.737626\pi\)
\(138\) −3.41871 −0.291020
\(139\) −9.90742 −0.840336 −0.420168 0.907446i \(-0.638029\pi\)
−0.420168 + 0.907446i \(0.638029\pi\)
\(140\) −0.414702 −0.0350487
\(141\) 18.3589 1.54610
\(142\) −2.18583 −0.183431
\(143\) −17.5039 −1.46375
\(144\) −0.443564 −0.0369636
\(145\) −0.547003 −0.0454261
\(146\) −10.2130 −0.845234
\(147\) −30.6460 −2.52764
\(148\) 2.01340 0.165501
\(149\) 12.9827 1.06358 0.531792 0.846875i \(-0.321519\pi\)
0.531792 + 0.846875i \(0.321519\pi\)
\(150\) −7.98392 −0.651884
\(151\) −15.0873 −1.22779 −0.613895 0.789388i \(-0.710398\pi\)
−0.613895 + 0.789388i \(0.710398\pi\)
\(152\) −1.42100 −0.115258
\(153\) −2.54304 −0.205593
\(154\) −25.3059 −2.03920
\(155\) −0.468062 −0.0375956
\(156\) 5.65730 0.452947
\(157\) −4.03544 −0.322063 −0.161032 0.986949i \(-0.551482\pi\)
−0.161032 + 0.986949i \(0.551482\pi\)
\(158\) −5.27760 −0.419863
\(159\) −20.2593 −1.60667
\(160\) 0.0810696 0.00640912
\(161\) −10.9376 −0.862005
\(162\) 7.47256 0.587100
\(163\) −2.12563 −0.166492 −0.0832459 0.996529i \(-0.526529\pi\)
−0.0832459 + 0.996529i \(0.526529\pi\)
\(164\) −7.93357 −0.619508
\(165\) 0.641238 0.0499203
\(166\) −9.28936 −0.720994
\(167\) 11.1445 0.862386 0.431193 0.902260i \(-0.358093\pi\)
0.431193 + 0.902260i \(0.358093\pi\)
\(168\) 8.17891 0.631017
\(169\) −0.480591 −0.0369685
\(170\) 0.464789 0.0356477
\(171\) −0.630303 −0.0482005
\(172\) 6.63296 0.505758
\(173\) −19.7120 −1.49868 −0.749340 0.662186i \(-0.769629\pi\)
−0.749340 + 0.662186i \(0.769629\pi\)
\(174\) 10.7882 0.817851
\(175\) −25.5433 −1.93089
\(176\) 4.94702 0.372895
\(177\) 15.2532 1.14650
\(178\) −10.9623 −0.821661
\(179\) −9.17355 −0.685664 −0.342832 0.939397i \(-0.611386\pi\)
−0.342832 + 0.939397i \(0.611386\pi\)
\(180\) 0.0359595 0.00268027
\(181\) −13.3949 −0.995638 −0.497819 0.867281i \(-0.665866\pi\)
−0.497819 + 0.867281i \(0.665866\pi\)
\(182\) 18.0996 1.34163
\(183\) 2.56998 0.189978
\(184\) 2.13818 0.157629
\(185\) −0.163226 −0.0120006
\(186\) 9.23129 0.676871
\(187\) 28.3623 2.07406
\(188\) −11.4823 −0.837433
\(189\) 28.1646 2.04867
\(190\) 0.115200 0.00835747
\(191\) −21.7988 −1.57731 −0.788654 0.614837i \(-0.789222\pi\)
−0.788654 + 0.614837i \(0.789222\pi\)
\(192\) −1.59889 −0.115390
\(193\) 11.1587 0.803219 0.401610 0.915811i \(-0.368451\pi\)
0.401610 + 0.915811i \(0.368451\pi\)
\(194\) 3.18214 0.228465
\(195\) −0.458635 −0.0328436
\(196\) 19.1671 1.36908
\(197\) 6.63930 0.473031 0.236515 0.971628i \(-0.423995\pi\)
0.236515 + 0.971628i \(0.423995\pi\)
\(198\) 2.19432 0.155943
\(199\) 17.3870 1.23253 0.616266 0.787538i \(-0.288645\pi\)
0.616266 + 0.787538i \(0.288645\pi\)
\(200\) 4.99343 0.353089
\(201\) 12.2496 0.864018
\(202\) −7.96263 −0.560249
\(203\) 34.5151 2.42249
\(204\) −9.16675 −0.641801
\(205\) 0.643172 0.0449210
\(206\) −6.91916 −0.482081
\(207\) 0.948419 0.0659197
\(208\) −3.53828 −0.245335
\(209\) 7.02970 0.486255
\(210\) −0.663061 −0.0457556
\(211\) −14.0080 −0.964348 −0.482174 0.876075i \(-0.660153\pi\)
−0.482174 + 0.876075i \(0.660153\pi\)
\(212\) 12.6709 0.870241
\(213\) −3.49489 −0.239466
\(214\) −3.67855 −0.251461
\(215\) −0.537731 −0.0366730
\(216\) −5.50587 −0.374627
\(217\) 29.5340 2.00490
\(218\) 10.0586 0.681251
\(219\) −16.3294 −1.10344
\(220\) −0.401053 −0.0270390
\(221\) −20.2857 −1.36456
\(222\) 3.21920 0.216059
\(223\) −10.1595 −0.680331 −0.340165 0.940366i \(-0.610483\pi\)
−0.340165 + 0.940366i \(0.610483\pi\)
\(224\) −5.11538 −0.341786
\(225\) 2.21490 0.147660
\(226\) −9.08743 −0.604487
\(227\) −26.0019 −1.72581 −0.862905 0.505367i \(-0.831357\pi\)
−0.862905 + 0.505367i \(0.831357\pi\)
\(228\) −2.27201 −0.150468
\(229\) −8.17539 −0.540245 −0.270122 0.962826i \(-0.587064\pi\)
−0.270122 + 0.962826i \(0.587064\pi\)
\(230\) −0.173342 −0.0114298
\(231\) −40.4612 −2.66215
\(232\) −6.74732 −0.442983
\(233\) 4.98481 0.326566 0.163283 0.986579i \(-0.447792\pi\)
0.163283 + 0.986579i \(0.447792\pi\)
\(234\) −1.56945 −0.102598
\(235\) 0.930866 0.0607230
\(236\) −9.53989 −0.620994
\(237\) −8.43828 −0.548125
\(238\) −29.3276 −1.90102
\(239\) −28.5845 −1.84898 −0.924488 0.381211i \(-0.875507\pi\)
−0.924488 + 0.381211i \(0.875507\pi\)
\(240\) 0.129621 0.00836701
\(241\) 14.6289 0.942330 0.471165 0.882045i \(-0.343834\pi\)
0.471165 + 0.882045i \(0.343834\pi\)
\(242\) −13.4730 −0.866075
\(243\) −4.56982 −0.293154
\(244\) −1.60736 −0.102900
\(245\) −1.55387 −0.0992732
\(246\) −12.6849 −0.808758
\(247\) −5.02789 −0.319917
\(248\) −5.77357 −0.366622
\(249\) −14.8526 −0.941247
\(250\) −0.810164 −0.0512392
\(251\) 5.61535 0.354438 0.177219 0.984171i \(-0.443290\pi\)
0.177219 + 0.984171i \(0.443290\pi\)
\(252\) −2.26900 −0.142933
\(253\) −10.5776 −0.665009
\(254\) −0.538264 −0.0337737
\(255\) 0.743145 0.0465376
\(256\) 1.00000 0.0625000
\(257\) −24.8358 −1.54921 −0.774606 0.632444i \(-0.782052\pi\)
−0.774606 + 0.632444i \(0.782052\pi\)
\(258\) 10.6053 0.660260
\(259\) 10.2993 0.639969
\(260\) 0.286847 0.0177895
\(261\) −2.99287 −0.185254
\(262\) −20.0788 −1.24047
\(263\) 12.8171 0.790336 0.395168 0.918609i \(-0.370686\pi\)
0.395168 + 0.918609i \(0.370686\pi\)
\(264\) 7.90971 0.486809
\(265\) −1.02723 −0.0631020
\(266\) −7.26895 −0.445688
\(267\) −17.5275 −1.07267
\(268\) −7.66131 −0.467989
\(269\) 10.8805 0.663397 0.331699 0.943385i \(-0.392378\pi\)
0.331699 + 0.943385i \(0.392378\pi\)
\(270\) 0.446358 0.0271645
\(271\) −24.9074 −1.51302 −0.756508 0.653984i \(-0.773096\pi\)
−0.756508 + 0.653984i \(0.773096\pi\)
\(272\) 5.73321 0.347627
\(273\) 28.9393 1.75148
\(274\) 15.8971 0.960379
\(275\) −24.7026 −1.48962
\(276\) 3.41871 0.205782
\(277\) −16.4322 −0.987315 −0.493658 0.869656i \(-0.664340\pi\)
−0.493658 + 0.869656i \(0.664340\pi\)
\(278\) 9.90742 0.594208
\(279\) −2.56095 −0.153320
\(280\) 0.414702 0.0247832
\(281\) 27.7773 1.65706 0.828528 0.559948i \(-0.189179\pi\)
0.828528 + 0.559948i \(0.189179\pi\)
\(282\) −18.3589 −1.09326
\(283\) −3.96193 −0.235512 −0.117756 0.993043i \(-0.537570\pi\)
−0.117756 + 0.993043i \(0.537570\pi\)
\(284\) 2.18583 0.129705
\(285\) 0.184191 0.0109106
\(286\) 17.5039 1.03503
\(287\) −40.5832 −2.39555
\(288\) 0.443564 0.0261372
\(289\) 15.8697 0.933514
\(290\) 0.547003 0.0321211
\(291\) 5.08789 0.298257
\(292\) 10.2130 0.597671
\(293\) 0.996102 0.0581929 0.0290965 0.999577i \(-0.490737\pi\)
0.0290965 + 0.999577i \(0.490737\pi\)
\(294\) 30.6460 1.78731
\(295\) 0.773395 0.0450288
\(296\) −2.01340 −0.117027
\(297\) 27.2376 1.58049
\(298\) −12.9827 −0.752067
\(299\) 7.56548 0.437523
\(300\) 7.98392 0.460952
\(301\) 33.9301 1.95570
\(302\) 15.0873 0.868179
\(303\) −12.7313 −0.731396
\(304\) 1.42100 0.0814999
\(305\) 0.130308 0.00746140
\(306\) 2.54304 0.145376
\(307\) 15.1927 0.867091 0.433546 0.901132i \(-0.357262\pi\)
0.433546 + 0.901132i \(0.357262\pi\)
\(308\) 25.3059 1.44194
\(309\) −11.0629 −0.629349
\(310\) 0.468062 0.0265841
\(311\) 24.6107 1.39554 0.697772 0.716320i \(-0.254175\pi\)
0.697772 + 0.716320i \(0.254175\pi\)
\(312\) −5.65730 −0.320282
\(313\) 27.1636 1.53538 0.767689 0.640823i \(-0.221407\pi\)
0.767689 + 0.640823i \(0.221407\pi\)
\(314\) 4.03544 0.227733
\(315\) 0.183947 0.0103642
\(316\) 5.27760 0.296888
\(317\) 2.21758 0.124552 0.0622758 0.998059i \(-0.480164\pi\)
0.0622758 + 0.998059i \(0.480164\pi\)
\(318\) 20.2593 1.13609
\(319\) 33.3791 1.86887
\(320\) −0.0810696 −0.00453193
\(321\) −5.88159 −0.328278
\(322\) 10.9376 0.609529
\(323\) 8.14689 0.453305
\(324\) −7.47256 −0.415142
\(325\) 17.6681 0.980052
\(326\) 2.12563 0.117728
\(327\) 16.0825 0.889363
\(328\) 7.93357 0.438058
\(329\) −58.7363 −3.23824
\(330\) −0.641238 −0.0352990
\(331\) −35.5813 −1.95573 −0.977864 0.209243i \(-0.932900\pi\)
−0.977864 + 0.209243i \(0.932900\pi\)
\(332\) 9.28936 0.509820
\(333\) −0.893072 −0.0489400
\(334\) −11.1445 −0.609799
\(335\) 0.621100 0.0339343
\(336\) −8.17891 −0.446196
\(337\) −18.1041 −0.986191 −0.493095 0.869975i \(-0.664135\pi\)
−0.493095 + 0.869975i \(0.664135\pi\)
\(338\) 0.480591 0.0261407
\(339\) −14.5298 −0.789148
\(340\) −0.464789 −0.0252067
\(341\) 28.5620 1.54672
\(342\) 0.630303 0.0340829
\(343\) 62.2394 3.36061
\(344\) −6.63296 −0.357625
\(345\) −0.277153 −0.0149214
\(346\) 19.7120 1.05973
\(347\) −7.60352 −0.408178 −0.204089 0.978952i \(-0.565423\pi\)
−0.204089 + 0.978952i \(0.565423\pi\)
\(348\) −10.7882 −0.578308
\(349\) −20.0290 −1.07213 −0.536065 0.844177i \(-0.680090\pi\)
−0.536065 + 0.844177i \(0.680090\pi\)
\(350\) 25.5433 1.36535
\(351\) −19.4813 −1.03983
\(352\) −4.94702 −0.263677
\(353\) 18.7407 0.997465 0.498732 0.866756i \(-0.333799\pi\)
0.498732 + 0.866756i \(0.333799\pi\)
\(354\) −15.2532 −0.810698
\(355\) −0.177204 −0.00940503
\(356\) 10.9623 0.581002
\(357\) −46.8914 −2.48176
\(358\) 9.17355 0.484837
\(359\) −1.50254 −0.0793013 −0.0396506 0.999214i \(-0.512625\pi\)
−0.0396506 + 0.999214i \(0.512625\pi\)
\(360\) −0.0359595 −0.00189523
\(361\) −16.9808 −0.893724
\(362\) 13.3949 0.704022
\(363\) −21.5417 −1.13065
\(364\) −18.0996 −0.948679
\(365\) −0.827964 −0.0433376
\(366\) −2.56998 −0.134335
\(367\) 19.0944 0.996719 0.498359 0.866970i \(-0.333936\pi\)
0.498359 + 0.866970i \(0.333936\pi\)
\(368\) −2.13818 −0.111460
\(369\) 3.51904 0.183194
\(370\) 0.163226 0.00848571
\(371\) 64.8165 3.36510
\(372\) −9.23129 −0.478620
\(373\) 16.4712 0.852847 0.426424 0.904524i \(-0.359773\pi\)
0.426424 + 0.904524i \(0.359773\pi\)
\(374\) −28.3623 −1.46658
\(375\) −1.29536 −0.0668921
\(376\) 11.4823 0.592154
\(377\) −23.8739 −1.22957
\(378\) −28.1646 −1.44863
\(379\) −16.9224 −0.869243 −0.434621 0.900613i \(-0.643118\pi\)
−0.434621 + 0.900613i \(0.643118\pi\)
\(380\) −0.115200 −0.00590963
\(381\) −0.860623 −0.0440911
\(382\) 21.7988 1.11533
\(383\) 20.7139 1.05843 0.529217 0.848487i \(-0.322486\pi\)
0.529217 + 0.848487i \(0.322486\pi\)
\(384\) 1.59889 0.0815928
\(385\) −2.05154 −0.104556
\(386\) −11.1587 −0.567962
\(387\) −2.94214 −0.149557
\(388\) −3.18214 −0.161549
\(389\) 7.81849 0.396413 0.198206 0.980160i \(-0.436488\pi\)
0.198206 + 0.980160i \(0.436488\pi\)
\(390\) 0.458635 0.0232239
\(391\) −12.2587 −0.619947
\(392\) −19.1671 −0.968085
\(393\) −32.1038 −1.61942
\(394\) −6.63930 −0.334483
\(395\) −0.427853 −0.0215276
\(396\) −2.19432 −0.110269
\(397\) 26.4079 1.32537 0.662686 0.748897i \(-0.269416\pi\)
0.662686 + 0.748897i \(0.269416\pi\)
\(398\) −17.3870 −0.871532
\(399\) −11.6222 −0.581839
\(400\) −4.99343 −0.249671
\(401\) 14.6894 0.733551 0.366776 0.930309i \(-0.380462\pi\)
0.366776 + 0.930309i \(0.380462\pi\)
\(402\) −12.2496 −0.610953
\(403\) −20.4285 −1.01762
\(404\) 7.96263 0.396156
\(405\) 0.605798 0.0301023
\(406\) −34.5151 −1.71296
\(407\) 9.96034 0.493716
\(408\) 9.16675 0.453822
\(409\) −11.0819 −0.547964 −0.273982 0.961735i \(-0.588341\pi\)
−0.273982 + 0.961735i \(0.588341\pi\)
\(410\) −0.643172 −0.0317640
\(411\) 25.4176 1.25376
\(412\) 6.91916 0.340883
\(413\) −48.8002 −2.40130
\(414\) −0.948419 −0.0466123
\(415\) −0.753085 −0.0369675
\(416\) 3.53828 0.173478
\(417\) 15.8408 0.775729
\(418\) −7.02970 −0.343834
\(419\) 38.9966 1.90511 0.952554 0.304370i \(-0.0984459\pi\)
0.952554 + 0.304370i \(0.0984459\pi\)
\(420\) 0.663061 0.0323541
\(421\) −16.6285 −0.810423 −0.405211 0.914223i \(-0.632802\pi\)
−0.405211 + 0.914223i \(0.632802\pi\)
\(422\) 14.0080 0.681897
\(423\) 5.09313 0.247636
\(424\) −12.6709 −0.615353
\(425\) −28.6284 −1.38868
\(426\) 3.49489 0.169328
\(427\) −8.22223 −0.397902
\(428\) 3.67855 0.177810
\(429\) 27.9868 1.35121
\(430\) 0.537731 0.0259317
\(431\) 25.2496 1.21623 0.608114 0.793850i \(-0.291926\pi\)
0.608114 + 0.793850i \(0.291926\pi\)
\(432\) 5.50587 0.264901
\(433\) −4.70461 −0.226089 −0.113044 0.993590i \(-0.536060\pi\)
−0.113044 + 0.993590i \(0.536060\pi\)
\(434\) −29.5340 −1.41768
\(435\) 0.874595 0.0419336
\(436\) −10.0586 −0.481717
\(437\) −3.03835 −0.145344
\(438\) 16.3294 0.780250
\(439\) 31.9801 1.52633 0.763163 0.646207i \(-0.223646\pi\)
0.763163 + 0.646207i \(0.223646\pi\)
\(440\) 0.401053 0.0191194
\(441\) −8.50183 −0.404849
\(442\) 20.2857 0.964892
\(443\) −11.5314 −0.547872 −0.273936 0.961748i \(-0.588326\pi\)
−0.273936 + 0.961748i \(0.588326\pi\)
\(444\) −3.21920 −0.152777
\(445\) −0.888712 −0.0421290
\(446\) 10.1595 0.481067
\(447\) −20.7578 −0.981812
\(448\) 5.11538 0.241679
\(449\) −2.96772 −0.140055 −0.0700276 0.997545i \(-0.522309\pi\)
−0.0700276 + 0.997545i \(0.522309\pi\)
\(450\) −2.21490 −0.104411
\(451\) −39.2475 −1.84809
\(452\) 9.08743 0.427437
\(453\) 24.1229 1.13339
\(454\) 26.0019 1.22033
\(455\) 1.46733 0.0687895
\(456\) 2.27201 0.106397
\(457\) 24.2063 1.13232 0.566161 0.824295i \(-0.308428\pi\)
0.566161 + 0.824295i \(0.308428\pi\)
\(458\) 8.17539 0.382011
\(459\) 31.5663 1.47339
\(460\) 0.173342 0.00808209
\(461\) −0.672850 −0.0313378 −0.0156689 0.999877i \(-0.504988\pi\)
−0.0156689 + 0.999877i \(0.504988\pi\)
\(462\) 40.4612 1.88243
\(463\) −31.8160 −1.47861 −0.739307 0.673368i \(-0.764847\pi\)
−0.739307 + 0.673368i \(0.764847\pi\)
\(464\) 6.74732 0.313237
\(465\) 0.748377 0.0347052
\(466\) −4.98481 −0.230917
\(467\) −9.93985 −0.459961 −0.229981 0.973195i \(-0.573866\pi\)
−0.229981 + 0.973195i \(0.573866\pi\)
\(468\) 1.56945 0.0725479
\(469\) −39.1905 −1.80965
\(470\) −0.930866 −0.0429376
\(471\) 6.45221 0.297302
\(472\) 9.53989 0.439109
\(473\) 32.8133 1.50876
\(474\) 8.43828 0.387583
\(475\) −7.09565 −0.325571
\(476\) 29.3276 1.34423
\(477\) −5.62035 −0.257338
\(478\) 28.5845 1.30742
\(479\) 8.34110 0.381115 0.190557 0.981676i \(-0.438970\pi\)
0.190557 + 0.981676i \(0.438970\pi\)
\(480\) −0.129621 −0.00591637
\(481\) −7.12398 −0.324825
\(482\) −14.6289 −0.666328
\(483\) 17.4880 0.795731
\(484\) 13.4730 0.612408
\(485\) 0.257975 0.0117141
\(486\) 4.56982 0.207291
\(487\) 28.7540 1.30297 0.651484 0.758663i \(-0.274147\pi\)
0.651484 + 0.758663i \(0.274147\pi\)
\(488\) 1.60736 0.0727616
\(489\) 3.39863 0.153692
\(490\) 1.55387 0.0701967
\(491\) −2.61550 −0.118036 −0.0590179 0.998257i \(-0.518797\pi\)
−0.0590179 + 0.998257i \(0.518797\pi\)
\(492\) 12.6849 0.571878
\(493\) 38.6838 1.74223
\(494\) 5.02789 0.226215
\(495\) 0.177892 0.00799567
\(496\) 5.77357 0.259241
\(497\) 11.1813 0.501552
\(498\) 14.8526 0.665562
\(499\) 31.6139 1.41523 0.707617 0.706596i \(-0.249770\pi\)
0.707617 + 0.706596i \(0.249770\pi\)
\(500\) 0.810164 0.0362316
\(501\) −17.8188 −0.796084
\(502\) −5.61535 −0.250626
\(503\) −28.6885 −1.27916 −0.639579 0.768726i \(-0.720891\pi\)
−0.639579 + 0.768726i \(0.720891\pi\)
\(504\) 2.26900 0.101069
\(505\) −0.645527 −0.0287256
\(506\) 10.5776 0.470233
\(507\) 0.768410 0.0341263
\(508\) 0.538264 0.0238816
\(509\) −35.9946 −1.59543 −0.797716 0.603033i \(-0.793959\pi\)
−0.797716 + 0.603033i \(0.793959\pi\)
\(510\) −0.743145 −0.0329070
\(511\) 52.2434 2.31111
\(512\) −1.00000 −0.0441942
\(513\) 7.82383 0.345430
\(514\) 24.8358 1.09546
\(515\) −0.560934 −0.0247177
\(516\) −10.6053 −0.466874
\(517\) −56.8031 −2.49820
\(518\) −10.2993 −0.452526
\(519\) 31.5173 1.38346
\(520\) −0.286847 −0.0125791
\(521\) 26.4206 1.15751 0.578753 0.815503i \(-0.303540\pi\)
0.578753 + 0.815503i \(0.303540\pi\)
\(522\) 2.99287 0.130994
\(523\) −25.0310 −1.09453 −0.547264 0.836960i \(-0.684331\pi\)
−0.547264 + 0.836960i \(0.684331\pi\)
\(524\) 20.0788 0.877148
\(525\) 40.8408 1.78244
\(526\) −12.8171 −0.558852
\(527\) 33.1011 1.44191
\(528\) −7.90971 −0.344226
\(529\) −18.4282 −0.801225
\(530\) 1.02723 0.0446198
\(531\) 4.23155 0.183633
\(532\) 7.26895 0.315149
\(533\) 28.0712 1.21590
\(534\) 17.5275 0.758490
\(535\) −0.298219 −0.0128931
\(536\) 7.66131 0.330918
\(537\) 14.6675 0.632948
\(538\) −10.8805 −0.469093
\(539\) 94.8200 4.08419
\(540\) −0.446358 −0.0192082
\(541\) −3.17513 −0.136509 −0.0682547 0.997668i \(-0.521743\pi\)
−0.0682547 + 0.997668i \(0.521743\pi\)
\(542\) 24.9074 1.06986
\(543\) 21.4170 0.919090
\(544\) −5.73321 −0.245809
\(545\) 0.815443 0.0349298
\(546\) −28.9393 −1.23849
\(547\) −38.2775 −1.63663 −0.818314 0.574771i \(-0.805091\pi\)
−0.818314 + 0.574771i \(0.805091\pi\)
\(548\) −15.8971 −0.679090
\(549\) 0.712964 0.0304286
\(550\) 24.7026 1.05332
\(551\) 9.58793 0.408460
\(552\) −3.41871 −0.145510
\(553\) 26.9969 1.14803
\(554\) 16.4322 0.698137
\(555\) 0.260979 0.0110780
\(556\) −9.90742 −0.420168
\(557\) −12.8325 −0.543732 −0.271866 0.962335i \(-0.587641\pi\)
−0.271866 + 0.962335i \(0.587641\pi\)
\(558\) 2.56095 0.108414
\(559\) −23.4692 −0.992643
\(560\) −0.414702 −0.0175244
\(561\) −45.3481 −1.91460
\(562\) −27.7773 −1.17171
\(563\) 3.85797 0.162594 0.0812969 0.996690i \(-0.474094\pi\)
0.0812969 + 0.996690i \(0.474094\pi\)
\(564\) 18.3589 0.773049
\(565\) −0.736715 −0.0309938
\(566\) 3.96193 0.166532
\(567\) −38.2250 −1.60530
\(568\) −2.18583 −0.0917154
\(569\) 6.99385 0.293197 0.146599 0.989196i \(-0.453167\pi\)
0.146599 + 0.989196i \(0.453167\pi\)
\(570\) −0.184191 −0.00771493
\(571\) 21.7809 0.911502 0.455751 0.890107i \(-0.349371\pi\)
0.455751 + 0.890107i \(0.349371\pi\)
\(572\) −17.5039 −0.731876
\(573\) 34.8538 1.45604
\(574\) 40.5832 1.69391
\(575\) 10.6769 0.445256
\(576\) −0.443564 −0.0184818
\(577\) −19.9728 −0.831477 −0.415739 0.909484i \(-0.636477\pi\)
−0.415739 + 0.909484i \(0.636477\pi\)
\(578\) −15.8697 −0.660094
\(579\) −17.8415 −0.741466
\(580\) −0.547003 −0.0227131
\(581\) 47.5186 1.97140
\(582\) −5.08789 −0.210900
\(583\) 62.6832 2.59607
\(584\) −10.2130 −0.422617
\(585\) −0.127235 −0.00526051
\(586\) −0.996102 −0.0411486
\(587\) 34.5331 1.42533 0.712667 0.701503i \(-0.247487\pi\)
0.712667 + 0.701503i \(0.247487\pi\)
\(588\) −30.6460 −1.26382
\(589\) 8.20424 0.338050
\(590\) −0.773395 −0.0318402
\(591\) −10.6155 −0.436663
\(592\) 2.01340 0.0827503
\(593\) 46.6260 1.91470 0.957350 0.288932i \(-0.0933002\pi\)
0.957350 + 0.288932i \(0.0933002\pi\)
\(594\) −27.2376 −1.11757
\(595\) −2.37757 −0.0974711
\(596\) 12.9827 0.531792
\(597\) −27.7998 −1.13777
\(598\) −7.56548 −0.309375
\(599\) 3.36927 0.137665 0.0688323 0.997628i \(-0.478073\pi\)
0.0688323 + 0.997628i \(0.478073\pi\)
\(600\) −7.98392 −0.325942
\(601\) −23.0910 −0.941903 −0.470951 0.882159i \(-0.656089\pi\)
−0.470951 + 0.882159i \(0.656089\pi\)
\(602\) −33.9301 −1.38289
\(603\) 3.39828 0.138389
\(604\) −15.0873 −0.613895
\(605\) −1.09225 −0.0444062
\(606\) 12.7313 0.517175
\(607\) 35.6262 1.44602 0.723012 0.690835i \(-0.242757\pi\)
0.723012 + 0.690835i \(0.242757\pi\)
\(608\) −1.42100 −0.0576291
\(609\) −55.1857 −2.23624
\(610\) −0.130308 −0.00527601
\(611\) 40.6276 1.64362
\(612\) −2.54304 −0.102796
\(613\) 18.2231 0.736025 0.368013 0.929821i \(-0.380038\pi\)
0.368013 + 0.929821i \(0.380038\pi\)
\(614\) −15.1927 −0.613126
\(615\) −1.02836 −0.0414674
\(616\) −25.3059 −1.01960
\(617\) −25.7308 −1.03588 −0.517942 0.855416i \(-0.673302\pi\)
−0.517942 + 0.855416i \(0.673302\pi\)
\(618\) 11.0629 0.445017
\(619\) −21.5242 −0.865129 −0.432564 0.901603i \(-0.642391\pi\)
−0.432564 + 0.901603i \(0.642391\pi\)
\(620\) −0.468062 −0.0187978
\(621\) −11.7725 −0.472416
\(622\) −24.6107 −0.986799
\(623\) 56.0765 2.24666
\(624\) 5.65730 0.226473
\(625\) 24.9015 0.996058
\(626\) −27.1636 −1.08568
\(627\) −11.2397 −0.448870
\(628\) −4.03544 −0.161032
\(629\) 11.5433 0.460260
\(630\) −0.183947 −0.00732861
\(631\) −11.0081 −0.438224 −0.219112 0.975700i \(-0.570316\pi\)
−0.219112 + 0.975700i \(0.570316\pi\)
\(632\) −5.27760 −0.209932
\(633\) 22.3971 0.890207
\(634\) −2.21758 −0.0880713
\(635\) −0.0436369 −0.00173168
\(636\) −20.2593 −0.803335
\(637\) −67.8186 −2.68707
\(638\) −33.3791 −1.32149
\(639\) −0.969554 −0.0383550
\(640\) 0.0810696 0.00320456
\(641\) −43.5653 −1.72073 −0.860364 0.509681i \(-0.829763\pi\)
−0.860364 + 0.509681i \(0.829763\pi\)
\(642\) 5.88159 0.232128
\(643\) 2.16211 0.0852651 0.0426326 0.999091i \(-0.486426\pi\)
0.0426326 + 0.999091i \(0.486426\pi\)
\(644\) −10.9376 −0.431002
\(645\) 0.859771 0.0338535
\(646\) −8.14689 −0.320535
\(647\) 42.1789 1.65822 0.829111 0.559084i \(-0.188847\pi\)
0.829111 + 0.559084i \(0.188847\pi\)
\(648\) 7.47256 0.293550
\(649\) −47.1940 −1.85253
\(650\) −17.6681 −0.693001
\(651\) −47.2215 −1.85076
\(652\) −2.12563 −0.0832459
\(653\) 14.2973 0.559497 0.279748 0.960073i \(-0.409749\pi\)
0.279748 + 0.960073i \(0.409749\pi\)
\(654\) −16.0825 −0.628875
\(655\) −1.62778 −0.0636028
\(656\) −7.93357 −0.309754
\(657\) −4.53012 −0.176737
\(658\) 58.7363 2.28978
\(659\) 23.1568 0.902061 0.451031 0.892508i \(-0.351056\pi\)
0.451031 + 0.892508i \(0.351056\pi\)
\(660\) 0.641238 0.0249601
\(661\) 21.8169 0.848581 0.424290 0.905526i \(-0.360524\pi\)
0.424290 + 0.905526i \(0.360524\pi\)
\(662\) 35.5813 1.38291
\(663\) 32.4345 1.25965
\(664\) −9.28936 −0.360497
\(665\) −0.589291 −0.0228517
\(666\) 0.893072 0.0346058
\(667\) −14.4270 −0.558616
\(668\) 11.1445 0.431193
\(669\) 16.2439 0.628025
\(670\) −0.621100 −0.0239952
\(671\) −7.95161 −0.306969
\(672\) 8.17891 0.315508
\(673\) 16.5286 0.637129 0.318564 0.947901i \(-0.396799\pi\)
0.318564 + 0.947901i \(0.396799\pi\)
\(674\) 18.1041 0.697342
\(675\) −27.4931 −1.05821
\(676\) −0.480591 −0.0184843
\(677\) 26.0031 0.999379 0.499690 0.866205i \(-0.333447\pi\)
0.499690 + 0.866205i \(0.333447\pi\)
\(678\) 14.5298 0.558012
\(679\) −16.2779 −0.624688
\(680\) 0.464789 0.0178239
\(681\) 41.5741 1.59312
\(682\) −28.5620 −1.09369
\(683\) 17.0134 0.650998 0.325499 0.945542i \(-0.394468\pi\)
0.325499 + 0.945542i \(0.394468\pi\)
\(684\) −0.630303 −0.0241002
\(685\) 1.28877 0.0492414
\(686\) −62.2394 −2.37631
\(687\) 13.0715 0.498709
\(688\) 6.63296 0.252879
\(689\) −44.8332 −1.70801
\(690\) 0.277153 0.0105511
\(691\) 35.9731 1.36848 0.684240 0.729257i \(-0.260134\pi\)
0.684240 + 0.729257i \(0.260134\pi\)
\(692\) −19.7120 −0.749340
\(693\) −11.2248 −0.426393
\(694\) 7.60352 0.288626
\(695\) 0.803191 0.0304668
\(696\) 10.7882 0.408926
\(697\) −45.4848 −1.72286
\(698\) 20.0290 0.758111
\(699\) −7.97014 −0.301458
\(700\) −25.5433 −0.965445
\(701\) 44.3811 1.67625 0.838125 0.545478i \(-0.183652\pi\)
0.838125 + 0.545478i \(0.183652\pi\)
\(702\) 19.4813 0.735274
\(703\) 2.86104 0.107906
\(704\) 4.94702 0.186448
\(705\) −1.48835 −0.0560544
\(706\) −18.7407 −0.705314
\(707\) 40.7319 1.53188
\(708\) 15.2532 0.573250
\(709\) 14.4085 0.541123 0.270561 0.962703i \(-0.412791\pi\)
0.270561 + 0.962703i \(0.412791\pi\)
\(710\) 0.177204 0.00665036
\(711\) −2.34095 −0.0877925
\(712\) −10.9623 −0.410831
\(713\) −12.3450 −0.462322
\(714\) 46.8914 1.75487
\(715\) 1.41904 0.0530689
\(716\) −9.17355 −0.342832
\(717\) 45.7033 1.70682
\(718\) 1.50254 0.0560745
\(719\) 44.6201 1.66405 0.832024 0.554740i \(-0.187182\pi\)
0.832024 + 0.554740i \(0.187182\pi\)
\(720\) 0.0359595 0.00134013
\(721\) 35.3941 1.31815
\(722\) 16.9808 0.631959
\(723\) −23.3899 −0.869881
\(724\) −13.3949 −0.497819
\(725\) −33.6923 −1.25130
\(726\) 21.5417 0.799489
\(727\) 26.8368 0.995322 0.497661 0.867372i \(-0.334192\pi\)
0.497661 + 0.867372i \(0.334192\pi\)
\(728\) 18.0996 0.670817
\(729\) 29.7243 1.10090
\(730\) 0.827964 0.0306443
\(731\) 38.0282 1.40652
\(732\) 2.56998 0.0949891
\(733\) 24.7307 0.913448 0.456724 0.889608i \(-0.349023\pi\)
0.456724 + 0.889608i \(0.349023\pi\)
\(734\) −19.0944 −0.704787
\(735\) 2.48446 0.0916408
\(736\) 2.13818 0.0788144
\(737\) −37.9006 −1.39609
\(738\) −3.51904 −0.129538
\(739\) −20.0689 −0.738248 −0.369124 0.929380i \(-0.620342\pi\)
−0.369124 + 0.929380i \(0.620342\pi\)
\(740\) −0.163226 −0.00600030
\(741\) 8.03902 0.295321
\(742\) −64.8165 −2.37949
\(743\) 29.8892 1.09653 0.548265 0.836305i \(-0.315289\pi\)
0.548265 + 0.836305i \(0.315289\pi\)
\(744\) 9.23129 0.338435
\(745\) −1.05250 −0.0385607
\(746\) −16.4712 −0.603054
\(747\) −4.12042 −0.150758
\(748\) 28.3623 1.03703
\(749\) 18.8172 0.687565
\(750\) 1.29536 0.0472998
\(751\) −16.0114 −0.584263 −0.292131 0.956378i \(-0.594364\pi\)
−0.292131 + 0.956378i \(0.594364\pi\)
\(752\) −11.4823 −0.418716
\(753\) −8.97831 −0.327188
\(754\) 23.8739 0.869436
\(755\) 1.22313 0.0445141
\(756\) 28.1646 1.02434
\(757\) −45.5951 −1.65718 −0.828592 0.559853i \(-0.810858\pi\)
−0.828592 + 0.559853i \(0.810858\pi\)
\(758\) 16.9224 0.614647
\(759\) 16.9124 0.613881
\(760\) 0.115200 0.00417874
\(761\) −3.51592 −0.127452 −0.0637260 0.997967i \(-0.520298\pi\)
−0.0637260 + 0.997967i \(0.520298\pi\)
\(762\) 0.860623 0.0311771
\(763\) −51.4533 −1.86274
\(764\) −21.7988 −0.788654
\(765\) 0.206164 0.00745386
\(766\) −20.7139 −0.748425
\(767\) 33.7548 1.21881
\(768\) −1.59889 −0.0576948
\(769\) −16.8093 −0.606160 −0.303080 0.952965i \(-0.598015\pi\)
−0.303080 + 0.952965i \(0.598015\pi\)
\(770\) 2.05154 0.0739323
\(771\) 39.7096 1.43010
\(772\) 11.1587 0.401610
\(773\) 21.0790 0.758161 0.379080 0.925364i \(-0.376240\pi\)
0.379080 + 0.925364i \(0.376240\pi\)
\(774\) 2.94214 0.105753
\(775\) −28.8299 −1.03560
\(776\) 3.18214 0.114232
\(777\) −16.4674 −0.590766
\(778\) −7.81849 −0.280306
\(779\) −11.2736 −0.403918
\(780\) −0.458635 −0.0164218
\(781\) 10.8133 0.386932
\(782\) 12.2587 0.438368
\(783\) 37.1498 1.32763
\(784\) 19.1671 0.684540
\(785\) 0.327152 0.0116765
\(786\) 32.1038 1.14510
\(787\) −9.48100 −0.337961 −0.168981 0.985619i \(-0.554048\pi\)
−0.168981 + 0.985619i \(0.554048\pi\)
\(788\) 6.63930 0.236515
\(789\) −20.4931 −0.729572
\(790\) 0.427853 0.0152223
\(791\) 46.4857 1.65284
\(792\) 2.19432 0.0779716
\(793\) 5.68727 0.201961
\(794\) −26.4079 −0.937180
\(795\) 1.64242 0.0582505
\(796\) 17.3870 0.616266
\(797\) −45.2964 −1.60448 −0.802240 0.597001i \(-0.796359\pi\)
−0.802240 + 0.597001i \(0.796359\pi\)
\(798\) 11.6222 0.411422
\(799\) −65.8305 −2.32891
\(800\) 4.99343 0.176544
\(801\) −4.86249 −0.171808
\(802\) −14.6894 −0.518699
\(803\) 50.5239 1.78295
\(804\) 12.2496 0.432009
\(805\) 0.886708 0.0312524
\(806\) 20.4285 0.719564
\(807\) −17.3967 −0.612394
\(808\) −7.96263 −0.280124
\(809\) 16.5330 0.581270 0.290635 0.956834i \(-0.406133\pi\)
0.290635 + 0.956834i \(0.406133\pi\)
\(810\) −0.605798 −0.0212856
\(811\) 12.3068 0.432149 0.216075 0.976377i \(-0.430675\pi\)
0.216075 + 0.976377i \(0.430675\pi\)
\(812\) 34.5151 1.21124
\(813\) 39.8241 1.39669
\(814\) −9.96034 −0.349110
\(815\) 0.172324 0.00603624
\(816\) −9.16675 −0.320901
\(817\) 9.42542 0.329754
\(818\) 11.0819 0.387469
\(819\) 8.02834 0.280533
\(820\) 0.643172 0.0224605
\(821\) −13.7517 −0.479939 −0.239969 0.970780i \(-0.577137\pi\)
−0.239969 + 0.970780i \(0.577137\pi\)
\(822\) −25.4176 −0.886542
\(823\) −15.1260 −0.527258 −0.263629 0.964624i \(-0.584919\pi\)
−0.263629 + 0.964624i \(0.584919\pi\)
\(824\) −6.91916 −0.241040
\(825\) 39.4966 1.37509
\(826\) 48.8002 1.69797
\(827\) −18.2930 −0.636108 −0.318054 0.948073i \(-0.603029\pi\)
−0.318054 + 0.948073i \(0.603029\pi\)
\(828\) 0.948419 0.0329599
\(829\) −38.2577 −1.32874 −0.664372 0.747402i \(-0.731301\pi\)
−0.664372 + 0.747402i \(0.731301\pi\)
\(830\) 0.753085 0.0261400
\(831\) 26.2732 0.911408
\(832\) −3.53828 −0.122668
\(833\) 109.889 3.80743
\(834\) −15.8408 −0.548523
\(835\) −0.903480 −0.0312662
\(836\) 7.02970 0.243127
\(837\) 31.7885 1.09877
\(838\) −38.9966 −1.34711
\(839\) 7.23928 0.249928 0.124964 0.992161i \(-0.460118\pi\)
0.124964 + 0.992161i \(0.460118\pi\)
\(840\) −0.663061 −0.0228778
\(841\) 16.5263 0.569874
\(842\) 16.6285 0.573055
\(843\) −44.4127 −1.52966
\(844\) −14.0080 −0.482174
\(845\) 0.0389613 0.00134031
\(846\) −5.09313 −0.175105
\(847\) 68.9194 2.36810
\(848\) 12.6709 0.435121
\(849\) 6.33467 0.217405
\(850\) 28.6284 0.981946
\(851\) −4.30502 −0.147574
\(852\) −3.49489 −0.119733
\(853\) 21.9317 0.750926 0.375463 0.926837i \(-0.377484\pi\)
0.375463 + 0.926837i \(0.377484\pi\)
\(854\) 8.22223 0.281359
\(855\) 0.0510984 0.00174753
\(856\) −3.67855 −0.125730
\(857\) −19.3792 −0.661982 −0.330991 0.943634i \(-0.607383\pi\)
−0.330991 + 0.943634i \(0.607383\pi\)
\(858\) −27.9868 −0.955453
\(859\) −18.6194 −0.635285 −0.317642 0.948211i \(-0.602891\pi\)
−0.317642 + 0.948211i \(0.602891\pi\)
\(860\) −0.537731 −0.0183365
\(861\) 64.8879 2.21138
\(862\) −25.2496 −0.860003
\(863\) 57.8962 1.97081 0.985405 0.170228i \(-0.0544505\pi\)
0.985405 + 0.170228i \(0.0544505\pi\)
\(864\) −5.50587 −0.187313
\(865\) 1.59805 0.0543353
\(866\) 4.70461 0.159869
\(867\) −25.3739 −0.861743
\(868\) 29.5340 1.00245
\(869\) 26.1084 0.885666
\(870\) −0.874595 −0.0296516
\(871\) 27.1079 0.918515
\(872\) 10.0586 0.340626
\(873\) 1.41148 0.0477715
\(874\) 3.03835 0.102774
\(875\) 4.14429 0.140103
\(876\) −16.3294 −0.551720
\(877\) 22.8229 0.770675 0.385338 0.922776i \(-0.374085\pi\)
0.385338 + 0.922776i \(0.374085\pi\)
\(878\) −31.9801 −1.07927
\(879\) −1.59265 −0.0537189
\(880\) −0.401053 −0.0135195
\(881\) −2.07138 −0.0697867 −0.0348934 0.999391i \(-0.511109\pi\)
−0.0348934 + 0.999391i \(0.511109\pi\)
\(882\) 8.50183 0.286272
\(883\) −19.1325 −0.643861 −0.321930 0.946763i \(-0.604332\pi\)
−0.321930 + 0.946763i \(0.604332\pi\)
\(884\) −20.2857 −0.682282
\(885\) −1.23657 −0.0415669
\(886\) 11.5314 0.387404
\(887\) −42.2241 −1.41775 −0.708873 0.705336i \(-0.750796\pi\)
−0.708873 + 0.705336i \(0.750796\pi\)
\(888\) 3.21920 0.108029
\(889\) 2.75343 0.0923470
\(890\) 0.888712 0.0297897
\(891\) −36.9669 −1.23844
\(892\) −10.1595 −0.340165
\(893\) −16.3163 −0.546005
\(894\) 20.7578 0.694246
\(895\) 0.743697 0.0248590
\(896\) −5.11538 −0.170893
\(897\) −12.0963 −0.403885
\(898\) 2.96772 0.0990340
\(899\) 38.9562 1.29926
\(900\) 2.21490 0.0738301
\(901\) 72.6450 2.42016
\(902\) 39.2475 1.30680
\(903\) −54.2504 −1.80534
\(904\) −9.08743 −0.302243
\(905\) 1.08592 0.0360973
\(906\) −24.1229 −0.801431
\(907\) −26.6129 −0.883666 −0.441833 0.897097i \(-0.645672\pi\)
−0.441833 + 0.897097i \(0.645672\pi\)
\(908\) −26.0019 −0.862905
\(909\) −3.53193 −0.117147
\(910\) −1.46733 −0.0486415
\(911\) −13.7049 −0.454065 −0.227032 0.973887i \(-0.572902\pi\)
−0.227032 + 0.973887i \(0.572902\pi\)
\(912\) −2.27201 −0.0752339
\(913\) 45.9546 1.52088
\(914\) −24.2063 −0.800673
\(915\) −0.208347 −0.00688775
\(916\) −8.17539 −0.270122
\(917\) 102.711 3.39181
\(918\) −31.5663 −1.04184
\(919\) −29.8538 −0.984785 −0.492392 0.870373i \(-0.663877\pi\)
−0.492392 + 0.870373i \(0.663877\pi\)
\(920\) −0.173342 −0.00571490
\(921\) −24.2913 −0.800427
\(922\) 0.672850 0.0221591
\(923\) −7.73407 −0.254570
\(924\) −40.4612 −1.33108
\(925\) −10.0538 −0.330566
\(926\) 31.8160 1.04554
\(927\) −3.06909 −0.100802
\(928\) −6.74732 −0.221492
\(929\) 23.5111 0.771374 0.385687 0.922630i \(-0.373964\pi\)
0.385687 + 0.922630i \(0.373964\pi\)
\(930\) −0.748377 −0.0245403
\(931\) 27.2364 0.892638
\(932\) 4.98481 0.163283
\(933\) −39.3497 −1.28825
\(934\) 9.93985 0.325242
\(935\) −2.29932 −0.0751958
\(936\) −1.56945 −0.0512991
\(937\) 9.25385 0.302310 0.151155 0.988510i \(-0.451701\pi\)
0.151155 + 0.988510i \(0.451701\pi\)
\(938\) 39.1905 1.27962
\(939\) −43.4315 −1.41733
\(940\) 0.930866 0.0303615
\(941\) −58.4736 −1.90619 −0.953093 0.302678i \(-0.902119\pi\)
−0.953093 + 0.302678i \(0.902119\pi\)
\(942\) −6.45221 −0.210224
\(943\) 16.9634 0.552405
\(944\) −9.53989 −0.310497
\(945\) −2.28329 −0.0742755
\(946\) −32.8133 −1.06685
\(947\) −7.44707 −0.241997 −0.120999 0.992653i \(-0.538610\pi\)
−0.120999 + 0.992653i \(0.538610\pi\)
\(948\) −8.43828 −0.274063
\(949\) −36.1364 −1.17304
\(950\) 7.09565 0.230213
\(951\) −3.54566 −0.114976
\(952\) −29.3276 −0.950512
\(953\) 3.10104 0.100452 0.0502262 0.998738i \(-0.484006\pi\)
0.0502262 + 0.998738i \(0.484006\pi\)
\(954\) 5.62035 0.181966
\(955\) 1.76722 0.0571860
\(956\) −28.5845 −0.924488
\(957\) −53.3694 −1.72519
\(958\) −8.34110 −0.269489
\(959\) −81.3197 −2.62595
\(960\) 0.129621 0.00418350
\(961\) 2.33416 0.0752955
\(962\) 7.12398 0.229686
\(963\) −1.63167 −0.0525799
\(964\) 14.6289 0.471165
\(965\) −0.904630 −0.0291211
\(966\) −17.4880 −0.562667
\(967\) −23.7592 −0.764045 −0.382023 0.924153i \(-0.624772\pi\)
−0.382023 + 0.924153i \(0.624772\pi\)
\(968\) −13.4730 −0.433038
\(969\) −13.0259 −0.418454
\(970\) −0.257975 −0.00828309
\(971\) 27.7041 0.889068 0.444534 0.895762i \(-0.353369\pi\)
0.444534 + 0.895762i \(0.353369\pi\)
\(972\) −4.56982 −0.146577
\(973\) −50.6802 −1.62473
\(974\) −28.7540 −0.921337
\(975\) −28.2493 −0.904703
\(976\) −1.60736 −0.0514502
\(977\) 2.31334 0.0740104 0.0370052 0.999315i \(-0.488218\pi\)
0.0370052 + 0.999315i \(0.488218\pi\)
\(978\) −3.39863 −0.108676
\(979\) 54.2308 1.73322
\(980\) −1.55387 −0.0496366
\(981\) 4.46161 0.142448
\(982\) 2.61550 0.0834639
\(983\) 45.1949 1.44149 0.720746 0.693199i \(-0.243799\pi\)
0.720746 + 0.693199i \(0.243799\pi\)
\(984\) −12.6849 −0.404379
\(985\) −0.538246 −0.0171499
\(986\) −38.6838 −1.23194
\(987\) 93.9127 2.98927
\(988\) −5.02789 −0.159958
\(989\) −14.1825 −0.450976
\(990\) −0.177892 −0.00565379
\(991\) −8.10229 −0.257378 −0.128689 0.991685i \(-0.541077\pi\)
−0.128689 + 0.991685i \(0.541077\pi\)
\(992\) −5.77357 −0.183311
\(993\) 56.8905 1.80537
\(994\) −11.1813 −0.354651
\(995\) −1.40956 −0.0446860
\(996\) −14.8526 −0.470623
\(997\) −11.0872 −0.351135 −0.175567 0.984467i \(-0.556176\pi\)
−0.175567 + 0.984467i \(0.556176\pi\)
\(998\) −31.6139 −1.00072
\(999\) 11.0855 0.350731
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 \(a_p\))