Properties

Label 8002.2.a.e.1.5
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 1.5
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.91842 q^{3} +1.00000 q^{4} +3.04954 q^{5} +2.91842 q^{6} +3.39338 q^{7} -1.00000 q^{8} +5.51716 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.91842 q^{3} +1.00000 q^{4} +3.04954 q^{5} +2.91842 q^{6} +3.39338 q^{7} -1.00000 q^{8} +5.51716 q^{9} -3.04954 q^{10} +3.24275 q^{11} -2.91842 q^{12} -3.02838 q^{13} -3.39338 q^{14} -8.89983 q^{15} +1.00000 q^{16} +2.71304 q^{17} -5.51716 q^{18} +1.92519 q^{19} +3.04954 q^{20} -9.90330 q^{21} -3.24275 q^{22} +1.77570 q^{23} +2.91842 q^{24} +4.29970 q^{25} +3.02838 q^{26} -7.34612 q^{27} +3.39338 q^{28} +1.39033 q^{29} +8.89983 q^{30} -9.18702 q^{31} -1.00000 q^{32} -9.46369 q^{33} -2.71304 q^{34} +10.3482 q^{35} +5.51716 q^{36} +4.71373 q^{37} -1.92519 q^{38} +8.83807 q^{39} -3.04954 q^{40} -11.1910 q^{41} +9.90330 q^{42} -12.0232 q^{43} +3.24275 q^{44} +16.8248 q^{45} -1.77570 q^{46} +6.09693 q^{47} -2.91842 q^{48} +4.51503 q^{49} -4.29970 q^{50} -7.91777 q^{51} -3.02838 q^{52} -8.04949 q^{53} +7.34612 q^{54} +9.88889 q^{55} -3.39338 q^{56} -5.61851 q^{57} -1.39033 q^{58} +6.52281 q^{59} -8.89983 q^{60} +6.23515 q^{61} +9.18702 q^{62} +18.7218 q^{63} +1.00000 q^{64} -9.23516 q^{65} +9.46369 q^{66} +11.9464 q^{67} +2.71304 q^{68} -5.18223 q^{69} -10.3482 q^{70} -1.32813 q^{71} -5.51716 q^{72} +5.31705 q^{73} -4.71373 q^{74} -12.5483 q^{75} +1.92519 q^{76} +11.0039 q^{77} -8.83807 q^{78} +10.2976 q^{79} +3.04954 q^{80} +4.88755 q^{81} +11.1910 q^{82} +11.8365 q^{83} -9.90330 q^{84} +8.27351 q^{85} +12.0232 q^{86} -4.05757 q^{87} -3.24275 q^{88} -1.96091 q^{89} -16.8248 q^{90} -10.2764 q^{91} +1.77570 q^{92} +26.8116 q^{93} -6.09693 q^{94} +5.87095 q^{95} +2.91842 q^{96} +17.6719 q^{97} -4.51503 q^{98} +17.8907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.91842 −1.68495 −0.842474 0.538736i \(-0.818902\pi\)
−0.842474 + 0.538736i \(0.818902\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.04954 1.36380 0.681898 0.731447i \(-0.261155\pi\)
0.681898 + 0.731447i \(0.261155\pi\)
\(6\) 2.91842 1.19144
\(7\) 3.39338 1.28258 0.641289 0.767300i \(-0.278400\pi\)
0.641289 + 0.767300i \(0.278400\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.51716 1.83905
\(10\) −3.04954 −0.964349
\(11\) 3.24275 0.977725 0.488862 0.872361i \(-0.337412\pi\)
0.488862 + 0.872361i \(0.337412\pi\)
\(12\) −2.91842 −0.842474
\(13\) −3.02838 −0.839921 −0.419960 0.907542i \(-0.637956\pi\)
−0.419960 + 0.907542i \(0.637956\pi\)
\(14\) −3.39338 −0.906919
\(15\) −8.89983 −2.29793
\(16\) 1.00000 0.250000
\(17\) 2.71304 0.658008 0.329004 0.944329i \(-0.393287\pi\)
0.329004 + 0.944329i \(0.393287\pi\)
\(18\) −5.51716 −1.30041
\(19\) 1.92519 0.441669 0.220835 0.975311i \(-0.429122\pi\)
0.220835 + 0.975311i \(0.429122\pi\)
\(20\) 3.04954 0.681898
\(21\) −9.90330 −2.16108
\(22\) −3.24275 −0.691356
\(23\) 1.77570 0.370259 0.185129 0.982714i \(-0.440730\pi\)
0.185129 + 0.982714i \(0.440730\pi\)
\(24\) 2.91842 0.595719
\(25\) 4.29970 0.859939
\(26\) 3.02838 0.593914
\(27\) −7.34612 −1.41376
\(28\) 3.39338 0.641289
\(29\) 1.39033 0.258178 0.129089 0.991633i \(-0.458795\pi\)
0.129089 + 0.991633i \(0.458795\pi\)
\(30\) 8.89983 1.62488
\(31\) −9.18702 −1.65004 −0.825019 0.565105i \(-0.808836\pi\)
−0.825019 + 0.565105i \(0.808836\pi\)
\(32\) −1.00000 −0.176777
\(33\) −9.46369 −1.64742
\(34\) −2.71304 −0.465282
\(35\) 10.3482 1.74917
\(36\) 5.51716 0.919526
\(37\) 4.71373 0.774933 0.387467 0.921884i \(-0.373350\pi\)
0.387467 + 0.921884i \(0.373350\pi\)
\(38\) −1.92519 −0.312307
\(39\) 8.83807 1.41522
\(40\) −3.04954 −0.482175
\(41\) −11.1910 −1.74774 −0.873869 0.486161i \(-0.838397\pi\)
−0.873869 + 0.486161i \(0.838397\pi\)
\(42\) 9.90330 1.52811
\(43\) −12.0232 −1.83353 −0.916764 0.399430i \(-0.869208\pi\)
−0.916764 + 0.399430i \(0.869208\pi\)
\(44\) 3.24275 0.488862
\(45\) 16.8248 2.50809
\(46\) −1.77570 −0.261812
\(47\) 6.09693 0.889328 0.444664 0.895697i \(-0.353323\pi\)
0.444664 + 0.895697i \(0.353323\pi\)
\(48\) −2.91842 −0.421237
\(49\) 4.51503 0.645004
\(50\) −4.29970 −0.608069
\(51\) −7.91777 −1.10871
\(52\) −3.02838 −0.419960
\(53\) −8.04949 −1.10568 −0.552841 0.833287i \(-0.686456\pi\)
−0.552841 + 0.833287i \(0.686456\pi\)
\(54\) 7.34612 0.999680
\(55\) 9.88889 1.33342
\(56\) −3.39338 −0.453460
\(57\) −5.61851 −0.744190
\(58\) −1.39033 −0.182559
\(59\) 6.52281 0.849197 0.424599 0.905382i \(-0.360415\pi\)
0.424599 + 0.905382i \(0.360415\pi\)
\(60\) −8.89983 −1.14896
\(61\) 6.23515 0.798330 0.399165 0.916879i \(-0.369300\pi\)
0.399165 + 0.916879i \(0.369300\pi\)
\(62\) 9.18702 1.16675
\(63\) 18.7218 2.35873
\(64\) 1.00000 0.125000
\(65\) −9.23516 −1.14548
\(66\) 9.46369 1.16490
\(67\) 11.9464 1.45948 0.729742 0.683723i \(-0.239640\pi\)
0.729742 + 0.683723i \(0.239640\pi\)
\(68\) 2.71304 0.329004
\(69\) −5.18223 −0.623867
\(70\) −10.3482 −1.23685
\(71\) −1.32813 −0.157620 −0.0788098 0.996890i \(-0.525112\pi\)
−0.0788098 + 0.996890i \(0.525112\pi\)
\(72\) −5.51716 −0.650203
\(73\) 5.31705 0.622314 0.311157 0.950359i \(-0.399284\pi\)
0.311157 + 0.950359i \(0.399284\pi\)
\(74\) −4.71373 −0.547961
\(75\) −12.5483 −1.44895
\(76\) 1.92519 0.220835
\(77\) 11.0039 1.25401
\(78\) −8.83807 −1.00071
\(79\) 10.2976 1.15857 0.579285 0.815125i \(-0.303332\pi\)
0.579285 + 0.815125i \(0.303332\pi\)
\(80\) 3.04954 0.340949
\(81\) 4.88755 0.543062
\(82\) 11.1910 1.23584
\(83\) 11.8365 1.29922 0.649610 0.760267i \(-0.274932\pi\)
0.649610 + 0.760267i \(0.274932\pi\)
\(84\) −9.90330 −1.08054
\(85\) 8.27351 0.897389
\(86\) 12.0232 1.29650
\(87\) −4.05757 −0.435017
\(88\) −3.24275 −0.345678
\(89\) −1.96091 −0.207856 −0.103928 0.994585i \(-0.533141\pi\)
−0.103928 + 0.994585i \(0.533141\pi\)
\(90\) −16.8248 −1.77349
\(91\) −10.2764 −1.07726
\(92\) 1.77570 0.185129
\(93\) 26.8116 2.78023
\(94\) −6.09693 −0.628850
\(95\) 5.87095 0.602347
\(96\) 2.91842 0.297860
\(97\) 17.6719 1.79431 0.897153 0.441721i \(-0.145632\pi\)
0.897153 + 0.441721i \(0.145632\pi\)
\(98\) −4.51503 −0.456087
\(99\) 17.8907 1.79809
\(100\) 4.29970 0.429970
\(101\) −12.1834 −1.21229 −0.606144 0.795355i \(-0.707285\pi\)
−0.606144 + 0.795355i \(0.707285\pi\)
\(102\) 7.91777 0.783976
\(103\) 9.85463 0.971006 0.485503 0.874235i \(-0.338637\pi\)
0.485503 + 0.874235i \(0.338637\pi\)
\(104\) 3.02838 0.296957
\(105\) −30.2005 −2.94727
\(106\) 8.04949 0.781836
\(107\) −16.3987 −1.58532 −0.792660 0.609664i \(-0.791305\pi\)
−0.792660 + 0.609664i \(0.791305\pi\)
\(108\) −7.34612 −0.706880
\(109\) 20.1882 1.93368 0.966838 0.255389i \(-0.0822036\pi\)
0.966838 + 0.255389i \(0.0822036\pi\)
\(110\) −9.88889 −0.942868
\(111\) −13.7566 −1.30572
\(112\) 3.39338 0.320644
\(113\) 2.38781 0.224626 0.112313 0.993673i \(-0.464174\pi\)
0.112313 + 0.993673i \(0.464174\pi\)
\(114\) 5.61851 0.526222
\(115\) 5.41506 0.504957
\(116\) 1.39033 0.129089
\(117\) −16.7080 −1.54466
\(118\) −6.52281 −0.600473
\(119\) 9.20637 0.843946
\(120\) 8.89983 0.812440
\(121\) −0.484593 −0.0440539
\(122\) −6.23515 −0.564504
\(123\) 32.6600 2.94485
\(124\) −9.18702 −0.825019
\(125\) −2.13561 −0.191015
\(126\) −18.7218 −1.66787
\(127\) 1.82067 0.161558 0.0807791 0.996732i \(-0.474259\pi\)
0.0807791 + 0.996732i \(0.474259\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 35.0888 3.08940
\(130\) 9.23516 0.809977
\(131\) 10.1233 0.884480 0.442240 0.896897i \(-0.354184\pi\)
0.442240 + 0.896897i \(0.354184\pi\)
\(132\) −9.46369 −0.823708
\(133\) 6.53291 0.566475
\(134\) −11.9464 −1.03201
\(135\) −22.4023 −1.92808
\(136\) −2.71304 −0.232641
\(137\) 5.59503 0.478016 0.239008 0.971018i \(-0.423178\pi\)
0.239008 + 0.971018i \(0.423178\pi\)
\(138\) 5.18223 0.441140
\(139\) 11.3239 0.960481 0.480241 0.877137i \(-0.340549\pi\)
0.480241 + 0.877137i \(0.340549\pi\)
\(140\) 10.3482 0.874587
\(141\) −17.7934 −1.49847
\(142\) 1.32813 0.111454
\(143\) −9.82026 −0.821211
\(144\) 5.51716 0.459763
\(145\) 4.23987 0.352102
\(146\) −5.31705 −0.440042
\(147\) −13.1767 −1.08680
\(148\) 4.71373 0.387467
\(149\) −3.07453 −0.251876 −0.125938 0.992038i \(-0.540194\pi\)
−0.125938 + 0.992038i \(0.540194\pi\)
\(150\) 12.5483 1.02456
\(151\) −0.609059 −0.0495646 −0.0247823 0.999693i \(-0.507889\pi\)
−0.0247823 + 0.999693i \(0.507889\pi\)
\(152\) −1.92519 −0.156154
\(153\) 14.9683 1.21011
\(154\) −11.0039 −0.886717
\(155\) −28.0162 −2.25032
\(156\) 8.83807 0.707612
\(157\) 11.0608 0.882747 0.441374 0.897323i \(-0.354491\pi\)
0.441374 + 0.897323i \(0.354491\pi\)
\(158\) −10.2976 −0.819233
\(159\) 23.4918 1.86302
\(160\) −3.04954 −0.241087
\(161\) 6.02562 0.474885
\(162\) −4.88755 −0.384003
\(163\) 15.4803 1.21251 0.606255 0.795270i \(-0.292671\pi\)
0.606255 + 0.795270i \(0.292671\pi\)
\(164\) −11.1910 −0.873869
\(165\) −28.8599 −2.24674
\(166\) −11.8365 −0.918688
\(167\) −0.310574 −0.0240329 −0.0120165 0.999928i \(-0.503825\pi\)
−0.0120165 + 0.999928i \(0.503825\pi\)
\(168\) 9.90330 0.764056
\(169\) −3.82893 −0.294533
\(170\) −8.27351 −0.634550
\(171\) 10.6216 0.812253
\(172\) −12.0232 −0.916764
\(173\) −2.50587 −0.190518 −0.0952588 0.995453i \(-0.530368\pi\)
−0.0952588 + 0.995453i \(0.530368\pi\)
\(174\) 4.05757 0.307603
\(175\) 14.5905 1.10294
\(176\) 3.24275 0.244431
\(177\) −19.0363 −1.43085
\(178\) 1.96091 0.146976
\(179\) −3.41102 −0.254951 −0.127476 0.991842i \(-0.540687\pi\)
−0.127476 + 0.991842i \(0.540687\pi\)
\(180\) 16.8248 1.25405
\(181\) −19.0067 −1.41276 −0.706380 0.707833i \(-0.749673\pi\)
−0.706380 + 0.707833i \(0.749673\pi\)
\(182\) 10.2764 0.761740
\(183\) −18.1968 −1.34514
\(184\) −1.77570 −0.130906
\(185\) 14.3747 1.05685
\(186\) −26.8116 −1.96592
\(187\) 8.79769 0.643351
\(188\) 6.09693 0.444664
\(189\) −24.9282 −1.81326
\(190\) −5.87095 −0.425924
\(191\) 5.35334 0.387354 0.193677 0.981065i \(-0.437959\pi\)
0.193677 + 0.981065i \(0.437959\pi\)
\(192\) −2.91842 −0.210619
\(193\) 9.31689 0.670644 0.335322 0.942103i \(-0.391155\pi\)
0.335322 + 0.942103i \(0.391155\pi\)
\(194\) −17.6719 −1.26877
\(195\) 26.9520 1.93008
\(196\) 4.51503 0.322502
\(197\) 16.2169 1.15541 0.577703 0.816247i \(-0.303949\pi\)
0.577703 + 0.816247i \(0.303949\pi\)
\(198\) −17.8907 −1.27144
\(199\) 3.69204 0.261722 0.130861 0.991401i \(-0.458226\pi\)
0.130861 + 0.991401i \(0.458226\pi\)
\(200\) −4.29970 −0.304034
\(201\) −34.8645 −2.45915
\(202\) 12.1834 0.857218
\(203\) 4.71792 0.331133
\(204\) −7.91777 −0.554355
\(205\) −34.1274 −2.38356
\(206\) −9.85463 −0.686605
\(207\) 9.79681 0.680925
\(208\) −3.02838 −0.209980
\(209\) 6.24291 0.431831
\(210\) 30.2005 2.08403
\(211\) −15.4489 −1.06355 −0.531773 0.846887i \(-0.678474\pi\)
−0.531773 + 0.846887i \(0.678474\pi\)
\(212\) −8.04949 −0.552841
\(213\) 3.87603 0.265581
\(214\) 16.3987 1.12099
\(215\) −36.6654 −2.50056
\(216\) 7.34612 0.499840
\(217\) −31.1751 −2.11630
\(218\) −20.1882 −1.36732
\(219\) −15.5174 −1.04857
\(220\) 9.88889 0.666709
\(221\) −8.21610 −0.552675
\(222\) 13.7566 0.923285
\(223\) −13.5607 −0.908094 −0.454047 0.890978i \(-0.650020\pi\)
−0.454047 + 0.890978i \(0.650020\pi\)
\(224\) −3.39338 −0.226730
\(225\) 23.7221 1.58147
\(226\) −2.38781 −0.158835
\(227\) 8.04828 0.534183 0.267091 0.963671i \(-0.413937\pi\)
0.267091 + 0.963671i \(0.413937\pi\)
\(228\) −5.61851 −0.372095
\(229\) −14.2222 −0.939829 −0.469914 0.882712i \(-0.655715\pi\)
−0.469914 + 0.882712i \(0.655715\pi\)
\(230\) −5.41506 −0.357059
\(231\) −32.1139 −2.11294
\(232\) −1.39033 −0.0912797
\(233\) 2.83488 0.185719 0.0928597 0.995679i \(-0.470399\pi\)
0.0928597 + 0.995679i \(0.470399\pi\)
\(234\) 16.7080 1.09224
\(235\) 18.5928 1.21286
\(236\) 6.52281 0.424599
\(237\) −30.0527 −1.95213
\(238\) −9.20637 −0.596760
\(239\) 0.659329 0.0426485 0.0213242 0.999773i \(-0.493212\pi\)
0.0213242 + 0.999773i \(0.493212\pi\)
\(240\) −8.89983 −0.574482
\(241\) −5.93920 −0.382577 −0.191289 0.981534i \(-0.561267\pi\)
−0.191289 + 0.981534i \(0.561267\pi\)
\(242\) 0.484593 0.0311508
\(243\) 7.77442 0.498729
\(244\) 6.23515 0.399165
\(245\) 13.7688 0.879654
\(246\) −32.6600 −2.08232
\(247\) −5.83021 −0.370967
\(248\) 9.18702 0.583377
\(249\) −34.5437 −2.18912
\(250\) 2.13561 0.135068
\(251\) 16.9407 1.06929 0.534644 0.845077i \(-0.320446\pi\)
0.534644 + 0.845077i \(0.320446\pi\)
\(252\) 18.7218 1.17936
\(253\) 5.75814 0.362011
\(254\) −1.82067 −0.114239
\(255\) −24.1456 −1.51205
\(256\) 1.00000 0.0625000
\(257\) 11.0742 0.690792 0.345396 0.938457i \(-0.387745\pi\)
0.345396 + 0.938457i \(0.387745\pi\)
\(258\) −35.0888 −2.18454
\(259\) 15.9955 0.993912
\(260\) −9.23516 −0.572740
\(261\) 7.67068 0.474803
\(262\) −10.1233 −0.625422
\(263\) 17.3168 1.06780 0.533899 0.845548i \(-0.320726\pi\)
0.533899 + 0.845548i \(0.320726\pi\)
\(264\) 9.46369 0.582450
\(265\) −24.5472 −1.50793
\(266\) −6.53291 −0.400558
\(267\) 5.72274 0.350226
\(268\) 11.9464 0.729742
\(269\) −0.794480 −0.0484403 −0.0242201 0.999707i \(-0.507710\pi\)
−0.0242201 + 0.999707i \(0.507710\pi\)
\(270\) 22.4023 1.36336
\(271\) 8.63822 0.524735 0.262367 0.964968i \(-0.415497\pi\)
0.262367 + 0.964968i \(0.415497\pi\)
\(272\) 2.71304 0.164502
\(273\) 29.9909 1.81513
\(274\) −5.59503 −0.338008
\(275\) 13.9428 0.840784
\(276\) −5.18223 −0.311933
\(277\) −16.8967 −1.01522 −0.507612 0.861586i \(-0.669472\pi\)
−0.507612 + 0.861586i \(0.669472\pi\)
\(278\) −11.3239 −0.679163
\(279\) −50.6863 −3.03451
\(280\) −10.3482 −0.618426
\(281\) 12.0704 0.720058 0.360029 0.932941i \(-0.382767\pi\)
0.360029 + 0.932941i \(0.382767\pi\)
\(282\) 17.7934 1.05958
\(283\) −7.86758 −0.467679 −0.233839 0.972275i \(-0.575129\pi\)
−0.233839 + 0.972275i \(0.575129\pi\)
\(284\) −1.32813 −0.0788098
\(285\) −17.1339 −1.01492
\(286\) 9.82026 0.580684
\(287\) −37.9753 −2.24161
\(288\) −5.51716 −0.325102
\(289\) −9.63943 −0.567025
\(290\) −4.23987 −0.248974
\(291\) −51.5738 −3.02331
\(292\) 5.31705 0.311157
\(293\) 8.28476 0.484001 0.242000 0.970276i \(-0.422196\pi\)
0.242000 + 0.970276i \(0.422196\pi\)
\(294\) 13.1767 0.768483
\(295\) 19.8916 1.15813
\(296\) −4.71373 −0.273980
\(297\) −23.8216 −1.38227
\(298\) 3.07453 0.178103
\(299\) −5.37748 −0.310988
\(300\) −12.5483 −0.724477
\(301\) −40.7994 −2.35164
\(302\) 0.609059 0.0350474
\(303\) 35.5561 2.04264
\(304\) 1.92519 0.110417
\(305\) 19.0143 1.08876
\(306\) −14.9683 −0.855678
\(307\) −9.29988 −0.530772 −0.265386 0.964142i \(-0.585499\pi\)
−0.265386 + 0.964142i \(0.585499\pi\)
\(308\) 11.0039 0.627004
\(309\) −28.7599 −1.63609
\(310\) 28.0162 1.59121
\(311\) 18.1058 1.02668 0.513342 0.858184i \(-0.328407\pi\)
0.513342 + 0.858184i \(0.328407\pi\)
\(312\) −8.83807 −0.500357
\(313\) −19.7732 −1.11765 −0.558825 0.829286i \(-0.688748\pi\)
−0.558825 + 0.829286i \(0.688748\pi\)
\(314\) −11.0608 −0.624196
\(315\) 57.0929 3.21682
\(316\) 10.2976 0.579285
\(317\) −25.3471 −1.42363 −0.711817 0.702365i \(-0.752127\pi\)
−0.711817 + 0.702365i \(0.752127\pi\)
\(318\) −23.4918 −1.31735
\(319\) 4.50849 0.252427
\(320\) 3.04954 0.170474
\(321\) 47.8582 2.67118
\(322\) −6.02562 −0.335795
\(323\) 5.22312 0.290622
\(324\) 4.88755 0.271531
\(325\) −13.0211 −0.722280
\(326\) −15.4803 −0.857374
\(327\) −58.9175 −3.25815
\(328\) 11.1910 0.617919
\(329\) 20.6892 1.14063
\(330\) 28.8599 1.58868
\(331\) 12.8359 0.705522 0.352761 0.935713i \(-0.385243\pi\)
0.352761 + 0.935713i \(0.385243\pi\)
\(332\) 11.8365 0.649610
\(333\) 26.0064 1.42514
\(334\) 0.310574 0.0169938
\(335\) 36.4310 1.99044
\(336\) −9.90330 −0.540269
\(337\) 12.4219 0.676663 0.338332 0.941027i \(-0.390137\pi\)
0.338332 + 0.941027i \(0.390137\pi\)
\(338\) 3.82893 0.208267
\(339\) −6.96862 −0.378483
\(340\) 8.27351 0.448694
\(341\) −29.7912 −1.61328
\(342\) −10.6216 −0.574350
\(343\) −8.43245 −0.455309
\(344\) 12.0232 0.648250
\(345\) −15.8034 −0.850827
\(346\) 2.50587 0.134716
\(347\) 15.7866 0.847468 0.423734 0.905787i \(-0.360719\pi\)
0.423734 + 0.905787i \(0.360719\pi\)
\(348\) −4.05757 −0.217508
\(349\) −30.6239 −1.63926 −0.819630 0.572893i \(-0.805821\pi\)
−0.819630 + 0.572893i \(0.805821\pi\)
\(350\) −14.5905 −0.779895
\(351\) 22.2468 1.18745
\(352\) −3.24275 −0.172839
\(353\) −1.54201 −0.0820731 −0.0410366 0.999158i \(-0.513066\pi\)
−0.0410366 + 0.999158i \(0.513066\pi\)
\(354\) 19.0363 1.01177
\(355\) −4.05017 −0.214961
\(356\) −1.96091 −0.103928
\(357\) −26.8680 −1.42201
\(358\) 3.41102 0.180278
\(359\) 5.82488 0.307425 0.153713 0.988116i \(-0.450877\pi\)
0.153713 + 0.988116i \(0.450877\pi\)
\(360\) −16.8248 −0.886744
\(361\) −15.2936 −0.804928
\(362\) 19.0067 0.998972
\(363\) 1.41424 0.0742286
\(364\) −10.2764 −0.538632
\(365\) 16.2146 0.848709
\(366\) 18.1968 0.951161
\(367\) 30.0128 1.56665 0.783327 0.621610i \(-0.213521\pi\)
0.783327 + 0.621610i \(0.213521\pi\)
\(368\) 1.77570 0.0925647
\(369\) −61.7425 −3.21418
\(370\) −14.3747 −0.747306
\(371\) −27.3150 −1.41812
\(372\) 26.8116 1.39011
\(373\) −22.8789 −1.18463 −0.592313 0.805708i \(-0.701785\pi\)
−0.592313 + 0.805708i \(0.701785\pi\)
\(374\) −8.79769 −0.454918
\(375\) 6.23259 0.321850
\(376\) −6.09693 −0.314425
\(377\) −4.21045 −0.216849
\(378\) 24.9282 1.28217
\(379\) 5.67831 0.291675 0.145838 0.989309i \(-0.453412\pi\)
0.145838 + 0.989309i \(0.453412\pi\)
\(380\) 5.87095 0.301173
\(381\) −5.31347 −0.272217
\(382\) −5.35334 −0.273901
\(383\) 17.1966 0.878703 0.439352 0.898315i \(-0.355208\pi\)
0.439352 + 0.898315i \(0.355208\pi\)
\(384\) 2.91842 0.148930
\(385\) 33.5568 1.71021
\(386\) −9.31689 −0.474217
\(387\) −66.3341 −3.37195
\(388\) 17.6719 0.897153
\(389\) 37.2248 1.88737 0.943686 0.330843i \(-0.107333\pi\)
0.943686 + 0.330843i \(0.107333\pi\)
\(390\) −26.9520 −1.36477
\(391\) 4.81753 0.243633
\(392\) −4.51503 −0.228043
\(393\) −29.5441 −1.49030
\(394\) −16.2169 −0.816996
\(395\) 31.4029 1.58005
\(396\) 17.8907 0.899044
\(397\) −14.7102 −0.738286 −0.369143 0.929373i \(-0.620349\pi\)
−0.369143 + 0.929373i \(0.620349\pi\)
\(398\) −3.69204 −0.185065
\(399\) −19.0658 −0.954482
\(400\) 4.29970 0.214985
\(401\) −29.6325 −1.47978 −0.739889 0.672729i \(-0.765122\pi\)
−0.739889 + 0.672729i \(0.765122\pi\)
\(402\) 34.8645 1.73888
\(403\) 27.8218 1.38590
\(404\) −12.1834 −0.606144
\(405\) 14.9048 0.740625
\(406\) −4.71792 −0.234147
\(407\) 15.2854 0.757672
\(408\) 7.91777 0.391988
\(409\) 31.4794 1.55656 0.778278 0.627919i \(-0.216093\pi\)
0.778278 + 0.627919i \(0.216093\pi\)
\(410\) 34.1274 1.68543
\(411\) −16.3286 −0.805432
\(412\) 9.85463 0.485503
\(413\) 22.1344 1.08916
\(414\) −9.79681 −0.481487
\(415\) 36.0958 1.77187
\(416\) 3.02838 0.148478
\(417\) −33.0479 −1.61836
\(418\) −6.24291 −0.305351
\(419\) −6.87683 −0.335955 −0.167978 0.985791i \(-0.553724\pi\)
−0.167978 + 0.985791i \(0.553724\pi\)
\(420\) −30.2005 −1.47363
\(421\) −14.7388 −0.718325 −0.359163 0.933275i \(-0.616938\pi\)
−0.359163 + 0.933275i \(0.616938\pi\)
\(422\) 15.4489 0.752041
\(423\) 33.6377 1.63552
\(424\) 8.04949 0.390918
\(425\) 11.6652 0.565847
\(426\) −3.87603 −0.187794
\(427\) 21.1582 1.02392
\(428\) −16.3987 −0.792660
\(429\) 28.6596 1.38370
\(430\) 36.6654 1.76816
\(431\) −0.510707 −0.0245999 −0.0122999 0.999924i \(-0.503915\pi\)
−0.0122999 + 0.999924i \(0.503915\pi\)
\(432\) −7.34612 −0.353440
\(433\) 13.0265 0.626013 0.313006 0.949751i \(-0.398664\pi\)
0.313006 + 0.949751i \(0.398664\pi\)
\(434\) 31.1751 1.49645
\(435\) −12.3737 −0.593274
\(436\) 20.1882 0.966838
\(437\) 3.41856 0.163532
\(438\) 15.5174 0.741449
\(439\) 15.0265 0.717175 0.358587 0.933496i \(-0.383259\pi\)
0.358587 + 0.933496i \(0.383259\pi\)
\(440\) −9.88889 −0.471434
\(441\) 24.9101 1.18620
\(442\) 8.21610 0.390800
\(443\) 24.2179 1.15063 0.575313 0.817934i \(-0.304880\pi\)
0.575313 + 0.817934i \(0.304880\pi\)
\(444\) −13.7566 −0.652861
\(445\) −5.97986 −0.283473
\(446\) 13.5607 0.642119
\(447\) 8.97277 0.424397
\(448\) 3.39338 0.160322
\(449\) 3.31168 0.156288 0.0781439 0.996942i \(-0.475101\pi\)
0.0781439 + 0.996942i \(0.475101\pi\)
\(450\) −23.7221 −1.11827
\(451\) −36.2895 −1.70881
\(452\) 2.38781 0.112313
\(453\) 1.77749 0.0835137
\(454\) −8.04828 −0.377724
\(455\) −31.3384 −1.46917
\(456\) 5.61851 0.263111
\(457\) 7.98224 0.373393 0.186697 0.982418i \(-0.440222\pi\)
0.186697 + 0.982418i \(0.440222\pi\)
\(458\) 14.2222 0.664559
\(459\) −19.9303 −0.930266
\(460\) 5.41506 0.252479
\(461\) 32.5697 1.51692 0.758461 0.651719i \(-0.225952\pi\)
0.758461 + 0.651719i \(0.225952\pi\)
\(462\) 32.1139 1.49407
\(463\) −30.9159 −1.43678 −0.718391 0.695640i \(-0.755121\pi\)
−0.718391 + 0.695640i \(0.755121\pi\)
\(464\) 1.39033 0.0645445
\(465\) 81.7629 3.79167
\(466\) −2.83488 −0.131323
\(467\) 26.2417 1.21432 0.607160 0.794580i \(-0.292309\pi\)
0.607160 + 0.794580i \(0.292309\pi\)
\(468\) −16.7080 −0.772329
\(469\) 40.5386 1.87190
\(470\) −18.5928 −0.857623
\(471\) −32.2800 −1.48738
\(472\) −6.52281 −0.300237
\(473\) −38.9883 −1.79269
\(474\) 30.0527 1.38037
\(475\) 8.27774 0.379809
\(476\) 9.20637 0.421973
\(477\) −44.4103 −2.03341
\(478\) −0.659329 −0.0301570
\(479\) −5.21508 −0.238283 −0.119142 0.992877i \(-0.538014\pi\)
−0.119142 + 0.992877i \(0.538014\pi\)
\(480\) 8.89983 0.406220
\(481\) −14.2750 −0.650882
\(482\) 5.93920 0.270523
\(483\) −17.5853 −0.800157
\(484\) −0.484593 −0.0220270
\(485\) 53.8910 2.44707
\(486\) −7.77442 −0.352655
\(487\) 41.3148 1.87215 0.936077 0.351796i \(-0.114429\pi\)
0.936077 + 0.351796i \(0.114429\pi\)
\(488\) −6.23515 −0.282252
\(489\) −45.1779 −2.04302
\(490\) −13.7688 −0.622010
\(491\) −43.2059 −1.94985 −0.974927 0.222525i \(-0.928570\pi\)
−0.974927 + 0.222525i \(0.928570\pi\)
\(492\) 32.6600 1.47243
\(493\) 3.77202 0.169883
\(494\) 5.83021 0.262313
\(495\) 54.5585 2.45222
\(496\) −9.18702 −0.412510
\(497\) −4.50684 −0.202159
\(498\) 34.5437 1.54794
\(499\) 2.55810 0.114516 0.0572582 0.998359i \(-0.481764\pi\)
0.0572582 + 0.998359i \(0.481764\pi\)
\(500\) −2.13561 −0.0955073
\(501\) 0.906384 0.0404942
\(502\) −16.9407 −0.756101
\(503\) 29.5012 1.31540 0.657698 0.753282i \(-0.271530\pi\)
0.657698 + 0.753282i \(0.271530\pi\)
\(504\) −18.7218 −0.833936
\(505\) −37.1536 −1.65331
\(506\) −5.75814 −0.255981
\(507\) 11.1744 0.496274
\(508\) 1.82067 0.0807791
\(509\) 7.95135 0.352438 0.176219 0.984351i \(-0.443613\pi\)
0.176219 + 0.984351i \(0.443613\pi\)
\(510\) 24.1456 1.06918
\(511\) 18.0428 0.798166
\(512\) −1.00000 −0.0441942
\(513\) −14.1427 −0.624415
\(514\) −11.0742 −0.488464
\(515\) 30.0521 1.32425
\(516\) 35.0888 1.54470
\(517\) 19.7708 0.869519
\(518\) −15.9955 −0.702802
\(519\) 7.31317 0.321013
\(520\) 9.23516 0.404988
\(521\) −6.42823 −0.281626 −0.140813 0.990036i \(-0.544972\pi\)
−0.140813 + 0.990036i \(0.544972\pi\)
\(522\) −7.67068 −0.335736
\(523\) 30.1877 1.32001 0.660007 0.751259i \(-0.270553\pi\)
0.660007 + 0.751259i \(0.270553\pi\)
\(524\) 10.1233 0.442240
\(525\) −42.5812 −1.85839
\(526\) −17.3168 −0.755047
\(527\) −24.9247 −1.08574
\(528\) −9.46369 −0.411854
\(529\) −19.8469 −0.862909
\(530\) 24.5472 1.06626
\(531\) 35.9874 1.56172
\(532\) 6.53291 0.283238
\(533\) 33.8905 1.46796
\(534\) −5.72274 −0.247647
\(535\) −50.0084 −2.16205
\(536\) −11.9464 −0.516005
\(537\) 9.95477 0.429580
\(538\) 0.794480 0.0342524
\(539\) 14.6411 0.630637
\(540\) −22.4023 −0.964040
\(541\) 27.8226 1.19619 0.598093 0.801427i \(-0.295925\pi\)
0.598093 + 0.801427i \(0.295925\pi\)
\(542\) −8.63822 −0.371044
\(543\) 55.4696 2.38043
\(544\) −2.71304 −0.116320
\(545\) 61.5647 2.63714
\(546\) −29.9909 −1.28349
\(547\) −22.2276 −0.950382 −0.475191 0.879883i \(-0.657621\pi\)
−0.475191 + 0.879883i \(0.657621\pi\)
\(548\) 5.59503 0.239008
\(549\) 34.4003 1.46817
\(550\) −13.9428 −0.594524
\(551\) 2.67665 0.114029
\(552\) 5.18223 0.220570
\(553\) 34.9437 1.48596
\(554\) 16.8967 0.717872
\(555\) −41.9514 −1.78074
\(556\) 11.3239 0.480241
\(557\) 28.1460 1.19258 0.596291 0.802768i \(-0.296640\pi\)
0.596291 + 0.802768i \(0.296640\pi\)
\(558\) 50.6863 2.14572
\(559\) 36.4109 1.54002
\(560\) 10.3482 0.437293
\(561\) −25.6753 −1.08401
\(562\) −12.0704 −0.509158
\(563\) −17.9140 −0.754986 −0.377493 0.926013i \(-0.623214\pi\)
−0.377493 + 0.926013i \(0.623214\pi\)
\(564\) −17.7934 −0.749236
\(565\) 7.28171 0.306344
\(566\) 7.86758 0.330699
\(567\) 16.5853 0.696519
\(568\) 1.32813 0.0557269
\(569\) 10.7515 0.450726 0.225363 0.974275i \(-0.427643\pi\)
0.225363 + 0.974275i \(0.427643\pi\)
\(570\) 17.1339 0.717659
\(571\) 5.07165 0.212242 0.106121 0.994353i \(-0.466157\pi\)
0.106121 + 0.994353i \(0.466157\pi\)
\(572\) −9.82026 −0.410606
\(573\) −15.6233 −0.652672
\(574\) 37.9753 1.58506
\(575\) 7.63496 0.318400
\(576\) 5.51716 0.229882
\(577\) 18.2492 0.759724 0.379862 0.925043i \(-0.375971\pi\)
0.379862 + 0.925043i \(0.375971\pi\)
\(578\) 9.63943 0.400947
\(579\) −27.1906 −1.13000
\(580\) 4.23987 0.176051
\(581\) 40.1656 1.66635
\(582\) 51.5738 2.13780
\(583\) −26.1025 −1.08105
\(584\) −5.31705 −0.220021
\(585\) −50.9518 −2.10660
\(586\) −8.28476 −0.342240
\(587\) −10.1541 −0.419105 −0.209552 0.977797i \(-0.567201\pi\)
−0.209552 + 0.977797i \(0.567201\pi\)
\(588\) −13.1767 −0.543400
\(589\) −17.6868 −0.728771
\(590\) −19.8916 −0.818923
\(591\) −47.3277 −1.94680
\(592\) 4.71373 0.193733
\(593\) 4.77348 0.196023 0.0980117 0.995185i \(-0.468752\pi\)
0.0980117 + 0.995185i \(0.468752\pi\)
\(594\) 23.8216 0.977412
\(595\) 28.0752 1.15097
\(596\) −3.07453 −0.125938
\(597\) −10.7749 −0.440988
\(598\) 5.37748 0.219902
\(599\) −27.4626 −1.12209 −0.561047 0.827784i \(-0.689601\pi\)
−0.561047 + 0.827784i \(0.689601\pi\)
\(600\) 12.5483 0.512282
\(601\) 32.7509 1.33594 0.667969 0.744189i \(-0.267164\pi\)
0.667969 + 0.744189i \(0.267164\pi\)
\(602\) 40.7994 1.66286
\(603\) 65.9101 2.68407
\(604\) −0.609059 −0.0247823
\(605\) −1.47779 −0.0600805
\(606\) −35.5561 −1.44437
\(607\) 41.0293 1.66533 0.832665 0.553777i \(-0.186814\pi\)
0.832665 + 0.553777i \(0.186814\pi\)
\(608\) −1.92519 −0.0780769
\(609\) −13.7689 −0.557943
\(610\) −19.0143 −0.769869
\(611\) −18.4638 −0.746965
\(612\) 14.9683 0.605056
\(613\) 23.1268 0.934083 0.467041 0.884235i \(-0.345320\pi\)
0.467041 + 0.884235i \(0.345320\pi\)
\(614\) 9.29988 0.375313
\(615\) 99.5979 4.01618
\(616\) −11.0039 −0.443359
\(617\) −9.09422 −0.366119 −0.183060 0.983102i \(-0.558600\pi\)
−0.183060 + 0.983102i \(0.558600\pi\)
\(618\) 28.7599 1.15689
\(619\) −22.7072 −0.912678 −0.456339 0.889806i \(-0.650840\pi\)
−0.456339 + 0.889806i \(0.650840\pi\)
\(620\) −28.0162 −1.12516
\(621\) −13.0445 −0.523457
\(622\) −18.1058 −0.725975
\(623\) −6.65410 −0.266591
\(624\) 8.83807 0.353806
\(625\) −28.0111 −1.12044
\(626\) 19.7732 0.790298
\(627\) −18.2194 −0.727613
\(628\) 11.0608 0.441374
\(629\) 12.7885 0.509912
\(630\) −57.0929 −2.27464
\(631\) 29.3641 1.16897 0.584484 0.811405i \(-0.301297\pi\)
0.584484 + 0.811405i \(0.301297\pi\)
\(632\) −10.2976 −0.409616
\(633\) 45.0863 1.79202
\(634\) 25.3471 1.00666
\(635\) 5.55220 0.220332
\(636\) 23.4918 0.931509
\(637\) −13.6732 −0.541752
\(638\) −4.50849 −0.178493
\(639\) −7.32748 −0.289871
\(640\) −3.04954 −0.120544
\(641\) 40.8880 1.61498 0.807489 0.589883i \(-0.200826\pi\)
0.807489 + 0.589883i \(0.200826\pi\)
\(642\) −47.8582 −1.88881
\(643\) −30.6968 −1.21056 −0.605282 0.796011i \(-0.706939\pi\)
−0.605282 + 0.796011i \(0.706939\pi\)
\(644\) 6.02562 0.237443
\(645\) 107.005 4.21331
\(646\) −5.22312 −0.205501
\(647\) 17.6111 0.692363 0.346181 0.938168i \(-0.387478\pi\)
0.346181 + 0.938168i \(0.387478\pi\)
\(648\) −4.88755 −0.192001
\(649\) 21.1518 0.830281
\(650\) 13.0211 0.510729
\(651\) 90.9818 3.56586
\(652\) 15.4803 0.606255
\(653\) −34.1366 −1.33587 −0.667934 0.744221i \(-0.732821\pi\)
−0.667934 + 0.744221i \(0.732821\pi\)
\(654\) 58.9175 2.30386
\(655\) 30.8715 1.20625
\(656\) −11.1910 −0.436935
\(657\) 29.3350 1.14447
\(658\) −20.6892 −0.806549
\(659\) −15.5750 −0.606717 −0.303359 0.952876i \(-0.598108\pi\)
−0.303359 + 0.952876i \(0.598108\pi\)
\(660\) −28.8599 −1.12337
\(661\) −47.6998 −1.85531 −0.927653 0.373444i \(-0.878177\pi\)
−0.927653 + 0.373444i \(0.878177\pi\)
\(662\) −12.8359 −0.498880
\(663\) 23.9780 0.931228
\(664\) −11.8365 −0.459344
\(665\) 19.9224 0.772556
\(666\) −26.0064 −1.00773
\(667\) 2.46881 0.0955926
\(668\) −0.310574 −0.0120165
\(669\) 39.5759 1.53009
\(670\) −36.4310 −1.40745
\(671\) 20.2190 0.780547
\(672\) 9.90330 0.382028
\(673\) −43.1214 −1.66221 −0.831104 0.556116i \(-0.812291\pi\)
−0.831104 + 0.556116i \(0.812291\pi\)
\(674\) −12.4219 −0.478473
\(675\) −31.5861 −1.21575
\(676\) −3.82893 −0.147267
\(677\) −15.3548 −0.590134 −0.295067 0.955477i \(-0.595342\pi\)
−0.295067 + 0.955477i \(0.595342\pi\)
\(678\) 6.96862 0.267628
\(679\) 59.9673 2.30134
\(680\) −8.27351 −0.317275
\(681\) −23.4882 −0.900071
\(682\) 29.7912 1.14076
\(683\) 16.1837 0.619252 0.309626 0.950858i \(-0.399796\pi\)
0.309626 + 0.950858i \(0.399796\pi\)
\(684\) 10.6216 0.406127
\(685\) 17.0623 0.651916
\(686\) 8.43245 0.321952
\(687\) 41.5063 1.58356
\(688\) −12.0232 −0.458382
\(689\) 24.3769 0.928685
\(690\) 15.8034 0.601626
\(691\) −33.0997 −1.25917 −0.629586 0.776931i \(-0.716775\pi\)
−0.629586 + 0.776931i \(0.716775\pi\)
\(692\) −2.50587 −0.0952588
\(693\) 60.7101 2.30619
\(694\) −15.7866 −0.599250
\(695\) 34.5327 1.30990
\(696\) 4.05757 0.153802
\(697\) −30.3616 −1.15003
\(698\) 30.6239 1.15913
\(699\) −8.27337 −0.312928
\(700\) 14.5905 0.551469
\(701\) −22.7439 −0.859026 −0.429513 0.903061i \(-0.641315\pi\)
−0.429513 + 0.903061i \(0.641315\pi\)
\(702\) −22.2468 −0.839652
\(703\) 9.07485 0.342264
\(704\) 3.24275 0.122216
\(705\) −54.2616 −2.04361
\(706\) 1.54201 0.0580345
\(707\) −41.3427 −1.55485
\(708\) −19.0363 −0.715427
\(709\) −40.2044 −1.50991 −0.754955 0.655777i \(-0.772341\pi\)
−0.754955 + 0.655777i \(0.772341\pi\)
\(710\) 4.05017 0.152000
\(711\) 56.8135 2.13067
\(712\) 1.96091 0.0734881
\(713\) −16.3134 −0.610941
\(714\) 26.8680 1.00551
\(715\) −29.9473 −1.11996
\(716\) −3.41102 −0.127476
\(717\) −1.92420 −0.0718605
\(718\) −5.82488 −0.217383
\(719\) −4.50222 −0.167904 −0.0839521 0.996470i \(-0.526754\pi\)
−0.0839521 + 0.996470i \(0.526754\pi\)
\(720\) 16.8248 0.627023
\(721\) 33.4405 1.24539
\(722\) 15.2936 0.569170
\(723\) 17.3331 0.644623
\(724\) −19.0067 −0.706380
\(725\) 5.97800 0.222017
\(726\) −1.41424 −0.0524875
\(727\) 48.7315 1.80735 0.903675 0.428219i \(-0.140859\pi\)
0.903675 + 0.428219i \(0.140859\pi\)
\(728\) 10.2764 0.380870
\(729\) −37.3517 −1.38340
\(730\) −16.2146 −0.600128
\(731\) −32.6195 −1.20648
\(732\) −18.1968 −0.672572
\(733\) −52.0038 −1.92081 −0.960403 0.278616i \(-0.910124\pi\)
−0.960403 + 0.278616i \(0.910124\pi\)
\(734\) −30.0128 −1.10779
\(735\) −40.1830 −1.48217
\(736\) −1.77570 −0.0654531
\(737\) 38.7391 1.42697
\(738\) 61.7425 2.27277
\(739\) 1.30695 0.0480768 0.0240384 0.999711i \(-0.492348\pi\)
0.0240384 + 0.999711i \(0.492348\pi\)
\(740\) 14.3747 0.528425
\(741\) 17.0150 0.625061
\(742\) 27.3150 1.00276
\(743\) −25.6873 −0.942376 −0.471188 0.882033i \(-0.656175\pi\)
−0.471188 + 0.882033i \(0.656175\pi\)
\(744\) −26.8116 −0.982960
\(745\) −9.37591 −0.343507
\(746\) 22.8789 0.837657
\(747\) 65.3036 2.38934
\(748\) 8.79769 0.321675
\(749\) −55.6470 −2.03330
\(750\) −6.23259 −0.227582
\(751\) −41.3433 −1.50864 −0.754319 0.656508i \(-0.772033\pi\)
−0.754319 + 0.656508i \(0.772033\pi\)
\(752\) 6.09693 0.222332
\(753\) −49.4401 −1.80170
\(754\) 4.21045 0.153335
\(755\) −1.85735 −0.0675959
\(756\) −24.9282 −0.906629
\(757\) −25.9620 −0.943603 −0.471802 0.881705i \(-0.656396\pi\)
−0.471802 + 0.881705i \(0.656396\pi\)
\(758\) −5.67831 −0.206246
\(759\) −16.8047 −0.609970
\(760\) −5.87095 −0.212962
\(761\) −12.6899 −0.460008 −0.230004 0.973190i \(-0.573874\pi\)
−0.230004 + 0.973190i \(0.573874\pi\)
\(762\) 5.31347 0.192487
\(763\) 68.5062 2.48009
\(764\) 5.35334 0.193677
\(765\) 45.6463 1.65034
\(766\) −17.1966 −0.621337
\(767\) −19.7535 −0.713258
\(768\) −2.91842 −0.105309
\(769\) −42.6967 −1.53968 −0.769842 0.638235i \(-0.779665\pi\)
−0.769842 + 0.638235i \(0.779665\pi\)
\(770\) −33.5568 −1.20930
\(771\) −32.3193 −1.16395
\(772\) 9.31689 0.335322
\(773\) −6.04844 −0.217547 −0.108774 0.994067i \(-0.534692\pi\)
−0.108774 + 0.994067i \(0.534692\pi\)
\(774\) 66.3341 2.38433
\(775\) −39.5014 −1.41893
\(776\) −17.6719 −0.634383
\(777\) −46.6815 −1.67469
\(778\) −37.2248 −1.33457
\(779\) −21.5448 −0.771923
\(780\) 26.9520 0.965038
\(781\) −4.30678 −0.154109
\(782\) −4.81753 −0.172275
\(783\) −10.2135 −0.365002
\(784\) 4.51503 0.161251
\(785\) 33.7303 1.20389
\(786\) 29.5441 1.05380
\(787\) 49.7478 1.77332 0.886659 0.462424i \(-0.153020\pi\)
0.886659 + 0.462424i \(0.153020\pi\)
\(788\) 16.2169 0.577703
\(789\) −50.5376 −1.79918
\(790\) −31.4029 −1.11727
\(791\) 8.10274 0.288100
\(792\) −17.8907 −0.635720
\(793\) −18.8824 −0.670533
\(794\) 14.7102 0.522047
\(795\) 71.6391 2.54078
\(796\) 3.69204 0.130861
\(797\) 28.0085 0.992112 0.496056 0.868291i \(-0.334781\pi\)
0.496056 + 0.868291i \(0.334781\pi\)
\(798\) 19.0658 0.674920
\(799\) 16.5412 0.585185
\(800\) −4.29970 −0.152017
\(801\) −10.8186 −0.382257
\(802\) 29.6325 1.04636
\(803\) 17.2419 0.608452
\(804\) −34.8645 −1.22958
\(805\) 18.3754 0.647647
\(806\) −27.8218 −0.979980
\(807\) 2.31862 0.0816194
\(808\) 12.1834 0.428609
\(809\) 13.1264 0.461498 0.230749 0.973013i \(-0.425882\pi\)
0.230749 + 0.973013i \(0.425882\pi\)
\(810\) −14.9048 −0.523701
\(811\) −17.1909 −0.603655 −0.301828 0.953363i \(-0.597597\pi\)
−0.301828 + 0.953363i \(0.597597\pi\)
\(812\) 4.71792 0.165567
\(813\) −25.2099 −0.884151
\(814\) −15.2854 −0.535755
\(815\) 47.2078 1.65362
\(816\) −7.91777 −0.277177
\(817\) −23.1471 −0.809813
\(818\) −31.4794 −1.10065
\(819\) −56.6967 −1.98114
\(820\) −34.1274 −1.19178
\(821\) 14.6297 0.510582 0.255291 0.966864i \(-0.417829\pi\)
0.255291 + 0.966864i \(0.417829\pi\)
\(822\) 16.3286 0.569526
\(823\) −17.4531 −0.608378 −0.304189 0.952612i \(-0.598385\pi\)
−0.304189 + 0.952612i \(0.598385\pi\)
\(824\) −9.85463 −0.343302
\(825\) −40.6910 −1.41668
\(826\) −22.1344 −0.770153
\(827\) 14.1441 0.491840 0.245920 0.969290i \(-0.420910\pi\)
0.245920 + 0.969290i \(0.420910\pi\)
\(828\) 9.79681 0.340463
\(829\) 3.27491 0.113742 0.0568711 0.998382i \(-0.481888\pi\)
0.0568711 + 0.998382i \(0.481888\pi\)
\(830\) −36.0958 −1.25290
\(831\) 49.3116 1.71060
\(832\) −3.02838 −0.104990
\(833\) 12.2494 0.424418
\(834\) 33.0479 1.14435
\(835\) −0.947107 −0.0327760
\(836\) 6.24291 0.215916
\(837\) 67.4889 2.33276
\(838\) 6.87683 0.237556
\(839\) 15.8008 0.545504 0.272752 0.962084i \(-0.412066\pi\)
0.272752 + 0.962084i \(0.412066\pi\)
\(840\) 30.2005 1.04202
\(841\) −27.0670 −0.933344
\(842\) 14.7388 0.507933
\(843\) −35.2264 −1.21326
\(844\) −15.4489 −0.531773
\(845\) −11.6765 −0.401683
\(846\) −33.6377 −1.15649
\(847\) −1.64441 −0.0565025
\(848\) −8.04949 −0.276421
\(849\) 22.9609 0.788015
\(850\) −11.6652 −0.400114
\(851\) 8.37017 0.286926
\(852\) 3.87603 0.132790
\(853\) −2.67157 −0.0914727 −0.0457364 0.998954i \(-0.514563\pi\)
−0.0457364 + 0.998954i \(0.514563\pi\)
\(854\) −21.1582 −0.724020
\(855\) 32.3910 1.10775
\(856\) 16.3987 0.560495
\(857\) 17.3020 0.591026 0.295513 0.955339i \(-0.404509\pi\)
0.295513 + 0.955339i \(0.404509\pi\)
\(858\) −28.6596 −0.978423
\(859\) 35.3105 1.20478 0.602389 0.798203i \(-0.294216\pi\)
0.602389 + 0.798203i \(0.294216\pi\)
\(860\) −36.6654 −1.25028
\(861\) 110.828 3.77700
\(862\) 0.510707 0.0173947
\(863\) 28.3673 0.965633 0.482817 0.875721i \(-0.339614\pi\)
0.482817 + 0.875721i \(0.339614\pi\)
\(864\) 7.34612 0.249920
\(865\) −7.64175 −0.259827
\(866\) −13.0265 −0.442658
\(867\) 28.1319 0.955409
\(868\) −31.1751 −1.05815
\(869\) 33.3925 1.13276
\(870\) 12.3737 0.419508
\(871\) −36.1782 −1.22585
\(872\) −20.1882 −0.683658
\(873\) 97.4984 3.29982
\(874\) −3.41856 −0.115635
\(875\) −7.24693 −0.244991
\(876\) −15.5174 −0.524284
\(877\) 13.3551 0.450968 0.225484 0.974247i \(-0.427604\pi\)
0.225484 + 0.974247i \(0.427604\pi\)
\(878\) −15.0265 −0.507119
\(879\) −24.1784 −0.815517
\(880\) 9.88889 0.333354
\(881\) 33.5661 1.13087 0.565435 0.824793i \(-0.308708\pi\)
0.565435 + 0.824793i \(0.308708\pi\)
\(882\) −24.9101 −0.838768
\(883\) −41.6195 −1.40061 −0.700303 0.713846i \(-0.746952\pi\)
−0.700303 + 0.713846i \(0.746952\pi\)
\(884\) −8.21610 −0.276337
\(885\) −58.0519 −1.95139
\(886\) −24.2179 −0.813615
\(887\) −29.2027 −0.980531 −0.490265 0.871573i \(-0.663100\pi\)
−0.490265 + 0.871573i \(0.663100\pi\)
\(888\) 13.7566 0.461643
\(889\) 6.17822 0.207211
\(890\) 5.97986 0.200445
\(891\) 15.8491 0.530965
\(892\) −13.5607 −0.454047
\(893\) 11.7378 0.392789
\(894\) −8.97277 −0.300094
\(895\) −10.4020 −0.347702
\(896\) −3.39338 −0.113365
\(897\) 15.6937 0.523999
\(898\) −3.31168 −0.110512
\(899\) −12.7730 −0.426004
\(900\) 23.7221 0.790737
\(901\) −21.8386 −0.727548
\(902\) 36.2895 1.20831
\(903\) 119.070 3.96239
\(904\) −2.38781 −0.0794173
\(905\) −57.9618 −1.92672
\(906\) −1.77749 −0.0590531
\(907\) 18.8095 0.624559 0.312279 0.949990i \(-0.398907\pi\)
0.312279 + 0.949990i \(0.398907\pi\)
\(908\) 8.04828 0.267091
\(909\) −67.2175 −2.22946
\(910\) 31.3384 1.03886
\(911\) −46.1255 −1.52821 −0.764103 0.645094i \(-0.776818\pi\)
−0.764103 + 0.645094i \(0.776818\pi\)
\(912\) −5.61851 −0.186048
\(913\) 38.3827 1.27028
\(914\) −7.98224 −0.264029
\(915\) −55.4918 −1.83450
\(916\) −14.2222 −0.469914
\(917\) 34.3523 1.13441
\(918\) 19.9303 0.657797
\(919\) 1.42934 0.0471497 0.0235748 0.999722i \(-0.492495\pi\)
0.0235748 + 0.999722i \(0.492495\pi\)
\(920\) −5.41506 −0.178529
\(921\) 27.1409 0.894324
\(922\) −32.5697 −1.07263
\(923\) 4.02207 0.132388
\(924\) −32.1139 −1.05647
\(925\) 20.2676 0.666395
\(926\) 30.9159 1.01596
\(927\) 54.3696 1.78573
\(928\) −1.39033 −0.0456399
\(929\) 8.45362 0.277354 0.138677 0.990338i \(-0.455715\pi\)
0.138677 + 0.990338i \(0.455715\pi\)
\(930\) −81.7629 −2.68111
\(931\) 8.69230 0.284879
\(932\) 2.83488 0.0928597
\(933\) −52.8402 −1.72991
\(934\) −26.2417 −0.858654
\(935\) 26.8289 0.877399
\(936\) 16.7080 0.546119
\(937\) −2.89589 −0.0946048 −0.0473024 0.998881i \(-0.515062\pi\)
−0.0473024 + 0.998881i \(0.515062\pi\)
\(938\) −40.5386 −1.32363
\(939\) 57.7066 1.88318
\(940\) 18.5928 0.606431
\(941\) 44.8877 1.46330 0.731649 0.681682i \(-0.238751\pi\)
0.731649 + 0.681682i \(0.238751\pi\)
\(942\) 32.2800 1.05174
\(943\) −19.8718 −0.647115
\(944\) 6.52281 0.212299
\(945\) −76.0194 −2.47291
\(946\) 38.9883 1.26762
\(947\) −1.36305 −0.0442930 −0.0221465 0.999755i \(-0.507050\pi\)
−0.0221465 + 0.999755i \(0.507050\pi\)
\(948\) −30.0527 −0.976066
\(949\) −16.1020 −0.522694
\(950\) −8.27774 −0.268565
\(951\) 73.9733 2.39875
\(952\) −9.20637 −0.298380
\(953\) 40.5528 1.31363 0.656817 0.754050i \(-0.271902\pi\)
0.656817 + 0.754050i \(0.271902\pi\)
\(954\) 44.4103 1.43784
\(955\) 16.3252 0.528272
\(956\) 0.659329 0.0213242
\(957\) −13.1577 −0.425327
\(958\) 5.21508 0.168492
\(959\) 18.9861 0.613092
\(960\) −8.89983 −0.287241
\(961\) 53.4014 1.72263
\(962\) 14.2750 0.460243
\(963\) −90.4741 −2.91549
\(964\) −5.93920 −0.191289
\(965\) 28.4122 0.914622
\(966\) 17.5853 0.565797
\(967\) 12.1999 0.392322 0.196161 0.980572i \(-0.437153\pi\)
0.196161 + 0.980572i \(0.437153\pi\)
\(968\) 0.484593 0.0155754
\(969\) −15.2432 −0.489683
\(970\) −53.8910 −1.73034
\(971\) −34.4508 −1.10558 −0.552789 0.833321i \(-0.686436\pi\)
−0.552789 + 0.833321i \(0.686436\pi\)
\(972\) 7.77442 0.249365
\(973\) 38.4263 1.23189
\(974\) −41.3148 −1.32381
\(975\) 38.0010 1.21701
\(976\) 6.23515 0.199582
\(977\) 3.84417 0.122986 0.0614930 0.998108i \(-0.480414\pi\)
0.0614930 + 0.998108i \(0.480414\pi\)
\(978\) 45.1779 1.44463
\(979\) −6.35872 −0.203226
\(980\) 13.7688 0.439827
\(981\) 111.381 3.55613
\(982\) 43.2059 1.37875
\(983\) 62.0659 1.97959 0.989797 0.142486i \(-0.0455095\pi\)
0.989797 + 0.142486i \(0.0455095\pi\)
\(984\) −32.6600 −1.04116
\(985\) 49.4541 1.57574
\(986\) −3.77202 −0.120126
\(987\) −60.3797 −1.92191
\(988\) −5.83021 −0.185484
\(989\) −21.3497 −0.678880
\(990\) −54.5585 −1.73398
\(991\) −10.0605 −0.319584 −0.159792 0.987151i \(-0.551082\pi\)
−0.159792 + 0.987151i \(0.551082\pi\)
\(992\) 9.18702 0.291688
\(993\) −37.4604 −1.18877
\(994\) 4.50684 0.142948
\(995\) 11.2590 0.356935
\(996\) −34.5437 −1.09456
\(997\) 7.89603 0.250070 0.125035 0.992152i \(-0.460096\pi\)
0.125035 + 0.992152i \(0.460096\pi\)
\(998\) −2.55810 −0.0809754
\(999\) −34.6276 −1.09557
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 \(a_p\))