Properties

Label 4030.2.a.f.1.5
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.467757\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} -1.00000 q^{10} -4.96352 q^{11} +0.300926 q^{12} +1.00000 q^{13} +3.15038 q^{14} -0.300926 q^{15} +1.00000 q^{16} +1.88940 q^{17} -2.90944 q^{18} -4.66561 q^{19} -1.00000 q^{20} +0.948034 q^{21} -4.96352 q^{22} -4.45581 q^{23} +0.300926 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.77831 q^{27} +3.15038 q^{28} -2.08163 q^{29} -0.300926 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.49365 q^{33} +1.88940 q^{34} -3.15038 q^{35} -2.90944 q^{36} -5.70317 q^{37} -4.66561 q^{38} +0.300926 q^{39} -1.00000 q^{40} +6.80470 q^{41} +0.948034 q^{42} -0.777730 q^{43} -4.96352 q^{44} +2.90944 q^{45} -4.45581 q^{46} -6.80921 q^{47} +0.300926 q^{48} +2.92492 q^{49} +1.00000 q^{50} +0.568571 q^{51} +1.00000 q^{52} -3.39123 q^{53} -1.77831 q^{54} +4.96352 q^{55} +3.15038 q^{56} -1.40400 q^{57} -2.08163 q^{58} -13.2811 q^{59} -0.300926 q^{60} -3.23767 q^{61} -1.00000 q^{62} -9.16587 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.49365 q^{66} -8.44633 q^{67} +1.88940 q^{68} -1.34087 q^{69} -3.15038 q^{70} +13.1139 q^{71} -2.90944 q^{72} +11.3045 q^{73} -5.70317 q^{74} +0.300926 q^{75} -4.66561 q^{76} -15.6370 q^{77} +0.300926 q^{78} -2.47892 q^{79} -1.00000 q^{80} +8.19319 q^{81} +6.80470 q^{82} -2.94456 q^{83} +0.948034 q^{84} -1.88940 q^{85} -0.777730 q^{86} -0.626417 q^{87} -4.96352 q^{88} +8.26456 q^{89} +2.90944 q^{90} +3.15038 q^{91} -4.45581 q^{92} -0.300926 q^{93} -6.80921 q^{94} +4.66561 q^{95} +0.300926 q^{96} -10.2891 q^{97} +2.92492 q^{98} +14.4411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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
\(3\) 0.300926 0.173740 0.0868700 0.996220i \(-0.472314\pi\)
0.0868700 + 0.996220i \(0.472314\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.300926 0.122853
\(7\) 3.15038 1.19073 0.595367 0.803454i \(-0.297007\pi\)
0.595367 + 0.803454i \(0.297007\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.90944 −0.969814
\(10\) −1.00000 −0.316228
\(11\) −4.96352 −1.49656 −0.748278 0.663385i \(-0.769119\pi\)
−0.748278 + 0.663385i \(0.769119\pi\)
\(12\) 0.300926 0.0868700
\(13\) 1.00000 0.277350
\(14\) 3.15038 0.841976
\(15\) −0.300926 −0.0776989
\(16\) 1.00000 0.250000
\(17\) 1.88940 0.458248 0.229124 0.973397i \(-0.426414\pi\)
0.229124 + 0.973397i \(0.426414\pi\)
\(18\) −2.90944 −0.685762
\(19\) −4.66561 −1.07036 −0.535182 0.844737i \(-0.679757\pi\)
−0.535182 + 0.844737i \(0.679757\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.948034 0.206878
\(22\) −4.96352 −1.05822
\(23\) −4.45581 −0.929101 −0.464551 0.885547i \(-0.653784\pi\)
−0.464551 + 0.885547i \(0.653784\pi\)
\(24\) 0.300926 0.0614263
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) −1.77831 −0.342235
\(28\) 3.15038 0.595367
\(29\) −2.08163 −0.386549 −0.193274 0.981145i \(-0.561911\pi\)
−0.193274 + 0.981145i \(0.561911\pi\)
\(30\) −0.300926 −0.0549414
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −1.49365 −0.260012
\(34\) 1.88940 0.324030
\(35\) −3.15038 −0.532512
\(36\) −2.90944 −0.484907
\(37\) −5.70317 −0.937595 −0.468798 0.883306i \(-0.655313\pi\)
−0.468798 + 0.883306i \(0.655313\pi\)
\(38\) −4.66561 −0.756861
\(39\) 0.300926 0.0481868
\(40\) −1.00000 −0.158114
\(41\) 6.80470 1.06272 0.531358 0.847147i \(-0.321682\pi\)
0.531358 + 0.847147i \(0.321682\pi\)
\(42\) 0.948034 0.146285
\(43\) −0.777730 −0.118603 −0.0593014 0.998240i \(-0.518887\pi\)
−0.0593014 + 0.998240i \(0.518887\pi\)
\(44\) −4.96352 −0.748278
\(45\) 2.90944 0.433714
\(46\) −4.45581 −0.656974
\(47\) −6.80921 −0.993225 −0.496612 0.867972i \(-0.665423\pi\)
−0.496612 + 0.867972i \(0.665423\pi\)
\(48\) 0.300926 0.0434350
\(49\) 2.92492 0.417846
\(50\) 1.00000 0.141421
\(51\) 0.568571 0.0796159
\(52\) 1.00000 0.138675
\(53\) −3.39123 −0.465822 −0.232911 0.972498i \(-0.574825\pi\)
−0.232911 + 0.972498i \(0.574825\pi\)
\(54\) −1.77831 −0.241997
\(55\) 4.96352 0.669280
\(56\) 3.15038 0.420988
\(57\) −1.40400 −0.185965
\(58\) −2.08163 −0.273331
\(59\) −13.2811 −1.72905 −0.864523 0.502593i \(-0.832379\pi\)
−0.864523 + 0.502593i \(0.832379\pi\)
\(60\) −0.300926 −0.0388494
\(61\) −3.23767 −0.414542 −0.207271 0.978284i \(-0.566458\pi\)
−0.207271 + 0.978284i \(0.566458\pi\)
\(62\) −1.00000 −0.127000
\(63\) −9.16587 −1.15479
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −1.49365 −0.183856
\(67\) −8.44633 −1.03188 −0.515941 0.856624i \(-0.672558\pi\)
−0.515941 + 0.856624i \(0.672558\pi\)
\(68\) 1.88940 0.229124
\(69\) −1.34087 −0.161422
\(70\) −3.15038 −0.376543
\(71\) 13.1139 1.55633 0.778165 0.628060i \(-0.216151\pi\)
0.778165 + 0.628060i \(0.216151\pi\)
\(72\) −2.90944 −0.342881
\(73\) 11.3045 1.32309 0.661545 0.749906i \(-0.269901\pi\)
0.661545 + 0.749906i \(0.269901\pi\)
\(74\) −5.70317 −0.662980
\(75\) 0.300926 0.0347480
\(76\) −4.66561 −0.535182
\(77\) −15.6370 −1.78200
\(78\) 0.300926 0.0340732
\(79\) −2.47892 −0.278901 −0.139450 0.990229i \(-0.544534\pi\)
−0.139450 + 0.990229i \(0.544534\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.19319 0.910354
\(82\) 6.80470 0.751454
\(83\) −2.94456 −0.323207 −0.161604 0.986856i \(-0.551667\pi\)
−0.161604 + 0.986856i \(0.551667\pi\)
\(84\) 0.948034 0.103439
\(85\) −1.88940 −0.204935
\(86\) −0.777730 −0.0838648
\(87\) −0.626417 −0.0671590
\(88\) −4.96352 −0.529112
\(89\) 8.26456 0.876042 0.438021 0.898965i \(-0.355680\pi\)
0.438021 + 0.898965i \(0.355680\pi\)
\(90\) 2.90944 0.306682
\(91\) 3.15038 0.330250
\(92\) −4.45581 −0.464551
\(93\) −0.300926 −0.0312046
\(94\) −6.80921 −0.702316
\(95\) 4.66561 0.478681
\(96\) 0.300926 0.0307132
\(97\) −10.2891 −1.04470 −0.522351 0.852731i \(-0.674945\pi\)
−0.522351 + 0.852731i \(0.674945\pi\)
\(98\) 2.92492 0.295462
\(99\) 14.4411 1.45138
\(100\) 1.00000 0.100000
\(101\) −14.3862 −1.43148 −0.715739 0.698368i \(-0.753910\pi\)
−0.715739 + 0.698368i \(0.753910\pi\)
\(102\) 0.568571 0.0562970
\(103\) −5.54509 −0.546374 −0.273187 0.961961i \(-0.588078\pi\)
−0.273187 + 0.961961i \(0.588078\pi\)
\(104\) 1.00000 0.0980581
\(105\) −0.948034 −0.0925186
\(106\) −3.39123 −0.329386
\(107\) −11.4428 −1.10621 −0.553107 0.833110i \(-0.686558\pi\)
−0.553107 + 0.833110i \(0.686558\pi\)
\(108\) −1.77831 −0.171118
\(109\) −1.00382 −0.0961489 −0.0480745 0.998844i \(-0.515308\pi\)
−0.0480745 + 0.998844i \(0.515308\pi\)
\(110\) 4.96352 0.473253
\(111\) −1.71623 −0.162898
\(112\) 3.15038 0.297683
\(113\) 14.6751 1.38052 0.690261 0.723561i \(-0.257496\pi\)
0.690261 + 0.723561i \(0.257496\pi\)
\(114\) −1.40400 −0.131497
\(115\) 4.45581 0.415507
\(116\) −2.08163 −0.193274
\(117\) −2.90944 −0.268978
\(118\) −13.2811 −1.22262
\(119\) 5.95235 0.545651
\(120\) −0.300926 −0.0274707
\(121\) 13.6365 1.23968
\(122\) −3.23767 −0.293125
\(123\) 2.04772 0.184636
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −9.16587 −0.816560
\(127\) −0.378647 −0.0335995 −0.0167998 0.999859i \(-0.505348\pi\)
−0.0167998 + 0.999859i \(0.505348\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.234040 −0.0206060
\(130\) −1.00000 −0.0877058
\(131\) −18.5959 −1.62473 −0.812366 0.583148i \(-0.801821\pi\)
−0.812366 + 0.583148i \(0.801821\pi\)
\(132\) −1.49365 −0.130006
\(133\) −14.6985 −1.27452
\(134\) −8.44633 −0.729651
\(135\) 1.77831 0.153052
\(136\) 1.88940 0.162015
\(137\) −2.27913 −0.194719 −0.0973594 0.995249i \(-0.531040\pi\)
−0.0973594 + 0.995249i \(0.531040\pi\)
\(138\) −1.34087 −0.114143
\(139\) 9.01897 0.764979 0.382490 0.923960i \(-0.375067\pi\)
0.382490 + 0.923960i \(0.375067\pi\)
\(140\) −3.15038 −0.266256
\(141\) −2.04907 −0.172563
\(142\) 13.1139 1.10049
\(143\) −4.96352 −0.415070
\(144\) −2.90944 −0.242454
\(145\) 2.08163 0.172870
\(146\) 11.3045 0.935566
\(147\) 0.880187 0.0725966
\(148\) −5.70317 −0.468798
\(149\) −4.37620 −0.358512 −0.179256 0.983802i \(-0.557369\pi\)
−0.179256 + 0.983802i \(0.557369\pi\)
\(150\) 0.300926 0.0245705
\(151\) 19.7761 1.60935 0.804677 0.593712i \(-0.202338\pi\)
0.804677 + 0.593712i \(0.202338\pi\)
\(152\) −4.66561 −0.378431
\(153\) −5.49711 −0.444415
\(154\) −15.6370 −1.26006
\(155\) 1.00000 0.0803219
\(156\) 0.300926 0.0240934
\(157\) 0.100858 0.00804936 0.00402468 0.999992i \(-0.498719\pi\)
0.00402468 + 0.999992i \(0.498719\pi\)
\(158\) −2.47892 −0.197212
\(159\) −1.02051 −0.0809318
\(160\) −1.00000 −0.0790569
\(161\) −14.0375 −1.10631
\(162\) 8.19319 0.643718
\(163\) 2.69300 0.210932 0.105466 0.994423i \(-0.466367\pi\)
0.105466 + 0.994423i \(0.466367\pi\)
\(164\) 6.80470 0.531358
\(165\) 1.49365 0.116281
\(166\) −2.94456 −0.228542
\(167\) 0.159566 0.0123476 0.00617378 0.999981i \(-0.498035\pi\)
0.00617378 + 0.999981i \(0.498035\pi\)
\(168\) 0.948034 0.0731424
\(169\) 1.00000 0.0769231
\(170\) −1.88940 −0.144911
\(171\) 13.5743 1.03805
\(172\) −0.777730 −0.0593014
\(173\) −4.88183 −0.371159 −0.185579 0.982629i \(-0.559416\pi\)
−0.185579 + 0.982629i \(0.559416\pi\)
\(174\) −0.626417 −0.0474886
\(175\) 3.15038 0.238147
\(176\) −4.96352 −0.374139
\(177\) −3.99662 −0.300404
\(178\) 8.26456 0.619455
\(179\) −17.8316 −1.33279 −0.666397 0.745597i \(-0.732165\pi\)
−0.666397 + 0.745597i \(0.732165\pi\)
\(180\) 2.90944 0.216857
\(181\) 14.7311 1.09496 0.547478 0.836820i \(-0.315588\pi\)
0.547478 + 0.836820i \(0.315588\pi\)
\(182\) 3.15038 0.233522
\(183\) −0.974302 −0.0720224
\(184\) −4.45581 −0.328487
\(185\) 5.70317 0.419305
\(186\) −0.300926 −0.0220650
\(187\) −9.37808 −0.685793
\(188\) −6.80921 −0.496612
\(189\) −5.60235 −0.407511
\(190\) 4.66561 0.338479
\(191\) 21.2023 1.53415 0.767073 0.641560i \(-0.221712\pi\)
0.767073 + 0.641560i \(0.221712\pi\)
\(192\) 0.300926 0.0217175
\(193\) −24.9474 −1.79576 −0.897878 0.440244i \(-0.854892\pi\)
−0.897878 + 0.440244i \(0.854892\pi\)
\(194\) −10.2891 −0.738716
\(195\) −0.300926 −0.0215498
\(196\) 2.92492 0.208923
\(197\) 12.9775 0.924612 0.462306 0.886720i \(-0.347022\pi\)
0.462306 + 0.886720i \(0.347022\pi\)
\(198\) 14.4411 1.02628
\(199\) −7.29756 −0.517310 −0.258655 0.965970i \(-0.583279\pi\)
−0.258655 + 0.965970i \(0.583279\pi\)
\(200\) 1.00000 0.0707107
\(201\) −2.54172 −0.179279
\(202\) −14.3862 −1.01221
\(203\) −6.55794 −0.460277
\(204\) 0.568571 0.0398080
\(205\) −6.80470 −0.475261
\(206\) −5.54509 −0.386345
\(207\) 12.9639 0.901056
\(208\) 1.00000 0.0693375
\(209\) 23.1578 1.60186
\(210\) −0.948034 −0.0654206
\(211\) 7.95412 0.547584 0.273792 0.961789i \(-0.411722\pi\)
0.273792 + 0.961789i \(0.411722\pi\)
\(212\) −3.39123 −0.232911
\(213\) 3.94631 0.270397
\(214\) −11.4428 −0.782211
\(215\) 0.777730 0.0530408
\(216\) −1.77831 −0.120998
\(217\) −3.15038 −0.213862
\(218\) −1.00382 −0.0679876
\(219\) 3.40182 0.229873
\(220\) 4.96352 0.334640
\(221\) 1.88940 0.127095
\(222\) −1.71623 −0.115186
\(223\) −8.84055 −0.592007 −0.296004 0.955187i \(-0.595654\pi\)
−0.296004 + 0.955187i \(0.595654\pi\)
\(224\) 3.15038 0.210494
\(225\) −2.90944 −0.193963
\(226\) 14.6751 0.976176
\(227\) −13.1740 −0.874388 −0.437194 0.899367i \(-0.644028\pi\)
−0.437194 + 0.899367i \(0.644028\pi\)
\(228\) −1.40400 −0.0929824
\(229\) 24.5085 1.61957 0.809783 0.586730i \(-0.199585\pi\)
0.809783 + 0.586730i \(0.199585\pi\)
\(230\) 4.45581 0.293808
\(231\) −4.70558 −0.309604
\(232\) −2.08163 −0.136666
\(233\) −4.33762 −0.284167 −0.142084 0.989855i \(-0.545380\pi\)
−0.142084 + 0.989855i \(0.545380\pi\)
\(234\) −2.90944 −0.190196
\(235\) 6.80921 0.444184
\(236\) −13.2811 −0.864523
\(237\) −0.745973 −0.0484562
\(238\) 5.95235 0.385833
\(239\) −0.415754 −0.0268929 −0.0134465 0.999910i \(-0.504280\pi\)
−0.0134465 + 0.999910i \(0.504280\pi\)
\(240\) −0.300926 −0.0194247
\(241\) −24.1094 −1.55303 −0.776513 0.630102i \(-0.783013\pi\)
−0.776513 + 0.630102i \(0.783013\pi\)
\(242\) 13.6365 0.876586
\(243\) 7.80047 0.500400
\(244\) −3.23767 −0.207271
\(245\) −2.92492 −0.186867
\(246\) 2.04772 0.130558
\(247\) −4.66561 −0.296865
\(248\) −1.00000 −0.0635001
\(249\) −0.886096 −0.0561540
\(250\) −1.00000 −0.0632456
\(251\) 0.649253 0.0409805 0.0204902 0.999790i \(-0.493477\pi\)
0.0204902 + 0.999790i \(0.493477\pi\)
\(252\) −9.16587 −0.577395
\(253\) 22.1165 1.39045
\(254\) −0.378647 −0.0237584
\(255\) −0.568571 −0.0356053
\(256\) 1.00000 0.0625000
\(257\) −18.8917 −1.17843 −0.589215 0.807977i \(-0.700563\pi\)
−0.589215 + 0.807977i \(0.700563\pi\)
\(258\) −0.234040 −0.0145707
\(259\) −17.9672 −1.11643
\(260\) −1.00000 −0.0620174
\(261\) 6.05638 0.374881
\(262\) −18.5959 −1.14886
\(263\) 1.96769 0.121333 0.0606666 0.998158i \(-0.480677\pi\)
0.0606666 + 0.998158i \(0.480677\pi\)
\(264\) −1.49365 −0.0919280
\(265\) 3.39123 0.208322
\(266\) −14.6985 −0.901220
\(267\) 2.48702 0.152203
\(268\) −8.44633 −0.515941
\(269\) −8.70926 −0.531013 −0.265507 0.964109i \(-0.585539\pi\)
−0.265507 + 0.964109i \(0.585539\pi\)
\(270\) 1.77831 0.108224
\(271\) 25.4247 1.54444 0.772221 0.635354i \(-0.219146\pi\)
0.772221 + 0.635354i \(0.219146\pi\)
\(272\) 1.88940 0.114562
\(273\) 0.948034 0.0573776
\(274\) −2.27913 −0.137687
\(275\) −4.96352 −0.299311
\(276\) −1.34087 −0.0807110
\(277\) 14.1698 0.851380 0.425690 0.904869i \(-0.360031\pi\)
0.425690 + 0.904869i \(0.360031\pi\)
\(278\) 9.01897 0.540922
\(279\) 2.90944 0.174184
\(280\) −3.15038 −0.188272
\(281\) −7.09200 −0.423073 −0.211537 0.977370i \(-0.567847\pi\)
−0.211537 + 0.977370i \(0.567847\pi\)
\(282\) −2.04907 −0.122020
\(283\) 29.6798 1.76428 0.882140 0.470987i \(-0.156102\pi\)
0.882140 + 0.470987i \(0.156102\pi\)
\(284\) 13.1139 0.778165
\(285\) 1.40400 0.0831660
\(286\) −4.96352 −0.293499
\(287\) 21.4374 1.26541
\(288\) −2.90944 −0.171441
\(289\) −13.4302 −0.790009
\(290\) 2.08163 0.122238
\(291\) −3.09627 −0.181506
\(292\) 11.3045 0.661545
\(293\) 15.1271 0.883733 0.441867 0.897081i \(-0.354316\pi\)
0.441867 + 0.897081i \(0.354316\pi\)
\(294\) 0.880187 0.0513335
\(295\) 13.2811 0.773253
\(296\) −5.70317 −0.331490
\(297\) 8.82666 0.512175
\(298\) −4.37620 −0.253506
\(299\) −4.45581 −0.257686
\(300\) 0.300926 0.0173740
\(301\) −2.45015 −0.141224
\(302\) 19.7761 1.13799
\(303\) −4.32918 −0.248705
\(304\) −4.66561 −0.267591
\(305\) 3.23767 0.185389
\(306\) −5.49711 −0.314249
\(307\) 17.6312 1.00626 0.503132 0.864210i \(-0.332181\pi\)
0.503132 + 0.864210i \(0.332181\pi\)
\(308\) −15.6370 −0.891000
\(309\) −1.66866 −0.0949270
\(310\) 1.00000 0.0567962
\(311\) −28.8907 −1.63824 −0.819120 0.573623i \(-0.805538\pi\)
−0.819120 + 0.573623i \(0.805538\pi\)
\(312\) 0.300926 0.0170366
\(313\) −5.63644 −0.318590 −0.159295 0.987231i \(-0.550922\pi\)
−0.159295 + 0.987231i \(0.550922\pi\)
\(314\) 0.100858 0.00569176
\(315\) 9.16587 0.516438
\(316\) −2.47892 −0.139450
\(317\) −18.9402 −1.06379 −0.531893 0.846811i \(-0.678519\pi\)
−0.531893 + 0.846811i \(0.678519\pi\)
\(318\) −1.02051 −0.0572274
\(319\) 10.3322 0.578492
\(320\) −1.00000 −0.0559017
\(321\) −3.44343 −0.192194
\(322\) −14.0375 −0.782281
\(323\) −8.81521 −0.490492
\(324\) 8.19319 0.455177
\(325\) 1.00000 0.0554700
\(326\) 2.69300 0.149152
\(327\) −0.302077 −0.0167049
\(328\) 6.80470 0.375727
\(329\) −21.4516 −1.18267
\(330\) 1.49365 0.0822229
\(331\) 32.0008 1.75892 0.879462 0.475968i \(-0.157902\pi\)
0.879462 + 0.475968i \(0.157902\pi\)
\(332\) −2.94456 −0.161604
\(333\) 16.5930 0.909293
\(334\) 0.159566 0.00873104
\(335\) 8.44633 0.461472
\(336\) 0.948034 0.0517195
\(337\) 24.8686 1.35468 0.677339 0.735671i \(-0.263133\pi\)
0.677339 + 0.735671i \(0.263133\pi\)
\(338\) 1.00000 0.0543928
\(339\) 4.41614 0.239852
\(340\) −1.88940 −0.102467
\(341\) 4.96352 0.268789
\(342\) 13.5743 0.734015
\(343\) −12.8381 −0.693190
\(344\) −0.777730 −0.0419324
\(345\) 1.34087 0.0721901
\(346\) −4.88183 −0.262449
\(347\) −25.6965 −1.37946 −0.689729 0.724067i \(-0.742271\pi\)
−0.689729 + 0.724067i \(0.742271\pi\)
\(348\) −0.626417 −0.0335795
\(349\) −15.7290 −0.841952 −0.420976 0.907072i \(-0.638312\pi\)
−0.420976 + 0.907072i \(0.638312\pi\)
\(350\) 3.15038 0.168395
\(351\) −1.77831 −0.0949190
\(352\) −4.96352 −0.264556
\(353\) −16.3575 −0.870621 −0.435311 0.900280i \(-0.643361\pi\)
−0.435311 + 0.900280i \(0.643361\pi\)
\(354\) −3.99662 −0.212418
\(355\) −13.1139 −0.696012
\(356\) 8.26456 0.438021
\(357\) 1.79122 0.0948014
\(358\) −17.8316 −0.942428
\(359\) 17.3047 0.913308 0.456654 0.889644i \(-0.349048\pi\)
0.456654 + 0.889644i \(0.349048\pi\)
\(360\) 2.90944 0.153341
\(361\) 2.76787 0.145678
\(362\) 14.7311 0.774250
\(363\) 4.10358 0.215382
\(364\) 3.15038 0.165125
\(365\) −11.3045 −0.591704
\(366\) −0.974302 −0.0509276
\(367\) −19.3654 −1.01086 −0.505432 0.862866i \(-0.668667\pi\)
−0.505432 + 0.862866i \(0.668667\pi\)
\(368\) −4.45581 −0.232275
\(369\) −19.7979 −1.03064
\(370\) 5.70317 0.296494
\(371\) −10.6837 −0.554669
\(372\) −0.300926 −0.0156023
\(373\) 13.0357 0.674965 0.337483 0.941332i \(-0.390425\pi\)
0.337483 + 0.941332i \(0.390425\pi\)
\(374\) −9.37808 −0.484929
\(375\) −0.300926 −0.0155398
\(376\) −6.80921 −0.351158
\(377\) −2.08163 −0.107209
\(378\) −5.60235 −0.288154
\(379\) −21.3118 −1.09471 −0.547357 0.836899i \(-0.684366\pi\)
−0.547357 + 0.836899i \(0.684366\pi\)
\(380\) 4.66561 0.239341
\(381\) −0.113945 −0.00583758
\(382\) 21.2023 1.08480
\(383\) −19.3110 −0.986745 −0.493372 0.869818i \(-0.664236\pi\)
−0.493372 + 0.869818i \(0.664236\pi\)
\(384\) 0.300926 0.0153566
\(385\) 15.6370 0.796934
\(386\) −24.9474 −1.26979
\(387\) 2.26276 0.115023
\(388\) −10.2891 −0.522351
\(389\) −9.71130 −0.492382 −0.246191 0.969221i \(-0.579179\pi\)
−0.246191 + 0.969221i \(0.579179\pi\)
\(390\) −0.300926 −0.0152380
\(391\) −8.41883 −0.425759
\(392\) 2.92492 0.147731
\(393\) −5.59600 −0.282281
\(394\) 12.9775 0.653799
\(395\) 2.47892 0.124728
\(396\) 14.4411 0.725691
\(397\) 20.9972 1.05382 0.526910 0.849921i \(-0.323350\pi\)
0.526910 + 0.849921i \(0.323350\pi\)
\(398\) −7.29756 −0.365794
\(399\) −4.42315 −0.221435
\(400\) 1.00000 0.0500000
\(401\) −34.9041 −1.74303 −0.871515 0.490369i \(-0.836862\pi\)
−0.871515 + 0.490369i \(0.836862\pi\)
\(402\) −2.54172 −0.126770
\(403\) −1.00000 −0.0498135
\(404\) −14.3862 −0.715739
\(405\) −8.19319 −0.407123
\(406\) −6.55794 −0.325465
\(407\) 28.3078 1.40316
\(408\) 0.568571 0.0281485
\(409\) −23.7803 −1.17586 −0.587930 0.808912i \(-0.700057\pi\)
−0.587930 + 0.808912i \(0.700057\pi\)
\(410\) −6.80470 −0.336060
\(411\) −0.685849 −0.0338304
\(412\) −5.54509 −0.273187
\(413\) −41.8404 −2.05883
\(414\) 12.9639 0.637143
\(415\) 2.94456 0.144543
\(416\) 1.00000 0.0490290
\(417\) 2.71405 0.132907
\(418\) 23.1578 1.13269
\(419\) −27.3830 −1.33775 −0.668873 0.743377i \(-0.733223\pi\)
−0.668873 + 0.743377i \(0.733223\pi\)
\(420\) −0.948034 −0.0462593
\(421\) 26.3343 1.28346 0.641728 0.766933i \(-0.278218\pi\)
0.641728 + 0.766933i \(0.278218\pi\)
\(422\) 7.95412 0.387200
\(423\) 19.8110 0.963244
\(424\) −3.39123 −0.164693
\(425\) 1.88940 0.0916495
\(426\) 3.94631 0.191199
\(427\) −10.1999 −0.493609
\(428\) −11.4428 −0.553107
\(429\) −1.49365 −0.0721142
\(430\) 0.777730 0.0375055
\(431\) 29.5386 1.42283 0.711413 0.702775i \(-0.248056\pi\)
0.711413 + 0.702775i \(0.248056\pi\)
\(432\) −1.77831 −0.0855589
\(433\) 24.3047 1.16801 0.584004 0.811751i \(-0.301485\pi\)
0.584004 + 0.811751i \(0.301485\pi\)
\(434\) −3.15038 −0.151223
\(435\) 0.626417 0.0300344
\(436\) −1.00382 −0.0480745
\(437\) 20.7891 0.994476
\(438\) 3.40182 0.162545
\(439\) 12.1983 0.582194 0.291097 0.956694i \(-0.405980\pi\)
0.291097 + 0.956694i \(0.405980\pi\)
\(440\) 4.96352 0.236626
\(441\) −8.50990 −0.405233
\(442\) 1.88940 0.0898698
\(443\) −32.0859 −1.52445 −0.762223 0.647315i \(-0.775892\pi\)
−0.762223 + 0.647315i \(0.775892\pi\)
\(444\) −1.71623 −0.0814489
\(445\) −8.26456 −0.391778
\(446\) −8.84055 −0.418612
\(447\) −1.31691 −0.0622879
\(448\) 3.15038 0.148842
\(449\) 9.39473 0.443365 0.221682 0.975119i \(-0.428845\pi\)
0.221682 + 0.975119i \(0.428845\pi\)
\(450\) −2.90944 −0.137152
\(451\) −33.7753 −1.59041
\(452\) 14.6751 0.690261
\(453\) 5.95114 0.279609
\(454\) −13.1740 −0.618285
\(455\) −3.15038 −0.147692
\(456\) −1.40400 −0.0657485
\(457\) −3.32286 −0.155437 −0.0777185 0.996975i \(-0.524764\pi\)
−0.0777185 + 0.996975i \(0.524764\pi\)
\(458\) 24.5085 1.14521
\(459\) −3.35994 −0.156829
\(460\) 4.45581 0.207753
\(461\) −8.51704 −0.396678 −0.198339 0.980133i \(-0.563555\pi\)
−0.198339 + 0.980133i \(0.563555\pi\)
\(462\) −4.70558 −0.218923
\(463\) 20.7368 0.963721 0.481861 0.876248i \(-0.339961\pi\)
0.481861 + 0.876248i \(0.339961\pi\)
\(464\) −2.08163 −0.0966372
\(465\) 0.300926 0.0139551
\(466\) −4.33762 −0.200937
\(467\) 11.5796 0.535838 0.267919 0.963441i \(-0.413664\pi\)
0.267919 + 0.963441i \(0.413664\pi\)
\(468\) −2.90944 −0.134489
\(469\) −26.6092 −1.22870
\(470\) 6.80921 0.314085
\(471\) 0.0303509 0.00139850
\(472\) −13.2811 −0.611310
\(473\) 3.86028 0.177496
\(474\) −0.745973 −0.0342637
\(475\) −4.66561 −0.214073
\(476\) 5.95235 0.272825
\(477\) 9.86660 0.451760
\(478\) −0.415754 −0.0190162
\(479\) 7.74388 0.353827 0.176913 0.984226i \(-0.443389\pi\)
0.176913 + 0.984226i \(0.443389\pi\)
\(480\) −0.300926 −0.0137353
\(481\) −5.70317 −0.260042
\(482\) −24.1094 −1.09815
\(483\) −4.22426 −0.192211
\(484\) 13.6365 0.619840
\(485\) 10.2891 0.467205
\(486\) 7.80047 0.353836
\(487\) 2.14030 0.0969862 0.0484931 0.998824i \(-0.484558\pi\)
0.0484931 + 0.998824i \(0.484558\pi\)
\(488\) −3.23767 −0.146563
\(489\) 0.810396 0.0366474
\(490\) −2.92492 −0.132135
\(491\) 15.5236 0.700570 0.350285 0.936643i \(-0.386085\pi\)
0.350285 + 0.936643i \(0.386085\pi\)
\(492\) 2.04772 0.0923181
\(493\) −3.93304 −0.177135
\(494\) −4.66561 −0.209916
\(495\) −14.4411 −0.649078
\(496\) −1.00000 −0.0449013
\(497\) 41.3137 1.85317
\(498\) −0.886096 −0.0397069
\(499\) 22.9404 1.02695 0.513476 0.858104i \(-0.328357\pi\)
0.513476 + 0.858104i \(0.328357\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0.0480175 0.00214526
\(502\) 0.649253 0.0289776
\(503\) −10.8543 −0.483968 −0.241984 0.970280i \(-0.577798\pi\)
−0.241984 + 0.970280i \(0.577798\pi\)
\(504\) −9.16587 −0.408280
\(505\) 14.3862 0.640176
\(506\) 22.1165 0.983198
\(507\) 0.300926 0.0133646
\(508\) −0.378647 −0.0167998
\(509\) 16.8325 0.746087 0.373043 0.927814i \(-0.378314\pi\)
0.373043 + 0.927814i \(0.378314\pi\)
\(510\) −0.568571 −0.0251768
\(511\) 35.6135 1.57545
\(512\) 1.00000 0.0441942
\(513\) 8.29688 0.366316
\(514\) −18.8917 −0.833275
\(515\) 5.54509 0.244346
\(516\) −0.234040 −0.0103030
\(517\) 33.7976 1.48642
\(518\) −17.9672 −0.789432
\(519\) −1.46907 −0.0644851
\(520\) −1.00000 −0.0438529
\(521\) 33.3980 1.46319 0.731596 0.681738i \(-0.238776\pi\)
0.731596 + 0.681738i \(0.238776\pi\)
\(522\) 6.05638 0.265081
\(523\) 40.2347 1.75934 0.879669 0.475586i \(-0.157764\pi\)
0.879669 + 0.475586i \(0.157764\pi\)
\(524\) −18.5959 −0.812366
\(525\) 0.948034 0.0413756
\(526\) 1.96769 0.0857955
\(527\) −1.88940 −0.0823037
\(528\) −1.49365 −0.0650029
\(529\) −3.14573 −0.136771
\(530\) 3.39123 0.147306
\(531\) 38.6405 1.67685
\(532\) −14.6985 −0.637259
\(533\) 6.80470 0.294744
\(534\) 2.48702 0.107624
\(535\) 11.4428 0.494714
\(536\) −8.44633 −0.364826
\(537\) −5.36599 −0.231560
\(538\) −8.70926 −0.375483
\(539\) −14.5179 −0.625331
\(540\) 1.77831 0.0765262
\(541\) −36.7918 −1.58180 −0.790901 0.611945i \(-0.790388\pi\)
−0.790901 + 0.611945i \(0.790388\pi\)
\(542\) 25.4247 1.09209
\(543\) 4.43298 0.190237
\(544\) 1.88940 0.0810075
\(545\) 1.00382 0.0429991
\(546\) 0.948034 0.0405721
\(547\) 25.0106 1.06938 0.534688 0.845050i \(-0.320429\pi\)
0.534688 + 0.845050i \(0.320429\pi\)
\(548\) −2.27913 −0.0973594
\(549\) 9.41983 0.402028
\(550\) −4.96352 −0.211645
\(551\) 9.71206 0.413748
\(552\) −1.34087 −0.0570713
\(553\) −7.80956 −0.332096
\(554\) 14.1698 0.602017
\(555\) 1.71623 0.0728501
\(556\) 9.01897 0.382490
\(557\) 9.36989 0.397015 0.198507 0.980099i \(-0.436391\pi\)
0.198507 + 0.980099i \(0.436391\pi\)
\(558\) 2.90944 0.123167
\(559\) −0.777730 −0.0328945
\(560\) −3.15038 −0.133128
\(561\) −2.82211 −0.119150
\(562\) −7.09200 −0.299158
\(563\) 29.5032 1.24341 0.621705 0.783252i \(-0.286440\pi\)
0.621705 + 0.783252i \(0.286440\pi\)
\(564\) −2.04907 −0.0862814
\(565\) −14.6751 −0.617388
\(566\) 29.6798 1.24753
\(567\) 25.8117 1.08399
\(568\) 13.1139 0.550245
\(569\) 31.1992 1.30794 0.653969 0.756521i \(-0.273103\pi\)
0.653969 + 0.756521i \(0.273103\pi\)
\(570\) 1.40400 0.0588073
\(571\) −9.14924 −0.382884 −0.191442 0.981504i \(-0.561316\pi\)
−0.191442 + 0.981504i \(0.561316\pi\)
\(572\) −4.96352 −0.207535
\(573\) 6.38034 0.266542
\(574\) 21.4374 0.894781
\(575\) −4.45581 −0.185820
\(576\) −2.90944 −0.121227
\(577\) 27.5281 1.14601 0.573004 0.819553i \(-0.305778\pi\)
0.573004 + 0.819553i \(0.305778\pi\)
\(578\) −13.4302 −0.558621
\(579\) −7.50734 −0.311995
\(580\) 2.08163 0.0864350
\(581\) −9.27650 −0.384854
\(582\) −3.09627 −0.128344
\(583\) 16.8324 0.697128
\(584\) 11.3045 0.467783
\(585\) 2.90944 0.120291
\(586\) 15.1271 0.624894
\(587\) 29.6183 1.22248 0.611239 0.791446i \(-0.290671\pi\)
0.611239 + 0.791446i \(0.290671\pi\)
\(588\) 0.880187 0.0362983
\(589\) 4.66561 0.192243
\(590\) 13.2811 0.546772
\(591\) 3.90529 0.160642
\(592\) −5.70317 −0.234399
\(593\) −17.1957 −0.706141 −0.353071 0.935597i \(-0.614862\pi\)
−0.353071 + 0.935597i \(0.614862\pi\)
\(594\) 8.82666 0.362162
\(595\) −5.95235 −0.244023
\(596\) −4.37620 −0.179256
\(597\) −2.19603 −0.0898774
\(598\) −4.45581 −0.182212
\(599\) −13.5475 −0.553538 −0.276769 0.960937i \(-0.589264\pi\)
−0.276769 + 0.960937i \(0.589264\pi\)
\(600\) 0.300926 0.0122853
\(601\) −28.3499 −1.15642 −0.578209 0.815889i \(-0.696248\pi\)
−0.578209 + 0.815889i \(0.696248\pi\)
\(602\) −2.45015 −0.0998606
\(603\) 24.5741 1.00073
\(604\) 19.7761 0.804677
\(605\) −13.6365 −0.554402
\(606\) −4.32918 −0.175861
\(607\) 21.5229 0.873587 0.436794 0.899562i \(-0.356114\pi\)
0.436794 + 0.899562i \(0.356114\pi\)
\(608\) −4.66561 −0.189215
\(609\) −1.97346 −0.0799685
\(610\) 3.23767 0.131090
\(611\) −6.80921 −0.275471
\(612\) −5.49711 −0.222208
\(613\) 13.9442 0.563202 0.281601 0.959532i \(-0.409135\pi\)
0.281601 + 0.959532i \(0.409135\pi\)
\(614\) 17.6312 0.711536
\(615\) −2.04772 −0.0825718
\(616\) −15.6370 −0.630032
\(617\) 20.3340 0.818616 0.409308 0.912396i \(-0.365770\pi\)
0.409308 + 0.912396i \(0.365770\pi\)
\(618\) −1.66866 −0.0671235
\(619\) −40.4260 −1.62486 −0.812428 0.583061i \(-0.801855\pi\)
−0.812428 + 0.583061i \(0.801855\pi\)
\(620\) 1.00000 0.0401610
\(621\) 7.92381 0.317971
\(622\) −28.8907 −1.15841
\(623\) 26.0366 1.04313
\(624\) 0.300926 0.0120467
\(625\) 1.00000 0.0400000
\(626\) −5.63644 −0.225277
\(627\) 6.96879 0.278307
\(628\) 0.100858 0.00402468
\(629\) −10.7756 −0.429651
\(630\) 9.16587 0.365177
\(631\) −2.10823 −0.0839273 −0.0419637 0.999119i \(-0.513361\pi\)
−0.0419637 + 0.999119i \(0.513361\pi\)
\(632\) −2.47892 −0.0986062
\(633\) 2.39360 0.0951372
\(634\) −18.9402 −0.752211
\(635\) 0.378647 0.0150262
\(636\) −1.02051 −0.0404659
\(637\) 2.92492 0.115890
\(638\) 10.3322 0.409056
\(639\) −38.1540 −1.50935
\(640\) −1.00000 −0.0395285
\(641\) −9.15240 −0.361498 −0.180749 0.983529i \(-0.557852\pi\)
−0.180749 + 0.983529i \(0.557852\pi\)
\(642\) −3.44343 −0.135901
\(643\) 5.66423 0.223375 0.111688 0.993743i \(-0.464374\pi\)
0.111688 + 0.993743i \(0.464374\pi\)
\(644\) −14.0375 −0.553156
\(645\) 0.234040 0.00921530
\(646\) −8.81521 −0.346830
\(647\) −35.4275 −1.39280 −0.696400 0.717654i \(-0.745216\pi\)
−0.696400 + 0.717654i \(0.745216\pi\)
\(648\) 8.19319 0.321859
\(649\) 65.9207 2.58761
\(650\) 1.00000 0.0392232
\(651\) −0.948034 −0.0371564
\(652\) 2.69300 0.105466
\(653\) −7.47777 −0.292628 −0.146314 0.989238i \(-0.546741\pi\)
−0.146314 + 0.989238i \(0.546741\pi\)
\(654\) −0.302077 −0.0118122
\(655\) 18.5959 0.726602
\(656\) 6.80470 0.265679
\(657\) −32.8897 −1.28315
\(658\) −21.4516 −0.836271
\(659\) −3.69306 −0.143861 −0.0719306 0.997410i \(-0.522916\pi\)
−0.0719306 + 0.997410i \(0.522916\pi\)
\(660\) 1.49365 0.0581404
\(661\) 36.4497 1.41773 0.708865 0.705344i \(-0.249207\pi\)
0.708865 + 0.705344i \(0.249207\pi\)
\(662\) 32.0008 1.24375
\(663\) 0.568571 0.0220815
\(664\) −2.94456 −0.114271
\(665\) 14.6985 0.569982
\(666\) 16.5930 0.642967
\(667\) 9.27535 0.359143
\(668\) 0.159566 0.00617378
\(669\) −2.66036 −0.102855
\(670\) 8.44633 0.326310
\(671\) 16.0702 0.620385
\(672\) 0.948034 0.0365712
\(673\) 29.3390 1.13093 0.565467 0.824771i \(-0.308696\pi\)
0.565467 + 0.824771i \(0.308696\pi\)
\(674\) 24.8686 0.957902
\(675\) −1.77831 −0.0684471
\(676\) 1.00000 0.0384615
\(677\) 32.2186 1.23826 0.619130 0.785289i \(-0.287485\pi\)
0.619130 + 0.785289i \(0.287485\pi\)
\(678\) 4.41614 0.169601
\(679\) −32.4147 −1.24396
\(680\) −1.88940 −0.0724553
\(681\) −3.96440 −0.151916
\(682\) 4.96352 0.190063
\(683\) −17.1496 −0.656213 −0.328107 0.944641i \(-0.606410\pi\)
−0.328107 + 0.944641i \(0.606410\pi\)
\(684\) 13.5743 0.519027
\(685\) 2.27913 0.0870809
\(686\) −12.8381 −0.490159
\(687\) 7.37525 0.281383
\(688\) −0.777730 −0.0296507
\(689\) −3.39123 −0.129196
\(690\) 1.34087 0.0510461
\(691\) 33.3329 1.26804 0.634022 0.773315i \(-0.281403\pi\)
0.634022 + 0.773315i \(0.281403\pi\)
\(692\) −4.88183 −0.185579
\(693\) 45.4949 1.72821
\(694\) −25.6965 −0.975425
\(695\) −9.01897 −0.342109
\(696\) −0.626417 −0.0237443
\(697\) 12.8568 0.486987
\(698\) −15.7290 −0.595350
\(699\) −1.30531 −0.0493712
\(700\) 3.15038 0.119073
\(701\) 13.2118 0.499003 0.249502 0.968374i \(-0.419733\pi\)
0.249502 + 0.968374i \(0.419733\pi\)
\(702\) −1.77831 −0.0671179
\(703\) 26.6087 1.00357
\(704\) −4.96352 −0.187070
\(705\) 2.04907 0.0771724
\(706\) −16.3575 −0.615622
\(707\) −45.3220 −1.70451
\(708\) −3.99662 −0.150202
\(709\) 11.9859 0.450141 0.225070 0.974342i \(-0.427739\pi\)
0.225070 + 0.974342i \(0.427739\pi\)
\(710\) −13.1139 −0.492155
\(711\) 7.21228 0.270482
\(712\) 8.26456 0.309728
\(713\) 4.45581 0.166872
\(714\) 1.79122 0.0670347
\(715\) 4.96352 0.185625
\(716\) −17.8316 −0.666397
\(717\) −0.125111 −0.00467237
\(718\) 17.3047 0.645806
\(719\) −31.2726 −1.16627 −0.583136 0.812375i \(-0.698175\pi\)
−0.583136 + 0.812375i \(0.698175\pi\)
\(720\) 2.90944 0.108429
\(721\) −17.4692 −0.650586
\(722\) 2.76787 0.103010
\(723\) −7.25517 −0.269823
\(724\) 14.7311 0.547478
\(725\) −2.08163 −0.0773098
\(726\) 4.10358 0.152298
\(727\) −21.0644 −0.781237 −0.390618 0.920553i \(-0.627739\pi\)
−0.390618 + 0.920553i \(0.627739\pi\)
\(728\) 3.15038 0.116761
\(729\) −22.2322 −0.823415
\(730\) −11.3045 −0.418398
\(731\) −1.46945 −0.0543494
\(732\) −0.974302 −0.0360112
\(733\) 7.83389 0.289351 0.144676 0.989479i \(-0.453786\pi\)
0.144676 + 0.989479i \(0.453786\pi\)
\(734\) −19.3654 −0.714789
\(735\) −0.880187 −0.0324662
\(736\) −4.45581 −0.164243
\(737\) 41.9235 1.54427
\(738\) −19.7979 −0.728771
\(739\) −19.2833 −0.709348 −0.354674 0.934990i \(-0.615408\pi\)
−0.354674 + 0.934990i \(0.615408\pi\)
\(740\) 5.70317 0.209653
\(741\) −1.40400 −0.0515774
\(742\) −10.6837 −0.392210
\(743\) −48.4537 −1.77759 −0.888797 0.458302i \(-0.848458\pi\)
−0.888797 + 0.458302i \(0.848458\pi\)
\(744\) −0.300926 −0.0110325
\(745\) 4.37620 0.160332
\(746\) 13.0357 0.477272
\(747\) 8.56703 0.313451
\(748\) −9.37808 −0.342897
\(749\) −36.0491 −1.31721
\(750\) −0.300926 −0.0109883
\(751\) −3.92584 −0.143256 −0.0716280 0.997431i \(-0.522819\pi\)
−0.0716280 + 0.997431i \(0.522819\pi\)
\(752\) −6.80921 −0.248306
\(753\) 0.195377 0.00711994
\(754\) −2.08163 −0.0758085
\(755\) −19.7761 −0.719725
\(756\) −5.60235 −0.203756
\(757\) −42.7038 −1.55210 −0.776048 0.630674i \(-0.782779\pi\)
−0.776048 + 0.630674i \(0.782779\pi\)
\(758\) −21.3118 −0.774080
\(759\) 6.65544 0.241577
\(760\) 4.66561 0.169239
\(761\) 30.0194 1.08820 0.544101 0.839020i \(-0.316871\pi\)
0.544101 + 0.839020i \(0.316871\pi\)
\(762\) −0.113945 −0.00412779
\(763\) −3.16243 −0.114488
\(764\) 21.2023 0.767073
\(765\) 5.49711 0.198749
\(766\) −19.3110 −0.697734
\(767\) −13.2811 −0.479551
\(768\) 0.300926 0.0108587
\(769\) 33.6907 1.21492 0.607459 0.794351i \(-0.292189\pi\)
0.607459 + 0.794351i \(0.292189\pi\)
\(770\) 15.6370 0.563518
\(771\) −5.68500 −0.204740
\(772\) −24.9474 −0.897878
\(773\) −36.9590 −1.32932 −0.664662 0.747144i \(-0.731424\pi\)
−0.664662 + 0.747144i \(0.731424\pi\)
\(774\) 2.26276 0.0813333
\(775\) −1.00000 −0.0359211
\(776\) −10.2891 −0.369358
\(777\) −5.40680 −0.193968
\(778\) −9.71130 −0.348167
\(779\) −31.7481 −1.13749
\(780\) −0.300926 −0.0107749
\(781\) −65.0909 −2.32913
\(782\) −8.41883 −0.301057
\(783\) 3.70178 0.132291
\(784\) 2.92492 0.104462
\(785\) −0.100858 −0.00359978
\(786\) −5.59600 −0.199603
\(787\) 24.2241 0.863494 0.431747 0.901995i \(-0.357897\pi\)
0.431747 + 0.901995i \(0.357897\pi\)
\(788\) 12.9775 0.462306
\(789\) 0.592131 0.0210804
\(790\) 2.47892 0.0881961
\(791\) 46.2324 1.64383
\(792\) 14.4411 0.513141
\(793\) −3.23767 −0.114973
\(794\) 20.9972 0.745164
\(795\) 1.02051 0.0361938
\(796\) −7.29756 −0.258655
\(797\) 51.6621 1.82997 0.914983 0.403493i \(-0.132204\pi\)
0.914983 + 0.403493i \(0.132204\pi\)
\(798\) −4.42315 −0.156578
\(799\) −12.8653 −0.455143
\(800\) 1.00000 0.0353553
\(801\) −24.0453 −0.849598
\(802\) −34.9041 −1.23251
\(803\) −56.1100 −1.98008
\(804\) −2.54172 −0.0896396
\(805\) 14.0375 0.494758
\(806\) −1.00000 −0.0352235
\(807\) −2.62085 −0.0922582
\(808\) −14.3862 −0.506104
\(809\) −13.9235 −0.489526 −0.244763 0.969583i \(-0.578710\pi\)
−0.244763 + 0.969583i \(0.578710\pi\)
\(810\) −8.19319 −0.287879
\(811\) −48.2518 −1.69435 −0.847175 0.531313i \(-0.821699\pi\)
−0.847175 + 0.531313i \(0.821699\pi\)
\(812\) −6.55794 −0.230138
\(813\) 7.65097 0.268331
\(814\) 28.3078 0.992186
\(815\) −2.69300 −0.0943318
\(816\) 0.568571 0.0199040
\(817\) 3.62858 0.126948
\(818\) −23.7803 −0.831458
\(819\) −9.16587 −0.320281
\(820\) −6.80470 −0.237631
\(821\) 15.3268 0.534910 0.267455 0.963570i \(-0.413817\pi\)
0.267455 + 0.963570i \(0.413817\pi\)
\(822\) −0.685849 −0.0239217
\(823\) 11.5724 0.403388 0.201694 0.979449i \(-0.435355\pi\)
0.201694 + 0.979449i \(0.435355\pi\)
\(824\) −5.54509 −0.193172
\(825\) −1.49365 −0.0520023
\(826\) −41.8404 −1.45582
\(827\) −24.5182 −0.852580 −0.426290 0.904586i \(-0.640180\pi\)
−0.426290 + 0.904586i \(0.640180\pi\)
\(828\) 12.9639 0.450528
\(829\) 24.8568 0.863313 0.431656 0.902038i \(-0.357929\pi\)
0.431656 + 0.902038i \(0.357929\pi\)
\(830\) 2.94456 0.102207
\(831\) 4.26406 0.147919
\(832\) 1.00000 0.0346688
\(833\) 5.52636 0.191477
\(834\) 2.71405 0.0939798
\(835\) −0.159566 −0.00552199
\(836\) 23.1578 0.800929
\(837\) 1.77831 0.0614673
\(838\) −27.3830 −0.945930
\(839\) −35.1576 −1.21377 −0.606887 0.794788i \(-0.707582\pi\)
−0.606887 + 0.794788i \(0.707582\pi\)
\(840\) −0.948034 −0.0327103
\(841\) −24.6668 −0.850580
\(842\) 26.3343 0.907540
\(843\) −2.13417 −0.0735047
\(844\) 7.95412 0.273792
\(845\) −1.00000 −0.0344010
\(846\) 19.8110 0.681116
\(847\) 42.9602 1.47613
\(848\) −3.39123 −0.116455
\(849\) 8.93143 0.306526
\(850\) 1.88940 0.0648060
\(851\) 25.4123 0.871121
\(852\) 3.94631 0.135198
\(853\) 28.6515 0.981008 0.490504 0.871439i \(-0.336813\pi\)
0.490504 + 0.871439i \(0.336813\pi\)
\(854\) −10.1999 −0.349034
\(855\) −13.5743 −0.464232
\(856\) −11.4428 −0.391106
\(857\) 53.8463 1.83935 0.919677 0.392675i \(-0.128450\pi\)
0.919677 + 0.392675i \(0.128450\pi\)
\(858\) −1.49365 −0.0509925
\(859\) −2.64326 −0.0901869 −0.0450934 0.998983i \(-0.514359\pi\)
−0.0450934 + 0.998983i \(0.514359\pi\)
\(860\) 0.777730 0.0265204
\(861\) 6.45109 0.219853
\(862\) 29.5386 1.00609
\(863\) −37.2858 −1.26922 −0.634612 0.772831i \(-0.718840\pi\)
−0.634612 + 0.772831i \(0.718840\pi\)
\(864\) −1.77831 −0.0604992
\(865\) 4.88183 0.165987
\(866\) 24.3047 0.825907
\(867\) −4.04149 −0.137256
\(868\) −3.15038 −0.106931
\(869\) 12.3042 0.417390
\(870\) 0.626417 0.0212375
\(871\) −8.44633 −0.286193
\(872\) −1.00382 −0.0339938
\(873\) 29.9356 1.01317
\(874\) 20.7891 0.703201
\(875\) −3.15038 −0.106502
\(876\) 3.40182 0.114937
\(877\) −30.0955 −1.01625 −0.508127 0.861282i \(-0.669662\pi\)
−0.508127 + 0.861282i \(0.669662\pi\)
\(878\) 12.1983 0.411673
\(879\) 4.55214 0.153540
\(880\) 4.96352 0.167320
\(881\) 6.48049 0.218333 0.109167 0.994023i \(-0.465182\pi\)
0.109167 + 0.994023i \(0.465182\pi\)
\(882\) −8.50990 −0.286543
\(883\) −24.8652 −0.836781 −0.418390 0.908267i \(-0.637406\pi\)
−0.418390 + 0.908267i \(0.637406\pi\)
\(884\) 1.88940 0.0635475
\(885\) 3.99662 0.134345
\(886\) −32.0859 −1.07795
\(887\) −9.47569 −0.318163 −0.159081 0.987265i \(-0.550853\pi\)
−0.159081 + 0.987265i \(0.550853\pi\)
\(888\) −1.71623 −0.0575930
\(889\) −1.19288 −0.0400081
\(890\) −8.26456 −0.277029
\(891\) −40.6670 −1.36240
\(892\) −8.84055 −0.296004
\(893\) 31.7691 1.06311
\(894\) −1.31691 −0.0440442
\(895\) 17.8316 0.596044
\(896\) 3.15038 0.105247
\(897\) −1.34087 −0.0447704
\(898\) 9.39473 0.313506
\(899\) 2.08163 0.0694262
\(900\) −2.90944 −0.0969814
\(901\) −6.40741 −0.213462
\(902\) −33.7753 −1.12459
\(903\) −0.737315 −0.0245363
\(904\) 14.6751 0.488088
\(905\) −14.7311 −0.489679
\(906\) 5.95114 0.197714
\(907\) −38.7436 −1.28646 −0.643231 0.765672i \(-0.722406\pi\)
−0.643231 + 0.765672i \(0.722406\pi\)
\(908\) −13.1740 −0.437194
\(909\) 41.8557 1.38827
\(910\) −3.15038 −0.104434
\(911\) 30.5601 1.01250 0.506251 0.862386i \(-0.331031\pi\)
0.506251 + 0.862386i \(0.331031\pi\)
\(912\) −1.40400 −0.0464912
\(913\) 14.6154 0.483698
\(914\) −3.32286 −0.109910
\(915\) 0.974302 0.0322094
\(916\) 24.5085 0.809783
\(917\) −58.5843 −1.93462
\(918\) −3.35994 −0.110895
\(919\) 42.6592 1.40720 0.703598 0.710598i \(-0.251575\pi\)
0.703598 + 0.710598i \(0.251575\pi\)
\(920\) 4.45581 0.146904
\(921\) 5.30568 0.174828
\(922\) −8.51704 −0.280494
\(923\) 13.1139 0.431648
\(924\) −4.70558 −0.154802
\(925\) −5.70317 −0.187519
\(926\) 20.7368 0.681454
\(927\) 16.1331 0.529881
\(928\) −2.08163 −0.0683329
\(929\) −14.9660 −0.491018 −0.245509 0.969394i \(-0.578955\pi\)
−0.245509 + 0.969394i \(0.578955\pi\)
\(930\) 0.300926 0.00986777
\(931\) −13.6465 −0.447247
\(932\) −4.33762 −0.142084
\(933\) −8.69397 −0.284628
\(934\) 11.5796 0.378894
\(935\) 9.37808 0.306696
\(936\) −2.90944 −0.0950981
\(937\) −2.06773 −0.0675496 −0.0337748 0.999429i \(-0.510753\pi\)
−0.0337748 + 0.999429i \(0.510753\pi\)
\(938\) −26.6092 −0.868820
\(939\) −1.69615 −0.0553519
\(940\) 6.80921 0.222092
\(941\) 43.2291 1.40923 0.704615 0.709590i \(-0.251120\pi\)
0.704615 + 0.709590i \(0.251120\pi\)
\(942\) 0.0303509 0.000988886 0
\(943\) −30.3205 −0.987371
\(944\) −13.2811 −0.432262
\(945\) 5.60235 0.182245
\(946\) 3.86028 0.125508
\(947\) 17.5363 0.569852 0.284926 0.958550i \(-0.408031\pi\)
0.284926 + 0.958550i \(0.408031\pi\)
\(948\) −0.745973 −0.0242281
\(949\) 11.3045 0.366959
\(950\) −4.66561 −0.151372
\(951\) −5.69960 −0.184822
\(952\) 5.95235 0.192917
\(953\) −0.0617556 −0.00200046 −0.00100023 0.999999i \(-0.500318\pi\)
−0.00100023 + 0.999999i \(0.500318\pi\)
\(954\) 9.86660 0.319443
\(955\) −21.2023 −0.686091
\(956\) −0.415754 −0.0134465
\(957\) 3.10923 0.100507
\(958\) 7.74388 0.250193
\(959\) −7.18012 −0.231858
\(960\) −0.300926 −0.00971236
\(961\) 1.00000 0.0322581
\(962\) −5.70317 −0.183878
\(963\) 33.2921 1.07282
\(964\) −24.1094 −0.776513
\(965\) 24.9474 0.803087
\(966\) −4.22426 −0.135913
\(967\) −36.8990 −1.18659 −0.593296 0.804984i \(-0.702174\pi\)
−0.593296 + 0.804984i \(0.702174\pi\)
\(968\) 13.6365 0.438293
\(969\) −2.65273 −0.0852180
\(970\) 10.2891 0.330364
\(971\) −33.8502 −1.08631 −0.543153 0.839634i \(-0.682770\pi\)
−0.543153 + 0.839634i \(0.682770\pi\)
\(972\) 7.80047 0.250200
\(973\) 28.4132 0.910887
\(974\) 2.14030 0.0685796
\(975\) 0.300926 0.00963736
\(976\) −3.23767 −0.103635
\(977\) 6.14025 0.196444 0.0982221 0.995165i \(-0.468684\pi\)
0.0982221 + 0.995165i \(0.468684\pi\)
\(978\) 0.810396 0.0259136
\(979\) −41.0213 −1.31105
\(980\) −2.92492 −0.0934333
\(981\) 2.92057 0.0932466
\(982\) 15.5236 0.495378
\(983\) 3.72011 0.118653 0.0593266 0.998239i \(-0.481105\pi\)
0.0593266 + 0.998239i \(0.481105\pi\)
\(984\) 2.04772 0.0652788
\(985\) −12.9775 −0.413499
\(986\) −3.93304 −0.125254
\(987\) −6.45536 −0.205476
\(988\) −4.66561 −0.148433
\(989\) 3.46542 0.110194
\(990\) −14.4411 −0.458967
\(991\) 11.0600 0.351331 0.175665 0.984450i \(-0.443792\pi\)
0.175665 + 0.984450i \(0.443792\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 9.62989 0.305595
\(994\) 41.3137 1.31039
\(995\) 7.29756 0.231348
\(996\) −0.886096 −0.0280770
\(997\) −44.6240 −1.41326 −0.706629 0.707585i \(-0.749785\pi\)
−0.706629 + 0.707585i \(0.749785\pi\)
\(998\) 22.9404 0.726165
\(999\) 10.1420 0.320878
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 \(a_p\))