Properties

Label 8041.2.a.i.1.10
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.28473 q^{2} -0.648502 q^{3} +3.22000 q^{4} -1.19117 q^{5} +1.48165 q^{6} +3.55276 q^{7} -2.78738 q^{8} -2.57944 q^{9} +O(q^{10})\) \(q-2.28473 q^{2} -0.648502 q^{3} +3.22000 q^{4} -1.19117 q^{5} +1.48165 q^{6} +3.55276 q^{7} -2.78738 q^{8} -2.57944 q^{9} +2.72151 q^{10} +1.00000 q^{11} -2.08818 q^{12} +2.20951 q^{13} -8.11710 q^{14} +0.772478 q^{15} -0.0715963 q^{16} -1.00000 q^{17} +5.89334 q^{18} -2.00734 q^{19} -3.83558 q^{20} -2.30397 q^{21} -2.28473 q^{22} +3.40797 q^{23} +1.80762 q^{24} -3.58111 q^{25} -5.04814 q^{26} +3.61828 q^{27} +11.4399 q^{28} +7.34415 q^{29} -1.76491 q^{30} -2.81936 q^{31} +5.73833 q^{32} -0.648502 q^{33} +2.28473 q^{34} -4.23195 q^{35} -8.30581 q^{36} -6.89242 q^{37} +4.58623 q^{38} -1.43287 q^{39} +3.32025 q^{40} +2.63626 q^{41} +5.26396 q^{42} -1.00000 q^{43} +3.22000 q^{44} +3.07256 q^{45} -7.78629 q^{46} -0.309786 q^{47} +0.0464303 q^{48} +5.62208 q^{49} +8.18187 q^{50} +0.648502 q^{51} +7.11463 q^{52} +3.94179 q^{53} -8.26681 q^{54} -1.19117 q^{55} -9.90286 q^{56} +1.30176 q^{57} -16.7794 q^{58} -11.6969 q^{59} +2.48738 q^{60} -6.80995 q^{61} +6.44148 q^{62} -9.16414 q^{63} -12.9674 q^{64} -2.63191 q^{65} +1.48165 q^{66} +1.66914 q^{67} -3.22000 q^{68} -2.21007 q^{69} +9.66886 q^{70} +5.91650 q^{71} +7.18988 q^{72} +7.52804 q^{73} +15.7473 q^{74} +2.32236 q^{75} -6.46363 q^{76} +3.55276 q^{77} +3.27373 q^{78} +7.35099 q^{79} +0.0852835 q^{80} +5.39187 q^{81} -6.02316 q^{82} +8.75805 q^{83} -7.41879 q^{84} +1.19117 q^{85} +2.28473 q^{86} -4.76270 q^{87} -2.78738 q^{88} -13.9073 q^{89} -7.01999 q^{90} +7.84985 q^{91} +10.9737 q^{92} +1.82836 q^{93} +0.707779 q^{94} +2.39109 q^{95} -3.72132 q^{96} -12.7362 q^{97} -12.8449 q^{98} -2.57944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28473 −1.61555 −0.807775 0.589491i \(-0.799328\pi\)
−0.807775 + 0.589491i \(0.799328\pi\)
\(3\) −0.648502 −0.374413 −0.187207 0.982321i \(-0.559943\pi\)
−0.187207 + 0.982321i \(0.559943\pi\)
\(4\) 3.22000 1.61000
\(5\) −1.19117 −0.532709 −0.266354 0.963875i \(-0.585819\pi\)
−0.266354 + 0.963875i \(0.585819\pi\)
\(6\) 1.48165 0.604883
\(7\) 3.55276 1.34282 0.671408 0.741088i \(-0.265690\pi\)
0.671408 + 0.741088i \(0.265690\pi\)
\(8\) −2.78738 −0.985486
\(9\) −2.57944 −0.859815
\(10\) 2.72151 0.860617
\(11\) 1.00000 0.301511
\(12\) −2.08818 −0.602805
\(13\) 2.20951 0.612808 0.306404 0.951902i \(-0.400874\pi\)
0.306404 + 0.951902i \(0.400874\pi\)
\(14\) −8.11710 −2.16939
\(15\) 0.772478 0.199453
\(16\) −0.0715963 −0.0178991
\(17\) −1.00000 −0.242536
\(18\) 5.89334 1.38907
\(19\) −2.00734 −0.460515 −0.230258 0.973130i \(-0.573957\pi\)
−0.230258 + 0.973130i \(0.573957\pi\)
\(20\) −3.83558 −0.857661
\(21\) −2.30397 −0.502768
\(22\) −2.28473 −0.487107
\(23\) 3.40797 0.710610 0.355305 0.934750i \(-0.384377\pi\)
0.355305 + 0.934750i \(0.384377\pi\)
\(24\) 1.80762 0.368979
\(25\) −3.58111 −0.716221
\(26\) −5.04814 −0.990022
\(27\) 3.61828 0.696339
\(28\) 11.4399 2.16193
\(29\) 7.34415 1.36377 0.681887 0.731457i \(-0.261159\pi\)
0.681887 + 0.731457i \(0.261159\pi\)
\(30\) −1.76491 −0.322226
\(31\) −2.81936 −0.506371 −0.253186 0.967418i \(-0.581478\pi\)
−0.253186 + 0.967418i \(0.581478\pi\)
\(32\) 5.73833 1.01440
\(33\) −0.648502 −0.112890
\(34\) 2.28473 0.391828
\(35\) −4.23195 −0.715330
\(36\) −8.30581 −1.38430
\(37\) −6.89242 −1.13311 −0.566553 0.824025i \(-0.691723\pi\)
−0.566553 + 0.824025i \(0.691723\pi\)
\(38\) 4.58623 0.743985
\(39\) −1.43287 −0.229443
\(40\) 3.32025 0.524977
\(41\) 2.63626 0.411715 0.205858 0.978582i \(-0.434002\pi\)
0.205858 + 0.978582i \(0.434002\pi\)
\(42\) 5.26396 0.812246
\(43\) −1.00000 −0.152499
\(44\) 3.22000 0.485433
\(45\) 3.07256 0.458031
\(46\) −7.78629 −1.14803
\(47\) −0.309786 −0.0451870 −0.0225935 0.999745i \(-0.507192\pi\)
−0.0225935 + 0.999745i \(0.507192\pi\)
\(48\) 0.0464303 0.00670164
\(49\) 5.62208 0.803154
\(50\) 8.18187 1.15709
\(51\) 0.648502 0.0908085
\(52\) 7.11463 0.986621
\(53\) 3.94179 0.541447 0.270723 0.962657i \(-0.412737\pi\)
0.270723 + 0.962657i \(0.412737\pi\)
\(54\) −8.26681 −1.12497
\(55\) −1.19117 −0.160618
\(56\) −9.90286 −1.32333
\(57\) 1.30176 0.172423
\(58\) −16.7794 −2.20325
\(59\) −11.6969 −1.52280 −0.761402 0.648280i \(-0.775489\pi\)
−0.761402 + 0.648280i \(0.775489\pi\)
\(60\) 2.48738 0.321120
\(61\) −6.80995 −0.871925 −0.435962 0.899965i \(-0.643592\pi\)
−0.435962 + 0.899965i \(0.643592\pi\)
\(62\) 6.44148 0.818068
\(63\) −9.16414 −1.15457
\(64\) −12.9674 −1.62092
\(65\) −2.63191 −0.326448
\(66\) 1.48165 0.182379
\(67\) 1.66914 0.203918 0.101959 0.994789i \(-0.467489\pi\)
0.101959 + 0.994789i \(0.467489\pi\)
\(68\) −3.22000 −0.390482
\(69\) −2.21007 −0.266062
\(70\) 9.66886 1.15565
\(71\) 5.91650 0.702159 0.351080 0.936346i \(-0.385815\pi\)
0.351080 + 0.936346i \(0.385815\pi\)
\(72\) 7.18988 0.847335
\(73\) 7.52804 0.881091 0.440545 0.897730i \(-0.354785\pi\)
0.440545 + 0.897730i \(0.354785\pi\)
\(74\) 15.7473 1.83059
\(75\) 2.32236 0.268163
\(76\) −6.46363 −0.741429
\(77\) 3.55276 0.404874
\(78\) 3.27373 0.370677
\(79\) 7.35099 0.827051 0.413526 0.910492i \(-0.364297\pi\)
0.413526 + 0.910492i \(0.364297\pi\)
\(80\) 0.0852835 0.00953499
\(81\) 5.39187 0.599097
\(82\) −6.02316 −0.665146
\(83\) 8.75805 0.961320 0.480660 0.876907i \(-0.340397\pi\)
0.480660 + 0.876907i \(0.340397\pi\)
\(84\) −7.41879 −0.809456
\(85\) 1.19117 0.129201
\(86\) 2.28473 0.246369
\(87\) −4.76270 −0.510615
\(88\) −2.78738 −0.297135
\(89\) −13.9073 −1.47417 −0.737087 0.675798i \(-0.763799\pi\)
−0.737087 + 0.675798i \(0.763799\pi\)
\(90\) −7.01999 −0.739972
\(91\) 7.84985 0.822888
\(92\) 10.9737 1.14408
\(93\) 1.82836 0.189592
\(94\) 0.707779 0.0730018
\(95\) 2.39109 0.245320
\(96\) −3.72132 −0.379806
\(97\) −12.7362 −1.29317 −0.646584 0.762843i \(-0.723803\pi\)
−0.646584 + 0.762843i \(0.723803\pi\)
\(98\) −12.8449 −1.29753
\(99\) −2.57944 −0.259244
\(100\) −11.5312 −1.15312
\(101\) 9.09598 0.905084 0.452542 0.891743i \(-0.350517\pi\)
0.452542 + 0.891743i \(0.350517\pi\)
\(102\) −1.48165 −0.146706
\(103\) −2.34909 −0.231462 −0.115731 0.993281i \(-0.536921\pi\)
−0.115731 + 0.993281i \(0.536921\pi\)
\(104\) −6.15873 −0.603914
\(105\) 2.74443 0.267829
\(106\) −9.00594 −0.874734
\(107\) 11.3911 1.10122 0.550609 0.834763i \(-0.314395\pi\)
0.550609 + 0.834763i \(0.314395\pi\)
\(108\) 11.6509 1.12111
\(109\) 10.8657 1.04074 0.520371 0.853940i \(-0.325794\pi\)
0.520371 + 0.853940i \(0.325794\pi\)
\(110\) 2.72151 0.259486
\(111\) 4.46975 0.424250
\(112\) −0.254364 −0.0240351
\(113\) 0.532901 0.0501311 0.0250656 0.999686i \(-0.492021\pi\)
0.0250656 + 0.999686i \(0.492021\pi\)
\(114\) −2.97418 −0.278558
\(115\) −4.05948 −0.378548
\(116\) 23.6482 2.19568
\(117\) −5.69931 −0.526901
\(118\) 26.7242 2.46017
\(119\) −3.55276 −0.325681
\(120\) −2.15319 −0.196558
\(121\) 1.00000 0.0909091
\(122\) 15.5589 1.40864
\(123\) −1.70962 −0.154152
\(124\) −9.07833 −0.815258
\(125\) 10.2216 0.914246
\(126\) 20.9376 1.86527
\(127\) 21.2140 1.88243 0.941217 0.337802i \(-0.109683\pi\)
0.941217 + 0.337802i \(0.109683\pi\)
\(128\) 18.1503 1.60427
\(129\) 0.648502 0.0570974
\(130\) 6.01321 0.527393
\(131\) −22.6848 −1.98198 −0.990989 0.133945i \(-0.957235\pi\)
−0.990989 + 0.133945i \(0.957235\pi\)
\(132\) −2.08818 −0.181753
\(133\) −7.13159 −0.618387
\(134\) −3.81354 −0.329440
\(135\) −4.31000 −0.370946
\(136\) 2.78738 0.239015
\(137\) 17.7104 1.51310 0.756552 0.653934i \(-0.226883\pi\)
0.756552 + 0.653934i \(0.226883\pi\)
\(138\) 5.04943 0.429836
\(139\) 13.0865 1.10998 0.554992 0.831855i \(-0.312721\pi\)
0.554992 + 0.831855i \(0.312721\pi\)
\(140\) −13.6269 −1.15168
\(141\) 0.200897 0.0169186
\(142\) −13.5176 −1.13437
\(143\) 2.20951 0.184769
\(144\) 0.184679 0.0153899
\(145\) −8.74815 −0.726495
\(146\) −17.1996 −1.42345
\(147\) −3.64593 −0.300711
\(148\) −22.1936 −1.82430
\(149\) 5.89280 0.482757 0.241378 0.970431i \(-0.422401\pi\)
0.241378 + 0.970431i \(0.422401\pi\)
\(150\) −5.30596 −0.433230
\(151\) −3.39079 −0.275939 −0.137969 0.990436i \(-0.544058\pi\)
−0.137969 + 0.990436i \(0.544058\pi\)
\(152\) 5.59521 0.453831
\(153\) 2.57944 0.208536
\(154\) −8.11710 −0.654094
\(155\) 3.35834 0.269748
\(156\) −4.61385 −0.369404
\(157\) −7.08938 −0.565794 −0.282897 0.959150i \(-0.591296\pi\)
−0.282897 + 0.959150i \(0.591296\pi\)
\(158\) −16.7950 −1.33614
\(159\) −2.55626 −0.202725
\(160\) −6.83534 −0.540381
\(161\) 12.1077 0.954218
\(162\) −12.3190 −0.967870
\(163\) −0.823931 −0.0645353 −0.0322676 0.999479i \(-0.510273\pi\)
−0.0322676 + 0.999479i \(0.510273\pi\)
\(164\) 8.48877 0.662862
\(165\) 0.772478 0.0601374
\(166\) −20.0098 −1.55306
\(167\) 11.4728 0.887788 0.443894 0.896079i \(-0.353597\pi\)
0.443894 + 0.896079i \(0.353597\pi\)
\(168\) 6.42203 0.495470
\(169\) −8.11806 −0.624466
\(170\) −2.72151 −0.208730
\(171\) 5.17782 0.395958
\(172\) −3.22000 −0.245523
\(173\) −21.8738 −1.66303 −0.831517 0.555499i \(-0.812527\pi\)
−0.831517 + 0.555499i \(0.812527\pi\)
\(174\) 10.8815 0.824924
\(175\) −12.7228 −0.961753
\(176\) −0.0715963 −0.00539677
\(177\) 7.58545 0.570158
\(178\) 31.7745 2.38160
\(179\) 3.95534 0.295636 0.147818 0.989015i \(-0.452775\pi\)
0.147818 + 0.989015i \(0.452775\pi\)
\(180\) 9.89366 0.737430
\(181\) −18.4422 −1.37080 −0.685398 0.728169i \(-0.740372\pi\)
−0.685398 + 0.728169i \(0.740372\pi\)
\(182\) −17.9348 −1.32942
\(183\) 4.41627 0.326460
\(184\) −9.49928 −0.700296
\(185\) 8.21006 0.603616
\(186\) −4.17731 −0.306295
\(187\) −1.00000 −0.0731272
\(188\) −0.997512 −0.0727511
\(189\) 12.8549 0.935055
\(190\) −5.46299 −0.396327
\(191\) 9.97761 0.721954 0.360977 0.932575i \(-0.382443\pi\)
0.360977 + 0.932575i \(0.382443\pi\)
\(192\) 8.40936 0.606893
\(193\) 14.4311 1.03877 0.519385 0.854540i \(-0.326161\pi\)
0.519385 + 0.854540i \(0.326161\pi\)
\(194\) 29.0989 2.08918
\(195\) 1.70680 0.122226
\(196\) 18.1031 1.29308
\(197\) 19.7895 1.40995 0.704973 0.709234i \(-0.250959\pi\)
0.704973 + 0.709234i \(0.250959\pi\)
\(198\) 5.89334 0.418821
\(199\) −19.0828 −1.35274 −0.676371 0.736561i \(-0.736448\pi\)
−0.676371 + 0.736561i \(0.736448\pi\)
\(200\) 9.98189 0.705826
\(201\) −1.08244 −0.0763496
\(202\) −20.7819 −1.46221
\(203\) 26.0920 1.83130
\(204\) 2.08818 0.146202
\(205\) −3.14025 −0.219324
\(206\) 5.36703 0.373939
\(207\) −8.79066 −0.610993
\(208\) −0.158193 −0.0109687
\(209\) −2.00734 −0.138851
\(210\) −6.27028 −0.432691
\(211\) 4.30128 0.296113 0.148056 0.988979i \(-0.452698\pi\)
0.148056 + 0.988979i \(0.452698\pi\)
\(212\) 12.6926 0.871730
\(213\) −3.83686 −0.262898
\(214\) −26.0256 −1.77907
\(215\) 1.19117 0.0812373
\(216\) −10.0855 −0.686232
\(217\) −10.0165 −0.679964
\(218\) −24.8251 −1.68137
\(219\) −4.88195 −0.329892
\(220\) −3.83558 −0.258595
\(221\) −2.20951 −0.148628
\(222\) −10.2122 −0.685397
\(223\) −13.9198 −0.932137 −0.466069 0.884749i \(-0.654330\pi\)
−0.466069 + 0.884749i \(0.654330\pi\)
\(224\) 20.3869 1.36216
\(225\) 9.23727 0.615818
\(226\) −1.21754 −0.0809893
\(227\) 3.26121 0.216454 0.108227 0.994126i \(-0.465483\pi\)
0.108227 + 0.994126i \(0.465483\pi\)
\(228\) 4.19168 0.277601
\(229\) −4.43344 −0.292970 −0.146485 0.989213i \(-0.546796\pi\)
−0.146485 + 0.989213i \(0.546796\pi\)
\(230\) 9.27481 0.611563
\(231\) −2.30397 −0.151590
\(232\) −20.4709 −1.34398
\(233\) 1.04788 0.0686488 0.0343244 0.999411i \(-0.489072\pi\)
0.0343244 + 0.999411i \(0.489072\pi\)
\(234\) 13.0214 0.851235
\(235\) 0.369009 0.0240715
\(236\) −37.6640 −2.45171
\(237\) −4.76714 −0.309659
\(238\) 8.11710 0.526153
\(239\) −8.56665 −0.554130 −0.277065 0.960851i \(-0.589362\pi\)
−0.277065 + 0.960851i \(0.589362\pi\)
\(240\) −0.0553066 −0.00357002
\(241\) −3.14689 −0.202709 −0.101354 0.994850i \(-0.532318\pi\)
−0.101354 + 0.994850i \(0.532318\pi\)
\(242\) −2.28473 −0.146868
\(243\) −14.3515 −0.920648
\(244\) −21.9280 −1.40380
\(245\) −6.69687 −0.427847
\(246\) 3.90603 0.249039
\(247\) −4.43524 −0.282207
\(248\) 7.85861 0.499022
\(249\) −5.67961 −0.359931
\(250\) −23.3536 −1.47701
\(251\) −21.3698 −1.34885 −0.674424 0.738344i \(-0.735608\pi\)
−0.674424 + 0.738344i \(0.735608\pi\)
\(252\) −29.5085 −1.85886
\(253\) 3.40797 0.214257
\(254\) −48.4682 −3.04117
\(255\) −0.772478 −0.0483745
\(256\) −15.5338 −0.970862
\(257\) 17.3554 1.08260 0.541301 0.840829i \(-0.317932\pi\)
0.541301 + 0.840829i \(0.317932\pi\)
\(258\) −1.48165 −0.0922438
\(259\) −24.4871 −1.52155
\(260\) −8.47475 −0.525582
\(261\) −18.9438 −1.17259
\(262\) 51.8286 3.20198
\(263\) 9.40210 0.579759 0.289879 0.957063i \(-0.406385\pi\)
0.289879 + 0.957063i \(0.406385\pi\)
\(264\) 1.80762 0.111251
\(265\) −4.69536 −0.288433
\(266\) 16.2938 0.999035
\(267\) 9.01894 0.551950
\(268\) 5.37464 0.328308
\(269\) −22.5602 −1.37552 −0.687760 0.725938i \(-0.741406\pi\)
−0.687760 + 0.725938i \(0.741406\pi\)
\(270\) 9.84720 0.599281
\(271\) 28.6420 1.73988 0.869938 0.493161i \(-0.164159\pi\)
0.869938 + 0.493161i \(0.164159\pi\)
\(272\) 0.0715963 0.00434116
\(273\) −5.09065 −0.308100
\(274\) −40.4636 −2.44449
\(275\) −3.58111 −0.215949
\(276\) −7.11644 −0.428359
\(277\) 7.54784 0.453506 0.226753 0.973952i \(-0.427189\pi\)
0.226753 + 0.973952i \(0.427189\pi\)
\(278\) −29.8992 −1.79324
\(279\) 7.27238 0.435386
\(280\) 11.7960 0.704947
\(281\) 24.1984 1.44356 0.721778 0.692125i \(-0.243325\pi\)
0.721778 + 0.692125i \(0.243325\pi\)
\(282\) −0.458996 −0.0273328
\(283\) −5.84037 −0.347174 −0.173587 0.984819i \(-0.555536\pi\)
−0.173587 + 0.984819i \(0.555536\pi\)
\(284\) 19.0511 1.13048
\(285\) −1.55063 −0.0918511
\(286\) −5.04814 −0.298503
\(287\) 9.36600 0.552858
\(288\) −14.8017 −0.872199
\(289\) 1.00000 0.0588235
\(290\) 19.9872 1.17369
\(291\) 8.25947 0.484179
\(292\) 24.2403 1.41856
\(293\) 21.5392 1.25833 0.629165 0.777272i \(-0.283397\pi\)
0.629165 + 0.777272i \(0.283397\pi\)
\(294\) 8.32997 0.485814
\(295\) 13.9330 0.811211
\(296\) 19.2118 1.11666
\(297\) 3.61828 0.209954
\(298\) −13.4635 −0.779917
\(299\) 7.52993 0.435467
\(300\) 7.47799 0.431742
\(301\) −3.55276 −0.204777
\(302\) 7.74705 0.445793
\(303\) −5.89876 −0.338875
\(304\) 0.143718 0.00824279
\(305\) 8.11183 0.464482
\(306\) −5.89334 −0.336900
\(307\) −31.2816 −1.78533 −0.892666 0.450718i \(-0.851168\pi\)
−0.892666 + 0.450718i \(0.851168\pi\)
\(308\) 11.4399 0.651848
\(309\) 1.52339 0.0866625
\(310\) −7.67291 −0.435792
\(311\) 8.11131 0.459950 0.229975 0.973197i \(-0.426136\pi\)
0.229975 + 0.973197i \(0.426136\pi\)
\(312\) 3.99395 0.226113
\(313\) −9.34692 −0.528319 −0.264160 0.964479i \(-0.585095\pi\)
−0.264160 + 0.964479i \(0.585095\pi\)
\(314\) 16.1973 0.914069
\(315\) 10.9161 0.615051
\(316\) 23.6702 1.33155
\(317\) 23.1945 1.30273 0.651367 0.758763i \(-0.274196\pi\)
0.651367 + 0.758763i \(0.274196\pi\)
\(318\) 5.84037 0.327512
\(319\) 7.34415 0.411193
\(320\) 15.4464 0.863478
\(321\) −7.38715 −0.412311
\(322\) −27.6628 −1.54159
\(323\) 2.00734 0.111691
\(324\) 17.3618 0.964546
\(325\) −7.91249 −0.438906
\(326\) 1.88246 0.104260
\(327\) −7.04641 −0.389667
\(328\) −7.34825 −0.405740
\(329\) −1.10060 −0.0606778
\(330\) −1.76491 −0.0971549
\(331\) −7.80558 −0.429034 −0.214517 0.976720i \(-0.568818\pi\)
−0.214517 + 0.976720i \(0.568818\pi\)
\(332\) 28.2009 1.54773
\(333\) 17.7786 0.974262
\(334\) −26.2122 −1.43427
\(335\) −1.98824 −0.108629
\(336\) 0.164956 0.00899907
\(337\) −1.36060 −0.0741166 −0.0370583 0.999313i \(-0.511799\pi\)
−0.0370583 + 0.999313i \(0.511799\pi\)
\(338\) 18.5476 1.00886
\(339\) −0.345588 −0.0187697
\(340\) 3.83558 0.208013
\(341\) −2.81936 −0.152677
\(342\) −11.8299 −0.639689
\(343\) −4.89542 −0.264328
\(344\) 2.78738 0.150285
\(345\) 2.63258 0.141733
\(346\) 49.9758 2.68671
\(347\) −15.7178 −0.843774 −0.421887 0.906648i \(-0.638632\pi\)
−0.421887 + 0.906648i \(0.638632\pi\)
\(348\) −15.3359 −0.822090
\(349\) −17.6120 −0.942747 −0.471373 0.881934i \(-0.656242\pi\)
−0.471373 + 0.881934i \(0.656242\pi\)
\(350\) 29.0682 1.55376
\(351\) 7.99463 0.426722
\(352\) 5.73833 0.305854
\(353\) −9.92305 −0.528151 −0.264075 0.964502i \(-0.585067\pi\)
−0.264075 + 0.964502i \(0.585067\pi\)
\(354\) −17.3307 −0.921118
\(355\) −7.04757 −0.374046
\(356\) −44.7816 −2.37342
\(357\) 2.30397 0.121939
\(358\) −9.03689 −0.477615
\(359\) −24.5876 −1.29768 −0.648842 0.760923i \(-0.724746\pi\)
−0.648842 + 0.760923i \(0.724746\pi\)
\(360\) −8.56439 −0.451383
\(361\) −14.9706 −0.787926
\(362\) 42.1354 2.21459
\(363\) −0.648502 −0.0340375
\(364\) 25.2765 1.32485
\(365\) −8.96720 −0.469365
\(366\) −10.0900 −0.527412
\(367\) −15.7572 −0.822517 −0.411258 0.911519i \(-0.634911\pi\)
−0.411258 + 0.911519i \(0.634911\pi\)
\(368\) −0.243998 −0.0127193
\(369\) −6.80010 −0.353999
\(370\) −18.7578 −0.975171
\(371\) 14.0042 0.727063
\(372\) 5.88732 0.305243
\(373\) 22.1275 1.14572 0.572858 0.819654i \(-0.305835\pi\)
0.572858 + 0.819654i \(0.305835\pi\)
\(374\) 2.28473 0.118141
\(375\) −6.62872 −0.342306
\(376\) 0.863491 0.0445311
\(377\) 16.2270 0.835732
\(378\) −29.3700 −1.51063
\(379\) 13.2418 0.680184 0.340092 0.940392i \(-0.389542\pi\)
0.340092 + 0.940392i \(0.389542\pi\)
\(380\) 7.69930 0.394966
\(381\) −13.7573 −0.704808
\(382\) −22.7962 −1.16635
\(383\) −15.4977 −0.791897 −0.395948 0.918273i \(-0.629584\pi\)
−0.395948 + 0.918273i \(0.629584\pi\)
\(384\) −11.7705 −0.600660
\(385\) −4.23195 −0.215680
\(386\) −32.9711 −1.67819
\(387\) 2.57944 0.131121
\(388\) −41.0107 −2.08200
\(389\) 28.7306 1.45670 0.728350 0.685205i \(-0.240287\pi\)
0.728350 + 0.685205i \(0.240287\pi\)
\(390\) −3.89958 −0.197463
\(391\) −3.40797 −0.172348
\(392\) −15.6708 −0.791497
\(393\) 14.7111 0.742078
\(394\) −45.2138 −2.27784
\(395\) −8.75630 −0.440577
\(396\) −8.30581 −0.417383
\(397\) 2.46298 0.123613 0.0618067 0.998088i \(-0.480314\pi\)
0.0618067 + 0.998088i \(0.480314\pi\)
\(398\) 43.5990 2.18542
\(399\) 4.62485 0.231532
\(400\) 0.256394 0.0128197
\(401\) −1.07935 −0.0539001 −0.0269500 0.999637i \(-0.508580\pi\)
−0.0269500 + 0.999637i \(0.508580\pi\)
\(402\) 2.47309 0.123347
\(403\) −6.22940 −0.310308
\(404\) 29.2891 1.45719
\(405\) −6.42265 −0.319144
\(406\) −59.6132 −2.95855
\(407\) −6.89242 −0.341644
\(408\) −1.80762 −0.0894905
\(409\) −5.14552 −0.254430 −0.127215 0.991875i \(-0.540604\pi\)
−0.127215 + 0.991875i \(0.540604\pi\)
\(410\) 7.17462 0.354329
\(411\) −11.4853 −0.566526
\(412\) −7.56406 −0.372654
\(413\) −41.5562 −2.04484
\(414\) 20.0843 0.987089
\(415\) −10.4323 −0.512104
\(416\) 12.6789 0.621634
\(417\) −8.48664 −0.415593
\(418\) 4.58623 0.224320
\(419\) 21.3971 1.04532 0.522658 0.852543i \(-0.324941\pi\)
0.522658 + 0.852543i \(0.324941\pi\)
\(420\) 8.83706 0.431204
\(421\) −0.216598 −0.0105563 −0.00527817 0.999986i \(-0.501680\pi\)
−0.00527817 + 0.999986i \(0.501680\pi\)
\(422\) −9.82728 −0.478384
\(423\) 0.799077 0.0388524
\(424\) −10.9873 −0.533588
\(425\) 3.58111 0.173709
\(426\) 8.76620 0.424724
\(427\) −24.1941 −1.17083
\(428\) 36.6793 1.77296
\(429\) −1.43287 −0.0691797
\(430\) −2.72151 −0.131243
\(431\) −24.3837 −1.17452 −0.587262 0.809397i \(-0.699794\pi\)
−0.587262 + 0.809397i \(0.699794\pi\)
\(432\) −0.259056 −0.0124638
\(433\) 19.2679 0.925955 0.462977 0.886370i \(-0.346781\pi\)
0.462977 + 0.886370i \(0.346781\pi\)
\(434\) 22.8850 1.09851
\(435\) 5.67320 0.272009
\(436\) 34.9874 1.67559
\(437\) −6.84094 −0.327247
\(438\) 11.1540 0.532957
\(439\) −27.0559 −1.29131 −0.645653 0.763631i \(-0.723415\pi\)
−0.645653 + 0.763631i \(0.723415\pi\)
\(440\) 3.32025 0.158286
\(441\) −14.5018 −0.690564
\(442\) 5.04814 0.240116
\(443\) 16.8591 0.801000 0.400500 0.916297i \(-0.368836\pi\)
0.400500 + 0.916297i \(0.368836\pi\)
\(444\) 14.3926 0.683042
\(445\) 16.5660 0.785305
\(446\) 31.8030 1.50591
\(447\) −3.82149 −0.180750
\(448\) −46.0698 −2.17660
\(449\) 7.60495 0.358900 0.179450 0.983767i \(-0.442568\pi\)
0.179450 + 0.983767i \(0.442568\pi\)
\(450\) −21.1047 −0.994884
\(451\) 2.63626 0.124137
\(452\) 1.71594 0.0807111
\(453\) 2.19894 0.103315
\(454\) −7.45099 −0.349692
\(455\) −9.35053 −0.438360
\(456\) −3.62850 −0.169920
\(457\) 7.17726 0.335738 0.167869 0.985809i \(-0.446311\pi\)
0.167869 + 0.985809i \(0.446311\pi\)
\(458\) 10.1292 0.473307
\(459\) −3.61828 −0.168887
\(460\) −13.0715 −0.609463
\(461\) 34.7799 1.61986 0.809930 0.586526i \(-0.199505\pi\)
0.809930 + 0.586526i \(0.199505\pi\)
\(462\) 5.26396 0.244901
\(463\) 16.9796 0.789110 0.394555 0.918872i \(-0.370899\pi\)
0.394555 + 0.918872i \(0.370899\pi\)
\(464\) −0.525814 −0.0244103
\(465\) −2.17789 −0.100997
\(466\) −2.39412 −0.110905
\(467\) 27.7214 1.28280 0.641398 0.767209i \(-0.278355\pi\)
0.641398 + 0.767209i \(0.278355\pi\)
\(468\) −18.3518 −0.848312
\(469\) 5.93006 0.273825
\(470\) −0.843087 −0.0388887
\(471\) 4.59748 0.211841
\(472\) 32.6036 1.50070
\(473\) −1.00000 −0.0459800
\(474\) 10.8916 0.500269
\(475\) 7.18850 0.329831
\(476\) −11.4399 −0.524346
\(477\) −10.1676 −0.465544
\(478\) 19.5725 0.895225
\(479\) −26.0165 −1.18873 −0.594363 0.804197i \(-0.702596\pi\)
−0.594363 + 0.804197i \(0.702596\pi\)
\(480\) 4.43273 0.202326
\(481\) −15.2289 −0.694377
\(482\) 7.18980 0.327486
\(483\) −7.85185 −0.357272
\(484\) 3.22000 0.146364
\(485\) 15.1711 0.688882
\(486\) 32.7893 1.48735
\(487\) −19.4282 −0.880377 −0.440188 0.897905i \(-0.645088\pi\)
−0.440188 + 0.897905i \(0.645088\pi\)
\(488\) 18.9819 0.859270
\(489\) 0.534321 0.0241628
\(490\) 15.3005 0.691208
\(491\) 25.5428 1.15273 0.576365 0.817192i \(-0.304470\pi\)
0.576365 + 0.817192i \(0.304470\pi\)
\(492\) −5.50499 −0.248184
\(493\) −7.34415 −0.330764
\(494\) 10.1333 0.455920
\(495\) 3.07256 0.138102
\(496\) 0.201855 0.00906358
\(497\) 21.0199 0.942870
\(498\) 12.9764 0.581486
\(499\) 17.4977 0.783306 0.391653 0.920113i \(-0.371903\pi\)
0.391653 + 0.920113i \(0.371903\pi\)
\(500\) 32.9135 1.47194
\(501\) −7.44011 −0.332400
\(502\) 48.8242 2.17913
\(503\) −15.8960 −0.708769 −0.354385 0.935100i \(-0.615310\pi\)
−0.354385 + 0.935100i \(0.615310\pi\)
\(504\) 25.5439 1.13782
\(505\) −10.8349 −0.482146
\(506\) −7.78629 −0.346143
\(507\) 5.26458 0.233808
\(508\) 68.3090 3.03072
\(509\) 16.1262 0.714783 0.357392 0.933955i \(-0.383666\pi\)
0.357392 + 0.933955i \(0.383666\pi\)
\(510\) 1.76491 0.0781514
\(511\) 26.7453 1.18314
\(512\) −0.809974 −0.0357961
\(513\) −7.26312 −0.320675
\(514\) −39.6525 −1.74900
\(515\) 2.79817 0.123302
\(516\) 2.08818 0.0919269
\(517\) −0.309786 −0.0136244
\(518\) 55.9464 2.45814
\(519\) 14.1852 0.622662
\(520\) 7.33612 0.321710
\(521\) 33.4431 1.46517 0.732585 0.680676i \(-0.238314\pi\)
0.732585 + 0.680676i \(0.238314\pi\)
\(522\) 43.2816 1.89438
\(523\) −14.7468 −0.644830 −0.322415 0.946598i \(-0.604495\pi\)
−0.322415 + 0.946598i \(0.604495\pi\)
\(524\) −73.0450 −3.19098
\(525\) 8.25077 0.360093
\(526\) −21.4813 −0.936629
\(527\) 2.81936 0.122813
\(528\) 0.0464303 0.00202062
\(529\) −11.3858 −0.495034
\(530\) 10.7276 0.465979
\(531\) 30.1715 1.30933
\(532\) −22.9637 −0.995603
\(533\) 5.82485 0.252302
\(534\) −20.6059 −0.891702
\(535\) −13.5688 −0.586629
\(536\) −4.65253 −0.200958
\(537\) −2.56505 −0.110690
\(538\) 51.5440 2.22222
\(539\) 5.62208 0.242160
\(540\) −13.8782 −0.597223
\(541\) 24.8653 1.06904 0.534520 0.845156i \(-0.320492\pi\)
0.534520 + 0.845156i \(0.320492\pi\)
\(542\) −65.4392 −2.81086
\(543\) 11.9598 0.513244
\(544\) −5.73833 −0.246029
\(545\) −12.9429 −0.554412
\(546\) 11.6308 0.497751
\(547\) −6.56693 −0.280782 −0.140391 0.990096i \(-0.544836\pi\)
−0.140391 + 0.990096i \(0.544836\pi\)
\(548\) 57.0276 2.43610
\(549\) 17.5659 0.749694
\(550\) 8.18187 0.348876
\(551\) −14.7422 −0.628039
\(552\) 6.16030 0.262200
\(553\) 26.1163 1.11058
\(554\) −17.2448 −0.732661
\(555\) −5.32424 −0.226002
\(556\) 42.1386 1.78708
\(557\) −37.0106 −1.56819 −0.784096 0.620640i \(-0.786873\pi\)
−0.784096 + 0.620640i \(0.786873\pi\)
\(558\) −16.6154 −0.703387
\(559\) −2.20951 −0.0934523
\(560\) 0.302992 0.0128037
\(561\) 0.648502 0.0273798
\(562\) −55.2869 −2.33214
\(563\) −9.00574 −0.379547 −0.189773 0.981828i \(-0.560775\pi\)
−0.189773 + 0.981828i \(0.560775\pi\)
\(564\) 0.646889 0.0272389
\(565\) −0.634777 −0.0267053
\(566\) 13.3437 0.560877
\(567\) 19.1560 0.804476
\(568\) −16.4915 −0.691968
\(569\) −3.64279 −0.152714 −0.0763569 0.997081i \(-0.524329\pi\)
−0.0763569 + 0.997081i \(0.524329\pi\)
\(570\) 3.54276 0.148390
\(571\) 39.3205 1.64551 0.822755 0.568395i \(-0.192436\pi\)
0.822755 + 0.568395i \(0.192436\pi\)
\(572\) 7.11463 0.297477
\(573\) −6.47050 −0.270309
\(574\) −21.3988 −0.893169
\(575\) −12.2043 −0.508954
\(576\) 33.4486 1.39369
\(577\) 18.6552 0.776627 0.388314 0.921527i \(-0.373058\pi\)
0.388314 + 0.921527i \(0.373058\pi\)
\(578\) −2.28473 −0.0950323
\(579\) −9.35858 −0.388929
\(580\) −28.1691 −1.16966
\(581\) 31.1152 1.29088
\(582\) −18.8707 −0.782215
\(583\) 3.94179 0.163252
\(584\) −20.9835 −0.868303
\(585\) 6.78886 0.280685
\(586\) −49.2112 −2.03290
\(587\) −12.3832 −0.511107 −0.255554 0.966795i \(-0.582258\pi\)
−0.255554 + 0.966795i \(0.582258\pi\)
\(588\) −11.7399 −0.484145
\(589\) 5.65940 0.233192
\(590\) −31.8332 −1.31055
\(591\) −12.8336 −0.527902
\(592\) 0.493471 0.0202815
\(593\) 21.1433 0.868253 0.434126 0.900852i \(-0.357057\pi\)
0.434126 + 0.900852i \(0.357057\pi\)
\(594\) −8.26681 −0.339191
\(595\) 4.23195 0.173493
\(596\) 18.9748 0.777239
\(597\) 12.3752 0.506484
\(598\) −17.2039 −0.703519
\(599\) −5.00603 −0.204541 −0.102270 0.994757i \(-0.532611\pi\)
−0.102270 + 0.994757i \(0.532611\pi\)
\(600\) −6.47328 −0.264270
\(601\) 29.7526 1.21363 0.606817 0.794841i \(-0.292446\pi\)
0.606817 + 0.794841i \(0.292446\pi\)
\(602\) 8.11710 0.330828
\(603\) −4.30546 −0.175332
\(604\) −10.9184 −0.444262
\(605\) −1.19117 −0.0484281
\(606\) 13.4771 0.547470
\(607\) 11.3253 0.459680 0.229840 0.973228i \(-0.426180\pi\)
0.229840 + 0.973228i \(0.426180\pi\)
\(608\) −11.5188 −0.467148
\(609\) −16.9207 −0.685662
\(610\) −18.5334 −0.750394
\(611\) −0.684476 −0.0276909
\(612\) 8.30581 0.335743
\(613\) 26.1633 1.05672 0.528362 0.849019i \(-0.322806\pi\)
0.528362 + 0.849019i \(0.322806\pi\)
\(614\) 71.4700 2.88429
\(615\) 2.03646 0.0821179
\(616\) −9.90286 −0.398998
\(617\) −4.15687 −0.167349 −0.0836747 0.996493i \(-0.526666\pi\)
−0.0836747 + 0.996493i \(0.526666\pi\)
\(618\) −3.48053 −0.140008
\(619\) 14.6889 0.590398 0.295199 0.955436i \(-0.404614\pi\)
0.295199 + 0.955436i \(0.404614\pi\)
\(620\) 10.8139 0.434295
\(621\) 12.3310 0.494825
\(622\) −18.5322 −0.743072
\(623\) −49.4093 −1.97954
\(624\) 0.102588 0.00410682
\(625\) 5.72987 0.229195
\(626\) 21.3552 0.853526
\(627\) 1.30176 0.0519874
\(628\) −22.8278 −0.910929
\(629\) 6.89242 0.274819
\(630\) −24.9403 −0.993645
\(631\) −21.1440 −0.841729 −0.420864 0.907124i \(-0.638273\pi\)
−0.420864 + 0.907124i \(0.638273\pi\)
\(632\) −20.4900 −0.815047
\(633\) −2.78939 −0.110868
\(634\) −52.9933 −2.10463
\(635\) −25.2695 −1.00279
\(636\) −8.23117 −0.326387
\(637\) 12.4220 0.492179
\(638\) −16.7794 −0.664303
\(639\) −15.2613 −0.603727
\(640\) −21.6201 −0.854610
\(641\) 10.2656 0.405468 0.202734 0.979234i \(-0.435017\pi\)
0.202734 + 0.979234i \(0.435017\pi\)
\(642\) 16.8777 0.666108
\(643\) −24.3254 −0.959302 −0.479651 0.877459i \(-0.659237\pi\)
−0.479651 + 0.877459i \(0.659237\pi\)
\(644\) 38.9867 1.53629
\(645\) −0.772478 −0.0304163
\(646\) −4.58623 −0.180443
\(647\) 23.4820 0.923172 0.461586 0.887095i \(-0.347281\pi\)
0.461586 + 0.887095i \(0.347281\pi\)
\(648\) −15.0292 −0.590401
\(649\) −11.6969 −0.459143
\(650\) 18.0779 0.709075
\(651\) 6.49572 0.254587
\(652\) −2.65306 −0.103902
\(653\) −28.6780 −1.12226 −0.561128 0.827729i \(-0.689633\pi\)
−0.561128 + 0.827729i \(0.689633\pi\)
\(654\) 16.0991 0.629527
\(655\) 27.0215 1.05582
\(656\) −0.188747 −0.00736932
\(657\) −19.4182 −0.757575
\(658\) 2.51457 0.0980280
\(659\) 1.22280 0.0476334 0.0238167 0.999716i \(-0.492418\pi\)
0.0238167 + 0.999716i \(0.492418\pi\)
\(660\) 2.48738 0.0968212
\(661\) 12.0950 0.470441 0.235221 0.971942i \(-0.424419\pi\)
0.235221 + 0.971942i \(0.424419\pi\)
\(662\) 17.8337 0.693125
\(663\) 1.43287 0.0556482
\(664\) −24.4120 −0.947368
\(665\) 8.49495 0.329420
\(666\) −40.6194 −1.57397
\(667\) 25.0286 0.969112
\(668\) 36.9423 1.42934
\(669\) 9.02701 0.349004
\(670\) 4.54259 0.175496
\(671\) −6.80995 −0.262895
\(672\) −13.2209 −0.510009
\(673\) −4.39274 −0.169328 −0.0846639 0.996410i \(-0.526982\pi\)
−0.0846639 + 0.996410i \(0.526982\pi\)
\(674\) 3.10861 0.119739
\(675\) −12.9575 −0.498733
\(676\) −26.1402 −1.00539
\(677\) −23.5799 −0.906248 −0.453124 0.891447i \(-0.649691\pi\)
−0.453124 + 0.891447i \(0.649691\pi\)
\(678\) 0.789575 0.0303234
\(679\) −45.2487 −1.73649
\(680\) −3.32025 −0.127326
\(681\) −2.11490 −0.0810432
\(682\) 6.44148 0.246657
\(683\) −10.9734 −0.419886 −0.209943 0.977714i \(-0.567328\pi\)
−0.209943 + 0.977714i \(0.567328\pi\)
\(684\) 16.6726 0.637492
\(685\) −21.0962 −0.806043
\(686\) 11.1847 0.427035
\(687\) 2.87509 0.109692
\(688\) 0.0715963 0.00272958
\(689\) 8.70943 0.331803
\(690\) −6.01474 −0.228977
\(691\) −22.2785 −0.847515 −0.423757 0.905776i \(-0.639289\pi\)
−0.423757 + 0.905776i \(0.639289\pi\)
\(692\) −70.4337 −2.67749
\(693\) −9.16414 −0.348117
\(694\) 35.9109 1.36316
\(695\) −15.5883 −0.591298
\(696\) 13.2754 0.503204
\(697\) −2.63626 −0.0998556
\(698\) 40.2386 1.52305
\(699\) −0.679551 −0.0257030
\(700\) −40.9674 −1.54842
\(701\) 40.7156 1.53781 0.768904 0.639364i \(-0.220802\pi\)
0.768904 + 0.639364i \(0.220802\pi\)
\(702\) −18.2656 −0.689391
\(703\) 13.8354 0.521813
\(704\) −12.9674 −0.488725
\(705\) −0.239303 −0.00901268
\(706\) 22.6715 0.853253
\(707\) 32.3158 1.21536
\(708\) 24.4252 0.917954
\(709\) 4.72375 0.177404 0.0887021 0.996058i \(-0.471728\pi\)
0.0887021 + 0.996058i \(0.471728\pi\)
\(710\) 16.1018 0.604290
\(711\) −18.9615 −0.711111
\(712\) 38.7649 1.45278
\(713\) −9.60827 −0.359833
\(714\) −5.26396 −0.196999
\(715\) −2.63191 −0.0984278
\(716\) 12.7362 0.475974
\(717\) 5.55549 0.207474
\(718\) 56.1761 2.09647
\(719\) 47.5144 1.77199 0.885995 0.463695i \(-0.153477\pi\)
0.885995 + 0.463695i \(0.153477\pi\)
\(720\) −0.219984 −0.00819832
\(721\) −8.34573 −0.310811
\(722\) 34.2038 1.27293
\(723\) 2.04077 0.0758969
\(724\) −59.3838 −2.20698
\(725\) −26.3002 −0.976765
\(726\) 1.48165 0.0549893
\(727\) −5.62245 −0.208525 −0.104263 0.994550i \(-0.533248\pi\)
−0.104263 + 0.994550i \(0.533248\pi\)
\(728\) −21.8805 −0.810945
\(729\) −6.86863 −0.254394
\(730\) 20.4877 0.758282
\(731\) 1.00000 0.0369863
\(732\) 14.2204 0.525601
\(733\) 13.3269 0.492239 0.246119 0.969240i \(-0.420844\pi\)
0.246119 + 0.969240i \(0.420844\pi\)
\(734\) 36.0009 1.32882
\(735\) 4.34293 0.160191
\(736\) 19.5560 0.720845
\(737\) 1.66914 0.0614836
\(738\) 15.5364 0.571903
\(739\) 34.5361 1.27043 0.635216 0.772334i \(-0.280911\pi\)
0.635216 + 0.772334i \(0.280911\pi\)
\(740\) 26.4364 0.971821
\(741\) 2.87626 0.105662
\(742\) −31.9959 −1.17461
\(743\) 2.33458 0.0856474 0.0428237 0.999083i \(-0.486365\pi\)
0.0428237 + 0.999083i \(0.486365\pi\)
\(744\) −5.09632 −0.186840
\(745\) −7.01934 −0.257169
\(746\) −50.5553 −1.85096
\(747\) −22.5909 −0.826558
\(748\) −3.22000 −0.117735
\(749\) 40.4698 1.47873
\(750\) 15.1448 0.553012
\(751\) 38.9039 1.41962 0.709811 0.704392i \(-0.248780\pi\)
0.709811 + 0.704392i \(0.248780\pi\)
\(752\) 0.0221795 0.000808805 0
\(753\) 13.8583 0.505026
\(754\) −37.0743 −1.35017
\(755\) 4.03902 0.146995
\(756\) 41.3927 1.50544
\(757\) −7.57459 −0.275303 −0.137652 0.990481i \(-0.543955\pi\)
−0.137652 + 0.990481i \(0.543955\pi\)
\(758\) −30.2539 −1.09887
\(759\) −2.21007 −0.0802206
\(760\) −6.66486 −0.241760
\(761\) 19.0910 0.692048 0.346024 0.938226i \(-0.387532\pi\)
0.346024 + 0.938226i \(0.387532\pi\)
\(762\) 31.4318 1.13865
\(763\) 38.6030 1.39752
\(764\) 32.1279 1.16235
\(765\) −3.07256 −0.111089
\(766\) 35.4082 1.27935
\(767\) −25.8444 −0.933186
\(768\) 10.0737 0.363503
\(769\) 12.9331 0.466378 0.233189 0.972431i \(-0.425084\pi\)
0.233189 + 0.972431i \(0.425084\pi\)
\(770\) 9.66886 0.348442
\(771\) −11.2550 −0.405340
\(772\) 46.4680 1.67242
\(773\) −9.68816 −0.348459 −0.174230 0.984705i \(-0.555743\pi\)
−0.174230 + 0.984705i \(0.555743\pi\)
\(774\) −5.89334 −0.211832
\(775\) 10.0964 0.362674
\(776\) 35.5006 1.27440
\(777\) 15.8799 0.569689
\(778\) −65.6418 −2.35337
\(779\) −5.29187 −0.189601
\(780\) 5.49589 0.196785
\(781\) 5.91650 0.211709
\(782\) 7.78629 0.278437
\(783\) 26.5732 0.949649
\(784\) −0.402520 −0.0143757
\(785\) 8.44468 0.301404
\(786\) −33.6110 −1.19886
\(787\) −10.0288 −0.357487 −0.178744 0.983896i \(-0.557203\pi\)
−0.178744 + 0.983896i \(0.557203\pi\)
\(788\) 63.7224 2.27001
\(789\) −6.09729 −0.217069
\(790\) 20.0058 0.711775
\(791\) 1.89327 0.0673168
\(792\) 7.18988 0.255481
\(793\) −15.0467 −0.534322
\(794\) −5.62725 −0.199704
\(795\) 3.04495 0.107993
\(796\) −61.4465 −2.17791
\(797\) 20.4095 0.722941 0.361470 0.932384i \(-0.382275\pi\)
0.361470 + 0.932384i \(0.382275\pi\)
\(798\) −10.5665 −0.374052
\(799\) 0.309786 0.0109595
\(800\) −20.5496 −0.726537
\(801\) 35.8732 1.26752
\(802\) 2.46602 0.0870782
\(803\) 7.52804 0.265659
\(804\) −3.48547 −0.122923
\(805\) −14.4223 −0.508320
\(806\) 14.2325 0.501319
\(807\) 14.6304 0.515013
\(808\) −25.3539 −0.891947
\(809\) 32.7107 1.15005 0.575024 0.818137i \(-0.304993\pi\)
0.575024 + 0.818137i \(0.304993\pi\)
\(810\) 14.6740 0.515593
\(811\) 45.7942 1.60805 0.804025 0.594595i \(-0.202688\pi\)
0.804025 + 0.594595i \(0.202688\pi\)
\(812\) 84.0162 2.94839
\(813\) −18.5744 −0.651432
\(814\) 15.7473 0.551943
\(815\) 0.981444 0.0343785
\(816\) −0.0464303 −0.00162539
\(817\) 2.00734 0.0702279
\(818\) 11.7561 0.411044
\(819\) −20.2483 −0.707531
\(820\) −10.1116 −0.353112
\(821\) 10.2577 0.357996 0.178998 0.983849i \(-0.442714\pi\)
0.178998 + 0.983849i \(0.442714\pi\)
\(822\) 26.2407 0.915250
\(823\) 27.4487 0.956802 0.478401 0.878141i \(-0.341216\pi\)
0.478401 + 0.878141i \(0.341216\pi\)
\(824\) 6.54778 0.228103
\(825\) 2.32236 0.0808541
\(826\) 94.9447 3.30355
\(827\) −53.6382 −1.86518 −0.932592 0.360931i \(-0.882459\pi\)
−0.932592 + 0.360931i \(0.882459\pi\)
\(828\) −28.3059 −0.983699
\(829\) 37.6464 1.30751 0.653756 0.756705i \(-0.273192\pi\)
0.653756 + 0.756705i \(0.273192\pi\)
\(830\) 23.8351 0.827329
\(831\) −4.89480 −0.169799
\(832\) −28.6515 −0.993312
\(833\) −5.62208 −0.194793
\(834\) 19.3897 0.671411
\(835\) −13.6660 −0.472933
\(836\) −6.46363 −0.223549
\(837\) −10.2012 −0.352606
\(838\) −48.8866 −1.68876
\(839\) 25.8381 0.892031 0.446016 0.895025i \(-0.352843\pi\)
0.446016 + 0.895025i \(0.352843\pi\)
\(840\) −7.64975 −0.263941
\(841\) 24.9365 0.859881
\(842\) 0.494868 0.0170543
\(843\) −15.6927 −0.540486
\(844\) 13.8501 0.476741
\(845\) 9.67002 0.332659
\(846\) −1.82568 −0.0627680
\(847\) 3.55276 0.122074
\(848\) −0.282218 −0.00969139
\(849\) 3.78749 0.129986
\(850\) −8.18187 −0.280636
\(851\) −23.4891 −0.805197
\(852\) −12.3547 −0.423265
\(853\) 30.6675 1.05003 0.525017 0.851092i \(-0.324059\pi\)
0.525017 + 0.851092i \(0.324059\pi\)
\(854\) 55.2770 1.89154
\(855\) −6.16768 −0.210930
\(856\) −31.7513 −1.08524
\(857\) −4.19736 −0.143379 −0.0716896 0.997427i \(-0.522839\pi\)
−0.0716896 + 0.997427i \(0.522839\pi\)
\(858\) 3.27373 0.111763
\(859\) 37.1928 1.26900 0.634501 0.772922i \(-0.281205\pi\)
0.634501 + 0.772922i \(0.281205\pi\)
\(860\) 3.83558 0.130792
\(861\) −6.07387 −0.206997
\(862\) 55.7103 1.89750
\(863\) −9.66577 −0.329027 −0.164513 0.986375i \(-0.552605\pi\)
−0.164513 + 0.986375i \(0.552605\pi\)
\(864\) 20.7629 0.706368
\(865\) 26.0555 0.885913
\(866\) −44.0219 −1.49593
\(867\) −0.648502 −0.0220243
\(868\) −32.2531 −1.09474
\(869\) 7.35099 0.249365
\(870\) −12.9617 −0.439444
\(871\) 3.68799 0.124963
\(872\) −30.2867 −1.02564
\(873\) 32.8524 1.11189
\(874\) 15.6297 0.528683
\(875\) 36.3148 1.22766
\(876\) −15.7199 −0.531126
\(877\) −42.0305 −1.41927 −0.709635 0.704569i \(-0.751140\pi\)
−0.709635 + 0.704569i \(0.751140\pi\)
\(878\) 61.8154 2.08617
\(879\) −13.9682 −0.471135
\(880\) 0.0852835 0.00287491
\(881\) 20.1381 0.678468 0.339234 0.940702i \(-0.389832\pi\)
0.339234 + 0.940702i \(0.389832\pi\)
\(882\) 33.1328 1.11564
\(883\) −16.5777 −0.557885 −0.278943 0.960308i \(-0.589984\pi\)
−0.278943 + 0.960308i \(0.589984\pi\)
\(884\) −7.11463 −0.239291
\(885\) −9.03559 −0.303728
\(886\) −38.5185 −1.29406
\(887\) 15.3506 0.515424 0.257712 0.966222i \(-0.417031\pi\)
0.257712 + 0.966222i \(0.417031\pi\)
\(888\) −12.4589 −0.418092
\(889\) 75.3680 2.52776
\(890\) −37.8489 −1.26870
\(891\) 5.39187 0.180634
\(892\) −44.8217 −1.50074
\(893\) 0.621846 0.0208093
\(894\) 8.73109 0.292011
\(895\) −4.71149 −0.157488
\(896\) 64.4835 2.15424
\(897\) −4.88318 −0.163045
\(898\) −17.3753 −0.579820
\(899\) −20.7058 −0.690577
\(900\) 29.7440 0.991467
\(901\) −3.94179 −0.131320
\(902\) −6.02316 −0.200549
\(903\) 2.30397 0.0766713
\(904\) −1.48540 −0.0494035
\(905\) 21.9678 0.730235
\(906\) −5.02398 −0.166911
\(907\) 22.9954 0.763551 0.381776 0.924255i \(-0.375313\pi\)
0.381776 + 0.924255i \(0.375313\pi\)
\(908\) 10.5011 0.348491
\(909\) −23.4626 −0.778204
\(910\) 21.3635 0.708192
\(911\) 30.4863 1.01006 0.505029 0.863103i \(-0.331482\pi\)
0.505029 + 0.863103i \(0.331482\pi\)
\(912\) −0.0932014 −0.00308621
\(913\) 8.75805 0.289849
\(914\) −16.3981 −0.542401
\(915\) −5.26054 −0.173908
\(916\) −14.2757 −0.471681
\(917\) −80.5935 −2.66143
\(918\) 8.26681 0.272845
\(919\) −6.58041 −0.217068 −0.108534 0.994093i \(-0.534616\pi\)
−0.108534 + 0.994093i \(0.534616\pi\)
\(920\) 11.3153 0.373054
\(921\) 20.2862 0.668452
\(922\) −79.4627 −2.61697
\(923\) 13.0726 0.430289
\(924\) −7.41879 −0.244060
\(925\) 24.6825 0.811555
\(926\) −38.7939 −1.27485
\(927\) 6.05933 0.199015
\(928\) 42.1431 1.38342
\(929\) 48.2706 1.58371 0.791853 0.610712i \(-0.209117\pi\)
0.791853 + 0.610712i \(0.209117\pi\)
\(930\) 4.97590 0.163166
\(931\) −11.2854 −0.369864
\(932\) 3.37417 0.110525
\(933\) −5.26020 −0.172211
\(934\) −63.3361 −2.07242
\(935\) 1.19117 0.0389555
\(936\) 15.8861 0.519254
\(937\) 26.9123 0.879188 0.439594 0.898197i \(-0.355122\pi\)
0.439594 + 0.898197i \(0.355122\pi\)
\(938\) −13.5486 −0.442377
\(939\) 6.06150 0.197810
\(940\) 1.18821 0.0387551
\(941\) 52.7134 1.71841 0.859204 0.511634i \(-0.170960\pi\)
0.859204 + 0.511634i \(0.170960\pi\)
\(942\) −10.5040 −0.342239
\(943\) 8.98429 0.292569
\(944\) 0.837453 0.0272568
\(945\) −15.3124 −0.498112
\(946\) 2.28473 0.0742830
\(947\) −10.8298 −0.351922 −0.175961 0.984397i \(-0.556303\pi\)
−0.175961 + 0.984397i \(0.556303\pi\)
\(948\) −15.3502 −0.498551
\(949\) 16.6333 0.539940
\(950\) −16.4238 −0.532858
\(951\) −15.0417 −0.487761
\(952\) 9.90286 0.320954
\(953\) 38.8834 1.25956 0.629778 0.776775i \(-0.283146\pi\)
0.629778 + 0.776775i \(0.283146\pi\)
\(954\) 23.2303 0.752110
\(955\) −11.8851 −0.384591
\(956\) −27.5846 −0.892150
\(957\) −4.76270 −0.153956
\(958\) 59.4408 1.92045
\(959\) 62.9208 2.03182
\(960\) −10.0170 −0.323297
\(961\) −23.0512 −0.743588
\(962\) 34.7939 1.12180
\(963\) −29.3827 −0.946844
\(964\) −10.1330 −0.326362
\(965\) −17.1899 −0.553362
\(966\) 17.9394 0.577190
\(967\) 51.8598 1.66770 0.833850 0.551991i \(-0.186132\pi\)
0.833850 + 0.551991i \(0.186132\pi\)
\(968\) −2.78738 −0.0895896
\(969\) −1.30176 −0.0418187
\(970\) −34.6618 −1.11292
\(971\) −4.51303 −0.144830 −0.0724150 0.997375i \(-0.523071\pi\)
−0.0724150 + 0.997375i \(0.523071\pi\)
\(972\) −46.2118 −1.48224
\(973\) 46.4932 1.49050
\(974\) 44.3883 1.42229
\(975\) 5.13127 0.164332
\(976\) 0.487567 0.0156066
\(977\) −52.9686 −1.69462 −0.847308 0.531102i \(-0.821778\pi\)
−0.847308 + 0.531102i \(0.821778\pi\)
\(978\) −1.22078 −0.0390363
\(979\) −13.9073 −0.444480
\(980\) −21.5639 −0.688834
\(981\) −28.0274 −0.894845
\(982\) −58.3585 −1.86229
\(983\) 28.3015 0.902677 0.451339 0.892353i \(-0.350947\pi\)
0.451339 + 0.892353i \(0.350947\pi\)
\(984\) 4.76536 0.151914
\(985\) −23.5728 −0.751091
\(986\) 16.7794 0.534365
\(987\) 0.713739 0.0227186
\(988\) −14.2815 −0.454354
\(989\) −3.40797 −0.108367
\(990\) −7.01999 −0.223110
\(991\) −18.8636 −0.599222 −0.299611 0.954061i \(-0.596857\pi\)
−0.299611 + 0.954061i \(0.596857\pi\)
\(992\) −16.1784 −0.513665
\(993\) 5.06194 0.160636
\(994\) −48.0248 −1.52325
\(995\) 22.7309 0.720617
\(996\) −18.2884 −0.579489
\(997\) −21.3459 −0.676030 −0.338015 0.941141i \(-0.609756\pi\)
−0.338015 + 0.941141i \(0.609756\pi\)
\(998\) −39.9776 −1.26547
\(999\) −24.9387 −0.789026
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 \(a_p\))