Properties

Label 8041.2.a.g.1.5
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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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: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56568 q^{2} -3.40788 q^{3} +4.58273 q^{4} +3.86072 q^{5} +8.74353 q^{6} +2.70727 q^{7} -6.62646 q^{8} +8.61362 q^{9} +O(q^{10})\) \(q-2.56568 q^{2} -3.40788 q^{3} +4.58273 q^{4} +3.86072 q^{5} +8.74353 q^{6} +2.70727 q^{7} -6.62646 q^{8} +8.61362 q^{9} -9.90537 q^{10} -1.00000 q^{11} -15.6174 q^{12} +2.11448 q^{13} -6.94599 q^{14} -13.1568 q^{15} +7.83593 q^{16} +1.00000 q^{17} -22.0998 q^{18} -1.30765 q^{19} +17.6926 q^{20} -9.22603 q^{21} +2.56568 q^{22} -2.98860 q^{23} +22.5821 q^{24} +9.90513 q^{25} -5.42507 q^{26} -19.1305 q^{27} +12.4067 q^{28} -10.3624 q^{29} +33.7563 q^{30} -6.85908 q^{31} -6.85160 q^{32} +3.40788 q^{33} -2.56568 q^{34} +10.4520 q^{35} +39.4739 q^{36} +10.9443 q^{37} +3.35500 q^{38} -7.20587 q^{39} -25.5829 q^{40} +2.34438 q^{41} +23.6711 q^{42} +1.00000 q^{43} -4.58273 q^{44} +33.2548 q^{45} +7.66779 q^{46} -3.62217 q^{47} -26.7039 q^{48} +0.329292 q^{49} -25.4134 q^{50} -3.40788 q^{51} +9.69007 q^{52} -5.18840 q^{53} +49.0829 q^{54} -3.86072 q^{55} -17.9396 q^{56} +4.45630 q^{57} +26.5865 q^{58} -3.01490 q^{59} -60.2942 q^{60} -0.942345 q^{61} +17.5982 q^{62} +23.3194 q^{63} +1.90716 q^{64} +8.16339 q^{65} -8.74353 q^{66} +8.07080 q^{67} +4.58273 q^{68} +10.1848 q^{69} -26.8165 q^{70} +1.22037 q^{71} -57.0778 q^{72} +0.756085 q^{73} -28.0795 q^{74} -33.7555 q^{75} -5.99258 q^{76} -2.70727 q^{77} +18.4880 q^{78} +7.66163 q^{79} +30.2523 q^{80} +39.3537 q^{81} -6.01494 q^{82} -0.00863659 q^{83} -42.2804 q^{84} +3.86072 q^{85} -2.56568 q^{86} +35.3137 q^{87} +6.62646 q^{88} -0.141453 q^{89} -85.3212 q^{90} +5.72445 q^{91} -13.6959 q^{92} +23.3749 q^{93} +9.29334 q^{94} -5.04845 q^{95} +23.3494 q^{96} -12.3113 q^{97} -0.844859 q^{98} -8.61362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56568 −1.81421 −0.907106 0.420903i \(-0.861713\pi\)
−0.907106 + 0.420903i \(0.861713\pi\)
\(3\) −3.40788 −1.96754 −0.983769 0.179438i \(-0.942572\pi\)
−0.983769 + 0.179438i \(0.942572\pi\)
\(4\) 4.58273 2.29136
\(5\) 3.86072 1.72656 0.863282 0.504721i \(-0.168405\pi\)
0.863282 + 0.504721i \(0.168405\pi\)
\(6\) 8.74353 3.56953
\(7\) 2.70727 1.02325 0.511625 0.859209i \(-0.329044\pi\)
0.511625 + 0.859209i \(0.329044\pi\)
\(8\) −6.62646 −2.34281
\(9\) 8.61362 2.87121
\(10\) −9.90537 −3.13235
\(11\) −1.00000 −0.301511
\(12\) −15.6174 −4.50835
\(13\) 2.11448 0.586450 0.293225 0.956043i \(-0.405271\pi\)
0.293225 + 0.956043i \(0.405271\pi\)
\(14\) −6.94599 −1.85639
\(15\) −13.1568 −3.39708
\(16\) 7.83593 1.95898
\(17\) 1.00000 0.242536
\(18\) −22.0998 −5.20898
\(19\) −1.30765 −0.299995 −0.149997 0.988686i \(-0.547926\pi\)
−0.149997 + 0.988686i \(0.547926\pi\)
\(20\) 17.6926 3.95619
\(21\) −9.22603 −2.01329
\(22\) 2.56568 0.547005
\(23\) −2.98860 −0.623165 −0.311583 0.950219i \(-0.600859\pi\)
−0.311583 + 0.950219i \(0.600859\pi\)
\(24\) 22.5821 4.60956
\(25\) 9.90513 1.98103
\(26\) −5.42507 −1.06394
\(27\) −19.1305 −3.68167
\(28\) 12.4067 2.34464
\(29\) −10.3624 −1.92424 −0.962121 0.272622i \(-0.912109\pi\)
−0.962121 + 0.272622i \(0.912109\pi\)
\(30\) 33.7563 6.16303
\(31\) −6.85908 −1.23193 −0.615963 0.787775i \(-0.711233\pi\)
−0.615963 + 0.787775i \(0.711233\pi\)
\(32\) −6.85160 −1.21120
\(33\) 3.40788 0.593235
\(34\) −2.56568 −0.440011
\(35\) 10.4520 1.76671
\(36\) 39.4739 6.57898
\(37\) 10.9443 1.79922 0.899612 0.436690i \(-0.143849\pi\)
0.899612 + 0.436690i \(0.143849\pi\)
\(38\) 3.35500 0.544254
\(39\) −7.20587 −1.15386
\(40\) −25.5829 −4.04501
\(41\) 2.34438 0.366131 0.183065 0.983101i \(-0.441398\pi\)
0.183065 + 0.983101i \(0.441398\pi\)
\(42\) 23.6711 3.65252
\(43\) 1.00000 0.152499
\(44\) −4.58273 −0.690872
\(45\) 33.2548 4.95733
\(46\) 7.66779 1.13055
\(47\) −3.62217 −0.528348 −0.264174 0.964475i \(-0.585099\pi\)
−0.264174 + 0.964475i \(0.585099\pi\)
\(48\) −26.7039 −3.85437
\(49\) 0.329292 0.0470417
\(50\) −25.4134 −3.59400
\(51\) −3.40788 −0.477198
\(52\) 9.69007 1.34377
\(53\) −5.18840 −0.712681 −0.356341 0.934356i \(-0.615976\pi\)
−0.356341 + 0.934356i \(0.615976\pi\)
\(54\) 49.0829 6.67934
\(55\) −3.86072 −0.520579
\(56\) −17.9396 −2.39728
\(57\) 4.45630 0.590251
\(58\) 26.5865 3.49098
\(59\) −3.01490 −0.392506 −0.196253 0.980553i \(-0.562877\pi\)
−0.196253 + 0.980553i \(0.562877\pi\)
\(60\) −60.2942 −7.78395
\(61\) −0.942345 −0.120655 −0.0603275 0.998179i \(-0.519214\pi\)
−0.0603275 + 0.998179i \(0.519214\pi\)
\(62\) 17.5982 2.23498
\(63\) 23.3194 2.93797
\(64\) 1.90716 0.238395
\(65\) 8.16339 1.01254
\(66\) −8.74353 −1.07625
\(67\) 8.07080 0.986005 0.493003 0.870028i \(-0.335899\pi\)
0.493003 + 0.870028i \(0.335899\pi\)
\(68\) 4.58273 0.555737
\(69\) 10.1848 1.22610
\(70\) −26.8165 −3.20518
\(71\) 1.22037 0.144832 0.0724158 0.997375i \(-0.476929\pi\)
0.0724158 + 0.997375i \(0.476929\pi\)
\(72\) −57.0778 −6.72668
\(73\) 0.756085 0.0884931 0.0442465 0.999021i \(-0.485911\pi\)
0.0442465 + 0.999021i \(0.485911\pi\)
\(74\) −28.0795 −3.26417
\(75\) −33.7555 −3.89775
\(76\) −5.99258 −0.687397
\(77\) −2.70727 −0.308522
\(78\) 18.4880 2.09335
\(79\) 7.66163 0.862001 0.431000 0.902352i \(-0.358161\pi\)
0.431000 + 0.902352i \(0.358161\pi\)
\(80\) 30.2523 3.38231
\(81\) 39.3537 4.37263
\(82\) −6.01494 −0.664239
\(83\) −0.00863659 −0.000947989 0 −0.000473995 1.00000i \(-0.500151\pi\)
−0.000473995 1.00000i \(0.500151\pi\)
\(84\) −42.2804 −4.61317
\(85\) 3.86072 0.418753
\(86\) −2.56568 −0.276665
\(87\) 35.3137 3.78602
\(88\) 6.62646 0.706383
\(89\) −0.141453 −0.0149940 −0.00749698 0.999972i \(-0.502386\pi\)
−0.00749698 + 0.999972i \(0.502386\pi\)
\(90\) −85.3212 −8.99364
\(91\) 5.72445 0.600086
\(92\) −13.6959 −1.42790
\(93\) 23.3749 2.42386
\(94\) 9.29334 0.958535
\(95\) −5.04845 −0.517960
\(96\) 23.3494 2.38309
\(97\) −12.3113 −1.25002 −0.625011 0.780616i \(-0.714905\pi\)
−0.625011 + 0.780616i \(0.714905\pi\)
\(98\) −0.844859 −0.0853436
\(99\) −8.61362 −0.865702
\(100\) 45.3925 4.53925
\(101\) −9.54345 −0.949609 −0.474804 0.880091i \(-0.657481\pi\)
−0.474804 + 0.880091i \(0.657481\pi\)
\(102\) 8.74353 0.865738
\(103\) −17.1049 −1.68539 −0.842696 0.538390i \(-0.819033\pi\)
−0.842696 + 0.538390i \(0.819033\pi\)
\(104\) −14.0115 −1.37394
\(105\) −35.6191 −3.47607
\(106\) 13.3118 1.29295
\(107\) −8.20583 −0.793287 −0.396644 0.917973i \(-0.629825\pi\)
−0.396644 + 0.917973i \(0.629825\pi\)
\(108\) −87.6700 −8.43605
\(109\) −13.7576 −1.31774 −0.658872 0.752255i \(-0.728966\pi\)
−0.658872 + 0.752255i \(0.728966\pi\)
\(110\) 9.90537 0.944440
\(111\) −37.2967 −3.54004
\(112\) 21.2140 2.00453
\(113\) −1.41681 −0.133282 −0.0666411 0.997777i \(-0.521228\pi\)
−0.0666411 + 0.997777i \(0.521228\pi\)
\(114\) −11.4334 −1.07084
\(115\) −11.5381 −1.07594
\(116\) −47.4879 −4.40914
\(117\) 18.2133 1.68382
\(118\) 7.73527 0.712089
\(119\) 2.70727 0.248175
\(120\) 87.1833 7.95871
\(121\) 1.00000 0.0909091
\(122\) 2.41776 0.218894
\(123\) −7.98936 −0.720376
\(124\) −31.4333 −2.82279
\(125\) 18.9373 1.69381
\(126\) −59.8301 −5.33009
\(127\) −18.2538 −1.61976 −0.809881 0.586594i \(-0.800469\pi\)
−0.809881 + 0.586594i \(0.800469\pi\)
\(128\) 8.81002 0.778703
\(129\) −3.40788 −0.300047
\(130\) −20.9447 −1.83697
\(131\) −16.5568 −1.44657 −0.723285 0.690549i \(-0.757369\pi\)
−0.723285 + 0.690549i \(0.757369\pi\)
\(132\) 15.6174 1.35932
\(133\) −3.54015 −0.306970
\(134\) −20.7071 −1.78882
\(135\) −73.8576 −6.35665
\(136\) −6.62646 −0.568214
\(137\) −2.11635 −0.180812 −0.0904058 0.995905i \(-0.528816\pi\)
−0.0904058 + 0.995905i \(0.528816\pi\)
\(138\) −26.1309 −2.22441
\(139\) 0.360905 0.0306115 0.0153058 0.999883i \(-0.495128\pi\)
0.0153058 + 0.999883i \(0.495128\pi\)
\(140\) 47.8986 4.04817
\(141\) 12.3439 1.03955
\(142\) −3.13109 −0.262755
\(143\) −2.11448 −0.176821
\(144\) 67.4958 5.62465
\(145\) −40.0061 −3.32233
\(146\) −1.93987 −0.160545
\(147\) −1.12219 −0.0925564
\(148\) 50.1545 4.12268
\(149\) −21.5462 −1.76514 −0.882568 0.470184i \(-0.844188\pi\)
−0.882568 + 0.470184i \(0.844188\pi\)
\(150\) 86.6058 7.07133
\(151\) −16.0295 −1.30446 −0.652231 0.758021i \(-0.726167\pi\)
−0.652231 + 0.758021i \(0.726167\pi\)
\(152\) 8.66506 0.702829
\(153\) 8.61362 0.696370
\(154\) 6.94599 0.559724
\(155\) −26.4810 −2.12700
\(156\) −33.0226 −2.64392
\(157\) 21.0322 1.67855 0.839275 0.543707i \(-0.182980\pi\)
0.839275 + 0.543707i \(0.182980\pi\)
\(158\) −19.6573 −1.56385
\(159\) 17.6814 1.40223
\(160\) −26.4521 −2.09122
\(161\) −8.09093 −0.637654
\(162\) −100.969 −7.93287
\(163\) −14.9750 −1.17293 −0.586464 0.809975i \(-0.699481\pi\)
−0.586464 + 0.809975i \(0.699481\pi\)
\(164\) 10.7437 0.838939
\(165\) 13.1568 1.02426
\(166\) 0.0221588 0.00171985
\(167\) 0.440321 0.0340731 0.0170365 0.999855i \(-0.494577\pi\)
0.0170365 + 0.999855i \(0.494577\pi\)
\(168\) 61.1359 4.71674
\(169\) −8.52899 −0.656076
\(170\) −9.90537 −0.759707
\(171\) −11.2636 −0.861347
\(172\) 4.58273 0.349430
\(173\) 10.8300 0.823386 0.411693 0.911322i \(-0.364938\pi\)
0.411693 + 0.911322i \(0.364938\pi\)
\(174\) −90.6036 −6.86864
\(175\) 26.8158 2.02709
\(176\) −7.83593 −0.590656
\(177\) 10.2744 0.772271
\(178\) 0.362923 0.0272022
\(179\) 16.0754 1.20153 0.600765 0.799426i \(-0.294863\pi\)
0.600765 + 0.799426i \(0.294863\pi\)
\(180\) 152.397 11.3590
\(181\) 18.6761 1.38818 0.694091 0.719887i \(-0.255807\pi\)
0.694091 + 0.719887i \(0.255807\pi\)
\(182\) −14.6871 −1.08868
\(183\) 3.21140 0.237393
\(184\) 19.8038 1.45996
\(185\) 42.2526 3.10648
\(186\) −59.9726 −4.39740
\(187\) −1.00000 −0.0731272
\(188\) −16.5994 −1.21064
\(189\) −51.7915 −3.76728
\(190\) 12.9527 0.939689
\(191\) 1.25058 0.0904885 0.0452443 0.998976i \(-0.485593\pi\)
0.0452443 + 0.998976i \(0.485593\pi\)
\(192\) −6.49937 −0.469052
\(193\) −6.39972 −0.460662 −0.230331 0.973112i \(-0.573981\pi\)
−0.230331 + 0.973112i \(0.573981\pi\)
\(194\) 31.5868 2.26780
\(195\) −27.8198 −1.99222
\(196\) 1.50906 0.107790
\(197\) 17.0074 1.21173 0.605863 0.795569i \(-0.292828\pi\)
0.605863 + 0.795569i \(0.292828\pi\)
\(198\) 22.0998 1.57057
\(199\) −6.05693 −0.429364 −0.214682 0.976684i \(-0.568872\pi\)
−0.214682 + 0.976684i \(0.568872\pi\)
\(200\) −65.6359 −4.64116
\(201\) −27.5043 −1.94000
\(202\) 24.4855 1.72279
\(203\) −28.0537 −1.96898
\(204\) −15.6174 −1.09343
\(205\) 9.05099 0.632148
\(206\) 43.8856 3.05766
\(207\) −25.7427 −1.78924
\(208\) 16.5689 1.14885
\(209\) 1.30765 0.0904518
\(210\) 91.3873 6.30632
\(211\) −1.15209 −0.0793133 −0.0396566 0.999213i \(-0.512626\pi\)
−0.0396566 + 0.999213i \(0.512626\pi\)
\(212\) −23.7770 −1.63301
\(213\) −4.15888 −0.284962
\(214\) 21.0535 1.43919
\(215\) 3.86072 0.263299
\(216\) 126.768 8.62545
\(217\) −18.5694 −1.26057
\(218\) 35.2977 2.39066
\(219\) −2.57664 −0.174113
\(220\) −17.6926 −1.19284
\(221\) 2.11448 0.142235
\(222\) 95.6914 6.42239
\(223\) 25.4941 1.70721 0.853606 0.520919i \(-0.174411\pi\)
0.853606 + 0.520919i \(0.174411\pi\)
\(224\) −18.5491 −1.23936
\(225\) 85.3191 5.68794
\(226\) 3.63508 0.241802
\(227\) 19.0502 1.26441 0.632203 0.774803i \(-0.282151\pi\)
0.632203 + 0.774803i \(0.282151\pi\)
\(228\) 20.4220 1.35248
\(229\) −10.5112 −0.694598 −0.347299 0.937754i \(-0.612901\pi\)
−0.347299 + 0.937754i \(0.612901\pi\)
\(230\) 29.6032 1.95197
\(231\) 9.22603 0.607028
\(232\) 68.6658 4.50813
\(233\) −17.6216 −1.15443 −0.577215 0.816592i \(-0.695860\pi\)
−0.577215 + 0.816592i \(0.695860\pi\)
\(234\) −46.7296 −3.05481
\(235\) −13.9842 −0.912227
\(236\) −13.8164 −0.899374
\(237\) −26.1099 −1.69602
\(238\) −6.94599 −0.450241
\(239\) −6.19205 −0.400530 −0.200265 0.979742i \(-0.564180\pi\)
−0.200265 + 0.979742i \(0.564180\pi\)
\(240\) −103.096 −6.65483
\(241\) 9.01722 0.580850 0.290425 0.956898i \(-0.406203\pi\)
0.290425 + 0.956898i \(0.406203\pi\)
\(242\) −2.56568 −0.164928
\(243\) −76.7208 −4.92164
\(244\) −4.31851 −0.276464
\(245\) 1.27130 0.0812206
\(246\) 20.4982 1.30692
\(247\) −2.76499 −0.175932
\(248\) 45.4514 2.88617
\(249\) 0.0294325 0.00186521
\(250\) −48.5871 −3.07292
\(251\) 5.54169 0.349789 0.174894 0.984587i \(-0.444042\pi\)
0.174894 + 0.984587i \(0.444042\pi\)
\(252\) 106.866 6.73195
\(253\) 2.98860 0.187891
\(254\) 46.8335 2.93859
\(255\) −13.1568 −0.823914
\(256\) −26.4180 −1.65113
\(257\) −28.4209 −1.77285 −0.886424 0.462874i \(-0.846818\pi\)
−0.886424 + 0.462874i \(0.846818\pi\)
\(258\) 8.74353 0.544348
\(259\) 29.6290 1.84106
\(260\) 37.4106 2.32011
\(261\) −89.2575 −5.52490
\(262\) 42.4794 2.62438
\(263\) 9.97055 0.614811 0.307405 0.951579i \(-0.400539\pi\)
0.307405 + 0.951579i \(0.400539\pi\)
\(264\) −22.5821 −1.38984
\(265\) −20.0309 −1.23049
\(266\) 9.08289 0.556908
\(267\) 0.482053 0.0295012
\(268\) 36.9863 2.25930
\(269\) −32.1793 −1.96201 −0.981004 0.193989i \(-0.937857\pi\)
−0.981004 + 0.193989i \(0.937857\pi\)
\(270\) 189.495 11.5323
\(271\) −10.8929 −0.661697 −0.330849 0.943684i \(-0.607335\pi\)
−0.330849 + 0.943684i \(0.607335\pi\)
\(272\) 7.83593 0.475123
\(273\) −19.5082 −1.18069
\(274\) 5.42987 0.328030
\(275\) −9.90513 −0.597302
\(276\) 46.6740 2.80945
\(277\) 3.98110 0.239201 0.119600 0.992822i \(-0.461839\pi\)
0.119600 + 0.992822i \(0.461839\pi\)
\(278\) −0.925967 −0.0555358
\(279\) −59.0815 −3.53712
\(280\) −69.2596 −4.13906
\(281\) −19.8292 −1.18291 −0.591456 0.806337i \(-0.701447\pi\)
−0.591456 + 0.806337i \(0.701447\pi\)
\(282\) −31.6706 −1.88596
\(283\) 17.4932 1.03986 0.519931 0.854208i \(-0.325958\pi\)
0.519931 + 0.854208i \(0.325958\pi\)
\(284\) 5.59264 0.331862
\(285\) 17.2045 1.01911
\(286\) 5.42507 0.320791
\(287\) 6.34686 0.374643
\(288\) −59.0171 −3.47762
\(289\) 1.00000 0.0588235
\(290\) 102.643 6.02741
\(291\) 41.9553 2.45947
\(292\) 3.46493 0.202770
\(293\) −16.1550 −0.943783 −0.471891 0.881657i \(-0.656429\pi\)
−0.471891 + 0.881657i \(0.656429\pi\)
\(294\) 2.87918 0.167917
\(295\) −11.6397 −0.677687
\(296\) −72.5216 −4.21523
\(297\) 19.1305 1.11007
\(298\) 55.2808 3.20233
\(299\) −6.31932 −0.365456
\(300\) −154.692 −8.93115
\(301\) 2.70727 0.156044
\(302\) 41.1266 2.36657
\(303\) 32.5229 1.86839
\(304\) −10.2466 −0.587684
\(305\) −3.63813 −0.208319
\(306\) −22.0998 −1.26336
\(307\) −27.0549 −1.54411 −0.772053 0.635558i \(-0.780770\pi\)
−0.772053 + 0.635558i \(0.780770\pi\)
\(308\) −12.4067 −0.706935
\(309\) 58.2913 3.31607
\(310\) 67.9417 3.85883
\(311\) 1.31805 0.0747399 0.0373700 0.999301i \(-0.488102\pi\)
0.0373700 + 0.999301i \(0.488102\pi\)
\(312\) 47.7494 2.70328
\(313\) 24.6020 1.39059 0.695293 0.718727i \(-0.255275\pi\)
0.695293 + 0.718727i \(0.255275\pi\)
\(314\) −53.9619 −3.04525
\(315\) 90.0295 5.07259
\(316\) 35.1112 1.97516
\(317\) 18.4036 1.03365 0.516824 0.856092i \(-0.327114\pi\)
0.516824 + 0.856092i \(0.327114\pi\)
\(318\) −45.3649 −2.54394
\(319\) 10.3624 0.580181
\(320\) 7.36301 0.411605
\(321\) 27.9644 1.56082
\(322\) 20.7588 1.15684
\(323\) −1.30765 −0.0727594
\(324\) 180.347 10.0193
\(325\) 20.9442 1.16177
\(326\) 38.4210 2.12794
\(327\) 46.8844 2.59271
\(328\) −15.5349 −0.857773
\(329\) −9.80619 −0.540632
\(330\) −33.7563 −1.85822
\(331\) −0.955814 −0.0525363 −0.0262681 0.999655i \(-0.508362\pi\)
−0.0262681 + 0.999655i \(0.508362\pi\)
\(332\) −0.0395792 −0.00217219
\(333\) 94.2697 5.16595
\(334\) −1.12972 −0.0618158
\(335\) 31.1591 1.70240
\(336\) −72.2945 −3.94399
\(337\) −9.94283 −0.541621 −0.270810 0.962633i \(-0.587292\pi\)
−0.270810 + 0.962633i \(0.587292\pi\)
\(338\) 21.8827 1.19026
\(339\) 4.82831 0.262238
\(340\) 17.6926 0.959516
\(341\) 6.85908 0.371440
\(342\) 28.8987 1.56267
\(343\) −18.0594 −0.975115
\(344\) −6.62646 −0.357275
\(345\) 39.3205 2.11694
\(346\) −27.7862 −1.49380
\(347\) −2.24529 −0.120534 −0.0602668 0.998182i \(-0.519195\pi\)
−0.0602668 + 0.998182i \(0.519195\pi\)
\(348\) 161.833 8.67515
\(349\) −2.51558 −0.134656 −0.0673279 0.997731i \(-0.521447\pi\)
−0.0673279 + 0.997731i \(0.521447\pi\)
\(350\) −68.8009 −3.67756
\(351\) −40.4511 −2.15912
\(352\) 6.85160 0.365191
\(353\) 19.7090 1.04900 0.524501 0.851410i \(-0.324252\pi\)
0.524501 + 0.851410i \(0.324252\pi\)
\(354\) −26.3608 −1.40106
\(355\) 4.71151 0.250061
\(356\) −0.648239 −0.0343566
\(357\) −9.22603 −0.488293
\(358\) −41.2443 −2.17983
\(359\) −35.9132 −1.89543 −0.947714 0.319120i \(-0.896613\pi\)
−0.947714 + 0.319120i \(0.896613\pi\)
\(360\) −220.361 −11.6141
\(361\) −17.2901 −0.910003
\(362\) −47.9169 −2.51846
\(363\) −3.40788 −0.178867
\(364\) 26.2336 1.37501
\(365\) 2.91903 0.152789
\(366\) −8.23942 −0.430682
\(367\) 6.06250 0.316460 0.158230 0.987402i \(-0.449421\pi\)
0.158230 + 0.987402i \(0.449421\pi\)
\(368\) −23.4184 −1.22077
\(369\) 20.1936 1.05124
\(370\) −108.407 −5.63581
\(371\) −14.0464 −0.729252
\(372\) 107.121 5.55395
\(373\) 13.4398 0.695889 0.347944 0.937515i \(-0.386880\pi\)
0.347944 + 0.937515i \(0.386880\pi\)
\(374\) 2.56568 0.132668
\(375\) −64.5360 −3.33263
\(376\) 24.0022 1.23782
\(377\) −21.9110 −1.12847
\(378\) 132.880 6.83463
\(379\) 10.1209 0.519875 0.259937 0.965626i \(-0.416298\pi\)
0.259937 + 0.965626i \(0.416298\pi\)
\(380\) −23.1357 −1.18683
\(381\) 62.2067 3.18695
\(382\) −3.20858 −0.164165
\(383\) −4.32059 −0.220772 −0.110386 0.993889i \(-0.535209\pi\)
−0.110386 + 0.993889i \(0.535209\pi\)
\(384\) −30.0235 −1.53213
\(385\) −10.4520 −0.532683
\(386\) 16.4197 0.835739
\(387\) 8.61362 0.437855
\(388\) −56.4192 −2.86425
\(389\) −7.04567 −0.357229 −0.178615 0.983919i \(-0.557162\pi\)
−0.178615 + 0.983919i \(0.557162\pi\)
\(390\) 71.3769 3.61431
\(391\) −2.98860 −0.151140
\(392\) −2.18204 −0.110210
\(393\) 56.4234 2.84618
\(394\) −43.6355 −2.19833
\(395\) 29.5794 1.48830
\(396\) −39.4739 −1.98364
\(397\) 14.7016 0.737850 0.368925 0.929459i \(-0.379726\pi\)
0.368925 + 0.929459i \(0.379726\pi\)
\(398\) 15.5402 0.778958
\(399\) 12.0644 0.603975
\(400\) 77.6159 3.88080
\(401\) 0.564011 0.0281653 0.0140827 0.999901i \(-0.495517\pi\)
0.0140827 + 0.999901i \(0.495517\pi\)
\(402\) 70.5673 3.51958
\(403\) −14.5034 −0.722464
\(404\) −43.7350 −2.17590
\(405\) 151.933 7.54963
\(406\) 71.9768 3.57215
\(407\) −10.9443 −0.542486
\(408\) 22.5821 1.11798
\(409\) −24.8056 −1.22656 −0.613279 0.789866i \(-0.710150\pi\)
−0.613279 + 0.789866i \(0.710150\pi\)
\(410\) −23.2220 −1.14685
\(411\) 7.21224 0.355754
\(412\) −78.3869 −3.86185
\(413\) −8.16213 −0.401632
\(414\) 66.0475 3.24606
\(415\) −0.0333434 −0.00163677
\(416\) −14.4875 −0.710310
\(417\) −1.22992 −0.0602294
\(418\) −3.35500 −0.164099
\(419\) −29.2810 −1.43047 −0.715234 0.698885i \(-0.753680\pi\)
−0.715234 + 0.698885i \(0.753680\pi\)
\(420\) −163.233 −7.96493
\(421\) 16.2275 0.790882 0.395441 0.918491i \(-0.370592\pi\)
0.395441 + 0.918491i \(0.370592\pi\)
\(422\) 2.95590 0.143891
\(423\) −31.2000 −1.51700
\(424\) 34.3807 1.66967
\(425\) 9.90513 0.480469
\(426\) 10.6704 0.516981
\(427\) −2.55118 −0.123460
\(428\) −37.6051 −1.81771
\(429\) 7.20587 0.347903
\(430\) −9.90537 −0.477679
\(431\) 7.83107 0.377209 0.188605 0.982053i \(-0.439604\pi\)
0.188605 + 0.982053i \(0.439604\pi\)
\(432\) −149.906 −7.21234
\(433\) −28.5758 −1.37327 −0.686633 0.727004i \(-0.740912\pi\)
−0.686633 + 0.727004i \(0.740912\pi\)
\(434\) 47.6431 2.28694
\(435\) 136.336 6.53681
\(436\) −63.0475 −3.01943
\(437\) 3.90803 0.186946
\(438\) 6.61085 0.315879
\(439\) −20.2106 −0.964599 −0.482300 0.876006i \(-0.660198\pi\)
−0.482300 + 0.876006i \(0.660198\pi\)
\(440\) 25.5829 1.21962
\(441\) 2.83640 0.135067
\(442\) −5.42507 −0.258044
\(443\) −34.1256 −1.62136 −0.810678 0.585492i \(-0.800901\pi\)
−0.810678 + 0.585492i \(0.800901\pi\)
\(444\) −170.920 −8.11152
\(445\) −0.546109 −0.0258880
\(446\) −65.4098 −3.09724
\(447\) 73.4269 3.47298
\(448\) 5.16319 0.243938
\(449\) −35.3516 −1.66834 −0.834172 0.551505i \(-0.814054\pi\)
−0.834172 + 0.551505i \(0.814054\pi\)
\(450\) −218.902 −10.3191
\(451\) −2.34438 −0.110393
\(452\) −6.49285 −0.305398
\(453\) 54.6265 2.56658
\(454\) −48.8767 −2.29390
\(455\) 22.1005 1.03609
\(456\) −29.5295 −1.38284
\(457\) 27.6520 1.29350 0.646752 0.762700i \(-0.276127\pi\)
0.646752 + 0.762700i \(0.276127\pi\)
\(458\) 26.9683 1.26015
\(459\) −19.1305 −0.892937
\(460\) −52.8761 −2.46536
\(461\) 21.7082 1.01105 0.505527 0.862811i \(-0.331298\pi\)
0.505527 + 0.862811i \(0.331298\pi\)
\(462\) −23.6711 −1.10128
\(463\) 16.8349 0.782383 0.391192 0.920309i \(-0.372063\pi\)
0.391192 + 0.920309i \(0.372063\pi\)
\(464\) −81.1988 −3.76956
\(465\) 90.2438 4.18496
\(466\) 45.2114 2.09438
\(467\) −19.3987 −0.897666 −0.448833 0.893616i \(-0.648160\pi\)
−0.448833 + 0.893616i \(0.648160\pi\)
\(468\) 83.4666 3.85825
\(469\) 21.8498 1.00893
\(470\) 35.8790 1.65497
\(471\) −71.6751 −3.30261
\(472\) 19.9781 0.919566
\(473\) −1.00000 −0.0459800
\(474\) 66.9897 3.07694
\(475\) −12.9524 −0.594297
\(476\) 12.4067 0.568658
\(477\) −44.6909 −2.04626
\(478\) 15.8868 0.726646
\(479\) −31.8295 −1.45433 −0.727163 0.686465i \(-0.759161\pi\)
−0.727163 + 0.686465i \(0.759161\pi\)
\(480\) 90.1454 4.11456
\(481\) 23.1414 1.05516
\(482\) −23.1353 −1.05378
\(483\) 27.5729 1.25461
\(484\) 4.58273 0.208306
\(485\) −47.5304 −2.15824
\(486\) 196.841 8.92890
\(487\) 12.8515 0.582355 0.291177 0.956669i \(-0.405953\pi\)
0.291177 + 0.956669i \(0.405953\pi\)
\(488\) 6.24441 0.282671
\(489\) 51.0328 2.30778
\(490\) −3.26176 −0.147351
\(491\) −22.7255 −1.02559 −0.512794 0.858512i \(-0.671390\pi\)
−0.512794 + 0.858512i \(0.671390\pi\)
\(492\) −36.6131 −1.65064
\(493\) −10.3624 −0.466697
\(494\) 7.09408 0.319178
\(495\) −33.2548 −1.49469
\(496\) −53.7473 −2.41332
\(497\) 3.30388 0.148199
\(498\) −0.0755143 −0.00338388
\(499\) 39.9822 1.78985 0.894924 0.446219i \(-0.147230\pi\)
0.894924 + 0.446219i \(0.147230\pi\)
\(500\) 86.7846 3.88112
\(501\) −1.50056 −0.0670401
\(502\) −14.2182 −0.634590
\(503\) 37.8385 1.68713 0.843567 0.537024i \(-0.180452\pi\)
0.843567 + 0.537024i \(0.180452\pi\)
\(504\) −154.525 −6.88308
\(505\) −36.8446 −1.63956
\(506\) −7.66779 −0.340875
\(507\) 29.0657 1.29086
\(508\) −83.6522 −3.71147
\(509\) 36.9633 1.63837 0.819185 0.573529i \(-0.194426\pi\)
0.819185 + 0.573529i \(0.194426\pi\)
\(510\) 33.7563 1.49475
\(511\) 2.04692 0.0905506
\(512\) 50.1603 2.21679
\(513\) 25.0160 1.10448
\(514\) 72.9190 3.21632
\(515\) −66.0370 −2.90994
\(516\) −15.6174 −0.687516
\(517\) 3.62217 0.159303
\(518\) −76.0186 −3.34007
\(519\) −36.9072 −1.62004
\(520\) −54.0944 −2.37220
\(521\) −0.366090 −0.0160387 −0.00801935 0.999968i \(-0.502553\pi\)
−0.00801935 + 0.999968i \(0.502553\pi\)
\(522\) 229.006 10.0233
\(523\) −28.1275 −1.22993 −0.614965 0.788554i \(-0.710830\pi\)
−0.614965 + 0.788554i \(0.710830\pi\)
\(524\) −75.8751 −3.31462
\(525\) −91.3850 −3.98837
\(526\) −25.5813 −1.11540
\(527\) −6.85908 −0.298786
\(528\) 26.7039 1.16214
\(529\) −14.0683 −0.611665
\(530\) 51.3930 2.23237
\(531\) −25.9692 −1.12697
\(532\) −16.2235 −0.703379
\(533\) 4.95714 0.214717
\(534\) −1.23680 −0.0535214
\(535\) −31.6804 −1.36966
\(536\) −53.4808 −2.31002
\(537\) −54.7829 −2.36406
\(538\) 82.5619 3.55950
\(539\) −0.329292 −0.0141836
\(540\) −338.469 −14.5654
\(541\) 34.4124 1.47951 0.739753 0.672879i \(-0.234943\pi\)
0.739753 + 0.672879i \(0.234943\pi\)
\(542\) 27.9477 1.20046
\(543\) −63.6458 −2.73130
\(544\) −6.85160 −0.293760
\(545\) −53.1144 −2.27517
\(546\) 50.0519 2.14202
\(547\) −1.29007 −0.0551594 −0.0275797 0.999620i \(-0.508780\pi\)
−0.0275797 + 0.999620i \(0.508780\pi\)
\(548\) −9.69863 −0.414305
\(549\) −8.11701 −0.346425
\(550\) 25.4134 1.08363
\(551\) 13.5503 0.577262
\(552\) −67.4889 −2.87252
\(553\) 20.7421 0.882043
\(554\) −10.2142 −0.433961
\(555\) −143.992 −6.11211
\(556\) 1.65393 0.0701422
\(557\) −45.4436 −1.92551 −0.962754 0.270378i \(-0.912851\pi\)
−0.962754 + 0.270378i \(0.912851\pi\)
\(558\) 151.584 6.41708
\(559\) 2.11448 0.0894328
\(560\) 81.9011 3.46095
\(561\) 3.40788 0.143881
\(562\) 50.8755 2.14605
\(563\) 8.41519 0.354658 0.177329 0.984152i \(-0.443254\pi\)
0.177329 + 0.984152i \(0.443254\pi\)
\(564\) 56.5688 2.38198
\(565\) −5.46990 −0.230120
\(566\) −44.8820 −1.88653
\(567\) 106.541 4.47429
\(568\) −8.08675 −0.339313
\(569\) −46.3552 −1.94331 −0.971656 0.236399i \(-0.924033\pi\)
−0.971656 + 0.236399i \(0.924033\pi\)
\(570\) −44.1413 −1.84887
\(571\) 7.28218 0.304750 0.152375 0.988323i \(-0.451308\pi\)
0.152375 + 0.988323i \(0.451308\pi\)
\(572\) −9.69007 −0.405162
\(573\) −4.26181 −0.178040
\(574\) −16.2840 −0.679683
\(575\) −29.6024 −1.23451
\(576\) 16.4276 0.684482
\(577\) 11.9159 0.496064 0.248032 0.968752i \(-0.420216\pi\)
0.248032 + 0.968752i \(0.420216\pi\)
\(578\) −2.56568 −0.106718
\(579\) 21.8095 0.906371
\(580\) −183.337 −7.61266
\(581\) −0.0233816 −0.000970031 0
\(582\) −107.644 −4.46199
\(583\) 5.18840 0.214882
\(584\) −5.01016 −0.207322
\(585\) 70.3164 2.90723
\(586\) 41.4485 1.71222
\(587\) 10.1705 0.419781 0.209890 0.977725i \(-0.432689\pi\)
0.209890 + 0.977725i \(0.432689\pi\)
\(588\) −5.14268 −0.212080
\(589\) 8.96925 0.369571
\(590\) 29.8637 1.22947
\(591\) −57.9591 −2.38412
\(592\) 85.7584 3.52465
\(593\) 30.9156 1.26955 0.634775 0.772697i \(-0.281093\pi\)
0.634775 + 0.772697i \(0.281093\pi\)
\(594\) −49.0829 −2.01390
\(595\) 10.4520 0.428490
\(596\) −98.7405 −4.04457
\(597\) 20.6413 0.844791
\(598\) 16.2134 0.663014
\(599\) −0.676568 −0.0276438 −0.0138219 0.999904i \(-0.504400\pi\)
−0.0138219 + 0.999904i \(0.504400\pi\)
\(600\) 223.679 9.13166
\(601\) −29.3939 −1.19900 −0.599502 0.800374i \(-0.704634\pi\)
−0.599502 + 0.800374i \(0.704634\pi\)
\(602\) −6.94599 −0.283097
\(603\) 69.5188 2.83103
\(604\) −73.4588 −2.98900
\(605\) 3.86072 0.156960
\(606\) −83.4434 −3.38966
\(607\) 29.0313 1.17834 0.589172 0.808008i \(-0.299454\pi\)
0.589172 + 0.808008i \(0.299454\pi\)
\(608\) 8.95946 0.363354
\(609\) 95.6035 3.87405
\(610\) 9.33428 0.377934
\(611\) −7.65900 −0.309850
\(612\) 39.4739 1.59564
\(613\) −3.04225 −0.122875 −0.0614376 0.998111i \(-0.519569\pi\)
−0.0614376 + 0.998111i \(0.519569\pi\)
\(614\) 69.4143 2.80134
\(615\) −30.8447 −1.24378
\(616\) 17.9396 0.722806
\(617\) 40.9708 1.64942 0.824712 0.565553i \(-0.191337\pi\)
0.824712 + 0.565553i \(0.191337\pi\)
\(618\) −149.557 −6.01606
\(619\) 40.1960 1.61561 0.807807 0.589447i \(-0.200654\pi\)
0.807807 + 0.589447i \(0.200654\pi\)
\(620\) −121.355 −4.87373
\(621\) 57.1735 2.29429
\(622\) −3.38170 −0.135594
\(623\) −0.382950 −0.0153426
\(624\) −56.4647 −2.26040
\(625\) 23.5860 0.943438
\(626\) −63.1208 −2.52282
\(627\) −4.45630 −0.177967
\(628\) 96.3847 3.84617
\(629\) 10.9443 0.436376
\(630\) −230.987 −9.20275
\(631\) 41.3771 1.64720 0.823598 0.567173i \(-0.191963\pi\)
0.823598 + 0.567173i \(0.191963\pi\)
\(632\) −50.7695 −2.01950
\(633\) 3.92619 0.156052
\(634\) −47.2177 −1.87526
\(635\) −70.4727 −2.79663
\(636\) 81.0291 3.21301
\(637\) 0.696280 0.0275876
\(638\) −26.5865 −1.05257
\(639\) 10.5118 0.415842
\(640\) 34.0130 1.34448
\(641\) 21.9811 0.868203 0.434101 0.900864i \(-0.357066\pi\)
0.434101 + 0.900864i \(0.357066\pi\)
\(642\) −71.7479 −2.83166
\(643\) −1.54304 −0.0608517 −0.0304258 0.999537i \(-0.509686\pi\)
−0.0304258 + 0.999537i \(0.509686\pi\)
\(644\) −37.0785 −1.46110
\(645\) −13.1568 −0.518050
\(646\) 3.35500 0.132001
\(647\) 26.3907 1.03753 0.518763 0.854918i \(-0.326393\pi\)
0.518763 + 0.854918i \(0.326393\pi\)
\(648\) −260.775 −10.2442
\(649\) 3.01490 0.118345
\(650\) −53.7361 −2.10770
\(651\) 63.2821 2.48022
\(652\) −68.6261 −2.68761
\(653\) 2.11721 0.0828529 0.0414265 0.999142i \(-0.486810\pi\)
0.0414265 + 0.999142i \(0.486810\pi\)
\(654\) −120.290 −4.70373
\(655\) −63.9209 −2.49760
\(656\) 18.3704 0.717244
\(657\) 6.51263 0.254082
\(658\) 25.1596 0.980822
\(659\) 37.8061 1.47272 0.736359 0.676591i \(-0.236544\pi\)
0.736359 + 0.676591i \(0.236544\pi\)
\(660\) 60.2942 2.34695
\(661\) −35.6988 −1.38852 −0.694261 0.719723i \(-0.744269\pi\)
−0.694261 + 0.719723i \(0.744269\pi\)
\(662\) 2.45231 0.0953119
\(663\) −7.20587 −0.279853
\(664\) 0.0572300 0.00222096
\(665\) −13.6675 −0.530003
\(666\) −241.866 −9.37212
\(667\) 30.9689 1.19912
\(668\) 2.01787 0.0780738
\(669\) −86.8808 −3.35901
\(670\) −79.9443 −3.08852
\(671\) 0.942345 0.0363788
\(672\) 63.2130 2.43850
\(673\) 4.92558 0.189867 0.0949336 0.995484i \(-0.469736\pi\)
0.0949336 + 0.995484i \(0.469736\pi\)
\(674\) 25.5101 0.982614
\(675\) −189.491 −7.29349
\(676\) −39.0860 −1.50331
\(677\) −5.70818 −0.219383 −0.109692 0.993966i \(-0.534986\pi\)
−0.109692 + 0.993966i \(0.534986\pi\)
\(678\) −12.3879 −0.475755
\(679\) −33.3299 −1.27909
\(680\) −25.5829 −0.981058
\(681\) −64.9207 −2.48777
\(682\) −17.5982 −0.673871
\(683\) −0.00484862 −0.000185527 0 −9.27636e−5 1.00000i \(-0.500030\pi\)
−9.27636e−5 1.00000i \(0.500030\pi\)
\(684\) −51.6179 −1.97366
\(685\) −8.17061 −0.312183
\(686\) 46.3346 1.76907
\(687\) 35.8208 1.36665
\(688\) 7.83593 0.298742
\(689\) −10.9707 −0.417952
\(690\) −100.884 −3.84059
\(691\) 27.5741 1.04897 0.524485 0.851420i \(-0.324258\pi\)
0.524485 + 0.851420i \(0.324258\pi\)
\(692\) 49.6307 1.88668
\(693\) −23.3194 −0.885830
\(694\) 5.76071 0.218674
\(695\) 1.39335 0.0528528
\(696\) −234.004 −8.86991
\(697\) 2.34438 0.0887997
\(698\) 6.45418 0.244294
\(699\) 60.0522 2.27138
\(700\) 122.890 4.64479
\(701\) −17.1734 −0.648630 −0.324315 0.945949i \(-0.605134\pi\)
−0.324315 + 0.945949i \(0.605134\pi\)
\(702\) 103.785 3.91710
\(703\) −14.3112 −0.539757
\(704\) −1.90716 −0.0718789
\(705\) 47.6564 1.79484
\(706\) −50.5670 −1.90311
\(707\) −25.8367 −0.971688
\(708\) 47.0847 1.76955
\(709\) −44.5725 −1.67396 −0.836978 0.547237i \(-0.815680\pi\)
−0.836978 + 0.547237i \(0.815680\pi\)
\(710\) −12.0883 −0.453664
\(711\) 65.9944 2.47498
\(712\) 0.937330 0.0351279
\(713\) 20.4990 0.767694
\(714\) 23.6711 0.885867
\(715\) −8.16339 −0.305294
\(716\) 73.6691 2.75314
\(717\) 21.1017 0.788059
\(718\) 92.1420 3.43871
\(719\) 16.7672 0.625310 0.312655 0.949867i \(-0.398782\pi\)
0.312655 + 0.949867i \(0.398782\pi\)
\(720\) 260.582 9.71132
\(721\) −46.3074 −1.72458
\(722\) 44.3608 1.65094
\(723\) −30.7296 −1.14284
\(724\) 85.5874 3.18083
\(725\) −102.641 −3.81197
\(726\) 8.74353 0.324503
\(727\) −22.9888 −0.852609 −0.426304 0.904580i \(-0.640185\pi\)
−0.426304 + 0.904580i \(0.640185\pi\)
\(728\) −37.9328 −1.40588
\(729\) 143.394 5.31089
\(730\) −7.48930 −0.277192
\(731\) 1.00000 0.0369863
\(732\) 14.7170 0.543954
\(733\) −5.52678 −0.204136 −0.102068 0.994777i \(-0.532546\pi\)
−0.102068 + 0.994777i \(0.532546\pi\)
\(734\) −15.5545 −0.574126
\(735\) −4.33245 −0.159805
\(736\) 20.4767 0.754780
\(737\) −8.07080 −0.297292
\(738\) −51.8104 −1.90717
\(739\) 8.55475 0.314692 0.157346 0.987544i \(-0.449706\pi\)
0.157346 + 0.987544i \(0.449706\pi\)
\(740\) 193.632 7.11807
\(741\) 9.42273 0.346153
\(742\) 36.0385 1.32302
\(743\) −14.7440 −0.540904 −0.270452 0.962734i \(-0.587173\pi\)
−0.270452 + 0.962734i \(0.587173\pi\)
\(744\) −154.893 −5.67864
\(745\) −83.1839 −3.04762
\(746\) −34.4824 −1.26249
\(747\) −0.0743924 −0.00272187
\(748\) −4.58273 −0.167561
\(749\) −22.2154 −0.811732
\(750\) 165.579 6.04609
\(751\) −10.7666 −0.392879 −0.196440 0.980516i \(-0.562938\pi\)
−0.196440 + 0.980516i \(0.562938\pi\)
\(752\) −28.3831 −1.03502
\(753\) −18.8854 −0.688222
\(754\) 56.2166 2.04729
\(755\) −61.8853 −2.25224
\(756\) −237.346 −8.63220
\(757\) −19.4914 −0.708426 −0.354213 0.935165i \(-0.615251\pi\)
−0.354213 + 0.935165i \(0.615251\pi\)
\(758\) −25.9670 −0.943162
\(759\) −10.1848 −0.369684
\(760\) 33.4533 1.21348
\(761\) −31.5916 −1.14519 −0.572597 0.819837i \(-0.694064\pi\)
−0.572597 + 0.819837i \(0.694064\pi\)
\(762\) −159.603 −5.78179
\(763\) −37.2456 −1.34838
\(764\) 5.73105 0.207342
\(765\) 33.2548 1.20233
\(766\) 11.0853 0.400527
\(767\) −6.37493 −0.230185
\(768\) 90.0295 3.24866
\(769\) 31.8259 1.14767 0.573835 0.818971i \(-0.305455\pi\)
0.573835 + 0.818971i \(0.305455\pi\)
\(770\) 26.8165 0.966399
\(771\) 96.8550 3.48815
\(772\) −29.3282 −1.05554
\(773\) 53.1704 1.91241 0.956203 0.292705i \(-0.0945554\pi\)
0.956203 + 0.292705i \(0.0945554\pi\)
\(774\) −22.0998 −0.794362
\(775\) −67.9401 −2.44048
\(776\) 81.5802 2.92856
\(777\) −100.972 −3.62235
\(778\) 18.0769 0.648090
\(779\) −3.06562 −0.109837
\(780\) −127.491 −4.56490
\(781\) −1.22037 −0.0436684
\(782\) 7.66779 0.274200
\(783\) 198.238 7.08443
\(784\) 2.58031 0.0921539
\(785\) 81.1993 2.89813
\(786\) −144.764 −5.16358
\(787\) −3.52470 −0.125642 −0.0628210 0.998025i \(-0.520010\pi\)
−0.0628210 + 0.998025i \(0.520010\pi\)
\(788\) 77.9402 2.77650
\(789\) −33.9784 −1.20966
\(790\) −75.8913 −2.70009
\(791\) −3.83568 −0.136381
\(792\) 57.0778 2.02817
\(793\) −1.99257 −0.0707581
\(794\) −37.7195 −1.33862
\(795\) 68.2630 2.42104
\(796\) −27.7573 −0.983830
\(797\) −0.945700 −0.0334984 −0.0167492 0.999860i \(-0.505332\pi\)
−0.0167492 + 0.999860i \(0.505332\pi\)
\(798\) −30.9534 −1.09574
\(799\) −3.62217 −0.128143
\(800\) −67.8660 −2.39942
\(801\) −1.21842 −0.0430508
\(802\) −1.44707 −0.0510979
\(803\) −0.756085 −0.0266817
\(804\) −126.045 −4.44525
\(805\) −31.2368 −1.10095
\(806\) 37.2110 1.31070
\(807\) 109.663 3.86033
\(808\) 63.2393 2.22475
\(809\) 12.0201 0.422605 0.211303 0.977421i \(-0.432229\pi\)
0.211303 + 0.977421i \(0.432229\pi\)
\(810\) −389.813 −13.6966
\(811\) 21.9589 0.771082 0.385541 0.922691i \(-0.374015\pi\)
0.385541 + 0.922691i \(0.374015\pi\)
\(812\) −128.562 −4.51165
\(813\) 37.1217 1.30191
\(814\) 28.0795 0.984185
\(815\) −57.8140 −2.02514
\(816\) −26.7039 −0.934823
\(817\) −1.30765 −0.0457487
\(818\) 63.6433 2.22524
\(819\) 49.3083 1.72297
\(820\) 41.4782 1.44848
\(821\) −11.8731 −0.414376 −0.207188 0.978301i \(-0.566431\pi\)
−0.207188 + 0.978301i \(0.566431\pi\)
\(822\) −18.5043 −0.645413
\(823\) −6.29351 −0.219378 −0.109689 0.993966i \(-0.534986\pi\)
−0.109689 + 0.993966i \(0.534986\pi\)
\(824\) 113.345 3.94855
\(825\) 33.7555 1.17521
\(826\) 20.9414 0.728646
\(827\) −29.2252 −1.01626 −0.508131 0.861280i \(-0.669663\pi\)
−0.508131 + 0.861280i \(0.669663\pi\)
\(828\) −117.972 −4.09979
\(829\) −1.43924 −0.0499869 −0.0249935 0.999688i \(-0.507956\pi\)
−0.0249935 + 0.999688i \(0.507956\pi\)
\(830\) 0.0855487 0.00296944
\(831\) −13.5671 −0.470637
\(832\) 4.03265 0.139807
\(833\) 0.329292 0.0114093
\(834\) 3.15558 0.109269
\(835\) 1.69996 0.0588294
\(836\) 5.99258 0.207258
\(837\) 131.218 4.53555
\(838\) 75.1256 2.59517
\(839\) 10.1147 0.349199 0.174600 0.984639i \(-0.444137\pi\)
0.174600 + 0.984639i \(0.444137\pi\)
\(840\) 236.028 8.14375
\(841\) 78.3786 2.70271
\(842\) −41.6347 −1.43483
\(843\) 67.5756 2.32743
\(844\) −5.27972 −0.181736
\(845\) −32.9280 −1.13276
\(846\) 80.0494 2.75215
\(847\) 2.70727 0.0930228
\(848\) −40.6559 −1.39613
\(849\) −59.6146 −2.04597
\(850\) −25.4134 −0.871673
\(851\) −32.7080 −1.12121
\(852\) −19.0590 −0.652951
\(853\) 20.9007 0.715625 0.357812 0.933793i \(-0.383523\pi\)
0.357812 + 0.933793i \(0.383523\pi\)
\(854\) 6.54552 0.223983
\(855\) −43.4855 −1.48717
\(856\) 54.3756 1.85852
\(857\) −52.1008 −1.77973 −0.889864 0.456225i \(-0.849201\pi\)
−0.889864 + 0.456225i \(0.849201\pi\)
\(858\) −18.4880 −0.631169
\(859\) −1.88418 −0.0642873 −0.0321436 0.999483i \(-0.510233\pi\)
−0.0321436 + 0.999483i \(0.510233\pi\)
\(860\) 17.6926 0.603313
\(861\) −21.6293 −0.737126
\(862\) −20.0920 −0.684338
\(863\) −22.6315 −0.770385 −0.385193 0.922836i \(-0.625865\pi\)
−0.385193 + 0.922836i \(0.625865\pi\)
\(864\) 131.075 4.45925
\(865\) 41.8114 1.42163
\(866\) 73.3164 2.49139
\(867\) −3.40788 −0.115738
\(868\) −85.0983 −2.88842
\(869\) −7.66163 −0.259903
\(870\) −349.795 −11.8592
\(871\) 17.0655 0.578243
\(872\) 91.1644 3.08722
\(873\) −106.045 −3.58907
\(874\) −10.0268 −0.339160
\(875\) 51.2684 1.73319
\(876\) −11.8081 −0.398957
\(877\) 11.3175 0.382165 0.191083 0.981574i \(-0.438800\pi\)
0.191083 + 0.981574i \(0.438800\pi\)
\(878\) 51.8540 1.74999
\(879\) 55.0541 1.85693
\(880\) −30.2523 −1.01981
\(881\) 50.7352 1.70931 0.854656 0.519194i \(-0.173768\pi\)
0.854656 + 0.519194i \(0.173768\pi\)
\(882\) −7.27730 −0.245039
\(883\) 4.87912 0.164195 0.0820977 0.996624i \(-0.473838\pi\)
0.0820977 + 0.996624i \(0.473838\pi\)
\(884\) 9.69007 0.325912
\(885\) 39.6665 1.33338
\(886\) 87.5555 2.94148
\(887\) −35.6547 −1.19717 −0.598584 0.801060i \(-0.704270\pi\)
−0.598584 + 0.801060i \(0.704270\pi\)
\(888\) 247.145 8.29363
\(889\) −49.4179 −1.65742
\(890\) 1.40114 0.0469664
\(891\) −39.3537 −1.31840
\(892\) 116.833 3.91184
\(893\) 4.73652 0.158502
\(894\) −188.390 −6.30071
\(895\) 62.0625 2.07452
\(896\) 23.8511 0.796809
\(897\) 21.5355 0.719048
\(898\) 90.7009 3.02673
\(899\) 71.0763 2.37053
\(900\) 390.994 13.0331
\(901\) −5.18840 −0.172851
\(902\) 6.01494 0.200275
\(903\) −9.22603 −0.307023
\(904\) 9.38842 0.312254
\(905\) 72.1030 2.39679
\(906\) −140.154 −4.65632
\(907\) 36.0153 1.19587 0.597934 0.801546i \(-0.295989\pi\)
0.597934 + 0.801546i \(0.295989\pi\)
\(908\) 87.3018 2.89721
\(909\) −82.2037 −2.72652
\(910\) −56.7028 −1.87968
\(911\) 13.9844 0.463322 0.231661 0.972797i \(-0.425584\pi\)
0.231661 + 0.972797i \(0.425584\pi\)
\(912\) 34.9192 1.15629
\(913\) 0.00863659 0.000285830 0
\(914\) −70.9462 −2.34669
\(915\) 12.3983 0.409875
\(916\) −48.1698 −1.59158
\(917\) −44.8235 −1.48020
\(918\) 49.0829 1.61998
\(919\) −32.3409 −1.06683 −0.533413 0.845855i \(-0.679091\pi\)
−0.533413 + 0.845855i \(0.679091\pi\)
\(920\) 76.4569 2.52071
\(921\) 92.1999 3.03809
\(922\) −55.6965 −1.83426
\(923\) 2.58045 0.0849366
\(924\) 42.2804 1.39092
\(925\) 108.404 3.56431
\(926\) −43.1930 −1.41941
\(927\) −147.335 −4.83911
\(928\) 70.9987 2.33065
\(929\) −21.1655 −0.694416 −0.347208 0.937788i \(-0.612870\pi\)
−0.347208 + 0.937788i \(0.612870\pi\)
\(930\) −231.537 −7.59240
\(931\) −0.430597 −0.0141123
\(932\) −80.7550 −2.64522
\(933\) −4.49176 −0.147054
\(934\) 49.7710 1.62856
\(935\) −3.86072 −0.126259
\(936\) −120.690 −3.94487
\(937\) −7.21528 −0.235713 −0.117856 0.993031i \(-0.537602\pi\)
−0.117856 + 0.993031i \(0.537602\pi\)
\(938\) −56.0597 −1.83041
\(939\) −83.8405 −2.73603
\(940\) −64.0857 −2.09024
\(941\) 20.6129 0.671962 0.335981 0.941869i \(-0.390932\pi\)
0.335981 + 0.941869i \(0.390932\pi\)
\(942\) 183.895 5.99164
\(943\) −7.00641 −0.228160
\(944\) −23.6245 −0.768913
\(945\) −199.952 −6.50445
\(946\) 2.56568 0.0834175
\(947\) −58.1824 −1.89067 −0.945337 0.326095i \(-0.894267\pi\)
−0.945337 + 0.326095i \(0.894267\pi\)
\(948\) −119.655 −3.88620
\(949\) 1.59872 0.0518968
\(950\) 33.2318 1.07818
\(951\) −62.7171 −2.03374
\(952\) −17.9396 −0.581425
\(953\) 43.2160 1.39990 0.699952 0.714190i \(-0.253205\pi\)
0.699952 + 0.714190i \(0.253205\pi\)
\(954\) 114.663 3.71234
\(955\) 4.82812 0.156234
\(956\) −28.3765 −0.917760
\(957\) −35.3137 −1.14153
\(958\) 81.6643 2.63845
\(959\) −5.72951 −0.185016
\(960\) −25.0922 −0.809848
\(961\) 16.0470 0.517644
\(962\) −59.3734 −1.91427
\(963\) −70.6819 −2.27769
\(964\) 41.3234 1.33094
\(965\) −24.7075 −0.795363
\(966\) −70.7433 −2.27613
\(967\) −49.2721 −1.58448 −0.792242 0.610208i \(-0.791086\pi\)
−0.792242 + 0.610208i \(0.791086\pi\)
\(968\) −6.62646 −0.212982
\(969\) 4.45630 0.143157
\(970\) 121.948 3.91551
\(971\) 59.4975 1.90937 0.954683 0.297624i \(-0.0961943\pi\)
0.954683 + 0.297624i \(0.0961943\pi\)
\(972\) −351.590 −11.2773
\(973\) 0.977065 0.0313233
\(974\) −32.9727 −1.05651
\(975\) −71.3751 −2.28583
\(976\) −7.38415 −0.236361
\(977\) 34.9544 1.11829 0.559145 0.829070i \(-0.311129\pi\)
0.559145 + 0.829070i \(0.311129\pi\)
\(978\) −130.934 −4.18681
\(979\) 0.141453 0.00452085
\(980\) 5.82604 0.186106
\(981\) −118.503 −3.78352
\(982\) 58.3065 1.86063
\(983\) −19.3716 −0.617859 −0.308929 0.951085i \(-0.599971\pi\)
−0.308929 + 0.951085i \(0.599971\pi\)
\(984\) 52.9412 1.68770
\(985\) 65.6607 2.09212
\(986\) 26.5865 0.846688
\(987\) 33.4183 1.06372
\(988\) −12.6712 −0.403124
\(989\) −2.98860 −0.0950318
\(990\) 85.3212 2.71168
\(991\) 9.99236 0.317418 0.158709 0.987325i \(-0.449267\pi\)
0.158709 + 0.987325i \(0.449267\pi\)
\(992\) 46.9956 1.49211
\(993\) 3.25729 0.103367
\(994\) −8.47670 −0.268864
\(995\) −23.3841 −0.741325
\(996\) 0.134881 0.00427386
\(997\) 20.6367 0.653571 0.326786 0.945098i \(-0.394034\pi\)
0.326786 + 0.945098i \(0.394034\pi\)
\(998\) −102.582 −3.24716
\(999\) −209.369 −6.62416
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 \(a_p\))