Properties

Label 6019.2.a.c.1.18
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} +O(q^{10})\) \(q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} -4.75637 q^{10} -3.00332 q^{11} +5.79563 q^{12} -1.00000 q^{13} +5.12619 q^{14} +4.55941 q^{15} -1.87184 q^{16} +3.33571 q^{17} -3.01768 q^{18} -3.57317 q^{19} +6.03042 q^{20} -4.91391 q^{21} +6.55844 q^{22} +4.76590 q^{23} -3.51369 q^{24} -0.255882 q^{25} +2.18373 q^{26} -3.38717 q^{27} -6.49929 q^{28} +2.11920 q^{29} -9.95651 q^{30} +5.73883 q^{31} +7.44468 q^{32} -6.28685 q^{33} -7.28428 q^{34} -5.11298 q^{35} +3.82600 q^{36} -9.29779 q^{37} +7.80283 q^{38} -2.09330 q^{39} -3.65603 q^{40} +2.20335 q^{41} +10.7306 q^{42} -10.4981 q^{43} -8.31518 q^{44} +3.00991 q^{45} -10.4074 q^{46} +5.22842 q^{47} -3.91833 q^{48} -1.48948 q^{49} +0.558776 q^{50} +6.98263 q^{51} -2.76866 q^{52} +8.52718 q^{53} +7.39666 q^{54} -6.54154 q^{55} +3.94029 q^{56} -7.47972 q^{57} -4.62775 q^{58} -6.83343 q^{59} +12.6235 q^{60} +10.1192 q^{61} -12.5320 q^{62} -3.24393 q^{63} -12.5134 q^{64} -2.17810 q^{65} +13.7288 q^{66} -4.03486 q^{67} +9.23544 q^{68} +9.97644 q^{69} +11.1653 q^{70} +5.45532 q^{71} -2.31957 q^{72} +5.46706 q^{73} +20.3038 q^{74} -0.535637 q^{75} -9.89290 q^{76} +7.05015 q^{77} +4.57119 q^{78} +5.08897 q^{79} -4.07706 q^{80} -11.2361 q^{81} -4.81151 q^{82} -7.60495 q^{83} -13.6049 q^{84} +7.26551 q^{85} +22.9251 q^{86} +4.43612 q^{87} +5.04120 q^{88} -10.7414 q^{89} -6.57281 q^{90} +2.34745 q^{91} +13.1951 q^{92} +12.0131 q^{93} -11.4174 q^{94} -7.78273 q^{95} +15.5839 q^{96} -19.4503 q^{97} +3.25262 q^{98} -4.15028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} + O(q^{10}) \) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} - q^{10} - 45q^{11} - 6q^{12} - 108q^{13} - 31q^{14} - 39q^{15} + 73q^{16} + 21q^{17} - 35q^{18} - 19q^{19} - 79q^{20} - 72q^{21} - 26q^{23} - 23q^{24} + 92q^{25} + 11q^{26} + 7q^{27} - 21q^{28} - 94q^{29} - 24q^{30} - 36q^{31} - 77q^{32} - 32q^{33} - 58q^{34} - 10q^{35} + 17q^{36} - 54q^{37} - 12q^{38} - q^{39} - 4q^{40} - 68q^{41} - 11q^{42} - 32q^{43} - 151q^{44} - 121q^{45} - 33q^{46} - 51q^{47} - 27q^{48} + 72q^{49} - 45q^{50} - 24q^{51} - 95q^{52} - 81q^{53} - 29q^{54} + 4q^{55} - 68q^{56} - 45q^{57} - 30q^{58} - 94q^{59} - 108q^{60} - 39q^{61} - 9q^{62} - 52q^{63} + 31q^{64} + 40q^{65} - 40q^{66} - 47q^{67} + 24q^{68} - 60q^{69} - 66q^{70} - 86q^{71} - 91q^{72} - 51q^{73} - 110q^{74} - 7q^{75} - 51q^{76} - 96q^{77} + 10q^{78} - 18q^{79} - 136q^{80} - 24q^{81} - 33q^{82} - 77q^{83} - 113q^{84} - 95q^{85} - 137q^{86} + 23q^{87} + 19q^{88} - 112q^{89} - 19q^{90} + 8q^{91} - 111q^{92} - 124q^{93} - 20q^{94} - 73q^{95} - 77q^{96} - 41q^{97} - 80q^{98} - 154q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18373 −1.54413 −0.772064 0.635545i \(-0.780775\pi\)
−0.772064 + 0.635545i \(0.780775\pi\)
\(3\) 2.09330 1.20857 0.604283 0.796770i \(-0.293460\pi\)
0.604283 + 0.796770i \(0.293460\pi\)
\(4\) 2.76866 1.38433
\(5\) 2.17810 0.974076 0.487038 0.873381i \(-0.338077\pi\)
0.487038 + 0.873381i \(0.338077\pi\)
\(6\) −4.57119 −1.86618
\(7\) −2.34745 −0.887252 −0.443626 0.896212i \(-0.646308\pi\)
−0.443626 + 0.896212i \(0.646308\pi\)
\(8\) −1.67854 −0.593454
\(9\) 1.38190 0.460632
\(10\) −4.75637 −1.50410
\(11\) −3.00332 −0.905536 −0.452768 0.891628i \(-0.649563\pi\)
−0.452768 + 0.891628i \(0.649563\pi\)
\(12\) 5.79563 1.67305
\(13\) −1.00000 −0.277350
\(14\) 5.12619 1.37003
\(15\) 4.55941 1.17723
\(16\) −1.87184 −0.467961
\(17\) 3.33571 0.809028 0.404514 0.914532i \(-0.367441\pi\)
0.404514 + 0.914532i \(0.367441\pi\)
\(18\) −3.01768 −0.711275
\(19\) −3.57317 −0.819742 −0.409871 0.912143i \(-0.634426\pi\)
−0.409871 + 0.912143i \(0.634426\pi\)
\(20\) 6.03042 1.34844
\(21\) −4.91391 −1.07230
\(22\) 6.55844 1.39826
\(23\) 4.76590 0.993758 0.496879 0.867820i \(-0.334479\pi\)
0.496879 + 0.867820i \(0.334479\pi\)
\(24\) −3.51369 −0.717229
\(25\) −0.255882 −0.0511764
\(26\) 2.18373 0.428264
\(27\) −3.38717 −0.651862
\(28\) −6.49929 −1.22825
\(29\) 2.11920 0.393526 0.196763 0.980451i \(-0.436957\pi\)
0.196763 + 0.980451i \(0.436957\pi\)
\(30\) −9.95651 −1.81780
\(31\) 5.73883 1.03072 0.515362 0.856973i \(-0.327658\pi\)
0.515362 + 0.856973i \(0.327658\pi\)
\(32\) 7.44468 1.31605
\(33\) −6.28685 −1.09440
\(34\) −7.28428 −1.24924
\(35\) −5.11298 −0.864251
\(36\) 3.82600 0.637667
\(37\) −9.29779 −1.52855 −0.764274 0.644892i \(-0.776902\pi\)
−0.764274 + 0.644892i \(0.776902\pi\)
\(38\) 7.80283 1.26579
\(39\) −2.09330 −0.335196
\(40\) −3.65603 −0.578069
\(41\) 2.20335 0.344105 0.172053 0.985088i \(-0.444960\pi\)
0.172053 + 0.985088i \(0.444960\pi\)
\(42\) 10.7306 1.65577
\(43\) −10.4981 −1.60095 −0.800475 0.599366i \(-0.795420\pi\)
−0.800475 + 0.599366i \(0.795420\pi\)
\(44\) −8.31518 −1.25356
\(45\) 3.00991 0.448691
\(46\) −10.4074 −1.53449
\(47\) 5.22842 0.762643 0.381322 0.924442i \(-0.375469\pi\)
0.381322 + 0.924442i \(0.375469\pi\)
\(48\) −3.91833 −0.565562
\(49\) −1.48948 −0.212783
\(50\) 0.558776 0.0790228
\(51\) 6.98263 0.977764
\(52\) −2.76866 −0.383944
\(53\) 8.52718 1.17130 0.585649 0.810565i \(-0.300840\pi\)
0.585649 + 0.810565i \(0.300840\pi\)
\(54\) 7.39666 1.00656
\(55\) −6.54154 −0.882061
\(56\) 3.94029 0.526544
\(57\) −7.47972 −0.990713
\(58\) −4.62775 −0.607654
\(59\) −6.83343 −0.889637 −0.444818 0.895621i \(-0.646732\pi\)
−0.444818 + 0.895621i \(0.646732\pi\)
\(60\) 12.6235 1.62968
\(61\) 10.1192 1.29563 0.647813 0.761799i \(-0.275684\pi\)
0.647813 + 0.761799i \(0.275684\pi\)
\(62\) −12.5320 −1.59157
\(63\) −3.24393 −0.408697
\(64\) −12.5134 −1.56418
\(65\) −2.17810 −0.270160
\(66\) 13.7288 1.68989
\(67\) −4.03486 −0.492937 −0.246469 0.969151i \(-0.579270\pi\)
−0.246469 + 0.969151i \(0.579270\pi\)
\(68\) 9.23544 1.11996
\(69\) 9.97644 1.20102
\(70\) 11.1653 1.33451
\(71\) 5.45532 0.647428 0.323714 0.946155i \(-0.395069\pi\)
0.323714 + 0.946155i \(0.395069\pi\)
\(72\) −2.31957 −0.273364
\(73\) 5.46706 0.639871 0.319935 0.947439i \(-0.396339\pi\)
0.319935 + 0.947439i \(0.396339\pi\)
\(74\) 20.3038 2.36027
\(75\) −0.535637 −0.0618500
\(76\) −9.89290 −1.13479
\(77\) 7.05015 0.803439
\(78\) 4.57119 0.517585
\(79\) 5.08897 0.572553 0.286277 0.958147i \(-0.407582\pi\)
0.286277 + 0.958147i \(0.407582\pi\)
\(80\) −4.07706 −0.455829
\(81\) −11.2361 −1.24845
\(82\) −4.81151 −0.531342
\(83\) −7.60495 −0.834752 −0.417376 0.908734i \(-0.637050\pi\)
−0.417376 + 0.908734i \(0.637050\pi\)
\(84\) −13.6049 −1.48442
\(85\) 7.26551 0.788055
\(86\) 22.9251 2.47207
\(87\) 4.43612 0.475602
\(88\) 5.04120 0.537394
\(89\) −10.7414 −1.13859 −0.569295 0.822133i \(-0.692784\pi\)
−0.569295 + 0.822133i \(0.692784\pi\)
\(90\) −6.57281 −0.692835
\(91\) 2.34745 0.246080
\(92\) 13.1951 1.37569
\(93\) 12.0131 1.24570
\(94\) −11.4174 −1.17762
\(95\) −7.78273 −0.798491
\(96\) 15.5839 1.59053
\(97\) −19.4503 −1.97488 −0.987438 0.158009i \(-0.949492\pi\)
−0.987438 + 0.158009i \(0.949492\pi\)
\(98\) 3.25262 0.328565
\(99\) −4.15028 −0.417119
\(100\) −0.708450 −0.0708450
\(101\) −14.2729 −1.42020 −0.710102 0.704099i \(-0.751351\pi\)
−0.710102 + 0.704099i \(0.751351\pi\)
\(102\) −15.2482 −1.50979
\(103\) 3.35740 0.330814 0.165407 0.986225i \(-0.447106\pi\)
0.165407 + 0.986225i \(0.447106\pi\)
\(104\) 1.67854 0.164595
\(105\) −10.7030 −1.04450
\(106\) −18.6210 −1.80863
\(107\) 19.7245 1.90684 0.953421 0.301643i \(-0.0975349\pi\)
0.953421 + 0.301643i \(0.0975349\pi\)
\(108\) −9.37793 −0.902392
\(109\) 6.59222 0.631420 0.315710 0.948856i \(-0.397757\pi\)
0.315710 + 0.948856i \(0.397757\pi\)
\(110\) 14.2849 1.36201
\(111\) −19.4630 −1.84735
\(112\) 4.39406 0.415199
\(113\) −8.62881 −0.811730 −0.405865 0.913933i \(-0.633030\pi\)
−0.405865 + 0.913933i \(0.633030\pi\)
\(114\) 16.3337 1.52979
\(115\) 10.3806 0.967995
\(116\) 5.86735 0.544769
\(117\) −1.38190 −0.127756
\(118\) 14.9223 1.37371
\(119\) −7.83041 −0.717812
\(120\) −7.65316 −0.698635
\(121\) −1.98005 −0.180005
\(122\) −22.0975 −2.00061
\(123\) 4.61226 0.415874
\(124\) 15.8889 1.42686
\(125\) −11.4478 −1.02393
\(126\) 7.08386 0.631080
\(127\) 5.80001 0.514668 0.257334 0.966323i \(-0.417156\pi\)
0.257334 + 0.966323i \(0.417156\pi\)
\(128\) 12.4366 1.09925
\(129\) −21.9757 −1.93485
\(130\) 4.75637 0.417162
\(131\) −3.79863 −0.331888 −0.165944 0.986135i \(-0.553067\pi\)
−0.165944 + 0.986135i \(0.553067\pi\)
\(132\) −17.4061 −1.51501
\(133\) 8.38784 0.727318
\(134\) 8.81104 0.761158
\(135\) −7.37760 −0.634963
\(136\) −5.59913 −0.480121
\(137\) −17.8462 −1.52470 −0.762352 0.647162i \(-0.775956\pi\)
−0.762352 + 0.647162i \(0.775956\pi\)
\(138\) −21.7858 −1.85453
\(139\) 6.28181 0.532817 0.266408 0.963860i \(-0.414163\pi\)
0.266408 + 0.963860i \(0.414163\pi\)
\(140\) −14.1561 −1.19641
\(141\) 10.9446 0.921705
\(142\) −11.9129 −0.999711
\(143\) 3.00332 0.251151
\(144\) −2.58669 −0.215558
\(145\) 4.61583 0.383324
\(146\) −11.9386 −0.988042
\(147\) −3.11793 −0.257163
\(148\) −25.7424 −2.11601
\(149\) −3.21520 −0.263400 −0.131700 0.991290i \(-0.542044\pi\)
−0.131700 + 0.991290i \(0.542044\pi\)
\(150\) 1.16968 0.0955043
\(151\) −16.0929 −1.30962 −0.654812 0.755792i \(-0.727252\pi\)
−0.654812 + 0.755792i \(0.727252\pi\)
\(152\) 5.99772 0.486479
\(153\) 4.60960 0.372664
\(154\) −15.3956 −1.24061
\(155\) 12.4997 1.00400
\(156\) −5.79563 −0.464022
\(157\) −8.74228 −0.697710 −0.348855 0.937177i \(-0.613429\pi\)
−0.348855 + 0.937177i \(0.613429\pi\)
\(158\) −11.1129 −0.884096
\(159\) 17.8499 1.41559
\(160\) 16.2152 1.28193
\(161\) −11.1877 −0.881714
\(162\) 24.5365 1.92777
\(163\) −20.2942 −1.58956 −0.794782 0.606895i \(-0.792415\pi\)
−0.794782 + 0.606895i \(0.792415\pi\)
\(164\) 6.10032 0.476355
\(165\) −13.6934 −1.06603
\(166\) 16.6071 1.28896
\(167\) 7.88128 0.609872 0.304936 0.952373i \(-0.401365\pi\)
0.304936 + 0.952373i \(0.401365\pi\)
\(168\) 8.24820 0.636363
\(169\) 1.00000 0.0769231
\(170\) −15.8659 −1.21686
\(171\) −4.93775 −0.377600
\(172\) −29.0658 −2.21624
\(173\) 0.615966 0.0468310 0.0234155 0.999726i \(-0.492546\pi\)
0.0234155 + 0.999726i \(0.492546\pi\)
\(174\) −9.68727 −0.734390
\(175\) 0.600670 0.0454063
\(176\) 5.62175 0.423755
\(177\) −14.3044 −1.07519
\(178\) 23.4564 1.75813
\(179\) −2.26361 −0.169190 −0.0845952 0.996415i \(-0.526960\pi\)
−0.0845952 + 0.996415i \(0.526960\pi\)
\(180\) 8.33341 0.621136
\(181\) −15.7833 −1.17316 −0.586581 0.809891i \(-0.699526\pi\)
−0.586581 + 0.809891i \(0.699526\pi\)
\(182\) −5.12619 −0.379978
\(183\) 21.1824 1.56585
\(184\) −7.99975 −0.589750
\(185\) −20.2515 −1.48892
\(186\) −26.2333 −1.92352
\(187\) −10.0182 −0.732604
\(188\) 14.4757 1.05575
\(189\) 7.95122 0.578366
\(190\) 16.9953 1.23297
\(191\) −2.48808 −0.180031 −0.0900157 0.995940i \(-0.528692\pi\)
−0.0900157 + 0.995940i \(0.528692\pi\)
\(192\) −26.1944 −1.89042
\(193\) −10.1355 −0.729572 −0.364786 0.931091i \(-0.618858\pi\)
−0.364786 + 0.931091i \(0.618858\pi\)
\(194\) 42.4741 3.04946
\(195\) −4.55941 −0.326506
\(196\) −4.12387 −0.294562
\(197\) 8.26887 0.589133 0.294566 0.955631i \(-0.404825\pi\)
0.294566 + 0.955631i \(0.404825\pi\)
\(198\) 9.06308 0.644085
\(199\) 7.54357 0.534750 0.267375 0.963593i \(-0.413844\pi\)
0.267375 + 0.963593i \(0.413844\pi\)
\(200\) 0.429508 0.0303708
\(201\) −8.44617 −0.595747
\(202\) 31.1681 2.19298
\(203\) −4.97472 −0.349157
\(204\) 19.3325 1.35355
\(205\) 4.79911 0.335184
\(206\) −7.33163 −0.510819
\(207\) 6.58597 0.457757
\(208\) 1.87184 0.129789
\(209\) 10.7314 0.742306
\(210\) 23.3724 1.61285
\(211\) −27.8060 −1.91424 −0.957120 0.289690i \(-0.906448\pi\)
−0.957120 + 0.289690i \(0.906448\pi\)
\(212\) 23.6088 1.62146
\(213\) 11.4196 0.782459
\(214\) −43.0730 −2.94441
\(215\) −22.8660 −1.55945
\(216\) 5.68551 0.386850
\(217\) −13.4716 −0.914512
\(218\) −14.3956 −0.974993
\(219\) 11.4442 0.773326
\(220\) −18.1113 −1.22106
\(221\) −3.33571 −0.224384
\(222\) 42.5020 2.85254
\(223\) −29.0789 −1.94726 −0.973632 0.228123i \(-0.926741\pi\)
−0.973632 + 0.228123i \(0.926741\pi\)
\(224\) −17.4760 −1.16766
\(225\) −0.353602 −0.0235735
\(226\) 18.8430 1.25341
\(227\) −5.05251 −0.335347 −0.167673 0.985843i \(-0.553625\pi\)
−0.167673 + 0.985843i \(0.553625\pi\)
\(228\) −20.7088 −1.37147
\(229\) −16.0092 −1.05792 −0.528958 0.848648i \(-0.677417\pi\)
−0.528958 + 0.848648i \(0.677417\pi\)
\(230\) −22.6684 −1.49471
\(231\) 14.7581 0.971009
\(232\) −3.55717 −0.233539
\(233\) −28.3613 −1.85801 −0.929005 0.370068i \(-0.879334\pi\)
−0.929005 + 0.370068i \(0.879334\pi\)
\(234\) 3.01768 0.197272
\(235\) 11.3880 0.742872
\(236\) −18.9194 −1.23155
\(237\) 10.6527 0.691969
\(238\) 17.0995 1.10839
\(239\) −6.83617 −0.442195 −0.221098 0.975252i \(-0.570964\pi\)
−0.221098 + 0.975252i \(0.570964\pi\)
\(240\) −8.53450 −0.550900
\(241\) −4.25768 −0.274261 −0.137130 0.990553i \(-0.543788\pi\)
−0.137130 + 0.990553i \(0.543788\pi\)
\(242\) 4.32389 0.277950
\(243\) −13.3589 −0.856973
\(244\) 28.0165 1.79357
\(245\) −3.24424 −0.207267
\(246\) −10.0719 −0.642162
\(247\) 3.57317 0.227356
\(248\) −9.63286 −0.611687
\(249\) −15.9194 −1.00885
\(250\) 24.9989 1.58107
\(251\) −18.6978 −1.18019 −0.590097 0.807332i \(-0.700911\pi\)
−0.590097 + 0.807332i \(0.700911\pi\)
\(252\) −8.98134 −0.565771
\(253\) −14.3135 −0.899884
\(254\) −12.6656 −0.794713
\(255\) 15.2089 0.952416
\(256\) −2.13121 −0.133200
\(257\) 13.2574 0.826977 0.413488 0.910509i \(-0.364310\pi\)
0.413488 + 0.910509i \(0.364310\pi\)
\(258\) 47.9890 2.98766
\(259\) 21.8261 1.35621
\(260\) −6.03042 −0.373991
\(261\) 2.92852 0.181271
\(262\) 8.29516 0.512477
\(263\) −25.9900 −1.60261 −0.801307 0.598254i \(-0.795861\pi\)
−0.801307 + 0.598254i \(0.795861\pi\)
\(264\) 10.5527 0.649476
\(265\) 18.5730 1.14093
\(266\) −18.3167 −1.12307
\(267\) −22.4850 −1.37606
\(268\) −11.1712 −0.682387
\(269\) 0.968877 0.0590735 0.0295367 0.999564i \(-0.490597\pi\)
0.0295367 + 0.999564i \(0.490597\pi\)
\(270\) 16.1107 0.980464
\(271\) 7.99952 0.485936 0.242968 0.970034i \(-0.421879\pi\)
0.242968 + 0.970034i \(0.421879\pi\)
\(272\) −6.24393 −0.378594
\(273\) 4.91391 0.297403
\(274\) 38.9712 2.35434
\(275\) 0.768496 0.0463420
\(276\) 27.6214 1.66261
\(277\) 23.0850 1.38704 0.693521 0.720437i \(-0.256059\pi\)
0.693521 + 0.720437i \(0.256059\pi\)
\(278\) −13.7178 −0.822737
\(279\) 7.93046 0.474784
\(280\) 8.58235 0.512893
\(281\) −12.9659 −0.773480 −0.386740 0.922189i \(-0.626399\pi\)
−0.386740 + 0.922189i \(0.626399\pi\)
\(282\) −23.9001 −1.42323
\(283\) 22.3983 1.33144 0.665721 0.746201i \(-0.268124\pi\)
0.665721 + 0.746201i \(0.268124\pi\)
\(284\) 15.1039 0.896253
\(285\) −16.2916 −0.965029
\(286\) −6.55844 −0.387808
\(287\) −5.17225 −0.305308
\(288\) 10.2878 0.606213
\(289\) −5.87304 −0.345473
\(290\) −10.0797 −0.591901
\(291\) −40.7152 −2.38677
\(292\) 15.1364 0.885792
\(293\) 6.87255 0.401498 0.200749 0.979643i \(-0.435662\pi\)
0.200749 + 0.979643i \(0.435662\pi\)
\(294\) 6.80871 0.397092
\(295\) −14.8839 −0.866574
\(296\) 15.6067 0.907123
\(297\) 10.1728 0.590284
\(298\) 7.02113 0.406723
\(299\) −4.76590 −0.275619
\(300\) −1.48300 −0.0856208
\(301\) 24.6438 1.42045
\(302\) 35.1425 2.02223
\(303\) −29.8774 −1.71641
\(304\) 6.68842 0.383607
\(305\) 22.0406 1.26204
\(306\) −10.0661 −0.575441
\(307\) 0.130484 0.00744713 0.00372357 0.999993i \(-0.498815\pi\)
0.00372357 + 0.999993i \(0.498815\pi\)
\(308\) 19.5195 1.11222
\(309\) 7.02803 0.399811
\(310\) −27.2960 −1.55031
\(311\) 34.7139 1.96845 0.984223 0.176932i \(-0.0566173\pi\)
0.984223 + 0.176932i \(0.0566173\pi\)
\(312\) 3.51369 0.198923
\(313\) 6.24031 0.352723 0.176362 0.984325i \(-0.443567\pi\)
0.176362 + 0.984325i \(0.443567\pi\)
\(314\) 19.0908 1.07735
\(315\) −7.06560 −0.398102
\(316\) 14.0896 0.792603
\(317\) −8.42010 −0.472920 −0.236460 0.971641i \(-0.575987\pi\)
−0.236460 + 0.971641i \(0.575987\pi\)
\(318\) −38.9793 −2.18585
\(319\) −6.36465 −0.356352
\(320\) −27.2555 −1.52363
\(321\) 41.2893 2.30454
\(322\) 24.4309 1.36148
\(323\) −11.9191 −0.663195
\(324\) −31.1088 −1.72827
\(325\) 0.255882 0.0141938
\(326\) 44.3170 2.45449
\(327\) 13.7995 0.763112
\(328\) −3.69841 −0.204211
\(329\) −12.2734 −0.676657
\(330\) 29.9026 1.64608
\(331\) 28.6634 1.57548 0.787742 0.616005i \(-0.211250\pi\)
0.787742 + 0.616005i \(0.211250\pi\)
\(332\) −21.0555 −1.15557
\(333\) −12.8486 −0.704098
\(334\) −17.2106 −0.941720
\(335\) −8.78834 −0.480158
\(336\) 9.19807 0.501796
\(337\) 13.8780 0.755984 0.377992 0.925809i \(-0.376615\pi\)
0.377992 + 0.925809i \(0.376615\pi\)
\(338\) −2.18373 −0.118779
\(339\) −18.0627 −0.981029
\(340\) 20.1157 1.09093
\(341\) −17.2355 −0.933357
\(342\) 10.7827 0.583062
\(343\) 19.9286 1.07604
\(344\) 17.6216 0.950091
\(345\) 21.7297 1.16989
\(346\) −1.34510 −0.0723131
\(347\) 6.07364 0.326050 0.163025 0.986622i \(-0.447875\pi\)
0.163025 + 0.986622i \(0.447875\pi\)
\(348\) 12.2821 0.658390
\(349\) 25.6713 1.37415 0.687077 0.726585i \(-0.258894\pi\)
0.687077 + 0.726585i \(0.258894\pi\)
\(350\) −1.31170 −0.0701132
\(351\) 3.38717 0.180794
\(352\) −22.3588 −1.19173
\(353\) −23.4828 −1.24986 −0.624932 0.780679i \(-0.714873\pi\)
−0.624932 + 0.780679i \(0.714873\pi\)
\(354\) 31.2369 1.66022
\(355\) 11.8822 0.630643
\(356\) −29.7394 −1.57618
\(357\) −16.3914 −0.867524
\(358\) 4.94311 0.261252
\(359\) 15.9297 0.840738 0.420369 0.907353i \(-0.361901\pi\)
0.420369 + 0.907353i \(0.361901\pi\)
\(360\) −5.05226 −0.266277
\(361\) −6.23243 −0.328023
\(362\) 34.4664 1.81151
\(363\) −4.14483 −0.217547
\(364\) 6.49929 0.340655
\(365\) 11.9078 0.623282
\(366\) −46.2566 −2.41787
\(367\) 2.39775 0.125162 0.0625808 0.998040i \(-0.480067\pi\)
0.0625808 + 0.998040i \(0.480067\pi\)
\(368\) −8.92101 −0.465040
\(369\) 3.04480 0.158506
\(370\) 44.2238 2.29908
\(371\) −20.0171 −1.03924
\(372\) 33.2601 1.72446
\(373\) −5.88945 −0.304944 −0.152472 0.988308i \(-0.548723\pi\)
−0.152472 + 0.988308i \(0.548723\pi\)
\(374\) 21.8770 1.13123
\(375\) −23.9637 −1.23748
\(376\) −8.77612 −0.452594
\(377\) −2.11920 −0.109144
\(378\) −17.3633 −0.893071
\(379\) −5.47100 −0.281026 −0.140513 0.990079i \(-0.544875\pi\)
−0.140513 + 0.990079i \(0.544875\pi\)
\(380\) −21.5477 −1.10537
\(381\) 12.1412 0.622010
\(382\) 5.43330 0.277992
\(383\) −6.70387 −0.342552 −0.171276 0.985223i \(-0.554789\pi\)
−0.171276 + 0.985223i \(0.554789\pi\)
\(384\) 26.0335 1.32852
\(385\) 15.3559 0.782610
\(386\) 22.1333 1.12655
\(387\) −14.5073 −0.737449
\(388\) −53.8512 −2.73388
\(389\) 3.63301 0.184201 0.0921006 0.995750i \(-0.470642\pi\)
0.0921006 + 0.995750i \(0.470642\pi\)
\(390\) 9.95651 0.504167
\(391\) 15.8976 0.803978
\(392\) 2.50016 0.126277
\(393\) −7.95166 −0.401108
\(394\) −18.0570 −0.909696
\(395\) 11.0843 0.557710
\(396\) −11.4907 −0.577430
\(397\) −15.2955 −0.767659 −0.383830 0.923404i \(-0.625395\pi\)
−0.383830 + 0.923404i \(0.625395\pi\)
\(398\) −16.4731 −0.825722
\(399\) 17.5583 0.879012
\(400\) 0.478971 0.0239485
\(401\) −4.08771 −0.204130 −0.102065 0.994778i \(-0.532545\pi\)
−0.102065 + 0.994778i \(0.532545\pi\)
\(402\) 18.4441 0.919909
\(403\) −5.73883 −0.285871
\(404\) −39.5167 −1.96603
\(405\) −24.4732 −1.21609
\(406\) 10.8634 0.539142
\(407\) 27.9243 1.38415
\(408\) −11.7206 −0.580258
\(409\) 30.0340 1.48508 0.742542 0.669800i \(-0.233620\pi\)
0.742542 + 0.669800i \(0.233620\pi\)
\(410\) −10.4799 −0.517567
\(411\) −37.3574 −1.84271
\(412\) 9.29548 0.457956
\(413\) 16.0411 0.789332
\(414\) −14.3820 −0.706835
\(415\) −16.5643 −0.813112
\(416\) −7.44468 −0.365005
\(417\) 13.1497 0.643944
\(418\) −23.4344 −1.14622
\(419\) 11.2123 0.547755 0.273877 0.961765i \(-0.411694\pi\)
0.273877 + 0.961765i \(0.411694\pi\)
\(420\) −29.6329 −1.44594
\(421\) 18.5660 0.904850 0.452425 0.891803i \(-0.350559\pi\)
0.452425 + 0.891803i \(0.350559\pi\)
\(422\) 60.7206 2.95583
\(423\) 7.22513 0.351298
\(424\) −14.3132 −0.695111
\(425\) −0.853547 −0.0414031
\(426\) −24.9373 −1.20822
\(427\) −23.7542 −1.14955
\(428\) 54.6105 2.63970
\(429\) 6.28685 0.303532
\(430\) 49.9331 2.40799
\(431\) 6.08107 0.292915 0.146457 0.989217i \(-0.453213\pi\)
0.146457 + 0.989217i \(0.453213\pi\)
\(432\) 6.34026 0.305046
\(433\) −34.4568 −1.65589 −0.827944 0.560811i \(-0.810489\pi\)
−0.827944 + 0.560811i \(0.810489\pi\)
\(434\) 29.4183 1.41212
\(435\) 9.66231 0.463272
\(436\) 18.2516 0.874093
\(437\) −17.0294 −0.814625
\(438\) −24.9910 −1.19411
\(439\) 8.01169 0.382377 0.191189 0.981553i \(-0.438766\pi\)
0.191189 + 0.981553i \(0.438766\pi\)
\(440\) 10.9802 0.523463
\(441\) −2.05831 −0.0980148
\(442\) 7.28428 0.346478
\(443\) 23.0945 1.09725 0.548626 0.836068i \(-0.315151\pi\)
0.548626 + 0.836068i \(0.315151\pi\)
\(444\) −53.8865 −2.55734
\(445\) −23.3959 −1.10907
\(446\) 63.5003 3.00683
\(447\) −6.73038 −0.318336
\(448\) 29.3747 1.38782
\(449\) −12.1921 −0.575381 −0.287690 0.957723i \(-0.592887\pi\)
−0.287690 + 0.957723i \(0.592887\pi\)
\(450\) 0.772170 0.0364004
\(451\) −6.61736 −0.311600
\(452\) −23.8902 −1.12370
\(453\) −33.6873 −1.58277
\(454\) 11.0333 0.517818
\(455\) 5.11298 0.239700
\(456\) 12.5550 0.587943
\(457\) −29.6083 −1.38502 −0.692508 0.721410i \(-0.743494\pi\)
−0.692508 + 0.721410i \(0.743494\pi\)
\(458\) 34.9597 1.63356
\(459\) −11.2986 −0.527375
\(460\) 28.7403 1.34002
\(461\) 33.4297 1.55698 0.778489 0.627658i \(-0.215987\pi\)
0.778489 + 0.627658i \(0.215987\pi\)
\(462\) −32.2276 −1.49936
\(463\) −1.00000 −0.0464739
\(464\) −3.96681 −0.184155
\(465\) 26.1657 1.21340
\(466\) 61.9333 2.86900
\(467\) 28.7629 1.33099 0.665494 0.746403i \(-0.268221\pi\)
0.665494 + 0.746403i \(0.268221\pi\)
\(468\) −3.82600 −0.176857
\(469\) 9.47164 0.437360
\(470\) −24.8683 −1.14709
\(471\) −18.3002 −0.843229
\(472\) 11.4702 0.527959
\(473\) 31.5293 1.44972
\(474\) −23.2626 −1.06849
\(475\) 0.914310 0.0419514
\(476\) −21.6797 −0.993689
\(477\) 11.7837 0.539537
\(478\) 14.9283 0.682806
\(479\) 25.7355 1.17589 0.587943 0.808902i \(-0.299938\pi\)
0.587943 + 0.808902i \(0.299938\pi\)
\(480\) 33.9433 1.54929
\(481\) 9.29779 0.423943
\(482\) 9.29760 0.423494
\(483\) −23.4192 −1.06561
\(484\) −5.48208 −0.249186
\(485\) −42.3646 −1.92368
\(486\) 29.1721 1.32328
\(487\) 2.73349 0.123866 0.0619331 0.998080i \(-0.480273\pi\)
0.0619331 + 0.998080i \(0.480273\pi\)
\(488\) −16.9854 −0.768895
\(489\) −42.4818 −1.92109
\(490\) 7.08454 0.320047
\(491\) 27.4268 1.23776 0.618878 0.785487i \(-0.287588\pi\)
0.618878 + 0.785487i \(0.287588\pi\)
\(492\) 12.7698 0.575706
\(493\) 7.06904 0.318373
\(494\) −7.80283 −0.351066
\(495\) −9.03973 −0.406305
\(496\) −10.7422 −0.482338
\(497\) −12.8061 −0.574432
\(498\) 34.7637 1.55780
\(499\) −10.1759 −0.455536 −0.227768 0.973715i \(-0.573143\pi\)
−0.227768 + 0.973715i \(0.573143\pi\)
\(500\) −31.6952 −1.41745
\(501\) 16.4979 0.737070
\(502\) 40.8309 1.82237
\(503\) −37.3694 −1.66622 −0.833109 0.553110i \(-0.813441\pi\)
−0.833109 + 0.553110i \(0.813441\pi\)
\(504\) 5.44507 0.242543
\(505\) −31.0877 −1.38339
\(506\) 31.2568 1.38953
\(507\) 2.09330 0.0929666
\(508\) 16.0583 0.712470
\(509\) −29.7009 −1.31647 −0.658235 0.752813i \(-0.728696\pi\)
−0.658235 + 0.752813i \(0.728696\pi\)
\(510\) −33.2120 −1.47065
\(511\) −12.8336 −0.567727
\(512\) −20.2192 −0.893571
\(513\) 12.1030 0.534359
\(514\) −28.9506 −1.27696
\(515\) 7.31274 0.322238
\(516\) −60.8433 −2.67848
\(517\) −15.7026 −0.690601
\(518\) −47.6622 −2.09416
\(519\) 1.28940 0.0565984
\(520\) 3.65603 0.160328
\(521\) −4.20101 −0.184050 −0.0920248 0.995757i \(-0.529334\pi\)
−0.0920248 + 0.995757i \(0.529334\pi\)
\(522\) −6.39508 −0.279905
\(523\) −24.2796 −1.06167 −0.530836 0.847475i \(-0.678122\pi\)
−0.530836 + 0.847475i \(0.678122\pi\)
\(524\) −10.5171 −0.459442
\(525\) 1.25738 0.0548766
\(526\) 56.7551 2.47464
\(527\) 19.1431 0.833885
\(528\) 11.7680 0.512136
\(529\) −0.286242 −0.0124453
\(530\) −40.5584 −1.76175
\(531\) −9.44309 −0.409795
\(532\) 23.2231 1.00685
\(533\) −2.20335 −0.0954376
\(534\) 49.1012 2.12481
\(535\) 42.9620 1.85741
\(536\) 6.77269 0.292536
\(537\) −4.73842 −0.204478
\(538\) −2.11576 −0.0912170
\(539\) 4.47340 0.192683
\(540\) −20.4261 −0.878998
\(541\) 2.14389 0.0921730 0.0460865 0.998937i \(-0.485325\pi\)
0.0460865 + 0.998937i \(0.485325\pi\)
\(542\) −17.4688 −0.750348
\(543\) −33.0391 −1.41784
\(544\) 24.8333 1.06472
\(545\) 14.3585 0.615051
\(546\) −10.7306 −0.459229
\(547\) 31.5265 1.34798 0.673988 0.738743i \(-0.264580\pi\)
0.673988 + 0.738743i \(0.264580\pi\)
\(548\) −49.4101 −2.11069
\(549\) 13.9836 0.596807
\(550\) −1.67818 −0.0715580
\(551\) −7.57227 −0.322590
\(552\) −16.7459 −0.712752
\(553\) −11.9461 −0.507999
\(554\) −50.4113 −2.14177
\(555\) −42.3925 −1.79946
\(556\) 17.3922 0.737594
\(557\) −35.7375 −1.51425 −0.757123 0.653273i \(-0.773395\pi\)
−0.757123 + 0.653273i \(0.773395\pi\)
\(558\) −17.3180 −0.733127
\(559\) 10.4981 0.444024
\(560\) 9.57069 0.404436
\(561\) −20.9711 −0.885401
\(562\) 28.3139 1.19435
\(563\) −41.2103 −1.73681 −0.868404 0.495857i \(-0.834854\pi\)
−0.868404 + 0.495857i \(0.834854\pi\)
\(564\) 30.3020 1.27594
\(565\) −18.7944 −0.790687
\(566\) −48.9118 −2.05592
\(567\) 26.3761 1.10769
\(568\) −9.15699 −0.384219
\(569\) −6.87590 −0.288253 −0.144126 0.989559i \(-0.546037\pi\)
−0.144126 + 0.989559i \(0.546037\pi\)
\(570\) 35.5763 1.49013
\(571\) 33.8843 1.41801 0.709007 0.705202i \(-0.249144\pi\)
0.709007 + 0.705202i \(0.249144\pi\)
\(572\) 8.31518 0.347675
\(573\) −5.20830 −0.217580
\(574\) 11.2948 0.471435
\(575\) −1.21951 −0.0508569
\(576\) −17.2923 −0.720512
\(577\) 27.1688 1.13105 0.565526 0.824730i \(-0.308673\pi\)
0.565526 + 0.824730i \(0.308673\pi\)
\(578\) 12.8251 0.533455
\(579\) −21.2167 −0.881736
\(580\) 12.7797 0.530647
\(581\) 17.8522 0.740636
\(582\) 88.9108 3.68547
\(583\) −25.6099 −1.06065
\(584\) −9.17668 −0.379734
\(585\) −3.00991 −0.124444
\(586\) −15.0078 −0.619965
\(587\) 3.11809 0.128697 0.0643486 0.997927i \(-0.479503\pi\)
0.0643486 + 0.997927i \(0.479503\pi\)
\(588\) −8.63249 −0.355998
\(589\) −20.5058 −0.844928
\(590\) 32.5023 1.33810
\(591\) 17.3092 0.712006
\(592\) 17.4040 0.715300
\(593\) 30.9213 1.26979 0.634893 0.772600i \(-0.281044\pi\)
0.634893 + 0.772600i \(0.281044\pi\)
\(594\) −22.2146 −0.911474
\(595\) −17.0554 −0.699204
\(596\) −8.90181 −0.364632
\(597\) 15.7909 0.646280
\(598\) 10.4074 0.425591
\(599\) 27.0857 1.10669 0.553345 0.832952i \(-0.313351\pi\)
0.553345 + 0.832952i \(0.313351\pi\)
\(600\) 0.899089 0.0367052
\(601\) −10.6669 −0.435110 −0.217555 0.976048i \(-0.569808\pi\)
−0.217555 + 0.976048i \(0.569808\pi\)
\(602\) −53.8154 −2.19335
\(603\) −5.57576 −0.227063
\(604\) −44.5558 −1.81295
\(605\) −4.31275 −0.175338
\(606\) 65.2440 2.65036
\(607\) 17.6255 0.715397 0.357699 0.933837i \(-0.383561\pi\)
0.357699 + 0.933837i \(0.383561\pi\)
\(608\) −26.6011 −1.07882
\(609\) −10.4136 −0.421979
\(610\) −48.1305 −1.94875
\(611\) −5.22842 −0.211519
\(612\) 12.7624 0.515890
\(613\) −0.351865 −0.0142117 −0.00710585 0.999975i \(-0.502262\pi\)
−0.00710585 + 0.999975i \(0.502262\pi\)
\(614\) −0.284942 −0.0114993
\(615\) 10.0460 0.405093
\(616\) −11.8340 −0.476804
\(617\) 43.7378 1.76082 0.880410 0.474214i \(-0.157268\pi\)
0.880410 + 0.474214i \(0.157268\pi\)
\(618\) −15.3473 −0.617359
\(619\) −19.1649 −0.770302 −0.385151 0.922854i \(-0.625851\pi\)
−0.385151 + 0.922854i \(0.625851\pi\)
\(620\) 34.6075 1.38987
\(621\) −16.1429 −0.647793
\(622\) −75.8057 −3.03953
\(623\) 25.2150 1.01022
\(624\) 3.91833 0.156859
\(625\) −23.6551 −0.946205
\(626\) −13.6271 −0.544650
\(627\) 22.4640 0.897126
\(628\) −24.2044 −0.965861
\(629\) −31.0147 −1.23664
\(630\) 15.4293 0.614720
\(631\) −24.4022 −0.971437 −0.485719 0.874115i \(-0.661442\pi\)
−0.485719 + 0.874115i \(0.661442\pi\)
\(632\) −8.54204 −0.339784
\(633\) −58.2061 −2.31349
\(634\) 18.3872 0.730249
\(635\) 12.6330 0.501326
\(636\) 49.4203 1.95964
\(637\) 1.48948 0.0590155
\(638\) 13.8986 0.550253
\(639\) 7.53869 0.298226
\(640\) 27.0881 1.07075
\(641\) −8.63890 −0.341216 −0.170608 0.985339i \(-0.554573\pi\)
−0.170608 + 0.985339i \(0.554573\pi\)
\(642\) −90.1646 −3.55851
\(643\) 47.7235 1.88203 0.941015 0.338366i \(-0.109874\pi\)
0.941015 + 0.338366i \(0.109874\pi\)
\(644\) −30.9749 −1.22058
\(645\) −47.8653 −1.88470
\(646\) 26.0280 1.02406
\(647\) −8.96305 −0.352374 −0.176187 0.984357i \(-0.556376\pi\)
−0.176187 + 0.984357i \(0.556376\pi\)
\(648\) 18.8602 0.740898
\(649\) 20.5230 0.805598
\(650\) −0.558776 −0.0219170
\(651\) −28.2001 −1.10525
\(652\) −56.1877 −2.20048
\(653\) −11.5514 −0.452041 −0.226020 0.974123i \(-0.572572\pi\)
−0.226020 + 0.974123i \(0.572572\pi\)
\(654\) −30.1343 −1.17834
\(655\) −8.27379 −0.323284
\(656\) −4.12432 −0.161028
\(657\) 7.55490 0.294745
\(658\) 26.8018 1.04484
\(659\) 1.60792 0.0626355 0.0313177 0.999509i \(-0.490030\pi\)
0.0313177 + 0.999509i \(0.490030\pi\)
\(660\) −37.9123 −1.47574
\(661\) −38.0373 −1.47948 −0.739740 0.672893i \(-0.765052\pi\)
−0.739740 + 0.672893i \(0.765052\pi\)
\(662\) −62.5931 −2.43275
\(663\) −6.98263 −0.271183
\(664\) 12.7652 0.495387
\(665\) 18.2696 0.708463
\(666\) 28.0578 1.08722
\(667\) 10.0999 0.391069
\(668\) 21.8206 0.844263
\(669\) −60.8707 −2.35340
\(670\) 19.1913 0.741425
\(671\) −30.3911 −1.17324
\(672\) −36.5825 −1.41120
\(673\) 8.60104 0.331546 0.165773 0.986164i \(-0.446988\pi\)
0.165773 + 0.986164i \(0.446988\pi\)
\(674\) −30.3058 −1.16733
\(675\) 0.866716 0.0333599
\(676\) 2.76866 0.106487
\(677\) −0.585977 −0.0225209 −0.0112605 0.999937i \(-0.503584\pi\)
−0.0112605 + 0.999937i \(0.503584\pi\)
\(678\) 39.4439 1.51483
\(679\) 45.6585 1.75221
\(680\) −12.1955 −0.467674
\(681\) −10.5764 −0.405289
\(682\) 37.6377 1.44122
\(683\) −27.6086 −1.05641 −0.528206 0.849116i \(-0.677135\pi\)
−0.528206 + 0.849116i \(0.677135\pi\)
\(684\) −13.6710 −0.522722
\(685\) −38.8708 −1.48518
\(686\) −43.5187 −1.66155
\(687\) −33.5120 −1.27856
\(688\) 19.6509 0.749182
\(689\) −8.52718 −0.324860
\(690\) −47.4517 −1.80645
\(691\) −3.95559 −0.150478 −0.0752389 0.997166i \(-0.523972\pi\)
−0.0752389 + 0.997166i \(0.523972\pi\)
\(692\) 1.70540 0.0648296
\(693\) 9.74257 0.370090
\(694\) −13.2632 −0.503463
\(695\) 13.6824 0.519004
\(696\) −7.44621 −0.282248
\(697\) 7.34973 0.278391
\(698\) −56.0591 −2.12187
\(699\) −59.3686 −2.24553
\(700\) 1.66305 0.0628574
\(701\) −16.6680 −0.629541 −0.314770 0.949168i \(-0.601928\pi\)
−0.314770 + 0.949168i \(0.601928\pi\)
\(702\) −7.39666 −0.279169
\(703\) 33.2226 1.25301
\(704\) 37.5819 1.41642
\(705\) 23.8385 0.897810
\(706\) 51.2801 1.92995
\(707\) 33.5048 1.26008
\(708\) −39.6040 −1.48841
\(709\) 26.4805 0.994496 0.497248 0.867609i \(-0.334344\pi\)
0.497248 + 0.867609i \(0.334344\pi\)
\(710\) −25.9475 −0.973794
\(711\) 7.03242 0.263736
\(712\) 18.0300 0.675701
\(713\) 27.3506 1.02429
\(714\) 35.7943 1.33957
\(715\) 6.54154 0.244640
\(716\) −6.26717 −0.234215
\(717\) −14.3101 −0.534422
\(718\) −34.7861 −1.29821
\(719\) −15.1419 −0.564699 −0.282349 0.959312i \(-0.591114\pi\)
−0.282349 + 0.959312i \(0.591114\pi\)
\(720\) −5.63408 −0.209970
\(721\) −7.88131 −0.293515
\(722\) 13.6099 0.506509
\(723\) −8.91258 −0.331462
\(724\) −43.6985 −1.62404
\(725\) −0.542265 −0.0201392
\(726\) 9.05118 0.335921
\(727\) 39.9807 1.48280 0.741402 0.671062i \(-0.234161\pi\)
0.741402 + 0.671062i \(0.234161\pi\)
\(728\) −3.94029 −0.146037
\(729\) 5.74403 0.212742
\(730\) −26.0034 −0.962428
\(731\) −35.0187 −1.29521
\(732\) 58.6470 2.16765
\(733\) −31.4396 −1.16125 −0.580623 0.814172i \(-0.697191\pi\)
−0.580623 + 0.814172i \(0.697191\pi\)
\(734\) −5.23603 −0.193266
\(735\) −6.79117 −0.250496
\(736\) 35.4806 1.30783
\(737\) 12.1180 0.446372
\(738\) −6.64900 −0.244753
\(739\) 2.18516 0.0803823 0.0401911 0.999192i \(-0.487203\pi\)
0.0401911 + 0.999192i \(0.487203\pi\)
\(740\) −56.0695 −2.06116
\(741\) 7.47972 0.274774
\(742\) 43.7119 1.60471
\(743\) 22.7250 0.833699 0.416850 0.908975i \(-0.363134\pi\)
0.416850 + 0.908975i \(0.363134\pi\)
\(744\) −20.1644 −0.739264
\(745\) −7.00304 −0.256571
\(746\) 12.8609 0.470873
\(747\) −10.5093 −0.384513
\(748\) −27.7370 −1.01417
\(749\) −46.3023 −1.69185
\(750\) 52.3302 1.91083
\(751\) 28.6412 1.04513 0.522566 0.852599i \(-0.324975\pi\)
0.522566 + 0.852599i \(0.324975\pi\)
\(752\) −9.78678 −0.356887
\(753\) −39.1401 −1.42634
\(754\) 4.62775 0.168533
\(755\) −35.0520 −1.27567
\(756\) 22.0142 0.800649
\(757\) 20.2347 0.735441 0.367721 0.929936i \(-0.380138\pi\)
0.367721 + 0.929936i \(0.380138\pi\)
\(758\) 11.9472 0.433941
\(759\) −29.9625 −1.08757
\(760\) 13.0636 0.473868
\(761\) 24.1931 0.877001 0.438500 0.898731i \(-0.355510\pi\)
0.438500 + 0.898731i \(0.355510\pi\)
\(762\) −26.5130 −0.960463
\(763\) −15.4749 −0.560229
\(764\) −6.88866 −0.249223
\(765\) 10.0402 0.363003
\(766\) 14.6394 0.528944
\(767\) 6.83343 0.246741
\(768\) −4.46125 −0.160982
\(769\) −32.8115 −1.18321 −0.591606 0.806227i \(-0.701506\pi\)
−0.591606 + 0.806227i \(0.701506\pi\)
\(770\) −33.5331 −1.20845
\(771\) 27.7518 0.999456
\(772\) −28.0619 −1.00997
\(773\) 7.68910 0.276558 0.138279 0.990393i \(-0.455843\pi\)
0.138279 + 0.990393i \(0.455843\pi\)
\(774\) 31.6800 1.13872
\(775\) −1.46846 −0.0527487
\(776\) 32.6481 1.17200
\(777\) 45.6885 1.63907
\(778\) −7.93351 −0.284430
\(779\) −7.87294 −0.282077
\(780\) −12.6235 −0.451992
\(781\) −16.3841 −0.586269
\(782\) −34.7161 −1.24145
\(783\) −7.17810 −0.256524
\(784\) 2.78808 0.0995743
\(785\) −19.0416 −0.679623
\(786\) 17.3642 0.619362
\(787\) −51.2261 −1.82601 −0.913006 0.407945i \(-0.866245\pi\)
−0.913006 + 0.407945i \(0.866245\pi\)
\(788\) 22.8937 0.815554
\(789\) −54.4049 −1.93686
\(790\) −24.2050 −0.861176
\(791\) 20.2557 0.720209
\(792\) 6.96642 0.247541
\(793\) −10.1192 −0.359342
\(794\) 33.4012 1.18536
\(795\) 38.8789 1.37889
\(796\) 20.8856 0.740270
\(797\) 17.8258 0.631423 0.315712 0.948855i \(-0.397757\pi\)
0.315712 + 0.948855i \(0.397757\pi\)
\(798\) −38.3424 −1.35731
\(799\) 17.4405 0.617000
\(800\) −1.90496 −0.0673504
\(801\) −14.8436 −0.524471
\(802\) 8.92644 0.315203
\(803\) −16.4193 −0.579426
\(804\) −23.3846 −0.824710
\(805\) −24.3679 −0.858856
\(806\) 12.5320 0.441422
\(807\) 2.02815 0.0713942
\(808\) 23.9576 0.842826
\(809\) −11.3384 −0.398637 −0.199319 0.979935i \(-0.563873\pi\)
−0.199319 + 0.979935i \(0.563873\pi\)
\(810\) 53.4429 1.87779
\(811\) −43.0631 −1.51215 −0.756075 0.654485i \(-0.772885\pi\)
−0.756075 + 0.654485i \(0.772885\pi\)
\(812\) −13.7733 −0.483348
\(813\) 16.7454 0.587286
\(814\) −60.9790 −2.13731
\(815\) −44.2028 −1.54836
\(816\) −13.0704 −0.457555
\(817\) 37.5117 1.31237
\(818\) −65.5859 −2.29316
\(819\) 3.24393 0.113352
\(820\) 13.2871 0.464006
\(821\) −28.4867 −0.994192 −0.497096 0.867695i \(-0.665600\pi\)
−0.497096 + 0.867695i \(0.665600\pi\)
\(822\) 81.5784 2.84537
\(823\) 28.4013 0.990008 0.495004 0.868891i \(-0.335167\pi\)
0.495004 + 0.868891i \(0.335167\pi\)
\(824\) −5.63553 −0.196323
\(825\) 1.60869 0.0560074
\(826\) −35.0294 −1.21883
\(827\) −41.1758 −1.43182 −0.715912 0.698191i \(-0.753989\pi\)
−0.715912 + 0.698191i \(0.753989\pi\)
\(828\) 18.2343 0.633686
\(829\) 10.4542 0.363090 0.181545 0.983383i \(-0.441890\pi\)
0.181545 + 0.983383i \(0.441890\pi\)
\(830\) 36.1720 1.25555
\(831\) 48.3237 1.67633
\(832\) 12.5134 0.433826
\(833\) −4.96848 −0.172148
\(834\) −28.7154 −0.994332
\(835\) 17.1662 0.594061
\(836\) 29.7116 1.02760
\(837\) −19.4384 −0.671889
\(838\) −24.4845 −0.845803
\(839\) 5.27533 0.182125 0.0910623 0.995845i \(-0.470974\pi\)
0.0910623 + 0.995845i \(0.470974\pi\)
\(840\) 17.9654 0.619866
\(841\) −24.5090 −0.845137
\(842\) −40.5430 −1.39720
\(843\) −27.1415 −0.934802
\(844\) −76.9852 −2.64994
\(845\) 2.17810 0.0749289
\(846\) −15.7777 −0.542449
\(847\) 4.64807 0.159709
\(848\) −15.9615 −0.548121
\(849\) 46.8864 1.60914
\(850\) 1.86391 0.0639317
\(851\) −44.3123 −1.51901
\(852\) 31.6170 1.08318
\(853\) −27.6990 −0.948395 −0.474197 0.880419i \(-0.657262\pi\)
−0.474197 + 0.880419i \(0.657262\pi\)
\(854\) 51.8727 1.77505
\(855\) −10.7549 −0.367811
\(856\) −33.1084 −1.13162
\(857\) −2.25488 −0.0770252 −0.0385126 0.999258i \(-0.512262\pi\)
−0.0385126 + 0.999258i \(0.512262\pi\)
\(858\) −13.7288 −0.468692
\(859\) −20.7032 −0.706384 −0.353192 0.935551i \(-0.614904\pi\)
−0.353192 + 0.935551i \(0.614904\pi\)
\(860\) −63.3081 −2.15879
\(861\) −10.8271 −0.368985
\(862\) −13.2794 −0.452298
\(863\) 13.0053 0.442706 0.221353 0.975194i \(-0.428953\pi\)
0.221353 + 0.975194i \(0.428953\pi\)
\(864\) −25.2164 −0.857880
\(865\) 1.34164 0.0456170
\(866\) 75.2442 2.55690
\(867\) −12.2940 −0.417527
\(868\) −37.2983 −1.26599
\(869\) −15.2838 −0.518468
\(870\) −21.0998 −0.715351
\(871\) 4.03486 0.136716
\(872\) −11.0653 −0.374719
\(873\) −26.8782 −0.909691
\(874\) 37.1875 1.25789
\(875\) 26.8732 0.908480
\(876\) 31.6850 1.07054
\(877\) −31.5819 −1.06644 −0.533222 0.845975i \(-0.679019\pi\)
−0.533222 + 0.845975i \(0.679019\pi\)
\(878\) −17.4953 −0.590439
\(879\) 14.3863 0.485237
\(880\) 12.2447 0.412770
\(881\) −42.8466 −1.44354 −0.721770 0.692133i \(-0.756671\pi\)
−0.721770 + 0.692133i \(0.756671\pi\)
\(882\) 4.49479 0.151347
\(883\) −19.2358 −0.647335 −0.323667 0.946171i \(-0.604916\pi\)
−0.323667 + 0.946171i \(0.604916\pi\)
\(884\) −9.23544 −0.310622
\(885\) −31.1564 −1.04731
\(886\) −50.4321 −1.69430
\(887\) 43.0616 1.44587 0.722934 0.690917i \(-0.242793\pi\)
0.722934 + 0.690917i \(0.242793\pi\)
\(888\) 32.6695 1.09632
\(889\) −13.6152 −0.456640
\(890\) 51.0903 1.71255
\(891\) 33.7455 1.13052
\(892\) −80.5095 −2.69566
\(893\) −18.6820 −0.625171
\(894\) 14.6973 0.491552
\(895\) −4.93038 −0.164804
\(896\) −29.1943 −0.975312
\(897\) −9.97644 −0.333104
\(898\) 26.6242 0.888461
\(899\) 12.1617 0.405616
\(900\) −0.979004 −0.0326335
\(901\) 28.4442 0.947613
\(902\) 14.4505 0.481149
\(903\) 51.5869 1.71670
\(904\) 14.4838 0.481725
\(905\) −34.3775 −1.14275
\(906\) 73.5638 2.44399
\(907\) 40.9436 1.35951 0.679755 0.733439i \(-0.262086\pi\)
0.679755 + 0.733439i \(0.262086\pi\)
\(908\) −13.9887 −0.464230
\(909\) −19.7236 −0.654192
\(910\) −11.1653 −0.370128
\(911\) 13.5368 0.448494 0.224247 0.974532i \(-0.428008\pi\)
0.224247 + 0.974532i \(0.428008\pi\)
\(912\) 14.0009 0.463615
\(913\) 22.8401 0.755898
\(914\) 64.6563 2.13864
\(915\) 46.1375 1.52526
\(916\) −44.3240 −1.46451
\(917\) 8.91708 0.294468
\(918\) 24.6731 0.814334
\(919\) −46.9114 −1.54747 −0.773733 0.633512i \(-0.781613\pi\)
−0.773733 + 0.633512i \(0.781613\pi\)
\(920\) −17.4243 −0.574461
\(921\) 0.273143 0.00900035
\(922\) −73.0014 −2.40417
\(923\) −5.45532 −0.179564
\(924\) 40.8600 1.34420
\(925\) 2.37914 0.0782255
\(926\) 2.18373 0.0717617
\(927\) 4.63957 0.152384
\(928\) 15.7768 0.517898
\(929\) −18.8745 −0.619253 −0.309626 0.950858i \(-0.600204\pi\)
−0.309626 + 0.950858i \(0.600204\pi\)
\(930\) −57.1387 −1.87365
\(931\) 5.32218 0.174427
\(932\) −78.5227 −2.57210
\(933\) 72.6666 2.37900
\(934\) −62.8103 −2.05521
\(935\) −21.8207 −0.713612
\(936\) 2.31957 0.0758175
\(937\) 49.9205 1.63083 0.815415 0.578876i \(-0.196509\pi\)
0.815415 + 0.578876i \(0.196509\pi\)
\(938\) −20.6835 −0.675339
\(939\) 13.0628 0.426289
\(940\) 31.5295 1.02838
\(941\) −8.74673 −0.285135 −0.142568 0.989785i \(-0.545536\pi\)
−0.142568 + 0.989785i \(0.545536\pi\)
\(942\) 39.9626 1.30205
\(943\) 10.5009 0.341957
\(944\) 12.7911 0.416315
\(945\) 17.3185 0.563372
\(946\) −68.8513 −2.23855
\(947\) 37.0510 1.20400 0.601998 0.798498i \(-0.294371\pi\)
0.601998 + 0.798498i \(0.294371\pi\)
\(948\) 29.4938 0.957913
\(949\) −5.46706 −0.177468
\(950\) −1.99660 −0.0647783
\(951\) −17.6258 −0.571555
\(952\) 13.1437 0.425989
\(953\) 0.596845 0.0193337 0.00966685 0.999953i \(-0.496923\pi\)
0.00966685 + 0.999953i \(0.496923\pi\)
\(954\) −25.7323 −0.833114
\(955\) −5.41930 −0.175364
\(956\) −18.9270 −0.612144
\(957\) −13.3231 −0.430675
\(958\) −56.1993 −1.81572
\(959\) 41.8931 1.35280
\(960\) −57.0540 −1.84141
\(961\) 1.93412 0.0623910
\(962\) −20.3038 −0.654622
\(963\) 27.2572 0.878353
\(964\) −11.7881 −0.379668
\(965\) −22.0762 −0.710659
\(966\) 51.1411 1.64544
\(967\) 40.5001 1.30239 0.651197 0.758909i \(-0.274267\pi\)
0.651197 + 0.758909i \(0.274267\pi\)
\(968\) 3.32360 0.106824
\(969\) −24.9502 −0.801515
\(970\) 92.5127 2.97040
\(971\) 55.5060 1.78127 0.890636 0.454716i \(-0.150259\pi\)
0.890636 + 0.454716i \(0.150259\pi\)
\(972\) −36.9862 −1.18633
\(973\) −14.7462 −0.472743
\(974\) −5.96919 −0.191265
\(975\) 0.535637 0.0171541
\(976\) −18.9415 −0.606303
\(977\) 35.1795 1.12549 0.562746 0.826630i \(-0.309745\pi\)
0.562746 + 0.826630i \(0.309745\pi\)
\(978\) 92.7686 2.96641
\(979\) 32.2600 1.03103
\(980\) −8.98221 −0.286926
\(981\) 9.10976 0.290852
\(982\) −59.8927 −1.91125
\(983\) −24.2502 −0.773462 −0.386731 0.922193i \(-0.626396\pi\)
−0.386731 + 0.922193i \(0.626396\pi\)
\(984\) −7.74188 −0.246802
\(985\) 18.0104 0.573860
\(986\) −15.4368 −0.491609
\(987\) −25.6920 −0.817784
\(988\) 9.89290 0.314735
\(989\) −50.0330 −1.59096
\(990\) 19.7403 0.627387
\(991\) −22.2492 −0.706768 −0.353384 0.935478i \(-0.614969\pi\)
−0.353384 + 0.935478i \(0.614969\pi\)
\(992\) 42.7237 1.35648
\(993\) 60.0011 1.90408
\(994\) 27.9650 0.886996
\(995\) 16.4307 0.520887
\(996\) −44.0755 −1.39659
\(997\) −14.6775 −0.464841 −0.232420 0.972615i \(-0.574665\pi\)
−0.232420 + 0.972615i \(0.574665\pi\)
\(998\) 22.2214 0.703406
\(999\) 31.4932 0.996402
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 \(a_p\))