Properties

Label 8041.2.a.i.1.17
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
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: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73352 q^{2} +2.13034 q^{3} +1.00511 q^{4} -4.15912 q^{5} -3.69300 q^{6} -1.81917 q^{7} +1.72467 q^{8} +1.53836 q^{9} +O(q^{10})\) \(q-1.73352 q^{2} +2.13034 q^{3} +1.00511 q^{4} -4.15912 q^{5} -3.69300 q^{6} -1.81917 q^{7} +1.72467 q^{8} +1.53836 q^{9} +7.20994 q^{10} +1.00000 q^{11} +2.14123 q^{12} +3.34135 q^{13} +3.15357 q^{14} -8.86036 q^{15} -4.99997 q^{16} -1.00000 q^{17} -2.66679 q^{18} -0.395669 q^{19} -4.18037 q^{20} -3.87545 q^{21} -1.73352 q^{22} +3.74793 q^{23} +3.67414 q^{24} +12.2983 q^{25} -5.79231 q^{26} -3.11379 q^{27} -1.82846 q^{28} +6.92498 q^{29} +15.3597 q^{30} -4.77160 q^{31} +5.21824 q^{32} +2.13034 q^{33} +1.73352 q^{34} +7.56615 q^{35} +1.54622 q^{36} +12.0076 q^{37} +0.685902 q^{38} +7.11821 q^{39} -7.17311 q^{40} +3.93128 q^{41} +6.71820 q^{42} -1.00000 q^{43} +1.00511 q^{44} -6.39824 q^{45} -6.49714 q^{46} +0.482571 q^{47} -10.6517 q^{48} -3.69062 q^{49} -21.3194 q^{50} -2.13034 q^{51} +3.35841 q^{52} -5.31367 q^{53} +5.39783 q^{54} -4.15912 q^{55} -3.13746 q^{56} -0.842911 q^{57} -12.0046 q^{58} -5.33453 q^{59} -8.90562 q^{60} -14.4626 q^{61} +8.27168 q^{62} -2.79854 q^{63} +0.953998 q^{64} -13.8971 q^{65} -3.69300 q^{66} -9.55002 q^{67} -1.00511 q^{68} +7.98439 q^{69} -13.1161 q^{70} -10.8443 q^{71} +2.65317 q^{72} +0.787245 q^{73} -20.8154 q^{74} +26.1996 q^{75} -0.397690 q^{76} -1.81917 q^{77} -12.3396 q^{78} -13.0934 q^{79} +20.7955 q^{80} -11.2485 q^{81} -6.81497 q^{82} +6.37930 q^{83} -3.89525 q^{84} +4.15912 q^{85} +1.73352 q^{86} +14.7526 q^{87} +1.72467 q^{88} -6.94533 q^{89} +11.0915 q^{90} -6.07847 q^{91} +3.76708 q^{92} -10.1651 q^{93} -0.836549 q^{94} +1.64564 q^{95} +11.1166 q^{96} +9.60390 q^{97} +6.39779 q^{98} +1.53836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73352 −1.22579 −0.612894 0.790165i \(-0.709995\pi\)
−0.612894 + 0.790165i \(0.709995\pi\)
\(3\) 2.13034 1.22995 0.614977 0.788545i \(-0.289165\pi\)
0.614977 + 0.788545i \(0.289165\pi\)
\(4\) 1.00511 0.502554
\(5\) −4.15912 −1.86002 −0.930008 0.367539i \(-0.880200\pi\)
−0.930008 + 0.367539i \(0.880200\pi\)
\(6\) −3.69300 −1.50766
\(7\) −1.81917 −0.687581 −0.343791 0.939046i \(-0.611711\pi\)
−0.343791 + 0.939046i \(0.611711\pi\)
\(8\) 1.72467 0.609763
\(9\) 1.53836 0.512788
\(10\) 7.20994 2.27998
\(11\) 1.00000 0.301511
\(12\) 2.14123 0.618119
\(13\) 3.34135 0.926722 0.463361 0.886170i \(-0.346643\pi\)
0.463361 + 0.886170i \(0.346643\pi\)
\(14\) 3.15357 0.842828
\(15\) −8.86036 −2.28774
\(16\) −4.99997 −1.24999
\(17\) −1.00000 −0.242536
\(18\) −2.66679 −0.628569
\(19\) −0.395669 −0.0907727 −0.0453864 0.998970i \(-0.514452\pi\)
−0.0453864 + 0.998970i \(0.514452\pi\)
\(20\) −4.18037 −0.934759
\(21\) −3.87545 −0.845694
\(22\) −1.73352 −0.369589
\(23\) 3.74793 0.781498 0.390749 0.920497i \(-0.372216\pi\)
0.390749 + 0.920497i \(0.372216\pi\)
\(24\) 3.67414 0.749980
\(25\) 12.2983 2.45966
\(26\) −5.79231 −1.13596
\(27\) −3.11379 −0.599249
\(28\) −1.82846 −0.345547
\(29\) 6.92498 1.28594 0.642969 0.765893i \(-0.277703\pi\)
0.642969 + 0.765893i \(0.277703\pi\)
\(30\) 15.3597 2.80428
\(31\) −4.77160 −0.857004 −0.428502 0.903541i \(-0.640959\pi\)
−0.428502 + 0.903541i \(0.640959\pi\)
\(32\) 5.21824 0.922463
\(33\) 2.13034 0.370845
\(34\) 1.73352 0.297297
\(35\) 7.56615 1.27891
\(36\) 1.54622 0.257704
\(37\) 12.0076 1.97403 0.987015 0.160628i \(-0.0513518\pi\)
0.987015 + 0.160628i \(0.0513518\pi\)
\(38\) 0.685902 0.111268
\(39\) 7.11821 1.13983
\(40\) −7.17311 −1.13417
\(41\) 3.93128 0.613963 0.306981 0.951716i \(-0.400681\pi\)
0.306981 + 0.951716i \(0.400681\pi\)
\(42\) 6.71820 1.03664
\(43\) −1.00000 −0.152499
\(44\) 1.00511 0.151526
\(45\) −6.39824 −0.953794
\(46\) −6.49714 −0.957951
\(47\) 0.482571 0.0703902 0.0351951 0.999380i \(-0.488795\pi\)
0.0351951 + 0.999380i \(0.488795\pi\)
\(48\) −10.6517 −1.53743
\(49\) −3.69062 −0.527232
\(50\) −21.3194 −3.01502
\(51\) −2.13034 −0.298308
\(52\) 3.35841 0.465728
\(53\) −5.31367 −0.729888 −0.364944 0.931029i \(-0.618912\pi\)
−0.364944 + 0.931029i \(0.618912\pi\)
\(54\) 5.39783 0.734552
\(55\) −4.15912 −0.560816
\(56\) −3.13746 −0.419261
\(57\) −0.842911 −0.111646
\(58\) −12.0046 −1.57629
\(59\) −5.33453 −0.694496 −0.347248 0.937773i \(-0.612884\pi\)
−0.347248 + 0.937773i \(0.612884\pi\)
\(60\) −8.90562 −1.14971
\(61\) −14.4626 −1.85175 −0.925873 0.377834i \(-0.876669\pi\)
−0.925873 + 0.377834i \(0.876669\pi\)
\(62\) 8.27168 1.05050
\(63\) −2.79854 −0.352583
\(64\) 0.953998 0.119250
\(65\) −13.8971 −1.72372
\(66\) −3.69300 −0.454577
\(67\) −9.55002 −1.16672 −0.583360 0.812213i \(-0.698262\pi\)
−0.583360 + 0.812213i \(0.698262\pi\)
\(68\) −1.00511 −0.121887
\(69\) 7.98439 0.961207
\(70\) −13.1161 −1.56767
\(71\) −10.8443 −1.28698 −0.643489 0.765456i \(-0.722514\pi\)
−0.643489 + 0.765456i \(0.722514\pi\)
\(72\) 2.65317 0.312679
\(73\) 0.787245 0.0921400 0.0460700 0.998938i \(-0.485330\pi\)
0.0460700 + 0.998938i \(0.485330\pi\)
\(74\) −20.8154 −2.41974
\(75\) 26.1996 3.02527
\(76\) −0.397690 −0.0456182
\(77\) −1.81917 −0.207314
\(78\) −12.3396 −1.39718
\(79\) −13.0934 −1.47312 −0.736559 0.676373i \(-0.763551\pi\)
−0.736559 + 0.676373i \(0.763551\pi\)
\(80\) 20.7955 2.32501
\(81\) −11.2485 −1.24984
\(82\) −6.81497 −0.752588
\(83\) 6.37930 0.700219 0.350110 0.936709i \(-0.386144\pi\)
0.350110 + 0.936709i \(0.386144\pi\)
\(84\) −3.89525 −0.425007
\(85\) 4.15912 0.451120
\(86\) 1.73352 0.186931
\(87\) 14.7526 1.58164
\(88\) 1.72467 0.183850
\(89\) −6.94533 −0.736204 −0.368102 0.929785i \(-0.619992\pi\)
−0.368102 + 0.929785i \(0.619992\pi\)
\(90\) 11.0915 1.16915
\(91\) −6.07847 −0.637197
\(92\) 3.76708 0.392745
\(93\) −10.1651 −1.05408
\(94\) −0.836549 −0.0862834
\(95\) 1.64564 0.168839
\(96\) 11.1166 1.13459
\(97\) 9.60390 0.975129 0.487564 0.873087i \(-0.337885\pi\)
0.487564 + 0.873087i \(0.337885\pi\)
\(98\) 6.39779 0.646274
\(99\) 1.53836 0.154611
\(100\) 12.3611 1.23611
\(101\) 0.280169 0.0278778 0.0139389 0.999903i \(-0.495563\pi\)
0.0139389 + 0.999903i \(0.495563\pi\)
\(102\) 3.69300 0.365662
\(103\) −6.91930 −0.681778 −0.340889 0.940103i \(-0.610728\pi\)
−0.340889 + 0.940103i \(0.610728\pi\)
\(104\) 5.76272 0.565081
\(105\) 16.1185 1.57300
\(106\) 9.21137 0.894688
\(107\) −5.02302 −0.485594 −0.242797 0.970077i \(-0.578065\pi\)
−0.242797 + 0.970077i \(0.578065\pi\)
\(108\) −3.12970 −0.301155
\(109\) 13.0521 1.25016 0.625081 0.780560i \(-0.285066\pi\)
0.625081 + 0.780560i \(0.285066\pi\)
\(110\) 7.20994 0.687441
\(111\) 25.5802 2.42797
\(112\) 9.09580 0.859472
\(113\) 4.90543 0.461464 0.230732 0.973017i \(-0.425888\pi\)
0.230732 + 0.973017i \(0.425888\pi\)
\(114\) 1.46121 0.136855
\(115\) −15.5881 −1.45360
\(116\) 6.96036 0.646253
\(117\) 5.14020 0.475212
\(118\) 9.24753 0.851304
\(119\) 1.81917 0.166763
\(120\) −15.2812 −1.39498
\(121\) 1.00000 0.0909091
\(122\) 25.0713 2.26985
\(123\) 8.37498 0.755146
\(124\) −4.79597 −0.430691
\(125\) −30.3545 −2.71499
\(126\) 4.85134 0.432192
\(127\) 18.8511 1.67277 0.836384 0.548144i \(-0.184665\pi\)
0.836384 + 0.548144i \(0.184665\pi\)
\(128\) −12.0903 −1.06864
\(129\) −2.13034 −0.187566
\(130\) 24.0909 2.11291
\(131\) −0.920618 −0.0804348 −0.0402174 0.999191i \(-0.512805\pi\)
−0.0402174 + 0.999191i \(0.512805\pi\)
\(132\) 2.14123 0.186370
\(133\) 0.719789 0.0624136
\(134\) 16.5552 1.43015
\(135\) 12.9506 1.11461
\(136\) −1.72467 −0.147889
\(137\) −6.23598 −0.532776 −0.266388 0.963866i \(-0.585830\pi\)
−0.266388 + 0.963866i \(0.585830\pi\)
\(138\) −13.8411 −1.17824
\(139\) −5.62858 −0.477410 −0.238705 0.971092i \(-0.576723\pi\)
−0.238705 + 0.971092i \(0.576723\pi\)
\(140\) 7.60480 0.642723
\(141\) 1.02804 0.0865768
\(142\) 18.7988 1.57756
\(143\) 3.34135 0.279417
\(144\) −7.69178 −0.640981
\(145\) −28.8019 −2.39186
\(146\) −1.36471 −0.112944
\(147\) −7.86230 −0.648471
\(148\) 12.0689 0.992057
\(149\) 22.5681 1.84885 0.924425 0.381363i \(-0.124545\pi\)
0.924425 + 0.381363i \(0.124545\pi\)
\(150\) −45.4177 −3.70834
\(151\) −7.25551 −0.590445 −0.295223 0.955429i \(-0.595394\pi\)
−0.295223 + 0.955429i \(0.595394\pi\)
\(152\) −0.682398 −0.0553498
\(153\) −1.53836 −0.124369
\(154\) 3.15357 0.254122
\(155\) 19.8457 1.59404
\(156\) 7.15458 0.572825
\(157\) 12.6197 1.00716 0.503582 0.863947i \(-0.332015\pi\)
0.503582 + 0.863947i \(0.332015\pi\)
\(158\) 22.6977 1.80573
\(159\) −11.3199 −0.897729
\(160\) −21.7033 −1.71580
\(161\) −6.81813 −0.537344
\(162\) 19.4996 1.53203
\(163\) 22.8361 1.78866 0.894330 0.447409i \(-0.147653\pi\)
0.894330 + 0.447409i \(0.147653\pi\)
\(164\) 3.95136 0.308550
\(165\) −8.86036 −0.689778
\(166\) −11.0587 −0.858320
\(167\) 18.9126 1.46350 0.731749 0.681574i \(-0.238704\pi\)
0.731749 + 0.681574i \(0.238704\pi\)
\(168\) −6.68388 −0.515672
\(169\) −1.83541 −0.141186
\(170\) −7.20994 −0.552977
\(171\) −0.608683 −0.0465471
\(172\) −1.00511 −0.0766388
\(173\) 7.37677 0.560846 0.280423 0.959877i \(-0.409525\pi\)
0.280423 + 0.959877i \(0.409525\pi\)
\(174\) −25.5740 −1.93876
\(175\) −22.3727 −1.69122
\(176\) −4.99997 −0.376887
\(177\) −11.3644 −0.854199
\(178\) 12.0399 0.902429
\(179\) 2.42944 0.181585 0.0907925 0.995870i \(-0.471060\pi\)
0.0907925 + 0.995870i \(0.471060\pi\)
\(180\) −6.43093 −0.479333
\(181\) −7.53724 −0.560239 −0.280119 0.959965i \(-0.590374\pi\)
−0.280119 + 0.959965i \(0.590374\pi\)
\(182\) 10.5372 0.781068
\(183\) −30.8103 −2.27756
\(184\) 6.46395 0.476529
\(185\) −49.9409 −3.67173
\(186\) 17.6215 1.29207
\(187\) −1.00000 −0.0731272
\(188\) 0.485036 0.0353749
\(189\) 5.66451 0.412032
\(190\) −2.85275 −0.206960
\(191\) 24.2995 1.75825 0.879125 0.476591i \(-0.158128\pi\)
0.879125 + 0.476591i \(0.158128\pi\)
\(192\) 2.03234 0.146672
\(193\) −15.6469 −1.12629 −0.563144 0.826359i \(-0.690408\pi\)
−0.563144 + 0.826359i \(0.690408\pi\)
\(194\) −16.6486 −1.19530
\(195\) −29.6055 −2.12010
\(196\) −3.70948 −0.264963
\(197\) 11.5970 0.826252 0.413126 0.910674i \(-0.364437\pi\)
0.413126 + 0.910674i \(0.364437\pi\)
\(198\) −2.66679 −0.189521
\(199\) −16.7890 −1.19014 −0.595069 0.803674i \(-0.702875\pi\)
−0.595069 + 0.803674i \(0.702875\pi\)
\(200\) 21.2105 1.49981
\(201\) −20.3448 −1.43501
\(202\) −0.485679 −0.0341723
\(203\) −12.5977 −0.884186
\(204\) −2.14123 −0.149916
\(205\) −16.3507 −1.14198
\(206\) 11.9948 0.835715
\(207\) 5.76568 0.400743
\(208\) −16.7066 −1.15840
\(209\) −0.395669 −0.0273690
\(210\) −27.9418 −1.92817
\(211\) 25.0401 1.72383 0.861917 0.507049i \(-0.169264\pi\)
0.861917 + 0.507049i \(0.169264\pi\)
\(212\) −5.34081 −0.366808
\(213\) −23.1020 −1.58292
\(214\) 8.70753 0.595234
\(215\) 4.15912 0.283650
\(216\) −5.37026 −0.365400
\(217\) 8.68034 0.589260
\(218\) −22.6261 −1.53243
\(219\) 1.67710 0.113328
\(220\) −4.18037 −0.281840
\(221\) −3.34135 −0.224763
\(222\) −44.3439 −2.97617
\(223\) −1.55714 −0.104274 −0.0521368 0.998640i \(-0.516603\pi\)
−0.0521368 + 0.998640i \(0.516603\pi\)
\(224\) −9.49286 −0.634268
\(225\) 18.9193 1.26128
\(226\) −8.50369 −0.565657
\(227\) 19.2961 1.28072 0.640362 0.768073i \(-0.278784\pi\)
0.640362 + 0.768073i \(0.278784\pi\)
\(228\) −0.847217 −0.0561083
\(229\) 16.6755 1.10195 0.550974 0.834523i \(-0.314256\pi\)
0.550974 + 0.834523i \(0.314256\pi\)
\(230\) 27.0224 1.78180
\(231\) −3.87545 −0.254986
\(232\) 11.9433 0.784116
\(233\) 16.9746 1.11204 0.556022 0.831168i \(-0.312327\pi\)
0.556022 + 0.831168i \(0.312327\pi\)
\(234\) −8.91067 −0.582509
\(235\) −2.00707 −0.130927
\(236\) −5.36178 −0.349022
\(237\) −27.8934 −1.81187
\(238\) −3.15357 −0.204416
\(239\) −2.40411 −0.155509 −0.0777544 0.996973i \(-0.524775\pi\)
−0.0777544 + 0.996973i \(0.524775\pi\)
\(240\) 44.3016 2.85965
\(241\) −16.4944 −1.06250 −0.531249 0.847216i \(-0.678277\pi\)
−0.531249 + 0.847216i \(0.678277\pi\)
\(242\) −1.73352 −0.111435
\(243\) −14.6219 −0.937993
\(244\) −14.5365 −0.930603
\(245\) 15.3498 0.980660
\(246\) −14.5182 −0.925648
\(247\) −1.32207 −0.0841211
\(248\) −8.22943 −0.522569
\(249\) 13.5901 0.861238
\(250\) 52.6203 3.32800
\(251\) 19.0017 1.19938 0.599689 0.800233i \(-0.295291\pi\)
0.599689 + 0.800233i \(0.295291\pi\)
\(252\) −2.81284 −0.177192
\(253\) 3.74793 0.235631
\(254\) −32.6789 −2.05046
\(255\) 8.86036 0.554857
\(256\) 19.0508 1.19067
\(257\) 17.0767 1.06522 0.532608 0.846362i \(-0.321212\pi\)
0.532608 + 0.846362i \(0.321212\pi\)
\(258\) 3.69300 0.229916
\(259\) −21.8438 −1.35731
\(260\) −13.9681 −0.866262
\(261\) 10.6531 0.659413
\(262\) 1.59591 0.0985959
\(263\) −6.92502 −0.427015 −0.213508 0.976941i \(-0.568489\pi\)
−0.213508 + 0.976941i \(0.568489\pi\)
\(264\) 3.67414 0.226128
\(265\) 22.1002 1.35760
\(266\) −1.24777 −0.0765058
\(267\) −14.7959 −0.905497
\(268\) −9.59881 −0.586340
\(269\) −4.89486 −0.298445 −0.149223 0.988804i \(-0.547677\pi\)
−0.149223 + 0.988804i \(0.547677\pi\)
\(270\) −22.4502 −1.36628
\(271\) −8.59353 −0.522020 −0.261010 0.965336i \(-0.584055\pi\)
−0.261010 + 0.965336i \(0.584055\pi\)
\(272\) 4.99997 0.303168
\(273\) −12.9492 −0.783723
\(274\) 10.8102 0.653070
\(275\) 12.2983 0.741616
\(276\) 8.02518 0.483059
\(277\) −30.3758 −1.82511 −0.912553 0.408959i \(-0.865892\pi\)
−0.912553 + 0.408959i \(0.865892\pi\)
\(278\) 9.75728 0.585203
\(279\) −7.34045 −0.439461
\(280\) 13.0491 0.779833
\(281\) −10.8956 −0.649977 −0.324989 0.945718i \(-0.605360\pi\)
−0.324989 + 0.945718i \(0.605360\pi\)
\(282\) −1.78214 −0.106125
\(283\) −8.28555 −0.492525 −0.246262 0.969203i \(-0.579202\pi\)
−0.246262 + 0.969203i \(0.579202\pi\)
\(284\) −10.8997 −0.646776
\(285\) 3.50577 0.207664
\(286\) −5.79231 −0.342506
\(287\) −7.15166 −0.422149
\(288\) 8.02755 0.473028
\(289\) 1.00000 0.0588235
\(290\) 49.9287 2.93192
\(291\) 20.4596 1.19936
\(292\) 0.791267 0.0463054
\(293\) −13.1064 −0.765683 −0.382841 0.923814i \(-0.625054\pi\)
−0.382841 + 0.923814i \(0.625054\pi\)
\(294\) 13.6295 0.794888
\(295\) 22.1869 1.29177
\(296\) 20.7091 1.20369
\(297\) −3.11379 −0.180680
\(298\) −39.1224 −2.26630
\(299\) 12.5231 0.724232
\(300\) 26.3334 1.52036
\(301\) 1.81917 0.104855
\(302\) 12.5776 0.723760
\(303\) 0.596856 0.0342885
\(304\) 1.97834 0.113465
\(305\) 60.1517 3.44428
\(306\) 2.66679 0.152450
\(307\) −3.52390 −0.201120 −0.100560 0.994931i \(-0.532063\pi\)
−0.100560 + 0.994931i \(0.532063\pi\)
\(308\) −1.82846 −0.104186
\(309\) −14.7405 −0.838556
\(310\) −34.4029 −1.95396
\(311\) 6.21116 0.352203 0.176101 0.984372i \(-0.443651\pi\)
0.176101 + 0.984372i \(0.443651\pi\)
\(312\) 12.2766 0.695024
\(313\) −22.4968 −1.27160 −0.635798 0.771855i \(-0.719329\pi\)
−0.635798 + 0.771855i \(0.719329\pi\)
\(314\) −21.8766 −1.23457
\(315\) 11.6395 0.655811
\(316\) −13.1603 −0.740322
\(317\) −4.91928 −0.276294 −0.138147 0.990412i \(-0.544115\pi\)
−0.138147 + 0.990412i \(0.544115\pi\)
\(318\) 19.6234 1.10042
\(319\) 6.92498 0.387725
\(320\) −3.96780 −0.221807
\(321\) −10.7008 −0.597258
\(322\) 11.8194 0.658669
\(323\) 0.395669 0.0220156
\(324\) −11.3060 −0.628111
\(325\) 41.0929 2.27942
\(326\) −39.5869 −2.19252
\(327\) 27.8054 1.53764
\(328\) 6.78016 0.374372
\(329\) −0.877878 −0.0483990
\(330\) 15.3597 0.845521
\(331\) 29.0547 1.59699 0.798496 0.602000i \(-0.205629\pi\)
0.798496 + 0.602000i \(0.205629\pi\)
\(332\) 6.41189 0.351898
\(333\) 18.4720 1.01226
\(334\) −32.7854 −1.79394
\(335\) 39.7197 2.17012
\(336\) 19.3772 1.05711
\(337\) 9.54892 0.520163 0.260081 0.965587i \(-0.416251\pi\)
0.260081 + 0.965587i \(0.416251\pi\)
\(338\) 3.18173 0.173063
\(339\) 10.4503 0.567580
\(340\) 4.18037 0.226712
\(341\) −4.77160 −0.258396
\(342\) 1.05517 0.0570569
\(343\) 19.4481 1.05010
\(344\) −1.72467 −0.0929879
\(345\) −33.2080 −1.78786
\(346\) −12.7878 −0.687478
\(347\) 18.7629 1.00725 0.503624 0.863923i \(-0.332000\pi\)
0.503624 + 0.863923i \(0.332000\pi\)
\(348\) 14.8280 0.794862
\(349\) 5.88659 0.315102 0.157551 0.987511i \(-0.449640\pi\)
0.157551 + 0.987511i \(0.449640\pi\)
\(350\) 38.7836 2.07307
\(351\) −10.4042 −0.555337
\(352\) 5.21824 0.278133
\(353\) 18.7976 1.00049 0.500247 0.865883i \(-0.333243\pi\)
0.500247 + 0.865883i \(0.333243\pi\)
\(354\) 19.7004 1.04707
\(355\) 45.1026 2.39380
\(356\) −6.98081 −0.369982
\(357\) 3.87545 0.205111
\(358\) −4.21150 −0.222585
\(359\) 23.5778 1.24439 0.622193 0.782864i \(-0.286242\pi\)
0.622193 + 0.782864i \(0.286242\pi\)
\(360\) −11.0349 −0.581588
\(361\) −18.8434 −0.991760
\(362\) 13.0660 0.686733
\(363\) 2.13034 0.111814
\(364\) −6.10952 −0.320226
\(365\) −3.27425 −0.171382
\(366\) 53.4104 2.79181
\(367\) 30.9896 1.61764 0.808822 0.588054i \(-0.200106\pi\)
0.808822 + 0.588054i \(0.200106\pi\)
\(368\) −18.7396 −0.976868
\(369\) 6.04774 0.314833
\(370\) 86.5738 4.50076
\(371\) 9.66646 0.501857
\(372\) −10.2171 −0.529730
\(373\) −12.5384 −0.649213 −0.324607 0.945849i \(-0.605232\pi\)
−0.324607 + 0.945849i \(0.605232\pi\)
\(374\) 1.73352 0.0896384
\(375\) −64.6656 −3.33932
\(376\) 0.832275 0.0429213
\(377\) 23.1388 1.19171
\(378\) −9.81956 −0.505064
\(379\) 7.02346 0.360771 0.180385 0.983596i \(-0.442265\pi\)
0.180385 + 0.983596i \(0.442265\pi\)
\(380\) 1.65404 0.0848506
\(381\) 40.1594 2.05743
\(382\) −42.1238 −2.15524
\(383\) 3.15574 0.161251 0.0806254 0.996744i \(-0.474308\pi\)
0.0806254 + 0.996744i \(0.474308\pi\)
\(384\) −25.7564 −1.31438
\(385\) 7.56615 0.385607
\(386\) 27.1243 1.38059
\(387\) −1.53836 −0.0781994
\(388\) 9.65297 0.490055
\(389\) 19.4912 0.988241 0.494121 0.869393i \(-0.335490\pi\)
0.494121 + 0.869393i \(0.335490\pi\)
\(390\) 51.3219 2.59879
\(391\) −3.74793 −0.189541
\(392\) −6.36511 −0.321486
\(393\) −1.96123 −0.0989311
\(394\) −20.1037 −1.01281
\(395\) 54.4569 2.74002
\(396\) 1.54622 0.0777006
\(397\) 4.50829 0.226264 0.113132 0.993580i \(-0.463912\pi\)
0.113132 + 0.993580i \(0.463912\pi\)
\(398\) 29.1041 1.45886
\(399\) 1.53340 0.0767659
\(400\) −61.4912 −3.07456
\(401\) −19.4741 −0.972492 −0.486246 0.873822i \(-0.661634\pi\)
−0.486246 + 0.873822i \(0.661634\pi\)
\(402\) 35.2683 1.75902
\(403\) −15.9436 −0.794205
\(404\) 0.281600 0.0140101
\(405\) 46.7840 2.32472
\(406\) 21.8385 1.08382
\(407\) 12.0076 0.595192
\(408\) −3.67414 −0.181897
\(409\) −37.4564 −1.85210 −0.926051 0.377398i \(-0.876819\pi\)
−0.926051 + 0.377398i \(0.876819\pi\)
\(410\) 28.3443 1.39983
\(411\) −13.2848 −0.655290
\(412\) −6.95464 −0.342631
\(413\) 9.70440 0.477523
\(414\) −9.99496 −0.491225
\(415\) −26.5323 −1.30242
\(416\) 17.4359 0.854867
\(417\) −11.9908 −0.587192
\(418\) 0.685902 0.0335486
\(419\) −5.37835 −0.262750 −0.131375 0.991333i \(-0.541939\pi\)
−0.131375 + 0.991333i \(0.541939\pi\)
\(420\) 16.2008 0.790520
\(421\) −10.7539 −0.524112 −0.262056 0.965053i \(-0.584400\pi\)
−0.262056 + 0.965053i \(0.584400\pi\)
\(422\) −43.4077 −2.11305
\(423\) 0.742370 0.0360952
\(424\) −9.16432 −0.445059
\(425\) −12.2983 −0.596555
\(426\) 40.0479 1.94033
\(427\) 26.3099 1.27323
\(428\) −5.04868 −0.244037
\(429\) 7.11821 0.343671
\(430\) −7.20994 −0.347694
\(431\) 31.0868 1.49740 0.748700 0.662909i \(-0.230678\pi\)
0.748700 + 0.662909i \(0.230678\pi\)
\(432\) 15.5689 0.749057
\(433\) 24.9861 1.20075 0.600377 0.799717i \(-0.295017\pi\)
0.600377 + 0.799717i \(0.295017\pi\)
\(434\) −15.0476 −0.722307
\(435\) −61.3578 −2.94188
\(436\) 13.1187 0.628274
\(437\) −1.48294 −0.0709387
\(438\) −2.90730 −0.138916
\(439\) −14.7450 −0.703742 −0.351871 0.936049i \(-0.614454\pi\)
−0.351871 + 0.936049i \(0.614454\pi\)
\(440\) −7.17311 −0.341965
\(441\) −5.67752 −0.270358
\(442\) 5.79231 0.275512
\(443\) 7.33150 0.348330 0.174165 0.984716i \(-0.444277\pi\)
0.174165 + 0.984716i \(0.444277\pi\)
\(444\) 25.7109 1.22019
\(445\) 28.8865 1.36935
\(446\) 2.69933 0.127817
\(447\) 48.0778 2.27400
\(448\) −1.73548 −0.0819939
\(449\) 8.64688 0.408071 0.204036 0.978963i \(-0.434594\pi\)
0.204036 + 0.978963i \(0.434594\pi\)
\(450\) −32.7970 −1.54607
\(451\) 3.93128 0.185117
\(452\) 4.93049 0.231911
\(453\) −15.4567 −0.726220
\(454\) −33.4502 −1.56989
\(455\) 25.2811 1.18520
\(456\) −1.45374 −0.0680777
\(457\) 1.01564 0.0475096 0.0237548 0.999718i \(-0.492438\pi\)
0.0237548 + 0.999718i \(0.492438\pi\)
\(458\) −28.9074 −1.35075
\(459\) 3.11379 0.145339
\(460\) −15.6678 −0.730513
\(461\) −18.7447 −0.873027 −0.436514 0.899698i \(-0.643787\pi\)
−0.436514 + 0.899698i \(0.643787\pi\)
\(462\) 6.71820 0.312559
\(463\) −3.26052 −0.151529 −0.0757646 0.997126i \(-0.524140\pi\)
−0.0757646 + 0.997126i \(0.524140\pi\)
\(464\) −34.6247 −1.60741
\(465\) 42.2781 1.96060
\(466\) −29.4259 −1.36313
\(467\) −23.2079 −1.07393 −0.536967 0.843603i \(-0.680430\pi\)
−0.536967 + 0.843603i \(0.680430\pi\)
\(468\) 5.16646 0.238820
\(469\) 17.3731 0.802215
\(470\) 3.47931 0.160489
\(471\) 26.8844 1.23877
\(472\) −9.20029 −0.423478
\(473\) −1.00000 −0.0459800
\(474\) 48.3538 2.22097
\(475\) −4.86606 −0.223270
\(476\) 1.82846 0.0838074
\(477\) −8.17435 −0.374278
\(478\) 4.16758 0.190621
\(479\) −20.1309 −0.919803 −0.459902 0.887970i \(-0.652115\pi\)
−0.459902 + 0.887970i \(0.652115\pi\)
\(480\) −46.2355 −2.11035
\(481\) 40.1214 1.82938
\(482\) 28.5935 1.30240
\(483\) −14.5249 −0.660908
\(484\) 1.00511 0.0456867
\(485\) −39.9438 −1.81376
\(486\) 25.3474 1.14978
\(487\) 16.0837 0.728822 0.364411 0.931238i \(-0.381270\pi\)
0.364411 + 0.931238i \(0.381270\pi\)
\(488\) −24.9432 −1.12913
\(489\) 48.6487 2.19997
\(490\) −26.6092 −1.20208
\(491\) 24.4966 1.10552 0.552759 0.833341i \(-0.313575\pi\)
0.552759 + 0.833341i \(0.313575\pi\)
\(492\) 8.41776 0.379502
\(493\) −6.92498 −0.311886
\(494\) 2.29184 0.103115
\(495\) −6.39824 −0.287580
\(496\) 23.8579 1.07125
\(497\) 19.7276 0.884902
\(498\) −23.5588 −1.05569
\(499\) −10.6609 −0.477249 −0.238625 0.971112i \(-0.576697\pi\)
−0.238625 + 0.971112i \(0.576697\pi\)
\(500\) −30.5096 −1.36443
\(501\) 40.2903 1.80004
\(502\) −32.9400 −1.47018
\(503\) 3.94210 0.175770 0.0878849 0.996131i \(-0.471989\pi\)
0.0878849 + 0.996131i \(0.471989\pi\)
\(504\) −4.82656 −0.214992
\(505\) −1.16526 −0.0518532
\(506\) −6.49714 −0.288833
\(507\) −3.91006 −0.173652
\(508\) 18.9474 0.840657
\(509\) 24.0289 1.06506 0.532531 0.846410i \(-0.321241\pi\)
0.532531 + 0.846410i \(0.321241\pi\)
\(510\) −15.3597 −0.680137
\(511\) −1.43213 −0.0633538
\(512\) −8.84446 −0.390874
\(513\) 1.23203 0.0543955
\(514\) −29.6029 −1.30573
\(515\) 28.7782 1.26812
\(516\) −2.14123 −0.0942622
\(517\) 0.482571 0.0212235
\(518\) 37.8667 1.66377
\(519\) 15.7151 0.689815
\(520\) −23.9678 −1.05106
\(521\) −2.06632 −0.0905270 −0.0452635 0.998975i \(-0.514413\pi\)
−0.0452635 + 0.998975i \(0.514413\pi\)
\(522\) −18.4675 −0.808300
\(523\) −40.6133 −1.77589 −0.887947 0.459945i \(-0.847869\pi\)
−0.887947 + 0.459945i \(0.847869\pi\)
\(524\) −0.925321 −0.0404228
\(525\) −47.6615 −2.08012
\(526\) 12.0047 0.523430
\(527\) 4.77160 0.207854
\(528\) −10.6517 −0.463554
\(529\) −8.95299 −0.389260
\(530\) −38.3112 −1.66413
\(531\) −8.20644 −0.356129
\(532\) 0.723466 0.0313662
\(533\) 13.1358 0.568973
\(534\) 25.6491 1.10995
\(535\) 20.8914 0.903212
\(536\) −16.4706 −0.711423
\(537\) 5.17555 0.223341
\(538\) 8.48537 0.365830
\(539\) −3.69062 −0.158966
\(540\) 13.0168 0.560153
\(541\) 26.4953 1.13912 0.569561 0.821949i \(-0.307113\pi\)
0.569561 + 0.821949i \(0.307113\pi\)
\(542\) 14.8971 0.639885
\(543\) −16.0569 −0.689068
\(544\) −5.21824 −0.223730
\(545\) −54.2851 −2.32532
\(546\) 22.4478 0.960678
\(547\) −3.85418 −0.164793 −0.0823965 0.996600i \(-0.526257\pi\)
−0.0823965 + 0.996600i \(0.526257\pi\)
\(548\) −6.26784 −0.267749
\(549\) −22.2487 −0.949553
\(550\) −21.3194 −0.909063
\(551\) −2.74000 −0.116728
\(552\) 13.7704 0.586108
\(553\) 23.8190 1.01289
\(554\) 52.6572 2.23719
\(555\) −106.391 −4.51606
\(556\) −5.65733 −0.239924
\(557\) 17.8754 0.757403 0.378702 0.925519i \(-0.376371\pi\)
0.378702 + 0.925519i \(0.376371\pi\)
\(558\) 12.7249 0.538686
\(559\) −3.34135 −0.141324
\(560\) −37.8305 −1.59863
\(561\) −2.13034 −0.0899432
\(562\) 18.8878 0.796734
\(563\) 7.87441 0.331867 0.165933 0.986137i \(-0.446936\pi\)
0.165933 + 0.986137i \(0.446936\pi\)
\(564\) 1.03329 0.0435095
\(565\) −20.4023 −0.858331
\(566\) 14.3632 0.603731
\(567\) 20.4630 0.859364
\(568\) −18.7028 −0.784751
\(569\) −27.4812 −1.15207 −0.576036 0.817424i \(-0.695401\pi\)
−0.576036 + 0.817424i \(0.695401\pi\)
\(570\) −6.07734 −0.254552
\(571\) −44.0173 −1.84207 −0.921034 0.389482i \(-0.872654\pi\)
−0.921034 + 0.389482i \(0.872654\pi\)
\(572\) 3.35841 0.140422
\(573\) 51.7663 2.16257
\(574\) 12.3976 0.517465
\(575\) 46.0932 1.92222
\(576\) 1.46760 0.0611498
\(577\) 12.4992 0.520347 0.260174 0.965562i \(-0.416220\pi\)
0.260174 + 0.965562i \(0.416220\pi\)
\(578\) −1.73352 −0.0721051
\(579\) −33.3333 −1.38528
\(580\) −28.9490 −1.20204
\(581\) −11.6050 −0.481458
\(582\) −35.4673 −1.47016
\(583\) −5.31367 −0.220070
\(584\) 1.35774 0.0561836
\(585\) −21.3787 −0.883902
\(586\) 22.7202 0.938564
\(587\) 39.4789 1.62947 0.814735 0.579834i \(-0.196882\pi\)
0.814735 + 0.579834i \(0.196882\pi\)
\(588\) −7.90246 −0.325892
\(589\) 1.88797 0.0777926
\(590\) −38.4616 −1.58344
\(591\) 24.7056 1.01625
\(592\) −60.0375 −2.46752
\(593\) 37.1415 1.52522 0.762610 0.646858i \(-0.223917\pi\)
0.762610 + 0.646858i \(0.223917\pi\)
\(594\) 5.39783 0.221476
\(595\) −7.56615 −0.310182
\(596\) 22.6834 0.929148
\(597\) −35.7663 −1.46382
\(598\) −21.7092 −0.887754
\(599\) 15.8187 0.646334 0.323167 0.946342i \(-0.395253\pi\)
0.323167 + 0.946342i \(0.395253\pi\)
\(600\) 45.1857 1.84470
\(601\) 39.6107 1.61575 0.807877 0.589351i \(-0.200616\pi\)
0.807877 + 0.589351i \(0.200616\pi\)
\(602\) −3.15357 −0.128530
\(603\) −14.6914 −0.598280
\(604\) −7.29257 −0.296731
\(605\) −4.15912 −0.169092
\(606\) −1.03466 −0.0420304
\(607\) 14.5160 0.589188 0.294594 0.955622i \(-0.404816\pi\)
0.294594 + 0.955622i \(0.404816\pi\)
\(608\) −2.06470 −0.0837345
\(609\) −26.8375 −1.08751
\(610\) −104.275 −4.22195
\(611\) 1.61244 0.0652322
\(612\) −1.54622 −0.0625023
\(613\) −32.4613 −1.31110 −0.655550 0.755152i \(-0.727563\pi\)
−0.655550 + 0.755152i \(0.727563\pi\)
\(614\) 6.10878 0.246530
\(615\) −34.8326 −1.40458
\(616\) −3.13746 −0.126412
\(617\) −10.0335 −0.403935 −0.201967 0.979392i \(-0.564734\pi\)
−0.201967 + 0.979392i \(0.564734\pi\)
\(618\) 25.5530 1.02789
\(619\) 14.0314 0.563970 0.281985 0.959419i \(-0.409007\pi\)
0.281985 + 0.959419i \(0.409007\pi\)
\(620\) 19.9470 0.801092
\(621\) −11.6703 −0.468312
\(622\) −10.7672 −0.431725
\(623\) 12.6347 0.506200
\(624\) −35.5909 −1.42478
\(625\) 64.7567 2.59027
\(626\) 38.9988 1.55871
\(627\) −0.842911 −0.0336626
\(628\) 12.6842 0.506155
\(629\) −12.0076 −0.478773
\(630\) −20.1773 −0.803884
\(631\) 30.5604 1.21659 0.608294 0.793712i \(-0.291854\pi\)
0.608294 + 0.793712i \(0.291854\pi\)
\(632\) −22.5817 −0.898253
\(633\) 53.3441 2.12024
\(634\) 8.52769 0.338678
\(635\) −78.4042 −3.11138
\(636\) −11.3778 −0.451158
\(637\) −12.3317 −0.488598
\(638\) −12.0046 −0.475268
\(639\) −16.6824 −0.659946
\(640\) 50.2849 1.98768
\(641\) −37.1632 −1.46786 −0.733929 0.679226i \(-0.762315\pi\)
−0.733929 + 0.679226i \(0.762315\pi\)
\(642\) 18.5500 0.732111
\(643\) 48.4321 1.90997 0.954987 0.296648i \(-0.0958689\pi\)
0.954987 + 0.296648i \(0.0958689\pi\)
\(644\) −6.85296 −0.270044
\(645\) 8.86036 0.348876
\(646\) −0.685902 −0.0269865
\(647\) −6.47105 −0.254403 −0.127202 0.991877i \(-0.540600\pi\)
−0.127202 + 0.991877i \(0.540600\pi\)
\(648\) −19.4000 −0.762104
\(649\) −5.33453 −0.209398
\(650\) −71.2355 −2.79409
\(651\) 18.4921 0.724763
\(652\) 22.9527 0.898898
\(653\) −6.13116 −0.239931 −0.119965 0.992778i \(-0.538278\pi\)
−0.119965 + 0.992778i \(0.538278\pi\)
\(654\) −48.2013 −1.88482
\(655\) 3.82896 0.149610
\(656\) −19.6563 −0.767449
\(657\) 1.21107 0.0472483
\(658\) 1.52182 0.0593269
\(659\) 16.9276 0.659407 0.329703 0.944085i \(-0.393051\pi\)
0.329703 + 0.944085i \(0.393051\pi\)
\(660\) −8.90562 −0.346651
\(661\) −8.40237 −0.326814 −0.163407 0.986559i \(-0.552248\pi\)
−0.163407 + 0.986559i \(0.552248\pi\)
\(662\) −50.3671 −1.95757
\(663\) −7.11821 −0.276448
\(664\) 11.0022 0.426968
\(665\) −2.99369 −0.116090
\(666\) −32.0216 −1.24081
\(667\) 25.9544 1.00496
\(668\) 19.0092 0.735487
\(669\) −3.31723 −0.128252
\(670\) −68.8551 −2.66010
\(671\) −14.4626 −0.558323
\(672\) −20.2231 −0.780121
\(673\) −7.19800 −0.277462 −0.138731 0.990330i \(-0.544302\pi\)
−0.138731 + 0.990330i \(0.544302\pi\)
\(674\) −16.5533 −0.637609
\(675\) −38.2943 −1.47395
\(676\) −1.84479 −0.0709534
\(677\) 4.59262 0.176509 0.0882543 0.996098i \(-0.471871\pi\)
0.0882543 + 0.996098i \(0.471871\pi\)
\(678\) −18.1158 −0.695732
\(679\) −17.4711 −0.670480
\(680\) 7.17311 0.275076
\(681\) 41.1072 1.57523
\(682\) 8.27168 0.316739
\(683\) 20.3470 0.778557 0.389278 0.921120i \(-0.372724\pi\)
0.389278 + 0.921120i \(0.372724\pi\)
\(684\) −0.611792 −0.0233925
\(685\) 25.9362 0.990972
\(686\) −33.7137 −1.28719
\(687\) 35.5245 1.35534
\(688\) 4.99997 0.190622
\(689\) −17.7548 −0.676404
\(690\) 57.5670 2.19154
\(691\) −40.6621 −1.54686 −0.773429 0.633883i \(-0.781460\pi\)
−0.773429 + 0.633883i \(0.781460\pi\)
\(692\) 7.41446 0.281855
\(693\) −2.79854 −0.106308
\(694\) −32.5260 −1.23467
\(695\) 23.4099 0.887990
\(696\) 25.4433 0.964427
\(697\) −3.93128 −0.148908
\(698\) −10.2045 −0.386248
\(699\) 36.1618 1.36776
\(700\) −22.4870 −0.849928
\(701\) −3.56567 −0.134673 −0.0673367 0.997730i \(-0.521450\pi\)
−0.0673367 + 0.997730i \(0.521450\pi\)
\(702\) 18.0360 0.680725
\(703\) −4.75102 −0.179188
\(704\) 0.953998 0.0359552
\(705\) −4.27575 −0.161034
\(706\) −32.5861 −1.22639
\(707\) −0.509674 −0.0191683
\(708\) −11.4224 −0.429281
\(709\) 3.29202 0.123634 0.0618172 0.998087i \(-0.480310\pi\)
0.0618172 + 0.998087i \(0.480310\pi\)
\(710\) −78.1865 −2.93429
\(711\) −20.1423 −0.755397
\(712\) −11.9784 −0.448910
\(713\) −17.8836 −0.669747
\(714\) −6.71820 −0.251422
\(715\) −13.8971 −0.519721
\(716\) 2.44185 0.0912563
\(717\) −5.12158 −0.191269
\(718\) −40.8726 −1.52535
\(719\) 22.9828 0.857115 0.428558 0.903514i \(-0.359022\pi\)
0.428558 + 0.903514i \(0.359022\pi\)
\(720\) 31.9910 1.19224
\(721\) 12.5874 0.468778
\(722\) 32.6656 1.21569
\(723\) −35.1387 −1.30682
\(724\) −7.57574 −0.281550
\(725\) 85.1655 3.16297
\(726\) −3.69300 −0.137060
\(727\) 25.2996 0.938311 0.469155 0.883116i \(-0.344558\pi\)
0.469155 + 0.883116i \(0.344558\pi\)
\(728\) −10.4834 −0.388539
\(729\) 2.59599 0.0961479
\(730\) 5.67599 0.210078
\(731\) 1.00000 0.0369863
\(732\) −30.9677 −1.14460
\(733\) 9.34073 0.345008 0.172504 0.985009i \(-0.444814\pi\)
0.172504 + 0.985009i \(0.444814\pi\)
\(734\) −53.7212 −1.98289
\(735\) 32.7003 1.20617
\(736\) 19.5576 0.720904
\(737\) −9.55002 −0.351780
\(738\) −10.4839 −0.385918
\(739\) −15.6028 −0.573957 −0.286978 0.957937i \(-0.592651\pi\)
−0.286978 + 0.957937i \(0.592651\pi\)
\(740\) −50.1960 −1.84524
\(741\) −2.81646 −0.103465
\(742\) −16.7570 −0.615170
\(743\) −2.48960 −0.0913346 −0.0456673 0.998957i \(-0.514541\pi\)
−0.0456673 + 0.998957i \(0.514541\pi\)
\(744\) −17.5315 −0.642736
\(745\) −93.8635 −3.43889
\(746\) 21.7356 0.795797
\(747\) 9.81368 0.359064
\(748\) −1.00511 −0.0367504
\(749\) 9.13772 0.333885
\(750\) 112.099 4.09329
\(751\) 16.8503 0.614877 0.307438 0.951568i \(-0.400528\pi\)
0.307438 + 0.951568i \(0.400528\pi\)
\(752\) −2.41284 −0.0879873
\(753\) 40.4802 1.47518
\(754\) −40.1116 −1.46078
\(755\) 30.1766 1.09824
\(756\) 5.69344 0.207069
\(757\) 25.7264 0.935042 0.467521 0.883982i \(-0.345147\pi\)
0.467521 + 0.883982i \(0.345147\pi\)
\(758\) −12.1753 −0.442228
\(759\) 7.98439 0.289815
\(760\) 2.83818 0.102952
\(761\) 8.56334 0.310421 0.155210 0.987881i \(-0.450394\pi\)
0.155210 + 0.987881i \(0.450394\pi\)
\(762\) −69.6173 −2.52197
\(763\) −23.7439 −0.859587
\(764\) 24.4236 0.883616
\(765\) 6.39824 0.231329
\(766\) −5.47055 −0.197659
\(767\) −17.8245 −0.643605
\(768\) 40.5847 1.46447
\(769\) 12.4303 0.448248 0.224124 0.974561i \(-0.428048\pi\)
0.224124 + 0.974561i \(0.428048\pi\)
\(770\) −13.1161 −0.472672
\(771\) 36.3793 1.31017
\(772\) −15.7268 −0.566021
\(773\) 33.4064 1.20154 0.600772 0.799421i \(-0.294860\pi\)
0.600772 + 0.799421i \(0.294860\pi\)
\(774\) 2.66679 0.0958558
\(775\) −58.6826 −2.10794
\(776\) 16.5636 0.594597
\(777\) −46.5347 −1.66942
\(778\) −33.7884 −1.21137
\(779\) −1.55549 −0.0557311
\(780\) −29.7568 −1.06546
\(781\) −10.8443 −0.388038
\(782\) 6.49714 0.232337
\(783\) −21.5629 −0.770596
\(784\) 18.4530 0.659037
\(785\) −52.4870 −1.87334
\(786\) 3.39985 0.121268
\(787\) −6.95976 −0.248089 −0.124044 0.992277i \(-0.539587\pi\)
−0.124044 + 0.992277i \(0.539587\pi\)
\(788\) 11.6562 0.415236
\(789\) −14.7527 −0.525209
\(790\) −94.4024 −3.35869
\(791\) −8.92381 −0.317294
\(792\) 2.65317 0.0942762
\(793\) −48.3245 −1.71606
\(794\) −7.81523 −0.277352
\(795\) 47.0810 1.66979
\(796\) −16.8747 −0.598109
\(797\) 21.1866 0.750469 0.375234 0.926930i \(-0.377562\pi\)
0.375234 + 0.926930i \(0.377562\pi\)
\(798\) −2.65818 −0.0940987
\(799\) −0.482571 −0.0170721
\(800\) 64.1755 2.26895
\(801\) −10.6844 −0.377516
\(802\) 33.7589 1.19207
\(803\) 0.787245 0.0277813
\(804\) −20.4488 −0.721172
\(805\) 28.3574 0.999468
\(806\) 27.6385 0.973526
\(807\) −10.4277 −0.367074
\(808\) 0.483198 0.0169989
\(809\) −52.0591 −1.83030 −0.915151 0.403111i \(-0.867929\pi\)
−0.915151 + 0.403111i \(0.867929\pi\)
\(810\) −81.1012 −2.84961
\(811\) 18.3140 0.643092 0.321546 0.946894i \(-0.395798\pi\)
0.321546 + 0.946894i \(0.395798\pi\)
\(812\) −12.6621 −0.444352
\(813\) −18.3072 −0.642060
\(814\) −20.8154 −0.729579
\(815\) −94.9780 −3.32694
\(816\) 10.6517 0.372883
\(817\) 0.395669 0.0138427
\(818\) 64.9317 2.27028
\(819\) −9.35090 −0.326747
\(820\) −16.4342 −0.573907
\(821\) −21.6929 −0.757087 −0.378543 0.925584i \(-0.623575\pi\)
−0.378543 + 0.925584i \(0.623575\pi\)
\(822\) 23.0295 0.803246
\(823\) −34.8886 −1.21614 −0.608070 0.793884i \(-0.708056\pi\)
−0.608070 + 0.793884i \(0.708056\pi\)
\(824\) −11.9335 −0.415723
\(825\) 26.1996 0.912153
\(826\) −16.8228 −0.585341
\(827\) 18.4110 0.640213 0.320107 0.947382i \(-0.396281\pi\)
0.320107 + 0.947382i \(0.396281\pi\)
\(828\) 5.79514 0.201395
\(829\) 3.47139 0.120566 0.0602831 0.998181i \(-0.480800\pi\)
0.0602831 + 0.998181i \(0.480800\pi\)
\(830\) 45.9944 1.59649
\(831\) −64.7109 −2.24480
\(832\) 3.18764 0.110511
\(833\) 3.69062 0.127873
\(834\) 20.7864 0.719773
\(835\) −78.6597 −2.72213
\(836\) −0.397690 −0.0137544
\(837\) 14.8577 0.513559
\(838\) 9.32350 0.322075
\(839\) 32.6769 1.12813 0.564066 0.825729i \(-0.309236\pi\)
0.564066 + 0.825729i \(0.309236\pi\)
\(840\) 27.7991 0.959159
\(841\) 18.9554 0.653634
\(842\) 18.6421 0.642450
\(843\) −23.2114 −0.799442
\(844\) 25.1681 0.866320
\(845\) 7.63370 0.262607
\(846\) −1.28692 −0.0442451
\(847\) −1.81917 −0.0625074
\(848\) 26.5682 0.912355
\(849\) −17.6511 −0.605783
\(850\) 21.3194 0.731250
\(851\) 45.0035 1.54270
\(852\) −23.2200 −0.795505
\(853\) 14.5448 0.498004 0.249002 0.968503i \(-0.419897\pi\)
0.249002 + 0.968503i \(0.419897\pi\)
\(854\) −45.6089 −1.56070
\(855\) 2.53159 0.0865784
\(856\) −8.66305 −0.296097
\(857\) −57.2896 −1.95698 −0.978488 0.206303i \(-0.933857\pi\)
−0.978488 + 0.206303i \(0.933857\pi\)
\(858\) −12.3396 −0.421267
\(859\) 23.2202 0.792263 0.396131 0.918194i \(-0.370352\pi\)
0.396131 + 0.918194i \(0.370352\pi\)
\(860\) 4.18037 0.142549
\(861\) −15.2355 −0.519224
\(862\) −53.8898 −1.83549
\(863\) 41.9492 1.42797 0.713983 0.700163i \(-0.246889\pi\)
0.713983 + 0.700163i \(0.246889\pi\)
\(864\) −16.2485 −0.552785
\(865\) −30.6809 −1.04318
\(866\) −43.3139 −1.47187
\(867\) 2.13034 0.0723503
\(868\) 8.72468 0.296135
\(869\) −13.0934 −0.444162
\(870\) 106.365 3.60612
\(871\) −31.9099 −1.08123
\(872\) 22.5105 0.762302
\(873\) 14.7743 0.500034
\(874\) 2.57072 0.0869558
\(875\) 55.2200 1.86678
\(876\) 1.68567 0.0569535
\(877\) 0.187881 0.00634430 0.00317215 0.999995i \(-0.498990\pi\)
0.00317215 + 0.999995i \(0.498990\pi\)
\(878\) 25.5609 0.862638
\(879\) −27.9211 −0.941755
\(880\) 20.7955 0.701016
\(881\) −17.9792 −0.605736 −0.302868 0.953033i \(-0.597944\pi\)
−0.302868 + 0.953033i \(0.597944\pi\)
\(882\) 9.84212 0.331402
\(883\) 12.2957 0.413783 0.206891 0.978364i \(-0.433665\pi\)
0.206891 + 0.978364i \(0.433665\pi\)
\(884\) −3.35841 −0.112956
\(885\) 47.2658 1.58882
\(886\) −12.7093 −0.426978
\(887\) 15.8416 0.531909 0.265954 0.963986i \(-0.414313\pi\)
0.265954 + 0.963986i \(0.414313\pi\)
\(888\) 44.1174 1.48048
\(889\) −34.2934 −1.15016
\(890\) −50.0755 −1.67853
\(891\) −11.2485 −0.376840
\(892\) −1.56509 −0.0524031
\(893\) −0.190938 −0.00638951
\(894\) −83.3441 −2.78744
\(895\) −10.1043 −0.337751
\(896\) 21.9942 0.734776
\(897\) 26.6786 0.890772
\(898\) −14.9896 −0.500209
\(899\) −33.0432 −1.10205
\(900\) 19.0159 0.633863
\(901\) 5.31367 0.177024
\(902\) −6.81497 −0.226914
\(903\) 3.87545 0.128967
\(904\) 8.46025 0.281384
\(905\) 31.3483 1.04205
\(906\) 26.7946 0.890192
\(907\) −0.113375 −0.00376457 −0.00188228 0.999998i \(-0.500599\pi\)
−0.00188228 + 0.999998i \(0.500599\pi\)
\(908\) 19.3946 0.643633
\(909\) 0.431001 0.0142954
\(910\) −43.8254 −1.45280
\(911\) 50.7226 1.68051 0.840257 0.542188i \(-0.182404\pi\)
0.840257 + 0.542188i \(0.182404\pi\)
\(912\) 4.21453 0.139557
\(913\) 6.37930 0.211124
\(914\) −1.76064 −0.0582367
\(915\) 128.144 4.23631
\(916\) 16.7607 0.553788
\(917\) 1.67476 0.0553054
\(918\) −5.39783 −0.178155
\(919\) 1.42520 0.0470129 0.0235064 0.999724i \(-0.492517\pi\)
0.0235064 + 0.999724i \(0.492517\pi\)
\(920\) −26.8844 −0.886351
\(921\) −7.50713 −0.247368
\(922\) 32.4944 1.07015
\(923\) −36.2344 −1.19267
\(924\) −3.89525 −0.128144
\(925\) 147.673 4.85544
\(926\) 5.65219 0.185743
\(927\) −10.6444 −0.349608
\(928\) 36.1362 1.18623
\(929\) −6.45400 −0.211749 −0.105874 0.994380i \(-0.533764\pi\)
−0.105874 + 0.994380i \(0.533764\pi\)
\(930\) −73.2901 −2.40328
\(931\) 1.46027 0.0478583
\(932\) 17.0613 0.558862
\(933\) 13.2319 0.433193
\(934\) 40.2315 1.31641
\(935\) 4.15912 0.136018
\(936\) 8.86515 0.289766
\(937\) −36.7454 −1.20042 −0.600210 0.799843i \(-0.704916\pi\)
−0.600210 + 0.799843i \(0.704916\pi\)
\(938\) −30.1167 −0.983345
\(939\) −47.9260 −1.56401
\(940\) −2.01733 −0.0657979
\(941\) −51.8476 −1.69018 −0.845092 0.534622i \(-0.820454\pi\)
−0.845092 + 0.534622i \(0.820454\pi\)
\(942\) −46.6047 −1.51846
\(943\) 14.7342 0.479811
\(944\) 26.6725 0.868116
\(945\) −23.5594 −0.766387
\(946\) 1.73352 0.0563618
\(947\) 19.7023 0.640239 0.320120 0.947377i \(-0.396277\pi\)
0.320120 + 0.947377i \(0.396277\pi\)
\(948\) −28.0359 −0.910562
\(949\) 2.63046 0.0853882
\(950\) 8.43543 0.273682
\(951\) −10.4798 −0.339829
\(952\) 3.13746 0.101686
\(953\) 11.1653 0.361681 0.180841 0.983512i \(-0.442118\pi\)
0.180841 + 0.983512i \(0.442118\pi\)
\(954\) 14.1704 0.458785
\(955\) −101.065 −3.27037
\(956\) −2.41639 −0.0781516
\(957\) 14.7526 0.476884
\(958\) 34.8974 1.12748
\(959\) 11.3443 0.366327
\(960\) −8.45277 −0.272812
\(961\) −8.23186 −0.265544
\(962\) −69.5514 −2.24243
\(963\) −7.72723 −0.249006
\(964\) −16.5787 −0.533963
\(965\) 65.0773 2.09491
\(966\) 25.1794 0.810133
\(967\) 47.2611 1.51982 0.759908 0.650031i \(-0.225244\pi\)
0.759908 + 0.650031i \(0.225244\pi\)
\(968\) 1.72467 0.0554330
\(969\) 0.842911 0.0270782
\(970\) 69.2436 2.22328
\(971\) −53.2219 −1.70797 −0.853986 0.520295i \(-0.825822\pi\)
−0.853986 + 0.520295i \(0.825822\pi\)
\(972\) −14.6966 −0.471392
\(973\) 10.2393 0.328258
\(974\) −27.8815 −0.893381
\(975\) 87.5419 2.80359
\(976\) 72.3126 2.31467
\(977\) 39.1537 1.25264 0.626319 0.779567i \(-0.284561\pi\)
0.626319 + 0.779567i \(0.284561\pi\)
\(978\) −84.3337 −2.69669
\(979\) −6.94533 −0.221974
\(980\) 15.4282 0.492835
\(981\) 20.0788 0.641067
\(982\) −42.4655 −1.35513
\(983\) 20.0267 0.638752 0.319376 0.947628i \(-0.396527\pi\)
0.319376 + 0.947628i \(0.396527\pi\)
\(984\) 14.4441 0.460460
\(985\) −48.2334 −1.53684
\(986\) 12.0046 0.382305
\(987\) −1.87018 −0.0595286
\(988\) −1.32882 −0.0422754
\(989\) −3.74793 −0.119177
\(990\) 11.0915 0.352511
\(991\) 17.0975 0.543120 0.271560 0.962421i \(-0.412460\pi\)
0.271560 + 0.962421i \(0.412460\pi\)
\(992\) −24.8993 −0.790555
\(993\) 61.8965 1.96423
\(994\) −34.1982 −1.08470
\(995\) 69.8274 2.21368
\(996\) 13.6595 0.432819
\(997\) −14.4961 −0.459097 −0.229549 0.973297i \(-0.573725\pi\)
−0.229549 + 0.973297i \(0.573725\pi\)
\(998\) 18.4810 0.585006
\(999\) −37.3890 −1.18294
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 \(a_p\))