Properties

Label 6003.2.a.t.1.3
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24483 q^{2} +3.03928 q^{4} +2.70888 q^{5} -1.81542 q^{7} -2.33301 q^{8} +O(q^{10})\) \(q-2.24483 q^{2} +3.03928 q^{4} +2.70888 q^{5} -1.81542 q^{7} -2.33301 q^{8} -6.08099 q^{10} +1.28860 q^{11} +4.53826 q^{13} +4.07531 q^{14} -0.841340 q^{16} -4.48595 q^{17} +2.67238 q^{19} +8.23305 q^{20} -2.89270 q^{22} +1.00000 q^{23} +2.33804 q^{25} -10.1876 q^{26} -5.51756 q^{28} +1.00000 q^{29} -5.79860 q^{31} +6.55469 q^{32} +10.0702 q^{34} -4.91775 q^{35} -5.91943 q^{37} -5.99906 q^{38} -6.31985 q^{40} -7.82902 q^{41} -5.28362 q^{43} +3.91642 q^{44} -2.24483 q^{46} +2.52885 q^{47} -3.70427 q^{49} -5.24851 q^{50} +13.7930 q^{52} +7.14230 q^{53} +3.49067 q^{55} +4.23538 q^{56} -2.24483 q^{58} -7.87478 q^{59} +0.0192849 q^{61} +13.0169 q^{62} -13.0315 q^{64} +12.2936 q^{65} -15.5222 q^{67} -13.6340 q^{68} +11.0395 q^{70} +8.18804 q^{71} -16.8537 q^{73} +13.2881 q^{74} +8.12212 q^{76} -2.33935 q^{77} +2.32730 q^{79} -2.27909 q^{80} +17.5749 q^{82} +8.65460 q^{83} -12.1519 q^{85} +11.8608 q^{86} -3.00632 q^{88} +17.6714 q^{89} -8.23883 q^{91} +3.03928 q^{92} -5.67686 q^{94} +7.23917 q^{95} -7.50809 q^{97} +8.31546 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24483 −1.58734 −0.793669 0.608350i \(-0.791832\pi\)
−0.793669 + 0.608350i \(0.791832\pi\)
\(3\) 0 0
\(4\) 3.03928 1.51964
\(5\) 2.70888 1.21145 0.605724 0.795675i \(-0.292883\pi\)
0.605724 + 0.795675i \(0.292883\pi\)
\(6\) 0 0
\(7\) −1.81542 −0.686163 −0.343081 0.939306i \(-0.611471\pi\)
−0.343081 + 0.939306i \(0.611471\pi\)
\(8\) −2.33301 −0.824843
\(9\) 0 0
\(10\) −6.08099 −1.92298
\(11\) 1.28860 0.388528 0.194264 0.980949i \(-0.437768\pi\)
0.194264 + 0.980949i \(0.437768\pi\)
\(12\) 0 0
\(13\) 4.53826 1.25869 0.629343 0.777127i \(-0.283324\pi\)
0.629343 + 0.777127i \(0.283324\pi\)
\(14\) 4.07531 1.08917
\(15\) 0 0
\(16\) −0.841340 −0.210335
\(17\) −4.48595 −1.08800 −0.544001 0.839085i \(-0.683091\pi\)
−0.544001 + 0.839085i \(0.683091\pi\)
\(18\) 0 0
\(19\) 2.67238 0.613087 0.306543 0.951857i \(-0.400828\pi\)
0.306543 + 0.951857i \(0.400828\pi\)
\(20\) 8.23305 1.84097
\(21\) 0 0
\(22\) −2.89270 −0.616725
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 2.33804 0.467607
\(26\) −10.1876 −1.99796
\(27\) 0 0
\(28\) −5.51756 −1.04272
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −5.79860 −1.04146 −0.520730 0.853722i \(-0.674340\pi\)
−0.520730 + 0.853722i \(0.674340\pi\)
\(32\) 6.55469 1.15872
\(33\) 0 0
\(34\) 10.0702 1.72703
\(35\) −4.91775 −0.831251
\(36\) 0 0
\(37\) −5.91943 −0.973147 −0.486574 0.873640i \(-0.661754\pi\)
−0.486574 + 0.873640i \(0.661754\pi\)
\(38\) −5.99906 −0.973175
\(39\) 0 0
\(40\) −6.31985 −0.999255
\(41\) −7.82902 −1.22269 −0.611344 0.791365i \(-0.709371\pi\)
−0.611344 + 0.791365i \(0.709371\pi\)
\(42\) 0 0
\(43\) −5.28362 −0.805744 −0.402872 0.915256i \(-0.631988\pi\)
−0.402872 + 0.915256i \(0.631988\pi\)
\(44\) 3.91642 0.590423
\(45\) 0 0
\(46\) −2.24483 −0.330983
\(47\) 2.52885 0.368871 0.184436 0.982845i \(-0.440954\pi\)
0.184436 + 0.982845i \(0.440954\pi\)
\(48\) 0 0
\(49\) −3.70427 −0.529181
\(50\) −5.24851 −0.742251
\(51\) 0 0
\(52\) 13.7930 1.91275
\(53\) 7.14230 0.981070 0.490535 0.871421i \(-0.336801\pi\)
0.490535 + 0.871421i \(0.336801\pi\)
\(54\) 0 0
\(55\) 3.49067 0.470682
\(56\) 4.23538 0.565977
\(57\) 0 0
\(58\) −2.24483 −0.294761
\(59\) −7.87478 −1.02521 −0.512605 0.858625i \(-0.671319\pi\)
−0.512605 + 0.858625i \(0.671319\pi\)
\(60\) 0 0
\(61\) 0.0192849 0.00246918 0.00123459 0.999999i \(-0.499607\pi\)
0.00123459 + 0.999999i \(0.499607\pi\)
\(62\) 13.0169 1.65315
\(63\) 0 0
\(64\) −13.0315 −1.62894
\(65\) 12.2936 1.52483
\(66\) 0 0
\(67\) −15.5222 −1.89634 −0.948170 0.317764i \(-0.897068\pi\)
−0.948170 + 0.317764i \(0.897068\pi\)
\(68\) −13.6340 −1.65337
\(69\) 0 0
\(70\) 11.0395 1.31948
\(71\) 8.18804 0.971742 0.485871 0.874031i \(-0.338502\pi\)
0.485871 + 0.874031i \(0.338502\pi\)
\(72\) 0 0
\(73\) −16.8537 −1.97258 −0.986288 0.165035i \(-0.947226\pi\)
−0.986288 + 0.165035i \(0.947226\pi\)
\(74\) 13.2881 1.54471
\(75\) 0 0
\(76\) 8.12212 0.931671
\(77\) −2.33935 −0.266593
\(78\) 0 0
\(79\) 2.32730 0.261842 0.130921 0.991393i \(-0.458207\pi\)
0.130921 + 0.991393i \(0.458207\pi\)
\(80\) −2.27909 −0.254810
\(81\) 0 0
\(82\) 17.5749 1.94082
\(83\) 8.65460 0.949966 0.474983 0.879995i \(-0.342454\pi\)
0.474983 + 0.879995i \(0.342454\pi\)
\(84\) 0 0
\(85\) −12.1519 −1.31806
\(86\) 11.8608 1.27899
\(87\) 0 0
\(88\) −3.00632 −0.320475
\(89\) 17.6714 1.87316 0.936581 0.350451i \(-0.113972\pi\)
0.936581 + 0.350451i \(0.113972\pi\)
\(90\) 0 0
\(91\) −8.23883 −0.863664
\(92\) 3.03928 0.316867
\(93\) 0 0
\(94\) −5.67686 −0.585523
\(95\) 7.23917 0.742723
\(96\) 0 0
\(97\) −7.50809 −0.762331 −0.381166 0.924507i \(-0.624477\pi\)
−0.381166 + 0.924507i \(0.624477\pi\)
\(98\) 8.31546 0.839989
\(99\) 0 0
\(100\) 7.10595 0.710595
\(101\) −12.9202 −1.28561 −0.642804 0.766031i \(-0.722229\pi\)
−0.642804 + 0.766031i \(0.722229\pi\)
\(102\) 0 0
\(103\) 0.730126 0.0719415 0.0359707 0.999353i \(-0.488548\pi\)
0.0359707 + 0.999353i \(0.488548\pi\)
\(104\) −10.5878 −1.03822
\(105\) 0 0
\(106\) −16.0333 −1.55729
\(107\) −2.51770 −0.243395 −0.121697 0.992567i \(-0.538834\pi\)
−0.121697 + 0.992567i \(0.538834\pi\)
\(108\) 0 0
\(109\) 0.164640 0.0157696 0.00788481 0.999969i \(-0.497490\pi\)
0.00788481 + 0.999969i \(0.497490\pi\)
\(110\) −7.83597 −0.747131
\(111\) 0 0
\(112\) 1.52738 0.144324
\(113\) −12.0351 −1.13216 −0.566082 0.824349i \(-0.691541\pi\)
−0.566082 + 0.824349i \(0.691541\pi\)
\(114\) 0 0
\(115\) 2.70888 0.252604
\(116\) 3.03928 0.282190
\(117\) 0 0
\(118\) 17.6776 1.62735
\(119\) 8.14386 0.746546
\(120\) 0 0
\(121\) −9.33951 −0.849046
\(122\) −0.0432915 −0.00391942
\(123\) 0 0
\(124\) −17.6236 −1.58264
\(125\) −7.21094 −0.644966
\(126\) 0 0
\(127\) −12.8939 −1.14415 −0.572076 0.820201i \(-0.693862\pi\)
−0.572076 + 0.820201i \(0.693862\pi\)
\(128\) 16.1442 1.42696
\(129\) 0 0
\(130\) −27.5971 −2.42043
\(131\) −15.3953 −1.34510 −0.672549 0.740053i \(-0.734800\pi\)
−0.672549 + 0.740053i \(0.734800\pi\)
\(132\) 0 0
\(133\) −4.85149 −0.420677
\(134\) 34.8448 3.01013
\(135\) 0 0
\(136\) 10.4658 0.897431
\(137\) −4.85694 −0.414956 −0.207478 0.978240i \(-0.566526\pi\)
−0.207478 + 0.978240i \(0.566526\pi\)
\(138\) 0 0
\(139\) 8.76830 0.743718 0.371859 0.928289i \(-0.378721\pi\)
0.371859 + 0.928289i \(0.378721\pi\)
\(140\) −14.9464 −1.26320
\(141\) 0 0
\(142\) −18.3808 −1.54248
\(143\) 5.84801 0.489035
\(144\) 0 0
\(145\) 2.70888 0.224960
\(146\) 37.8337 3.13114
\(147\) 0 0
\(148\) −17.9908 −1.47883
\(149\) −1.66660 −0.136534 −0.0682668 0.997667i \(-0.521747\pi\)
−0.0682668 + 0.997667i \(0.521747\pi\)
\(150\) 0 0
\(151\) 15.6639 1.27471 0.637357 0.770569i \(-0.280028\pi\)
0.637357 + 0.770569i \(0.280028\pi\)
\(152\) −6.23469 −0.505701
\(153\) 0 0
\(154\) 5.25145 0.423174
\(155\) −15.7077 −1.26167
\(156\) 0 0
\(157\) −17.5561 −1.40113 −0.700563 0.713591i \(-0.747068\pi\)
−0.700563 + 0.713591i \(0.747068\pi\)
\(158\) −5.22441 −0.415632
\(159\) 0 0
\(160\) 17.7559 1.40372
\(161\) −1.81542 −0.143075
\(162\) 0 0
\(163\) 22.2450 1.74236 0.871180 0.490964i \(-0.163355\pi\)
0.871180 + 0.490964i \(0.163355\pi\)
\(164\) −23.7946 −1.85805
\(165\) 0 0
\(166\) −19.4281 −1.50792
\(167\) −20.9725 −1.62290 −0.811449 0.584423i \(-0.801321\pi\)
−0.811449 + 0.584423i \(0.801321\pi\)
\(168\) 0 0
\(169\) 7.59580 0.584292
\(170\) 27.2790 2.09220
\(171\) 0 0
\(172\) −16.0584 −1.22444
\(173\) 19.8975 1.51278 0.756389 0.654122i \(-0.226962\pi\)
0.756389 + 0.654122i \(0.226962\pi\)
\(174\) 0 0
\(175\) −4.24451 −0.320855
\(176\) −1.08415 −0.0817210
\(177\) 0 0
\(178\) −39.6693 −2.97334
\(179\) 0.697223 0.0521129 0.0260564 0.999660i \(-0.491705\pi\)
0.0260564 + 0.999660i \(0.491705\pi\)
\(180\) 0 0
\(181\) −21.7053 −1.61334 −0.806670 0.591001i \(-0.798733\pi\)
−0.806670 + 0.591001i \(0.798733\pi\)
\(182\) 18.4948 1.37093
\(183\) 0 0
\(184\) −2.33301 −0.171992
\(185\) −16.0350 −1.17892
\(186\) 0 0
\(187\) −5.78060 −0.422719
\(188\) 7.68589 0.560551
\(189\) 0 0
\(190\) −16.2507 −1.17895
\(191\) 14.0930 1.01974 0.509869 0.860252i \(-0.329694\pi\)
0.509869 + 0.860252i \(0.329694\pi\)
\(192\) 0 0
\(193\) 11.1691 0.803973 0.401986 0.915646i \(-0.368320\pi\)
0.401986 + 0.915646i \(0.368320\pi\)
\(194\) 16.8544 1.21008
\(195\) 0 0
\(196\) −11.2583 −0.804164
\(197\) 11.8308 0.842910 0.421455 0.906849i \(-0.361520\pi\)
0.421455 + 0.906849i \(0.361520\pi\)
\(198\) 0 0
\(199\) 7.23419 0.512818 0.256409 0.966568i \(-0.417461\pi\)
0.256409 + 0.966568i \(0.417461\pi\)
\(200\) −5.45466 −0.385703
\(201\) 0 0
\(202\) 29.0037 2.04069
\(203\) −1.81542 −0.127417
\(204\) 0 0
\(205\) −21.2079 −1.48122
\(206\) −1.63901 −0.114195
\(207\) 0 0
\(208\) −3.81822 −0.264746
\(209\) 3.44364 0.238201
\(210\) 0 0
\(211\) −4.94613 −0.340506 −0.170253 0.985400i \(-0.554458\pi\)
−0.170253 + 0.985400i \(0.554458\pi\)
\(212\) 21.7074 1.49087
\(213\) 0 0
\(214\) 5.65181 0.386350
\(215\) −14.3127 −0.976117
\(216\) 0 0
\(217\) 10.5269 0.714610
\(218\) −0.369589 −0.0250317
\(219\) 0 0
\(220\) 10.6091 0.715267
\(221\) −20.3584 −1.36945
\(222\) 0 0
\(223\) −12.4975 −0.836891 −0.418446 0.908242i \(-0.637425\pi\)
−0.418446 + 0.908242i \(0.637425\pi\)
\(224\) −11.8995 −0.795068
\(225\) 0 0
\(226\) 27.0167 1.79712
\(227\) −14.7488 −0.978911 −0.489456 0.872028i \(-0.662804\pi\)
−0.489456 + 0.872028i \(0.662804\pi\)
\(228\) 0 0
\(229\) −11.4103 −0.754016 −0.377008 0.926210i \(-0.623047\pi\)
−0.377008 + 0.926210i \(0.623047\pi\)
\(230\) −6.08099 −0.400969
\(231\) 0 0
\(232\) −2.33301 −0.153170
\(233\) −10.5481 −0.691029 −0.345514 0.938413i \(-0.612296\pi\)
−0.345514 + 0.938413i \(0.612296\pi\)
\(234\) 0 0
\(235\) 6.85036 0.446868
\(236\) −23.9337 −1.55795
\(237\) 0 0
\(238\) −18.2816 −1.18502
\(239\) −3.76141 −0.243306 −0.121653 0.992573i \(-0.538819\pi\)
−0.121653 + 0.992573i \(0.538819\pi\)
\(240\) 0 0
\(241\) −11.4984 −0.740677 −0.370339 0.928897i \(-0.620758\pi\)
−0.370339 + 0.928897i \(0.620758\pi\)
\(242\) 20.9656 1.34772
\(243\) 0 0
\(244\) 0.0586123 0.00375227
\(245\) −10.0344 −0.641075
\(246\) 0 0
\(247\) 12.1280 0.771684
\(248\) 13.5282 0.859041
\(249\) 0 0
\(250\) 16.1874 1.02378
\(251\) 1.24214 0.0784034 0.0392017 0.999231i \(-0.487519\pi\)
0.0392017 + 0.999231i \(0.487519\pi\)
\(252\) 0 0
\(253\) 1.28860 0.0810137
\(254\) 28.9447 1.81615
\(255\) 0 0
\(256\) −10.1780 −0.636126
\(257\) 11.4715 0.715575 0.357788 0.933803i \(-0.383531\pi\)
0.357788 + 0.933803i \(0.383531\pi\)
\(258\) 0 0
\(259\) 10.7462 0.667737
\(260\) 37.3637 2.31720
\(261\) 0 0
\(262\) 34.5600 2.13512
\(263\) 31.2502 1.92697 0.963486 0.267760i \(-0.0862836\pi\)
0.963486 + 0.267760i \(0.0862836\pi\)
\(264\) 0 0
\(265\) 19.3476 1.18852
\(266\) 10.8908 0.667757
\(267\) 0 0
\(268\) −47.1763 −2.88175
\(269\) 24.6573 1.50338 0.751691 0.659516i \(-0.229239\pi\)
0.751691 + 0.659516i \(0.229239\pi\)
\(270\) 0 0
\(271\) 26.4463 1.60650 0.803248 0.595644i \(-0.203103\pi\)
0.803248 + 0.595644i \(0.203103\pi\)
\(272\) 3.77421 0.228845
\(273\) 0 0
\(274\) 10.9030 0.658675
\(275\) 3.01280 0.181679
\(276\) 0 0
\(277\) 17.9981 1.08140 0.540702 0.841214i \(-0.318159\pi\)
0.540702 + 0.841214i \(0.318159\pi\)
\(278\) −19.6834 −1.18053
\(279\) 0 0
\(280\) 11.4731 0.685652
\(281\) −19.6129 −1.17001 −0.585004 0.811030i \(-0.698907\pi\)
−0.585004 + 0.811030i \(0.698907\pi\)
\(282\) 0 0
\(283\) 4.74374 0.281986 0.140993 0.990011i \(-0.454971\pi\)
0.140993 + 0.990011i \(0.454971\pi\)
\(284\) 24.8858 1.47670
\(285\) 0 0
\(286\) −13.1278 −0.776264
\(287\) 14.2129 0.838963
\(288\) 0 0
\(289\) 3.12372 0.183749
\(290\) −6.08099 −0.357088
\(291\) 0 0
\(292\) −51.2231 −2.99760
\(293\) 5.47082 0.319609 0.159804 0.987149i \(-0.448914\pi\)
0.159804 + 0.987149i \(0.448914\pi\)
\(294\) 0 0
\(295\) −21.3319 −1.24199
\(296\) 13.8101 0.802694
\(297\) 0 0
\(298\) 3.74125 0.216725
\(299\) 4.53826 0.262454
\(300\) 0 0
\(301\) 9.59196 0.552871
\(302\) −35.1629 −2.02340
\(303\) 0 0
\(304\) −2.24838 −0.128954
\(305\) 0.0522406 0.00299129
\(306\) 0 0
\(307\) −29.4112 −1.67858 −0.839292 0.543681i \(-0.817030\pi\)
−0.839292 + 0.543681i \(0.817030\pi\)
\(308\) −7.10993 −0.405126
\(309\) 0 0
\(310\) 35.2612 2.00270
\(311\) 0.290134 0.0164520 0.00822598 0.999966i \(-0.497382\pi\)
0.00822598 + 0.999966i \(0.497382\pi\)
\(312\) 0 0
\(313\) 2.75393 0.155661 0.0778306 0.996967i \(-0.475201\pi\)
0.0778306 + 0.996967i \(0.475201\pi\)
\(314\) 39.4104 2.22406
\(315\) 0 0
\(316\) 7.07332 0.397905
\(317\) −23.3102 −1.30923 −0.654617 0.755961i \(-0.727170\pi\)
−0.654617 + 0.755961i \(0.727170\pi\)
\(318\) 0 0
\(319\) 1.28860 0.0721478
\(320\) −35.3008 −1.97337
\(321\) 0 0
\(322\) 4.07531 0.227108
\(323\) −11.9882 −0.667040
\(324\) 0 0
\(325\) 10.6106 0.588571
\(326\) −49.9363 −2.76571
\(327\) 0 0
\(328\) 18.2652 1.00853
\(329\) −4.59092 −0.253106
\(330\) 0 0
\(331\) 28.6297 1.57363 0.786816 0.617187i \(-0.211728\pi\)
0.786816 + 0.617187i \(0.211728\pi\)
\(332\) 26.3038 1.44361
\(333\) 0 0
\(334\) 47.0797 2.57609
\(335\) −42.0478 −2.29732
\(336\) 0 0
\(337\) −23.8515 −1.29927 −0.649637 0.760245i \(-0.725079\pi\)
−0.649637 + 0.760245i \(0.725079\pi\)
\(338\) −17.0513 −0.927469
\(339\) 0 0
\(340\) −36.9330 −2.00297
\(341\) −7.47208 −0.404636
\(342\) 0 0
\(343\) 19.4327 1.04927
\(344\) 12.3267 0.664613
\(345\) 0 0
\(346\) −44.6666 −2.40129
\(347\) 12.6128 0.677093 0.338546 0.940950i \(-0.390065\pi\)
0.338546 + 0.940950i \(0.390065\pi\)
\(348\) 0 0
\(349\) 28.6656 1.53443 0.767216 0.641389i \(-0.221641\pi\)
0.767216 + 0.641389i \(0.221641\pi\)
\(350\) 9.52822 0.509305
\(351\) 0 0
\(352\) 8.44638 0.450194
\(353\) 9.85003 0.524264 0.262132 0.965032i \(-0.415574\pi\)
0.262132 + 0.965032i \(0.415574\pi\)
\(354\) 0 0
\(355\) 22.1804 1.17722
\(356\) 53.7082 2.84653
\(357\) 0 0
\(358\) −1.56515 −0.0827207
\(359\) −6.28877 −0.331909 −0.165954 0.986133i \(-0.553070\pi\)
−0.165954 + 0.986133i \(0.553070\pi\)
\(360\) 0 0
\(361\) −11.8584 −0.624125
\(362\) 48.7248 2.56092
\(363\) 0 0
\(364\) −25.0401 −1.31246
\(365\) −45.6546 −2.38967
\(366\) 0 0
\(367\) 34.2153 1.78602 0.893011 0.450034i \(-0.148588\pi\)
0.893011 + 0.450034i \(0.148588\pi\)
\(368\) −0.841340 −0.0438579
\(369\) 0 0
\(370\) 35.9960 1.87134
\(371\) −12.9662 −0.673174
\(372\) 0 0
\(373\) 6.32053 0.327264 0.163632 0.986521i \(-0.447679\pi\)
0.163632 + 0.986521i \(0.447679\pi\)
\(374\) 12.9765 0.670998
\(375\) 0 0
\(376\) −5.89984 −0.304261
\(377\) 4.53826 0.233732
\(378\) 0 0
\(379\) 24.3916 1.25291 0.626456 0.779457i \(-0.284505\pi\)
0.626456 + 0.779457i \(0.284505\pi\)
\(380\) 22.0019 1.12867
\(381\) 0 0
\(382\) −31.6366 −1.61867
\(383\) 1.48836 0.0760516 0.0380258 0.999277i \(-0.487893\pi\)
0.0380258 + 0.999277i \(0.487893\pi\)
\(384\) 0 0
\(385\) −6.33701 −0.322964
\(386\) −25.0729 −1.27618
\(387\) 0 0
\(388\) −22.8192 −1.15847
\(389\) 32.8601 1.66607 0.833036 0.553219i \(-0.186601\pi\)
0.833036 + 0.553219i \(0.186601\pi\)
\(390\) 0 0
\(391\) −4.48595 −0.226864
\(392\) 8.64209 0.436491
\(393\) 0 0
\(394\) −26.5582 −1.33798
\(395\) 6.30439 0.317208
\(396\) 0 0
\(397\) 6.95067 0.348844 0.174422 0.984671i \(-0.444194\pi\)
0.174422 + 0.984671i \(0.444194\pi\)
\(398\) −16.2396 −0.814015
\(399\) 0 0
\(400\) −1.96708 −0.0983542
\(401\) −2.64996 −0.132333 −0.0661664 0.997809i \(-0.521077\pi\)
−0.0661664 + 0.997809i \(0.521077\pi\)
\(402\) 0 0
\(403\) −26.3155 −1.31087
\(404\) −39.2681 −1.95366
\(405\) 0 0
\(406\) 4.07531 0.202254
\(407\) −7.62778 −0.378095
\(408\) 0 0
\(409\) −8.22912 −0.406904 −0.203452 0.979085i \(-0.565216\pi\)
−0.203452 + 0.979085i \(0.565216\pi\)
\(410\) 47.6082 2.35120
\(411\) 0 0
\(412\) 2.21906 0.109325
\(413\) 14.2960 0.703460
\(414\) 0 0
\(415\) 23.4443 1.15083
\(416\) 29.7469 1.45846
\(417\) 0 0
\(418\) −7.73039 −0.378106
\(419\) −17.7332 −0.866323 −0.433161 0.901316i \(-0.642602\pi\)
−0.433161 + 0.901316i \(0.642602\pi\)
\(420\) 0 0
\(421\) 19.8575 0.967795 0.483897 0.875125i \(-0.339221\pi\)
0.483897 + 0.875125i \(0.339221\pi\)
\(422\) 11.1032 0.540497
\(423\) 0 0
\(424\) −16.6631 −0.809229
\(425\) −10.4883 −0.508758
\(426\) 0 0
\(427\) −0.0350102 −0.00169426
\(428\) −7.65198 −0.369873
\(429\) 0 0
\(430\) 32.1296 1.54943
\(431\) 16.6485 0.801930 0.400965 0.916093i \(-0.368675\pi\)
0.400965 + 0.916093i \(0.368675\pi\)
\(432\) 0 0
\(433\) −33.5474 −1.61219 −0.806093 0.591789i \(-0.798422\pi\)
−0.806093 + 0.591789i \(0.798422\pi\)
\(434\) −23.6311 −1.13433
\(435\) 0 0
\(436\) 0.500386 0.0239641
\(437\) 2.67238 0.127837
\(438\) 0 0
\(439\) 18.1685 0.867134 0.433567 0.901121i \(-0.357255\pi\)
0.433567 + 0.901121i \(0.357255\pi\)
\(440\) −8.14376 −0.388239
\(441\) 0 0
\(442\) 45.7012 2.17379
\(443\) −26.5362 −1.26077 −0.630386 0.776282i \(-0.717103\pi\)
−0.630386 + 0.776282i \(0.717103\pi\)
\(444\) 0 0
\(445\) 47.8697 2.26924
\(446\) 28.0547 1.32843
\(447\) 0 0
\(448\) 23.6576 1.11772
\(449\) −31.8845 −1.50472 −0.752362 0.658750i \(-0.771085\pi\)
−0.752362 + 0.658750i \(0.771085\pi\)
\(450\) 0 0
\(451\) −10.0885 −0.475049
\(452\) −36.5779 −1.72048
\(453\) 0 0
\(454\) 33.1086 1.55386
\(455\) −22.3180 −1.04628
\(456\) 0 0
\(457\) −3.81457 −0.178438 −0.0892190 0.996012i \(-0.528437\pi\)
−0.0892190 + 0.996012i \(0.528437\pi\)
\(458\) 25.6143 1.19688
\(459\) 0 0
\(460\) 8.23305 0.383868
\(461\) 15.5993 0.726532 0.363266 0.931685i \(-0.381662\pi\)
0.363266 + 0.931685i \(0.381662\pi\)
\(462\) 0 0
\(463\) −32.0523 −1.48960 −0.744799 0.667289i \(-0.767455\pi\)
−0.744799 + 0.667289i \(0.767455\pi\)
\(464\) −0.841340 −0.0390582
\(465\) 0 0
\(466\) 23.6787 1.09690
\(467\) −27.7274 −1.28307 −0.641535 0.767094i \(-0.721702\pi\)
−0.641535 + 0.767094i \(0.721702\pi\)
\(468\) 0 0
\(469\) 28.1793 1.30120
\(470\) −15.3779 −0.709331
\(471\) 0 0
\(472\) 18.3719 0.845637
\(473\) −6.80848 −0.313054
\(474\) 0 0
\(475\) 6.24813 0.286684
\(476\) 24.7515 1.13448
\(477\) 0 0
\(478\) 8.44375 0.386208
\(479\) −28.8506 −1.31822 −0.659109 0.752048i \(-0.729066\pi\)
−0.659109 + 0.752048i \(0.729066\pi\)
\(480\) 0 0
\(481\) −26.8639 −1.22489
\(482\) 25.8120 1.17570
\(483\) 0 0
\(484\) −28.3854 −1.29024
\(485\) −20.3385 −0.923525
\(486\) 0 0
\(487\) −13.0525 −0.591467 −0.295734 0.955270i \(-0.595564\pi\)
−0.295734 + 0.955270i \(0.595564\pi\)
\(488\) −0.0449919 −0.00203669
\(489\) 0 0
\(490\) 22.5256 1.01760
\(491\) 16.7180 0.754472 0.377236 0.926117i \(-0.376875\pi\)
0.377236 + 0.926117i \(0.376875\pi\)
\(492\) 0 0
\(493\) −4.48595 −0.202037
\(494\) −27.2253 −1.22492
\(495\) 0 0
\(496\) 4.87859 0.219055
\(497\) −14.8647 −0.666773
\(498\) 0 0
\(499\) 5.64497 0.252704 0.126352 0.991985i \(-0.459673\pi\)
0.126352 + 0.991985i \(0.459673\pi\)
\(500\) −21.9161 −0.980116
\(501\) 0 0
\(502\) −2.78841 −0.124453
\(503\) −18.7912 −0.837858 −0.418929 0.908019i \(-0.637594\pi\)
−0.418929 + 0.908019i \(0.637594\pi\)
\(504\) 0 0
\(505\) −34.9993 −1.55745
\(506\) −2.89270 −0.128596
\(507\) 0 0
\(508\) −39.1883 −1.73870
\(509\) 38.1542 1.69116 0.845579 0.533851i \(-0.179256\pi\)
0.845579 + 0.533851i \(0.179256\pi\)
\(510\) 0 0
\(511\) 30.5965 1.35351
\(512\) −9.44042 −0.417212
\(513\) 0 0
\(514\) −25.7517 −1.13586
\(515\) 1.97783 0.0871534
\(516\) 0 0
\(517\) 3.25868 0.143317
\(518\) −24.1235 −1.05992
\(519\) 0 0
\(520\) −28.6811 −1.25775
\(521\) 20.7383 0.908564 0.454282 0.890858i \(-0.349896\pi\)
0.454282 + 0.890858i \(0.349896\pi\)
\(522\) 0 0
\(523\) −35.6601 −1.55931 −0.779654 0.626211i \(-0.784605\pi\)
−0.779654 + 0.626211i \(0.784605\pi\)
\(524\) −46.7907 −2.04406
\(525\) 0 0
\(526\) −70.1516 −3.05875
\(527\) 26.0122 1.13311
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −43.4322 −1.88658
\(531\) 0 0
\(532\) −14.7450 −0.639278
\(533\) −35.5301 −1.53898
\(534\) 0 0
\(535\) −6.82014 −0.294860
\(536\) 36.2135 1.56418
\(537\) 0 0
\(538\) −55.3515 −2.38637
\(539\) −4.77332 −0.205602
\(540\) 0 0
\(541\) −12.9936 −0.558640 −0.279320 0.960198i \(-0.590109\pi\)
−0.279320 + 0.960198i \(0.590109\pi\)
\(542\) −59.3675 −2.55005
\(543\) 0 0
\(544\) −29.4040 −1.26069
\(545\) 0.445989 0.0191041
\(546\) 0 0
\(547\) 35.0835 1.50006 0.750031 0.661403i \(-0.230039\pi\)
0.750031 + 0.661403i \(0.230039\pi\)
\(548\) −14.7616 −0.630584
\(549\) 0 0
\(550\) −6.76323 −0.288385
\(551\) 2.67238 0.113847
\(552\) 0 0
\(553\) −4.22502 −0.179666
\(554\) −40.4028 −1.71655
\(555\) 0 0
\(556\) 26.6493 1.13018
\(557\) 38.1951 1.61838 0.809190 0.587547i \(-0.199906\pi\)
0.809190 + 0.587547i \(0.199906\pi\)
\(558\) 0 0
\(559\) −23.9784 −1.01418
\(560\) 4.13749 0.174841
\(561\) 0 0
\(562\) 44.0277 1.85720
\(563\) 11.2679 0.474886 0.237443 0.971401i \(-0.423691\pi\)
0.237443 + 0.971401i \(0.423691\pi\)
\(564\) 0 0
\(565\) −32.6015 −1.37156
\(566\) −10.6489 −0.447607
\(567\) 0 0
\(568\) −19.1028 −0.801535
\(569\) −21.5961 −0.905356 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(570\) 0 0
\(571\) 8.89694 0.372325 0.186163 0.982519i \(-0.440395\pi\)
0.186163 + 0.982519i \(0.440395\pi\)
\(572\) 17.7737 0.743157
\(573\) 0 0
\(574\) −31.9057 −1.33172
\(575\) 2.33804 0.0975029
\(576\) 0 0
\(577\) −29.9448 −1.24662 −0.623308 0.781976i \(-0.714212\pi\)
−0.623308 + 0.781976i \(0.714212\pi\)
\(578\) −7.01224 −0.291671
\(579\) 0 0
\(580\) 8.23305 0.341859
\(581\) −15.7117 −0.651831
\(582\) 0 0
\(583\) 9.20358 0.381173
\(584\) 39.3198 1.62707
\(585\) 0 0
\(586\) −12.2811 −0.507327
\(587\) −23.3343 −0.963109 −0.481555 0.876416i \(-0.659928\pi\)
−0.481555 + 0.876416i \(0.659928\pi\)
\(588\) 0 0
\(589\) −15.4961 −0.638505
\(590\) 47.8865 1.97145
\(591\) 0 0
\(592\) 4.98025 0.204687
\(593\) −34.8623 −1.43162 −0.715811 0.698295i \(-0.753943\pi\)
−0.715811 + 0.698295i \(0.753943\pi\)
\(594\) 0 0
\(595\) 22.0607 0.904402
\(596\) −5.06528 −0.207482
\(597\) 0 0
\(598\) −10.1876 −0.416604
\(599\) −13.7736 −0.562775 −0.281387 0.959594i \(-0.590795\pi\)
−0.281387 + 0.959594i \(0.590795\pi\)
\(600\) 0 0
\(601\) −11.6882 −0.476772 −0.238386 0.971170i \(-0.576618\pi\)
−0.238386 + 0.971170i \(0.576618\pi\)
\(602\) −21.5324 −0.877593
\(603\) 0 0
\(604\) 47.6071 1.93710
\(605\) −25.2996 −1.02858
\(606\) 0 0
\(607\) −22.5491 −0.915238 −0.457619 0.889148i \(-0.651298\pi\)
−0.457619 + 0.889148i \(0.651298\pi\)
\(608\) 17.5166 0.710393
\(609\) 0 0
\(610\) −0.117271 −0.00474818
\(611\) 11.4766 0.464293
\(612\) 0 0
\(613\) −30.0844 −1.21510 −0.607549 0.794282i \(-0.707847\pi\)
−0.607549 + 0.794282i \(0.707847\pi\)
\(614\) 66.0232 2.66448
\(615\) 0 0
\(616\) 5.45772 0.219898
\(617\) −3.34573 −0.134694 −0.0673471 0.997730i \(-0.521453\pi\)
−0.0673471 + 0.997730i \(0.521453\pi\)
\(618\) 0 0
\(619\) −27.0042 −1.08539 −0.542694 0.839930i \(-0.682596\pi\)
−0.542694 + 0.839930i \(0.682596\pi\)
\(620\) −47.7401 −1.91729
\(621\) 0 0
\(622\) −0.651302 −0.0261148
\(623\) −32.0809 −1.28529
\(624\) 0 0
\(625\) −31.2238 −1.24895
\(626\) −6.18211 −0.247087
\(627\) 0 0
\(628\) −53.3578 −2.12921
\(629\) 26.5542 1.05879
\(630\) 0 0
\(631\) 17.3154 0.689316 0.344658 0.938728i \(-0.387995\pi\)
0.344658 + 0.938728i \(0.387995\pi\)
\(632\) −5.42962 −0.215979
\(633\) 0 0
\(634\) 52.3276 2.07819
\(635\) −34.9281 −1.38608
\(636\) 0 0
\(637\) −16.8109 −0.666073
\(638\) −2.89270 −0.114523
\(639\) 0 0
\(640\) 43.7327 1.72869
\(641\) −48.1364 −1.90128 −0.950638 0.310304i \(-0.899569\pi\)
−0.950638 + 0.310304i \(0.899569\pi\)
\(642\) 0 0
\(643\) −33.4951 −1.32092 −0.660460 0.750862i \(-0.729639\pi\)
−0.660460 + 0.750862i \(0.729639\pi\)
\(644\) −5.51756 −0.217422
\(645\) 0 0
\(646\) 26.9114 1.05882
\(647\) −15.8951 −0.624900 −0.312450 0.949934i \(-0.601150\pi\)
−0.312450 + 0.949934i \(0.601150\pi\)
\(648\) 0 0
\(649\) −10.1475 −0.398323
\(650\) −23.8191 −0.934261
\(651\) 0 0
\(652\) 67.6087 2.64776
\(653\) −28.6078 −1.11951 −0.559754 0.828659i \(-0.689104\pi\)
−0.559754 + 0.828659i \(0.689104\pi\)
\(654\) 0 0
\(655\) −41.7041 −1.62952
\(656\) 6.58687 0.257174
\(657\) 0 0
\(658\) 10.3059 0.401764
\(659\) 32.2194 1.25509 0.627545 0.778580i \(-0.284060\pi\)
0.627545 + 0.778580i \(0.284060\pi\)
\(660\) 0 0
\(661\) −7.50116 −0.291761 −0.145881 0.989302i \(-0.546602\pi\)
−0.145881 + 0.989302i \(0.546602\pi\)
\(662\) −64.2690 −2.49789
\(663\) 0 0
\(664\) −20.1913 −0.783573
\(665\) −13.1421 −0.509629
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −63.7412 −2.46622
\(669\) 0 0
\(670\) 94.3904 3.64662
\(671\) 0.0248506 0.000959346 0
\(672\) 0 0
\(673\) 13.3328 0.513941 0.256970 0.966419i \(-0.417276\pi\)
0.256970 + 0.966419i \(0.417276\pi\)
\(674\) 53.5426 2.06239
\(675\) 0 0
\(676\) 23.0858 0.887914
\(677\) 25.8323 0.992817 0.496408 0.868089i \(-0.334652\pi\)
0.496408 + 0.868089i \(0.334652\pi\)
\(678\) 0 0
\(679\) 13.6303 0.523083
\(680\) 28.3505 1.08719
\(681\) 0 0
\(682\) 16.7736 0.642294
\(683\) 2.67992 0.102544 0.0512722 0.998685i \(-0.483672\pi\)
0.0512722 + 0.998685i \(0.483672\pi\)
\(684\) 0 0
\(685\) −13.1569 −0.502698
\(686\) −43.6232 −1.66554
\(687\) 0 0
\(688\) 4.44532 0.169476
\(689\) 32.4136 1.23486
\(690\) 0 0
\(691\) −14.5615 −0.553945 −0.276972 0.960878i \(-0.589331\pi\)
−0.276972 + 0.960878i \(0.589331\pi\)
\(692\) 60.4740 2.29888
\(693\) 0 0
\(694\) −28.3137 −1.07477
\(695\) 23.7523 0.900976
\(696\) 0 0
\(697\) 35.1206 1.33029
\(698\) −64.3494 −2.43566
\(699\) 0 0
\(700\) −12.9003 −0.487584
\(701\) −12.8173 −0.484103 −0.242051 0.970263i \(-0.577820\pi\)
−0.242051 + 0.970263i \(0.577820\pi\)
\(702\) 0 0
\(703\) −15.8190 −0.596624
\(704\) −16.7924 −0.632888
\(705\) 0 0
\(706\) −22.1117 −0.832185
\(707\) 23.4555 0.882136
\(708\) 0 0
\(709\) −10.1202 −0.380073 −0.190036 0.981777i \(-0.560861\pi\)
−0.190036 + 0.981777i \(0.560861\pi\)
\(710\) −49.7914 −1.86864
\(711\) 0 0
\(712\) −41.2275 −1.54507
\(713\) −5.79860 −0.217159
\(714\) 0 0
\(715\) 15.8416 0.592441
\(716\) 2.11905 0.0791928
\(717\) 0 0
\(718\) 14.1172 0.526851
\(719\) 50.2292 1.87323 0.936616 0.350357i \(-0.113940\pi\)
0.936616 + 0.350357i \(0.113940\pi\)
\(720\) 0 0
\(721\) −1.32548 −0.0493636
\(722\) 26.6201 0.990697
\(723\) 0 0
\(724\) −65.9684 −2.45170
\(725\) 2.33804 0.0868325
\(726\) 0 0
\(727\) −30.3374 −1.12515 −0.562575 0.826746i \(-0.690189\pi\)
−0.562575 + 0.826746i \(0.690189\pi\)
\(728\) 19.2213 0.712387
\(729\) 0 0
\(730\) 102.487 3.79322
\(731\) 23.7020 0.876651
\(732\) 0 0
\(733\) −29.1824 −1.07788 −0.538939 0.842345i \(-0.681175\pi\)
−0.538939 + 0.842345i \(0.681175\pi\)
\(734\) −76.8076 −2.83502
\(735\) 0 0
\(736\) 6.55469 0.241609
\(737\) −20.0019 −0.736781
\(738\) 0 0
\(739\) −17.6927 −0.650837 −0.325419 0.945570i \(-0.605505\pi\)
−0.325419 + 0.945570i \(0.605505\pi\)
\(740\) −48.7349 −1.79153
\(741\) 0 0
\(742\) 29.1071 1.06855
\(743\) −25.7647 −0.945216 −0.472608 0.881273i \(-0.656687\pi\)
−0.472608 + 0.881273i \(0.656687\pi\)
\(744\) 0 0
\(745\) −4.51463 −0.165403
\(746\) −14.1885 −0.519479
\(747\) 0 0
\(748\) −17.5689 −0.642381
\(749\) 4.57067 0.167008
\(750\) 0 0
\(751\) 0.702382 0.0256303 0.0128151 0.999918i \(-0.495921\pi\)
0.0128151 + 0.999918i \(0.495921\pi\)
\(752\) −2.12762 −0.0775865
\(753\) 0 0
\(754\) −10.1876 −0.371012
\(755\) 42.4318 1.54425
\(756\) 0 0
\(757\) −33.7740 −1.22754 −0.613768 0.789486i \(-0.710347\pi\)
−0.613768 + 0.789486i \(0.710347\pi\)
\(758\) −54.7551 −1.98879
\(759\) 0 0
\(760\) −16.8890 −0.612630
\(761\) −33.2497 −1.20530 −0.602651 0.798005i \(-0.705889\pi\)
−0.602651 + 0.798005i \(0.705889\pi\)
\(762\) 0 0
\(763\) −0.298889 −0.0108205
\(764\) 42.8327 1.54963
\(765\) 0 0
\(766\) −3.34112 −0.120720
\(767\) −35.7378 −1.29042
\(768\) 0 0
\(769\) 27.8729 1.00512 0.502561 0.864542i \(-0.332391\pi\)
0.502561 + 0.864542i \(0.332391\pi\)
\(770\) 14.2255 0.512653
\(771\) 0 0
\(772\) 33.9462 1.22175
\(773\) −39.7315 −1.42904 −0.714522 0.699613i \(-0.753356\pi\)
−0.714522 + 0.699613i \(0.753356\pi\)
\(774\) 0 0
\(775\) −13.5573 −0.486994
\(776\) 17.5165 0.628804
\(777\) 0 0
\(778\) −73.7654 −2.64462
\(779\) −20.9222 −0.749614
\(780\) 0 0
\(781\) 10.5511 0.377549
\(782\) 10.0702 0.360110
\(783\) 0 0
\(784\) 3.11655 0.111305
\(785\) −47.5573 −1.69739
\(786\) 0 0
\(787\) 6.77874 0.241636 0.120818 0.992675i \(-0.461448\pi\)
0.120818 + 0.992675i \(0.461448\pi\)
\(788\) 35.9571 1.28092
\(789\) 0 0
\(790\) −14.1523 −0.503516
\(791\) 21.8486 0.776848
\(792\) 0 0
\(793\) 0.0875200 0.00310793
\(794\) −15.6031 −0.553734
\(795\) 0 0
\(796\) 21.9867 0.779299
\(797\) −45.6601 −1.61737 −0.808683 0.588245i \(-0.799819\pi\)
−0.808683 + 0.588245i \(0.799819\pi\)
\(798\) 0 0
\(799\) −11.3443 −0.401333
\(800\) 15.3251 0.541824
\(801\) 0 0
\(802\) 5.94872 0.210057
\(803\) −21.7177 −0.766401
\(804\) 0 0
\(805\) −4.91775 −0.173328
\(806\) 59.0740 2.08079
\(807\) 0 0
\(808\) 30.1429 1.06042
\(809\) 30.4752 1.07145 0.535725 0.844392i \(-0.320038\pi\)
0.535725 + 0.844392i \(0.320038\pi\)
\(810\) 0 0
\(811\) 49.2770 1.73035 0.865174 0.501472i \(-0.167208\pi\)
0.865174 + 0.501472i \(0.167208\pi\)
\(812\) −5.51756 −0.193628
\(813\) 0 0
\(814\) 17.1231 0.600164
\(815\) 60.2590 2.11078
\(816\) 0 0
\(817\) −14.1198 −0.493991
\(818\) 18.4730 0.645893
\(819\) 0 0
\(820\) −64.4567 −2.25093
\(821\) 11.2716 0.393382 0.196691 0.980466i \(-0.436980\pi\)
0.196691 + 0.980466i \(0.436980\pi\)
\(822\) 0 0
\(823\) −28.9336 −1.00856 −0.504282 0.863539i \(-0.668243\pi\)
−0.504282 + 0.863539i \(0.668243\pi\)
\(824\) −1.70339 −0.0593405
\(825\) 0 0
\(826\) −32.0922 −1.11663
\(827\) 28.1166 0.977711 0.488855 0.872365i \(-0.337415\pi\)
0.488855 + 0.872365i \(0.337415\pi\)
\(828\) 0 0
\(829\) −24.8841 −0.864262 −0.432131 0.901811i \(-0.642238\pi\)
−0.432131 + 0.901811i \(0.642238\pi\)
\(830\) −52.6285 −1.82676
\(831\) 0 0
\(832\) −59.1404 −2.05032
\(833\) 16.6171 0.575750
\(834\) 0 0
\(835\) −56.8119 −1.96606
\(836\) 10.4662 0.361980
\(837\) 0 0
\(838\) 39.8080 1.37515
\(839\) 1.16783 0.0403180 0.0201590 0.999797i \(-0.493583\pi\)
0.0201590 + 0.999797i \(0.493583\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −44.5768 −1.53622
\(843\) 0 0
\(844\) −15.0327 −0.517446
\(845\) 20.5761 0.707840
\(846\) 0 0
\(847\) 16.9551 0.582584
\(848\) −6.00910 −0.206353
\(849\) 0 0
\(850\) 23.5445 0.807570
\(851\) −5.91943 −0.202915
\(852\) 0 0
\(853\) 7.52282 0.257577 0.128788 0.991672i \(-0.458891\pi\)
0.128788 + 0.991672i \(0.458891\pi\)
\(854\) 0.0785920 0.00268936
\(855\) 0 0
\(856\) 5.87381 0.200763
\(857\) −37.9847 −1.29753 −0.648766 0.760988i \(-0.724715\pi\)
−0.648766 + 0.760988i \(0.724715\pi\)
\(858\) 0 0
\(859\) −20.5333 −0.700588 −0.350294 0.936640i \(-0.613918\pi\)
−0.350294 + 0.936640i \(0.613918\pi\)
\(860\) −43.5003 −1.48335
\(861\) 0 0
\(862\) −37.3731 −1.27293
\(863\) 22.2904 0.758773 0.379386 0.925238i \(-0.376135\pi\)
0.379386 + 0.925238i \(0.376135\pi\)
\(864\) 0 0
\(865\) 53.8999 1.83265
\(866\) 75.3084 2.55908
\(867\) 0 0
\(868\) 31.9941 1.08595
\(869\) 2.99897 0.101733
\(870\) 0 0
\(871\) −70.4438 −2.38690
\(872\) −0.384106 −0.0130075
\(873\) 0 0
\(874\) −5.99906 −0.202921
\(875\) 13.0909 0.442552
\(876\) 0 0
\(877\) −3.67076 −0.123953 −0.0619763 0.998078i \(-0.519740\pi\)
−0.0619763 + 0.998078i \(0.519740\pi\)
\(878\) −40.7852 −1.37643
\(879\) 0 0
\(880\) −2.93684 −0.0990008
\(881\) 6.66693 0.224615 0.112307 0.993674i \(-0.464176\pi\)
0.112307 + 0.993674i \(0.464176\pi\)
\(882\) 0 0
\(883\) 19.4496 0.654530 0.327265 0.944933i \(-0.393873\pi\)
0.327265 + 0.944933i \(0.393873\pi\)
\(884\) −61.8749 −2.08108
\(885\) 0 0
\(886\) 59.5693 2.00127
\(887\) 6.36719 0.213789 0.106895 0.994270i \(-0.465909\pi\)
0.106895 + 0.994270i \(0.465909\pi\)
\(888\) 0 0
\(889\) 23.4078 0.785074
\(890\) −107.459 −3.60205
\(891\) 0 0
\(892\) −37.9833 −1.27177
\(893\) 6.75806 0.226150
\(894\) 0 0
\(895\) 1.88869 0.0631320
\(896\) −29.3084 −0.979125
\(897\) 0 0
\(898\) 71.5754 2.38850
\(899\) −5.79860 −0.193394
\(900\) 0 0
\(901\) −32.0400 −1.06741
\(902\) 22.6470 0.754062
\(903\) 0 0
\(904\) 28.0779 0.933857
\(905\) −58.7970 −1.95448
\(906\) 0 0
\(907\) 50.3211 1.67089 0.835443 0.549578i \(-0.185211\pi\)
0.835443 + 0.549578i \(0.185211\pi\)
\(908\) −44.8257 −1.48759
\(909\) 0 0
\(910\) 50.1002 1.66081
\(911\) −44.4615 −1.47307 −0.736537 0.676397i \(-0.763541\pi\)
−0.736537 + 0.676397i \(0.763541\pi\)
\(912\) 0 0
\(913\) 11.1523 0.369088
\(914\) 8.56308 0.283241
\(915\) 0 0
\(916\) −34.6792 −1.14583
\(917\) 27.9489 0.922955
\(918\) 0 0
\(919\) 48.7767 1.60899 0.804497 0.593957i \(-0.202435\pi\)
0.804497 + 0.593957i \(0.202435\pi\)
\(920\) −6.31985 −0.208359
\(921\) 0 0
\(922\) −35.0179 −1.15325
\(923\) 37.1595 1.22312
\(924\) 0 0
\(925\) −13.8398 −0.455051
\(926\) 71.9522 2.36449
\(927\) 0 0
\(928\) 6.55469 0.215168
\(929\) −41.3850 −1.35780 −0.678898 0.734232i \(-0.737542\pi\)
−0.678898 + 0.734232i \(0.737542\pi\)
\(930\) 0 0
\(931\) −9.89922 −0.324434
\(932\) −32.0586 −1.05011
\(933\) 0 0
\(934\) 62.2433 2.03666
\(935\) −15.6590 −0.512103
\(936\) 0 0
\(937\) 15.0228 0.490774 0.245387 0.969425i \(-0.421085\pi\)
0.245387 + 0.969425i \(0.421085\pi\)
\(938\) −63.2578 −2.06544
\(939\) 0 0
\(940\) 20.8202 0.679079
\(941\) 28.3415 0.923907 0.461954 0.886904i \(-0.347149\pi\)
0.461954 + 0.886904i \(0.347149\pi\)
\(942\) 0 0
\(943\) −7.82902 −0.254948
\(944\) 6.62537 0.215637
\(945\) 0 0
\(946\) 15.2839 0.496922
\(947\) −14.4377 −0.469164 −0.234582 0.972096i \(-0.575372\pi\)
−0.234582 + 0.972096i \(0.575372\pi\)
\(948\) 0 0
\(949\) −76.4864 −2.48285
\(950\) −14.0260 −0.455064
\(951\) 0 0
\(952\) −18.9997 −0.615784
\(953\) 13.5038 0.437431 0.218715 0.975789i \(-0.429813\pi\)
0.218715 + 0.975789i \(0.429813\pi\)
\(954\) 0 0
\(955\) 38.1764 1.23536
\(956\) −11.4320 −0.369737
\(957\) 0 0
\(958\) 64.7648 2.09246
\(959\) 8.81736 0.284727
\(960\) 0 0
\(961\) 2.62375 0.0846371
\(962\) 60.3050 1.94431
\(963\) 0 0
\(964\) −34.9469 −1.12556
\(965\) 30.2559 0.973972
\(966\) 0 0
\(967\) 25.4673 0.818974 0.409487 0.912316i \(-0.365708\pi\)
0.409487 + 0.912316i \(0.365708\pi\)
\(968\) 21.7892 0.700330
\(969\) 0 0
\(970\) 45.6566 1.46595
\(971\) 13.8575 0.444708 0.222354 0.974966i \(-0.428626\pi\)
0.222354 + 0.974966i \(0.428626\pi\)
\(972\) 0 0
\(973\) −15.9181 −0.510311
\(974\) 29.3008 0.938858
\(975\) 0 0
\(976\) −0.0162252 −0.000519355 0
\(977\) −10.0587 −0.321805 −0.160902 0.986970i \(-0.551440\pi\)
−0.160902 + 0.986970i \(0.551440\pi\)
\(978\) 0 0
\(979\) 22.7714 0.727776
\(980\) −30.4974 −0.974204
\(981\) 0 0
\(982\) −37.5291 −1.19760
\(983\) 33.1846 1.05843 0.529213 0.848489i \(-0.322487\pi\)
0.529213 + 0.848489i \(0.322487\pi\)
\(984\) 0 0
\(985\) 32.0482 1.02114
\(986\) 10.0702 0.320701
\(987\) 0 0
\(988\) 36.8603 1.17268
\(989\) −5.28362 −0.168009
\(990\) 0 0
\(991\) −60.1166 −1.90967 −0.954834 0.297141i \(-0.903967\pi\)
−0.954834 + 0.297141i \(0.903967\pi\)
\(992\) −38.0080 −1.20676
\(993\) 0 0
\(994\) 33.3688 1.05839
\(995\) 19.5966 0.621253
\(996\) 0 0
\(997\) −6.86405 −0.217387 −0.108693 0.994075i \(-0.534667\pi\)
−0.108693 + 0.994075i \(0.534667\pi\)
\(998\) −12.6720 −0.401126
\(999\) 0 0
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 \(a_p\))