Properties

Label 6036.2.a.i.1.15
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.754498 q^{5}\) \(-4.03319 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.754498 q^{5}\) \(-4.03319 q^{7}\) \(+1.00000 q^{9}\) \(-3.82332 q^{11}\) \(-4.25616 q^{13}\) \(-0.754498 q^{15}\) \(-5.34396 q^{17}\) \(-3.06933 q^{19}\) \(+4.03319 q^{21}\) \(-3.68458 q^{23}\) \(-4.43073 q^{25}\) \(-1.00000 q^{27}\) \(-6.36746 q^{29}\) \(-10.0869 q^{31}\) \(+3.82332 q^{33}\) \(-3.04303 q^{35}\) \(+9.28645 q^{37}\) \(+4.25616 q^{39}\) \(+2.62840 q^{41}\) \(+7.26677 q^{43}\) \(+0.754498 q^{45}\) \(-10.3713 q^{47}\) \(+9.26663 q^{49}\) \(+5.34396 q^{51}\) \(+10.2864 q^{53}\) \(-2.88468 q^{55}\) \(+3.06933 q^{57}\) \(+6.42578 q^{59}\) \(+9.19171 q^{61}\) \(-4.03319 q^{63}\) \(-3.21126 q^{65}\) \(-6.71426 q^{67}\) \(+3.68458 q^{69}\) \(-0.934048 q^{71}\) \(-12.6801 q^{73}\) \(+4.43073 q^{75}\) \(+15.4202 q^{77}\) \(-0.170154 q^{79}\) \(+1.00000 q^{81}\) \(+10.4649 q^{83}\) \(-4.03201 q^{85}\) \(+6.36746 q^{87}\) \(+7.13287 q^{89}\) \(+17.1659 q^{91}\) \(+10.0869 q^{93}\) \(-2.31580 q^{95}\) \(-12.3455 q^{97}\) \(-3.82332 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0.754498 0.337422 0.168711 0.985666i \(-0.446040\pi\)
0.168711 + 0.985666i \(0.446040\pi\)
\(6\) 0 0
\(7\) −4.03319 −1.52440 −0.762201 0.647340i \(-0.775881\pi\)
−0.762201 + 0.647340i \(0.775881\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.82332 −1.15277 −0.576387 0.817177i \(-0.695538\pi\)
−0.576387 + 0.817177i \(0.695538\pi\)
\(12\) 0 0
\(13\) −4.25616 −1.18045 −0.590223 0.807240i \(-0.700960\pi\)
−0.590223 + 0.807240i \(0.700960\pi\)
\(14\) 0 0
\(15\) −0.754498 −0.194810
\(16\) 0 0
\(17\) −5.34396 −1.29610 −0.648051 0.761597i \(-0.724416\pi\)
−0.648051 + 0.761597i \(0.724416\pi\)
\(18\) 0 0
\(19\) −3.06933 −0.704152 −0.352076 0.935971i \(-0.614524\pi\)
−0.352076 + 0.935971i \(0.614524\pi\)
\(20\) 0 0
\(21\) 4.03319 0.880114
\(22\) 0 0
\(23\) −3.68458 −0.768288 −0.384144 0.923273i \(-0.625503\pi\)
−0.384144 + 0.923273i \(0.625503\pi\)
\(24\) 0 0
\(25\) −4.43073 −0.886147
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.36746 −1.18241 −0.591204 0.806522i \(-0.701347\pi\)
−0.591204 + 0.806522i \(0.701347\pi\)
\(30\) 0 0
\(31\) −10.0869 −1.81167 −0.905835 0.423631i \(-0.860755\pi\)
−0.905835 + 0.423631i \(0.860755\pi\)
\(32\) 0 0
\(33\) 3.82332 0.665554
\(34\) 0 0
\(35\) −3.04303 −0.514366
\(36\) 0 0
\(37\) 9.28645 1.52668 0.763341 0.645996i \(-0.223558\pi\)
0.763341 + 0.645996i \(0.223558\pi\)
\(38\) 0 0
\(39\) 4.25616 0.681531
\(40\) 0 0
\(41\) 2.62840 0.410487 0.205244 0.978711i \(-0.434201\pi\)
0.205244 + 0.978711i \(0.434201\pi\)
\(42\) 0 0
\(43\) 7.26677 1.10817 0.554086 0.832459i \(-0.313068\pi\)
0.554086 + 0.832459i \(0.313068\pi\)
\(44\) 0 0
\(45\) 0.754498 0.112474
\(46\) 0 0
\(47\) −10.3713 −1.51280 −0.756402 0.654107i \(-0.773044\pi\)
−0.756402 + 0.654107i \(0.773044\pi\)
\(48\) 0 0
\(49\) 9.26663 1.32380
\(50\) 0 0
\(51\) 5.34396 0.748305
\(52\) 0 0
\(53\) 10.2864 1.41295 0.706475 0.707738i \(-0.250284\pi\)
0.706475 + 0.707738i \(0.250284\pi\)
\(54\) 0 0
\(55\) −2.88468 −0.388971
\(56\) 0 0
\(57\) 3.06933 0.406542
\(58\) 0 0
\(59\) 6.42578 0.836565 0.418282 0.908317i \(-0.362632\pi\)
0.418282 + 0.908317i \(0.362632\pi\)
\(60\) 0 0
\(61\) 9.19171 1.17688 0.588439 0.808541i \(-0.299743\pi\)
0.588439 + 0.808541i \(0.299743\pi\)
\(62\) 0 0
\(63\) −4.03319 −0.508134
\(64\) 0 0
\(65\) −3.21126 −0.398308
\(66\) 0 0
\(67\) −6.71426 −0.820278 −0.410139 0.912023i \(-0.634520\pi\)
−0.410139 + 0.912023i \(0.634520\pi\)
\(68\) 0 0
\(69\) 3.68458 0.443571
\(70\) 0 0
\(71\) −0.934048 −0.110851 −0.0554255 0.998463i \(-0.517652\pi\)
−0.0554255 + 0.998463i \(0.517652\pi\)
\(72\) 0 0
\(73\) −12.6801 −1.48409 −0.742045 0.670351i \(-0.766144\pi\)
−0.742045 + 0.670351i \(0.766144\pi\)
\(74\) 0 0
\(75\) 4.43073 0.511617
\(76\) 0 0
\(77\) 15.4202 1.75729
\(78\) 0 0
\(79\) −0.170154 −0.0191438 −0.00957192 0.999954i \(-0.503047\pi\)
−0.00957192 + 0.999954i \(0.503047\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 10.4649 1.14867 0.574334 0.818621i \(-0.305261\pi\)
0.574334 + 0.818621i \(0.305261\pi\)
\(84\) 0 0
\(85\) −4.03201 −0.437333
\(86\) 0 0
\(87\) 6.36746 0.682663
\(88\) 0 0
\(89\) 7.13287 0.756083 0.378042 0.925789i \(-0.376598\pi\)
0.378042 + 0.925789i \(0.376598\pi\)
\(90\) 0 0
\(91\) 17.1659 1.79947
\(92\) 0 0
\(93\) 10.0869 1.04597
\(94\) 0 0
\(95\) −2.31580 −0.237596
\(96\) 0 0
\(97\) −12.3455 −1.25350 −0.626749 0.779221i \(-0.715615\pi\)
−0.626749 + 0.779221i \(0.715615\pi\)
\(98\) 0 0
\(99\) −3.82332 −0.384258
\(100\) 0 0
\(101\) 5.74355 0.571505 0.285752 0.958303i \(-0.407756\pi\)
0.285752 + 0.958303i \(0.407756\pi\)
\(102\) 0 0
\(103\) −6.83800 −0.673768 −0.336884 0.941546i \(-0.609373\pi\)
−0.336884 + 0.941546i \(0.609373\pi\)
\(104\) 0 0
\(105\) 3.04303 0.296970
\(106\) 0 0
\(107\) −5.41431 −0.523421 −0.261711 0.965146i \(-0.584287\pi\)
−0.261711 + 0.965146i \(0.584287\pi\)
\(108\) 0 0
\(109\) −15.8743 −1.52048 −0.760241 0.649642i \(-0.774919\pi\)
−0.760241 + 0.649642i \(0.774919\pi\)
\(110\) 0 0
\(111\) −9.28645 −0.881430
\(112\) 0 0
\(113\) −2.42307 −0.227943 −0.113971 0.993484i \(-0.536357\pi\)
−0.113971 + 0.993484i \(0.536357\pi\)
\(114\) 0 0
\(115\) −2.78001 −0.259237
\(116\) 0 0
\(117\) −4.25616 −0.393482
\(118\) 0 0
\(119\) 21.5532 1.97578
\(120\) 0 0
\(121\) 3.61776 0.328888
\(122\) 0 0
\(123\) −2.62840 −0.236995
\(124\) 0 0
\(125\) −7.11547 −0.636427
\(126\) 0 0
\(127\) 12.5823 1.11650 0.558250 0.829672i \(-0.311473\pi\)
0.558250 + 0.829672i \(0.311473\pi\)
\(128\) 0 0
\(129\) −7.26677 −0.639803
\(130\) 0 0
\(131\) 1.11476 0.0973967 0.0486983 0.998814i \(-0.484493\pi\)
0.0486983 + 0.998814i \(0.484493\pi\)
\(132\) 0 0
\(133\) 12.3792 1.07341
\(134\) 0 0
\(135\) −0.754498 −0.0649368
\(136\) 0 0
\(137\) 2.03806 0.174123 0.0870617 0.996203i \(-0.472252\pi\)
0.0870617 + 0.996203i \(0.472252\pi\)
\(138\) 0 0
\(139\) 2.61705 0.221975 0.110988 0.993822i \(-0.464599\pi\)
0.110988 + 0.993822i \(0.464599\pi\)
\(140\) 0 0
\(141\) 10.3713 0.873417
\(142\) 0 0
\(143\) 16.2726 1.36079
\(144\) 0 0
\(145\) −4.80423 −0.398970
\(146\) 0 0
\(147\) −9.26663 −0.764299
\(148\) 0 0
\(149\) −0.999867 −0.0819123 −0.0409561 0.999161i \(-0.513040\pi\)
−0.0409561 + 0.999161i \(0.513040\pi\)
\(150\) 0 0
\(151\) 1.18736 0.0966257 0.0483128 0.998832i \(-0.484616\pi\)
0.0483128 + 0.998832i \(0.484616\pi\)
\(152\) 0 0
\(153\) −5.34396 −0.432034
\(154\) 0 0
\(155\) −7.61058 −0.611296
\(156\) 0 0
\(157\) 2.87492 0.229443 0.114722 0.993398i \(-0.463402\pi\)
0.114722 + 0.993398i \(0.463402\pi\)
\(158\) 0 0
\(159\) −10.2864 −0.815767
\(160\) 0 0
\(161\) 14.8606 1.17118
\(162\) 0 0
\(163\) −15.3943 −1.20578 −0.602888 0.797826i \(-0.705984\pi\)
−0.602888 + 0.797826i \(0.705984\pi\)
\(164\) 0 0
\(165\) 2.88468 0.224572
\(166\) 0 0
\(167\) −10.8494 −0.839554 −0.419777 0.907627i \(-0.637892\pi\)
−0.419777 + 0.907627i \(0.637892\pi\)
\(168\) 0 0
\(169\) 5.11487 0.393452
\(170\) 0 0
\(171\) −3.06933 −0.234717
\(172\) 0 0
\(173\) 8.55402 0.650350 0.325175 0.945654i \(-0.394577\pi\)
0.325175 + 0.945654i \(0.394577\pi\)
\(174\) 0 0
\(175\) 17.8700 1.35084
\(176\) 0 0
\(177\) −6.42578 −0.482991
\(178\) 0 0
\(179\) −22.5055 −1.68214 −0.841070 0.540927i \(-0.818074\pi\)
−0.841070 + 0.540927i \(0.818074\pi\)
\(180\) 0 0
\(181\) 24.1911 1.79811 0.899057 0.437832i \(-0.144254\pi\)
0.899057 + 0.437832i \(0.144254\pi\)
\(182\) 0 0
\(183\) −9.19171 −0.679471
\(184\) 0 0
\(185\) 7.00660 0.515135
\(186\) 0 0
\(187\) 20.4317 1.49411
\(188\) 0 0
\(189\) 4.03319 0.293371
\(190\) 0 0
\(191\) −9.29327 −0.672438 −0.336219 0.941784i \(-0.609148\pi\)
−0.336219 + 0.941784i \(0.609148\pi\)
\(192\) 0 0
\(193\) −11.8415 −0.852368 −0.426184 0.904637i \(-0.640142\pi\)
−0.426184 + 0.904637i \(0.640142\pi\)
\(194\) 0 0
\(195\) 3.21126 0.229963
\(196\) 0 0
\(197\) 10.2965 0.733598 0.366799 0.930300i \(-0.380454\pi\)
0.366799 + 0.930300i \(0.380454\pi\)
\(198\) 0 0
\(199\) 25.1760 1.78468 0.892341 0.451362i \(-0.149062\pi\)
0.892341 + 0.451362i \(0.149062\pi\)
\(200\) 0 0
\(201\) 6.71426 0.473587
\(202\) 0 0
\(203\) 25.6812 1.80246
\(204\) 0 0
\(205\) 1.98312 0.138507
\(206\) 0 0
\(207\) −3.68458 −0.256096
\(208\) 0 0
\(209\) 11.7350 0.811728
\(210\) 0 0
\(211\) −16.7238 −1.15132 −0.575658 0.817691i \(-0.695254\pi\)
−0.575658 + 0.817691i \(0.695254\pi\)
\(212\) 0 0
\(213\) 0.934048 0.0639999
\(214\) 0 0
\(215\) 5.48276 0.373921
\(216\) 0 0
\(217\) 40.6826 2.76171
\(218\) 0 0
\(219\) 12.6801 0.856839
\(220\) 0 0
\(221\) 22.7448 1.52998
\(222\) 0 0
\(223\) 6.83098 0.457436 0.228718 0.973493i \(-0.426547\pi\)
0.228718 + 0.973493i \(0.426547\pi\)
\(224\) 0 0
\(225\) −4.43073 −0.295382
\(226\) 0 0
\(227\) −27.7479 −1.84169 −0.920845 0.389929i \(-0.872500\pi\)
−0.920845 + 0.389929i \(0.872500\pi\)
\(228\) 0 0
\(229\) −8.72641 −0.576657 −0.288329 0.957532i \(-0.593100\pi\)
−0.288329 + 0.957532i \(0.593100\pi\)
\(230\) 0 0
\(231\) −15.4202 −1.01457
\(232\) 0 0
\(233\) −12.2730 −0.804030 −0.402015 0.915633i \(-0.631690\pi\)
−0.402015 + 0.915633i \(0.631690\pi\)
\(234\) 0 0
\(235\) −7.82509 −0.510452
\(236\) 0 0
\(237\) 0.170154 0.0110527
\(238\) 0 0
\(239\) −18.0522 −1.16770 −0.583851 0.811861i \(-0.698455\pi\)
−0.583851 + 0.811861i \(0.698455\pi\)
\(240\) 0 0
\(241\) 25.8028 1.66211 0.831054 0.556192i \(-0.187738\pi\)
0.831054 + 0.556192i \(0.187738\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 6.99165 0.446680
\(246\) 0 0
\(247\) 13.0635 0.831213
\(248\) 0 0
\(249\) −10.4649 −0.663184
\(250\) 0 0
\(251\) 25.0414 1.58060 0.790299 0.612721i \(-0.209925\pi\)
0.790299 + 0.612721i \(0.209925\pi\)
\(252\) 0 0
\(253\) 14.0873 0.885663
\(254\) 0 0
\(255\) 4.03201 0.252494
\(256\) 0 0
\(257\) 14.6320 0.912716 0.456358 0.889796i \(-0.349154\pi\)
0.456358 + 0.889796i \(0.349154\pi\)
\(258\) 0 0
\(259\) −37.4540 −2.32728
\(260\) 0 0
\(261\) −6.36746 −0.394136
\(262\) 0 0
\(263\) −27.1264 −1.67268 −0.836342 0.548208i \(-0.815310\pi\)
−0.836342 + 0.548208i \(0.815310\pi\)
\(264\) 0 0
\(265\) 7.76109 0.476760
\(266\) 0 0
\(267\) −7.13287 −0.436525
\(268\) 0 0
\(269\) −15.5230 −0.946457 −0.473228 0.880940i \(-0.656911\pi\)
−0.473228 + 0.880940i \(0.656911\pi\)
\(270\) 0 0
\(271\) −3.76129 −0.228482 −0.114241 0.993453i \(-0.536444\pi\)
−0.114241 + 0.993453i \(0.536444\pi\)
\(272\) 0 0
\(273\) −17.1659 −1.03893
\(274\) 0 0
\(275\) 16.9401 1.02153
\(276\) 0 0
\(277\) −7.82723 −0.470293 −0.235146 0.971960i \(-0.575557\pi\)
−0.235146 + 0.971960i \(0.575557\pi\)
\(278\) 0 0
\(279\) −10.0869 −0.603890
\(280\) 0 0
\(281\) −11.0898 −0.661565 −0.330782 0.943707i \(-0.607313\pi\)
−0.330782 + 0.943707i \(0.607313\pi\)
\(282\) 0 0
\(283\) −28.4603 −1.69179 −0.845895 0.533349i \(-0.820933\pi\)
−0.845895 + 0.533349i \(0.820933\pi\)
\(284\) 0 0
\(285\) 2.31580 0.137176
\(286\) 0 0
\(287\) −10.6008 −0.625748
\(288\) 0 0
\(289\) 11.5580 0.679880
\(290\) 0 0
\(291\) 12.3455 0.723707
\(292\) 0 0
\(293\) −31.1011 −1.81695 −0.908473 0.417943i \(-0.862751\pi\)
−0.908473 + 0.417943i \(0.862751\pi\)
\(294\) 0 0
\(295\) 4.84823 0.282275
\(296\) 0 0
\(297\) 3.82332 0.221851
\(298\) 0 0
\(299\) 15.6822 0.906922
\(300\) 0 0
\(301\) −29.3083 −1.68930
\(302\) 0 0
\(303\) −5.74355 −0.329959
\(304\) 0 0
\(305\) 6.93513 0.397104
\(306\) 0 0
\(307\) 22.1359 1.26336 0.631680 0.775229i \(-0.282366\pi\)
0.631680 + 0.775229i \(0.282366\pi\)
\(308\) 0 0
\(309\) 6.83800 0.389000
\(310\) 0 0
\(311\) −20.5369 −1.16454 −0.582270 0.812995i \(-0.697835\pi\)
−0.582270 + 0.812995i \(0.697835\pi\)
\(312\) 0 0
\(313\) 16.4172 0.927957 0.463978 0.885847i \(-0.346422\pi\)
0.463978 + 0.885847i \(0.346422\pi\)
\(314\) 0 0
\(315\) −3.04303 −0.171455
\(316\) 0 0
\(317\) −9.49952 −0.533546 −0.266773 0.963759i \(-0.585957\pi\)
−0.266773 + 0.963759i \(0.585957\pi\)
\(318\) 0 0
\(319\) 24.3448 1.36305
\(320\) 0 0
\(321\) 5.41431 0.302197
\(322\) 0 0
\(323\) 16.4024 0.912653
\(324\) 0 0
\(325\) 18.8579 1.04605
\(326\) 0 0
\(327\) 15.8743 0.877850
\(328\) 0 0
\(329\) 41.8293 2.30612
\(330\) 0 0
\(331\) −21.9003 −1.20375 −0.601874 0.798591i \(-0.705579\pi\)
−0.601874 + 0.798591i \(0.705579\pi\)
\(332\) 0 0
\(333\) 9.28645 0.508894
\(334\) 0 0
\(335\) −5.06589 −0.276779
\(336\) 0 0
\(337\) 10.5657 0.575551 0.287776 0.957698i \(-0.407084\pi\)
0.287776 + 0.957698i \(0.407084\pi\)
\(338\) 0 0
\(339\) 2.42307 0.131603
\(340\) 0 0
\(341\) 38.5656 2.08845
\(342\) 0 0
\(343\) −9.14174 −0.493608
\(344\) 0 0
\(345\) 2.78001 0.149671
\(346\) 0 0
\(347\) −27.8517 −1.49516 −0.747578 0.664174i \(-0.768783\pi\)
−0.747578 + 0.664174i \(0.768783\pi\)
\(348\) 0 0
\(349\) 4.34629 0.232652 0.116326 0.993211i \(-0.462888\pi\)
0.116326 + 0.993211i \(0.462888\pi\)
\(350\) 0 0
\(351\) 4.25616 0.227177
\(352\) 0 0
\(353\) 12.6797 0.674874 0.337437 0.941348i \(-0.390440\pi\)
0.337437 + 0.941348i \(0.390440\pi\)
\(354\) 0 0
\(355\) −0.704737 −0.0374035
\(356\) 0 0
\(357\) −21.5532 −1.14072
\(358\) 0 0
\(359\) 28.9983 1.53047 0.765236 0.643750i \(-0.222622\pi\)
0.765236 + 0.643750i \(0.222622\pi\)
\(360\) 0 0
\(361\) −9.57923 −0.504170
\(362\) 0 0
\(363\) −3.61776 −0.189883
\(364\) 0 0
\(365\) −9.56708 −0.500764
\(366\) 0 0
\(367\) −10.5490 −0.550652 −0.275326 0.961351i \(-0.588786\pi\)
−0.275326 + 0.961351i \(0.588786\pi\)
\(368\) 0 0
\(369\) 2.62840 0.136829
\(370\) 0 0
\(371\) −41.4872 −2.15391
\(372\) 0 0
\(373\) 4.24418 0.219755 0.109878 0.993945i \(-0.464954\pi\)
0.109878 + 0.993945i \(0.464954\pi\)
\(374\) 0 0
\(375\) 7.11547 0.367441
\(376\) 0 0
\(377\) 27.1009 1.39577
\(378\) 0 0
\(379\) −1.87745 −0.0964381 −0.0482190 0.998837i \(-0.515355\pi\)
−0.0482190 + 0.998837i \(0.515355\pi\)
\(380\) 0 0
\(381\) −12.5823 −0.644612
\(382\) 0 0
\(383\) 31.6065 1.61502 0.807509 0.589855i \(-0.200815\pi\)
0.807509 + 0.589855i \(0.200815\pi\)
\(384\) 0 0
\(385\) 11.6345 0.592948
\(386\) 0 0
\(387\) 7.26677 0.369391
\(388\) 0 0
\(389\) 0.510967 0.0259070 0.0129535 0.999916i \(-0.495877\pi\)
0.0129535 + 0.999916i \(0.495877\pi\)
\(390\) 0 0
\(391\) 19.6903 0.995780
\(392\) 0 0
\(393\) −1.11476 −0.0562320
\(394\) 0 0
\(395\) −0.128381 −0.00645955
\(396\) 0 0
\(397\) −29.8037 −1.49580 −0.747902 0.663809i \(-0.768939\pi\)
−0.747902 + 0.663809i \(0.768939\pi\)
\(398\) 0 0
\(399\) −12.3792 −0.619734
\(400\) 0 0
\(401\) −15.9732 −0.797663 −0.398832 0.917024i \(-0.630584\pi\)
−0.398832 + 0.917024i \(0.630584\pi\)
\(402\) 0 0
\(403\) 42.9316 2.13858
\(404\) 0 0
\(405\) 0.754498 0.0374913
\(406\) 0 0
\(407\) −35.5050 −1.75992
\(408\) 0 0
\(409\) −5.71498 −0.282587 −0.141294 0.989968i \(-0.545126\pi\)
−0.141294 + 0.989968i \(0.545126\pi\)
\(410\) 0 0
\(411\) −2.03806 −0.100530
\(412\) 0 0
\(413\) −25.9164 −1.27526
\(414\) 0 0
\(415\) 7.89572 0.387586
\(416\) 0 0
\(417\) −2.61705 −0.128158
\(418\) 0 0
\(419\) 11.8180 0.577349 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(420\) 0 0
\(421\) 17.6267 0.859073 0.429537 0.903049i \(-0.358677\pi\)
0.429537 + 0.903049i \(0.358677\pi\)
\(422\) 0 0
\(423\) −10.3713 −0.504268
\(424\) 0 0
\(425\) 23.6777 1.14854
\(426\) 0 0
\(427\) −37.0719 −1.79404
\(428\) 0 0
\(429\) −16.2726 −0.785651
\(430\) 0 0
\(431\) 30.5333 1.47074 0.735369 0.677667i \(-0.237009\pi\)
0.735369 + 0.677667i \(0.237009\pi\)
\(432\) 0 0
\(433\) 30.9147 1.48567 0.742833 0.669477i \(-0.233482\pi\)
0.742833 + 0.669477i \(0.233482\pi\)
\(434\) 0 0
\(435\) 4.80423 0.230345
\(436\) 0 0
\(437\) 11.3092 0.540992
\(438\) 0 0
\(439\) −3.50027 −0.167059 −0.0835294 0.996505i \(-0.526619\pi\)
−0.0835294 + 0.996505i \(0.526619\pi\)
\(440\) 0 0
\(441\) 9.26663 0.441268
\(442\) 0 0
\(443\) 10.5864 0.502977 0.251489 0.967860i \(-0.419080\pi\)
0.251489 + 0.967860i \(0.419080\pi\)
\(444\) 0 0
\(445\) 5.38174 0.255119
\(446\) 0 0
\(447\) 0.999867 0.0472921
\(448\) 0 0
\(449\) −19.7803 −0.933491 −0.466745 0.884392i \(-0.654574\pi\)
−0.466745 + 0.884392i \(0.654574\pi\)
\(450\) 0 0
\(451\) −10.0492 −0.473199
\(452\) 0 0
\(453\) −1.18736 −0.0557869
\(454\) 0 0
\(455\) 12.9516 0.607181
\(456\) 0 0
\(457\) 25.1346 1.17575 0.587875 0.808952i \(-0.299965\pi\)
0.587875 + 0.808952i \(0.299965\pi\)
\(458\) 0 0
\(459\) 5.34396 0.249435
\(460\) 0 0
\(461\) 6.56388 0.305711 0.152855 0.988249i \(-0.451153\pi\)
0.152855 + 0.988249i \(0.451153\pi\)
\(462\) 0 0
\(463\) 10.4817 0.487125 0.243562 0.969885i \(-0.421684\pi\)
0.243562 + 0.969885i \(0.421684\pi\)
\(464\) 0 0
\(465\) 7.61058 0.352932
\(466\) 0 0
\(467\) −1.91751 −0.0887317 −0.0443659 0.999015i \(-0.514127\pi\)
−0.0443659 + 0.999015i \(0.514127\pi\)
\(468\) 0 0
\(469\) 27.0799 1.25043
\(470\) 0 0
\(471\) −2.87492 −0.132469
\(472\) 0 0
\(473\) −27.7832 −1.27747
\(474\) 0 0
\(475\) 13.5994 0.623982
\(476\) 0 0
\(477\) 10.2864 0.470983
\(478\) 0 0
\(479\) −13.4291 −0.613591 −0.306796 0.951775i \(-0.599257\pi\)
−0.306796 + 0.951775i \(0.599257\pi\)
\(480\) 0 0
\(481\) −39.5246 −1.80217
\(482\) 0 0
\(483\) −14.8606 −0.676182
\(484\) 0 0
\(485\) −9.31467 −0.422957
\(486\) 0 0
\(487\) −5.47244 −0.247980 −0.123990 0.992283i \(-0.539569\pi\)
−0.123990 + 0.992283i \(0.539569\pi\)
\(488\) 0 0
\(489\) 15.3943 0.696156
\(490\) 0 0
\(491\) −25.7816 −1.16351 −0.581754 0.813365i \(-0.697634\pi\)
−0.581754 + 0.813365i \(0.697634\pi\)
\(492\) 0 0
\(493\) 34.0275 1.53252
\(494\) 0 0
\(495\) −2.88468 −0.129657
\(496\) 0 0
\(497\) 3.76719 0.168982
\(498\) 0 0
\(499\) 33.2044 1.48643 0.743217 0.669051i \(-0.233299\pi\)
0.743217 + 0.669051i \(0.233299\pi\)
\(500\) 0 0
\(501\) 10.8494 0.484717
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 4.33350 0.192838
\(506\) 0 0
\(507\) −5.11487 −0.227159
\(508\) 0 0
\(509\) 9.72689 0.431137 0.215568 0.976489i \(-0.430840\pi\)
0.215568 + 0.976489i \(0.430840\pi\)
\(510\) 0 0
\(511\) 51.1411 2.26235
\(512\) 0 0
\(513\) 3.06933 0.135514
\(514\) 0 0
\(515\) −5.15926 −0.227344
\(516\) 0 0
\(517\) 39.6526 1.74392
\(518\) 0 0
\(519\) −8.55402 −0.375480
\(520\) 0 0
\(521\) 37.5389 1.64461 0.822305 0.569047i \(-0.192688\pi\)
0.822305 + 0.569047i \(0.192688\pi\)
\(522\) 0 0
\(523\) 39.2063 1.71437 0.857185 0.515009i \(-0.172211\pi\)
0.857185 + 0.515009i \(0.172211\pi\)
\(524\) 0 0
\(525\) −17.8700 −0.779910
\(526\) 0 0
\(527\) 53.9043 2.34811
\(528\) 0 0
\(529\) −9.42386 −0.409733
\(530\) 0 0
\(531\) 6.42578 0.278855
\(532\) 0 0
\(533\) −11.1869 −0.484558
\(534\) 0 0
\(535\) −4.08508 −0.176614
\(536\) 0 0
\(537\) 22.5055 0.971184
\(538\) 0 0
\(539\) −35.4293 −1.52605
\(540\) 0 0
\(541\) −1.64741 −0.0708278 −0.0354139 0.999373i \(-0.511275\pi\)
−0.0354139 + 0.999373i \(0.511275\pi\)
\(542\) 0 0
\(543\) −24.1911 −1.03814
\(544\) 0 0
\(545\) −11.9771 −0.513043
\(546\) 0 0
\(547\) −33.6132 −1.43720 −0.718598 0.695425i \(-0.755216\pi\)
−0.718598 + 0.695425i \(0.755216\pi\)
\(548\) 0 0
\(549\) 9.19171 0.392293
\(550\) 0 0
\(551\) 19.5438 0.832595
\(552\) 0 0
\(553\) 0.686264 0.0291829
\(554\) 0 0
\(555\) −7.00660 −0.297414
\(556\) 0 0
\(557\) −23.9974 −1.01680 −0.508402 0.861120i \(-0.669763\pi\)
−0.508402 + 0.861120i \(0.669763\pi\)
\(558\) 0 0
\(559\) −30.9285 −1.30814
\(560\) 0 0
\(561\) −20.4317 −0.862626
\(562\) 0 0
\(563\) −22.3031 −0.939965 −0.469983 0.882676i \(-0.655740\pi\)
−0.469983 + 0.882676i \(0.655740\pi\)
\(564\) 0 0
\(565\) −1.82820 −0.0769128
\(566\) 0 0
\(567\) −4.03319 −0.169378
\(568\) 0 0
\(569\) −40.6422 −1.70381 −0.851905 0.523696i \(-0.824553\pi\)
−0.851905 + 0.523696i \(0.824553\pi\)
\(570\) 0 0
\(571\) 33.4244 1.39877 0.699385 0.714746i \(-0.253458\pi\)
0.699385 + 0.714746i \(0.253458\pi\)
\(572\) 0 0
\(573\) 9.29327 0.388232
\(574\) 0 0
\(575\) 16.3254 0.680816
\(576\) 0 0
\(577\) −28.7613 −1.19735 −0.598674 0.800993i \(-0.704306\pi\)
−0.598674 + 0.800993i \(0.704306\pi\)
\(578\) 0 0
\(579\) 11.8415 0.492115
\(580\) 0 0
\(581\) −42.2068 −1.75103
\(582\) 0 0
\(583\) −39.3283 −1.62881
\(584\) 0 0
\(585\) −3.21126 −0.132769
\(586\) 0 0
\(587\) −11.3654 −0.469102 −0.234551 0.972104i \(-0.575362\pi\)
−0.234551 + 0.972104i \(0.575362\pi\)
\(588\) 0 0
\(589\) 30.9602 1.27569
\(590\) 0 0
\(591\) −10.2965 −0.423543
\(592\) 0 0
\(593\) −21.3119 −0.875177 −0.437588 0.899175i \(-0.644167\pi\)
−0.437588 + 0.899175i \(0.644167\pi\)
\(594\) 0 0
\(595\) 16.2619 0.666671
\(596\) 0 0
\(597\) −25.1760 −1.03039
\(598\) 0 0
\(599\) −7.58424 −0.309884 −0.154942 0.987924i \(-0.549519\pi\)
−0.154942 + 0.987924i \(0.549519\pi\)
\(600\) 0 0
\(601\) 35.3001 1.43992 0.719960 0.694015i \(-0.244160\pi\)
0.719960 + 0.694015i \(0.244160\pi\)
\(602\) 0 0
\(603\) −6.71426 −0.273426
\(604\) 0 0
\(605\) 2.72959 0.110974
\(606\) 0 0
\(607\) 16.6902 0.677435 0.338718 0.940888i \(-0.390007\pi\)
0.338718 + 0.940888i \(0.390007\pi\)
\(608\) 0 0
\(609\) −25.6812 −1.04065
\(610\) 0 0
\(611\) 44.1417 1.78578
\(612\) 0 0
\(613\) −2.92515 −0.118146 −0.0590729 0.998254i \(-0.518814\pi\)
−0.0590729 + 0.998254i \(0.518814\pi\)
\(614\) 0 0
\(615\) −1.98312 −0.0799672
\(616\) 0 0
\(617\) −15.7400 −0.633670 −0.316835 0.948481i \(-0.602620\pi\)
−0.316835 + 0.948481i \(0.602620\pi\)
\(618\) 0 0
\(619\) 7.76427 0.312072 0.156036 0.987751i \(-0.450128\pi\)
0.156036 + 0.987751i \(0.450128\pi\)
\(620\) 0 0
\(621\) 3.68458 0.147857
\(622\) 0 0
\(623\) −28.7682 −1.15258
\(624\) 0 0
\(625\) 16.7851 0.671403
\(626\) 0 0
\(627\) −11.7350 −0.468651
\(628\) 0 0
\(629\) −49.6264 −1.97874
\(630\) 0 0
\(631\) 14.0859 0.560749 0.280375 0.959891i \(-0.409541\pi\)
0.280375 + 0.959891i \(0.409541\pi\)
\(632\) 0 0
\(633\) 16.7238 0.664713
\(634\) 0 0
\(635\) 9.49333 0.376731
\(636\) 0 0
\(637\) −39.4402 −1.56268
\(638\) 0 0
\(639\) −0.934048 −0.0369504
\(640\) 0 0
\(641\) −8.77631 −0.346643 −0.173322 0.984865i \(-0.555450\pi\)
−0.173322 + 0.984865i \(0.555450\pi\)
\(642\) 0 0
\(643\) 2.86752 0.113084 0.0565419 0.998400i \(-0.481993\pi\)
0.0565419 + 0.998400i \(0.481993\pi\)
\(644\) 0 0
\(645\) −5.48276 −0.215883
\(646\) 0 0
\(647\) −25.7123 −1.01085 −0.505427 0.862869i \(-0.668665\pi\)
−0.505427 + 0.862869i \(0.668665\pi\)
\(648\) 0 0
\(649\) −24.5678 −0.964370
\(650\) 0 0
\(651\) −40.6826 −1.59448
\(652\) 0 0
\(653\) 38.3735 1.50167 0.750835 0.660490i \(-0.229651\pi\)
0.750835 + 0.660490i \(0.229651\pi\)
\(654\) 0 0
\(655\) 0.841081 0.0328637
\(656\) 0 0
\(657\) −12.6801 −0.494696
\(658\) 0 0
\(659\) 27.4948 1.07105 0.535523 0.844521i \(-0.320115\pi\)
0.535523 + 0.844521i \(0.320115\pi\)
\(660\) 0 0
\(661\) 31.4337 1.22263 0.611314 0.791388i \(-0.290641\pi\)
0.611314 + 0.791388i \(0.290641\pi\)
\(662\) 0 0
\(663\) −22.7448 −0.883333
\(664\) 0 0
\(665\) 9.34006 0.362192
\(666\) 0 0
\(667\) 23.4614 0.908430
\(668\) 0 0
\(669\) −6.83098 −0.264101
\(670\) 0 0
\(671\) −35.1429 −1.35667
\(672\) 0 0
\(673\) −28.9440 −1.11571 −0.557855 0.829939i \(-0.688375\pi\)
−0.557855 + 0.829939i \(0.688375\pi\)
\(674\) 0 0
\(675\) 4.43073 0.170539
\(676\) 0 0
\(677\) −11.5512 −0.443950 −0.221975 0.975052i \(-0.571250\pi\)
−0.221975 + 0.975052i \(0.571250\pi\)
\(678\) 0 0
\(679\) 49.7918 1.91084
\(680\) 0 0
\(681\) 27.7479 1.06330
\(682\) 0 0
\(683\) −27.8711 −1.06646 −0.533229 0.845971i \(-0.679022\pi\)
−0.533229 + 0.845971i \(0.679022\pi\)
\(684\) 0 0
\(685\) 1.53771 0.0587530
\(686\) 0 0
\(687\) 8.72641 0.332933
\(688\) 0 0
\(689\) −43.7807 −1.66791
\(690\) 0 0
\(691\) −3.75815 −0.142967 −0.0714834 0.997442i \(-0.522773\pi\)
−0.0714834 + 0.997442i \(0.522773\pi\)
\(692\) 0 0
\(693\) 15.4202 0.585764
\(694\) 0 0
\(695\) 1.97456 0.0748993
\(696\) 0 0
\(697\) −14.0461 −0.532033
\(698\) 0 0
\(699\) 12.2730 0.464207
\(700\) 0 0
\(701\) 5.02223 0.189687 0.0948435 0.995492i \(-0.469765\pi\)
0.0948435 + 0.995492i \(0.469765\pi\)
\(702\) 0 0
\(703\) −28.5031 −1.07502
\(704\) 0 0
\(705\) 7.82509 0.294710
\(706\) 0 0
\(707\) −23.1648 −0.871204
\(708\) 0 0
\(709\) 36.4816 1.37009 0.685047 0.728499i \(-0.259782\pi\)
0.685047 + 0.728499i \(0.259782\pi\)
\(710\) 0 0
\(711\) −0.170154 −0.00638128
\(712\) 0 0
\(713\) 37.1662 1.39188
\(714\) 0 0
\(715\) 12.2777 0.459159
\(716\) 0 0
\(717\) 18.0522 0.674173
\(718\) 0 0
\(719\) 43.9651 1.63962 0.819812 0.572633i \(-0.194078\pi\)
0.819812 + 0.572633i \(0.194078\pi\)
\(720\) 0 0
\(721\) 27.5790 1.02709
\(722\) 0 0
\(723\) −25.8028 −0.959618
\(724\) 0 0
\(725\) 28.2125 1.04779
\(726\) 0 0
\(727\) −9.53527 −0.353643 −0.176822 0.984243i \(-0.556582\pi\)
−0.176822 + 0.984243i \(0.556582\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −38.8334 −1.43630
\(732\) 0 0
\(733\) −33.9700 −1.25471 −0.627355 0.778733i \(-0.715863\pi\)
−0.627355 + 0.778733i \(0.715863\pi\)
\(734\) 0 0
\(735\) −6.99165 −0.257891
\(736\) 0 0
\(737\) 25.6708 0.945594
\(738\) 0 0
\(739\) −32.4665 −1.19430 −0.597150 0.802130i \(-0.703700\pi\)
−0.597150 + 0.802130i \(0.703700\pi\)
\(740\) 0 0
\(741\) −13.0635 −0.479901
\(742\) 0 0
\(743\) −34.4226 −1.26284 −0.631422 0.775440i \(-0.717528\pi\)
−0.631422 + 0.775440i \(0.717528\pi\)
\(744\) 0 0
\(745\) −0.754397 −0.0276390
\(746\) 0 0
\(747\) 10.4649 0.382890
\(748\) 0 0
\(749\) 21.8369 0.797905
\(750\) 0 0
\(751\) 6.75620 0.246537 0.123269 0.992373i \(-0.460662\pi\)
0.123269 + 0.992373i \(0.460662\pi\)
\(752\) 0 0
\(753\) −25.0414 −0.912559
\(754\) 0 0
\(755\) 0.895857 0.0326036
\(756\) 0 0
\(757\) 26.7652 0.972797 0.486398 0.873737i \(-0.338310\pi\)
0.486398 + 0.873737i \(0.338310\pi\)
\(758\) 0 0
\(759\) −14.0873 −0.511338
\(760\) 0 0
\(761\) 2.22026 0.0804843 0.0402422 0.999190i \(-0.487187\pi\)
0.0402422 + 0.999190i \(0.487187\pi\)
\(762\) 0 0
\(763\) 64.0240 2.31783
\(764\) 0 0
\(765\) −4.03201 −0.145778
\(766\) 0 0
\(767\) −27.3491 −0.987519
\(768\) 0 0
\(769\) 15.8742 0.572438 0.286219 0.958164i \(-0.407601\pi\)
0.286219 + 0.958164i \(0.407601\pi\)
\(770\) 0 0
\(771\) −14.6320 −0.526957
\(772\) 0 0
\(773\) 41.1692 1.48075 0.740377 0.672192i \(-0.234647\pi\)
0.740377 + 0.672192i \(0.234647\pi\)
\(774\) 0 0
\(775\) 44.6926 1.60540
\(776\) 0 0
\(777\) 37.4540 1.34366
\(778\) 0 0
\(779\) −8.06742 −0.289045
\(780\) 0 0
\(781\) 3.57116 0.127786
\(782\) 0 0
\(783\) 6.36746 0.227554
\(784\) 0 0
\(785\) 2.16912 0.0774192
\(786\) 0 0
\(787\) −13.3361 −0.475380 −0.237690 0.971341i \(-0.576390\pi\)
−0.237690 + 0.971341i \(0.576390\pi\)
\(788\) 0 0
\(789\) 27.1264 0.965725
\(790\) 0 0
\(791\) 9.77269 0.347477
\(792\) 0 0
\(793\) −39.1214 −1.38924
\(794\) 0 0
\(795\) −7.76109 −0.275257
\(796\) 0 0
\(797\) −39.2316 −1.38965 −0.694827 0.719177i \(-0.744519\pi\)
−0.694827 + 0.719177i \(0.744519\pi\)
\(798\) 0 0
\(799\) 55.4236 1.96075
\(800\) 0 0
\(801\) 7.13287 0.252028
\(802\) 0 0
\(803\) 48.4799 1.71082
\(804\) 0 0
\(805\) 11.2123 0.395182
\(806\) 0 0
\(807\) 15.5230 0.546437
\(808\) 0 0
\(809\) 43.5715 1.53189 0.765947 0.642904i \(-0.222271\pi\)
0.765947 + 0.642904i \(0.222271\pi\)
\(810\) 0 0
\(811\) 14.9480 0.524897 0.262448 0.964946i \(-0.415470\pi\)
0.262448 + 0.964946i \(0.415470\pi\)
\(812\) 0 0
\(813\) 3.76129 0.131914
\(814\) 0 0
\(815\) −11.6150 −0.406855
\(816\) 0 0
\(817\) −22.3041 −0.780322
\(818\) 0 0
\(819\) 17.1659 0.599825
\(820\) 0 0
\(821\) −49.1473 −1.71525 −0.857626 0.514274i \(-0.828061\pi\)
−0.857626 + 0.514274i \(0.828061\pi\)
\(822\) 0 0
\(823\) 30.1302 1.05027 0.525137 0.851018i \(-0.324014\pi\)
0.525137 + 0.851018i \(0.324014\pi\)
\(824\) 0 0
\(825\) −16.9401 −0.589779
\(826\) 0 0
\(827\) 28.8177 1.00209 0.501045 0.865421i \(-0.332949\pi\)
0.501045 + 0.865421i \(0.332949\pi\)
\(828\) 0 0
\(829\) −26.4605 −0.919010 −0.459505 0.888175i \(-0.651973\pi\)
−0.459505 + 0.888175i \(0.651973\pi\)
\(830\) 0 0
\(831\) 7.82723 0.271524
\(832\) 0 0
\(833\) −49.5205 −1.71578
\(834\) 0 0
\(835\) −8.18586 −0.283283
\(836\) 0 0
\(837\) 10.0869 0.348656
\(838\) 0 0
\(839\) −23.6556 −0.816680 −0.408340 0.912830i \(-0.633892\pi\)
−0.408340 + 0.912830i \(0.633892\pi\)
\(840\) 0 0
\(841\) 11.5445 0.398087
\(842\) 0 0
\(843\) 11.0898 0.381954
\(844\) 0 0
\(845\) 3.85916 0.132759
\(846\) 0 0
\(847\) −14.5911 −0.501357
\(848\) 0 0
\(849\) 28.4603 0.976755
\(850\) 0 0
\(851\) −34.2167 −1.17293
\(852\) 0 0
\(853\) −29.0652 −0.995174 −0.497587 0.867414i \(-0.665780\pi\)
−0.497587 + 0.867414i \(0.665780\pi\)
\(854\) 0 0
\(855\) −2.31580 −0.0791987
\(856\) 0 0
\(857\) −6.11549 −0.208901 −0.104451 0.994530i \(-0.533308\pi\)
−0.104451 + 0.994530i \(0.533308\pi\)
\(858\) 0 0
\(859\) −18.6271 −0.635548 −0.317774 0.948166i \(-0.602935\pi\)
−0.317774 + 0.948166i \(0.602935\pi\)
\(860\) 0 0
\(861\) 10.6008 0.361276
\(862\) 0 0
\(863\) −55.7750 −1.89860 −0.949302 0.314366i \(-0.898208\pi\)
−0.949302 + 0.314366i \(0.898208\pi\)
\(864\) 0 0
\(865\) 6.45399 0.219442
\(866\) 0 0
\(867\) −11.5580 −0.392529
\(868\) 0 0
\(869\) 0.650554 0.0220685
\(870\) 0 0
\(871\) 28.5769 0.968293
\(872\) 0 0
\(873\) −12.3455 −0.417833
\(874\) 0 0
\(875\) 28.6980 0.970170
\(876\) 0 0
\(877\) −47.5083 −1.60424 −0.802121 0.597162i \(-0.796295\pi\)
−0.802121 + 0.597162i \(0.796295\pi\)
\(878\) 0 0
\(879\) 31.1011 1.04901
\(880\) 0 0
\(881\) 2.62666 0.0884944 0.0442472 0.999021i \(-0.485911\pi\)
0.0442472 + 0.999021i \(0.485911\pi\)
\(882\) 0 0
\(883\) 3.16601 0.106545 0.0532724 0.998580i \(-0.483035\pi\)
0.0532724 + 0.998580i \(0.483035\pi\)
\(884\) 0 0
\(885\) −4.84823 −0.162972
\(886\) 0 0
\(887\) −15.4145 −0.517569 −0.258785 0.965935i \(-0.583322\pi\)
−0.258785 + 0.965935i \(0.583322\pi\)
\(888\) 0 0
\(889\) −50.7469 −1.70200
\(890\) 0 0
\(891\) −3.82332 −0.128086
\(892\) 0 0
\(893\) 31.8328 1.06524
\(894\) 0 0
\(895\) −16.9803 −0.567590
\(896\) 0 0
\(897\) −15.6822 −0.523612
\(898\) 0 0
\(899\) 64.2282 2.14213
\(900\) 0 0
\(901\) −54.9703 −1.83133
\(902\) 0 0
\(903\) 29.3083 0.975318
\(904\) 0 0
\(905\) 18.2522 0.606722
\(906\) 0 0
\(907\) 48.5123 1.61083 0.805413 0.592714i \(-0.201944\pi\)
0.805413 + 0.592714i \(0.201944\pi\)
\(908\) 0 0
\(909\) 5.74355 0.190502
\(910\) 0 0
\(911\) 3.30195 0.109398 0.0546992 0.998503i \(-0.482580\pi\)
0.0546992 + 0.998503i \(0.482580\pi\)
\(912\) 0 0
\(913\) −40.0105 −1.32416
\(914\) 0 0
\(915\) −6.93513 −0.229268
\(916\) 0 0
\(917\) −4.49602 −0.148472
\(918\) 0 0
\(919\) 16.4454 0.542482 0.271241 0.962511i \(-0.412566\pi\)
0.271241 + 0.962511i \(0.412566\pi\)
\(920\) 0 0
\(921\) −22.1359 −0.729402
\(922\) 0 0
\(923\) 3.97545 0.130854
\(924\) 0 0
\(925\) −41.1458 −1.35286
\(926\) 0 0
\(927\) −6.83800 −0.224589
\(928\) 0 0
\(929\) 4.67293 0.153314 0.0766569 0.997058i \(-0.475575\pi\)
0.0766569 + 0.997058i \(0.475575\pi\)
\(930\) 0 0
\(931\) −28.4423 −0.932159
\(932\) 0 0
\(933\) 20.5369 0.672348
\(934\) 0 0
\(935\) 15.4156 0.504146
\(936\) 0 0
\(937\) −36.3883 −1.18875 −0.594376 0.804187i \(-0.702601\pi\)
−0.594376 + 0.804187i \(0.702601\pi\)
\(938\) 0 0
\(939\) −16.4172 −0.535756
\(940\) 0 0
\(941\) 41.0935 1.33961 0.669805 0.742537i \(-0.266378\pi\)
0.669805 + 0.742537i \(0.266378\pi\)
\(942\) 0 0
\(943\) −9.68456 −0.315373
\(944\) 0 0
\(945\) 3.04303 0.0989899
\(946\) 0 0
\(947\) −27.5567 −0.895473 −0.447737 0.894165i \(-0.647770\pi\)
−0.447737 + 0.894165i \(0.647770\pi\)
\(948\) 0 0
\(949\) 53.9683 1.75189
\(950\) 0 0
\(951\) 9.49952 0.308043
\(952\) 0 0
\(953\) 23.2999 0.754758 0.377379 0.926059i \(-0.376825\pi\)
0.377379 + 0.926059i \(0.376825\pi\)
\(954\) 0 0
\(955\) −7.01175 −0.226895
\(956\) 0 0
\(957\) −24.3448 −0.786956
\(958\) 0 0
\(959\) −8.21989 −0.265434
\(960\) 0 0
\(961\) 70.7465 2.28215
\(962\) 0 0
\(963\) −5.41431 −0.174474
\(964\) 0 0
\(965\) −8.93436 −0.287607
\(966\) 0 0
\(967\) 46.7910 1.50470 0.752349 0.658765i \(-0.228921\pi\)
0.752349 + 0.658765i \(0.228921\pi\)
\(968\) 0 0
\(969\) −16.4024 −0.526920
\(970\) 0 0
\(971\) −38.9878 −1.25118 −0.625590 0.780152i \(-0.715142\pi\)
−0.625590 + 0.780152i \(0.715142\pi\)
\(972\) 0 0
\(973\) −10.5551 −0.338380
\(974\) 0 0
\(975\) −18.8579 −0.603936
\(976\) 0 0
\(977\) −19.9510 −0.638289 −0.319144 0.947706i \(-0.603396\pi\)
−0.319144 + 0.947706i \(0.603396\pi\)
\(978\) 0 0
\(979\) −27.2712 −0.871593
\(980\) 0 0
\(981\) −15.8743 −0.506827
\(982\) 0 0
\(983\) −29.4924 −0.940663 −0.470331 0.882490i \(-0.655866\pi\)
−0.470331 + 0.882490i \(0.655866\pi\)
\(984\) 0 0
\(985\) 7.76871 0.247532
\(986\) 0 0
\(987\) −41.8293 −1.33144
\(988\) 0 0
\(989\) −26.7750 −0.851396
\(990\) 0 0
\(991\) −43.7780 −1.39065 −0.695327 0.718693i \(-0.744741\pi\)
−0.695327 + 0.718693i \(0.744741\pi\)
\(992\) 0 0
\(993\) 21.9003 0.694984
\(994\) 0 0
\(995\) 18.9953 0.602190
\(996\) 0 0
\(997\) 21.0399 0.666339 0.333170 0.942867i \(-0.391882\pi\)
0.333170 + 0.942867i \(0.391882\pi\)
\(998\) 0 0
\(999\) −9.28645 −0.293810
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 \(a_p\))