Properties

Label 6036.2.a.g.1.12
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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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: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(1.40631\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.406311 q^{5}\) \(-3.65793 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.406311 q^{5}\) \(-3.65793 q^{7}\) \(+1.00000 q^{9}\) \(+2.14503 q^{11}\) \(+3.44501 q^{13}\) \(+0.406311 q^{15}\) \(-3.83373 q^{17}\) \(-3.34349 q^{19}\) \(-3.65793 q^{21}\) \(-3.64859 q^{23}\) \(-4.83491 q^{25}\) \(+1.00000 q^{27}\) \(+9.24385 q^{29}\) \(+1.08272 q^{31}\) \(+2.14503 q^{33}\) \(-1.48626 q^{35}\) \(-2.54793 q^{37}\) \(+3.44501 q^{39}\) \(-8.54300 q^{41}\) \(+9.55542 q^{43}\) \(+0.406311 q^{45}\) \(+0.898817 q^{47}\) \(+6.38045 q^{49}\) \(-3.83373 q^{51}\) \(-1.91334 q^{53}\) \(+0.871548 q^{55}\) \(-3.34349 q^{57}\) \(+0.219503 q^{59}\) \(-11.3053 q^{61}\) \(-3.65793 q^{63}\) \(+1.39975 q^{65}\) \(-7.20894 q^{67}\) \(-3.64859 q^{69}\) \(-7.59769 q^{71}\) \(-13.9530 q^{73}\) \(-4.83491 q^{75}\) \(-7.84637 q^{77}\) \(-2.82794 q^{79}\) \(+1.00000 q^{81}\) \(+13.0368 q^{83}\) \(-1.55768 q^{85}\) \(+9.24385 q^{87}\) \(+5.24068 q^{89}\) \(-12.6016 q^{91}\) \(+1.08272 q^{93}\) \(-1.35849 q^{95}\) \(+3.08960 q^{97}\) \(+2.14503 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 0.406311 0.181708 0.0908538 0.995864i \(-0.471040\pi\)
0.0908538 + 0.995864i \(0.471040\pi\)
\(6\) 0 0
\(7\) −3.65793 −1.38257 −0.691284 0.722583i \(-0.742955\pi\)
−0.691284 + 0.722583i \(0.742955\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.14503 0.646751 0.323375 0.946271i \(-0.395182\pi\)
0.323375 + 0.946271i \(0.395182\pi\)
\(12\) 0 0
\(13\) 3.44501 0.955475 0.477737 0.878503i \(-0.341457\pi\)
0.477737 + 0.878503i \(0.341457\pi\)
\(14\) 0 0
\(15\) 0.406311 0.104909
\(16\) 0 0
\(17\) −3.83373 −0.929816 −0.464908 0.885359i \(-0.653913\pi\)
−0.464908 + 0.885359i \(0.653913\pi\)
\(18\) 0 0
\(19\) −3.34349 −0.767049 −0.383524 0.923531i \(-0.625290\pi\)
−0.383524 + 0.923531i \(0.625290\pi\)
\(20\) 0 0
\(21\) −3.65793 −0.798226
\(22\) 0 0
\(23\) −3.64859 −0.760783 −0.380391 0.924826i \(-0.624211\pi\)
−0.380391 + 0.924826i \(0.624211\pi\)
\(24\) 0 0
\(25\) −4.83491 −0.966982
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.24385 1.71654 0.858270 0.513199i \(-0.171540\pi\)
0.858270 + 0.513199i \(0.171540\pi\)
\(30\) 0 0
\(31\) 1.08272 0.194463 0.0972315 0.995262i \(-0.469001\pi\)
0.0972315 + 0.995262i \(0.469001\pi\)
\(32\) 0 0
\(33\) 2.14503 0.373402
\(34\) 0 0
\(35\) −1.48626 −0.251223
\(36\) 0 0
\(37\) −2.54793 −0.418876 −0.209438 0.977822i \(-0.567163\pi\)
−0.209438 + 0.977822i \(0.567163\pi\)
\(38\) 0 0
\(39\) 3.44501 0.551643
\(40\) 0 0
\(41\) −8.54300 −1.33419 −0.667096 0.744972i \(-0.732463\pi\)
−0.667096 + 0.744972i \(0.732463\pi\)
\(42\) 0 0
\(43\) 9.55542 1.45719 0.728594 0.684946i \(-0.240174\pi\)
0.728594 + 0.684946i \(0.240174\pi\)
\(44\) 0 0
\(45\) 0.406311 0.0605692
\(46\) 0 0
\(47\) 0.898817 0.131106 0.0655530 0.997849i \(-0.479119\pi\)
0.0655530 + 0.997849i \(0.479119\pi\)
\(48\) 0 0
\(49\) 6.38045 0.911493
\(50\) 0 0
\(51\) −3.83373 −0.536829
\(52\) 0 0
\(53\) −1.91334 −0.262818 −0.131409 0.991328i \(-0.541950\pi\)
−0.131409 + 0.991328i \(0.541950\pi\)
\(54\) 0 0
\(55\) 0.871548 0.117520
\(56\) 0 0
\(57\) −3.34349 −0.442856
\(58\) 0 0
\(59\) 0.219503 0.0285769 0.0142884 0.999898i \(-0.495452\pi\)
0.0142884 + 0.999898i \(0.495452\pi\)
\(60\) 0 0
\(61\) −11.3053 −1.44750 −0.723748 0.690064i \(-0.757582\pi\)
−0.723748 + 0.690064i \(0.757582\pi\)
\(62\) 0 0
\(63\) −3.65793 −0.460856
\(64\) 0 0
\(65\) 1.39975 0.173617
\(66\) 0 0
\(67\) −7.20894 −0.880712 −0.440356 0.897823i \(-0.645148\pi\)
−0.440356 + 0.897823i \(0.645148\pi\)
\(68\) 0 0
\(69\) −3.64859 −0.439238
\(70\) 0 0
\(71\) −7.59769 −0.901680 −0.450840 0.892605i \(-0.648876\pi\)
−0.450840 + 0.892605i \(0.648876\pi\)
\(72\) 0 0
\(73\) −13.9530 −1.63308 −0.816538 0.577292i \(-0.804109\pi\)
−0.816538 + 0.577292i \(0.804109\pi\)
\(74\) 0 0
\(75\) −4.83491 −0.558288
\(76\) 0 0
\(77\) −7.84637 −0.894176
\(78\) 0 0
\(79\) −2.82794 −0.318168 −0.159084 0.987265i \(-0.550854\pi\)
−0.159084 + 0.987265i \(0.550854\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 13.0368 1.43097 0.715485 0.698628i \(-0.246206\pi\)
0.715485 + 0.698628i \(0.246206\pi\)
\(84\) 0 0
\(85\) −1.55768 −0.168955
\(86\) 0 0
\(87\) 9.24385 0.991044
\(88\) 0 0
\(89\) 5.24068 0.555511 0.277756 0.960652i \(-0.410409\pi\)
0.277756 + 0.960652i \(0.410409\pi\)
\(90\) 0 0
\(91\) −12.6016 −1.32101
\(92\) 0 0
\(93\) 1.08272 0.112273
\(94\) 0 0
\(95\) −1.35849 −0.139379
\(96\) 0 0
\(97\) 3.08960 0.313701 0.156851 0.987622i \(-0.449866\pi\)
0.156851 + 0.987622i \(0.449866\pi\)
\(98\) 0 0
\(99\) 2.14503 0.215584
\(100\) 0 0
\(101\) −8.72529 −0.868199 −0.434099 0.900865i \(-0.642933\pi\)
−0.434099 + 0.900865i \(0.642933\pi\)
\(102\) 0 0
\(103\) 12.0716 1.18945 0.594726 0.803928i \(-0.297260\pi\)
0.594726 + 0.803928i \(0.297260\pi\)
\(104\) 0 0
\(105\) −1.48626 −0.145044
\(106\) 0 0
\(107\) −13.3086 −1.28659 −0.643294 0.765619i \(-0.722433\pi\)
−0.643294 + 0.765619i \(0.722433\pi\)
\(108\) 0 0
\(109\) −14.2247 −1.36248 −0.681240 0.732061i \(-0.738559\pi\)
−0.681240 + 0.732061i \(0.738559\pi\)
\(110\) 0 0
\(111\) −2.54793 −0.241838
\(112\) 0 0
\(113\) 1.63423 0.153735 0.0768676 0.997041i \(-0.475508\pi\)
0.0768676 + 0.997041i \(0.475508\pi\)
\(114\) 0 0
\(115\) −1.48246 −0.138240
\(116\) 0 0
\(117\) 3.44501 0.318492
\(118\) 0 0
\(119\) 14.0235 1.28553
\(120\) 0 0
\(121\) −6.39885 −0.581714
\(122\) 0 0
\(123\) −8.54300 −0.770296
\(124\) 0 0
\(125\) −3.99603 −0.357416
\(126\) 0 0
\(127\) −9.63369 −0.854851 −0.427426 0.904050i \(-0.640579\pi\)
−0.427426 + 0.904050i \(0.640579\pi\)
\(128\) 0 0
\(129\) 9.55542 0.841307
\(130\) 0 0
\(131\) 0.830899 0.0725959 0.0362980 0.999341i \(-0.488443\pi\)
0.0362980 + 0.999341i \(0.488443\pi\)
\(132\) 0 0
\(133\) 12.2302 1.06050
\(134\) 0 0
\(135\) 0.406311 0.0349696
\(136\) 0 0
\(137\) 1.91974 0.164014 0.0820072 0.996632i \(-0.473867\pi\)
0.0820072 + 0.996632i \(0.473867\pi\)
\(138\) 0 0
\(139\) 18.9417 1.60662 0.803308 0.595563i \(-0.203071\pi\)
0.803308 + 0.595563i \(0.203071\pi\)
\(140\) 0 0
\(141\) 0.898817 0.0756941
\(142\) 0 0
\(143\) 7.38965 0.617954
\(144\) 0 0
\(145\) 3.75587 0.311908
\(146\) 0 0
\(147\) 6.38045 0.526251
\(148\) 0 0
\(149\) −9.30578 −0.762359 −0.381179 0.924501i \(-0.624482\pi\)
−0.381179 + 0.924501i \(0.624482\pi\)
\(150\) 0 0
\(151\) 9.88578 0.804493 0.402247 0.915531i \(-0.368229\pi\)
0.402247 + 0.915531i \(0.368229\pi\)
\(152\) 0 0
\(153\) −3.83373 −0.309939
\(154\) 0 0
\(155\) 0.439922 0.0353354
\(156\) 0 0
\(157\) −14.3508 −1.14532 −0.572659 0.819794i \(-0.694088\pi\)
−0.572659 + 0.819794i \(0.694088\pi\)
\(158\) 0 0
\(159\) −1.91334 −0.151738
\(160\) 0 0
\(161\) 13.3463 1.05183
\(162\) 0 0
\(163\) −7.32959 −0.574097 −0.287049 0.957916i \(-0.592674\pi\)
−0.287049 + 0.957916i \(0.592674\pi\)
\(164\) 0 0
\(165\) 0.871548 0.0678499
\(166\) 0 0
\(167\) 16.5604 1.28148 0.640741 0.767757i \(-0.278627\pi\)
0.640741 + 0.767757i \(0.278627\pi\)
\(168\) 0 0
\(169\) −1.13189 −0.0870684
\(170\) 0 0
\(171\) −3.34349 −0.255683
\(172\) 0 0
\(173\) −14.0530 −1.06843 −0.534214 0.845349i \(-0.679392\pi\)
−0.534214 + 0.845349i \(0.679392\pi\)
\(174\) 0 0
\(175\) 17.6858 1.33692
\(176\) 0 0
\(177\) 0.219503 0.0164989
\(178\) 0 0
\(179\) −6.28478 −0.469746 −0.234873 0.972026i \(-0.575467\pi\)
−0.234873 + 0.972026i \(0.575467\pi\)
\(180\) 0 0
\(181\) −15.6909 −1.16629 −0.583146 0.812367i \(-0.698178\pi\)
−0.583146 + 0.812367i \(0.698178\pi\)
\(182\) 0 0
\(183\) −11.3053 −0.835713
\(184\) 0 0
\(185\) −1.03525 −0.0761130
\(186\) 0 0
\(187\) −8.22346 −0.601359
\(188\) 0 0
\(189\) −3.65793 −0.266075
\(190\) 0 0
\(191\) −14.9019 −1.07827 −0.539133 0.842221i \(-0.681248\pi\)
−0.539133 + 0.842221i \(0.681248\pi\)
\(192\) 0 0
\(193\) −9.98140 −0.718477 −0.359238 0.933246i \(-0.616964\pi\)
−0.359238 + 0.933246i \(0.616964\pi\)
\(194\) 0 0
\(195\) 1.39975 0.100238
\(196\) 0 0
\(197\) −0.547736 −0.0390246 −0.0195123 0.999810i \(-0.506211\pi\)
−0.0195123 + 0.999810i \(0.506211\pi\)
\(198\) 0 0
\(199\) 4.41343 0.312860 0.156430 0.987689i \(-0.450001\pi\)
0.156430 + 0.987689i \(0.450001\pi\)
\(200\) 0 0
\(201\) −7.20894 −0.508480
\(202\) 0 0
\(203\) −33.8133 −2.37323
\(204\) 0 0
\(205\) −3.47111 −0.242433
\(206\) 0 0
\(207\) −3.64859 −0.253594
\(208\) 0 0
\(209\) −7.17188 −0.496089
\(210\) 0 0
\(211\) 4.69009 0.322879 0.161440 0.986883i \(-0.448386\pi\)
0.161440 + 0.986883i \(0.448386\pi\)
\(212\) 0 0
\(213\) −7.59769 −0.520585
\(214\) 0 0
\(215\) 3.88247 0.264782
\(216\) 0 0
\(217\) −3.96053 −0.268858
\(218\) 0 0
\(219\) −13.9530 −0.942857
\(220\) 0 0
\(221\) −13.2072 −0.888415
\(222\) 0 0
\(223\) 5.27468 0.353218 0.176609 0.984281i \(-0.443487\pi\)
0.176609 + 0.984281i \(0.443487\pi\)
\(224\) 0 0
\(225\) −4.83491 −0.322327
\(226\) 0 0
\(227\) −21.5479 −1.43019 −0.715094 0.699029i \(-0.753616\pi\)
−0.715094 + 0.699029i \(0.753616\pi\)
\(228\) 0 0
\(229\) 24.2138 1.60009 0.800046 0.599938i \(-0.204808\pi\)
0.800046 + 0.599938i \(0.204808\pi\)
\(230\) 0 0
\(231\) −7.84637 −0.516253
\(232\) 0 0
\(233\) 22.4540 1.47101 0.735505 0.677519i \(-0.236945\pi\)
0.735505 + 0.677519i \(0.236945\pi\)
\(234\) 0 0
\(235\) 0.365199 0.0238230
\(236\) 0 0
\(237\) −2.82794 −0.183694
\(238\) 0 0
\(239\) −6.86087 −0.443793 −0.221896 0.975070i \(-0.571225\pi\)
−0.221896 + 0.975070i \(0.571225\pi\)
\(240\) 0 0
\(241\) 0.0687447 0.00442823 0.00221412 0.999998i \(-0.499295\pi\)
0.00221412 + 0.999998i \(0.499295\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 2.59244 0.165625
\(246\) 0 0
\(247\) −11.5184 −0.732895
\(248\) 0 0
\(249\) 13.0368 0.826171
\(250\) 0 0
\(251\) −3.14820 −0.198713 −0.0993564 0.995052i \(-0.531678\pi\)
−0.0993564 + 0.995052i \(0.531678\pi\)
\(252\) 0 0
\(253\) −7.82632 −0.492037
\(254\) 0 0
\(255\) −1.55768 −0.0975460
\(256\) 0 0
\(257\) −17.2997 −1.07913 −0.539563 0.841945i \(-0.681411\pi\)
−0.539563 + 0.841945i \(0.681411\pi\)
\(258\) 0 0
\(259\) 9.32013 0.579125
\(260\) 0 0
\(261\) 9.24385 0.572180
\(262\) 0 0
\(263\) 7.74904 0.477827 0.238913 0.971041i \(-0.423209\pi\)
0.238913 + 0.971041i \(0.423209\pi\)
\(264\) 0 0
\(265\) −0.777411 −0.0477560
\(266\) 0 0
\(267\) 5.24068 0.320724
\(268\) 0 0
\(269\) −28.5783 −1.74245 −0.871224 0.490886i \(-0.836673\pi\)
−0.871224 + 0.490886i \(0.836673\pi\)
\(270\) 0 0
\(271\) −20.5574 −1.24878 −0.624388 0.781115i \(-0.714651\pi\)
−0.624388 + 0.781115i \(0.714651\pi\)
\(272\) 0 0
\(273\) −12.6016 −0.762684
\(274\) 0 0
\(275\) −10.3710 −0.625396
\(276\) 0 0
\(277\) −1.90200 −0.114280 −0.0571401 0.998366i \(-0.518198\pi\)
−0.0571401 + 0.998366i \(0.518198\pi\)
\(278\) 0 0
\(279\) 1.08272 0.0648210
\(280\) 0 0
\(281\) −1.02847 −0.0613533 −0.0306767 0.999529i \(-0.509766\pi\)
−0.0306767 + 0.999529i \(0.509766\pi\)
\(282\) 0 0
\(283\) 17.2609 1.02606 0.513028 0.858372i \(-0.328524\pi\)
0.513028 + 0.858372i \(0.328524\pi\)
\(284\) 0 0
\(285\) −1.35849 −0.0804703
\(286\) 0 0
\(287\) 31.2497 1.84461
\(288\) 0 0
\(289\) −2.30253 −0.135443
\(290\) 0 0
\(291\) 3.08960 0.181116
\(292\) 0 0
\(293\) 6.28937 0.367429 0.183715 0.982980i \(-0.441188\pi\)
0.183715 + 0.982980i \(0.441188\pi\)
\(294\) 0 0
\(295\) 0.0891864 0.00519263
\(296\) 0 0
\(297\) 2.14503 0.124467
\(298\) 0 0
\(299\) −12.5694 −0.726909
\(300\) 0 0
\(301\) −34.9530 −2.01466
\(302\) 0 0
\(303\) −8.72529 −0.501255
\(304\) 0 0
\(305\) −4.59347 −0.263021
\(306\) 0 0
\(307\) −6.09689 −0.347968 −0.173984 0.984748i \(-0.555664\pi\)
−0.173984 + 0.984748i \(0.555664\pi\)
\(308\) 0 0
\(309\) 12.0716 0.686731
\(310\) 0 0
\(311\) −23.3022 −1.32135 −0.660673 0.750674i \(-0.729729\pi\)
−0.660673 + 0.750674i \(0.729729\pi\)
\(312\) 0 0
\(313\) −26.5747 −1.50209 −0.751046 0.660250i \(-0.770450\pi\)
−0.751046 + 0.660250i \(0.770450\pi\)
\(314\) 0 0
\(315\) −1.48626 −0.0837410
\(316\) 0 0
\(317\) 10.2513 0.575772 0.287886 0.957665i \(-0.407048\pi\)
0.287886 + 0.957665i \(0.407048\pi\)
\(318\) 0 0
\(319\) 19.8283 1.11017
\(320\) 0 0
\(321\) −13.3086 −0.742812
\(322\) 0 0
\(323\) 12.8180 0.713214
\(324\) 0 0
\(325\) −16.6563 −0.923927
\(326\) 0 0
\(327\) −14.2247 −0.786628
\(328\) 0 0
\(329\) −3.28781 −0.181263
\(330\) 0 0
\(331\) −7.48821 −0.411589 −0.205795 0.978595i \(-0.565978\pi\)
−0.205795 + 0.978595i \(0.565978\pi\)
\(332\) 0 0
\(333\) −2.54793 −0.139625
\(334\) 0 0
\(335\) −2.92907 −0.160032
\(336\) 0 0
\(337\) 12.4765 0.679638 0.339819 0.940491i \(-0.389634\pi\)
0.339819 + 0.940491i \(0.389634\pi\)
\(338\) 0 0
\(339\) 1.63423 0.0887591
\(340\) 0 0
\(341\) 2.32248 0.125769
\(342\) 0 0
\(343\) 2.26627 0.122367
\(344\) 0 0
\(345\) −1.48246 −0.0798129
\(346\) 0 0
\(347\) −13.0082 −0.698315 −0.349158 0.937064i \(-0.613532\pi\)
−0.349158 + 0.937064i \(0.613532\pi\)
\(348\) 0 0
\(349\) −24.7891 −1.32693 −0.663464 0.748208i \(-0.730914\pi\)
−0.663464 + 0.748208i \(0.730914\pi\)
\(350\) 0 0
\(351\) 3.44501 0.183881
\(352\) 0 0
\(353\) 14.9658 0.796551 0.398276 0.917266i \(-0.369609\pi\)
0.398276 + 0.917266i \(0.369609\pi\)
\(354\) 0 0
\(355\) −3.08702 −0.163842
\(356\) 0 0
\(357\) 14.0235 0.742203
\(358\) 0 0
\(359\) −25.8342 −1.36348 −0.681738 0.731596i \(-0.738776\pi\)
−0.681738 + 0.731596i \(0.738776\pi\)
\(360\) 0 0
\(361\) −7.82109 −0.411637
\(362\) 0 0
\(363\) −6.39885 −0.335853
\(364\) 0 0
\(365\) −5.66925 −0.296742
\(366\) 0 0
\(367\) 4.02532 0.210120 0.105060 0.994466i \(-0.466497\pi\)
0.105060 + 0.994466i \(0.466497\pi\)
\(368\) 0 0
\(369\) −8.54300 −0.444731
\(370\) 0 0
\(371\) 6.99887 0.363363
\(372\) 0 0
\(373\) −0.839469 −0.0434660 −0.0217330 0.999764i \(-0.506918\pi\)
−0.0217330 + 0.999764i \(0.506918\pi\)
\(374\) 0 0
\(375\) −3.99603 −0.206354
\(376\) 0 0
\(377\) 31.8452 1.64011
\(378\) 0 0
\(379\) 25.0804 1.28830 0.644148 0.764901i \(-0.277212\pi\)
0.644148 + 0.764901i \(0.277212\pi\)
\(380\) 0 0
\(381\) −9.63369 −0.493549
\(382\) 0 0
\(383\) 16.7374 0.855243 0.427621 0.903958i \(-0.359352\pi\)
0.427621 + 0.903958i \(0.359352\pi\)
\(384\) 0 0
\(385\) −3.18806 −0.162479
\(386\) 0 0
\(387\) 9.55542 0.485729
\(388\) 0 0
\(389\) 2.54922 0.129250 0.0646252 0.997910i \(-0.479415\pi\)
0.0646252 + 0.997910i \(0.479415\pi\)
\(390\) 0 0
\(391\) 13.9877 0.707388
\(392\) 0 0
\(393\) 0.830899 0.0419133
\(394\) 0 0
\(395\) −1.14902 −0.0578135
\(396\) 0 0
\(397\) 20.7992 1.04388 0.521941 0.852982i \(-0.325208\pi\)
0.521941 + 0.852982i \(0.325208\pi\)
\(398\) 0 0
\(399\) 12.2302 0.612278
\(400\) 0 0
\(401\) 22.5961 1.12840 0.564198 0.825639i \(-0.309185\pi\)
0.564198 + 0.825639i \(0.309185\pi\)
\(402\) 0 0
\(403\) 3.73000 0.185805
\(404\) 0 0
\(405\) 0.406311 0.0201897
\(406\) 0 0
\(407\) −5.46537 −0.270909
\(408\) 0 0
\(409\) −14.2372 −0.703983 −0.351991 0.936003i \(-0.614495\pi\)
−0.351991 + 0.936003i \(0.614495\pi\)
\(410\) 0 0
\(411\) 1.91974 0.0946937
\(412\) 0 0
\(413\) −0.802927 −0.0395094
\(414\) 0 0
\(415\) 5.29697 0.260018
\(416\) 0 0
\(417\) 18.9417 0.927581
\(418\) 0 0
\(419\) −6.78220 −0.331332 −0.165666 0.986182i \(-0.552977\pi\)
−0.165666 + 0.986182i \(0.552977\pi\)
\(420\) 0 0
\(421\) 23.9079 1.16520 0.582600 0.812759i \(-0.302035\pi\)
0.582600 + 0.812759i \(0.302035\pi\)
\(422\) 0 0
\(423\) 0.898817 0.0437020
\(424\) 0 0
\(425\) 18.5357 0.899115
\(426\) 0 0
\(427\) 41.3540 2.00126
\(428\) 0 0
\(429\) 7.38965 0.356776
\(430\) 0 0
\(431\) 24.0546 1.15867 0.579334 0.815090i \(-0.303313\pi\)
0.579334 + 0.815090i \(0.303313\pi\)
\(432\) 0 0
\(433\) 22.2211 1.06788 0.533939 0.845523i \(-0.320711\pi\)
0.533939 + 0.845523i \(0.320711\pi\)
\(434\) 0 0
\(435\) 3.75587 0.180080
\(436\) 0 0
\(437\) 12.1990 0.583557
\(438\) 0 0
\(439\) 14.6703 0.700175 0.350087 0.936717i \(-0.386152\pi\)
0.350087 + 0.936717i \(0.386152\pi\)
\(440\) 0 0
\(441\) 6.38045 0.303831
\(442\) 0 0
\(443\) −16.5212 −0.784944 −0.392472 0.919764i \(-0.628380\pi\)
−0.392472 + 0.919764i \(0.628380\pi\)
\(444\) 0 0
\(445\) 2.12934 0.100941
\(446\) 0 0
\(447\) −9.30578 −0.440148
\(448\) 0 0
\(449\) −2.49155 −0.117583 −0.0587917 0.998270i \(-0.518725\pi\)
−0.0587917 + 0.998270i \(0.518725\pi\)
\(450\) 0 0
\(451\) −18.3250 −0.862890
\(452\) 0 0
\(453\) 9.88578 0.464474
\(454\) 0 0
\(455\) −5.12017 −0.240037
\(456\) 0 0
\(457\) 13.1799 0.616532 0.308266 0.951300i \(-0.400251\pi\)
0.308266 + 0.951300i \(0.400251\pi\)
\(458\) 0 0
\(459\) −3.83373 −0.178943
\(460\) 0 0
\(461\) −29.1718 −1.35867 −0.679333 0.733830i \(-0.737731\pi\)
−0.679333 + 0.733830i \(0.737731\pi\)
\(462\) 0 0
\(463\) 9.74846 0.453049 0.226525 0.974005i \(-0.427264\pi\)
0.226525 + 0.974005i \(0.427264\pi\)
\(464\) 0 0
\(465\) 0.439922 0.0204009
\(466\) 0 0
\(467\) 3.62671 0.167824 0.0839120 0.996473i \(-0.473259\pi\)
0.0839120 + 0.996473i \(0.473259\pi\)
\(468\) 0 0
\(469\) 26.3698 1.21764
\(470\) 0 0
\(471\) −14.3508 −0.661250
\(472\) 0 0
\(473\) 20.4966 0.942437
\(474\) 0 0
\(475\) 16.1655 0.741722
\(476\) 0 0
\(477\) −1.91334 −0.0876059
\(478\) 0 0
\(479\) −17.3619 −0.793286 −0.396643 0.917973i \(-0.629825\pi\)
−0.396643 + 0.917973i \(0.629825\pi\)
\(480\) 0 0
\(481\) −8.77763 −0.400226
\(482\) 0 0
\(483\) 13.3463 0.607276
\(484\) 0 0
\(485\) 1.25534 0.0570020
\(486\) 0 0
\(487\) 12.0909 0.547891 0.273946 0.961745i \(-0.411671\pi\)
0.273946 + 0.961745i \(0.411671\pi\)
\(488\) 0 0
\(489\) −7.32959 −0.331455
\(490\) 0 0
\(491\) 12.3346 0.556655 0.278327 0.960486i \(-0.410220\pi\)
0.278327 + 0.960486i \(0.410220\pi\)
\(492\) 0 0
\(493\) −35.4384 −1.59606
\(494\) 0 0
\(495\) 0.871548 0.0391732
\(496\) 0 0
\(497\) 27.7918 1.24663
\(498\) 0 0
\(499\) 11.8077 0.528585 0.264293 0.964443i \(-0.414862\pi\)
0.264293 + 0.964443i \(0.414862\pi\)
\(500\) 0 0
\(501\) 16.5604 0.739865
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −3.54518 −0.157758
\(506\) 0 0
\(507\) −1.13189 −0.0502689
\(508\) 0 0
\(509\) −39.3128 −1.74251 −0.871255 0.490830i \(-0.836693\pi\)
−0.871255 + 0.490830i \(0.836693\pi\)
\(510\) 0 0
\(511\) 51.0391 2.25784
\(512\) 0 0
\(513\) −3.34349 −0.147619
\(514\) 0 0
\(515\) 4.90483 0.216133
\(516\) 0 0
\(517\) 1.92799 0.0847929
\(518\) 0 0
\(519\) −14.0530 −0.616857
\(520\) 0 0
\(521\) −19.6475 −0.860773 −0.430387 0.902645i \(-0.641623\pi\)
−0.430387 + 0.902645i \(0.641623\pi\)
\(522\) 0 0
\(523\) 15.6466 0.684180 0.342090 0.939667i \(-0.388865\pi\)
0.342090 + 0.939667i \(0.388865\pi\)
\(524\) 0 0
\(525\) 17.6858 0.771870
\(526\) 0 0
\(527\) −4.15087 −0.180815
\(528\) 0 0
\(529\) −9.68782 −0.421210
\(530\) 0 0
\(531\) 0.219503 0.00952562
\(532\) 0 0
\(533\) −29.4307 −1.27479
\(534\) 0 0
\(535\) −5.40741 −0.233783
\(536\) 0 0
\(537\) −6.28478 −0.271208
\(538\) 0 0
\(539\) 13.6863 0.589509
\(540\) 0 0
\(541\) 33.2755 1.43062 0.715312 0.698805i \(-0.246285\pi\)
0.715312 + 0.698805i \(0.246285\pi\)
\(542\) 0 0
\(543\) −15.6909 −0.673359
\(544\) 0 0
\(545\) −5.77965 −0.247573
\(546\) 0 0
\(547\) 34.0810 1.45720 0.728599 0.684940i \(-0.240172\pi\)
0.728599 + 0.684940i \(0.240172\pi\)
\(548\) 0 0
\(549\) −11.3053 −0.482499
\(550\) 0 0
\(551\) −30.9067 −1.31667
\(552\) 0 0
\(553\) 10.3444 0.439889
\(554\) 0 0
\(555\) −1.03525 −0.0439439
\(556\) 0 0
\(557\) 11.8757 0.503188 0.251594 0.967833i \(-0.419045\pi\)
0.251594 + 0.967833i \(0.419045\pi\)
\(558\) 0 0
\(559\) 32.9185 1.39231
\(560\) 0 0
\(561\) −8.22346 −0.347195
\(562\) 0 0
\(563\) −15.7880 −0.665386 −0.332693 0.943035i \(-0.607957\pi\)
−0.332693 + 0.943035i \(0.607957\pi\)
\(564\) 0 0
\(565\) 0.664004 0.0279349
\(566\) 0 0
\(567\) −3.65793 −0.153619
\(568\) 0 0
\(569\) 11.6496 0.488378 0.244189 0.969728i \(-0.421478\pi\)
0.244189 + 0.969728i \(0.421478\pi\)
\(570\) 0 0
\(571\) −31.6615 −1.32499 −0.662496 0.749066i \(-0.730503\pi\)
−0.662496 + 0.749066i \(0.730503\pi\)
\(572\) 0 0
\(573\) −14.9019 −0.622537
\(574\) 0 0
\(575\) 17.6406 0.735664
\(576\) 0 0
\(577\) 4.00850 0.166876 0.0834380 0.996513i \(-0.473410\pi\)
0.0834380 + 0.996513i \(0.473410\pi\)
\(578\) 0 0
\(579\) −9.98140 −0.414813
\(580\) 0 0
\(581\) −47.6875 −1.97841
\(582\) 0 0
\(583\) −4.10418 −0.169978
\(584\) 0 0
\(585\) 1.39975 0.0578723
\(586\) 0 0
\(587\) −8.18405 −0.337792 −0.168896 0.985634i \(-0.554020\pi\)
−0.168896 + 0.985634i \(0.554020\pi\)
\(588\) 0 0
\(589\) −3.62008 −0.149163
\(590\) 0 0
\(591\) −0.547736 −0.0225308
\(592\) 0 0
\(593\) −21.4944 −0.882669 −0.441334 0.897343i \(-0.645495\pi\)
−0.441334 + 0.897343i \(0.645495\pi\)
\(594\) 0 0
\(595\) 5.69790 0.233591
\(596\) 0 0
\(597\) 4.41343 0.180630
\(598\) 0 0
\(599\) −33.2767 −1.35965 −0.679824 0.733375i \(-0.737944\pi\)
−0.679824 + 0.733375i \(0.737944\pi\)
\(600\) 0 0
\(601\) 30.8617 1.25888 0.629438 0.777051i \(-0.283285\pi\)
0.629438 + 0.777051i \(0.283285\pi\)
\(602\) 0 0
\(603\) −7.20894 −0.293571
\(604\) 0 0
\(605\) −2.59992 −0.105702
\(606\) 0 0
\(607\) 25.1748 1.02182 0.510908 0.859636i \(-0.329309\pi\)
0.510908 + 0.859636i \(0.329309\pi\)
\(608\) 0 0
\(609\) −33.8133 −1.37019
\(610\) 0 0
\(611\) 3.09644 0.125268
\(612\) 0 0
\(613\) −15.1119 −0.610364 −0.305182 0.952294i \(-0.598717\pi\)
−0.305182 + 0.952294i \(0.598717\pi\)
\(614\) 0 0
\(615\) −3.47111 −0.139969
\(616\) 0 0
\(617\) −15.8617 −0.638570 −0.319285 0.947659i \(-0.603443\pi\)
−0.319285 + 0.947659i \(0.603443\pi\)
\(618\) 0 0
\(619\) 40.0301 1.60895 0.804473 0.593989i \(-0.202448\pi\)
0.804473 + 0.593989i \(0.202448\pi\)
\(620\) 0 0
\(621\) −3.64859 −0.146413
\(622\) 0 0
\(623\) −19.1700 −0.768032
\(624\) 0 0
\(625\) 22.5509 0.902037
\(626\) 0 0
\(627\) −7.17188 −0.286417
\(628\) 0 0
\(629\) 9.76805 0.389478
\(630\) 0 0
\(631\) 3.76994 0.150079 0.0750395 0.997181i \(-0.476092\pi\)
0.0750395 + 0.997181i \(0.476092\pi\)
\(632\) 0 0
\(633\) 4.69009 0.186414
\(634\) 0 0
\(635\) −3.91427 −0.155333
\(636\) 0 0
\(637\) 21.9807 0.870908
\(638\) 0 0
\(639\) −7.59769 −0.300560
\(640\) 0 0
\(641\) 22.3026 0.880901 0.440451 0.897777i \(-0.354819\pi\)
0.440451 + 0.897777i \(0.354819\pi\)
\(642\) 0 0
\(643\) −19.0145 −0.749857 −0.374929 0.927054i \(-0.622333\pi\)
−0.374929 + 0.927054i \(0.622333\pi\)
\(644\) 0 0
\(645\) 3.88247 0.152872
\(646\) 0 0
\(647\) −35.1435 −1.38163 −0.690816 0.723031i \(-0.742749\pi\)
−0.690816 + 0.723031i \(0.742749\pi\)
\(648\) 0 0
\(649\) 0.470840 0.0184821
\(650\) 0 0
\(651\) −3.96053 −0.155225
\(652\) 0 0
\(653\) −29.6822 −1.16155 −0.580777 0.814063i \(-0.697251\pi\)
−0.580777 + 0.814063i \(0.697251\pi\)
\(654\) 0 0
\(655\) 0.337603 0.0131912
\(656\) 0 0
\(657\) −13.9530 −0.544359
\(658\) 0 0
\(659\) −6.28017 −0.244641 −0.122320 0.992491i \(-0.539034\pi\)
−0.122320 + 0.992491i \(0.539034\pi\)
\(660\) 0 0
\(661\) −13.2371 −0.514865 −0.257433 0.966296i \(-0.582877\pi\)
−0.257433 + 0.966296i \(0.582877\pi\)
\(662\) 0 0
\(663\) −13.2072 −0.512927
\(664\) 0 0
\(665\) 4.96928 0.192700
\(666\) 0 0
\(667\) −33.7270 −1.30591
\(668\) 0 0
\(669\) 5.27468 0.203931
\(670\) 0 0
\(671\) −24.2502 −0.936169
\(672\) 0 0
\(673\) 32.6171 1.25730 0.628648 0.777690i \(-0.283609\pi\)
0.628648 + 0.777690i \(0.283609\pi\)
\(674\) 0 0
\(675\) −4.83491 −0.186096
\(676\) 0 0
\(677\) −3.86931 −0.148710 −0.0743549 0.997232i \(-0.523690\pi\)
−0.0743549 + 0.997232i \(0.523690\pi\)
\(678\) 0 0
\(679\) −11.3015 −0.433713
\(680\) 0 0
\(681\) −21.5479 −0.825719
\(682\) 0 0
\(683\) −4.26938 −0.163363 −0.0816817 0.996658i \(-0.526029\pi\)
−0.0816817 + 0.996658i \(0.526029\pi\)
\(684\) 0 0
\(685\) 0.780010 0.0298027
\(686\) 0 0
\(687\) 24.2138 0.923814
\(688\) 0 0
\(689\) −6.59149 −0.251116
\(690\) 0 0
\(691\) −4.54311 −0.172828 −0.0864140 0.996259i \(-0.527541\pi\)
−0.0864140 + 0.996259i \(0.527541\pi\)
\(692\) 0 0
\(693\) −7.84637 −0.298059
\(694\) 0 0
\(695\) 7.69623 0.291935
\(696\) 0 0
\(697\) 32.7515 1.24055
\(698\) 0 0
\(699\) 22.4540 0.849288
\(700\) 0 0
\(701\) −1.64863 −0.0622679 −0.0311339 0.999515i \(-0.509912\pi\)
−0.0311339 + 0.999515i \(0.509912\pi\)
\(702\) 0 0
\(703\) 8.51896 0.321298
\(704\) 0 0
\(705\) 0.365199 0.0137542
\(706\) 0 0
\(707\) 31.9165 1.20034
\(708\) 0 0
\(709\) 28.9639 1.08776 0.543880 0.839163i \(-0.316955\pi\)
0.543880 + 0.839163i \(0.316955\pi\)
\(710\) 0 0
\(711\) −2.82794 −0.106056
\(712\) 0 0
\(713\) −3.95041 −0.147944
\(714\) 0 0
\(715\) 3.00249 0.112287
\(716\) 0 0
\(717\) −6.86087 −0.256224
\(718\) 0 0
\(719\) −32.2589 −1.20305 −0.601527 0.798853i \(-0.705441\pi\)
−0.601527 + 0.798853i \(0.705441\pi\)
\(720\) 0 0
\(721\) −44.1572 −1.64450
\(722\) 0 0
\(723\) 0.0687447 0.00255664
\(724\) 0 0
\(725\) −44.6932 −1.65986
\(726\) 0 0
\(727\) −36.8934 −1.36830 −0.684149 0.729342i \(-0.739826\pi\)
−0.684149 + 0.729342i \(0.739826\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −36.6329 −1.35492
\(732\) 0 0
\(733\) −17.4675 −0.645176 −0.322588 0.946539i \(-0.604553\pi\)
−0.322588 + 0.946539i \(0.604553\pi\)
\(734\) 0 0
\(735\) 2.59244 0.0956238
\(736\) 0 0
\(737\) −15.4634 −0.569601
\(738\) 0 0
\(739\) 9.14408 0.336371 0.168185 0.985755i \(-0.446209\pi\)
0.168185 + 0.985755i \(0.446209\pi\)
\(740\) 0 0
\(741\) −11.5184 −0.423137
\(742\) 0 0
\(743\) −1.90908 −0.0700373 −0.0350187 0.999387i \(-0.511149\pi\)
−0.0350187 + 0.999387i \(0.511149\pi\)
\(744\) 0 0
\(745\) −3.78104 −0.138526
\(746\) 0 0
\(747\) 13.0368 0.476990
\(748\) 0 0
\(749\) 48.6818 1.77879
\(750\) 0 0
\(751\) −2.87431 −0.104885 −0.0524426 0.998624i \(-0.516701\pi\)
−0.0524426 + 0.998624i \(0.516701\pi\)
\(752\) 0 0
\(753\) −3.14820 −0.114727
\(754\) 0 0
\(755\) 4.01670 0.146183
\(756\) 0 0
\(757\) 10.3723 0.376986 0.188493 0.982075i \(-0.439640\pi\)
0.188493 + 0.982075i \(0.439640\pi\)
\(758\) 0 0
\(759\) −7.82632 −0.284078
\(760\) 0 0
\(761\) 31.1830 1.13038 0.565191 0.824960i \(-0.308802\pi\)
0.565191 + 0.824960i \(0.308802\pi\)
\(762\) 0 0
\(763\) 52.0330 1.88372
\(764\) 0 0
\(765\) −1.55768 −0.0563182
\(766\) 0 0
\(767\) 0.756191 0.0273045
\(768\) 0 0
\(769\) 8.37913 0.302159 0.151080 0.988522i \(-0.451725\pi\)
0.151080 + 0.988522i \(0.451725\pi\)
\(770\) 0 0
\(771\) −17.2997 −0.623034
\(772\) 0 0
\(773\) 18.2922 0.657924 0.328962 0.944343i \(-0.393301\pi\)
0.328962 + 0.944343i \(0.393301\pi\)
\(774\) 0 0
\(775\) −5.23488 −0.188042
\(776\) 0 0
\(777\) 9.32013 0.334358
\(778\) 0 0
\(779\) 28.5634 1.02339
\(780\) 0 0
\(781\) −16.2973 −0.583162
\(782\) 0 0
\(783\) 9.24385 0.330348
\(784\) 0 0
\(785\) −5.83088 −0.208113
\(786\) 0 0
\(787\) 12.8034 0.456392 0.228196 0.973615i \(-0.426717\pi\)
0.228196 + 0.973615i \(0.426717\pi\)
\(788\) 0 0
\(789\) 7.74904 0.275873
\(790\) 0 0
\(791\) −5.97789 −0.212549
\(792\) 0 0
\(793\) −38.9469 −1.38305
\(794\) 0 0
\(795\) −0.777411 −0.0275719
\(796\) 0 0
\(797\) 11.4139 0.404302 0.202151 0.979354i \(-0.435207\pi\)
0.202151 + 0.979354i \(0.435207\pi\)
\(798\) 0 0
\(799\) −3.44582 −0.121904
\(800\) 0 0
\(801\) 5.24068 0.185170
\(802\) 0 0
\(803\) −29.9296 −1.05619
\(804\) 0 0
\(805\) 5.42273 0.191126
\(806\) 0 0
\(807\) −28.5783 −1.00600
\(808\) 0 0
\(809\) 47.3479 1.66466 0.832332 0.554277i \(-0.187005\pi\)
0.832332 + 0.554277i \(0.187005\pi\)
\(810\) 0 0
\(811\) 23.2769 0.817361 0.408680 0.912678i \(-0.365989\pi\)
0.408680 + 0.912678i \(0.365989\pi\)
\(812\) 0 0
\(813\) −20.5574 −0.720981
\(814\) 0 0
\(815\) −2.97809 −0.104318
\(816\) 0 0
\(817\) −31.9484 −1.11773
\(818\) 0 0
\(819\) −12.6016 −0.440336
\(820\) 0 0
\(821\) 18.6905 0.652302 0.326151 0.945318i \(-0.394248\pi\)
0.326151 + 0.945318i \(0.394248\pi\)
\(822\) 0 0
\(823\) −16.2117 −0.565105 −0.282553 0.959252i \(-0.591181\pi\)
−0.282553 + 0.959252i \(0.591181\pi\)
\(824\) 0 0
\(825\) −10.3710 −0.361073
\(826\) 0 0
\(827\) −4.92285 −0.171184 −0.0855921 0.996330i \(-0.527278\pi\)
−0.0855921 + 0.996330i \(0.527278\pi\)
\(828\) 0 0
\(829\) −33.1013 −1.14966 −0.574828 0.818274i \(-0.694931\pi\)
−0.574828 + 0.818274i \(0.694931\pi\)
\(830\) 0 0
\(831\) −1.90200 −0.0659797
\(832\) 0 0
\(833\) −24.4609 −0.847520
\(834\) 0 0
\(835\) 6.72867 0.232855
\(836\) 0 0
\(837\) 1.08272 0.0374244
\(838\) 0 0
\(839\) −28.8189 −0.994941 −0.497470 0.867481i \(-0.665738\pi\)
−0.497470 + 0.867481i \(0.665738\pi\)
\(840\) 0 0
\(841\) 56.4487 1.94651
\(842\) 0 0
\(843\) −1.02847 −0.0354224
\(844\) 0 0
\(845\) −0.459898 −0.0158210
\(846\) 0 0
\(847\) 23.4065 0.804258
\(848\) 0 0
\(849\) 17.2609 0.592394
\(850\) 0 0
\(851\) 9.29632 0.318674
\(852\) 0 0
\(853\) −10.3896 −0.355733 −0.177867 0.984055i \(-0.556920\pi\)
−0.177867 + 0.984055i \(0.556920\pi\)
\(854\) 0 0
\(855\) −1.35849 −0.0464595
\(856\) 0 0
\(857\) 50.3343 1.71939 0.859693 0.510811i \(-0.170655\pi\)
0.859693 + 0.510811i \(0.170655\pi\)
\(858\) 0 0
\(859\) 24.6385 0.840655 0.420327 0.907372i \(-0.361915\pi\)
0.420327 + 0.907372i \(0.361915\pi\)
\(860\) 0 0
\(861\) 31.2497 1.06499
\(862\) 0 0
\(863\) 31.3490 1.06713 0.533567 0.845758i \(-0.320851\pi\)
0.533567 + 0.845758i \(0.320851\pi\)
\(864\) 0 0
\(865\) −5.70987 −0.194142
\(866\) 0 0
\(867\) −2.30253 −0.0781981
\(868\) 0 0
\(869\) −6.06601 −0.205775
\(870\) 0 0
\(871\) −24.8349 −0.841498
\(872\) 0 0
\(873\) 3.08960 0.104567
\(874\) 0 0
\(875\) 14.6172 0.494151
\(876\) 0 0
\(877\) 10.5485 0.356197 0.178098 0.984013i \(-0.443005\pi\)
0.178098 + 0.984013i \(0.443005\pi\)
\(878\) 0 0
\(879\) 6.28937 0.212135
\(880\) 0 0
\(881\) 32.2167 1.08541 0.542704 0.839924i \(-0.317400\pi\)
0.542704 + 0.839924i \(0.317400\pi\)
\(882\) 0 0
\(883\) 24.4657 0.823336 0.411668 0.911334i \(-0.364946\pi\)
0.411668 + 0.911334i \(0.364946\pi\)
\(884\) 0 0
\(885\) 0.0891864 0.00299797
\(886\) 0 0
\(887\) 42.5837 1.42982 0.714910 0.699216i \(-0.246468\pi\)
0.714910 + 0.699216i \(0.246468\pi\)
\(888\) 0 0
\(889\) 35.2393 1.18189
\(890\) 0 0
\(891\) 2.14503 0.0718612
\(892\) 0 0
\(893\) −3.00518 −0.100565
\(894\) 0 0
\(895\) −2.55357 −0.0853565
\(896\) 0 0
\(897\) −12.5694 −0.419681
\(898\) 0 0
\(899\) 10.0085 0.333803
\(900\) 0 0
\(901\) 7.33523 0.244372
\(902\) 0 0
\(903\) −34.9530 −1.16316
\(904\) 0 0
\(905\) −6.37536 −0.211924
\(906\) 0 0
\(907\) −41.2043 −1.36817 −0.684083 0.729404i \(-0.739797\pi\)
−0.684083 + 0.729404i \(0.739797\pi\)
\(908\) 0 0
\(909\) −8.72529 −0.289400
\(910\) 0 0
\(911\) −39.4233 −1.30615 −0.653076 0.757293i \(-0.726522\pi\)
−0.653076 + 0.757293i \(0.726522\pi\)
\(912\) 0 0
\(913\) 27.9642 0.925481
\(914\) 0 0
\(915\) −4.59347 −0.151855
\(916\) 0 0
\(917\) −3.03937 −0.100369
\(918\) 0 0
\(919\) −2.55207 −0.0841850 −0.0420925 0.999114i \(-0.513402\pi\)
−0.0420925 + 0.999114i \(0.513402\pi\)
\(920\) 0 0
\(921\) −6.09689 −0.200899
\(922\) 0 0
\(923\) −26.1741 −0.861532
\(924\) 0 0
\(925\) 12.3190 0.405046
\(926\) 0 0
\(927\) 12.0716 0.396484
\(928\) 0 0
\(929\) −40.9415 −1.34325 −0.671624 0.740892i \(-0.734403\pi\)
−0.671624 + 0.740892i \(0.734403\pi\)
\(930\) 0 0
\(931\) −21.3330 −0.699159
\(932\) 0 0
\(933\) −23.3022 −0.762879
\(934\) 0 0
\(935\) −3.34128 −0.109271
\(936\) 0 0
\(937\) 49.5459 1.61859 0.809297 0.587400i \(-0.199848\pi\)
0.809297 + 0.587400i \(0.199848\pi\)
\(938\) 0 0
\(939\) −26.5747 −0.867233
\(940\) 0 0
\(941\) −40.6325 −1.32458 −0.662291 0.749246i \(-0.730416\pi\)
−0.662291 + 0.749246i \(0.730416\pi\)
\(942\) 0 0
\(943\) 31.1699 1.01503
\(944\) 0 0
\(945\) −1.48626 −0.0483479
\(946\) 0 0
\(947\) 40.3218 1.31028 0.655141 0.755507i \(-0.272609\pi\)
0.655141 + 0.755507i \(0.272609\pi\)
\(948\) 0 0
\(949\) −48.0683 −1.56036
\(950\) 0 0
\(951\) 10.2513 0.332422
\(952\) 0 0
\(953\) −40.6134 −1.31560 −0.657798 0.753195i \(-0.728512\pi\)
−0.657798 + 0.753195i \(0.728512\pi\)
\(954\) 0 0
\(955\) −6.05481 −0.195929
\(956\) 0 0
\(957\) 19.8283 0.640959
\(958\) 0 0
\(959\) −7.02227 −0.226761
\(960\) 0 0
\(961\) −29.8277 −0.962184
\(962\) 0 0
\(963\) −13.3086 −0.428862
\(964\) 0 0
\(965\) −4.05555 −0.130553
\(966\) 0 0
\(967\) −11.1040 −0.357081 −0.178540 0.983933i \(-0.557138\pi\)
−0.178540 + 0.983933i \(0.557138\pi\)
\(968\) 0 0
\(969\) 12.8180 0.411774
\(970\) 0 0
\(971\) 40.5525 1.30139 0.650696 0.759339i \(-0.274477\pi\)
0.650696 + 0.759339i \(0.274477\pi\)
\(972\) 0 0
\(973\) −69.2875 −2.22126
\(974\) 0 0
\(975\) −16.6563 −0.533430
\(976\) 0 0
\(977\) −1.56212 −0.0499767 −0.0249883 0.999688i \(-0.507955\pi\)
−0.0249883 + 0.999688i \(0.507955\pi\)
\(978\) 0 0
\(979\) 11.2414 0.359277
\(980\) 0 0
\(981\) −14.2247 −0.454160
\(982\) 0 0
\(983\) 25.6312 0.817509 0.408755 0.912644i \(-0.365963\pi\)
0.408755 + 0.912644i \(0.365963\pi\)
\(984\) 0 0
\(985\) −0.222551 −0.00709106
\(986\) 0 0
\(987\) −3.28781 −0.104652
\(988\) 0 0
\(989\) −34.8638 −1.10860
\(990\) 0 0
\(991\) −21.5294 −0.683903 −0.341951 0.939718i \(-0.611088\pi\)
−0.341951 + 0.939718i \(0.611088\pi\)
\(992\) 0 0
\(993\) −7.48821 −0.237631
\(994\) 0 0
\(995\) 1.79322 0.0568490
\(996\) 0 0
\(997\) 46.6509 1.47745 0.738725 0.674007i \(-0.235428\pi\)
0.738725 + 0.674007i \(0.235428\pi\)
\(998\) 0 0
\(999\) −2.54793 −0.0806128
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 \(a_p\))