Properties

Label 6036.2.a.i.1.8
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 1.8
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-1.79097 q^{5}\) \(-4.44185 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-1.79097 q^{5}\) \(-4.44185 q^{7}\) \(+1.00000 q^{9}\) \(-1.81330 q^{11}\) \(-2.51558 q^{13}\) \(+1.79097 q^{15}\) \(+2.41675 q^{17}\) \(-3.57055 q^{19}\) \(+4.44185 q^{21}\) \(-5.16993 q^{23}\) \(-1.79244 q^{25}\) \(-1.00000 q^{27}\) \(+7.45747 q^{29}\) \(-1.28896 q^{31}\) \(+1.81330 q^{33}\) \(+7.95521 q^{35}\) \(-9.97766 q^{37}\) \(+2.51558 q^{39}\) \(-10.2535 q^{41}\) \(-11.0743 q^{43}\) \(-1.79097 q^{45}\) \(-10.6910 q^{47}\) \(+12.7300 q^{49}\) \(-2.41675 q^{51}\) \(-5.98775 q^{53}\) \(+3.24757 q^{55}\) \(+3.57055 q^{57}\) \(-0.0586743 q^{59}\) \(-4.61631 q^{61}\) \(-4.44185 q^{63}\) \(+4.50531 q^{65}\) \(-3.96605 q^{67}\) \(+5.16993 q^{69}\) \(+6.41945 q^{71}\) \(+3.78184 q^{73}\) \(+1.79244 q^{75}\) \(+8.05443 q^{77}\) \(-13.8661 q^{79}\) \(+1.00000 q^{81}\) \(-14.9798 q^{83}\) \(-4.32832 q^{85}\) \(-7.45747 q^{87}\) \(-3.96709 q^{89}\) \(+11.1738 q^{91}\) \(+1.28896 q^{93}\) \(+6.39474 q^{95}\) \(-7.68234 q^{97}\) \(-1.81330 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.79097 −0.800944 −0.400472 0.916309i \(-0.631154\pi\)
−0.400472 + 0.916309i \(0.631154\pi\)
\(6\) 0 0
\(7\) −4.44185 −1.67886 −0.839431 0.543466i \(-0.817112\pi\)
−0.839431 + 0.543466i \(0.817112\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.81330 −0.546732 −0.273366 0.961910i \(-0.588137\pi\)
−0.273366 + 0.961910i \(0.588137\pi\)
\(12\) 0 0
\(13\) −2.51558 −0.697696 −0.348848 0.937179i \(-0.613427\pi\)
−0.348848 + 0.937179i \(0.613427\pi\)
\(14\) 0 0
\(15\) 1.79097 0.462425
\(16\) 0 0
\(17\) 2.41675 0.586148 0.293074 0.956090i \(-0.405322\pi\)
0.293074 + 0.956090i \(0.405322\pi\)
\(18\) 0 0
\(19\) −3.57055 −0.819141 −0.409571 0.912278i \(-0.634322\pi\)
−0.409571 + 0.912278i \(0.634322\pi\)
\(20\) 0 0
\(21\) 4.44185 0.969291
\(22\) 0 0
\(23\) −5.16993 −1.07801 −0.539003 0.842304i \(-0.681199\pi\)
−0.539003 + 0.842304i \(0.681199\pi\)
\(24\) 0 0
\(25\) −1.79244 −0.358488
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.45747 1.38482 0.692408 0.721506i \(-0.256550\pi\)
0.692408 + 0.721506i \(0.256550\pi\)
\(30\) 0 0
\(31\) −1.28896 −0.231504 −0.115752 0.993278i \(-0.536928\pi\)
−0.115752 + 0.993278i \(0.536928\pi\)
\(32\) 0 0
\(33\) 1.81330 0.315656
\(34\) 0 0
\(35\) 7.95521 1.34468
\(36\) 0 0
\(37\) −9.97766 −1.64032 −0.820158 0.572137i \(-0.806115\pi\)
−0.820158 + 0.572137i \(0.806115\pi\)
\(38\) 0 0
\(39\) 2.51558 0.402815
\(40\) 0 0
\(41\) −10.2535 −1.60133 −0.800667 0.599110i \(-0.795521\pi\)
−0.800667 + 0.599110i \(0.795521\pi\)
\(42\) 0 0
\(43\) −11.0743 −1.68881 −0.844406 0.535703i \(-0.820047\pi\)
−0.844406 + 0.535703i \(0.820047\pi\)
\(44\) 0 0
\(45\) −1.79097 −0.266981
\(46\) 0 0
\(47\) −10.6910 −1.55945 −0.779725 0.626122i \(-0.784641\pi\)
−0.779725 + 0.626122i \(0.784641\pi\)
\(48\) 0 0
\(49\) 12.7300 1.81858
\(50\) 0 0
\(51\) −2.41675 −0.338413
\(52\) 0 0
\(53\) −5.98775 −0.822481 −0.411241 0.911527i \(-0.634904\pi\)
−0.411241 + 0.911527i \(0.634904\pi\)
\(54\) 0 0
\(55\) 3.24757 0.437902
\(56\) 0 0
\(57\) 3.57055 0.472932
\(58\) 0 0
\(59\) −0.0586743 −0.00763874 −0.00381937 0.999993i \(-0.501216\pi\)
−0.00381937 + 0.999993i \(0.501216\pi\)
\(60\) 0 0
\(61\) −4.61631 −0.591057 −0.295529 0.955334i \(-0.595496\pi\)
−0.295529 + 0.955334i \(0.595496\pi\)
\(62\) 0 0
\(63\) −4.44185 −0.559621
\(64\) 0 0
\(65\) 4.50531 0.558816
\(66\) 0 0
\(67\) −3.96605 −0.484530 −0.242265 0.970210i \(-0.577890\pi\)
−0.242265 + 0.970210i \(0.577890\pi\)
\(68\) 0 0
\(69\) 5.16993 0.622387
\(70\) 0 0
\(71\) 6.41945 0.761849 0.380924 0.924606i \(-0.375606\pi\)
0.380924 + 0.924606i \(0.375606\pi\)
\(72\) 0 0
\(73\) 3.78184 0.442631 0.221315 0.975202i \(-0.428965\pi\)
0.221315 + 0.975202i \(0.428965\pi\)
\(74\) 0 0
\(75\) 1.79244 0.206973
\(76\) 0 0
\(77\) 8.05443 0.917887
\(78\) 0 0
\(79\) −13.8661 −1.56006 −0.780029 0.625743i \(-0.784796\pi\)
−0.780029 + 0.625743i \(0.784796\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.9798 −1.64424 −0.822122 0.569311i \(-0.807210\pi\)
−0.822122 + 0.569311i \(0.807210\pi\)
\(84\) 0 0
\(85\) −4.32832 −0.469472
\(86\) 0 0
\(87\) −7.45747 −0.799524
\(88\) 0 0
\(89\) −3.96709 −0.420510 −0.210255 0.977647i \(-0.567429\pi\)
−0.210255 + 0.977647i \(0.567429\pi\)
\(90\) 0 0
\(91\) 11.1738 1.17134
\(92\) 0 0
\(93\) 1.28896 0.133659
\(94\) 0 0
\(95\) 6.39474 0.656087
\(96\) 0 0
\(97\) −7.68234 −0.780023 −0.390012 0.920810i \(-0.627529\pi\)
−0.390012 + 0.920810i \(0.627529\pi\)
\(98\) 0 0
\(99\) −1.81330 −0.182244
\(100\) 0 0
\(101\) 15.3196 1.52436 0.762179 0.647366i \(-0.224130\pi\)
0.762179 + 0.647366i \(0.224130\pi\)
\(102\) 0 0
\(103\) 5.87011 0.578399 0.289200 0.957269i \(-0.406611\pi\)
0.289200 + 0.957269i \(0.406611\pi\)
\(104\) 0 0
\(105\) −7.95521 −0.776349
\(106\) 0 0
\(107\) 6.35078 0.613954 0.306977 0.951717i \(-0.400683\pi\)
0.306977 + 0.951717i \(0.400683\pi\)
\(108\) 0 0
\(109\) 12.8531 1.23110 0.615551 0.788097i \(-0.288933\pi\)
0.615551 + 0.788097i \(0.288933\pi\)
\(110\) 0 0
\(111\) 9.97766 0.947037
\(112\) 0 0
\(113\) −14.2890 −1.34419 −0.672096 0.740464i \(-0.734606\pi\)
−0.672096 + 0.740464i \(0.734606\pi\)
\(114\) 0 0
\(115\) 9.25917 0.863422
\(116\) 0 0
\(117\) −2.51558 −0.232565
\(118\) 0 0
\(119\) −10.7349 −0.984062
\(120\) 0 0
\(121\) −7.71193 −0.701085
\(122\) 0 0
\(123\) 10.2535 0.924530
\(124\) 0 0
\(125\) 12.1650 1.08807
\(126\) 0 0
\(127\) 13.1129 1.16358 0.581791 0.813338i \(-0.302352\pi\)
0.581791 + 0.813338i \(0.302352\pi\)
\(128\) 0 0
\(129\) 11.0743 0.975037
\(130\) 0 0
\(131\) −10.2950 −0.899475 −0.449738 0.893161i \(-0.648482\pi\)
−0.449738 + 0.893161i \(0.648482\pi\)
\(132\) 0 0
\(133\) 15.8599 1.37523
\(134\) 0 0
\(135\) 1.79097 0.154142
\(136\) 0 0
\(137\) 10.1710 0.868968 0.434484 0.900680i \(-0.356931\pi\)
0.434484 + 0.900680i \(0.356931\pi\)
\(138\) 0 0
\(139\) 3.72509 0.315958 0.157979 0.987442i \(-0.449502\pi\)
0.157979 + 0.987442i \(0.449502\pi\)
\(140\) 0 0
\(141\) 10.6910 0.900349
\(142\) 0 0
\(143\) 4.56151 0.381452
\(144\) 0 0
\(145\) −13.3561 −1.10916
\(146\) 0 0
\(147\) −12.7300 −1.04996
\(148\) 0 0
\(149\) −1.87390 −0.153516 −0.0767579 0.997050i \(-0.524457\pi\)
−0.0767579 + 0.997050i \(0.524457\pi\)
\(150\) 0 0
\(151\) 15.8972 1.29370 0.646849 0.762618i \(-0.276086\pi\)
0.646849 + 0.762618i \(0.276086\pi\)
\(152\) 0 0
\(153\) 2.41675 0.195383
\(154\) 0 0
\(155\) 2.30849 0.185422
\(156\) 0 0
\(157\) 17.9023 1.42876 0.714378 0.699760i \(-0.246710\pi\)
0.714378 + 0.699760i \(0.246710\pi\)
\(158\) 0 0
\(159\) 5.98775 0.474860
\(160\) 0 0
\(161\) 22.9641 1.80982
\(162\) 0 0
\(163\) −11.2246 −0.879177 −0.439588 0.898199i \(-0.644876\pi\)
−0.439588 + 0.898199i \(0.644876\pi\)
\(164\) 0 0
\(165\) −3.24757 −0.252823
\(166\) 0 0
\(167\) 5.50349 0.425873 0.212937 0.977066i \(-0.431697\pi\)
0.212937 + 0.977066i \(0.431697\pi\)
\(168\) 0 0
\(169\) −6.67187 −0.513221
\(170\) 0 0
\(171\) −3.57055 −0.273047
\(172\) 0 0
\(173\) −12.6287 −0.960144 −0.480072 0.877229i \(-0.659390\pi\)
−0.480072 + 0.877229i \(0.659390\pi\)
\(174\) 0 0
\(175\) 7.96176 0.601852
\(176\) 0 0
\(177\) 0.0586743 0.00441023
\(178\) 0 0
\(179\) −17.4659 −1.30547 −0.652733 0.757588i \(-0.726378\pi\)
−0.652733 + 0.757588i \(0.726378\pi\)
\(180\) 0 0
\(181\) 9.96334 0.740569 0.370284 0.928918i \(-0.379260\pi\)
0.370284 + 0.928918i \(0.379260\pi\)
\(182\) 0 0
\(183\) 4.61631 0.341247
\(184\) 0 0
\(185\) 17.8696 1.31380
\(186\) 0 0
\(187\) −4.38230 −0.320466
\(188\) 0 0
\(189\) 4.44185 0.323097
\(190\) 0 0
\(191\) 4.00549 0.289827 0.144914 0.989444i \(-0.453710\pi\)
0.144914 + 0.989444i \(0.453710\pi\)
\(192\) 0 0
\(193\) 19.2439 1.38521 0.692604 0.721318i \(-0.256463\pi\)
0.692604 + 0.721318i \(0.256463\pi\)
\(194\) 0 0
\(195\) −4.50531 −0.322632
\(196\) 0 0
\(197\) −25.0976 −1.78813 −0.894063 0.447941i \(-0.852158\pi\)
−0.894063 + 0.447941i \(0.852158\pi\)
\(198\) 0 0
\(199\) 10.1127 0.716867 0.358434 0.933555i \(-0.383311\pi\)
0.358434 + 0.933555i \(0.383311\pi\)
\(200\) 0 0
\(201\) 3.96605 0.279744
\(202\) 0 0
\(203\) −33.1250 −2.32492
\(204\) 0 0
\(205\) 18.3637 1.28258
\(206\) 0 0
\(207\) −5.16993 −0.359335
\(208\) 0 0
\(209\) 6.47450 0.447851
\(210\) 0 0
\(211\) −12.0164 −0.827240 −0.413620 0.910450i \(-0.635736\pi\)
−0.413620 + 0.910450i \(0.635736\pi\)
\(212\) 0 0
\(213\) −6.41945 −0.439853
\(214\) 0 0
\(215\) 19.8337 1.35265
\(216\) 0 0
\(217\) 5.72538 0.388664
\(218\) 0 0
\(219\) −3.78184 −0.255553
\(220\) 0 0
\(221\) −6.07953 −0.408953
\(222\) 0 0
\(223\) −20.8248 −1.39453 −0.697265 0.716813i \(-0.745600\pi\)
−0.697265 + 0.716813i \(0.745600\pi\)
\(224\) 0 0
\(225\) −1.79244 −0.119496
\(226\) 0 0
\(227\) 18.9517 1.25787 0.628935 0.777458i \(-0.283491\pi\)
0.628935 + 0.777458i \(0.283491\pi\)
\(228\) 0 0
\(229\) 21.4258 1.41585 0.707927 0.706285i \(-0.249630\pi\)
0.707927 + 0.706285i \(0.249630\pi\)
\(230\) 0 0
\(231\) −8.05443 −0.529942
\(232\) 0 0
\(233\) 12.0637 0.790320 0.395160 0.918612i \(-0.370689\pi\)
0.395160 + 0.918612i \(0.370689\pi\)
\(234\) 0 0
\(235\) 19.1473 1.24903
\(236\) 0 0
\(237\) 13.8661 0.900700
\(238\) 0 0
\(239\) −5.05208 −0.326792 −0.163396 0.986561i \(-0.552245\pi\)
−0.163396 + 0.986561i \(0.552245\pi\)
\(240\) 0 0
\(241\) −21.1868 −1.36476 −0.682382 0.730996i \(-0.739056\pi\)
−0.682382 + 0.730996i \(0.739056\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −22.7991 −1.45658
\(246\) 0 0
\(247\) 8.98201 0.571512
\(248\) 0 0
\(249\) 14.9798 0.949305
\(250\) 0 0
\(251\) −11.5889 −0.731482 −0.365741 0.930717i \(-0.619184\pi\)
−0.365741 + 0.930717i \(0.619184\pi\)
\(252\) 0 0
\(253\) 9.37466 0.589380
\(254\) 0 0
\(255\) 4.32832 0.271050
\(256\) 0 0
\(257\) 0.593402 0.0370154 0.0185077 0.999829i \(-0.494108\pi\)
0.0185077 + 0.999829i \(0.494108\pi\)
\(258\) 0 0
\(259\) 44.3193 2.75387
\(260\) 0 0
\(261\) 7.45747 0.461606
\(262\) 0 0
\(263\) 8.07853 0.498143 0.249072 0.968485i \(-0.419875\pi\)
0.249072 + 0.968485i \(0.419875\pi\)
\(264\) 0 0
\(265\) 10.7239 0.658762
\(266\) 0 0
\(267\) 3.96709 0.242782
\(268\) 0 0
\(269\) 4.59074 0.279903 0.139951 0.990158i \(-0.455305\pi\)
0.139951 + 0.990158i \(0.455305\pi\)
\(270\) 0 0
\(271\) 19.0274 1.15583 0.577915 0.816097i \(-0.303867\pi\)
0.577915 + 0.816097i \(0.303867\pi\)
\(272\) 0 0
\(273\) −11.1738 −0.676271
\(274\) 0 0
\(275\) 3.25024 0.195997
\(276\) 0 0
\(277\) −32.5295 −1.95451 −0.977254 0.212072i \(-0.931979\pi\)
−0.977254 + 0.212072i \(0.931979\pi\)
\(278\) 0 0
\(279\) −1.28896 −0.0771681
\(280\) 0 0
\(281\) 25.3406 1.51169 0.755847 0.654748i \(-0.227225\pi\)
0.755847 + 0.654748i \(0.227225\pi\)
\(282\) 0 0
\(283\) 0.181596 0.0107948 0.00539738 0.999985i \(-0.498282\pi\)
0.00539738 + 0.999985i \(0.498282\pi\)
\(284\) 0 0
\(285\) −6.39474 −0.378792
\(286\) 0 0
\(287\) 45.5447 2.68842
\(288\) 0 0
\(289\) −11.1593 −0.656430
\(290\) 0 0
\(291\) 7.68234 0.450347
\(292\) 0 0
\(293\) −19.5225 −1.14051 −0.570257 0.821466i \(-0.693156\pi\)
−0.570257 + 0.821466i \(0.693156\pi\)
\(294\) 0 0
\(295\) 0.105084 0.00611820
\(296\) 0 0
\(297\) 1.81330 0.105219
\(298\) 0 0
\(299\) 13.0054 0.752120
\(300\) 0 0
\(301\) 49.1903 2.83528
\(302\) 0 0
\(303\) −15.3196 −0.880089
\(304\) 0 0
\(305\) 8.26765 0.473404
\(306\) 0 0
\(307\) −7.67738 −0.438171 −0.219086 0.975706i \(-0.570307\pi\)
−0.219086 + 0.975706i \(0.570307\pi\)
\(308\) 0 0
\(309\) −5.87011 −0.333939
\(310\) 0 0
\(311\) 22.8409 1.29519 0.647594 0.761985i \(-0.275775\pi\)
0.647594 + 0.761985i \(0.275775\pi\)
\(312\) 0 0
\(313\) −4.51047 −0.254947 −0.127473 0.991842i \(-0.540687\pi\)
−0.127473 + 0.991842i \(0.540687\pi\)
\(314\) 0 0
\(315\) 7.95521 0.448225
\(316\) 0 0
\(317\) −8.22120 −0.461748 −0.230874 0.972984i \(-0.574159\pi\)
−0.230874 + 0.972984i \(0.574159\pi\)
\(318\) 0 0
\(319\) −13.5226 −0.757123
\(320\) 0 0
\(321\) −6.35078 −0.354466
\(322\) 0 0
\(323\) −8.62914 −0.480138
\(324\) 0 0
\(325\) 4.50903 0.250116
\(326\) 0 0
\(327\) −12.8531 −0.710777
\(328\) 0 0
\(329\) 47.4881 2.61810
\(330\) 0 0
\(331\) 25.5035 1.40180 0.700898 0.713261i \(-0.252783\pi\)
0.700898 + 0.713261i \(0.252783\pi\)
\(332\) 0 0
\(333\) −9.97766 −0.546772
\(334\) 0 0
\(335\) 7.10306 0.388082
\(336\) 0 0
\(337\) 1.14378 0.0623056 0.0311528 0.999515i \(-0.490082\pi\)
0.0311528 + 0.999515i \(0.490082\pi\)
\(338\) 0 0
\(339\) 14.2890 0.776070
\(340\) 0 0
\(341\) 2.33728 0.126571
\(342\) 0 0
\(343\) −25.4520 −1.37428
\(344\) 0 0
\(345\) −9.25917 −0.498497
\(346\) 0 0
\(347\) −34.5902 −1.85690 −0.928450 0.371458i \(-0.878858\pi\)
−0.928450 + 0.371458i \(0.878858\pi\)
\(348\) 0 0
\(349\) −14.3435 −0.767790 −0.383895 0.923377i \(-0.625417\pi\)
−0.383895 + 0.923377i \(0.625417\pi\)
\(350\) 0 0
\(351\) 2.51558 0.134272
\(352\) 0 0
\(353\) −0.480704 −0.0255853 −0.0127926 0.999918i \(-0.504072\pi\)
−0.0127926 + 0.999918i \(0.504072\pi\)
\(354\) 0 0
\(355\) −11.4970 −0.610198
\(356\) 0 0
\(357\) 10.7349 0.568149
\(358\) 0 0
\(359\) −6.57158 −0.346835 −0.173417 0.984848i \(-0.555481\pi\)
−0.173417 + 0.984848i \(0.555481\pi\)
\(360\) 0 0
\(361\) −6.25114 −0.329007
\(362\) 0 0
\(363\) 7.71193 0.404771
\(364\) 0 0
\(365\) −6.77315 −0.354523
\(366\) 0 0
\(367\) 17.3002 0.903063 0.451532 0.892255i \(-0.350878\pi\)
0.451532 + 0.892255i \(0.350878\pi\)
\(368\) 0 0
\(369\) −10.2535 −0.533778
\(370\) 0 0
\(371\) 26.5967 1.38083
\(372\) 0 0
\(373\) 36.3387 1.88155 0.940773 0.339036i \(-0.110101\pi\)
0.940773 + 0.339036i \(0.110101\pi\)
\(374\) 0 0
\(375\) −12.1650 −0.628199
\(376\) 0 0
\(377\) −18.7598 −0.966181
\(378\) 0 0
\(379\) −24.4654 −1.25670 −0.628350 0.777930i \(-0.716270\pi\)
−0.628350 + 0.777930i \(0.716270\pi\)
\(380\) 0 0
\(381\) −13.1129 −0.671795
\(382\) 0 0
\(383\) −19.1310 −0.977547 −0.488773 0.872411i \(-0.662555\pi\)
−0.488773 + 0.872411i \(0.662555\pi\)
\(384\) 0 0
\(385\) −14.4252 −0.735176
\(386\) 0 0
\(387\) −11.0743 −0.562938
\(388\) 0 0
\(389\) −14.2551 −0.722762 −0.361381 0.932418i \(-0.617695\pi\)
−0.361381 + 0.932418i \(0.617695\pi\)
\(390\) 0 0
\(391\) −12.4944 −0.631871
\(392\) 0 0
\(393\) 10.2950 0.519312
\(394\) 0 0
\(395\) 24.8337 1.24952
\(396\) 0 0
\(397\) 23.3027 1.16953 0.584764 0.811203i \(-0.301187\pi\)
0.584764 + 0.811203i \(0.301187\pi\)
\(398\) 0 0
\(399\) −15.8599 −0.793987
\(400\) 0 0
\(401\) −6.67183 −0.333175 −0.166588 0.986027i \(-0.553275\pi\)
−0.166588 + 0.986027i \(0.553275\pi\)
\(402\) 0 0
\(403\) 3.24248 0.161520
\(404\) 0 0
\(405\) −1.79097 −0.0889938
\(406\) 0 0
\(407\) 18.0925 0.896813
\(408\) 0 0
\(409\) −10.9559 −0.541736 −0.270868 0.962617i \(-0.587311\pi\)
−0.270868 + 0.962617i \(0.587311\pi\)
\(410\) 0 0
\(411\) −10.1710 −0.501699
\(412\) 0 0
\(413\) 0.260622 0.0128244
\(414\) 0 0
\(415\) 26.8283 1.31695
\(416\) 0 0
\(417\) −3.72509 −0.182418
\(418\) 0 0
\(419\) −17.0127 −0.831127 −0.415564 0.909564i \(-0.636416\pi\)
−0.415564 + 0.909564i \(0.636416\pi\)
\(420\) 0 0
\(421\) −33.3469 −1.62523 −0.812613 0.582803i \(-0.801956\pi\)
−0.812613 + 0.582803i \(0.801956\pi\)
\(422\) 0 0
\(423\) −10.6910 −0.519817
\(424\) 0 0
\(425\) −4.33188 −0.210127
\(426\) 0 0
\(427\) 20.5049 0.992304
\(428\) 0 0
\(429\) −4.56151 −0.220232
\(430\) 0 0
\(431\) −38.5757 −1.85813 −0.929063 0.369921i \(-0.879385\pi\)
−0.929063 + 0.369921i \(0.879385\pi\)
\(432\) 0 0
\(433\) 16.3071 0.783671 0.391836 0.920035i \(-0.371840\pi\)
0.391836 + 0.920035i \(0.371840\pi\)
\(434\) 0 0
\(435\) 13.3561 0.640374
\(436\) 0 0
\(437\) 18.4595 0.883039
\(438\) 0 0
\(439\) 21.7738 1.03921 0.519603 0.854408i \(-0.326080\pi\)
0.519603 + 0.854408i \(0.326080\pi\)
\(440\) 0 0
\(441\) 12.7300 0.606193
\(442\) 0 0
\(443\) 6.04240 0.287083 0.143541 0.989644i \(-0.454151\pi\)
0.143541 + 0.989644i \(0.454151\pi\)
\(444\) 0 0
\(445\) 7.10492 0.336805
\(446\) 0 0
\(447\) 1.87390 0.0886323
\(448\) 0 0
\(449\) 2.44696 0.115479 0.0577395 0.998332i \(-0.481611\pi\)
0.0577395 + 0.998332i \(0.481611\pi\)
\(450\) 0 0
\(451\) 18.5928 0.875500
\(452\) 0 0
\(453\) −15.8972 −0.746917
\(454\) 0 0
\(455\) −20.0119 −0.938174
\(456\) 0 0
\(457\) −2.29158 −0.107195 −0.0535977 0.998563i \(-0.517069\pi\)
−0.0535977 + 0.998563i \(0.517069\pi\)
\(458\) 0 0
\(459\) −2.41675 −0.112804
\(460\) 0 0
\(461\) 6.40370 0.298250 0.149125 0.988818i \(-0.452354\pi\)
0.149125 + 0.988818i \(0.452354\pi\)
\(462\) 0 0
\(463\) 1.72070 0.0799677 0.0399838 0.999200i \(-0.487269\pi\)
0.0399838 + 0.999200i \(0.487269\pi\)
\(464\) 0 0
\(465\) −2.30849 −0.107054
\(466\) 0 0
\(467\) −28.5008 −1.31886 −0.659429 0.751767i \(-0.729202\pi\)
−0.659429 + 0.751767i \(0.729202\pi\)
\(468\) 0 0
\(469\) 17.6166 0.813459
\(470\) 0 0
\(471\) −17.9023 −0.824893
\(472\) 0 0
\(473\) 20.0810 0.923327
\(474\) 0 0
\(475\) 6.40001 0.293653
\(476\) 0 0
\(477\) −5.98775 −0.274160
\(478\) 0 0
\(479\) −37.4969 −1.71328 −0.856638 0.515919i \(-0.827451\pi\)
−0.856638 + 0.515919i \(0.827451\pi\)
\(480\) 0 0
\(481\) 25.0996 1.14444
\(482\) 0 0
\(483\) −22.9641 −1.04490
\(484\) 0 0
\(485\) 13.7588 0.624755
\(486\) 0 0
\(487\) 12.5097 0.566866 0.283433 0.958992i \(-0.408527\pi\)
0.283433 + 0.958992i \(0.408527\pi\)
\(488\) 0 0
\(489\) 11.2246 0.507593
\(490\) 0 0
\(491\) −11.3268 −0.511172 −0.255586 0.966786i \(-0.582268\pi\)
−0.255586 + 0.966786i \(0.582268\pi\)
\(492\) 0 0
\(493\) 18.0228 0.811708
\(494\) 0 0
\(495\) 3.24757 0.145967
\(496\) 0 0
\(497\) −28.5142 −1.27904
\(498\) 0 0
\(499\) 29.6999 1.32955 0.664774 0.747044i \(-0.268528\pi\)
0.664774 + 0.747044i \(0.268528\pi\)
\(500\) 0 0
\(501\) −5.50349 −0.245878
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −27.4369 −1.22093
\(506\) 0 0
\(507\) 6.67187 0.296308
\(508\) 0 0
\(509\) 17.6491 0.782281 0.391141 0.920331i \(-0.372081\pi\)
0.391141 + 0.920331i \(0.372081\pi\)
\(510\) 0 0
\(511\) −16.7984 −0.743116
\(512\) 0 0
\(513\) 3.57055 0.157644
\(514\) 0 0
\(515\) −10.5132 −0.463266
\(516\) 0 0
\(517\) 19.3861 0.852600
\(518\) 0 0
\(519\) 12.6287 0.554340
\(520\) 0 0
\(521\) −20.6893 −0.906414 −0.453207 0.891405i \(-0.649720\pi\)
−0.453207 + 0.891405i \(0.649720\pi\)
\(522\) 0 0
\(523\) 14.0143 0.612803 0.306401 0.951902i \(-0.400875\pi\)
0.306401 + 0.951902i \(0.400875\pi\)
\(524\) 0 0
\(525\) −7.96176 −0.347480
\(526\) 0 0
\(527\) −3.11510 −0.135696
\(528\) 0 0
\(529\) 3.72820 0.162096
\(530\) 0 0
\(531\) −0.0586743 −0.00254625
\(532\) 0 0
\(533\) 25.7936 1.11724
\(534\) 0 0
\(535\) −11.3740 −0.491743
\(536\) 0 0
\(537\) 17.4659 0.753711
\(538\) 0 0
\(539\) −23.0834 −0.994274
\(540\) 0 0
\(541\) 11.1304 0.478531 0.239266 0.970954i \(-0.423093\pi\)
0.239266 + 0.970954i \(0.423093\pi\)
\(542\) 0 0
\(543\) −9.96334 −0.427568
\(544\) 0 0
\(545\) −23.0194 −0.986045
\(546\) 0 0
\(547\) 3.91069 0.167209 0.0836046 0.996499i \(-0.473357\pi\)
0.0836046 + 0.996499i \(0.473357\pi\)
\(548\) 0 0
\(549\) −4.61631 −0.197019
\(550\) 0 0
\(551\) −26.6273 −1.13436
\(552\) 0 0
\(553\) 61.5912 2.61912
\(554\) 0 0
\(555\) −17.8696 −0.758524
\(556\) 0 0
\(557\) 21.0319 0.891152 0.445576 0.895244i \(-0.352999\pi\)
0.445576 + 0.895244i \(0.352999\pi\)
\(558\) 0 0
\(559\) 27.8582 1.17828
\(560\) 0 0
\(561\) 4.38230 0.185021
\(562\) 0 0
\(563\) 2.87046 0.120976 0.0604878 0.998169i \(-0.480734\pi\)
0.0604878 + 0.998169i \(0.480734\pi\)
\(564\) 0 0
\(565\) 25.5910 1.07662
\(566\) 0 0
\(567\) −4.44185 −0.186540
\(568\) 0 0
\(569\) −17.4112 −0.729916 −0.364958 0.931024i \(-0.618917\pi\)
−0.364958 + 0.931024i \(0.618917\pi\)
\(570\) 0 0
\(571\) −43.3984 −1.81616 −0.908082 0.418791i \(-0.862454\pi\)
−0.908082 + 0.418791i \(0.862454\pi\)
\(572\) 0 0
\(573\) −4.00549 −0.167332
\(574\) 0 0
\(575\) 9.26680 0.386452
\(576\) 0 0
\(577\) −25.7678 −1.07273 −0.536364 0.843987i \(-0.680203\pi\)
−0.536364 + 0.843987i \(0.680203\pi\)
\(578\) 0 0
\(579\) −19.2439 −0.799750
\(580\) 0 0
\(581\) 66.5379 2.76046
\(582\) 0 0
\(583\) 10.8576 0.449677
\(584\) 0 0
\(585\) 4.50531 0.186272
\(586\) 0 0
\(587\) −32.4582 −1.33969 −0.669847 0.742499i \(-0.733640\pi\)
−0.669847 + 0.742499i \(0.733640\pi\)
\(588\) 0 0
\(589\) 4.60231 0.189635
\(590\) 0 0
\(591\) 25.0976 1.03238
\(592\) 0 0
\(593\) 20.9474 0.860206 0.430103 0.902780i \(-0.358477\pi\)
0.430103 + 0.902780i \(0.358477\pi\)
\(594\) 0 0
\(595\) 19.2258 0.788179
\(596\) 0 0
\(597\) −10.1127 −0.413884
\(598\) 0 0
\(599\) −11.7101 −0.478463 −0.239232 0.970962i \(-0.576896\pi\)
−0.239232 + 0.970962i \(0.576896\pi\)
\(600\) 0 0
\(601\) −21.5160 −0.877658 −0.438829 0.898571i \(-0.644607\pi\)
−0.438829 + 0.898571i \(0.644607\pi\)
\(602\) 0 0
\(603\) −3.96605 −0.161510
\(604\) 0 0
\(605\) 13.8118 0.561530
\(606\) 0 0
\(607\) 21.1856 0.859898 0.429949 0.902853i \(-0.358532\pi\)
0.429949 + 0.902853i \(0.358532\pi\)
\(608\) 0 0
\(609\) 33.1250 1.34229
\(610\) 0 0
\(611\) 26.8942 1.08802
\(612\) 0 0
\(613\) −12.5879 −0.508419 −0.254209 0.967149i \(-0.581815\pi\)
−0.254209 + 0.967149i \(0.581815\pi\)
\(614\) 0 0
\(615\) −18.3637 −0.740497
\(616\) 0 0
\(617\) 4.35448 0.175305 0.0876524 0.996151i \(-0.472064\pi\)
0.0876524 + 0.996151i \(0.472064\pi\)
\(618\) 0 0
\(619\) 34.8826 1.40205 0.701025 0.713136i \(-0.252726\pi\)
0.701025 + 0.713136i \(0.252726\pi\)
\(620\) 0 0
\(621\) 5.16993 0.207462
\(622\) 0 0
\(623\) 17.6212 0.705979
\(624\) 0 0
\(625\) −12.8250 −0.512998
\(626\) 0 0
\(627\) −6.47450 −0.258567
\(628\) 0 0
\(629\) −24.1135 −0.961469
\(630\) 0 0
\(631\) 24.6950 0.983092 0.491546 0.870852i \(-0.336432\pi\)
0.491546 + 0.870852i \(0.336432\pi\)
\(632\) 0 0
\(633\) 12.0164 0.477607
\(634\) 0 0
\(635\) −23.4848 −0.931965
\(636\) 0 0
\(637\) −32.0234 −1.26881
\(638\) 0 0
\(639\) 6.41945 0.253950
\(640\) 0 0
\(641\) 9.85763 0.389353 0.194676 0.980868i \(-0.437634\pi\)
0.194676 + 0.980868i \(0.437634\pi\)
\(642\) 0 0
\(643\) 19.9394 0.786335 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(644\) 0 0
\(645\) −19.8337 −0.780950
\(646\) 0 0
\(647\) −17.2156 −0.676813 −0.338407 0.941000i \(-0.609888\pi\)
−0.338407 + 0.941000i \(0.609888\pi\)
\(648\) 0 0
\(649\) 0.106394 0.00417634
\(650\) 0 0
\(651\) −5.72538 −0.224395
\(652\) 0 0
\(653\) 28.8272 1.12810 0.564049 0.825742i \(-0.309243\pi\)
0.564049 + 0.825742i \(0.309243\pi\)
\(654\) 0 0
\(655\) 18.4379 0.720429
\(656\) 0 0
\(657\) 3.78184 0.147544
\(658\) 0 0
\(659\) 11.0092 0.428858 0.214429 0.976740i \(-0.431211\pi\)
0.214429 + 0.976740i \(0.431211\pi\)
\(660\) 0 0
\(661\) −27.6456 −1.07529 −0.537644 0.843172i \(-0.680686\pi\)
−0.537644 + 0.843172i \(0.680686\pi\)
\(662\) 0 0
\(663\) 6.07953 0.236109
\(664\) 0 0
\(665\) −28.4045 −1.10148
\(666\) 0 0
\(667\) −38.5546 −1.49284
\(668\) 0 0
\(669\) 20.8248 0.805132
\(670\) 0 0
\(671\) 8.37077 0.323150
\(672\) 0 0
\(673\) −14.2899 −0.550835 −0.275418 0.961325i \(-0.588816\pi\)
−0.275418 + 0.961325i \(0.588816\pi\)
\(674\) 0 0
\(675\) 1.79244 0.0689911
\(676\) 0 0
\(677\) −24.7177 −0.949979 −0.474990 0.879991i \(-0.657548\pi\)
−0.474990 + 0.879991i \(0.657548\pi\)
\(678\) 0 0
\(679\) 34.1238 1.30955
\(680\) 0 0
\(681\) −18.9517 −0.726231
\(682\) 0 0
\(683\) −28.6300 −1.09550 −0.547748 0.836644i \(-0.684515\pi\)
−0.547748 + 0.836644i \(0.684515\pi\)
\(684\) 0 0
\(685\) −18.2159 −0.695995
\(686\) 0 0
\(687\) −21.4258 −0.817444
\(688\) 0 0
\(689\) 15.0627 0.573842
\(690\) 0 0
\(691\) −11.3159 −0.430477 −0.215238 0.976562i \(-0.569053\pi\)
−0.215238 + 0.976562i \(0.569053\pi\)
\(692\) 0 0
\(693\) 8.05443 0.305962
\(694\) 0 0
\(695\) −6.67151 −0.253065
\(696\) 0 0
\(697\) −24.7803 −0.938619
\(698\) 0 0
\(699\) −12.0637 −0.456292
\(700\) 0 0
\(701\) 11.8584 0.447886 0.223943 0.974602i \(-0.428107\pi\)
0.223943 + 0.974602i \(0.428107\pi\)
\(702\) 0 0
\(703\) 35.6258 1.34365
\(704\) 0 0
\(705\) −19.1473 −0.721129
\(706\) 0 0
\(707\) −68.0474 −2.55919
\(708\) 0 0
\(709\) −4.79744 −0.180172 −0.0900858 0.995934i \(-0.528714\pi\)
−0.0900858 + 0.995934i \(0.528714\pi\)
\(710\) 0 0
\(711\) −13.8661 −0.520019
\(712\) 0 0
\(713\) 6.66385 0.249563
\(714\) 0 0
\(715\) −8.16950 −0.305522
\(716\) 0 0
\(717\) 5.05208 0.188673
\(718\) 0 0
\(719\) −14.1635 −0.528209 −0.264105 0.964494i \(-0.585076\pi\)
−0.264105 + 0.964494i \(0.585076\pi\)
\(720\) 0 0
\(721\) −26.0742 −0.971053
\(722\) 0 0
\(723\) 21.1868 0.787946
\(724\) 0 0
\(725\) −13.3671 −0.496440
\(726\) 0 0
\(727\) 15.5322 0.576059 0.288029 0.957622i \(-0.407000\pi\)
0.288029 + 0.957622i \(0.407000\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −26.7638 −0.989895
\(732\) 0 0
\(733\) −1.35869 −0.0501843 −0.0250922 0.999685i \(-0.507988\pi\)
−0.0250922 + 0.999685i \(0.507988\pi\)
\(734\) 0 0
\(735\) 22.7991 0.840957
\(736\) 0 0
\(737\) 7.19165 0.264908
\(738\) 0 0
\(739\) −36.0815 −1.32728 −0.663640 0.748052i \(-0.730989\pi\)
−0.663640 + 0.748052i \(0.730989\pi\)
\(740\) 0 0
\(741\) −8.98201 −0.329962
\(742\) 0 0
\(743\) 5.48440 0.201203 0.100602 0.994927i \(-0.467923\pi\)
0.100602 + 0.994927i \(0.467923\pi\)
\(744\) 0 0
\(745\) 3.35609 0.122958
\(746\) 0 0
\(747\) −14.9798 −0.548081
\(748\) 0 0
\(749\) −28.2092 −1.03074
\(750\) 0 0
\(751\) −31.8666 −1.16283 −0.581414 0.813608i \(-0.697500\pi\)
−0.581414 + 0.813608i \(0.697500\pi\)
\(752\) 0 0
\(753\) 11.5889 0.422322
\(754\) 0 0
\(755\) −28.4714 −1.03618
\(756\) 0 0
\(757\) −15.4940 −0.563138 −0.281569 0.959541i \(-0.590855\pi\)
−0.281569 + 0.959541i \(0.590855\pi\)
\(758\) 0 0
\(759\) −9.37466 −0.340278
\(760\) 0 0
\(761\) 13.7765 0.499399 0.249700 0.968323i \(-0.419668\pi\)
0.249700 + 0.968323i \(0.419668\pi\)
\(762\) 0 0
\(763\) −57.0915 −2.06685
\(764\) 0 0
\(765\) −4.32832 −0.156491
\(766\) 0 0
\(767\) 0.147600 0.00532952
\(768\) 0 0
\(769\) 47.7485 1.72185 0.860927 0.508728i \(-0.169884\pi\)
0.860927 + 0.508728i \(0.169884\pi\)
\(770\) 0 0
\(771\) −0.593402 −0.0213708
\(772\) 0 0
\(773\) −7.91160 −0.284560 −0.142280 0.989826i \(-0.545443\pi\)
−0.142280 + 0.989826i \(0.545443\pi\)
\(774\) 0 0
\(775\) 2.31039 0.0829916
\(776\) 0 0
\(777\) −44.3193 −1.58994
\(778\) 0 0
\(779\) 36.6108 1.31172
\(780\) 0 0
\(781\) −11.6404 −0.416527
\(782\) 0 0
\(783\) −7.45747 −0.266508
\(784\) 0 0
\(785\) −32.0624 −1.14435
\(786\) 0 0
\(787\) 6.04807 0.215590 0.107795 0.994173i \(-0.465621\pi\)
0.107795 + 0.994173i \(0.465621\pi\)
\(788\) 0 0
\(789\) −8.07853 −0.287603
\(790\) 0 0
\(791\) 63.4694 2.25671
\(792\) 0 0
\(793\) 11.6127 0.412378
\(794\) 0 0
\(795\) −10.7239 −0.380336
\(796\) 0 0
\(797\) 10.3854 0.367870 0.183935 0.982938i \(-0.441116\pi\)
0.183935 + 0.982938i \(0.441116\pi\)
\(798\) 0 0
\(799\) −25.8376 −0.914069
\(800\) 0 0
\(801\) −3.96709 −0.140170
\(802\) 0 0
\(803\) −6.85762 −0.242000
\(804\) 0 0
\(805\) −41.1279 −1.44957
\(806\) 0 0
\(807\) −4.59074 −0.161602
\(808\) 0 0
\(809\) 29.8024 1.04780 0.523899 0.851781i \(-0.324477\pi\)
0.523899 + 0.851781i \(0.324477\pi\)
\(810\) 0 0
\(811\) −13.7347 −0.482291 −0.241145 0.970489i \(-0.577523\pi\)
−0.241145 + 0.970489i \(0.577523\pi\)
\(812\) 0 0
\(813\) −19.0274 −0.667318
\(814\) 0 0
\(815\) 20.1028 0.704172
\(816\) 0 0
\(817\) 39.5413 1.38338
\(818\) 0 0
\(819\) 11.1738 0.390445
\(820\) 0 0
\(821\) 25.5908 0.893124 0.446562 0.894753i \(-0.352648\pi\)
0.446562 + 0.894753i \(0.352648\pi\)
\(822\) 0 0
\(823\) −41.5326 −1.44774 −0.723868 0.689939i \(-0.757638\pi\)
−0.723868 + 0.689939i \(0.757638\pi\)
\(824\) 0 0
\(825\) −3.25024 −0.113159
\(826\) 0 0
\(827\) −30.5733 −1.06314 −0.531569 0.847015i \(-0.678397\pi\)
−0.531569 + 0.847015i \(0.678397\pi\)
\(828\) 0 0
\(829\) 40.1329 1.39387 0.696937 0.717132i \(-0.254546\pi\)
0.696937 + 0.717132i \(0.254546\pi\)
\(830\) 0 0
\(831\) 32.5295 1.12844
\(832\) 0 0
\(833\) 30.7654 1.06596
\(834\) 0 0
\(835\) −9.85657 −0.341101
\(836\) 0 0
\(837\) 1.28896 0.0445530
\(838\) 0 0
\(839\) 30.1065 1.03939 0.519695 0.854352i \(-0.326046\pi\)
0.519695 + 0.854352i \(0.326046\pi\)
\(840\) 0 0
\(841\) 26.6138 0.917717
\(842\) 0 0
\(843\) −25.3406 −0.872777
\(844\) 0 0
\(845\) 11.9491 0.411061
\(846\) 0 0
\(847\) 34.2552 1.17702
\(848\) 0 0
\(849\) −0.181596 −0.00623235
\(850\) 0 0
\(851\) 51.5838 1.76827
\(852\) 0 0
\(853\) −19.3786 −0.663509 −0.331755 0.943366i \(-0.607641\pi\)
−0.331755 + 0.943366i \(0.607641\pi\)
\(854\) 0 0
\(855\) 6.39474 0.218696
\(856\) 0 0
\(857\) 9.55876 0.326521 0.163260 0.986583i \(-0.447799\pi\)
0.163260 + 0.986583i \(0.447799\pi\)
\(858\) 0 0
\(859\) −22.2422 −0.758894 −0.379447 0.925213i \(-0.623886\pi\)
−0.379447 + 0.925213i \(0.623886\pi\)
\(860\) 0 0
\(861\) −45.5447 −1.55216
\(862\) 0 0
\(863\) 54.9012 1.86886 0.934430 0.356147i \(-0.115910\pi\)
0.934430 + 0.356147i \(0.115910\pi\)
\(864\) 0 0
\(865\) 22.6176 0.769022
\(866\) 0 0
\(867\) 11.1593 0.378990
\(868\) 0 0
\(869\) 25.1435 0.852933
\(870\) 0 0
\(871\) 9.97691 0.338055
\(872\) 0 0
\(873\) −7.68234 −0.260008
\(874\) 0 0
\(875\) −54.0353 −1.82673
\(876\) 0 0
\(877\) −3.61018 −0.121907 −0.0609536 0.998141i \(-0.519414\pi\)
−0.0609536 + 0.998141i \(0.519414\pi\)
\(878\) 0 0
\(879\) 19.5225 0.658476
\(880\) 0 0
\(881\) 53.6558 1.80771 0.903856 0.427838i \(-0.140724\pi\)
0.903856 + 0.427838i \(0.140724\pi\)
\(882\) 0 0
\(883\) 41.4251 1.39407 0.697033 0.717039i \(-0.254503\pi\)
0.697033 + 0.717039i \(0.254503\pi\)
\(884\) 0 0
\(885\) −0.105084 −0.00353235
\(886\) 0 0
\(887\) 21.8980 0.735263 0.367632 0.929971i \(-0.380169\pi\)
0.367632 + 0.929971i \(0.380169\pi\)
\(888\) 0 0
\(889\) −58.2456 −1.95349
\(890\) 0 0
\(891\) −1.81330 −0.0607480
\(892\) 0 0
\(893\) 38.1730 1.27741
\(894\) 0 0
\(895\) 31.2809 1.04561
\(896\) 0 0
\(897\) −13.0054 −0.434237
\(898\) 0 0
\(899\) −9.61239 −0.320591
\(900\) 0 0
\(901\) −14.4709 −0.482096
\(902\) 0 0
\(903\) −49.1903 −1.63695
\(904\) 0 0
\(905\) −17.8440 −0.593154
\(906\) 0 0
\(907\) 56.1990 1.86606 0.933028 0.359803i \(-0.117156\pi\)
0.933028 + 0.359803i \(0.117156\pi\)
\(908\) 0 0
\(909\) 15.3196 0.508119
\(910\) 0 0
\(911\) −51.2043 −1.69648 −0.848238 0.529616i \(-0.822336\pi\)
−0.848238 + 0.529616i \(0.822336\pi\)
\(912\) 0 0
\(913\) 27.1629 0.898960
\(914\) 0 0
\(915\) −8.26765 −0.273320
\(916\) 0 0
\(917\) 45.7287 1.51009
\(918\) 0 0
\(919\) 20.6079 0.679792 0.339896 0.940463i \(-0.389608\pi\)
0.339896 + 0.940463i \(0.389608\pi\)
\(920\) 0 0
\(921\) 7.67738 0.252978
\(922\) 0 0
\(923\) −16.1486 −0.531539
\(924\) 0 0
\(925\) 17.8844 0.588034
\(926\) 0 0
\(927\) 5.87011 0.192800
\(928\) 0 0
\(929\) −25.6208 −0.840591 −0.420295 0.907387i \(-0.638074\pi\)
−0.420295 + 0.907387i \(0.638074\pi\)
\(930\) 0 0
\(931\) −45.4533 −1.48967
\(932\) 0 0
\(933\) −22.8409 −0.747778
\(934\) 0 0
\(935\) 7.84856 0.256675
\(936\) 0 0
\(937\) −15.7353 −0.514049 −0.257025 0.966405i \(-0.582742\pi\)
−0.257025 + 0.966405i \(0.582742\pi\)
\(938\) 0 0
\(939\) 4.51047 0.147194
\(940\) 0 0
\(941\) −58.0599 −1.89270 −0.946349 0.323145i \(-0.895260\pi\)
−0.946349 + 0.323145i \(0.895260\pi\)
\(942\) 0 0
\(943\) 53.0101 1.72625
\(944\) 0 0
\(945\) −7.95521 −0.258783
\(946\) 0 0
\(947\) −29.5628 −0.960661 −0.480330 0.877088i \(-0.659483\pi\)
−0.480330 + 0.877088i \(0.659483\pi\)
\(948\) 0 0
\(949\) −9.51351 −0.308822
\(950\) 0 0
\(951\) 8.22120 0.266591
\(952\) 0 0
\(953\) 36.0784 1.16869 0.584347 0.811504i \(-0.301351\pi\)
0.584347 + 0.811504i \(0.301351\pi\)
\(954\) 0 0
\(955\) −7.17370 −0.232136
\(956\) 0 0
\(957\) 13.5226 0.437125
\(958\) 0 0
\(959\) −45.1781 −1.45888
\(960\) 0 0
\(961\) −29.3386 −0.946406
\(962\) 0 0
\(963\) 6.35078 0.204651
\(964\) 0 0
\(965\) −34.4652 −1.10947
\(966\) 0 0
\(967\) −12.6440 −0.406603 −0.203302 0.979116i \(-0.565167\pi\)
−0.203302 + 0.979116i \(0.565167\pi\)
\(968\) 0 0
\(969\) 8.62914 0.277208
\(970\) 0 0
\(971\) −27.0916 −0.869412 −0.434706 0.900572i \(-0.643148\pi\)
−0.434706 + 0.900572i \(0.643148\pi\)
\(972\) 0 0
\(973\) −16.5463 −0.530450
\(974\) 0 0
\(975\) −4.50903 −0.144404
\(976\) 0 0
\(977\) −6.89384 −0.220554 −0.110277 0.993901i \(-0.535174\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(978\) 0 0
\(979\) 7.19353 0.229906
\(980\) 0 0
\(981\) 12.8531 0.410367
\(982\) 0 0
\(983\) −32.8660 −1.04826 −0.524131 0.851637i \(-0.675610\pi\)
−0.524131 + 0.851637i \(0.675610\pi\)
\(984\) 0 0
\(985\) 44.9489 1.43219
\(986\) 0 0
\(987\) −47.4881 −1.51156
\(988\) 0 0
\(989\) 57.2533 1.82055
\(990\) 0 0
\(991\) 29.5094 0.937398 0.468699 0.883358i \(-0.344723\pi\)
0.468699 + 0.883358i \(0.344723\pi\)
\(992\) 0 0
\(993\) −25.5035 −0.809328
\(994\) 0 0
\(995\) −18.1114 −0.574171
\(996\) 0 0
\(997\) −11.5507 −0.365815 −0.182907 0.983130i \(-0.558551\pi\)
−0.182907 + 0.983130i \(0.558551\pi\)
\(998\) 0 0
\(999\) 9.97766 0.315679
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 \(a_p\))