Properties

Label 9450.2.a.el.1.1
Level 9450
Weight 2
Character 9450.1
Self dual Yes
Analytic conductor 75.459
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9450.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(75.4586299101\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{97}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.42443\)
Character \(\chi\) = 9450.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-3.42443 q^{11}\) \(-1.00000 q^{13}\) \(-1.00000 q^{14}\) \(+1.00000 q^{16}\) \(-4.42443 q^{17}\) \(-1.42443 q^{19}\) \(+3.42443 q^{22}\) \(-6.42443 q^{23}\) \(+1.00000 q^{26}\) \(+1.00000 q^{28}\) \(+6.42443 q^{29}\) \(+8.42443 q^{31}\) \(-1.00000 q^{32}\) \(+4.42443 q^{34}\) \(-10.8489 q^{37}\) \(+1.42443 q^{38}\) \(+0.575571 q^{41}\) \(+7.00000 q^{43}\) \(-3.42443 q^{44}\) \(+6.42443 q^{46}\) \(-0.575571 q^{47}\) \(+1.00000 q^{49}\) \(-1.00000 q^{52}\) \(-5.00000 q^{53}\) \(-1.00000 q^{56}\) \(-6.42443 q^{58}\) \(-2.42443 q^{59}\) \(-8.84886 q^{61}\) \(-8.42443 q^{62}\) \(+1.00000 q^{64}\) \(+3.00000 q^{67}\) \(-4.42443 q^{68}\) \(-4.42443 q^{71}\) \(+7.42443 q^{73}\) \(+10.8489 q^{74}\) \(-1.42443 q^{76}\) \(-3.42443 q^{77}\) \(-8.00000 q^{79}\) \(-0.575571 q^{82}\) \(-17.4244 q^{83}\) \(-7.00000 q^{86}\) \(+3.42443 q^{88}\) \(+1.00000 q^{89}\) \(-1.00000 q^{91}\) \(-6.42443 q^{92}\) \(+0.575571 q^{94}\) \(+10.0000 q^{97}\) \(-1.00000 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut q^{34} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut +\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 5q^{59} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 7q^{62} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{76} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 11q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut -\mathstrut 3q^{88} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 11q^{94} \) \(\mathstrut +\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −3.42443 −1.03250 −0.516252 0.856437i \(-0.672673\pi\)
−0.516252 + 0.856437i \(0.672673\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.42443 −1.07308 −0.536541 0.843874i \(-0.680269\pi\)
−0.536541 + 0.843874i \(0.680269\pi\)
\(18\) 0 0
\(19\) −1.42443 −0.326786 −0.163393 0.986561i \(-0.552244\pi\)
−0.163393 + 0.986561i \(0.552244\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.42443 0.730091
\(23\) −6.42443 −1.33959 −0.669793 0.742548i \(-0.733617\pi\)
−0.669793 + 0.742548i \(0.733617\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 6.42443 1.19299 0.596493 0.802618i \(-0.296560\pi\)
0.596493 + 0.802618i \(0.296560\pi\)
\(30\) 0 0
\(31\) 8.42443 1.51307 0.756536 0.653952i \(-0.226890\pi\)
0.756536 + 0.653952i \(0.226890\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.42443 0.758783
\(35\) 0 0
\(36\) 0 0
\(37\) −10.8489 −1.78354 −0.891771 0.452488i \(-0.850537\pi\)
−0.891771 + 0.452488i \(0.850537\pi\)
\(38\) 1.42443 0.231073
\(39\) 0 0
\(40\) 0 0
\(41\) 0.575571 0.0898891 0.0449446 0.998989i \(-0.485689\pi\)
0.0449446 + 0.998989i \(0.485689\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) −3.42443 −0.516252
\(45\) 0 0
\(46\) 6.42443 0.947230
\(47\) −0.575571 −0.0839557 −0.0419778 0.999119i \(-0.513366\pi\)
−0.0419778 + 0.999119i \(0.513366\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) −5.00000 −0.686803 −0.343401 0.939189i \(-0.611579\pi\)
−0.343401 + 0.939189i \(0.611579\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −6.42443 −0.843569
\(59\) −2.42443 −0.315634 −0.157817 0.987468i \(-0.550446\pi\)
−0.157817 + 0.987468i \(0.550446\pi\)
\(60\) 0 0
\(61\) −8.84886 −1.13298 −0.566490 0.824069i \(-0.691699\pi\)
−0.566490 + 0.824069i \(0.691699\pi\)
\(62\) −8.42443 −1.06990
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) −4.42443 −0.536541
\(69\) 0 0
\(70\) 0 0
\(71\) −4.42443 −0.525083 −0.262542 0.964921i \(-0.584561\pi\)
−0.262542 + 0.964921i \(0.584561\pi\)
\(72\) 0 0
\(73\) 7.42443 0.868964 0.434482 0.900681i \(-0.356932\pi\)
0.434482 + 0.900681i \(0.356932\pi\)
\(74\) 10.8489 1.26115
\(75\) 0 0
\(76\) −1.42443 −0.163393
\(77\) −3.42443 −0.390250
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.575571 −0.0635612
\(83\) −17.4244 −1.91258 −0.956290 0.292421i \(-0.905539\pi\)
−0.956290 + 0.292421i \(0.905539\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −7.00000 −0.754829
\(87\) 0 0
\(88\) 3.42443 0.365045
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) −6.42443 −0.669793
\(93\) 0 0
\(94\) 0.575571 0.0593656
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 16.2733 1.61925 0.809626 0.586946i \(-0.199670\pi\)
0.809626 + 0.586946i \(0.199670\pi\)
\(102\) 0 0
\(103\) −0.424429 −0.0418202 −0.0209101 0.999781i \(-0.506656\pi\)
−0.0209101 + 0.999781i \(0.506656\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) 16.8489 1.62884 0.814420 0.580275i \(-0.197055\pi\)
0.814420 + 0.580275i \(0.197055\pi\)
\(108\) 0 0
\(109\) 7.42443 0.711131 0.355566 0.934651i \(-0.384288\pi\)
0.355566 + 0.934651i \(0.384288\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) 10.2733 0.966430 0.483215 0.875502i \(-0.339469\pi\)
0.483215 + 0.875502i \(0.339469\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.42443 0.596493
\(117\) 0 0
\(118\) 2.42443 0.223187
\(119\) −4.42443 −0.405587
\(120\) 0 0
\(121\) 0.726713 0.0660648
\(122\) 8.84886 0.801138
\(123\) 0 0
\(124\) 8.42443 0.756536
\(125\) 0 0
\(126\) 0 0
\(127\) 21.4244 1.90111 0.950555 0.310555i \(-0.100515\pi\)
0.950555 + 0.310555i \(0.100515\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 9.27329 0.810211 0.405105 0.914270i \(-0.367235\pi\)
0.405105 + 0.914270i \(0.367235\pi\)
\(132\) 0 0
\(133\) −1.42443 −0.123514
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) 4.42443 0.379392
\(137\) 7.42443 0.634312 0.317156 0.948373i \(-0.397272\pi\)
0.317156 + 0.948373i \(0.397272\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.42443 0.371290
\(143\) 3.42443 0.286365
\(144\) 0 0
\(145\) 0 0
\(146\) −7.42443 −0.614450
\(147\) 0 0
\(148\) −10.8489 −0.891771
\(149\) 10.4244 0.854002 0.427001 0.904251i \(-0.359570\pi\)
0.427001 + 0.904251i \(0.359570\pi\)
\(150\) 0 0
\(151\) 2.84886 0.231837 0.115918 0.993259i \(-0.463019\pi\)
0.115918 + 0.993259i \(0.463019\pi\)
\(152\) 1.42443 0.115536
\(153\) 0 0
\(154\) 3.42443 0.275948
\(155\) 0 0
\(156\) 0 0
\(157\) 2.42443 0.193490 0.0967452 0.995309i \(-0.469157\pi\)
0.0967452 + 0.995309i \(0.469157\pi\)
\(158\) 8.00000 0.636446
\(159\) 0 0
\(160\) 0 0
\(161\) −6.42443 −0.506316
\(162\) 0 0
\(163\) 12.4244 0.973156 0.486578 0.873637i \(-0.338245\pi\)
0.486578 + 0.873637i \(0.338245\pi\)
\(164\) 0.575571 0.0449446
\(165\) 0 0
\(166\) 17.4244 1.35240
\(167\) −20.8489 −1.61333 −0.806667 0.591007i \(-0.798731\pi\)
−0.806667 + 0.591007i \(0.798731\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 7.00000 0.533745
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.42443 −0.258126
\(177\) 0 0
\(178\) −1.00000 −0.0749532
\(179\) 8.27329 0.618374 0.309187 0.951001i \(-0.399943\pi\)
0.309187 + 0.951001i \(0.399943\pi\)
\(180\) 0 0
\(181\) 7.27329 0.540619 0.270310 0.962773i \(-0.412874\pi\)
0.270310 + 0.962773i \(0.412874\pi\)
\(182\) 1.00000 0.0741249
\(183\) 0 0
\(184\) 6.42443 0.473615
\(185\) 0 0
\(186\) 0 0
\(187\) 15.1511 1.10796
\(188\) −0.575571 −0.0419778
\(189\) 0 0
\(190\) 0 0
\(191\) −10.5756 −0.765221 −0.382611 0.923910i \(-0.624975\pi\)
−0.382611 + 0.923910i \(0.624975\pi\)
\(192\) 0 0
\(193\) −5.57557 −0.401338 −0.200669 0.979659i \(-0.564312\pi\)
−0.200669 + 0.979659i \(0.564312\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 12.5756 0.895972 0.447986 0.894040i \(-0.352141\pi\)
0.447986 + 0.894040i \(0.352141\pi\)
\(198\) 0 0
\(199\) −3.00000 −0.212664 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −16.2733 −1.14498
\(203\) 6.42443 0.450907
\(204\) 0 0
\(205\) 0 0
\(206\) 0.424429 0.0295714
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 4.87786 0.337408
\(210\) 0 0
\(211\) −2.42443 −0.166905 −0.0834523 0.996512i \(-0.526595\pi\)
−0.0834523 + 0.996512i \(0.526595\pi\)
\(212\) −5.00000 −0.343401
\(213\) 0 0
\(214\) −16.8489 −1.15176
\(215\) 0 0
\(216\) 0 0
\(217\) 8.42443 0.571887
\(218\) −7.42443 −0.502846
\(219\) 0 0
\(220\) 0 0
\(221\) 4.42443 0.297619
\(222\) 0 0
\(223\) 26.8489 1.79793 0.898966 0.438018i \(-0.144319\pi\)
0.898966 + 0.438018i \(0.144319\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −10.2733 −0.683369
\(227\) 11.0000 0.730096 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.42443 −0.421784
\(233\) 4.57557 0.299756 0.149878 0.988705i \(-0.452112\pi\)
0.149878 + 0.988705i \(0.452112\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.42443 −0.157817
\(237\) 0 0
\(238\) 4.42443 0.286793
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 16.0000 1.03065 0.515325 0.856995i \(-0.327671\pi\)
0.515325 + 0.856995i \(0.327671\pi\)
\(242\) −0.726713 −0.0467149
\(243\) 0 0
\(244\) −8.84886 −0.566490
\(245\) 0 0
\(246\) 0 0
\(247\) 1.42443 0.0906342
\(248\) −8.42443 −0.534952
\(249\) 0 0
\(250\) 0 0
\(251\) 10.8489 0.684774 0.342387 0.939559i \(-0.388765\pi\)
0.342387 + 0.939559i \(0.388765\pi\)
\(252\) 0 0
\(253\) 22.0000 1.38313
\(254\) −21.4244 −1.34429
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.8489 0.801490 0.400745 0.916190i \(-0.368751\pi\)
0.400745 + 0.916190i \(0.368751\pi\)
\(258\) 0 0
\(259\) −10.8489 −0.674115
\(260\) 0 0
\(261\) 0 0
\(262\) −9.27329 −0.572906
\(263\) −28.4244 −1.75273 −0.876363 0.481652i \(-0.840037\pi\)
−0.876363 + 0.481652i \(0.840037\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.42443 0.0873373
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) −10.8489 −0.661467 −0.330733 0.943724i \(-0.607296\pi\)
−0.330733 + 0.943724i \(0.607296\pi\)
\(270\) 0 0
\(271\) 16.6977 1.01431 0.507157 0.861854i \(-0.330696\pi\)
0.507157 + 0.861854i \(0.330696\pi\)
\(272\) −4.42443 −0.268270
\(273\) 0 0
\(274\) −7.42443 −0.448526
\(275\) 0 0
\(276\) 0 0
\(277\) 30.8489 1.85353 0.926764 0.375644i \(-0.122578\pi\)
0.926764 + 0.375644i \(0.122578\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) −22.8489 −1.36305 −0.681524 0.731795i \(-0.738683\pi\)
−0.681524 + 0.731795i \(0.738683\pi\)
\(282\) 0 0
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) −4.42443 −0.262542
\(285\) 0 0
\(286\) −3.42443 −0.202491
\(287\) 0.575571 0.0339749
\(288\) 0 0
\(289\) 2.57557 0.151504
\(290\) 0 0
\(291\) 0 0
\(292\) 7.42443 0.434482
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 10.8489 0.630577
\(297\) 0 0
\(298\) −10.4244 −0.603871
\(299\) 6.42443 0.371534
\(300\) 0 0
\(301\) 7.00000 0.403473
\(302\) −2.84886 −0.163933
\(303\) 0 0
\(304\) −1.42443 −0.0816966
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −3.42443 −0.195125
\(309\) 0 0
\(310\) 0 0
\(311\) −11.6977 −0.663317 −0.331658 0.943400i \(-0.607608\pi\)
−0.331658 + 0.943400i \(0.607608\pi\)
\(312\) 0 0
\(313\) −16.2733 −0.919821 −0.459910 0.887965i \(-0.652118\pi\)
−0.459910 + 0.887965i \(0.652118\pi\)
\(314\) −2.42443 −0.136818
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 31.4244 1.76497 0.882486 0.470339i \(-0.155868\pi\)
0.882486 + 0.470339i \(0.155868\pi\)
\(318\) 0 0
\(319\) −22.0000 −1.23176
\(320\) 0 0
\(321\) 0 0
\(322\) 6.42443 0.358019
\(323\) 6.30228 0.350668
\(324\) 0 0
\(325\) 0 0
\(326\) −12.4244 −0.688125
\(327\) 0 0
\(328\) −0.575571 −0.0317806
\(329\) −0.575571 −0.0317323
\(330\) 0 0
\(331\) 24.1221 1.32587 0.662936 0.748676i \(-0.269310\pi\)
0.662936 + 0.748676i \(0.269310\pi\)
\(332\) −17.4244 −0.956290
\(333\) 0 0
\(334\) 20.8489 1.14080
\(335\) 0 0
\(336\) 0 0
\(337\) −25.2733 −1.37672 −0.688362 0.725367i \(-0.741670\pi\)
−0.688362 + 0.725367i \(0.741670\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) −28.8489 −1.56225
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −7.00000 −0.377415
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 19.6977 1.05743 0.528714 0.848800i \(-0.322674\pi\)
0.528714 + 0.848800i \(0.322674\pi\)
\(348\) 0 0
\(349\) −13.5756 −0.726684 −0.363342 0.931656i \(-0.618364\pi\)
−0.363342 + 0.931656i \(0.618364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.42443 0.182523
\(353\) −7.57557 −0.403207 −0.201603 0.979467i \(-0.564615\pi\)
−0.201603 + 0.979467i \(0.564615\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) −8.27329 −0.437257
\(359\) −4.15114 −0.219089 −0.109544 0.993982i \(-0.534939\pi\)
−0.109544 + 0.993982i \(0.534939\pi\)
\(360\) 0 0
\(361\) −16.9710 −0.893211
\(362\) −7.27329 −0.382275
\(363\) 0 0
\(364\) −1.00000 −0.0524142
\(365\) 0 0
\(366\) 0 0
\(367\) 27.2733 1.42365 0.711827 0.702355i \(-0.247868\pi\)
0.711827 + 0.702355i \(0.247868\pi\)
\(368\) −6.42443 −0.334897
\(369\) 0 0
\(370\) 0 0
\(371\) −5.00000 −0.259587
\(372\) 0 0
\(373\) −29.6977 −1.53769 −0.768845 0.639436i \(-0.779168\pi\)
−0.768845 + 0.639436i \(0.779168\pi\)
\(374\) −15.1511 −0.783447
\(375\) 0 0
\(376\) 0.575571 0.0296828
\(377\) −6.42443 −0.330875
\(378\) 0 0
\(379\) 1.69772 0.0872058 0.0436029 0.999049i \(-0.486116\pi\)
0.0436029 + 0.999049i \(0.486116\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 10.5756 0.541093
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5.57557 0.283789
\(387\) 0 0
\(388\) 10.0000 0.507673
\(389\) 7.69772 0.390290 0.195145 0.980774i \(-0.437482\pi\)
0.195145 + 0.980774i \(0.437482\pi\)
\(390\) 0 0
\(391\) 28.4244 1.43749
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −12.5756 −0.633548
\(395\) 0 0
\(396\) 0 0
\(397\) 27.6977 1.39011 0.695054 0.718957i \(-0.255380\pi\)
0.695054 + 0.718957i \(0.255380\pi\)
\(398\) 3.00000 0.150376
\(399\) 0 0
\(400\) 0 0
\(401\) −24.8489 −1.24089 −0.620446 0.784249i \(-0.713049\pi\)
−0.620446 + 0.784249i \(0.713049\pi\)
\(402\) 0 0
\(403\) −8.42443 −0.419651
\(404\) 16.2733 0.809626
\(405\) 0 0
\(406\) −6.42443 −0.318839
\(407\) 37.1511 1.84151
\(408\) 0 0
\(409\) 31.6977 1.56735 0.783676 0.621170i \(-0.213342\pi\)
0.783676 + 0.621170i \(0.213342\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.424429 −0.0209101
\(413\) −2.42443 −0.119298
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) −4.87786 −0.238584
\(419\) 27.2733 1.33239 0.666194 0.745779i \(-0.267922\pi\)
0.666194 + 0.745779i \(0.267922\pi\)
\(420\) 0 0
\(421\) 5.72671 0.279103 0.139551 0.990215i \(-0.455434\pi\)
0.139551 + 0.990215i \(0.455434\pi\)
\(422\) 2.42443 0.118019
\(423\) 0 0
\(424\) 5.00000 0.242821
\(425\) 0 0
\(426\) 0 0
\(427\) −8.84886 −0.428226
\(428\) 16.8489 0.814420
\(429\) 0 0
\(430\) 0 0
\(431\) 7.72671 0.372183 0.186091 0.982532i \(-0.440418\pi\)
0.186091 + 0.982532i \(0.440418\pi\)
\(432\) 0 0
\(433\) 3.72671 0.179094 0.0895472 0.995983i \(-0.471458\pi\)
0.0895472 + 0.995983i \(0.471458\pi\)
\(434\) −8.42443 −0.404386
\(435\) 0 0
\(436\) 7.42443 0.355566
\(437\) 9.15114 0.437758
\(438\) 0 0
\(439\) −33.8489 −1.61552 −0.807759 0.589513i \(-0.799320\pi\)
−0.807759 + 0.589513i \(0.799320\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.42443 −0.210449
\(443\) 33.6977 1.60103 0.800513 0.599315i \(-0.204560\pi\)
0.800513 + 0.599315i \(0.204560\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −26.8489 −1.27133
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) −25.6977 −1.21275 −0.606375 0.795179i \(-0.707377\pi\)
−0.606375 + 0.795179i \(0.707377\pi\)
\(450\) 0 0
\(451\) −1.97100 −0.0928109
\(452\) 10.2733 0.483215
\(453\) 0 0
\(454\) −11.0000 −0.516256
\(455\) 0 0
\(456\) 0 0
\(457\) −7.57557 −0.354370 −0.177185 0.984178i \(-0.556699\pi\)
−0.177185 + 0.984178i \(0.556699\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 0 0
\(460\) 0 0
\(461\) −16.5756 −0.772001 −0.386001 0.922499i \(-0.626144\pi\)
−0.386001 + 0.922499i \(0.626144\pi\)
\(462\) 0 0
\(463\) 25.9710 1.20697 0.603487 0.797373i \(-0.293777\pi\)
0.603487 + 0.797373i \(0.293777\pi\)
\(464\) 6.42443 0.298247
\(465\) 0 0
\(466\) −4.57557 −0.211959
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 3.00000 0.138527
\(470\) 0 0
\(471\) 0 0
\(472\) 2.42443 0.111593
\(473\) −23.9710 −1.10219
\(474\) 0 0
\(475\) 0 0
\(476\) −4.42443 −0.202793
\(477\) 0 0
\(478\) 0 0
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 0 0
\(481\) 10.8489 0.494665
\(482\) −16.0000 −0.728780
\(483\) 0 0
\(484\) 0.726713 0.0330324
\(485\) 0 0
\(486\) 0 0
\(487\) −3.42443 −0.155176 −0.0775878 0.996986i \(-0.524722\pi\)
−0.0775878 + 0.996986i \(0.524722\pi\)
\(488\) 8.84886 0.400569
\(489\) 0 0
\(490\) 0 0
\(491\) 21.6977 0.979204 0.489602 0.871946i \(-0.337142\pi\)
0.489602 + 0.871946i \(0.337142\pi\)
\(492\) 0 0
\(493\) −28.4244 −1.28017
\(494\) −1.42443 −0.0640881
\(495\) 0 0
\(496\) 8.42443 0.378268
\(497\) −4.42443 −0.198463
\(498\) 0 0
\(499\) −22.8489 −1.02286 −0.511428 0.859326i \(-0.670883\pi\)
−0.511428 + 0.859326i \(0.670883\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10.8489 −0.484208
\(503\) 39.9710 1.78222 0.891109 0.453788i \(-0.149928\pi\)
0.891109 + 0.453788i \(0.149928\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −22.0000 −0.978019
\(507\) 0 0
\(508\) 21.4244 0.950555
\(509\) −22.8489 −1.01276 −0.506379 0.862311i \(-0.669016\pi\)
−0.506379 + 0.862311i \(0.669016\pi\)
\(510\) 0 0
\(511\) 7.42443 0.328437
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −12.8489 −0.566739
\(515\) 0 0
\(516\) 0 0
\(517\) 1.97100 0.0866846
\(518\) 10.8489 0.476671
\(519\) 0 0
\(520\) 0 0
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) 0 0
\(523\) 6.84886 0.299480 0.149740 0.988725i \(-0.452156\pi\)
0.149740 + 0.988725i \(0.452156\pi\)
\(524\) 9.27329 0.405105
\(525\) 0 0
\(526\) 28.4244 1.23936
\(527\) −37.2733 −1.62365
\(528\) 0 0
\(529\) 18.2733 0.794491
\(530\) 0 0
\(531\) 0 0
\(532\) −1.42443 −0.0617568
\(533\) −0.575571 −0.0249308
\(534\) 0 0
\(535\) 0 0
\(536\) −3.00000 −0.129580
\(537\) 0 0
\(538\) 10.8489 0.467727
\(539\) −3.42443 −0.147501
\(540\) 0 0
\(541\) 42.2733 1.81747 0.908735 0.417373i \(-0.137049\pi\)
0.908735 + 0.417373i \(0.137049\pi\)
\(542\) −16.6977 −0.717228
\(543\) 0 0
\(544\) 4.42443 0.189696
\(545\) 0 0
\(546\) 0 0
\(547\) −9.69772 −0.414644 −0.207322 0.978273i \(-0.566475\pi\)
−0.207322 + 0.978273i \(0.566475\pi\)
\(548\) 7.42443 0.317156
\(549\) 0 0
\(550\) 0 0
\(551\) −9.15114 −0.389852
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) −30.8489 −1.31064
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) −19.2733 −0.816635 −0.408318 0.912840i \(-0.633884\pi\)
−0.408318 + 0.912840i \(0.633884\pi\)
\(558\) 0 0
\(559\) −7.00000 −0.296068
\(560\) 0 0
\(561\) 0 0
\(562\) 22.8489 0.963821
\(563\) −5.00000 −0.210725 −0.105362 0.994434i \(-0.533600\pi\)
−0.105362 + 0.994434i \(0.533600\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 4.42443 0.185645
\(569\) 11.6977 0.490394 0.245197 0.969473i \(-0.421147\pi\)
0.245197 + 0.969473i \(0.421147\pi\)
\(570\) 0 0
\(571\) 5.27329 0.220680 0.110340 0.993894i \(-0.464806\pi\)
0.110340 + 0.993894i \(0.464806\pi\)
\(572\) 3.42443 0.143183
\(573\) 0 0
\(574\) −0.575571 −0.0240239
\(575\) 0 0
\(576\) 0 0
\(577\) 3.72671 0.155145 0.0775726 0.996987i \(-0.475283\pi\)
0.0775726 + 0.996987i \(0.475283\pi\)
\(578\) −2.57557 −0.107130
\(579\) 0 0
\(580\) 0 0
\(581\) −17.4244 −0.722887
\(582\) 0 0
\(583\) 17.1221 0.709127
\(584\) −7.42443 −0.307225
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) −25.2733 −1.04314 −0.521570 0.853208i \(-0.674653\pi\)
−0.521570 + 0.853208i \(0.674653\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −10.8489 −0.445885
\(593\) 19.1511 0.786443 0.393222 0.919444i \(-0.371361\pi\)
0.393222 + 0.919444i \(0.371361\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.4244 0.427001
\(597\) 0 0
\(598\) −6.42443 −0.262714
\(599\) 10.1511 0.414764 0.207382 0.978260i \(-0.433506\pi\)
0.207382 + 0.978260i \(0.433506\pi\)
\(600\) 0 0
\(601\) 28.0000 1.14214 0.571072 0.820900i \(-0.306528\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(602\) −7.00000 −0.285299
\(603\) 0 0
\(604\) 2.84886 0.115918
\(605\) 0 0
\(606\) 0 0
\(607\) 29.5756 1.20044 0.600218 0.799837i \(-0.295081\pi\)
0.600218 + 0.799837i \(0.295081\pi\)
\(608\) 1.42443 0.0577682
\(609\) 0 0
\(610\) 0 0
\(611\) 0.575571 0.0232851
\(612\) 0 0
\(613\) −45.6977 −1.84571 −0.922857 0.385144i \(-0.874152\pi\)
−0.922857 + 0.385144i \(0.874152\pi\)
\(614\) −16.0000 −0.645707
\(615\) 0 0
\(616\) 3.42443 0.137974
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 0 0
\(619\) 42.2733 1.69911 0.849553 0.527503i \(-0.176871\pi\)
0.849553 + 0.527503i \(0.176871\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.6977 0.469036
\(623\) 1.00000 0.0400642
\(624\) 0 0
\(625\) 0 0
\(626\) 16.2733 0.650411
\(627\) 0 0
\(628\) 2.42443 0.0967452
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) −5.15114 −0.205064 −0.102532 0.994730i \(-0.532694\pi\)
−0.102532 + 0.994730i \(0.532694\pi\)
\(632\) 8.00000 0.318223
\(633\) 0 0
\(634\) −31.4244 −1.24802
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 22.0000 0.870988
\(639\) 0 0
\(640\) 0 0
\(641\) 8.84886 0.349509 0.174754 0.984612i \(-0.444087\pi\)
0.174754 + 0.984612i \(0.444087\pi\)
\(642\) 0 0
\(643\) −22.5466 −0.889150 −0.444575 0.895742i \(-0.646645\pi\)
−0.444575 + 0.895742i \(0.646645\pi\)
\(644\) −6.42443 −0.253158
\(645\) 0 0
\(646\) −6.30228 −0.247960
\(647\) −0.575571 −0.0226280 −0.0113140 0.999936i \(-0.503601\pi\)
−0.0113140 + 0.999936i \(0.503601\pi\)
\(648\) 0 0
\(649\) 8.30228 0.325893
\(650\) 0 0
\(651\) 0 0
\(652\) 12.4244 0.486578
\(653\) 11.2733 0.441158 0.220579 0.975369i \(-0.429205\pi\)
0.220579 + 0.975369i \(0.429205\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.575571 0.0224723
\(657\) 0 0
\(658\) 0.575571 0.0224381
\(659\) −50.5466 −1.96901 −0.984507 0.175343i \(-0.943897\pi\)
−0.984507 + 0.175343i \(0.943897\pi\)
\(660\) 0 0
\(661\) 47.6977 1.85523 0.927613 0.373543i \(-0.121857\pi\)
0.927613 + 0.373543i \(0.121857\pi\)
\(662\) −24.1221 −0.937534
\(663\) 0 0
\(664\) 17.4244 0.676199
\(665\) 0 0
\(666\) 0 0
\(667\) −41.2733 −1.59811
\(668\) −20.8489 −0.806667
\(669\) 0 0
\(670\) 0 0
\(671\) 30.3023 1.16981
\(672\) 0 0
\(673\) 6.12214 0.235991 0.117996 0.993014i \(-0.462353\pi\)
0.117996 + 0.993014i \(0.462353\pi\)
\(674\) 25.2733 0.973491
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 28.5466 1.09713 0.548567 0.836107i \(-0.315174\pi\)
0.548567 + 0.836107i \(0.315174\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) 28.8489 1.10468
\(683\) 15.6977 0.600656 0.300328 0.953836i \(-0.402904\pi\)
0.300328 + 0.953836i \(0.402904\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) 7.00000 0.266872
\(689\) 5.00000 0.190485
\(690\) 0 0
\(691\) −36.8199 −1.40069 −0.700347 0.713803i \(-0.746971\pi\)
−0.700347 + 0.713803i \(0.746971\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −19.6977 −0.747715
\(695\) 0 0
\(696\) 0 0
\(697\) −2.54657 −0.0964583
\(698\) 13.5756 0.513843
\(699\) 0 0
\(700\) 0 0
\(701\) 50.5466 1.90912 0.954559 0.298022i \(-0.0963270\pi\)
0.954559 + 0.298022i \(0.0963270\pi\)
\(702\) 0 0
\(703\) 15.4534 0.582837
\(704\) −3.42443 −0.129063
\(705\) 0 0
\(706\) 7.57557 0.285110
\(707\) 16.2733 0.612020
\(708\) 0 0
\(709\) −41.1221 −1.54437 −0.772187 0.635395i \(-0.780837\pi\)
−0.772187 + 0.635395i \(0.780837\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.00000 −0.0374766
\(713\) −54.1221 −2.02689
\(714\) 0 0
\(715\) 0 0
\(716\) 8.27329 0.309187
\(717\) 0 0
\(718\) 4.15114 0.154919
\(719\) 12.8489 0.479182 0.239591 0.970874i \(-0.422987\pi\)
0.239591 + 0.970874i \(0.422987\pi\)
\(720\) 0 0
\(721\) −0.424429 −0.0158066
\(722\) 16.9710 0.631595
\(723\) 0 0
\(724\) 7.27329 0.270310
\(725\) 0 0
\(726\) 0 0
\(727\) −33.2733 −1.23404 −0.617019 0.786948i \(-0.711660\pi\)
−0.617019 + 0.786948i \(0.711660\pi\)
\(728\) 1.00000 0.0370625
\(729\) 0 0
\(730\) 0 0
\(731\) −30.9710 −1.14550
\(732\) 0 0
\(733\) 15.8489 0.585391 0.292695 0.956206i \(-0.405448\pi\)
0.292695 + 0.956206i \(0.405448\pi\)
\(734\) −27.2733 −1.00668
\(735\) 0 0
\(736\) 6.42443 0.236808
\(737\) −10.2733 −0.378421
\(738\) 0 0
\(739\) 32.0000 1.17714 0.588570 0.808447i \(-0.299691\pi\)
0.588570 + 0.808447i \(0.299691\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 5.00000 0.183556
\(743\) −24.1221 −0.884956 −0.442478 0.896779i \(-0.645900\pi\)
−0.442478 + 0.896779i \(0.645900\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 29.6977 1.08731
\(747\) 0 0
\(748\) 15.1511 0.553981
\(749\) 16.8489 0.615644
\(750\) 0 0
\(751\) −30.8489 −1.12569 −0.562845 0.826562i \(-0.690293\pi\)
−0.562845 + 0.826562i \(0.690293\pi\)
\(752\) −0.575571 −0.0209889
\(753\) 0 0
\(754\) 6.42443 0.233964
\(755\) 0 0
\(756\) 0 0
\(757\) 39.3954 1.43185 0.715926 0.698177i \(-0.246005\pi\)
0.715926 + 0.698177i \(0.246005\pi\)
\(758\) −1.69772 −0.0616638
\(759\) 0 0
\(760\) 0 0
\(761\) −22.4244 −0.812885 −0.406442 0.913676i \(-0.633231\pi\)
−0.406442 + 0.913676i \(0.633231\pi\)
\(762\) 0 0
\(763\) 7.42443 0.268782
\(764\) −10.5756 −0.382611
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) 2.42443 0.0875411
\(768\) 0 0
\(769\) −34.5466 −1.24578 −0.622891 0.782309i \(-0.714042\pi\)
−0.622891 + 0.782309i \(0.714042\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.57557 −0.200669
\(773\) −2.84886 −0.102466 −0.0512331 0.998687i \(-0.516315\pi\)
−0.0512331 + 0.998687i \(0.516315\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) −7.69772 −0.275976
\(779\) −0.819860 −0.0293745
\(780\) 0 0
\(781\) 15.1511 0.542150
\(782\) −28.4244 −1.01646
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −0.848858 −0.0302585 −0.0151293 0.999886i \(-0.504816\pi\)
−0.0151293 + 0.999886i \(0.504816\pi\)
\(788\) 12.5756 0.447986
\(789\) 0 0
\(790\) 0 0
\(791\) 10.2733 0.365276
\(792\) 0 0
\(793\) 8.84886 0.314232
\(794\) −27.6977 −0.982955
\(795\) 0 0
\(796\) −3.00000 −0.106332
\(797\) 14.5466 0.515266 0.257633 0.966243i \(-0.417057\pi\)
0.257633 + 0.966243i \(0.417057\pi\)
\(798\) 0 0
\(799\) 2.54657 0.0900913
\(800\) 0 0
\(801\) 0 0
\(802\) 24.8489 0.877444
\(803\) −25.4244 −0.897209
\(804\) 0 0
\(805\) 0 0
\(806\) 8.42443 0.296738
\(807\) 0 0
\(808\) −16.2733 −0.572492
\(809\) 9.15114 0.321737 0.160869 0.986976i \(-0.448570\pi\)
0.160869 + 0.986976i \(0.448570\pi\)
\(810\) 0 0
\(811\) −27.9710 −0.982195 −0.491097 0.871105i \(-0.663404\pi\)
−0.491097 + 0.871105i \(0.663404\pi\)
\(812\) 6.42443 0.225453
\(813\) 0 0
\(814\) −37.1511 −1.30215
\(815\) 0 0
\(816\) 0 0
\(817\) −9.97100 −0.348841
\(818\) −31.6977 −1.10828
\(819\) 0 0
\(820\) 0 0
\(821\) −22.4244 −0.782618 −0.391309 0.920259i \(-0.627978\pi\)
−0.391309 + 0.920259i \(0.627978\pi\)
\(822\) 0 0
\(823\) 4.27329 0.148957 0.0744787 0.997223i \(-0.476271\pi\)
0.0744787 + 0.997223i \(0.476271\pi\)
\(824\) 0.424429 0.0147857
\(825\) 0 0
\(826\) 2.42443 0.0843567
\(827\) 22.5466 0.784021 0.392011 0.919961i \(-0.371780\pi\)
0.392011 + 0.919961i \(0.371780\pi\)
\(828\) 0 0
\(829\) 19.1511 0.665147 0.332573 0.943077i \(-0.392083\pi\)
0.332573 + 0.943077i \(0.392083\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) −4.42443 −0.153297
\(834\) 0 0
\(835\) 0 0
\(836\) 4.87786 0.168704
\(837\) 0 0
\(838\) −27.2733 −0.942140
\(839\) 18.8489 0.650735 0.325367 0.945588i \(-0.394512\pi\)
0.325367 + 0.945588i \(0.394512\pi\)
\(840\) 0 0
\(841\) 12.2733 0.423217
\(842\) −5.72671 −0.197356
\(843\) 0 0
\(844\) −2.42443 −0.0834523
\(845\) 0 0
\(846\) 0 0
\(847\) 0.726713 0.0249702
\(848\) −5.00000 −0.171701
\(849\) 0 0
\(850\) 0 0
\(851\) 69.6977 2.38921
\(852\) 0 0
\(853\) −11.2733 −0.385990 −0.192995 0.981200i \(-0.561820\pi\)
−0.192995 + 0.981200i \(0.561820\pi\)
\(854\) 8.84886 0.302802
\(855\) 0 0
\(856\) −16.8489 −0.575882
\(857\) 11.2733 0.385088 0.192544 0.981288i \(-0.438326\pi\)
0.192544 + 0.981288i \(0.438326\pi\)
\(858\) 0 0
\(859\) −25.4244 −0.867470 −0.433735 0.901040i \(-0.642805\pi\)
−0.433735 + 0.901040i \(0.642805\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −7.72671 −0.263173
\(863\) 20.7267 0.705546 0.352773 0.935709i \(-0.385239\pi\)
0.352773 + 0.935709i \(0.385239\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −3.72671 −0.126639
\(867\) 0 0
\(868\) 8.42443 0.285944
\(869\) 27.3954 0.929326
\(870\) 0 0
\(871\) −3.00000 −0.101651
\(872\) −7.42443 −0.251423
\(873\) 0 0
\(874\) −9.15114 −0.309542
\(875\) 0 0
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 33.8489 1.14234
\(879\) 0 0
\(880\) 0 0
\(881\) 3.27329 0.110280 0.0551399 0.998479i \(-0.482440\pi\)
0.0551399 + 0.998479i \(0.482440\pi\)
\(882\) 0 0
\(883\) 7.57557 0.254938 0.127469 0.991843i \(-0.459315\pi\)
0.127469 + 0.991843i \(0.459315\pi\)
\(884\) 4.42443 0.148810
\(885\) 0 0
\(886\) −33.6977 −1.13210
\(887\) −47.1221 −1.58221 −0.791103 0.611682i \(-0.790493\pi\)
−0.791103 + 0.611682i \(0.790493\pi\)
\(888\) 0 0
\(889\) 21.4244 0.718552
\(890\) 0 0
\(891\) 0 0
\(892\) 26.8489 0.898966
\(893\) 0.819860 0.0274356
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 25.6977 0.857544
\(899\) 54.1221 1.80507
\(900\) 0 0
\(901\) 22.1221 0.736995
\(902\) 1.97100 0.0656272
\(903\) 0 0
\(904\) −10.2733 −0.341684
\(905\) 0 0
\(906\) 0 0
\(907\) 55.6687 1.84845 0.924225 0.381849i \(-0.124713\pi\)
0.924225 + 0.381849i \(0.124713\pi\)
\(908\) 11.0000 0.365048
\(909\) 0 0
\(910\) 0 0
\(911\) 24.2733 0.804210 0.402105 0.915594i \(-0.368279\pi\)
0.402105 + 0.915594i \(0.368279\pi\)
\(912\) 0 0
\(913\) 59.6687 1.97475
\(914\) 7.57557 0.250578
\(915\) 0 0
\(916\) 2.00000 0.0660819
\(917\) 9.27329 0.306231
\(918\) 0 0
\(919\) −15.1511 −0.499790 −0.249895 0.968273i \(-0.580396\pi\)
−0.249895 + 0.968273i \(0.580396\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 16.5756 0.545887
\(923\) 4.42443 0.145632
\(924\) 0 0
\(925\) 0 0
\(926\) −25.9710 −0.853460
\(927\) 0 0
\(928\) −6.42443 −0.210892
\(929\) 25.1221 0.824231 0.412115 0.911132i \(-0.364790\pi\)
0.412115 + 0.911132i \(0.364790\pi\)
\(930\) 0 0
\(931\) −1.42443 −0.0466838
\(932\) 4.57557 0.149878
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) 7.42443 0.242546 0.121273 0.992619i \(-0.461302\pi\)
0.121273 + 0.992619i \(0.461302\pi\)
\(938\) −3.00000 −0.0979535
\(939\) 0 0
\(940\) 0 0
\(941\) 34.2733 1.11728 0.558639 0.829411i \(-0.311324\pi\)
0.558639 + 0.829411i \(0.311324\pi\)
\(942\) 0 0
\(943\) −3.69772 −0.120414
\(944\) −2.42443 −0.0789084
\(945\) 0 0
\(946\) 23.9710 0.779365
\(947\) 10.3023 0.334779 0.167390 0.985891i \(-0.446466\pi\)
0.167390 + 0.985891i \(0.446466\pi\)
\(948\) 0 0
\(949\) −7.42443 −0.241007
\(950\) 0 0
\(951\) 0 0
\(952\) 4.42443 0.143397
\(953\) 36.5466 1.18386 0.591930 0.805990i \(-0.298366\pi\)
0.591930 + 0.805990i \(0.298366\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −8.00000 −0.258468
\(959\) 7.42443 0.239747
\(960\) 0 0
\(961\) 39.9710 1.28939
\(962\) −10.8489 −0.349781
\(963\) 0 0
\(964\) 16.0000 0.515325
\(965\) 0 0
\(966\) 0 0
\(967\) 36.2733 1.16647 0.583235 0.812303i \(-0.301787\pi\)
0.583235 + 0.812303i \(0.301787\pi\)
\(968\) −0.726713 −0.0233575
\(969\) 0 0
\(970\) 0 0
\(971\) 7.57557 0.243112 0.121556 0.992585i \(-0.461212\pi\)
0.121556 + 0.992585i \(0.461212\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 3.42443 0.109726
\(975\) 0 0
\(976\) −8.84886 −0.283245
\(977\) 34.2733 1.09650 0.548250 0.836315i \(-0.315294\pi\)
0.548250 + 0.836315i \(0.315294\pi\)
\(978\) 0 0
\(979\) −3.42443 −0.109445
\(980\) 0 0
\(981\) 0 0
\(982\) −21.6977 −0.692402
\(983\) −43.3954 −1.38410 −0.692050 0.721850i \(-0.743292\pi\)
−0.692050 + 0.721850i \(0.743292\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 28.4244 0.905218
\(987\) 0 0
\(988\) 1.42443 0.0453171
\(989\) −44.9710 −1.42999
\(990\) 0 0
\(991\) 54.5466 1.73273 0.866365 0.499412i \(-0.166451\pi\)
0.866365 + 0.499412i \(0.166451\pi\)
\(992\) −8.42443 −0.267476
\(993\) 0 0
\(994\) 4.42443 0.140334
\(995\) 0 0
\(996\) 0 0
\(997\) −6.42443 −0.203464 −0.101732 0.994812i \(-0.532438\pi\)
−0.101732 + 0.994812i \(0.532438\pi\)
\(998\) 22.8489 0.723268
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))