Properties

Label 9450.2.a.el.1.2
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 1.2
Root \(5.42443\)
Character \(\chi\) = 9450.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+6.42443 q^{11}\) \(-1.00000 q^{13}\) \(-1.00000 q^{14}\) \(+1.00000 q^{16}\) \(+5.42443 q^{17}\) \(+8.42443 q^{19}\) \(-6.42443 q^{22}\) \(+3.42443 q^{23}\) \(+1.00000 q^{26}\) \(+1.00000 q^{28}\) \(-3.42443 q^{29}\) \(-1.42443 q^{31}\) \(-1.00000 q^{32}\) \(-5.42443 q^{34}\) \(+8.84886 q^{37}\) \(-8.42443 q^{38}\) \(+10.4244 q^{41}\) \(+7.00000 q^{43}\) \(+6.42443 q^{44}\) \(-3.42443 q^{46}\) \(-10.4244 q^{47}\) \(+1.00000 q^{49}\) \(-1.00000 q^{52}\) \(-5.00000 q^{53}\) \(-1.00000 q^{56}\) \(+3.42443 q^{58}\) \(+7.42443 q^{59}\) \(+10.8489 q^{61}\) \(+1.42443 q^{62}\) \(+1.00000 q^{64}\) \(+3.00000 q^{67}\) \(+5.42443 q^{68}\) \(+5.42443 q^{71}\) \(-2.42443 q^{73}\) \(-8.84886 q^{74}\) \(+8.42443 q^{76}\) \(+6.42443 q^{77}\) \(-8.00000 q^{79}\) \(-10.4244 q^{82}\) \(-7.57557 q^{83}\) \(-7.00000 q^{86}\) \(-6.42443 q^{88}\) \(+1.00000 q^{89}\) \(-1.00000 q^{91}\) \(+3.42443 q^{92}\) \(+10.4244 q^{94}\) \(+10.0000 q^{97}\) \(-1.00000 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut q^{34} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut +\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 5q^{59} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 7q^{62} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{76} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 11q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut -\mathstrut 3q^{88} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 11q^{94} \) \(\mathstrut +\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(11\) 6.42443 1.93704 0.968519 0.248939i \(-0.0800820\pi\)
0.968519 + 0.248939i \(0.0800820\pi\)
\(12\) 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
\(17\) 5.42443 1.31562 0.657809 0.753185i \(-0.271484\pi\)
0.657809 + 0.753185i \(0.271484\pi\)
\(18\) 0 0
\(19\) 8.42443 1.93270 0.966348 0.257237i \(-0.0828122\pi\)
0.966348 + 0.257237i \(0.0828122\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −6.42443 −1.36969
\(23\) 3.42443 0.714043 0.357021 0.934096i \(-0.383792\pi\)
0.357021 + 0.934096i \(0.383792\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −3.42443 −0.635900 −0.317950 0.948107i \(-0.602994\pi\)
−0.317950 + 0.948107i \(0.602994\pi\)
\(30\) 0 0
\(31\) −1.42443 −0.255835 −0.127917 0.991785i \(-0.540829\pi\)
−0.127917 + 0.991785i \(0.540829\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −5.42443 −0.930282
\(35\) 0 0
\(36\) 0 0
\(37\) 8.84886 1.45474 0.727372 0.686244i \(-0.240742\pi\)
0.727372 + 0.686244i \(0.240742\pi\)
\(38\) −8.42443 −1.36662
\(39\) 0 0
\(40\) 0 0
\(41\) 10.4244 1.62802 0.814011 0.580849i \(-0.197279\pi\)
0.814011 + 0.580849i \(0.197279\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 6.42443 0.968519
\(45\) 0 0
\(46\) −3.42443 −0.504904
\(47\) −10.4244 −1.52056 −0.760280 0.649596i \(-0.774938\pi\)
−0.760280 + 0.649596i \(0.774938\pi\)
\(48\) 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
\(58\) 3.42443 0.449650
\(59\) 7.42443 0.966578 0.483289 0.875461i \(-0.339442\pi\)
0.483289 + 0.875461i \(0.339442\pi\)
\(60\) 0 0
\(61\) 10.8489 1.38905 0.694527 0.719467i \(-0.255614\pi\)
0.694527 + 0.719467i \(0.255614\pi\)
\(62\) 1.42443 0.180903
\(63\) 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 \(0.441337\pi\)
\(68\) 5.42443 0.657809
\(69\) 0 0
\(70\) 0 0
\(71\) 5.42443 0.643761 0.321881 0.946780i \(-0.395685\pi\)
0.321881 + 0.946780i \(0.395685\pi\)
\(72\) 0 0
\(73\) −2.42443 −0.283758 −0.141879 0.989884i \(-0.545314\pi\)
−0.141879 + 0.989884i \(0.545314\pi\)
\(74\) −8.84886 −1.02866
\(75\) 0 0
\(76\) 8.42443 0.966348
\(77\) 6.42443 0.732132
\(78\) 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
\(82\) −10.4244 −1.15119
\(83\) −7.57557 −0.831527 −0.415763 0.909473i \(-0.636486\pi\)
−0.415763 + 0.909473i \(0.636486\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −7.00000 −0.754829
\(87\) 0 0
\(88\) −6.42443 −0.684846
\(89\) 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
\(92\) 3.42443 0.357021
\(93\) 0 0
\(94\) 10.4244 1.07520
\(95\) 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
\(101\) −13.2733 −1.32074 −0.660371 0.750940i \(-0.729601\pi\)
−0.660371 + 0.750940i \(0.729601\pi\)
\(102\) 0 0
\(103\) 9.42443 0.928617 0.464308 0.885674i \(-0.346303\pi\)
0.464308 + 0.885674i \(0.346303\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 5.00000 0.485643
\(107\) −2.84886 −0.275409 −0.137705 0.990473i \(-0.543973\pi\)
−0.137705 + 0.990473i \(0.543973\pi\)
\(108\) 0 0
\(109\) −2.42443 −0.232218 −0.116109 0.993236i \(-0.537042\pi\)
−0.116109 + 0.993236i \(0.537042\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −19.2733 −1.81308 −0.906539 0.422122i \(-0.861285\pi\)
−0.906539 + 0.422122i \(0.861285\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.42443 −0.317950
\(117\) 0 0
\(118\) −7.42443 −0.683474
\(119\) 5.42443 0.497257
\(120\) 0 0
\(121\) 30.2733 2.75212
\(122\) −10.8489 −0.982209
\(123\) 0 0
\(124\) −1.42443 −0.127917
\(125\) 0 0
\(126\) 0 0
\(127\) 11.5756 1.02717 0.513583 0.858040i \(-0.328318\pi\)
0.513583 + 0.858040i \(0.328318\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −20.2733 −1.77129 −0.885643 0.464367i \(-0.846282\pi\)
−0.885643 + 0.464367i \(0.846282\pi\)
\(132\) 0 0
\(133\) 8.42443 0.730491
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −5.42443 −0.465141
\(137\) −2.42443 −0.207133 −0.103566 0.994623i \(-0.533025\pi\)
−0.103566 + 0.994623i \(0.533025\pi\)
\(138\) 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
\(142\) −5.42443 −0.455208
\(143\) −6.42443 −0.537238
\(144\) 0 0
\(145\) 0 0
\(146\) 2.42443 0.200647
\(147\) 0 0
\(148\) 8.84886 0.727372
\(149\) 0.575571 0.0471526 0.0235763 0.999722i \(-0.492495\pi\)
0.0235763 + 0.999722i \(0.492495\pi\)
\(150\) 0 0
\(151\) −16.8489 −1.37114 −0.685570 0.728006i \(-0.740447\pi\)
−0.685570 + 0.728006i \(0.740447\pi\)
\(152\) −8.42443 −0.683311
\(153\) 0 0
\(154\) −6.42443 −0.517695
\(155\) 0 0
\(156\) 0 0
\(157\) −7.42443 −0.592534 −0.296267 0.955105i \(-0.595742\pi\)
−0.296267 + 0.955105i \(0.595742\pi\)
\(158\) 8.00000 0.636446
\(159\) 0 0
\(160\) 0 0
\(161\) 3.42443 0.269883
\(162\) 0 0
\(163\) 2.57557 0.201734 0.100867 0.994900i \(-0.467838\pi\)
0.100867 + 0.994900i \(0.467838\pi\)
\(164\) 10.4244 0.814011
\(165\) 0 0
\(166\) 7.57557 0.587978
\(167\) −1.15114 −0.0890781 −0.0445390 0.999008i \(-0.514182\pi\)
−0.0445390 + 0.999008i \(0.514182\pi\)
\(168\) 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
\(176\) 6.42443 0.484260
\(177\) 0 0
\(178\) −1.00000 −0.0749532
\(179\) −21.2733 −1.59004 −0.795020 0.606583i \(-0.792540\pi\)
−0.795020 + 0.606583i \(0.792540\pi\)
\(180\) 0 0
\(181\) −22.2733 −1.65556 −0.827780 0.561053i \(-0.810397\pi\)
−0.827780 + 0.561053i \(0.810397\pi\)
\(182\) 1.00000 0.0741249
\(183\) 0 0
\(184\) −3.42443 −0.252452
\(185\) 0 0
\(186\) 0 0
\(187\) 34.8489 2.54840
\(188\) −10.4244 −0.760280
\(189\) 0 0
\(190\) 0 0
\(191\) −20.4244 −1.47786 −0.738930 0.673782i \(-0.764669\pi\)
−0.738930 + 0.673782i \(0.764669\pi\)
\(192\) 0 0
\(193\) −15.4244 −1.11027 −0.555137 0.831759i \(-0.687334\pi\)
−0.555137 + 0.831759i \(0.687334\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 22.4244 1.59767 0.798837 0.601547i \(-0.205449\pi\)
0.798837 + 0.601547i \(0.205449\pi\)
\(198\) 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
\(202\) 13.2733 0.933905
\(203\) −3.42443 −0.240348
\(204\) 0 0
\(205\) 0 0
\(206\) −9.42443 −0.656631
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 54.1221 3.74371
\(210\) 0 0
\(211\) 7.42443 0.511119 0.255559 0.966793i \(-0.417740\pi\)
0.255559 + 0.966793i \(0.417740\pi\)
\(212\) −5.00000 −0.343401
\(213\) 0 0
\(214\) 2.84886 0.194744
\(215\) 0 0
\(216\) 0 0
\(217\) −1.42443 −0.0966965
\(218\) 2.42443 0.164203
\(219\) 0 0
\(220\) 0 0
\(221\) −5.42443 −0.364887
\(222\) 0 0
\(223\) 7.15114 0.478876 0.239438 0.970912i \(-0.423037\pi\)
0.239438 + 0.970912i \(0.423037\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 19.2733 1.28204
\(227\) 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
\(232\) 3.42443 0.224825
\(233\) 14.4244 0.944976 0.472488 0.881337i \(-0.343356\pi\)
0.472488 + 0.881337i \(0.343356\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.42443 0.483289
\(237\) 0 0
\(238\) −5.42443 −0.351614
\(239\) 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 \(0.327671\pi\)
\(242\) −30.2733 −1.94604
\(243\) 0 0
\(244\) 10.8489 0.694527
\(245\) 0 0
\(246\) 0 0
\(247\) −8.42443 −0.536034
\(248\) 1.42443 0.0904513
\(249\) 0 0
\(250\) 0 0
\(251\) −8.84886 −0.558535 −0.279267 0.960213i \(-0.590092\pi\)
−0.279267 + 0.960213i \(0.590092\pi\)
\(252\) 0 0
\(253\) 22.0000 1.38313
\(254\) −11.5756 −0.726316
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.84886 −0.427220 −0.213610 0.976919i \(-0.568522\pi\)
−0.213610 + 0.976919i \(0.568522\pi\)
\(258\) 0 0
\(259\) 8.84886 0.549841
\(260\) 0 0
\(261\) 0 0
\(262\) 20.2733 1.25249
\(263\) −18.5756 −1.14542 −0.572709 0.819758i \(-0.694108\pi\)
−0.572709 + 0.819758i \(0.694108\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.42443 −0.516535
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) 8.84886 0.539524 0.269762 0.962927i \(-0.413055\pi\)
0.269762 + 0.962927i \(0.413055\pi\)
\(270\) 0 0
\(271\) −22.6977 −1.37879 −0.689394 0.724387i \(-0.742123\pi\)
−0.689394 + 0.724387i \(0.742123\pi\)
\(272\) 5.42443 0.328904
\(273\) 0 0
\(274\) 2.42443 0.146465
\(275\) 0 0
\(276\) 0 0
\(277\) 11.1511 0.670007 0.335004 0.942217i \(-0.391262\pi\)
0.335004 + 0.942217i \(0.391262\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) −3.15114 −0.187981 −0.0939907 0.995573i \(-0.529962\pi\)
−0.0939907 + 0.995573i \(0.529962\pi\)
\(282\) 0 0
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 5.42443 0.321881
\(285\) 0 0
\(286\) 6.42443 0.379884
\(287\) 10.4244 0.615335
\(288\) 0 0
\(289\) 12.4244 0.730849
\(290\) 0 0
\(291\) 0 0
\(292\) −2.42443 −0.141879
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.84886 −0.514329
\(297\) 0 0
\(298\) −0.575571 −0.0333419
\(299\) −3.42443 −0.198040
\(300\) 0 0
\(301\) 7.00000 0.403473
\(302\) 16.8489 0.969543
\(303\) 0 0
\(304\) 8.42443 0.483174
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 6.42443 0.366066
\(309\) 0 0
\(310\) 0 0
\(311\) 27.6977 1.57059 0.785297 0.619120i \(-0.212510\pi\)
0.785297 + 0.619120i \(0.212510\pi\)
\(312\) 0 0
\(313\) 13.2733 0.750251 0.375125 0.926974i \(-0.377600\pi\)
0.375125 + 0.926974i \(0.377600\pi\)
\(314\) 7.42443 0.418985
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 21.5756 1.21180 0.605902 0.795539i \(-0.292812\pi\)
0.605902 + 0.795539i \(0.292812\pi\)
\(318\) 0 0
\(319\) −22.0000 −1.23176
\(320\) 0 0
\(321\) 0 0
\(322\) −3.42443 −0.190836
\(323\) 45.6977 2.54269
\(324\) 0 0
\(325\) 0 0
\(326\) −2.57557 −0.142648
\(327\) 0 0
\(328\) −10.4244 −0.575593
\(329\) −10.4244 −0.574717
\(330\) 0 0
\(331\) −25.1221 −1.38084 −0.690419 0.723410i \(-0.742574\pi\)
−0.690419 + 0.723410i \(0.742574\pi\)
\(332\) −7.57557 −0.415763
\(333\) 0 0
\(334\) 1.15114 0.0629877
\(335\) 0 0
\(336\) 0 0
\(337\) 4.27329 0.232781 0.116390 0.993204i \(-0.462868\pi\)
0.116390 + 0.993204i \(0.462868\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) −9.15114 −0.495562
\(342\) 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 \(-0.677326\pi\)
−0.528714 + 0.848800i \(0.677326\pi\)
\(348\) 0 0
\(349\) −23.4244 −1.25388 −0.626940 0.779067i \(-0.715693\pi\)
−0.626940 + 0.779067i \(0.715693\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.42443 −0.342423
\(353\) −17.4244 −0.927409 −0.463704 0.885990i \(-0.653480\pi\)
−0.463704 + 0.885990i \(0.653480\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 21.2733 1.12433
\(359\) −23.8489 −1.25869 −0.629347 0.777124i \(-0.716678\pi\)
−0.629347 + 0.777124i \(0.716678\pi\)
\(360\) 0 0
\(361\) 51.9710 2.73532
\(362\) 22.2733 1.17066
\(363\) 0 0
\(364\) −1.00000 −0.0524142
\(365\) 0 0
\(366\) 0 0
\(367\) −2.27329 −0.118665 −0.0593323 0.998238i \(-0.518897\pi\)
−0.0593323 + 0.998238i \(0.518897\pi\)
\(368\) 3.42443 0.178511
\(369\) 0 0
\(370\) 0 0
\(371\) −5.00000 −0.259587
\(372\) 0 0
\(373\) 9.69772 0.502129 0.251064 0.967970i \(-0.419219\pi\)
0.251064 + 0.967970i \(0.419219\pi\)
\(374\) −34.8489 −1.80199
\(375\) 0 0
\(376\) 10.4244 0.537599
\(377\) 3.42443 0.176367
\(378\) 0 0
\(379\) −37.6977 −1.93640 −0.968201 0.250174i \(-0.919512\pi\)
−0.968201 + 0.250174i \(0.919512\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 20.4244 1.04500
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.4244 0.785083
\(387\) 0 0
\(388\) 10.0000 0.507673
\(389\) −31.6977 −1.60714 −0.803569 0.595212i \(-0.797068\pi\)
−0.803569 + 0.595212i \(0.797068\pi\)
\(390\) 0 0
\(391\) 18.5756 0.939407
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −22.4244 −1.12973
\(395\) 0 0
\(396\) 0 0
\(397\) −11.6977 −0.587092 −0.293546 0.955945i \(-0.594835\pi\)
−0.293546 + 0.955945i \(0.594835\pi\)
\(398\) 3.00000 0.150376
\(399\) 0 0
\(400\) 0 0
\(401\) −5.15114 −0.257236 −0.128618 0.991694i \(-0.541054\pi\)
−0.128618 + 0.991694i \(0.541054\pi\)
\(402\) 0 0
\(403\) 1.42443 0.0709559
\(404\) −13.2733 −0.660371
\(405\) 0 0
\(406\) 3.42443 0.169952
\(407\) 56.8489 2.81789
\(408\) 0 0
\(409\) −7.69772 −0.380628 −0.190314 0.981723i \(-0.560951\pi\)
−0.190314 + 0.981723i \(0.560951\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 9.42443 0.464308
\(413\) 7.42443 0.365332
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) −54.1221 −2.64720
\(419\) −2.27329 −0.111057 −0.0555287 0.998457i \(-0.517684\pi\)
−0.0555287 + 0.998457i \(0.517684\pi\)
\(420\) 0 0
\(421\) 35.2733 1.71911 0.859557 0.511039i \(-0.170739\pi\)
0.859557 + 0.511039i \(0.170739\pi\)
\(422\) −7.42443 −0.361416
\(423\) 0 0
\(424\) 5.00000 0.242821
\(425\) 0 0
\(426\) 0 0
\(427\) 10.8489 0.525013
\(428\) −2.84886 −0.137705
\(429\) 0 0
\(430\) 0 0
\(431\) 37.2733 1.79539 0.897696 0.440616i \(-0.145240\pi\)
0.897696 + 0.440616i \(0.145240\pi\)
\(432\) 0 0
\(433\) 33.2733 1.59901 0.799506 0.600658i \(-0.205095\pi\)
0.799506 + 0.600658i \(0.205095\pi\)
\(434\) 1.42443 0.0683748
\(435\) 0 0
\(436\) −2.42443 −0.116109
\(437\) 28.8489 1.38003
\(438\) 0 0
\(439\) −14.1511 −0.675397 −0.337699 0.941254i \(-0.609648\pi\)
−0.337699 + 0.941254i \(0.609648\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 5.42443 0.258014
\(443\) −5.69772 −0.270707 −0.135353 0.990797i \(-0.543217\pi\)
−0.135353 + 0.990797i \(0.543217\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.15114 −0.338616
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 13.6977 0.646435 0.323218 0.946325i \(-0.395235\pi\)
0.323218 + 0.946325i \(0.395235\pi\)
\(450\) 0 0
\(451\) 66.9710 3.15354
\(452\) −19.2733 −0.906539
\(453\) 0 0
\(454\) −11.0000 −0.516256
\(455\) 0 0
\(456\) 0 0
\(457\) −17.4244 −0.815080 −0.407540 0.913187i \(-0.633613\pi\)
−0.407540 + 0.913187i \(0.633613\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 0 0
\(460\) 0 0
\(461\) −26.4244 −1.23071 −0.615354 0.788251i \(-0.710987\pi\)
−0.615354 + 0.788251i \(0.710987\pi\)
\(462\) 0 0
\(463\) −42.9710 −1.99703 −0.998516 0.0544606i \(-0.982656\pi\)
−0.998516 + 0.0544606i \(0.982656\pi\)
\(464\) −3.42443 −0.158975
\(465\) 0 0
\(466\) −14.4244 −0.668199
\(467\) 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
\(472\) −7.42443 −0.341737
\(473\) 44.9710 2.06777
\(474\) 0 0
\(475\) 0 0
\(476\) 5.42443 0.248628
\(477\) 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
\(481\) −8.84886 −0.403473
\(482\) −16.0000 −0.728780
\(483\) 0 0
\(484\) 30.2733 1.37606
\(485\) 0 0
\(486\) 0 0
\(487\) 6.42443 0.291119 0.145559 0.989350i \(-0.453502\pi\)
0.145559 + 0.989350i \(0.453502\pi\)
\(488\) −10.8489 −0.491105
\(489\) 0 0
\(490\) 0 0
\(491\) −17.6977 −0.798687 −0.399343 0.916801i \(-0.630762\pi\)
−0.399343 + 0.916801i \(0.630762\pi\)
\(492\) 0 0
\(493\) −18.5756 −0.836602
\(494\) 8.42443 0.379033
\(495\) 0 0
\(496\) −1.42443 −0.0639587
\(497\) 5.42443 0.243319
\(498\) 0 0
\(499\) −3.15114 −0.141064 −0.0705322 0.997509i \(-0.522470\pi\)
−0.0705322 + 0.997509i \(0.522470\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 8.84886 0.394944
\(503\) −28.9710 −1.29175 −0.645877 0.763442i \(-0.723508\pi\)
−0.645877 + 0.763442i \(0.723508\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −22.0000 −0.978019
\(507\) 0 0
\(508\) 11.5756 0.513583
\(509\) −3.15114 −0.139672 −0.0698360 0.997558i \(-0.522248\pi\)
−0.0698360 + 0.997558i \(0.522248\pi\)
\(510\) 0 0
\(511\) −2.42443 −0.107250
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.84886 0.302090
\(515\) 0 0
\(516\) 0 0
\(517\) −66.9710 −2.94538
\(518\) −8.84886 −0.388796
\(519\) 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
\(523\) −12.8489 −0.561841 −0.280921 0.959731i \(-0.590640\pi\)
−0.280921 + 0.959731i \(0.590640\pi\)
\(524\) −20.2733 −0.885643
\(525\) 0 0
\(526\) 18.5756 0.809933
\(527\) −7.72671 −0.336581
\(528\) 0 0
\(529\) −11.2733 −0.490143
\(530\) 0 0
\(531\) 0 0
\(532\) 8.42443 0.365245
\(533\) −10.4244 −0.451532
\(534\) 0 0
\(535\) 0 0
\(536\) −3.00000 −0.129580
\(537\) 0 0
\(538\) −8.84886 −0.381501
\(539\) 6.42443 0.276720
\(540\) 0 0
\(541\) 12.7267 0.547164 0.273582 0.961849i \(-0.411791\pi\)
0.273582 + 0.961849i \(0.411791\pi\)
\(542\) 22.6977 0.974950
\(543\) 0 0
\(544\) −5.42443 −0.232570
\(545\) 0 0
\(546\) 0 0
\(547\) 29.6977 1.26978 0.634891 0.772601i \(-0.281045\pi\)
0.634891 + 0.772601i \(0.281045\pi\)
\(548\) −2.42443 −0.103566
\(549\) 0 0
\(550\) 0 0
\(551\) −28.8489 −1.22900
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) −11.1511 −0.473767
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) 10.2733 0.435293 0.217647 0.976028i \(-0.430162\pi\)
0.217647 + 0.976028i \(0.430162\pi\)
\(558\) 0 0
\(559\) −7.00000 −0.296068
\(560\) 0 0
\(561\) 0 0
\(562\) 3.15114 0.132923
\(563\) −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
\(568\) −5.42443 −0.227604
\(569\) −27.6977 −1.16115 −0.580574 0.814207i \(-0.697172\pi\)
−0.580574 + 0.814207i \(0.697172\pi\)
\(570\) 0 0
\(571\) −24.2733 −1.01581 −0.507903 0.861414i \(-0.669579\pi\)
−0.507903 + 0.861414i \(0.669579\pi\)
\(572\) −6.42443 −0.268619
\(573\) 0 0
\(574\) −10.4244 −0.435107
\(575\) 0 0
\(576\) 0 0
\(577\) 33.2733 1.38519 0.692593 0.721329i \(-0.256468\pi\)
0.692593 + 0.721329i \(0.256468\pi\)
\(578\) −12.4244 −0.516788
\(579\) 0 0
\(580\) 0 0
\(581\) −7.57557 −0.314288
\(582\) 0 0
\(583\) −32.1221 −1.33036
\(584\) 2.42443 0.100324
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) 4.27329 0.176377 0.0881887 0.996104i \(-0.471892\pi\)
0.0881887 + 0.996104i \(0.471892\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) 8.84886 0.363686
\(593\) 38.8489 1.59533 0.797666 0.603100i \(-0.206068\pi\)
0.797666 + 0.603100i \(0.206068\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.575571 0.0235763
\(597\) 0 0
\(598\) 3.42443 0.140035
\(599\) 29.8489 1.21959 0.609796 0.792559i \(-0.291252\pi\)
0.609796 + 0.792559i \(0.291252\pi\)
\(600\) 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
\(604\) −16.8489 −0.685570
\(605\) 0 0
\(606\) 0 0
\(607\) 39.4244 1.60019 0.800094 0.599875i \(-0.204783\pi\)
0.800094 + 0.599875i \(0.204783\pi\)
\(608\) −8.42443 −0.341656
\(609\) 0 0
\(610\) 0 0
\(611\) 10.4244 0.421727
\(612\) 0 0
\(613\) −6.30228 −0.254547 −0.127273 0.991868i \(-0.540623\pi\)
−0.127273 + 0.991868i \(0.540623\pi\)
\(614\) −16.0000 −0.645707
\(615\) 0 0
\(616\) −6.42443 −0.258848
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 0 0
\(619\) 12.7267 0.511530 0.255765 0.966739i \(-0.417673\pi\)
0.255765 + 0.966739i \(0.417673\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −27.6977 −1.11058
\(623\) 1.00000 0.0400642
\(624\) 0 0
\(625\) 0 0
\(626\) −13.2733 −0.530507
\(627\) 0 0
\(628\) −7.42443 −0.296267
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) −24.8489 −0.989217 −0.494609 0.869116i \(-0.664689\pi\)
−0.494609 + 0.869116i \(0.664689\pi\)
\(632\) 8.00000 0.318223
\(633\) 0 0
\(634\) −21.5756 −0.856875
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 22.0000 0.870988
\(639\) 0 0
\(640\) 0 0
\(641\) −10.8489 −0.428504 −0.214252 0.976778i \(-0.568731\pi\)
−0.214252 + 0.976778i \(0.568731\pi\)
\(642\) 0 0
\(643\) 36.5466 1.44126 0.720628 0.693322i \(-0.243854\pi\)
0.720628 + 0.693322i \(0.243854\pi\)
\(644\) 3.42443 0.134941
\(645\) 0 0
\(646\) −45.6977 −1.79795
\(647\) −10.4244 −0.409827 −0.204913 0.978780i \(-0.565691\pi\)
−0.204913 + 0.978780i \(0.565691\pi\)
\(648\) 0 0
\(649\) 47.6977 1.87230
\(650\) 0 0
\(651\) 0 0
\(652\) 2.57557 0.100867
\(653\) −18.2733 −0.715089 −0.357544 0.933896i \(-0.616386\pi\)
−0.357544 + 0.933896i \(0.616386\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 10.4244 0.407006
\(657\) 0 0
\(658\) 10.4244 0.406387
\(659\) 8.54657 0.332927 0.166464 0.986048i \(-0.446765\pi\)
0.166464 + 0.986048i \(0.446765\pi\)
\(660\) 0 0
\(661\) 8.30228 0.322921 0.161461 0.986879i \(-0.448379\pi\)
0.161461 + 0.986879i \(0.448379\pi\)
\(662\) 25.1221 0.976400
\(663\) 0 0
\(664\) 7.57557 0.293989
\(665\) 0 0
\(666\) 0 0
\(667\) −11.7267 −0.454060
\(668\) −1.15114 −0.0445390
\(669\) 0 0
\(670\) 0 0
\(671\) 69.6977 2.69065
\(672\) 0 0
\(673\) −43.1221 −1.66224 −0.831118 0.556096i \(-0.812299\pi\)
−0.831118 + 0.556096i \(0.812299\pi\)
\(674\) −4.27329 −0.164601
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −30.5466 −1.17400 −0.587000 0.809587i \(-0.699691\pi\)
−0.587000 + 0.809587i \(0.699691\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) 9.15114 0.350415
\(683\) −23.6977 −0.906768 −0.453384 0.891315i \(-0.649783\pi\)
−0.453384 + 0.891315i \(0.649783\pi\)
\(684\) 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
\(691\) 51.8199 1.97132 0.985660 0.168742i \(-0.0539706\pi\)
0.985660 + 0.168742i \(0.0539706\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 19.6977 0.747715
\(695\) 0 0
\(696\) 0 0
\(697\) 56.5466 2.14185
\(698\) 23.4244 0.886628
\(699\) 0 0
\(700\) 0 0
\(701\) −8.54657 −0.322800 −0.161400 0.986889i \(-0.551601\pi\)
−0.161400 + 0.986889i \(0.551601\pi\)
\(702\) 0 0
\(703\) 74.5466 2.81158
\(704\) 6.42443 0.242130
\(705\) 0 0
\(706\) 17.4244 0.655777
\(707\) −13.2733 −0.499193
\(708\) 0 0
\(709\) 8.12214 0.305034 0.152517 0.988301i \(-0.451262\pi\)
0.152517 + 0.988301i \(0.451262\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.00000 −0.0374766
\(713\) −4.87786 −0.182677
\(714\) 0 0
\(715\) 0 0
\(716\) −21.2733 −0.795020
\(717\) 0 0
\(718\) 23.8489 0.890031
\(719\) −6.84886 −0.255419 −0.127710 0.991812i \(-0.540763\pi\)
−0.127710 + 0.991812i \(0.540763\pi\)
\(720\) 0 0
\(721\) 9.42443 0.350984
\(722\) −51.9710 −1.93416
\(723\) 0 0
\(724\) −22.2733 −0.827780
\(725\) 0 0
\(726\) 0 0
\(727\) −3.72671 −0.138216 −0.0691081 0.997609i \(-0.522015\pi\)
−0.0691081 + 0.997609i \(0.522015\pi\)
\(728\) 1.00000 0.0370625
\(729\) 0 0
\(730\) 0 0
\(731\) 37.9710 1.40441
\(732\) 0 0
\(733\) −3.84886 −0.142161 −0.0710804 0.997471i \(-0.522645\pi\)
−0.0710804 + 0.997471i \(0.522645\pi\)
\(734\) 2.27329 0.0839085
\(735\) 0 0
\(736\) −3.42443 −0.126226
\(737\) 19.2733 0.709941
\(738\) 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
\(743\) 25.1221 0.921642 0.460821 0.887493i \(-0.347555\pi\)
0.460821 + 0.887493i \(0.347555\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −9.69772 −0.355059
\(747\) 0 0
\(748\) 34.8489 1.27420
\(749\) −2.84886 −0.104095
\(750\) 0 0
\(751\) −11.1511 −0.406911 −0.203455 0.979084i \(-0.565217\pi\)
−0.203455 + 0.979084i \(0.565217\pi\)
\(752\) −10.4244 −0.380140
\(753\) 0 0
\(754\) −3.42443 −0.124710
\(755\) 0 0
\(756\) 0 0
\(757\) −39.3954 −1.43185 −0.715926 0.698177i \(-0.753995\pi\)
−0.715926 + 0.698177i \(0.753995\pi\)
\(758\) 37.6977 1.36924
\(759\) 0 0
\(760\) 0 0
\(761\) −12.5756 −0.455864 −0.227932 0.973677i \(-0.573196\pi\)
−0.227932 + 0.973677i \(0.573196\pi\)
\(762\) 0 0
\(763\) −2.42443 −0.0877702
\(764\) −20.4244 −0.738930
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) −7.42443 −0.268081
\(768\) 0 0
\(769\) 24.5466 0.885172 0.442586 0.896726i \(-0.354061\pi\)
0.442586 + 0.896726i \(0.354061\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −15.4244 −0.555137
\(773\) 16.8489 0.606011 0.303006 0.952989i \(-0.402010\pi\)
0.303006 + 0.952989i \(0.402010\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 31.6977 1.13642
\(779\) 87.8199 3.14647
\(780\) 0 0
\(781\) 34.8489 1.24699
\(782\) −18.5756 −0.664261
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 18.8489 0.671889 0.335945 0.941882i \(-0.390945\pi\)
0.335945 + 0.941882i \(0.390945\pi\)
\(788\) 22.4244 0.798837
\(789\) 0 0
\(790\) 0 0
\(791\) −19.2733 −0.685279
\(792\) 0 0
\(793\) −10.8489 −0.385254
\(794\) 11.6977 0.415136
\(795\) 0 0
\(796\) −3.00000 −0.106332
\(797\) −44.5466 −1.57792 −0.788960 0.614444i \(-0.789380\pi\)
−0.788960 + 0.614444i \(0.789380\pi\)
\(798\) 0 0
\(799\) −56.5466 −2.00047
\(800\) 0 0
\(801\) 0 0
\(802\) 5.15114 0.181893
\(803\) −15.5756 −0.549650
\(804\) 0 0
\(805\) 0 0
\(806\) −1.42443 −0.0501734
\(807\) 0 0
\(808\) 13.2733 0.466953
\(809\) 28.8489 1.01427 0.507136 0.861866i \(-0.330704\pi\)
0.507136 + 0.861866i \(0.330704\pi\)
\(810\) 0 0
\(811\) 40.9710 1.43869 0.719343 0.694655i \(-0.244443\pi\)
0.719343 + 0.694655i \(0.244443\pi\)
\(812\) −3.42443 −0.120174
\(813\) 0 0
\(814\) −56.8489 −1.99255
\(815\) 0 0
\(816\) 0 0
\(817\) 58.9710 2.06313
\(818\) 7.69772 0.269144
\(819\) 0 0
\(820\) 0 0
\(821\) −12.5756 −0.438890 −0.219445 0.975625i \(-0.570425\pi\)
−0.219445 + 0.975625i \(0.570425\pi\)
\(822\) 0 0
\(823\) −25.2733 −0.880971 −0.440486 0.897760i \(-0.645194\pi\)
−0.440486 + 0.897760i \(0.645194\pi\)
\(824\) −9.42443 −0.328316
\(825\) 0 0
\(826\) −7.42443 −0.258329
\(827\) −36.5466 −1.27085 −0.635424 0.772163i \(-0.719175\pi\)
−0.635424 + 0.772163i \(0.719175\pi\)
\(828\) 0 0
\(829\) 38.8489 1.34928 0.674638 0.738148i \(-0.264300\pi\)
0.674638 + 0.738148i \(0.264300\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) 5.42443 0.187945
\(834\) 0 0
\(835\) 0 0
\(836\) 54.1221 1.87185
\(837\) 0 0
\(838\) 2.27329 0.0785294
\(839\) −0.848858 −0.0293058 −0.0146529 0.999893i \(-0.504664\pi\)
−0.0146529 + 0.999893i \(0.504664\pi\)
\(840\) 0 0
\(841\) −17.2733 −0.595631
\(842\) −35.2733 −1.21560
\(843\) 0 0
\(844\) 7.42443 0.255559
\(845\) 0 0
\(846\) 0 0
\(847\) 30.2733 1.04020
\(848\) −5.00000 −0.171701
\(849\) 0 0
\(850\) 0 0
\(851\) 30.3023 1.03875
\(852\) 0 0
\(853\) 18.2733 0.625665 0.312833 0.949808i \(-0.398722\pi\)
0.312833 + 0.949808i \(0.398722\pi\)
\(854\) −10.8489 −0.371240
\(855\) 0 0
\(856\) 2.84886 0.0973720
\(857\) −18.2733 −0.624204 −0.312102 0.950049i \(-0.601033\pi\)
−0.312102 + 0.950049i \(0.601033\pi\)
\(858\) 0 0
\(859\) −15.5756 −0.531432 −0.265716 0.964051i \(-0.585608\pi\)
−0.265716 + 0.964051i \(0.585608\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −37.2733 −1.26953
\(863\) 50.2733 1.71132 0.855661 0.517536i \(-0.173151\pi\)
0.855661 + 0.517536i \(0.173151\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −33.2733 −1.13067
\(867\) 0 0
\(868\) −1.42443 −0.0483483
\(869\) −51.3954 −1.74347
\(870\) 0 0
\(871\) −3.00000 −0.101651
\(872\) 2.42443 0.0821015
\(873\) 0 0
\(874\) −28.8489 −0.975827
\(875\) 0 0
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 14.1511 0.477578
\(879\) 0 0
\(880\) 0 0
\(881\) −26.2733 −0.885170 −0.442585 0.896727i \(-0.645938\pi\)
−0.442585 + 0.896727i \(0.645938\pi\)
\(882\) 0 0
\(883\) 17.4244 0.586379 0.293189 0.956054i \(-0.405283\pi\)
0.293189 + 0.956054i \(0.405283\pi\)
\(884\) −5.42443 −0.182443
\(885\) 0 0
\(886\) 5.69772 0.191418
\(887\) 2.12214 0.0712546 0.0356273 0.999365i \(-0.488657\pi\)
0.0356273 + 0.999365i \(0.488657\pi\)
\(888\) 0 0
\(889\) 11.5756 0.388232
\(890\) 0 0
\(891\) 0 0
\(892\) 7.15114 0.239438
\(893\) −87.8199 −2.93878
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −13.6977 −0.457099
\(899\) 4.87786 0.162686
\(900\) 0 0
\(901\) −27.1221 −0.903570
\(902\) −66.9710 −2.22989
\(903\) 0 0
\(904\) 19.2733 0.641020
\(905\) 0 0
\(906\) 0 0
\(907\) −52.6687 −1.74884 −0.874418 0.485173i \(-0.838757\pi\)
−0.874418 + 0.485173i \(0.838757\pi\)
\(908\) 11.0000 0.365048
\(909\) 0 0
\(910\) 0 0
\(911\) −5.27329 −0.174712 −0.0873559 0.996177i \(-0.527842\pi\)
−0.0873559 + 0.996177i \(0.527842\pi\)
\(912\) 0 0
\(913\) −48.6687 −1.61070
\(914\) 17.4244 0.576349
\(915\) 0 0
\(916\) 2.00000 0.0660819
\(917\) −20.2733 −0.669483
\(918\) 0 0
\(919\) −34.8489 −1.14956 −0.574779 0.818309i \(-0.694912\pi\)
−0.574779 + 0.818309i \(0.694912\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 26.4244 0.870242
\(923\) −5.42443 −0.178547
\(924\) 0 0
\(925\) 0 0
\(926\) 42.9710 1.41211
\(927\) 0 0
\(928\) 3.42443 0.112412
\(929\) −24.1221 −0.791422 −0.395711 0.918375i \(-0.629502\pi\)
−0.395711 + 0.918375i \(0.629502\pi\)
\(930\) 0 0
\(931\) 8.42443 0.276100
\(932\) 14.4244 0.472488
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) −2.42443 −0.0792026 −0.0396013 0.999216i \(-0.512609\pi\)
−0.0396013 + 0.999216i \(0.512609\pi\)
\(938\) −3.00000 −0.0979535
\(939\) 0 0
\(940\) 0 0
\(941\) 4.72671 0.154086 0.0770432 0.997028i \(-0.475452\pi\)
0.0770432 + 0.997028i \(0.475452\pi\)
\(942\) 0 0
\(943\) 35.6977 1.16248
\(944\) 7.42443 0.241645
\(945\) 0 0
\(946\) −44.9710 −1.46213
\(947\) 49.6977 1.61496 0.807479 0.589896i \(-0.200831\pi\)
0.807479 + 0.589896i \(0.200831\pi\)
\(948\) 0 0
\(949\) 2.42443 0.0787003
\(950\) 0 0
\(951\) 0 0
\(952\) −5.42443 −0.175807
\(953\) −22.5466 −0.730355 −0.365178 0.930938i \(-0.618992\pi\)
−0.365178 + 0.930938i \(0.618992\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −8.00000 −0.258468
\(959\) −2.42443 −0.0782889
\(960\) 0 0
\(961\) −28.9710 −0.934548
\(962\) 8.84886 0.285299
\(963\) 0 0
\(964\) 16.0000 0.515325
\(965\) 0 0
\(966\) 0 0
\(967\) 6.72671 0.216317 0.108158 0.994134i \(-0.465505\pi\)
0.108158 + 0.994134i \(0.465505\pi\)
\(968\) −30.2733 −0.973020
\(969\) 0 0
\(970\) 0 0
\(971\) 17.4244 0.559177 0.279588 0.960120i \(-0.409802\pi\)
0.279588 + 0.960120i \(0.409802\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) −6.42443 −0.205852
\(975\) 0 0
\(976\) 10.8489 0.347263
\(977\) 4.72671 0.151221 0.0756105 0.997137i \(-0.475909\pi\)
0.0756105 + 0.997137i \(0.475909\pi\)
\(978\) 0 0
\(979\) 6.42443 0.205326
\(980\) 0 0
\(981\) 0 0
\(982\) 17.6977 0.564757
\(983\) 35.3954 1.12894 0.564469 0.825454i \(-0.309081\pi\)
0.564469 + 0.825454i \(0.309081\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 18.5756 0.591567
\(987\) 0 0
\(988\) −8.42443 −0.268017
\(989\) 23.9710 0.762234
\(990\) 0 0
\(991\) −4.54657 −0.144427 −0.0722133 0.997389i \(-0.523006\pi\)
−0.0722133 + 0.997389i \(0.523006\pi\)
\(992\) 1.42443 0.0452257
\(993\) 0 0
\(994\) −5.42443 −0.172052
\(995\) 0 0
\(996\) 0 0
\(997\) 3.42443 0.108453 0.0542264 0.998529i \(-0.482731\pi\)
0.0542264 + 0.998529i \(0.482731\pi\)
\(998\) 3.15114 0.0997477
\(999\) 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 \(a_p\))