Properties

Label 8020.2.a.c.1.14
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.0547853 q^{3}\) \(-1.00000 q^{5}\) \(+3.87235 q^{7}\) \(-2.99700 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.0547853 q^{3}\) \(-1.00000 q^{5}\) \(+3.87235 q^{7}\) \(-2.99700 q^{9}\) \(+3.25314 q^{11}\) \(-6.91309 q^{13}\) \(-0.0547853 q^{15}\) \(+0.379841 q^{17}\) \(+4.37288 q^{19}\) \(+0.212148 q^{21}\) \(+1.01656 q^{23}\) \(+1.00000 q^{25}\) \(-0.328547 q^{27}\) \(-3.37707 q^{29}\) \(-6.22792 q^{31}\) \(+0.178224 q^{33}\) \(-3.87235 q^{35}\) \(-0.791545 q^{37}\) \(-0.378736 q^{39}\) \(+2.36327 q^{41}\) \(+0.241812 q^{43}\) \(+2.99700 q^{45}\) \(-6.57722 q^{47}\) \(+7.99512 q^{49}\) \(+0.0208097 q^{51}\) \(+9.52720 q^{53}\) \(-3.25314 q^{55}\) \(+0.239569 q^{57}\) \(+1.22289 q^{59}\) \(-9.03747 q^{61}\) \(-11.6054 q^{63}\) \(+6.91309 q^{65}\) \(-12.4260 q^{67}\) \(+0.0556924 q^{69}\) \(-11.8150 q^{71}\) \(-1.03700 q^{73}\) \(+0.0547853 q^{75}\) \(+12.5973 q^{77}\) \(+1.42411 q^{79}\) \(+8.97300 q^{81}\) \(+10.0097 q^{83}\) \(-0.379841 q^{85}\) \(-0.185014 q^{87}\) \(-0.256993 q^{89}\) \(-26.7699 q^{91}\) \(-0.341199 q^{93}\) \(-4.37288 q^{95}\) \(+4.05385 q^{97}\) \(-9.74965 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.0547853 0.0316303 0.0158152 0.999875i \(-0.494966\pi\)
0.0158152 + 0.999875i \(0.494966\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.87235 1.46361 0.731806 0.681513i \(-0.238678\pi\)
0.731806 + 0.681513i \(0.238678\pi\)
\(8\) 0 0
\(9\) −2.99700 −0.999000
\(10\) 0 0
\(11\) 3.25314 0.980858 0.490429 0.871481i \(-0.336840\pi\)
0.490429 + 0.871481i \(0.336840\pi\)
\(12\) 0 0
\(13\) −6.91309 −1.91735 −0.958674 0.284508i \(-0.908170\pi\)
−0.958674 + 0.284508i \(0.908170\pi\)
\(14\) 0 0
\(15\) −0.0547853 −0.0141455
\(16\) 0 0
\(17\) 0.379841 0.0921251 0.0460625 0.998939i \(-0.485333\pi\)
0.0460625 + 0.998939i \(0.485333\pi\)
\(18\) 0 0
\(19\) 4.37288 1.00321 0.501603 0.865098i \(-0.332744\pi\)
0.501603 + 0.865098i \(0.332744\pi\)
\(20\) 0 0
\(21\) 0.212148 0.0462945
\(22\) 0 0
\(23\) 1.01656 0.211967 0.105983 0.994368i \(-0.466201\pi\)
0.105983 + 0.994368i \(0.466201\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −0.328547 −0.0632290
\(28\) 0 0
\(29\) −3.37707 −0.627106 −0.313553 0.949571i \(-0.601519\pi\)
−0.313553 + 0.949571i \(0.601519\pi\)
\(30\) 0 0
\(31\) −6.22792 −1.11857 −0.559284 0.828976i \(-0.688924\pi\)
−0.559284 + 0.828976i \(0.688924\pi\)
\(32\) 0 0
\(33\) 0.178224 0.0310248
\(34\) 0 0
\(35\) −3.87235 −0.654547
\(36\) 0 0
\(37\) −0.791545 −0.130129 −0.0650646 0.997881i \(-0.520725\pi\)
−0.0650646 + 0.997881i \(0.520725\pi\)
\(38\) 0 0
\(39\) −0.378736 −0.0606463
\(40\) 0 0
\(41\) 2.36327 0.369080 0.184540 0.982825i \(-0.440920\pi\)
0.184540 + 0.982825i \(0.440920\pi\)
\(42\) 0 0
\(43\) 0.241812 0.0368760 0.0184380 0.999830i \(-0.494131\pi\)
0.0184380 + 0.999830i \(0.494131\pi\)
\(44\) 0 0
\(45\) 2.99700 0.446766
\(46\) 0 0
\(47\) −6.57722 −0.959386 −0.479693 0.877436i \(-0.659252\pi\)
−0.479693 + 0.877436i \(0.659252\pi\)
\(48\) 0 0
\(49\) 7.99512 1.14216
\(50\) 0 0
\(51\) 0.0208097 0.00291394
\(52\) 0 0
\(53\) 9.52720 1.30866 0.654331 0.756208i \(-0.272950\pi\)
0.654331 + 0.756208i \(0.272950\pi\)
\(54\) 0 0
\(55\) −3.25314 −0.438653
\(56\) 0 0
\(57\) 0.239569 0.0317317
\(58\) 0 0
\(59\) 1.22289 0.159207 0.0796034 0.996827i \(-0.474635\pi\)
0.0796034 + 0.996827i \(0.474635\pi\)
\(60\) 0 0
\(61\) −9.03747 −1.15713 −0.578565 0.815636i \(-0.696387\pi\)
−0.578565 + 0.815636i \(0.696387\pi\)
\(62\) 0 0
\(63\) −11.6054 −1.46215
\(64\) 0 0
\(65\) 6.91309 0.857464
\(66\) 0 0
\(67\) −12.4260 −1.51807 −0.759036 0.651048i \(-0.774330\pi\)
−0.759036 + 0.651048i \(0.774330\pi\)
\(68\) 0 0
\(69\) 0.0556924 0.00670458
\(70\) 0 0
\(71\) −11.8150 −1.40219 −0.701093 0.713070i \(-0.747304\pi\)
−0.701093 + 0.713070i \(0.747304\pi\)
\(72\) 0 0
\(73\) −1.03700 −0.121372 −0.0606861 0.998157i \(-0.519329\pi\)
−0.0606861 + 0.998157i \(0.519329\pi\)
\(74\) 0 0
\(75\) 0.0547853 0.00632606
\(76\) 0 0
\(77\) 12.5973 1.43560
\(78\) 0 0
\(79\) 1.42411 0.160225 0.0801124 0.996786i \(-0.474472\pi\)
0.0801124 + 0.996786i \(0.474472\pi\)
\(80\) 0 0
\(81\) 8.97300 0.997000
\(82\) 0 0
\(83\) 10.0097 1.09871 0.549356 0.835588i \(-0.314873\pi\)
0.549356 + 0.835588i \(0.314873\pi\)
\(84\) 0 0
\(85\) −0.379841 −0.0411996
\(86\) 0 0
\(87\) −0.185014 −0.0198356
\(88\) 0 0
\(89\) −0.256993 −0.0272412 −0.0136206 0.999907i \(-0.504336\pi\)
−0.0136206 + 0.999907i \(0.504336\pi\)
\(90\) 0 0
\(91\) −26.7699 −2.80625
\(92\) 0 0
\(93\) −0.341199 −0.0353807
\(94\) 0 0
\(95\) −4.37288 −0.448648
\(96\) 0 0
\(97\) 4.05385 0.411606 0.205803 0.978593i \(-0.434019\pi\)
0.205803 + 0.978593i \(0.434019\pi\)
\(98\) 0 0
\(99\) −9.74965 −0.979876
\(100\) 0 0
\(101\) −1.29284 −0.128642 −0.0643211 0.997929i \(-0.520488\pi\)
−0.0643211 + 0.997929i \(0.520488\pi\)
\(102\) 0 0
\(103\) 4.69720 0.462828 0.231414 0.972855i \(-0.425665\pi\)
0.231414 + 0.972855i \(0.425665\pi\)
\(104\) 0 0
\(105\) −0.212148 −0.0207035
\(106\) 0 0
\(107\) 2.90373 0.280714 0.140357 0.990101i \(-0.455175\pi\)
0.140357 + 0.990101i \(0.455175\pi\)
\(108\) 0 0
\(109\) −3.52516 −0.337649 −0.168824 0.985646i \(-0.553997\pi\)
−0.168824 + 0.985646i \(0.553997\pi\)
\(110\) 0 0
\(111\) −0.0433650 −0.00411603
\(112\) 0 0
\(113\) −4.53383 −0.426507 −0.213253 0.976997i \(-0.568406\pi\)
−0.213253 + 0.976997i \(0.568406\pi\)
\(114\) 0 0
\(115\) −1.01656 −0.0947945
\(116\) 0 0
\(117\) 20.7185 1.91543
\(118\) 0 0
\(119\) 1.47088 0.134835
\(120\) 0 0
\(121\) −0.417101 −0.0379183
\(122\) 0 0
\(123\) 0.129472 0.0116741
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −13.8505 −1.22903 −0.614514 0.788906i \(-0.710648\pi\)
−0.614514 + 0.788906i \(0.710648\pi\)
\(128\) 0 0
\(129\) 0.0132477 0.00116640
\(130\) 0 0
\(131\) −11.4760 −1.00267 −0.501333 0.865255i \(-0.667157\pi\)
−0.501333 + 0.865255i \(0.667157\pi\)
\(132\) 0 0
\(133\) 16.9333 1.46831
\(134\) 0 0
\(135\) 0.328547 0.0282769
\(136\) 0 0
\(137\) −13.2569 −1.13262 −0.566308 0.824194i \(-0.691629\pi\)
−0.566308 + 0.824194i \(0.691629\pi\)
\(138\) 0 0
\(139\) −2.87929 −0.244218 −0.122109 0.992517i \(-0.538966\pi\)
−0.122109 + 0.992517i \(0.538966\pi\)
\(140\) 0 0
\(141\) −0.360335 −0.0303457
\(142\) 0 0
\(143\) −22.4892 −1.88064
\(144\) 0 0
\(145\) 3.37707 0.280450
\(146\) 0 0
\(147\) 0.438015 0.0361269
\(148\) 0 0
\(149\) 5.39273 0.441790 0.220895 0.975298i \(-0.429102\pi\)
0.220895 + 0.975298i \(0.429102\pi\)
\(150\) 0 0
\(151\) −2.42119 −0.197033 −0.0985167 0.995135i \(-0.531410\pi\)
−0.0985167 + 0.995135i \(0.531410\pi\)
\(152\) 0 0
\(153\) −1.13838 −0.0920329
\(154\) 0 0
\(155\) 6.22792 0.500239
\(156\) 0 0
\(157\) 0.904608 0.0721956 0.0360978 0.999348i \(-0.488507\pi\)
0.0360978 + 0.999348i \(0.488507\pi\)
\(158\) 0 0
\(159\) 0.521951 0.0413934
\(160\) 0 0
\(161\) 3.93647 0.310237
\(162\) 0 0
\(163\) 6.73871 0.527817 0.263908 0.964548i \(-0.414988\pi\)
0.263908 + 0.964548i \(0.414988\pi\)
\(164\) 0 0
\(165\) −0.178224 −0.0138747
\(166\) 0 0
\(167\) −20.2600 −1.56777 −0.783885 0.620907i \(-0.786765\pi\)
−0.783885 + 0.620907i \(0.786765\pi\)
\(168\) 0 0
\(169\) 34.7909 2.67622
\(170\) 0 0
\(171\) −13.1055 −1.00220
\(172\) 0 0
\(173\) −5.63353 −0.428309 −0.214155 0.976800i \(-0.568700\pi\)
−0.214155 + 0.976800i \(0.568700\pi\)
\(174\) 0 0
\(175\) 3.87235 0.292722
\(176\) 0 0
\(177\) 0.0669965 0.00503576
\(178\) 0 0
\(179\) 14.2014 1.06147 0.530733 0.847539i \(-0.321917\pi\)
0.530733 + 0.847539i \(0.321917\pi\)
\(180\) 0 0
\(181\) −20.5197 −1.52522 −0.762608 0.646860i \(-0.776082\pi\)
−0.762608 + 0.646860i \(0.776082\pi\)
\(182\) 0 0
\(183\) −0.495121 −0.0366004
\(184\) 0 0
\(185\) 0.791545 0.0581955
\(186\) 0 0
\(187\) 1.23568 0.0903616
\(188\) 0 0
\(189\) −1.27225 −0.0925427
\(190\) 0 0
\(191\) −21.5800 −1.56147 −0.780736 0.624861i \(-0.785156\pi\)
−0.780736 + 0.624861i \(0.785156\pi\)
\(192\) 0 0
\(193\) 13.6158 0.980090 0.490045 0.871697i \(-0.336980\pi\)
0.490045 + 0.871697i \(0.336980\pi\)
\(194\) 0 0
\(195\) 0.378736 0.0271218
\(196\) 0 0
\(197\) −17.2022 −1.22561 −0.612804 0.790235i \(-0.709958\pi\)
−0.612804 + 0.790235i \(0.709958\pi\)
\(198\) 0 0
\(199\) 19.4704 1.38022 0.690109 0.723705i \(-0.257562\pi\)
0.690109 + 0.723705i \(0.257562\pi\)
\(200\) 0 0
\(201\) −0.680760 −0.0480171
\(202\) 0 0
\(203\) −13.0772 −0.917840
\(204\) 0 0
\(205\) −2.36327 −0.165058
\(206\) 0 0
\(207\) −3.04662 −0.211755
\(208\) 0 0
\(209\) 14.2256 0.984003
\(210\) 0 0
\(211\) −12.7402 −0.877072 −0.438536 0.898714i \(-0.644503\pi\)
−0.438536 + 0.898714i \(0.644503\pi\)
\(212\) 0 0
\(213\) −0.647290 −0.0443516
\(214\) 0 0
\(215\) −0.241812 −0.0164914
\(216\) 0 0
\(217\) −24.1167 −1.63715
\(218\) 0 0
\(219\) −0.0568126 −0.00383904
\(220\) 0 0
\(221\) −2.62588 −0.176636
\(222\) 0 0
\(223\) −2.58615 −0.173181 −0.0865906 0.996244i \(-0.527597\pi\)
−0.0865906 + 0.996244i \(0.527597\pi\)
\(224\) 0 0
\(225\) −2.99700 −0.199800
\(226\) 0 0
\(227\) 15.8804 1.05402 0.527009 0.849860i \(-0.323313\pi\)
0.527009 + 0.849860i \(0.323313\pi\)
\(228\) 0 0
\(229\) −4.44561 −0.293774 −0.146887 0.989153i \(-0.546925\pi\)
−0.146887 + 0.989153i \(0.546925\pi\)
\(230\) 0 0
\(231\) 0.690147 0.0454083
\(232\) 0 0
\(233\) −14.1850 −0.929292 −0.464646 0.885497i \(-0.653818\pi\)
−0.464646 + 0.885497i \(0.653818\pi\)
\(234\) 0 0
\(235\) 6.57722 0.429051
\(236\) 0 0
\(237\) 0.0780202 0.00506796
\(238\) 0 0
\(239\) −7.56239 −0.489170 −0.244585 0.969628i \(-0.578652\pi\)
−0.244585 + 0.969628i \(0.578652\pi\)
\(240\) 0 0
\(241\) 9.87453 0.636074 0.318037 0.948078i \(-0.396976\pi\)
0.318037 + 0.948078i \(0.396976\pi\)
\(242\) 0 0
\(243\) 1.47723 0.0947644
\(244\) 0 0
\(245\) −7.99512 −0.510789
\(246\) 0 0
\(247\) −30.2301 −1.92350
\(248\) 0 0
\(249\) 0.548387 0.0347526
\(250\) 0 0
\(251\) −22.0552 −1.39211 −0.696056 0.717988i \(-0.745063\pi\)
−0.696056 + 0.717988i \(0.745063\pi\)
\(252\) 0 0
\(253\) 3.30700 0.207909
\(254\) 0 0
\(255\) −0.0208097 −0.00130316
\(256\) 0 0
\(257\) 17.3588 1.08281 0.541405 0.840762i \(-0.317892\pi\)
0.541405 + 0.840762i \(0.317892\pi\)
\(258\) 0 0
\(259\) −3.06514 −0.190459
\(260\) 0 0
\(261\) 10.1211 0.626478
\(262\) 0 0
\(263\) −18.2110 −1.12294 −0.561468 0.827498i \(-0.689763\pi\)
−0.561468 + 0.827498i \(0.689763\pi\)
\(264\) 0 0
\(265\) −9.52720 −0.585251
\(266\) 0 0
\(267\) −0.0140795 −0.000861648 0
\(268\) 0 0
\(269\) 4.83629 0.294874 0.147437 0.989071i \(-0.452898\pi\)
0.147437 + 0.989071i \(0.452898\pi\)
\(270\) 0 0
\(271\) 14.0413 0.852949 0.426474 0.904500i \(-0.359755\pi\)
0.426474 + 0.904500i \(0.359755\pi\)
\(272\) 0 0
\(273\) −1.46660 −0.0887626
\(274\) 0 0
\(275\) 3.25314 0.196172
\(276\) 0 0
\(277\) −16.8843 −1.01448 −0.507238 0.861806i \(-0.669334\pi\)
−0.507238 + 0.861806i \(0.669334\pi\)
\(278\) 0 0
\(279\) 18.6651 1.11745
\(280\) 0 0
\(281\) −17.8389 −1.06418 −0.532091 0.846687i \(-0.678593\pi\)
−0.532091 + 0.846687i \(0.678593\pi\)
\(282\) 0 0
\(283\) 29.4099 1.74824 0.874119 0.485711i \(-0.161439\pi\)
0.874119 + 0.485711i \(0.161439\pi\)
\(284\) 0 0
\(285\) −0.239569 −0.0141909
\(286\) 0 0
\(287\) 9.15141 0.540191
\(288\) 0 0
\(289\) −16.8557 −0.991513
\(290\) 0 0
\(291\) 0.222091 0.0130192
\(292\) 0 0
\(293\) −11.2205 −0.655507 −0.327754 0.944763i \(-0.606292\pi\)
−0.327754 + 0.944763i \(0.606292\pi\)
\(294\) 0 0
\(295\) −1.22289 −0.0711995
\(296\) 0 0
\(297\) −1.06881 −0.0620186
\(298\) 0 0
\(299\) −7.02756 −0.406414
\(300\) 0 0
\(301\) 0.936382 0.0539722
\(302\) 0 0
\(303\) −0.0708285 −0.00406899
\(304\) 0 0
\(305\) 9.03747 0.517484
\(306\) 0 0
\(307\) 16.0714 0.917244 0.458622 0.888631i \(-0.348343\pi\)
0.458622 + 0.888631i \(0.348343\pi\)
\(308\) 0 0
\(309\) 0.257337 0.0146394
\(310\) 0 0
\(311\) −23.5345 −1.33452 −0.667259 0.744825i \(-0.732533\pi\)
−0.667259 + 0.744825i \(0.732533\pi\)
\(312\) 0 0
\(313\) −2.46325 −0.139231 −0.0696155 0.997574i \(-0.522177\pi\)
−0.0696155 + 0.997574i \(0.522177\pi\)
\(314\) 0 0
\(315\) 11.6054 0.653892
\(316\) 0 0
\(317\) 2.74184 0.153997 0.0769984 0.997031i \(-0.475466\pi\)
0.0769984 + 0.997031i \(0.475466\pi\)
\(318\) 0 0
\(319\) −10.9861 −0.615102
\(320\) 0 0
\(321\) 0.159082 0.00887908
\(322\) 0 0
\(323\) 1.66100 0.0924205
\(324\) 0 0
\(325\) −6.91309 −0.383469
\(326\) 0 0
\(327\) −0.193127 −0.0106799
\(328\) 0 0
\(329\) −25.4693 −1.40417
\(330\) 0 0
\(331\) 20.1919 1.10985 0.554924 0.831901i \(-0.312747\pi\)
0.554924 + 0.831901i \(0.312747\pi\)
\(332\) 0 0
\(333\) 2.37226 0.129999
\(334\) 0 0
\(335\) 12.4260 0.678903
\(336\) 0 0
\(337\) 26.5295 1.44516 0.722578 0.691290i \(-0.242957\pi\)
0.722578 + 0.691290i \(0.242957\pi\)
\(338\) 0 0
\(339\) −0.248387 −0.0134905
\(340\) 0 0
\(341\) −20.2603 −1.09716
\(342\) 0 0
\(343\) 3.85346 0.208067
\(344\) 0 0
\(345\) −0.0556924 −0.00299838
\(346\) 0 0
\(347\) −1.16729 −0.0626634 −0.0313317 0.999509i \(-0.509975\pi\)
−0.0313317 + 0.999509i \(0.509975\pi\)
\(348\) 0 0
\(349\) 13.6879 0.732698 0.366349 0.930477i \(-0.380608\pi\)
0.366349 + 0.930477i \(0.380608\pi\)
\(350\) 0 0
\(351\) 2.27128 0.121232
\(352\) 0 0
\(353\) −0.960426 −0.0511183 −0.0255591 0.999673i \(-0.508137\pi\)
−0.0255591 + 0.999673i \(0.508137\pi\)
\(354\) 0 0
\(355\) 11.8150 0.627077
\(356\) 0 0
\(357\) 0.0805826 0.00426488
\(358\) 0 0
\(359\) 20.7589 1.09561 0.547807 0.836605i \(-0.315463\pi\)
0.547807 + 0.836605i \(0.315463\pi\)
\(360\) 0 0
\(361\) 0.122051 0.00642376
\(362\) 0 0
\(363\) −0.0228510 −0.00119937
\(364\) 0 0
\(365\) 1.03700 0.0542793
\(366\) 0 0
\(367\) −23.1120 −1.20643 −0.603217 0.797577i \(-0.706115\pi\)
−0.603217 + 0.797577i \(0.706115\pi\)
\(368\) 0 0
\(369\) −7.08271 −0.368711
\(370\) 0 0
\(371\) 36.8927 1.91537
\(372\) 0 0
\(373\) −1.77344 −0.0918255 −0.0459127 0.998945i \(-0.514620\pi\)
−0.0459127 + 0.998945i \(0.514620\pi\)
\(374\) 0 0
\(375\) −0.0547853 −0.00282910
\(376\) 0 0
\(377\) 23.3460 1.20238
\(378\) 0 0
\(379\) −12.4511 −0.639572 −0.319786 0.947490i \(-0.603611\pi\)
−0.319786 + 0.947490i \(0.603611\pi\)
\(380\) 0 0
\(381\) −0.758801 −0.0388746
\(382\) 0 0
\(383\) −11.6751 −0.596569 −0.298284 0.954477i \(-0.596414\pi\)
−0.298284 + 0.954477i \(0.596414\pi\)
\(384\) 0 0
\(385\) −12.5973 −0.642018
\(386\) 0 0
\(387\) −0.724711 −0.0368391
\(388\) 0 0
\(389\) 22.6275 1.14726 0.573629 0.819115i \(-0.305535\pi\)
0.573629 + 0.819115i \(0.305535\pi\)
\(390\) 0 0
\(391\) 0.386131 0.0195275
\(392\) 0 0
\(393\) −0.628718 −0.0317146
\(394\) 0 0
\(395\) −1.42411 −0.0716547
\(396\) 0 0
\(397\) 20.7266 1.04024 0.520118 0.854094i \(-0.325888\pi\)
0.520118 + 0.854094i \(0.325888\pi\)
\(398\) 0 0
\(399\) 0.927697 0.0464430
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 43.0542 2.14468
\(404\) 0 0
\(405\) −8.97300 −0.445872
\(406\) 0 0
\(407\) −2.57500 −0.127638
\(408\) 0 0
\(409\) −14.5502 −0.719461 −0.359730 0.933056i \(-0.617131\pi\)
−0.359730 + 0.933056i \(0.617131\pi\)
\(410\) 0 0
\(411\) −0.726285 −0.0358250
\(412\) 0 0
\(413\) 4.73547 0.233017
\(414\) 0 0
\(415\) −10.0097 −0.491359
\(416\) 0 0
\(417\) −0.157743 −0.00772469
\(418\) 0 0
\(419\) 0.495617 0.0242125 0.0121062 0.999927i \(-0.496146\pi\)
0.0121062 + 0.999927i \(0.496146\pi\)
\(420\) 0 0
\(421\) −36.0564 −1.75728 −0.878640 0.477486i \(-0.841548\pi\)
−0.878640 + 0.477486i \(0.841548\pi\)
\(422\) 0 0
\(423\) 19.7119 0.958427
\(424\) 0 0
\(425\) 0.379841 0.0184250
\(426\) 0 0
\(427\) −34.9963 −1.69359
\(428\) 0 0
\(429\) −1.23208 −0.0594854
\(430\) 0 0
\(431\) 25.2202 1.21481 0.607406 0.794391i \(-0.292210\pi\)
0.607406 + 0.794391i \(0.292210\pi\)
\(432\) 0 0
\(433\) 11.8649 0.570193 0.285096 0.958499i \(-0.407974\pi\)
0.285096 + 0.958499i \(0.407974\pi\)
\(434\) 0 0
\(435\) 0.185014 0.00887073
\(436\) 0 0
\(437\) 4.44528 0.212647
\(438\) 0 0
\(439\) 16.7449 0.799191 0.399595 0.916692i \(-0.369151\pi\)
0.399595 + 0.916692i \(0.369151\pi\)
\(440\) 0 0
\(441\) −23.9614 −1.14102
\(442\) 0 0
\(443\) 17.4045 0.826912 0.413456 0.910524i \(-0.364322\pi\)
0.413456 + 0.910524i \(0.364322\pi\)
\(444\) 0 0
\(445\) 0.256993 0.0121826
\(446\) 0 0
\(447\) 0.295443 0.0139740
\(448\) 0 0
\(449\) −4.06051 −0.191627 −0.0958136 0.995399i \(-0.530545\pi\)
−0.0958136 + 0.995399i \(0.530545\pi\)
\(450\) 0 0
\(451\) 7.68803 0.362015
\(452\) 0 0
\(453\) −0.132645 −0.00623223
\(454\) 0 0
\(455\) 26.7699 1.25499
\(456\) 0 0
\(457\) −23.7234 −1.10973 −0.554867 0.831939i \(-0.687231\pi\)
−0.554867 + 0.831939i \(0.687231\pi\)
\(458\) 0 0
\(459\) −0.124796 −0.00582497
\(460\) 0 0
\(461\) 2.02394 0.0942642 0.0471321 0.998889i \(-0.484992\pi\)
0.0471321 + 0.998889i \(0.484992\pi\)
\(462\) 0 0
\(463\) −12.4483 −0.578520 −0.289260 0.957251i \(-0.593409\pi\)
−0.289260 + 0.957251i \(0.593409\pi\)
\(464\) 0 0
\(465\) 0.341199 0.0158227
\(466\) 0 0
\(467\) −21.4461 −0.992406 −0.496203 0.868206i \(-0.665273\pi\)
−0.496203 + 0.868206i \(0.665273\pi\)
\(468\) 0 0
\(469\) −48.1177 −2.22187
\(470\) 0 0
\(471\) 0.0495592 0.00228357
\(472\) 0 0
\(473\) 0.786648 0.0361701
\(474\) 0 0
\(475\) 4.37288 0.200641
\(476\) 0 0
\(477\) −28.5530 −1.30735
\(478\) 0 0
\(479\) −31.3565 −1.43271 −0.716357 0.697734i \(-0.754192\pi\)
−0.716357 + 0.697734i \(0.754192\pi\)
\(480\) 0 0
\(481\) 5.47202 0.249503
\(482\) 0 0
\(483\) 0.215661 0.00981290
\(484\) 0 0
\(485\) −4.05385 −0.184076
\(486\) 0 0
\(487\) −34.6622 −1.57069 −0.785347 0.619056i \(-0.787515\pi\)
−0.785347 + 0.619056i \(0.787515\pi\)
\(488\) 0 0
\(489\) 0.369182 0.0166950
\(490\) 0 0
\(491\) −26.3685 −1.18999 −0.594997 0.803728i \(-0.702847\pi\)
−0.594997 + 0.803728i \(0.702847\pi\)
\(492\) 0 0
\(493\) −1.28275 −0.0577722
\(494\) 0 0
\(495\) 9.74965 0.438214
\(496\) 0 0
\(497\) −45.7520 −2.05226
\(498\) 0 0
\(499\) −31.7512 −1.42138 −0.710689 0.703506i \(-0.751617\pi\)
−0.710689 + 0.703506i \(0.751617\pi\)
\(500\) 0 0
\(501\) −1.10995 −0.0495890
\(502\) 0 0
\(503\) −23.5992 −1.05224 −0.526118 0.850411i \(-0.676353\pi\)
−0.526118 + 0.850411i \(0.676353\pi\)
\(504\) 0 0
\(505\) 1.29284 0.0575305
\(506\) 0 0
\(507\) 1.90603 0.0846497
\(508\) 0 0
\(509\) 33.4949 1.48463 0.742317 0.670048i \(-0.233727\pi\)
0.742317 + 0.670048i \(0.233727\pi\)
\(510\) 0 0
\(511\) −4.01565 −0.177642
\(512\) 0 0
\(513\) −1.43670 −0.0634317
\(514\) 0 0
\(515\) −4.69720 −0.206983
\(516\) 0 0
\(517\) −21.3966 −0.941022
\(518\) 0 0
\(519\) −0.308635 −0.0135476
\(520\) 0 0
\(521\) −40.2923 −1.76524 −0.882620 0.470087i \(-0.844222\pi\)
−0.882620 + 0.470087i \(0.844222\pi\)
\(522\) 0 0
\(523\) −41.1087 −1.79756 −0.898778 0.438404i \(-0.855544\pi\)
−0.898778 + 0.438404i \(0.855544\pi\)
\(524\) 0 0
\(525\) 0.212148 0.00925890
\(526\) 0 0
\(527\) −2.36562 −0.103048
\(528\) 0 0
\(529\) −21.9666 −0.955070
\(530\) 0 0
\(531\) −3.66500 −0.159048
\(532\) 0 0
\(533\) −16.3375 −0.707655
\(534\) 0 0
\(535\) −2.90373 −0.125539
\(536\) 0 0
\(537\) 0.778030 0.0335745
\(538\) 0 0
\(539\) 26.0092 1.12030
\(540\) 0 0
\(541\) −15.0005 −0.644923 −0.322461 0.946583i \(-0.604510\pi\)
−0.322461 + 0.946583i \(0.604510\pi\)
\(542\) 0 0
\(543\) −1.12418 −0.0482431
\(544\) 0 0
\(545\) 3.52516 0.151001
\(546\) 0 0
\(547\) 8.48196 0.362662 0.181331 0.983422i \(-0.441959\pi\)
0.181331 + 0.983422i \(0.441959\pi\)
\(548\) 0 0
\(549\) 27.0853 1.15597
\(550\) 0 0
\(551\) −14.7675 −0.629117
\(552\) 0 0
\(553\) 5.51465 0.234507
\(554\) 0 0
\(555\) 0.0433650 0.00184074
\(556\) 0 0
\(557\) −12.8347 −0.543823 −0.271911 0.962322i \(-0.587656\pi\)
−0.271911 + 0.962322i \(0.587656\pi\)
\(558\) 0 0
\(559\) −1.67167 −0.0707041
\(560\) 0 0
\(561\) 0.0676969 0.00285816
\(562\) 0 0
\(563\) −37.1619 −1.56619 −0.783094 0.621903i \(-0.786360\pi\)
−0.783094 + 0.621903i \(0.786360\pi\)
\(564\) 0 0
\(565\) 4.53383 0.190740
\(566\) 0 0
\(567\) 34.7466 1.45922
\(568\) 0 0
\(569\) −10.6682 −0.447234 −0.223617 0.974677i \(-0.571786\pi\)
−0.223617 + 0.974677i \(0.571786\pi\)
\(570\) 0 0
\(571\) 2.83451 0.118620 0.0593102 0.998240i \(-0.481110\pi\)
0.0593102 + 0.998240i \(0.481110\pi\)
\(572\) 0 0
\(573\) −1.18227 −0.0493898
\(574\) 0 0
\(575\) 1.01656 0.0423934
\(576\) 0 0
\(577\) −8.54980 −0.355933 −0.177966 0.984037i \(-0.556952\pi\)
−0.177966 + 0.984037i \(0.556952\pi\)
\(578\) 0 0
\(579\) 0.745948 0.0310005
\(580\) 0 0
\(581\) 38.7613 1.60809
\(582\) 0 0
\(583\) 30.9933 1.28361
\(584\) 0 0
\(585\) −20.7185 −0.856606
\(586\) 0 0
\(587\) −28.2948 −1.16785 −0.583926 0.811807i \(-0.698484\pi\)
−0.583926 + 0.811807i \(0.698484\pi\)
\(588\) 0 0
\(589\) −27.2339 −1.12216
\(590\) 0 0
\(591\) −0.942429 −0.0387663
\(592\) 0 0
\(593\) −2.04491 −0.0839743 −0.0419872 0.999118i \(-0.513369\pi\)
−0.0419872 + 0.999118i \(0.513369\pi\)
\(594\) 0 0
\(595\) −1.47088 −0.0603002
\(596\) 0 0
\(597\) 1.06669 0.0436567
\(598\) 0 0
\(599\) −0.317784 −0.0129843 −0.00649215 0.999979i \(-0.502067\pi\)
−0.00649215 + 0.999979i \(0.502067\pi\)
\(600\) 0 0
\(601\) 7.97661 0.325373 0.162686 0.986678i \(-0.447984\pi\)
0.162686 + 0.986678i \(0.447984\pi\)
\(602\) 0 0
\(603\) 37.2406 1.51655
\(604\) 0 0
\(605\) 0.417101 0.0169576
\(606\) 0 0
\(607\) 38.9256 1.57994 0.789971 0.613144i \(-0.210096\pi\)
0.789971 + 0.613144i \(0.210096\pi\)
\(608\) 0 0
\(609\) −0.716438 −0.0290315
\(610\) 0 0
\(611\) 45.4690 1.83948
\(612\) 0 0
\(613\) −36.6279 −1.47939 −0.739694 0.672943i \(-0.765030\pi\)
−0.739694 + 0.672943i \(0.765030\pi\)
\(614\) 0 0
\(615\) −0.129472 −0.00522083
\(616\) 0 0
\(617\) −23.0675 −0.928662 −0.464331 0.885662i \(-0.653705\pi\)
−0.464331 + 0.885662i \(0.653705\pi\)
\(618\) 0 0
\(619\) 13.1149 0.527131 0.263565 0.964642i \(-0.415102\pi\)
0.263565 + 0.964642i \(0.415102\pi\)
\(620\) 0 0
\(621\) −0.333987 −0.0134024
\(622\) 0 0
\(623\) −0.995169 −0.0398706
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0.779352 0.0311243
\(628\) 0 0
\(629\) −0.300662 −0.0119882
\(630\) 0 0
\(631\) 22.8199 0.908444 0.454222 0.890888i \(-0.349917\pi\)
0.454222 + 0.890888i \(0.349917\pi\)
\(632\) 0 0
\(633\) −0.697976 −0.0277420
\(634\) 0 0
\(635\) 13.8505 0.549638
\(636\) 0 0
\(637\) −55.2710 −2.18992
\(638\) 0 0
\(639\) 35.4096 1.40078
\(640\) 0 0
\(641\) −2.76533 −0.109224 −0.0546121 0.998508i \(-0.517392\pi\)
−0.0546121 + 0.998508i \(0.517392\pi\)
\(642\) 0 0
\(643\) 48.3052 1.90497 0.952485 0.304585i \(-0.0985179\pi\)
0.952485 + 0.304585i \(0.0985179\pi\)
\(644\) 0 0
\(645\) −0.0132477 −0.000521630 0
\(646\) 0 0
\(647\) −23.1138 −0.908699 −0.454349 0.890824i \(-0.650128\pi\)
−0.454349 + 0.890824i \(0.650128\pi\)
\(648\) 0 0
\(649\) 3.97823 0.156159
\(650\) 0 0
\(651\) −1.32124 −0.0517835
\(652\) 0 0
\(653\) −39.2971 −1.53781 −0.768907 0.639360i \(-0.779199\pi\)
−0.768907 + 0.639360i \(0.779199\pi\)
\(654\) 0 0
\(655\) 11.4760 0.448405
\(656\) 0 0
\(657\) 3.10790 0.121251
\(658\) 0 0
\(659\) −20.7465 −0.808171 −0.404085 0.914721i \(-0.632410\pi\)
−0.404085 + 0.914721i \(0.632410\pi\)
\(660\) 0 0
\(661\) 27.1256 1.05506 0.527531 0.849536i \(-0.323118\pi\)
0.527531 + 0.849536i \(0.323118\pi\)
\(662\) 0 0
\(663\) −0.143860 −0.00558704
\(664\) 0 0
\(665\) −16.9333 −0.656646
\(666\) 0 0
\(667\) −3.43298 −0.132926
\(668\) 0 0
\(669\) −0.141683 −0.00547778
\(670\) 0 0
\(671\) −29.4001 −1.13498
\(672\) 0 0
\(673\) 4.95240 0.190901 0.0954505 0.995434i \(-0.469571\pi\)
0.0954505 + 0.995434i \(0.469571\pi\)
\(674\) 0 0
\(675\) −0.328547 −0.0126458
\(676\) 0 0
\(677\) 35.1674 1.35159 0.675796 0.737089i \(-0.263800\pi\)
0.675796 + 0.737089i \(0.263800\pi\)
\(678\) 0 0
\(679\) 15.6979 0.602431
\(680\) 0 0
\(681\) 0.870011 0.0333389
\(682\) 0 0
\(683\) −33.0119 −1.26317 −0.631584 0.775308i \(-0.717595\pi\)
−0.631584 + 0.775308i \(0.717595\pi\)
\(684\) 0 0
\(685\) 13.2569 0.506521
\(686\) 0 0
\(687\) −0.243554 −0.00929216
\(688\) 0 0
\(689\) −65.8624 −2.50916
\(690\) 0 0
\(691\) −0.394264 −0.0149985 −0.00749926 0.999972i \(-0.502387\pi\)
−0.00749926 + 0.999972i \(0.502387\pi\)
\(692\) 0 0
\(693\) −37.7541 −1.43416
\(694\) 0 0
\(695\) 2.87929 0.109218
\(696\) 0 0
\(697\) 0.897667 0.0340016
\(698\) 0 0
\(699\) −0.777131 −0.0293938
\(700\) 0 0
\(701\) 30.2131 1.14113 0.570566 0.821252i \(-0.306724\pi\)
0.570566 + 0.821252i \(0.306724\pi\)
\(702\) 0 0
\(703\) −3.46133 −0.130546
\(704\) 0 0
\(705\) 0.360335 0.0135710
\(706\) 0 0
\(707\) −5.00633 −0.188282
\(708\) 0 0
\(709\) −13.2139 −0.496260 −0.248130 0.968727i \(-0.579816\pi\)
−0.248130 + 0.968727i \(0.579816\pi\)
\(710\) 0 0
\(711\) −4.26805 −0.160064
\(712\) 0 0
\(713\) −6.33104 −0.237099
\(714\) 0 0
\(715\) 22.4892 0.841050
\(716\) 0 0
\(717\) −0.414308 −0.0154726
\(718\) 0 0
\(719\) 9.77985 0.364727 0.182363 0.983231i \(-0.441625\pi\)
0.182363 + 0.983231i \(0.441625\pi\)
\(720\) 0 0
\(721\) 18.1892 0.677401
\(722\) 0 0
\(723\) 0.540979 0.0201192
\(724\) 0 0
\(725\) −3.37707 −0.125421
\(726\) 0 0
\(727\) 13.0727 0.484839 0.242420 0.970172i \(-0.422059\pi\)
0.242420 + 0.970172i \(0.422059\pi\)
\(728\) 0 0
\(729\) −26.8381 −0.994002
\(730\) 0 0
\(731\) 0.0918503 0.00339720
\(732\) 0 0
\(733\) −1.89623 −0.0700389 −0.0350194 0.999387i \(-0.511149\pi\)
−0.0350194 + 0.999387i \(0.511149\pi\)
\(734\) 0 0
\(735\) −0.438015 −0.0161564
\(736\) 0 0
\(737\) −40.4233 −1.48901
\(738\) 0 0
\(739\) −7.42230 −0.273034 −0.136517 0.990638i \(-0.543591\pi\)
−0.136517 + 0.990638i \(0.543591\pi\)
\(740\) 0 0
\(741\) −1.65617 −0.0608408
\(742\) 0 0
\(743\) −26.4765 −0.971328 −0.485664 0.874146i \(-0.661422\pi\)
−0.485664 + 0.874146i \(0.661422\pi\)
\(744\) 0 0
\(745\) −5.39273 −0.197574
\(746\) 0 0
\(747\) −29.9992 −1.09761
\(748\) 0 0
\(749\) 11.2443 0.410857
\(750\) 0 0
\(751\) 36.3315 1.32576 0.662879 0.748727i \(-0.269335\pi\)
0.662879 + 0.748727i \(0.269335\pi\)
\(752\) 0 0
\(753\) −1.20830 −0.0440329
\(754\) 0 0
\(755\) 2.42119 0.0881160
\(756\) 0 0
\(757\) 40.6604 1.47783 0.738913 0.673801i \(-0.235340\pi\)
0.738913 + 0.673801i \(0.235340\pi\)
\(758\) 0 0
\(759\) 0.181175 0.00657623
\(760\) 0 0
\(761\) −27.3976 −0.993162 −0.496581 0.867990i \(-0.665411\pi\)
−0.496581 + 0.867990i \(0.665411\pi\)
\(762\) 0 0
\(763\) −13.6507 −0.494187
\(764\) 0 0
\(765\) 1.13838 0.0411584
\(766\) 0 0
\(767\) −8.45396 −0.305255
\(768\) 0 0
\(769\) −26.4027 −0.952104 −0.476052 0.879417i \(-0.657933\pi\)
−0.476052 + 0.879417i \(0.657933\pi\)
\(770\) 0 0
\(771\) 0.951006 0.0342496
\(772\) 0 0
\(773\) 45.6528 1.64202 0.821008 0.570917i \(-0.193412\pi\)
0.821008 + 0.570917i \(0.193412\pi\)
\(774\) 0 0
\(775\) −6.22792 −0.223714
\(776\) 0 0
\(777\) −0.167925 −0.00602426
\(778\) 0 0
\(779\) 10.3343 0.370264
\(780\) 0 0
\(781\) −38.4359 −1.37534
\(782\) 0 0
\(783\) 1.10953 0.0396513
\(784\) 0 0
\(785\) −0.904608 −0.0322869
\(786\) 0 0
\(787\) 4.23031 0.150794 0.0753971 0.997154i \(-0.475978\pi\)
0.0753971 + 0.997154i \(0.475978\pi\)
\(788\) 0 0
\(789\) −0.997694 −0.0355188
\(790\) 0 0
\(791\) −17.5566 −0.624241
\(792\) 0 0
\(793\) 62.4769 2.21862
\(794\) 0 0
\(795\) −0.521951 −0.0185117
\(796\) 0 0
\(797\) 22.6939 0.803860 0.401930 0.915670i \(-0.368340\pi\)
0.401930 + 0.915670i \(0.368340\pi\)
\(798\) 0 0
\(799\) −2.49830 −0.0883836
\(800\) 0 0
\(801\) 0.770208 0.0272140
\(802\) 0 0
\(803\) −3.37352 −0.119049
\(804\) 0 0
\(805\) −3.93647 −0.138742
\(806\) 0 0
\(807\) 0.264957 0.00932694
\(808\) 0 0
\(809\) −44.9292 −1.57963 −0.789814 0.613347i \(-0.789823\pi\)
−0.789814 + 0.613347i \(0.789823\pi\)
\(810\) 0 0
\(811\) −38.6415 −1.35689 −0.678443 0.734653i \(-0.737345\pi\)
−0.678443 + 0.734653i \(0.737345\pi\)
\(812\) 0 0
\(813\) 0.769257 0.0269790
\(814\) 0 0
\(815\) −6.73871 −0.236047
\(816\) 0 0
\(817\) 1.05741 0.0369943
\(818\) 0 0
\(819\) 80.2295 2.80344
\(820\) 0 0
\(821\) 11.7155 0.408873 0.204437 0.978880i \(-0.434464\pi\)
0.204437 + 0.978880i \(0.434464\pi\)
\(822\) 0 0
\(823\) 31.5615 1.10017 0.550083 0.835110i \(-0.314596\pi\)
0.550083 + 0.835110i \(0.314596\pi\)
\(824\) 0 0
\(825\) 0.178224 0.00620497
\(826\) 0 0
\(827\) 35.7491 1.24312 0.621559 0.783368i \(-0.286500\pi\)
0.621559 + 0.783368i \(0.286500\pi\)
\(828\) 0 0
\(829\) 29.0953 1.01052 0.505261 0.862967i \(-0.331396\pi\)
0.505261 + 0.862967i \(0.331396\pi\)
\(830\) 0 0
\(831\) −0.925009 −0.0320882
\(832\) 0 0
\(833\) 3.03688 0.105222
\(834\) 0 0
\(835\) 20.2600 0.701128
\(836\) 0 0
\(837\) 2.04617 0.0707259
\(838\) 0 0
\(839\) −30.2324 −1.04374 −0.521870 0.853025i \(-0.674765\pi\)
−0.521870 + 0.853025i \(0.674765\pi\)
\(840\) 0 0
\(841\) −17.5954 −0.606738
\(842\) 0 0
\(843\) −0.977311 −0.0336604
\(844\) 0 0
\(845\) −34.7909 −1.19684
\(846\) 0 0
\(847\) −1.61516 −0.0554976
\(848\) 0 0
\(849\) 1.61123 0.0552973
\(850\) 0 0
\(851\) −0.804651 −0.0275831
\(852\) 0 0
\(853\) 34.3299 1.17543 0.587716 0.809067i \(-0.300027\pi\)
0.587716 + 0.809067i \(0.300027\pi\)
\(854\) 0 0
\(855\) 13.1055 0.448199
\(856\) 0 0
\(857\) 52.8787 1.80630 0.903152 0.429322i \(-0.141247\pi\)
0.903152 + 0.429322i \(0.141247\pi\)
\(858\) 0 0
\(859\) 4.06326 0.138637 0.0693183 0.997595i \(-0.477918\pi\)
0.0693183 + 0.997595i \(0.477918\pi\)
\(860\) 0 0
\(861\) 0.501363 0.0170864
\(862\) 0 0
\(863\) 41.0841 1.39852 0.699260 0.714867i \(-0.253513\pi\)
0.699260 + 0.714867i \(0.253513\pi\)
\(864\) 0 0
\(865\) 5.63353 0.191546
\(866\) 0 0
\(867\) −0.923446 −0.0313619
\(868\) 0 0
\(869\) 4.63282 0.157158
\(870\) 0 0
\(871\) 85.9018 2.91067
\(872\) 0 0
\(873\) −12.1494 −0.411194
\(874\) 0 0
\(875\) −3.87235 −0.130909
\(876\) 0 0
\(877\) 42.3791 1.43104 0.715521 0.698592i \(-0.246190\pi\)
0.715521 + 0.698592i \(0.246190\pi\)
\(878\) 0 0
\(879\) −0.614717 −0.0207339
\(880\) 0 0
\(881\) 8.82835 0.297435 0.148717 0.988880i \(-0.452486\pi\)
0.148717 + 0.988880i \(0.452486\pi\)
\(882\) 0 0
\(883\) 9.06826 0.305171 0.152586 0.988290i \(-0.451240\pi\)
0.152586 + 0.988290i \(0.451240\pi\)
\(884\) 0 0
\(885\) −0.0669965 −0.00225206
\(886\) 0 0
\(887\) 5.34816 0.179574 0.0897869 0.995961i \(-0.471381\pi\)
0.0897869 + 0.995961i \(0.471381\pi\)
\(888\) 0 0
\(889\) −53.6338 −1.79882
\(890\) 0 0
\(891\) 29.1904 0.977915
\(892\) 0 0
\(893\) −28.7614 −0.962463
\(894\) 0 0
\(895\) −14.2014 −0.474702
\(896\) 0 0
\(897\) −0.385007 −0.0128550
\(898\) 0 0
\(899\) 21.0321 0.701461
\(900\) 0 0
\(901\) 3.61883 0.120561
\(902\) 0 0
\(903\) 0.0513000 0.00170716
\(904\) 0 0
\(905\) 20.5197 0.682098
\(906\) 0 0
\(907\) −12.5206 −0.415740 −0.207870 0.978156i \(-0.566653\pi\)
−0.207870 + 0.978156i \(0.566653\pi\)
\(908\) 0 0
\(909\) 3.87463 0.128514
\(910\) 0 0
\(911\) −19.9114 −0.659695 −0.329847 0.944034i \(-0.606997\pi\)
−0.329847 + 0.944034i \(0.606997\pi\)
\(912\) 0 0
\(913\) 32.5631 1.07768
\(914\) 0 0
\(915\) 0.495121 0.0163682
\(916\) 0 0
\(917\) −44.4392 −1.46751
\(918\) 0 0
\(919\) −7.90519 −0.260768 −0.130384 0.991464i \(-0.541621\pi\)
−0.130384 + 0.991464i \(0.541621\pi\)
\(920\) 0 0
\(921\) 0.880477 0.0290127
\(922\) 0 0
\(923\) 81.6784 2.68848
\(924\) 0 0
\(925\) −0.791545 −0.0260258
\(926\) 0 0
\(927\) −14.0775 −0.462365
\(928\) 0 0
\(929\) 22.7571 0.746637 0.373319 0.927703i \(-0.378220\pi\)
0.373319 + 0.927703i \(0.378220\pi\)
\(930\) 0 0
\(931\) 34.9617 1.14582
\(932\) 0 0
\(933\) −1.28934 −0.0422112
\(934\) 0 0
\(935\) −1.23568 −0.0404109
\(936\) 0 0
\(937\) −6.31048 −0.206154 −0.103077 0.994673i \(-0.532869\pi\)
−0.103077 + 0.994673i \(0.532869\pi\)
\(938\) 0 0
\(939\) −0.134950 −0.00440392
\(940\) 0 0
\(941\) 9.34624 0.304679 0.152339 0.988328i \(-0.451319\pi\)
0.152339 + 0.988328i \(0.451319\pi\)
\(942\) 0 0
\(943\) 2.40240 0.0782328
\(944\) 0 0
\(945\) 1.27225 0.0413863
\(946\) 0 0
\(947\) 3.05680 0.0993326 0.0496663 0.998766i \(-0.484184\pi\)
0.0496663 + 0.998766i \(0.484184\pi\)
\(948\) 0 0
\(949\) 7.16890 0.232712
\(950\) 0 0
\(951\) 0.150212 0.00487097
\(952\) 0 0
\(953\) −14.6885 −0.475808 −0.237904 0.971289i \(-0.576460\pi\)
−0.237904 + 0.971289i \(0.576460\pi\)
\(954\) 0 0
\(955\) 21.5800 0.698312
\(956\) 0 0
\(957\) −0.601875 −0.0194559
\(958\) 0 0
\(959\) −51.3355 −1.65771
\(960\) 0 0
\(961\) 7.78703 0.251195
\(962\) 0 0
\(963\) −8.70248 −0.280433
\(964\) 0 0
\(965\) −13.6158 −0.438309
\(966\) 0 0
\(967\) −3.07041 −0.0987377 −0.0493689 0.998781i \(-0.515721\pi\)
−0.0493689 + 0.998781i \(0.515721\pi\)
\(968\) 0 0
\(969\) 0.0909984 0.00292329
\(970\) 0 0
\(971\) 26.1214 0.838275 0.419137 0.907923i \(-0.362333\pi\)
0.419137 + 0.907923i \(0.362333\pi\)
\(972\) 0 0
\(973\) −11.1496 −0.357440
\(974\) 0 0
\(975\) −0.378736 −0.0121293
\(976\) 0 0
\(977\) 22.7437 0.727634 0.363817 0.931470i \(-0.381473\pi\)
0.363817 + 0.931470i \(0.381473\pi\)
\(978\) 0 0
\(979\) −0.836034 −0.0267198
\(980\) 0 0
\(981\) 10.5649 0.337311
\(982\) 0 0
\(983\) 11.1823 0.356660 0.178330 0.983971i \(-0.442931\pi\)
0.178330 + 0.983971i \(0.442931\pi\)
\(984\) 0 0
\(985\) 17.2022 0.548108
\(986\) 0 0
\(987\) −1.39534 −0.0444143
\(988\) 0 0
\(989\) 0.245816 0.00781649
\(990\) 0 0
\(991\) −39.2303 −1.24619 −0.623096 0.782145i \(-0.714125\pi\)
−0.623096 + 0.782145i \(0.714125\pi\)
\(992\) 0 0
\(993\) 1.10622 0.0351048
\(994\) 0 0
\(995\) −19.4704 −0.617253
\(996\) 0 0
\(997\) 44.3720 1.40527 0.702637 0.711549i \(-0.252006\pi\)
0.702637 + 0.711549i \(0.252006\pi\)
\(998\) 0 0
\(999\) 0.260060 0.00822793
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 \(a_p\))