Properties

Label 8020.2.a.c.1.8
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 1.8
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.53415 q^{3}\) \(-1.00000 q^{5}\) \(+0.759833 q^{7}\) \(-0.646394 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.53415 q^{3}\) \(-1.00000 q^{5}\) \(+0.759833 q^{7}\) \(-0.646394 q^{9}\) \(-2.75985 q^{11}\) \(-4.86468 q^{13}\) \(+1.53415 q^{15}\) \(+0.830882 q^{17}\) \(-3.43525 q^{19}\) \(-1.16570 q^{21}\) \(-1.12980 q^{23}\) \(+1.00000 q^{25}\) \(+5.59410 q^{27}\) \(+9.75363 q^{29}\) \(+8.03408 q^{31}\) \(+4.23402 q^{33}\) \(-0.759833 q^{35}\) \(+5.57488 q^{37}\) \(+7.46314 q^{39}\) \(-4.04451 q^{41}\) \(+6.17253 q^{43}\) \(+0.646394 q^{45}\) \(+3.41376 q^{47}\) \(-6.42265 q^{49}\) \(-1.27469 q^{51}\) \(+5.80300 q^{53}\) \(+2.75985 q^{55}\) \(+5.27017 q^{57}\) \(+0.686320 q^{59}\) \(+7.65711 q^{61}\) \(-0.491151 q^{63}\) \(+4.86468 q^{65}\) \(-0.747223 q^{67}\) \(+1.73328 q^{69}\) \(-11.8382 q^{71}\) \(-2.72697 q^{73}\) \(-1.53415 q^{75}\) \(-2.09703 q^{77}\) \(+14.7572 q^{79}\) \(-6.64299 q^{81}\) \(-10.0970 q^{83}\) \(-0.830882 q^{85}\) \(-14.9635 q^{87}\) \(+0.776847 q^{89}\) \(-3.69635 q^{91}\) \(-12.3255 q^{93}\) \(+3.43525 q^{95}\) \(-1.20228 q^{97}\) \(+1.78395 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.53415 −0.885740 −0.442870 0.896586i \(-0.646040\pi\)
−0.442870 + 0.896586i \(0.646040\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.759833 0.287190 0.143595 0.989637i \(-0.454134\pi\)
0.143595 + 0.989637i \(0.454134\pi\)
\(8\) 0 0
\(9\) −0.646394 −0.215465
\(10\) 0 0
\(11\) −2.75985 −0.832127 −0.416064 0.909335i \(-0.636591\pi\)
−0.416064 + 0.909335i \(0.636591\pi\)
\(12\) 0 0
\(13\) −4.86468 −1.34922 −0.674610 0.738174i \(-0.735688\pi\)
−0.674610 + 0.738174i \(0.735688\pi\)
\(14\) 0 0
\(15\) 1.53415 0.396115
\(16\) 0 0
\(17\) 0.830882 0.201518 0.100759 0.994911i \(-0.467873\pi\)
0.100759 + 0.994911i \(0.467873\pi\)
\(18\) 0 0
\(19\) −3.43525 −0.788099 −0.394050 0.919089i \(-0.628926\pi\)
−0.394050 + 0.919089i \(0.628926\pi\)
\(20\) 0 0
\(21\) −1.16570 −0.254376
\(22\) 0 0
\(23\) −1.12980 −0.235579 −0.117790 0.993039i \(-0.537581\pi\)
−0.117790 + 0.993039i \(0.537581\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.59410 1.07659
\(28\) 0 0
\(29\) 9.75363 1.81120 0.905602 0.424130i \(-0.139420\pi\)
0.905602 + 0.424130i \(0.139420\pi\)
\(30\) 0 0
\(31\) 8.03408 1.44296 0.721482 0.692434i \(-0.243461\pi\)
0.721482 + 0.692434i \(0.243461\pi\)
\(32\) 0 0
\(33\) 4.23402 0.737049
\(34\) 0 0
\(35\) −0.759833 −0.128435
\(36\) 0 0
\(37\) 5.57488 0.916505 0.458252 0.888822i \(-0.348476\pi\)
0.458252 + 0.888822i \(0.348476\pi\)
\(38\) 0 0
\(39\) 7.46314 1.19506
\(40\) 0 0
\(41\) −4.04451 −0.631646 −0.315823 0.948818i \(-0.602281\pi\)
−0.315823 + 0.948818i \(0.602281\pi\)
\(42\) 0 0
\(43\) 6.17253 0.941302 0.470651 0.882320i \(-0.344019\pi\)
0.470651 + 0.882320i \(0.344019\pi\)
\(44\) 0 0
\(45\) 0.646394 0.0963587
\(46\) 0 0
\(47\) 3.41376 0.497948 0.248974 0.968510i \(-0.419907\pi\)
0.248974 + 0.968510i \(0.419907\pi\)
\(48\) 0 0
\(49\) −6.42265 −0.917522
\(50\) 0 0
\(51\) −1.27469 −0.178493
\(52\) 0 0
\(53\) 5.80300 0.797103 0.398552 0.917146i \(-0.369513\pi\)
0.398552 + 0.917146i \(0.369513\pi\)
\(54\) 0 0
\(55\) 2.75985 0.372139
\(56\) 0 0
\(57\) 5.27017 0.698051
\(58\) 0 0
\(59\) 0.686320 0.0893513 0.0446756 0.999002i \(-0.485775\pi\)
0.0446756 + 0.999002i \(0.485775\pi\)
\(60\) 0 0
\(61\) 7.65711 0.980393 0.490196 0.871612i \(-0.336925\pi\)
0.490196 + 0.871612i \(0.336925\pi\)
\(62\) 0 0
\(63\) −0.491151 −0.0618793
\(64\) 0 0
\(65\) 4.86468 0.603390
\(66\) 0 0
\(67\) −0.747223 −0.0912879 −0.0456439 0.998958i \(-0.514534\pi\)
−0.0456439 + 0.998958i \(0.514534\pi\)
\(68\) 0 0
\(69\) 1.73328 0.208662
\(70\) 0 0
\(71\) −11.8382 −1.40493 −0.702465 0.711718i \(-0.747917\pi\)
−0.702465 + 0.711718i \(0.747917\pi\)
\(72\) 0 0
\(73\) −2.72697 −0.319168 −0.159584 0.987184i \(-0.551015\pi\)
−0.159584 + 0.987184i \(0.551015\pi\)
\(74\) 0 0
\(75\) −1.53415 −0.177148
\(76\) 0 0
\(77\) −2.09703 −0.238979
\(78\) 0 0
\(79\) 14.7572 1.66032 0.830159 0.557526i \(-0.188249\pi\)
0.830159 + 0.557526i \(0.188249\pi\)
\(80\) 0 0
\(81\) −6.64299 −0.738111
\(82\) 0 0
\(83\) −10.0970 −1.10829 −0.554145 0.832420i \(-0.686955\pi\)
−0.554145 + 0.832420i \(0.686955\pi\)
\(84\) 0 0
\(85\) −0.830882 −0.0901218
\(86\) 0 0
\(87\) −14.9635 −1.60426
\(88\) 0 0
\(89\) 0.776847 0.0823456 0.0411728 0.999152i \(-0.486891\pi\)
0.0411728 + 0.999152i \(0.486891\pi\)
\(90\) 0 0
\(91\) −3.69635 −0.387483
\(92\) 0 0
\(93\) −12.3255 −1.27809
\(94\) 0 0
\(95\) 3.43525 0.352449
\(96\) 0 0
\(97\) −1.20228 −0.122073 −0.0610365 0.998136i \(-0.519441\pi\)
−0.0610365 + 0.998136i \(0.519441\pi\)
\(98\) 0 0
\(99\) 1.78395 0.179294
\(100\) 0 0
\(101\) 6.46240 0.643032 0.321516 0.946904i \(-0.395808\pi\)
0.321516 + 0.946904i \(0.395808\pi\)
\(102\) 0 0
\(103\) −3.29037 −0.324209 −0.162105 0.986774i \(-0.551828\pi\)
−0.162105 + 0.986774i \(0.551828\pi\)
\(104\) 0 0
\(105\) 1.16570 0.113760
\(106\) 0 0
\(107\) −5.44880 −0.526755 −0.263378 0.964693i \(-0.584837\pi\)
−0.263378 + 0.964693i \(0.584837\pi\)
\(108\) 0 0
\(109\) −0.521292 −0.0499307 −0.0249653 0.999688i \(-0.507948\pi\)
−0.0249653 + 0.999688i \(0.507948\pi\)
\(110\) 0 0
\(111\) −8.55268 −0.811785
\(112\) 0 0
\(113\) −7.94408 −0.747316 −0.373658 0.927567i \(-0.621897\pi\)
−0.373658 + 0.927567i \(0.621897\pi\)
\(114\) 0 0
\(115\) 1.12980 0.105354
\(116\) 0 0
\(117\) 3.14450 0.290709
\(118\) 0 0
\(119\) 0.631332 0.0578741
\(120\) 0 0
\(121\) −3.38321 −0.307564
\(122\) 0 0
\(123\) 6.20487 0.559474
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.24379 −0.287840 −0.143920 0.989589i \(-0.545971\pi\)
−0.143920 + 0.989589i \(0.545971\pi\)
\(128\) 0 0
\(129\) −9.46956 −0.833749
\(130\) 0 0
\(131\) −9.24112 −0.807400 −0.403700 0.914891i \(-0.632276\pi\)
−0.403700 + 0.914891i \(0.632276\pi\)
\(132\) 0 0
\(133\) −2.61021 −0.226334
\(134\) 0 0
\(135\) −5.59410 −0.481464
\(136\) 0 0
\(137\) −15.6925 −1.34070 −0.670349 0.742046i \(-0.733856\pi\)
−0.670349 + 0.742046i \(0.733856\pi\)
\(138\) 0 0
\(139\) 4.81186 0.408137 0.204069 0.978957i \(-0.434583\pi\)
0.204069 + 0.978957i \(0.434583\pi\)
\(140\) 0 0
\(141\) −5.23721 −0.441053
\(142\) 0 0
\(143\) 13.4258 1.12272
\(144\) 0 0
\(145\) −9.75363 −0.809995
\(146\) 0 0
\(147\) 9.85329 0.812686
\(148\) 0 0
\(149\) −5.22558 −0.428096 −0.214048 0.976823i \(-0.568665\pi\)
−0.214048 + 0.976823i \(0.568665\pi\)
\(150\) 0 0
\(151\) −13.9772 −1.13745 −0.568723 0.822529i \(-0.692562\pi\)
−0.568723 + 0.822529i \(0.692562\pi\)
\(152\) 0 0
\(153\) −0.537077 −0.0434201
\(154\) 0 0
\(155\) −8.03408 −0.645313
\(156\) 0 0
\(157\) 13.2320 1.05603 0.528013 0.849236i \(-0.322937\pi\)
0.528013 + 0.849236i \(0.322937\pi\)
\(158\) 0 0
\(159\) −8.90265 −0.706026
\(160\) 0 0
\(161\) −0.858459 −0.0676560
\(162\) 0 0
\(163\) −7.04005 −0.551419 −0.275710 0.961241i \(-0.588913\pi\)
−0.275710 + 0.961241i \(0.588913\pi\)
\(164\) 0 0
\(165\) −4.23402 −0.329618
\(166\) 0 0
\(167\) 13.0422 1.00924 0.504619 0.863342i \(-0.331633\pi\)
0.504619 + 0.863342i \(0.331633\pi\)
\(168\) 0 0
\(169\) 10.6652 0.820396
\(170\) 0 0
\(171\) 2.22052 0.169807
\(172\) 0 0
\(173\) 16.8374 1.28012 0.640060 0.768325i \(-0.278909\pi\)
0.640060 + 0.768325i \(0.278909\pi\)
\(174\) 0 0
\(175\) 0.759833 0.0574380
\(176\) 0 0
\(177\) −1.05292 −0.0791420
\(178\) 0 0
\(179\) 4.08801 0.305552 0.152776 0.988261i \(-0.451179\pi\)
0.152776 + 0.988261i \(0.451179\pi\)
\(180\) 0 0
\(181\) −20.0459 −1.49000 −0.745000 0.667064i \(-0.767551\pi\)
−0.745000 + 0.667064i \(0.767551\pi\)
\(182\) 0 0
\(183\) −11.7471 −0.868373
\(184\) 0 0
\(185\) −5.57488 −0.409873
\(186\) 0 0
\(187\) −2.29311 −0.167689
\(188\) 0 0
\(189\) 4.25059 0.309185
\(190\) 0 0
\(191\) 11.6572 0.843487 0.421743 0.906715i \(-0.361418\pi\)
0.421743 + 0.906715i \(0.361418\pi\)
\(192\) 0 0
\(193\) −17.4242 −1.25422 −0.627109 0.778931i \(-0.715762\pi\)
−0.627109 + 0.778931i \(0.715762\pi\)
\(194\) 0 0
\(195\) −7.46314 −0.534447
\(196\) 0 0
\(197\) −3.97131 −0.282944 −0.141472 0.989942i \(-0.545184\pi\)
−0.141472 + 0.989942i \(0.545184\pi\)
\(198\) 0 0
\(199\) −13.8110 −0.979035 −0.489517 0.871994i \(-0.662827\pi\)
−0.489517 + 0.871994i \(0.662827\pi\)
\(200\) 0 0
\(201\) 1.14635 0.0808573
\(202\) 0 0
\(203\) 7.41113 0.520159
\(204\) 0 0
\(205\) 4.04451 0.282481
\(206\) 0 0
\(207\) 0.730295 0.0507590
\(208\) 0 0
\(209\) 9.48078 0.655799
\(210\) 0 0
\(211\) −3.28172 −0.225923 −0.112962 0.993599i \(-0.536034\pi\)
−0.112962 + 0.993599i \(0.536034\pi\)
\(212\) 0 0
\(213\) 18.1615 1.24440
\(214\) 0 0
\(215\) −6.17253 −0.420963
\(216\) 0 0
\(217\) 6.10456 0.414405
\(218\) 0 0
\(219\) 4.18358 0.282700
\(220\) 0 0
\(221\) −4.04198 −0.271893
\(222\) 0 0
\(223\) 18.7777 1.25745 0.628725 0.777628i \(-0.283577\pi\)
0.628725 + 0.777628i \(0.283577\pi\)
\(224\) 0 0
\(225\) −0.646394 −0.0430929
\(226\) 0 0
\(227\) 11.9728 0.794662 0.397331 0.917675i \(-0.369936\pi\)
0.397331 + 0.917675i \(0.369936\pi\)
\(228\) 0 0
\(229\) −23.4706 −1.55098 −0.775491 0.631358i \(-0.782498\pi\)
−0.775491 + 0.631358i \(0.782498\pi\)
\(230\) 0 0
\(231\) 3.21715 0.211673
\(232\) 0 0
\(233\) −8.02403 −0.525672 −0.262836 0.964841i \(-0.584658\pi\)
−0.262836 + 0.964841i \(0.584658\pi\)
\(234\) 0 0
\(235\) −3.41376 −0.222689
\(236\) 0 0
\(237\) −22.6398 −1.47061
\(238\) 0 0
\(239\) 12.8059 0.828344 0.414172 0.910199i \(-0.364071\pi\)
0.414172 + 0.910199i \(0.364071\pi\)
\(240\) 0 0
\(241\) −22.4734 −1.44764 −0.723818 0.689991i \(-0.757614\pi\)
−0.723818 + 0.689991i \(0.757614\pi\)
\(242\) 0 0
\(243\) −6.59098 −0.422812
\(244\) 0 0
\(245\) 6.42265 0.410328
\(246\) 0 0
\(247\) 16.7114 1.06332
\(248\) 0 0
\(249\) 15.4903 0.981656
\(250\) 0 0
\(251\) −5.19371 −0.327824 −0.163912 0.986475i \(-0.552411\pi\)
−0.163912 + 0.986475i \(0.552411\pi\)
\(252\) 0 0
\(253\) 3.11808 0.196032
\(254\) 0 0
\(255\) 1.27469 0.0798245
\(256\) 0 0
\(257\) 19.3741 1.20852 0.604262 0.796785i \(-0.293468\pi\)
0.604262 + 0.796785i \(0.293468\pi\)
\(258\) 0 0
\(259\) 4.23598 0.263211
\(260\) 0 0
\(261\) −6.30468 −0.390250
\(262\) 0 0
\(263\) −10.7948 −0.665635 −0.332817 0.942991i \(-0.607999\pi\)
−0.332817 + 0.942991i \(0.607999\pi\)
\(264\) 0 0
\(265\) −5.80300 −0.356475
\(266\) 0 0
\(267\) −1.19180 −0.0729368
\(268\) 0 0
\(269\) 3.85567 0.235084 0.117542 0.993068i \(-0.462498\pi\)
0.117542 + 0.993068i \(0.462498\pi\)
\(270\) 0 0
\(271\) 28.3032 1.71930 0.859650 0.510884i \(-0.170682\pi\)
0.859650 + 0.510884i \(0.170682\pi\)
\(272\) 0 0
\(273\) 5.67074 0.343209
\(274\) 0 0
\(275\) −2.75985 −0.166425
\(276\) 0 0
\(277\) 31.7035 1.90488 0.952441 0.304724i \(-0.0985641\pi\)
0.952441 + 0.304724i \(0.0985641\pi\)
\(278\) 0 0
\(279\) −5.19318 −0.310907
\(280\) 0 0
\(281\) −19.1110 −1.14007 −0.570034 0.821621i \(-0.693070\pi\)
−0.570034 + 0.821621i \(0.693070\pi\)
\(282\) 0 0
\(283\) 28.9062 1.71829 0.859147 0.511729i \(-0.170995\pi\)
0.859147 + 0.511729i \(0.170995\pi\)
\(284\) 0 0
\(285\) −5.27017 −0.312178
\(286\) 0 0
\(287\) −3.07315 −0.181402
\(288\) 0 0
\(289\) −16.3096 −0.959390
\(290\) 0 0
\(291\) 1.84447 0.108125
\(292\) 0 0
\(293\) 23.4457 1.36971 0.684857 0.728677i \(-0.259865\pi\)
0.684857 + 0.728677i \(0.259865\pi\)
\(294\) 0 0
\(295\) −0.686320 −0.0399591
\(296\) 0 0
\(297\) −15.4389 −0.895856
\(298\) 0 0
\(299\) 5.49612 0.317849
\(300\) 0 0
\(301\) 4.69009 0.270332
\(302\) 0 0
\(303\) −9.91427 −0.569560
\(304\) 0 0
\(305\) −7.65711 −0.438445
\(306\) 0 0
\(307\) 13.3216 0.760305 0.380153 0.924924i \(-0.375871\pi\)
0.380153 + 0.924924i \(0.375871\pi\)
\(308\) 0 0
\(309\) 5.04790 0.287165
\(310\) 0 0
\(311\) −22.8500 −1.29570 −0.647851 0.761767i \(-0.724332\pi\)
−0.647851 + 0.761767i \(0.724332\pi\)
\(312\) 0 0
\(313\) −14.0076 −0.791759 −0.395879 0.918303i \(-0.629560\pi\)
−0.395879 + 0.918303i \(0.629560\pi\)
\(314\) 0 0
\(315\) 0.491151 0.0276732
\(316\) 0 0
\(317\) 10.7526 0.603924 0.301962 0.953320i \(-0.402358\pi\)
0.301962 + 0.953320i \(0.402358\pi\)
\(318\) 0 0
\(319\) −26.9186 −1.50715
\(320\) 0 0
\(321\) 8.35926 0.466568
\(322\) 0 0
\(323\) −2.85428 −0.158817
\(324\) 0 0
\(325\) −4.86468 −0.269844
\(326\) 0 0
\(327\) 0.799738 0.0442256
\(328\) 0 0
\(329\) 2.59389 0.143006
\(330\) 0 0
\(331\) 15.8279 0.869979 0.434989 0.900436i \(-0.356752\pi\)
0.434989 + 0.900436i \(0.356752\pi\)
\(332\) 0 0
\(333\) −3.60357 −0.197474
\(334\) 0 0
\(335\) 0.747223 0.0408252
\(336\) 0 0
\(337\) −35.6496 −1.94196 −0.970979 0.239164i \(-0.923127\pi\)
−0.970979 + 0.239164i \(0.923127\pi\)
\(338\) 0 0
\(339\) 12.1874 0.661928
\(340\) 0 0
\(341\) −22.1729 −1.20073
\(342\) 0 0
\(343\) −10.1990 −0.550693
\(344\) 0 0
\(345\) −1.73328 −0.0933165
\(346\) 0 0
\(347\) −27.9865 −1.50239 −0.751196 0.660079i \(-0.770523\pi\)
−0.751196 + 0.660079i \(0.770523\pi\)
\(348\) 0 0
\(349\) 31.2666 1.67366 0.836831 0.547461i \(-0.184405\pi\)
0.836831 + 0.547461i \(0.184405\pi\)
\(350\) 0 0
\(351\) −27.2135 −1.45255
\(352\) 0 0
\(353\) 13.7901 0.733973 0.366986 0.930226i \(-0.380390\pi\)
0.366986 + 0.930226i \(0.380390\pi\)
\(354\) 0 0
\(355\) 11.8382 0.628304
\(356\) 0 0
\(357\) −0.968555 −0.0512614
\(358\) 0 0
\(359\) −10.5760 −0.558180 −0.279090 0.960265i \(-0.590033\pi\)
−0.279090 + 0.960265i \(0.590033\pi\)
\(360\) 0 0
\(361\) −7.19909 −0.378900
\(362\) 0 0
\(363\) 5.19033 0.272422
\(364\) 0 0
\(365\) 2.72697 0.142736
\(366\) 0 0
\(367\) 6.01748 0.314110 0.157055 0.987590i \(-0.449800\pi\)
0.157055 + 0.987590i \(0.449800\pi\)
\(368\) 0 0
\(369\) 2.61434 0.136097
\(370\) 0 0
\(371\) 4.40931 0.228920
\(372\) 0 0
\(373\) −11.1189 −0.575715 −0.287858 0.957673i \(-0.592943\pi\)
−0.287858 + 0.957673i \(0.592943\pi\)
\(374\) 0 0
\(375\) 1.53415 0.0792230
\(376\) 0 0
\(377\) −47.4483 −2.44371
\(378\) 0 0
\(379\) −27.3547 −1.40512 −0.702559 0.711626i \(-0.747959\pi\)
−0.702559 + 0.711626i \(0.747959\pi\)
\(380\) 0 0
\(381\) 4.97646 0.254952
\(382\) 0 0
\(383\) −35.7722 −1.82788 −0.913938 0.405855i \(-0.866974\pi\)
−0.913938 + 0.405855i \(0.866974\pi\)
\(384\) 0 0
\(385\) 2.09703 0.106874
\(386\) 0 0
\(387\) −3.98988 −0.202817
\(388\) 0 0
\(389\) −30.2658 −1.53454 −0.767269 0.641325i \(-0.778385\pi\)
−0.767269 + 0.641325i \(0.778385\pi\)
\(390\) 0 0
\(391\) −0.938729 −0.0474736
\(392\) 0 0
\(393\) 14.1772 0.715147
\(394\) 0 0
\(395\) −14.7572 −0.742517
\(396\) 0 0
\(397\) −13.6559 −0.685370 −0.342685 0.939450i \(-0.611336\pi\)
−0.342685 + 0.939450i \(0.611336\pi\)
\(398\) 0 0
\(399\) 4.00445 0.200473
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −39.0833 −1.94688
\(404\) 0 0
\(405\) 6.64299 0.330093
\(406\) 0 0
\(407\) −15.3859 −0.762649
\(408\) 0 0
\(409\) 3.69437 0.182675 0.0913373 0.995820i \(-0.470886\pi\)
0.0913373 + 0.995820i \(0.470886\pi\)
\(410\) 0 0
\(411\) 24.0746 1.18751
\(412\) 0 0
\(413\) 0.521489 0.0256608
\(414\) 0 0
\(415\) 10.0970 0.495642
\(416\) 0 0
\(417\) −7.38211 −0.361503
\(418\) 0 0
\(419\) 8.55113 0.417750 0.208875 0.977942i \(-0.433020\pi\)
0.208875 + 0.977942i \(0.433020\pi\)
\(420\) 0 0
\(421\) −16.6874 −0.813294 −0.406647 0.913585i \(-0.633302\pi\)
−0.406647 + 0.913585i \(0.633302\pi\)
\(422\) 0 0
\(423\) −2.20663 −0.107290
\(424\) 0 0
\(425\) 0.830882 0.0403037
\(426\) 0 0
\(427\) 5.81813 0.281559
\(428\) 0 0
\(429\) −20.5972 −0.994441
\(430\) 0 0
\(431\) −18.8109 −0.906089 −0.453045 0.891488i \(-0.649662\pi\)
−0.453045 + 0.891488i \(0.649662\pi\)
\(432\) 0 0
\(433\) −15.7460 −0.756703 −0.378352 0.925662i \(-0.623509\pi\)
−0.378352 + 0.925662i \(0.623509\pi\)
\(434\) 0 0
\(435\) 14.9635 0.717445
\(436\) 0 0
\(437\) 3.88114 0.185660
\(438\) 0 0
\(439\) −0.595803 −0.0284361 −0.0142181 0.999899i \(-0.504526\pi\)
−0.0142181 + 0.999899i \(0.504526\pi\)
\(440\) 0 0
\(441\) 4.15156 0.197693
\(442\) 0 0
\(443\) −3.15079 −0.149698 −0.0748492 0.997195i \(-0.523848\pi\)
−0.0748492 + 0.997195i \(0.523848\pi\)
\(444\) 0 0
\(445\) −0.776847 −0.0368261
\(446\) 0 0
\(447\) 8.01681 0.379182
\(448\) 0 0
\(449\) 28.8574 1.36187 0.680933 0.732346i \(-0.261575\pi\)
0.680933 + 0.732346i \(0.261575\pi\)
\(450\) 0 0
\(451\) 11.1623 0.525610
\(452\) 0 0
\(453\) 21.4430 1.00748
\(454\) 0 0
\(455\) 3.69635 0.173288
\(456\) 0 0
\(457\) 0.990165 0.0463179 0.0231590 0.999732i \(-0.492628\pi\)
0.0231590 + 0.999732i \(0.492628\pi\)
\(458\) 0 0
\(459\) 4.64804 0.216952
\(460\) 0 0
\(461\) 0.967691 0.0450699 0.0225349 0.999746i \(-0.492826\pi\)
0.0225349 + 0.999746i \(0.492826\pi\)
\(462\) 0 0
\(463\) 20.3287 0.944755 0.472378 0.881396i \(-0.343396\pi\)
0.472378 + 0.881396i \(0.343396\pi\)
\(464\) 0 0
\(465\) 12.3255 0.571579
\(466\) 0 0
\(467\) −38.8600 −1.79823 −0.899114 0.437714i \(-0.855788\pi\)
−0.899114 + 0.437714i \(0.855788\pi\)
\(468\) 0 0
\(469\) −0.567765 −0.0262170
\(470\) 0 0
\(471\) −20.2998 −0.935365
\(472\) 0 0
\(473\) −17.0353 −0.783283
\(474\) 0 0
\(475\) −3.43525 −0.157620
\(476\) 0 0
\(477\) −3.75102 −0.171747
\(478\) 0 0
\(479\) −1.66519 −0.0760844 −0.0380422 0.999276i \(-0.512112\pi\)
−0.0380422 + 0.999276i \(0.512112\pi\)
\(480\) 0 0
\(481\) −27.1200 −1.23657
\(482\) 0 0
\(483\) 1.31700 0.0599257
\(484\) 0 0
\(485\) 1.20228 0.0545927
\(486\) 0 0
\(487\) 4.83758 0.219212 0.109606 0.993975i \(-0.465041\pi\)
0.109606 + 0.993975i \(0.465041\pi\)
\(488\) 0 0
\(489\) 10.8005 0.488414
\(490\) 0 0
\(491\) 31.0655 1.40197 0.700984 0.713177i \(-0.252745\pi\)
0.700984 + 0.713177i \(0.252745\pi\)
\(492\) 0 0
\(493\) 8.10411 0.364991
\(494\) 0 0
\(495\) −1.78395 −0.0801827
\(496\) 0 0
\(497\) −8.99502 −0.403482
\(498\) 0 0
\(499\) 22.5844 1.01102 0.505509 0.862821i \(-0.331305\pi\)
0.505509 + 0.862821i \(0.331305\pi\)
\(500\) 0 0
\(501\) −20.0087 −0.893923
\(502\) 0 0
\(503\) 20.1548 0.898660 0.449330 0.893366i \(-0.351663\pi\)
0.449330 + 0.893366i \(0.351663\pi\)
\(504\) 0 0
\(505\) −6.46240 −0.287573
\(506\) 0 0
\(507\) −16.3619 −0.726658
\(508\) 0 0
\(509\) −28.5080 −1.26359 −0.631797 0.775134i \(-0.717682\pi\)
−0.631797 + 0.775134i \(0.717682\pi\)
\(510\) 0 0
\(511\) −2.07204 −0.0916618
\(512\) 0 0
\(513\) −19.2171 −0.848456
\(514\) 0 0
\(515\) 3.29037 0.144991
\(516\) 0 0
\(517\) −9.42148 −0.414356
\(518\) 0 0
\(519\) −25.8310 −1.13385
\(520\) 0 0
\(521\) −11.3868 −0.498866 −0.249433 0.968392i \(-0.580244\pi\)
−0.249433 + 0.968392i \(0.580244\pi\)
\(522\) 0 0
\(523\) −13.3107 −0.582036 −0.291018 0.956718i \(-0.593994\pi\)
−0.291018 + 0.956718i \(0.593994\pi\)
\(524\) 0 0
\(525\) −1.16570 −0.0508751
\(526\) 0 0
\(527\) 6.67537 0.290784
\(528\) 0 0
\(529\) −21.7236 −0.944502
\(530\) 0 0
\(531\) −0.443633 −0.0192520
\(532\) 0 0
\(533\) 19.6753 0.852230
\(534\) 0 0
\(535\) 5.44880 0.235572
\(536\) 0 0
\(537\) −6.27160 −0.270640
\(538\) 0 0
\(539\) 17.7256 0.763495
\(540\) 0 0
\(541\) 2.85131 0.122587 0.0612936 0.998120i \(-0.480477\pi\)
0.0612936 + 0.998120i \(0.480477\pi\)
\(542\) 0 0
\(543\) 30.7534 1.31975
\(544\) 0 0
\(545\) 0.521292 0.0223297
\(546\) 0 0
\(547\) 25.4604 1.08861 0.544305 0.838887i \(-0.316793\pi\)
0.544305 + 0.838887i \(0.316793\pi\)
\(548\) 0 0
\(549\) −4.94951 −0.211240
\(550\) 0 0
\(551\) −33.5061 −1.42741
\(552\) 0 0
\(553\) 11.2130 0.476827
\(554\) 0 0
\(555\) 8.55268 0.363041
\(556\) 0 0
\(557\) −8.97044 −0.380090 −0.190045 0.981775i \(-0.560863\pi\)
−0.190045 + 0.981775i \(0.560863\pi\)
\(558\) 0 0
\(559\) −30.0274 −1.27002
\(560\) 0 0
\(561\) 3.51797 0.148529
\(562\) 0 0
\(563\) 27.9367 1.17739 0.588695 0.808355i \(-0.299642\pi\)
0.588695 + 0.808355i \(0.299642\pi\)
\(564\) 0 0
\(565\) 7.94408 0.334210
\(566\) 0 0
\(567\) −5.04757 −0.211978
\(568\) 0 0
\(569\) −41.2323 −1.72855 −0.864274 0.503021i \(-0.832222\pi\)
−0.864274 + 0.503021i \(0.832222\pi\)
\(570\) 0 0
\(571\) 39.1954 1.64028 0.820139 0.572164i \(-0.193896\pi\)
0.820139 + 0.572164i \(0.193896\pi\)
\(572\) 0 0
\(573\) −17.8839 −0.747110
\(574\) 0 0
\(575\) −1.12980 −0.0471159
\(576\) 0 0
\(577\) 38.7606 1.61363 0.806813 0.590807i \(-0.201190\pi\)
0.806813 + 0.590807i \(0.201190\pi\)
\(578\) 0 0
\(579\) 26.7312 1.11091
\(580\) 0 0
\(581\) −7.67203 −0.318290
\(582\) 0 0
\(583\) −16.0154 −0.663291
\(584\) 0 0
\(585\) −3.14450 −0.130009
\(586\) 0 0
\(587\) −22.5665 −0.931418 −0.465709 0.884938i \(-0.654201\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(588\) 0 0
\(589\) −27.5990 −1.13720
\(590\) 0 0
\(591\) 6.09257 0.250615
\(592\) 0 0
\(593\) 47.7257 1.95986 0.979929 0.199347i \(-0.0638820\pi\)
0.979929 + 0.199347i \(0.0638820\pi\)
\(594\) 0 0
\(595\) −0.631332 −0.0258821
\(596\) 0 0
\(597\) 21.1881 0.867170
\(598\) 0 0
\(599\) 28.1861 1.15165 0.575826 0.817572i \(-0.304681\pi\)
0.575826 + 0.817572i \(0.304681\pi\)
\(600\) 0 0
\(601\) −45.3474 −1.84976 −0.924880 0.380259i \(-0.875835\pi\)
−0.924880 + 0.380259i \(0.875835\pi\)
\(602\) 0 0
\(603\) 0.483000 0.0196693
\(604\) 0 0
\(605\) 3.38321 0.137547
\(606\) 0 0
\(607\) 28.2277 1.14573 0.572864 0.819651i \(-0.305832\pi\)
0.572864 + 0.819651i \(0.305832\pi\)
\(608\) 0 0
\(609\) −11.3698 −0.460726
\(610\) 0 0
\(611\) −16.6069 −0.671842
\(612\) 0 0
\(613\) −25.9000 −1.04609 −0.523046 0.852304i \(-0.675204\pi\)
−0.523046 + 0.852304i \(0.675204\pi\)
\(614\) 0 0
\(615\) −6.20487 −0.250204
\(616\) 0 0
\(617\) 0.401050 0.0161457 0.00807283 0.999967i \(-0.497430\pi\)
0.00807283 + 0.999967i \(0.497430\pi\)
\(618\) 0 0
\(619\) −25.8802 −1.04021 −0.520107 0.854101i \(-0.674108\pi\)
−0.520107 + 0.854101i \(0.674108\pi\)
\(620\) 0 0
\(621\) −6.32021 −0.253621
\(622\) 0 0
\(623\) 0.590274 0.0236488
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −14.5449 −0.580867
\(628\) 0 0
\(629\) 4.63207 0.184693
\(630\) 0 0
\(631\) 14.7018 0.585271 0.292636 0.956224i \(-0.405468\pi\)
0.292636 + 0.956224i \(0.405468\pi\)
\(632\) 0 0
\(633\) 5.03465 0.200109
\(634\) 0 0
\(635\) 3.24379 0.128726
\(636\) 0 0
\(637\) 31.2442 1.23794
\(638\) 0 0
\(639\) 7.65211 0.302713
\(640\) 0 0
\(641\) −34.8309 −1.37574 −0.687868 0.725836i \(-0.741453\pi\)
−0.687868 + 0.725836i \(0.741453\pi\)
\(642\) 0 0
\(643\) −2.39935 −0.0946213 −0.0473107 0.998880i \(-0.515065\pi\)
−0.0473107 + 0.998880i \(0.515065\pi\)
\(644\) 0 0
\(645\) 9.46956 0.372864
\(646\) 0 0
\(647\) −44.7501 −1.75931 −0.879653 0.475616i \(-0.842225\pi\)
−0.879653 + 0.475616i \(0.842225\pi\)
\(648\) 0 0
\(649\) −1.89414 −0.0743517
\(650\) 0 0
\(651\) −9.36529 −0.367055
\(652\) 0 0
\(653\) −13.7635 −0.538606 −0.269303 0.963056i \(-0.586793\pi\)
−0.269303 + 0.963056i \(0.586793\pi\)
\(654\) 0 0
\(655\) 9.24112 0.361080
\(656\) 0 0
\(657\) 1.76270 0.0687694
\(658\) 0 0
\(659\) −13.1460 −0.512096 −0.256048 0.966664i \(-0.582421\pi\)
−0.256048 + 0.966664i \(0.582421\pi\)
\(660\) 0 0
\(661\) −38.0880 −1.48145 −0.740726 0.671808i \(-0.765518\pi\)
−0.740726 + 0.671808i \(0.765518\pi\)
\(662\) 0 0
\(663\) 6.20099 0.240826
\(664\) 0 0
\(665\) 2.61021 0.101220
\(666\) 0 0
\(667\) −11.0196 −0.426682
\(668\) 0 0
\(669\) −28.8078 −1.11377
\(670\) 0 0
\(671\) −21.1325 −0.815812
\(672\) 0 0
\(673\) −5.93599 −0.228816 −0.114408 0.993434i \(-0.536497\pi\)
−0.114408 + 0.993434i \(0.536497\pi\)
\(674\) 0 0
\(675\) 5.59410 0.215317
\(676\) 0 0
\(677\) −3.80771 −0.146342 −0.0731712 0.997319i \(-0.523312\pi\)
−0.0731712 + 0.997319i \(0.523312\pi\)
\(678\) 0 0
\(679\) −0.913531 −0.0350581
\(680\) 0 0
\(681\) −18.3680 −0.703864
\(682\) 0 0
\(683\) 8.79800 0.336646 0.168323 0.985732i \(-0.446165\pi\)
0.168323 + 0.985732i \(0.446165\pi\)
\(684\) 0 0
\(685\) 15.6925 0.599579
\(686\) 0 0
\(687\) 36.0074 1.37377
\(688\) 0 0
\(689\) −28.2297 −1.07547
\(690\) 0 0
\(691\) 13.0002 0.494551 0.247276 0.968945i \(-0.420465\pi\)
0.247276 + 0.968945i \(0.420465\pi\)
\(692\) 0 0
\(693\) 1.35551 0.0514914
\(694\) 0 0
\(695\) −4.81186 −0.182524
\(696\) 0 0
\(697\) −3.36051 −0.127288
\(698\) 0 0
\(699\) 12.3100 0.465609
\(700\) 0 0
\(701\) −17.2602 −0.651910 −0.325955 0.945385i \(-0.605686\pi\)
−0.325955 + 0.945385i \(0.605686\pi\)
\(702\) 0 0
\(703\) −19.1511 −0.722297
\(704\) 0 0
\(705\) 5.23721 0.197245
\(706\) 0 0
\(707\) 4.91034 0.184672
\(708\) 0 0
\(709\) −11.0965 −0.416739 −0.208369 0.978050i \(-0.566816\pi\)
−0.208369 + 0.978050i \(0.566816\pi\)
\(710\) 0 0
\(711\) −9.53898 −0.357740
\(712\) 0 0
\(713\) −9.07690 −0.339932
\(714\) 0 0
\(715\) −13.4258 −0.502097
\(716\) 0 0
\(717\) −19.6461 −0.733697
\(718\) 0 0
\(719\) −27.0873 −1.01019 −0.505093 0.863065i \(-0.668542\pi\)
−0.505093 + 0.863065i \(0.668542\pi\)
\(720\) 0 0
\(721\) −2.50013 −0.0931097
\(722\) 0 0
\(723\) 34.4774 1.28223
\(724\) 0 0
\(725\) 9.75363 0.362241
\(726\) 0 0
\(727\) 36.4438 1.35163 0.675813 0.737074i \(-0.263793\pi\)
0.675813 + 0.737074i \(0.263793\pi\)
\(728\) 0 0
\(729\) 30.0405 1.11261
\(730\) 0 0
\(731\) 5.12864 0.189690
\(732\) 0 0
\(733\) −3.67189 −0.135624 −0.0678122 0.997698i \(-0.521602\pi\)
−0.0678122 + 0.997698i \(0.521602\pi\)
\(734\) 0 0
\(735\) −9.85329 −0.363444
\(736\) 0 0
\(737\) 2.06223 0.0759631
\(738\) 0 0
\(739\) 26.8919 0.989233 0.494617 0.869111i \(-0.335308\pi\)
0.494617 + 0.869111i \(0.335308\pi\)
\(740\) 0 0
\(741\) −25.6377 −0.941825
\(742\) 0 0
\(743\) −31.6345 −1.16056 −0.580279 0.814418i \(-0.697056\pi\)
−0.580279 + 0.814418i \(0.697056\pi\)
\(744\) 0 0
\(745\) 5.22558 0.191450
\(746\) 0 0
\(747\) 6.52663 0.238797
\(748\) 0 0
\(749\) −4.14018 −0.151279
\(750\) 0 0
\(751\) −25.7965 −0.941329 −0.470664 0.882312i \(-0.655986\pi\)
−0.470664 + 0.882312i \(0.655986\pi\)
\(752\) 0 0
\(753\) 7.96791 0.290367
\(754\) 0 0
\(755\) 13.9772 0.508682
\(756\) 0 0
\(757\) −8.21800 −0.298688 −0.149344 0.988785i \(-0.547716\pi\)
−0.149344 + 0.988785i \(0.547716\pi\)
\(758\) 0 0
\(759\) −4.78359 −0.173633
\(760\) 0 0
\(761\) −30.7715 −1.11547 −0.557733 0.830020i \(-0.688329\pi\)
−0.557733 + 0.830020i \(0.688329\pi\)
\(762\) 0 0
\(763\) −0.396095 −0.0143396
\(764\) 0 0
\(765\) 0.537077 0.0194180
\(766\) 0 0
\(767\) −3.33873 −0.120555
\(768\) 0 0
\(769\) −2.79781 −0.100892 −0.0504458 0.998727i \(-0.516064\pi\)
−0.0504458 + 0.998727i \(0.516064\pi\)
\(770\) 0 0
\(771\) −29.7228 −1.07044
\(772\) 0 0
\(773\) 18.1152 0.651559 0.325779 0.945446i \(-0.394373\pi\)
0.325779 + 0.945446i \(0.394373\pi\)
\(774\) 0 0
\(775\) 8.03408 0.288593
\(776\) 0 0
\(777\) −6.49861 −0.233136
\(778\) 0 0
\(779\) 13.8939 0.497800
\(780\) 0 0
\(781\) 32.6716 1.16908
\(782\) 0 0
\(783\) 54.5628 1.94992
\(784\) 0 0
\(785\) −13.2320 −0.472269
\(786\) 0 0
\(787\) 10.7805 0.384282 0.192141 0.981367i \(-0.438457\pi\)
0.192141 + 0.981367i \(0.438457\pi\)
\(788\) 0 0
\(789\) 16.5608 0.589580
\(790\) 0 0
\(791\) −6.03618 −0.214622
\(792\) 0 0
\(793\) −37.2494 −1.32277
\(794\) 0 0
\(795\) 8.90265 0.315744
\(796\) 0 0
\(797\) −0.891987 −0.0315958 −0.0157979 0.999875i \(-0.505029\pi\)
−0.0157979 + 0.999875i \(0.505029\pi\)
\(798\) 0 0
\(799\) 2.83643 0.100346
\(800\) 0 0
\(801\) −0.502149 −0.0177426
\(802\) 0 0
\(803\) 7.52605 0.265588
\(804\) 0 0
\(805\) 0.858459 0.0302567
\(806\) 0 0
\(807\) −5.91517 −0.208224
\(808\) 0 0
\(809\) −53.9355 −1.89627 −0.948135 0.317867i \(-0.897033\pi\)
−0.948135 + 0.317867i \(0.897033\pi\)
\(810\) 0 0
\(811\) 20.2727 0.711872 0.355936 0.934510i \(-0.384162\pi\)
0.355936 + 0.934510i \(0.384162\pi\)
\(812\) 0 0
\(813\) −43.4213 −1.52285
\(814\) 0 0
\(815\) 7.04005 0.246602
\(816\) 0 0
\(817\) −21.2041 −0.741839
\(818\) 0 0
\(819\) 2.38930 0.0834888
\(820\) 0 0
\(821\) 11.7045 0.408490 0.204245 0.978920i \(-0.434526\pi\)
0.204245 + 0.978920i \(0.434526\pi\)
\(822\) 0 0
\(823\) −6.24375 −0.217643 −0.108822 0.994061i \(-0.534708\pi\)
−0.108822 + 0.994061i \(0.534708\pi\)
\(824\) 0 0
\(825\) 4.23402 0.147410
\(826\) 0 0
\(827\) −20.8295 −0.724314 −0.362157 0.932117i \(-0.617960\pi\)
−0.362157 + 0.932117i \(0.617960\pi\)
\(828\) 0 0
\(829\) −31.3402 −1.08849 −0.544245 0.838926i \(-0.683184\pi\)
−0.544245 + 0.838926i \(0.683184\pi\)
\(830\) 0 0
\(831\) −48.6379 −1.68723
\(832\) 0 0
\(833\) −5.33647 −0.184898
\(834\) 0 0
\(835\) −13.0422 −0.451345
\(836\) 0 0
\(837\) 44.9435 1.55347
\(838\) 0 0
\(839\) 46.5853 1.60830 0.804151 0.594425i \(-0.202620\pi\)
0.804151 + 0.594425i \(0.202620\pi\)
\(840\) 0 0
\(841\) 66.1332 2.28046
\(842\) 0 0
\(843\) 29.3191 1.00980
\(844\) 0 0
\(845\) −10.6652 −0.366892
\(846\) 0 0
\(847\) −2.57067 −0.0883293
\(848\) 0 0
\(849\) −44.3463 −1.52196
\(850\) 0 0
\(851\) −6.29849 −0.215910
\(852\) 0 0
\(853\) 25.7874 0.882945 0.441472 0.897275i \(-0.354456\pi\)
0.441472 + 0.897275i \(0.354456\pi\)
\(854\) 0 0
\(855\) −2.22052 −0.0759402
\(856\) 0 0
\(857\) −31.3117 −1.06959 −0.534793 0.844983i \(-0.679610\pi\)
−0.534793 + 0.844983i \(0.679610\pi\)
\(858\) 0 0
\(859\) −2.00145 −0.0682887 −0.0341443 0.999417i \(-0.510871\pi\)
−0.0341443 + 0.999417i \(0.510871\pi\)
\(860\) 0 0
\(861\) 4.71467 0.160675
\(862\) 0 0
\(863\) −28.2136 −0.960402 −0.480201 0.877158i \(-0.659436\pi\)
−0.480201 + 0.877158i \(0.659436\pi\)
\(864\) 0 0
\(865\) −16.8374 −0.572487
\(866\) 0 0
\(867\) 25.0214 0.849770
\(868\) 0 0
\(869\) −40.7278 −1.38160
\(870\) 0 0
\(871\) 3.63501 0.123167
\(872\) 0 0
\(873\) 0.777145 0.0263024
\(874\) 0 0
\(875\) −0.759833 −0.0256871
\(876\) 0 0
\(877\) 53.4420 1.80461 0.902303 0.431102i \(-0.141875\pi\)
0.902303 + 0.431102i \(0.141875\pi\)
\(878\) 0 0
\(879\) −35.9692 −1.21321
\(880\) 0 0
\(881\) −32.6836 −1.10114 −0.550569 0.834790i \(-0.685589\pi\)
−0.550569 + 0.834790i \(0.685589\pi\)
\(882\) 0 0
\(883\) 53.8651 1.81271 0.906353 0.422521i \(-0.138855\pi\)
0.906353 + 0.422521i \(0.138855\pi\)
\(884\) 0 0
\(885\) 1.05292 0.0353934
\(886\) 0 0
\(887\) −21.7792 −0.731275 −0.365638 0.930757i \(-0.619149\pi\)
−0.365638 + 0.930757i \(0.619149\pi\)
\(888\) 0 0
\(889\) −2.46474 −0.0826648
\(890\) 0 0
\(891\) 18.3337 0.614202
\(892\) 0 0
\(893\) −11.7271 −0.392432
\(894\) 0 0
\(895\) −4.08801 −0.136647
\(896\) 0 0
\(897\) −8.43185 −0.281531
\(898\) 0 0
\(899\) 78.3614 2.61350
\(900\) 0 0
\(901\) 4.82160 0.160631
\(902\) 0 0
\(903\) −7.19529 −0.239444
\(904\) 0 0
\(905\) 20.0459 0.666348
\(906\) 0 0
\(907\) −33.0195 −1.09639 −0.548197 0.836349i \(-0.684686\pi\)
−0.548197 + 0.836349i \(0.684686\pi\)
\(908\) 0 0
\(909\) −4.17725 −0.138551
\(910\) 0 0
\(911\) −0.911206 −0.0301896 −0.0150948 0.999886i \(-0.504805\pi\)
−0.0150948 + 0.999886i \(0.504805\pi\)
\(912\) 0 0
\(913\) 27.8662 0.922238
\(914\) 0 0
\(915\) 11.7471 0.388348
\(916\) 0 0
\(917\) −7.02171 −0.231877
\(918\) 0 0
\(919\) 8.51531 0.280894 0.140447 0.990088i \(-0.455146\pi\)
0.140447 + 0.990088i \(0.455146\pi\)
\(920\) 0 0
\(921\) −20.4373 −0.673433
\(922\) 0 0
\(923\) 57.5889 1.89556
\(924\) 0 0
\(925\) 5.57488 0.183301
\(926\) 0 0
\(927\) 2.12687 0.0698556
\(928\) 0 0
\(929\) 29.6015 0.971195 0.485598 0.874182i \(-0.338602\pi\)
0.485598 + 0.874182i \(0.338602\pi\)
\(930\) 0 0
\(931\) 22.0634 0.723098
\(932\) 0 0
\(933\) 35.0552 1.14766
\(934\) 0 0
\(935\) 2.29311 0.0749928
\(936\) 0 0
\(937\) −4.12820 −0.134863 −0.0674313 0.997724i \(-0.521480\pi\)
−0.0674313 + 0.997724i \(0.521480\pi\)
\(938\) 0 0
\(939\) 21.4898 0.701292
\(940\) 0 0
\(941\) 8.36517 0.272697 0.136348 0.990661i \(-0.456463\pi\)
0.136348 + 0.990661i \(0.456463\pi\)
\(942\) 0 0
\(943\) 4.56948 0.148803
\(944\) 0 0
\(945\) −4.25059 −0.138272
\(946\) 0 0
\(947\) 49.6566 1.61362 0.806811 0.590810i \(-0.201192\pi\)
0.806811 + 0.590810i \(0.201192\pi\)
\(948\) 0 0
\(949\) 13.2659 0.430628
\(950\) 0 0
\(951\) −16.4960 −0.534920
\(952\) 0 0
\(953\) −46.3342 −1.50091 −0.750457 0.660920i \(-0.770166\pi\)
−0.750457 + 0.660920i \(0.770166\pi\)
\(954\) 0 0
\(955\) −11.6572 −0.377219
\(956\) 0 0
\(957\) 41.2971 1.33494
\(958\) 0 0
\(959\) −11.9237 −0.385035
\(960\) 0 0
\(961\) 33.5464 1.08214
\(962\) 0 0
\(963\) 3.52207 0.113497
\(964\) 0 0
\(965\) 17.4242 0.560904
\(966\) 0 0
\(967\) −12.3455 −0.397005 −0.198503 0.980100i \(-0.563608\pi\)
−0.198503 + 0.980100i \(0.563608\pi\)
\(968\) 0 0
\(969\) 4.37889 0.140670
\(970\) 0 0
\(971\) −44.2040 −1.41857 −0.709287 0.704920i \(-0.750983\pi\)
−0.709287 + 0.704920i \(0.750983\pi\)
\(972\) 0 0
\(973\) 3.65621 0.117213
\(974\) 0 0
\(975\) 7.46314 0.239012
\(976\) 0 0
\(977\) −47.6278 −1.52375 −0.761875 0.647724i \(-0.775721\pi\)
−0.761875 + 0.647724i \(0.775721\pi\)
\(978\) 0 0
\(979\) −2.14399 −0.0685221
\(980\) 0 0
\(981\) 0.336960 0.0107583
\(982\) 0 0
\(983\) 49.1756 1.56846 0.784229 0.620471i \(-0.213059\pi\)
0.784229 + 0.620471i \(0.213059\pi\)
\(984\) 0 0
\(985\) 3.97131 0.126536
\(986\) 0 0
\(987\) −3.97941 −0.126666
\(988\) 0 0
\(989\) −6.97372 −0.221751
\(990\) 0 0
\(991\) −11.9666 −0.380131 −0.190065 0.981771i \(-0.560870\pi\)
−0.190065 + 0.981771i \(0.560870\pi\)
\(992\) 0 0
\(993\) −24.2823 −0.770575
\(994\) 0 0
\(995\) 13.8110 0.437838
\(996\) 0 0
\(997\) −25.2431 −0.799456 −0.399728 0.916634i \(-0.630895\pi\)
−0.399728 + 0.916634i \(0.630895\pi\)
\(998\) 0 0
\(999\) 31.1865 0.986696
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 \(a_p\))