Properties

Label 8036.2.a.t.1.7
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.915292\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.915292 q^{3}\) \(-1.31004 q^{5}\) \(-2.16224 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.915292 q^{3}\) \(-1.31004 q^{5}\) \(-2.16224 q^{9}\) \(+2.72778 q^{11}\) \(+6.20323 q^{13}\) \(+1.19907 q^{15}\) \(-6.76678 q^{17}\) \(+5.15682 q^{19}\) \(+6.76186 q^{23}\) \(-3.28379 q^{25}\) \(+4.72496 q^{27}\) \(-6.37080 q^{29}\) \(+2.28883 q^{31}\) \(-2.49672 q^{33}\) \(+9.35867 q^{37}\) \(-5.67776 q^{39}\) \(-1.00000 q^{41}\) \(-6.74692 q^{43}\) \(+2.83262 q^{45}\) \(+8.15236 q^{47}\) \(+6.19357 q^{51}\) \(-12.5686 q^{53}\) \(-3.57351 q^{55}\) \(-4.72000 q^{57}\) \(+1.48363 q^{59}\) \(-2.36836 q^{61}\) \(-8.12648 q^{65}\) \(+2.61180 q^{67}\) \(-6.18908 q^{69}\) \(-1.28105 q^{71}\) \(+3.81398 q^{73}\) \(+3.00563 q^{75}\) \(+4.28357 q^{79}\) \(+2.16201 q^{81}\) \(-2.35962 q^{83}\) \(+8.86476 q^{85}\) \(+5.83114 q^{87}\) \(+3.98293 q^{89}\) \(-2.09495 q^{93}\) \(-6.75565 q^{95}\) \(-7.03488 q^{97}\) \(-5.89813 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.915292 −0.528444 −0.264222 0.964462i \(-0.585115\pi\)
−0.264222 + 0.964462i \(0.585115\pi\)
\(4\) 0 0
\(5\) −1.31004 −0.585868 −0.292934 0.956133i \(-0.594632\pi\)
−0.292934 + 0.956133i \(0.594632\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.16224 −0.720747
\(10\) 0 0
\(11\) 2.72778 0.822458 0.411229 0.911532i \(-0.365100\pi\)
0.411229 + 0.911532i \(0.365100\pi\)
\(12\) 0 0
\(13\) 6.20323 1.72047 0.860233 0.509902i \(-0.170318\pi\)
0.860233 + 0.509902i \(0.170318\pi\)
\(14\) 0 0
\(15\) 1.19907 0.309598
\(16\) 0 0
\(17\) −6.76678 −1.64118 −0.820592 0.571514i \(-0.806356\pi\)
−0.820592 + 0.571514i \(0.806356\pi\)
\(18\) 0 0
\(19\) 5.15682 1.18306 0.591528 0.806284i \(-0.298525\pi\)
0.591528 + 0.806284i \(0.298525\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.76186 1.40995 0.704973 0.709234i \(-0.250959\pi\)
0.704973 + 0.709234i \(0.250959\pi\)
\(24\) 0 0
\(25\) −3.28379 −0.656758
\(26\) 0 0
\(27\) 4.72496 0.909318
\(28\) 0 0
\(29\) −6.37080 −1.18303 −0.591514 0.806295i \(-0.701470\pi\)
−0.591514 + 0.806295i \(0.701470\pi\)
\(30\) 0 0
\(31\) 2.28883 0.411086 0.205543 0.978648i \(-0.434104\pi\)
0.205543 + 0.978648i \(0.434104\pi\)
\(32\) 0 0
\(33\) −2.49672 −0.434623
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.35867 1.53856 0.769278 0.638915i \(-0.220616\pi\)
0.769278 + 0.638915i \(0.220616\pi\)
\(38\) 0 0
\(39\) −5.67776 −0.909169
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −6.74692 −1.02890 −0.514448 0.857521i \(-0.672003\pi\)
−0.514448 + 0.857521i \(0.672003\pi\)
\(44\) 0 0
\(45\) 2.83262 0.422263
\(46\) 0 0
\(47\) 8.15236 1.18914 0.594572 0.804042i \(-0.297322\pi\)
0.594572 + 0.804042i \(0.297322\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 6.19357 0.867274
\(52\) 0 0
\(53\) −12.5686 −1.72643 −0.863215 0.504837i \(-0.831552\pi\)
−0.863215 + 0.504837i \(0.831552\pi\)
\(54\) 0 0
\(55\) −3.57351 −0.481852
\(56\) 0 0
\(57\) −4.72000 −0.625179
\(58\) 0 0
\(59\) 1.48363 0.193152 0.0965759 0.995326i \(-0.469211\pi\)
0.0965759 + 0.995326i \(0.469211\pi\)
\(60\) 0 0
\(61\) −2.36836 −0.303237 −0.151619 0.988439i \(-0.548449\pi\)
−0.151619 + 0.988439i \(0.548449\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.12648 −1.00797
\(66\) 0 0
\(67\) 2.61180 0.319083 0.159541 0.987191i \(-0.448998\pi\)
0.159541 + 0.987191i \(0.448998\pi\)
\(68\) 0 0
\(69\) −6.18908 −0.745077
\(70\) 0 0
\(71\) −1.28105 −0.152033 −0.0760164 0.997107i \(-0.524220\pi\)
−0.0760164 + 0.997107i \(0.524220\pi\)
\(72\) 0 0
\(73\) 3.81398 0.446393 0.223196 0.974774i \(-0.428351\pi\)
0.223196 + 0.974774i \(0.428351\pi\)
\(74\) 0 0
\(75\) 3.00563 0.347060
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.28357 0.481940 0.240970 0.970533i \(-0.422535\pi\)
0.240970 + 0.970533i \(0.422535\pi\)
\(80\) 0 0
\(81\) 2.16201 0.240223
\(82\) 0 0
\(83\) −2.35962 −0.259002 −0.129501 0.991579i \(-0.541338\pi\)
−0.129501 + 0.991579i \(0.541338\pi\)
\(84\) 0 0
\(85\) 8.86476 0.961518
\(86\) 0 0
\(87\) 5.83114 0.625164
\(88\) 0 0
\(89\) 3.98293 0.422190 0.211095 0.977466i \(-0.432297\pi\)
0.211095 + 0.977466i \(0.432297\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.09495 −0.217236
\(94\) 0 0
\(95\) −6.75565 −0.693115
\(96\) 0 0
\(97\) −7.03488 −0.714284 −0.357142 0.934050i \(-0.616249\pi\)
−0.357142 + 0.934050i \(0.616249\pi\)
\(98\) 0 0
\(99\) −5.89813 −0.592784
\(100\) 0 0
\(101\) −6.24828 −0.621727 −0.310864 0.950455i \(-0.600618\pi\)
−0.310864 + 0.950455i \(0.600618\pi\)
\(102\) 0 0
\(103\) 7.53553 0.742498 0.371249 0.928533i \(-0.378930\pi\)
0.371249 + 0.928533i \(0.378930\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.8145 −1.72220 −0.861098 0.508439i \(-0.830223\pi\)
−0.861098 + 0.508439i \(0.830223\pi\)
\(108\) 0 0
\(109\) −7.83067 −0.750042 −0.375021 0.927016i \(-0.622365\pi\)
−0.375021 + 0.927016i \(0.622365\pi\)
\(110\) 0 0
\(111\) −8.56591 −0.813040
\(112\) 0 0
\(113\) 5.31934 0.500401 0.250201 0.968194i \(-0.419503\pi\)
0.250201 + 0.968194i \(0.419503\pi\)
\(114\) 0 0
\(115\) −8.85832 −0.826042
\(116\) 0 0
\(117\) −13.4129 −1.24002
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −3.55920 −0.323563
\(122\) 0 0
\(123\) 0.915292 0.0825291
\(124\) 0 0
\(125\) 10.8521 0.970642
\(126\) 0 0
\(127\) 9.66189 0.857354 0.428677 0.903458i \(-0.358980\pi\)
0.428677 + 0.903458i \(0.358980\pi\)
\(128\) 0 0
\(129\) 6.17540 0.543714
\(130\) 0 0
\(131\) 17.2464 1.50683 0.753413 0.657547i \(-0.228406\pi\)
0.753413 + 0.657547i \(0.228406\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −6.18989 −0.532741
\(136\) 0 0
\(137\) −8.10990 −0.692875 −0.346438 0.938073i \(-0.612609\pi\)
−0.346438 + 0.938073i \(0.612609\pi\)
\(138\) 0 0
\(139\) −2.72783 −0.231372 −0.115686 0.993286i \(-0.536907\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(140\) 0 0
\(141\) −7.46179 −0.628396
\(142\) 0 0
\(143\) 16.9211 1.41501
\(144\) 0 0
\(145\) 8.34601 0.693099
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.82784 −0.395512 −0.197756 0.980251i \(-0.563365\pi\)
−0.197756 + 0.980251i \(0.563365\pi\)
\(150\) 0 0
\(151\) 2.35596 0.191726 0.0958628 0.995395i \(-0.469439\pi\)
0.0958628 + 0.995395i \(0.469439\pi\)
\(152\) 0 0
\(153\) 14.6314 1.18288
\(154\) 0 0
\(155\) −2.99846 −0.240842
\(156\) 0 0
\(157\) 12.6689 1.01109 0.505543 0.862801i \(-0.331292\pi\)
0.505543 + 0.862801i \(0.331292\pi\)
\(158\) 0 0
\(159\) 11.5039 0.912321
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.78527 0.688115 0.344058 0.938949i \(-0.388198\pi\)
0.344058 + 0.938949i \(0.388198\pi\)
\(164\) 0 0
\(165\) 3.27080 0.254632
\(166\) 0 0
\(167\) −3.24661 −0.251230 −0.125615 0.992079i \(-0.540090\pi\)
−0.125615 + 0.992079i \(0.540090\pi\)
\(168\) 0 0
\(169\) 25.4800 1.96000
\(170\) 0 0
\(171\) −11.1503 −0.852684
\(172\) 0 0
\(173\) −0.370585 −0.0281751 −0.0140875 0.999901i \(-0.504484\pi\)
−0.0140875 + 0.999901i \(0.504484\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.35795 −0.102070
\(178\) 0 0
\(179\) −24.0644 −1.79866 −0.899330 0.437271i \(-0.855945\pi\)
−0.899330 + 0.437271i \(0.855945\pi\)
\(180\) 0 0
\(181\) −1.03031 −0.0765824 −0.0382912 0.999267i \(-0.512191\pi\)
−0.0382912 + 0.999267i \(0.512191\pi\)
\(182\) 0 0
\(183\) 2.16774 0.160244
\(184\) 0 0
\(185\) −12.2602 −0.901391
\(186\) 0 0
\(187\) −18.4583 −1.34980
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.25690 0.597448 0.298724 0.954340i \(-0.403439\pi\)
0.298724 + 0.954340i \(0.403439\pi\)
\(192\) 0 0
\(193\) 9.77019 0.703274 0.351637 0.936137i \(-0.385625\pi\)
0.351637 + 0.936137i \(0.385625\pi\)
\(194\) 0 0
\(195\) 7.43810 0.532653
\(196\) 0 0
\(197\) 2.63912 0.188030 0.0940149 0.995571i \(-0.470030\pi\)
0.0940149 + 0.995571i \(0.470030\pi\)
\(198\) 0 0
\(199\) 7.19404 0.509972 0.254986 0.966945i \(-0.417929\pi\)
0.254986 + 0.966945i \(0.417929\pi\)
\(200\) 0 0
\(201\) −2.39056 −0.168617
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.31004 0.0914972
\(206\) 0 0
\(207\) −14.6208 −1.01621
\(208\) 0 0
\(209\) 14.0667 0.973014
\(210\) 0 0
\(211\) −19.7516 −1.35976 −0.679879 0.733324i \(-0.737968\pi\)
−0.679879 + 0.733324i \(0.737968\pi\)
\(212\) 0 0
\(213\) 1.17254 0.0803409
\(214\) 0 0
\(215\) 8.83875 0.602798
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.49090 −0.235893
\(220\) 0 0
\(221\) −41.9758 −2.82360
\(222\) 0 0
\(223\) 19.8914 1.33203 0.666014 0.745939i \(-0.267999\pi\)
0.666014 + 0.745939i \(0.267999\pi\)
\(224\) 0 0
\(225\) 7.10035 0.473357
\(226\) 0 0
\(227\) 16.0483 1.06516 0.532581 0.846379i \(-0.321222\pi\)
0.532581 + 0.846379i \(0.321222\pi\)
\(228\) 0 0
\(229\) 20.4940 1.35428 0.677142 0.735852i \(-0.263218\pi\)
0.677142 + 0.735852i \(0.263218\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.2859 −1.00141 −0.500705 0.865618i \(-0.666926\pi\)
−0.500705 + 0.865618i \(0.666926\pi\)
\(234\) 0 0
\(235\) −10.6799 −0.696682
\(236\) 0 0
\(237\) −3.92072 −0.254678
\(238\) 0 0
\(239\) 27.3135 1.76676 0.883380 0.468657i \(-0.155262\pi\)
0.883380 + 0.468657i \(0.155262\pi\)
\(240\) 0 0
\(241\) −15.7932 −1.01733 −0.508663 0.860965i \(-0.669860\pi\)
−0.508663 + 0.860965i \(0.669860\pi\)
\(242\) 0 0
\(243\) −16.1537 −1.03626
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 31.9889 2.03541
\(248\) 0 0
\(249\) 2.15974 0.136868
\(250\) 0 0
\(251\) 15.7718 0.995505 0.497753 0.867319i \(-0.334159\pi\)
0.497753 + 0.867319i \(0.334159\pi\)
\(252\) 0 0
\(253\) 18.4449 1.15962
\(254\) 0 0
\(255\) −8.11384 −0.508108
\(256\) 0 0
\(257\) −7.38691 −0.460783 −0.230391 0.973098i \(-0.574001\pi\)
−0.230391 + 0.973098i \(0.574001\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 13.7752 0.852664
\(262\) 0 0
\(263\) −7.79849 −0.480875 −0.240438 0.970665i \(-0.577291\pi\)
−0.240438 + 0.970665i \(0.577291\pi\)
\(264\) 0 0
\(265\) 16.4654 1.01146
\(266\) 0 0
\(267\) −3.64555 −0.223104
\(268\) 0 0
\(269\) 11.3794 0.693815 0.346907 0.937899i \(-0.387232\pi\)
0.346907 + 0.937899i \(0.387232\pi\)
\(270\) 0 0
\(271\) −20.2606 −1.23075 −0.615373 0.788236i \(-0.710995\pi\)
−0.615373 + 0.788236i \(0.710995\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.95747 −0.540156
\(276\) 0 0
\(277\) 22.4498 1.34888 0.674440 0.738330i \(-0.264385\pi\)
0.674440 + 0.738330i \(0.264385\pi\)
\(278\) 0 0
\(279\) −4.94900 −0.296289
\(280\) 0 0
\(281\) 28.7285 1.71380 0.856898 0.515485i \(-0.172388\pi\)
0.856898 + 0.515485i \(0.172388\pi\)
\(282\) 0 0
\(283\) 25.3840 1.50892 0.754462 0.656344i \(-0.227898\pi\)
0.754462 + 0.656344i \(0.227898\pi\)
\(284\) 0 0
\(285\) 6.18339 0.366272
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 28.7893 1.69349
\(290\) 0 0
\(291\) 6.43897 0.377459
\(292\) 0 0
\(293\) 26.3359 1.53856 0.769280 0.638912i \(-0.220615\pi\)
0.769280 + 0.638912i \(0.220615\pi\)
\(294\) 0 0
\(295\) −1.94361 −0.113161
\(296\) 0 0
\(297\) 12.8887 0.747876
\(298\) 0 0
\(299\) 41.9454 2.42576
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 5.71900 0.328548
\(304\) 0 0
\(305\) 3.10265 0.177657
\(306\) 0 0
\(307\) −29.8539 −1.70385 −0.851926 0.523663i \(-0.824565\pi\)
−0.851926 + 0.523663i \(0.824565\pi\)
\(308\) 0 0
\(309\) −6.89721 −0.392369
\(310\) 0 0
\(311\) 1.09275 0.0619642 0.0309821 0.999520i \(-0.490137\pi\)
0.0309821 + 0.999520i \(0.490137\pi\)
\(312\) 0 0
\(313\) 25.8202 1.45945 0.729723 0.683743i \(-0.239649\pi\)
0.729723 + 0.683743i \(0.239649\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.09034 0.342067 0.171034 0.985265i \(-0.445289\pi\)
0.171034 + 0.985265i \(0.445289\pi\)
\(318\) 0 0
\(319\) −17.3782 −0.972991
\(320\) 0 0
\(321\) 16.3055 0.910084
\(322\) 0 0
\(323\) −34.8951 −1.94161
\(324\) 0 0
\(325\) −20.3701 −1.12993
\(326\) 0 0
\(327\) 7.16735 0.396355
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.7596 0.756298 0.378149 0.925745i \(-0.376561\pi\)
0.378149 + 0.925745i \(0.376561\pi\)
\(332\) 0 0
\(333\) −20.2357 −1.10891
\(334\) 0 0
\(335\) −3.42157 −0.186940
\(336\) 0 0
\(337\) −28.3125 −1.54228 −0.771141 0.636664i \(-0.780314\pi\)
−0.771141 + 0.636664i \(0.780314\pi\)
\(338\) 0 0
\(339\) −4.86875 −0.264434
\(340\) 0 0
\(341\) 6.24343 0.338101
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 8.10794 0.436517
\(346\) 0 0
\(347\) −14.3979 −0.772920 −0.386460 0.922306i \(-0.626302\pi\)
−0.386460 + 0.922306i \(0.626302\pi\)
\(348\) 0 0
\(349\) 15.5569 0.832741 0.416371 0.909195i \(-0.363302\pi\)
0.416371 + 0.909195i \(0.363302\pi\)
\(350\) 0 0
\(351\) 29.3100 1.56445
\(352\) 0 0
\(353\) 4.63356 0.246620 0.123310 0.992368i \(-0.460649\pi\)
0.123310 + 0.992368i \(0.460649\pi\)
\(354\) 0 0
\(355\) 1.67823 0.0890712
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.24826 −0.329771 −0.164885 0.986313i \(-0.552725\pi\)
−0.164885 + 0.986313i \(0.552725\pi\)
\(360\) 0 0
\(361\) 7.59281 0.399622
\(362\) 0 0
\(363\) 3.25770 0.170985
\(364\) 0 0
\(365\) −4.99647 −0.261527
\(366\) 0 0
\(367\) 35.2894 1.84209 0.921047 0.389452i \(-0.127336\pi\)
0.921047 + 0.389452i \(0.127336\pi\)
\(368\) 0 0
\(369\) 2.16224 0.112562
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 29.5655 1.53084 0.765421 0.643530i \(-0.222531\pi\)
0.765421 + 0.643530i \(0.222531\pi\)
\(374\) 0 0
\(375\) −9.93284 −0.512930
\(376\) 0 0
\(377\) −39.5195 −2.03536
\(378\) 0 0
\(379\) −9.02380 −0.463522 −0.231761 0.972773i \(-0.574449\pi\)
−0.231761 + 0.972773i \(0.574449\pi\)
\(380\) 0 0
\(381\) −8.84344 −0.453063
\(382\) 0 0
\(383\) −20.0681 −1.02543 −0.512716 0.858559i \(-0.671360\pi\)
−0.512716 + 0.858559i \(0.671360\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 14.5885 0.741574
\(388\) 0 0
\(389\) 35.4162 1.79567 0.897836 0.440330i \(-0.145139\pi\)
0.897836 + 0.440330i \(0.145139\pi\)
\(390\) 0 0
\(391\) −45.7560 −2.31398
\(392\) 0 0
\(393\) −15.7855 −0.796273
\(394\) 0 0
\(395\) −5.61166 −0.282353
\(396\) 0 0
\(397\) 20.8612 1.04699 0.523496 0.852028i \(-0.324628\pi\)
0.523496 + 0.852028i \(0.324628\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.68818 0.483805 0.241902 0.970301i \(-0.422229\pi\)
0.241902 + 0.970301i \(0.422229\pi\)
\(402\) 0 0
\(403\) 14.1981 0.707259
\(404\) 0 0
\(405\) −2.83232 −0.140739
\(406\) 0 0
\(407\) 25.5284 1.26540
\(408\) 0 0
\(409\) −14.5208 −0.718009 −0.359004 0.933336i \(-0.616884\pi\)
−0.359004 + 0.933336i \(0.616884\pi\)
\(410\) 0 0
\(411\) 7.42292 0.366146
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 3.09120 0.151741
\(416\) 0 0
\(417\) 2.49676 0.122267
\(418\) 0 0
\(419\) −7.75224 −0.378721 −0.189361 0.981908i \(-0.560642\pi\)
−0.189361 + 0.981908i \(0.560642\pi\)
\(420\) 0 0
\(421\) 6.10905 0.297737 0.148869 0.988857i \(-0.452437\pi\)
0.148869 + 0.988857i \(0.452437\pi\)
\(422\) 0 0
\(423\) −17.6274 −0.857072
\(424\) 0 0
\(425\) 22.2207 1.07786
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −15.4877 −0.747753
\(430\) 0 0
\(431\) 20.0724 0.966853 0.483427 0.875385i \(-0.339392\pi\)
0.483427 + 0.875385i \(0.339392\pi\)
\(432\) 0 0
\(433\) 18.0613 0.867973 0.433986 0.900919i \(-0.357107\pi\)
0.433986 + 0.900919i \(0.357107\pi\)
\(434\) 0 0
\(435\) −7.63904 −0.366264
\(436\) 0 0
\(437\) 34.8697 1.66804
\(438\) 0 0
\(439\) −4.24242 −0.202480 −0.101240 0.994862i \(-0.532281\pi\)
−0.101240 + 0.994862i \(0.532281\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.3712 0.777819 0.388909 0.921276i \(-0.372852\pi\)
0.388909 + 0.921276i \(0.372852\pi\)
\(444\) 0 0
\(445\) −5.21781 −0.247348
\(446\) 0 0
\(447\) 4.41888 0.209006
\(448\) 0 0
\(449\) −14.4030 −0.679721 −0.339860 0.940476i \(-0.610380\pi\)
−0.339860 + 0.940476i \(0.610380\pi\)
\(450\) 0 0
\(451\) −2.72778 −0.128446
\(452\) 0 0
\(453\) −2.15639 −0.101316
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.7736 −0.597523 −0.298761 0.954328i \(-0.596573\pi\)
−0.298761 + 0.954328i \(0.596573\pi\)
\(458\) 0 0
\(459\) −31.9727 −1.49236
\(460\) 0 0
\(461\) −3.83939 −0.178818 −0.0894092 0.995995i \(-0.528498\pi\)
−0.0894092 + 0.995995i \(0.528498\pi\)
\(462\) 0 0
\(463\) 42.3474 1.96805 0.984025 0.178030i \(-0.0569723\pi\)
0.984025 + 0.178030i \(0.0569723\pi\)
\(464\) 0 0
\(465\) 2.74447 0.127272
\(466\) 0 0
\(467\) −27.2929 −1.26296 −0.631482 0.775390i \(-0.717553\pi\)
−0.631482 + 0.775390i \(0.717553\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −11.5957 −0.534302
\(472\) 0 0
\(473\) −18.4041 −0.846224
\(474\) 0 0
\(475\) −16.9339 −0.776982
\(476\) 0 0
\(477\) 27.1763 1.24432
\(478\) 0 0
\(479\) 24.9162 1.13845 0.569225 0.822182i \(-0.307243\pi\)
0.569225 + 0.822182i \(0.307243\pi\)
\(480\) 0 0
\(481\) 58.0539 2.64703
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.21598 0.418476
\(486\) 0 0
\(487\) 17.1545 0.777346 0.388673 0.921376i \(-0.372934\pi\)
0.388673 + 0.921376i \(0.372934\pi\)
\(488\) 0 0
\(489\) −8.04108 −0.363630
\(490\) 0 0
\(491\) 20.8028 0.938815 0.469408 0.882982i \(-0.344468\pi\)
0.469408 + 0.882982i \(0.344468\pi\)
\(492\) 0 0
\(493\) 43.1098 1.94157
\(494\) 0 0
\(495\) 7.72679 0.347293
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.8858 0.666380 0.333190 0.942860i \(-0.391875\pi\)
0.333190 + 0.942860i \(0.391875\pi\)
\(500\) 0 0
\(501\) 2.97159 0.132761
\(502\) 0 0
\(503\) −4.55717 −0.203194 −0.101597 0.994826i \(-0.532395\pi\)
−0.101597 + 0.994826i \(0.532395\pi\)
\(504\) 0 0
\(505\) 8.18550 0.364250
\(506\) 0 0
\(507\) −23.3216 −1.03575
\(508\) 0 0
\(509\) 5.37084 0.238058 0.119029 0.992891i \(-0.462022\pi\)
0.119029 + 0.992891i \(0.462022\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 24.3658 1.07577
\(514\) 0 0
\(515\) −9.87186 −0.435006
\(516\) 0 0
\(517\) 22.2379 0.978021
\(518\) 0 0
\(519\) 0.339193 0.0148889
\(520\) 0 0
\(521\) −14.7276 −0.645228 −0.322614 0.946531i \(-0.604562\pi\)
−0.322614 + 0.946531i \(0.604562\pi\)
\(522\) 0 0
\(523\) −39.0551 −1.70776 −0.853880 0.520470i \(-0.825757\pi\)
−0.853880 + 0.520470i \(0.825757\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.4880 −0.674668
\(528\) 0 0
\(529\) 22.7228 0.987947
\(530\) 0 0
\(531\) −3.20796 −0.139214
\(532\) 0 0
\(533\) −6.20323 −0.268692
\(534\) 0 0
\(535\) 23.3378 1.00898
\(536\) 0 0
\(537\) 22.0260 0.950490
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11.7979 −0.507230 −0.253615 0.967305i \(-0.581620\pi\)
−0.253615 + 0.967305i \(0.581620\pi\)
\(542\) 0 0
\(543\) 0.943034 0.0404695
\(544\) 0 0
\(545\) 10.2585 0.439426
\(546\) 0 0
\(547\) −16.4776 −0.704530 −0.352265 0.935900i \(-0.614588\pi\)
−0.352265 + 0.935900i \(0.614588\pi\)
\(548\) 0 0
\(549\) 5.12097 0.218557
\(550\) 0 0
\(551\) −32.8531 −1.39959
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 11.2217 0.476334
\(556\) 0 0
\(557\) −29.7784 −1.26175 −0.630876 0.775884i \(-0.717304\pi\)
−0.630876 + 0.775884i \(0.717304\pi\)
\(558\) 0 0
\(559\) −41.8527 −1.77018
\(560\) 0 0
\(561\) 16.8947 0.713296
\(562\) 0 0
\(563\) 27.9737 1.17895 0.589476 0.807786i \(-0.299334\pi\)
0.589476 + 0.807786i \(0.299334\pi\)
\(564\) 0 0
\(565\) −6.96856 −0.293169
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −39.1698 −1.64208 −0.821041 0.570870i \(-0.806606\pi\)
−0.821041 + 0.570870i \(0.806606\pi\)
\(570\) 0 0
\(571\) −9.58472 −0.401108 −0.200554 0.979683i \(-0.564274\pi\)
−0.200554 + 0.979683i \(0.564274\pi\)
\(572\) 0 0
\(573\) −7.55747 −0.315718
\(574\) 0 0
\(575\) −22.2045 −0.925994
\(576\) 0 0
\(577\) 17.4043 0.724549 0.362275 0.932071i \(-0.382000\pi\)
0.362275 + 0.932071i \(0.382000\pi\)
\(578\) 0 0
\(579\) −8.94257 −0.371641
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −34.2844 −1.41991
\(584\) 0 0
\(585\) 17.5714 0.726488
\(586\) 0 0
\(587\) 26.8005 1.10617 0.553087 0.833123i \(-0.313450\pi\)
0.553087 + 0.833123i \(0.313450\pi\)
\(588\) 0 0
\(589\) 11.8031 0.486338
\(590\) 0 0
\(591\) −2.41557 −0.0993632
\(592\) 0 0
\(593\) 4.07921 0.167513 0.0837564 0.996486i \(-0.473308\pi\)
0.0837564 + 0.996486i \(0.473308\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.58465 −0.269492
\(598\) 0 0
\(599\) 0.348239 0.0142287 0.00711434 0.999975i \(-0.497735\pi\)
0.00711434 + 0.999975i \(0.497735\pi\)
\(600\) 0 0
\(601\) 12.9913 0.529924 0.264962 0.964259i \(-0.414641\pi\)
0.264962 + 0.964259i \(0.414641\pi\)
\(602\) 0 0
\(603\) −5.64735 −0.229978
\(604\) 0 0
\(605\) 4.66269 0.189565
\(606\) 0 0
\(607\) −32.8925 −1.33506 −0.667532 0.744581i \(-0.732649\pi\)
−0.667532 + 0.744581i \(0.732649\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 50.5709 2.04588
\(612\) 0 0
\(613\) −47.5587 −1.92088 −0.960439 0.278490i \(-0.910166\pi\)
−0.960439 + 0.278490i \(0.910166\pi\)
\(614\) 0 0
\(615\) −1.19907 −0.0483512
\(616\) 0 0
\(617\) 14.3219 0.576578 0.288289 0.957544i \(-0.406914\pi\)
0.288289 + 0.957544i \(0.406914\pi\)
\(618\) 0 0
\(619\) 0.567473 0.0228087 0.0114043 0.999935i \(-0.496370\pi\)
0.0114043 + 0.999935i \(0.496370\pi\)
\(620\) 0 0
\(621\) 31.9495 1.28209
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2.20225 0.0880900
\(626\) 0 0
\(627\) −12.8751 −0.514183
\(628\) 0 0
\(629\) −63.3280 −2.52505
\(630\) 0 0
\(631\) 19.5021 0.776366 0.388183 0.921582i \(-0.373103\pi\)
0.388183 + 0.921582i \(0.373103\pi\)
\(632\) 0 0
\(633\) 18.0785 0.718556
\(634\) 0 0
\(635\) −12.6575 −0.502296
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.76994 0.109577
\(640\) 0 0
\(641\) −19.0255 −0.751461 −0.375731 0.926729i \(-0.622608\pi\)
−0.375731 + 0.926729i \(0.622608\pi\)
\(642\) 0 0
\(643\) 44.8947 1.77047 0.885237 0.465141i \(-0.153996\pi\)
0.885237 + 0.465141i \(0.153996\pi\)
\(644\) 0 0
\(645\) −8.09003 −0.318545
\(646\) 0 0
\(647\) 5.67864 0.223250 0.111625 0.993750i \(-0.464394\pi\)
0.111625 + 0.993750i \(0.464394\pi\)
\(648\) 0 0
\(649\) 4.04701 0.158859
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.31189 −0.168737 −0.0843686 0.996435i \(-0.526887\pi\)
−0.0843686 + 0.996435i \(0.526887\pi\)
\(654\) 0 0
\(655\) −22.5935 −0.882802
\(656\) 0 0
\(657\) −8.24674 −0.321736
\(658\) 0 0
\(659\) 42.9372 1.67260 0.836298 0.548275i \(-0.184715\pi\)
0.836298 + 0.548275i \(0.184715\pi\)
\(660\) 0 0
\(661\) 14.6588 0.570160 0.285080 0.958504i \(-0.407980\pi\)
0.285080 + 0.958504i \(0.407980\pi\)
\(662\) 0 0
\(663\) 38.4201 1.49211
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −43.0785 −1.66801
\(668\) 0 0
\(669\) −18.2065 −0.703902
\(670\) 0 0
\(671\) −6.46037 −0.249400
\(672\) 0 0
\(673\) −26.0296 −1.00337 −0.501684 0.865051i \(-0.667286\pi\)
−0.501684 + 0.865051i \(0.667286\pi\)
\(674\) 0 0
\(675\) −15.5158 −0.597202
\(676\) 0 0
\(677\) −36.3578 −1.39735 −0.698673 0.715441i \(-0.746226\pi\)
−0.698673 + 0.715441i \(0.746226\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.6889 −0.562878
\(682\) 0 0
\(683\) 17.5708 0.672328 0.336164 0.941803i \(-0.390870\pi\)
0.336164 + 0.941803i \(0.390870\pi\)
\(684\) 0 0
\(685\) 10.6243 0.405934
\(686\) 0 0
\(687\) −18.7580 −0.715663
\(688\) 0 0
\(689\) −77.9658 −2.97026
\(690\) 0 0
\(691\) 25.1288 0.955944 0.477972 0.878375i \(-0.341372\pi\)
0.477972 + 0.878375i \(0.341372\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.57357 0.135553
\(696\) 0 0
\(697\) 6.76678 0.256310
\(698\) 0 0
\(699\) 13.9910 0.529189
\(700\) 0 0
\(701\) −12.8610 −0.485753 −0.242877 0.970057i \(-0.578091\pi\)
−0.242877 + 0.970057i \(0.578091\pi\)
\(702\) 0 0
\(703\) 48.2610 1.82020
\(704\) 0 0
\(705\) 9.77525 0.368157
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −23.9369 −0.898969 −0.449484 0.893288i \(-0.648392\pi\)
−0.449484 + 0.893288i \(0.648392\pi\)
\(710\) 0 0
\(711\) −9.26212 −0.347357
\(712\) 0 0
\(713\) 15.4767 0.579609
\(714\) 0 0
\(715\) −22.1673 −0.829009
\(716\) 0 0
\(717\) −24.9998 −0.933634
\(718\) 0 0
\(719\) 38.7742 1.44603 0.723017 0.690830i \(-0.242755\pi\)
0.723017 + 0.690830i \(0.242755\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 14.4553 0.537600
\(724\) 0 0
\(725\) 20.9204 0.776964
\(726\) 0 0
\(727\) 19.6322 0.728117 0.364059 0.931376i \(-0.381391\pi\)
0.364059 + 0.931376i \(0.381391\pi\)
\(728\) 0 0
\(729\) 8.29935 0.307383
\(730\) 0 0
\(731\) 45.6549 1.68861
\(732\) 0 0
\(733\) 35.7663 1.32106 0.660529 0.750801i \(-0.270332\pi\)
0.660529 + 0.750801i \(0.270332\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.12444 0.262432
\(738\) 0 0
\(739\) −22.6233 −0.832212 −0.416106 0.909316i \(-0.636606\pi\)
−0.416106 + 0.909316i \(0.636606\pi\)
\(740\) 0 0
\(741\) −29.2792 −1.07560
\(742\) 0 0
\(743\) 16.9685 0.622515 0.311257 0.950326i \(-0.399250\pi\)
0.311257 + 0.950326i \(0.399250\pi\)
\(744\) 0 0
\(745\) 6.32467 0.231718
\(746\) 0 0
\(747\) 5.10207 0.186675
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 38.1262 1.39124 0.695622 0.718408i \(-0.255129\pi\)
0.695622 + 0.718408i \(0.255129\pi\)
\(752\) 0 0
\(753\) −14.4358 −0.526069
\(754\) 0 0
\(755\) −3.08641 −0.112326
\(756\) 0 0
\(757\) 15.1230 0.549656 0.274828 0.961493i \(-0.411379\pi\)
0.274828 + 0.961493i \(0.411379\pi\)
\(758\) 0 0
\(759\) −16.8825 −0.612794
\(760\) 0 0
\(761\) −43.5322 −1.57804 −0.789020 0.614367i \(-0.789411\pi\)
−0.789020 + 0.614367i \(0.789411\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −19.1677 −0.693011
\(766\) 0 0
\(767\) 9.20327 0.332311
\(768\) 0 0
\(769\) 5.22236 0.188323 0.0941616 0.995557i \(-0.469983\pi\)
0.0941616 + 0.995557i \(0.469983\pi\)
\(770\) 0 0
\(771\) 6.76118 0.243498
\(772\) 0 0
\(773\) −5.83438 −0.209848 −0.104924 0.994480i \(-0.533460\pi\)
−0.104924 + 0.994480i \(0.533460\pi\)
\(774\) 0 0
\(775\) −7.51604 −0.269984
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.15682 −0.184762
\(780\) 0 0
\(781\) −3.49443 −0.125041
\(782\) 0 0
\(783\) −30.1018 −1.07575
\(784\) 0 0
\(785\) −16.5967 −0.592363
\(786\) 0 0
\(787\) −54.2719 −1.93459 −0.967293 0.253662i \(-0.918365\pi\)
−0.967293 + 0.253662i \(0.918365\pi\)
\(788\) 0 0
\(789\) 7.13789 0.254116
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −14.6915 −0.521709
\(794\) 0 0
\(795\) −15.0706 −0.534500
\(796\) 0 0
\(797\) 20.7610 0.735393 0.367697 0.929946i \(-0.380146\pi\)
0.367697 + 0.929946i \(0.380146\pi\)
\(798\) 0 0
\(799\) −55.1652 −1.95160
\(800\) 0 0
\(801\) −8.61206 −0.304292
\(802\) 0 0
\(803\) 10.4037 0.367139
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −10.4155 −0.366642
\(808\) 0 0
\(809\) 2.74903 0.0966509 0.0483254 0.998832i \(-0.484612\pi\)
0.0483254 + 0.998832i \(0.484612\pi\)
\(810\) 0 0
\(811\) −38.6188 −1.35609 −0.678045 0.735020i \(-0.737173\pi\)
−0.678045 + 0.735020i \(0.737173\pi\)
\(812\) 0 0
\(813\) 18.5444 0.650380
\(814\) 0 0
\(815\) −11.5091 −0.403145
\(816\) 0 0
\(817\) −34.7927 −1.21724
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 32.0655 1.11910 0.559548 0.828798i \(-0.310975\pi\)
0.559548 + 0.828798i \(0.310975\pi\)
\(822\) 0 0
\(823\) 24.9174 0.868566 0.434283 0.900776i \(-0.357002\pi\)
0.434283 + 0.900776i \(0.357002\pi\)
\(824\) 0 0
\(825\) 8.19870 0.285442
\(826\) 0 0
\(827\) 16.0445 0.557924 0.278962 0.960302i \(-0.410010\pi\)
0.278962 + 0.960302i \(0.410010\pi\)
\(828\) 0 0
\(829\) −23.2341 −0.806955 −0.403477 0.914990i \(-0.632199\pi\)
−0.403477 + 0.914990i \(0.632199\pi\)
\(830\) 0 0
\(831\) −20.5481 −0.712807
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 4.25319 0.147188
\(836\) 0 0
\(837\) 10.8146 0.373808
\(838\) 0 0
\(839\) −9.97240 −0.344286 −0.172143 0.985072i \(-0.555069\pi\)
−0.172143 + 0.985072i \(0.555069\pi\)
\(840\) 0 0
\(841\) 11.5871 0.399556
\(842\) 0 0
\(843\) −26.2949 −0.905645
\(844\) 0 0
\(845\) −33.3799 −1.14830
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −23.2338 −0.797382
\(850\) 0 0
\(851\) 63.2820 2.16928
\(852\) 0 0
\(853\) 20.8869 0.715155 0.357577 0.933883i \(-0.383603\pi\)
0.357577 + 0.933883i \(0.383603\pi\)
\(854\) 0 0
\(855\) 14.6073 0.499561
\(856\) 0 0
\(857\) 25.0377 0.855272 0.427636 0.903951i \(-0.359347\pi\)
0.427636 + 0.903951i \(0.359347\pi\)
\(858\) 0 0
\(859\) 33.8628 1.15538 0.577692 0.816255i \(-0.303953\pi\)
0.577692 + 0.816255i \(0.303953\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 47.2687 1.60905 0.804523 0.593922i \(-0.202421\pi\)
0.804523 + 0.593922i \(0.202421\pi\)
\(864\) 0 0
\(865\) 0.485482 0.0165069
\(866\) 0 0
\(867\) −26.3506 −0.894912
\(868\) 0 0
\(869\) 11.6847 0.396375
\(870\) 0 0
\(871\) 16.2016 0.548971
\(872\) 0 0
\(873\) 15.2111 0.514818
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 24.3287 0.821522 0.410761 0.911743i \(-0.365263\pi\)
0.410761 + 0.911743i \(0.365263\pi\)
\(878\) 0 0
\(879\) −24.1050 −0.813042
\(880\) 0 0
\(881\) 46.4242 1.56407 0.782035 0.623235i \(-0.214182\pi\)
0.782035 + 0.623235i \(0.214182\pi\)
\(882\) 0 0
\(883\) −4.22330 −0.142125 −0.0710626 0.997472i \(-0.522639\pi\)
−0.0710626 + 0.997472i \(0.522639\pi\)
\(884\) 0 0
\(885\) 1.77897 0.0597995
\(886\) 0 0
\(887\) −5.72536 −0.192239 −0.0961194 0.995370i \(-0.530643\pi\)
−0.0961194 + 0.995370i \(0.530643\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 5.89750 0.197574
\(892\) 0 0
\(893\) 42.0403 1.40682
\(894\) 0 0
\(895\) 31.5254 1.05378
\(896\) 0 0
\(897\) −38.3922 −1.28188
\(898\) 0 0
\(899\) −14.5817 −0.486326
\(900\) 0 0
\(901\) 85.0489 2.83339
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.34975 0.0448672
\(906\) 0 0
\(907\) −18.2656 −0.606501 −0.303250 0.952911i \(-0.598072\pi\)
−0.303250 + 0.952911i \(0.598072\pi\)
\(908\) 0 0
\(909\) 13.5103 0.448108
\(910\) 0 0
\(911\) −22.8893 −0.758356 −0.379178 0.925324i \(-0.623793\pi\)
−0.379178 + 0.925324i \(0.623793\pi\)
\(912\) 0 0
\(913\) −6.43654 −0.213018
\(914\) 0 0
\(915\) −2.83983 −0.0938819
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 4.67612 0.154251 0.0771254 0.997021i \(-0.475426\pi\)
0.0771254 + 0.997021i \(0.475426\pi\)
\(920\) 0 0
\(921\) 27.3250 0.900390
\(922\) 0 0
\(923\) −7.94665 −0.261567
\(924\) 0 0
\(925\) −30.7319 −1.01046
\(926\) 0 0
\(927\) −16.2936 −0.535153
\(928\) 0 0
\(929\) 33.1752 1.08844 0.544222 0.838941i \(-0.316825\pi\)
0.544222 + 0.838941i \(0.316825\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −1.00019 −0.0327446
\(934\) 0 0
\(935\) 24.1811 0.790808
\(936\) 0 0
\(937\) −54.1119 −1.76776 −0.883879 0.467715i \(-0.845077\pi\)
−0.883879 + 0.467715i \(0.845077\pi\)
\(938\) 0 0
\(939\) −23.6330 −0.771235
\(940\) 0 0
\(941\) −19.1721 −0.624993 −0.312497 0.949919i \(-0.601165\pi\)
−0.312497 + 0.949919i \(0.601165\pi\)
\(942\) 0 0
\(943\) −6.76186 −0.220197
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.20600 −0.0391898 −0.0195949 0.999808i \(-0.506238\pi\)
−0.0195949 + 0.999808i \(0.506238\pi\)
\(948\) 0 0
\(949\) 23.6590 0.768003
\(950\) 0 0
\(951\) −5.57443 −0.180763
\(952\) 0 0
\(953\) 35.0276 1.13466 0.567328 0.823492i \(-0.307977\pi\)
0.567328 + 0.823492i \(0.307977\pi\)
\(954\) 0 0
\(955\) −10.8169 −0.350026
\(956\) 0 0
\(957\) 15.9061 0.514171
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −25.7613 −0.831008
\(962\) 0 0
\(963\) 38.5193 1.24127
\(964\) 0 0
\(965\) −12.7993 −0.412026
\(966\) 0 0
\(967\) −36.8246 −1.18420 −0.592099 0.805865i \(-0.701701\pi\)
−0.592099 + 0.805865i \(0.701701\pi\)
\(968\) 0 0
\(969\) 31.9392 1.02603
\(970\) 0 0
\(971\) −3.28648 −0.105468 −0.0527341 0.998609i \(-0.516794\pi\)
−0.0527341 + 0.998609i \(0.516794\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 18.6446 0.597105
\(976\) 0 0
\(977\) −9.64478 −0.308564 −0.154282 0.988027i \(-0.549306\pi\)
−0.154282 + 0.988027i \(0.549306\pi\)
\(978\) 0 0
\(979\) 10.8646 0.347234
\(980\) 0 0
\(981\) 16.9318 0.540591
\(982\) 0 0
\(983\) −29.4596 −0.939615 −0.469808 0.882769i \(-0.655677\pi\)
−0.469808 + 0.882769i \(0.655677\pi\)
\(984\) 0 0
\(985\) −3.45736 −0.110161
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −45.6218 −1.45069
\(990\) 0 0
\(991\) −18.9223 −0.601086 −0.300543 0.953768i \(-0.597168\pi\)
−0.300543 + 0.953768i \(0.597168\pi\)
\(992\) 0 0
\(993\) −12.5941 −0.399661
\(994\) 0 0
\(995\) −9.42449 −0.298777
\(996\) 0 0
\(997\) −50.4615 −1.59813 −0.799066 0.601243i \(-0.794672\pi\)
−0.799066 + 0.601243i \(0.794672\pi\)
\(998\) 0 0
\(999\) 44.2193 1.39904
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 \(a_p\))