Properties

Label 8040.2.a.t.1.5
Level 8040
Weight 2
Character 8040.1
Self dual Yes
Analytic conductor 64.200
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1997232251\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.211675\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} +3.61083 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} +3.61083 q^{7} +1.00000 q^{9} -3.95191 q^{11} +5.10788 q^{13} -1.00000 q^{15} +4.16687 q^{17} +2.79100 q^{19} +3.61083 q^{21} +3.13197 q^{23} +1.00000 q^{25} +1.00000 q^{27} -1.00339 q^{29} +2.03151 q^{31} -3.95191 q^{33} -3.61083 q^{35} -6.39738 q^{37} +5.10788 q^{39} -0.0315111 q^{41} +1.97592 q^{43} -1.00000 q^{45} +3.94924 q^{47} +6.03811 q^{49} +4.16687 q^{51} -2.86080 q^{53} +3.95191 q^{55} +2.79100 q^{57} -3.52446 q^{59} +3.00606 q^{61} +3.61083 q^{63} -5.10788 q^{65} +1.00000 q^{67} +3.13197 q^{69} +13.2515 q^{71} +4.27398 q^{73} +1.00000 q^{75} -14.2697 q^{77} -2.34696 q^{79} +1.00000 q^{81} -1.02480 q^{83} -4.16687 q^{85} -1.00339 q^{87} +3.28609 q^{89} +18.4437 q^{91} +2.03151 q^{93} -2.79100 q^{95} +15.8180 q^{97} -3.95191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} + O(q^{10}) \) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} - q^{13} - 7q^{15} - 2q^{17} + 9q^{19} + 10q^{21} + 2q^{23} + 7q^{25} + 7q^{27} - q^{29} + 9q^{31} - 10q^{35} + 23q^{37} - q^{39} + 5q^{41} - 3q^{43} - 7q^{45} + 11q^{47} + 13q^{49} - 2q^{51} + 13q^{53} + 9q^{57} + q^{59} + 4q^{61} + 10q^{63} + q^{65} + 7q^{67} + 2q^{69} + q^{71} + 14q^{73} + 7q^{75} + 18q^{77} + 25q^{79} + 7q^{81} - 29q^{83} + 2q^{85} - q^{87} + 7q^{89} + 27q^{91} + 9q^{93} - 9q^{95} + 38q^{97} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.61083 1.36477 0.682383 0.730995i \(-0.260944\pi\)
0.682383 + 0.730995i \(0.260944\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.95191 −1.19155 −0.595773 0.803153i \(-0.703154\pi\)
−0.595773 + 0.803153i \(0.703154\pi\)
\(12\) 0 0
\(13\) 5.10788 1.41667 0.708336 0.705875i \(-0.249446\pi\)
0.708336 + 0.705875i \(0.249446\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 4.16687 1.01061 0.505307 0.862940i \(-0.331379\pi\)
0.505307 + 0.862940i \(0.331379\pi\)
\(18\) 0 0
\(19\) 2.79100 0.640299 0.320149 0.947367i \(-0.396267\pi\)
0.320149 + 0.947367i \(0.396267\pi\)
\(20\) 0 0
\(21\) 3.61083 0.787948
\(22\) 0 0
\(23\) 3.13197 0.653061 0.326530 0.945187i \(-0.394120\pi\)
0.326530 + 0.945187i \(0.394120\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00339 −0.186325 −0.0931623 0.995651i \(-0.529698\pi\)
−0.0931623 + 0.995651i \(0.529698\pi\)
\(30\) 0 0
\(31\) 2.03151 0.364870 0.182435 0.983218i \(-0.441602\pi\)
0.182435 + 0.983218i \(0.441602\pi\)
\(32\) 0 0
\(33\) −3.95191 −0.687940
\(34\) 0 0
\(35\) −3.61083 −0.610342
\(36\) 0 0
\(37\) −6.39738 −1.05172 −0.525861 0.850570i \(-0.676257\pi\)
−0.525861 + 0.850570i \(0.676257\pi\)
\(38\) 0 0
\(39\) 5.10788 0.817916
\(40\) 0 0
\(41\) −0.0315111 −0.00492120 −0.00246060 0.999997i \(-0.500783\pi\)
−0.00246060 + 0.999997i \(0.500783\pi\)
\(42\) 0 0
\(43\) 1.97592 0.301324 0.150662 0.988585i \(-0.451859\pi\)
0.150662 + 0.988585i \(0.451859\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 3.94924 0.576056 0.288028 0.957622i \(-0.407000\pi\)
0.288028 + 0.957622i \(0.407000\pi\)
\(48\) 0 0
\(49\) 6.03811 0.862588
\(50\) 0 0
\(51\) 4.16687 0.583478
\(52\) 0 0
\(53\) −2.86080 −0.392960 −0.196480 0.980508i \(-0.562951\pi\)
−0.196480 + 0.980508i \(0.562951\pi\)
\(54\) 0 0
\(55\) 3.95191 0.532876
\(56\) 0 0
\(57\) 2.79100 0.369677
\(58\) 0 0
\(59\) −3.52446 −0.458845 −0.229423 0.973327i \(-0.573684\pi\)
−0.229423 + 0.973327i \(0.573684\pi\)
\(60\) 0 0
\(61\) 3.00606 0.384886 0.192443 0.981308i \(-0.438359\pi\)
0.192443 + 0.981308i \(0.438359\pi\)
\(62\) 0 0
\(63\) 3.61083 0.454922
\(64\) 0 0
\(65\) −5.10788 −0.633555
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) 3.13197 0.377045
\(70\) 0 0
\(71\) 13.2515 1.57266 0.786332 0.617804i \(-0.211977\pi\)
0.786332 + 0.617804i \(0.211977\pi\)
\(72\) 0 0
\(73\) 4.27398 0.500231 0.250116 0.968216i \(-0.419531\pi\)
0.250116 + 0.968216i \(0.419531\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −14.2697 −1.62618
\(78\) 0 0
\(79\) −2.34696 −0.264054 −0.132027 0.991246i \(-0.542149\pi\)
−0.132027 + 0.991246i \(0.542149\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.02480 −0.112487 −0.0562433 0.998417i \(-0.517912\pi\)
−0.0562433 + 0.998417i \(0.517912\pi\)
\(84\) 0 0
\(85\) −4.16687 −0.451960
\(86\) 0 0
\(87\) −1.00339 −0.107575
\(88\) 0 0
\(89\) 3.28609 0.348325 0.174163 0.984717i \(-0.444278\pi\)
0.174163 + 0.984717i \(0.444278\pi\)
\(90\) 0 0
\(91\) 18.4437 1.93343
\(92\) 0 0
\(93\) 2.03151 0.210658
\(94\) 0 0
\(95\) −2.79100 −0.286350
\(96\) 0 0
\(97\) 15.8180 1.60607 0.803037 0.595929i \(-0.203216\pi\)
0.803037 + 0.595929i \(0.203216\pi\)
\(98\) 0 0
\(99\) −3.95191 −0.397182
\(100\) 0 0
\(101\) −13.4986 −1.34316 −0.671580 0.740932i \(-0.734384\pi\)
−0.671580 + 0.740932i \(0.734384\pi\)
\(102\) 0 0
\(103\) −9.21508 −0.907989 −0.453994 0.891005i \(-0.650001\pi\)
−0.453994 + 0.891005i \(0.650001\pi\)
\(104\) 0 0
\(105\) −3.61083 −0.352381
\(106\) 0 0
\(107\) −17.4978 −1.69157 −0.845786 0.533522i \(-0.820868\pi\)
−0.845786 + 0.533522i \(0.820868\pi\)
\(108\) 0 0
\(109\) −7.36518 −0.705456 −0.352728 0.935726i \(-0.614746\pi\)
−0.352728 + 0.935726i \(0.614746\pi\)
\(110\) 0 0
\(111\) −6.39738 −0.607213
\(112\) 0 0
\(113\) −4.23653 −0.398539 −0.199270 0.979945i \(-0.563857\pi\)
−0.199270 + 0.979945i \(0.563857\pi\)
\(114\) 0 0
\(115\) −3.13197 −0.292058
\(116\) 0 0
\(117\) 5.10788 0.472224
\(118\) 0 0
\(119\) 15.0459 1.37925
\(120\) 0 0
\(121\) 4.61761 0.419783
\(122\) 0 0
\(123\) −0.0315111 −0.00284126
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −13.1095 −1.16328 −0.581642 0.813445i \(-0.697589\pi\)
−0.581642 + 0.813445i \(0.697589\pi\)
\(128\) 0 0
\(129\) 1.97592 0.173970
\(130\) 0 0
\(131\) 9.93669 0.868172 0.434086 0.900871i \(-0.357071\pi\)
0.434086 + 0.900871i \(0.357071\pi\)
\(132\) 0 0
\(133\) 10.0778 0.873858
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 7.49781 0.640581 0.320290 0.947319i \(-0.396219\pi\)
0.320290 + 0.947319i \(0.396219\pi\)
\(138\) 0 0
\(139\) 7.33834 0.622430 0.311215 0.950340i \(-0.399264\pi\)
0.311215 + 0.950340i \(0.399264\pi\)
\(140\) 0 0
\(141\) 3.94924 0.332586
\(142\) 0 0
\(143\) −20.1859 −1.68803
\(144\) 0 0
\(145\) 1.00339 0.0833269
\(146\) 0 0
\(147\) 6.03811 0.498015
\(148\) 0 0
\(149\) −14.1055 −1.15557 −0.577784 0.816190i \(-0.696082\pi\)
−0.577784 + 0.816190i \(0.696082\pi\)
\(150\) 0 0
\(151\) −0.577475 −0.0469942 −0.0234971 0.999724i \(-0.507480\pi\)
−0.0234971 + 0.999724i \(0.507480\pi\)
\(152\) 0 0
\(153\) 4.16687 0.336871
\(154\) 0 0
\(155\) −2.03151 −0.163175
\(156\) 0 0
\(157\) 11.7978 0.941566 0.470783 0.882249i \(-0.343971\pi\)
0.470783 + 0.882249i \(0.343971\pi\)
\(158\) 0 0
\(159\) −2.86080 −0.226876
\(160\) 0 0
\(161\) 11.3090 0.891275
\(162\) 0 0
\(163\) 18.7219 1.46641 0.733204 0.680008i \(-0.238024\pi\)
0.733204 + 0.680008i \(0.238024\pi\)
\(164\) 0 0
\(165\) 3.95191 0.307656
\(166\) 0 0
\(167\) −14.7169 −1.13883 −0.569416 0.822050i \(-0.692830\pi\)
−0.569416 + 0.822050i \(0.692830\pi\)
\(168\) 0 0
\(169\) 13.0905 1.00696
\(170\) 0 0
\(171\) 2.79100 0.213433
\(172\) 0 0
\(173\) −21.1994 −1.61176 −0.805880 0.592079i \(-0.798307\pi\)
−0.805880 + 0.592079i \(0.798307\pi\)
\(174\) 0 0
\(175\) 3.61083 0.272953
\(176\) 0 0
\(177\) −3.52446 −0.264914
\(178\) 0 0
\(179\) 9.65922 0.721964 0.360982 0.932573i \(-0.382442\pi\)
0.360982 + 0.932573i \(0.382442\pi\)
\(180\) 0 0
\(181\) 12.6152 0.937684 0.468842 0.883282i \(-0.344671\pi\)
0.468842 + 0.883282i \(0.344671\pi\)
\(182\) 0 0
\(183\) 3.00606 0.222214
\(184\) 0 0
\(185\) 6.39738 0.470345
\(186\) 0 0
\(187\) −16.4671 −1.20419
\(188\) 0 0
\(189\) 3.61083 0.262649
\(190\) 0 0
\(191\) 10.9695 0.793724 0.396862 0.917878i \(-0.370099\pi\)
0.396862 + 0.917878i \(0.370099\pi\)
\(192\) 0 0
\(193\) 0.722848 0.0520317 0.0260159 0.999662i \(-0.491718\pi\)
0.0260159 + 0.999662i \(0.491718\pi\)
\(194\) 0 0
\(195\) −5.10788 −0.365783
\(196\) 0 0
\(197\) 18.6212 1.32671 0.663354 0.748306i \(-0.269133\pi\)
0.663354 + 0.748306i \(0.269133\pi\)
\(198\) 0 0
\(199\) 20.9803 1.48725 0.743626 0.668596i \(-0.233104\pi\)
0.743626 + 0.668596i \(0.233104\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) −3.62307 −0.254290
\(204\) 0 0
\(205\) 0.0315111 0.00220083
\(206\) 0 0
\(207\) 3.13197 0.217687
\(208\) 0 0
\(209\) −11.0298 −0.762945
\(210\) 0 0
\(211\) 19.2534 1.32546 0.662729 0.748859i \(-0.269398\pi\)
0.662729 + 0.748859i \(0.269398\pi\)
\(212\) 0 0
\(213\) 13.2515 0.907978
\(214\) 0 0
\(215\) −1.97592 −0.134756
\(216\) 0 0
\(217\) 7.33545 0.497963
\(218\) 0 0
\(219\) 4.27398 0.288809
\(220\) 0 0
\(221\) 21.2839 1.43171
\(222\) 0 0
\(223\) −0.0434167 −0.00290740 −0.00145370 0.999999i \(-0.500463\pi\)
−0.00145370 + 0.999999i \(0.500463\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −24.1183 −1.60079 −0.800393 0.599476i \(-0.795376\pi\)
−0.800393 + 0.599476i \(0.795376\pi\)
\(228\) 0 0
\(229\) 15.1106 0.998539 0.499270 0.866447i \(-0.333602\pi\)
0.499270 + 0.866447i \(0.333602\pi\)
\(230\) 0 0
\(231\) −14.2697 −0.938877
\(232\) 0 0
\(233\) −10.5699 −0.692457 −0.346228 0.938150i \(-0.612538\pi\)
−0.346228 + 0.938150i \(0.612538\pi\)
\(234\) 0 0
\(235\) −3.94924 −0.257620
\(236\) 0 0
\(237\) −2.34696 −0.152452
\(238\) 0 0
\(239\) 12.5167 0.809640 0.404820 0.914396i \(-0.367334\pi\)
0.404820 + 0.914396i \(0.367334\pi\)
\(240\) 0 0
\(241\) 8.76911 0.564868 0.282434 0.959287i \(-0.408858\pi\)
0.282434 + 0.959287i \(0.408858\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −6.03811 −0.385761
\(246\) 0 0
\(247\) 14.2561 0.907093
\(248\) 0 0
\(249\) −1.02480 −0.0649442
\(250\) 0 0
\(251\) −15.7157 −0.991965 −0.495982 0.868333i \(-0.665192\pi\)
−0.495982 + 0.868333i \(0.665192\pi\)
\(252\) 0 0
\(253\) −12.3773 −0.778152
\(254\) 0 0
\(255\) −4.16687 −0.260939
\(256\) 0 0
\(257\) 6.71788 0.419050 0.209525 0.977803i \(-0.432808\pi\)
0.209525 + 0.977803i \(0.432808\pi\)
\(258\) 0 0
\(259\) −23.0999 −1.43536
\(260\) 0 0
\(261\) −1.00339 −0.0621082
\(262\) 0 0
\(263\) 21.6126 1.33269 0.666346 0.745642i \(-0.267857\pi\)
0.666346 + 0.745642i \(0.267857\pi\)
\(264\) 0 0
\(265\) 2.86080 0.175737
\(266\) 0 0
\(267\) 3.28609 0.201106
\(268\) 0 0
\(269\) 30.1299 1.83705 0.918527 0.395359i \(-0.129380\pi\)
0.918527 + 0.395359i \(0.129380\pi\)
\(270\) 0 0
\(271\) −12.7627 −0.775279 −0.387640 0.921811i \(-0.626710\pi\)
−0.387640 + 0.921811i \(0.626710\pi\)
\(272\) 0 0
\(273\) 18.4437 1.11626
\(274\) 0 0
\(275\) −3.95191 −0.238309
\(276\) 0 0
\(277\) 14.1883 0.852490 0.426245 0.904608i \(-0.359836\pi\)
0.426245 + 0.904608i \(0.359836\pi\)
\(278\) 0 0
\(279\) 2.03151 0.121623
\(280\) 0 0
\(281\) 11.6888 0.697296 0.348648 0.937254i \(-0.386641\pi\)
0.348648 + 0.937254i \(0.386641\pi\)
\(282\) 0 0
\(283\) 14.3802 0.854813 0.427407 0.904060i \(-0.359427\pi\)
0.427407 + 0.904060i \(0.359427\pi\)
\(284\) 0 0
\(285\) −2.79100 −0.165324
\(286\) 0 0
\(287\) −0.113781 −0.00671629
\(288\) 0 0
\(289\) 0.362793 0.0213408
\(290\) 0 0
\(291\) 15.8180 0.927267
\(292\) 0 0
\(293\) −13.3640 −0.780733 −0.390366 0.920660i \(-0.627652\pi\)
−0.390366 + 0.920660i \(0.627652\pi\)
\(294\) 0 0
\(295\) 3.52446 0.205202
\(296\) 0 0
\(297\) −3.95191 −0.229313
\(298\) 0 0
\(299\) 15.9977 0.925173
\(300\) 0 0
\(301\) 7.13470 0.411237
\(302\) 0 0
\(303\) −13.4986 −0.775474
\(304\) 0 0
\(305\) −3.00606 −0.172126
\(306\) 0 0
\(307\) −2.55156 −0.145625 −0.0728125 0.997346i \(-0.523197\pi\)
−0.0728125 + 0.997346i \(0.523197\pi\)
\(308\) 0 0
\(309\) −9.21508 −0.524228
\(310\) 0 0
\(311\) −28.0850 −1.59255 −0.796276 0.604933i \(-0.793200\pi\)
−0.796276 + 0.604933i \(0.793200\pi\)
\(312\) 0 0
\(313\) −5.73874 −0.324372 −0.162186 0.986760i \(-0.551855\pi\)
−0.162186 + 0.986760i \(0.551855\pi\)
\(314\) 0 0
\(315\) −3.61083 −0.203447
\(316\) 0 0
\(317\) 13.6975 0.769330 0.384665 0.923056i \(-0.374317\pi\)
0.384665 + 0.923056i \(0.374317\pi\)
\(318\) 0 0
\(319\) 3.96530 0.222014
\(320\) 0 0
\(321\) −17.4978 −0.976630
\(322\) 0 0
\(323\) 11.6297 0.647095
\(324\) 0 0
\(325\) 5.10788 0.283334
\(326\) 0 0
\(327\) −7.36518 −0.407295
\(328\) 0 0
\(329\) 14.2600 0.786182
\(330\) 0 0
\(331\) 5.77430 0.317384 0.158692 0.987328i \(-0.449272\pi\)
0.158692 + 0.987328i \(0.449272\pi\)
\(332\) 0 0
\(333\) −6.39738 −0.350574
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) −11.9573 −0.651358 −0.325679 0.945480i \(-0.605593\pi\)
−0.325679 + 0.945480i \(0.605593\pi\)
\(338\) 0 0
\(339\) −4.23653 −0.230097
\(340\) 0 0
\(341\) −8.02835 −0.434760
\(342\) 0 0
\(343\) −3.47321 −0.187536
\(344\) 0 0
\(345\) −3.13197 −0.168620
\(346\) 0 0
\(347\) −21.1534 −1.13557 −0.567787 0.823176i \(-0.692200\pi\)
−0.567787 + 0.823176i \(0.692200\pi\)
\(348\) 0 0
\(349\) −10.9858 −0.588056 −0.294028 0.955797i \(-0.594996\pi\)
−0.294028 + 0.955797i \(0.594996\pi\)
\(350\) 0 0
\(351\) 5.10788 0.272639
\(352\) 0 0
\(353\) −18.7880 −0.999986 −0.499993 0.866029i \(-0.666664\pi\)
−0.499993 + 0.866029i \(0.666664\pi\)
\(354\) 0 0
\(355\) −13.2515 −0.703317
\(356\) 0 0
\(357\) 15.0459 0.796312
\(358\) 0 0
\(359\) 5.24991 0.277080 0.138540 0.990357i \(-0.455759\pi\)
0.138540 + 0.990357i \(0.455759\pi\)
\(360\) 0 0
\(361\) −11.2103 −0.590018
\(362\) 0 0
\(363\) 4.61761 0.242362
\(364\) 0 0
\(365\) −4.27398 −0.223710
\(366\) 0 0
\(367\) 29.3062 1.52977 0.764885 0.644167i \(-0.222796\pi\)
0.764885 + 0.644167i \(0.222796\pi\)
\(368\) 0 0
\(369\) −0.0315111 −0.00164040
\(370\) 0 0
\(371\) −10.3299 −0.536299
\(372\) 0 0
\(373\) −12.5199 −0.648257 −0.324129 0.946013i \(-0.605071\pi\)
−0.324129 + 0.946013i \(0.605071\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −5.12519 −0.263961
\(378\) 0 0
\(379\) −34.4168 −1.76787 −0.883936 0.467609i \(-0.845116\pi\)
−0.883936 + 0.467609i \(0.845116\pi\)
\(380\) 0 0
\(381\) −13.1095 −0.671622
\(382\) 0 0
\(383\) −9.25280 −0.472796 −0.236398 0.971656i \(-0.575967\pi\)
−0.236398 + 0.971656i \(0.575967\pi\)
\(384\) 0 0
\(385\) 14.2697 0.727251
\(386\) 0 0
\(387\) 1.97592 0.100441
\(388\) 0 0
\(389\) −0.256374 −0.0129987 −0.00649934 0.999979i \(-0.502069\pi\)
−0.00649934 + 0.999979i \(0.502069\pi\)
\(390\) 0 0
\(391\) 13.0505 0.659992
\(392\) 0 0
\(393\) 9.93669 0.501240
\(394\) 0 0
\(395\) 2.34696 0.118089
\(396\) 0 0
\(397\) −33.6329 −1.68799 −0.843994 0.536352i \(-0.819802\pi\)
−0.843994 + 0.536352i \(0.819802\pi\)
\(398\) 0 0
\(399\) 10.0778 0.504522
\(400\) 0 0
\(401\) −0.467824 −0.0233620 −0.0116810 0.999932i \(-0.503718\pi\)
−0.0116810 + 0.999932i \(0.503718\pi\)
\(402\) 0 0
\(403\) 10.3767 0.516901
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 25.2819 1.25318
\(408\) 0 0
\(409\) −3.09058 −0.152819 −0.0764096 0.997077i \(-0.524346\pi\)
−0.0764096 + 0.997077i \(0.524346\pi\)
\(410\) 0 0
\(411\) 7.49781 0.369840
\(412\) 0 0
\(413\) −12.7262 −0.626217
\(414\) 0 0
\(415\) 1.02480 0.0503055
\(416\) 0 0
\(417\) 7.33834 0.359360
\(418\) 0 0
\(419\) −1.43962 −0.0703298 −0.0351649 0.999382i \(-0.511196\pi\)
−0.0351649 + 0.999382i \(0.511196\pi\)
\(420\) 0 0
\(421\) 12.2803 0.598507 0.299253 0.954174i \(-0.403262\pi\)
0.299253 + 0.954174i \(0.403262\pi\)
\(422\) 0 0
\(423\) 3.94924 0.192019
\(424\) 0 0
\(425\) 4.16687 0.202123
\(426\) 0 0
\(427\) 10.8544 0.525280
\(428\) 0 0
\(429\) −20.1859 −0.974585
\(430\) 0 0
\(431\) 25.1887 1.21330 0.606649 0.794970i \(-0.292513\pi\)
0.606649 + 0.794970i \(0.292513\pi\)
\(432\) 0 0
\(433\) 22.8480 1.09800 0.549001 0.835822i \(-0.315008\pi\)
0.549001 + 0.835822i \(0.315008\pi\)
\(434\) 0 0
\(435\) 1.00339 0.0481088
\(436\) 0 0
\(437\) 8.74131 0.418154
\(438\) 0 0
\(439\) 35.7813 1.70775 0.853875 0.520478i \(-0.174246\pi\)
0.853875 + 0.520478i \(0.174246\pi\)
\(440\) 0 0
\(441\) 6.03811 0.287529
\(442\) 0 0
\(443\) 16.5541 0.786509 0.393255 0.919430i \(-0.371349\pi\)
0.393255 + 0.919430i \(0.371349\pi\)
\(444\) 0 0
\(445\) −3.28609 −0.155776
\(446\) 0 0
\(447\) −14.1055 −0.667167
\(448\) 0 0
\(449\) −0.552445 −0.0260715 −0.0130357 0.999915i \(-0.504150\pi\)
−0.0130357 + 0.999915i \(0.504150\pi\)
\(450\) 0 0
\(451\) 0.124529 0.00586384
\(452\) 0 0
\(453\) −0.577475 −0.0271321
\(454\) 0 0
\(455\) −18.4437 −0.864655
\(456\) 0 0
\(457\) −15.3560 −0.718322 −0.359161 0.933276i \(-0.616937\pi\)
−0.359161 + 0.933276i \(0.616937\pi\)
\(458\) 0 0
\(459\) 4.16687 0.194493
\(460\) 0 0
\(461\) −17.6577 −0.822401 −0.411201 0.911545i \(-0.634890\pi\)
−0.411201 + 0.911545i \(0.634890\pi\)
\(462\) 0 0
\(463\) −15.0420 −0.699060 −0.349530 0.936925i \(-0.613659\pi\)
−0.349530 + 0.936925i \(0.613659\pi\)
\(464\) 0 0
\(465\) −2.03151 −0.0942091
\(466\) 0 0
\(467\) 3.60120 0.166644 0.0833218 0.996523i \(-0.473447\pi\)
0.0833218 + 0.996523i \(0.473447\pi\)
\(468\) 0 0
\(469\) 3.61083 0.166733
\(470\) 0 0
\(471\) 11.7978 0.543613
\(472\) 0 0
\(473\) −7.80864 −0.359042
\(474\) 0 0
\(475\) 2.79100 0.128060
\(476\) 0 0
\(477\) −2.86080 −0.130987
\(478\) 0 0
\(479\) 7.78569 0.355737 0.177869 0.984054i \(-0.443080\pi\)
0.177869 + 0.984054i \(0.443080\pi\)
\(480\) 0 0
\(481\) −32.6771 −1.48995
\(482\) 0 0
\(483\) 11.3090 0.514578
\(484\) 0 0
\(485\) −15.8180 −0.718258
\(486\) 0 0
\(487\) 12.0734 0.547098 0.273549 0.961858i \(-0.411802\pi\)
0.273549 + 0.961858i \(0.411802\pi\)
\(488\) 0 0
\(489\) 18.7219 0.846632
\(490\) 0 0
\(491\) 34.8500 1.57276 0.786378 0.617745i \(-0.211954\pi\)
0.786378 + 0.617745i \(0.211954\pi\)
\(492\) 0 0
\(493\) −4.18099 −0.188302
\(494\) 0 0
\(495\) 3.95191 0.177625
\(496\) 0 0
\(497\) 47.8490 2.14632
\(498\) 0 0
\(499\) 32.4794 1.45398 0.726989 0.686649i \(-0.240919\pi\)
0.726989 + 0.686649i \(0.240919\pi\)
\(500\) 0 0
\(501\) −14.7169 −0.657504
\(502\) 0 0
\(503\) 27.5356 1.22775 0.613875 0.789403i \(-0.289610\pi\)
0.613875 + 0.789403i \(0.289610\pi\)
\(504\) 0 0
\(505\) 13.4986 0.600680
\(506\) 0 0
\(507\) 13.0905 0.581369
\(508\) 0 0
\(509\) −24.8007 −1.09927 −0.549636 0.835404i \(-0.685233\pi\)
−0.549636 + 0.835404i \(0.685233\pi\)
\(510\) 0 0
\(511\) 15.4326 0.682699
\(512\) 0 0
\(513\) 2.79100 0.123226
\(514\) 0 0
\(515\) 9.21508 0.406065
\(516\) 0 0
\(517\) −15.6071 −0.686397
\(518\) 0 0
\(519\) −21.1994 −0.930550
\(520\) 0 0
\(521\) 6.88070 0.301449 0.150724 0.988576i \(-0.451839\pi\)
0.150724 + 0.988576i \(0.451839\pi\)
\(522\) 0 0
\(523\) −4.50396 −0.196944 −0.0984722 0.995140i \(-0.531396\pi\)
−0.0984722 + 0.995140i \(0.531396\pi\)
\(524\) 0 0
\(525\) 3.61083 0.157590
\(526\) 0 0
\(527\) 8.46504 0.368743
\(528\) 0 0
\(529\) −13.1908 −0.573512
\(530\) 0 0
\(531\) −3.52446 −0.152948
\(532\) 0 0
\(533\) −0.160955 −0.00697173
\(534\) 0 0
\(535\) 17.4978 0.756494
\(536\) 0 0
\(537\) 9.65922 0.416826
\(538\) 0 0
\(539\) −23.8621 −1.02781
\(540\) 0 0
\(541\) −11.1324 −0.478619 −0.239310 0.970943i \(-0.576921\pi\)
−0.239310 + 0.970943i \(0.576921\pi\)
\(542\) 0 0
\(543\) 12.6152 0.541372
\(544\) 0 0
\(545\) 7.36518 0.315490
\(546\) 0 0
\(547\) 17.2028 0.735538 0.367769 0.929917i \(-0.380122\pi\)
0.367769 + 0.929917i \(0.380122\pi\)
\(548\) 0 0
\(549\) 3.00606 0.128295
\(550\) 0 0
\(551\) −2.80045 −0.119303
\(552\) 0 0
\(553\) −8.47450 −0.360372
\(554\) 0 0
\(555\) 6.39738 0.271554
\(556\) 0 0
\(557\) 10.3509 0.438582 0.219291 0.975660i \(-0.429626\pi\)
0.219291 + 0.975660i \(0.429626\pi\)
\(558\) 0 0
\(559\) 10.0927 0.426878
\(560\) 0 0
\(561\) −16.4671 −0.695241
\(562\) 0 0
\(563\) −21.6520 −0.912521 −0.456261 0.889846i \(-0.650812\pi\)
−0.456261 + 0.889846i \(0.650812\pi\)
\(564\) 0 0
\(565\) 4.23653 0.178232
\(566\) 0 0
\(567\) 3.61083 0.151641
\(568\) 0 0
\(569\) 6.15642 0.258090 0.129045 0.991639i \(-0.458809\pi\)
0.129045 + 0.991639i \(0.458809\pi\)
\(570\) 0 0
\(571\) −25.4090 −1.06333 −0.531667 0.846954i \(-0.678434\pi\)
−0.531667 + 0.846954i \(0.678434\pi\)
\(572\) 0 0
\(573\) 10.9695 0.458257
\(574\) 0 0
\(575\) 3.13197 0.130612
\(576\) 0 0
\(577\) −45.7616 −1.90508 −0.952541 0.304411i \(-0.901540\pi\)
−0.952541 + 0.304411i \(0.901540\pi\)
\(578\) 0 0
\(579\) 0.722848 0.0300405
\(580\) 0 0
\(581\) −3.70039 −0.153518
\(582\) 0 0
\(583\) 11.3056 0.468231
\(584\) 0 0
\(585\) −5.10788 −0.211185
\(586\) 0 0
\(587\) 36.9664 1.52577 0.762883 0.646536i \(-0.223783\pi\)
0.762883 + 0.646536i \(0.223783\pi\)
\(588\) 0 0
\(589\) 5.66994 0.233626
\(590\) 0 0
\(591\) 18.6212 0.765975
\(592\) 0 0
\(593\) −20.8852 −0.857652 −0.428826 0.903387i \(-0.641073\pi\)
−0.428826 + 0.903387i \(0.641073\pi\)
\(594\) 0 0
\(595\) −15.0459 −0.616820
\(596\) 0 0
\(597\) 20.9803 0.858666
\(598\) 0 0
\(599\) −7.27017 −0.297051 −0.148526 0.988909i \(-0.547453\pi\)
−0.148526 + 0.988909i \(0.547453\pi\)
\(600\) 0 0
\(601\) −45.2676 −1.84650 −0.923252 0.384195i \(-0.874479\pi\)
−0.923252 + 0.384195i \(0.874479\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) −4.61761 −0.187733
\(606\) 0 0
\(607\) −23.9016 −0.970136 −0.485068 0.874476i \(-0.661205\pi\)
−0.485068 + 0.874476i \(0.661205\pi\)
\(608\) 0 0
\(609\) −3.62307 −0.146814
\(610\) 0 0
\(611\) 20.1723 0.816083
\(612\) 0 0
\(613\) 38.1502 1.54087 0.770435 0.637518i \(-0.220039\pi\)
0.770435 + 0.637518i \(0.220039\pi\)
\(614\) 0 0
\(615\) 0.0315111 0.00127065
\(616\) 0 0
\(617\) 8.40259 0.338276 0.169138 0.985592i \(-0.445902\pi\)
0.169138 + 0.985592i \(0.445902\pi\)
\(618\) 0 0
\(619\) 8.60518 0.345871 0.172936 0.984933i \(-0.444675\pi\)
0.172936 + 0.984933i \(0.444675\pi\)
\(620\) 0 0
\(621\) 3.13197 0.125682
\(622\) 0 0
\(623\) 11.8655 0.475383
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −11.0298 −0.440487
\(628\) 0 0
\(629\) −26.6570 −1.06289
\(630\) 0 0
\(631\) 22.2734 0.886692 0.443346 0.896351i \(-0.353791\pi\)
0.443346 + 0.896351i \(0.353791\pi\)
\(632\) 0 0
\(633\) 19.2534 0.765254
\(634\) 0 0
\(635\) 13.1095 0.520236
\(636\) 0 0
\(637\) 30.8420 1.22200
\(638\) 0 0
\(639\) 13.2515 0.524221
\(640\) 0 0
\(641\) 3.06312 0.120986 0.0604930 0.998169i \(-0.480733\pi\)
0.0604930 + 0.998169i \(0.480733\pi\)
\(642\) 0 0
\(643\) −1.68139 −0.0663074 −0.0331537 0.999450i \(-0.510555\pi\)
−0.0331537 + 0.999450i \(0.510555\pi\)
\(644\) 0 0
\(645\) −1.97592 −0.0778016
\(646\) 0 0
\(647\) 41.0726 1.61473 0.807366 0.590051i \(-0.200892\pi\)
0.807366 + 0.590051i \(0.200892\pi\)
\(648\) 0 0
\(649\) 13.9283 0.546735
\(650\) 0 0
\(651\) 7.33545 0.287499
\(652\) 0 0
\(653\) 26.2381 1.02677 0.513387 0.858157i \(-0.328390\pi\)
0.513387 + 0.858157i \(0.328390\pi\)
\(654\) 0 0
\(655\) −9.93669 −0.388259
\(656\) 0 0
\(657\) 4.27398 0.166744
\(658\) 0 0
\(659\) 1.61523 0.0629203 0.0314602 0.999505i \(-0.489984\pi\)
0.0314602 + 0.999505i \(0.489984\pi\)
\(660\) 0 0
\(661\) −38.7656 −1.50781 −0.753904 0.656985i \(-0.771831\pi\)
−0.753904 + 0.656985i \(0.771831\pi\)
\(662\) 0 0
\(663\) 21.2839 0.826598
\(664\) 0 0
\(665\) −10.0778 −0.390801
\(666\) 0 0
\(667\) −3.14258 −0.121681
\(668\) 0 0
\(669\) −0.0434167 −0.00167859
\(670\) 0 0
\(671\) −11.8797 −0.458610
\(672\) 0 0
\(673\) −0.441903 −0.0170341 −0.00851705 0.999964i \(-0.502711\pi\)
−0.00851705 + 0.999964i \(0.502711\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 19.6075 0.753578 0.376789 0.926299i \(-0.377028\pi\)
0.376789 + 0.926299i \(0.377028\pi\)
\(678\) 0 0
\(679\) 57.1161 2.19192
\(680\) 0 0
\(681\) −24.1183 −0.924214
\(682\) 0 0
\(683\) 9.12846 0.349291 0.174645 0.984631i \(-0.444122\pi\)
0.174645 + 0.984631i \(0.444122\pi\)
\(684\) 0 0
\(685\) −7.49781 −0.286477
\(686\) 0 0
\(687\) 15.1106 0.576507
\(688\) 0 0
\(689\) −14.6126 −0.556696
\(690\) 0 0
\(691\) −39.0546 −1.48571 −0.742853 0.669454i \(-0.766528\pi\)
−0.742853 + 0.669454i \(0.766528\pi\)
\(692\) 0 0
\(693\) −14.2697 −0.542061
\(694\) 0 0
\(695\) −7.33834 −0.278359
\(696\) 0 0
\(697\) −0.131302 −0.00497343
\(698\) 0 0
\(699\) −10.5699 −0.399790
\(700\) 0 0
\(701\) −25.8561 −0.976570 −0.488285 0.872684i \(-0.662377\pi\)
−0.488285 + 0.872684i \(0.662377\pi\)
\(702\) 0 0
\(703\) −17.8551 −0.673417
\(704\) 0 0
\(705\) −3.94924 −0.148737
\(706\) 0 0
\(707\) −48.7412 −1.83310
\(708\) 0 0
\(709\) 22.8391 0.857742 0.428871 0.903366i \(-0.358912\pi\)
0.428871 + 0.903366i \(0.358912\pi\)
\(710\) 0 0
\(711\) −2.34696 −0.0880180
\(712\) 0 0
\(713\) 6.36263 0.238282
\(714\) 0 0
\(715\) 20.1859 0.754910
\(716\) 0 0
\(717\) 12.5167 0.467446
\(718\) 0 0
\(719\) 12.1305 0.452390 0.226195 0.974082i \(-0.427371\pi\)
0.226195 + 0.974082i \(0.427371\pi\)
\(720\) 0 0
\(721\) −33.2741 −1.23919
\(722\) 0 0
\(723\) 8.76911 0.326127
\(724\) 0 0
\(725\) −1.00339 −0.0372649
\(726\) 0 0
\(727\) 31.6088 1.17230 0.586152 0.810201i \(-0.300642\pi\)
0.586152 + 0.810201i \(0.300642\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.23338 0.304523
\(732\) 0 0
\(733\) 9.22504 0.340735 0.170367 0.985381i \(-0.445505\pi\)
0.170367 + 0.985381i \(0.445505\pi\)
\(734\) 0 0
\(735\) −6.03811 −0.222719
\(736\) 0 0
\(737\) −3.95191 −0.145571
\(738\) 0 0
\(739\) 31.9265 1.17443 0.587217 0.809430i \(-0.300224\pi\)
0.587217 + 0.809430i \(0.300224\pi\)
\(740\) 0 0
\(741\) 14.2561 0.523710
\(742\) 0 0
\(743\) −8.41981 −0.308893 −0.154446 0.988001i \(-0.549359\pi\)
−0.154446 + 0.988001i \(0.549359\pi\)
\(744\) 0 0
\(745\) 14.1055 0.516785
\(746\) 0 0
\(747\) −1.02480 −0.0374955
\(748\) 0 0
\(749\) −63.1815 −2.30860
\(750\) 0 0
\(751\) −13.3140 −0.485833 −0.242917 0.970047i \(-0.578104\pi\)
−0.242917 + 0.970047i \(0.578104\pi\)
\(752\) 0 0
\(753\) −15.7157 −0.572711
\(754\) 0 0
\(755\) 0.577475 0.0210165
\(756\) 0 0
\(757\) −10.3061 −0.374581 −0.187291 0.982305i \(-0.559971\pi\)
−0.187291 + 0.982305i \(0.559971\pi\)
\(758\) 0 0
\(759\) −12.3773 −0.449266
\(760\) 0 0
\(761\) −25.6664 −0.930406 −0.465203 0.885204i \(-0.654019\pi\)
−0.465203 + 0.885204i \(0.654019\pi\)
\(762\) 0 0
\(763\) −26.5944 −0.962783
\(764\) 0 0
\(765\) −4.16687 −0.150653
\(766\) 0 0
\(767\) −18.0025 −0.650033
\(768\) 0 0
\(769\) 25.6427 0.924700 0.462350 0.886698i \(-0.347006\pi\)
0.462350 + 0.886698i \(0.347006\pi\)
\(770\) 0 0
\(771\) 6.71788 0.241939
\(772\) 0 0
\(773\) −36.2347 −1.30327 −0.651635 0.758532i \(-0.725917\pi\)
−0.651635 + 0.758532i \(0.725917\pi\)
\(774\) 0 0
\(775\) 2.03151 0.0729740
\(776\) 0 0
\(777\) −23.0999 −0.828703
\(778\) 0 0
\(779\) −0.0879472 −0.00315104
\(780\) 0 0
\(781\) −52.3688 −1.87390
\(782\) 0 0
\(783\) −1.00339 −0.0358582
\(784\) 0 0
\(785\) −11.7978 −0.421081
\(786\) 0 0
\(787\) 12.7835 0.455682 0.227841 0.973698i \(-0.426833\pi\)
0.227841 + 0.973698i \(0.426833\pi\)
\(788\) 0 0
\(789\) 21.6126 0.769431
\(790\) 0 0
\(791\) −15.2974 −0.543913
\(792\) 0 0
\(793\) 15.3546 0.545258
\(794\) 0 0
\(795\) 2.86080 0.101462
\(796\) 0 0
\(797\) −4.44142 −0.157323 −0.0786615 0.996901i \(-0.525065\pi\)
−0.0786615 + 0.996901i \(0.525065\pi\)
\(798\) 0 0
\(799\) 16.4560 0.582170
\(800\) 0 0
\(801\) 3.28609 0.116108
\(802\) 0 0
\(803\) −16.8904 −0.596049
\(804\) 0 0
\(805\) −11.3090 −0.398590
\(806\) 0 0
\(807\) 30.1299 1.06062
\(808\) 0 0
\(809\) 0.965317 0.0339387 0.0169694 0.999856i \(-0.494598\pi\)
0.0169694 + 0.999856i \(0.494598\pi\)
\(810\) 0 0
\(811\) 7.30046 0.256354 0.128177 0.991751i \(-0.459087\pi\)
0.128177 + 0.991751i \(0.459087\pi\)
\(812\) 0 0
\(813\) −12.7627 −0.447608
\(814\) 0 0
\(815\) −18.7219 −0.655798
\(816\) 0 0
\(817\) 5.51477 0.192937
\(818\) 0 0
\(819\) 18.4437 0.644476
\(820\) 0 0
\(821\) −26.8343 −0.936525 −0.468263 0.883589i \(-0.655120\pi\)
−0.468263 + 0.883589i \(0.655120\pi\)
\(822\) 0 0
\(823\) 15.2105 0.530206 0.265103 0.964220i \(-0.414594\pi\)
0.265103 + 0.964220i \(0.414594\pi\)
\(824\) 0 0
\(825\) −3.95191 −0.137588
\(826\) 0 0
\(827\) −19.8677 −0.690868 −0.345434 0.938443i \(-0.612268\pi\)
−0.345434 + 0.938443i \(0.612268\pi\)
\(828\) 0 0
\(829\) −15.1836 −0.527347 −0.263673 0.964612i \(-0.584934\pi\)
−0.263673 + 0.964612i \(0.584934\pi\)
\(830\) 0 0
\(831\) 14.1883 0.492185
\(832\) 0 0
\(833\) 25.1600 0.871743
\(834\) 0 0
\(835\) 14.7169 0.509301
\(836\) 0 0
\(837\) 2.03151 0.0702193
\(838\) 0 0
\(839\) 46.7563 1.61421 0.807104 0.590409i \(-0.201034\pi\)
0.807104 + 0.590409i \(0.201034\pi\)
\(840\) 0 0
\(841\) −27.9932 −0.965283
\(842\) 0 0
\(843\) 11.6888 0.402584
\(844\) 0 0
\(845\) −13.0905 −0.450326
\(846\) 0 0
\(847\) 16.6734 0.572905
\(848\) 0 0
\(849\) 14.3802 0.493527
\(850\) 0 0
\(851\) −20.0364 −0.686839
\(852\) 0 0
\(853\) −17.6156 −0.603148 −0.301574 0.953443i \(-0.597512\pi\)
−0.301574 + 0.953443i \(0.597512\pi\)
\(854\) 0 0
\(855\) −2.79100 −0.0954501
\(856\) 0 0
\(857\) 43.7808 1.49552 0.747762 0.663967i \(-0.231128\pi\)
0.747762 + 0.663967i \(0.231128\pi\)
\(858\) 0 0
\(859\) 31.6898 1.08124 0.540622 0.841266i \(-0.318189\pi\)
0.540622 + 0.841266i \(0.318189\pi\)
\(860\) 0 0
\(861\) −0.113781 −0.00387765
\(862\) 0 0
\(863\) 19.5685 0.666119 0.333059 0.942906i \(-0.391919\pi\)
0.333059 + 0.942906i \(0.391919\pi\)
\(864\) 0 0
\(865\) 21.1994 0.720801
\(866\) 0 0
\(867\) 0.362793 0.0123211
\(868\) 0 0
\(869\) 9.27500 0.314633
\(870\) 0 0
\(871\) 5.10788 0.173074
\(872\) 0 0
\(873\) 15.8180 0.535358
\(874\) 0 0
\(875\) −3.61083 −0.122068
\(876\) 0 0
\(877\) 26.9226 0.909112 0.454556 0.890718i \(-0.349798\pi\)
0.454556 + 0.890718i \(0.349798\pi\)
\(878\) 0 0
\(879\) −13.3640 −0.450756
\(880\) 0 0
\(881\) 16.9281 0.570323 0.285162 0.958479i \(-0.407953\pi\)
0.285162 + 0.958479i \(0.407953\pi\)
\(882\) 0 0
\(883\) −19.0415 −0.640798 −0.320399 0.947283i \(-0.603817\pi\)
−0.320399 + 0.947283i \(0.603817\pi\)
\(884\) 0 0
\(885\) 3.52446 0.118473
\(886\) 0 0
\(887\) −2.80958 −0.0943364 −0.0471682 0.998887i \(-0.515020\pi\)
−0.0471682 + 0.998887i \(0.515020\pi\)
\(888\) 0 0
\(889\) −47.3363 −1.58761
\(890\) 0 0
\(891\) −3.95191 −0.132394
\(892\) 0 0
\(893\) 11.0223 0.368848
\(894\) 0 0
\(895\) −9.65922 −0.322872
\(896\) 0 0
\(897\) 15.9977 0.534149
\(898\) 0 0
\(899\) −2.03839 −0.0679843
\(900\) 0 0
\(901\) −11.9206 −0.397131
\(902\) 0 0
\(903\) 7.13470 0.237428
\(904\) 0 0
\(905\) −12.6152 −0.419345
\(906\) 0 0
\(907\) −31.8586 −1.05785 −0.528923 0.848670i \(-0.677404\pi\)
−0.528923 + 0.848670i \(0.677404\pi\)
\(908\) 0 0
\(909\) −13.4986 −0.447720
\(910\) 0 0
\(911\) −42.9667 −1.42355 −0.711775 0.702407i \(-0.752109\pi\)
−0.711775 + 0.702407i \(0.752109\pi\)
\(912\) 0 0
\(913\) 4.04993 0.134033
\(914\) 0 0
\(915\) −3.00606 −0.0993773
\(916\) 0 0
\(917\) 35.8797 1.18485
\(918\) 0 0
\(919\) 13.0441 0.430284 0.215142 0.976583i \(-0.430979\pi\)
0.215142 + 0.976583i \(0.430979\pi\)
\(920\) 0 0
\(921\) −2.55156 −0.0840766
\(922\) 0 0
\(923\) 67.6872 2.22795
\(924\) 0 0
\(925\) −6.39738 −0.210345
\(926\) 0 0
\(927\) −9.21508 −0.302663
\(928\) 0 0
\(929\) −0.0287500 −0.000943257 0 −0.000471629 1.00000i \(-0.500150\pi\)
−0.000471629 1.00000i \(0.500150\pi\)
\(930\) 0 0
\(931\) 16.8524 0.552314
\(932\) 0 0
\(933\) −28.0850 −0.919460
\(934\) 0 0
\(935\) 16.4671 0.538532
\(936\) 0 0
\(937\) −22.2736 −0.727648 −0.363824 0.931468i \(-0.618529\pi\)
−0.363824 + 0.931468i \(0.618529\pi\)
\(938\) 0 0
\(939\) −5.73874 −0.187277
\(940\) 0 0
\(941\) 16.2045 0.528253 0.264126 0.964488i \(-0.414916\pi\)
0.264126 + 0.964488i \(0.414916\pi\)
\(942\) 0 0
\(943\) −0.0986916 −0.00321384
\(944\) 0 0
\(945\) −3.61083 −0.117460
\(946\) 0 0
\(947\) −3.07154 −0.0998117 −0.0499059 0.998754i \(-0.515892\pi\)
−0.0499059 + 0.998754i \(0.515892\pi\)
\(948\) 0 0
\(949\) 21.8310 0.708664
\(950\) 0 0
\(951\) 13.6975 0.444173
\(952\) 0 0
\(953\) 25.3892 0.822437 0.411219 0.911537i \(-0.365103\pi\)
0.411219 + 0.911537i \(0.365103\pi\)
\(954\) 0 0
\(955\) −10.9695 −0.354964
\(956\) 0 0
\(957\) 3.96530 0.128180
\(958\) 0 0
\(959\) 27.0733 0.874243
\(960\) 0 0
\(961\) −26.8730 −0.866870
\(962\) 0 0
\(963\) −17.4978 −0.563857
\(964\) 0 0
\(965\) −0.722848 −0.0232693
\(966\) 0 0
\(967\) 6.48762 0.208628 0.104314 0.994544i \(-0.466735\pi\)
0.104314 + 0.994544i \(0.466735\pi\)
\(968\) 0 0
\(969\) 11.6297 0.373600
\(970\) 0 0
\(971\) −35.5113 −1.13961 −0.569806 0.821779i \(-0.692982\pi\)
−0.569806 + 0.821779i \(0.692982\pi\)
\(972\) 0 0
\(973\) 26.4975 0.849472
\(974\) 0 0
\(975\) 5.10788 0.163583
\(976\) 0 0
\(977\) −5.88536 −0.188289 −0.0941447 0.995559i \(-0.530012\pi\)
−0.0941447 + 0.995559i \(0.530012\pi\)
\(978\) 0 0
\(979\) −12.9864 −0.415046
\(980\) 0 0
\(981\) −7.36518 −0.235152
\(982\) 0 0
\(983\) 2.21530 0.0706571 0.0353285 0.999376i \(-0.488752\pi\)
0.0353285 + 0.999376i \(0.488752\pi\)
\(984\) 0 0
\(985\) −18.6212 −0.593321
\(986\) 0 0
\(987\) 14.2600 0.453902
\(988\) 0 0
\(989\) 6.18851 0.196783
\(990\) 0 0
\(991\) −57.2636 −1.81904 −0.909519 0.415663i \(-0.863550\pi\)
−0.909519 + 0.415663i \(0.863550\pi\)
\(992\) 0 0
\(993\) 5.77430 0.183242
\(994\) 0 0
\(995\) −20.9803 −0.665120
\(996\) 0 0
\(997\) 1.19804 0.0379423 0.0189711 0.999820i \(-0.493961\pi\)
0.0189711 + 0.999820i \(0.493961\pi\)
\(998\) 0 0
\(999\) −6.39738 −0.202404
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 \(a_p\))