Properties

Label 8040.2.a.t.1.7
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 1.7
Root \(0.922407\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(+4.52856 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(+4.52856 q^{7}\) \(+1.00000 q^{9}\) \(+3.01746 q^{11}\) \(-4.99509 q^{13}\) \(-1.00000 q^{15}\) \(+4.07157 q^{17}\) \(+1.78959 q^{19}\) \(+4.52856 q^{21}\) \(+4.12194 q^{23}\) \(+1.00000 q^{25}\) \(+1.00000 q^{27}\) \(+2.71175 q^{29}\) \(+4.66138 q^{31}\) \(+3.01746 q^{33}\) \(-4.52856 q^{35}\) \(+4.96844 q^{37}\) \(-4.99509 q^{39}\) \(-2.66138 q^{41}\) \(-9.11704 q^{43}\) \(-1.00000 q^{45}\) \(-2.72945 q^{47}\) \(+13.5078 q^{49}\) \(+4.07157 q^{51}\) \(+0.311159 q^{53}\) \(-3.01746 q^{55}\) \(+1.78959 q^{57}\) \(-2.27322 q^{59}\) \(-0.999758 q^{61}\) \(+4.52856 q^{63}\) \(+4.99509 q^{65}\) \(+1.00000 q^{67}\) \(+4.12194 q^{69}\) \(-3.73447 q^{71}\) \(+13.6689 q^{73}\) \(+1.00000 q^{75}\) \(+13.6647 q^{77}\) \(-2.72419 q^{79}\) \(+1.00000 q^{81}\) \(-8.69329 q^{83}\) \(-4.07157 q^{85}\) \(+2.71175 q^{87}\) \(-11.8698 q^{89}\) \(-22.6206 q^{91}\) \(+4.66138 q^{93}\) \(-1.78959 q^{95}\) \(+8.55597 q^{97}\) \(+3.01746 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 13q^{53} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 25q^{79} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 29q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut q^{87} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 9q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.52856 1.71163 0.855817 0.517279i \(-0.173055\pi\)
0.855817 + 0.517279i \(0.173055\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.01746 0.909798 0.454899 0.890543i \(-0.349675\pi\)
0.454899 + 0.890543i \(0.349675\pi\)
\(12\) 0 0
\(13\) −4.99509 −1.38539 −0.692695 0.721231i \(-0.743577\pi\)
−0.692695 + 0.721231i \(0.743577\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 4.07157 0.987501 0.493751 0.869603i \(-0.335626\pi\)
0.493751 + 0.869603i \(0.335626\pi\)
\(18\) 0 0
\(19\) 1.78959 0.410559 0.205280 0.978703i \(-0.434190\pi\)
0.205280 + 0.978703i \(0.434190\pi\)
\(20\) 0 0
\(21\) 4.52856 0.988212
\(22\) 0 0
\(23\) 4.12194 0.859485 0.429742 0.902951i \(-0.358604\pi\)
0.429742 + 0.902951i \(0.358604\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.71175 0.503560 0.251780 0.967785i \(-0.418984\pi\)
0.251780 + 0.967785i \(0.418984\pi\)
\(30\) 0 0
\(31\) 4.66138 0.837208 0.418604 0.908169i \(-0.362519\pi\)
0.418604 + 0.908169i \(0.362519\pi\)
\(32\) 0 0
\(33\) 3.01746 0.525272
\(34\) 0 0
\(35\) −4.52856 −0.765466
\(36\) 0 0
\(37\) 4.96844 0.816807 0.408403 0.912802i \(-0.366086\pi\)
0.408403 + 0.912802i \(0.366086\pi\)
\(38\) 0 0
\(39\) −4.99509 −0.799855
\(40\) 0 0
\(41\) −2.66138 −0.415638 −0.207819 0.978167i \(-0.566636\pi\)
−0.207819 + 0.978167i \(0.566636\pi\)
\(42\) 0 0
\(43\) −9.11704 −1.39034 −0.695168 0.718848i \(-0.744670\pi\)
−0.695168 + 0.718848i \(0.744670\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −2.72945 −0.398131 −0.199066 0.979986i \(-0.563791\pi\)
−0.199066 + 0.979986i \(0.563791\pi\)
\(48\) 0 0
\(49\) 13.5078 1.92969
\(50\) 0 0
\(51\) 4.07157 0.570134
\(52\) 0 0
\(53\) 0.311159 0.0427409 0.0213705 0.999772i \(-0.493197\pi\)
0.0213705 + 0.999772i \(0.493197\pi\)
\(54\) 0 0
\(55\) −3.01746 −0.406874
\(56\) 0 0
\(57\) 1.78959 0.237036
\(58\) 0 0
\(59\) −2.27322 −0.295948 −0.147974 0.988991i \(-0.547275\pi\)
−0.147974 + 0.988991i \(0.547275\pi\)
\(60\) 0 0
\(61\) −0.999758 −0.128006 −0.0640030 0.997950i \(-0.520387\pi\)
−0.0640030 + 0.997950i \(0.520387\pi\)
\(62\) 0 0
\(63\) 4.52856 0.570545
\(64\) 0 0
\(65\) 4.99509 0.619565
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) 4.12194 0.496224
\(70\) 0 0
\(71\) −3.73447 −0.443200 −0.221600 0.975138i \(-0.571128\pi\)
−0.221600 + 0.975138i \(0.571128\pi\)
\(72\) 0 0
\(73\) 13.6689 1.59982 0.799912 0.600117i \(-0.204879\pi\)
0.799912 + 0.600117i \(0.204879\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 13.6647 1.55724
\(78\) 0 0
\(79\) −2.72419 −0.306495 −0.153248 0.988188i \(-0.548973\pi\)
−0.153248 + 0.988188i \(0.548973\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −8.69329 −0.954213 −0.477106 0.878846i \(-0.658314\pi\)
−0.477106 + 0.878846i \(0.658314\pi\)
\(84\) 0 0
\(85\) −4.07157 −0.441624
\(86\) 0 0
\(87\) 2.71175 0.290730
\(88\) 0 0
\(89\) −11.8698 −1.25820 −0.629098 0.777326i \(-0.716576\pi\)
−0.629098 + 0.777326i \(0.716576\pi\)
\(90\) 0 0
\(91\) −22.6206 −2.37128
\(92\) 0 0
\(93\) 4.66138 0.483362
\(94\) 0 0
\(95\) −1.78959 −0.183608
\(96\) 0 0
\(97\) 8.55597 0.868727 0.434363 0.900738i \(-0.356973\pi\)
0.434363 + 0.900738i \(0.356973\pi\)
\(98\) 0 0
\(99\) 3.01746 0.303266
\(100\) 0 0
\(101\) 10.4184 1.03667 0.518335 0.855178i \(-0.326552\pi\)
0.518335 + 0.855178i \(0.326552\pi\)
\(102\) 0 0
\(103\) −7.83575 −0.772079 −0.386040 0.922482i \(-0.626157\pi\)
−0.386040 + 0.922482i \(0.626157\pi\)
\(104\) 0 0
\(105\) −4.52856 −0.441942
\(106\) 0 0
\(107\) 10.7245 1.03678 0.518388 0.855146i \(-0.326532\pi\)
0.518388 + 0.855146i \(0.326532\pi\)
\(108\) 0 0
\(109\) −12.1961 −1.16818 −0.584088 0.811690i \(-0.698548\pi\)
−0.584088 + 0.811690i \(0.698548\pi\)
\(110\) 0 0
\(111\) 4.96844 0.471584
\(112\) 0 0
\(113\) 3.55298 0.334237 0.167118 0.985937i \(-0.446554\pi\)
0.167118 + 0.985937i \(0.446554\pi\)
\(114\) 0 0
\(115\) −4.12194 −0.384373
\(116\) 0 0
\(117\) −4.99509 −0.461796
\(118\) 0 0
\(119\) 18.4384 1.69024
\(120\) 0 0
\(121\) −1.89494 −0.172268
\(122\) 0 0
\(123\) −2.66138 −0.239968
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 19.7682 1.75415 0.877073 0.480357i \(-0.159493\pi\)
0.877073 + 0.480357i \(0.159493\pi\)
\(128\) 0 0
\(129\) −9.11704 −0.802710
\(130\) 0 0
\(131\) −3.62342 −0.316580 −0.158290 0.987393i \(-0.550598\pi\)
−0.158290 + 0.987393i \(0.550598\pi\)
\(132\) 0 0
\(133\) 8.10424 0.702727
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −14.4342 −1.23320 −0.616598 0.787278i \(-0.711489\pi\)
−0.616598 + 0.787278i \(0.711489\pi\)
\(138\) 0 0
\(139\) 2.13358 0.180968 0.0904839 0.995898i \(-0.471159\pi\)
0.0904839 + 0.995898i \(0.471159\pi\)
\(140\) 0 0
\(141\) −2.72945 −0.229861
\(142\) 0 0
\(143\) −15.0725 −1.26042
\(144\) 0 0
\(145\) −2.71175 −0.225199
\(146\) 0 0
\(147\) 13.5078 1.11411
\(148\) 0 0
\(149\) 14.0243 1.14892 0.574458 0.818534i \(-0.305213\pi\)
0.574458 + 0.818534i \(0.305213\pi\)
\(150\) 0 0
\(151\) 14.1469 1.15126 0.575631 0.817710i \(-0.304757\pi\)
0.575631 + 0.817710i \(0.304757\pi\)
\(152\) 0 0
\(153\) 4.07157 0.329167
\(154\) 0 0
\(155\) −4.66138 −0.374411
\(156\) 0 0
\(157\) 20.9743 1.67393 0.836965 0.547256i \(-0.184328\pi\)
0.836965 + 0.547256i \(0.184328\pi\)
\(158\) 0 0
\(159\) 0.311159 0.0246765
\(160\) 0 0
\(161\) 18.6665 1.47112
\(162\) 0 0
\(163\) −20.2727 −1.58788 −0.793941 0.607995i \(-0.791974\pi\)
−0.793941 + 0.607995i \(0.791974\pi\)
\(164\) 0 0
\(165\) −3.01746 −0.234909
\(166\) 0 0
\(167\) 6.04113 0.467476 0.233738 0.972300i \(-0.424904\pi\)
0.233738 + 0.972300i \(0.424904\pi\)
\(168\) 0 0
\(169\) 11.9509 0.919304
\(170\) 0 0
\(171\) 1.78959 0.136853
\(172\) 0 0
\(173\) −3.61707 −0.275001 −0.137500 0.990502i \(-0.543907\pi\)
−0.137500 + 0.990502i \(0.543907\pi\)
\(174\) 0 0
\(175\) 4.52856 0.342327
\(176\) 0 0
\(177\) −2.27322 −0.170866
\(178\) 0 0
\(179\) −2.97723 −0.222529 −0.111264 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(180\) 0 0
\(181\) 3.47802 0.258519 0.129260 0.991611i \(-0.458740\pi\)
0.129260 + 0.991611i \(0.458740\pi\)
\(182\) 0 0
\(183\) −0.999758 −0.0739043
\(184\) 0 0
\(185\) −4.96844 −0.365287
\(186\) 0 0
\(187\) 12.2858 0.898427
\(188\) 0 0
\(189\) 4.52856 0.329404
\(190\) 0 0
\(191\) 9.48662 0.686428 0.343214 0.939257i \(-0.388484\pi\)
0.343214 + 0.939257i \(0.388484\pi\)
\(192\) 0 0
\(193\) 15.7833 1.13610 0.568052 0.822992i \(-0.307697\pi\)
0.568052 + 0.822992i \(0.307697\pi\)
\(194\) 0 0
\(195\) 4.99509 0.357706
\(196\) 0 0
\(197\) −6.46333 −0.460493 −0.230247 0.973132i \(-0.573953\pi\)
−0.230247 + 0.973132i \(0.573953\pi\)
\(198\) 0 0
\(199\) 9.52523 0.675226 0.337613 0.941285i \(-0.390381\pi\)
0.337613 + 0.941285i \(0.390381\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) 12.2803 0.861910
\(204\) 0 0
\(205\) 2.66138 0.185879
\(206\) 0 0
\(207\) 4.12194 0.286495
\(208\) 0 0
\(209\) 5.40000 0.373526
\(210\) 0 0
\(211\) −18.4972 −1.27340 −0.636702 0.771110i \(-0.719702\pi\)
−0.636702 + 0.771110i \(0.719702\pi\)
\(212\) 0 0
\(213\) −3.73447 −0.255882
\(214\) 0 0
\(215\) 9.11704 0.621777
\(216\) 0 0
\(217\) 21.1093 1.43299
\(218\) 0 0
\(219\) 13.6689 0.923659
\(220\) 0 0
\(221\) −20.3379 −1.36807
\(222\) 0 0
\(223\) −14.4186 −0.965542 −0.482771 0.875747i \(-0.660370\pi\)
−0.482771 + 0.875747i \(0.660370\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −27.4412 −1.82134 −0.910668 0.413139i \(-0.864432\pi\)
−0.910668 + 0.413139i \(0.864432\pi\)
\(228\) 0 0
\(229\) 3.95040 0.261050 0.130525 0.991445i \(-0.458334\pi\)
0.130525 + 0.991445i \(0.458334\pi\)
\(230\) 0 0
\(231\) 13.6647 0.899074
\(232\) 0 0
\(233\) −18.2038 −1.19257 −0.596285 0.802773i \(-0.703357\pi\)
−0.596285 + 0.802773i \(0.703357\pi\)
\(234\) 0 0
\(235\) 2.72945 0.178050
\(236\) 0 0
\(237\) −2.72419 −0.176955
\(238\) 0 0
\(239\) −6.17999 −0.399750 −0.199875 0.979821i \(-0.564054\pi\)
−0.199875 + 0.979821i \(0.564054\pi\)
\(240\) 0 0
\(241\) 12.9358 0.833270 0.416635 0.909074i \(-0.363209\pi\)
0.416635 + 0.909074i \(0.363209\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −13.5078 −0.862984
\(246\) 0 0
\(247\) −8.93915 −0.568784
\(248\) 0 0
\(249\) −8.69329 −0.550915
\(250\) 0 0
\(251\) 10.4636 0.660457 0.330228 0.943901i \(-0.392874\pi\)
0.330228 + 0.943901i \(0.392874\pi\)
\(252\) 0 0
\(253\) 12.4378 0.781958
\(254\) 0 0
\(255\) −4.07157 −0.254972
\(256\) 0 0
\(257\) −6.77262 −0.422464 −0.211232 0.977436i \(-0.567748\pi\)
−0.211232 + 0.977436i \(0.567748\pi\)
\(258\) 0 0
\(259\) 22.4999 1.39807
\(260\) 0 0
\(261\) 2.71175 0.167853
\(262\) 0 0
\(263\) −26.2916 −1.62121 −0.810606 0.585592i \(-0.800862\pi\)
−0.810606 + 0.585592i \(0.800862\pi\)
\(264\) 0 0
\(265\) −0.311159 −0.0191143
\(266\) 0 0
\(267\) −11.8698 −0.726420
\(268\) 0 0
\(269\) −27.6254 −1.68435 −0.842175 0.539204i \(-0.818725\pi\)
−0.842175 + 0.539204i \(0.818725\pi\)
\(270\) 0 0
\(271\) 21.4445 1.30266 0.651330 0.758795i \(-0.274211\pi\)
0.651330 + 0.758795i \(0.274211\pi\)
\(272\) 0 0
\(273\) −22.6206 −1.36906
\(274\) 0 0
\(275\) 3.01746 0.181960
\(276\) 0 0
\(277\) −5.90868 −0.355018 −0.177509 0.984119i \(-0.556804\pi\)
−0.177509 + 0.984119i \(0.556804\pi\)
\(278\) 0 0
\(279\) 4.66138 0.279069
\(280\) 0 0
\(281\) −15.4143 −0.919537 −0.459769 0.888039i \(-0.652068\pi\)
−0.459769 + 0.888039i \(0.652068\pi\)
\(282\) 0 0
\(283\) 15.1098 0.898186 0.449093 0.893485i \(-0.351747\pi\)
0.449093 + 0.893485i \(0.351747\pi\)
\(284\) 0 0
\(285\) −1.78959 −0.106006
\(286\) 0 0
\(287\) −12.0522 −0.711419
\(288\) 0 0
\(289\) −0.422296 −0.0248410
\(290\) 0 0
\(291\) 8.55597 0.501560
\(292\) 0 0
\(293\) −10.3820 −0.606526 −0.303263 0.952907i \(-0.598076\pi\)
−0.303263 + 0.952907i \(0.598076\pi\)
\(294\) 0 0
\(295\) 2.27322 0.132352
\(296\) 0 0
\(297\) 3.01746 0.175091
\(298\) 0 0
\(299\) −20.5895 −1.19072
\(300\) 0 0
\(301\) −41.2870 −2.37975
\(302\) 0 0
\(303\) 10.4184 0.598522
\(304\) 0 0
\(305\) 0.999758 0.0572460
\(306\) 0 0
\(307\) 18.6699 1.06555 0.532773 0.846258i \(-0.321150\pi\)
0.532773 + 0.846258i \(0.321150\pi\)
\(308\) 0 0
\(309\) −7.83575 −0.445760
\(310\) 0 0
\(311\) 13.1111 0.743461 0.371730 0.928341i \(-0.378765\pi\)
0.371730 + 0.928341i \(0.378765\pi\)
\(312\) 0 0
\(313\) −7.29921 −0.412576 −0.206288 0.978491i \(-0.566138\pi\)
−0.206288 + 0.978491i \(0.566138\pi\)
\(314\) 0 0
\(315\) −4.52856 −0.255155
\(316\) 0 0
\(317\) 31.4771 1.76793 0.883964 0.467556i \(-0.154865\pi\)
0.883964 + 0.467556i \(0.154865\pi\)
\(318\) 0 0
\(319\) 8.18260 0.458137
\(320\) 0 0
\(321\) 10.7245 0.598583
\(322\) 0 0
\(323\) 7.28643 0.405428
\(324\) 0 0
\(325\) −4.99509 −0.277078
\(326\) 0 0
\(327\) −12.1961 −0.674447
\(328\) 0 0
\(329\) −12.3605 −0.681455
\(330\) 0 0
\(331\) −7.29632 −0.401042 −0.200521 0.979689i \(-0.564264\pi\)
−0.200521 + 0.979689i \(0.564264\pi\)
\(332\) 0 0
\(333\) 4.96844 0.272269
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) −4.70904 −0.256518 −0.128259 0.991741i \(-0.540939\pi\)
−0.128259 + 0.991741i \(0.540939\pi\)
\(338\) 0 0
\(339\) 3.55298 0.192972
\(340\) 0 0
\(341\) 14.0655 0.761690
\(342\) 0 0
\(343\) 29.4711 1.59129
\(344\) 0 0
\(345\) −4.12194 −0.221918
\(346\) 0 0
\(347\) −17.5439 −0.941805 −0.470902 0.882185i \(-0.656072\pi\)
−0.470902 + 0.882185i \(0.656072\pi\)
\(348\) 0 0
\(349\) 19.5530 1.04665 0.523323 0.852134i \(-0.324692\pi\)
0.523323 + 0.852134i \(0.324692\pi\)
\(350\) 0 0
\(351\) −4.99509 −0.266618
\(352\) 0 0
\(353\) 6.20618 0.330322 0.165161 0.986267i \(-0.447186\pi\)
0.165161 + 0.986267i \(0.447186\pi\)
\(354\) 0 0
\(355\) 3.73447 0.198205
\(356\) 0 0
\(357\) 18.4384 0.975861
\(358\) 0 0
\(359\) 10.8531 0.572804 0.286402 0.958110i \(-0.407541\pi\)
0.286402 + 0.958110i \(0.407541\pi\)
\(360\) 0 0
\(361\) −15.7974 −0.831441
\(362\) 0 0
\(363\) −1.89494 −0.0994588
\(364\) 0 0
\(365\) −13.6689 −0.715463
\(366\) 0 0
\(367\) −6.31956 −0.329878 −0.164939 0.986304i \(-0.552743\pi\)
−0.164939 + 0.986304i \(0.552743\pi\)
\(368\) 0 0
\(369\) −2.66138 −0.138546
\(370\) 0 0
\(371\) 1.40910 0.0731568
\(372\) 0 0
\(373\) −1.30921 −0.0677885 −0.0338943 0.999425i \(-0.510791\pi\)
−0.0338943 + 0.999425i \(0.510791\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −13.5454 −0.697626
\(378\) 0 0
\(379\) 18.6595 0.958472 0.479236 0.877686i \(-0.340914\pi\)
0.479236 + 0.877686i \(0.340914\pi\)
\(380\) 0 0
\(381\) 19.7682 1.01276
\(382\) 0 0
\(383\) 21.1748 1.08198 0.540990 0.841029i \(-0.318050\pi\)
0.540990 + 0.841029i \(0.318050\pi\)
\(384\) 0 0
\(385\) −13.6647 −0.696419
\(386\) 0 0
\(387\) −9.11704 −0.463445
\(388\) 0 0
\(389\) −11.6516 −0.590760 −0.295380 0.955380i \(-0.595446\pi\)
−0.295380 + 0.955380i \(0.595446\pi\)
\(390\) 0 0
\(391\) 16.7828 0.848743
\(392\) 0 0
\(393\) −3.62342 −0.182777
\(394\) 0 0
\(395\) 2.72419 0.137069
\(396\) 0 0
\(397\) 31.4764 1.57976 0.789879 0.613263i \(-0.210143\pi\)
0.789879 + 0.613263i \(0.210143\pi\)
\(398\) 0 0
\(399\) 8.10424 0.405720
\(400\) 0 0
\(401\) 38.6154 1.92836 0.964181 0.265246i \(-0.0854532\pi\)
0.964181 + 0.265246i \(0.0854532\pi\)
\(402\) 0 0
\(403\) −23.2840 −1.15986
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 14.9921 0.743129
\(408\) 0 0
\(409\) 25.5356 1.26266 0.631328 0.775516i \(-0.282510\pi\)
0.631328 + 0.775516i \(0.282510\pi\)
\(410\) 0 0
\(411\) −14.4342 −0.711986
\(412\) 0 0
\(413\) −10.2944 −0.506555
\(414\) 0 0
\(415\) 8.69329 0.426737
\(416\) 0 0
\(417\) 2.13358 0.104482
\(418\) 0 0
\(419\) −20.7202 −1.01225 −0.506124 0.862461i \(-0.668922\pi\)
−0.506124 + 0.862461i \(0.668922\pi\)
\(420\) 0 0
\(421\) −15.5622 −0.758454 −0.379227 0.925304i \(-0.623810\pi\)
−0.379227 + 0.925304i \(0.623810\pi\)
\(422\) 0 0
\(423\) −2.72945 −0.132710
\(424\) 0 0
\(425\) 4.07157 0.197500
\(426\) 0 0
\(427\) −4.52746 −0.219099
\(428\) 0 0
\(429\) −15.0725 −0.727706
\(430\) 0 0
\(431\) −31.7281 −1.52829 −0.764144 0.645046i \(-0.776838\pi\)
−0.764144 + 0.645046i \(0.776838\pi\)
\(432\) 0 0
\(433\) 4.49421 0.215978 0.107989 0.994152i \(-0.465559\pi\)
0.107989 + 0.994152i \(0.465559\pi\)
\(434\) 0 0
\(435\) −2.71175 −0.130019
\(436\) 0 0
\(437\) 7.37658 0.352869
\(438\) 0 0
\(439\) 15.8257 0.755321 0.377660 0.925944i \(-0.376729\pi\)
0.377660 + 0.925944i \(0.376729\pi\)
\(440\) 0 0
\(441\) 13.5078 0.643230
\(442\) 0 0
\(443\) 17.8635 0.848719 0.424360 0.905494i \(-0.360499\pi\)
0.424360 + 0.905494i \(0.360499\pi\)
\(444\) 0 0
\(445\) 11.8698 0.562683
\(446\) 0 0
\(447\) 14.0243 0.663327
\(448\) 0 0
\(449\) −0.122541 −0.00578308 −0.00289154 0.999996i \(-0.500920\pi\)
−0.00289154 + 0.999996i \(0.500920\pi\)
\(450\) 0 0
\(451\) −8.03060 −0.378146
\(452\) 0 0
\(453\) 14.1469 0.664681
\(454\) 0 0
\(455\) 22.6206 1.06047
\(456\) 0 0
\(457\) 23.4200 1.09554 0.547771 0.836628i \(-0.315477\pi\)
0.547771 + 0.836628i \(0.315477\pi\)
\(458\) 0 0
\(459\) 4.07157 0.190045
\(460\) 0 0
\(461\) −30.6749 −1.42867 −0.714337 0.699802i \(-0.753272\pi\)
−0.714337 + 0.699802i \(0.753272\pi\)
\(462\) 0 0
\(463\) 10.1660 0.472455 0.236227 0.971698i \(-0.424089\pi\)
0.236227 + 0.971698i \(0.424089\pi\)
\(464\) 0 0
\(465\) −4.66138 −0.216166
\(466\) 0 0
\(467\) 6.90183 0.319378 0.159689 0.987167i \(-0.448951\pi\)
0.159689 + 0.987167i \(0.448951\pi\)
\(468\) 0 0
\(469\) 4.52856 0.209109
\(470\) 0 0
\(471\) 20.9743 0.966444
\(472\) 0 0
\(473\) −27.5103 −1.26492
\(474\) 0 0
\(475\) 1.78959 0.0821118
\(476\) 0 0
\(477\) 0.311159 0.0142470
\(478\) 0 0
\(479\) −7.66608 −0.350272 −0.175136 0.984544i \(-0.556037\pi\)
−0.175136 + 0.984544i \(0.556037\pi\)
\(480\) 0 0
\(481\) −24.8178 −1.13160
\(482\) 0 0
\(483\) 18.6665 0.849354
\(484\) 0 0
\(485\) −8.55597 −0.388506
\(486\) 0 0
\(487\) 16.8798 0.764895 0.382447 0.923977i \(-0.375081\pi\)
0.382447 + 0.923977i \(0.375081\pi\)
\(488\) 0 0
\(489\) −20.2727 −0.916764
\(490\) 0 0
\(491\) −30.1301 −1.35975 −0.679875 0.733328i \(-0.737966\pi\)
−0.679875 + 0.733328i \(0.737966\pi\)
\(492\) 0 0
\(493\) 11.0411 0.497266
\(494\) 0 0
\(495\) −3.01746 −0.135625
\(496\) 0 0
\(497\) −16.9118 −0.758597
\(498\) 0 0
\(499\) 41.5501 1.86004 0.930019 0.367511i \(-0.119790\pi\)
0.930019 + 0.367511i \(0.119790\pi\)
\(500\) 0 0
\(501\) 6.04113 0.269898
\(502\) 0 0
\(503\) 36.2858 1.61790 0.808951 0.587876i \(-0.200036\pi\)
0.808951 + 0.587876i \(0.200036\pi\)
\(504\) 0 0
\(505\) −10.4184 −0.463613
\(506\) 0 0
\(507\) 11.9509 0.530760
\(508\) 0 0
\(509\) −29.7617 −1.31916 −0.659582 0.751633i \(-0.729267\pi\)
−0.659582 + 0.751633i \(0.729267\pi\)
\(510\) 0 0
\(511\) 61.9004 2.73831
\(512\) 0 0
\(513\) 1.78959 0.0790122
\(514\) 0 0
\(515\) 7.83575 0.345284
\(516\) 0 0
\(517\) −8.23601 −0.362219
\(518\) 0 0
\(519\) −3.61707 −0.158772
\(520\) 0 0
\(521\) 10.5559 0.462461 0.231230 0.972899i \(-0.425725\pi\)
0.231230 + 0.972899i \(0.425725\pi\)
\(522\) 0 0
\(523\) 21.1314 0.924013 0.462006 0.886877i \(-0.347130\pi\)
0.462006 + 0.886877i \(0.347130\pi\)
\(524\) 0 0
\(525\) 4.52856 0.197642
\(526\) 0 0
\(527\) 18.9791 0.826744
\(528\) 0 0
\(529\) −6.00957 −0.261286
\(530\) 0 0
\(531\) −2.27322 −0.0986495
\(532\) 0 0
\(533\) 13.2938 0.575820
\(534\) 0 0
\(535\) −10.7245 −0.463660
\(536\) 0 0
\(537\) −2.97723 −0.128477
\(538\) 0 0
\(539\) 40.7593 1.75563
\(540\) 0 0
\(541\) 9.65064 0.414913 0.207457 0.978244i \(-0.433481\pi\)
0.207457 + 0.978244i \(0.433481\pi\)
\(542\) 0 0
\(543\) 3.47802 0.149256
\(544\) 0 0
\(545\) 12.1961 0.522424
\(546\) 0 0
\(547\) −37.2906 −1.59443 −0.797216 0.603694i \(-0.793695\pi\)
−0.797216 + 0.603694i \(0.793695\pi\)
\(548\) 0 0
\(549\) −0.999758 −0.0426686
\(550\) 0 0
\(551\) 4.85291 0.206741
\(552\) 0 0
\(553\) −12.3366 −0.524607
\(554\) 0 0
\(555\) −4.96844 −0.210899
\(556\) 0 0
\(557\) 22.0909 0.936020 0.468010 0.883723i \(-0.344971\pi\)
0.468010 + 0.883723i \(0.344971\pi\)
\(558\) 0 0
\(559\) 45.5404 1.92616
\(560\) 0 0
\(561\) 12.2858 0.518707
\(562\) 0 0
\(563\) 21.4094 0.902300 0.451150 0.892448i \(-0.351014\pi\)
0.451150 + 0.892448i \(0.351014\pi\)
\(564\) 0 0
\(565\) −3.55298 −0.149475
\(566\) 0 0
\(567\) 4.52856 0.190182
\(568\) 0 0
\(569\) 21.6142 0.906116 0.453058 0.891481i \(-0.350333\pi\)
0.453058 + 0.891481i \(0.350333\pi\)
\(570\) 0 0
\(571\) 25.2151 1.05522 0.527609 0.849487i \(-0.323089\pi\)
0.527609 + 0.849487i \(0.323089\pi\)
\(572\) 0 0
\(573\) 9.48662 0.396309
\(574\) 0 0
\(575\) 4.12194 0.171897
\(576\) 0 0
\(577\) −9.50017 −0.395497 −0.197749 0.980253i \(-0.563363\pi\)
−0.197749 + 0.980253i \(0.563363\pi\)
\(578\) 0 0
\(579\) 15.7833 0.655930
\(580\) 0 0
\(581\) −39.3681 −1.63326
\(582\) 0 0
\(583\) 0.938908 0.0388856
\(584\) 0 0
\(585\) 4.99509 0.206522
\(586\) 0 0
\(587\) −33.1639 −1.36882 −0.684409 0.729098i \(-0.739940\pi\)
−0.684409 + 0.729098i \(0.739940\pi\)
\(588\) 0 0
\(589\) 8.34194 0.343724
\(590\) 0 0
\(591\) −6.46333 −0.265866
\(592\) 0 0
\(593\) 27.3144 1.12167 0.560835 0.827928i \(-0.310480\pi\)
0.560835 + 0.827928i \(0.310480\pi\)
\(594\) 0 0
\(595\) −18.4384 −0.755899
\(596\) 0 0
\(597\) 9.52523 0.389842
\(598\) 0 0
\(599\) 9.42693 0.385174 0.192587 0.981280i \(-0.438312\pi\)
0.192587 + 0.981280i \(0.438312\pi\)
\(600\) 0 0
\(601\) −33.1898 −1.35384 −0.676920 0.736057i \(-0.736686\pi\)
−0.676920 + 0.736057i \(0.736686\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) 1.89494 0.0770404
\(606\) 0 0
\(607\) 10.1532 0.412106 0.206053 0.978541i \(-0.433938\pi\)
0.206053 + 0.978541i \(0.433938\pi\)
\(608\) 0 0
\(609\) 12.2803 0.497624
\(610\) 0 0
\(611\) 13.6339 0.551567
\(612\) 0 0
\(613\) −23.0912 −0.932646 −0.466323 0.884615i \(-0.654421\pi\)
−0.466323 + 0.884615i \(0.654421\pi\)
\(614\) 0 0
\(615\) 2.66138 0.107317
\(616\) 0 0
\(617\) −1.52338 −0.0613288 −0.0306644 0.999530i \(-0.509762\pi\)
−0.0306644 + 0.999530i \(0.509762\pi\)
\(618\) 0 0
\(619\) −40.3184 −1.62053 −0.810266 0.586062i \(-0.800677\pi\)
−0.810266 + 0.586062i \(0.800677\pi\)
\(620\) 0 0
\(621\) 4.12194 0.165408
\(622\) 0 0
\(623\) −53.7531 −2.15357
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 5.40000 0.215655
\(628\) 0 0
\(629\) 20.2294 0.806598
\(630\) 0 0
\(631\) 0.363697 0.0144785 0.00723927 0.999974i \(-0.497696\pi\)
0.00723927 + 0.999974i \(0.497696\pi\)
\(632\) 0 0
\(633\) −18.4972 −0.735200
\(634\) 0 0
\(635\) −19.7682 −0.784478
\(636\) 0 0
\(637\) −67.4729 −2.67337
\(638\) 0 0
\(639\) −3.73447 −0.147733
\(640\) 0 0
\(641\) 25.1645 0.993937 0.496968 0.867769i \(-0.334447\pi\)
0.496968 + 0.867769i \(0.334447\pi\)
\(642\) 0 0
\(643\) −6.18919 −0.244078 −0.122039 0.992525i \(-0.538943\pi\)
−0.122039 + 0.992525i \(0.538943\pi\)
\(644\) 0 0
\(645\) 9.11704 0.358983
\(646\) 0 0
\(647\) −26.3079 −1.03427 −0.517135 0.855904i \(-0.673002\pi\)
−0.517135 + 0.855904i \(0.673002\pi\)
\(648\) 0 0
\(649\) −6.85936 −0.269253
\(650\) 0 0
\(651\) 21.1093 0.827340
\(652\) 0 0
\(653\) 24.9711 0.977196 0.488598 0.872509i \(-0.337509\pi\)
0.488598 + 0.872509i \(0.337509\pi\)
\(654\) 0 0
\(655\) 3.62342 0.141579
\(656\) 0 0
\(657\) 13.6689 0.533275
\(658\) 0 0
\(659\) 33.8149 1.31724 0.658621 0.752474i \(-0.271140\pi\)
0.658621 + 0.752474i \(0.271140\pi\)
\(660\) 0 0
\(661\) −9.02483 −0.351025 −0.175513 0.984477i \(-0.556158\pi\)
−0.175513 + 0.984477i \(0.556158\pi\)
\(662\) 0 0
\(663\) −20.3379 −0.789858
\(664\) 0 0
\(665\) −8.10424 −0.314269
\(666\) 0 0
\(667\) 11.1777 0.432802
\(668\) 0 0
\(669\) −14.4186 −0.557456
\(670\) 0 0
\(671\) −3.01673 −0.116460
\(672\) 0 0
\(673\) −28.0138 −1.07985 −0.539927 0.841712i \(-0.681548\pi\)
−0.539927 + 0.841712i \(0.681548\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −6.97519 −0.268078 −0.134039 0.990976i \(-0.542795\pi\)
−0.134039 + 0.990976i \(0.542795\pi\)
\(678\) 0 0
\(679\) 38.7462 1.48694
\(680\) 0 0
\(681\) −27.4412 −1.05155
\(682\) 0 0
\(683\) −34.0960 −1.30465 −0.652324 0.757940i \(-0.726206\pi\)
−0.652324 + 0.757940i \(0.726206\pi\)
\(684\) 0 0
\(685\) 14.4342 0.551502
\(686\) 0 0
\(687\) 3.95040 0.150717
\(688\) 0 0
\(689\) −1.55427 −0.0592128
\(690\) 0 0
\(691\) 41.2338 1.56861 0.784304 0.620377i \(-0.213020\pi\)
0.784304 + 0.620377i \(0.213020\pi\)
\(692\) 0 0
\(693\) 13.6647 0.519080
\(694\) 0 0
\(695\) −2.13358 −0.0809312
\(696\) 0 0
\(697\) −10.8360 −0.410443
\(698\) 0 0
\(699\) −18.2038 −0.688530
\(700\) 0 0
\(701\) 3.11548 0.117670 0.0588350 0.998268i \(-0.481261\pi\)
0.0588350 + 0.998268i \(0.481261\pi\)
\(702\) 0 0
\(703\) 8.89145 0.335347
\(704\) 0 0
\(705\) 2.72945 0.102797
\(706\) 0 0
\(707\) 47.1804 1.77440
\(708\) 0 0
\(709\) 9.97845 0.374749 0.187374 0.982289i \(-0.440002\pi\)
0.187374 + 0.982289i \(0.440002\pi\)
\(710\) 0 0
\(711\) −2.72419 −0.102165
\(712\) 0 0
\(713\) 19.2139 0.719568
\(714\) 0 0
\(715\) 15.0725 0.563679
\(716\) 0 0
\(717\) −6.17999 −0.230796
\(718\) 0 0
\(719\) 43.0440 1.60527 0.802635 0.596471i \(-0.203431\pi\)
0.802635 + 0.596471i \(0.203431\pi\)
\(720\) 0 0
\(721\) −35.4846 −1.32152
\(722\) 0 0
\(723\) 12.9358 0.481089
\(724\) 0 0
\(725\) 2.71175 0.100712
\(726\) 0 0
\(727\) −27.8439 −1.03267 −0.516336 0.856386i \(-0.672704\pi\)
−0.516336 + 0.856386i \(0.672704\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −37.1207 −1.37296
\(732\) 0 0
\(733\) 19.8584 0.733486 0.366743 0.930322i \(-0.380473\pi\)
0.366743 + 0.930322i \(0.380473\pi\)
\(734\) 0 0
\(735\) −13.5078 −0.498244
\(736\) 0 0
\(737\) 3.01746 0.111150
\(738\) 0 0
\(739\) −28.1107 −1.03407 −0.517035 0.855964i \(-0.672964\pi\)
−0.517035 + 0.855964i \(0.672964\pi\)
\(740\) 0 0
\(741\) −8.93915 −0.328388
\(742\) 0 0
\(743\) 6.81336 0.249958 0.124979 0.992159i \(-0.460114\pi\)
0.124979 + 0.992159i \(0.460114\pi\)
\(744\) 0 0
\(745\) −14.0243 −0.513811
\(746\) 0 0
\(747\) −8.69329 −0.318071
\(748\) 0 0
\(749\) 48.5665 1.77458
\(750\) 0 0
\(751\) 8.45304 0.308456 0.154228 0.988035i \(-0.450711\pi\)
0.154228 + 0.988035i \(0.450711\pi\)
\(752\) 0 0
\(753\) 10.4636 0.381315
\(754\) 0 0
\(755\) −14.1469 −0.514860
\(756\) 0 0
\(757\) 9.50624 0.345510 0.172755 0.984965i \(-0.444733\pi\)
0.172755 + 0.984965i \(0.444733\pi\)
\(758\) 0 0
\(759\) 12.4378 0.451463
\(760\) 0 0
\(761\) −17.3448 −0.628747 −0.314374 0.949299i \(-0.601794\pi\)
−0.314374 + 0.949299i \(0.601794\pi\)
\(762\) 0 0
\(763\) −55.2308 −1.99949
\(764\) 0 0
\(765\) −4.07157 −0.147208
\(766\) 0 0
\(767\) 11.3550 0.410004
\(768\) 0 0
\(769\) 36.8263 1.32799 0.663995 0.747737i \(-0.268860\pi\)
0.663995 + 0.747737i \(0.268860\pi\)
\(770\) 0 0
\(771\) −6.77262 −0.243910
\(772\) 0 0
\(773\) −5.48691 −0.197351 −0.0986753 0.995120i \(-0.531461\pi\)
−0.0986753 + 0.995120i \(0.531461\pi\)
\(774\) 0 0
\(775\) 4.66138 0.167442
\(776\) 0 0
\(777\) 22.4999 0.807178
\(778\) 0 0
\(779\) −4.76277 −0.170644
\(780\) 0 0
\(781\) −11.2686 −0.403223
\(782\) 0 0
\(783\) 2.71175 0.0969101
\(784\) 0 0
\(785\) −20.9743 −0.748604
\(786\) 0 0
\(787\) 41.7969 1.48990 0.744949 0.667121i \(-0.232474\pi\)
0.744949 + 0.667121i \(0.232474\pi\)
\(788\) 0 0
\(789\) −26.2916 −0.936007
\(790\) 0 0
\(791\) 16.0899 0.572091
\(792\) 0 0
\(793\) 4.99389 0.177338
\(794\) 0 0
\(795\) −0.311159 −0.0110357
\(796\) 0 0
\(797\) −6.99894 −0.247915 −0.123958 0.992288i \(-0.539559\pi\)
−0.123958 + 0.992288i \(0.539559\pi\)
\(798\) 0 0
\(799\) −11.1132 −0.393155
\(800\) 0 0
\(801\) −11.8698 −0.419399
\(802\) 0 0
\(803\) 41.2454 1.45552
\(804\) 0 0
\(805\) −18.6665 −0.657907
\(806\) 0 0
\(807\) −27.6254 −0.972460
\(808\) 0 0
\(809\) 22.7908 0.801282 0.400641 0.916235i \(-0.368787\pi\)
0.400641 + 0.916235i \(0.368787\pi\)
\(810\) 0 0
\(811\) −26.2680 −0.922395 −0.461197 0.887298i \(-0.652580\pi\)
−0.461197 + 0.887298i \(0.652580\pi\)
\(812\) 0 0
\(813\) 21.4445 0.752091
\(814\) 0 0
\(815\) 20.2727 0.710123
\(816\) 0 0
\(817\) −16.3157 −0.570815
\(818\) 0 0
\(819\) −22.6206 −0.790427
\(820\) 0 0
\(821\) −29.8917 −1.04323 −0.521614 0.853182i \(-0.674670\pi\)
−0.521614 + 0.853182i \(0.674670\pi\)
\(822\) 0 0
\(823\) 45.2087 1.57587 0.787937 0.615755i \(-0.211149\pi\)
0.787937 + 0.615755i \(0.211149\pi\)
\(824\) 0 0
\(825\) 3.01746 0.105054
\(826\) 0 0
\(827\) −24.5552 −0.853868 −0.426934 0.904283i \(-0.640406\pi\)
−0.426934 + 0.904283i \(0.640406\pi\)
\(828\) 0 0
\(829\) −26.0885 −0.906090 −0.453045 0.891488i \(-0.649662\pi\)
−0.453045 + 0.891488i \(0.649662\pi\)
\(830\) 0 0
\(831\) −5.90868 −0.204970
\(832\) 0 0
\(833\) 54.9982 1.90557
\(834\) 0 0
\(835\) −6.04113 −0.209062
\(836\) 0 0
\(837\) 4.66138 0.161121
\(838\) 0 0
\(839\) −25.3367 −0.874720 −0.437360 0.899286i \(-0.644086\pi\)
−0.437360 + 0.899286i \(0.644086\pi\)
\(840\) 0 0
\(841\) −21.6464 −0.746428
\(842\) 0 0
\(843\) −15.4143 −0.530895
\(844\) 0 0
\(845\) −11.9509 −0.411125
\(846\) 0 0
\(847\) −8.58136 −0.294859
\(848\) 0 0
\(849\) 15.1098 0.518568
\(850\) 0 0
\(851\) 20.4796 0.702033
\(852\) 0 0
\(853\) −4.49921 −0.154050 −0.0770250 0.997029i \(-0.524542\pi\)
−0.0770250 + 0.997029i \(0.524542\pi\)
\(854\) 0 0
\(855\) −1.78959 −0.0612026
\(856\) 0 0
\(857\) −31.5055 −1.07621 −0.538103 0.842879i \(-0.680859\pi\)
−0.538103 + 0.842879i \(0.680859\pi\)
\(858\) 0 0
\(859\) 14.2301 0.485524 0.242762 0.970086i \(-0.421947\pi\)
0.242762 + 0.970086i \(0.421947\pi\)
\(860\) 0 0
\(861\) −12.0522 −0.410738
\(862\) 0 0
\(863\) −37.2066 −1.26653 −0.633263 0.773936i \(-0.718285\pi\)
−0.633263 + 0.773936i \(0.718285\pi\)
\(864\) 0 0
\(865\) 3.61707 0.122984
\(866\) 0 0
\(867\) −0.422296 −0.0143419
\(868\) 0 0
\(869\) −8.22012 −0.278849
\(870\) 0 0
\(871\) −4.99509 −0.169252
\(872\) 0 0
\(873\) 8.55597 0.289576
\(874\) 0 0
\(875\) −4.52856 −0.153093
\(876\) 0 0
\(877\) −21.2708 −0.718262 −0.359131 0.933287i \(-0.616927\pi\)
−0.359131 + 0.933287i \(0.616927\pi\)
\(878\) 0 0
\(879\) −10.3820 −0.350178
\(880\) 0 0
\(881\) −40.8417 −1.37599 −0.687996 0.725714i \(-0.741509\pi\)
−0.687996 + 0.725714i \(0.741509\pi\)
\(882\) 0 0
\(883\) 16.0760 0.541000 0.270500 0.962720i \(-0.412811\pi\)
0.270500 + 0.962720i \(0.412811\pi\)
\(884\) 0 0
\(885\) 2.27322 0.0764136
\(886\) 0 0
\(887\) −23.5466 −0.790617 −0.395308 0.918548i \(-0.629362\pi\)
−0.395308 + 0.918548i \(0.629362\pi\)
\(888\) 0 0
\(889\) 89.5216 3.00246
\(890\) 0 0
\(891\) 3.01746 0.101089
\(892\) 0 0
\(893\) −4.88459 −0.163457
\(894\) 0 0
\(895\) 2.97723 0.0995179
\(896\) 0 0
\(897\) −20.5895 −0.687463
\(898\) 0 0
\(899\) 12.6405 0.421584
\(900\) 0 0
\(901\) 1.26690 0.0422067
\(902\) 0 0
\(903\) −41.2870 −1.37395
\(904\) 0 0
\(905\) −3.47802 −0.115613
\(906\) 0 0
\(907\) −42.8507 −1.42283 −0.711416 0.702771i \(-0.751946\pi\)
−0.711416 + 0.702771i \(0.751946\pi\)
\(908\) 0 0
\(909\) 10.4184 0.345557
\(910\) 0 0
\(911\) −29.3201 −0.971419 −0.485709 0.874120i \(-0.661439\pi\)
−0.485709 + 0.874120i \(0.661439\pi\)
\(912\) 0 0
\(913\) −26.2317 −0.868141
\(914\) 0 0
\(915\) 0.999758 0.0330510
\(916\) 0 0
\(917\) −16.4089 −0.541869
\(918\) 0 0
\(919\) 8.77825 0.289568 0.144784 0.989463i \(-0.453751\pi\)
0.144784 + 0.989463i \(0.453751\pi\)
\(920\) 0 0
\(921\) 18.6699 0.615193
\(922\) 0 0
\(923\) 18.6540 0.614005
\(924\) 0 0
\(925\) 4.96844 0.163361
\(926\) 0 0
\(927\) −7.83575 −0.257360
\(928\) 0 0
\(929\) 23.6432 0.775709 0.387855 0.921721i \(-0.373216\pi\)
0.387855 + 0.921721i \(0.373216\pi\)
\(930\) 0 0
\(931\) 24.1734 0.792253
\(932\) 0 0
\(933\) 13.1111 0.429237
\(934\) 0 0
\(935\) −12.2858 −0.401789
\(936\) 0 0
\(937\) 3.80530 0.124314 0.0621568 0.998066i \(-0.480202\pi\)
0.0621568 + 0.998066i \(0.480202\pi\)
\(938\) 0 0
\(939\) −7.29921 −0.238201
\(940\) 0 0
\(941\) 10.8919 0.355067 0.177534 0.984115i \(-0.443188\pi\)
0.177534 + 0.984115i \(0.443188\pi\)
\(942\) 0 0
\(943\) −10.9701 −0.357234
\(944\) 0 0
\(945\) −4.52856 −0.147314
\(946\) 0 0
\(947\) −53.9819 −1.75418 −0.877089 0.480329i \(-0.840517\pi\)
−0.877089 + 0.480329i \(0.840517\pi\)
\(948\) 0 0
\(949\) −68.2775 −2.21638
\(950\) 0 0
\(951\) 31.4771 1.02071
\(952\) 0 0
\(953\) −38.1294 −1.23513 −0.617566 0.786519i \(-0.711881\pi\)
−0.617566 + 0.786519i \(0.711881\pi\)
\(954\) 0 0
\(955\) −9.48662 −0.306980
\(956\) 0 0
\(957\) 8.18260 0.264506
\(958\) 0 0
\(959\) −65.3660 −2.11078
\(960\) 0 0
\(961\) −9.27155 −0.299082
\(962\) 0 0
\(963\) 10.7245 0.345592
\(964\) 0 0
\(965\) −15.7833 −0.508081
\(966\) 0 0
\(967\) −9.32514 −0.299876 −0.149938 0.988695i \(-0.547907\pi\)
−0.149938 + 0.988695i \(0.547907\pi\)
\(968\) 0 0
\(969\) 7.28643 0.234074
\(970\) 0 0
\(971\) 24.4385 0.784268 0.392134 0.919908i \(-0.371737\pi\)
0.392134 + 0.919908i \(0.371737\pi\)
\(972\) 0 0
\(973\) 9.66203 0.309751
\(974\) 0 0
\(975\) −4.99509 −0.159971
\(976\) 0 0
\(977\) −26.1127 −0.835419 −0.417710 0.908581i \(-0.637167\pi\)
−0.417710 + 0.908581i \(0.637167\pi\)
\(978\) 0 0
\(979\) −35.8166 −1.14470
\(980\) 0 0
\(981\) −12.1961 −0.389392
\(982\) 0 0
\(983\) 27.5111 0.877468 0.438734 0.898617i \(-0.355427\pi\)
0.438734 + 0.898617i \(0.355427\pi\)
\(984\) 0 0
\(985\) 6.46333 0.205939
\(986\) 0 0
\(987\) −12.3605 −0.393438
\(988\) 0 0
\(989\) −37.5799 −1.19497
\(990\) 0 0
\(991\) −46.5897 −1.47997 −0.739985 0.672623i \(-0.765167\pi\)
−0.739985 + 0.672623i \(0.765167\pi\)
\(992\) 0 0
\(993\) −7.29632 −0.231542
\(994\) 0 0
\(995\) −9.52523 −0.301970
\(996\) 0 0
\(997\) −48.9541 −1.55039 −0.775196 0.631721i \(-0.782349\pi\)
−0.775196 + 0.631721i \(0.782349\pi\)
\(998\) 0 0
\(999\) 4.96844 0.157195
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 \(a_p\))