Properties

Label 8020.2.a.c.1.7
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.58112 q^{3}\) \(-1.00000 q^{5}\) \(+3.33363 q^{7}\) \(-0.500055 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.58112 q^{3}\) \(-1.00000 q^{5}\) \(+3.33363 q^{7}\) \(-0.500055 q^{9}\) \(-4.48018 q^{11}\) \(+5.14806 q^{13}\) \(+1.58112 q^{15}\) \(-2.08313 q^{17}\) \(-1.21732 q^{19}\) \(-5.27087 q^{21}\) \(-6.31215 q^{23}\) \(+1.00000 q^{25}\) \(+5.53401 q^{27}\) \(-2.70237 q^{29}\) \(+9.30315 q^{31}\) \(+7.08371 q^{33}\) \(-3.33363 q^{35}\) \(-2.68867 q^{37}\) \(-8.13971 q^{39}\) \(+10.6715 q^{41}\) \(+9.65978 q^{43}\) \(+0.500055 q^{45}\) \(-12.9089 q^{47}\) \(+4.11307 q^{49}\) \(+3.29369 q^{51}\) \(-1.27197 q^{53}\) \(+4.48018 q^{55}\) \(+1.92473 q^{57}\) \(+6.58994 q^{59}\) \(-13.6691 q^{61}\) \(-1.66700 q^{63}\) \(-5.14806 q^{65}\) \(-3.07957 q^{67}\) \(+9.98027 q^{69}\) \(+6.24891 q^{71}\) \(-5.77379 q^{73}\) \(-1.58112 q^{75}\) \(-14.9353 q^{77}\) \(-4.70756 q^{79}\) \(-7.24978 q^{81}\) \(+8.49193 q^{83}\) \(+2.08313 q^{85}\) \(+4.27278 q^{87}\) \(+4.55626 q^{89}\) \(+17.1617 q^{91}\) \(-14.7094 q^{93}\) \(+1.21732 q^{95}\) \(-14.3702 q^{97}\) \(+2.24034 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.58112 −0.912861 −0.456430 0.889759i \(-0.650872\pi\)
−0.456430 + 0.889759i \(0.650872\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.33363 1.25999 0.629996 0.776598i \(-0.283056\pi\)
0.629996 + 0.776598i \(0.283056\pi\)
\(8\) 0 0
\(9\) −0.500055 −0.166685
\(10\) 0 0
\(11\) −4.48018 −1.35083 −0.675413 0.737440i \(-0.736035\pi\)
−0.675413 + 0.737440i \(0.736035\pi\)
\(12\) 0 0
\(13\) 5.14806 1.42782 0.713908 0.700240i \(-0.246923\pi\)
0.713908 + 0.700240i \(0.246923\pi\)
\(14\) 0 0
\(15\) 1.58112 0.408244
\(16\) 0 0
\(17\) −2.08313 −0.505234 −0.252617 0.967566i \(-0.581291\pi\)
−0.252617 + 0.967566i \(0.581291\pi\)
\(18\) 0 0
\(19\) −1.21732 −0.279272 −0.139636 0.990203i \(-0.544593\pi\)
−0.139636 + 0.990203i \(0.544593\pi\)
\(20\) 0 0
\(21\) −5.27087 −1.15020
\(22\) 0 0
\(23\) −6.31215 −1.31617 −0.658087 0.752942i \(-0.728634\pi\)
−0.658087 + 0.752942i \(0.728634\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.53401 1.06502
\(28\) 0 0
\(29\) −2.70237 −0.501818 −0.250909 0.968011i \(-0.580730\pi\)
−0.250909 + 0.968011i \(0.580730\pi\)
\(30\) 0 0
\(31\) 9.30315 1.67089 0.835447 0.549570i \(-0.185209\pi\)
0.835447 + 0.549570i \(0.185209\pi\)
\(32\) 0 0
\(33\) 7.08371 1.23312
\(34\) 0 0
\(35\) −3.33363 −0.563486
\(36\) 0 0
\(37\) −2.68867 −0.442015 −0.221008 0.975272i \(-0.570935\pi\)
−0.221008 + 0.975272i \(0.570935\pi\)
\(38\) 0 0
\(39\) −8.13971 −1.30340
\(40\) 0 0
\(41\) 10.6715 1.66661 0.833303 0.552817i \(-0.186447\pi\)
0.833303 + 0.552817i \(0.186447\pi\)
\(42\) 0 0
\(43\) 9.65978 1.47310 0.736552 0.676381i \(-0.236453\pi\)
0.736552 + 0.676381i \(0.236453\pi\)
\(44\) 0 0
\(45\) 0.500055 0.0745439
\(46\) 0 0
\(47\) −12.9089 −1.88295 −0.941476 0.337080i \(-0.890561\pi\)
−0.941476 + 0.337080i \(0.890561\pi\)
\(48\) 0 0
\(49\) 4.11307 0.587581
\(50\) 0 0
\(51\) 3.29369 0.461209
\(52\) 0 0
\(53\) −1.27197 −0.174718 −0.0873591 0.996177i \(-0.527843\pi\)
−0.0873591 + 0.996177i \(0.527843\pi\)
\(54\) 0 0
\(55\) 4.48018 0.604108
\(56\) 0 0
\(57\) 1.92473 0.254936
\(58\) 0 0
\(59\) 6.58994 0.857937 0.428969 0.903319i \(-0.358877\pi\)
0.428969 + 0.903319i \(0.358877\pi\)
\(60\) 0 0
\(61\) −13.6691 −1.75015 −0.875074 0.483989i \(-0.839188\pi\)
−0.875074 + 0.483989i \(0.839188\pi\)
\(62\) 0 0
\(63\) −1.66700 −0.210022
\(64\) 0 0
\(65\) −5.14806 −0.638539
\(66\) 0 0
\(67\) −3.07957 −0.376229 −0.188115 0.982147i \(-0.560238\pi\)
−0.188115 + 0.982147i \(0.560238\pi\)
\(68\) 0 0
\(69\) 9.98027 1.20148
\(70\) 0 0
\(71\) 6.24891 0.741609 0.370804 0.928711i \(-0.379082\pi\)
0.370804 + 0.928711i \(0.379082\pi\)
\(72\) 0 0
\(73\) −5.77379 −0.675771 −0.337886 0.941187i \(-0.609712\pi\)
−0.337886 + 0.941187i \(0.609712\pi\)
\(74\) 0 0
\(75\) −1.58112 −0.182572
\(76\) 0 0
\(77\) −14.9353 −1.70203
\(78\) 0 0
\(79\) −4.70756 −0.529642 −0.264821 0.964298i \(-0.585313\pi\)
−0.264821 + 0.964298i \(0.585313\pi\)
\(80\) 0 0
\(81\) −7.24978 −0.805531
\(82\) 0 0
\(83\) 8.49193 0.932111 0.466055 0.884756i \(-0.345675\pi\)
0.466055 + 0.884756i \(0.345675\pi\)
\(84\) 0 0
\(85\) 2.08313 0.225948
\(86\) 0 0
\(87\) 4.27278 0.458090
\(88\) 0 0
\(89\) 4.55626 0.482962 0.241481 0.970406i \(-0.422367\pi\)
0.241481 + 0.970406i \(0.422367\pi\)
\(90\) 0 0
\(91\) 17.1617 1.79904
\(92\) 0 0
\(93\) −14.7094 −1.52529
\(94\) 0 0
\(95\) 1.21732 0.124894
\(96\) 0 0
\(97\) −14.3702 −1.45907 −0.729534 0.683944i \(-0.760263\pi\)
−0.729534 + 0.683944i \(0.760263\pi\)
\(98\) 0 0
\(99\) 2.24034 0.225163
\(100\) 0 0
\(101\) −12.7935 −1.27300 −0.636498 0.771278i \(-0.719618\pi\)
−0.636498 + 0.771278i \(0.719618\pi\)
\(102\) 0 0
\(103\) −15.8202 −1.55881 −0.779406 0.626519i \(-0.784479\pi\)
−0.779406 + 0.626519i \(0.784479\pi\)
\(104\) 0 0
\(105\) 5.27087 0.514384
\(106\) 0 0
\(107\) −5.45121 −0.526988 −0.263494 0.964661i \(-0.584875\pi\)
−0.263494 + 0.964661i \(0.584875\pi\)
\(108\) 0 0
\(109\) 16.6376 1.59359 0.796795 0.604250i \(-0.206527\pi\)
0.796795 + 0.604250i \(0.206527\pi\)
\(110\) 0 0
\(111\) 4.25112 0.403498
\(112\) 0 0
\(113\) −3.45935 −0.325429 −0.162714 0.986673i \(-0.552025\pi\)
−0.162714 + 0.986673i \(0.552025\pi\)
\(114\) 0 0
\(115\) 6.31215 0.588611
\(116\) 0 0
\(117\) −2.57432 −0.237996
\(118\) 0 0
\(119\) −6.94439 −0.636591
\(120\) 0 0
\(121\) 9.07204 0.824731
\(122\) 0 0
\(123\) −16.8729 −1.52138
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 17.0434 1.51235 0.756177 0.654367i \(-0.227065\pi\)
0.756177 + 0.654367i \(0.227065\pi\)
\(128\) 0 0
\(129\) −15.2733 −1.34474
\(130\) 0 0
\(131\) −6.81219 −0.595184 −0.297592 0.954693i \(-0.596183\pi\)
−0.297592 + 0.954693i \(0.596183\pi\)
\(132\) 0 0
\(133\) −4.05808 −0.351880
\(134\) 0 0
\(135\) −5.53401 −0.476292
\(136\) 0 0
\(137\) 7.62695 0.651614 0.325807 0.945436i \(-0.394364\pi\)
0.325807 + 0.945436i \(0.394364\pi\)
\(138\) 0 0
\(139\) 19.2383 1.63177 0.815885 0.578214i \(-0.196250\pi\)
0.815885 + 0.578214i \(0.196250\pi\)
\(140\) 0 0
\(141\) 20.4105 1.71887
\(142\) 0 0
\(143\) −23.0643 −1.92873
\(144\) 0 0
\(145\) 2.70237 0.224420
\(146\) 0 0
\(147\) −6.50326 −0.536380
\(148\) 0 0
\(149\) 5.59856 0.458652 0.229326 0.973350i \(-0.426348\pi\)
0.229326 + 0.973350i \(0.426348\pi\)
\(150\) 0 0
\(151\) −10.5085 −0.855173 −0.427586 0.903975i \(-0.640636\pi\)
−0.427586 + 0.903975i \(0.640636\pi\)
\(152\) 0 0
\(153\) 1.04168 0.0842150
\(154\) 0 0
\(155\) −9.30315 −0.747247
\(156\) 0 0
\(157\) 11.5928 0.925208 0.462604 0.886565i \(-0.346915\pi\)
0.462604 + 0.886565i \(0.346915\pi\)
\(158\) 0 0
\(159\) 2.01113 0.159493
\(160\) 0 0
\(161\) −21.0424 −1.65837
\(162\) 0 0
\(163\) 19.5693 1.53278 0.766392 0.642374i \(-0.222050\pi\)
0.766392 + 0.642374i \(0.222050\pi\)
\(164\) 0 0
\(165\) −7.08371 −0.551466
\(166\) 0 0
\(167\) 8.84859 0.684724 0.342362 0.939568i \(-0.388773\pi\)
0.342362 + 0.939568i \(0.388773\pi\)
\(168\) 0 0
\(169\) 13.5026 1.03866
\(170\) 0 0
\(171\) 0.608726 0.0465504
\(172\) 0 0
\(173\) 6.19390 0.470914 0.235457 0.971885i \(-0.424341\pi\)
0.235457 + 0.971885i \(0.424341\pi\)
\(174\) 0 0
\(175\) 3.33363 0.251998
\(176\) 0 0
\(177\) −10.4195 −0.783178
\(178\) 0 0
\(179\) 6.66383 0.498078 0.249039 0.968493i \(-0.419885\pi\)
0.249039 + 0.968493i \(0.419885\pi\)
\(180\) 0 0
\(181\) −9.78563 −0.727360 −0.363680 0.931524i \(-0.618480\pi\)
−0.363680 + 0.931524i \(0.618480\pi\)
\(182\) 0 0
\(183\) 21.6125 1.59764
\(184\) 0 0
\(185\) 2.68867 0.197675
\(186\) 0 0
\(187\) 9.33282 0.682484
\(188\) 0 0
\(189\) 18.4483 1.34192
\(190\) 0 0
\(191\) −26.1568 −1.89264 −0.946322 0.323227i \(-0.895232\pi\)
−0.946322 + 0.323227i \(0.895232\pi\)
\(192\) 0 0
\(193\) −15.5525 −1.11949 −0.559745 0.828665i \(-0.689101\pi\)
−0.559745 + 0.828665i \(0.689101\pi\)
\(194\) 0 0
\(195\) 8.13971 0.582897
\(196\) 0 0
\(197\) 6.10796 0.435174 0.217587 0.976041i \(-0.430181\pi\)
0.217587 + 0.976041i \(0.430181\pi\)
\(198\) 0 0
\(199\) −12.9613 −0.918806 −0.459403 0.888228i \(-0.651937\pi\)
−0.459403 + 0.888228i \(0.651937\pi\)
\(200\) 0 0
\(201\) 4.86917 0.343445
\(202\) 0 0
\(203\) −9.00871 −0.632287
\(204\) 0 0
\(205\) −10.6715 −0.745329
\(206\) 0 0
\(207\) 3.15642 0.219387
\(208\) 0 0
\(209\) 5.45380 0.377247
\(210\) 0 0
\(211\) 12.2788 0.845310 0.422655 0.906291i \(-0.361098\pi\)
0.422655 + 0.906291i \(0.361098\pi\)
\(212\) 0 0
\(213\) −9.88028 −0.676986
\(214\) 0 0
\(215\) −9.65978 −0.658792
\(216\) 0 0
\(217\) 31.0132 2.10531
\(218\) 0 0
\(219\) 9.12907 0.616885
\(220\) 0 0
\(221\) −10.7241 −0.721382
\(222\) 0 0
\(223\) −6.97483 −0.467069 −0.233534 0.972349i \(-0.575029\pi\)
−0.233534 + 0.972349i \(0.575029\pi\)
\(224\) 0 0
\(225\) −0.500055 −0.0333370
\(226\) 0 0
\(227\) −17.1680 −1.13948 −0.569739 0.821825i \(-0.692956\pi\)
−0.569739 + 0.821825i \(0.692956\pi\)
\(228\) 0 0
\(229\) 15.6548 1.03450 0.517250 0.855834i \(-0.326956\pi\)
0.517250 + 0.855834i \(0.326956\pi\)
\(230\) 0 0
\(231\) 23.6145 1.55372
\(232\) 0 0
\(233\) 11.4766 0.751859 0.375930 0.926648i \(-0.377323\pi\)
0.375930 + 0.926648i \(0.377323\pi\)
\(234\) 0 0
\(235\) 12.9089 0.842082
\(236\) 0 0
\(237\) 7.44322 0.483489
\(238\) 0 0
\(239\) −20.2157 −1.30764 −0.653821 0.756649i \(-0.726835\pi\)
−0.653821 + 0.756649i \(0.726835\pi\)
\(240\) 0 0
\(241\) −15.2223 −0.980557 −0.490279 0.871566i \(-0.663105\pi\)
−0.490279 + 0.871566i \(0.663105\pi\)
\(242\) 0 0
\(243\) −5.13926 −0.329684
\(244\) 0 0
\(245\) −4.11307 −0.262774
\(246\) 0 0
\(247\) −6.26682 −0.398749
\(248\) 0 0
\(249\) −13.4268 −0.850887
\(250\) 0 0
\(251\) −13.0250 −0.822130 −0.411065 0.911606i \(-0.634843\pi\)
−0.411065 + 0.911606i \(0.634843\pi\)
\(252\) 0 0
\(253\) 28.2796 1.77792
\(254\) 0 0
\(255\) −3.29369 −0.206259
\(256\) 0 0
\(257\) 15.4276 0.962348 0.481174 0.876625i \(-0.340211\pi\)
0.481174 + 0.876625i \(0.340211\pi\)
\(258\) 0 0
\(259\) −8.96304 −0.556936
\(260\) 0 0
\(261\) 1.35134 0.0836457
\(262\) 0 0
\(263\) −10.0190 −0.617797 −0.308898 0.951095i \(-0.599960\pi\)
−0.308898 + 0.951095i \(0.599960\pi\)
\(264\) 0 0
\(265\) 1.27197 0.0781363
\(266\) 0 0
\(267\) −7.20399 −0.440877
\(268\) 0 0
\(269\) 6.18894 0.377346 0.188673 0.982040i \(-0.439581\pi\)
0.188673 + 0.982040i \(0.439581\pi\)
\(270\) 0 0
\(271\) 5.19686 0.315687 0.157844 0.987464i \(-0.449546\pi\)
0.157844 + 0.987464i \(0.449546\pi\)
\(272\) 0 0
\(273\) −27.1348 −1.64227
\(274\) 0 0
\(275\) −4.48018 −0.270165
\(276\) 0 0
\(277\) −16.1319 −0.969271 −0.484636 0.874716i \(-0.661048\pi\)
−0.484636 + 0.874716i \(0.661048\pi\)
\(278\) 0 0
\(279\) −4.65209 −0.278513
\(280\) 0 0
\(281\) −13.4448 −0.802052 −0.401026 0.916067i \(-0.631346\pi\)
−0.401026 + 0.916067i \(0.631346\pi\)
\(282\) 0 0
\(283\) −6.22533 −0.370058 −0.185029 0.982733i \(-0.559238\pi\)
−0.185029 + 0.982733i \(0.559238\pi\)
\(284\) 0 0
\(285\) −1.92473 −0.114011
\(286\) 0 0
\(287\) 35.5747 2.09991
\(288\) 0 0
\(289\) −12.6606 −0.744738
\(290\) 0 0
\(291\) 22.7210 1.33193
\(292\) 0 0
\(293\) −30.7314 −1.79535 −0.897673 0.440662i \(-0.854744\pi\)
−0.897673 + 0.440662i \(0.854744\pi\)
\(294\) 0 0
\(295\) −6.58994 −0.383681
\(296\) 0 0
\(297\) −24.7934 −1.43866
\(298\) 0 0
\(299\) −32.4953 −1.87925
\(300\) 0 0
\(301\) 32.2021 1.85610
\(302\) 0 0
\(303\) 20.2280 1.16207
\(304\) 0 0
\(305\) 13.6691 0.782690
\(306\) 0 0
\(307\) 19.2133 1.09656 0.548281 0.836294i \(-0.315282\pi\)
0.548281 + 0.836294i \(0.315282\pi\)
\(308\) 0 0
\(309\) 25.0137 1.42298
\(310\) 0 0
\(311\) −24.7589 −1.40395 −0.701975 0.712202i \(-0.747698\pi\)
−0.701975 + 0.712202i \(0.747698\pi\)
\(312\) 0 0
\(313\) −13.3884 −0.756757 −0.378378 0.925651i \(-0.623518\pi\)
−0.378378 + 0.925651i \(0.623518\pi\)
\(314\) 0 0
\(315\) 1.66700 0.0939247
\(316\) 0 0
\(317\) −3.06024 −0.171880 −0.0859401 0.996300i \(-0.527389\pi\)
−0.0859401 + 0.996300i \(0.527389\pi\)
\(318\) 0 0
\(319\) 12.1071 0.677869
\(320\) 0 0
\(321\) 8.61902 0.481067
\(322\) 0 0
\(323\) 2.53583 0.141098
\(324\) 0 0
\(325\) 5.14806 0.285563
\(326\) 0 0
\(327\) −26.3060 −1.45473
\(328\) 0 0
\(329\) −43.0333 −2.37251
\(330\) 0 0
\(331\) −5.46302 −0.300275 −0.150137 0.988665i \(-0.547972\pi\)
−0.150137 + 0.988665i \(0.547972\pi\)
\(332\) 0 0
\(333\) 1.34449 0.0736774
\(334\) 0 0
\(335\) 3.07957 0.168255
\(336\) 0 0
\(337\) 11.2431 0.612450 0.306225 0.951959i \(-0.400934\pi\)
0.306225 + 0.951959i \(0.400934\pi\)
\(338\) 0 0
\(339\) 5.46966 0.297071
\(340\) 0 0
\(341\) −41.6798 −2.25709
\(342\) 0 0
\(343\) −9.62396 −0.519645
\(344\) 0 0
\(345\) −9.98027 −0.537320
\(346\) 0 0
\(347\) 7.80699 0.419101 0.209551 0.977798i \(-0.432800\pi\)
0.209551 + 0.977798i \(0.432800\pi\)
\(348\) 0 0
\(349\) −18.6022 −0.995752 −0.497876 0.867248i \(-0.665886\pi\)
−0.497876 + 0.867248i \(0.665886\pi\)
\(350\) 0 0
\(351\) 28.4894 1.52065
\(352\) 0 0
\(353\) −30.5010 −1.62340 −0.811702 0.584072i \(-0.801458\pi\)
−0.811702 + 0.584072i \(0.801458\pi\)
\(354\) 0 0
\(355\) −6.24891 −0.331658
\(356\) 0 0
\(357\) 10.9799 0.581119
\(358\) 0 0
\(359\) −1.03237 −0.0544865 −0.0272432 0.999629i \(-0.508673\pi\)
−0.0272432 + 0.999629i \(0.508673\pi\)
\(360\) 0 0
\(361\) −17.5181 −0.922007
\(362\) 0 0
\(363\) −14.3440 −0.752865
\(364\) 0 0
\(365\) 5.77379 0.302214
\(366\) 0 0
\(367\) −3.60726 −0.188298 −0.0941488 0.995558i \(-0.530013\pi\)
−0.0941488 + 0.995558i \(0.530013\pi\)
\(368\) 0 0
\(369\) −5.33633 −0.277798
\(370\) 0 0
\(371\) −4.24026 −0.220144
\(372\) 0 0
\(373\) −26.8687 −1.39121 −0.695604 0.718425i \(-0.744863\pi\)
−0.695604 + 0.718425i \(0.744863\pi\)
\(374\) 0 0
\(375\) 1.58112 0.0816488
\(376\) 0 0
\(377\) −13.9120 −0.716504
\(378\) 0 0
\(379\) 15.3718 0.789597 0.394799 0.918768i \(-0.370814\pi\)
0.394799 + 0.918768i \(0.370814\pi\)
\(380\) 0 0
\(381\) −26.9476 −1.38057
\(382\) 0 0
\(383\) 2.18488 0.111642 0.0558210 0.998441i \(-0.482222\pi\)
0.0558210 + 0.998441i \(0.482222\pi\)
\(384\) 0 0
\(385\) 14.9353 0.761171
\(386\) 0 0
\(387\) −4.83043 −0.245544
\(388\) 0 0
\(389\) −18.6007 −0.943092 −0.471546 0.881841i \(-0.656304\pi\)
−0.471546 + 0.881841i \(0.656304\pi\)
\(390\) 0 0
\(391\) 13.1491 0.664976
\(392\) 0 0
\(393\) 10.7709 0.543320
\(394\) 0 0
\(395\) 4.70756 0.236863
\(396\) 0 0
\(397\) −16.0609 −0.806076 −0.403038 0.915183i \(-0.632046\pi\)
−0.403038 + 0.915183i \(0.632046\pi\)
\(398\) 0 0
\(399\) 6.41632 0.321218
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 47.8932 2.38573
\(404\) 0 0
\(405\) 7.24978 0.360244
\(406\) 0 0
\(407\) 12.0458 0.597086
\(408\) 0 0
\(409\) −7.21244 −0.356632 −0.178316 0.983973i \(-0.557065\pi\)
−0.178316 + 0.983973i \(0.557065\pi\)
\(410\) 0 0
\(411\) −12.0591 −0.594833
\(412\) 0 0
\(413\) 21.9684 1.08099
\(414\) 0 0
\(415\) −8.49193 −0.416853
\(416\) 0 0
\(417\) −30.4181 −1.48958
\(418\) 0 0
\(419\) −31.3528 −1.53168 −0.765841 0.643030i \(-0.777677\pi\)
−0.765841 + 0.643030i \(0.777677\pi\)
\(420\) 0 0
\(421\) −26.4448 −1.28884 −0.644420 0.764671i \(-0.722901\pi\)
−0.644420 + 0.764671i \(0.722901\pi\)
\(422\) 0 0
\(423\) 6.45515 0.313860
\(424\) 0 0
\(425\) −2.08313 −0.101047
\(426\) 0 0
\(427\) −45.5677 −2.20517
\(428\) 0 0
\(429\) 36.4674 1.76066
\(430\) 0 0
\(431\) 3.52695 0.169887 0.0849436 0.996386i \(-0.472929\pi\)
0.0849436 + 0.996386i \(0.472929\pi\)
\(432\) 0 0
\(433\) −35.8244 −1.72161 −0.860805 0.508934i \(-0.830040\pi\)
−0.860805 + 0.508934i \(0.830040\pi\)
\(434\) 0 0
\(435\) −4.27278 −0.204864
\(436\) 0 0
\(437\) 7.68389 0.367570
\(438\) 0 0
\(439\) 31.6303 1.50963 0.754816 0.655937i \(-0.227726\pi\)
0.754816 + 0.655937i \(0.227726\pi\)
\(440\) 0 0
\(441\) −2.05676 −0.0979410
\(442\) 0 0
\(443\) 33.1780 1.57634 0.788168 0.615460i \(-0.211030\pi\)
0.788168 + 0.615460i \(0.211030\pi\)
\(444\) 0 0
\(445\) −4.55626 −0.215987
\(446\) 0 0
\(447\) −8.85201 −0.418686
\(448\) 0 0
\(449\) 16.8498 0.795190 0.397595 0.917561i \(-0.369845\pi\)
0.397595 + 0.917561i \(0.369845\pi\)
\(450\) 0 0
\(451\) −47.8102 −2.25129
\(452\) 0 0
\(453\) 16.6153 0.780654
\(454\) 0 0
\(455\) −17.1617 −0.804554
\(456\) 0 0
\(457\) −3.51590 −0.164467 −0.0822334 0.996613i \(-0.526205\pi\)
−0.0822334 + 0.996613i \(0.526205\pi\)
\(458\) 0 0
\(459\) −11.5281 −0.538085
\(460\) 0 0
\(461\) −30.0753 −1.40074 −0.700372 0.713778i \(-0.746983\pi\)
−0.700372 + 0.713778i \(0.746983\pi\)
\(462\) 0 0
\(463\) 3.00741 0.139766 0.0698831 0.997555i \(-0.477737\pi\)
0.0698831 + 0.997555i \(0.477737\pi\)
\(464\) 0 0
\(465\) 14.7094 0.682132
\(466\) 0 0
\(467\) −3.30093 −0.152749 −0.0763745 0.997079i \(-0.524334\pi\)
−0.0763745 + 0.997079i \(0.524334\pi\)
\(468\) 0 0
\(469\) −10.2661 −0.474046
\(470\) 0 0
\(471\) −18.3297 −0.844586
\(472\) 0 0
\(473\) −43.2776 −1.98991
\(474\) 0 0
\(475\) −1.21732 −0.0558543
\(476\) 0 0
\(477\) 0.636054 0.0291229
\(478\) 0 0
\(479\) −5.91575 −0.270298 −0.135149 0.990825i \(-0.543151\pi\)
−0.135149 + 0.990825i \(0.543151\pi\)
\(480\) 0 0
\(481\) −13.8415 −0.631117
\(482\) 0 0
\(483\) 33.2705 1.51386
\(484\) 0 0
\(485\) 14.3702 0.652515
\(486\) 0 0
\(487\) −18.8555 −0.854423 −0.427212 0.904152i \(-0.640504\pi\)
−0.427212 + 0.904152i \(0.640504\pi\)
\(488\) 0 0
\(489\) −30.9414 −1.39922
\(490\) 0 0
\(491\) 28.4685 1.28476 0.642382 0.766385i \(-0.277946\pi\)
0.642382 + 0.766385i \(0.277946\pi\)
\(492\) 0 0
\(493\) 5.62941 0.253536
\(494\) 0 0
\(495\) −2.24034 −0.100696
\(496\) 0 0
\(497\) 20.8315 0.934421
\(498\) 0 0
\(499\) −39.5742 −1.77159 −0.885793 0.464082i \(-0.846384\pi\)
−0.885793 + 0.464082i \(0.846384\pi\)
\(500\) 0 0
\(501\) −13.9907 −0.625058
\(502\) 0 0
\(503\) 23.0644 1.02839 0.514195 0.857673i \(-0.328091\pi\)
0.514195 + 0.857673i \(0.328091\pi\)
\(504\) 0 0
\(505\) 12.7935 0.569301
\(506\) 0 0
\(507\) −21.3492 −0.948151
\(508\) 0 0
\(509\) 36.0771 1.59909 0.799544 0.600607i \(-0.205075\pi\)
0.799544 + 0.600607i \(0.205075\pi\)
\(510\) 0 0
\(511\) −19.2477 −0.851467
\(512\) 0 0
\(513\) −6.73665 −0.297430
\(514\) 0 0
\(515\) 15.8202 0.697122
\(516\) 0 0
\(517\) 57.8341 2.54354
\(518\) 0 0
\(519\) −9.79331 −0.429879
\(520\) 0 0
\(521\) −14.7342 −0.645517 −0.322759 0.946481i \(-0.604610\pi\)
−0.322759 + 0.946481i \(0.604610\pi\)
\(522\) 0 0
\(523\) 13.3205 0.582464 0.291232 0.956652i \(-0.405935\pi\)
0.291232 + 0.956652i \(0.405935\pi\)
\(524\) 0 0
\(525\) −5.27087 −0.230040
\(526\) 0 0
\(527\) −19.3797 −0.844193
\(528\) 0 0
\(529\) 16.8432 0.732314
\(530\) 0 0
\(531\) −3.29534 −0.143005
\(532\) 0 0
\(533\) 54.9375 2.37961
\(534\) 0 0
\(535\) 5.45121 0.235676
\(536\) 0 0
\(537\) −10.5363 −0.454676
\(538\) 0 0
\(539\) −18.4273 −0.793720
\(540\) 0 0
\(541\) −19.4187 −0.834877 −0.417438 0.908705i \(-0.637072\pi\)
−0.417438 + 0.908705i \(0.637072\pi\)
\(542\) 0 0
\(543\) 15.4723 0.663979
\(544\) 0 0
\(545\) −16.6376 −0.712675
\(546\) 0 0
\(547\) 0.537700 0.0229904 0.0114952 0.999934i \(-0.496341\pi\)
0.0114952 + 0.999934i \(0.496341\pi\)
\(548\) 0 0
\(549\) 6.83531 0.291724
\(550\) 0 0
\(551\) 3.28965 0.140144
\(552\) 0 0
\(553\) −15.6932 −0.667344
\(554\) 0 0
\(555\) −4.25112 −0.180450
\(556\) 0 0
\(557\) −20.1125 −0.852193 −0.426097 0.904678i \(-0.640112\pi\)
−0.426097 + 0.904678i \(0.640112\pi\)
\(558\) 0 0
\(559\) 49.7292 2.10332
\(560\) 0 0
\(561\) −14.7563 −0.623013
\(562\) 0 0
\(563\) 0.0804882 0.00339217 0.00169609 0.999999i \(-0.499460\pi\)
0.00169609 + 0.999999i \(0.499460\pi\)
\(564\) 0 0
\(565\) 3.45935 0.145536
\(566\) 0 0
\(567\) −24.1681 −1.01496
\(568\) 0 0
\(569\) 11.9728 0.501925 0.250963 0.967997i \(-0.419253\pi\)
0.250963 + 0.967997i \(0.419253\pi\)
\(570\) 0 0
\(571\) −32.6082 −1.36461 −0.682305 0.731068i \(-0.739022\pi\)
−0.682305 + 0.731068i \(0.739022\pi\)
\(572\) 0 0
\(573\) 41.3572 1.72772
\(574\) 0 0
\(575\) −6.31215 −0.263235
\(576\) 0 0
\(577\) 14.4477 0.601465 0.300732 0.953709i \(-0.402769\pi\)
0.300732 + 0.953709i \(0.402769\pi\)
\(578\) 0 0
\(579\) 24.5903 1.02194
\(580\) 0 0
\(581\) 28.3089 1.17445
\(582\) 0 0
\(583\) 5.69865 0.236014
\(584\) 0 0
\(585\) 2.57432 0.106435
\(586\) 0 0
\(587\) −14.5432 −0.600261 −0.300131 0.953898i \(-0.597030\pi\)
−0.300131 + 0.953898i \(0.597030\pi\)
\(588\) 0 0
\(589\) −11.3249 −0.466634
\(590\) 0 0
\(591\) −9.65743 −0.397253
\(592\) 0 0
\(593\) 38.7817 1.59257 0.796286 0.604921i \(-0.206795\pi\)
0.796286 + 0.604921i \(0.206795\pi\)
\(594\) 0 0
\(595\) 6.94439 0.284692
\(596\) 0 0
\(597\) 20.4935 0.838742
\(598\) 0 0
\(599\) 0.763380 0.0311908 0.0155954 0.999878i \(-0.495036\pi\)
0.0155954 + 0.999878i \(0.495036\pi\)
\(600\) 0 0
\(601\) −8.15875 −0.332802 −0.166401 0.986058i \(-0.553215\pi\)
−0.166401 + 0.986058i \(0.553215\pi\)
\(602\) 0 0
\(603\) 1.53996 0.0627119
\(604\) 0 0
\(605\) −9.07204 −0.368831
\(606\) 0 0
\(607\) −13.6422 −0.553720 −0.276860 0.960910i \(-0.589294\pi\)
−0.276860 + 0.960910i \(0.589294\pi\)
\(608\) 0 0
\(609\) 14.2439 0.577190
\(610\) 0 0
\(611\) −66.4557 −2.68851
\(612\) 0 0
\(613\) −14.0134 −0.565998 −0.282999 0.959120i \(-0.591329\pi\)
−0.282999 + 0.959120i \(0.591329\pi\)
\(614\) 0 0
\(615\) 16.8729 0.680381
\(616\) 0 0
\(617\) −34.4494 −1.38688 −0.693440 0.720515i \(-0.743906\pi\)
−0.693440 + 0.720515i \(0.743906\pi\)
\(618\) 0 0
\(619\) 28.3073 1.13777 0.568883 0.822419i \(-0.307376\pi\)
0.568883 + 0.822419i \(0.307376\pi\)
\(620\) 0 0
\(621\) −34.9315 −1.40175
\(622\) 0 0
\(623\) 15.1889 0.608529
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −8.62312 −0.344374
\(628\) 0 0
\(629\) 5.60087 0.223321
\(630\) 0 0
\(631\) 18.9140 0.752956 0.376478 0.926425i \(-0.377135\pi\)
0.376478 + 0.926425i \(0.377135\pi\)
\(632\) 0 0
\(633\) −19.4143 −0.771650
\(634\) 0 0
\(635\) −17.0434 −0.676346
\(636\) 0 0
\(637\) 21.1743 0.838958
\(638\) 0 0
\(639\) −3.12480 −0.123615
\(640\) 0 0
\(641\) −36.1534 −1.42797 −0.713987 0.700159i \(-0.753113\pi\)
−0.713987 + 0.700159i \(0.753113\pi\)
\(642\) 0 0
\(643\) 10.9574 0.432119 0.216060 0.976380i \(-0.430679\pi\)
0.216060 + 0.976380i \(0.430679\pi\)
\(644\) 0 0
\(645\) 15.2733 0.601385
\(646\) 0 0
\(647\) 21.9336 0.862298 0.431149 0.902281i \(-0.358108\pi\)
0.431149 + 0.902281i \(0.358108\pi\)
\(648\) 0 0
\(649\) −29.5242 −1.15892
\(650\) 0 0
\(651\) −49.0357 −1.92186
\(652\) 0 0
\(653\) 26.8361 1.05018 0.525088 0.851048i \(-0.324032\pi\)
0.525088 + 0.851048i \(0.324032\pi\)
\(654\) 0 0
\(655\) 6.81219 0.266174
\(656\) 0 0
\(657\) 2.88722 0.112641
\(658\) 0 0
\(659\) −37.8865 −1.47585 −0.737925 0.674883i \(-0.764194\pi\)
−0.737925 + 0.674883i \(0.764194\pi\)
\(660\) 0 0
\(661\) −13.4541 −0.523302 −0.261651 0.965163i \(-0.584267\pi\)
−0.261651 + 0.965163i \(0.584267\pi\)
\(662\) 0 0
\(663\) 16.9561 0.658521
\(664\) 0 0
\(665\) 4.05808 0.157366
\(666\) 0 0
\(667\) 17.0578 0.660480
\(668\) 0 0
\(669\) 11.0280 0.426369
\(670\) 0 0
\(671\) 61.2401 2.36415
\(672\) 0 0
\(673\) −21.0749 −0.812378 −0.406189 0.913789i \(-0.633143\pi\)
−0.406189 + 0.913789i \(0.633143\pi\)
\(674\) 0 0
\(675\) 5.53401 0.213004
\(676\) 0 0
\(677\) 6.60271 0.253763 0.126881 0.991918i \(-0.459503\pi\)
0.126881 + 0.991918i \(0.459503\pi\)
\(678\) 0 0
\(679\) −47.9047 −1.83842
\(680\) 0 0
\(681\) 27.1447 1.04019
\(682\) 0 0
\(683\) −10.9345 −0.418395 −0.209198 0.977873i \(-0.567085\pi\)
−0.209198 + 0.977873i \(0.567085\pi\)
\(684\) 0 0
\(685\) −7.62695 −0.291411
\(686\) 0 0
\(687\) −24.7522 −0.944355
\(688\) 0 0
\(689\) −6.54817 −0.249465
\(690\) 0 0
\(691\) 45.5552 1.73300 0.866501 0.499176i \(-0.166364\pi\)
0.866501 + 0.499176i \(0.166364\pi\)
\(692\) 0 0
\(693\) 7.46846 0.283703
\(694\) 0 0
\(695\) −19.2383 −0.729750
\(696\) 0 0
\(697\) −22.2301 −0.842026
\(698\) 0 0
\(699\) −18.1460 −0.686343
\(700\) 0 0
\(701\) −18.6798 −0.705527 −0.352764 0.935712i \(-0.614758\pi\)
−0.352764 + 0.935712i \(0.614758\pi\)
\(702\) 0 0
\(703\) 3.27297 0.123442
\(704\) 0 0
\(705\) −20.4105 −0.768703
\(706\) 0 0
\(707\) −42.6486 −1.60397
\(708\) 0 0
\(709\) −24.1207 −0.905871 −0.452935 0.891543i \(-0.649623\pi\)
−0.452935 + 0.891543i \(0.649623\pi\)
\(710\) 0 0
\(711\) 2.35404 0.0882834
\(712\) 0 0
\(713\) −58.7229 −2.19919
\(714\) 0 0
\(715\) 23.0643 0.862555
\(716\) 0 0
\(717\) 31.9634 1.19370
\(718\) 0 0
\(719\) −8.94887 −0.333736 −0.166868 0.985979i \(-0.553365\pi\)
−0.166868 + 0.985979i \(0.553365\pi\)
\(720\) 0 0
\(721\) −52.7387 −1.96409
\(722\) 0 0
\(723\) 24.0684 0.895112
\(724\) 0 0
\(725\) −2.70237 −0.100364
\(726\) 0 0
\(727\) −41.9938 −1.55746 −0.778732 0.627357i \(-0.784137\pi\)
−0.778732 + 0.627357i \(0.784137\pi\)
\(728\) 0 0
\(729\) 29.8751 1.10649
\(730\) 0 0
\(731\) −20.1226 −0.744262
\(732\) 0 0
\(733\) −25.8416 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(734\) 0 0
\(735\) 6.50326 0.239876
\(736\) 0 0
\(737\) 13.7970 0.508221
\(738\) 0 0
\(739\) 35.4614 1.30447 0.652235 0.758017i \(-0.273832\pi\)
0.652235 + 0.758017i \(0.273832\pi\)
\(740\) 0 0
\(741\) 9.90861 0.364002
\(742\) 0 0
\(743\) 18.0214 0.661140 0.330570 0.943781i \(-0.392759\pi\)
0.330570 + 0.943781i \(0.392759\pi\)
\(744\) 0 0
\(745\) −5.59856 −0.205115
\(746\) 0 0
\(747\) −4.24644 −0.155369
\(748\) 0 0
\(749\) −18.1723 −0.664001
\(750\) 0 0
\(751\) 11.1189 0.405735 0.202868 0.979206i \(-0.434974\pi\)
0.202868 + 0.979206i \(0.434974\pi\)
\(752\) 0 0
\(753\) 20.5941 0.750490
\(754\) 0 0
\(755\) 10.5085 0.382445
\(756\) 0 0
\(757\) 15.7093 0.570964 0.285482 0.958384i \(-0.407846\pi\)
0.285482 + 0.958384i \(0.407846\pi\)
\(758\) 0 0
\(759\) −44.7135 −1.62300
\(760\) 0 0
\(761\) −38.3518 −1.39025 −0.695126 0.718888i \(-0.744651\pi\)
−0.695126 + 0.718888i \(0.744651\pi\)
\(762\) 0 0
\(763\) 55.4634 2.00791
\(764\) 0 0
\(765\) −1.04168 −0.0376621
\(766\) 0 0
\(767\) 33.9254 1.22498
\(768\) 0 0
\(769\) −2.57147 −0.0927297 −0.0463648 0.998925i \(-0.514764\pi\)
−0.0463648 + 0.998925i \(0.514764\pi\)
\(770\) 0 0
\(771\) −24.3929 −0.878490
\(772\) 0 0
\(773\) 5.36452 0.192948 0.0964741 0.995335i \(-0.469244\pi\)
0.0964741 + 0.995335i \(0.469244\pi\)
\(774\) 0 0
\(775\) 9.30315 0.334179
\(776\) 0 0
\(777\) 14.1716 0.508405
\(778\) 0 0
\(779\) −12.9906 −0.465436
\(780\) 0 0
\(781\) −27.9962 −1.00178
\(782\) 0 0
\(783\) −14.9550 −0.534447
\(784\) 0 0
\(785\) −11.5928 −0.413766
\(786\) 0 0
\(787\) −52.1708 −1.85969 −0.929845 0.367952i \(-0.880059\pi\)
−0.929845 + 0.367952i \(0.880059\pi\)
\(788\) 0 0
\(789\) 15.8412 0.563963
\(790\) 0 0
\(791\) −11.5322 −0.410038
\(792\) 0 0
\(793\) −70.3694 −2.49889
\(794\) 0 0
\(795\) −2.01113 −0.0713276
\(796\) 0 0
\(797\) −22.8205 −0.808345 −0.404173 0.914683i \(-0.632440\pi\)
−0.404173 + 0.914683i \(0.632440\pi\)
\(798\) 0 0
\(799\) 26.8909 0.951332
\(800\) 0 0
\(801\) −2.27838 −0.0805026
\(802\) 0 0
\(803\) 25.8677 0.912850
\(804\) 0 0
\(805\) 21.0424 0.741645
\(806\) 0 0
\(807\) −9.78546 −0.344465
\(808\) 0 0
\(809\) 31.5301 1.10854 0.554269 0.832338i \(-0.312998\pi\)
0.554269 + 0.832338i \(0.312998\pi\)
\(810\) 0 0
\(811\) −33.1959 −1.16567 −0.582833 0.812592i \(-0.698056\pi\)
−0.582833 + 0.812592i \(0.698056\pi\)
\(812\) 0 0
\(813\) −8.21687 −0.288178
\(814\) 0 0
\(815\) −19.5693 −0.685482
\(816\) 0 0
\(817\) −11.7590 −0.411396
\(818\) 0 0
\(819\) −8.58181 −0.299873
\(820\) 0 0
\(821\) −48.2413 −1.68363 −0.841816 0.539764i \(-0.818513\pi\)
−0.841816 + 0.539764i \(0.818513\pi\)
\(822\) 0 0
\(823\) 8.88606 0.309749 0.154874 0.987934i \(-0.450503\pi\)
0.154874 + 0.987934i \(0.450503\pi\)
\(824\) 0 0
\(825\) 7.08371 0.246623
\(826\) 0 0
\(827\) −50.7133 −1.76347 −0.881737 0.471742i \(-0.843625\pi\)
−0.881737 + 0.471742i \(0.843625\pi\)
\(828\) 0 0
\(829\) 13.3560 0.463874 0.231937 0.972731i \(-0.425494\pi\)
0.231937 + 0.972731i \(0.425494\pi\)
\(830\) 0 0
\(831\) 25.5065 0.884810
\(832\) 0 0
\(833\) −8.56807 −0.296866
\(834\) 0 0
\(835\) −8.84859 −0.306218
\(836\) 0 0
\(837\) 51.4837 1.77954
\(838\) 0 0
\(839\) −12.9792 −0.448090 −0.224045 0.974579i \(-0.571926\pi\)
−0.224045 + 0.974579i \(0.571926\pi\)
\(840\) 0 0
\(841\) −21.6972 −0.748178
\(842\) 0 0
\(843\) 21.2579 0.732162
\(844\) 0 0
\(845\) −13.5026 −0.464502
\(846\) 0 0
\(847\) 30.2428 1.03916
\(848\) 0 0
\(849\) 9.84301 0.337811
\(850\) 0 0
\(851\) 16.9713 0.581769
\(852\) 0 0
\(853\) 9.60993 0.329038 0.164519 0.986374i \(-0.447393\pi\)
0.164519 + 0.986374i \(0.447393\pi\)
\(854\) 0 0
\(855\) −0.608726 −0.0208180
\(856\) 0 0
\(857\) −8.27086 −0.282527 −0.141264 0.989972i \(-0.545117\pi\)
−0.141264 + 0.989972i \(0.545117\pi\)
\(858\) 0 0
\(859\) −10.8254 −0.369357 −0.184678 0.982799i \(-0.559124\pi\)
−0.184678 + 0.982799i \(0.559124\pi\)
\(860\) 0 0
\(861\) −56.2480 −1.91693
\(862\) 0 0
\(863\) −10.3887 −0.353636 −0.176818 0.984244i \(-0.556580\pi\)
−0.176818 + 0.984244i \(0.556580\pi\)
\(864\) 0 0
\(865\) −6.19390 −0.210599
\(866\) 0 0
\(867\) 20.0179 0.679842
\(868\) 0 0
\(869\) 21.0907 0.715454
\(870\) 0 0
\(871\) −15.8538 −0.537186
\(872\) 0 0
\(873\) 7.18587 0.243205
\(874\) 0 0
\(875\) −3.33363 −0.112697
\(876\) 0 0
\(877\) 14.1104 0.476473 0.238236 0.971207i \(-0.423431\pi\)
0.238236 + 0.971207i \(0.423431\pi\)
\(878\) 0 0
\(879\) 48.5900 1.63890
\(880\) 0 0
\(881\) −16.1368 −0.543664 −0.271832 0.962345i \(-0.587629\pi\)
−0.271832 + 0.962345i \(0.587629\pi\)
\(882\) 0 0
\(883\) −10.2405 −0.344621 −0.172310 0.985043i \(-0.555123\pi\)
−0.172310 + 0.985043i \(0.555123\pi\)
\(884\) 0 0
\(885\) 10.4195 0.350248
\(886\) 0 0
\(887\) 2.55618 0.0858283 0.0429141 0.999079i \(-0.486336\pi\)
0.0429141 + 0.999079i \(0.486336\pi\)
\(888\) 0 0
\(889\) 56.8162 1.90556
\(890\) 0 0
\(891\) 32.4803 1.08813
\(892\) 0 0
\(893\) 15.7142 0.525855
\(894\) 0 0
\(895\) −6.66383 −0.222747
\(896\) 0 0
\(897\) 51.3791 1.71550
\(898\) 0 0
\(899\) −25.1406 −0.838486
\(900\) 0 0
\(901\) 2.64968 0.0882736
\(902\) 0 0
\(903\) −50.9154 −1.69436
\(904\) 0 0
\(905\) 9.78563 0.325285
\(906\) 0 0
\(907\) 52.6337 1.74767 0.873837 0.486218i \(-0.161624\pi\)
0.873837 + 0.486218i \(0.161624\pi\)
\(908\) 0 0
\(909\) 6.39744 0.212190
\(910\) 0 0
\(911\) −43.1084 −1.42825 −0.714123 0.700020i \(-0.753174\pi\)
−0.714123 + 0.700020i \(0.753174\pi\)
\(912\) 0 0
\(913\) −38.0454 −1.25912
\(914\) 0 0
\(915\) −21.6125 −0.714487
\(916\) 0 0
\(917\) −22.7093 −0.749927
\(918\) 0 0
\(919\) 28.6885 0.946346 0.473173 0.880969i \(-0.343108\pi\)
0.473173 + 0.880969i \(0.343108\pi\)
\(920\) 0 0
\(921\) −30.3786 −1.00101
\(922\) 0 0
\(923\) 32.1698 1.05888
\(924\) 0 0
\(925\) −2.68867 −0.0884031
\(926\) 0 0
\(927\) 7.91098 0.259831
\(928\) 0 0
\(929\) −58.1269 −1.90708 −0.953540 0.301266i \(-0.902591\pi\)
−0.953540 + 0.301266i \(0.902591\pi\)
\(930\) 0 0
\(931\) −5.00691 −0.164095
\(932\) 0 0
\(933\) 39.1468 1.28161
\(934\) 0 0
\(935\) −9.33282 −0.305216
\(936\) 0 0
\(937\) −16.1199 −0.526613 −0.263307 0.964712i \(-0.584813\pi\)
−0.263307 + 0.964712i \(0.584813\pi\)
\(938\) 0 0
\(939\) 21.1687 0.690814
\(940\) 0 0
\(941\) 0.469047 0.0152905 0.00764524 0.999971i \(-0.497566\pi\)
0.00764524 + 0.999971i \(0.497566\pi\)
\(942\) 0 0
\(943\) −67.3600 −2.19354
\(944\) 0 0
\(945\) −18.4483 −0.600124
\(946\) 0 0
\(947\) 46.1472 1.49958 0.749791 0.661674i \(-0.230154\pi\)
0.749791 + 0.661674i \(0.230154\pi\)
\(948\) 0 0
\(949\) −29.7239 −0.964877
\(950\) 0 0
\(951\) 4.83861 0.156903
\(952\) 0 0
\(953\) 17.3350 0.561535 0.280768 0.959776i \(-0.409411\pi\)
0.280768 + 0.959776i \(0.409411\pi\)
\(954\) 0 0
\(955\) 26.1568 0.846416
\(956\) 0 0
\(957\) −19.1428 −0.618800
\(958\) 0 0
\(959\) 25.4254 0.821029
\(960\) 0 0
\(961\) 55.5486 1.79189
\(962\) 0 0
\(963\) 2.72591 0.0878411
\(964\) 0 0
\(965\) 15.5525 0.500651
\(966\) 0 0
\(967\) 50.1909 1.61403 0.807015 0.590531i \(-0.201082\pi\)
0.807015 + 0.590531i \(0.201082\pi\)
\(968\) 0 0
\(969\) −4.00946 −0.128802
\(970\) 0 0
\(971\) 0.641284 0.0205798 0.0102899 0.999947i \(-0.496725\pi\)
0.0102899 + 0.999947i \(0.496725\pi\)
\(972\) 0 0
\(973\) 64.1333 2.05602
\(974\) 0 0
\(975\) −8.13971 −0.260679
\(976\) 0 0
\(977\) −34.9365 −1.11772 −0.558858 0.829263i \(-0.688760\pi\)
−0.558858 + 0.829263i \(0.688760\pi\)
\(978\) 0 0
\(979\) −20.4129 −0.652398
\(980\) 0 0
\(981\) −8.31971 −0.265628
\(982\) 0 0
\(983\) 12.1249 0.386725 0.193363 0.981127i \(-0.438061\pi\)
0.193363 + 0.981127i \(0.438061\pi\)
\(984\) 0 0
\(985\) −6.10796 −0.194616
\(986\) 0 0
\(987\) 68.0409 2.16577
\(988\) 0 0
\(989\) −60.9740 −1.93886
\(990\) 0 0
\(991\) 16.6528 0.528992 0.264496 0.964387i \(-0.414794\pi\)
0.264496 + 0.964387i \(0.414794\pi\)
\(992\) 0 0
\(993\) 8.63769 0.274109
\(994\) 0 0
\(995\) 12.9613 0.410902
\(996\) 0 0
\(997\) 40.9160 1.29582 0.647911 0.761716i \(-0.275643\pi\)
0.647911 + 0.761716i \(0.275643\pi\)
\(998\) 0 0
\(999\) −14.8792 −0.470756
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 \(a_p\))