Properties

Label 8036.2.a.q.1.7
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.27444\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.27444 q^{3} +4.37429 q^{5} -1.37580 q^{9} +O(q^{10})\) \(q-1.27444 q^{3} +4.37429 q^{5} -1.37580 q^{9} +6.01391 q^{11} -5.59853 q^{13} -5.57477 q^{15} +6.15244 q^{17} +5.17601 q^{19} -4.66413 q^{23} +14.1344 q^{25} +5.57670 q^{27} -1.77771 q^{29} -4.02499 q^{31} -7.66437 q^{33} +8.25323 q^{37} +7.13499 q^{39} -1.00000 q^{41} +0.831106 q^{43} -6.01815 q^{45} +2.72099 q^{47} -7.84091 q^{51} -0.906871 q^{53} +26.3066 q^{55} -6.59652 q^{57} +7.92624 q^{59} -5.68627 q^{61} -24.4896 q^{65} -0.0872911 q^{67} +5.94416 q^{69} -8.10863 q^{71} -5.60866 q^{73} -18.0134 q^{75} +0.401351 q^{79} -2.97976 q^{81} -7.91362 q^{83} +26.9125 q^{85} +2.26558 q^{87} +13.4751 q^{89} +5.12960 q^{93} +22.6414 q^{95} -7.58525 q^{97} -8.27395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −1.27444 −0.735798 −0.367899 0.929866i \(-0.619923\pi\)
−0.367899 + 0.929866i \(0.619923\pi\)
\(4\) 0 0
\(5\) 4.37429 1.95624 0.978120 0.208040i \(-0.0667085\pi\)
0.978120 + 0.208040i \(0.0667085\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.37580 −0.458601
\(10\) 0 0
\(11\) 6.01391 1.81326 0.906631 0.421925i \(-0.138646\pi\)
0.906631 + 0.421925i \(0.138646\pi\)
\(12\) 0 0
\(13\) −5.59853 −1.55275 −0.776376 0.630270i \(-0.782944\pi\)
−0.776376 + 0.630270i \(0.782944\pi\)
\(14\) 0 0
\(15\) −5.57477 −1.43940
\(16\) 0 0
\(17\) 6.15244 1.49218 0.746092 0.665842i \(-0.231928\pi\)
0.746092 + 0.665842i \(0.231928\pi\)
\(18\) 0 0
\(19\) 5.17601 1.18746 0.593729 0.804665i \(-0.297655\pi\)
0.593729 + 0.804665i \(0.297655\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.66413 −0.972539 −0.486270 0.873809i \(-0.661643\pi\)
−0.486270 + 0.873809i \(0.661643\pi\)
\(24\) 0 0
\(25\) 14.1344 2.82688
\(26\) 0 0
\(27\) 5.57670 1.07324
\(28\) 0 0
\(29\) −1.77771 −0.330112 −0.165056 0.986284i \(-0.552781\pi\)
−0.165056 + 0.986284i \(0.552781\pi\)
\(30\) 0 0
\(31\) −4.02499 −0.722909 −0.361454 0.932390i \(-0.617720\pi\)
−0.361454 + 0.932390i \(0.617720\pi\)
\(32\) 0 0
\(33\) −7.66437 −1.33419
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.25323 1.35682 0.678411 0.734683i \(-0.262669\pi\)
0.678411 + 0.734683i \(0.262669\pi\)
\(38\) 0 0
\(39\) 7.13499 1.14251
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 0.831106 0.126743 0.0633713 0.997990i \(-0.479815\pi\)
0.0633713 + 0.997990i \(0.479815\pi\)
\(44\) 0 0
\(45\) −6.01815 −0.897133
\(46\) 0 0
\(47\) 2.72099 0.396896 0.198448 0.980111i \(-0.436410\pi\)
0.198448 + 0.980111i \(0.436410\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −7.84091 −1.09795
\(52\) 0 0
\(53\) −0.906871 −0.124568 −0.0622842 0.998058i \(-0.519839\pi\)
−0.0622842 + 0.998058i \(0.519839\pi\)
\(54\) 0 0
\(55\) 26.3066 3.54718
\(56\) 0 0
\(57\) −6.59652 −0.873730
\(58\) 0 0
\(59\) 7.92624 1.03191 0.515954 0.856616i \(-0.327437\pi\)
0.515954 + 0.856616i \(0.327437\pi\)
\(60\) 0 0
\(61\) −5.68627 −0.728053 −0.364026 0.931389i \(-0.618598\pi\)
−0.364026 + 0.931389i \(0.618598\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −24.4896 −3.03756
\(66\) 0 0
\(67\) −0.0872911 −0.0106643 −0.00533215 0.999986i \(-0.501697\pi\)
−0.00533215 + 0.999986i \(0.501697\pi\)
\(68\) 0 0
\(69\) 5.94416 0.715593
\(70\) 0 0
\(71\) −8.10863 −0.962317 −0.481158 0.876634i \(-0.659784\pi\)
−0.481158 + 0.876634i \(0.659784\pi\)
\(72\) 0 0
\(73\) −5.60866 −0.656444 −0.328222 0.944601i \(-0.606449\pi\)
−0.328222 + 0.944601i \(0.606449\pi\)
\(74\) 0 0
\(75\) −18.0134 −2.08001
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.401351 0.0451555 0.0225778 0.999745i \(-0.492813\pi\)
0.0225778 + 0.999745i \(0.492813\pi\)
\(80\) 0 0
\(81\) −2.97976 −0.331085
\(82\) 0 0
\(83\) −7.91362 −0.868633 −0.434317 0.900760i \(-0.643010\pi\)
−0.434317 + 0.900760i \(0.643010\pi\)
\(84\) 0 0
\(85\) 26.9125 2.91907
\(86\) 0 0
\(87\) 2.26558 0.242896
\(88\) 0 0
\(89\) 13.4751 1.42836 0.714181 0.699961i \(-0.246799\pi\)
0.714181 + 0.699961i \(0.246799\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.12960 0.531915
\(94\) 0 0
\(95\) 22.6414 2.32296
\(96\) 0 0
\(97\) −7.58525 −0.770165 −0.385083 0.922882i \(-0.625827\pi\)
−0.385083 + 0.922882i \(0.625827\pi\)
\(98\) 0 0
\(99\) −8.27395 −0.831563
\(100\) 0 0
\(101\) 8.69249 0.864935 0.432467 0.901650i \(-0.357643\pi\)
0.432467 + 0.901650i \(0.357643\pi\)
\(102\) 0 0
\(103\) 0.936858 0.0923113 0.0461557 0.998934i \(-0.485303\pi\)
0.0461557 + 0.998934i \(0.485303\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.950579 0.0918960 0.0459480 0.998944i \(-0.485369\pi\)
0.0459480 + 0.998944i \(0.485369\pi\)
\(108\) 0 0
\(109\) −4.22000 −0.404203 −0.202102 0.979365i \(-0.564777\pi\)
−0.202102 + 0.979365i \(0.564777\pi\)
\(110\) 0 0
\(111\) −10.5182 −0.998348
\(112\) 0 0
\(113\) 18.5506 1.74509 0.872546 0.488532i \(-0.162468\pi\)
0.872546 + 0.488532i \(0.162468\pi\)
\(114\) 0 0
\(115\) −20.4023 −1.90252
\(116\) 0 0
\(117\) 7.70246 0.712093
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 25.1671 2.28792
\(122\) 0 0
\(123\) 1.27444 0.114912
\(124\) 0 0
\(125\) 39.9564 3.57381
\(126\) 0 0
\(127\) 2.38798 0.211899 0.105949 0.994372i \(-0.466212\pi\)
0.105949 + 0.994372i \(0.466212\pi\)
\(128\) 0 0
\(129\) −1.05920 −0.0932570
\(130\) 0 0
\(131\) −4.47978 −0.391400 −0.195700 0.980664i \(-0.562698\pi\)
−0.195700 + 0.980664i \(0.562698\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 24.3941 2.09951
\(136\) 0 0
\(137\) 21.2025 1.81145 0.905726 0.423864i \(-0.139327\pi\)
0.905726 + 0.423864i \(0.139327\pi\)
\(138\) 0 0
\(139\) −6.76140 −0.573494 −0.286747 0.958006i \(-0.592574\pi\)
−0.286747 + 0.958006i \(0.592574\pi\)
\(140\) 0 0
\(141\) −3.46773 −0.292036
\(142\) 0 0
\(143\) −33.6690 −2.81554
\(144\) 0 0
\(145\) −7.77621 −0.645779
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.88005 −0.481712 −0.240856 0.970561i \(-0.577428\pi\)
−0.240856 + 0.970561i \(0.577428\pi\)
\(150\) 0 0
\(151\) −6.62898 −0.539459 −0.269729 0.962936i \(-0.586934\pi\)
−0.269729 + 0.962936i \(0.586934\pi\)
\(152\) 0 0
\(153\) −8.46453 −0.684317
\(154\) 0 0
\(155\) −17.6064 −1.41418
\(156\) 0 0
\(157\) 9.09576 0.725921 0.362960 0.931805i \(-0.381766\pi\)
0.362960 + 0.931805i \(0.381766\pi\)
\(158\) 0 0
\(159\) 1.15575 0.0916572
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −9.02020 −0.706517 −0.353258 0.935526i \(-0.614926\pi\)
−0.353258 + 0.935526i \(0.614926\pi\)
\(164\) 0 0
\(165\) −33.5261 −2.61001
\(166\) 0 0
\(167\) −24.7420 −1.91459 −0.957297 0.289105i \(-0.906642\pi\)
−0.957297 + 0.289105i \(0.906642\pi\)
\(168\) 0 0
\(169\) 18.3435 1.41104
\(170\) 0 0
\(171\) −7.12117 −0.544570
\(172\) 0 0
\(173\) −6.16366 −0.468615 −0.234307 0.972163i \(-0.575282\pi\)
−0.234307 + 0.972163i \(0.575282\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.1015 −0.759277
\(178\) 0 0
\(179\) 14.8825 1.11237 0.556184 0.831059i \(-0.312265\pi\)
0.556184 + 0.831059i \(0.312265\pi\)
\(180\) 0 0
\(181\) 6.30244 0.468457 0.234228 0.972182i \(-0.424744\pi\)
0.234228 + 0.972182i \(0.424744\pi\)
\(182\) 0 0
\(183\) 7.24682 0.535700
\(184\) 0 0
\(185\) 36.1020 2.65427
\(186\) 0 0
\(187\) 37.0002 2.70572
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.42229 −0.102913 −0.0514566 0.998675i \(-0.516386\pi\)
−0.0514566 + 0.998675i \(0.516386\pi\)
\(192\) 0 0
\(193\) −3.69210 −0.265763 −0.132882 0.991132i \(-0.542423\pi\)
−0.132882 + 0.991132i \(0.542423\pi\)
\(194\) 0 0
\(195\) 31.2105 2.23503
\(196\) 0 0
\(197\) −0.537968 −0.0383286 −0.0191643 0.999816i \(-0.506101\pi\)
−0.0191643 + 0.999816i \(0.506101\pi\)
\(198\) 0 0
\(199\) −17.9853 −1.27494 −0.637471 0.770474i \(-0.720019\pi\)
−0.637471 + 0.770474i \(0.720019\pi\)
\(200\) 0 0
\(201\) 0.111247 0.00784678
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −4.37429 −0.305513
\(206\) 0 0
\(207\) 6.41693 0.446007
\(208\) 0 0
\(209\) 31.1281 2.15317
\(210\) 0 0
\(211\) 4.08723 0.281377 0.140688 0.990054i \(-0.455068\pi\)
0.140688 + 0.990054i \(0.455068\pi\)
\(212\) 0 0
\(213\) 10.3340 0.708071
\(214\) 0 0
\(215\) 3.63550 0.247939
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 7.14791 0.483011
\(220\) 0 0
\(221\) −34.4446 −2.31699
\(222\) 0 0
\(223\) 5.20162 0.348326 0.174163 0.984717i \(-0.444278\pi\)
0.174163 + 0.984717i \(0.444278\pi\)
\(224\) 0 0
\(225\) −19.4461 −1.29641
\(226\) 0 0
\(227\) 8.82361 0.585644 0.292822 0.956167i \(-0.405406\pi\)
0.292822 + 0.956167i \(0.405406\pi\)
\(228\) 0 0
\(229\) −11.2314 −0.742194 −0.371097 0.928594i \(-0.621018\pi\)
−0.371097 + 0.928594i \(0.621018\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.1088 1.44840 0.724199 0.689591i \(-0.242210\pi\)
0.724199 + 0.689591i \(0.242210\pi\)
\(234\) 0 0
\(235\) 11.9024 0.776425
\(236\) 0 0
\(237\) −0.511498 −0.0332254
\(238\) 0 0
\(239\) 8.28588 0.535969 0.267984 0.963423i \(-0.413642\pi\)
0.267984 + 0.963423i \(0.413642\pi\)
\(240\) 0 0
\(241\) −5.86206 −0.377608 −0.188804 0.982015i \(-0.560461\pi\)
−0.188804 + 0.982015i \(0.560461\pi\)
\(242\) 0 0
\(243\) −12.9326 −0.829625
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −28.9780 −1.84383
\(248\) 0 0
\(249\) 10.0854 0.639139
\(250\) 0 0
\(251\) 0.584676 0.0369044 0.0184522 0.999830i \(-0.494126\pi\)
0.0184522 + 0.999830i \(0.494126\pi\)
\(252\) 0 0
\(253\) −28.0497 −1.76347
\(254\) 0 0
\(255\) −34.2984 −2.14785
\(256\) 0 0
\(257\) −7.48023 −0.466604 −0.233302 0.972404i \(-0.574953\pi\)
−0.233302 + 0.972404i \(0.574953\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2.44578 0.151390
\(262\) 0 0
\(263\) 1.93364 0.119233 0.0596167 0.998221i \(-0.481012\pi\)
0.0596167 + 0.998221i \(0.481012\pi\)
\(264\) 0 0
\(265\) −3.96691 −0.243686
\(266\) 0 0
\(267\) −17.1733 −1.05099
\(268\) 0 0
\(269\) 4.18817 0.255357 0.127679 0.991816i \(-0.459247\pi\)
0.127679 + 0.991816i \(0.459247\pi\)
\(270\) 0 0
\(271\) −22.5286 −1.36851 −0.684256 0.729241i \(-0.739873\pi\)
−0.684256 + 0.729241i \(0.739873\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 85.0029 5.12587
\(276\) 0 0
\(277\) 5.70409 0.342726 0.171363 0.985208i \(-0.445183\pi\)
0.171363 + 0.985208i \(0.445183\pi\)
\(278\) 0 0
\(279\) 5.53758 0.331526
\(280\) 0 0
\(281\) 16.7441 0.998871 0.499436 0.866351i \(-0.333541\pi\)
0.499436 + 0.866351i \(0.333541\pi\)
\(282\) 0 0
\(283\) −9.51746 −0.565754 −0.282877 0.959156i \(-0.591289\pi\)
−0.282877 + 0.959156i \(0.591289\pi\)
\(284\) 0 0
\(285\) −28.8551 −1.70923
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 20.8525 1.22662
\(290\) 0 0
\(291\) 9.66695 0.566686
\(292\) 0 0
\(293\) −27.4692 −1.60477 −0.802383 0.596809i \(-0.796435\pi\)
−0.802383 + 0.596809i \(0.796435\pi\)
\(294\) 0 0
\(295\) 34.6717 2.01866
\(296\) 0 0
\(297\) 33.5377 1.94606
\(298\) 0 0
\(299\) 26.1123 1.51011
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −11.0781 −0.636418
\(304\) 0 0
\(305\) −24.8734 −1.42425
\(306\) 0 0
\(307\) −27.7003 −1.58094 −0.790470 0.612500i \(-0.790164\pi\)
−0.790470 + 0.612500i \(0.790164\pi\)
\(308\) 0 0
\(309\) −1.19397 −0.0679225
\(310\) 0 0
\(311\) 0.0840665 0.00476697 0.00238349 0.999997i \(-0.499241\pi\)
0.00238349 + 0.999997i \(0.499241\pi\)
\(312\) 0 0
\(313\) −20.8627 −1.17923 −0.589615 0.807684i \(-0.700721\pi\)
−0.589615 + 0.807684i \(0.700721\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.1200 0.624563 0.312282 0.949990i \(-0.398907\pi\)
0.312282 + 0.949990i \(0.398907\pi\)
\(318\) 0 0
\(319\) −10.6910 −0.598580
\(320\) 0 0
\(321\) −1.21146 −0.0676169
\(322\) 0 0
\(323\) 31.8451 1.77191
\(324\) 0 0
\(325\) −79.1317 −4.38944
\(326\) 0 0
\(327\) 5.37814 0.297412
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 23.5550 1.29470 0.647350 0.762193i \(-0.275877\pi\)
0.647350 + 0.762193i \(0.275877\pi\)
\(332\) 0 0
\(333\) −11.3548 −0.622240
\(334\) 0 0
\(335\) −0.381836 −0.0208620
\(336\) 0 0
\(337\) 14.4817 0.788867 0.394433 0.918924i \(-0.370941\pi\)
0.394433 + 0.918924i \(0.370941\pi\)
\(338\) 0 0
\(339\) −23.6416 −1.28404
\(340\) 0 0
\(341\) −24.2059 −1.31082
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 26.0015 1.39987
\(346\) 0 0
\(347\) −11.8736 −0.637409 −0.318704 0.947854i \(-0.603248\pi\)
−0.318704 + 0.947854i \(0.603248\pi\)
\(348\) 0 0
\(349\) 1.47735 0.0790805 0.0395403 0.999218i \(-0.487411\pi\)
0.0395403 + 0.999218i \(0.487411\pi\)
\(350\) 0 0
\(351\) −31.2213 −1.66647
\(352\) 0 0
\(353\) 20.5859 1.09568 0.547838 0.836585i \(-0.315451\pi\)
0.547838 + 0.836585i \(0.315451\pi\)
\(354\) 0 0
\(355\) −35.4695 −1.88252
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 22.0198 1.16216 0.581080 0.813847i \(-0.302630\pi\)
0.581080 + 0.813847i \(0.302630\pi\)
\(360\) 0 0
\(361\) 7.79112 0.410059
\(362\) 0 0
\(363\) −32.0739 −1.68345
\(364\) 0 0
\(365\) −24.5339 −1.28416
\(366\) 0 0
\(367\) −11.1637 −0.582742 −0.291371 0.956610i \(-0.594111\pi\)
−0.291371 + 0.956610i \(0.594111\pi\)
\(368\) 0 0
\(369\) 1.37580 0.0716214
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −27.1833 −1.40750 −0.703750 0.710448i \(-0.748493\pi\)
−0.703750 + 0.710448i \(0.748493\pi\)
\(374\) 0 0
\(375\) −50.9221 −2.62960
\(376\) 0 0
\(377\) 9.95255 0.512582
\(378\) 0 0
\(379\) −17.6910 −0.908724 −0.454362 0.890817i \(-0.650133\pi\)
−0.454362 + 0.890817i \(0.650133\pi\)
\(380\) 0 0
\(381\) −3.04333 −0.155915
\(382\) 0 0
\(383\) 2.22193 0.113535 0.0567676 0.998387i \(-0.481921\pi\)
0.0567676 + 0.998387i \(0.481921\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.14344 −0.0581242
\(388\) 0 0
\(389\) 8.04637 0.407967 0.203983 0.978974i \(-0.434611\pi\)
0.203983 + 0.978974i \(0.434611\pi\)
\(390\) 0 0
\(391\) −28.6958 −1.45121
\(392\) 0 0
\(393\) 5.70921 0.287992
\(394\) 0 0
\(395\) 1.75563 0.0883351
\(396\) 0 0
\(397\) 31.8213 1.59707 0.798533 0.601951i \(-0.205610\pi\)
0.798533 + 0.601951i \(0.205610\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 27.3619 1.36639 0.683194 0.730237i \(-0.260590\pi\)
0.683194 + 0.730237i \(0.260590\pi\)
\(402\) 0 0
\(403\) 22.5340 1.12250
\(404\) 0 0
\(405\) −13.0343 −0.647681
\(406\) 0 0
\(407\) 49.6341 2.46027
\(408\) 0 0
\(409\) 18.8393 0.931542 0.465771 0.884905i \(-0.345777\pi\)
0.465771 + 0.884905i \(0.345777\pi\)
\(410\) 0 0
\(411\) −27.0213 −1.33286
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −34.6165 −1.69926
\(416\) 0 0
\(417\) 8.61700 0.421976
\(418\) 0 0
\(419\) −10.0834 −0.492606 −0.246303 0.969193i \(-0.579216\pi\)
−0.246303 + 0.969193i \(0.579216\pi\)
\(420\) 0 0
\(421\) 5.09516 0.248323 0.124161 0.992262i \(-0.460376\pi\)
0.124161 + 0.992262i \(0.460376\pi\)
\(422\) 0 0
\(423\) −3.74354 −0.182017
\(424\) 0 0
\(425\) 86.9609 4.21822
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 42.9091 2.07167
\(430\) 0 0
\(431\) −0.0144149 −0.000694344 0 −0.000347172 1.00000i \(-0.500111\pi\)
−0.000347172 1.00000i \(0.500111\pi\)
\(432\) 0 0
\(433\) −16.1368 −0.775483 −0.387741 0.921768i \(-0.626745\pi\)
−0.387741 + 0.921768i \(0.626745\pi\)
\(434\) 0 0
\(435\) 9.91031 0.475163
\(436\) 0 0
\(437\) −24.1416 −1.15485
\(438\) 0 0
\(439\) 4.51306 0.215397 0.107698 0.994184i \(-0.465652\pi\)
0.107698 + 0.994184i \(0.465652\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.3960 0.541438 0.270719 0.962658i \(-0.412739\pi\)
0.270719 + 0.962658i \(0.412739\pi\)
\(444\) 0 0
\(445\) 58.9441 2.79422
\(446\) 0 0
\(447\) 7.49377 0.354443
\(448\) 0 0
\(449\) 26.9657 1.27259 0.636295 0.771446i \(-0.280466\pi\)
0.636295 + 0.771446i \(0.280466\pi\)
\(450\) 0 0
\(451\) −6.01391 −0.283184
\(452\) 0 0
\(453\) 8.44824 0.396933
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.5826 −0.728922 −0.364461 0.931219i \(-0.618747\pi\)
−0.364461 + 0.931219i \(0.618747\pi\)
\(458\) 0 0
\(459\) 34.3103 1.60147
\(460\) 0 0
\(461\) 31.6708 1.47506 0.737529 0.675316i \(-0.235993\pi\)
0.737529 + 0.675316i \(0.235993\pi\)
\(462\) 0 0
\(463\) −15.8220 −0.735312 −0.367656 0.929962i \(-0.619840\pi\)
−0.367656 + 0.929962i \(0.619840\pi\)
\(464\) 0 0
\(465\) 22.4384 1.04055
\(466\) 0 0
\(467\) 11.4140 0.528179 0.264089 0.964498i \(-0.414929\pi\)
0.264089 + 0.964498i \(0.414929\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −11.5920 −0.534131
\(472\) 0 0
\(473\) 4.99820 0.229817
\(474\) 0 0
\(475\) 73.1598 3.35680
\(476\) 0 0
\(477\) 1.24768 0.0571271
\(478\) 0 0
\(479\) 18.2230 0.832631 0.416316 0.909220i \(-0.363321\pi\)
0.416316 + 0.909220i \(0.363321\pi\)
\(480\) 0 0
\(481\) −46.2059 −2.10681
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −33.1801 −1.50663
\(486\) 0 0
\(487\) −35.8062 −1.62254 −0.811268 0.584675i \(-0.801222\pi\)
−0.811268 + 0.584675i \(0.801222\pi\)
\(488\) 0 0
\(489\) 11.4957 0.519854
\(490\) 0 0
\(491\) 34.2707 1.54662 0.773309 0.634030i \(-0.218600\pi\)
0.773309 + 0.634030i \(0.218600\pi\)
\(492\) 0 0
\(493\) −10.9372 −0.492589
\(494\) 0 0
\(495\) −36.1926 −1.62674
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 30.9556 1.38576 0.692881 0.721052i \(-0.256341\pi\)
0.692881 + 0.721052i \(0.256341\pi\)
\(500\) 0 0
\(501\) 31.5322 1.40876
\(502\) 0 0
\(503\) 34.2582 1.52750 0.763748 0.645515i \(-0.223357\pi\)
0.763748 + 0.645515i \(0.223357\pi\)
\(504\) 0 0
\(505\) 38.0234 1.69202
\(506\) 0 0
\(507\) −23.3777 −1.03824
\(508\) 0 0
\(509\) −27.4575 −1.21703 −0.608517 0.793541i \(-0.708235\pi\)
−0.608517 + 0.793541i \(0.708235\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 28.8651 1.27442
\(514\) 0 0
\(515\) 4.09808 0.180583
\(516\) 0 0
\(517\) 16.3638 0.719677
\(518\) 0 0
\(519\) 7.85522 0.344806
\(520\) 0 0
\(521\) 12.1471 0.532174 0.266087 0.963949i \(-0.414269\pi\)
0.266087 + 0.963949i \(0.414269\pi\)
\(522\) 0 0
\(523\) −21.0692 −0.921291 −0.460646 0.887584i \(-0.652382\pi\)
−0.460646 + 0.887584i \(0.652382\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24.7635 −1.07871
\(528\) 0 0
\(529\) −1.24586 −0.0541678
\(530\) 0 0
\(531\) −10.9049 −0.473234
\(532\) 0 0
\(533\) 5.59853 0.242499
\(534\) 0 0
\(535\) 4.15811 0.179771
\(536\) 0 0
\(537\) −18.9668 −0.818479
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −22.3830 −0.962320 −0.481160 0.876633i \(-0.659784\pi\)
−0.481160 + 0.876633i \(0.659784\pi\)
\(542\) 0 0
\(543\) −8.03208 −0.344690
\(544\) 0 0
\(545\) −18.4595 −0.790718
\(546\) 0 0
\(547\) −41.7440 −1.78485 −0.892423 0.451200i \(-0.850996\pi\)
−0.892423 + 0.451200i \(0.850996\pi\)
\(548\) 0 0
\(549\) 7.82319 0.333886
\(550\) 0 0
\(551\) −9.20145 −0.391995
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −46.0098 −1.95301
\(556\) 0 0
\(557\) 21.6176 0.915965 0.457983 0.888961i \(-0.348572\pi\)
0.457983 + 0.888961i \(0.348572\pi\)
\(558\) 0 0
\(559\) −4.65297 −0.196800
\(560\) 0 0
\(561\) −47.1545 −1.99087
\(562\) 0 0
\(563\) −37.7846 −1.59243 −0.796215 0.605014i \(-0.793167\pi\)
−0.796215 + 0.605014i \(0.793167\pi\)
\(564\) 0 0
\(565\) 81.1456 3.41382
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.43234 0.227735 0.113868 0.993496i \(-0.463676\pi\)
0.113868 + 0.993496i \(0.463676\pi\)
\(570\) 0 0
\(571\) 38.9281 1.62909 0.814545 0.580101i \(-0.196987\pi\)
0.814545 + 0.580101i \(0.196987\pi\)
\(572\) 0 0
\(573\) 1.81262 0.0757234
\(574\) 0 0
\(575\) −65.9247 −2.74925
\(576\) 0 0
\(577\) 12.0099 0.499978 0.249989 0.968249i \(-0.419573\pi\)
0.249989 + 0.968249i \(0.419573\pi\)
\(578\) 0 0
\(579\) 4.70536 0.195548
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.45384 −0.225875
\(584\) 0 0
\(585\) 33.6928 1.39303
\(586\) 0 0
\(587\) −24.6756 −1.01847 −0.509235 0.860628i \(-0.670071\pi\)
−0.509235 + 0.860628i \(0.670071\pi\)
\(588\) 0 0
\(589\) −20.8334 −0.858425
\(590\) 0 0
\(591\) 0.685608 0.0282021
\(592\) 0 0
\(593\) −12.2525 −0.503151 −0.251575 0.967838i \(-0.580949\pi\)
−0.251575 + 0.967838i \(0.580949\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 22.9211 0.938100
\(598\) 0 0
\(599\) 7.84464 0.320523 0.160262 0.987075i \(-0.448766\pi\)
0.160262 + 0.987075i \(0.448766\pi\)
\(600\) 0 0
\(601\) 14.4302 0.588619 0.294310 0.955710i \(-0.404910\pi\)
0.294310 + 0.955710i \(0.404910\pi\)
\(602\) 0 0
\(603\) 0.120095 0.00489066
\(604\) 0 0
\(605\) 110.088 4.47572
\(606\) 0 0
\(607\) 13.4212 0.544751 0.272376 0.962191i \(-0.412191\pi\)
0.272376 + 0.962191i \(0.412191\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.2335 −0.616282
\(612\) 0 0
\(613\) 11.3835 0.459776 0.229888 0.973217i \(-0.426164\pi\)
0.229888 + 0.973217i \(0.426164\pi\)
\(614\) 0 0
\(615\) 5.57477 0.224796
\(616\) 0 0
\(617\) −7.68338 −0.309321 −0.154661 0.987968i \(-0.549428\pi\)
−0.154661 + 0.987968i \(0.549428\pi\)
\(618\) 0 0
\(619\) 1.76746 0.0710401 0.0355201 0.999369i \(-0.488691\pi\)
0.0355201 + 0.999369i \(0.488691\pi\)
\(620\) 0 0
\(621\) −26.0105 −1.04376
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 104.109 4.16436
\(626\) 0 0
\(627\) −39.6709 −1.58430
\(628\) 0 0
\(629\) 50.7774 2.02463
\(630\) 0 0
\(631\) 26.4941 1.05471 0.527356 0.849645i \(-0.323184\pi\)
0.527356 + 0.849645i \(0.323184\pi\)
\(632\) 0 0
\(633\) −5.20893 −0.207036
\(634\) 0 0
\(635\) 10.4457 0.414525
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 11.1559 0.441319
\(640\) 0 0
\(641\) −3.10746 −0.122737 −0.0613687 0.998115i \(-0.519547\pi\)
−0.0613687 + 0.998115i \(0.519547\pi\)
\(642\) 0 0
\(643\) 20.4230 0.805405 0.402702 0.915331i \(-0.368071\pi\)
0.402702 + 0.915331i \(0.368071\pi\)
\(644\) 0 0
\(645\) −4.63322 −0.182433
\(646\) 0 0
\(647\) 27.3520 1.07532 0.537660 0.843162i \(-0.319308\pi\)
0.537660 + 0.843162i \(0.319308\pi\)
\(648\) 0 0
\(649\) 47.6677 1.87112
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.1311 0.709525 0.354763 0.934956i \(-0.384562\pi\)
0.354763 + 0.934956i \(0.384562\pi\)
\(654\) 0 0
\(655\) −19.5958 −0.765673
\(656\) 0 0
\(657\) 7.71641 0.301046
\(658\) 0 0
\(659\) −3.67331 −0.143092 −0.0715458 0.997437i \(-0.522793\pi\)
−0.0715458 + 0.997437i \(0.522793\pi\)
\(660\) 0 0
\(661\) −4.34291 −0.168919 −0.0844597 0.996427i \(-0.526916\pi\)
−0.0844597 + 0.996427i \(0.526916\pi\)
\(662\) 0 0
\(663\) 43.8975 1.70484
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.29147 0.321047
\(668\) 0 0
\(669\) −6.62916 −0.256298
\(670\) 0 0
\(671\) −34.1967 −1.32015
\(672\) 0 0
\(673\) −17.9495 −0.691904 −0.345952 0.938252i \(-0.612444\pi\)
−0.345952 + 0.938252i \(0.612444\pi\)
\(674\) 0 0
\(675\) 78.8232 3.03391
\(676\) 0 0
\(677\) −47.2419 −1.81565 −0.907826 0.419347i \(-0.862259\pi\)
−0.907826 + 0.419347i \(0.862259\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11.2452 −0.430916
\(682\) 0 0
\(683\) −32.2394 −1.23361 −0.616803 0.787118i \(-0.711572\pi\)
−0.616803 + 0.787118i \(0.711572\pi\)
\(684\) 0 0
\(685\) 92.7458 3.54363
\(686\) 0 0
\(687\) 14.3138 0.546105
\(688\) 0 0
\(689\) 5.07714 0.193424
\(690\) 0 0
\(691\) −43.8664 −1.66876 −0.834378 0.551193i \(-0.814173\pi\)
−0.834378 + 0.551193i \(0.814173\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −29.5763 −1.12189
\(696\) 0 0
\(697\) −6.15244 −0.233040
\(698\) 0 0
\(699\) −28.1764 −1.06573
\(700\) 0 0
\(701\) 17.1256 0.646826 0.323413 0.946258i \(-0.395170\pi\)
0.323413 + 0.946258i \(0.395170\pi\)
\(702\) 0 0
\(703\) 42.7188 1.61117
\(704\) 0 0
\(705\) −15.1689 −0.571292
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −4.59653 −0.172626 −0.0863131 0.996268i \(-0.527509\pi\)
−0.0863131 + 0.996268i \(0.527509\pi\)
\(710\) 0 0
\(711\) −0.552180 −0.0207084
\(712\) 0 0
\(713\) 18.7731 0.703057
\(714\) 0 0
\(715\) −147.278 −5.50788
\(716\) 0 0
\(717\) −10.5599 −0.394365
\(718\) 0 0
\(719\) 48.2702 1.80018 0.900088 0.435708i \(-0.143502\pi\)
0.900088 + 0.435708i \(0.143502\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 7.47084 0.277844
\(724\) 0 0
\(725\) −25.1268 −0.933187
\(726\) 0 0
\(727\) 18.6128 0.690309 0.345154 0.938546i \(-0.387827\pi\)
0.345154 + 0.938546i \(0.387827\pi\)
\(728\) 0 0
\(729\) 25.4211 0.941521
\(730\) 0 0
\(731\) 5.11333 0.189123
\(732\) 0 0
\(733\) −20.7445 −0.766217 −0.383109 0.923703i \(-0.625147\pi\)
−0.383109 + 0.923703i \(0.625147\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.524961 −0.0193372
\(738\) 0 0
\(739\) 31.5512 1.16063 0.580316 0.814392i \(-0.302929\pi\)
0.580316 + 0.814392i \(0.302929\pi\)
\(740\) 0 0
\(741\) 36.9308 1.35669
\(742\) 0 0
\(743\) 25.9780 0.953041 0.476520 0.879163i \(-0.341898\pi\)
0.476520 + 0.879163i \(0.341898\pi\)
\(744\) 0 0
\(745\) −25.7210 −0.942345
\(746\) 0 0
\(747\) 10.8876 0.398356
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4.58963 −0.167478 −0.0837389 0.996488i \(-0.526686\pi\)
−0.0837389 + 0.996488i \(0.526686\pi\)
\(752\) 0 0
\(753\) −0.745134 −0.0271542
\(754\) 0 0
\(755\) −28.9971 −1.05531
\(756\) 0 0
\(757\) −1.12358 −0.0408371 −0.0204185 0.999792i \(-0.506500\pi\)
−0.0204185 + 0.999792i \(0.506500\pi\)
\(758\) 0 0
\(759\) 35.7476 1.29756
\(760\) 0 0
\(761\) −21.1890 −0.768099 −0.384049 0.923313i \(-0.625471\pi\)
−0.384049 + 0.923313i \(0.625471\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −37.0263 −1.33869
\(766\) 0 0
\(767\) −44.3753 −1.60230
\(768\) 0 0
\(769\) 17.2834 0.623257 0.311628 0.950204i \(-0.399126\pi\)
0.311628 + 0.950204i \(0.399126\pi\)
\(770\) 0 0
\(771\) 9.53310 0.343326
\(772\) 0 0
\(773\) 5.95952 0.214349 0.107175 0.994240i \(-0.465820\pi\)
0.107175 + 0.994240i \(0.465820\pi\)
\(774\) 0 0
\(775\) −56.8907 −2.04357
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.17601 −0.185450
\(780\) 0 0
\(781\) −48.7645 −1.74493
\(782\) 0 0
\(783\) −9.91375 −0.354288
\(784\) 0 0
\(785\) 39.7875 1.42008
\(786\) 0 0
\(787\) 48.0534 1.71292 0.856459 0.516216i \(-0.172660\pi\)
0.856459 + 0.516216i \(0.172660\pi\)
\(788\) 0 0
\(789\) −2.46431 −0.0877317
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 31.8348 1.13049
\(794\) 0 0
\(795\) 5.05559 0.179303
\(796\) 0 0
\(797\) 12.3574 0.437723 0.218862 0.975756i \(-0.429766\pi\)
0.218862 + 0.975756i \(0.429766\pi\)
\(798\) 0 0
\(799\) 16.7407 0.592243
\(800\) 0 0
\(801\) −18.5391 −0.655048
\(802\) 0 0
\(803\) −33.7300 −1.19031
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.33757 −0.187891
\(808\) 0 0
\(809\) 31.4203 1.10468 0.552340 0.833619i \(-0.313735\pi\)
0.552340 + 0.833619i \(0.313735\pi\)
\(810\) 0 0
\(811\) 50.3267 1.76721 0.883604 0.468235i \(-0.155110\pi\)
0.883604 + 0.468235i \(0.155110\pi\)
\(812\) 0 0
\(813\) 28.7113 1.00695
\(814\) 0 0
\(815\) −39.4569 −1.38212
\(816\) 0 0
\(817\) 4.30182 0.150502
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.0005 −1.22153 −0.610763 0.791813i \(-0.709137\pi\)
−0.610763 + 0.791813i \(0.709137\pi\)
\(822\) 0 0
\(823\) 42.6664 1.48726 0.743628 0.668594i \(-0.233104\pi\)
0.743628 + 0.668594i \(0.233104\pi\)
\(824\) 0 0
\(825\) −108.331 −3.77160
\(826\) 0 0
\(827\) −21.3960 −0.744013 −0.372007 0.928230i \(-0.621330\pi\)
−0.372007 + 0.928230i \(0.621330\pi\)
\(828\) 0 0
\(829\) −45.6668 −1.58607 −0.793036 0.609174i \(-0.791501\pi\)
−0.793036 + 0.609174i \(0.791501\pi\)
\(830\) 0 0
\(831\) −7.26952 −0.252177
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −108.229 −3.74541
\(836\) 0 0
\(837\) −22.4461 −0.775852
\(838\) 0 0
\(839\) 19.2945 0.666121 0.333060 0.942906i \(-0.391919\pi\)
0.333060 + 0.942906i \(0.391919\pi\)
\(840\) 0 0
\(841\) −25.8398 −0.891026
\(842\) 0 0
\(843\) −21.3394 −0.734968
\(844\) 0 0
\(845\) 80.2397 2.76033
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 12.1294 0.416281
\(850\) 0 0
\(851\) −38.4942 −1.31956
\(852\) 0 0
\(853\) −15.5000 −0.530709 −0.265355 0.964151i \(-0.585489\pi\)
−0.265355 + 0.964151i \(0.585489\pi\)
\(854\) 0 0
\(855\) −31.1500 −1.06531
\(856\) 0 0
\(857\) 36.0081 1.23001 0.615007 0.788522i \(-0.289153\pi\)
0.615007 + 0.788522i \(0.289153\pi\)
\(858\) 0 0
\(859\) 20.2200 0.689898 0.344949 0.938621i \(-0.387896\pi\)
0.344949 + 0.938621i \(0.387896\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22.1025 0.752377 0.376189 0.926543i \(-0.377234\pi\)
0.376189 + 0.926543i \(0.377234\pi\)
\(864\) 0 0
\(865\) −26.9616 −0.916723
\(866\) 0 0
\(867\) −26.5752 −0.902542
\(868\) 0 0
\(869\) 2.41369 0.0818788
\(870\) 0 0
\(871\) 0.488702 0.0165590
\(872\) 0 0
\(873\) 10.4358 0.353198
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −13.8589 −0.467981 −0.233991 0.972239i \(-0.575178\pi\)
−0.233991 + 0.972239i \(0.575178\pi\)
\(878\) 0 0
\(879\) 35.0078 1.18078
\(880\) 0 0
\(881\) 36.0284 1.21383 0.606914 0.794768i \(-0.292407\pi\)
0.606914 + 0.794768i \(0.292407\pi\)
\(882\) 0 0
\(883\) 10.3770 0.349213 0.174606 0.984638i \(-0.444135\pi\)
0.174606 + 0.984638i \(0.444135\pi\)
\(884\) 0 0
\(885\) −44.1869 −1.48533
\(886\) 0 0
\(887\) 5.36696 0.180205 0.0901025 0.995932i \(-0.471281\pi\)
0.0901025 + 0.995932i \(0.471281\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −17.9200 −0.600343
\(892\) 0 0
\(893\) 14.0839 0.471298
\(894\) 0 0
\(895\) 65.1002 2.17606
\(896\) 0 0
\(897\) −33.2785 −1.11114
\(898\) 0 0
\(899\) 7.15525 0.238641
\(900\) 0 0
\(901\) −5.57947 −0.185879
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 27.5687 0.916414
\(906\) 0 0
\(907\) 6.71146 0.222850 0.111425 0.993773i \(-0.464458\pi\)
0.111425 + 0.993773i \(0.464458\pi\)
\(908\) 0 0
\(909\) −11.9591 −0.396660
\(910\) 0 0
\(911\) −37.7515 −1.25076 −0.625381 0.780319i \(-0.715057\pi\)
−0.625381 + 0.780319i \(0.715057\pi\)
\(912\) 0 0
\(913\) −47.5918 −1.57506
\(914\) 0 0
\(915\) 31.6997 1.04796
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −27.9965 −0.923520 −0.461760 0.887005i \(-0.652782\pi\)
−0.461760 + 0.887005i \(0.652782\pi\)
\(920\) 0 0
\(921\) 35.3024 1.16325
\(922\) 0 0
\(923\) 45.3964 1.49424
\(924\) 0 0
\(925\) 116.654 3.83557
\(926\) 0 0
\(927\) −1.28893 −0.0423340
\(928\) 0 0
\(929\) −0.392973 −0.0128930 −0.00644652 0.999979i \(-0.502052\pi\)
−0.00644652 + 0.999979i \(0.502052\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.107138 −0.00350753
\(934\) 0 0
\(935\) 161.849 5.29304
\(936\) 0 0
\(937\) −48.7090 −1.59126 −0.795628 0.605786i \(-0.792859\pi\)
−0.795628 + 0.605786i \(0.792859\pi\)
\(938\) 0 0
\(939\) 26.5883 0.867675
\(940\) 0 0
\(941\) 50.3207 1.64041 0.820204 0.572071i \(-0.193860\pi\)
0.820204 + 0.572071i \(0.193860\pi\)
\(942\) 0 0
\(943\) 4.66413 0.151885
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −60.6072 −1.96947 −0.984735 0.174062i \(-0.944311\pi\)
−0.984735 + 0.174062i \(0.944311\pi\)
\(948\) 0 0
\(949\) 31.4003 1.01930
\(950\) 0 0
\(951\) −14.1718 −0.459553
\(952\) 0 0
\(953\) 49.8014 1.61322 0.806612 0.591081i \(-0.201299\pi\)
0.806612 + 0.591081i \(0.201299\pi\)
\(954\) 0 0
\(955\) −6.22150 −0.201323
\(956\) 0 0
\(957\) 13.6250 0.440434
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −14.7995 −0.477403
\(962\) 0 0
\(963\) −1.30781 −0.0421436
\(964\) 0 0
\(965\) −16.1503 −0.519896
\(966\) 0 0
\(967\) −54.0824 −1.73917 −0.869587 0.493780i \(-0.835615\pi\)
−0.869587 + 0.493780i \(0.835615\pi\)
\(968\) 0 0
\(969\) −40.5847 −1.30377
\(970\) 0 0
\(971\) −40.6144 −1.30338 −0.651690 0.758486i \(-0.725940\pi\)
−0.651690 + 0.758486i \(0.725940\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 100.849 3.22974
\(976\) 0 0
\(977\) −8.05354 −0.257656 −0.128828 0.991667i \(-0.541121\pi\)
−0.128828 + 0.991667i \(0.541121\pi\)
\(978\) 0 0
\(979\) 81.0382 2.58999
\(980\) 0 0
\(981\) 5.80589 0.185368
\(982\) 0 0
\(983\) −39.9017 −1.27267 −0.636333 0.771415i \(-0.719549\pi\)
−0.636333 + 0.771415i \(0.719549\pi\)
\(984\) 0 0
\(985\) −2.35323 −0.0749800
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.87639 −0.123262
\(990\) 0 0
\(991\) −31.0321 −0.985768 −0.492884 0.870095i \(-0.664057\pi\)
−0.492884 + 0.870095i \(0.664057\pi\)
\(992\) 0 0
\(993\) −30.0194 −0.952638
\(994\) 0 0
\(995\) −78.6727 −2.49409
\(996\) 0 0
\(997\) −46.2267 −1.46401 −0.732007 0.681297i \(-0.761416\pi\)
−0.732007 + 0.681297i \(0.761416\pi\)
\(998\) 0 0
\(999\) 46.0258 1.45619
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 \(a_p\))