Properties

Label 8048.2.a.p.1.9
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.40552\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.40552 q^{3} +0.590303 q^{5} -1.95900 q^{7} +2.78655 q^{9} +O(q^{10})\) \(q+2.40552 q^{3} +0.590303 q^{5} -1.95900 q^{7} +2.78655 q^{9} +1.52746 q^{11} -4.67738 q^{13} +1.41999 q^{15} -3.04913 q^{17} -0.338159 q^{19} -4.71242 q^{21} +7.98874 q^{23} -4.65154 q^{25} -0.513468 q^{27} +6.01794 q^{29} +4.17447 q^{31} +3.67434 q^{33} -1.15640 q^{35} -11.0654 q^{37} -11.2515 q^{39} -4.82359 q^{41} -12.4475 q^{43} +1.64491 q^{45} -11.0094 q^{47} -3.16233 q^{49} -7.33476 q^{51} -3.43684 q^{53} +0.901664 q^{55} -0.813449 q^{57} -2.63490 q^{59} +11.4908 q^{61} -5.45884 q^{63} -2.76107 q^{65} +10.2554 q^{67} +19.2171 q^{69} -9.66931 q^{71} -6.33688 q^{73} -11.1894 q^{75} -2.99229 q^{77} +0.667323 q^{79} -9.59480 q^{81} +2.26231 q^{83} -1.79991 q^{85} +14.4763 q^{87} +2.21979 q^{89} +9.16297 q^{91} +10.0418 q^{93} -0.199616 q^{95} +14.2878 q^{97} +4.25634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + O(q^{10}) \) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + 3q^{11} - 18q^{13} + 2q^{15} - 11q^{17} + q^{21} + 2q^{23} - 27q^{25} + 2q^{27} - 9q^{29} + 22q^{31} - 10q^{33} + 6q^{35} - 35q^{37} - 8q^{39} - 4q^{41} + 20q^{43} + 2q^{45} - 7q^{47} - 27q^{49} - 9q^{51} - 24q^{53} + 11q^{55} - 23q^{57} - 17q^{59} - 4q^{61} - 10q^{63} - 16q^{65} + 6q^{67} - 2q^{69} + q^{71} - 31q^{73} - 30q^{75} + 3q^{77} + 10q^{79} - 6q^{81} - 22q^{83} - 6q^{85} - 25q^{87} + q^{89} - 10q^{91} - 6q^{93} - 39q^{95} - 57q^{97} - 35q^{99} + O(q^{100}) \)

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
\(3\) 2.40552 1.38883 0.694415 0.719575i \(-0.255663\pi\)
0.694415 + 0.719575i \(0.255663\pi\)
\(4\) 0 0
\(5\) 0.590303 0.263991 0.131996 0.991250i \(-0.457861\pi\)
0.131996 + 0.991250i \(0.457861\pi\)
\(6\) 0 0
\(7\) −1.95900 −0.740431 −0.370216 0.928946i \(-0.620716\pi\)
−0.370216 + 0.928946i \(0.620716\pi\)
\(8\) 0 0
\(9\) 2.78655 0.928849
\(10\) 0 0
\(11\) 1.52746 0.460546 0.230273 0.973126i \(-0.426038\pi\)
0.230273 + 0.973126i \(0.426038\pi\)
\(12\) 0 0
\(13\) −4.67738 −1.29727 −0.648636 0.761099i \(-0.724660\pi\)
−0.648636 + 0.761099i \(0.724660\pi\)
\(14\) 0 0
\(15\) 1.41999 0.366639
\(16\) 0 0
\(17\) −3.04913 −0.739523 −0.369761 0.929127i \(-0.620561\pi\)
−0.369761 + 0.929127i \(0.620561\pi\)
\(18\) 0 0
\(19\) −0.338159 −0.0775789 −0.0387895 0.999247i \(-0.512350\pi\)
−0.0387895 + 0.999247i \(0.512350\pi\)
\(20\) 0 0
\(21\) −4.71242 −1.02833
\(22\) 0 0
\(23\) 7.98874 1.66577 0.832884 0.553448i \(-0.186688\pi\)
0.832884 + 0.553448i \(0.186688\pi\)
\(24\) 0 0
\(25\) −4.65154 −0.930309
\(26\) 0 0
\(27\) −0.513468 −0.0988170
\(28\) 0 0
\(29\) 6.01794 1.11750 0.558751 0.829335i \(-0.311281\pi\)
0.558751 + 0.829335i \(0.311281\pi\)
\(30\) 0 0
\(31\) 4.17447 0.749758 0.374879 0.927074i \(-0.377684\pi\)
0.374879 + 0.927074i \(0.377684\pi\)
\(32\) 0 0
\(33\) 3.67434 0.639621
\(34\) 0 0
\(35\) −1.15640 −0.195468
\(36\) 0 0
\(37\) −11.0654 −1.81914 −0.909569 0.415553i \(-0.863588\pi\)
−0.909569 + 0.415553i \(0.863588\pi\)
\(38\) 0 0
\(39\) −11.2515 −1.80169
\(40\) 0 0
\(41\) −4.82359 −0.753319 −0.376659 0.926352i \(-0.622927\pi\)
−0.376659 + 0.926352i \(0.622927\pi\)
\(42\) 0 0
\(43\) −12.4475 −1.89822 −0.949111 0.314941i \(-0.898015\pi\)
−0.949111 + 0.314941i \(0.898015\pi\)
\(44\) 0 0
\(45\) 1.64491 0.245208
\(46\) 0 0
\(47\) −11.0094 −1.60589 −0.802945 0.596052i \(-0.796735\pi\)
−0.802945 + 0.596052i \(0.796735\pi\)
\(48\) 0 0
\(49\) −3.16233 −0.451761
\(50\) 0 0
\(51\) −7.33476 −1.02707
\(52\) 0 0
\(53\) −3.43684 −0.472087 −0.236043 0.971743i \(-0.575851\pi\)
−0.236043 + 0.971743i \(0.575851\pi\)
\(54\) 0 0
\(55\) 0.901664 0.121580
\(56\) 0 0
\(57\) −0.813449 −0.107744
\(58\) 0 0
\(59\) −2.63490 −0.343034 −0.171517 0.985181i \(-0.554867\pi\)
−0.171517 + 0.985181i \(0.554867\pi\)
\(60\) 0 0
\(61\) 11.4908 1.47125 0.735625 0.677389i \(-0.236889\pi\)
0.735625 + 0.677389i \(0.236889\pi\)
\(62\) 0 0
\(63\) −5.45884 −0.687749
\(64\) 0 0
\(65\) −2.76107 −0.342469
\(66\) 0 0
\(67\) 10.2554 1.25289 0.626445 0.779465i \(-0.284509\pi\)
0.626445 + 0.779465i \(0.284509\pi\)
\(68\) 0 0
\(69\) 19.2171 2.31347
\(70\) 0 0
\(71\) −9.66931 −1.14754 −0.573768 0.819018i \(-0.694519\pi\)
−0.573768 + 0.819018i \(0.694519\pi\)
\(72\) 0 0
\(73\) −6.33688 −0.741676 −0.370838 0.928698i \(-0.620929\pi\)
−0.370838 + 0.928698i \(0.620929\pi\)
\(74\) 0 0
\(75\) −11.1894 −1.29204
\(76\) 0 0
\(77\) −2.99229 −0.341003
\(78\) 0 0
\(79\) 0.667323 0.0750798 0.0375399 0.999295i \(-0.488048\pi\)
0.0375399 + 0.999295i \(0.488048\pi\)
\(80\) 0 0
\(81\) −9.59480 −1.06609
\(82\) 0 0
\(83\) 2.26231 0.248321 0.124161 0.992262i \(-0.460376\pi\)
0.124161 + 0.992262i \(0.460376\pi\)
\(84\) 0 0
\(85\) −1.79991 −0.195228
\(86\) 0 0
\(87\) 14.4763 1.55202
\(88\) 0 0
\(89\) 2.21979 0.235297 0.117649 0.993055i \(-0.462464\pi\)
0.117649 + 0.993055i \(0.462464\pi\)
\(90\) 0 0
\(91\) 9.16297 0.960541
\(92\) 0 0
\(93\) 10.0418 1.04129
\(94\) 0 0
\(95\) −0.199616 −0.0204802
\(96\) 0 0
\(97\) 14.2878 1.45070 0.725352 0.688378i \(-0.241677\pi\)
0.725352 + 0.688378i \(0.241677\pi\)
\(98\) 0 0
\(99\) 4.25634 0.427778
\(100\) 0 0
\(101\) −0.629834 −0.0626708 −0.0313354 0.999509i \(-0.509976\pi\)
−0.0313354 + 0.999509i \(0.509976\pi\)
\(102\) 0 0
\(103\) 4.51410 0.444788 0.222394 0.974957i \(-0.428613\pi\)
0.222394 + 0.974957i \(0.428613\pi\)
\(104\) 0 0
\(105\) −2.78175 −0.271471
\(106\) 0 0
\(107\) −3.43562 −0.332134 −0.166067 0.986115i \(-0.553107\pi\)
−0.166067 + 0.986115i \(0.553107\pi\)
\(108\) 0 0
\(109\) 9.90039 0.948285 0.474142 0.880448i \(-0.342758\pi\)
0.474142 + 0.880448i \(0.342758\pi\)
\(110\) 0 0
\(111\) −26.6180 −2.52647
\(112\) 0 0
\(113\) −9.47684 −0.891506 −0.445753 0.895156i \(-0.647064\pi\)
−0.445753 + 0.895156i \(0.647064\pi\)
\(114\) 0 0
\(115\) 4.71578 0.439748
\(116\) 0 0
\(117\) −13.0337 −1.20497
\(118\) 0 0
\(119\) 5.97324 0.547566
\(120\) 0 0
\(121\) −8.66687 −0.787897
\(122\) 0 0
\(123\) −11.6033 −1.04623
\(124\) 0 0
\(125\) −5.69733 −0.509585
\(126\) 0 0
\(127\) 11.3574 1.00781 0.503904 0.863760i \(-0.331896\pi\)
0.503904 + 0.863760i \(0.331896\pi\)
\(128\) 0 0
\(129\) −29.9427 −2.63631
\(130\) 0 0
\(131\) −15.9119 −1.39023 −0.695113 0.718900i \(-0.744646\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(132\) 0 0
\(133\) 0.662452 0.0574419
\(134\) 0 0
\(135\) −0.303102 −0.0260868
\(136\) 0 0
\(137\) −15.0390 −1.28486 −0.642432 0.766343i \(-0.722075\pi\)
−0.642432 + 0.766343i \(0.722075\pi\)
\(138\) 0 0
\(139\) 16.6486 1.41212 0.706059 0.708153i \(-0.250471\pi\)
0.706059 + 0.708153i \(0.250471\pi\)
\(140\) 0 0
\(141\) −26.4835 −2.23031
\(142\) 0 0
\(143\) −7.14451 −0.597454
\(144\) 0 0
\(145\) 3.55241 0.295011
\(146\) 0 0
\(147\) −7.60706 −0.627420
\(148\) 0 0
\(149\) −12.0657 −0.988463 −0.494232 0.869330i \(-0.664550\pi\)
−0.494232 + 0.869330i \(0.664550\pi\)
\(150\) 0 0
\(151\) 16.4897 1.34192 0.670958 0.741495i \(-0.265883\pi\)
0.670958 + 0.741495i \(0.265883\pi\)
\(152\) 0 0
\(153\) −8.49655 −0.686905
\(154\) 0 0
\(155\) 2.46420 0.197930
\(156\) 0 0
\(157\) 4.10607 0.327700 0.163850 0.986485i \(-0.447609\pi\)
0.163850 + 0.986485i \(0.447609\pi\)
\(158\) 0 0
\(159\) −8.26741 −0.655648
\(160\) 0 0
\(161\) −15.6499 −1.23339
\(162\) 0 0
\(163\) −21.2459 −1.66411 −0.832053 0.554696i \(-0.812835\pi\)
−0.832053 + 0.554696i \(0.812835\pi\)
\(164\) 0 0
\(165\) 2.16897 0.168854
\(166\) 0 0
\(167\) 5.96545 0.461620 0.230810 0.972999i \(-0.425862\pi\)
0.230810 + 0.972999i \(0.425862\pi\)
\(168\) 0 0
\(169\) 8.87787 0.682913
\(170\) 0 0
\(171\) −0.942295 −0.0720591
\(172\) 0 0
\(173\) −16.2621 −1.23638 −0.618192 0.786027i \(-0.712135\pi\)
−0.618192 + 0.786027i \(0.712135\pi\)
\(174\) 0 0
\(175\) 9.11236 0.688830
\(176\) 0 0
\(177\) −6.33831 −0.476416
\(178\) 0 0
\(179\) −9.36724 −0.700140 −0.350070 0.936723i \(-0.613842\pi\)
−0.350070 + 0.936723i \(0.613842\pi\)
\(180\) 0 0
\(181\) 1.62885 0.121072 0.0605358 0.998166i \(-0.480719\pi\)
0.0605358 + 0.998166i \(0.480719\pi\)
\(182\) 0 0
\(183\) 27.6415 2.04332
\(184\) 0 0
\(185\) −6.53193 −0.480237
\(186\) 0 0
\(187\) −4.65742 −0.340585
\(188\) 0 0
\(189\) 1.00588 0.0731672
\(190\) 0 0
\(191\) 8.41952 0.609215 0.304607 0.952478i \(-0.401475\pi\)
0.304607 + 0.952478i \(0.401475\pi\)
\(192\) 0 0
\(193\) −24.9514 −1.79604 −0.898022 0.439950i \(-0.854996\pi\)
−0.898022 + 0.439950i \(0.854996\pi\)
\(194\) 0 0
\(195\) −6.64182 −0.475631
\(196\) 0 0
\(197\) 2.36559 0.168541 0.0842705 0.996443i \(-0.473144\pi\)
0.0842705 + 0.996443i \(0.473144\pi\)
\(198\) 0 0
\(199\) −11.7817 −0.835180 −0.417590 0.908636i \(-0.637125\pi\)
−0.417590 + 0.908636i \(0.637125\pi\)
\(200\) 0 0
\(201\) 24.6695 1.74005
\(202\) 0 0
\(203\) −11.7891 −0.827434
\(204\) 0 0
\(205\) −2.84738 −0.198870
\(206\) 0 0
\(207\) 22.2610 1.54725
\(208\) 0 0
\(209\) −0.516524 −0.0357287
\(210\) 0 0
\(211\) 16.8124 1.15742 0.578708 0.815535i \(-0.303557\pi\)
0.578708 + 0.815535i \(0.303557\pi\)
\(212\) 0 0
\(213\) −23.2597 −1.59373
\(214\) 0 0
\(215\) −7.34778 −0.501115
\(216\) 0 0
\(217\) −8.17778 −0.555144
\(218\) 0 0
\(219\) −15.2435 −1.03006
\(220\) 0 0
\(221\) 14.2619 0.959362
\(222\) 0 0
\(223\) −8.32490 −0.557476 −0.278738 0.960367i \(-0.589916\pi\)
−0.278738 + 0.960367i \(0.589916\pi\)
\(224\) 0 0
\(225\) −12.9617 −0.864116
\(226\) 0 0
\(227\) −6.35919 −0.422074 −0.211037 0.977478i \(-0.567684\pi\)
−0.211037 + 0.977478i \(0.567684\pi\)
\(228\) 0 0
\(229\) 11.4619 0.757426 0.378713 0.925514i \(-0.376367\pi\)
0.378713 + 0.925514i \(0.376367\pi\)
\(230\) 0 0
\(231\) −7.19802 −0.473595
\(232\) 0 0
\(233\) 21.5891 1.41435 0.707175 0.707039i \(-0.249969\pi\)
0.707175 + 0.707039i \(0.249969\pi\)
\(234\) 0 0
\(235\) −6.49890 −0.423941
\(236\) 0 0
\(237\) 1.60526 0.104273
\(238\) 0 0
\(239\) 4.52568 0.292742 0.146371 0.989230i \(-0.453241\pi\)
0.146371 + 0.989230i \(0.453241\pi\)
\(240\) 0 0
\(241\) −9.84982 −0.634483 −0.317241 0.948345i \(-0.602757\pi\)
−0.317241 + 0.948345i \(0.602757\pi\)
\(242\) 0 0
\(243\) −21.5401 −1.38180
\(244\) 0 0
\(245\) −1.86673 −0.119261
\(246\) 0 0
\(247\) 1.58170 0.100641
\(248\) 0 0
\(249\) 5.44205 0.344876
\(250\) 0 0
\(251\) −22.0558 −1.39215 −0.696075 0.717969i \(-0.745072\pi\)
−0.696075 + 0.717969i \(0.745072\pi\)
\(252\) 0 0
\(253\) 12.2025 0.767163
\(254\) 0 0
\(255\) −4.32973 −0.271138
\(256\) 0 0
\(257\) 25.3211 1.57948 0.789742 0.613439i \(-0.210214\pi\)
0.789742 + 0.613439i \(0.210214\pi\)
\(258\) 0 0
\(259\) 21.6771 1.34695
\(260\) 0 0
\(261\) 16.7693 1.03799
\(262\) 0 0
\(263\) −10.7243 −0.661289 −0.330644 0.943755i \(-0.607266\pi\)
−0.330644 + 0.943755i \(0.607266\pi\)
\(264\) 0 0
\(265\) −2.02878 −0.124627
\(266\) 0 0
\(267\) 5.33975 0.326788
\(268\) 0 0
\(269\) −11.9609 −0.729266 −0.364633 0.931151i \(-0.618806\pi\)
−0.364633 + 0.931151i \(0.618806\pi\)
\(270\) 0 0
\(271\) 11.7258 0.712295 0.356147 0.934430i \(-0.384090\pi\)
0.356147 + 0.934430i \(0.384090\pi\)
\(272\) 0 0
\(273\) 22.0418 1.33403
\(274\) 0 0
\(275\) −7.10504 −0.428450
\(276\) 0 0
\(277\) −0.916745 −0.0550819 −0.0275409 0.999621i \(-0.508768\pi\)
−0.0275409 + 0.999621i \(0.508768\pi\)
\(278\) 0 0
\(279\) 11.6324 0.696411
\(280\) 0 0
\(281\) 21.7464 1.29728 0.648640 0.761096i \(-0.275338\pi\)
0.648640 + 0.761096i \(0.275338\pi\)
\(282\) 0 0
\(283\) 8.06684 0.479524 0.239762 0.970832i \(-0.422931\pi\)
0.239762 + 0.970832i \(0.422931\pi\)
\(284\) 0 0
\(285\) −0.480181 −0.0284435
\(286\) 0 0
\(287\) 9.44941 0.557781
\(288\) 0 0
\(289\) −7.70280 −0.453106
\(290\) 0 0
\(291\) 34.3696 2.01478
\(292\) 0 0
\(293\) −2.16609 −0.126544 −0.0632722 0.997996i \(-0.520154\pi\)
−0.0632722 + 0.997996i \(0.520154\pi\)
\(294\) 0 0
\(295\) −1.55539 −0.0905581
\(296\) 0 0
\(297\) −0.784302 −0.0455098
\(298\) 0 0
\(299\) −37.3664 −2.16095
\(300\) 0 0
\(301\) 24.3846 1.40550
\(302\) 0 0
\(303\) −1.51508 −0.0870391
\(304\) 0 0
\(305\) 6.78307 0.388397
\(306\) 0 0
\(307\) −6.60523 −0.376980 −0.188490 0.982075i \(-0.560359\pi\)
−0.188490 + 0.982075i \(0.560359\pi\)
\(308\) 0 0
\(309\) 10.8588 0.617735
\(310\) 0 0
\(311\) −3.84184 −0.217851 −0.108925 0.994050i \(-0.534741\pi\)
−0.108925 + 0.994050i \(0.534741\pi\)
\(312\) 0 0
\(313\) −25.4617 −1.43918 −0.719591 0.694398i \(-0.755671\pi\)
−0.719591 + 0.694398i \(0.755671\pi\)
\(314\) 0 0
\(315\) −3.22237 −0.181560
\(316\) 0 0
\(317\) −8.23817 −0.462702 −0.231351 0.972870i \(-0.574314\pi\)
−0.231351 + 0.972870i \(0.574314\pi\)
\(318\) 0 0
\(319\) 9.19216 0.514662
\(320\) 0 0
\(321\) −8.26446 −0.461277
\(322\) 0 0
\(323\) 1.03109 0.0573714
\(324\) 0 0
\(325\) 21.7570 1.20686
\(326\) 0 0
\(327\) 23.8156 1.31701
\(328\) 0 0
\(329\) 21.5675 1.18905
\(330\) 0 0
\(331\) 6.68597 0.367494 0.183747 0.982974i \(-0.441177\pi\)
0.183747 + 0.982974i \(0.441177\pi\)
\(332\) 0 0
\(333\) −30.8342 −1.68970
\(334\) 0 0
\(335\) 6.05376 0.330752
\(336\) 0 0
\(337\) −34.9491 −1.90380 −0.951899 0.306411i \(-0.900872\pi\)
−0.951899 + 0.306411i \(0.900872\pi\)
\(338\) 0 0
\(339\) −22.7968 −1.23815
\(340\) 0 0
\(341\) 6.37634 0.345298
\(342\) 0 0
\(343\) 19.9080 1.07493
\(344\) 0 0
\(345\) 11.3439 0.610736
\(346\) 0 0
\(347\) 16.1317 0.865998 0.432999 0.901394i \(-0.357455\pi\)
0.432999 + 0.901394i \(0.357455\pi\)
\(348\) 0 0
\(349\) −16.2651 −0.870653 −0.435326 0.900273i \(-0.643367\pi\)
−0.435326 + 0.900273i \(0.643367\pi\)
\(350\) 0 0
\(351\) 2.40169 0.128192
\(352\) 0 0
\(353\) 15.5427 0.827254 0.413627 0.910446i \(-0.364262\pi\)
0.413627 + 0.910446i \(0.364262\pi\)
\(354\) 0 0
\(355\) −5.70782 −0.302940
\(356\) 0 0
\(357\) 14.3688 0.760476
\(358\) 0 0
\(359\) 16.5339 0.872625 0.436312 0.899795i \(-0.356284\pi\)
0.436312 + 0.899795i \(0.356284\pi\)
\(360\) 0 0
\(361\) −18.8856 −0.993982
\(362\) 0 0
\(363\) −20.8484 −1.09425
\(364\) 0 0
\(365\) −3.74068 −0.195796
\(366\) 0 0
\(367\) −5.62500 −0.293623 −0.146811 0.989165i \(-0.546901\pi\)
−0.146811 + 0.989165i \(0.546901\pi\)
\(368\) 0 0
\(369\) −13.4412 −0.699719
\(370\) 0 0
\(371\) 6.73277 0.349548
\(372\) 0 0
\(373\) −18.0602 −0.935122 −0.467561 0.883961i \(-0.654867\pi\)
−0.467561 + 0.883961i \(0.654867\pi\)
\(374\) 0 0
\(375\) −13.7051 −0.707727
\(376\) 0 0
\(377\) −28.1482 −1.44970
\(378\) 0 0
\(379\) 2.42773 0.124704 0.0623521 0.998054i \(-0.480140\pi\)
0.0623521 + 0.998054i \(0.480140\pi\)
\(380\) 0 0
\(381\) 27.3206 1.39967
\(382\) 0 0
\(383\) 16.2778 0.831757 0.415878 0.909420i \(-0.363474\pi\)
0.415878 + 0.909420i \(0.363474\pi\)
\(384\) 0 0
\(385\) −1.76636 −0.0900219
\(386\) 0 0
\(387\) −34.6855 −1.76316
\(388\) 0 0
\(389\) −15.0862 −0.764899 −0.382450 0.923976i \(-0.624919\pi\)
−0.382450 + 0.923976i \(0.624919\pi\)
\(390\) 0 0
\(391\) −24.3587 −1.23187
\(392\) 0 0
\(393\) −38.2764 −1.93079
\(394\) 0 0
\(395\) 0.393923 0.0198204
\(396\) 0 0
\(397\) −26.7523 −1.34266 −0.671329 0.741160i \(-0.734276\pi\)
−0.671329 + 0.741160i \(0.734276\pi\)
\(398\) 0 0
\(399\) 1.59354 0.0797770
\(400\) 0 0
\(401\) −21.1930 −1.05833 −0.529165 0.848519i \(-0.677495\pi\)
−0.529165 + 0.848519i \(0.677495\pi\)
\(402\) 0 0
\(403\) −19.5256 −0.972639
\(404\) 0 0
\(405\) −5.66384 −0.281438
\(406\) 0 0
\(407\) −16.9019 −0.837797
\(408\) 0 0
\(409\) 14.2178 0.703023 0.351511 0.936184i \(-0.385668\pi\)
0.351511 + 0.936184i \(0.385668\pi\)
\(410\) 0 0
\(411\) −36.1766 −1.78446
\(412\) 0 0
\(413\) 5.16176 0.253993
\(414\) 0 0
\(415\) 1.33545 0.0655547
\(416\) 0 0
\(417\) 40.0487 1.96119
\(418\) 0 0
\(419\) −40.7220 −1.98940 −0.994700 0.102818i \(-0.967214\pi\)
−0.994700 + 0.102818i \(0.967214\pi\)
\(420\) 0 0
\(421\) 30.2685 1.47519 0.737597 0.675241i \(-0.235960\pi\)
0.737597 + 0.675241i \(0.235960\pi\)
\(422\) 0 0
\(423\) −30.6783 −1.49163
\(424\) 0 0
\(425\) 14.1832 0.687984
\(426\) 0 0
\(427\) −22.5105 −1.08936
\(428\) 0 0
\(429\) −17.1863 −0.829762
\(430\) 0 0
\(431\) −14.3367 −0.690572 −0.345286 0.938497i \(-0.612218\pi\)
−0.345286 + 0.938497i \(0.612218\pi\)
\(432\) 0 0
\(433\) −26.4985 −1.27344 −0.636719 0.771096i \(-0.719709\pi\)
−0.636719 + 0.771096i \(0.719709\pi\)
\(434\) 0 0
\(435\) 8.54540 0.409720
\(436\) 0 0
\(437\) −2.70146 −0.129228
\(438\) 0 0
\(439\) −19.2176 −0.917208 −0.458604 0.888641i \(-0.651650\pi\)
−0.458604 + 0.888641i \(0.651650\pi\)
\(440\) 0 0
\(441\) −8.81198 −0.419618
\(442\) 0 0
\(443\) 5.97322 0.283796 0.141898 0.989881i \(-0.454679\pi\)
0.141898 + 0.989881i \(0.454679\pi\)
\(444\) 0 0
\(445\) 1.31035 0.0621164
\(446\) 0 0
\(447\) −29.0244 −1.37281
\(448\) 0 0
\(449\) 1.84304 0.0869784 0.0434892 0.999054i \(-0.486153\pi\)
0.0434892 + 0.999054i \(0.486153\pi\)
\(450\) 0 0
\(451\) −7.36785 −0.346938
\(452\) 0 0
\(453\) 39.6665 1.86369
\(454\) 0 0
\(455\) 5.40893 0.253575
\(456\) 0 0
\(457\) 27.3399 1.27891 0.639453 0.768830i \(-0.279161\pi\)
0.639453 + 0.768830i \(0.279161\pi\)
\(458\) 0 0
\(459\) 1.56563 0.0730774
\(460\) 0 0
\(461\) 35.1434 1.63679 0.818395 0.574656i \(-0.194864\pi\)
0.818395 + 0.574656i \(0.194864\pi\)
\(462\) 0 0
\(463\) 18.6765 0.867969 0.433984 0.900920i \(-0.357107\pi\)
0.433984 + 0.900920i \(0.357107\pi\)
\(464\) 0 0
\(465\) 5.92770 0.274891
\(466\) 0 0
\(467\) 16.9925 0.786318 0.393159 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(468\) 0 0
\(469\) −20.0902 −0.927680
\(470\) 0 0
\(471\) 9.87725 0.455120
\(472\) 0 0
\(473\) −19.0130 −0.874220
\(474\) 0 0
\(475\) 1.57296 0.0721723
\(476\) 0 0
\(477\) −9.57692 −0.438497
\(478\) 0 0
\(479\) 11.4554 0.523409 0.261705 0.965148i \(-0.415715\pi\)
0.261705 + 0.965148i \(0.415715\pi\)
\(480\) 0 0
\(481\) 51.7570 2.35992
\(482\) 0 0
\(483\) −37.6463 −1.71296
\(484\) 0 0
\(485\) 8.43411 0.382973
\(486\) 0 0
\(487\) 14.2183 0.644295 0.322147 0.946690i \(-0.395595\pi\)
0.322147 + 0.946690i \(0.395595\pi\)
\(488\) 0 0
\(489\) −51.1075 −2.31116
\(490\) 0 0
\(491\) 4.53402 0.204617 0.102309 0.994753i \(-0.467377\pi\)
0.102309 + 0.994753i \(0.467377\pi\)
\(492\) 0 0
\(493\) −18.3495 −0.826419
\(494\) 0 0
\(495\) 2.51253 0.112930
\(496\) 0 0
\(497\) 18.9421 0.849671
\(498\) 0 0
\(499\) 38.1411 1.70743 0.853715 0.520741i \(-0.174344\pi\)
0.853715 + 0.520741i \(0.174344\pi\)
\(500\) 0 0
\(501\) 14.3500 0.641112
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −0.371793 −0.0165446
\(506\) 0 0
\(507\) 21.3559 0.948451
\(508\) 0 0
\(509\) 34.3114 1.52083 0.760413 0.649440i \(-0.224997\pi\)
0.760413 + 0.649440i \(0.224997\pi\)
\(510\) 0 0
\(511\) 12.4139 0.549160
\(512\) 0 0
\(513\) 0.173634 0.00766612
\(514\) 0 0
\(515\) 2.66469 0.117420
\(516\) 0 0
\(517\) −16.8165 −0.739587
\(518\) 0 0
\(519\) −39.1189 −1.71713
\(520\) 0 0
\(521\) 23.8175 1.04346 0.521732 0.853110i \(-0.325286\pi\)
0.521732 + 0.853110i \(0.325286\pi\)
\(522\) 0 0
\(523\) 2.16718 0.0947643 0.0473821 0.998877i \(-0.484912\pi\)
0.0473821 + 0.998877i \(0.484912\pi\)
\(524\) 0 0
\(525\) 21.9200 0.956667
\(526\) 0 0
\(527\) −12.7285 −0.554463
\(528\) 0 0
\(529\) 40.8200 1.77478
\(530\) 0 0
\(531\) −7.34226 −0.318627
\(532\) 0 0
\(533\) 22.5618 0.977259
\(534\) 0 0
\(535\) −2.02805 −0.0876804
\(536\) 0 0
\(537\) −22.5331 −0.972376
\(538\) 0 0
\(539\) −4.83033 −0.208057
\(540\) 0 0
\(541\) 13.5019 0.580493 0.290246 0.956952i \(-0.406263\pi\)
0.290246 + 0.956952i \(0.406263\pi\)
\(542\) 0 0
\(543\) 3.91824 0.168148
\(544\) 0 0
\(545\) 5.84423 0.250339
\(546\) 0 0
\(547\) 1.05880 0.0452710 0.0226355 0.999744i \(-0.492794\pi\)
0.0226355 + 0.999744i \(0.492794\pi\)
\(548\) 0 0
\(549\) 32.0197 1.36657
\(550\) 0 0
\(551\) −2.03502 −0.0866947
\(552\) 0 0
\(553\) −1.30728 −0.0555914
\(554\) 0 0
\(555\) −15.7127 −0.666967
\(556\) 0 0
\(557\) −9.20176 −0.389891 −0.194946 0.980814i \(-0.562453\pi\)
−0.194946 + 0.980814i \(0.562453\pi\)
\(558\) 0 0
\(559\) 58.2216 2.46251
\(560\) 0 0
\(561\) −11.2035 −0.473014
\(562\) 0 0
\(563\) 29.6502 1.24961 0.624804 0.780782i \(-0.285179\pi\)
0.624804 + 0.780782i \(0.285179\pi\)
\(564\) 0 0
\(565\) −5.59420 −0.235350
\(566\) 0 0
\(567\) 18.7962 0.789366
\(568\) 0 0
\(569\) 22.6715 0.950439 0.475220 0.879867i \(-0.342369\pi\)
0.475220 + 0.879867i \(0.342369\pi\)
\(570\) 0 0
\(571\) 31.2013 1.30573 0.652866 0.757473i \(-0.273566\pi\)
0.652866 + 0.757473i \(0.273566\pi\)
\(572\) 0 0
\(573\) 20.2533 0.846096
\(574\) 0 0
\(575\) −37.1600 −1.54968
\(576\) 0 0
\(577\) −3.98191 −0.165769 −0.0828845 0.996559i \(-0.526413\pi\)
−0.0828845 + 0.996559i \(0.526413\pi\)
\(578\) 0 0
\(579\) −60.0213 −2.49440
\(580\) 0 0
\(581\) −4.43187 −0.183865
\(582\) 0 0
\(583\) −5.24964 −0.217418
\(584\) 0 0
\(585\) −7.69385 −0.318102
\(586\) 0 0
\(587\) 12.7494 0.526225 0.263113 0.964765i \(-0.415251\pi\)
0.263113 + 0.964765i \(0.415251\pi\)
\(588\) 0 0
\(589\) −1.41163 −0.0581654
\(590\) 0 0
\(591\) 5.69048 0.234075
\(592\) 0 0
\(593\) −3.27771 −0.134600 −0.0672998 0.997733i \(-0.521438\pi\)
−0.0672998 + 0.997733i \(0.521438\pi\)
\(594\) 0 0
\(595\) 3.52602 0.144553
\(596\) 0 0
\(597\) −28.3411 −1.15992
\(598\) 0 0
\(599\) −10.9237 −0.446332 −0.223166 0.974780i \(-0.571639\pi\)
−0.223166 + 0.974780i \(0.571639\pi\)
\(600\) 0 0
\(601\) −29.7446 −1.21331 −0.606653 0.794967i \(-0.707488\pi\)
−0.606653 + 0.794967i \(0.707488\pi\)
\(602\) 0 0
\(603\) 28.5770 1.16375
\(604\) 0 0
\(605\) −5.11608 −0.207998
\(606\) 0 0
\(607\) 43.8414 1.77947 0.889735 0.456478i \(-0.150889\pi\)
0.889735 + 0.456478i \(0.150889\pi\)
\(608\) 0 0
\(609\) −28.3590 −1.14917
\(610\) 0 0
\(611\) 51.4953 2.08328
\(612\) 0 0
\(613\) −32.3195 −1.30537 −0.652687 0.757628i \(-0.726358\pi\)
−0.652687 + 0.757628i \(0.726358\pi\)
\(614\) 0 0
\(615\) −6.84945 −0.276196
\(616\) 0 0
\(617\) 40.9696 1.64937 0.824687 0.565589i \(-0.191351\pi\)
0.824687 + 0.565589i \(0.191351\pi\)
\(618\) 0 0
\(619\) −22.5775 −0.907466 −0.453733 0.891138i \(-0.649908\pi\)
−0.453733 + 0.891138i \(0.649908\pi\)
\(620\) 0 0
\(621\) −4.10196 −0.164606
\(622\) 0 0
\(623\) −4.34856 −0.174221
\(624\) 0 0
\(625\) 19.8946 0.795782
\(626\) 0 0
\(627\) −1.24251 −0.0496211
\(628\) 0 0
\(629\) 33.7398 1.34529
\(630\) 0 0
\(631\) −33.9719 −1.35240 −0.676199 0.736719i \(-0.736374\pi\)
−0.676199 + 0.736719i \(0.736374\pi\)
\(632\) 0 0
\(633\) 40.4427 1.60745
\(634\) 0 0
\(635\) 6.70432 0.266053
\(636\) 0 0
\(637\) 14.7914 0.586057
\(638\) 0 0
\(639\) −26.9440 −1.06589
\(640\) 0 0
\(641\) −4.53431 −0.179095 −0.0895473 0.995983i \(-0.528542\pi\)
−0.0895473 + 0.995983i \(0.528542\pi\)
\(642\) 0 0
\(643\) −38.3929 −1.51407 −0.757033 0.653376i \(-0.773352\pi\)
−0.757033 + 0.653376i \(0.773352\pi\)
\(644\) 0 0
\(645\) −17.6753 −0.695963
\(646\) 0 0
\(647\) 0.255028 0.0100262 0.00501309 0.999987i \(-0.498404\pi\)
0.00501309 + 0.999987i \(0.498404\pi\)
\(648\) 0 0
\(649\) −4.02470 −0.157983
\(650\) 0 0
\(651\) −19.6719 −0.771001
\(652\) 0 0
\(653\) −2.04379 −0.0799797 −0.0399898 0.999200i \(-0.512733\pi\)
−0.0399898 + 0.999200i \(0.512733\pi\)
\(654\) 0 0
\(655\) −9.39282 −0.367008
\(656\) 0 0
\(657\) −17.6580 −0.688904
\(658\) 0 0
\(659\) −10.0768 −0.392534 −0.196267 0.980550i \(-0.562882\pi\)
−0.196267 + 0.980550i \(0.562882\pi\)
\(660\) 0 0
\(661\) −5.53010 −0.215096 −0.107548 0.994200i \(-0.534300\pi\)
−0.107548 + 0.994200i \(0.534300\pi\)
\(662\) 0 0
\(663\) 34.3074 1.33239
\(664\) 0 0
\(665\) 0.391047 0.0151642
\(666\) 0 0
\(667\) 48.0757 1.86150
\(668\) 0 0
\(669\) −20.0257 −0.774240
\(670\) 0 0
\(671\) 17.5518 0.677579
\(672\) 0 0
\(673\) −3.16280 −0.121917 −0.0609585 0.998140i \(-0.519416\pi\)
−0.0609585 + 0.998140i \(0.519416\pi\)
\(674\) 0 0
\(675\) 2.38842 0.0919303
\(676\) 0 0
\(677\) −47.8219 −1.83794 −0.918972 0.394323i \(-0.870979\pi\)
−0.918972 + 0.394323i \(0.870979\pi\)
\(678\) 0 0
\(679\) −27.9897 −1.07415
\(680\) 0 0
\(681\) −15.2972 −0.586190
\(682\) 0 0
\(683\) −13.2468 −0.506873 −0.253437 0.967352i \(-0.581561\pi\)
−0.253437 + 0.967352i \(0.581561\pi\)
\(684\) 0 0
\(685\) −8.87754 −0.339193
\(686\) 0 0
\(687\) 27.5720 1.05194
\(688\) 0 0
\(689\) 16.0754 0.612425
\(690\) 0 0
\(691\) 7.80850 0.297049 0.148525 0.988909i \(-0.452548\pi\)
0.148525 + 0.988909i \(0.452548\pi\)
\(692\) 0 0
\(693\) −8.33815 −0.316740
\(694\) 0 0
\(695\) 9.82774 0.372787
\(696\) 0 0
\(697\) 14.7078 0.557097
\(698\) 0 0
\(699\) 51.9331 1.96429
\(700\) 0 0
\(701\) 7.68972 0.290437 0.145218 0.989400i \(-0.453612\pi\)
0.145218 + 0.989400i \(0.453612\pi\)
\(702\) 0 0
\(703\) 3.74185 0.141127
\(704\) 0 0
\(705\) −15.6333 −0.588783
\(706\) 0 0
\(707\) 1.23384 0.0464034
\(708\) 0 0
\(709\) 31.0522 1.16619 0.583096 0.812403i \(-0.301841\pi\)
0.583096 + 0.812403i \(0.301841\pi\)
\(710\) 0 0
\(711\) 1.85953 0.0697377
\(712\) 0 0
\(713\) 33.3488 1.24892
\(714\) 0 0
\(715\) −4.21742 −0.157723
\(716\) 0 0
\(717\) 10.8866 0.406569
\(718\) 0 0
\(719\) 30.4494 1.13557 0.567786 0.823176i \(-0.307800\pi\)
0.567786 + 0.823176i \(0.307800\pi\)
\(720\) 0 0
\(721\) −8.84312 −0.329335
\(722\) 0 0
\(723\) −23.6940 −0.881189
\(724\) 0 0
\(725\) −27.9927 −1.03962
\(726\) 0 0
\(727\) 6.14587 0.227938 0.113969 0.993484i \(-0.463644\pi\)
0.113969 + 0.993484i \(0.463644\pi\)
\(728\) 0 0
\(729\) −23.0309 −0.852995
\(730\) 0 0
\(731\) 37.9540 1.40378
\(732\) 0 0
\(733\) −25.4237 −0.939046 −0.469523 0.882920i \(-0.655574\pi\)
−0.469523 + 0.882920i \(0.655574\pi\)
\(734\) 0 0
\(735\) −4.49047 −0.165633
\(736\) 0 0
\(737\) 15.6646 0.577014
\(738\) 0 0
\(739\) 19.8464 0.730063 0.365032 0.930995i \(-0.381058\pi\)
0.365032 + 0.930995i \(0.381058\pi\)
\(740\) 0 0
\(741\) 3.80481 0.139773
\(742\) 0 0
\(743\) 28.7154 1.05346 0.526732 0.850031i \(-0.323417\pi\)
0.526732 + 0.850031i \(0.323417\pi\)
\(744\) 0 0
\(745\) −7.12243 −0.260946
\(746\) 0 0
\(747\) 6.30404 0.230653
\(748\) 0 0
\(749\) 6.73036 0.245922
\(750\) 0 0
\(751\) −24.0374 −0.877139 −0.438569 0.898697i \(-0.644515\pi\)
−0.438569 + 0.898697i \(0.644515\pi\)
\(752\) 0 0
\(753\) −53.0558 −1.93346
\(754\) 0 0
\(755\) 9.73394 0.354254
\(756\) 0 0
\(757\) −23.2463 −0.844902 −0.422451 0.906386i \(-0.638830\pi\)
−0.422451 + 0.906386i \(0.638830\pi\)
\(758\) 0 0
\(759\) 29.3534 1.06546
\(760\) 0 0
\(761\) 44.3555 1.60789 0.803943 0.594706i \(-0.202732\pi\)
0.803943 + 0.594706i \(0.202732\pi\)
\(762\) 0 0
\(763\) −19.3948 −0.702140
\(764\) 0 0
\(765\) −5.01553 −0.181337
\(766\) 0 0
\(767\) 12.3244 0.445009
\(768\) 0 0
\(769\) −17.4534 −0.629385 −0.314693 0.949194i \(-0.601901\pi\)
−0.314693 + 0.949194i \(0.601901\pi\)
\(770\) 0 0
\(771\) 60.9104 2.19364
\(772\) 0 0
\(773\) −1.73607 −0.0624422 −0.0312211 0.999513i \(-0.509940\pi\)
−0.0312211 + 0.999513i \(0.509940\pi\)
\(774\) 0 0
\(775\) −19.4177 −0.697506
\(776\) 0 0
\(777\) 52.1447 1.87068
\(778\) 0 0
\(779\) 1.63114 0.0584417
\(780\) 0 0
\(781\) −14.7695 −0.528493
\(782\) 0 0
\(783\) −3.09002 −0.110428
\(784\) 0 0
\(785\) 2.42383 0.0865100
\(786\) 0 0
\(787\) 16.1636 0.576169 0.288085 0.957605i \(-0.406982\pi\)
0.288085 + 0.957605i \(0.406982\pi\)
\(788\) 0 0
\(789\) −25.7976 −0.918418
\(790\) 0 0
\(791\) 18.5651 0.660099
\(792\) 0 0
\(793\) −53.7469 −1.90861
\(794\) 0 0
\(795\) −4.88028 −0.173086
\(796\) 0 0
\(797\) −26.8208 −0.950040 −0.475020 0.879975i \(-0.657559\pi\)
−0.475020 + 0.879975i \(0.657559\pi\)
\(798\) 0 0
\(799\) 33.5692 1.18759
\(800\) 0 0
\(801\) 6.18554 0.218555
\(802\) 0 0
\(803\) −9.67933 −0.341576
\(804\) 0 0
\(805\) −9.23819 −0.325603
\(806\) 0 0
\(807\) −28.7721 −1.01283
\(808\) 0 0
\(809\) 33.4065 1.17451 0.587255 0.809402i \(-0.300209\pi\)
0.587255 + 0.809402i \(0.300209\pi\)
\(810\) 0 0
\(811\) −34.8499 −1.22375 −0.611873 0.790956i \(-0.709584\pi\)
−0.611873 + 0.790956i \(0.709584\pi\)
\(812\) 0 0
\(813\) 28.2068 0.989256
\(814\) 0 0
\(815\) −12.5415 −0.439310
\(816\) 0 0
\(817\) 4.20922 0.147262
\(818\) 0 0
\(819\) 25.5330 0.892197
\(820\) 0 0
\(821\) −24.4182 −0.852201 −0.426101 0.904676i \(-0.640113\pi\)
−0.426101 + 0.904676i \(0.640113\pi\)
\(822\) 0 0
\(823\) −4.51039 −0.157222 −0.0786112 0.996905i \(-0.525049\pi\)
−0.0786112 + 0.996905i \(0.525049\pi\)
\(824\) 0 0
\(825\) −17.0914 −0.595045
\(826\) 0 0
\(827\) 2.91499 0.101364 0.0506821 0.998715i \(-0.483860\pi\)
0.0506821 + 0.998715i \(0.483860\pi\)
\(828\) 0 0
\(829\) 35.2382 1.22387 0.611937 0.790906i \(-0.290390\pi\)
0.611937 + 0.790906i \(0.290390\pi\)
\(830\) 0 0
\(831\) −2.20525 −0.0764994
\(832\) 0 0
\(833\) 9.64236 0.334088
\(834\) 0 0
\(835\) 3.52142 0.121864
\(836\) 0 0
\(837\) −2.14346 −0.0740888
\(838\) 0 0
\(839\) 14.4876 0.500166 0.250083 0.968224i \(-0.419542\pi\)
0.250083 + 0.968224i \(0.419542\pi\)
\(840\) 0 0
\(841\) 7.21557 0.248813
\(842\) 0 0
\(843\) 52.3114 1.80170
\(844\) 0 0
\(845\) 5.24063 0.180283
\(846\) 0 0
\(847\) 16.9784 0.583384
\(848\) 0 0
\(849\) 19.4050 0.665977
\(850\) 0 0
\(851\) −88.3985 −3.03026
\(852\) 0 0
\(853\) 4.92917 0.168772 0.0843858 0.996433i \(-0.473107\pi\)
0.0843858 + 0.996433i \(0.473107\pi\)
\(854\) 0 0
\(855\) −0.556239 −0.0190230
\(856\) 0 0
\(857\) 52.5344 1.79454 0.897270 0.441482i \(-0.145547\pi\)
0.897270 + 0.441482i \(0.145547\pi\)
\(858\) 0 0
\(859\) −32.5431 −1.11036 −0.555179 0.831731i \(-0.687350\pi\)
−0.555179 + 0.831731i \(0.687350\pi\)
\(860\) 0 0
\(861\) 22.7308 0.774663
\(862\) 0 0
\(863\) −51.5604 −1.75514 −0.877568 0.479451i \(-0.840836\pi\)
−0.877568 + 0.479451i \(0.840836\pi\)
\(864\) 0 0
\(865\) −9.59956 −0.326395
\(866\) 0 0
\(867\) −18.5293 −0.629287
\(868\) 0 0
\(869\) 1.01931 0.0345777
\(870\) 0 0
\(871\) −47.9682 −1.62534
\(872\) 0 0
\(873\) 39.8135 1.34748
\(874\) 0 0
\(875\) 11.1611 0.377313
\(876\) 0 0
\(877\) 35.8616 1.21096 0.605481 0.795860i \(-0.292981\pi\)
0.605481 + 0.795860i \(0.292981\pi\)
\(878\) 0 0
\(879\) −5.21058 −0.175749
\(880\) 0 0
\(881\) −41.2432 −1.38952 −0.694759 0.719243i \(-0.744489\pi\)
−0.694759 + 0.719243i \(0.744489\pi\)
\(882\) 0 0
\(883\) −24.3041 −0.817898 −0.408949 0.912557i \(-0.634105\pi\)
−0.408949 + 0.912557i \(0.634105\pi\)
\(884\) 0 0
\(885\) −3.74152 −0.125770
\(886\) 0 0
\(887\) −51.7010 −1.73595 −0.867975 0.496608i \(-0.834579\pi\)
−0.867975 + 0.496608i \(0.834579\pi\)
\(888\) 0 0
\(889\) −22.2492 −0.746213
\(890\) 0 0
\(891\) −14.6557 −0.490983
\(892\) 0 0
\(893\) 3.72294 0.124583
\(894\) 0 0
\(895\) −5.52951 −0.184831
\(896\) 0 0
\(897\) −89.8857 −3.00120
\(898\) 0 0
\(899\) 25.1217 0.837856
\(900\) 0 0
\(901\) 10.4794 0.349119
\(902\) 0 0
\(903\) 58.6577 1.95201
\(904\) 0 0
\(905\) 0.961515 0.0319618
\(906\) 0 0
\(907\) 5.06194 0.168079 0.0840395 0.996462i \(-0.473218\pi\)
0.0840395 + 0.996462i \(0.473218\pi\)
\(908\) 0 0
\(909\) −1.75506 −0.0582117
\(910\) 0 0
\(911\) 40.4144 1.33899 0.669495 0.742817i \(-0.266511\pi\)
0.669495 + 0.742817i \(0.266511\pi\)
\(912\) 0 0
\(913\) 3.45559 0.114363
\(914\) 0 0
\(915\) 16.3168 0.539418
\(916\) 0 0
\(917\) 31.1713 1.02937
\(918\) 0 0
\(919\) −31.2276 −1.03010 −0.515052 0.857159i \(-0.672227\pi\)
−0.515052 + 0.857159i \(0.672227\pi\)
\(920\) 0 0
\(921\) −15.8890 −0.523562
\(922\) 0 0
\(923\) 45.2270 1.48867
\(924\) 0 0
\(925\) 51.4711 1.69236
\(926\) 0 0
\(927\) 12.5788 0.413141
\(928\) 0 0
\(929\) −51.3773 −1.68563 −0.842817 0.538201i \(-0.819104\pi\)
−0.842817 + 0.538201i \(0.819104\pi\)
\(930\) 0 0
\(931\) 1.06937 0.0350472
\(932\) 0 0
\(933\) −9.24164 −0.302558
\(934\) 0 0
\(935\) −2.74929 −0.0899114
\(936\) 0 0
\(937\) 22.6093 0.738614 0.369307 0.929307i \(-0.379595\pi\)
0.369307 + 0.929307i \(0.379595\pi\)
\(938\) 0 0
\(939\) −61.2488 −1.99878
\(940\) 0 0
\(941\) −51.2485 −1.67065 −0.835326 0.549754i \(-0.814721\pi\)
−0.835326 + 0.549754i \(0.814721\pi\)
\(942\) 0 0
\(943\) −38.5344 −1.25485
\(944\) 0 0
\(945\) 0.593776 0.0193155
\(946\) 0 0
\(947\) 54.1474 1.75955 0.879777 0.475387i \(-0.157692\pi\)
0.879777 + 0.475387i \(0.157692\pi\)
\(948\) 0 0
\(949\) 29.6400 0.962155
\(950\) 0 0
\(951\) −19.8171 −0.642614
\(952\) 0 0
\(953\) −34.0986 −1.10456 −0.552281 0.833658i \(-0.686242\pi\)
−0.552281 + 0.833658i \(0.686242\pi\)
\(954\) 0 0
\(955\) 4.97006 0.160827
\(956\) 0 0
\(957\) 22.1120 0.714778
\(958\) 0 0
\(959\) 29.4613 0.951354
\(960\) 0 0
\(961\) −13.5738 −0.437863
\(962\) 0 0
\(963\) −9.57350 −0.308502
\(964\) 0 0
\(965\) −14.7289 −0.474140
\(966\) 0 0
\(967\) −20.9385 −0.673336 −0.336668 0.941623i \(-0.609300\pi\)
−0.336668 + 0.941623i \(0.609300\pi\)
\(968\) 0 0
\(969\) 2.48031 0.0796791
\(970\) 0 0
\(971\) 5.00722 0.160689 0.0803447 0.996767i \(-0.474398\pi\)
0.0803447 + 0.996767i \(0.474398\pi\)
\(972\) 0 0
\(973\) −32.6146 −1.04558
\(974\) 0 0
\(975\) 52.3371 1.67613
\(976\) 0 0
\(977\) 12.5547 0.401662 0.200831 0.979626i \(-0.435636\pi\)
0.200831 + 0.979626i \(0.435636\pi\)
\(978\) 0 0
\(979\) 3.39064 0.108365
\(980\) 0 0
\(981\) 27.5879 0.880813
\(982\) 0 0
\(983\) −1.43810 −0.0458683 −0.0229341 0.999737i \(-0.507301\pi\)
−0.0229341 + 0.999737i \(0.507301\pi\)
\(984\) 0 0
\(985\) 1.39641 0.0444934
\(986\) 0 0
\(987\) 51.8810 1.65139
\(988\) 0 0
\(989\) −99.4397 −3.16200
\(990\) 0 0
\(991\) 41.6595 1.32336 0.661678 0.749788i \(-0.269845\pi\)
0.661678 + 0.749788i \(0.269845\pi\)
\(992\) 0 0
\(993\) 16.0833 0.510387
\(994\) 0 0
\(995\) −6.95475 −0.220480
\(996\) 0 0
\(997\) 46.5145 1.47313 0.736564 0.676367i \(-0.236447\pi\)
0.736564 + 0.676367i \(0.236447\pi\)
\(998\) 0 0
\(999\) 5.68172 0.179762
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 \(a_p\))