Properties

Label 6004.2.a.d.1.5
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.60188\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.60188 q^{5}\) \(-2.96099 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.60188 q^{5}\) \(-2.96099 q^{7}\) \(-3.00000 q^{9}\) \(-6.18049 q^{11}\) \(+3.15433 q^{13}\) \(-3.39245 q^{17}\) \(+1.00000 q^{19}\) \(-4.49250 q^{23}\) \(-2.43397 q^{25}\) \(-2.60902 q^{29}\) \(+1.91390 q^{31}\) \(-4.74316 q^{35}\) \(+2.15697 q^{37}\) \(+4.04381 q^{41}\) \(+10.3442 q^{43}\) \(-4.80565 q^{45}\) \(+9.46005 q^{47}\) \(+1.76746 q^{49}\) \(+6.85330 q^{53}\) \(-9.90041 q^{55}\) \(-11.9794 q^{59}\) \(-6.13105 q^{61}\) \(+8.88297 q^{63}\) \(+5.05286 q^{65}\) \(-0.994333 q^{67}\) \(+5.98261 q^{71}\) \(+0.489939 q^{73}\) \(+18.3004 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(-1.53735 q^{83}\) \(-5.43431 q^{85}\) \(+9.91571 q^{89}\) \(-9.33993 q^{91}\) \(+1.60188 q^{95}\) \(+4.02985 q^{97}\) \(+18.5415 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 1.60188 0.716384 0.358192 0.933648i \(-0.383393\pi\)
0.358192 + 0.933648i \(0.383393\pi\)
\(6\) 0 0
\(7\) −2.96099 −1.11915 −0.559575 0.828780i \(-0.689035\pi\)
−0.559575 + 0.828780i \(0.689035\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −6.18049 −1.86349 −0.931743 0.363117i \(-0.881712\pi\)
−0.931743 + 0.363117i \(0.881712\pi\)
\(12\) 0 0
\(13\) 3.15433 0.874852 0.437426 0.899254i \(-0.355890\pi\)
0.437426 + 0.899254i \(0.355890\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.39245 −0.822790 −0.411395 0.911457i \(-0.634958\pi\)
−0.411395 + 0.911457i \(0.634958\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.49250 −0.936752 −0.468376 0.883529i \(-0.655161\pi\)
−0.468376 + 0.883529i \(0.655161\pi\)
\(24\) 0 0
\(25\) −2.43397 −0.486794
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.60902 −0.484484 −0.242242 0.970216i \(-0.577883\pi\)
−0.242242 + 0.970216i \(0.577883\pi\)
\(30\) 0 0
\(31\) 1.91390 0.343747 0.171873 0.985119i \(-0.445018\pi\)
0.171873 + 0.985119i \(0.445018\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.74316 −0.801740
\(36\) 0 0
\(37\) 2.15697 0.354604 0.177302 0.984157i \(-0.443263\pi\)
0.177302 + 0.984157i \(0.443263\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.04381 0.631537 0.315768 0.948836i \(-0.397738\pi\)
0.315768 + 0.948836i \(0.397738\pi\)
\(42\) 0 0
\(43\) 10.3442 1.57748 0.788742 0.614725i \(-0.210733\pi\)
0.788742 + 0.614725i \(0.210733\pi\)
\(44\) 0 0
\(45\) −4.80565 −0.716384
\(46\) 0 0
\(47\) 9.46005 1.37989 0.689945 0.723861i \(-0.257635\pi\)
0.689945 + 0.723861i \(0.257635\pi\)
\(48\) 0 0
\(49\) 1.76746 0.252495
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.85330 0.941373 0.470686 0.882301i \(-0.344006\pi\)
0.470686 + 0.882301i \(0.344006\pi\)
\(54\) 0 0
\(55\) −9.90041 −1.33497
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.9794 −1.55959 −0.779795 0.626035i \(-0.784677\pi\)
−0.779795 + 0.626035i \(0.784677\pi\)
\(60\) 0 0
\(61\) −6.13105 −0.785000 −0.392500 0.919752i \(-0.628390\pi\)
−0.392500 + 0.919752i \(0.628390\pi\)
\(62\) 0 0
\(63\) 8.88297 1.11915
\(64\) 0 0
\(65\) 5.05286 0.626730
\(66\) 0 0
\(67\) −0.994333 −0.121477 −0.0607386 0.998154i \(-0.519346\pi\)
−0.0607386 + 0.998154i \(0.519346\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.98261 0.710005 0.355003 0.934865i \(-0.384480\pi\)
0.355003 + 0.934865i \(0.384480\pi\)
\(72\) 0 0
\(73\) 0.489939 0.0573430 0.0286715 0.999589i \(-0.490872\pi\)
0.0286715 + 0.999589i \(0.490872\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18.3004 2.08552
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −1.53735 −0.168746 −0.0843730 0.996434i \(-0.526889\pi\)
−0.0843730 + 0.996434i \(0.526889\pi\)
\(84\) 0 0
\(85\) −5.43431 −0.589433
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.91571 1.05106 0.525532 0.850774i \(-0.323866\pi\)
0.525532 + 0.850774i \(0.323866\pi\)
\(90\) 0 0
\(91\) −9.33993 −0.979090
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.60188 0.164350
\(96\) 0 0
\(97\) 4.02985 0.409170 0.204585 0.978849i \(-0.434416\pi\)
0.204585 + 0.978849i \(0.434416\pi\)
\(98\) 0 0
\(99\) 18.5415 1.86349
\(100\) 0 0
\(101\) 15.3528 1.52766 0.763832 0.645415i \(-0.223316\pi\)
0.763832 + 0.645415i \(0.223316\pi\)
\(102\) 0 0
\(103\) −15.9671 −1.57329 −0.786645 0.617406i \(-0.788184\pi\)
−0.786645 + 0.617406i \(0.788184\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.0808 1.65126 0.825631 0.564211i \(-0.190820\pi\)
0.825631 + 0.564211i \(0.190820\pi\)
\(108\) 0 0
\(109\) −1.50364 −0.144023 −0.0720113 0.997404i \(-0.522942\pi\)
−0.0720113 + 0.997404i \(0.522942\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.82323 0.924092 0.462046 0.886856i \(-0.347115\pi\)
0.462046 + 0.886856i \(0.347115\pi\)
\(114\) 0 0
\(115\) −7.19646 −0.671074
\(116\) 0 0
\(117\) −9.46298 −0.874852
\(118\) 0 0
\(119\) 10.0450 0.920825
\(120\) 0 0
\(121\) 27.1984 2.47258
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.9084 −1.06512
\(126\) 0 0
\(127\) −16.1749 −1.43529 −0.717646 0.696408i \(-0.754780\pi\)
−0.717646 + 0.696408i \(0.754780\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.08734 0.0950013 0.0475007 0.998871i \(-0.484874\pi\)
0.0475007 + 0.998871i \(0.484874\pi\)
\(132\) 0 0
\(133\) −2.96099 −0.256750
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.95999 −0.423760 −0.211880 0.977296i \(-0.567959\pi\)
−0.211880 + 0.977296i \(0.567959\pi\)
\(138\) 0 0
\(139\) 5.82121 0.493749 0.246874 0.969047i \(-0.420596\pi\)
0.246874 + 0.969047i \(0.420596\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −19.4953 −1.63028
\(144\) 0 0
\(145\) −4.17935 −0.347076
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.6060 1.19657 0.598286 0.801283i \(-0.295849\pi\)
0.598286 + 0.801283i \(0.295849\pi\)
\(150\) 0 0
\(151\) −20.7748 −1.69063 −0.845316 0.534266i \(-0.820588\pi\)
−0.845316 + 0.534266i \(0.820588\pi\)
\(152\) 0 0
\(153\) 10.1774 0.822790
\(154\) 0 0
\(155\) 3.06584 0.246254
\(156\) 0 0
\(157\) 22.6648 1.80885 0.904426 0.426631i \(-0.140300\pi\)
0.904426 + 0.426631i \(0.140300\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 13.3023 1.04837
\(162\) 0 0
\(163\) −4.04190 −0.316586 −0.158293 0.987392i \(-0.550599\pi\)
−0.158293 + 0.987392i \(0.550599\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.3609 1.57558 0.787788 0.615946i \(-0.211226\pi\)
0.787788 + 0.615946i \(0.211226\pi\)
\(168\) 0 0
\(169\) −3.05023 −0.234633
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) 21.4107 1.62783 0.813913 0.580986i \(-0.197333\pi\)
0.813913 + 0.580986i \(0.197333\pi\)
\(174\) 0 0
\(175\) 7.20697 0.544796
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.77997 0.432015 0.216008 0.976392i \(-0.430696\pi\)
0.216008 + 0.976392i \(0.430696\pi\)
\(180\) 0 0
\(181\) −14.1791 −1.05392 −0.526960 0.849890i \(-0.676668\pi\)
−0.526960 + 0.849890i \(0.676668\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.45521 0.254032
\(186\) 0 0
\(187\) 20.9670 1.53326
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.21884 −0.232907 −0.116454 0.993196i \(-0.537153\pi\)
−0.116454 + 0.993196i \(0.537153\pi\)
\(192\) 0 0
\(193\) 23.0991 1.66271 0.831354 0.555744i \(-0.187566\pi\)
0.831354 + 0.555744i \(0.187566\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.67837 −0.475814 −0.237907 0.971288i \(-0.576461\pi\)
−0.237907 + 0.971288i \(0.576461\pi\)
\(198\) 0 0
\(199\) −8.68196 −0.615448 −0.307724 0.951476i \(-0.599567\pi\)
−0.307724 + 0.951476i \(0.599567\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.72529 0.542209
\(204\) 0 0
\(205\) 6.47771 0.452423
\(206\) 0 0
\(207\) 13.4775 0.936752
\(208\) 0 0
\(209\) −6.18049 −0.427513
\(210\) 0 0
\(211\) −13.6971 −0.942946 −0.471473 0.881881i \(-0.656277\pi\)
−0.471473 + 0.881881i \(0.656277\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.5703 1.13008
\(216\) 0 0
\(217\) −5.66704 −0.384704
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −10.7009 −0.719820
\(222\) 0 0
\(223\) −25.5376 −1.71012 −0.855062 0.518525i \(-0.826481\pi\)
−0.855062 + 0.518525i \(0.826481\pi\)
\(224\) 0 0
\(225\) 7.30192 0.486794
\(226\) 0 0
\(227\) 11.3060 0.750405 0.375202 0.926943i \(-0.377573\pi\)
0.375202 + 0.926943i \(0.377573\pi\)
\(228\) 0 0
\(229\) 24.7018 1.63234 0.816171 0.577811i \(-0.196093\pi\)
0.816171 + 0.577811i \(0.196093\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.2147 −0.669186 −0.334593 0.942363i \(-0.608599\pi\)
−0.334593 + 0.942363i \(0.608599\pi\)
\(234\) 0 0
\(235\) 15.1539 0.988531
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.5094 −0.679797 −0.339899 0.940462i \(-0.610393\pi\)
−0.339899 + 0.940462i \(0.610393\pi\)
\(240\) 0 0
\(241\) −4.15386 −0.267573 −0.133787 0.991010i \(-0.542714\pi\)
−0.133787 + 0.991010i \(0.542714\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.83127 0.180883
\(246\) 0 0
\(247\) 3.15433 0.200705
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5040 1.04172 0.520862 0.853641i \(-0.325611\pi\)
0.520862 + 0.853641i \(0.325611\pi\)
\(252\) 0 0
\(253\) 27.7659 1.74562
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.8772 0.803260 0.401630 0.915802i \(-0.368444\pi\)
0.401630 + 0.915802i \(0.368444\pi\)
\(258\) 0 0
\(259\) −6.38677 −0.396854
\(260\) 0 0
\(261\) 7.82707 0.484484
\(262\) 0 0
\(263\) −21.4959 −1.32549 −0.662747 0.748844i \(-0.730609\pi\)
−0.662747 + 0.748844i \(0.730609\pi\)
\(264\) 0 0
\(265\) 10.9782 0.674384
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.95294 −0.301986 −0.150993 0.988535i \(-0.548247\pi\)
−0.150993 + 0.988535i \(0.548247\pi\)
\(270\) 0 0
\(271\) −16.4688 −1.00041 −0.500203 0.865908i \(-0.666741\pi\)
−0.500203 + 0.865908i \(0.666741\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.0431 0.907135
\(276\) 0 0
\(277\) 18.6690 1.12171 0.560855 0.827914i \(-0.310473\pi\)
0.560855 + 0.827914i \(0.310473\pi\)
\(278\) 0 0
\(279\) −5.74170 −0.343747
\(280\) 0 0
\(281\) −28.3257 −1.68977 −0.844886 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(282\) 0 0
\(283\) −8.93603 −0.531192 −0.265596 0.964084i \(-0.585569\pi\)
−0.265596 + 0.964084i \(0.585569\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.9737 −0.706784
\(288\) 0 0
\(289\) −5.49128 −0.323016
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.61796 −0.269784 −0.134892 0.990860i \(-0.543069\pi\)
−0.134892 + 0.990860i \(0.543069\pi\)
\(294\) 0 0
\(295\) −19.1896 −1.11726
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −14.1708 −0.819520
\(300\) 0 0
\(301\) −30.6292 −1.76544
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9.82122 −0.562361
\(306\) 0 0
\(307\) −21.7797 −1.24303 −0.621516 0.783401i \(-0.713483\pi\)
−0.621516 + 0.783401i \(0.713483\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.3867 −0.759089 −0.379544 0.925173i \(-0.623919\pi\)
−0.379544 + 0.925173i \(0.623919\pi\)
\(312\) 0 0
\(313\) 26.8251 1.51625 0.758123 0.652111i \(-0.226116\pi\)
0.758123 + 0.652111i \(0.226116\pi\)
\(314\) 0 0
\(315\) 14.2295 0.801740
\(316\) 0 0
\(317\) −0.190107 −0.0106775 −0.00533873 0.999986i \(-0.501699\pi\)
−0.00533873 + 0.999986i \(0.501699\pi\)
\(318\) 0 0
\(319\) 16.1250 0.902829
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.39245 −0.188761
\(324\) 0 0
\(325\) −7.67754 −0.425873
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −28.0111 −1.54430
\(330\) 0 0
\(331\) 7.71372 0.423984 0.211992 0.977271i \(-0.432005\pi\)
0.211992 + 0.977271i \(0.432005\pi\)
\(332\) 0 0
\(333\) −6.47091 −0.354604
\(334\) 0 0
\(335\) −1.59281 −0.0870242
\(336\) 0 0
\(337\) −28.6809 −1.56235 −0.781173 0.624314i \(-0.785379\pi\)
−0.781173 + 0.624314i \(0.785379\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11.8288 −0.640567
\(342\) 0 0
\(343\) 15.4935 0.836570
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.6441 1.26928 0.634640 0.772808i \(-0.281149\pi\)
0.634640 + 0.772808i \(0.281149\pi\)
\(348\) 0 0
\(349\) −17.0960 −0.915128 −0.457564 0.889177i \(-0.651278\pi\)
−0.457564 + 0.889177i \(0.651278\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.50478 −0.292990 −0.146495 0.989211i \(-0.546799\pi\)
−0.146495 + 0.989211i \(0.546799\pi\)
\(354\) 0 0
\(355\) 9.58344 0.508636
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.27449 −0.489489 −0.244745 0.969588i \(-0.578704\pi\)
−0.244745 + 0.969588i \(0.578704\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.784825 0.0410796
\(366\) 0 0
\(367\) 34.4748 1.79957 0.899784 0.436335i \(-0.143724\pi\)
0.899784 + 0.436335i \(0.143724\pi\)
\(368\) 0 0
\(369\) −12.1314 −0.631537
\(370\) 0 0
\(371\) −20.2925 −1.05354
\(372\) 0 0
\(373\) −36.8435 −1.90768 −0.953841 0.300313i \(-0.902909\pi\)
−0.953841 + 0.300313i \(0.902909\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.22971 −0.423852
\(378\) 0 0
\(379\) 18.8052 0.965956 0.482978 0.875632i \(-0.339555\pi\)
0.482978 + 0.875632i \(0.339555\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 19.9132 1.01752 0.508759 0.860909i \(-0.330104\pi\)
0.508759 + 0.860909i \(0.330104\pi\)
\(384\) 0 0
\(385\) 29.3150 1.49403
\(386\) 0 0
\(387\) −31.0327 −1.57748
\(388\) 0 0
\(389\) 33.5507 1.70109 0.850543 0.525905i \(-0.176273\pi\)
0.850543 + 0.525905i \(0.176273\pi\)
\(390\) 0 0
\(391\) 15.2406 0.770750
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.60188 0.0805995
\(396\) 0 0
\(397\) 17.9649 0.901632 0.450816 0.892617i \(-0.351133\pi\)
0.450816 + 0.892617i \(0.351133\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.13847 −0.456354 −0.228177 0.973620i \(-0.573276\pi\)
−0.228177 + 0.973620i \(0.573276\pi\)
\(402\) 0 0
\(403\) 6.03706 0.300727
\(404\) 0 0
\(405\) 14.4169 0.716384
\(406\) 0 0
\(407\) −13.3311 −0.660799
\(408\) 0 0
\(409\) 34.9748 1.72939 0.864696 0.502296i \(-0.167511\pi\)
0.864696 + 0.502296i \(0.167511\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 35.4710 1.74541
\(414\) 0 0
\(415\) −2.46265 −0.120887
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −31.1087 −1.51976 −0.759881 0.650063i \(-0.774743\pi\)
−0.759881 + 0.650063i \(0.774743\pi\)
\(420\) 0 0
\(421\) 16.1940 0.789248 0.394624 0.918843i \(-0.370875\pi\)
0.394624 + 0.918843i \(0.370875\pi\)
\(422\) 0 0
\(423\) −28.3802 −1.37989
\(424\) 0 0
\(425\) 8.25713 0.400530
\(426\) 0 0
\(427\) 18.1540 0.878532
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.36886 −0.114104 −0.0570520 0.998371i \(-0.518170\pi\)
−0.0570520 + 0.998371i \(0.518170\pi\)
\(432\) 0 0
\(433\) −1.65098 −0.0793411 −0.0396706 0.999213i \(-0.512631\pi\)
−0.0396706 + 0.999213i \(0.512631\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.49250 −0.214906
\(438\) 0 0
\(439\) −24.1570 −1.15295 −0.576475 0.817115i \(-0.695572\pi\)
−0.576475 + 0.817115i \(0.695572\pi\)
\(440\) 0 0
\(441\) −5.30239 −0.252495
\(442\) 0 0
\(443\) 31.1895 1.48186 0.740929 0.671583i \(-0.234385\pi\)
0.740929 + 0.671583i \(0.234385\pi\)
\(444\) 0 0
\(445\) 15.8838 0.752965
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 34.8012 1.64237 0.821185 0.570661i \(-0.193313\pi\)
0.821185 + 0.570661i \(0.193313\pi\)
\(450\) 0 0
\(451\) −24.9927 −1.17686
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14.9615 −0.701404
\(456\) 0 0
\(457\) 1.81118 0.0847235 0.0423617 0.999102i \(-0.486512\pi\)
0.0423617 + 0.999102i \(0.486512\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.01490 −0.326716 −0.163358 0.986567i \(-0.552233\pi\)
−0.163358 + 0.986567i \(0.552233\pi\)
\(462\) 0 0
\(463\) −20.2063 −0.939064 −0.469532 0.882915i \(-0.655577\pi\)
−0.469532 + 0.882915i \(0.655577\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.5724 −0.581782 −0.290891 0.956756i \(-0.593952\pi\)
−0.290891 + 0.956756i \(0.593952\pi\)
\(468\) 0 0
\(469\) 2.94421 0.135951
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −63.9325 −2.93962
\(474\) 0 0
\(475\) −2.43397 −0.111678
\(476\) 0 0
\(477\) −20.5599 −0.941373
\(478\) 0 0
\(479\) 19.8020 0.904775 0.452387 0.891822i \(-0.350572\pi\)
0.452387 + 0.891822i \(0.350572\pi\)
\(480\) 0 0
\(481\) 6.80378 0.310226
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.45535 0.293122
\(486\) 0 0
\(487\) 2.38065 0.107878 0.0539388 0.998544i \(-0.482822\pi\)
0.0539388 + 0.998544i \(0.482822\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 22.1657 1.00032 0.500162 0.865932i \(-0.333274\pi\)
0.500162 + 0.865932i \(0.333274\pi\)
\(492\) 0 0
\(493\) 8.85098 0.398628
\(494\) 0 0
\(495\) 29.7012 1.33497
\(496\) 0 0
\(497\) −17.7144 −0.794602
\(498\) 0 0
\(499\) −0.279456 −0.0125102 −0.00625509 0.999980i \(-0.501991\pi\)
−0.00625509 + 0.999980i \(0.501991\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0134 −0.535652 −0.267826 0.963467i \(-0.586305\pi\)
−0.267826 + 0.963467i \(0.586305\pi\)
\(504\) 0 0
\(505\) 24.5934 1.09439
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 31.7225 1.40608 0.703039 0.711152i \(-0.251826\pi\)
0.703039 + 0.711152i \(0.251826\pi\)
\(510\) 0 0
\(511\) −1.45070 −0.0641754
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25.5775 −1.12708
\(516\) 0 0
\(517\) −58.4677 −2.57141
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.57824 −0.419630 −0.209815 0.977741i \(-0.567286\pi\)
−0.209815 + 0.977741i \(0.567286\pi\)
\(522\) 0 0
\(523\) 24.1221 1.05479 0.527393 0.849622i \(-0.323170\pi\)
0.527393 + 0.849622i \(0.323170\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.49281 −0.282831
\(528\) 0 0
\(529\) −2.81741 −0.122496
\(530\) 0 0
\(531\) 35.9383 1.55959
\(532\) 0 0
\(533\) 12.7555 0.552501
\(534\) 0 0
\(535\) 27.3614 1.18294
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.9238 −0.470521
\(540\) 0 0
\(541\) −10.4239 −0.448157 −0.224079 0.974571i \(-0.571937\pi\)
−0.224079 + 0.974571i \(0.571937\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.40865 −0.103175
\(546\) 0 0
\(547\) 9.44329 0.403766 0.201883 0.979410i \(-0.435294\pi\)
0.201883 + 0.979410i \(0.435294\pi\)
\(548\) 0 0
\(549\) 18.3931 0.785000
\(550\) 0 0
\(551\) −2.60902 −0.111148
\(552\) 0 0
\(553\) −2.96099 −0.125914
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.95386 0.421759 0.210879 0.977512i \(-0.432367\pi\)
0.210879 + 0.977512i \(0.432367\pi\)
\(558\) 0 0
\(559\) 32.6291 1.38006
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.38192 0.226821 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(564\) 0 0
\(565\) 15.7357 0.662004
\(566\) 0 0
\(567\) −26.6489 −1.11915
\(568\) 0 0
\(569\) −5.26481 −0.220712 −0.110356 0.993892i \(-0.535199\pi\)
−0.110356 + 0.993892i \(0.535199\pi\)
\(570\) 0 0
\(571\) −35.7075 −1.49431 −0.747157 0.664648i \(-0.768582\pi\)
−0.747157 + 0.664648i \(0.768582\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.9346 0.456006
\(576\) 0 0
\(577\) 19.9138 0.829024 0.414512 0.910044i \(-0.363952\pi\)
0.414512 + 0.910044i \(0.363952\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.55207 0.188852
\(582\) 0 0
\(583\) −42.3567 −1.75424
\(584\) 0 0
\(585\) −15.1586 −0.626730
\(586\) 0 0
\(587\) 23.0599 0.951783 0.475892 0.879504i \(-0.342125\pi\)
0.475892 + 0.879504i \(0.342125\pi\)
\(588\) 0 0
\(589\) 1.91390 0.0788609
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 38.6058 1.58535 0.792676 0.609643i \(-0.208687\pi\)
0.792676 + 0.609643i \(0.208687\pi\)
\(594\) 0 0
\(595\) 16.0909 0.659664
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.97002 0.243928 0.121964 0.992534i \(-0.461081\pi\)
0.121964 + 0.992534i \(0.461081\pi\)
\(600\) 0 0
\(601\) −3.49599 −0.142604 −0.0713022 0.997455i \(-0.522715\pi\)
−0.0713022 + 0.997455i \(0.522715\pi\)
\(602\) 0 0
\(603\) 2.98300 0.121477
\(604\) 0 0
\(605\) 43.5687 1.77132
\(606\) 0 0
\(607\) 30.8392 1.25173 0.625863 0.779933i \(-0.284747\pi\)
0.625863 + 0.779933i \(0.284747\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29.8401 1.20720
\(612\) 0 0
\(613\) 5.13623 0.207450 0.103725 0.994606i \(-0.466924\pi\)
0.103725 + 0.994606i \(0.466924\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.8690 −0.518085 −0.259042 0.965866i \(-0.583407\pi\)
−0.259042 + 0.965866i \(0.583407\pi\)
\(618\) 0 0
\(619\) 36.3048 1.45921 0.729606 0.683868i \(-0.239704\pi\)
0.729606 + 0.683868i \(0.239704\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29.3603 −1.17630
\(624\) 0 0
\(625\) −6.90592 −0.276237
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.31741 −0.291764
\(630\) 0 0
\(631\) 2.57355 0.102451 0.0512256 0.998687i \(-0.483687\pi\)
0.0512256 + 0.998687i \(0.483687\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −25.9103 −1.02822
\(636\) 0 0
\(637\) 5.57515 0.220896
\(638\) 0 0
\(639\) −17.9478 −0.710005
\(640\) 0 0
\(641\) 32.4874 1.28317 0.641587 0.767050i \(-0.278276\pi\)
0.641587 + 0.767050i \(0.278276\pi\)
\(642\) 0 0
\(643\) 37.9261 1.49566 0.747831 0.663890i \(-0.231096\pi\)
0.747831 + 0.663890i \(0.231096\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.57368 0.297752 0.148876 0.988856i \(-0.452434\pi\)
0.148876 + 0.988856i \(0.452434\pi\)
\(648\) 0 0
\(649\) 74.0387 2.90627
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22.1701 −0.867583 −0.433792 0.901013i \(-0.642825\pi\)
−0.433792 + 0.901013i \(0.642825\pi\)
\(654\) 0 0
\(655\) 1.74179 0.0680574
\(656\) 0 0
\(657\) −1.46982 −0.0573430
\(658\) 0 0
\(659\) 23.9592 0.933319 0.466659 0.884437i \(-0.345457\pi\)
0.466659 + 0.884437i \(0.345457\pi\)
\(660\) 0 0
\(661\) −38.5426 −1.49913 −0.749566 0.661929i \(-0.769738\pi\)
−0.749566 + 0.661929i \(0.769738\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.74316 −0.183932
\(666\) 0 0
\(667\) 11.7210 0.453841
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 37.8929 1.46284
\(672\) 0 0
\(673\) −39.9549 −1.54015 −0.770075 0.637954i \(-0.779781\pi\)
−0.770075 + 0.637954i \(0.779781\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.5706 0.867457 0.433729 0.901044i \(-0.357198\pi\)
0.433729 + 0.901044i \(0.357198\pi\)
\(678\) 0 0
\(679\) −11.9324 −0.457922
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 27.4357 1.04980 0.524900 0.851164i \(-0.324103\pi\)
0.524900 + 0.851164i \(0.324103\pi\)
\(684\) 0 0
\(685\) −7.94532 −0.303575
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 21.6175 0.823562
\(690\) 0 0
\(691\) 20.5742 0.782681 0.391340 0.920246i \(-0.372012\pi\)
0.391340 + 0.920246i \(0.372012\pi\)
\(692\) 0 0
\(693\) −54.9011 −2.08552
\(694\) 0 0
\(695\) 9.32490 0.353714
\(696\) 0 0
\(697\) −13.7184 −0.519622
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21.0856 0.796394 0.398197 0.917300i \(-0.369636\pi\)
0.398197 + 0.917300i \(0.369636\pi\)
\(702\) 0 0
\(703\) 2.15697 0.0813517
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −45.4596 −1.70968
\(708\) 0 0
\(709\) 5.69713 0.213960 0.106980 0.994261i \(-0.465882\pi\)
0.106980 + 0.994261i \(0.465882\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −8.59820 −0.322005
\(714\) 0 0
\(715\) −31.2291 −1.16790
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.56754 0.0957531 0.0478766 0.998853i \(-0.484755\pi\)
0.0478766 + 0.998853i \(0.484755\pi\)
\(720\) 0 0
\(721\) 47.2786 1.76075
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.35029 0.235844
\(726\) 0 0
\(727\) 23.2307 0.861580 0.430790 0.902452i \(-0.358235\pi\)
0.430790 + 0.902452i \(0.358235\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −35.0924 −1.29794
\(732\) 0 0
\(733\) 0.138669 0.00512185 0.00256093 0.999997i \(-0.499185\pi\)
0.00256093 + 0.999997i \(0.499185\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.14546 0.226371
\(738\) 0 0
\(739\) −43.4978 −1.60009 −0.800046 0.599939i \(-0.795191\pi\)
−0.800046 + 0.599939i \(0.795191\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22.8136 0.836951 0.418475 0.908228i \(-0.362565\pi\)
0.418475 + 0.908228i \(0.362565\pi\)
\(744\) 0 0
\(745\) 23.3971 0.857205
\(746\) 0 0
\(747\) 4.61205 0.168746
\(748\) 0 0
\(749\) −50.5760 −1.84801
\(750\) 0 0
\(751\) 11.8560 0.432633 0.216316 0.976323i \(-0.430596\pi\)
0.216316 + 0.976323i \(0.430596\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −33.2789 −1.21114
\(756\) 0 0
\(757\) −40.7204 −1.48001 −0.740005 0.672602i \(-0.765177\pi\)
−0.740005 + 0.672602i \(0.765177\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.1068 1.63512 0.817561 0.575843i \(-0.195326\pi\)
0.817561 + 0.575843i \(0.195326\pi\)
\(762\) 0 0
\(763\) 4.45226 0.161183
\(764\) 0 0
\(765\) 16.3029 0.589433
\(766\) 0 0
\(767\) −37.7870 −1.36441
\(768\) 0 0
\(769\) 19.3550 0.697961 0.348980 0.937130i \(-0.386528\pi\)
0.348980 + 0.937130i \(0.386528\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.8207 −0.928707 −0.464353 0.885650i \(-0.653713\pi\)
−0.464353 + 0.885650i \(0.653713\pi\)
\(774\) 0 0
\(775\) −4.65838 −0.167334
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.04381 0.144884
\(780\) 0 0
\(781\) −36.9754 −1.32309
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 36.3064 1.29583
\(786\) 0 0
\(787\) −4.39178 −0.156550 −0.0782751 0.996932i \(-0.524941\pi\)
−0.0782751 + 0.996932i \(0.524941\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −29.0865 −1.03420
\(792\) 0 0
\(793\) −19.3393 −0.686759
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.64624 0.200000 0.100000 0.994987i \(-0.468116\pi\)
0.100000 + 0.994987i \(0.468116\pi\)
\(798\) 0 0
\(799\) −32.0928 −1.13536
\(800\) 0 0
\(801\) −29.7471 −1.05106
\(802\) 0 0
\(803\) −3.02806 −0.106858
\(804\) 0 0
\(805\) 21.3087 0.751032
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18.4943 −0.650227 −0.325113 0.945675i \(-0.605402\pi\)
−0.325113 + 0.945675i \(0.605402\pi\)
\(810\) 0 0
\(811\) 17.0901 0.600115 0.300057 0.953921i \(-0.402994\pi\)
0.300057 + 0.953921i \(0.402994\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −6.47464 −0.226797
\(816\) 0 0
\(817\) 10.3442 0.361899
\(818\) 0 0
\(819\) 28.0198 0.979090
\(820\) 0 0
\(821\) 27.8760 0.972880 0.486440 0.873714i \(-0.338295\pi\)
0.486440 + 0.873714i \(0.338295\pi\)
\(822\) 0 0
\(823\) 16.7731 0.584673 0.292337 0.956315i \(-0.405567\pi\)
0.292337 + 0.956315i \(0.405567\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −42.0722 −1.46300 −0.731498 0.681844i \(-0.761178\pi\)
−0.731498 + 0.681844i \(0.761178\pi\)
\(828\) 0 0
\(829\) 15.6729 0.544344 0.272172 0.962249i \(-0.412258\pi\)
0.272172 + 0.962249i \(0.412258\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.99603 −0.207750
\(834\) 0 0
\(835\) 32.6158 1.12872
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.7289 0.370401 0.185201 0.982701i \(-0.440707\pi\)
0.185201 + 0.982701i \(0.440707\pi\)
\(840\) 0 0
\(841\) −22.1930 −0.765276
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.88612 −0.168088
\(846\) 0 0
\(847\) −80.5343 −2.76719
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.69020 −0.332176
\(852\) 0 0
\(853\) 35.4097 1.21241 0.606203 0.795310i \(-0.292692\pi\)
0.606203 + 0.795310i \(0.292692\pi\)
\(854\) 0 0
\(855\) −4.80565 −0.164350
\(856\) 0 0
\(857\) 0.963968 0.0329285 0.0164643 0.999864i \(-0.494759\pi\)
0.0164643 + 0.999864i \(0.494759\pi\)
\(858\) 0 0
\(859\) 50.6832 1.72929 0.864645 0.502384i \(-0.167544\pi\)
0.864645 + 0.502384i \(0.167544\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −42.8580 −1.45890 −0.729452 0.684032i \(-0.760225\pi\)
−0.729452 + 0.684032i \(0.760225\pi\)
\(864\) 0 0
\(865\) 34.2975 1.16615
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −6.18049 −0.209659
\(870\) 0 0
\(871\) −3.13645 −0.106275
\(872\) 0 0
\(873\) −12.0896 −0.409170
\(874\) 0 0
\(875\) 35.2605 1.19202
\(876\) 0 0
\(877\) −17.7853 −0.600569 −0.300284 0.953850i \(-0.597082\pi\)
−0.300284 + 0.953850i \(0.597082\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −48.1540 −1.62235 −0.811176 0.584803i \(-0.801172\pi\)
−0.811176 + 0.584803i \(0.801172\pi\)
\(882\) 0 0
\(883\) −36.1943 −1.21804 −0.609018 0.793156i \(-0.708436\pi\)
−0.609018 + 0.793156i \(0.708436\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37.4004 1.25578 0.627891 0.778301i \(-0.283918\pi\)
0.627891 + 0.778301i \(0.283918\pi\)
\(888\) 0 0
\(889\) 47.8938 1.60631
\(890\) 0 0
\(891\) −55.6244 −1.86349
\(892\) 0 0
\(893\) 9.46005 0.316569
\(894\) 0 0
\(895\) 9.25883 0.309489
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.99341 −0.166540
\(900\) 0 0
\(901\) −23.2495 −0.774552
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −22.7132 −0.755011
\(906\) 0 0
\(907\) −25.2635 −0.838862 −0.419431 0.907787i \(-0.637770\pi\)
−0.419431 + 0.907787i \(0.637770\pi\)
\(908\) 0 0
\(909\) −46.0585 −1.52766
\(910\) 0 0
\(911\) −24.9132 −0.825410 −0.412705 0.910865i \(-0.635416\pi\)
−0.412705 + 0.910865i \(0.635416\pi\)
\(912\) 0 0
\(913\) 9.50156 0.314456
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.21960 −0.106321
\(918\) 0 0
\(919\) 18.8721 0.622533 0.311267 0.950323i \(-0.399247\pi\)
0.311267 + 0.950323i \(0.399247\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 18.8711 0.621150
\(924\) 0 0
\(925\) −5.25001 −0.172619
\(926\) 0 0
\(927\) 47.9014 1.57329
\(928\) 0 0
\(929\) −1.65253 −0.0542177 −0.0271088 0.999632i \(-0.508630\pi\)
−0.0271088 + 0.999632i \(0.508630\pi\)
\(930\) 0 0
\(931\) 1.76746 0.0579263
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 33.5867 1.09840
\(936\) 0 0
\(937\) 11.2763 0.368381 0.184190 0.982891i \(-0.441034\pi\)
0.184190 + 0.982891i \(0.441034\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −37.9473 −1.23705 −0.618523 0.785767i \(-0.712269\pi\)
−0.618523 + 0.785767i \(0.712269\pi\)
\(942\) 0 0
\(943\) −18.1668 −0.591593
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.7654 −1.19472 −0.597358 0.801975i \(-0.703783\pi\)
−0.597358 + 0.801975i \(0.703783\pi\)
\(948\) 0 0
\(949\) 1.54543 0.0501667
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −35.8155 −1.16018 −0.580088 0.814554i \(-0.696982\pi\)
−0.580088 + 0.814554i \(0.696982\pi\)
\(954\) 0 0
\(955\) −5.15620 −0.166851
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.6865 0.474251
\(960\) 0 0
\(961\) −27.3370 −0.881838
\(962\) 0 0
\(963\) −51.2423 −1.65126
\(964\) 0 0
\(965\) 37.0020 1.19114
\(966\) 0 0
\(967\) −43.6691 −1.40431 −0.702153 0.712026i \(-0.747778\pi\)
−0.702153 + 0.712026i \(0.747778\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 41.5533 1.33351 0.666755 0.745277i \(-0.267683\pi\)
0.666755 + 0.745277i \(0.267683\pi\)
\(972\) 0 0
\(973\) −17.2366 −0.552579
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.44477 0.142201 0.0711004 0.997469i \(-0.477349\pi\)
0.0711004 + 0.997469i \(0.477349\pi\)
\(978\) 0 0
\(979\) −61.2839 −1.95864
\(980\) 0 0
\(981\) 4.51092 0.144023
\(982\) 0 0
\(983\) −33.5915 −1.07140 −0.535701 0.844408i \(-0.679953\pi\)
−0.535701 + 0.844408i \(0.679953\pi\)
\(984\) 0 0
\(985\) −10.6980 −0.340866
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −46.4716 −1.47771
\(990\) 0 0
\(991\) 39.7079 1.26136 0.630682 0.776042i \(-0.282775\pi\)
0.630682 + 0.776042i \(0.282775\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −13.9075 −0.440897
\(996\) 0 0
\(997\) 32.8133 1.03921 0.519604 0.854407i \(-0.326080\pi\)
0.519604 + 0.854407i \(0.326080\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))