Properties

Label 6040.2.a.l.1.8
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
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 1.8
Root \(1.10659\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.35518 q^{3} +1.00000 q^{5} +0.202920 q^{7} +2.54689 q^{9} +O(q^{10})\) \(q+2.35518 q^{3} +1.00000 q^{5} +0.202920 q^{7} +2.54689 q^{9} -4.49118 q^{11} -0.979565 q^{13} +2.35518 q^{15} +0.563306 q^{17} -3.51749 q^{19} +0.477913 q^{21} -8.46590 q^{23} +1.00000 q^{25} -1.06715 q^{27} -3.31208 q^{29} +5.73102 q^{31} -10.5776 q^{33} +0.202920 q^{35} -8.46526 q^{37} -2.30706 q^{39} -6.59632 q^{41} -0.444501 q^{43} +2.54689 q^{45} +10.8979 q^{47} -6.95882 q^{49} +1.32669 q^{51} -6.63714 q^{53} -4.49118 q^{55} -8.28435 q^{57} +1.09121 q^{59} +0.633746 q^{61} +0.516815 q^{63} -0.979565 q^{65} +4.51926 q^{67} -19.9388 q^{69} -14.7218 q^{71} +0.361789 q^{73} +2.35518 q^{75} -0.911349 q^{77} +2.63388 q^{79} -10.1540 q^{81} +11.1266 q^{83} +0.563306 q^{85} -7.80055 q^{87} +6.68105 q^{89} -0.198773 q^{91} +13.4976 q^{93} -3.51749 q^{95} +10.1080 q^{97} -11.4386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} + O(q^{10}) \) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} - 6q^{11} - 9q^{13} - 2q^{17} - 10q^{19} - 9q^{21} - 6q^{23} + 9q^{25} + 12q^{27} - 6q^{29} + 9q^{31} - 11q^{33} - 2q^{35} - 12q^{37} - 3q^{39} - 20q^{41} + q^{43} - 3q^{45} + 22q^{47} - 29q^{49} + 2q^{51} - 35q^{53} - 6q^{55} - 20q^{57} + 14q^{59} - 22q^{61} - 12q^{63} - 9q^{65} + 4q^{67} + 5q^{69} - 22q^{71} - 34q^{73} - 5q^{77} + 8q^{79} - 31q^{81} - 3q^{83} - 2q^{85} - 5q^{89} - 7q^{91} - 21q^{93} - 10q^{95} - 33q^{97} - 15q^{99} + O(q^{100}) \)

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
\(3\) 2.35518 1.35977 0.679883 0.733320i \(-0.262030\pi\)
0.679883 + 0.733320i \(0.262030\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.202920 0.0766964 0.0383482 0.999264i \(-0.487790\pi\)
0.0383482 + 0.999264i \(0.487790\pi\)
\(8\) 0 0
\(9\) 2.54689 0.848965
\(10\) 0 0
\(11\) −4.49118 −1.35414 −0.677071 0.735918i \(-0.736751\pi\)
−0.677071 + 0.735918i \(0.736751\pi\)
\(12\) 0 0
\(13\) −0.979565 −0.271682 −0.135841 0.990731i \(-0.543374\pi\)
−0.135841 + 0.990731i \(0.543374\pi\)
\(14\) 0 0
\(15\) 2.35518 0.608106
\(16\) 0 0
\(17\) 0.563306 0.136622 0.0683109 0.997664i \(-0.478239\pi\)
0.0683109 + 0.997664i \(0.478239\pi\)
\(18\) 0 0
\(19\) −3.51749 −0.806968 −0.403484 0.914987i \(-0.632201\pi\)
−0.403484 + 0.914987i \(0.632201\pi\)
\(20\) 0 0
\(21\) 0.477913 0.104289
\(22\) 0 0
\(23\) −8.46590 −1.76526 −0.882631 0.470067i \(-0.844230\pi\)
−0.882631 + 0.470067i \(0.844230\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.06715 −0.205373
\(28\) 0 0
\(29\) −3.31208 −0.615037 −0.307519 0.951542i \(-0.599499\pi\)
−0.307519 + 0.951542i \(0.599499\pi\)
\(30\) 0 0
\(31\) 5.73102 1.02932 0.514660 0.857394i \(-0.327918\pi\)
0.514660 + 0.857394i \(0.327918\pi\)
\(32\) 0 0
\(33\) −10.5776 −1.84132
\(34\) 0 0
\(35\) 0.202920 0.0342997
\(36\) 0 0
\(37\) −8.46526 −1.39168 −0.695840 0.718197i \(-0.744968\pi\)
−0.695840 + 0.718197i \(0.744968\pi\)
\(38\) 0 0
\(39\) −2.30706 −0.369425
\(40\) 0 0
\(41\) −6.59632 −1.03017 −0.515086 0.857138i \(-0.672240\pi\)
−0.515086 + 0.857138i \(0.672240\pi\)
\(42\) 0 0
\(43\) −0.444501 −0.0677858 −0.0338929 0.999425i \(-0.510791\pi\)
−0.0338929 + 0.999425i \(0.510791\pi\)
\(44\) 0 0
\(45\) 2.54689 0.379668
\(46\) 0 0
\(47\) 10.8979 1.58962 0.794811 0.606857i \(-0.207570\pi\)
0.794811 + 0.606857i \(0.207570\pi\)
\(48\) 0 0
\(49\) −6.95882 −0.994118
\(50\) 0 0
\(51\) 1.32669 0.185774
\(52\) 0 0
\(53\) −6.63714 −0.911682 −0.455841 0.890061i \(-0.650661\pi\)
−0.455841 + 0.890061i \(0.650661\pi\)
\(54\) 0 0
\(55\) −4.49118 −0.605590
\(56\) 0 0
\(57\) −8.28435 −1.09729
\(58\) 0 0
\(59\) 1.09121 0.142063 0.0710315 0.997474i \(-0.477371\pi\)
0.0710315 + 0.997474i \(0.477371\pi\)
\(60\) 0 0
\(61\) 0.633746 0.0811429 0.0405714 0.999177i \(-0.487082\pi\)
0.0405714 + 0.999177i \(0.487082\pi\)
\(62\) 0 0
\(63\) 0.516815 0.0651126
\(64\) 0 0
\(65\) −0.979565 −0.121500
\(66\) 0 0
\(67\) 4.51926 0.552115 0.276057 0.961141i \(-0.410972\pi\)
0.276057 + 0.961141i \(0.410972\pi\)
\(68\) 0 0
\(69\) −19.9388 −2.40034
\(70\) 0 0
\(71\) −14.7218 −1.74715 −0.873577 0.486687i \(-0.838205\pi\)
−0.873577 + 0.486687i \(0.838205\pi\)
\(72\) 0 0
\(73\) 0.361789 0.0423442 0.0211721 0.999776i \(-0.493260\pi\)
0.0211721 + 0.999776i \(0.493260\pi\)
\(74\) 0 0
\(75\) 2.35518 0.271953
\(76\) 0 0
\(77\) −0.911349 −0.103858
\(78\) 0 0
\(79\) 2.63388 0.296334 0.148167 0.988962i \(-0.452663\pi\)
0.148167 + 0.988962i \(0.452663\pi\)
\(80\) 0 0
\(81\) −10.1540 −1.12822
\(82\) 0 0
\(83\) 11.1266 1.22130 0.610650 0.791901i \(-0.290908\pi\)
0.610650 + 0.791901i \(0.290908\pi\)
\(84\) 0 0
\(85\) 0.563306 0.0610991
\(86\) 0 0
\(87\) −7.80055 −0.836307
\(88\) 0 0
\(89\) 6.68105 0.708190 0.354095 0.935209i \(-0.384789\pi\)
0.354095 + 0.935209i \(0.384789\pi\)
\(90\) 0 0
\(91\) −0.198773 −0.0208371
\(92\) 0 0
\(93\) 13.4976 1.39964
\(94\) 0 0
\(95\) −3.51749 −0.360887
\(96\) 0 0
\(97\) 10.1080 1.02631 0.513154 0.858296i \(-0.328477\pi\)
0.513154 + 0.858296i \(0.328477\pi\)
\(98\) 0 0
\(99\) −11.4386 −1.14962
\(100\) 0 0
\(101\) −9.21387 −0.916814 −0.458407 0.888742i \(-0.651580\pi\)
−0.458407 + 0.888742i \(0.651580\pi\)
\(102\) 0 0
\(103\) −4.96729 −0.489441 −0.244721 0.969594i \(-0.578696\pi\)
−0.244721 + 0.969594i \(0.578696\pi\)
\(104\) 0 0
\(105\) 0.477913 0.0466396
\(106\) 0 0
\(107\) −7.94662 −0.768229 −0.384114 0.923285i \(-0.625493\pi\)
−0.384114 + 0.923285i \(0.625493\pi\)
\(108\) 0 0
\(109\) 12.1664 1.16533 0.582666 0.812711i \(-0.302009\pi\)
0.582666 + 0.812711i \(0.302009\pi\)
\(110\) 0 0
\(111\) −19.9372 −1.89236
\(112\) 0 0
\(113\) −14.9767 −1.40889 −0.704445 0.709758i \(-0.748804\pi\)
−0.704445 + 0.709758i \(0.748804\pi\)
\(114\) 0 0
\(115\) −8.46590 −0.789449
\(116\) 0 0
\(117\) −2.49485 −0.230649
\(118\) 0 0
\(119\) 0.114306 0.0104784
\(120\) 0 0
\(121\) 9.17068 0.833698
\(122\) 0 0
\(123\) −15.5356 −1.40079
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 5.31664 0.471776 0.235888 0.971780i \(-0.424200\pi\)
0.235888 + 0.971780i \(0.424200\pi\)
\(128\) 0 0
\(129\) −1.04688 −0.0921729
\(130\) 0 0
\(131\) 17.3314 1.51425 0.757127 0.653267i \(-0.226602\pi\)
0.757127 + 0.653267i \(0.226602\pi\)
\(132\) 0 0
\(133\) −0.713769 −0.0618916
\(134\) 0 0
\(135\) −1.06715 −0.0918456
\(136\) 0 0
\(137\) −3.42352 −0.292491 −0.146246 0.989248i \(-0.546719\pi\)
−0.146246 + 0.989248i \(0.546719\pi\)
\(138\) 0 0
\(139\) −2.58726 −0.219448 −0.109724 0.993962i \(-0.534997\pi\)
−0.109724 + 0.993962i \(0.534997\pi\)
\(140\) 0 0
\(141\) 25.6666 2.16152
\(142\) 0 0
\(143\) 4.39940 0.367896
\(144\) 0 0
\(145\) −3.31208 −0.275053
\(146\) 0 0
\(147\) −16.3893 −1.35177
\(148\) 0 0
\(149\) 7.04914 0.577488 0.288744 0.957406i \(-0.406762\pi\)
0.288744 + 0.957406i \(0.406762\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) 1.43468 0.115987
\(154\) 0 0
\(155\) 5.73102 0.460326
\(156\) 0 0
\(157\) −23.2092 −1.85229 −0.926147 0.377162i \(-0.876900\pi\)
−0.926147 + 0.377162i \(0.876900\pi\)
\(158\) 0 0
\(159\) −15.6317 −1.23967
\(160\) 0 0
\(161\) −1.71790 −0.135389
\(162\) 0 0
\(163\) 21.8289 1.70977 0.854884 0.518819i \(-0.173628\pi\)
0.854884 + 0.518819i \(0.173628\pi\)
\(164\) 0 0
\(165\) −10.5776 −0.823461
\(166\) 0 0
\(167\) −9.28307 −0.718346 −0.359173 0.933271i \(-0.616941\pi\)
−0.359173 + 0.933271i \(0.616941\pi\)
\(168\) 0 0
\(169\) −12.0405 −0.926189
\(170\) 0 0
\(171\) −8.95868 −0.685088
\(172\) 0 0
\(173\) 19.6824 1.49642 0.748211 0.663460i \(-0.230913\pi\)
0.748211 + 0.663460i \(0.230913\pi\)
\(174\) 0 0
\(175\) 0.202920 0.0153393
\(176\) 0 0
\(177\) 2.56999 0.193172
\(178\) 0 0
\(179\) −3.71951 −0.278009 −0.139005 0.990292i \(-0.544390\pi\)
−0.139005 + 0.990292i \(0.544390\pi\)
\(180\) 0 0
\(181\) 14.4230 1.07205 0.536027 0.844201i \(-0.319924\pi\)
0.536027 + 0.844201i \(0.319924\pi\)
\(182\) 0 0
\(183\) 1.49259 0.110335
\(184\) 0 0
\(185\) −8.46526 −0.622378
\(186\) 0 0
\(187\) −2.52991 −0.185005
\(188\) 0 0
\(189\) −0.216546 −0.0157514
\(190\) 0 0
\(191\) 13.1268 0.949820 0.474910 0.880034i \(-0.342481\pi\)
0.474910 + 0.880034i \(0.342481\pi\)
\(192\) 0 0
\(193\) −2.80478 −0.201893 −0.100946 0.994892i \(-0.532187\pi\)
−0.100946 + 0.994892i \(0.532187\pi\)
\(194\) 0 0
\(195\) −2.30706 −0.165212
\(196\) 0 0
\(197\) −24.0126 −1.71083 −0.855414 0.517945i \(-0.826697\pi\)
−0.855414 + 0.517945i \(0.826697\pi\)
\(198\) 0 0
\(199\) −25.4102 −1.80128 −0.900641 0.434564i \(-0.856902\pi\)
−0.900641 + 0.434564i \(0.856902\pi\)
\(200\) 0 0
\(201\) 10.6437 0.750747
\(202\) 0 0
\(203\) −0.672086 −0.0471712
\(204\) 0 0
\(205\) −6.59632 −0.460707
\(206\) 0 0
\(207\) −21.5617 −1.49864
\(208\) 0 0
\(209\) 15.7977 1.09275
\(210\) 0 0
\(211\) 7.42509 0.511164 0.255582 0.966787i \(-0.417733\pi\)
0.255582 + 0.966787i \(0.417733\pi\)
\(212\) 0 0
\(213\) −34.6725 −2.37572
\(214\) 0 0
\(215\) −0.444501 −0.0303147
\(216\) 0 0
\(217\) 1.16294 0.0789452
\(218\) 0 0
\(219\) 0.852079 0.0575782
\(220\) 0 0
\(221\) −0.551795 −0.0371177
\(222\) 0 0
\(223\) 10.6305 0.711874 0.355937 0.934510i \(-0.384162\pi\)
0.355937 + 0.934510i \(0.384162\pi\)
\(224\) 0 0
\(225\) 2.54689 0.169793
\(226\) 0 0
\(227\) −21.4230 −1.42190 −0.710949 0.703244i \(-0.751734\pi\)
−0.710949 + 0.703244i \(0.751734\pi\)
\(228\) 0 0
\(229\) 26.5539 1.75473 0.877365 0.479824i \(-0.159299\pi\)
0.877365 + 0.479824i \(0.159299\pi\)
\(230\) 0 0
\(231\) −2.14639 −0.141222
\(232\) 0 0
\(233\) −14.9502 −0.979419 −0.489709 0.871886i \(-0.662897\pi\)
−0.489709 + 0.871886i \(0.662897\pi\)
\(234\) 0 0
\(235\) 10.8979 0.710901
\(236\) 0 0
\(237\) 6.20327 0.402946
\(238\) 0 0
\(239\) 29.9489 1.93723 0.968617 0.248559i \(-0.0799569\pi\)
0.968617 + 0.248559i \(0.0799569\pi\)
\(240\) 0 0
\(241\) −11.1974 −0.721285 −0.360643 0.932704i \(-0.617443\pi\)
−0.360643 + 0.932704i \(0.617443\pi\)
\(242\) 0 0
\(243\) −20.7131 −1.32875
\(244\) 0 0
\(245\) −6.95882 −0.444583
\(246\) 0 0
\(247\) 3.44561 0.219239
\(248\) 0 0
\(249\) 26.2051 1.66068
\(250\) 0 0
\(251\) −14.2145 −0.897210 −0.448605 0.893730i \(-0.648079\pi\)
−0.448605 + 0.893730i \(0.648079\pi\)
\(252\) 0 0
\(253\) 38.0219 2.39041
\(254\) 0 0
\(255\) 1.32669 0.0830805
\(256\) 0 0
\(257\) −31.4537 −1.96203 −0.981015 0.193932i \(-0.937876\pi\)
−0.981015 + 0.193932i \(0.937876\pi\)
\(258\) 0 0
\(259\) −1.71777 −0.106737
\(260\) 0 0
\(261\) −8.43551 −0.522145
\(262\) 0 0
\(263\) 24.3949 1.50426 0.752128 0.659018i \(-0.229028\pi\)
0.752128 + 0.659018i \(0.229028\pi\)
\(264\) 0 0
\(265\) −6.63714 −0.407716
\(266\) 0 0
\(267\) 15.7351 0.962973
\(268\) 0 0
\(269\) 25.5613 1.55850 0.779250 0.626713i \(-0.215600\pi\)
0.779250 + 0.626713i \(0.215600\pi\)
\(270\) 0 0
\(271\) −16.2039 −0.984319 −0.492160 0.870505i \(-0.663792\pi\)
−0.492160 + 0.870505i \(0.663792\pi\)
\(272\) 0 0
\(273\) −0.468147 −0.0283336
\(274\) 0 0
\(275\) −4.49118 −0.270828
\(276\) 0 0
\(277\) 21.5615 1.29550 0.647752 0.761851i \(-0.275709\pi\)
0.647752 + 0.761851i \(0.275709\pi\)
\(278\) 0 0
\(279\) 14.5963 0.873857
\(280\) 0 0
\(281\) 0.415755 0.0248019 0.0124009 0.999923i \(-0.496053\pi\)
0.0124009 + 0.999923i \(0.496053\pi\)
\(282\) 0 0
\(283\) 15.8910 0.944620 0.472310 0.881433i \(-0.343420\pi\)
0.472310 + 0.881433i \(0.343420\pi\)
\(284\) 0 0
\(285\) −8.28435 −0.490722
\(286\) 0 0
\(287\) −1.33852 −0.0790106
\(288\) 0 0
\(289\) −16.6827 −0.981334
\(290\) 0 0
\(291\) 23.8061 1.39554
\(292\) 0 0
\(293\) 12.7581 0.745335 0.372668 0.927965i \(-0.378443\pi\)
0.372668 + 0.927965i \(0.378443\pi\)
\(294\) 0 0
\(295\) 1.09121 0.0635325
\(296\) 0 0
\(297\) 4.79276 0.278104
\(298\) 0 0
\(299\) 8.29290 0.479591
\(300\) 0 0
\(301\) −0.0901981 −0.00519893
\(302\) 0 0
\(303\) −21.7004 −1.24665
\(304\) 0 0
\(305\) 0.633746 0.0362882
\(306\) 0 0
\(307\) −15.6385 −0.892539 −0.446269 0.894899i \(-0.647248\pi\)
−0.446269 + 0.894899i \(0.647248\pi\)
\(308\) 0 0
\(309\) −11.6989 −0.665526
\(310\) 0 0
\(311\) −9.81184 −0.556378 −0.278189 0.960526i \(-0.589734\pi\)
−0.278189 + 0.960526i \(0.589734\pi\)
\(312\) 0 0
\(313\) 14.7719 0.834956 0.417478 0.908687i \(-0.362914\pi\)
0.417478 + 0.908687i \(0.362914\pi\)
\(314\) 0 0
\(315\) 0.516815 0.0291192
\(316\) 0 0
\(317\) −33.8917 −1.90355 −0.951773 0.306802i \(-0.900741\pi\)
−0.951773 + 0.306802i \(0.900741\pi\)
\(318\) 0 0
\(319\) 14.8751 0.832847
\(320\) 0 0
\(321\) −18.7158 −1.04461
\(322\) 0 0
\(323\) −1.98143 −0.110249
\(324\) 0 0
\(325\) −0.979565 −0.0543365
\(326\) 0 0
\(327\) 28.6542 1.58458
\(328\) 0 0
\(329\) 2.21140 0.121918
\(330\) 0 0
\(331\) 16.3916 0.900962 0.450481 0.892786i \(-0.351253\pi\)
0.450481 + 0.892786i \(0.351253\pi\)
\(332\) 0 0
\(333\) −21.5601 −1.18149
\(334\) 0 0
\(335\) 4.51926 0.246913
\(336\) 0 0
\(337\) 7.16366 0.390229 0.195115 0.980780i \(-0.437492\pi\)
0.195115 + 0.980780i \(0.437492\pi\)
\(338\) 0 0
\(339\) −35.2729 −1.91576
\(340\) 0 0
\(341\) −25.7390 −1.39385
\(342\) 0 0
\(343\) −2.83252 −0.152942
\(344\) 0 0
\(345\) −19.9388 −1.07347
\(346\) 0 0
\(347\) −3.68889 −0.198030 −0.0990150 0.995086i \(-0.531569\pi\)
−0.0990150 + 0.995086i \(0.531569\pi\)
\(348\) 0 0
\(349\) 18.3785 0.983777 0.491888 0.870658i \(-0.336307\pi\)
0.491888 + 0.870658i \(0.336307\pi\)
\(350\) 0 0
\(351\) 1.04534 0.0557962
\(352\) 0 0
\(353\) −23.9540 −1.27494 −0.637472 0.770473i \(-0.720020\pi\)
−0.637472 + 0.770473i \(0.720020\pi\)
\(354\) 0 0
\(355\) −14.7218 −0.781351
\(356\) 0 0
\(357\) 0.269212 0.0142482
\(358\) 0 0
\(359\) −1.35465 −0.0714959 −0.0357479 0.999361i \(-0.511381\pi\)
−0.0357479 + 0.999361i \(0.511381\pi\)
\(360\) 0 0
\(361\) −6.62724 −0.348802
\(362\) 0 0
\(363\) 21.5986 1.13363
\(364\) 0 0
\(365\) 0.361789 0.0189369
\(366\) 0 0
\(367\) 13.2011 0.689092 0.344546 0.938769i \(-0.388033\pi\)
0.344546 + 0.938769i \(0.388033\pi\)
\(368\) 0 0
\(369\) −16.8001 −0.874580
\(370\) 0 0
\(371\) −1.34681 −0.0699227
\(372\) 0 0
\(373\) −6.09681 −0.315681 −0.157840 0.987465i \(-0.550453\pi\)
−0.157840 + 0.987465i \(0.550453\pi\)
\(374\) 0 0
\(375\) 2.35518 0.121621
\(376\) 0 0
\(377\) 3.24439 0.167095
\(378\) 0 0
\(379\) −17.9581 −0.922447 −0.461224 0.887284i \(-0.652589\pi\)
−0.461224 + 0.887284i \(0.652589\pi\)
\(380\) 0 0
\(381\) 12.5217 0.641505
\(382\) 0 0
\(383\) 19.4959 0.996196 0.498098 0.867121i \(-0.334032\pi\)
0.498098 + 0.867121i \(0.334032\pi\)
\(384\) 0 0
\(385\) −0.911349 −0.0464466
\(386\) 0 0
\(387\) −1.13210 −0.0575477
\(388\) 0 0
\(389\) 31.7748 1.61105 0.805523 0.592564i \(-0.201884\pi\)
0.805523 + 0.592564i \(0.201884\pi\)
\(390\) 0 0
\(391\) −4.76889 −0.241173
\(392\) 0 0
\(393\) 40.8187 2.05903
\(394\) 0 0
\(395\) 2.63388 0.132525
\(396\) 0 0
\(397\) 27.9452 1.40253 0.701265 0.712900i \(-0.252619\pi\)
0.701265 + 0.712900i \(0.252619\pi\)
\(398\) 0 0
\(399\) −1.68106 −0.0841581
\(400\) 0 0
\(401\) −1.23547 −0.0616963 −0.0308482 0.999524i \(-0.509821\pi\)
−0.0308482 + 0.999524i \(0.509821\pi\)
\(402\) 0 0
\(403\) −5.61390 −0.279648
\(404\) 0 0
\(405\) −10.1540 −0.504557
\(406\) 0 0
\(407\) 38.0190 1.88453
\(408\) 0 0
\(409\) −25.5433 −1.26304 −0.631518 0.775361i \(-0.717568\pi\)
−0.631518 + 0.775361i \(0.717568\pi\)
\(410\) 0 0
\(411\) −8.06302 −0.397719
\(412\) 0 0
\(413\) 0.221427 0.0108957
\(414\) 0 0
\(415\) 11.1266 0.546182
\(416\) 0 0
\(417\) −6.09347 −0.298399
\(418\) 0 0
\(419\) −1.30024 −0.0635208 −0.0317604 0.999496i \(-0.510111\pi\)
−0.0317604 + 0.999496i \(0.510111\pi\)
\(420\) 0 0
\(421\) 9.81643 0.478423 0.239212 0.970967i \(-0.423111\pi\)
0.239212 + 0.970967i \(0.423111\pi\)
\(422\) 0 0
\(423\) 27.7558 1.34953
\(424\) 0 0
\(425\) 0.563306 0.0273244
\(426\) 0 0
\(427\) 0.128600 0.00622337
\(428\) 0 0
\(429\) 10.3614 0.500253
\(430\) 0 0
\(431\) −7.06097 −0.340115 −0.170057 0.985434i \(-0.554395\pi\)
−0.170057 + 0.985434i \(0.554395\pi\)
\(432\) 0 0
\(433\) −21.1737 −1.01754 −0.508771 0.860902i \(-0.669900\pi\)
−0.508771 + 0.860902i \(0.669900\pi\)
\(434\) 0 0
\(435\) −7.80055 −0.374008
\(436\) 0 0
\(437\) 29.7787 1.42451
\(438\) 0 0
\(439\) −26.3068 −1.25555 −0.627777 0.778393i \(-0.716035\pi\)
−0.627777 + 0.778393i \(0.716035\pi\)
\(440\) 0 0
\(441\) −17.7234 −0.843971
\(442\) 0 0
\(443\) −13.0573 −0.620371 −0.310186 0.950676i \(-0.600391\pi\)
−0.310186 + 0.950676i \(0.600391\pi\)
\(444\) 0 0
\(445\) 6.68105 0.316712
\(446\) 0 0
\(447\) 16.6020 0.785249
\(448\) 0 0
\(449\) 30.3665 1.43308 0.716541 0.697545i \(-0.245724\pi\)
0.716541 + 0.697545i \(0.245724\pi\)
\(450\) 0 0
\(451\) 29.6253 1.39500
\(452\) 0 0
\(453\) −2.35518 −0.110656
\(454\) 0 0
\(455\) −0.198773 −0.00931863
\(456\) 0 0
\(457\) −25.5804 −1.19660 −0.598301 0.801271i \(-0.704157\pi\)
−0.598301 + 0.801271i \(0.704157\pi\)
\(458\) 0 0
\(459\) −0.601132 −0.0280584
\(460\) 0 0
\(461\) −36.9012 −1.71866 −0.859330 0.511422i \(-0.829119\pi\)
−0.859330 + 0.511422i \(0.829119\pi\)
\(462\) 0 0
\(463\) −0.538716 −0.0250362 −0.0125181 0.999922i \(-0.503985\pi\)
−0.0125181 + 0.999922i \(0.503985\pi\)
\(464\) 0 0
\(465\) 13.4976 0.625936
\(466\) 0 0
\(467\) −3.12127 −0.144435 −0.0722176 0.997389i \(-0.523008\pi\)
−0.0722176 + 0.997389i \(0.523008\pi\)
\(468\) 0 0
\(469\) 0.917046 0.0423453
\(470\) 0 0
\(471\) −54.6619 −2.51869
\(472\) 0 0
\(473\) 1.99633 0.0917915
\(474\) 0 0
\(475\) −3.51749 −0.161394
\(476\) 0 0
\(477\) −16.9041 −0.773985
\(478\) 0 0
\(479\) −28.6507 −1.30908 −0.654542 0.756026i \(-0.727139\pi\)
−0.654542 + 0.756026i \(0.727139\pi\)
\(480\) 0 0
\(481\) 8.29227 0.378095
\(482\) 0 0
\(483\) −4.04597 −0.184098
\(484\) 0 0
\(485\) 10.1080 0.458979
\(486\) 0 0
\(487\) 1.67099 0.0757196 0.0378598 0.999283i \(-0.487946\pi\)
0.0378598 + 0.999283i \(0.487946\pi\)
\(488\) 0 0
\(489\) 51.4110 2.32489
\(490\) 0 0
\(491\) 9.05502 0.408647 0.204324 0.978903i \(-0.434501\pi\)
0.204324 + 0.978903i \(0.434501\pi\)
\(492\) 0 0
\(493\) −1.86571 −0.0840275
\(494\) 0 0
\(495\) −11.4386 −0.514125
\(496\) 0 0
\(497\) −2.98734 −0.134000
\(498\) 0 0
\(499\) 5.04777 0.225969 0.112985 0.993597i \(-0.463959\pi\)
0.112985 + 0.993597i \(0.463959\pi\)
\(500\) 0 0
\(501\) −21.8633 −0.976782
\(502\) 0 0
\(503\) 28.4586 1.26891 0.634453 0.772961i \(-0.281225\pi\)
0.634453 + 0.772961i \(0.281225\pi\)
\(504\) 0 0
\(505\) −9.21387 −0.410012
\(506\) 0 0
\(507\) −28.3575 −1.25940
\(508\) 0 0
\(509\) 14.6592 0.649756 0.324878 0.945756i \(-0.394677\pi\)
0.324878 + 0.945756i \(0.394677\pi\)
\(510\) 0 0
\(511\) 0.0734141 0.00324765
\(512\) 0 0
\(513\) 3.75369 0.165729
\(514\) 0 0
\(515\) −4.96729 −0.218885
\(516\) 0 0
\(517\) −48.9444 −2.15257
\(518\) 0 0
\(519\) 46.3556 2.03479
\(520\) 0 0
\(521\) −5.01177 −0.219570 −0.109785 0.993955i \(-0.535016\pi\)
−0.109785 + 0.993955i \(0.535016\pi\)
\(522\) 0 0
\(523\) −39.1308 −1.71107 −0.855535 0.517744i \(-0.826772\pi\)
−0.855535 + 0.517744i \(0.826772\pi\)
\(524\) 0 0
\(525\) 0.477913 0.0208579
\(526\) 0 0
\(527\) 3.22832 0.140628
\(528\) 0 0
\(529\) 48.6714 2.11615
\(530\) 0 0
\(531\) 2.77919 0.120606
\(532\) 0 0
\(533\) 6.46153 0.279880
\(534\) 0 0
\(535\) −7.94662 −0.343562
\(536\) 0 0
\(537\) −8.76014 −0.378028
\(538\) 0 0
\(539\) 31.2533 1.34618
\(540\) 0 0
\(541\) 6.96641 0.299509 0.149755 0.988723i \(-0.452152\pi\)
0.149755 + 0.988723i \(0.452152\pi\)
\(542\) 0 0
\(543\) 33.9689 1.45774
\(544\) 0 0
\(545\) 12.1664 0.521153
\(546\) 0 0
\(547\) 38.9850 1.66688 0.833439 0.552611i \(-0.186368\pi\)
0.833439 + 0.552611i \(0.186368\pi\)
\(548\) 0 0
\(549\) 1.61408 0.0688874
\(550\) 0 0
\(551\) 11.6502 0.496316
\(552\) 0 0
\(553\) 0.534466 0.0227278
\(554\) 0 0
\(555\) −19.9372 −0.846289
\(556\) 0 0
\(557\) −26.8368 −1.13711 −0.568557 0.822644i \(-0.692498\pi\)
−0.568557 + 0.822644i \(0.692498\pi\)
\(558\) 0 0
\(559\) 0.435418 0.0184162
\(560\) 0 0
\(561\) −5.95840 −0.251564
\(562\) 0 0
\(563\) −37.1806 −1.56697 −0.783487 0.621408i \(-0.786561\pi\)
−0.783487 + 0.621408i \(0.786561\pi\)
\(564\) 0 0
\(565\) −14.9767 −0.630075
\(566\) 0 0
\(567\) −2.06045 −0.0865308
\(568\) 0 0
\(569\) −20.6274 −0.864745 −0.432372 0.901695i \(-0.642323\pi\)
−0.432372 + 0.901695i \(0.642323\pi\)
\(570\) 0 0
\(571\) 1.64544 0.0688594 0.0344297 0.999407i \(-0.489039\pi\)
0.0344297 + 0.999407i \(0.489039\pi\)
\(572\) 0 0
\(573\) 30.9160 1.29153
\(574\) 0 0
\(575\) −8.46590 −0.353052
\(576\) 0 0
\(577\) 6.62015 0.275601 0.137800 0.990460i \(-0.455997\pi\)
0.137800 + 0.990460i \(0.455997\pi\)
\(578\) 0 0
\(579\) −6.60578 −0.274527
\(580\) 0 0
\(581\) 2.25780 0.0936693
\(582\) 0 0
\(583\) 29.8086 1.23455
\(584\) 0 0
\(585\) −2.49485 −0.103149
\(586\) 0 0
\(587\) 43.5390 1.79705 0.898523 0.438927i \(-0.144641\pi\)
0.898523 + 0.438927i \(0.144641\pi\)
\(588\) 0 0
\(589\) −20.1588 −0.830629
\(590\) 0 0
\(591\) −56.5541 −2.32633
\(592\) 0 0
\(593\) −7.30485 −0.299974 −0.149987 0.988688i \(-0.547923\pi\)
−0.149987 + 0.988688i \(0.547923\pi\)
\(594\) 0 0
\(595\) 0.114306 0.00468609
\(596\) 0 0
\(597\) −59.8457 −2.44932
\(598\) 0 0
\(599\) 27.2901 1.11504 0.557521 0.830163i \(-0.311753\pi\)
0.557521 + 0.830163i \(0.311753\pi\)
\(600\) 0 0
\(601\) −27.6305 −1.12707 −0.563535 0.826092i \(-0.690559\pi\)
−0.563535 + 0.826092i \(0.690559\pi\)
\(602\) 0 0
\(603\) 11.5101 0.468726
\(604\) 0 0
\(605\) 9.17068 0.372841
\(606\) 0 0
\(607\) −33.9348 −1.37737 −0.688685 0.725060i \(-0.741812\pi\)
−0.688685 + 0.725060i \(0.741812\pi\)
\(608\) 0 0
\(609\) −1.58289 −0.0641418
\(610\) 0 0
\(611\) −10.6752 −0.431873
\(612\) 0 0
\(613\) −44.6722 −1.80429 −0.902147 0.431428i \(-0.858010\pi\)
−0.902147 + 0.431428i \(0.858010\pi\)
\(614\) 0 0
\(615\) −15.5356 −0.626454
\(616\) 0 0
\(617\) 7.08617 0.285279 0.142639 0.989775i \(-0.454441\pi\)
0.142639 + 0.989775i \(0.454441\pi\)
\(618\) 0 0
\(619\) 32.3033 1.29838 0.649190 0.760626i \(-0.275108\pi\)
0.649190 + 0.760626i \(0.275108\pi\)
\(620\) 0 0
\(621\) 9.03438 0.362537
\(622\) 0 0
\(623\) 1.35572 0.0543157
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 37.2065 1.48588
\(628\) 0 0
\(629\) −4.76853 −0.190134
\(630\) 0 0
\(631\) −7.24903 −0.288579 −0.144290 0.989536i \(-0.546090\pi\)
−0.144290 + 0.989536i \(0.546090\pi\)
\(632\) 0 0
\(633\) 17.4875 0.695064
\(634\) 0 0
\(635\) 5.31664 0.210985
\(636\) 0 0
\(637\) 6.81662 0.270084
\(638\) 0 0
\(639\) −37.4948 −1.48327
\(640\) 0 0
\(641\) −3.98697 −0.157476 −0.0787379 0.996895i \(-0.525089\pi\)
−0.0787379 + 0.996895i \(0.525089\pi\)
\(642\) 0 0
\(643\) 5.46730 0.215609 0.107805 0.994172i \(-0.465618\pi\)
0.107805 + 0.994172i \(0.465618\pi\)
\(644\) 0 0
\(645\) −1.04688 −0.0412210
\(646\) 0 0
\(647\) 2.48685 0.0977683 0.0488842 0.998804i \(-0.484433\pi\)
0.0488842 + 0.998804i \(0.484433\pi\)
\(648\) 0 0
\(649\) −4.90080 −0.192373
\(650\) 0 0
\(651\) 2.73893 0.107347
\(652\) 0 0
\(653\) 5.39300 0.211045 0.105522 0.994417i \(-0.466349\pi\)
0.105522 + 0.994417i \(0.466349\pi\)
\(654\) 0 0
\(655\) 17.3314 0.677195
\(656\) 0 0
\(657\) 0.921438 0.0359487
\(658\) 0 0
\(659\) −6.08375 −0.236989 −0.118495 0.992955i \(-0.537807\pi\)
−0.118495 + 0.992955i \(0.537807\pi\)
\(660\) 0 0
\(661\) −37.6924 −1.46606 −0.733032 0.680194i \(-0.761896\pi\)
−0.733032 + 0.680194i \(0.761896\pi\)
\(662\) 0 0
\(663\) −1.29958 −0.0504715
\(664\) 0 0
\(665\) −0.713769 −0.0276788
\(666\) 0 0
\(667\) 28.0397 1.08570
\(668\) 0 0
\(669\) 25.0369 0.967983
\(670\) 0 0
\(671\) −2.84627 −0.109879
\(672\) 0 0
\(673\) −31.3561 −1.20869 −0.604343 0.796724i \(-0.706565\pi\)
−0.604343 + 0.796724i \(0.706565\pi\)
\(674\) 0 0
\(675\) −1.06715 −0.0410746
\(676\) 0 0
\(677\) 17.0170 0.654016 0.327008 0.945021i \(-0.393960\pi\)
0.327008 + 0.945021i \(0.393960\pi\)
\(678\) 0 0
\(679\) 2.05111 0.0787142
\(680\) 0 0
\(681\) −50.4552 −1.93345
\(682\) 0 0
\(683\) 19.7605 0.756116 0.378058 0.925782i \(-0.376592\pi\)
0.378058 + 0.925782i \(0.376592\pi\)
\(684\) 0 0
\(685\) −3.42352 −0.130806
\(686\) 0 0
\(687\) 62.5393 2.38602
\(688\) 0 0
\(689\) 6.50151 0.247688
\(690\) 0 0
\(691\) −3.84967 −0.146448 −0.0732242 0.997316i \(-0.523329\pi\)
−0.0732242 + 0.997316i \(0.523329\pi\)
\(692\) 0 0
\(693\) −2.32111 −0.0881716
\(694\) 0 0
\(695\) −2.58726 −0.0981403
\(696\) 0 0
\(697\) −3.71575 −0.140744
\(698\) 0 0
\(699\) −35.2104 −1.33178
\(700\) 0 0
\(701\) −39.6526 −1.49766 −0.748829 0.662763i \(-0.769384\pi\)
−0.748829 + 0.662763i \(0.769384\pi\)
\(702\) 0 0
\(703\) 29.7765 1.12304
\(704\) 0 0
\(705\) 25.6666 0.966659
\(706\) 0 0
\(707\) −1.86968 −0.0703164
\(708\) 0 0
\(709\) −8.24413 −0.309615 −0.154807 0.987945i \(-0.549476\pi\)
−0.154807 + 0.987945i \(0.549476\pi\)
\(710\) 0 0
\(711\) 6.70821 0.251577
\(712\) 0 0
\(713\) −48.5182 −1.81702
\(714\) 0 0
\(715\) 4.39940 0.164528
\(716\) 0 0
\(717\) 70.5352 2.63419
\(718\) 0 0
\(719\) −2.88559 −0.107614 −0.0538071 0.998551i \(-0.517136\pi\)
−0.0538071 + 0.998551i \(0.517136\pi\)
\(720\) 0 0
\(721\) −1.00796 −0.0375384
\(722\) 0 0
\(723\) −26.3718 −0.980779
\(724\) 0 0
\(725\) −3.31208 −0.123007
\(726\) 0 0
\(727\) 31.2477 1.15891 0.579457 0.815003i \(-0.303265\pi\)
0.579457 + 0.815003i \(0.303265\pi\)
\(728\) 0 0
\(729\) −18.3212 −0.678563
\(730\) 0 0
\(731\) −0.250390 −0.00926102
\(732\) 0 0
\(733\) −41.4275 −1.53016 −0.765079 0.643936i \(-0.777300\pi\)
−0.765079 + 0.643936i \(0.777300\pi\)
\(734\) 0 0
\(735\) −16.3893 −0.604529
\(736\) 0 0
\(737\) −20.2968 −0.747642
\(738\) 0 0
\(739\) 0.263160 0.00968051 0.00484025 0.999988i \(-0.498459\pi\)
0.00484025 + 0.999988i \(0.498459\pi\)
\(740\) 0 0
\(741\) 8.11506 0.298114
\(742\) 0 0
\(743\) 3.12566 0.114669 0.0573347 0.998355i \(-0.481740\pi\)
0.0573347 + 0.998355i \(0.481740\pi\)
\(744\) 0 0
\(745\) 7.04914 0.258260
\(746\) 0 0
\(747\) 28.3382 1.03684
\(748\) 0 0
\(749\) −1.61253 −0.0589204
\(750\) 0 0
\(751\) 17.9728 0.655835 0.327918 0.944706i \(-0.393653\pi\)
0.327918 + 0.944706i \(0.393653\pi\)
\(752\) 0 0
\(753\) −33.4777 −1.22000
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 36.5849 1.32970 0.664850 0.746977i \(-0.268495\pi\)
0.664850 + 0.746977i \(0.268495\pi\)
\(758\) 0 0
\(759\) 89.5485 3.25040
\(760\) 0 0
\(761\) −23.3244 −0.845509 −0.422755 0.906244i \(-0.638937\pi\)
−0.422755 + 0.906244i \(0.638937\pi\)
\(762\) 0 0
\(763\) 2.46881 0.0893769
\(764\) 0 0
\(765\) 1.43468 0.0518710
\(766\) 0 0
\(767\) −1.06891 −0.0385960
\(768\) 0 0
\(769\) 42.3109 1.52577 0.762886 0.646533i \(-0.223782\pi\)
0.762886 + 0.646533i \(0.223782\pi\)
\(770\) 0 0
\(771\) −74.0793 −2.66790
\(772\) 0 0
\(773\) 39.9119 1.43553 0.717766 0.696284i \(-0.245165\pi\)
0.717766 + 0.696284i \(0.245165\pi\)
\(774\) 0 0
\(775\) 5.73102 0.205864
\(776\) 0 0
\(777\) −4.04566 −0.145137
\(778\) 0 0
\(779\) 23.2025 0.831317
\(780\) 0 0
\(781\) 66.1181 2.36589
\(782\) 0 0
\(783\) 3.53448 0.126312
\(784\) 0 0
\(785\) −23.2092 −0.828371
\(786\) 0 0
\(787\) 7.41388 0.264276 0.132138 0.991231i \(-0.457816\pi\)
0.132138 + 0.991231i \(0.457816\pi\)
\(788\) 0 0
\(789\) 57.4545 2.04544
\(790\) 0 0
\(791\) −3.03907 −0.108057
\(792\) 0 0
\(793\) −0.620795 −0.0220451
\(794\) 0 0
\(795\) −15.6317 −0.554399
\(796\) 0 0
\(797\) −37.4922 −1.32804 −0.664022 0.747713i \(-0.731152\pi\)
−0.664022 + 0.747713i \(0.731152\pi\)
\(798\) 0 0
\(799\) 6.13886 0.217177
\(800\) 0 0
\(801\) 17.0159 0.601228
\(802\) 0 0
\(803\) −1.62486 −0.0573400
\(804\) 0 0
\(805\) −1.71790 −0.0605479
\(806\) 0 0
\(807\) 60.2016 2.11920
\(808\) 0 0
\(809\) −14.2543 −0.501155 −0.250578 0.968097i \(-0.580621\pi\)
−0.250578 + 0.968097i \(0.580621\pi\)
\(810\) 0 0
\(811\) 15.1211 0.530972 0.265486 0.964115i \(-0.414468\pi\)
0.265486 + 0.964115i \(0.414468\pi\)
\(812\) 0 0
\(813\) −38.1633 −1.33844
\(814\) 0 0
\(815\) 21.8289 0.764632
\(816\) 0 0
\(817\) 1.56353 0.0547010
\(818\) 0 0
\(819\) −0.506254 −0.0176899
\(820\) 0 0
\(821\) −43.2687 −1.51009 −0.755043 0.655675i \(-0.772384\pi\)
−0.755043 + 0.655675i \(0.772384\pi\)
\(822\) 0 0
\(823\) 55.4572 1.93312 0.966558 0.256450i \(-0.0825528\pi\)
0.966558 + 0.256450i \(0.0825528\pi\)
\(824\) 0 0
\(825\) −10.5776 −0.368263
\(826\) 0 0
\(827\) −14.8934 −0.517896 −0.258948 0.965891i \(-0.583376\pi\)
−0.258948 + 0.965891i \(0.583376\pi\)
\(828\) 0 0
\(829\) −17.0618 −0.592581 −0.296290 0.955098i \(-0.595750\pi\)
−0.296290 + 0.955098i \(0.595750\pi\)
\(830\) 0 0
\(831\) 50.7813 1.76158
\(832\) 0 0
\(833\) −3.91995 −0.135818
\(834\) 0 0
\(835\) −9.28307 −0.321254
\(836\) 0 0
\(837\) −6.11585 −0.211395
\(838\) 0 0
\(839\) 29.1530 1.00647 0.503236 0.864149i \(-0.332143\pi\)
0.503236 + 0.864149i \(0.332143\pi\)
\(840\) 0 0
\(841\) −18.0302 −0.621729
\(842\) 0 0
\(843\) 0.979179 0.0337247
\(844\) 0 0
\(845\) −12.0405 −0.414204
\(846\) 0 0
\(847\) 1.86091 0.0639417
\(848\) 0 0
\(849\) 37.4261 1.28446
\(850\) 0 0
\(851\) 71.6660 2.45668
\(852\) 0 0
\(853\) −11.1847 −0.382957 −0.191478 0.981497i \(-0.561328\pi\)
−0.191478 + 0.981497i \(0.561328\pi\)
\(854\) 0 0
\(855\) −8.95868 −0.306380
\(856\) 0 0
\(857\) 7.86905 0.268802 0.134401 0.990927i \(-0.457089\pi\)
0.134401 + 0.990927i \(0.457089\pi\)
\(858\) 0 0
\(859\) −38.1597 −1.30199 −0.650996 0.759082i \(-0.725648\pi\)
−0.650996 + 0.759082i \(0.725648\pi\)
\(860\) 0 0
\(861\) −3.15247 −0.107436
\(862\) 0 0
\(863\) 39.0500 1.32928 0.664639 0.747164i \(-0.268585\pi\)
0.664639 + 0.747164i \(0.268585\pi\)
\(864\) 0 0
\(865\) 19.6824 0.669221
\(866\) 0 0
\(867\) −39.2908 −1.33439
\(868\) 0 0
\(869\) −11.8292 −0.401279
\(870\) 0 0
\(871\) −4.42690 −0.150000
\(872\) 0 0
\(873\) 25.7439 0.871300
\(874\) 0 0
\(875\) 0.202920 0.00685994
\(876\) 0 0
\(877\) −24.6150 −0.831190 −0.415595 0.909550i \(-0.636427\pi\)
−0.415595 + 0.909550i \(0.636427\pi\)
\(878\) 0 0
\(879\) 30.0476 1.01348
\(880\) 0 0
\(881\) 28.1672 0.948977 0.474489 0.880262i \(-0.342633\pi\)
0.474489 + 0.880262i \(0.342633\pi\)
\(882\) 0 0
\(883\) 34.7308 1.16878 0.584392 0.811471i \(-0.301333\pi\)
0.584392 + 0.811471i \(0.301333\pi\)
\(884\) 0 0
\(885\) 2.56999 0.0863893
\(886\) 0 0
\(887\) −8.95032 −0.300522 −0.150261 0.988646i \(-0.548011\pi\)
−0.150261 + 0.988646i \(0.548011\pi\)
\(888\) 0 0
\(889\) 1.07885 0.0361835
\(890\) 0 0
\(891\) 45.6035 1.52777
\(892\) 0 0
\(893\) −38.3333 −1.28278
\(894\) 0 0
\(895\) −3.71951 −0.124330
\(896\) 0 0
\(897\) 19.5313 0.652131
\(898\) 0 0
\(899\) −18.9816 −0.633070
\(900\) 0 0
\(901\) −3.73874 −0.124556
\(902\) 0 0
\(903\) −0.212433 −0.00706933
\(904\) 0 0
\(905\) 14.4230 0.479437
\(906\) 0 0
\(907\) −49.6056 −1.64713 −0.823563 0.567225i \(-0.808017\pi\)
−0.823563 + 0.567225i \(0.808017\pi\)
\(908\) 0 0
\(909\) −23.4667 −0.778343
\(910\) 0 0
\(911\) 9.01846 0.298795 0.149398 0.988777i \(-0.452267\pi\)
0.149398 + 0.988777i \(0.452267\pi\)
\(912\) 0 0
\(913\) −49.9714 −1.65381
\(914\) 0 0
\(915\) 1.49259 0.0493435
\(916\) 0 0
\(917\) 3.51689 0.116138
\(918\) 0 0
\(919\) 4.94530 0.163130 0.0815652 0.996668i \(-0.474008\pi\)
0.0815652 + 0.996668i \(0.474008\pi\)
\(920\) 0 0
\(921\) −36.8317 −1.21364
\(922\) 0 0
\(923\) 14.4209 0.474671
\(924\) 0 0
\(925\) −8.46526 −0.278336
\(926\) 0 0
\(927\) −12.6511 −0.415518
\(928\) 0 0
\(929\) 12.0661 0.395875 0.197938 0.980215i \(-0.436576\pi\)
0.197938 + 0.980215i \(0.436576\pi\)
\(930\) 0 0
\(931\) 24.4776 0.802222
\(932\) 0 0
\(933\) −23.1087 −0.756544
\(934\) 0 0
\(935\) −2.52991 −0.0827368
\(936\) 0 0
\(937\) −0.272066 −0.00888800 −0.00444400 0.999990i \(-0.501415\pi\)
−0.00444400 + 0.999990i \(0.501415\pi\)
\(938\) 0 0
\(939\) 34.7905 1.13534
\(940\) 0 0
\(941\) −19.8673 −0.647656 −0.323828 0.946116i \(-0.604970\pi\)
−0.323828 + 0.946116i \(0.604970\pi\)
\(942\) 0 0
\(943\) 55.8438 1.81852
\(944\) 0 0
\(945\) −0.216546 −0.00704423
\(946\) 0 0
\(947\) −36.7169 −1.19314 −0.596569 0.802562i \(-0.703470\pi\)
−0.596569 + 0.802562i \(0.703470\pi\)
\(948\) 0 0
\(949\) −0.354396 −0.0115042
\(950\) 0 0
\(951\) −79.8212 −2.58838
\(952\) 0 0
\(953\) −41.4553 −1.34287 −0.671434 0.741065i \(-0.734321\pi\)
−0.671434 + 0.741065i \(0.734321\pi\)
\(954\) 0 0
\(955\) 13.1268 0.424773
\(956\) 0 0
\(957\) 35.0337 1.13248
\(958\) 0 0
\(959\) −0.694700 −0.0224330
\(960\) 0 0
\(961\) 1.84454 0.0595012
\(962\) 0 0
\(963\) −20.2392 −0.652199
\(964\) 0 0
\(965\) −2.80478 −0.0902891
\(966\) 0 0
\(967\) −33.6334 −1.08158 −0.540788 0.841159i \(-0.681874\pi\)
−0.540788 + 0.841159i \(0.681874\pi\)
\(968\) 0 0
\(969\) −4.66662 −0.149914
\(970\) 0 0
\(971\) −17.7577 −0.569871 −0.284935 0.958547i \(-0.591972\pi\)
−0.284935 + 0.958547i \(0.591972\pi\)
\(972\) 0 0
\(973\) −0.525006 −0.0168309
\(974\) 0 0
\(975\) −2.30706 −0.0738849
\(976\) 0 0
\(977\) −15.0637 −0.481930 −0.240965 0.970534i \(-0.577464\pi\)
−0.240965 + 0.970534i \(0.577464\pi\)
\(978\) 0 0
\(979\) −30.0058 −0.958989
\(980\) 0 0
\(981\) 30.9866 0.989326
\(982\) 0 0
\(983\) −37.5910 −1.19897 −0.599484 0.800387i \(-0.704627\pi\)
−0.599484 + 0.800387i \(0.704627\pi\)
\(984\) 0 0
\(985\) −24.0126 −0.765105
\(986\) 0 0
\(987\) 5.20825 0.165781
\(988\) 0 0
\(989\) 3.76310 0.119660
\(990\) 0 0
\(991\) 36.0602 1.14549 0.572745 0.819734i \(-0.305879\pi\)
0.572745 + 0.819734i \(0.305879\pi\)
\(992\) 0 0
\(993\) 38.6052 1.22510
\(994\) 0 0
\(995\) −25.4102 −0.805558
\(996\) 0 0
\(997\) 13.8167 0.437578 0.218789 0.975772i \(-0.429789\pi\)
0.218789 + 0.975772i \(0.429789\pi\)
\(998\) 0 0
\(999\) 9.03370 0.285813
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 \(a_p\))