Properties

Label 8048.2.a.p.1.7
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 1.7
Root \(-0.510671\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.51067 q^{3}\) \(-2.23445 q^{5}\) \(+3.60329 q^{7}\) \(-0.717874 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.51067 q^{3}\) \(-2.23445 q^{5}\) \(+3.60329 q^{7}\) \(-0.717874 q^{9}\) \(+1.50306 q^{11}\) \(+0.00459548 q^{13}\) \(-3.37551 q^{15}\) \(+1.11927 q^{17}\) \(-2.49963 q^{19}\) \(+5.44339 q^{21}\) \(-1.72480 q^{23}\) \(-0.00724425 q^{25}\) \(-5.61648 q^{27}\) \(-0.572061 q^{29}\) \(-3.25375 q^{31}\) \(+2.27063 q^{33}\) \(-8.05137 q^{35}\) \(-6.13809 q^{37}\) \(+0.00694226 q^{39}\) \(-5.89549 q^{41}\) \(+7.66800 q^{43}\) \(+1.60405 q^{45}\) \(-6.44840 q^{47}\) \(+5.98373 q^{49}\) \(+1.69085 q^{51}\) \(-7.82500 q^{53}\) \(-3.35851 q^{55}\) \(-3.77612 q^{57}\) \(-0.253382 q^{59}\) \(+7.08244 q^{61}\) \(-2.58671 q^{63}\) \(-0.0102684 q^{65}\) \(-6.16046 q^{67}\) \(-2.60561 q^{69}\) \(+9.32311 q^{71}\) \(-15.2654 q^{73}\) \(-0.0109437 q^{75}\) \(+5.41596 q^{77}\) \(+1.99661 q^{79}\) \(-6.33104 q^{81}\) \(-6.91660 q^{83}\) \(-2.50096 q^{85}\) \(-0.864195 q^{87}\) \(+3.37422 q^{89}\) \(+0.0165589 q^{91}\) \(-4.91534 q^{93}\) \(+5.58529 q^{95}\) \(-14.8842 q^{97}\) \(-1.07901 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.51067 0.872186 0.436093 0.899902i \(-0.356362\pi\)
0.436093 + 0.899902i \(0.356362\pi\)
\(4\) 0 0
\(5\) −2.23445 −0.999275 −0.499638 0.866235i \(-0.666534\pi\)
−0.499638 + 0.866235i \(0.666534\pi\)
\(6\) 0 0
\(7\) 3.60329 1.36192 0.680959 0.732322i \(-0.261563\pi\)
0.680959 + 0.732322i \(0.261563\pi\)
\(8\) 0 0
\(9\) −0.717874 −0.239291
\(10\) 0 0
\(11\) 1.50306 0.453189 0.226595 0.973989i \(-0.427241\pi\)
0.226595 + 0.973989i \(0.427241\pi\)
\(12\) 0 0
\(13\) 0.00459548 0.00127456 0.000637279 1.00000i \(-0.499797\pi\)
0.000637279 1.00000i \(0.499797\pi\)
\(14\) 0 0
\(15\) −3.37551 −0.871554
\(16\) 0 0
\(17\) 1.11927 0.271464 0.135732 0.990746i \(-0.456661\pi\)
0.135732 + 0.990746i \(0.456661\pi\)
\(18\) 0 0
\(19\) −2.49963 −0.573454 −0.286727 0.958012i \(-0.592567\pi\)
−0.286727 + 0.958012i \(0.592567\pi\)
\(20\) 0 0
\(21\) 5.44339 1.18785
\(22\) 0 0
\(23\) −1.72480 −0.359646 −0.179823 0.983699i \(-0.557553\pi\)
−0.179823 + 0.983699i \(0.557553\pi\)
\(24\) 0 0
\(25\) −0.00724425 −0.00144885
\(26\) 0 0
\(27\) −5.61648 −1.08089
\(28\) 0 0
\(29\) −0.572061 −0.106229 −0.0531145 0.998588i \(-0.516915\pi\)
−0.0531145 + 0.998588i \(0.516915\pi\)
\(30\) 0 0
\(31\) −3.25375 −0.584390 −0.292195 0.956359i \(-0.594386\pi\)
−0.292195 + 0.956359i \(0.594386\pi\)
\(32\) 0 0
\(33\) 2.27063 0.395266
\(34\) 0 0
\(35\) −8.05137 −1.36093
\(36\) 0 0
\(37\) −6.13809 −1.00910 −0.504548 0.863384i \(-0.668341\pi\)
−0.504548 + 0.863384i \(0.668341\pi\)
\(38\) 0 0
\(39\) 0.00694226 0.00111165
\(40\) 0 0
\(41\) −5.89549 −0.920721 −0.460360 0.887732i \(-0.652280\pi\)
−0.460360 + 0.887732i \(0.652280\pi\)
\(42\) 0 0
\(43\) 7.66800 1.16936 0.584680 0.811264i \(-0.301220\pi\)
0.584680 + 0.811264i \(0.301220\pi\)
\(44\) 0 0
\(45\) 1.60405 0.239118
\(46\) 0 0
\(47\) −6.44840 −0.940596 −0.470298 0.882508i \(-0.655854\pi\)
−0.470298 + 0.882508i \(0.655854\pi\)
\(48\) 0 0
\(49\) 5.98373 0.854819
\(50\) 0 0
\(51\) 1.69085 0.236767
\(52\) 0 0
\(53\) −7.82500 −1.07485 −0.537423 0.843313i \(-0.680602\pi\)
−0.537423 + 0.843313i \(0.680602\pi\)
\(54\) 0 0
\(55\) −3.35851 −0.452861
\(56\) 0 0
\(57\) −3.77612 −0.500159
\(58\) 0 0
\(59\) −0.253382 −0.0329875 −0.0164938 0.999864i \(-0.505250\pi\)
−0.0164938 + 0.999864i \(0.505250\pi\)
\(60\) 0 0
\(61\) 7.08244 0.906814 0.453407 0.891304i \(-0.350208\pi\)
0.453407 + 0.891304i \(0.350208\pi\)
\(62\) 0 0
\(63\) −2.58671 −0.325895
\(64\) 0 0
\(65\) −0.0102684 −0.00127363
\(66\) 0 0
\(67\) −6.16046 −0.752621 −0.376310 0.926494i \(-0.622807\pi\)
−0.376310 + 0.926494i \(0.622807\pi\)
\(68\) 0 0
\(69\) −2.60561 −0.313678
\(70\) 0 0
\(71\) 9.32311 1.10645 0.553225 0.833032i \(-0.313397\pi\)
0.553225 + 0.833032i \(0.313397\pi\)
\(72\) 0 0
\(73\) −15.2654 −1.78668 −0.893338 0.449385i \(-0.851643\pi\)
−0.893338 + 0.449385i \(0.851643\pi\)
\(74\) 0 0
\(75\) −0.0109437 −0.00126367
\(76\) 0 0
\(77\) 5.41596 0.617206
\(78\) 0 0
\(79\) 1.99661 0.224636 0.112318 0.993672i \(-0.464172\pi\)
0.112318 + 0.993672i \(0.464172\pi\)
\(80\) 0 0
\(81\) −6.33104 −0.703448
\(82\) 0 0
\(83\) −6.91660 −0.759196 −0.379598 0.925152i \(-0.623938\pi\)
−0.379598 + 0.925152i \(0.623938\pi\)
\(84\) 0 0
\(85\) −2.50096 −0.271267
\(86\) 0 0
\(87\) −0.864195 −0.0926514
\(88\) 0 0
\(89\) 3.37422 0.357666 0.178833 0.983879i \(-0.442768\pi\)
0.178833 + 0.983879i \(0.442768\pi\)
\(90\) 0 0
\(91\) 0.0165589 0.00173584
\(92\) 0 0
\(93\) −4.91534 −0.509697
\(94\) 0 0
\(95\) 5.58529 0.573039
\(96\) 0 0
\(97\) −14.8842 −1.51126 −0.755631 0.654997i \(-0.772670\pi\)
−0.755631 + 0.654997i \(0.772670\pi\)
\(98\) 0 0
\(99\) −1.07901 −0.108444
\(100\) 0 0
\(101\) 11.2591 1.12032 0.560159 0.828385i \(-0.310740\pi\)
0.560159 + 0.828385i \(0.310740\pi\)
\(102\) 0 0
\(103\) −4.65004 −0.458182 −0.229091 0.973405i \(-0.573575\pi\)
−0.229091 + 0.973405i \(0.573575\pi\)
\(104\) 0 0
\(105\) −12.1630 −1.18698
\(106\) 0 0
\(107\) 8.08323 0.781435 0.390718 0.920511i \(-0.372227\pi\)
0.390718 + 0.920511i \(0.372227\pi\)
\(108\) 0 0
\(109\) −1.20991 −0.115889 −0.0579444 0.998320i \(-0.518455\pi\)
−0.0579444 + 0.998320i \(0.518455\pi\)
\(110\) 0 0
\(111\) −9.27264 −0.880120
\(112\) 0 0
\(113\) 7.68412 0.722861 0.361431 0.932399i \(-0.382288\pi\)
0.361431 + 0.932399i \(0.382288\pi\)
\(114\) 0 0
\(115\) 3.85398 0.359386
\(116\) 0 0
\(117\) −0.00329898 −0.000304991 0
\(118\) 0 0
\(119\) 4.03307 0.369711
\(120\) 0 0
\(121\) −8.74081 −0.794619
\(122\) 0 0
\(123\) −8.90614 −0.803040
\(124\) 0 0
\(125\) 11.1884 1.00072
\(126\) 0 0
\(127\) −8.83928 −0.784360 −0.392180 0.919889i \(-0.628279\pi\)
−0.392180 + 0.919889i \(0.628279\pi\)
\(128\) 0 0
\(129\) 11.5838 1.01990
\(130\) 0 0
\(131\) 12.9102 1.12797 0.563984 0.825786i \(-0.309268\pi\)
0.563984 + 0.825786i \(0.309268\pi\)
\(132\) 0 0
\(133\) −9.00690 −0.780998
\(134\) 0 0
\(135\) 12.5497 1.08011
\(136\) 0 0
\(137\) 3.83616 0.327745 0.163873 0.986482i \(-0.447601\pi\)
0.163873 + 0.986482i \(0.447601\pi\)
\(138\) 0 0
\(139\) −9.22921 −0.782811 −0.391406 0.920218i \(-0.628011\pi\)
−0.391406 + 0.920218i \(0.628011\pi\)
\(140\) 0 0
\(141\) −9.74142 −0.820375
\(142\) 0 0
\(143\) 0.00690728 0.000577616 0
\(144\) 0 0
\(145\) 1.27824 0.106152
\(146\) 0 0
\(147\) 9.03945 0.745561
\(148\) 0 0
\(149\) 22.6884 1.85871 0.929353 0.369191i \(-0.120365\pi\)
0.929353 + 0.369191i \(0.120365\pi\)
\(150\) 0 0
\(151\) 2.22521 0.181085 0.0905427 0.995893i \(-0.471140\pi\)
0.0905427 + 0.995893i \(0.471140\pi\)
\(152\) 0 0
\(153\) −0.803497 −0.0649589
\(154\) 0 0
\(155\) 7.27033 0.583967
\(156\) 0 0
\(157\) −22.3177 −1.78114 −0.890571 0.454844i \(-0.849695\pi\)
−0.890571 + 0.454844i \(0.849695\pi\)
\(158\) 0 0
\(159\) −11.8210 −0.937466
\(160\) 0 0
\(161\) −6.21497 −0.489808
\(162\) 0 0
\(163\) −7.22321 −0.565765 −0.282883 0.959155i \(-0.591291\pi\)
−0.282883 + 0.959155i \(0.591291\pi\)
\(164\) 0 0
\(165\) −5.07360 −0.394979
\(166\) 0 0
\(167\) 11.4485 0.885915 0.442958 0.896543i \(-0.353929\pi\)
0.442958 + 0.896543i \(0.353929\pi\)
\(168\) 0 0
\(169\) −13.0000 −0.999998
\(170\) 0 0
\(171\) 1.79442 0.137223
\(172\) 0 0
\(173\) −12.5821 −0.956599 −0.478300 0.878197i \(-0.658747\pi\)
−0.478300 + 0.878197i \(0.658747\pi\)
\(174\) 0 0
\(175\) −0.0261032 −0.00197321
\(176\) 0 0
\(177\) −0.382777 −0.0287713
\(178\) 0 0
\(179\) −1.23407 −0.0922389 −0.0461194 0.998936i \(-0.514685\pi\)
−0.0461194 + 0.998936i \(0.514685\pi\)
\(180\) 0 0
\(181\) −17.0030 −1.26382 −0.631911 0.775041i \(-0.717729\pi\)
−0.631911 + 0.775041i \(0.717729\pi\)
\(182\) 0 0
\(183\) 10.6992 0.790910
\(184\) 0 0
\(185\) 13.7152 1.00836
\(186\) 0 0
\(187\) 1.68233 0.123024
\(188\) 0 0
\(189\) −20.2378 −1.47209
\(190\) 0 0
\(191\) −0.213652 −0.0154593 −0.00772966 0.999970i \(-0.502460\pi\)
−0.00772966 + 0.999970i \(0.502460\pi\)
\(192\) 0 0
\(193\) −3.51336 −0.252897 −0.126449 0.991973i \(-0.540358\pi\)
−0.126449 + 0.991973i \(0.540358\pi\)
\(194\) 0 0
\(195\) −0.0155121 −0.00111085
\(196\) 0 0
\(197\) −11.5456 −0.822587 −0.411294 0.911503i \(-0.634923\pi\)
−0.411294 + 0.911503i \(0.634923\pi\)
\(198\) 0 0
\(199\) 4.63698 0.328707 0.164353 0.986402i \(-0.447446\pi\)
0.164353 + 0.986402i \(0.447446\pi\)
\(200\) 0 0
\(201\) −9.30643 −0.656425
\(202\) 0 0
\(203\) −2.06130 −0.144675
\(204\) 0 0
\(205\) 13.1732 0.920054
\(206\) 0 0
\(207\) 1.23819 0.0860602
\(208\) 0 0
\(209\) −3.75709 −0.259883
\(210\) 0 0
\(211\) 0.622411 0.0428485 0.0214243 0.999770i \(-0.493180\pi\)
0.0214243 + 0.999770i \(0.493180\pi\)
\(212\) 0 0
\(213\) 14.0841 0.965030
\(214\) 0 0
\(215\) −17.1338 −1.16851
\(216\) 0 0
\(217\) −11.7242 −0.795891
\(218\) 0 0
\(219\) −23.0609 −1.55831
\(220\) 0 0
\(221\) 0.00514360 0.000345996 0
\(222\) 0 0
\(223\) −0.0281489 −0.00188499 −0.000942495 1.00000i \(-0.500300\pi\)
−0.000942495 1.00000i \(0.500300\pi\)
\(224\) 0 0
\(225\) 0.00520046 0.000346697 0
\(226\) 0 0
\(227\) 8.12837 0.539499 0.269749 0.962931i \(-0.413059\pi\)
0.269749 + 0.962931i \(0.413059\pi\)
\(228\) 0 0
\(229\) 23.9995 1.58593 0.792966 0.609266i \(-0.208536\pi\)
0.792966 + 0.609266i \(0.208536\pi\)
\(230\) 0 0
\(231\) 8.18174 0.538319
\(232\) 0 0
\(233\) −12.5903 −0.824819 −0.412410 0.910999i \(-0.635313\pi\)
−0.412410 + 0.910999i \(0.635313\pi\)
\(234\) 0 0
\(235\) 14.4086 0.939915
\(236\) 0 0
\(237\) 3.01622 0.195925
\(238\) 0 0
\(239\) −24.1351 −1.56117 −0.780586 0.625049i \(-0.785079\pi\)
−0.780586 + 0.625049i \(0.785079\pi\)
\(240\) 0 0
\(241\) 25.4713 1.64075 0.820374 0.571827i \(-0.193765\pi\)
0.820374 + 0.571827i \(0.193765\pi\)
\(242\) 0 0
\(243\) 7.28534 0.467355
\(244\) 0 0
\(245\) −13.3703 −0.854199
\(246\) 0 0
\(247\) −0.0114870 −0.000730901 0
\(248\) 0 0
\(249\) −10.4487 −0.662160
\(250\) 0 0
\(251\) −4.12389 −0.260298 −0.130149 0.991494i \(-0.541546\pi\)
−0.130149 + 0.991494i \(0.541546\pi\)
\(252\) 0 0
\(253\) −2.59248 −0.162988
\(254\) 0 0
\(255\) −3.77812 −0.236595
\(256\) 0 0
\(257\) −16.7266 −1.04337 −0.521687 0.853137i \(-0.674697\pi\)
−0.521687 + 0.853137i \(0.674697\pi\)
\(258\) 0 0
\(259\) −22.1174 −1.37431
\(260\) 0 0
\(261\) 0.410667 0.0254197
\(262\) 0 0
\(263\) −28.7329 −1.77174 −0.885872 0.463930i \(-0.846439\pi\)
−0.885872 + 0.463930i \(0.846439\pi\)
\(264\) 0 0
\(265\) 17.4845 1.07407
\(266\) 0 0
\(267\) 5.09733 0.311951
\(268\) 0 0
\(269\) 28.6099 1.74438 0.872189 0.489169i \(-0.162700\pi\)
0.872189 + 0.489169i \(0.162700\pi\)
\(270\) 0 0
\(271\) 13.8852 0.843467 0.421733 0.906720i \(-0.361422\pi\)
0.421733 + 0.906720i \(0.361422\pi\)
\(272\) 0 0
\(273\) 0.0250150 0.00151398
\(274\) 0 0
\(275\) −0.0108885 −0.000656603 0
\(276\) 0 0
\(277\) −14.4664 −0.869200 −0.434600 0.900624i \(-0.643110\pi\)
−0.434600 + 0.900624i \(0.643110\pi\)
\(278\) 0 0
\(279\) 2.33578 0.139839
\(280\) 0 0
\(281\) −15.4967 −0.924456 −0.462228 0.886761i \(-0.652950\pi\)
−0.462228 + 0.886761i \(0.652950\pi\)
\(282\) 0 0
\(283\) −10.4295 −0.619970 −0.309985 0.950741i \(-0.600324\pi\)
−0.309985 + 0.950741i \(0.600324\pi\)
\(284\) 0 0
\(285\) 8.43754 0.499797
\(286\) 0 0
\(287\) −21.2432 −1.25395
\(288\) 0 0
\(289\) −15.7472 −0.926307
\(290\) 0 0
\(291\) −22.4851 −1.31810
\(292\) 0 0
\(293\) −1.90244 −0.111142 −0.0555708 0.998455i \(-0.517698\pi\)
−0.0555708 + 0.998455i \(0.517698\pi\)
\(294\) 0 0
\(295\) 0.566169 0.0329636
\(296\) 0 0
\(297\) −8.44191 −0.489849
\(298\) 0 0
\(299\) −0.00792630 −0.000458390 0
\(300\) 0 0
\(301\) 27.6301 1.59257
\(302\) 0 0
\(303\) 17.0087 0.977127
\(304\) 0 0
\(305\) −15.8253 −0.906157
\(306\) 0 0
\(307\) 17.6876 1.00949 0.504744 0.863269i \(-0.331587\pi\)
0.504744 + 0.863269i \(0.331587\pi\)
\(308\) 0 0
\(309\) −7.02468 −0.399620
\(310\) 0 0
\(311\) 28.0074 1.58815 0.794076 0.607818i \(-0.207955\pi\)
0.794076 + 0.607818i \(0.207955\pi\)
\(312\) 0 0
\(313\) 5.02123 0.283817 0.141908 0.989880i \(-0.454676\pi\)
0.141908 + 0.989880i \(0.454676\pi\)
\(314\) 0 0
\(315\) 5.77987 0.325659
\(316\) 0 0
\(317\) 0.356974 0.0200496 0.0100248 0.999950i \(-0.496809\pi\)
0.0100248 + 0.999950i \(0.496809\pi\)
\(318\) 0 0
\(319\) −0.859841 −0.0481418
\(320\) 0 0
\(321\) 12.2111 0.681557
\(322\) 0 0
\(323\) −2.79777 −0.155672
\(324\) 0 0
\(325\) −3.32908e−5 0 −1.84664e−6 0
\(326\) 0 0
\(327\) −1.82778 −0.101077
\(328\) 0 0
\(329\) −23.2355 −1.28101
\(330\) 0 0
\(331\) −16.2490 −0.893123 −0.446562 0.894753i \(-0.647352\pi\)
−0.446562 + 0.894753i \(0.647352\pi\)
\(332\) 0 0
\(333\) 4.40637 0.241468
\(334\) 0 0
\(335\) 13.7652 0.752075
\(336\) 0 0
\(337\) −24.0444 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(338\) 0 0
\(339\) 11.6082 0.630469
\(340\) 0 0
\(341\) −4.89057 −0.264839
\(342\) 0 0
\(343\) −3.66192 −0.197725
\(344\) 0 0
\(345\) 5.82210 0.313451
\(346\) 0 0
\(347\) 10.7861 0.579028 0.289514 0.957174i \(-0.406506\pi\)
0.289514 + 0.957174i \(0.406506\pi\)
\(348\) 0 0
\(349\) 17.2044 0.920933 0.460466 0.887677i \(-0.347682\pi\)
0.460466 + 0.887677i \(0.347682\pi\)
\(350\) 0 0
\(351\) −0.0258105 −0.00137766
\(352\) 0 0
\(353\) −2.83276 −0.150773 −0.0753863 0.997154i \(-0.524019\pi\)
−0.0753863 + 0.997154i \(0.524019\pi\)
\(354\) 0 0
\(355\) −20.8320 −1.10565
\(356\) 0 0
\(357\) 6.09264 0.322457
\(358\) 0 0
\(359\) −23.3759 −1.23373 −0.616867 0.787068i \(-0.711598\pi\)
−0.616867 + 0.787068i \(0.711598\pi\)
\(360\) 0 0
\(361\) −12.7518 −0.671150
\(362\) 0 0
\(363\) −13.2045 −0.693056
\(364\) 0 0
\(365\) 34.1097 1.78538
\(366\) 0 0
\(367\) 21.8406 1.14007 0.570034 0.821621i \(-0.306930\pi\)
0.570034 + 0.821621i \(0.306930\pi\)
\(368\) 0 0
\(369\) 4.23222 0.220320
\(370\) 0 0
\(371\) −28.1958 −1.46385
\(372\) 0 0
\(373\) 0.594294 0.0307714 0.0153857 0.999882i \(-0.495102\pi\)
0.0153857 + 0.999882i \(0.495102\pi\)
\(374\) 0 0
\(375\) 16.9020 0.872817
\(376\) 0 0
\(377\) −0.00262890 −0.000135395 0
\(378\) 0 0
\(379\) 16.0631 0.825105 0.412553 0.910934i \(-0.364637\pi\)
0.412553 + 0.910934i \(0.364637\pi\)
\(380\) 0 0
\(381\) −13.3532 −0.684108
\(382\) 0 0
\(383\) −15.0745 −0.770271 −0.385135 0.922860i \(-0.625845\pi\)
−0.385135 + 0.922860i \(0.625845\pi\)
\(384\) 0 0
\(385\) −12.1017 −0.616759
\(386\) 0 0
\(387\) −5.50466 −0.279818
\(388\) 0 0
\(389\) 8.06793 0.409060 0.204530 0.978860i \(-0.434433\pi\)
0.204530 + 0.978860i \(0.434433\pi\)
\(390\) 0 0
\(391\) −1.93053 −0.0976309
\(392\) 0 0
\(393\) 19.5030 0.983797
\(394\) 0 0
\(395\) −4.46132 −0.224473
\(396\) 0 0
\(397\) 7.64285 0.383583 0.191792 0.981436i \(-0.438570\pi\)
0.191792 + 0.981436i \(0.438570\pi\)
\(398\) 0 0
\(399\) −13.6065 −0.681175
\(400\) 0 0
\(401\) 37.0556 1.85047 0.925234 0.379397i \(-0.123868\pi\)
0.925234 + 0.379397i \(0.123868\pi\)
\(402\) 0 0
\(403\) −0.0149525 −0.000744839 0
\(404\) 0 0
\(405\) 14.1464 0.702939
\(406\) 0 0
\(407\) −9.22591 −0.457312
\(408\) 0 0
\(409\) −29.1516 −1.44145 −0.720726 0.693220i \(-0.756191\pi\)
−0.720726 + 0.693220i \(0.756191\pi\)
\(410\) 0 0
\(411\) 5.79518 0.285855
\(412\) 0 0
\(413\) −0.913010 −0.0449263
\(414\) 0 0
\(415\) 15.4548 0.758645
\(416\) 0 0
\(417\) −13.9423 −0.682757
\(418\) 0 0
\(419\) −31.8690 −1.55690 −0.778451 0.627705i \(-0.783994\pi\)
−0.778451 + 0.627705i \(0.783994\pi\)
\(420\) 0 0
\(421\) −26.0459 −1.26940 −0.634699 0.772759i \(-0.718876\pi\)
−0.634699 + 0.772759i \(0.718876\pi\)
\(422\) 0 0
\(423\) 4.62914 0.225077
\(424\) 0 0
\(425\) −0.00810829 −0.000393310 0
\(426\) 0 0
\(427\) 25.5201 1.23501
\(428\) 0 0
\(429\) 0.0104346 0.000503789 0
\(430\) 0 0
\(431\) 22.6196 1.08955 0.544774 0.838583i \(-0.316616\pi\)
0.544774 + 0.838583i \(0.316616\pi\)
\(432\) 0 0
\(433\) −22.7272 −1.09220 −0.546099 0.837720i \(-0.683888\pi\)
−0.546099 + 0.837720i \(0.683888\pi\)
\(434\) 0 0
\(435\) 1.93100 0.0925843
\(436\) 0 0
\(437\) 4.31137 0.206241
\(438\) 0 0
\(439\) −24.5936 −1.17379 −0.586895 0.809663i \(-0.699650\pi\)
−0.586895 + 0.809663i \(0.699650\pi\)
\(440\) 0 0
\(441\) −4.29556 −0.204551
\(442\) 0 0
\(443\) −23.4765 −1.11540 −0.557702 0.830041i \(-0.688317\pi\)
−0.557702 + 0.830041i \(0.688317\pi\)
\(444\) 0 0
\(445\) −7.53951 −0.357407
\(446\) 0 0
\(447\) 34.2747 1.62114
\(448\) 0 0
\(449\) −13.6452 −0.643958 −0.321979 0.946747i \(-0.604348\pi\)
−0.321979 + 0.946747i \(0.604348\pi\)
\(450\) 0 0
\(451\) −8.86127 −0.417261
\(452\) 0 0
\(453\) 3.36157 0.157940
\(454\) 0 0
\(455\) −0.0370000 −0.00173458
\(456\) 0 0
\(457\) −2.17967 −0.101960 −0.0509802 0.998700i \(-0.516235\pi\)
−0.0509802 + 0.998700i \(0.516235\pi\)
\(458\) 0 0
\(459\) −6.28638 −0.293423
\(460\) 0 0
\(461\) 12.2229 0.569276 0.284638 0.958635i \(-0.408127\pi\)
0.284638 + 0.958635i \(0.408127\pi\)
\(462\) 0 0
\(463\) 1.99436 0.0926860 0.0463430 0.998926i \(-0.485243\pi\)
0.0463430 + 0.998926i \(0.485243\pi\)
\(464\) 0 0
\(465\) 10.9831 0.509328
\(466\) 0 0
\(467\) −41.2601 −1.90929 −0.954645 0.297747i \(-0.903765\pi\)
−0.954645 + 0.297747i \(0.903765\pi\)
\(468\) 0 0
\(469\) −22.1980 −1.02501
\(470\) 0 0
\(471\) −33.7146 −1.55349
\(472\) 0 0
\(473\) 11.5255 0.529941
\(474\) 0 0
\(475\) 0.0181079 0.000830849 0
\(476\) 0 0
\(477\) 5.61736 0.257201
\(478\) 0 0
\(479\) −23.4921 −1.07338 −0.536691 0.843779i \(-0.680326\pi\)
−0.536691 + 0.843779i \(0.680326\pi\)
\(480\) 0 0
\(481\) −0.0282075 −0.00128615
\(482\) 0 0
\(483\) −9.38878 −0.427204
\(484\) 0 0
\(485\) 33.2580 1.51017
\(486\) 0 0
\(487\) −6.09387 −0.276139 −0.138070 0.990423i \(-0.544090\pi\)
−0.138070 + 0.990423i \(0.544090\pi\)
\(488\) 0 0
\(489\) −10.9119 −0.493453
\(490\) 0 0
\(491\) 7.88983 0.356063 0.178032 0.984025i \(-0.443027\pi\)
0.178032 + 0.984025i \(0.443027\pi\)
\(492\) 0 0
\(493\) −0.640292 −0.0288373
\(494\) 0 0
\(495\) 2.41098 0.108366
\(496\) 0 0
\(497\) 33.5939 1.50689
\(498\) 0 0
\(499\) 0.289120 0.0129428 0.00647139 0.999979i \(-0.497940\pi\)
0.00647139 + 0.999979i \(0.497940\pi\)
\(500\) 0 0
\(501\) 17.2950 0.772683
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −25.1578 −1.11951
\(506\) 0 0
\(507\) −19.6387 −0.872185
\(508\) 0 0
\(509\) 27.0889 1.20069 0.600346 0.799740i \(-0.295030\pi\)
0.600346 + 0.799740i \(0.295030\pi\)
\(510\) 0 0
\(511\) −55.0056 −2.43331
\(512\) 0 0
\(513\) 14.0391 0.619843
\(514\) 0 0
\(515\) 10.3903 0.457850
\(516\) 0 0
\(517\) −9.69233 −0.426268
\(518\) 0 0
\(519\) −19.0074 −0.834333
\(520\) 0 0
\(521\) 21.1689 0.927424 0.463712 0.885986i \(-0.346517\pi\)
0.463712 + 0.885986i \(0.346517\pi\)
\(522\) 0 0
\(523\) 0.868369 0.0379711 0.0189856 0.999820i \(-0.493956\pi\)
0.0189856 + 0.999820i \(0.493956\pi\)
\(524\) 0 0
\(525\) −0.0394333 −0.00172101
\(526\) 0 0
\(527\) −3.64183 −0.158641
\(528\) 0 0
\(529\) −20.0251 −0.870655
\(530\) 0 0
\(531\) 0.181896 0.00789363
\(532\) 0 0
\(533\) −0.0270926 −0.00117351
\(534\) 0 0
\(535\) −18.0616 −0.780869
\(536\) 0 0
\(537\) −1.86428 −0.0804495
\(538\) 0 0
\(539\) 8.99390 0.387395
\(540\) 0 0
\(541\) 14.8513 0.638508 0.319254 0.947669i \(-0.396568\pi\)
0.319254 + 0.947669i \(0.396568\pi\)
\(542\) 0 0
\(543\) −25.6859 −1.10229
\(544\) 0 0
\(545\) 2.70349 0.115805
\(546\) 0 0
\(547\) 18.8256 0.804925 0.402463 0.915436i \(-0.368154\pi\)
0.402463 + 0.915436i \(0.368154\pi\)
\(548\) 0 0
\(549\) −5.08430 −0.216993
\(550\) 0 0
\(551\) 1.42994 0.0609175
\(552\) 0 0
\(553\) 7.19437 0.305936
\(554\) 0 0
\(555\) 20.7192 0.879482
\(556\) 0 0
\(557\) 11.9201 0.505071 0.252535 0.967588i \(-0.418736\pi\)
0.252535 + 0.967588i \(0.418736\pi\)
\(558\) 0 0
\(559\) 0.0352382 0.00149042
\(560\) 0 0
\(561\) 2.54145 0.107300
\(562\) 0 0
\(563\) 22.7172 0.957414 0.478707 0.877975i \(-0.341106\pi\)
0.478707 + 0.877975i \(0.341106\pi\)
\(564\) 0 0
\(565\) −17.1698 −0.722337
\(566\) 0 0
\(567\) −22.8126 −0.958039
\(568\) 0 0
\(569\) −16.9403 −0.710176 −0.355088 0.934833i \(-0.615549\pi\)
−0.355088 + 0.934833i \(0.615549\pi\)
\(570\) 0 0
\(571\) −16.2940 −0.681883 −0.340941 0.940085i \(-0.610746\pi\)
−0.340941 + 0.940085i \(0.610746\pi\)
\(572\) 0 0
\(573\) −0.322758 −0.0134834
\(574\) 0 0
\(575\) 0.0124949 0.000521073 0
\(576\) 0 0
\(577\) −44.3876 −1.84788 −0.923941 0.382535i \(-0.875051\pi\)
−0.923941 + 0.382535i \(0.875051\pi\)
\(578\) 0 0
\(579\) −5.30753 −0.220574
\(580\) 0 0
\(581\) −24.9226 −1.03396
\(582\) 0 0
\(583\) −11.7614 −0.487109
\(584\) 0 0
\(585\) 0.00737139 0.000304770 0
\(586\) 0 0
\(587\) −33.6221 −1.38773 −0.693865 0.720105i \(-0.744094\pi\)
−0.693865 + 0.720105i \(0.744094\pi\)
\(588\) 0 0
\(589\) 8.13316 0.335121
\(590\) 0 0
\(591\) −17.4415 −0.717449
\(592\) 0 0
\(593\) 14.3513 0.589336 0.294668 0.955600i \(-0.404791\pi\)
0.294668 + 0.955600i \(0.404791\pi\)
\(594\) 0 0
\(595\) −9.01169 −0.369443
\(596\) 0 0
\(597\) 7.00495 0.286694
\(598\) 0 0
\(599\) 4.26954 0.174449 0.0872243 0.996189i \(-0.472200\pi\)
0.0872243 + 0.996189i \(0.472200\pi\)
\(600\) 0 0
\(601\) 18.2764 0.745510 0.372755 0.927930i \(-0.378413\pi\)
0.372755 + 0.927930i \(0.378413\pi\)
\(602\) 0 0
\(603\) 4.42244 0.180096
\(604\) 0 0
\(605\) 19.5309 0.794044
\(606\) 0 0
\(607\) 29.2048 1.18539 0.592694 0.805428i \(-0.298064\pi\)
0.592694 + 0.805428i \(0.298064\pi\)
\(608\) 0 0
\(609\) −3.11395 −0.126184
\(610\) 0 0
\(611\) −0.0296335 −0.00119884
\(612\) 0 0
\(613\) −24.0622 −0.971861 −0.485931 0.873997i \(-0.661519\pi\)
−0.485931 + 0.873997i \(0.661519\pi\)
\(614\) 0 0
\(615\) 19.9003 0.802458
\(616\) 0 0
\(617\) −20.7734 −0.836307 −0.418154 0.908376i \(-0.637323\pi\)
−0.418154 + 0.908376i \(0.637323\pi\)
\(618\) 0 0
\(619\) 6.43218 0.258531 0.129266 0.991610i \(-0.458738\pi\)
0.129266 + 0.991610i \(0.458738\pi\)
\(620\) 0 0
\(621\) 9.68732 0.388739
\(622\) 0 0
\(623\) 12.1583 0.487112
\(624\) 0 0
\(625\) −24.9637 −0.998549
\(626\) 0 0
\(627\) −5.67573 −0.226667
\(628\) 0 0
\(629\) −6.87020 −0.273933
\(630\) 0 0
\(631\) 43.2199 1.72056 0.860279 0.509824i \(-0.170290\pi\)
0.860279 + 0.509824i \(0.170290\pi\)
\(632\) 0 0
\(633\) 0.940258 0.0373719
\(634\) 0 0
\(635\) 19.7509 0.783791
\(636\) 0 0
\(637\) 0.0274981 0.00108952
\(638\) 0 0
\(639\) −6.69281 −0.264764
\(640\) 0 0
\(641\) −49.6276 −1.96017 −0.980086 0.198574i \(-0.936369\pi\)
−0.980086 + 0.198574i \(0.936369\pi\)
\(642\) 0 0
\(643\) 45.1377 1.78006 0.890028 0.455906i \(-0.150685\pi\)
0.890028 + 0.455906i \(0.150685\pi\)
\(644\) 0 0
\(645\) −25.8835 −1.01916
\(646\) 0 0
\(647\) 29.7930 1.17128 0.585642 0.810570i \(-0.300843\pi\)
0.585642 + 0.810570i \(0.300843\pi\)
\(648\) 0 0
\(649\) −0.380848 −0.0149496
\(650\) 0 0
\(651\) −17.7114 −0.694165
\(652\) 0 0
\(653\) 29.1127 1.13927 0.569635 0.821898i \(-0.307085\pi\)
0.569635 + 0.821898i \(0.307085\pi\)
\(654\) 0 0
\(655\) −28.8471 −1.12715
\(656\) 0 0
\(657\) 10.9586 0.427536
\(658\) 0 0
\(659\) −17.1327 −0.667395 −0.333697 0.942680i \(-0.608296\pi\)
−0.333697 + 0.942680i \(0.608296\pi\)
\(660\) 0 0
\(661\) −0.266846 −0.0103791 −0.00518956 0.999987i \(-0.501652\pi\)
−0.00518956 + 0.999987i \(0.501652\pi\)
\(662\) 0 0
\(663\) 0.00777029 0.000301773 0
\(664\) 0 0
\(665\) 20.1255 0.780432
\(666\) 0 0
\(667\) 0.986691 0.0382048
\(668\) 0 0
\(669\) −0.0425237 −0.00164406
\(670\) 0 0
\(671\) 10.6453 0.410958
\(672\) 0 0
\(673\) 41.4814 1.59899 0.799495 0.600673i \(-0.205101\pi\)
0.799495 + 0.600673i \(0.205101\pi\)
\(674\) 0 0
\(675\) 0.0406872 0.00156605
\(676\) 0 0
\(677\) 33.0242 1.26922 0.634611 0.772832i \(-0.281160\pi\)
0.634611 + 0.772832i \(0.281160\pi\)
\(678\) 0 0
\(679\) −53.6322 −2.05822
\(680\) 0 0
\(681\) 12.2793 0.470543
\(682\) 0 0
\(683\) −0.471704 −0.0180492 −0.00902462 0.999959i \(-0.502873\pi\)
−0.00902462 + 0.999959i \(0.502873\pi\)
\(684\) 0 0
\(685\) −8.57170 −0.327508
\(686\) 0 0
\(687\) 36.2553 1.38323
\(688\) 0 0
\(689\) −0.0359597 −0.00136995
\(690\) 0 0
\(691\) 12.1972 0.464003 0.232002 0.972715i \(-0.425473\pi\)
0.232002 + 0.972715i \(0.425473\pi\)
\(692\) 0 0
\(693\) −3.88798 −0.147692
\(694\) 0 0
\(695\) 20.6222 0.782244
\(696\) 0 0
\(697\) −6.59866 −0.249942
\(698\) 0 0
\(699\) −19.0198 −0.719396
\(700\) 0 0
\(701\) −47.0220 −1.77600 −0.887999 0.459846i \(-0.847905\pi\)
−0.887999 + 0.459846i \(0.847905\pi\)
\(702\) 0 0
\(703\) 15.3430 0.578671
\(704\) 0 0
\(705\) 21.7667 0.819781
\(706\) 0 0
\(707\) 40.5697 1.52578
\(708\) 0 0
\(709\) 26.6796 1.00197 0.500986 0.865455i \(-0.332971\pi\)
0.500986 + 0.865455i \(0.332971\pi\)
\(710\) 0 0
\(711\) −1.43331 −0.0537535
\(712\) 0 0
\(713\) 5.61207 0.210174
\(714\) 0 0
\(715\) −0.0154340 −0.000577198 0
\(716\) 0 0
\(717\) −36.4602 −1.36163
\(718\) 0 0
\(719\) −12.7457 −0.475336 −0.237668 0.971346i \(-0.576383\pi\)
−0.237668 + 0.971346i \(0.576383\pi\)
\(720\) 0 0
\(721\) −16.7555 −0.624006
\(722\) 0 0
\(723\) 38.4787 1.43104
\(724\) 0 0
\(725\) 0.00414415 0.000153910 0
\(726\) 0 0
\(727\) −1.14219 −0.0423614 −0.0211807 0.999776i \(-0.506743\pi\)
−0.0211807 + 0.999776i \(0.506743\pi\)
\(728\) 0 0
\(729\) 29.9989 1.11107
\(730\) 0 0
\(731\) 8.58259 0.317439
\(732\) 0 0
\(733\) −20.6111 −0.761289 −0.380644 0.924721i \(-0.624298\pi\)
−0.380644 + 0.924721i \(0.624298\pi\)
\(734\) 0 0
\(735\) −20.1982 −0.745021
\(736\) 0 0
\(737\) −9.25954 −0.341080
\(738\) 0 0
\(739\) 40.1054 1.47530 0.737651 0.675182i \(-0.235935\pi\)
0.737651 + 0.675182i \(0.235935\pi\)
\(740\) 0 0
\(741\) −0.0173531 −0.000637482 0
\(742\) 0 0
\(743\) 31.7658 1.16538 0.582688 0.812696i \(-0.302001\pi\)
0.582688 + 0.812696i \(0.302001\pi\)
\(744\) 0 0
\(745\) −50.6961 −1.85736
\(746\) 0 0
\(747\) 4.96525 0.181669
\(748\) 0 0
\(749\) 29.1263 1.06425
\(750\) 0 0
\(751\) −3.19661 −0.116646 −0.0583230 0.998298i \(-0.518575\pi\)
−0.0583230 + 0.998298i \(0.518575\pi\)
\(752\) 0 0
\(753\) −6.22984 −0.227028
\(754\) 0 0
\(755\) −4.97212 −0.180954
\(756\) 0 0
\(757\) 45.6783 1.66021 0.830103 0.557610i \(-0.188281\pi\)
0.830103 + 0.557610i \(0.188281\pi\)
\(758\) 0 0
\(759\) −3.91638 −0.142156
\(760\) 0 0
\(761\) 37.7902 1.36989 0.684946 0.728594i \(-0.259826\pi\)
0.684946 + 0.728594i \(0.259826\pi\)
\(762\) 0 0
\(763\) −4.35968 −0.157831
\(764\) 0 0
\(765\) 1.79537 0.0649118
\(766\) 0 0
\(767\) −0.00116441 −4.20445e−5 0
\(768\) 0 0
\(769\) 11.6770 0.421084 0.210542 0.977585i \(-0.432477\pi\)
0.210542 + 0.977585i \(0.432477\pi\)
\(770\) 0 0
\(771\) −25.2683 −0.910017
\(772\) 0 0
\(773\) −43.2250 −1.55470 −0.777348 0.629070i \(-0.783436\pi\)
−0.777348 + 0.629070i \(0.783436\pi\)
\(774\) 0 0
\(775\) 0.0235710 0.000846694 0
\(776\) 0 0
\(777\) −33.4120 −1.19865
\(778\) 0 0
\(779\) 14.7365 0.527992
\(780\) 0 0
\(781\) 14.0132 0.501431
\(782\) 0 0
\(783\) 3.21297 0.114822
\(784\) 0 0
\(785\) 49.8676 1.77985
\(786\) 0 0
\(787\) −41.6501 −1.48467 −0.742334 0.670030i \(-0.766281\pi\)
−0.742334 + 0.670030i \(0.766281\pi\)
\(788\) 0 0
\(789\) −43.4059 −1.54529
\(790\) 0 0
\(791\) 27.6881 0.984477
\(792\) 0 0
\(793\) 0.0325473 0.00115579
\(794\) 0 0
\(795\) 26.4134 0.936787
\(796\) 0 0
\(797\) 20.0955 0.711819 0.355910 0.934520i \(-0.384171\pi\)
0.355910 + 0.934520i \(0.384171\pi\)
\(798\) 0 0
\(799\) −7.21753 −0.255338
\(800\) 0 0
\(801\) −2.42226 −0.0855864
\(802\) 0 0
\(803\) −22.9448 −0.809703
\(804\) 0 0
\(805\) 13.8870 0.489453
\(806\) 0 0
\(807\) 43.2202 1.52142
\(808\) 0 0
\(809\) −10.5903 −0.372334 −0.186167 0.982518i \(-0.559607\pi\)
−0.186167 + 0.982518i \(0.559607\pi\)
\(810\) 0 0
\(811\) −29.9332 −1.05110 −0.525549 0.850764i \(-0.676140\pi\)
−0.525549 + 0.850764i \(0.676140\pi\)
\(812\) 0 0
\(813\) 20.9760 0.735660
\(814\) 0 0
\(815\) 16.1399 0.565355
\(816\) 0 0
\(817\) −19.1672 −0.670575
\(818\) 0 0
\(819\) −0.0118872 −0.000415372 0
\(820\) 0 0
\(821\) 1.47970 0.0516419 0.0258209 0.999667i \(-0.491780\pi\)
0.0258209 + 0.999667i \(0.491780\pi\)
\(822\) 0 0
\(823\) 20.9277 0.729494 0.364747 0.931107i \(-0.381155\pi\)
0.364747 + 0.931107i \(0.381155\pi\)
\(824\) 0 0
\(825\) −0.0164490 −0.000572680 0
\(826\) 0 0
\(827\) −14.8863 −0.517646 −0.258823 0.965925i \(-0.583335\pi\)
−0.258823 + 0.965925i \(0.583335\pi\)
\(828\) 0 0
\(829\) 54.9732 1.90930 0.954649 0.297733i \(-0.0962304\pi\)
0.954649 + 0.297733i \(0.0962304\pi\)
\(830\) 0 0
\(831\) −21.8539 −0.758104
\(832\) 0 0
\(833\) 6.69743 0.232052
\(834\) 0 0
\(835\) −25.5812 −0.885273
\(836\) 0 0
\(837\) 18.2746 0.631663
\(838\) 0 0
\(839\) 40.8460 1.41016 0.705080 0.709128i \(-0.250911\pi\)
0.705080 + 0.709128i \(0.250911\pi\)
\(840\) 0 0
\(841\) −28.6727 −0.988715
\(842\) 0 0
\(843\) −23.4104 −0.806298
\(844\) 0 0
\(845\) 29.0478 0.999274
\(846\) 0 0
\(847\) −31.4957 −1.08221
\(848\) 0 0
\(849\) −15.7556 −0.540729
\(850\) 0 0
\(851\) 10.5870 0.362918
\(852\) 0 0
\(853\) −8.90994 −0.305071 −0.152535 0.988298i \(-0.548744\pi\)
−0.152535 + 0.988298i \(0.548744\pi\)
\(854\) 0 0
\(855\) −4.00953 −0.137123
\(856\) 0 0
\(857\) 32.1479 1.09815 0.549076 0.835773i \(-0.314980\pi\)
0.549076 + 0.835773i \(0.314980\pi\)
\(858\) 0 0
\(859\) 25.4577 0.868606 0.434303 0.900767i \(-0.356995\pi\)
0.434303 + 0.900767i \(0.356995\pi\)
\(860\) 0 0
\(861\) −32.0915 −1.09367
\(862\) 0 0
\(863\) 42.3500 1.44161 0.720805 0.693138i \(-0.243772\pi\)
0.720805 + 0.693138i \(0.243772\pi\)
\(864\) 0 0
\(865\) 28.1140 0.955906
\(866\) 0 0
\(867\) −23.7889 −0.807913
\(868\) 0 0
\(869\) 3.00102 0.101803
\(870\) 0 0
\(871\) −0.0283103 −0.000959259 0
\(872\) 0 0
\(873\) 10.6850 0.361632
\(874\) 0 0
\(875\) 40.3152 1.36290
\(876\) 0 0
\(877\) −54.7498 −1.84877 −0.924385 0.381461i \(-0.875421\pi\)
−0.924385 + 0.381461i \(0.875421\pi\)
\(878\) 0 0
\(879\) −2.87396 −0.0969361
\(880\) 0 0
\(881\) −42.7752 −1.44113 −0.720566 0.693386i \(-0.756118\pi\)
−0.720566 + 0.693386i \(0.756118\pi\)
\(882\) 0 0
\(883\) 51.0453 1.71781 0.858906 0.512133i \(-0.171144\pi\)
0.858906 + 0.512133i \(0.171144\pi\)
\(884\) 0 0
\(885\) 0.855295 0.0287504
\(886\) 0 0
\(887\) 15.6713 0.526191 0.263096 0.964770i \(-0.415256\pi\)
0.263096 + 0.964770i \(0.415256\pi\)
\(888\) 0 0
\(889\) −31.8505 −1.06823
\(890\) 0 0
\(891\) −9.51592 −0.318795
\(892\) 0 0
\(893\) 16.1186 0.539389
\(894\) 0 0
\(895\) 2.75747 0.0921720
\(896\) 0 0
\(897\) −0.0119740 −0.000399801 0
\(898\) 0 0
\(899\) 1.86134 0.0620792
\(900\) 0 0
\(901\) −8.75831 −0.291782
\(902\) 0 0
\(903\) 41.7400 1.38902
\(904\) 0 0
\(905\) 37.9923 1.26291
\(906\) 0 0
\(907\) −50.8029 −1.68688 −0.843442 0.537221i \(-0.819474\pi\)
−0.843442 + 0.537221i \(0.819474\pi\)
\(908\) 0 0
\(909\) −8.08259 −0.268083
\(910\) 0 0
\(911\) 47.4669 1.57265 0.786324 0.617815i \(-0.211982\pi\)
0.786324 + 0.617815i \(0.211982\pi\)
\(912\) 0 0
\(913\) −10.3961 −0.344059
\(914\) 0 0
\(915\) −23.9069 −0.790337
\(916\) 0 0
\(917\) 46.5192 1.53620
\(918\) 0 0
\(919\) −18.1424 −0.598462 −0.299231 0.954181i \(-0.596730\pi\)
−0.299231 + 0.954181i \(0.596730\pi\)
\(920\) 0 0
\(921\) 26.7202 0.880461
\(922\) 0 0
\(923\) 0.0428442 0.00141023
\(924\) 0 0
\(925\) 0.0444659 0.00146203
\(926\) 0 0
\(927\) 3.33814 0.109639
\(928\) 0 0
\(929\) −36.7632 −1.20616 −0.603081 0.797680i \(-0.706060\pi\)
−0.603081 + 0.797680i \(0.706060\pi\)
\(930\) 0 0
\(931\) −14.9571 −0.490200
\(932\) 0 0
\(933\) 42.3099 1.38516
\(934\) 0 0
\(935\) −3.75909 −0.122935
\(936\) 0 0
\(937\) −29.1597 −0.952607 −0.476304 0.879281i \(-0.658024\pi\)
−0.476304 + 0.879281i \(0.658024\pi\)
\(938\) 0 0
\(939\) 7.58543 0.247541
\(940\) 0 0
\(941\) −11.1041 −0.361983 −0.180991 0.983485i \(-0.557931\pi\)
−0.180991 + 0.983485i \(0.557931\pi\)
\(942\) 0 0
\(943\) 10.1686 0.331134
\(944\) 0 0
\(945\) 45.2204 1.47102
\(946\) 0 0
\(947\) −7.44473 −0.241921 −0.120961 0.992657i \(-0.538597\pi\)
−0.120961 + 0.992657i \(0.538597\pi\)
\(948\) 0 0
\(949\) −0.0701518 −0.00227722
\(950\) 0 0
\(951\) 0.539270 0.0174870
\(952\) 0 0
\(953\) −40.8632 −1.32369 −0.661844 0.749641i \(-0.730226\pi\)
−0.661844 + 0.749641i \(0.730226\pi\)
\(954\) 0 0
\(955\) 0.477394 0.0154481
\(956\) 0 0
\(957\) −1.29894 −0.0419886
\(958\) 0 0
\(959\) 13.8228 0.446362
\(960\) 0 0
\(961\) −20.4131 −0.658488
\(962\) 0 0
\(963\) −5.80274 −0.186991
\(964\) 0 0
\(965\) 7.85042 0.252714
\(966\) 0 0
\(967\) −2.29088 −0.0736697 −0.0368349 0.999321i \(-0.511728\pi\)
−0.0368349 + 0.999321i \(0.511728\pi\)
\(968\) 0 0
\(969\) −4.22651 −0.135775
\(970\) 0 0
\(971\) 27.8481 0.893689 0.446845 0.894612i \(-0.352548\pi\)
0.446845 + 0.894612i \(0.352548\pi\)
\(972\) 0 0
\(973\) −33.2556 −1.06612
\(974\) 0 0
\(975\) −5.02915e−5 0 −1.61062e−6 0
\(976\) 0 0
\(977\) 2.65190 0.0848419 0.0424209 0.999100i \(-0.486493\pi\)
0.0424209 + 0.999100i \(0.486493\pi\)
\(978\) 0 0
\(979\) 5.07165 0.162090
\(980\) 0 0
\(981\) 0.868565 0.0277312
\(982\) 0 0
\(983\) −17.5940 −0.561162 −0.280581 0.959830i \(-0.590527\pi\)
−0.280581 + 0.959830i \(0.590527\pi\)
\(984\) 0 0
\(985\) 25.7980 0.821991
\(986\) 0 0
\(987\) −35.1012 −1.11728
\(988\) 0 0
\(989\) −13.2258 −0.420556
\(990\) 0 0
\(991\) 40.1464 1.27529 0.637646 0.770329i \(-0.279908\pi\)
0.637646 + 0.770329i \(0.279908\pi\)
\(992\) 0 0
\(993\) −24.5468 −0.778970
\(994\) 0 0
\(995\) −10.3611 −0.328469
\(996\) 0 0
\(997\) −52.3474 −1.65786 −0.828930 0.559353i \(-0.811050\pi\)
−0.828930 + 0.559353i \(0.811050\pi\)
\(998\) 0 0
\(999\) 34.4745 1.09072
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 \(a_p\))