Properties

Label 4008.2.a.i.1.6
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.41388\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.413878 q^{5}\) \(+2.72537 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.413878 q^{5}\) \(+2.72537 q^{7}\) \(+1.00000 q^{9}\) \(-3.29320 q^{11}\) \(-3.51462 q^{13}\) \(+0.413878 q^{15}\) \(-2.04345 q^{17}\) \(+0.104243 q^{19}\) \(+2.72537 q^{21}\) \(-7.14941 q^{23}\) \(-4.82870 q^{25}\) \(+1.00000 q^{27}\) \(+3.94939 q^{29}\) \(-6.72301 q^{31}\) \(-3.29320 q^{33}\) \(+1.12797 q^{35}\) \(-11.8427 q^{37}\) \(-3.51462 q^{39}\) \(+1.68403 q^{41}\) \(-3.25044 q^{43}\) \(+0.413878 q^{45}\) \(-1.28674 q^{47}\) \(+0.427633 q^{49}\) \(-2.04345 q^{51}\) \(-2.39006 q^{53}\) \(-1.36298 q^{55}\) \(+0.104243 q^{57}\) \(+4.83514 q^{59}\) \(-0.869119 q^{61}\) \(+2.72537 q^{63}\) \(-1.45463 q^{65}\) \(+0.884563 q^{67}\) \(-7.14941 q^{69}\) \(+5.76105 q^{71}\) \(-9.55384 q^{73}\) \(-4.82870 q^{75}\) \(-8.97519 q^{77}\) \(+8.30282 q^{79}\) \(+1.00000 q^{81}\) \(-9.73510 q^{83}\) \(-0.845741 q^{85}\) \(+3.94939 q^{87}\) \(+15.7470 q^{89}\) \(-9.57864 q^{91}\) \(-6.72301 q^{93}\) \(+0.0431440 q^{95}\) \(-15.3694 q^{97}\) \(-3.29320 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.413878 0.185092 0.0925460 0.995708i \(-0.470499\pi\)
0.0925460 + 0.995708i \(0.470499\pi\)
\(6\) 0 0
\(7\) 2.72537 1.03009 0.515046 0.857162i \(-0.327775\pi\)
0.515046 + 0.857162i \(0.327775\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.29320 −0.992938 −0.496469 0.868054i \(-0.665370\pi\)
−0.496469 + 0.868054i \(0.665370\pi\)
\(12\) 0 0
\(13\) −3.51462 −0.974781 −0.487391 0.873184i \(-0.662051\pi\)
−0.487391 + 0.873184i \(0.662051\pi\)
\(14\) 0 0
\(15\) 0.413878 0.106863
\(16\) 0 0
\(17\) −2.04345 −0.495611 −0.247805 0.968810i \(-0.579709\pi\)
−0.247805 + 0.968810i \(0.579709\pi\)
\(18\) 0 0
\(19\) 0.104243 0.0239150 0.0119575 0.999929i \(-0.496194\pi\)
0.0119575 + 0.999929i \(0.496194\pi\)
\(20\) 0 0
\(21\) 2.72537 0.594724
\(22\) 0 0
\(23\) −7.14941 −1.49075 −0.745377 0.666643i \(-0.767731\pi\)
−0.745377 + 0.666643i \(0.767731\pi\)
\(24\) 0 0
\(25\) −4.82870 −0.965741
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.94939 0.733383 0.366692 0.930343i \(-0.380490\pi\)
0.366692 + 0.930343i \(0.380490\pi\)
\(30\) 0 0
\(31\) −6.72301 −1.20749 −0.603744 0.797178i \(-0.706325\pi\)
−0.603744 + 0.797178i \(0.706325\pi\)
\(32\) 0 0
\(33\) −3.29320 −0.573273
\(34\) 0 0
\(35\) 1.12797 0.190662
\(36\) 0 0
\(37\) −11.8427 −1.94693 −0.973467 0.228828i \(-0.926511\pi\)
−0.973467 + 0.228828i \(0.926511\pi\)
\(38\) 0 0
\(39\) −3.51462 −0.562790
\(40\) 0 0
\(41\) 1.68403 0.263001 0.131500 0.991316i \(-0.458021\pi\)
0.131500 + 0.991316i \(0.458021\pi\)
\(42\) 0 0
\(43\) −3.25044 −0.495687 −0.247843 0.968800i \(-0.579722\pi\)
−0.247843 + 0.968800i \(0.579722\pi\)
\(44\) 0 0
\(45\) 0.413878 0.0616973
\(46\) 0 0
\(47\) −1.28674 −0.187691 −0.0938453 0.995587i \(-0.529916\pi\)
−0.0938453 + 0.995587i \(0.529916\pi\)
\(48\) 0 0
\(49\) 0.427633 0.0610904
\(50\) 0 0
\(51\) −2.04345 −0.286141
\(52\) 0 0
\(53\) −2.39006 −0.328300 −0.164150 0.986435i \(-0.552488\pi\)
−0.164150 + 0.986435i \(0.552488\pi\)
\(54\) 0 0
\(55\) −1.36298 −0.183785
\(56\) 0 0
\(57\) 0.104243 0.0138073
\(58\) 0 0
\(59\) 4.83514 0.629482 0.314741 0.949178i \(-0.398082\pi\)
0.314741 + 0.949178i \(0.398082\pi\)
\(60\) 0 0
\(61\) −0.869119 −0.111279 −0.0556397 0.998451i \(-0.517720\pi\)
−0.0556397 + 0.998451i \(0.517720\pi\)
\(62\) 0 0
\(63\) 2.72537 0.343364
\(64\) 0 0
\(65\) −1.45463 −0.180424
\(66\) 0 0
\(67\) 0.884563 0.108067 0.0540333 0.998539i \(-0.482792\pi\)
0.0540333 + 0.998539i \(0.482792\pi\)
\(68\) 0 0
\(69\) −7.14941 −0.860688
\(70\) 0 0
\(71\) 5.76105 0.683711 0.341856 0.939752i \(-0.388945\pi\)
0.341856 + 0.939752i \(0.388945\pi\)
\(72\) 0 0
\(73\) −9.55384 −1.11819 −0.559096 0.829103i \(-0.688852\pi\)
−0.559096 + 0.829103i \(0.688852\pi\)
\(74\) 0 0
\(75\) −4.82870 −0.557571
\(76\) 0 0
\(77\) −8.97519 −1.02282
\(78\) 0 0
\(79\) 8.30282 0.934140 0.467070 0.884220i \(-0.345310\pi\)
0.467070 + 0.884220i \(0.345310\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −9.73510 −1.06857 −0.534283 0.845306i \(-0.679418\pi\)
−0.534283 + 0.845306i \(0.679418\pi\)
\(84\) 0 0
\(85\) −0.845741 −0.0917335
\(86\) 0 0
\(87\) 3.94939 0.423419
\(88\) 0 0
\(89\) 15.7470 1.66917 0.834587 0.550876i \(-0.185706\pi\)
0.834587 + 0.550876i \(0.185706\pi\)
\(90\) 0 0
\(91\) −9.57864 −1.00411
\(92\) 0 0
\(93\) −6.72301 −0.697143
\(94\) 0 0
\(95\) 0.0431440 0.00442648
\(96\) 0 0
\(97\) −15.3694 −1.56052 −0.780262 0.625453i \(-0.784914\pi\)
−0.780262 + 0.625453i \(0.784914\pi\)
\(98\) 0 0
\(99\) −3.29320 −0.330979
\(100\) 0 0
\(101\) 14.3982 1.43268 0.716338 0.697753i \(-0.245817\pi\)
0.716338 + 0.697753i \(0.245817\pi\)
\(102\) 0 0
\(103\) −5.67716 −0.559387 −0.279693 0.960089i \(-0.590233\pi\)
−0.279693 + 0.960089i \(0.590233\pi\)
\(104\) 0 0
\(105\) 1.12797 0.110079
\(106\) 0 0
\(107\) −0.767992 −0.0742446 −0.0371223 0.999311i \(-0.511819\pi\)
−0.0371223 + 0.999311i \(0.511819\pi\)
\(108\) 0 0
\(109\) 4.64735 0.445136 0.222568 0.974917i \(-0.428556\pi\)
0.222568 + 0.974917i \(0.428556\pi\)
\(110\) 0 0
\(111\) −11.8427 −1.12406
\(112\) 0 0
\(113\) 19.5981 1.84364 0.921819 0.387621i \(-0.126703\pi\)
0.921819 + 0.387621i \(0.126703\pi\)
\(114\) 0 0
\(115\) −2.95898 −0.275927
\(116\) 0 0
\(117\) −3.51462 −0.324927
\(118\) 0 0
\(119\) −5.56917 −0.510525
\(120\) 0 0
\(121\) −0.154818 −0.0140744
\(122\) 0 0
\(123\) 1.68403 0.151844
\(124\) 0 0
\(125\) −4.06789 −0.363843
\(126\) 0 0
\(127\) −16.0424 −1.42353 −0.711766 0.702417i \(-0.752104\pi\)
−0.711766 + 0.702417i \(0.752104\pi\)
\(128\) 0 0
\(129\) −3.25044 −0.286185
\(130\) 0 0
\(131\) −5.16033 −0.450860 −0.225430 0.974259i \(-0.572379\pi\)
−0.225430 + 0.974259i \(0.572379\pi\)
\(132\) 0 0
\(133\) 0.284101 0.0246347
\(134\) 0 0
\(135\) 0.413878 0.0356210
\(136\) 0 0
\(137\) −9.88061 −0.844158 −0.422079 0.906559i \(-0.638699\pi\)
−0.422079 + 0.906559i \(0.638699\pi\)
\(138\) 0 0
\(139\) 17.9804 1.52508 0.762540 0.646941i \(-0.223952\pi\)
0.762540 + 0.646941i \(0.223952\pi\)
\(140\) 0 0
\(141\) −1.28674 −0.108363
\(142\) 0 0
\(143\) 11.5744 0.967897
\(144\) 0 0
\(145\) 1.63457 0.135743
\(146\) 0 0
\(147\) 0.427633 0.0352705
\(148\) 0 0
\(149\) 15.3576 1.25815 0.629073 0.777346i \(-0.283435\pi\)
0.629073 + 0.777346i \(0.283435\pi\)
\(150\) 0 0
\(151\) 12.7460 1.03725 0.518626 0.855001i \(-0.326444\pi\)
0.518626 + 0.855001i \(0.326444\pi\)
\(152\) 0 0
\(153\) −2.04345 −0.165204
\(154\) 0 0
\(155\) −2.78251 −0.223496
\(156\) 0 0
\(157\) 19.3249 1.54230 0.771148 0.636656i \(-0.219683\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(158\) 0 0
\(159\) −2.39006 −0.189544
\(160\) 0 0
\(161\) −19.4848 −1.53562
\(162\) 0 0
\(163\) 15.3454 1.20195 0.600973 0.799269i \(-0.294780\pi\)
0.600973 + 0.799269i \(0.294780\pi\)
\(164\) 0 0
\(165\) −1.36298 −0.106108
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −0.647425 −0.0498019
\(170\) 0 0
\(171\) 0.104243 0.00797167
\(172\) 0 0
\(173\) −3.18370 −0.242053 −0.121026 0.992649i \(-0.538619\pi\)
−0.121026 + 0.992649i \(0.538619\pi\)
\(174\) 0 0
\(175\) −13.1600 −0.994802
\(176\) 0 0
\(177\) 4.83514 0.363431
\(178\) 0 0
\(179\) −10.5301 −0.787058 −0.393529 0.919312i \(-0.628746\pi\)
−0.393529 + 0.919312i \(0.628746\pi\)
\(180\) 0 0
\(181\) 15.5951 1.15918 0.579588 0.814910i \(-0.303214\pi\)
0.579588 + 0.814910i \(0.303214\pi\)
\(182\) 0 0
\(183\) −0.869119 −0.0642471
\(184\) 0 0
\(185\) −4.90145 −0.360362
\(186\) 0 0
\(187\) 6.72951 0.492111
\(188\) 0 0
\(189\) 2.72537 0.198241
\(190\) 0 0
\(191\) −1.21547 −0.0879483 −0.0439741 0.999033i \(-0.514002\pi\)
−0.0439741 + 0.999033i \(0.514002\pi\)
\(192\) 0 0
\(193\) −1.45639 −0.104833 −0.0524165 0.998625i \(-0.516692\pi\)
−0.0524165 + 0.998625i \(0.516692\pi\)
\(194\) 0 0
\(195\) −1.45463 −0.104168
\(196\) 0 0
\(197\) −9.70373 −0.691362 −0.345681 0.938352i \(-0.612352\pi\)
−0.345681 + 0.938352i \(0.612352\pi\)
\(198\) 0 0
\(199\) −9.90201 −0.701935 −0.350967 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(200\) 0 0
\(201\) 0.884563 0.0623923
\(202\) 0 0
\(203\) 10.7635 0.755452
\(204\) 0 0
\(205\) 0.696982 0.0486794
\(206\) 0 0
\(207\) −7.14941 −0.496918
\(208\) 0 0
\(209\) −0.343294 −0.0237461
\(210\) 0 0
\(211\) −13.7202 −0.944536 −0.472268 0.881455i \(-0.656564\pi\)
−0.472268 + 0.881455i \(0.656564\pi\)
\(212\) 0 0
\(213\) 5.76105 0.394741
\(214\) 0 0
\(215\) −1.34528 −0.0917476
\(216\) 0 0
\(217\) −18.3227 −1.24382
\(218\) 0 0
\(219\) −9.55384 −0.645589
\(220\) 0 0
\(221\) 7.18197 0.483112
\(222\) 0 0
\(223\) −25.3126 −1.69505 −0.847527 0.530752i \(-0.821910\pi\)
−0.847527 + 0.530752i \(0.821910\pi\)
\(224\) 0 0
\(225\) −4.82870 −0.321914
\(226\) 0 0
\(227\) 12.8035 0.849799 0.424899 0.905241i \(-0.360309\pi\)
0.424899 + 0.905241i \(0.360309\pi\)
\(228\) 0 0
\(229\) 25.4832 1.68397 0.841987 0.539497i \(-0.181386\pi\)
0.841987 + 0.539497i \(0.181386\pi\)
\(230\) 0 0
\(231\) −8.97519 −0.590524
\(232\) 0 0
\(233\) 16.0993 1.05470 0.527351 0.849648i \(-0.323185\pi\)
0.527351 + 0.849648i \(0.323185\pi\)
\(234\) 0 0
\(235\) −0.532554 −0.0347400
\(236\) 0 0
\(237\) 8.30282 0.539326
\(238\) 0 0
\(239\) 1.30980 0.0847238 0.0423619 0.999102i \(-0.486512\pi\)
0.0423619 + 0.999102i \(0.486512\pi\)
\(240\) 0 0
\(241\) −9.56647 −0.616231 −0.308115 0.951349i \(-0.599698\pi\)
−0.308115 + 0.951349i \(0.599698\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.176988 0.0113073
\(246\) 0 0
\(247\) −0.366375 −0.0233119
\(248\) 0 0
\(249\) −9.73510 −0.616937
\(250\) 0 0
\(251\) −8.83575 −0.557707 −0.278854 0.960334i \(-0.589954\pi\)
−0.278854 + 0.960334i \(0.589954\pi\)
\(252\) 0 0
\(253\) 23.5445 1.48023
\(254\) 0 0
\(255\) −0.845741 −0.0529624
\(256\) 0 0
\(257\) −9.44156 −0.588949 −0.294474 0.955659i \(-0.595145\pi\)
−0.294474 + 0.955659i \(0.595145\pi\)
\(258\) 0 0
\(259\) −32.2758 −2.00552
\(260\) 0 0
\(261\) 3.94939 0.244461
\(262\) 0 0
\(263\) −16.1240 −0.994248 −0.497124 0.867680i \(-0.665611\pi\)
−0.497124 + 0.867680i \(0.665611\pi\)
\(264\) 0 0
\(265\) −0.989192 −0.0607656
\(266\) 0 0
\(267\) 15.7470 0.963698
\(268\) 0 0
\(269\) −8.94717 −0.545519 −0.272759 0.962082i \(-0.587936\pi\)
−0.272759 + 0.962082i \(0.587936\pi\)
\(270\) 0 0
\(271\) 1.65772 0.100699 0.0503496 0.998732i \(-0.483966\pi\)
0.0503496 + 0.998732i \(0.483966\pi\)
\(272\) 0 0
\(273\) −9.57864 −0.579726
\(274\) 0 0
\(275\) 15.9019 0.958921
\(276\) 0 0
\(277\) −24.8633 −1.49389 −0.746945 0.664885i \(-0.768480\pi\)
−0.746945 + 0.664885i \(0.768480\pi\)
\(278\) 0 0
\(279\) −6.72301 −0.402496
\(280\) 0 0
\(281\) 16.2065 0.966802 0.483401 0.875399i \(-0.339401\pi\)
0.483401 + 0.875399i \(0.339401\pi\)
\(282\) 0 0
\(283\) 1.21553 0.0722555 0.0361278 0.999347i \(-0.488498\pi\)
0.0361278 + 0.999347i \(0.488498\pi\)
\(284\) 0 0
\(285\) 0.0431440 0.00255563
\(286\) 0 0
\(287\) 4.58960 0.270915
\(288\) 0 0
\(289\) −12.8243 −0.754370
\(290\) 0 0
\(291\) −15.3694 −0.900969
\(292\) 0 0
\(293\) −9.99666 −0.584011 −0.292006 0.956417i \(-0.594323\pi\)
−0.292006 + 0.956417i \(0.594323\pi\)
\(294\) 0 0
\(295\) 2.00116 0.116512
\(296\) 0 0
\(297\) −3.29320 −0.191091
\(298\) 0 0
\(299\) 25.1275 1.45316
\(300\) 0 0
\(301\) −8.85863 −0.510603
\(302\) 0 0
\(303\) 14.3982 0.827156
\(304\) 0 0
\(305\) −0.359709 −0.0205969
\(306\) 0 0
\(307\) −1.87030 −0.106744 −0.0533720 0.998575i \(-0.516997\pi\)
−0.0533720 + 0.998575i \(0.516997\pi\)
\(308\) 0 0
\(309\) −5.67716 −0.322962
\(310\) 0 0
\(311\) −31.7848 −1.80235 −0.901175 0.433455i \(-0.857294\pi\)
−0.901175 + 0.433455i \(0.857294\pi\)
\(312\) 0 0
\(313\) 8.24201 0.465866 0.232933 0.972493i \(-0.425168\pi\)
0.232933 + 0.972493i \(0.425168\pi\)
\(314\) 0 0
\(315\) 1.12797 0.0635539
\(316\) 0 0
\(317\) −8.89475 −0.499579 −0.249789 0.968300i \(-0.580361\pi\)
−0.249789 + 0.968300i \(0.580361\pi\)
\(318\) 0 0
\(319\) −13.0061 −0.728204
\(320\) 0 0
\(321\) −0.767992 −0.0428652
\(322\) 0 0
\(323\) −0.213016 −0.0118525
\(324\) 0 0
\(325\) 16.9711 0.941386
\(326\) 0 0
\(327\) 4.64735 0.256999
\(328\) 0 0
\(329\) −3.50685 −0.193339
\(330\) 0 0
\(331\) −10.2141 −0.561417 −0.280708 0.959793i \(-0.590569\pi\)
−0.280708 + 0.959793i \(0.590569\pi\)
\(332\) 0 0
\(333\) −11.8427 −0.648978
\(334\) 0 0
\(335\) 0.366101 0.0200022
\(336\) 0 0
\(337\) 11.3679 0.619246 0.309623 0.950859i \(-0.399797\pi\)
0.309623 + 0.950859i \(0.399797\pi\)
\(338\) 0 0
\(339\) 19.5981 1.06442
\(340\) 0 0
\(341\) 22.1402 1.19896
\(342\) 0 0
\(343\) −17.9121 −0.967164
\(344\) 0 0
\(345\) −2.95898 −0.159306
\(346\) 0 0
\(347\) −5.88839 −0.316105 −0.158053 0.987431i \(-0.550522\pi\)
−0.158053 + 0.987431i \(0.550522\pi\)
\(348\) 0 0
\(349\) 6.42996 0.344188 0.172094 0.985081i \(-0.444947\pi\)
0.172094 + 0.985081i \(0.444947\pi\)
\(350\) 0 0
\(351\) −3.51462 −0.187597
\(352\) 0 0
\(353\) 27.5192 1.46470 0.732349 0.680929i \(-0.238424\pi\)
0.732349 + 0.680929i \(0.238424\pi\)
\(354\) 0 0
\(355\) 2.38437 0.126549
\(356\) 0 0
\(357\) −5.56917 −0.294752
\(358\) 0 0
\(359\) 11.3372 0.598354 0.299177 0.954198i \(-0.403288\pi\)
0.299177 + 0.954198i \(0.403288\pi\)
\(360\) 0 0
\(361\) −18.9891 −0.999428
\(362\) 0 0
\(363\) −0.154818 −0.00812583
\(364\) 0 0
\(365\) −3.95413 −0.206968
\(366\) 0 0
\(367\) −19.7364 −1.03023 −0.515116 0.857120i \(-0.672251\pi\)
−0.515116 + 0.857120i \(0.672251\pi\)
\(368\) 0 0
\(369\) 1.68403 0.0876670
\(370\) 0 0
\(371\) −6.51378 −0.338179
\(372\) 0 0
\(373\) −17.5585 −0.909143 −0.454571 0.890710i \(-0.650208\pi\)
−0.454571 + 0.890710i \(0.650208\pi\)
\(374\) 0 0
\(375\) −4.06789 −0.210065
\(376\) 0 0
\(377\) −13.8806 −0.714888
\(378\) 0 0
\(379\) −22.9151 −1.17707 −0.588535 0.808471i \(-0.700295\pi\)
−0.588535 + 0.808471i \(0.700295\pi\)
\(380\) 0 0
\(381\) −16.0424 −0.821876
\(382\) 0 0
\(383\) −29.0263 −1.48318 −0.741588 0.670856i \(-0.765927\pi\)
−0.741588 + 0.670856i \(0.765927\pi\)
\(384\) 0 0
\(385\) −3.71463 −0.189315
\(386\) 0 0
\(387\) −3.25044 −0.165229
\(388\) 0 0
\(389\) −17.6204 −0.893390 −0.446695 0.894686i \(-0.647399\pi\)
−0.446695 + 0.894686i \(0.647399\pi\)
\(390\) 0 0
\(391\) 14.6095 0.738834
\(392\) 0 0
\(393\) −5.16033 −0.260304
\(394\) 0 0
\(395\) 3.43635 0.172902
\(396\) 0 0
\(397\) 4.09900 0.205723 0.102862 0.994696i \(-0.467200\pi\)
0.102862 + 0.994696i \(0.467200\pi\)
\(398\) 0 0
\(399\) 0.284101 0.0142228
\(400\) 0 0
\(401\) 34.1968 1.70771 0.853855 0.520512i \(-0.174259\pi\)
0.853855 + 0.520512i \(0.174259\pi\)
\(402\) 0 0
\(403\) 23.6288 1.17704
\(404\) 0 0
\(405\) 0.413878 0.0205658
\(406\) 0 0
\(407\) 39.0005 1.93318
\(408\) 0 0
\(409\) 34.9430 1.72782 0.863911 0.503645i \(-0.168008\pi\)
0.863911 + 0.503645i \(0.168008\pi\)
\(410\) 0 0
\(411\) −9.88061 −0.487375
\(412\) 0 0
\(413\) 13.1775 0.648424
\(414\) 0 0
\(415\) −4.02914 −0.197783
\(416\) 0 0
\(417\) 17.9804 0.880506
\(418\) 0 0
\(419\) 10.1622 0.496456 0.248228 0.968702i \(-0.420152\pi\)
0.248228 + 0.968702i \(0.420152\pi\)
\(420\) 0 0
\(421\) 2.04565 0.0996988 0.0498494 0.998757i \(-0.484126\pi\)
0.0498494 + 0.998757i \(0.484126\pi\)
\(422\) 0 0
\(423\) −1.28674 −0.0625635
\(424\) 0 0
\(425\) 9.86724 0.478631
\(426\) 0 0
\(427\) −2.36867 −0.114628
\(428\) 0 0
\(429\) 11.5744 0.558816
\(430\) 0 0
\(431\) −35.7674 −1.72285 −0.861427 0.507881i \(-0.830429\pi\)
−0.861427 + 0.507881i \(0.830429\pi\)
\(432\) 0 0
\(433\) 1.18675 0.0570317 0.0285158 0.999593i \(-0.490922\pi\)
0.0285158 + 0.999593i \(0.490922\pi\)
\(434\) 0 0
\(435\) 1.63457 0.0783714
\(436\) 0 0
\(437\) −0.745277 −0.0356514
\(438\) 0 0
\(439\) −1.60398 −0.0765537 −0.0382768 0.999267i \(-0.512187\pi\)
−0.0382768 + 0.999267i \(0.512187\pi\)
\(440\) 0 0
\(441\) 0.427633 0.0203635
\(442\) 0 0
\(443\) −4.90700 −0.233139 −0.116569 0.993183i \(-0.537190\pi\)
−0.116569 + 0.993183i \(0.537190\pi\)
\(444\) 0 0
\(445\) 6.51732 0.308951
\(446\) 0 0
\(447\) 15.3576 0.726391
\(448\) 0 0
\(449\) 10.6462 0.502423 0.251212 0.967932i \(-0.419171\pi\)
0.251212 + 0.967932i \(0.419171\pi\)
\(450\) 0 0
\(451\) −5.54584 −0.261144
\(452\) 0 0
\(453\) 12.7460 0.598858
\(454\) 0 0
\(455\) −3.96439 −0.185854
\(456\) 0 0
\(457\) −1.35862 −0.0635535 −0.0317768 0.999495i \(-0.510117\pi\)
−0.0317768 + 0.999495i \(0.510117\pi\)
\(458\) 0 0
\(459\) −2.04345 −0.0953803
\(460\) 0 0
\(461\) −9.30249 −0.433260 −0.216630 0.976254i \(-0.569507\pi\)
−0.216630 + 0.976254i \(0.569507\pi\)
\(462\) 0 0
\(463\) −26.4887 −1.23103 −0.615517 0.788123i \(-0.711053\pi\)
−0.615517 + 0.788123i \(0.711053\pi\)
\(464\) 0 0
\(465\) −2.78251 −0.129036
\(466\) 0 0
\(467\) 13.3061 0.615731 0.307865 0.951430i \(-0.400385\pi\)
0.307865 + 0.951430i \(0.400385\pi\)
\(468\) 0 0
\(469\) 2.41076 0.111319
\(470\) 0 0
\(471\) 19.3249 0.890445
\(472\) 0 0
\(473\) 10.7043 0.492186
\(474\) 0 0
\(475\) −0.503359 −0.0230957
\(476\) 0 0
\(477\) −2.39006 −0.109433
\(478\) 0 0
\(479\) −32.2772 −1.47478 −0.737391 0.675467i \(-0.763942\pi\)
−0.737391 + 0.675467i \(0.763942\pi\)
\(480\) 0 0
\(481\) 41.6228 1.89783
\(482\) 0 0
\(483\) −19.4848 −0.886588
\(484\) 0 0
\(485\) −6.36105 −0.288840
\(486\) 0 0
\(487\) −22.2588 −1.00864 −0.504322 0.863516i \(-0.668257\pi\)
−0.504322 + 0.863516i \(0.668257\pi\)
\(488\) 0 0
\(489\) 15.3454 0.693944
\(490\) 0 0
\(491\) 8.40910 0.379497 0.189749 0.981833i \(-0.439233\pi\)
0.189749 + 0.981833i \(0.439233\pi\)
\(492\) 0 0
\(493\) −8.07040 −0.363472
\(494\) 0 0
\(495\) −1.36298 −0.0612616
\(496\) 0 0
\(497\) 15.7010 0.704286
\(498\) 0 0
\(499\) −2.47029 −0.110585 −0.0552927 0.998470i \(-0.517609\pi\)
−0.0552927 + 0.998470i \(0.517609\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 38.9349 1.73602 0.868011 0.496545i \(-0.165398\pi\)
0.868011 + 0.496545i \(0.165398\pi\)
\(504\) 0 0
\(505\) 5.95911 0.265177
\(506\) 0 0
\(507\) −0.647425 −0.0287532
\(508\) 0 0
\(509\) 22.0390 0.976864 0.488432 0.872602i \(-0.337569\pi\)
0.488432 + 0.872602i \(0.337569\pi\)
\(510\) 0 0
\(511\) −26.0377 −1.15184
\(512\) 0 0
\(513\) 0.104243 0.00460245
\(514\) 0 0
\(515\) −2.34965 −0.103538
\(516\) 0 0
\(517\) 4.23750 0.186365
\(518\) 0 0
\(519\) −3.18370 −0.139749
\(520\) 0 0
\(521\) −0.635065 −0.0278227 −0.0139114 0.999903i \(-0.504428\pi\)
−0.0139114 + 0.999903i \(0.504428\pi\)
\(522\) 0 0
\(523\) 29.1785 1.27589 0.637944 0.770083i \(-0.279785\pi\)
0.637944 + 0.770083i \(0.279785\pi\)
\(524\) 0 0
\(525\) −13.1600 −0.574349
\(526\) 0 0
\(527\) 13.7382 0.598444
\(528\) 0 0
\(529\) 28.1141 1.22235
\(530\) 0 0
\(531\) 4.83514 0.209827
\(532\) 0 0
\(533\) −5.91872 −0.256368
\(534\) 0 0
\(535\) −0.317855 −0.0137421
\(536\) 0 0
\(537\) −10.5301 −0.454408
\(538\) 0 0
\(539\) −1.40828 −0.0606590
\(540\) 0 0
\(541\) 35.8099 1.53959 0.769793 0.638294i \(-0.220359\pi\)
0.769793 + 0.638294i \(0.220359\pi\)
\(542\) 0 0
\(543\) 15.5951 0.669250
\(544\) 0 0
\(545\) 1.92344 0.0823910
\(546\) 0 0
\(547\) −22.1170 −0.945653 −0.472827 0.881156i \(-0.656766\pi\)
−0.472827 + 0.881156i \(0.656766\pi\)
\(548\) 0 0
\(549\) −0.869119 −0.0370931
\(550\) 0 0
\(551\) 0.411697 0.0175389
\(552\) 0 0
\(553\) 22.6282 0.962250
\(554\) 0 0
\(555\) −4.90145 −0.208055
\(556\) 0 0
\(557\) 38.9219 1.64917 0.824586 0.565737i \(-0.191408\pi\)
0.824586 + 0.565737i \(0.191408\pi\)
\(558\) 0 0
\(559\) 11.4241 0.483186
\(560\) 0 0
\(561\) 6.72951 0.284120
\(562\) 0 0
\(563\) 21.4736 0.905006 0.452503 0.891763i \(-0.350531\pi\)
0.452503 + 0.891763i \(0.350531\pi\)
\(564\) 0 0
\(565\) 8.11124 0.341242
\(566\) 0 0
\(567\) 2.72537 0.114455
\(568\) 0 0
\(569\) −24.5335 −1.02850 −0.514248 0.857642i \(-0.671929\pi\)
−0.514248 + 0.857642i \(0.671929\pi\)
\(570\) 0 0
\(571\) 37.9527 1.58827 0.794136 0.607740i \(-0.207924\pi\)
0.794136 + 0.607740i \(0.207924\pi\)
\(572\) 0 0
\(573\) −1.21547 −0.0507770
\(574\) 0 0
\(575\) 34.5224 1.43968
\(576\) 0 0
\(577\) 27.0677 1.12684 0.563421 0.826170i \(-0.309485\pi\)
0.563421 + 0.826170i \(0.309485\pi\)
\(578\) 0 0
\(579\) −1.45639 −0.0605253
\(580\) 0 0
\(581\) −26.5317 −1.10072
\(582\) 0 0
\(583\) 7.87094 0.325981
\(584\) 0 0
\(585\) −1.45463 −0.0601414
\(586\) 0 0
\(587\) −18.7964 −0.775812 −0.387906 0.921699i \(-0.626802\pi\)
−0.387906 + 0.921699i \(0.626802\pi\)
\(588\) 0 0
\(589\) −0.700827 −0.0288771
\(590\) 0 0
\(591\) −9.70373 −0.399158
\(592\) 0 0
\(593\) −34.2880 −1.40804 −0.704020 0.710180i \(-0.748614\pi\)
−0.704020 + 0.710180i \(0.748614\pi\)
\(594\) 0 0
\(595\) −2.30496 −0.0944940
\(596\) 0 0
\(597\) −9.90201 −0.405262
\(598\) 0 0
\(599\) −11.9335 −0.487592 −0.243796 0.969827i \(-0.578393\pi\)
−0.243796 + 0.969827i \(0.578393\pi\)
\(600\) 0 0
\(601\) −12.4330 −0.507152 −0.253576 0.967315i \(-0.581607\pi\)
−0.253576 + 0.967315i \(0.581607\pi\)
\(602\) 0 0
\(603\) 0.884563 0.0360222
\(604\) 0 0
\(605\) −0.0640758 −0.00260505
\(606\) 0 0
\(607\) −19.2350 −0.780726 −0.390363 0.920661i \(-0.627650\pi\)
−0.390363 + 0.920661i \(0.627650\pi\)
\(608\) 0 0
\(609\) 10.7635 0.436161
\(610\) 0 0
\(611\) 4.52241 0.182957
\(612\) 0 0
\(613\) −10.4268 −0.421135 −0.210568 0.977579i \(-0.567531\pi\)
−0.210568 + 0.977579i \(0.567531\pi\)
\(614\) 0 0
\(615\) 0.696982 0.0281050
\(616\) 0 0
\(617\) −20.7139 −0.833911 −0.416956 0.908927i \(-0.636903\pi\)
−0.416956 + 0.908927i \(0.636903\pi\)
\(618\) 0 0
\(619\) −2.86053 −0.114974 −0.0574871 0.998346i \(-0.518309\pi\)
−0.0574871 + 0.998346i \(0.518309\pi\)
\(620\) 0 0
\(621\) −7.14941 −0.286896
\(622\) 0 0
\(623\) 42.9163 1.71940
\(624\) 0 0
\(625\) 22.4599 0.898397
\(626\) 0 0
\(627\) −0.343294 −0.0137098
\(628\) 0 0
\(629\) 24.2001 0.964921
\(630\) 0 0
\(631\) 11.9113 0.474180 0.237090 0.971488i \(-0.423806\pi\)
0.237090 + 0.971488i \(0.423806\pi\)
\(632\) 0 0
\(633\) −13.7202 −0.545328
\(634\) 0 0
\(635\) −6.63959 −0.263484
\(636\) 0 0
\(637\) −1.50297 −0.0595497
\(638\) 0 0
\(639\) 5.76105 0.227904
\(640\) 0 0
\(641\) 13.2323 0.522644 0.261322 0.965252i \(-0.415842\pi\)
0.261322 + 0.965252i \(0.415842\pi\)
\(642\) 0 0
\(643\) −35.7086 −1.40821 −0.704105 0.710096i \(-0.748652\pi\)
−0.704105 + 0.710096i \(0.748652\pi\)
\(644\) 0 0
\(645\) −1.34528 −0.0529705
\(646\) 0 0
\(647\) −5.04495 −0.198337 −0.0991687 0.995071i \(-0.531618\pi\)
−0.0991687 + 0.995071i \(0.531618\pi\)
\(648\) 0 0
\(649\) −15.9231 −0.625036
\(650\) 0 0
\(651\) −18.3227 −0.718122
\(652\) 0 0
\(653\) −23.5847 −0.922939 −0.461470 0.887156i \(-0.652678\pi\)
−0.461470 + 0.887156i \(0.652678\pi\)
\(654\) 0 0
\(655\) −2.13575 −0.0834505
\(656\) 0 0
\(657\) −9.55384 −0.372731
\(658\) 0 0
\(659\) −17.3871 −0.677307 −0.338653 0.940911i \(-0.609971\pi\)
−0.338653 + 0.940911i \(0.609971\pi\)
\(660\) 0 0
\(661\) −35.6429 −1.38635 −0.693174 0.720770i \(-0.743788\pi\)
−0.693174 + 0.720770i \(0.743788\pi\)
\(662\) 0 0
\(663\) 7.18197 0.278925
\(664\) 0 0
\(665\) 0.117583 0.00455968
\(666\) 0 0
\(667\) −28.2358 −1.09329
\(668\) 0 0
\(669\) −25.3126 −0.978640
\(670\) 0 0
\(671\) 2.86219 0.110493
\(672\) 0 0
\(673\) 2.77695 0.107043 0.0535217 0.998567i \(-0.482955\pi\)
0.0535217 + 0.998567i \(0.482955\pi\)
\(674\) 0 0
\(675\) −4.82870 −0.185857
\(676\) 0 0
\(677\) 0.941133 0.0361707 0.0180853 0.999836i \(-0.494243\pi\)
0.0180853 + 0.999836i \(0.494243\pi\)
\(678\) 0 0
\(679\) −41.8872 −1.60748
\(680\) 0 0
\(681\) 12.8035 0.490632
\(682\) 0 0
\(683\) 17.2667 0.660693 0.330347 0.943860i \(-0.392834\pi\)
0.330347 + 0.943860i \(0.392834\pi\)
\(684\) 0 0
\(685\) −4.08937 −0.156247
\(686\) 0 0
\(687\) 25.4832 0.972243
\(688\) 0 0
\(689\) 8.40015 0.320020
\(690\) 0 0
\(691\) −21.2233 −0.807372 −0.403686 0.914898i \(-0.632271\pi\)
−0.403686 + 0.914898i \(0.632271\pi\)
\(692\) 0 0
\(693\) −8.97519 −0.340939
\(694\) 0 0
\(695\) 7.44171 0.282280
\(696\) 0 0
\(697\) −3.44123 −0.130346
\(698\) 0 0
\(699\) 16.0993 0.608932
\(700\) 0 0
\(701\) 11.1597 0.421496 0.210748 0.977540i \(-0.432410\pi\)
0.210748 + 0.977540i \(0.432410\pi\)
\(702\) 0 0
\(703\) −1.23452 −0.0465610
\(704\) 0 0
\(705\) −0.532554 −0.0200572
\(706\) 0 0
\(707\) 39.2405 1.47579
\(708\) 0 0
\(709\) −37.0151 −1.39013 −0.695066 0.718946i \(-0.744625\pi\)
−0.695066 + 0.718946i \(0.744625\pi\)
\(710\) 0 0
\(711\) 8.30282 0.311380
\(712\) 0 0
\(713\) 48.0655 1.80007
\(714\) 0 0
\(715\) 4.79038 0.179150
\(716\) 0 0
\(717\) 1.30980 0.0489153
\(718\) 0 0
\(719\) 18.2002 0.678754 0.339377 0.940650i \(-0.389784\pi\)
0.339377 + 0.940650i \(0.389784\pi\)
\(720\) 0 0
\(721\) −15.4723 −0.576220
\(722\) 0 0
\(723\) −9.56647 −0.355781
\(724\) 0 0
\(725\) −19.0704 −0.708258
\(726\) 0 0
\(727\) −13.9170 −0.516152 −0.258076 0.966125i \(-0.583088\pi\)
−0.258076 + 0.966125i \(0.583088\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 6.64212 0.245668
\(732\) 0 0
\(733\) 49.0066 1.81010 0.905050 0.425305i \(-0.139833\pi\)
0.905050 + 0.425305i \(0.139833\pi\)
\(734\) 0 0
\(735\) 0.176988 0.00652829
\(736\) 0 0
\(737\) −2.91304 −0.107303
\(738\) 0 0
\(739\) −7.12817 −0.262214 −0.131107 0.991368i \(-0.541853\pi\)
−0.131107 + 0.991368i \(0.541853\pi\)
\(740\) 0 0
\(741\) −0.366375 −0.0134591
\(742\) 0 0
\(743\) −12.4421 −0.456456 −0.228228 0.973608i \(-0.573293\pi\)
−0.228228 + 0.973608i \(0.573293\pi\)
\(744\) 0 0
\(745\) 6.35618 0.232873
\(746\) 0 0
\(747\) −9.73510 −0.356189
\(748\) 0 0
\(749\) −2.09306 −0.0764788
\(750\) 0 0
\(751\) −41.7220 −1.52246 −0.761228 0.648484i \(-0.775403\pi\)
−0.761228 + 0.648484i \(0.775403\pi\)
\(752\) 0 0
\(753\) −8.83575 −0.321992
\(754\) 0 0
\(755\) 5.27528 0.191987
\(756\) 0 0
\(757\) −38.0972 −1.38467 −0.692333 0.721578i \(-0.743417\pi\)
−0.692333 + 0.721578i \(0.743417\pi\)
\(758\) 0 0
\(759\) 23.5445 0.854610
\(760\) 0 0
\(761\) 24.5395 0.889556 0.444778 0.895641i \(-0.353283\pi\)
0.444778 + 0.895641i \(0.353283\pi\)
\(762\) 0 0
\(763\) 12.6657 0.458531
\(764\) 0 0
\(765\) −0.845741 −0.0305778
\(766\) 0 0
\(767\) −16.9937 −0.613607
\(768\) 0 0
\(769\) 51.4319 1.85468 0.927341 0.374218i \(-0.122089\pi\)
0.927341 + 0.374218i \(0.122089\pi\)
\(770\) 0 0
\(771\) −9.44156 −0.340030
\(772\) 0 0
\(773\) −6.41003 −0.230553 −0.115276 0.993333i \(-0.536775\pi\)
−0.115276 + 0.993333i \(0.536775\pi\)
\(774\) 0 0
\(775\) 32.4634 1.16612
\(776\) 0 0
\(777\) −32.2758 −1.15789
\(778\) 0 0
\(779\) 0.175548 0.00628967
\(780\) 0 0
\(781\) −18.9723 −0.678883
\(782\) 0 0
\(783\) 3.94939 0.141140
\(784\) 0 0
\(785\) 7.99816 0.285466
\(786\) 0 0
\(787\) 18.4276 0.656872 0.328436 0.944526i \(-0.393479\pi\)
0.328436 + 0.944526i \(0.393479\pi\)
\(788\) 0 0
\(789\) −16.1240 −0.574029
\(790\) 0 0
\(791\) 53.4121 1.89912
\(792\) 0 0
\(793\) 3.05463 0.108473
\(794\) 0 0
\(795\) −0.989192 −0.0350830
\(796\) 0 0
\(797\) −17.0923 −0.605439 −0.302720 0.953080i \(-0.597895\pi\)
−0.302720 + 0.953080i \(0.597895\pi\)
\(798\) 0 0
\(799\) 2.62940 0.0930214
\(800\) 0 0
\(801\) 15.7470 0.556391
\(802\) 0 0
\(803\) 31.4627 1.11030
\(804\) 0 0
\(805\) −8.06432 −0.284230
\(806\) 0 0
\(807\) −8.94717 −0.314955
\(808\) 0 0
\(809\) 45.7133 1.60720 0.803598 0.595173i \(-0.202916\pi\)
0.803598 + 0.595173i \(0.202916\pi\)
\(810\) 0 0
\(811\) −36.5328 −1.28284 −0.641419 0.767190i \(-0.721654\pi\)
−0.641419 + 0.767190i \(0.721654\pi\)
\(812\) 0 0
\(813\) 1.65772 0.0581387
\(814\) 0 0
\(815\) 6.35113 0.222470
\(816\) 0 0
\(817\) −0.338836 −0.0118544
\(818\) 0 0
\(819\) −9.57864 −0.334705
\(820\) 0 0
\(821\) 21.0829 0.735797 0.367898 0.929866i \(-0.380077\pi\)
0.367898 + 0.929866i \(0.380077\pi\)
\(822\) 0 0
\(823\) −3.25974 −0.113627 −0.0568137 0.998385i \(-0.518094\pi\)
−0.0568137 + 0.998385i \(0.518094\pi\)
\(824\) 0 0
\(825\) 15.9019 0.553633
\(826\) 0 0
\(827\) 37.0262 1.28753 0.643764 0.765224i \(-0.277372\pi\)
0.643764 + 0.765224i \(0.277372\pi\)
\(828\) 0 0
\(829\) −38.6796 −1.34340 −0.671698 0.740825i \(-0.734435\pi\)
−0.671698 + 0.740825i \(0.734435\pi\)
\(830\) 0 0
\(831\) −24.8633 −0.862498
\(832\) 0 0
\(833\) −0.873848 −0.0302770
\(834\) 0 0
\(835\) −0.413878 −0.0143228
\(836\) 0 0
\(837\) −6.72301 −0.232381
\(838\) 0 0
\(839\) −30.1061 −1.03938 −0.519690 0.854355i \(-0.673952\pi\)
−0.519690 + 0.854355i \(0.673952\pi\)
\(840\) 0 0
\(841\) −13.4023 −0.462149
\(842\) 0 0
\(843\) 16.2065 0.558183
\(844\) 0 0
\(845\) −0.267955 −0.00921794
\(846\) 0 0
\(847\) −0.421936 −0.0144979
\(848\) 0 0
\(849\) 1.21553 0.0417168
\(850\) 0 0
\(851\) 84.6686 2.90240
\(852\) 0 0
\(853\) 31.8542 1.09067 0.545334 0.838219i \(-0.316403\pi\)
0.545334 + 0.838219i \(0.316403\pi\)
\(854\) 0 0
\(855\) 0.0431440 0.00147549
\(856\) 0 0
\(857\) 37.0715 1.26634 0.633170 0.774013i \(-0.281754\pi\)
0.633170 + 0.774013i \(0.281754\pi\)
\(858\) 0 0
\(859\) 16.9884 0.579638 0.289819 0.957081i \(-0.406405\pi\)
0.289819 + 0.957081i \(0.406405\pi\)
\(860\) 0 0
\(861\) 4.58960 0.156413
\(862\) 0 0
\(863\) −37.9003 −1.29014 −0.645071 0.764123i \(-0.723172\pi\)
−0.645071 + 0.764123i \(0.723172\pi\)
\(864\) 0 0
\(865\) −1.31767 −0.0448020
\(866\) 0 0
\(867\) −12.8243 −0.435536
\(868\) 0 0
\(869\) −27.3429 −0.927543
\(870\) 0 0
\(871\) −3.10891 −0.105341
\(872\) 0 0
\(873\) −15.3694 −0.520175
\(874\) 0 0
\(875\) −11.0865 −0.374792
\(876\) 0 0
\(877\) 18.4949 0.624529 0.312265 0.949995i \(-0.398912\pi\)
0.312265 + 0.949995i \(0.398912\pi\)
\(878\) 0 0
\(879\) −9.99666 −0.337179
\(880\) 0 0
\(881\) −27.6699 −0.932223 −0.466111 0.884726i \(-0.654345\pi\)
−0.466111 + 0.884726i \(0.654345\pi\)
\(882\) 0 0
\(883\) 12.2872 0.413499 0.206749 0.978394i \(-0.433712\pi\)
0.206749 + 0.978394i \(0.433712\pi\)
\(884\) 0 0
\(885\) 2.00116 0.0672682
\(886\) 0 0
\(887\) 46.6301 1.56569 0.782843 0.622219i \(-0.213769\pi\)
0.782843 + 0.622219i \(0.213769\pi\)
\(888\) 0 0
\(889\) −43.7214 −1.46637
\(890\) 0 0
\(891\) −3.29320 −0.110326
\(892\) 0 0
\(893\) −0.134134 −0.00448862
\(894\) 0 0
\(895\) −4.35819 −0.145678
\(896\) 0 0
\(897\) 25.1275 0.838982
\(898\) 0 0
\(899\) −26.5518 −0.885551
\(900\) 0 0
\(901\) 4.88397 0.162709
\(902\) 0 0
\(903\) −8.85863 −0.294797
\(904\) 0 0
\(905\) 6.45448 0.214554
\(906\) 0 0
\(907\) 21.8370 0.725084 0.362542 0.931967i \(-0.381909\pi\)
0.362542 + 0.931967i \(0.381909\pi\)
\(908\) 0 0
\(909\) 14.3982 0.477559
\(910\) 0 0
\(911\) 23.8654 0.790698 0.395349 0.918531i \(-0.370624\pi\)
0.395349 + 0.918531i \(0.370624\pi\)
\(912\) 0 0
\(913\) 32.0597 1.06102
\(914\) 0 0
\(915\) −0.359709 −0.0118916
\(916\) 0 0
\(917\) −14.0638 −0.464427
\(918\) 0 0
\(919\) 12.8967 0.425422 0.212711 0.977115i \(-0.431771\pi\)
0.212711 + 0.977115i \(0.431771\pi\)
\(920\) 0 0
\(921\) −1.87030 −0.0616286
\(922\) 0 0
\(923\) −20.2479 −0.666469
\(924\) 0 0
\(925\) 57.1851 1.88023
\(926\) 0 0
\(927\) −5.67716 −0.186462
\(928\) 0 0
\(929\) 28.1515 0.923621 0.461810 0.886979i \(-0.347200\pi\)
0.461810 + 0.886979i \(0.347200\pi\)
\(930\) 0 0
\(931\) 0.0445778 0.00146098
\(932\) 0 0
\(933\) −31.7848 −1.04059
\(934\) 0 0
\(935\) 2.78520 0.0910857
\(936\) 0 0
\(937\) −42.3504 −1.38353 −0.691764 0.722124i \(-0.743166\pi\)
−0.691764 + 0.722124i \(0.743166\pi\)
\(938\) 0 0
\(939\) 8.24201 0.268968
\(940\) 0 0
\(941\) −54.5165 −1.77719 −0.888593 0.458696i \(-0.848317\pi\)
−0.888593 + 0.458696i \(0.848317\pi\)
\(942\) 0 0
\(943\) −12.0398 −0.392070
\(944\) 0 0
\(945\) 1.12797 0.0366929
\(946\) 0 0
\(947\) 2.10003 0.0682417 0.0341209 0.999418i \(-0.489137\pi\)
0.0341209 + 0.999418i \(0.489137\pi\)
\(948\) 0 0
\(949\) 33.5782 1.08999
\(950\) 0 0
\(951\) −8.89475 −0.288432
\(952\) 0 0
\(953\) 35.3650 1.14559 0.572793 0.819700i \(-0.305860\pi\)
0.572793 + 0.819700i \(0.305860\pi\)
\(954\) 0 0
\(955\) −0.503056 −0.0162785
\(956\) 0 0
\(957\) −13.0061 −0.420429
\(958\) 0 0
\(959\) −26.9283 −0.869560
\(960\) 0 0
\(961\) 14.1988 0.458027
\(962\) 0 0
\(963\) −0.767992 −0.0247482
\(964\) 0 0
\(965\) −0.602766 −0.0194037
\(966\) 0 0
\(967\) 46.6270 1.49942 0.749712 0.661764i \(-0.230192\pi\)
0.749712 + 0.661764i \(0.230192\pi\)
\(968\) 0 0
\(969\) −0.213016 −0.00684306
\(970\) 0 0
\(971\) 9.30578 0.298637 0.149318 0.988789i \(-0.452292\pi\)
0.149318 + 0.988789i \(0.452292\pi\)
\(972\) 0 0
\(973\) 49.0033 1.57097
\(974\) 0 0
\(975\) 16.9711 0.543509
\(976\) 0 0
\(977\) −13.0655 −0.418001 −0.209001 0.977915i \(-0.567021\pi\)
−0.209001 + 0.977915i \(0.567021\pi\)
\(978\) 0 0
\(979\) −51.8579 −1.65739
\(980\) 0 0
\(981\) 4.64735 0.148379
\(982\) 0 0
\(983\) 7.31552 0.233329 0.116664 0.993171i \(-0.462780\pi\)
0.116664 + 0.993171i \(0.462780\pi\)
\(984\) 0 0
\(985\) −4.01616 −0.127966
\(986\) 0 0
\(987\) −3.50685 −0.111624
\(988\) 0 0
\(989\) 23.2387 0.738947
\(990\) 0 0
\(991\) −25.7439 −0.817782 −0.408891 0.912583i \(-0.634084\pi\)
−0.408891 + 0.912583i \(0.634084\pi\)
\(992\) 0 0
\(993\) −10.2141 −0.324134
\(994\) 0 0
\(995\) −4.09823 −0.129922
\(996\) 0 0
\(997\) 39.6667 1.25626 0.628129 0.778109i \(-0.283821\pi\)
0.628129 + 0.778109i \(0.283821\pi\)
\(998\) 0 0
\(999\) −11.8427 −0.374688
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 \(a_p\))