Properties

Label 6040.2.a.l.1.7
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 1.7
Root \(0.289144\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.17504 q^{3}\) \(+1.00000 q^{5}\) \(-3.16934 q^{7}\) \(-1.61928 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.17504 q^{3}\) \(+1.00000 q^{5}\) \(-3.16934 q^{7}\) \(-1.61928 q^{9}\) \(-0.427027 q^{11}\) \(+0.986358 q^{13}\) \(+1.17504 q^{15}\) \(+2.72436 q^{17}\) \(-1.41788 q^{19}\) \(-3.72410 q^{21}\) \(+6.25478 q^{23}\) \(+1.00000 q^{25}\) \(-5.42784 q^{27}\) \(+1.45051 q^{29}\) \(+0.966761 q^{31}\) \(-0.501774 q^{33}\) \(-3.16934 q^{35}\) \(-7.21828 q^{37}\) \(+1.15901 q^{39}\) \(-10.4859 q^{41}\) \(+9.12613 q^{43}\) \(-1.61928 q^{45}\) \(-12.8071 q^{47}\) \(+3.04470 q^{49}\) \(+3.20123 q^{51}\) \(-3.99178 q^{53}\) \(-0.427027 q^{55}\) \(-1.66607 q^{57}\) \(-0.170213 q^{59}\) \(-0.957779 q^{61}\) \(+5.13204 q^{63}\) \(+0.986358 q^{65}\) \(+1.61642 q^{67}\) \(+7.34963 q^{69}\) \(+7.83411 q^{71}\) \(-11.4466 q^{73}\) \(+1.17504 q^{75}\) \(+1.35339 q^{77}\) \(+3.09972 q^{79}\) \(-1.52011 q^{81}\) \(+6.07419 q^{83}\) \(+2.72436 q^{85}\) \(+1.70441 q^{87}\) \(+5.74911 q^{89}\) \(-3.12610 q^{91}\) \(+1.13598 q^{93}\) \(-1.41788 q^{95}\) \(-5.12793 q^{97}\) \(+0.691475 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.17504 0.678410 0.339205 0.940712i \(-0.389842\pi\)
0.339205 + 0.940712i \(0.389842\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −3.16934 −1.19790 −0.598949 0.800787i \(-0.704415\pi\)
−0.598949 + 0.800787i \(0.704415\pi\)
\(8\) 0 0
\(9\) −1.61928 −0.539759
\(10\) 0 0
\(11\) −0.427027 −0.128753 −0.0643767 0.997926i \(-0.520506\pi\)
−0.0643767 + 0.997926i \(0.520506\pi\)
\(12\) 0 0
\(13\) 0.986358 0.273566 0.136783 0.990601i \(-0.456324\pi\)
0.136783 + 0.990601i \(0.456324\pi\)
\(14\) 0 0
\(15\) 1.17504 0.303394
\(16\) 0 0
\(17\) 2.72436 0.660754 0.330377 0.943849i \(-0.392824\pi\)
0.330377 + 0.943849i \(0.392824\pi\)
\(18\) 0 0
\(19\) −1.41788 −0.325284 −0.162642 0.986685i \(-0.552002\pi\)
−0.162642 + 0.986685i \(0.552002\pi\)
\(20\) 0 0
\(21\) −3.72410 −0.812666
\(22\) 0 0
\(23\) 6.25478 1.30421 0.652106 0.758128i \(-0.273886\pi\)
0.652106 + 0.758128i \(0.273886\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.42784 −1.04459
\(28\) 0 0
\(29\) 1.45051 0.269353 0.134676 0.990890i \(-0.457001\pi\)
0.134676 + 0.990890i \(0.457001\pi\)
\(30\) 0 0
\(31\) 0.966761 0.173635 0.0868177 0.996224i \(-0.472330\pi\)
0.0868177 + 0.996224i \(0.472330\pi\)
\(32\) 0 0
\(33\) −0.501774 −0.0873477
\(34\) 0 0
\(35\) −3.16934 −0.535716
\(36\) 0 0
\(37\) −7.21828 −1.18668 −0.593339 0.804952i \(-0.702191\pi\)
−0.593339 + 0.804952i \(0.702191\pi\)
\(38\) 0 0
\(39\) 1.15901 0.185590
\(40\) 0 0
\(41\) −10.4859 −1.63763 −0.818813 0.574061i \(-0.805367\pi\)
−0.818813 + 0.574061i \(0.805367\pi\)
\(42\) 0 0
\(43\) 9.12613 1.39172 0.695861 0.718176i \(-0.255023\pi\)
0.695861 + 0.718176i \(0.255023\pi\)
\(44\) 0 0
\(45\) −1.61928 −0.241388
\(46\) 0 0
\(47\) −12.8071 −1.86811 −0.934056 0.357126i \(-0.883757\pi\)
−0.934056 + 0.357126i \(0.883757\pi\)
\(48\) 0 0
\(49\) 3.04470 0.434958
\(50\) 0 0
\(51\) 3.20123 0.448262
\(52\) 0 0
\(53\) −3.99178 −0.548312 −0.274156 0.961685i \(-0.588399\pi\)
−0.274156 + 0.961685i \(0.588399\pi\)
\(54\) 0 0
\(55\) −0.427027 −0.0575803
\(56\) 0 0
\(57\) −1.66607 −0.220676
\(58\) 0 0
\(59\) −0.170213 −0.0221598 −0.0110799 0.999939i \(-0.503527\pi\)
−0.0110799 + 0.999939i \(0.503527\pi\)
\(60\) 0 0
\(61\) −0.957779 −0.122631 −0.0613155 0.998118i \(-0.519530\pi\)
−0.0613155 + 0.998118i \(0.519530\pi\)
\(62\) 0 0
\(63\) 5.13204 0.646576
\(64\) 0 0
\(65\) 0.986358 0.122343
\(66\) 0 0
\(67\) 1.61642 0.197477 0.0987386 0.995113i \(-0.468519\pi\)
0.0987386 + 0.995113i \(0.468519\pi\)
\(68\) 0 0
\(69\) 7.34963 0.884791
\(70\) 0 0
\(71\) 7.83411 0.929738 0.464869 0.885380i \(-0.346101\pi\)
0.464869 + 0.885380i \(0.346101\pi\)
\(72\) 0 0
\(73\) −11.4466 −1.33972 −0.669862 0.742485i \(-0.733647\pi\)
−0.669862 + 0.742485i \(0.733647\pi\)
\(74\) 0 0
\(75\) 1.17504 0.135682
\(76\) 0 0
\(77\) 1.35339 0.154233
\(78\) 0 0
\(79\) 3.09972 0.348746 0.174373 0.984680i \(-0.444210\pi\)
0.174373 + 0.984680i \(0.444210\pi\)
\(80\) 0 0
\(81\) −1.52011 −0.168901
\(82\) 0 0
\(83\) 6.07419 0.666729 0.333364 0.942798i \(-0.391816\pi\)
0.333364 + 0.942798i \(0.391816\pi\)
\(84\) 0 0
\(85\) 2.72436 0.295498
\(86\) 0 0
\(87\) 1.70441 0.182732
\(88\) 0 0
\(89\) 5.74911 0.609404 0.304702 0.952448i \(-0.401443\pi\)
0.304702 + 0.952448i \(0.401443\pi\)
\(90\) 0 0
\(91\) −3.12610 −0.327704
\(92\) 0 0
\(93\) 1.13598 0.117796
\(94\) 0 0
\(95\) −1.41788 −0.145472
\(96\) 0 0
\(97\) −5.12793 −0.520663 −0.260331 0.965519i \(-0.583832\pi\)
−0.260331 + 0.965519i \(0.583832\pi\)
\(98\) 0 0
\(99\) 0.691475 0.0694958
\(100\) 0 0
\(101\) −5.85485 −0.582579 −0.291290 0.956635i \(-0.594084\pi\)
−0.291290 + 0.956635i \(0.594084\pi\)
\(102\) 0 0
\(103\) −10.7737 −1.06156 −0.530780 0.847509i \(-0.678101\pi\)
−0.530780 + 0.847509i \(0.678101\pi\)
\(104\) 0 0
\(105\) −3.72410 −0.363435
\(106\) 0 0
\(107\) −14.0100 −1.35439 −0.677197 0.735802i \(-0.736805\pi\)
−0.677197 + 0.735802i \(0.736805\pi\)
\(108\) 0 0
\(109\) −6.17284 −0.591251 −0.295625 0.955304i \(-0.595528\pi\)
−0.295625 + 0.955304i \(0.595528\pi\)
\(110\) 0 0
\(111\) −8.48178 −0.805055
\(112\) 0 0
\(113\) −9.37358 −0.881792 −0.440896 0.897558i \(-0.645339\pi\)
−0.440896 + 0.897558i \(0.645339\pi\)
\(114\) 0 0
\(115\) 6.25478 0.583262
\(116\) 0 0
\(117\) −1.59719 −0.147660
\(118\) 0 0
\(119\) −8.63441 −0.791515
\(120\) 0 0
\(121\) −10.8176 −0.983423
\(122\) 0 0
\(123\) −12.3214 −1.11098
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.60784 −0.408880 −0.204440 0.978879i \(-0.565537\pi\)
−0.204440 + 0.978879i \(0.565537\pi\)
\(128\) 0 0
\(129\) 10.7236 0.944159
\(130\) 0 0
\(131\) 13.2285 1.15578 0.577889 0.816116i \(-0.303877\pi\)
0.577889 + 0.816116i \(0.303877\pi\)
\(132\) 0 0
\(133\) 4.49374 0.389657
\(134\) 0 0
\(135\) −5.42784 −0.467154
\(136\) 0 0
\(137\) −1.13567 −0.0970272 −0.0485136 0.998823i \(-0.515448\pi\)
−0.0485136 + 0.998823i \(0.515448\pi\)
\(138\) 0 0
\(139\) −13.0821 −1.10961 −0.554804 0.831981i \(-0.687207\pi\)
−0.554804 + 0.831981i \(0.687207\pi\)
\(140\) 0 0
\(141\) −15.0489 −1.26735
\(142\) 0 0
\(143\) −0.421201 −0.0352226
\(144\) 0 0
\(145\) 1.45051 0.120458
\(146\) 0 0
\(147\) 3.57765 0.295080
\(148\) 0 0
\(149\) −9.90859 −0.811744 −0.405872 0.913930i \(-0.633032\pi\)
−0.405872 + 0.913930i \(0.633032\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −4.41149 −0.356648
\(154\) 0 0
\(155\) 0.966761 0.0776521
\(156\) 0 0
\(157\) −5.25629 −0.419497 −0.209749 0.977755i \(-0.567265\pi\)
−0.209749 + 0.977755i \(0.567265\pi\)
\(158\) 0 0
\(159\) −4.69050 −0.371981
\(160\) 0 0
\(161\) −19.8235 −1.56231
\(162\) 0 0
\(163\) −19.8537 −1.55506 −0.777532 0.628843i \(-0.783529\pi\)
−0.777532 + 0.628843i \(0.783529\pi\)
\(164\) 0 0
\(165\) −0.501774 −0.0390631
\(166\) 0 0
\(167\) 19.6267 1.51876 0.759382 0.650645i \(-0.225502\pi\)
0.759382 + 0.650645i \(0.225502\pi\)
\(168\) 0 0
\(169\) −12.0271 −0.925161
\(170\) 0 0
\(171\) 2.29594 0.175575
\(172\) 0 0
\(173\) −12.1620 −0.924658 −0.462329 0.886708i \(-0.652986\pi\)
−0.462329 + 0.886708i \(0.652986\pi\)
\(174\) 0 0
\(175\) −3.16934 −0.239579
\(176\) 0 0
\(177\) −0.200007 −0.0150334
\(178\) 0 0
\(179\) 24.8680 1.85872 0.929362 0.369169i \(-0.120358\pi\)
0.929362 + 0.369169i \(0.120358\pi\)
\(180\) 0 0
\(181\) 4.91718 0.365491 0.182746 0.983160i \(-0.441502\pi\)
0.182746 + 0.983160i \(0.441502\pi\)
\(182\) 0 0
\(183\) −1.12543 −0.0831942
\(184\) 0 0
\(185\) −7.21828 −0.530699
\(186\) 0 0
\(187\) −1.16337 −0.0850743
\(188\) 0 0
\(189\) 17.2027 1.25131
\(190\) 0 0
\(191\) −8.85924 −0.641032 −0.320516 0.947243i \(-0.603856\pi\)
−0.320516 + 0.947243i \(0.603856\pi\)
\(192\) 0 0
\(193\) 15.4026 1.10870 0.554352 0.832282i \(-0.312966\pi\)
0.554352 + 0.832282i \(0.312966\pi\)
\(194\) 0 0
\(195\) 1.15901 0.0829985
\(196\) 0 0
\(197\) 2.98189 0.212451 0.106225 0.994342i \(-0.466123\pi\)
0.106225 + 0.994342i \(0.466123\pi\)
\(198\) 0 0
\(199\) 0.598893 0.0424544 0.0212272 0.999775i \(-0.493243\pi\)
0.0212272 + 0.999775i \(0.493243\pi\)
\(200\) 0 0
\(201\) 1.89936 0.133971
\(202\) 0 0
\(203\) −4.59715 −0.322657
\(204\) 0 0
\(205\) −10.4859 −0.732368
\(206\) 0 0
\(207\) −10.1282 −0.703961
\(208\) 0 0
\(209\) 0.605473 0.0418815
\(210\) 0 0
\(211\) −24.9124 −1.71504 −0.857520 0.514450i \(-0.827996\pi\)
−0.857520 + 0.514450i \(0.827996\pi\)
\(212\) 0 0
\(213\) 9.20540 0.630744
\(214\) 0 0
\(215\) 9.12613 0.622397
\(216\) 0 0
\(217\) −3.06399 −0.207997
\(218\) 0 0
\(219\) −13.4502 −0.908883
\(220\) 0 0
\(221\) 2.68719 0.180760
\(222\) 0 0
\(223\) 5.18089 0.346938 0.173469 0.984839i \(-0.444502\pi\)
0.173469 + 0.984839i \(0.444502\pi\)
\(224\) 0 0
\(225\) −1.61928 −0.107952
\(226\) 0 0
\(227\) −17.7665 −1.17921 −0.589603 0.807693i \(-0.700716\pi\)
−0.589603 + 0.807693i \(0.700716\pi\)
\(228\) 0 0
\(229\) −26.3735 −1.74281 −0.871404 0.490565i \(-0.836790\pi\)
−0.871404 + 0.490565i \(0.836790\pi\)
\(230\) 0 0
\(231\) 1.59029 0.104634
\(232\) 0 0
\(233\) 1.67310 0.109609 0.0548043 0.998497i \(-0.482547\pi\)
0.0548043 + 0.998497i \(0.482547\pi\)
\(234\) 0 0
\(235\) −12.8071 −0.835445
\(236\) 0 0
\(237\) 3.64230 0.236593
\(238\) 0 0
\(239\) −11.3808 −0.736163 −0.368082 0.929793i \(-0.619985\pi\)
−0.368082 + 0.929793i \(0.619985\pi\)
\(240\) 0 0
\(241\) −20.7998 −1.33983 −0.669916 0.742437i \(-0.733670\pi\)
−0.669916 + 0.742437i \(0.733670\pi\)
\(242\) 0 0
\(243\) 14.4973 0.930005
\(244\) 0 0
\(245\) 3.04470 0.194519
\(246\) 0 0
\(247\) −1.39854 −0.0889869
\(248\) 0 0
\(249\) 7.13742 0.452316
\(250\) 0 0
\(251\) −9.71231 −0.613035 −0.306518 0.951865i \(-0.599164\pi\)
−0.306518 + 0.951865i \(0.599164\pi\)
\(252\) 0 0
\(253\) −2.67096 −0.167922
\(254\) 0 0
\(255\) 3.20123 0.200469
\(256\) 0 0
\(257\) 8.95226 0.558427 0.279213 0.960229i \(-0.409926\pi\)
0.279213 + 0.960229i \(0.409926\pi\)
\(258\) 0 0
\(259\) 22.8772 1.42152
\(260\) 0 0
\(261\) −2.34878 −0.145386
\(262\) 0 0
\(263\) −3.37823 −0.208311 −0.104155 0.994561i \(-0.533214\pi\)
−0.104155 + 0.994561i \(0.533214\pi\)
\(264\) 0 0
\(265\) −3.99178 −0.245213
\(266\) 0 0
\(267\) 6.75544 0.413426
\(268\) 0 0
\(269\) 5.67714 0.346142 0.173071 0.984909i \(-0.444631\pi\)
0.173071 + 0.984909i \(0.444631\pi\)
\(270\) 0 0
\(271\) 24.9587 1.51613 0.758066 0.652178i \(-0.226145\pi\)
0.758066 + 0.652178i \(0.226145\pi\)
\(272\) 0 0
\(273\) −3.67330 −0.222318
\(274\) 0 0
\(275\) −0.427027 −0.0257507
\(276\) 0 0
\(277\) 6.13041 0.368341 0.184170 0.982894i \(-0.441040\pi\)
0.184170 + 0.982894i \(0.441040\pi\)
\(278\) 0 0
\(279\) −1.56545 −0.0937213
\(280\) 0 0
\(281\) 21.8729 1.30483 0.652414 0.757863i \(-0.273756\pi\)
0.652414 + 0.757863i \(0.273756\pi\)
\(282\) 0 0
\(283\) −1.01538 −0.0603580 −0.0301790 0.999545i \(-0.509608\pi\)
−0.0301790 + 0.999545i \(0.509608\pi\)
\(284\) 0 0
\(285\) −1.66607 −0.0986894
\(286\) 0 0
\(287\) 33.2334 1.96171
\(288\) 0 0
\(289\) −9.57788 −0.563405
\(290\) 0 0
\(291\) −6.02553 −0.353223
\(292\) 0 0
\(293\) 5.11293 0.298700 0.149350 0.988784i \(-0.452282\pi\)
0.149350 + 0.988784i \(0.452282\pi\)
\(294\) 0 0
\(295\) −0.170213 −0.00991016
\(296\) 0 0
\(297\) 2.31783 0.134494
\(298\) 0 0
\(299\) 6.16945 0.356789
\(300\) 0 0
\(301\) −28.9238 −1.66714
\(302\) 0 0
\(303\) −6.87969 −0.395228
\(304\) 0 0
\(305\) −0.957779 −0.0548423
\(306\) 0 0
\(307\) 8.89561 0.507699 0.253850 0.967244i \(-0.418303\pi\)
0.253850 + 0.967244i \(0.418303\pi\)
\(308\) 0 0
\(309\) −12.6595 −0.720174
\(310\) 0 0
\(311\) −12.0643 −0.684103 −0.342052 0.939681i \(-0.611122\pi\)
−0.342052 + 0.939681i \(0.611122\pi\)
\(312\) 0 0
\(313\) −0.387425 −0.0218986 −0.0109493 0.999940i \(-0.503485\pi\)
−0.0109493 + 0.999940i \(0.503485\pi\)
\(314\) 0 0
\(315\) 5.13204 0.289158
\(316\) 0 0
\(317\) −11.1148 −0.624270 −0.312135 0.950038i \(-0.601044\pi\)
−0.312135 + 0.950038i \(0.601044\pi\)
\(318\) 0 0
\(319\) −0.619406 −0.0346801
\(320\) 0 0
\(321\) −16.4623 −0.918835
\(322\) 0 0
\(323\) −3.86281 −0.214933
\(324\) 0 0
\(325\) 0.986358 0.0547133
\(326\) 0 0
\(327\) −7.25334 −0.401111
\(328\) 0 0
\(329\) 40.5901 2.23781
\(330\) 0 0
\(331\) −9.10033 −0.500200 −0.250100 0.968220i \(-0.580463\pi\)
−0.250100 + 0.968220i \(0.580463\pi\)
\(332\) 0 0
\(333\) 11.6884 0.640521
\(334\) 0 0
\(335\) 1.61642 0.0883145
\(336\) 0 0
\(337\) −18.6524 −1.01606 −0.508031 0.861339i \(-0.669626\pi\)
−0.508031 + 0.861339i \(0.669626\pi\)
\(338\) 0 0
\(339\) −11.0143 −0.598217
\(340\) 0 0
\(341\) −0.412833 −0.0223561
\(342\) 0 0
\(343\) 12.5357 0.676863
\(344\) 0 0
\(345\) 7.34963 0.395691
\(346\) 0 0
\(347\) −14.9451 −0.802294 −0.401147 0.916014i \(-0.631388\pi\)
−0.401147 + 0.916014i \(0.631388\pi\)
\(348\) 0 0
\(349\) −0.652865 −0.0349471 −0.0174735 0.999847i \(-0.505562\pi\)
−0.0174735 + 0.999847i \(0.505562\pi\)
\(350\) 0 0
\(351\) −5.35380 −0.285764
\(352\) 0 0
\(353\) 7.87628 0.419212 0.209606 0.977786i \(-0.432782\pi\)
0.209606 + 0.977786i \(0.432782\pi\)
\(354\) 0 0
\(355\) 7.83411 0.415791
\(356\) 0 0
\(357\) −10.1458 −0.536972
\(358\) 0 0
\(359\) −17.1984 −0.907698 −0.453849 0.891079i \(-0.649950\pi\)
−0.453849 + 0.891079i \(0.649950\pi\)
\(360\) 0 0
\(361\) −16.9896 −0.894190
\(362\) 0 0
\(363\) −12.7112 −0.667164
\(364\) 0 0
\(365\) −11.4466 −0.599143
\(366\) 0 0
\(367\) 18.6758 0.974870 0.487435 0.873159i \(-0.337933\pi\)
0.487435 + 0.873159i \(0.337933\pi\)
\(368\) 0 0
\(369\) 16.9796 0.883923
\(370\) 0 0
\(371\) 12.6513 0.656822
\(372\) 0 0
\(373\) 16.6540 0.862312 0.431156 0.902277i \(-0.358106\pi\)
0.431156 + 0.902277i \(0.358106\pi\)
\(374\) 0 0
\(375\) 1.17504 0.0606789
\(376\) 0 0
\(377\) 1.43072 0.0736858
\(378\) 0 0
\(379\) 0.503692 0.0258729 0.0129365 0.999916i \(-0.495882\pi\)
0.0129365 + 0.999916i \(0.495882\pi\)
\(380\) 0 0
\(381\) −5.41441 −0.277388
\(382\) 0 0
\(383\) 35.2898 1.80322 0.901612 0.432546i \(-0.142385\pi\)
0.901612 + 0.432546i \(0.142385\pi\)
\(384\) 0 0
\(385\) 1.35339 0.0689753
\(386\) 0 0
\(387\) −14.7777 −0.751195
\(388\) 0 0
\(389\) 28.8139 1.46092 0.730462 0.682953i \(-0.239305\pi\)
0.730462 + 0.682953i \(0.239305\pi\)
\(390\) 0 0
\(391\) 17.0403 0.861763
\(392\) 0 0
\(393\) 15.5440 0.784092
\(394\) 0 0
\(395\) 3.09972 0.155964
\(396\) 0 0
\(397\) 6.10962 0.306633 0.153317 0.988177i \(-0.451005\pi\)
0.153317 + 0.988177i \(0.451005\pi\)
\(398\) 0 0
\(399\) 5.28034 0.264347
\(400\) 0 0
\(401\) 0.820697 0.0409837 0.0204918 0.999790i \(-0.493477\pi\)
0.0204918 + 0.999790i \(0.493477\pi\)
\(402\) 0 0
\(403\) 0.953572 0.0475008
\(404\) 0 0
\(405\) −1.52011 −0.0755347
\(406\) 0 0
\(407\) 3.08240 0.152789
\(408\) 0 0
\(409\) −2.75770 −0.136360 −0.0681798 0.997673i \(-0.521719\pi\)
−0.0681798 + 0.997673i \(0.521719\pi\)
\(410\) 0 0
\(411\) −1.33446 −0.0658243
\(412\) 0 0
\(413\) 0.539461 0.0265452
\(414\) 0 0
\(415\) 6.07419 0.298170
\(416\) 0 0
\(417\) −15.3720 −0.752769
\(418\) 0 0
\(419\) −22.2389 −1.08644 −0.543221 0.839590i \(-0.682795\pi\)
−0.543221 + 0.839590i \(0.682795\pi\)
\(420\) 0 0
\(421\) −16.6929 −0.813561 −0.406780 0.913526i \(-0.633349\pi\)
−0.406780 + 0.913526i \(0.633349\pi\)
\(422\) 0 0
\(423\) 20.7383 1.00833
\(424\) 0 0
\(425\) 2.72436 0.132151
\(426\) 0 0
\(427\) 3.03553 0.146899
\(428\) 0 0
\(429\) −0.494929 −0.0238954
\(430\) 0 0
\(431\) −23.7039 −1.14177 −0.570887 0.821028i \(-0.693401\pi\)
−0.570887 + 0.821028i \(0.693401\pi\)
\(432\) 0 0
\(433\) 32.6007 1.56669 0.783346 0.621586i \(-0.213512\pi\)
0.783346 + 0.621586i \(0.213512\pi\)
\(434\) 0 0
\(435\) 1.70441 0.0817201
\(436\) 0 0
\(437\) −8.86854 −0.424240
\(438\) 0 0
\(439\) 36.4425 1.73930 0.869652 0.493665i \(-0.164343\pi\)
0.869652 + 0.493665i \(0.164343\pi\)
\(440\) 0 0
\(441\) −4.93022 −0.234772
\(442\) 0 0
\(443\) 1.34033 0.0636808 0.0318404 0.999493i \(-0.489863\pi\)
0.0318404 + 0.999493i \(0.489863\pi\)
\(444\) 0 0
\(445\) 5.74911 0.272534
\(446\) 0 0
\(447\) −11.6430 −0.550695
\(448\) 0 0
\(449\) 23.2915 1.09920 0.549598 0.835429i \(-0.314781\pi\)
0.549598 + 0.835429i \(0.314781\pi\)
\(450\) 0 0
\(451\) 4.47777 0.210850
\(452\) 0 0
\(453\) −1.17504 −0.0552083
\(454\) 0 0
\(455\) −3.12610 −0.146554
\(456\) 0 0
\(457\) −12.6627 −0.592337 −0.296169 0.955136i \(-0.595709\pi\)
−0.296169 + 0.955136i \(0.595709\pi\)
\(458\) 0 0
\(459\) −14.7874 −0.690216
\(460\) 0 0
\(461\) 3.42109 0.159336 0.0796679 0.996821i \(-0.474614\pi\)
0.0796679 + 0.996821i \(0.474614\pi\)
\(462\) 0 0
\(463\) 2.71122 0.126001 0.0630006 0.998013i \(-0.479933\pi\)
0.0630006 + 0.998013i \(0.479933\pi\)
\(464\) 0 0
\(465\) 1.13598 0.0526800
\(466\) 0 0
\(467\) 19.3245 0.894233 0.447117 0.894476i \(-0.352451\pi\)
0.447117 + 0.894476i \(0.352451\pi\)
\(468\) 0 0
\(469\) −5.12299 −0.236557
\(470\) 0 0
\(471\) −6.17635 −0.284591
\(472\) 0 0
\(473\) −3.89710 −0.179189
\(474\) 0 0
\(475\) −1.41788 −0.0650568
\(476\) 0 0
\(477\) 6.46379 0.295957
\(478\) 0 0
\(479\) −2.10285 −0.0960815 −0.0480407 0.998845i \(-0.515298\pi\)
−0.0480407 + 0.998845i \(0.515298\pi\)
\(480\) 0 0
\(481\) −7.11981 −0.324635
\(482\) 0 0
\(483\) −23.2935 −1.05989
\(484\) 0 0
\(485\) −5.12793 −0.232847
\(486\) 0 0
\(487\) 23.8368 1.08015 0.540075 0.841617i \(-0.318396\pi\)
0.540075 + 0.841617i \(0.318396\pi\)
\(488\) 0 0
\(489\) −23.3290 −1.05497
\(490\) 0 0
\(491\) −4.27990 −0.193149 −0.0965747 0.995326i \(-0.530789\pi\)
−0.0965747 + 0.995326i \(0.530789\pi\)
\(492\) 0 0
\(493\) 3.95170 0.177976
\(494\) 0 0
\(495\) 0.691475 0.0310795
\(496\) 0 0
\(497\) −24.8289 −1.11373
\(498\) 0 0
\(499\) −30.7519 −1.37664 −0.688321 0.725406i \(-0.741652\pi\)
−0.688321 + 0.725406i \(0.741652\pi\)
\(500\) 0 0
\(501\) 23.0622 1.03034
\(502\) 0 0
\(503\) 40.1919 1.79207 0.896033 0.443987i \(-0.146436\pi\)
0.896033 + 0.443987i \(0.146436\pi\)
\(504\) 0 0
\(505\) −5.85485 −0.260537
\(506\) 0 0
\(507\) −14.1323 −0.627639
\(508\) 0 0
\(509\) −3.26068 −0.144527 −0.0722635 0.997386i \(-0.523022\pi\)
−0.0722635 + 0.997386i \(0.523022\pi\)
\(510\) 0 0
\(511\) 36.2782 1.60485
\(512\) 0 0
\(513\) 7.69604 0.339788
\(514\) 0 0
\(515\) −10.7737 −0.474744
\(516\) 0 0
\(517\) 5.46899 0.240526
\(518\) 0 0
\(519\) −14.2908 −0.627298
\(520\) 0 0
\(521\) −11.6652 −0.511061 −0.255530 0.966801i \(-0.582250\pi\)
−0.255530 + 0.966801i \(0.582250\pi\)
\(522\) 0 0
\(523\) −29.9462 −1.30946 −0.654728 0.755864i \(-0.727217\pi\)
−0.654728 + 0.755864i \(0.727217\pi\)
\(524\) 0 0
\(525\) −3.72410 −0.162533
\(526\) 0 0
\(527\) 2.63380 0.114730
\(528\) 0 0
\(529\) 16.1223 0.700970
\(530\) 0 0
\(531\) 0.275622 0.0119610
\(532\) 0 0
\(533\) −10.3429 −0.447999
\(534\) 0 0
\(535\) −14.0100 −0.605703
\(536\) 0 0
\(537\) 29.2210 1.26098
\(538\) 0 0
\(539\) −1.30017 −0.0560023
\(540\) 0 0
\(541\) 20.3922 0.876728 0.438364 0.898797i \(-0.355558\pi\)
0.438364 + 0.898797i \(0.355558\pi\)
\(542\) 0 0
\(543\) 5.77789 0.247953
\(544\) 0 0
\(545\) −6.17284 −0.264415
\(546\) 0 0
\(547\) 36.2171 1.54853 0.774266 0.632861i \(-0.218119\pi\)
0.774266 + 0.632861i \(0.218119\pi\)
\(548\) 0 0
\(549\) 1.55091 0.0661913
\(550\) 0 0
\(551\) −2.05665 −0.0876162
\(552\) 0 0
\(553\) −9.82407 −0.417762
\(554\) 0 0
\(555\) −8.48178 −0.360032
\(556\) 0 0
\(557\) 20.0950 0.851451 0.425725 0.904852i \(-0.360019\pi\)
0.425725 + 0.904852i \(0.360019\pi\)
\(558\) 0 0
\(559\) 9.00164 0.380729
\(560\) 0 0
\(561\) −1.36701 −0.0577153
\(562\) 0 0
\(563\) 5.37970 0.226727 0.113364 0.993554i \(-0.463838\pi\)
0.113364 + 0.993554i \(0.463838\pi\)
\(564\) 0 0
\(565\) −9.37358 −0.394349
\(566\) 0 0
\(567\) 4.81773 0.202326
\(568\) 0 0
\(569\) 9.81333 0.411396 0.205698 0.978615i \(-0.434054\pi\)
0.205698 + 0.978615i \(0.434054\pi\)
\(570\) 0 0
\(571\) −24.8128 −1.03838 −0.519191 0.854658i \(-0.673767\pi\)
−0.519191 + 0.854658i \(0.673767\pi\)
\(572\) 0 0
\(573\) −10.4100 −0.434883
\(574\) 0 0
\(575\) 6.25478 0.260842
\(576\) 0 0
\(577\) 2.53942 0.105717 0.0528587 0.998602i \(-0.483167\pi\)
0.0528587 + 0.998602i \(0.483167\pi\)
\(578\) 0 0
\(579\) 18.0987 0.752157
\(580\) 0 0
\(581\) −19.2512 −0.798673
\(582\) 0 0
\(583\) 1.70459 0.0705971
\(584\) 0 0
\(585\) −1.59719 −0.0660356
\(586\) 0 0
\(587\) −20.8740 −0.861561 −0.430781 0.902457i \(-0.641762\pi\)
−0.430781 + 0.902457i \(0.641762\pi\)
\(588\) 0 0
\(589\) −1.37075 −0.0564808
\(590\) 0 0
\(591\) 3.50384 0.144129
\(592\) 0 0
\(593\) −37.9045 −1.55655 −0.778275 0.627923i \(-0.783905\pi\)
−0.778275 + 0.627923i \(0.783905\pi\)
\(594\) 0 0
\(595\) −8.63441 −0.353976
\(596\) 0 0
\(597\) 0.703724 0.0288015
\(598\) 0 0
\(599\) 36.7416 1.50122 0.750611 0.660745i \(-0.229759\pi\)
0.750611 + 0.660745i \(0.229759\pi\)
\(600\) 0 0
\(601\) 9.24141 0.376965 0.188482 0.982077i \(-0.439643\pi\)
0.188482 + 0.982077i \(0.439643\pi\)
\(602\) 0 0
\(603\) −2.61743 −0.106590
\(604\) 0 0
\(605\) −10.8176 −0.439800
\(606\) 0 0
\(607\) 35.2763 1.43182 0.715911 0.698191i \(-0.246011\pi\)
0.715911 + 0.698191i \(0.246011\pi\)
\(608\) 0 0
\(609\) −5.40184 −0.218894
\(610\) 0 0
\(611\) −12.6324 −0.511053
\(612\) 0 0
\(613\) −2.66967 −0.107827 −0.0539135 0.998546i \(-0.517170\pi\)
−0.0539135 + 0.998546i \(0.517170\pi\)
\(614\) 0 0
\(615\) −12.3214 −0.496846
\(616\) 0 0
\(617\) −46.6323 −1.87734 −0.938672 0.344811i \(-0.887943\pi\)
−0.938672 + 0.344811i \(0.887943\pi\)
\(618\) 0 0
\(619\) 19.9463 0.801711 0.400856 0.916141i \(-0.368713\pi\)
0.400856 + 0.916141i \(0.368713\pi\)
\(620\) 0 0
\(621\) −33.9500 −1.36237
\(622\) 0 0
\(623\) −18.2209 −0.730003
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0.711456 0.0284128
\(628\) 0 0
\(629\) −19.6652 −0.784102
\(630\) 0 0
\(631\) 24.4020 0.971430 0.485715 0.874117i \(-0.338559\pi\)
0.485715 + 0.874117i \(0.338559\pi\)
\(632\) 0 0
\(633\) −29.2731 −1.16350
\(634\) 0 0
\(635\) −4.60784 −0.182857
\(636\) 0 0
\(637\) 3.00317 0.118990
\(638\) 0 0
\(639\) −12.6856 −0.501834
\(640\) 0 0
\(641\) −31.0743 −1.22736 −0.613681 0.789554i \(-0.710312\pi\)
−0.613681 + 0.789554i \(0.710312\pi\)
\(642\) 0 0
\(643\) 34.3485 1.35457 0.677286 0.735719i \(-0.263156\pi\)
0.677286 + 0.735719i \(0.263156\pi\)
\(644\) 0 0
\(645\) 10.7236 0.422241
\(646\) 0 0
\(647\) −6.04723 −0.237741 −0.118871 0.992910i \(-0.537927\pi\)
−0.118871 + 0.992910i \(0.537927\pi\)
\(648\) 0 0
\(649\) 0.0726854 0.00285315
\(650\) 0 0
\(651\) −3.60032 −0.141108
\(652\) 0 0
\(653\) 9.94652 0.389237 0.194619 0.980879i \(-0.437653\pi\)
0.194619 + 0.980879i \(0.437653\pi\)
\(654\) 0 0
\(655\) 13.2285 0.516879
\(656\) 0 0
\(657\) 18.5352 0.723129
\(658\) 0 0
\(659\) 20.2365 0.788301 0.394150 0.919046i \(-0.371039\pi\)
0.394150 + 0.919046i \(0.371039\pi\)
\(660\) 0 0
\(661\) 26.9120 1.04676 0.523378 0.852100i \(-0.324671\pi\)
0.523378 + 0.852100i \(0.324671\pi\)
\(662\) 0 0
\(663\) 3.15756 0.122629
\(664\) 0 0
\(665\) 4.49374 0.174260
\(666\) 0 0
\(667\) 9.07261 0.351293
\(668\) 0 0
\(669\) 6.08776 0.235366
\(670\) 0 0
\(671\) 0.408997 0.0157892
\(672\) 0 0
\(673\) −9.27576 −0.357554 −0.178777 0.983890i \(-0.557214\pi\)
−0.178777 + 0.983890i \(0.557214\pi\)
\(674\) 0 0
\(675\) −5.42784 −0.208918
\(676\) 0 0
\(677\) −19.0912 −0.733734 −0.366867 0.930273i \(-0.619570\pi\)
−0.366867 + 0.930273i \(0.619570\pi\)
\(678\) 0 0
\(679\) 16.2521 0.623700
\(680\) 0 0
\(681\) −20.8764 −0.799985
\(682\) 0 0
\(683\) −29.1105 −1.11388 −0.556941 0.830552i \(-0.688025\pi\)
−0.556941 + 0.830552i \(0.688025\pi\)
\(684\) 0 0
\(685\) −1.13567 −0.0433919
\(686\) 0 0
\(687\) −30.9899 −1.18234
\(688\) 0 0
\(689\) −3.93732 −0.150000
\(690\) 0 0
\(691\) −12.7571 −0.485301 −0.242651 0.970114i \(-0.578017\pi\)
−0.242651 + 0.970114i \(0.578017\pi\)
\(692\) 0 0
\(693\) −2.19152 −0.0832489
\(694\) 0 0
\(695\) −13.0821 −0.496232
\(696\) 0 0
\(697\) −28.5674 −1.08207
\(698\) 0 0
\(699\) 1.96597 0.0743596
\(700\) 0 0
\(701\) −50.7407 −1.91645 −0.958225 0.286014i \(-0.907670\pi\)
−0.958225 + 0.286014i \(0.907670\pi\)
\(702\) 0 0
\(703\) 10.2347 0.386008
\(704\) 0 0
\(705\) −15.0489 −0.566775
\(706\) 0 0
\(707\) 18.5560 0.697870
\(708\) 0 0
\(709\) −31.6528 −1.18875 −0.594373 0.804189i \(-0.702600\pi\)
−0.594373 + 0.804189i \(0.702600\pi\)
\(710\) 0 0
\(711\) −5.01931 −0.188239
\(712\) 0 0
\(713\) 6.04688 0.226457
\(714\) 0 0
\(715\) −0.421201 −0.0157520
\(716\) 0 0
\(717\) −13.3729 −0.499421
\(718\) 0 0
\(719\) −10.9392 −0.407961 −0.203981 0.978975i \(-0.565388\pi\)
−0.203981 + 0.978975i \(0.565388\pi\)
\(720\) 0 0
\(721\) 34.1454 1.27164
\(722\) 0 0
\(723\) −24.4406 −0.908956
\(724\) 0 0
\(725\) 1.45051 0.0538705
\(726\) 0 0
\(727\) 20.9839 0.778252 0.389126 0.921185i \(-0.372777\pi\)
0.389126 + 0.921185i \(0.372777\pi\)
\(728\) 0 0
\(729\) 21.5953 0.799826
\(730\) 0 0
\(731\) 24.8628 0.919586
\(732\) 0 0
\(733\) 3.32568 0.122837 0.0614184 0.998112i \(-0.480438\pi\)
0.0614184 + 0.998112i \(0.480438\pi\)
\(734\) 0 0
\(735\) 3.57765 0.131964
\(736\) 0 0
\(737\) −0.690255 −0.0254259
\(738\) 0 0
\(739\) −38.1043 −1.40169 −0.700844 0.713314i \(-0.747193\pi\)
−0.700844 + 0.713314i \(0.747193\pi\)
\(740\) 0 0
\(741\) −1.64334 −0.0603696
\(742\) 0 0
\(743\) 3.14344 0.115322 0.0576608 0.998336i \(-0.481636\pi\)
0.0576608 + 0.998336i \(0.481636\pi\)
\(744\) 0 0
\(745\) −9.90859 −0.363023
\(746\) 0 0
\(747\) −9.83580 −0.359873
\(748\) 0 0
\(749\) 44.4023 1.62242
\(750\) 0 0
\(751\) 7.09907 0.259049 0.129524 0.991576i \(-0.458655\pi\)
0.129524 + 0.991576i \(0.458655\pi\)
\(752\) 0 0
\(753\) −11.4124 −0.415890
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 51.7148 1.87961 0.939803 0.341716i \(-0.111008\pi\)
0.939803 + 0.341716i \(0.111008\pi\)
\(758\) 0 0
\(759\) −3.13849 −0.113920
\(760\) 0 0
\(761\) −13.9623 −0.506132 −0.253066 0.967449i \(-0.581439\pi\)
−0.253066 + 0.967449i \(0.581439\pi\)
\(762\) 0 0
\(763\) 19.5638 0.708258
\(764\) 0 0
\(765\) −4.41149 −0.159498
\(766\) 0 0
\(767\) −0.167891 −0.00606218
\(768\) 0 0
\(769\) −9.79049 −0.353054 −0.176527 0.984296i \(-0.556486\pi\)
−0.176527 + 0.984296i \(0.556486\pi\)
\(770\) 0 0
\(771\) 10.5193 0.378843
\(772\) 0 0
\(773\) −40.9284 −1.47209 −0.736047 0.676931i \(-0.763310\pi\)
−0.736047 + 0.676931i \(0.763310\pi\)
\(774\) 0 0
\(775\) 0.966761 0.0347271
\(776\) 0 0
\(777\) 26.8816 0.964373
\(778\) 0 0
\(779\) 14.8678 0.532694
\(780\) 0 0
\(781\) −3.34537 −0.119707
\(782\) 0 0
\(783\) −7.87313 −0.281363
\(784\) 0 0
\(785\) −5.25629 −0.187605
\(786\) 0 0
\(787\) −6.75722 −0.240869 −0.120434 0.992721i \(-0.538429\pi\)
−0.120434 + 0.992721i \(0.538429\pi\)
\(788\) 0 0
\(789\) −3.96956 −0.141320
\(790\) 0 0
\(791\) 29.7080 1.05630
\(792\) 0 0
\(793\) −0.944713 −0.0335478
\(794\) 0 0
\(795\) −4.69050 −0.166355
\(796\) 0 0
\(797\) 34.2553 1.21338 0.606692 0.794937i \(-0.292496\pi\)
0.606692 + 0.794937i \(0.292496\pi\)
\(798\) 0 0
\(799\) −34.8912 −1.23436
\(800\) 0 0
\(801\) −9.30940 −0.328931
\(802\) 0 0
\(803\) 4.88801 0.172494
\(804\) 0 0
\(805\) −19.8235 −0.698687
\(806\) 0 0
\(807\) 6.67088 0.234826
\(808\) 0 0
\(809\) 13.5765 0.477323 0.238661 0.971103i \(-0.423291\pi\)
0.238661 + 0.971103i \(0.423291\pi\)
\(810\) 0 0
\(811\) −10.3874 −0.364749 −0.182375 0.983229i \(-0.558378\pi\)
−0.182375 + 0.983229i \(0.558378\pi\)
\(812\) 0 0
\(813\) 29.3275 1.02856
\(814\) 0 0
\(815\) −19.8537 −0.695446
\(816\) 0 0
\(817\) −12.9398 −0.452705
\(818\) 0 0
\(819\) 5.06203 0.176882
\(820\) 0 0
\(821\) −1.14951 −0.0401180 −0.0200590 0.999799i \(-0.506385\pi\)
−0.0200590 + 0.999799i \(0.506385\pi\)
\(822\) 0 0
\(823\) 18.5671 0.647208 0.323604 0.946193i \(-0.395105\pi\)
0.323604 + 0.946193i \(0.395105\pi\)
\(824\) 0 0
\(825\) −0.501774 −0.0174695
\(826\) 0 0
\(827\) 24.1854 0.841009 0.420505 0.907290i \(-0.361853\pi\)
0.420505 + 0.907290i \(0.361853\pi\)
\(828\) 0 0
\(829\) 32.1554 1.11680 0.558402 0.829571i \(-0.311415\pi\)
0.558402 + 0.829571i \(0.311415\pi\)
\(830\) 0 0
\(831\) 7.20349 0.249886
\(832\) 0 0
\(833\) 8.29486 0.287400
\(834\) 0 0
\(835\) 19.6267 0.679212
\(836\) 0 0
\(837\) −5.24742 −0.181378
\(838\) 0 0
\(839\) −13.6812 −0.472327 −0.236164 0.971713i \(-0.575890\pi\)
−0.236164 + 0.971713i \(0.575890\pi\)
\(840\) 0 0
\(841\) −26.8960 −0.927449
\(842\) 0 0
\(843\) 25.7016 0.885209
\(844\) 0 0
\(845\) −12.0271 −0.413745
\(846\) 0 0
\(847\) 34.2848 1.17804
\(848\) 0 0
\(849\) −1.19311 −0.0409475
\(850\) 0 0
\(851\) −45.1488 −1.54768
\(852\) 0 0
\(853\) −54.9847 −1.88264 −0.941321 0.337514i \(-0.890414\pi\)
−0.941321 + 0.337514i \(0.890414\pi\)
\(854\) 0 0
\(855\) 2.29594 0.0785196
\(856\) 0 0
\(857\) −11.8360 −0.404310 −0.202155 0.979354i \(-0.564794\pi\)
−0.202155 + 0.979354i \(0.564794\pi\)
\(858\) 0 0
\(859\) 29.5375 1.00781 0.503904 0.863760i \(-0.331897\pi\)
0.503904 + 0.863760i \(0.331897\pi\)
\(860\) 0 0
\(861\) 39.0506 1.33084
\(862\) 0 0
\(863\) −54.3220 −1.84914 −0.924571 0.381011i \(-0.875576\pi\)
−0.924571 + 0.381011i \(0.875576\pi\)
\(864\) 0 0
\(865\) −12.1620 −0.413520
\(866\) 0 0
\(867\) −11.2544 −0.382220
\(868\) 0 0
\(869\) −1.32366 −0.0449022
\(870\) 0 0
\(871\) 1.59437 0.0540232
\(872\) 0 0
\(873\) 8.30355 0.281032
\(874\) 0 0
\(875\) −3.16934 −0.107143
\(876\) 0 0
\(877\) 35.0100 1.18220 0.591102 0.806597i \(-0.298693\pi\)
0.591102 + 0.806597i \(0.298693\pi\)
\(878\) 0 0
\(879\) 6.00790 0.202641
\(880\) 0 0
\(881\) 39.0946 1.31713 0.658565 0.752524i \(-0.271164\pi\)
0.658565 + 0.752524i \(0.271164\pi\)
\(882\) 0 0
\(883\) 29.9179 1.00682 0.503408 0.864049i \(-0.332079\pi\)
0.503408 + 0.864049i \(0.332079\pi\)
\(884\) 0 0
\(885\) −0.200007 −0.00672316
\(886\) 0 0
\(887\) −16.5945 −0.557187 −0.278594 0.960409i \(-0.589868\pi\)
−0.278594 + 0.960409i \(0.589868\pi\)
\(888\) 0 0
\(889\) 14.6038 0.489796
\(890\) 0 0
\(891\) 0.649126 0.0217466
\(892\) 0 0
\(893\) 18.1590 0.607668
\(894\) 0 0
\(895\) 24.8680 0.831247
\(896\) 0 0
\(897\) 7.24936 0.242049
\(898\) 0 0
\(899\) 1.40229 0.0467691
\(900\) 0 0
\(901\) −10.8750 −0.362299
\(902\) 0 0
\(903\) −33.9867 −1.13101
\(904\) 0 0
\(905\) 4.91718 0.163453
\(906\) 0 0
\(907\) 42.5089 1.41148 0.705742 0.708469i \(-0.250614\pi\)
0.705742 + 0.708469i \(0.250614\pi\)
\(908\) 0 0
\(909\) 9.48063 0.314453
\(910\) 0 0
\(911\) −4.01732 −0.133100 −0.0665499 0.997783i \(-0.521199\pi\)
−0.0665499 + 0.997783i \(0.521199\pi\)
\(912\) 0 0
\(913\) −2.59384 −0.0858436
\(914\) 0 0
\(915\) −1.12543 −0.0372056
\(916\) 0 0
\(917\) −41.9255 −1.38450
\(918\) 0 0
\(919\) −29.1594 −0.961879 −0.480939 0.876754i \(-0.659704\pi\)
−0.480939 + 0.876754i \(0.659704\pi\)
\(920\) 0 0
\(921\) 10.4527 0.344429
\(922\) 0 0
\(923\) 7.72724 0.254345
\(924\) 0 0
\(925\) −7.21828 −0.237336
\(926\) 0 0
\(927\) 17.4456 0.572987
\(928\) 0 0
\(929\) −38.2351 −1.25445 −0.627227 0.778836i \(-0.715810\pi\)
−0.627227 + 0.778836i \(0.715810\pi\)
\(930\) 0 0
\(931\) −4.31703 −0.141485
\(932\) 0 0
\(933\) −14.1760 −0.464103
\(934\) 0 0
\(935\) −1.16337 −0.0380464
\(936\) 0 0
\(937\) −51.1890 −1.67227 −0.836136 0.548522i \(-0.815191\pi\)
−0.836136 + 0.548522i \(0.815191\pi\)
\(938\) 0 0
\(939\) −0.455241 −0.0148562
\(940\) 0 0
\(941\) 27.0683 0.882400 0.441200 0.897409i \(-0.354553\pi\)
0.441200 + 0.897409i \(0.354553\pi\)
\(942\) 0 0
\(943\) −65.5871 −2.13581
\(944\) 0 0
\(945\) 17.2027 0.559603
\(946\) 0 0
\(947\) 18.5559 0.602985 0.301493 0.953468i \(-0.402515\pi\)
0.301493 + 0.953468i \(0.402515\pi\)
\(948\) 0 0
\(949\) −11.2905 −0.366504
\(950\) 0 0
\(951\) −13.0604 −0.423511
\(952\) 0 0
\(953\) 56.4681 1.82918 0.914590 0.404381i \(-0.132513\pi\)
0.914590 + 0.404381i \(0.132513\pi\)
\(954\) 0 0
\(955\) −8.85924 −0.286678
\(956\) 0 0
\(957\) −0.727828 −0.0235273
\(958\) 0 0
\(959\) 3.59934 0.116229
\(960\) 0 0
\(961\) −30.0654 −0.969851
\(962\) 0 0
\(963\) 22.6860 0.731046
\(964\) 0 0
\(965\) 15.4026 0.495828
\(966\) 0 0
\(967\) −21.6045 −0.694753 −0.347376 0.937726i \(-0.612927\pi\)
−0.347376 + 0.937726i \(0.612927\pi\)
\(968\) 0 0
\(969\) −4.53897 −0.145813
\(970\) 0 0
\(971\) 45.7906 1.46949 0.734746 0.678342i \(-0.237301\pi\)
0.734746 + 0.678342i \(0.237301\pi\)
\(972\) 0 0
\(973\) 41.4615 1.32920
\(974\) 0 0
\(975\) 1.15901 0.0371181
\(976\) 0 0
\(977\) −57.5657 −1.84169 −0.920845 0.389929i \(-0.872499\pi\)
−0.920845 + 0.389929i \(0.872499\pi\)
\(978\) 0 0
\(979\) −2.45502 −0.0784629
\(980\) 0 0
\(981\) 9.99554 0.319133
\(982\) 0 0
\(983\) 5.00960 0.159781 0.0798907 0.996804i \(-0.474543\pi\)
0.0798907 + 0.996804i \(0.474543\pi\)
\(984\) 0 0
\(985\) 2.98189 0.0950109
\(986\) 0 0
\(987\) 47.6951 1.51815
\(988\) 0 0
\(989\) 57.0820 1.81510
\(990\) 0 0
\(991\) 36.9350 1.17328 0.586640 0.809848i \(-0.300450\pi\)
0.586640 + 0.809848i \(0.300450\pi\)
\(992\) 0 0
\(993\) −10.6933 −0.339341
\(994\) 0 0
\(995\) 0.598893 0.0189862
\(996\) 0 0
\(997\) −45.8385 −1.45172 −0.725860 0.687842i \(-0.758558\pi\)
−0.725860 + 0.687842i \(0.758558\pi\)
\(998\) 0 0
\(999\) 39.1797 1.23959
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 \(a_p\))