Properties

Label 8008.2.a.k.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-3.25115\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.25115 q^{3}\) \(-0.215704 q^{5}\) \(+1.00000 q^{7}\) \(+7.56995 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.25115 q^{3}\) \(-0.215704 q^{5}\) \(+1.00000 q^{7}\) \(+7.56995 q^{9}\) \(-1.00000 q^{11}\) \(-1.00000 q^{13}\) \(-0.701286 q^{15}\) \(-1.35393 q^{17}\) \(+5.10414 q^{19}\) \(+3.25115 q^{21}\) \(+4.33416 q^{23}\) \(-4.95347 q^{25}\) \(+14.8576 q^{27}\) \(-0.702326 q^{29}\) \(+9.03648 q^{31}\) \(-3.25115 q^{33}\) \(-0.215704 q^{35}\) \(-2.18611 q^{37}\) \(-3.25115 q^{39}\) \(+3.79997 q^{41}\) \(+2.91699 q^{43}\) \(-1.63287 q^{45}\) \(+10.5856 q^{47}\) \(+1.00000 q^{49}\) \(-4.40181 q^{51}\) \(-8.94833 q^{53}\) \(+0.215704 q^{55}\) \(+16.5943 q^{57}\) \(-6.12859 q^{59}\) \(-1.26507 q^{61}\) \(+7.56995 q^{63}\) \(+0.215704 q^{65}\) \(-10.2368 q^{67}\) \(+14.0910 q^{69}\) \(+11.0722 q^{71}\) \(-10.6272 q^{73}\) \(-16.1045 q^{75}\) \(-1.00000 q^{77}\) \(+11.7524 q^{79}\) \(+25.5943 q^{81}\) \(-13.6773 q^{83}\) \(+0.292048 q^{85}\) \(-2.28336 q^{87}\) \(+6.89690 q^{89}\) \(-1.00000 q^{91}\) \(+29.3789 q^{93}\) \(-1.10098 q^{95}\) \(-9.18517 q^{97}\) \(-7.56995 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 46q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 55q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 3.25115 1.87705 0.938525 0.345211i \(-0.112193\pi\)
0.938525 + 0.345211i \(0.112193\pi\)
\(4\) 0 0
\(5\) −0.215704 −0.0964658 −0.0482329 0.998836i \(-0.515359\pi\)
−0.0482329 + 0.998836i \(0.515359\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 7.56995 2.52332
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.701286 −0.181071
\(16\) 0 0
\(17\) −1.35393 −0.328376 −0.164188 0.986429i \(-0.552500\pi\)
−0.164188 + 0.986429i \(0.552500\pi\)
\(18\) 0 0
\(19\) 5.10414 1.17097 0.585485 0.810683i \(-0.300904\pi\)
0.585485 + 0.810683i \(0.300904\pi\)
\(20\) 0 0
\(21\) 3.25115 0.709458
\(22\) 0 0
\(23\) 4.33416 0.903734 0.451867 0.892085i \(-0.350758\pi\)
0.451867 + 0.892085i \(0.350758\pi\)
\(24\) 0 0
\(25\) −4.95347 −0.990694
\(26\) 0 0
\(27\) 14.8576 2.85934
\(28\) 0 0
\(29\) −0.702326 −0.130419 −0.0652093 0.997872i \(-0.520772\pi\)
−0.0652093 + 0.997872i \(0.520772\pi\)
\(30\) 0 0
\(31\) 9.03648 1.62300 0.811500 0.584352i \(-0.198651\pi\)
0.811500 + 0.584352i \(0.198651\pi\)
\(32\) 0 0
\(33\) −3.25115 −0.565952
\(34\) 0 0
\(35\) −0.215704 −0.0364607
\(36\) 0 0
\(37\) −2.18611 −0.359394 −0.179697 0.983722i \(-0.557512\pi\)
−0.179697 + 0.983722i \(0.557512\pi\)
\(38\) 0 0
\(39\) −3.25115 −0.520600
\(40\) 0 0
\(41\) 3.79997 0.593455 0.296728 0.954962i \(-0.404105\pi\)
0.296728 + 0.954962i \(0.404105\pi\)
\(42\) 0 0
\(43\) 2.91699 0.444837 0.222418 0.974951i \(-0.428605\pi\)
0.222418 + 0.974951i \(0.428605\pi\)
\(44\) 0 0
\(45\) −1.63287 −0.243414
\(46\) 0 0
\(47\) 10.5856 1.54407 0.772036 0.635579i \(-0.219239\pi\)
0.772036 + 0.635579i \(0.219239\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −4.40181 −0.616377
\(52\) 0 0
\(53\) −8.94833 −1.22915 −0.614574 0.788859i \(-0.710672\pi\)
−0.614574 + 0.788859i \(0.710672\pi\)
\(54\) 0 0
\(55\) 0.215704 0.0290855
\(56\) 0 0
\(57\) 16.5943 2.19797
\(58\) 0 0
\(59\) −6.12859 −0.797875 −0.398937 0.916978i \(-0.630621\pi\)
−0.398937 + 0.916978i \(0.630621\pi\)
\(60\) 0 0
\(61\) −1.26507 −0.161975 −0.0809877 0.996715i \(-0.525807\pi\)
−0.0809877 + 0.996715i \(0.525807\pi\)
\(62\) 0 0
\(63\) 7.56995 0.953724
\(64\) 0 0
\(65\) 0.215704 0.0267548
\(66\) 0 0
\(67\) −10.2368 −1.25063 −0.625314 0.780373i \(-0.715029\pi\)
−0.625314 + 0.780373i \(0.715029\pi\)
\(68\) 0 0
\(69\) 14.0910 1.69635
\(70\) 0 0
\(71\) 11.0722 1.31403 0.657017 0.753876i \(-0.271818\pi\)
0.657017 + 0.753876i \(0.271818\pi\)
\(72\) 0 0
\(73\) −10.6272 −1.24382 −0.621912 0.783087i \(-0.713644\pi\)
−0.621912 + 0.783087i \(0.713644\pi\)
\(74\) 0 0
\(75\) −16.1045 −1.85958
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 11.7524 1.32225 0.661124 0.750277i \(-0.270080\pi\)
0.661124 + 0.750277i \(0.270080\pi\)
\(80\) 0 0
\(81\) 25.5943 2.84381
\(82\) 0 0
\(83\) −13.6773 −1.50128 −0.750640 0.660711i \(-0.770255\pi\)
−0.750640 + 0.660711i \(0.770255\pi\)
\(84\) 0 0
\(85\) 0.292048 0.0316770
\(86\) 0 0
\(87\) −2.28336 −0.244802
\(88\) 0 0
\(89\) 6.89690 0.731070 0.365535 0.930798i \(-0.380886\pi\)
0.365535 + 0.930798i \(0.380886\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 29.3789 3.04645
\(94\) 0 0
\(95\) −1.10098 −0.112959
\(96\) 0 0
\(97\) −9.18517 −0.932612 −0.466306 0.884623i \(-0.654415\pi\)
−0.466306 + 0.884623i \(0.654415\pi\)
\(98\) 0 0
\(99\) −7.56995 −0.760809
\(100\) 0 0
\(101\) −10.2727 −1.02217 −0.511084 0.859531i \(-0.670756\pi\)
−0.511084 + 0.859531i \(0.670756\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) −0.701286 −0.0684385
\(106\) 0 0
\(107\) 12.9900 1.25579 0.627893 0.778300i \(-0.283918\pi\)
0.627893 + 0.778300i \(0.283918\pi\)
\(108\) 0 0
\(109\) −1.59819 −0.153078 −0.0765392 0.997067i \(-0.524387\pi\)
−0.0765392 + 0.997067i \(0.524387\pi\)
\(110\) 0 0
\(111\) −7.10737 −0.674601
\(112\) 0 0
\(113\) 4.77551 0.449242 0.224621 0.974446i \(-0.427886\pi\)
0.224621 + 0.974446i \(0.427886\pi\)
\(114\) 0 0
\(115\) −0.934896 −0.0871795
\(116\) 0 0
\(117\) −7.56995 −0.699842
\(118\) 0 0
\(119\) −1.35393 −0.124114
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 12.3542 1.11394
\(124\) 0 0
\(125\) 2.14701 0.192034
\(126\) 0 0
\(127\) −5.68359 −0.504337 −0.252169 0.967683i \(-0.581144\pi\)
−0.252169 + 0.967683i \(0.581144\pi\)
\(128\) 0 0
\(129\) 9.48356 0.834981
\(130\) 0 0
\(131\) −6.86899 −0.600146 −0.300073 0.953916i \(-0.597011\pi\)
−0.300073 + 0.953916i \(0.597011\pi\)
\(132\) 0 0
\(133\) 5.10414 0.442585
\(134\) 0 0
\(135\) −3.20484 −0.275829
\(136\) 0 0
\(137\) 15.0365 1.28465 0.642327 0.766431i \(-0.277969\pi\)
0.642327 + 0.766431i \(0.277969\pi\)
\(138\) 0 0
\(139\) 8.93370 0.757747 0.378873 0.925449i \(-0.376312\pi\)
0.378873 + 0.925449i \(0.376312\pi\)
\(140\) 0 0
\(141\) 34.4154 2.89830
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 0.151495 0.0125809
\(146\) 0 0
\(147\) 3.25115 0.268150
\(148\) 0 0
\(149\) 18.6028 1.52400 0.761999 0.647578i \(-0.224218\pi\)
0.761999 + 0.647578i \(0.224218\pi\)
\(150\) 0 0
\(151\) −21.5665 −1.75505 −0.877527 0.479527i \(-0.840808\pi\)
−0.877527 + 0.479527i \(0.840808\pi\)
\(152\) 0 0
\(153\) −10.2492 −0.828596
\(154\) 0 0
\(155\) −1.94921 −0.156564
\(156\) 0 0
\(157\) 12.8997 1.02951 0.514755 0.857337i \(-0.327883\pi\)
0.514755 + 0.857337i \(0.327883\pi\)
\(158\) 0 0
\(159\) −29.0923 −2.30717
\(160\) 0 0
\(161\) 4.33416 0.341579
\(162\) 0 0
\(163\) 20.7694 1.62679 0.813394 0.581714i \(-0.197618\pi\)
0.813394 + 0.581714i \(0.197618\pi\)
\(164\) 0 0
\(165\) 0.701286 0.0545950
\(166\) 0 0
\(167\) 24.0229 1.85895 0.929473 0.368890i \(-0.120262\pi\)
0.929473 + 0.368890i \(0.120262\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 38.6381 2.95473
\(172\) 0 0
\(173\) −9.90044 −0.752717 −0.376358 0.926474i \(-0.622824\pi\)
−0.376358 + 0.926474i \(0.622824\pi\)
\(174\) 0 0
\(175\) −4.95347 −0.374447
\(176\) 0 0
\(177\) −19.9250 −1.49765
\(178\) 0 0
\(179\) −0.900882 −0.0673351 −0.0336675 0.999433i \(-0.510719\pi\)
−0.0336675 + 0.999433i \(0.510719\pi\)
\(180\) 0 0
\(181\) −14.5169 −1.07903 −0.539515 0.841976i \(-0.681392\pi\)
−0.539515 + 0.841976i \(0.681392\pi\)
\(182\) 0 0
\(183\) −4.11292 −0.304036
\(184\) 0 0
\(185\) 0.471553 0.0346693
\(186\) 0 0
\(187\) 1.35393 0.0990090
\(188\) 0 0
\(189\) 14.8576 1.08073
\(190\) 0 0
\(191\) 12.7425 0.922013 0.461006 0.887397i \(-0.347489\pi\)
0.461006 + 0.887397i \(0.347489\pi\)
\(192\) 0 0
\(193\) −16.5772 −1.19325 −0.596625 0.802520i \(-0.703492\pi\)
−0.596625 + 0.802520i \(0.703492\pi\)
\(194\) 0 0
\(195\) 0.701286 0.0502201
\(196\) 0 0
\(197\) 17.6276 1.25591 0.627956 0.778249i \(-0.283892\pi\)
0.627956 + 0.778249i \(0.283892\pi\)
\(198\) 0 0
\(199\) 8.17828 0.579743 0.289871 0.957066i \(-0.406387\pi\)
0.289871 + 0.957066i \(0.406387\pi\)
\(200\) 0 0
\(201\) −33.2814 −2.34749
\(202\) 0 0
\(203\) −0.702326 −0.0492936
\(204\) 0 0
\(205\) −0.819669 −0.0572481
\(206\) 0 0
\(207\) 32.8093 2.28041
\(208\) 0 0
\(209\) −5.10414 −0.353061
\(210\) 0 0
\(211\) −17.9751 −1.23746 −0.618728 0.785605i \(-0.712352\pi\)
−0.618728 + 0.785605i \(0.712352\pi\)
\(212\) 0 0
\(213\) 35.9975 2.46651
\(214\) 0 0
\(215\) −0.629207 −0.0429116
\(216\) 0 0
\(217\) 9.03648 0.613436
\(218\) 0 0
\(219\) −34.5507 −2.33472
\(220\) 0 0
\(221\) 1.35393 0.0910750
\(222\) 0 0
\(223\) 21.3676 1.43088 0.715441 0.698673i \(-0.246226\pi\)
0.715441 + 0.698673i \(0.246226\pi\)
\(224\) 0 0
\(225\) −37.4975 −2.49984
\(226\) 0 0
\(227\) −9.91374 −0.657998 −0.328999 0.944330i \(-0.606711\pi\)
−0.328999 + 0.944330i \(0.606711\pi\)
\(228\) 0 0
\(229\) −17.0346 −1.12568 −0.562840 0.826566i \(-0.690291\pi\)
−0.562840 + 0.826566i \(0.690291\pi\)
\(230\) 0 0
\(231\) −3.25115 −0.213910
\(232\) 0 0
\(233\) −13.9903 −0.916533 −0.458267 0.888815i \(-0.651530\pi\)
−0.458267 + 0.888815i \(0.651530\pi\)
\(234\) 0 0
\(235\) −2.28336 −0.148950
\(236\) 0 0
\(237\) 38.2088 2.48193
\(238\) 0 0
\(239\) 3.31371 0.214346 0.107173 0.994240i \(-0.465820\pi\)
0.107173 + 0.994240i \(0.465820\pi\)
\(240\) 0 0
\(241\) 10.5209 0.677711 0.338856 0.940838i \(-0.389960\pi\)
0.338856 + 0.940838i \(0.389960\pi\)
\(242\) 0 0
\(243\) 38.6381 2.47863
\(244\) 0 0
\(245\) −0.215704 −0.0137808
\(246\) 0 0
\(247\) −5.10414 −0.324769
\(248\) 0 0
\(249\) −44.4670 −2.81798
\(250\) 0 0
\(251\) −10.8840 −0.686993 −0.343497 0.939154i \(-0.611611\pi\)
−0.343497 + 0.939154i \(0.611611\pi\)
\(252\) 0 0
\(253\) −4.33416 −0.272486
\(254\) 0 0
\(255\) 0.949490 0.0594594
\(256\) 0 0
\(257\) −22.0396 −1.37479 −0.687396 0.726283i \(-0.741246\pi\)
−0.687396 + 0.726283i \(0.741246\pi\)
\(258\) 0 0
\(259\) −2.18611 −0.135838
\(260\) 0 0
\(261\) −5.31657 −0.329087
\(262\) 0 0
\(263\) −3.88772 −0.239727 −0.119863 0.992790i \(-0.538246\pi\)
−0.119863 + 0.992790i \(0.538246\pi\)
\(264\) 0 0
\(265\) 1.93019 0.118571
\(266\) 0 0
\(267\) 22.4228 1.37225
\(268\) 0 0
\(269\) −20.9399 −1.27673 −0.638363 0.769735i \(-0.720388\pi\)
−0.638363 + 0.769735i \(0.720388\pi\)
\(270\) 0 0
\(271\) 16.5926 1.00793 0.503963 0.863725i \(-0.331875\pi\)
0.503963 + 0.863725i \(0.331875\pi\)
\(272\) 0 0
\(273\) −3.25115 −0.196768
\(274\) 0 0
\(275\) 4.95347 0.298706
\(276\) 0 0
\(277\) 14.1362 0.849364 0.424682 0.905343i \(-0.360386\pi\)
0.424682 + 0.905343i \(0.360386\pi\)
\(278\) 0 0
\(279\) 68.4057 4.09534
\(280\) 0 0
\(281\) 8.49250 0.506620 0.253310 0.967385i \(-0.418481\pi\)
0.253310 + 0.967385i \(0.418481\pi\)
\(282\) 0 0
\(283\) 11.4242 0.679097 0.339549 0.940588i \(-0.389726\pi\)
0.339549 + 0.940588i \(0.389726\pi\)
\(284\) 0 0
\(285\) −3.57946 −0.212029
\(286\) 0 0
\(287\) 3.79997 0.224305
\(288\) 0 0
\(289\) −15.1669 −0.892169
\(290\) 0 0
\(291\) −29.8623 −1.75056
\(292\) 0 0
\(293\) −28.5641 −1.66873 −0.834366 0.551211i \(-0.814166\pi\)
−0.834366 + 0.551211i \(0.814166\pi\)
\(294\) 0 0
\(295\) 1.32196 0.0769677
\(296\) 0 0
\(297\) −14.8576 −0.862124
\(298\) 0 0
\(299\) −4.33416 −0.250651
\(300\) 0 0
\(301\) 2.91699 0.168133
\(302\) 0 0
\(303\) −33.3979 −1.91866
\(304\) 0 0
\(305\) 0.272881 0.0156251
\(306\) 0 0
\(307\) −15.3257 −0.874682 −0.437341 0.899296i \(-0.644080\pi\)
−0.437341 + 0.899296i \(0.644080\pi\)
\(308\) 0 0
\(309\) 26.0092 1.47961
\(310\) 0 0
\(311\) 16.7201 0.948111 0.474055 0.880495i \(-0.342790\pi\)
0.474055 + 0.880495i \(0.342790\pi\)
\(312\) 0 0
\(313\) −22.1688 −1.25305 −0.626527 0.779400i \(-0.715524\pi\)
−0.626527 + 0.779400i \(0.715524\pi\)
\(314\) 0 0
\(315\) −1.63287 −0.0920018
\(316\) 0 0
\(317\) 4.11034 0.230860 0.115430 0.993316i \(-0.463175\pi\)
0.115430 + 0.993316i \(0.463175\pi\)
\(318\) 0 0
\(319\) 0.702326 0.0393227
\(320\) 0 0
\(321\) 42.2322 2.35717
\(322\) 0 0
\(323\) −6.91063 −0.384518
\(324\) 0 0
\(325\) 4.95347 0.274769
\(326\) 0 0
\(327\) −5.19593 −0.287336
\(328\) 0 0
\(329\) 10.5856 0.583604
\(330\) 0 0
\(331\) −9.19240 −0.505260 −0.252630 0.967563i \(-0.581296\pi\)
−0.252630 + 0.967563i \(0.581296\pi\)
\(332\) 0 0
\(333\) −16.5488 −0.906866
\(334\) 0 0
\(335\) 2.20813 0.120643
\(336\) 0 0
\(337\) −16.8468 −0.917704 −0.458852 0.888513i \(-0.651739\pi\)
−0.458852 + 0.888513i \(0.651739\pi\)
\(338\) 0 0
\(339\) 15.5259 0.843251
\(340\) 0 0
\(341\) −9.03648 −0.489353
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −3.03948 −0.163640
\(346\) 0 0
\(347\) −0.693747 −0.0372423 −0.0186211 0.999827i \(-0.505928\pi\)
−0.0186211 + 0.999827i \(0.505928\pi\)
\(348\) 0 0
\(349\) −21.6150 −1.15703 −0.578513 0.815674i \(-0.696367\pi\)
−0.578513 + 0.815674i \(0.696367\pi\)
\(350\) 0 0
\(351\) −14.8576 −0.793039
\(352\) 0 0
\(353\) 33.7393 1.79576 0.897882 0.440236i \(-0.145105\pi\)
0.897882 + 0.440236i \(0.145105\pi\)
\(354\) 0 0
\(355\) −2.38833 −0.126759
\(356\) 0 0
\(357\) −4.40181 −0.232969
\(358\) 0 0
\(359\) −15.5388 −0.820107 −0.410054 0.912061i \(-0.634490\pi\)
−0.410054 + 0.912061i \(0.634490\pi\)
\(360\) 0 0
\(361\) 7.05225 0.371171
\(362\) 0 0
\(363\) 3.25115 0.170641
\(364\) 0 0
\(365\) 2.29234 0.119987
\(366\) 0 0
\(367\) −10.9705 −0.572656 −0.286328 0.958132i \(-0.592435\pi\)
−0.286328 + 0.958132i \(0.592435\pi\)
\(368\) 0 0
\(369\) 28.7656 1.49748
\(370\) 0 0
\(371\) −8.94833 −0.464574
\(372\) 0 0
\(373\) −7.36436 −0.381312 −0.190656 0.981657i \(-0.561062\pi\)
−0.190656 + 0.981657i \(0.561062\pi\)
\(374\) 0 0
\(375\) 6.98023 0.360457
\(376\) 0 0
\(377\) 0.702326 0.0361716
\(378\) 0 0
\(379\) −10.7926 −0.554381 −0.277190 0.960815i \(-0.589403\pi\)
−0.277190 + 0.960815i \(0.589403\pi\)
\(380\) 0 0
\(381\) −18.4782 −0.946667
\(382\) 0 0
\(383\) 21.0587 1.07605 0.538024 0.842929i \(-0.319171\pi\)
0.538024 + 0.842929i \(0.319171\pi\)
\(384\) 0 0
\(385\) 0.215704 0.0109933
\(386\) 0 0
\(387\) 22.0815 1.12246
\(388\) 0 0
\(389\) −8.12674 −0.412042 −0.206021 0.978548i \(-0.566052\pi\)
−0.206021 + 0.978548i \(0.566052\pi\)
\(390\) 0 0
\(391\) −5.86813 −0.296764
\(392\) 0 0
\(393\) −22.3321 −1.12650
\(394\) 0 0
\(395\) −2.53504 −0.127552
\(396\) 0 0
\(397\) −32.7843 −1.64540 −0.822698 0.568479i \(-0.807532\pi\)
−0.822698 + 0.568479i \(0.807532\pi\)
\(398\) 0 0
\(399\) 16.5943 0.830754
\(400\) 0 0
\(401\) 3.80205 0.189865 0.0949326 0.995484i \(-0.469736\pi\)
0.0949326 + 0.995484i \(0.469736\pi\)
\(402\) 0 0
\(403\) −9.03648 −0.450139
\(404\) 0 0
\(405\) −5.52080 −0.274331
\(406\) 0 0
\(407\) 2.18611 0.108361
\(408\) 0 0
\(409\) −12.4744 −0.616822 −0.308411 0.951253i \(-0.599797\pi\)
−0.308411 + 0.951253i \(0.599797\pi\)
\(410\) 0 0
\(411\) 48.8858 2.41136
\(412\) 0 0
\(413\) −6.12859 −0.301568
\(414\) 0 0
\(415\) 2.95025 0.144822
\(416\) 0 0
\(417\) 29.0448 1.42233
\(418\) 0 0
\(419\) 8.41603 0.411150 0.205575 0.978641i \(-0.434094\pi\)
0.205575 + 0.978641i \(0.434094\pi\)
\(420\) 0 0
\(421\) 30.1244 1.46818 0.734088 0.679055i \(-0.237610\pi\)
0.734088 + 0.679055i \(0.237610\pi\)
\(422\) 0 0
\(423\) 80.1326 3.89618
\(424\) 0 0
\(425\) 6.70664 0.325320
\(426\) 0 0
\(427\) −1.26507 −0.0612210
\(428\) 0 0
\(429\) 3.25115 0.156967
\(430\) 0 0
\(431\) 26.1605 1.26011 0.630054 0.776551i \(-0.283033\pi\)
0.630054 + 0.776551i \(0.283033\pi\)
\(432\) 0 0
\(433\) 18.3284 0.880808 0.440404 0.897800i \(-0.354835\pi\)
0.440404 + 0.897800i \(0.354835\pi\)
\(434\) 0 0
\(435\) 0.492531 0.0236151
\(436\) 0 0
\(437\) 22.1221 1.05825
\(438\) 0 0
\(439\) −18.5239 −0.884098 −0.442049 0.896991i \(-0.645748\pi\)
−0.442049 + 0.896991i \(0.645748\pi\)
\(440\) 0 0
\(441\) 7.56995 0.360474
\(442\) 0 0
\(443\) −7.89994 −0.375337 −0.187669 0.982232i \(-0.560093\pi\)
−0.187669 + 0.982232i \(0.560093\pi\)
\(444\) 0 0
\(445\) −1.48769 −0.0705233
\(446\) 0 0
\(447\) 60.4803 2.86062
\(448\) 0 0
\(449\) 2.05604 0.0970305 0.0485153 0.998822i \(-0.484551\pi\)
0.0485153 + 0.998822i \(0.484551\pi\)
\(450\) 0 0
\(451\) −3.79997 −0.178933
\(452\) 0 0
\(453\) −70.1158 −3.29433
\(454\) 0 0
\(455\) 0.215704 0.0101124
\(456\) 0 0
\(457\) −8.68043 −0.406053 −0.203027 0.979173i \(-0.565078\pi\)
−0.203027 + 0.979173i \(0.565078\pi\)
\(458\) 0 0
\(459\) −20.1161 −0.938938
\(460\) 0 0
\(461\) 0.873465 0.0406813 0.0203407 0.999793i \(-0.493525\pi\)
0.0203407 + 0.999793i \(0.493525\pi\)
\(462\) 0 0
\(463\) −17.6693 −0.821160 −0.410580 0.911825i \(-0.634674\pi\)
−0.410580 + 0.911825i \(0.634674\pi\)
\(464\) 0 0
\(465\) −6.33716 −0.293879
\(466\) 0 0
\(467\) 13.7534 0.636433 0.318217 0.948018i \(-0.396916\pi\)
0.318217 + 0.948018i \(0.396916\pi\)
\(468\) 0 0
\(469\) −10.2368 −0.472693
\(470\) 0 0
\(471\) 41.9389 1.93244
\(472\) 0 0
\(473\) −2.91699 −0.134123
\(474\) 0 0
\(475\) −25.2832 −1.16007
\(476\) 0 0
\(477\) −67.7384 −3.10153
\(478\) 0 0
\(479\) −36.2058 −1.65429 −0.827143 0.561991i \(-0.810036\pi\)
−0.827143 + 0.561991i \(0.810036\pi\)
\(480\) 0 0
\(481\) 2.18611 0.0996781
\(482\) 0 0
\(483\) 14.0910 0.641162
\(484\) 0 0
\(485\) 1.98128 0.0899652
\(486\) 0 0
\(487\) 2.21948 0.100574 0.0502872 0.998735i \(-0.483986\pi\)
0.0502872 + 0.998735i \(0.483986\pi\)
\(488\) 0 0
\(489\) 67.5244 3.05356
\(490\) 0 0
\(491\) −38.9913 −1.75965 −0.879825 0.475297i \(-0.842341\pi\)
−0.879825 + 0.475297i \(0.842341\pi\)
\(492\) 0 0
\(493\) 0.950898 0.0428263
\(494\) 0 0
\(495\) 1.63287 0.0733921
\(496\) 0 0
\(497\) 11.0722 0.496658
\(498\) 0 0
\(499\) 41.4187 1.85416 0.927079 0.374867i \(-0.122312\pi\)
0.927079 + 0.374867i \(0.122312\pi\)
\(500\) 0 0
\(501\) 78.1019 3.48934
\(502\) 0 0
\(503\) −9.03035 −0.402643 −0.201322 0.979525i \(-0.564524\pi\)
−0.201322 + 0.979525i \(0.564524\pi\)
\(504\) 0 0
\(505\) 2.21586 0.0986043
\(506\) 0 0
\(507\) 3.25115 0.144388
\(508\) 0 0
\(509\) 32.4570 1.43863 0.719316 0.694683i \(-0.244455\pi\)
0.719316 + 0.694683i \(0.244455\pi\)
\(510\) 0 0
\(511\) −10.6272 −0.470122
\(512\) 0 0
\(513\) 75.8352 3.34820
\(514\) 0 0
\(515\) −1.72563 −0.0760405
\(516\) 0 0
\(517\) −10.5856 −0.465555
\(518\) 0 0
\(519\) −32.1878 −1.41289
\(520\) 0 0
\(521\) 15.6556 0.685883 0.342941 0.939357i \(-0.388577\pi\)
0.342941 + 0.939357i \(0.388577\pi\)
\(522\) 0 0
\(523\) 20.8745 0.912779 0.456389 0.889780i \(-0.349142\pi\)
0.456389 + 0.889780i \(0.349142\pi\)
\(524\) 0 0
\(525\) −16.1045 −0.702856
\(526\) 0 0
\(527\) −12.2347 −0.532954
\(528\) 0 0
\(529\) −4.21509 −0.183265
\(530\) 0 0
\(531\) −46.3932 −2.01329
\(532\) 0 0
\(533\) −3.79997 −0.164595
\(534\) 0 0
\(535\) −2.80199 −0.121140
\(536\) 0 0
\(537\) −2.92890 −0.126391
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 31.5755 1.35754 0.678768 0.734353i \(-0.262514\pi\)
0.678768 + 0.734353i \(0.262514\pi\)
\(542\) 0 0
\(543\) −47.1964 −2.02539
\(544\) 0 0
\(545\) 0.344735 0.0147668
\(546\) 0 0
\(547\) −16.2961 −0.696771 −0.348385 0.937351i \(-0.613270\pi\)
−0.348385 + 0.937351i \(0.613270\pi\)
\(548\) 0 0
\(549\) −9.57651 −0.408715
\(550\) 0 0
\(551\) −3.58477 −0.152716
\(552\) 0 0
\(553\) 11.7524 0.499763
\(554\) 0 0
\(555\) 1.53309 0.0650760
\(556\) 0 0
\(557\) 17.0716 0.723349 0.361674 0.932305i \(-0.382205\pi\)
0.361674 + 0.932305i \(0.382205\pi\)
\(558\) 0 0
\(559\) −2.91699 −0.123376
\(560\) 0 0
\(561\) 4.40181 0.185845
\(562\) 0 0
\(563\) −32.5537 −1.37197 −0.685987 0.727614i \(-0.740629\pi\)
−0.685987 + 0.727614i \(0.740629\pi\)
\(564\) 0 0
\(565\) −1.03010 −0.0433366
\(566\) 0 0
\(567\) 25.5943 1.07486
\(568\) 0 0
\(569\) −36.9412 −1.54866 −0.774328 0.632785i \(-0.781912\pi\)
−0.774328 + 0.632785i \(0.781912\pi\)
\(570\) 0 0
\(571\) −27.3288 −1.14368 −0.571838 0.820367i \(-0.693769\pi\)
−0.571838 + 0.820367i \(0.693769\pi\)
\(572\) 0 0
\(573\) 41.4276 1.73066
\(574\) 0 0
\(575\) −21.4691 −0.895324
\(576\) 0 0
\(577\) 4.97239 0.207003 0.103502 0.994629i \(-0.466995\pi\)
0.103502 + 0.994629i \(0.466995\pi\)
\(578\) 0 0
\(579\) −53.8948 −2.23979
\(580\) 0 0
\(581\) −13.6773 −0.567431
\(582\) 0 0
\(583\) 8.94833 0.370602
\(584\) 0 0
\(585\) 1.63287 0.0675109
\(586\) 0 0
\(587\) 6.25355 0.258112 0.129056 0.991637i \(-0.458805\pi\)
0.129056 + 0.991637i \(0.458805\pi\)
\(588\) 0 0
\(589\) 46.1235 1.90048
\(590\) 0 0
\(591\) 57.3098 2.35741
\(592\) 0 0
\(593\) −5.49143 −0.225506 −0.112753 0.993623i \(-0.535967\pi\)
−0.112753 + 0.993623i \(0.535967\pi\)
\(594\) 0 0
\(595\) 0.292048 0.0119728
\(596\) 0 0
\(597\) 26.5888 1.08821
\(598\) 0 0
\(599\) 12.4086 0.507001 0.253501 0.967335i \(-0.418418\pi\)
0.253501 + 0.967335i \(0.418418\pi\)
\(600\) 0 0
\(601\) −46.9461 −1.91497 −0.957486 0.288481i \(-0.906850\pi\)
−0.957486 + 0.288481i \(0.906850\pi\)
\(602\) 0 0
\(603\) −77.4923 −3.15573
\(604\) 0 0
\(605\) −0.215704 −0.00876962
\(606\) 0 0
\(607\) −6.31974 −0.256510 −0.128255 0.991741i \(-0.540938\pi\)
−0.128255 + 0.991741i \(0.540938\pi\)
\(608\) 0 0
\(609\) −2.28336 −0.0925265
\(610\) 0 0
\(611\) −10.5856 −0.428248
\(612\) 0 0
\(613\) 3.89919 0.157487 0.0787434 0.996895i \(-0.474909\pi\)
0.0787434 + 0.996895i \(0.474909\pi\)
\(614\) 0 0
\(615\) −2.66486 −0.107458
\(616\) 0 0
\(617\) 18.3877 0.740260 0.370130 0.928980i \(-0.379313\pi\)
0.370130 + 0.928980i \(0.379313\pi\)
\(618\) 0 0
\(619\) −30.8782 −1.24110 −0.620549 0.784168i \(-0.713090\pi\)
−0.620549 + 0.784168i \(0.713090\pi\)
\(620\) 0 0
\(621\) 64.3951 2.58408
\(622\) 0 0
\(623\) 6.89690 0.276318
\(624\) 0 0
\(625\) 24.3042 0.972170
\(626\) 0 0
\(627\) −16.5943 −0.662713
\(628\) 0 0
\(629\) 2.95983 0.118016
\(630\) 0 0
\(631\) −16.0835 −0.640276 −0.320138 0.947371i \(-0.603729\pi\)
−0.320138 + 0.947371i \(0.603729\pi\)
\(632\) 0 0
\(633\) −58.4396 −2.32277
\(634\) 0 0
\(635\) 1.22598 0.0486513
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 83.8163 3.31572
\(640\) 0 0
\(641\) −3.38611 −0.133743 −0.0668716 0.997762i \(-0.521302\pi\)
−0.0668716 + 0.997762i \(0.521302\pi\)
\(642\) 0 0
\(643\) 45.0545 1.77678 0.888388 0.459094i \(-0.151826\pi\)
0.888388 + 0.459094i \(0.151826\pi\)
\(644\) 0 0
\(645\) −2.04564 −0.0805471
\(646\) 0 0
\(647\) 2.86125 0.112487 0.0562437 0.998417i \(-0.482088\pi\)
0.0562437 + 0.998417i \(0.482088\pi\)
\(648\) 0 0
\(649\) 6.12859 0.240568
\(650\) 0 0
\(651\) 29.3789 1.15145
\(652\) 0 0
\(653\) −23.6377 −0.925013 −0.462506 0.886616i \(-0.653050\pi\)
−0.462506 + 0.886616i \(0.653050\pi\)
\(654\) 0 0
\(655\) 1.48167 0.0578936
\(656\) 0 0
\(657\) −80.4477 −3.13856
\(658\) 0 0
\(659\) 7.87286 0.306683 0.153342 0.988173i \(-0.450997\pi\)
0.153342 + 0.988173i \(0.450997\pi\)
\(660\) 0 0
\(661\) −33.0419 −1.28518 −0.642591 0.766210i \(-0.722140\pi\)
−0.642591 + 0.766210i \(0.722140\pi\)
\(662\) 0 0
\(663\) 4.40181 0.170952
\(664\) 0 0
\(665\) −1.10098 −0.0426943
\(666\) 0 0
\(667\) −3.04399 −0.117864
\(668\) 0 0
\(669\) 69.4693 2.68584
\(670\) 0 0
\(671\) 1.26507 0.0488374
\(672\) 0 0
\(673\) 13.1226 0.505838 0.252919 0.967487i \(-0.418609\pi\)
0.252919 + 0.967487i \(0.418609\pi\)
\(674\) 0 0
\(675\) −73.5966 −2.83273
\(676\) 0 0
\(677\) −8.59089 −0.330175 −0.165087 0.986279i \(-0.552791\pi\)
−0.165087 + 0.986279i \(0.552791\pi\)
\(678\) 0 0
\(679\) −9.18517 −0.352494
\(680\) 0 0
\(681\) −32.2310 −1.23509
\(682\) 0 0
\(683\) −17.9611 −0.687263 −0.343632 0.939105i \(-0.611657\pi\)
−0.343632 + 0.939105i \(0.611657\pi\)
\(684\) 0 0
\(685\) −3.24343 −0.123925
\(686\) 0 0
\(687\) −55.3821 −2.11296
\(688\) 0 0
\(689\) 8.94833 0.340904
\(690\) 0 0
\(691\) −3.51104 −0.133566 −0.0667831 0.997768i \(-0.521274\pi\)
−0.0667831 + 0.997768i \(0.521274\pi\)
\(692\) 0 0
\(693\) −7.56995 −0.287559
\(694\) 0 0
\(695\) −1.92704 −0.0730967
\(696\) 0 0
\(697\) −5.14488 −0.194876
\(698\) 0 0
\(699\) −45.4844 −1.72038
\(700\) 0 0
\(701\) −27.1928 −1.02706 −0.513529 0.858072i \(-0.671662\pi\)
−0.513529 + 0.858072i \(0.671662\pi\)
\(702\) 0 0
\(703\) −11.1582 −0.420840
\(704\) 0 0
\(705\) −7.42355 −0.279587
\(706\) 0 0
\(707\) −10.2727 −0.386343
\(708\) 0 0
\(709\) −29.4670 −1.10666 −0.553328 0.832963i \(-0.686642\pi\)
−0.553328 + 0.832963i \(0.686642\pi\)
\(710\) 0 0
\(711\) 88.9651 3.33645
\(712\) 0 0
\(713\) 39.1655 1.46676
\(714\) 0 0
\(715\) −0.215704 −0.00806688
\(716\) 0 0
\(717\) 10.7734 0.402339
\(718\) 0 0
\(719\) −52.3195 −1.95119 −0.975593 0.219585i \(-0.929530\pi\)
−0.975593 + 0.219585i \(0.929530\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) 34.2050 1.27210
\(724\) 0 0
\(725\) 3.47895 0.129205
\(726\) 0 0
\(727\) −9.69341 −0.359509 −0.179754 0.983712i \(-0.557530\pi\)
−0.179754 + 0.983712i \(0.557530\pi\)
\(728\) 0 0
\(729\) 48.8352 1.80871
\(730\) 0 0
\(731\) −3.94939 −0.146074
\(732\) 0 0
\(733\) 25.6850 0.948696 0.474348 0.880337i \(-0.342684\pi\)
0.474348 + 0.880337i \(0.342684\pi\)
\(734\) 0 0
\(735\) −0.701286 −0.0258673
\(736\) 0 0
\(737\) 10.2368 0.377079
\(738\) 0 0
\(739\) 32.7900 1.20620 0.603100 0.797665i \(-0.293932\pi\)
0.603100 + 0.797665i \(0.293932\pi\)
\(740\) 0 0
\(741\) −16.5943 −0.609607
\(742\) 0 0
\(743\) 25.6814 0.942158 0.471079 0.882091i \(-0.343865\pi\)
0.471079 + 0.882091i \(0.343865\pi\)
\(744\) 0 0
\(745\) −4.01270 −0.147014
\(746\) 0 0
\(747\) −103.537 −3.78821
\(748\) 0 0
\(749\) 12.9900 0.474643
\(750\) 0 0
\(751\) −34.6188 −1.26326 −0.631629 0.775271i \(-0.717613\pi\)
−0.631629 + 0.775271i \(0.717613\pi\)
\(752\) 0 0
\(753\) −35.3855 −1.28952
\(754\) 0 0
\(755\) 4.65198 0.169303
\(756\) 0 0
\(757\) −33.9348 −1.23338 −0.616691 0.787205i \(-0.711527\pi\)
−0.616691 + 0.787205i \(0.711527\pi\)
\(758\) 0 0
\(759\) −14.0910 −0.511470
\(760\) 0 0
\(761\) −42.4495 −1.53879 −0.769396 0.638772i \(-0.779443\pi\)
−0.769396 + 0.638772i \(0.779443\pi\)
\(762\) 0 0
\(763\) −1.59819 −0.0578582
\(764\) 0 0
\(765\) 2.21079 0.0799312
\(766\) 0 0
\(767\) 6.12859 0.221291
\(768\) 0 0
\(769\) −23.4062 −0.844050 −0.422025 0.906584i \(-0.638680\pi\)
−0.422025 + 0.906584i \(0.638680\pi\)
\(770\) 0 0
\(771\) −71.6539 −2.58055
\(772\) 0 0
\(773\) 52.7928 1.89883 0.949413 0.314031i \(-0.101680\pi\)
0.949413 + 0.314031i \(0.101680\pi\)
\(774\) 0 0
\(775\) −44.7620 −1.60790
\(776\) 0 0
\(777\) −7.10737 −0.254975
\(778\) 0 0
\(779\) 19.3956 0.694918
\(780\) 0 0
\(781\) −11.0722 −0.396196
\(782\) 0 0
\(783\) −10.4349 −0.372911
\(784\) 0 0
\(785\) −2.78252 −0.0993126
\(786\) 0 0
\(787\) 45.2805 1.61408 0.807039 0.590499i \(-0.201069\pi\)
0.807039 + 0.590499i \(0.201069\pi\)
\(788\) 0 0
\(789\) −12.6395 −0.449979
\(790\) 0 0
\(791\) 4.77551 0.169798
\(792\) 0 0
\(793\) 1.26507 0.0449239
\(794\) 0 0
\(795\) 6.27534 0.222563
\(796\) 0 0
\(797\) −17.2169 −0.609855 −0.304927 0.952376i \(-0.598632\pi\)
−0.304927 + 0.952376i \(0.598632\pi\)
\(798\) 0 0
\(799\) −14.3322 −0.507035
\(800\) 0 0
\(801\) 52.2092 1.84472
\(802\) 0 0
\(803\) 10.6272 0.375027
\(804\) 0 0
\(805\) −0.934896 −0.0329507
\(806\) 0 0
\(807\) −68.0786 −2.39648
\(808\) 0 0
\(809\) −37.0834 −1.30378 −0.651892 0.758312i \(-0.726024\pi\)
−0.651892 + 0.758312i \(0.726024\pi\)
\(810\) 0 0
\(811\) −39.9009 −1.40111 −0.700555 0.713599i \(-0.747064\pi\)
−0.700555 + 0.713599i \(0.747064\pi\)
\(812\) 0 0
\(813\) 53.9448 1.89193
\(814\) 0 0
\(815\) −4.48005 −0.156929
\(816\) 0 0
\(817\) 14.8887 0.520891
\(818\) 0 0
\(819\) −7.56995 −0.264515
\(820\) 0 0
\(821\) −23.1435 −0.807713 −0.403856 0.914822i \(-0.632330\pi\)
−0.403856 + 0.914822i \(0.632330\pi\)
\(822\) 0 0
\(823\) 11.0615 0.385581 0.192791 0.981240i \(-0.438246\pi\)
0.192791 + 0.981240i \(0.438246\pi\)
\(824\) 0 0
\(825\) 16.1045 0.560685
\(826\) 0 0
\(827\) 41.4752 1.44223 0.721117 0.692813i \(-0.243629\pi\)
0.721117 + 0.692813i \(0.243629\pi\)
\(828\) 0 0
\(829\) −32.8401 −1.14058 −0.570292 0.821442i \(-0.693170\pi\)
−0.570292 + 0.821442i \(0.693170\pi\)
\(830\) 0 0
\(831\) 45.9590 1.59430
\(832\) 0 0
\(833\) −1.35393 −0.0469108
\(834\) 0 0
\(835\) −5.18184 −0.179325
\(836\) 0 0
\(837\) 134.260 4.64071
\(838\) 0 0
\(839\) −53.0612 −1.83188 −0.915938 0.401319i \(-0.868552\pi\)
−0.915938 + 0.401319i \(0.868552\pi\)
\(840\) 0 0
\(841\) −28.5067 −0.982991
\(842\) 0 0
\(843\) 27.6104 0.950951
\(844\) 0 0
\(845\) −0.215704 −0.00742045
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 37.1417 1.27470
\(850\) 0 0
\(851\) −9.47495 −0.324797
\(852\) 0 0
\(853\) 50.0001 1.71197 0.855985 0.517000i \(-0.172951\pi\)
0.855985 + 0.517000i \(0.172951\pi\)
\(854\) 0 0
\(855\) −8.33440 −0.285030
\(856\) 0 0
\(857\) −18.5101 −0.632294 −0.316147 0.948710i \(-0.602389\pi\)
−0.316147 + 0.948710i \(0.602389\pi\)
\(858\) 0 0
\(859\) −16.3202 −0.556838 −0.278419 0.960460i \(-0.589810\pi\)
−0.278419 + 0.960460i \(0.589810\pi\)
\(860\) 0 0
\(861\) 12.3542 0.421032
\(862\) 0 0
\(863\) 29.9243 1.01863 0.509317 0.860579i \(-0.329898\pi\)
0.509317 + 0.860579i \(0.329898\pi\)
\(864\) 0 0
\(865\) 2.13557 0.0726115
\(866\) 0 0
\(867\) −49.3097 −1.67465
\(868\) 0 0
\(869\) −11.7524 −0.398673
\(870\) 0 0
\(871\) 10.2368 0.346862
\(872\) 0 0
\(873\) −69.5313 −2.35328
\(874\) 0 0
\(875\) 2.14701 0.0725820
\(876\) 0 0
\(877\) −50.8390 −1.71671 −0.858355 0.513056i \(-0.828513\pi\)
−0.858355 + 0.513056i \(0.828513\pi\)
\(878\) 0 0
\(879\) −92.8660 −3.13229
\(880\) 0 0
\(881\) 45.9576 1.54835 0.774176 0.632971i \(-0.218165\pi\)
0.774176 + 0.632971i \(0.218165\pi\)
\(882\) 0 0
\(883\) −24.6131 −0.828298 −0.414149 0.910209i \(-0.635921\pi\)
−0.414149 + 0.910209i \(0.635921\pi\)
\(884\) 0 0
\(885\) 4.29790 0.144472
\(886\) 0 0
\(887\) −13.3357 −0.447770 −0.223885 0.974616i \(-0.571874\pi\)
−0.223885 + 0.974616i \(0.571874\pi\)
\(888\) 0 0
\(889\) −5.68359 −0.190622
\(890\) 0 0
\(891\) −25.5943 −0.857442
\(892\) 0 0
\(893\) 54.0305 1.80806
\(894\) 0 0
\(895\) 0.194324 0.00649554
\(896\) 0 0
\(897\) −14.0910 −0.470484
\(898\) 0 0
\(899\) −6.34655 −0.211669
\(900\) 0 0
\(901\) 12.1154 0.403622
\(902\) 0 0
\(903\) 9.48356 0.315593
\(904\) 0 0
\(905\) 3.13135 0.104089
\(906\) 0 0
\(907\) −33.8554 −1.12415 −0.562074 0.827087i \(-0.689997\pi\)
−0.562074 + 0.827087i \(0.689997\pi\)
\(908\) 0 0
\(909\) −77.7636 −2.57925
\(910\) 0 0
\(911\) −6.15681 −0.203984 −0.101992 0.994785i \(-0.532522\pi\)
−0.101992 + 0.994785i \(0.532522\pi\)
\(912\) 0 0
\(913\) 13.6773 0.452653
\(914\) 0 0
\(915\) 0.887175 0.0293291
\(916\) 0 0
\(917\) −6.86899 −0.226834
\(918\) 0 0
\(919\) 16.1255 0.531930 0.265965 0.963983i \(-0.414309\pi\)
0.265965 + 0.963983i \(0.414309\pi\)
\(920\) 0 0
\(921\) −49.8260 −1.64182
\(922\) 0 0
\(923\) −11.0722 −0.364447
\(924\) 0 0
\(925\) 10.8288 0.356050
\(926\) 0 0
\(927\) 60.5596 1.98904
\(928\) 0 0
\(929\) −10.5610 −0.346495 −0.173247 0.984878i \(-0.555426\pi\)
−0.173247 + 0.984878i \(0.555426\pi\)
\(930\) 0 0
\(931\) 5.10414 0.167281
\(932\) 0 0
\(933\) 54.3595 1.77965
\(934\) 0 0
\(935\) −0.292048 −0.00955098
\(936\) 0 0
\(937\) 21.5682 0.704603 0.352302 0.935887i \(-0.385399\pi\)
0.352302 + 0.935887i \(0.385399\pi\)
\(938\) 0 0
\(939\) −72.0739 −2.35204
\(940\) 0 0
\(941\) 12.6688 0.412991 0.206496 0.978448i \(-0.433794\pi\)
0.206496 + 0.978448i \(0.433794\pi\)
\(942\) 0 0
\(943\) 16.4696 0.536326
\(944\) 0 0
\(945\) −3.20484 −0.104254
\(946\) 0 0
\(947\) 11.0177 0.358026 0.179013 0.983847i \(-0.442710\pi\)
0.179013 + 0.983847i \(0.442710\pi\)
\(948\) 0 0
\(949\) 10.6272 0.344975
\(950\) 0 0
\(951\) 13.3633 0.433335
\(952\) 0 0
\(953\) 50.3089 1.62967 0.814833 0.579695i \(-0.196828\pi\)
0.814833 + 0.579695i \(0.196828\pi\)
\(954\) 0 0
\(955\) −2.74860 −0.0889427
\(956\) 0 0
\(957\) 2.28336 0.0738106
\(958\) 0 0
\(959\) 15.0365 0.485553
\(960\) 0 0
\(961\) 50.6580 1.63413
\(962\) 0 0
\(963\) 98.3333 3.16875
\(964\) 0 0
\(965\) 3.57576 0.115108
\(966\) 0 0
\(967\) −50.5440 −1.62539 −0.812694 0.582691i \(-0.802000\pi\)
−0.812694 + 0.582691i \(0.802000\pi\)
\(968\) 0 0
\(969\) −22.4675 −0.721760
\(970\) 0 0
\(971\) −11.0514 −0.354657 −0.177328 0.984152i \(-0.556745\pi\)
−0.177328 + 0.984152i \(0.556745\pi\)
\(972\) 0 0
\(973\) 8.93370 0.286401
\(974\) 0 0
\(975\) 16.1045 0.515755
\(976\) 0 0
\(977\) −46.4909 −1.48737 −0.743687 0.668528i \(-0.766925\pi\)
−0.743687 + 0.668528i \(0.766925\pi\)
\(978\) 0 0
\(979\) −6.89690 −0.220426
\(980\) 0 0
\(981\) −12.0982 −0.386265
\(982\) 0 0
\(983\) 42.7163 1.36244 0.681219 0.732080i \(-0.261450\pi\)
0.681219 + 0.732080i \(0.261450\pi\)
\(984\) 0 0
\(985\) −3.80234 −0.121153
\(986\) 0 0
\(987\) 34.4154 1.09545
\(988\) 0 0
\(989\) 12.6427 0.402014
\(990\) 0 0
\(991\) −33.2073 −1.05487 −0.527433 0.849597i \(-0.676845\pi\)
−0.527433 + 0.849597i \(0.676845\pi\)
\(992\) 0 0
\(993\) −29.8858 −0.948398
\(994\) 0 0
\(995\) −1.76409 −0.0559254
\(996\) 0 0
\(997\) −27.7407 −0.878556 −0.439278 0.898351i \(-0.644766\pi\)
−0.439278 + 0.898351i \(0.644766\pi\)
\(998\) 0 0
\(999\) −32.4803 −1.02763
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 \(a_p\))