Properties

Label 6008.2.a.e.1.18
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.691575 q^{3}\) \(-1.88995 q^{5}\) \(+4.98805 q^{7}\) \(-2.52172 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.691575 q^{3}\) \(-1.88995 q^{5}\) \(+4.98805 q^{7}\) \(-2.52172 q^{9}\) \(-4.24294 q^{11}\) \(+0.255617 q^{13}\) \(+1.30704 q^{15}\) \(-8.15886 q^{17}\) \(-0.0286100 q^{19}\) \(-3.44961 q^{21}\) \(+6.59610 q^{23}\) \(-1.42810 q^{25}\) \(+3.81869 q^{27}\) \(-2.26352 q^{29}\) \(-4.18850 q^{31}\) \(+2.93431 q^{33}\) \(-9.42715 q^{35}\) \(-4.27456 q^{37}\) \(-0.176779 q^{39}\) \(-7.77543 q^{41}\) \(+11.8738 q^{43}\) \(+4.76593 q^{45}\) \(+0.0979024 q^{47}\) \(+17.8806 q^{49}\) \(+5.64246 q^{51}\) \(+2.31292 q^{53}\) \(+8.01894 q^{55}\) \(+0.0197859 q^{57}\) \(+4.83165 q^{59}\) \(+3.40707 q^{61}\) \(-12.5785 q^{63}\) \(-0.483103 q^{65}\) \(+12.2867 q^{67}\) \(-4.56170 q^{69}\) \(-11.4325 q^{71}\) \(-5.63184 q^{73}\) \(+0.987638 q^{75}\) \(-21.1640 q^{77}\) \(+7.59380 q^{79}\) \(+4.92426 q^{81}\) \(+12.0138 q^{83}\) \(+15.4198 q^{85}\) \(+1.56539 q^{87}\) \(-2.68427 q^{89}\) \(+1.27503 q^{91}\) \(+2.89666 q^{93}\) \(+0.0540713 q^{95}\) \(-1.68885 q^{97}\) \(+10.6995 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.691575 −0.399281 −0.199641 0.979869i \(-0.563977\pi\)
−0.199641 + 0.979869i \(0.563977\pi\)
\(4\) 0 0
\(5\) −1.88995 −0.845210 −0.422605 0.906314i \(-0.638884\pi\)
−0.422605 + 0.906314i \(0.638884\pi\)
\(6\) 0 0
\(7\) 4.98805 1.88531 0.942653 0.333775i \(-0.108323\pi\)
0.942653 + 0.333775i \(0.108323\pi\)
\(8\) 0 0
\(9\) −2.52172 −0.840575
\(10\) 0 0
\(11\) −4.24294 −1.27930 −0.639648 0.768668i \(-0.720920\pi\)
−0.639648 + 0.768668i \(0.720920\pi\)
\(12\) 0 0
\(13\) 0.255617 0.0708955 0.0354477 0.999372i \(-0.488714\pi\)
0.0354477 + 0.999372i \(0.488714\pi\)
\(14\) 0 0
\(15\) 1.30704 0.337476
\(16\) 0 0
\(17\) −8.15886 −1.97881 −0.989407 0.145170i \(-0.953627\pi\)
−0.989407 + 0.145170i \(0.953627\pi\)
\(18\) 0 0
\(19\) −0.0286100 −0.00656358 −0.00328179 0.999995i \(-0.501045\pi\)
−0.00328179 + 0.999995i \(0.501045\pi\)
\(20\) 0 0
\(21\) −3.44961 −0.752767
\(22\) 0 0
\(23\) 6.59610 1.37538 0.687691 0.726004i \(-0.258624\pi\)
0.687691 + 0.726004i \(0.258624\pi\)
\(24\) 0 0
\(25\) −1.42810 −0.285620
\(26\) 0 0
\(27\) 3.81869 0.734907
\(28\) 0 0
\(29\) −2.26352 −0.420325 −0.210163 0.977666i \(-0.567399\pi\)
−0.210163 + 0.977666i \(0.567399\pi\)
\(30\) 0 0
\(31\) −4.18850 −0.752277 −0.376139 0.926563i \(-0.622748\pi\)
−0.376139 + 0.926563i \(0.622748\pi\)
\(32\) 0 0
\(33\) 2.93431 0.510798
\(34\) 0 0
\(35\) −9.42715 −1.59348
\(36\) 0 0
\(37\) −4.27456 −0.702733 −0.351366 0.936238i \(-0.614283\pi\)
−0.351366 + 0.936238i \(0.614283\pi\)
\(38\) 0 0
\(39\) −0.176779 −0.0283072
\(40\) 0 0
\(41\) −7.77543 −1.21432 −0.607159 0.794580i \(-0.707691\pi\)
−0.607159 + 0.794580i \(0.707691\pi\)
\(42\) 0 0
\(43\) 11.8738 1.81075 0.905373 0.424618i \(-0.139592\pi\)
0.905373 + 0.424618i \(0.139592\pi\)
\(44\) 0 0
\(45\) 4.76593 0.710462
\(46\) 0 0
\(47\) 0.0979024 0.0142805 0.00714027 0.999975i \(-0.497727\pi\)
0.00714027 + 0.999975i \(0.497727\pi\)
\(48\) 0 0
\(49\) 17.8806 2.55438
\(50\) 0 0
\(51\) 5.64246 0.790103
\(52\) 0 0
\(53\) 2.31292 0.317703 0.158852 0.987302i \(-0.449221\pi\)
0.158852 + 0.987302i \(0.449221\pi\)
\(54\) 0 0
\(55\) 8.01894 1.08127
\(56\) 0 0
\(57\) 0.0197859 0.00262071
\(58\) 0 0
\(59\) 4.83165 0.629027 0.314514 0.949253i \(-0.398159\pi\)
0.314514 + 0.949253i \(0.398159\pi\)
\(60\) 0 0
\(61\) 3.40707 0.436230 0.218115 0.975923i \(-0.430009\pi\)
0.218115 + 0.975923i \(0.430009\pi\)
\(62\) 0 0
\(63\) −12.5785 −1.58474
\(64\) 0 0
\(65\) −0.483103 −0.0599216
\(66\) 0 0
\(67\) 12.2867 1.50107 0.750533 0.660833i \(-0.229797\pi\)
0.750533 + 0.660833i \(0.229797\pi\)
\(68\) 0 0
\(69\) −4.56170 −0.549164
\(70\) 0 0
\(71\) −11.4325 −1.35679 −0.678393 0.734699i \(-0.737323\pi\)
−0.678393 + 0.734699i \(0.737323\pi\)
\(72\) 0 0
\(73\) −5.63184 −0.659158 −0.329579 0.944128i \(-0.606907\pi\)
−0.329579 + 0.944128i \(0.606907\pi\)
\(74\) 0 0
\(75\) 0.987638 0.114043
\(76\) 0 0
\(77\) −21.1640 −2.41186
\(78\) 0 0
\(79\) 7.59380 0.854369 0.427184 0.904165i \(-0.359506\pi\)
0.427184 + 0.904165i \(0.359506\pi\)
\(80\) 0 0
\(81\) 4.92426 0.547140
\(82\) 0 0
\(83\) 12.0138 1.31869 0.659345 0.751841i \(-0.270834\pi\)
0.659345 + 0.751841i \(0.270834\pi\)
\(84\) 0 0
\(85\) 15.4198 1.67251
\(86\) 0 0
\(87\) 1.56539 0.167828
\(88\) 0 0
\(89\) −2.68427 −0.284533 −0.142266 0.989828i \(-0.545439\pi\)
−0.142266 + 0.989828i \(0.545439\pi\)
\(90\) 0 0
\(91\) 1.27503 0.133660
\(92\) 0 0
\(93\) 2.89666 0.300370
\(94\) 0 0
\(95\) 0.0540713 0.00554760
\(96\) 0 0
\(97\) −1.68885 −0.171477 −0.0857386 0.996318i \(-0.527325\pi\)
−0.0857386 + 0.996318i \(0.527325\pi\)
\(98\) 0 0
\(99\) 10.6995 1.07534
\(100\) 0 0
\(101\) 13.6186 1.35510 0.677551 0.735476i \(-0.263041\pi\)
0.677551 + 0.735476i \(0.263041\pi\)
\(102\) 0 0
\(103\) 4.91857 0.484641 0.242320 0.970196i \(-0.422091\pi\)
0.242320 + 0.970196i \(0.422091\pi\)
\(104\) 0 0
\(105\) 6.51958 0.636246
\(106\) 0 0
\(107\) −4.92934 −0.476537 −0.238268 0.971199i \(-0.576580\pi\)
−0.238268 + 0.971199i \(0.576580\pi\)
\(108\) 0 0
\(109\) 3.25276 0.311557 0.155779 0.987792i \(-0.450211\pi\)
0.155779 + 0.987792i \(0.450211\pi\)
\(110\) 0 0
\(111\) 2.95618 0.280588
\(112\) 0 0
\(113\) −20.6477 −1.94237 −0.971187 0.238320i \(-0.923403\pi\)
−0.971187 + 0.238320i \(0.923403\pi\)
\(114\) 0 0
\(115\) −12.4663 −1.16249
\(116\) 0 0
\(117\) −0.644596 −0.0595929
\(118\) 0 0
\(119\) −40.6968 −3.73067
\(120\) 0 0
\(121\) 7.00257 0.636597
\(122\) 0 0
\(123\) 5.37729 0.484854
\(124\) 0 0
\(125\) 12.1488 1.08662
\(126\) 0 0
\(127\) −11.8670 −1.05303 −0.526513 0.850167i \(-0.676501\pi\)
−0.526513 + 0.850167i \(0.676501\pi\)
\(128\) 0 0
\(129\) −8.21166 −0.722996
\(130\) 0 0
\(131\) 11.3654 0.993002 0.496501 0.868036i \(-0.334618\pi\)
0.496501 + 0.868036i \(0.334618\pi\)
\(132\) 0 0
\(133\) −0.142708 −0.0123743
\(134\) 0 0
\(135\) −7.21712 −0.621151
\(136\) 0 0
\(137\) 19.5731 1.67224 0.836121 0.548545i \(-0.184818\pi\)
0.836121 + 0.548545i \(0.184818\pi\)
\(138\) 0 0
\(139\) 12.3930 1.05116 0.525580 0.850744i \(-0.323848\pi\)
0.525580 + 0.850744i \(0.323848\pi\)
\(140\) 0 0
\(141\) −0.0677069 −0.00570195
\(142\) 0 0
\(143\) −1.08457 −0.0906963
\(144\) 0 0
\(145\) 4.27793 0.355263
\(146\) 0 0
\(147\) −12.3658 −1.01991
\(148\) 0 0
\(149\) −3.77070 −0.308908 −0.154454 0.988000i \(-0.549362\pi\)
−0.154454 + 0.988000i \(0.549362\pi\)
\(150\) 0 0
\(151\) −0.819040 −0.0666526 −0.0333263 0.999445i \(-0.510610\pi\)
−0.0333263 + 0.999445i \(0.510610\pi\)
\(152\) 0 0
\(153\) 20.5744 1.66334
\(154\) 0 0
\(155\) 7.91605 0.635832
\(156\) 0 0
\(157\) −21.9452 −1.75142 −0.875709 0.482839i \(-0.839605\pi\)
−0.875709 + 0.482839i \(0.839605\pi\)
\(158\) 0 0
\(159\) −1.59955 −0.126853
\(160\) 0 0
\(161\) 32.9017 2.59301
\(162\) 0 0
\(163\) −4.46062 −0.349383 −0.174691 0.984623i \(-0.555893\pi\)
−0.174691 + 0.984623i \(0.555893\pi\)
\(164\) 0 0
\(165\) −5.54570 −0.431732
\(166\) 0 0
\(167\) −4.98379 −0.385658 −0.192829 0.981232i \(-0.561766\pi\)
−0.192829 + 0.981232i \(0.561766\pi\)
\(168\) 0 0
\(169\) −12.9347 −0.994974
\(170\) 0 0
\(171\) 0.0721464 0.00551718
\(172\) 0 0
\(173\) 25.3664 1.92857 0.964287 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(174\) 0 0
\(175\) −7.12343 −0.538481
\(176\) 0 0
\(177\) −3.34145 −0.251159
\(178\) 0 0
\(179\) 13.2611 0.991182 0.495591 0.868556i \(-0.334951\pi\)
0.495591 + 0.868556i \(0.334951\pi\)
\(180\) 0 0
\(181\) 1.86567 0.138674 0.0693372 0.997593i \(-0.477912\pi\)
0.0693372 + 0.997593i \(0.477912\pi\)
\(182\) 0 0
\(183\) −2.35624 −0.174178
\(184\) 0 0
\(185\) 8.07869 0.593957
\(186\) 0 0
\(187\) 34.6176 2.53149
\(188\) 0 0
\(189\) 19.0478 1.38552
\(190\) 0 0
\(191\) 17.8772 1.29355 0.646773 0.762682i \(-0.276118\pi\)
0.646773 + 0.762682i \(0.276118\pi\)
\(192\) 0 0
\(193\) 5.12261 0.368734 0.184367 0.982857i \(-0.440977\pi\)
0.184367 + 0.982857i \(0.440977\pi\)
\(194\) 0 0
\(195\) 0.334102 0.0239256
\(196\) 0 0
\(197\) −12.8588 −0.916152 −0.458076 0.888913i \(-0.651461\pi\)
−0.458076 + 0.888913i \(0.651461\pi\)
\(198\) 0 0
\(199\) 7.73338 0.548205 0.274103 0.961700i \(-0.411619\pi\)
0.274103 + 0.961700i \(0.411619\pi\)
\(200\) 0 0
\(201\) −8.49721 −0.599347
\(202\) 0 0
\(203\) −11.2906 −0.792441
\(204\) 0 0
\(205\) 14.6952 1.02635
\(206\) 0 0
\(207\) −16.6335 −1.15611
\(208\) 0 0
\(209\) 0.121390 0.00839675
\(210\) 0 0
\(211\) −1.74255 −0.119962 −0.0599810 0.998200i \(-0.519104\pi\)
−0.0599810 + 0.998200i \(0.519104\pi\)
\(212\) 0 0
\(213\) 7.90642 0.541739
\(214\) 0 0
\(215\) −22.4410 −1.53046
\(216\) 0 0
\(217\) −20.8925 −1.41827
\(218\) 0 0
\(219\) 3.89484 0.263189
\(220\) 0 0
\(221\) −2.08555 −0.140289
\(222\) 0 0
\(223\) −4.25485 −0.284926 −0.142463 0.989800i \(-0.545502\pi\)
−0.142463 + 0.989800i \(0.545502\pi\)
\(224\) 0 0
\(225\) 3.60127 0.240085
\(226\) 0 0
\(227\) 20.2454 1.34373 0.671866 0.740673i \(-0.265493\pi\)
0.671866 + 0.740673i \(0.265493\pi\)
\(228\) 0 0
\(229\) 3.96675 0.262130 0.131065 0.991374i \(-0.458160\pi\)
0.131065 + 0.991374i \(0.458160\pi\)
\(230\) 0 0
\(231\) 14.6365 0.963011
\(232\) 0 0
\(233\) −17.4979 −1.14633 −0.573164 0.819441i \(-0.694284\pi\)
−0.573164 + 0.819441i \(0.694284\pi\)
\(234\) 0 0
\(235\) −0.185030 −0.0120701
\(236\) 0 0
\(237\) −5.25168 −0.341133
\(238\) 0 0
\(239\) −22.8325 −1.47691 −0.738456 0.674301i \(-0.764445\pi\)
−0.738456 + 0.674301i \(0.764445\pi\)
\(240\) 0 0
\(241\) 27.9795 1.80232 0.901160 0.433486i \(-0.142717\pi\)
0.901160 + 0.433486i \(0.142717\pi\)
\(242\) 0 0
\(243\) −14.8616 −0.953369
\(244\) 0 0
\(245\) −33.7935 −2.15899
\(246\) 0 0
\(247\) −0.00731320 −0.000465328 0
\(248\) 0 0
\(249\) −8.30847 −0.526528
\(250\) 0 0
\(251\) −16.2334 −1.02464 −0.512320 0.858794i \(-0.671214\pi\)
−0.512320 + 0.858794i \(0.671214\pi\)
\(252\) 0 0
\(253\) −27.9869 −1.75952
\(254\) 0 0
\(255\) −10.6640 −0.667803
\(256\) 0 0
\(257\) −8.22214 −0.512883 −0.256442 0.966560i \(-0.582550\pi\)
−0.256442 + 0.966560i \(0.582550\pi\)
\(258\) 0 0
\(259\) −21.3217 −1.32487
\(260\) 0 0
\(261\) 5.70797 0.353315
\(262\) 0 0
\(263\) 16.2834 1.00408 0.502038 0.864846i \(-0.332584\pi\)
0.502038 + 0.864846i \(0.332584\pi\)
\(264\) 0 0
\(265\) −4.37129 −0.268526
\(266\) 0 0
\(267\) 1.85638 0.113608
\(268\) 0 0
\(269\) −10.7345 −0.654495 −0.327248 0.944939i \(-0.606121\pi\)
−0.327248 + 0.944939i \(0.606121\pi\)
\(270\) 0 0
\(271\) −17.5461 −1.06585 −0.532925 0.846163i \(-0.678907\pi\)
−0.532925 + 0.846163i \(0.678907\pi\)
\(272\) 0 0
\(273\) −0.881780 −0.0533678
\(274\) 0 0
\(275\) 6.05934 0.365392
\(276\) 0 0
\(277\) −13.6792 −0.821906 −0.410953 0.911657i \(-0.634804\pi\)
−0.410953 + 0.911657i \(0.634804\pi\)
\(278\) 0 0
\(279\) 10.5622 0.632345
\(280\) 0 0
\(281\) 9.60169 0.572789 0.286394 0.958112i \(-0.407543\pi\)
0.286394 + 0.958112i \(0.407543\pi\)
\(282\) 0 0
\(283\) 19.4532 1.15638 0.578188 0.815904i \(-0.303760\pi\)
0.578188 + 0.815904i \(0.303760\pi\)
\(284\) 0 0
\(285\) −0.0373944 −0.00221505
\(286\) 0 0
\(287\) −38.7842 −2.28936
\(288\) 0 0
\(289\) 49.5670 2.91570
\(290\) 0 0
\(291\) 1.16797 0.0684676
\(292\) 0 0
\(293\) 8.99532 0.525512 0.262756 0.964862i \(-0.415369\pi\)
0.262756 + 0.964862i \(0.415369\pi\)
\(294\) 0 0
\(295\) −9.13157 −0.531660
\(296\) 0 0
\(297\) −16.2025 −0.940163
\(298\) 0 0
\(299\) 1.68608 0.0975084
\(300\) 0 0
\(301\) 59.2274 3.41381
\(302\) 0 0
\(303\) −9.41828 −0.541066
\(304\) 0 0
\(305\) −6.43918 −0.368706
\(306\) 0 0
\(307\) 15.7568 0.899285 0.449643 0.893209i \(-0.351551\pi\)
0.449643 + 0.893209i \(0.351551\pi\)
\(308\) 0 0
\(309\) −3.40156 −0.193508
\(310\) 0 0
\(311\) 23.2569 1.31878 0.659388 0.751803i \(-0.270816\pi\)
0.659388 + 0.751803i \(0.270816\pi\)
\(312\) 0 0
\(313\) 25.0317 1.41488 0.707438 0.706775i \(-0.249851\pi\)
0.707438 + 0.706775i \(0.249851\pi\)
\(314\) 0 0
\(315\) 23.7727 1.33944
\(316\) 0 0
\(317\) 16.7785 0.942375 0.471188 0.882033i \(-0.343825\pi\)
0.471188 + 0.882033i \(0.343825\pi\)
\(318\) 0 0
\(319\) 9.60399 0.537720
\(320\) 0 0
\(321\) 3.40901 0.190272
\(322\) 0 0
\(323\) 0.233425 0.0129881
\(324\) 0 0
\(325\) −0.365047 −0.0202492
\(326\) 0 0
\(327\) −2.24952 −0.124399
\(328\) 0 0
\(329\) 0.488342 0.0269232
\(330\) 0 0
\(331\) −3.53931 −0.194538 −0.0972690 0.995258i \(-0.531011\pi\)
−0.0972690 + 0.995258i \(0.531011\pi\)
\(332\) 0 0
\(333\) 10.7793 0.590699
\(334\) 0 0
\(335\) −23.2213 −1.26872
\(336\) 0 0
\(337\) 34.0094 1.85261 0.926305 0.376776i \(-0.122967\pi\)
0.926305 + 0.376776i \(0.122967\pi\)
\(338\) 0 0
\(339\) 14.2794 0.775553
\(340\) 0 0
\(341\) 17.7716 0.962385
\(342\) 0 0
\(343\) 54.2732 2.93048
\(344\) 0 0
\(345\) 8.62137 0.464159
\(346\) 0 0
\(347\) −10.5553 −0.566636 −0.283318 0.959026i \(-0.591435\pi\)
−0.283318 + 0.959026i \(0.591435\pi\)
\(348\) 0 0
\(349\) 14.0269 0.750842 0.375421 0.926854i \(-0.377498\pi\)
0.375421 + 0.926854i \(0.377498\pi\)
\(350\) 0 0
\(351\) 0.976122 0.0521016
\(352\) 0 0
\(353\) −26.8192 −1.42744 −0.713721 0.700430i \(-0.752992\pi\)
−0.713721 + 0.700430i \(0.752992\pi\)
\(354\) 0 0
\(355\) 21.6068 1.14677
\(356\) 0 0
\(357\) 28.1449 1.48959
\(358\) 0 0
\(359\) 15.7200 0.829672 0.414836 0.909896i \(-0.363839\pi\)
0.414836 + 0.909896i \(0.363839\pi\)
\(360\) 0 0
\(361\) −18.9992 −0.999957
\(362\) 0 0
\(363\) −4.84280 −0.254181
\(364\) 0 0
\(365\) 10.6439 0.557127
\(366\) 0 0
\(367\) 19.6533 1.02589 0.512947 0.858420i \(-0.328554\pi\)
0.512947 + 0.858420i \(0.328554\pi\)
\(368\) 0 0
\(369\) 19.6075 1.02073
\(370\) 0 0
\(371\) 11.5369 0.598968
\(372\) 0 0
\(373\) −10.2903 −0.532811 −0.266406 0.963861i \(-0.585836\pi\)
−0.266406 + 0.963861i \(0.585836\pi\)
\(374\) 0 0
\(375\) −8.40179 −0.433866
\(376\) 0 0
\(377\) −0.578595 −0.0297992
\(378\) 0 0
\(379\) 13.7445 0.706008 0.353004 0.935622i \(-0.385160\pi\)
0.353004 + 0.935622i \(0.385160\pi\)
\(380\) 0 0
\(381\) 8.20691 0.420453
\(382\) 0 0
\(383\) 8.82959 0.451171 0.225585 0.974223i \(-0.427571\pi\)
0.225585 + 0.974223i \(0.427571\pi\)
\(384\) 0 0
\(385\) 39.9989 2.03853
\(386\) 0 0
\(387\) −29.9426 −1.52207
\(388\) 0 0
\(389\) −21.9808 −1.11447 −0.557235 0.830355i \(-0.688138\pi\)
−0.557235 + 0.830355i \(0.688138\pi\)
\(390\) 0 0
\(391\) −53.8166 −2.72162
\(392\) 0 0
\(393\) −7.86005 −0.396487
\(394\) 0 0
\(395\) −14.3519 −0.722121
\(396\) 0 0
\(397\) 19.2475 0.966003 0.483002 0.875620i \(-0.339547\pi\)
0.483002 + 0.875620i \(0.339547\pi\)
\(398\) 0 0
\(399\) 0.0986932 0.00494084
\(400\) 0 0
\(401\) 2.85175 0.142410 0.0712049 0.997462i \(-0.477316\pi\)
0.0712049 + 0.997462i \(0.477316\pi\)
\(402\) 0 0
\(403\) −1.07065 −0.0533331
\(404\) 0 0
\(405\) −9.30660 −0.462449
\(406\) 0 0
\(407\) 18.1367 0.899003
\(408\) 0 0
\(409\) −16.1676 −0.799435 −0.399717 0.916638i \(-0.630892\pi\)
−0.399717 + 0.916638i \(0.630892\pi\)
\(410\) 0 0
\(411\) −13.5363 −0.667695
\(412\) 0 0
\(413\) 24.1005 1.18591
\(414\) 0 0
\(415\) −22.7055 −1.11457
\(416\) 0 0
\(417\) −8.57069 −0.419709
\(418\) 0 0
\(419\) −12.7360 −0.622195 −0.311097 0.950378i \(-0.600697\pi\)
−0.311097 + 0.950378i \(0.600697\pi\)
\(420\) 0 0
\(421\) 20.2736 0.988074 0.494037 0.869441i \(-0.335521\pi\)
0.494037 + 0.869441i \(0.335521\pi\)
\(422\) 0 0
\(423\) −0.246883 −0.0120039
\(424\) 0 0
\(425\) 11.6517 0.565188
\(426\) 0 0
\(427\) 16.9946 0.822427
\(428\) 0 0
\(429\) 0.750061 0.0362133
\(430\) 0 0
\(431\) −6.82368 −0.328685 −0.164343 0.986403i \(-0.552550\pi\)
−0.164343 + 0.986403i \(0.552550\pi\)
\(432\) 0 0
\(433\) 16.9063 0.812467 0.406234 0.913769i \(-0.366842\pi\)
0.406234 + 0.913769i \(0.366842\pi\)
\(434\) 0 0
\(435\) −2.95851 −0.141850
\(436\) 0 0
\(437\) −0.188714 −0.00902742
\(438\) 0 0
\(439\) 29.1028 1.38900 0.694501 0.719492i \(-0.255625\pi\)
0.694501 + 0.719492i \(0.255625\pi\)
\(440\) 0 0
\(441\) −45.0900 −2.14714
\(442\) 0 0
\(443\) 9.52297 0.452450 0.226225 0.974075i \(-0.427362\pi\)
0.226225 + 0.974075i \(0.427362\pi\)
\(444\) 0 0
\(445\) 5.07314 0.240490
\(446\) 0 0
\(447\) 2.60772 0.123341
\(448\) 0 0
\(449\) 39.5773 1.86777 0.933884 0.357575i \(-0.116396\pi\)
0.933884 + 0.357575i \(0.116396\pi\)
\(450\) 0 0
\(451\) 32.9907 1.55347
\(452\) 0 0
\(453\) 0.566428 0.0266131
\(454\) 0 0
\(455\) −2.40974 −0.112970
\(456\) 0 0
\(457\) 8.83127 0.413110 0.206555 0.978435i \(-0.433775\pi\)
0.206555 + 0.978435i \(0.433775\pi\)
\(458\) 0 0
\(459\) −31.1561 −1.45424
\(460\) 0 0
\(461\) 40.2058 1.87257 0.936285 0.351242i \(-0.114241\pi\)
0.936285 + 0.351242i \(0.114241\pi\)
\(462\) 0 0
\(463\) −22.7668 −1.05806 −0.529031 0.848603i \(-0.677444\pi\)
−0.529031 + 0.848603i \(0.677444\pi\)
\(464\) 0 0
\(465\) −5.47454 −0.253876
\(466\) 0 0
\(467\) −2.17948 −0.100854 −0.0504272 0.998728i \(-0.516058\pi\)
−0.0504272 + 0.998728i \(0.516058\pi\)
\(468\) 0 0
\(469\) 61.2869 2.82997
\(470\) 0 0
\(471\) 15.1768 0.699308
\(472\) 0 0
\(473\) −50.3801 −2.31648
\(474\) 0 0
\(475\) 0.0408579 0.00187469
\(476\) 0 0
\(477\) −5.83253 −0.267053
\(478\) 0 0
\(479\) 21.4534 0.980232 0.490116 0.871657i \(-0.336954\pi\)
0.490116 + 0.871657i \(0.336954\pi\)
\(480\) 0 0
\(481\) −1.09265 −0.0498206
\(482\) 0 0
\(483\) −22.7540 −1.03534
\(484\) 0 0
\(485\) 3.19185 0.144934
\(486\) 0 0
\(487\) −11.8786 −0.538269 −0.269134 0.963103i \(-0.586738\pi\)
−0.269134 + 0.963103i \(0.586738\pi\)
\(488\) 0 0
\(489\) 3.08485 0.139502
\(490\) 0 0
\(491\) −5.35041 −0.241461 −0.120730 0.992685i \(-0.538524\pi\)
−0.120730 + 0.992685i \(0.538524\pi\)
\(492\) 0 0
\(493\) 18.4677 0.831745
\(494\) 0 0
\(495\) −20.2215 −0.908891
\(496\) 0 0
\(497\) −57.0258 −2.55796
\(498\) 0 0
\(499\) 6.43138 0.287908 0.143954 0.989584i \(-0.454018\pi\)
0.143954 + 0.989584i \(0.454018\pi\)
\(500\) 0 0
\(501\) 3.44667 0.153986
\(502\) 0 0
\(503\) −29.1140 −1.29813 −0.649064 0.760734i \(-0.724839\pi\)
−0.649064 + 0.760734i \(0.724839\pi\)
\(504\) 0 0
\(505\) −25.7384 −1.14535
\(506\) 0 0
\(507\) 8.94529 0.397274
\(508\) 0 0
\(509\) 16.1478 0.715737 0.357869 0.933772i \(-0.383504\pi\)
0.357869 + 0.933772i \(0.383504\pi\)
\(510\) 0 0
\(511\) −28.0919 −1.24271
\(512\) 0 0
\(513\) −0.109252 −0.00482362
\(514\) 0 0
\(515\) −9.29583 −0.409623
\(516\) 0 0
\(517\) −0.415394 −0.0182690
\(518\) 0 0
\(519\) −17.5428 −0.770043
\(520\) 0 0
\(521\) 33.7289 1.47769 0.738845 0.673876i \(-0.235372\pi\)
0.738845 + 0.673876i \(0.235372\pi\)
\(522\) 0 0
\(523\) −12.4235 −0.543242 −0.271621 0.962404i \(-0.587560\pi\)
−0.271621 + 0.962404i \(0.587560\pi\)
\(524\) 0 0
\(525\) 4.92639 0.215005
\(526\) 0 0
\(527\) 34.1734 1.48862
\(528\) 0 0
\(529\) 20.5085 0.891675
\(530\) 0 0
\(531\) −12.1841 −0.528744
\(532\) 0 0
\(533\) −1.98753 −0.0860897
\(534\) 0 0
\(535\) 9.31619 0.402774
\(536\) 0 0
\(537\) −9.17106 −0.395760
\(538\) 0 0
\(539\) −75.8665 −3.26780
\(540\) 0 0
\(541\) −4.64455 −0.199685 −0.0998423 0.995003i \(-0.531834\pi\)
−0.0998423 + 0.995003i \(0.531834\pi\)
\(542\) 0 0
\(543\) −1.29025 −0.0553700
\(544\) 0 0
\(545\) −6.14754 −0.263332
\(546\) 0 0
\(547\) −8.77503 −0.375193 −0.187597 0.982246i \(-0.560070\pi\)
−0.187597 + 0.982246i \(0.560070\pi\)
\(548\) 0 0
\(549\) −8.59168 −0.366684
\(550\) 0 0
\(551\) 0.0647592 0.00275884
\(552\) 0 0
\(553\) 37.8782 1.61075
\(554\) 0 0
\(555\) −5.58702 −0.237156
\(556\) 0 0
\(557\) 22.7624 0.964475 0.482238 0.876040i \(-0.339824\pi\)
0.482238 + 0.876040i \(0.339824\pi\)
\(558\) 0 0
\(559\) 3.03516 0.128374
\(560\) 0 0
\(561\) −23.9406 −1.01077
\(562\) 0 0
\(563\) −25.5518 −1.07688 −0.538441 0.842664i \(-0.680986\pi\)
−0.538441 + 0.842664i \(0.680986\pi\)
\(564\) 0 0
\(565\) 39.0231 1.64171
\(566\) 0 0
\(567\) 24.5625 1.03153
\(568\) 0 0
\(569\) 42.2344 1.77056 0.885278 0.465062i \(-0.153968\pi\)
0.885278 + 0.465062i \(0.153968\pi\)
\(570\) 0 0
\(571\) 8.50536 0.355938 0.177969 0.984036i \(-0.443047\pi\)
0.177969 + 0.984036i \(0.443047\pi\)
\(572\) 0 0
\(573\) −12.3634 −0.516489
\(574\) 0 0
\(575\) −9.41988 −0.392836
\(576\) 0 0
\(577\) −0.547439 −0.0227902 −0.0113951 0.999935i \(-0.503627\pi\)
−0.0113951 + 0.999935i \(0.503627\pi\)
\(578\) 0 0
\(579\) −3.54267 −0.147228
\(580\) 0 0
\(581\) 59.9256 2.48613
\(582\) 0 0
\(583\) −9.81357 −0.406436
\(584\) 0 0
\(585\) 1.21825 0.0503686
\(586\) 0 0
\(587\) −8.52515 −0.351871 −0.175935 0.984402i \(-0.556295\pi\)
−0.175935 + 0.984402i \(0.556295\pi\)
\(588\) 0 0
\(589\) 0.119833 0.00493763
\(590\) 0 0
\(591\) 8.89283 0.365802
\(592\) 0 0
\(593\) 22.7567 0.934504 0.467252 0.884124i \(-0.345244\pi\)
0.467252 + 0.884124i \(0.345244\pi\)
\(594\) 0 0
\(595\) 76.9148 3.15320
\(596\) 0 0
\(597\) −5.34822 −0.218888
\(598\) 0 0
\(599\) −7.10721 −0.290393 −0.145196 0.989403i \(-0.546381\pi\)
−0.145196 + 0.989403i \(0.546381\pi\)
\(600\) 0 0
\(601\) −12.5116 −0.510359 −0.255180 0.966894i \(-0.582135\pi\)
−0.255180 + 0.966894i \(0.582135\pi\)
\(602\) 0 0
\(603\) −30.9838 −1.26176
\(604\) 0 0
\(605\) −13.2345 −0.538058
\(606\) 0 0
\(607\) −25.6990 −1.04309 −0.521545 0.853224i \(-0.674644\pi\)
−0.521545 + 0.853224i \(0.674644\pi\)
\(608\) 0 0
\(609\) 7.80826 0.316407
\(610\) 0 0
\(611\) 0.0250256 0.00101243
\(612\) 0 0
\(613\) −3.43544 −0.138756 −0.0693780 0.997590i \(-0.522101\pi\)
−0.0693780 + 0.997590i \(0.522101\pi\)
\(614\) 0 0
\(615\) −10.1628 −0.409804
\(616\) 0 0
\(617\) −18.1933 −0.732436 −0.366218 0.930529i \(-0.619348\pi\)
−0.366218 + 0.930529i \(0.619348\pi\)
\(618\) 0 0
\(619\) 21.9770 0.883329 0.441665 0.897180i \(-0.354388\pi\)
0.441665 + 0.897180i \(0.354388\pi\)
\(620\) 0 0
\(621\) 25.1884 1.01078
\(622\) 0 0
\(623\) −13.3893 −0.536431
\(624\) 0 0
\(625\) −15.8200 −0.632801
\(626\) 0 0
\(627\) −0.0839506 −0.00335266
\(628\) 0 0
\(629\) 34.8755 1.39058
\(630\) 0 0
\(631\) −10.6174 −0.422670 −0.211335 0.977414i \(-0.567781\pi\)
−0.211335 + 0.977414i \(0.567781\pi\)
\(632\) 0 0
\(633\) 1.20510 0.0478986
\(634\) 0 0
\(635\) 22.4280 0.890027
\(636\) 0 0
\(637\) 4.57060 0.181094
\(638\) 0 0
\(639\) 28.8296 1.14048
\(640\) 0 0
\(641\) −11.1469 −0.440274 −0.220137 0.975469i \(-0.570650\pi\)
−0.220137 + 0.975469i \(0.570650\pi\)
\(642\) 0 0
\(643\) −6.25517 −0.246680 −0.123340 0.992364i \(-0.539361\pi\)
−0.123340 + 0.992364i \(0.539361\pi\)
\(644\) 0 0
\(645\) 15.5196 0.611084
\(646\) 0 0
\(647\) −12.9942 −0.510854 −0.255427 0.966828i \(-0.582216\pi\)
−0.255427 + 0.966828i \(0.582216\pi\)
\(648\) 0 0
\(649\) −20.5004 −0.804712
\(650\) 0 0
\(651\) 14.4487 0.566289
\(652\) 0 0
\(653\) −36.6494 −1.43420 −0.717100 0.696970i \(-0.754531\pi\)
−0.717100 + 0.696970i \(0.754531\pi\)
\(654\) 0 0
\(655\) −21.4801 −0.839296
\(656\) 0 0
\(657\) 14.2020 0.554071
\(658\) 0 0
\(659\) 30.5912 1.19166 0.595831 0.803110i \(-0.296823\pi\)
0.595831 + 0.803110i \(0.296823\pi\)
\(660\) 0 0
\(661\) −28.3480 −1.10261 −0.551305 0.834304i \(-0.685870\pi\)
−0.551305 + 0.834304i \(0.685870\pi\)
\(662\) 0 0
\(663\) 1.44231 0.0560147
\(664\) 0 0
\(665\) 0.269710 0.0104589
\(666\) 0 0
\(667\) −14.9304 −0.578108
\(668\) 0 0
\(669\) 2.94255 0.113765
\(670\) 0 0
\(671\) −14.4560 −0.558067
\(672\) 0 0
\(673\) 15.9364 0.614304 0.307152 0.951661i \(-0.400624\pi\)
0.307152 + 0.951661i \(0.400624\pi\)
\(674\) 0 0
\(675\) −5.45346 −0.209904
\(676\) 0 0
\(677\) −27.8347 −1.06977 −0.534887 0.844923i \(-0.679646\pi\)
−0.534887 + 0.844923i \(0.679646\pi\)
\(678\) 0 0
\(679\) −8.42409 −0.323287
\(680\) 0 0
\(681\) −14.0012 −0.536526
\(682\) 0 0
\(683\) −38.7950 −1.48445 −0.742225 0.670150i \(-0.766230\pi\)
−0.742225 + 0.670150i \(0.766230\pi\)
\(684\) 0 0
\(685\) −36.9921 −1.41340
\(686\) 0 0
\(687\) −2.74331 −0.104664
\(688\) 0 0
\(689\) 0.591221 0.0225237
\(690\) 0 0
\(691\) −4.98620 −0.189684 −0.0948420 0.995492i \(-0.530235\pi\)
−0.0948420 + 0.995492i \(0.530235\pi\)
\(692\) 0 0
\(693\) 53.3698 2.02735
\(694\) 0 0
\(695\) −23.4221 −0.888452
\(696\) 0 0
\(697\) 63.4386 2.40291
\(698\) 0 0
\(699\) 12.1011 0.457707
\(700\) 0 0
\(701\) −3.35330 −0.126652 −0.0633262 0.997993i \(-0.520171\pi\)
−0.0633262 + 0.997993i \(0.520171\pi\)
\(702\) 0 0
\(703\) 0.122295 0.00461244
\(704\) 0 0
\(705\) 0.127962 0.00481934
\(706\) 0 0
\(707\) 67.9302 2.55478
\(708\) 0 0
\(709\) −11.8302 −0.444291 −0.222145 0.975014i \(-0.571306\pi\)
−0.222145 + 0.975014i \(0.571306\pi\)
\(710\) 0 0
\(711\) −19.1495 −0.718161
\(712\) 0 0
\(713\) −27.6278 −1.03467
\(714\) 0 0
\(715\) 2.04978 0.0766574
\(716\) 0 0
\(717\) 15.7904 0.589703
\(718\) 0 0
\(719\) 15.0120 0.559853 0.279926 0.960021i \(-0.409690\pi\)
0.279926 + 0.960021i \(0.409690\pi\)
\(720\) 0 0
\(721\) 24.5341 0.913696
\(722\) 0 0
\(723\) −19.3500 −0.719632
\(724\) 0 0
\(725\) 3.23253 0.120053
\(726\) 0 0
\(727\) 45.4234 1.68466 0.842331 0.538961i \(-0.181183\pi\)
0.842331 + 0.538961i \(0.181183\pi\)
\(728\) 0 0
\(729\) −4.49490 −0.166478
\(730\) 0 0
\(731\) −96.8770 −3.58313
\(732\) 0 0
\(733\) −29.7212 −1.09778 −0.548889 0.835895i \(-0.684949\pi\)
−0.548889 + 0.835895i \(0.684949\pi\)
\(734\) 0 0
\(735\) 23.3707 0.862042
\(736\) 0 0
\(737\) −52.1320 −1.92031
\(738\) 0 0
\(739\) 38.4850 1.41569 0.707847 0.706366i \(-0.249667\pi\)
0.707847 + 0.706366i \(0.249667\pi\)
\(740\) 0 0
\(741\) 0.00505763 0.000185797 0
\(742\) 0 0
\(743\) 24.2057 0.888022 0.444011 0.896021i \(-0.353555\pi\)
0.444011 + 0.896021i \(0.353555\pi\)
\(744\) 0 0
\(745\) 7.12643 0.261092
\(746\) 0 0
\(747\) −30.2956 −1.10846
\(748\) 0 0
\(749\) −24.5878 −0.898418
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 11.2266 0.409120
\(754\) 0 0
\(755\) 1.54794 0.0563354
\(756\) 0 0
\(757\) −51.0242 −1.85451 −0.927253 0.374435i \(-0.877837\pi\)
−0.927253 + 0.374435i \(0.877837\pi\)
\(758\) 0 0
\(759\) 19.3550 0.702543
\(760\) 0 0
\(761\) 3.22601 0.116943 0.0584715 0.998289i \(-0.481377\pi\)
0.0584715 + 0.998289i \(0.481377\pi\)
\(762\) 0 0
\(763\) 16.2249 0.587381
\(764\) 0 0
\(765\) −38.8845 −1.40587
\(766\) 0 0
\(767\) 1.23505 0.0445952
\(768\) 0 0
\(769\) −44.9237 −1.61999 −0.809994 0.586437i \(-0.800530\pi\)
−0.809994 + 0.586437i \(0.800530\pi\)
\(770\) 0 0
\(771\) 5.68623 0.204785
\(772\) 0 0
\(773\) −45.3400 −1.63077 −0.815384 0.578921i \(-0.803474\pi\)
−0.815384 + 0.578921i \(0.803474\pi\)
\(774\) 0 0
\(775\) 5.98160 0.214865
\(776\) 0 0
\(777\) 14.7456 0.528994
\(778\) 0 0
\(779\) 0.222455 0.00797027
\(780\) 0 0
\(781\) 48.5074 1.73573
\(782\) 0 0
\(783\) −8.64367 −0.308900
\(784\) 0 0
\(785\) 41.4753 1.48032
\(786\) 0 0
\(787\) −3.44124 −0.122667 −0.0613334 0.998117i \(-0.519535\pi\)
−0.0613334 + 0.998117i \(0.519535\pi\)
\(788\) 0 0
\(789\) −11.2612 −0.400908
\(790\) 0 0
\(791\) −102.992 −3.66197
\(792\) 0 0
\(793\) 0.870905 0.0309268
\(794\) 0 0
\(795\) 3.02307 0.107217
\(796\) 0 0
\(797\) 25.1118 0.889507 0.444754 0.895653i \(-0.353291\pi\)
0.444754 + 0.895653i \(0.353291\pi\)
\(798\) 0 0
\(799\) −0.798772 −0.0282585
\(800\) 0 0
\(801\) 6.76900 0.239171
\(802\) 0 0
\(803\) 23.8956 0.843257
\(804\) 0 0
\(805\) −62.1824 −2.19164
\(806\) 0 0
\(807\) 7.42373 0.261328
\(808\) 0 0
\(809\) −40.0871 −1.40939 −0.704693 0.709512i \(-0.748915\pi\)
−0.704693 + 0.709512i \(0.748915\pi\)
\(810\) 0 0
\(811\) −28.4538 −0.999148 −0.499574 0.866271i \(-0.666510\pi\)
−0.499574 + 0.866271i \(0.666510\pi\)
\(812\) 0 0
\(813\) 12.1344 0.425573
\(814\) 0 0
\(815\) 8.43034 0.295302
\(816\) 0 0
\(817\) −0.339710 −0.0118850
\(818\) 0 0
\(819\) −3.21528 −0.112351
\(820\) 0 0
\(821\) 20.5338 0.716636 0.358318 0.933600i \(-0.383350\pi\)
0.358318 + 0.933600i \(0.383350\pi\)
\(822\) 0 0
\(823\) −12.3222 −0.429526 −0.214763 0.976666i \(-0.568898\pi\)
−0.214763 + 0.976666i \(0.568898\pi\)
\(824\) 0 0
\(825\) −4.19049 −0.145894
\(826\) 0 0
\(827\) 43.5681 1.51501 0.757505 0.652829i \(-0.226418\pi\)
0.757505 + 0.652829i \(0.226418\pi\)
\(828\) 0 0
\(829\) −25.7521 −0.894409 −0.447204 0.894432i \(-0.647580\pi\)
−0.447204 + 0.894432i \(0.647580\pi\)
\(830\) 0 0
\(831\) 9.46022 0.328171
\(832\) 0 0
\(833\) −145.886 −5.05464
\(834\) 0 0
\(835\) 9.41911 0.325962
\(836\) 0 0
\(837\) −15.9946 −0.552853
\(838\) 0 0
\(839\) 32.2700 1.11408 0.557042 0.830484i \(-0.311936\pi\)
0.557042 + 0.830484i \(0.311936\pi\)
\(840\) 0 0
\(841\) −23.8765 −0.823327
\(842\) 0 0
\(843\) −6.64029 −0.228704
\(844\) 0 0
\(845\) 24.4458 0.840962
\(846\) 0 0
\(847\) 34.9291 1.20018
\(848\) 0 0
\(849\) −13.4534 −0.461719
\(850\) 0 0
\(851\) −28.1954 −0.966526
\(852\) 0 0
\(853\) 45.6516 1.56308 0.781540 0.623855i \(-0.214434\pi\)
0.781540 + 0.623855i \(0.214434\pi\)
\(854\) 0 0
\(855\) −0.136353 −0.00466317
\(856\) 0 0
\(857\) −23.7515 −0.811336 −0.405668 0.914020i \(-0.632961\pi\)
−0.405668 + 0.914020i \(0.632961\pi\)
\(858\) 0 0
\(859\) −7.30524 −0.249252 −0.124626 0.992204i \(-0.539773\pi\)
−0.124626 + 0.992204i \(0.539773\pi\)
\(860\) 0 0
\(861\) 26.8222 0.914098
\(862\) 0 0
\(863\) 39.8543 1.35666 0.678329 0.734759i \(-0.262705\pi\)
0.678329 + 0.734759i \(0.262705\pi\)
\(864\) 0 0
\(865\) −47.9412 −1.63005
\(866\) 0 0
\(867\) −34.2793 −1.16419
\(868\) 0 0
\(869\) −32.2200 −1.09299
\(870\) 0 0
\(871\) 3.14071 0.106419
\(872\) 0 0
\(873\) 4.25882 0.144139
\(874\) 0 0
\(875\) 60.5987 2.04861
\(876\) 0 0
\(877\) 55.1439 1.86208 0.931038 0.364922i \(-0.118904\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(878\) 0 0
\(879\) −6.22094 −0.209827
\(880\) 0 0
\(881\) −35.8420 −1.20755 −0.603774 0.797156i \(-0.706337\pi\)
−0.603774 + 0.797156i \(0.706337\pi\)
\(882\) 0 0
\(883\) −32.0233 −1.07767 −0.538835 0.842411i \(-0.681135\pi\)
−0.538835 + 0.842411i \(0.681135\pi\)
\(884\) 0 0
\(885\) 6.31516 0.212282
\(886\) 0 0
\(887\) 29.9790 1.00660 0.503298 0.864113i \(-0.332120\pi\)
0.503298 + 0.864113i \(0.332120\pi\)
\(888\) 0 0
\(889\) −59.1931 −1.98527
\(890\) 0 0
\(891\) −20.8934 −0.699954
\(892\) 0 0
\(893\) −0.00280098 −9.37314e−5 0
\(894\) 0 0
\(895\) −25.0628 −0.837757
\(896\) 0 0
\(897\) −1.16605 −0.0389332
\(898\) 0 0
\(899\) 9.48076 0.316201
\(900\) 0 0
\(901\) −18.8707 −0.628676
\(902\) 0 0
\(903\) −40.9602 −1.36307
\(904\) 0 0
\(905\) −3.52602 −0.117209
\(906\) 0 0
\(907\) 15.4473 0.512919 0.256460 0.966555i \(-0.417444\pi\)
0.256460 + 0.966555i \(0.417444\pi\)
\(908\) 0 0
\(909\) −34.3423 −1.13906
\(910\) 0 0
\(911\) 27.3375 0.905732 0.452866 0.891579i \(-0.350402\pi\)
0.452866 + 0.891579i \(0.350402\pi\)
\(912\) 0 0
\(913\) −50.9740 −1.68699
\(914\) 0 0
\(915\) 4.45317 0.147217
\(916\) 0 0
\(917\) 56.6913 1.87211
\(918\) 0 0
\(919\) −23.3324 −0.769665 −0.384833 0.922986i \(-0.625741\pi\)
−0.384833 + 0.922986i \(0.625741\pi\)
\(920\) 0 0
\(921\) −10.8970 −0.359068
\(922\) 0 0
\(923\) −2.92234 −0.0961900
\(924\) 0 0
\(925\) 6.10449 0.200714
\(926\) 0 0
\(927\) −12.4033 −0.407377
\(928\) 0 0
\(929\) −38.6280 −1.26734 −0.633671 0.773602i \(-0.718453\pi\)
−0.633671 + 0.773602i \(0.718453\pi\)
\(930\) 0 0
\(931\) −0.511564 −0.0167658
\(932\) 0 0
\(933\) −16.0839 −0.526562
\(934\) 0 0
\(935\) −65.4254 −2.13964
\(936\) 0 0
\(937\) −55.8195 −1.82354 −0.911772 0.410696i \(-0.865286\pi\)
−0.911772 + 0.410696i \(0.865286\pi\)
\(938\) 0 0
\(939\) −17.3113 −0.564933
\(940\) 0 0
\(941\) −39.2474 −1.27943 −0.639714 0.768613i \(-0.720947\pi\)
−0.639714 + 0.768613i \(0.720947\pi\)
\(942\) 0 0
\(943\) −51.2875 −1.67015
\(944\) 0 0
\(945\) −35.9993 −1.17106
\(946\) 0 0
\(947\) 40.4075 1.31307 0.656534 0.754297i \(-0.272022\pi\)
0.656534 + 0.754297i \(0.272022\pi\)
\(948\) 0 0
\(949\) −1.43960 −0.0467313
\(950\) 0 0
\(951\) −11.6036 −0.376273
\(952\) 0 0
\(953\) −33.6187 −1.08902 −0.544508 0.838756i \(-0.683283\pi\)
−0.544508 + 0.838756i \(0.683283\pi\)
\(954\) 0 0
\(955\) −33.7869 −1.09332
\(956\) 0 0
\(957\) −6.64188 −0.214701
\(958\) 0 0
\(959\) 97.6316 3.15269
\(960\) 0 0
\(961\) −13.4564 −0.434079
\(962\) 0 0
\(963\) 12.4304 0.400565
\(964\) 0 0
\(965\) −9.68147 −0.311658
\(966\) 0 0
\(967\) −41.7754 −1.34341 −0.671704 0.740820i \(-0.734437\pi\)
−0.671704 + 0.740820i \(0.734437\pi\)
\(968\) 0 0
\(969\) −0.161431 −0.00518590
\(970\) 0 0
\(971\) 46.9780 1.50760 0.753798 0.657107i \(-0.228220\pi\)
0.753798 + 0.657107i \(0.228220\pi\)
\(972\) 0 0
\(973\) 61.8169 1.98176
\(974\) 0 0
\(975\) 0.252457 0.00808511
\(976\) 0 0
\(977\) 26.7190 0.854816 0.427408 0.904059i \(-0.359427\pi\)
0.427408 + 0.904059i \(0.359427\pi\)
\(978\) 0 0
\(979\) 11.3892 0.364001
\(980\) 0 0
\(981\) −8.20255 −0.261887
\(982\) 0 0
\(983\) 7.71854 0.246183 0.123092 0.992395i \(-0.460719\pi\)
0.123092 + 0.992395i \(0.460719\pi\)
\(984\) 0 0
\(985\) 24.3025 0.774341
\(986\) 0 0
\(987\) −0.337725 −0.0107499
\(988\) 0 0
\(989\) 78.3211 2.49047
\(990\) 0 0
\(991\) 45.7678 1.45386 0.726931 0.686710i \(-0.240946\pi\)
0.726931 + 0.686710i \(0.240946\pi\)
\(992\) 0 0
\(993\) 2.44770 0.0776753
\(994\) 0 0
\(995\) −14.6157 −0.463348
\(996\) 0 0
\(997\) −8.69495 −0.275372 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(998\) 0 0
\(999\) −16.3232 −0.516443
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 \(a_p\))