Properties

Label 8048.2.a.v.1.2
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.89723 q^{3}\) \(-1.96349 q^{5}\) \(-2.82850 q^{7}\) \(+5.39392 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.89723 q^{3}\) \(-1.96349 q^{5}\) \(-2.82850 q^{7}\) \(+5.39392 q^{9}\) \(+5.91397 q^{11}\) \(-5.24542 q^{13}\) \(+5.68869 q^{15}\) \(-0.885173 q^{17}\) \(+6.74515 q^{19}\) \(+8.19481 q^{21}\) \(-5.73298 q^{23}\) \(-1.14469 q^{25}\) \(-6.93574 q^{27}\) \(-9.96134 q^{29}\) \(-0.549277 q^{31}\) \(-17.1341 q^{33}\) \(+5.55375 q^{35}\) \(+6.03248 q^{37}\) \(+15.1972 q^{39}\) \(+2.81883 q^{41}\) \(-11.4268 q^{43}\) \(-10.5909 q^{45}\) \(+8.25534 q^{47}\) \(+1.00042 q^{49}\) \(+2.56455 q^{51}\) \(-4.66698 q^{53}\) \(-11.6120 q^{55}\) \(-19.5422 q^{57}\) \(+1.78874 q^{59}\) \(-7.68018 q^{61}\) \(-15.2567 q^{63}\) \(+10.2994 q^{65}\) \(+2.96915 q^{67}\) \(+16.6097 q^{69}\) \(+15.7082 q^{71}\) \(+10.8478 q^{73}\) \(+3.31643 q^{75}\) \(-16.7277 q^{77}\) \(+16.2472 q^{79}\) \(+3.91265 q^{81}\) \(+9.57081 q^{83}\) \(+1.73803 q^{85}\) \(+28.8603 q^{87}\) \(+7.66435 q^{89}\) \(+14.8367 q^{91}\) \(+1.59138 q^{93}\) \(-13.2441 q^{95}\) \(-2.26689 q^{97}\) \(+31.8995 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.89723 −1.67271 −0.836357 0.548185i \(-0.815319\pi\)
−0.836357 + 0.548185i \(0.815319\pi\)
\(4\) 0 0
\(5\) −1.96349 −0.878101 −0.439051 0.898462i \(-0.644685\pi\)
−0.439051 + 0.898462i \(0.644685\pi\)
\(6\) 0 0
\(7\) −2.82850 −1.06907 −0.534537 0.845145i \(-0.679514\pi\)
−0.534537 + 0.845145i \(0.679514\pi\)
\(8\) 0 0
\(9\) 5.39392 1.79797
\(10\) 0 0
\(11\) 5.91397 1.78313 0.891564 0.452895i \(-0.149609\pi\)
0.891564 + 0.452895i \(0.149609\pi\)
\(12\) 0 0
\(13\) −5.24542 −1.45482 −0.727409 0.686204i \(-0.759276\pi\)
−0.727409 + 0.686204i \(0.759276\pi\)
\(14\) 0 0
\(15\) 5.68869 1.46881
\(16\) 0 0
\(17\) −0.885173 −0.214686 −0.107343 0.994222i \(-0.534234\pi\)
−0.107343 + 0.994222i \(0.534234\pi\)
\(18\) 0 0
\(19\) 6.74515 1.54744 0.773722 0.633526i \(-0.218393\pi\)
0.773722 + 0.633526i \(0.218393\pi\)
\(20\) 0 0
\(21\) 8.19481 1.78825
\(22\) 0 0
\(23\) −5.73298 −1.19541 −0.597704 0.801717i \(-0.703920\pi\)
−0.597704 + 0.801717i \(0.703920\pi\)
\(24\) 0 0
\(25\) −1.14469 −0.228938
\(26\) 0 0
\(27\) −6.93574 −1.33478
\(28\) 0 0
\(29\) −9.96134 −1.84977 −0.924887 0.380242i \(-0.875841\pi\)
−0.924887 + 0.380242i \(0.875841\pi\)
\(30\) 0 0
\(31\) −0.549277 −0.0986530 −0.0493265 0.998783i \(-0.515707\pi\)
−0.0493265 + 0.998783i \(0.515707\pi\)
\(32\) 0 0
\(33\) −17.1341 −2.98266
\(34\) 0 0
\(35\) 5.55375 0.938754
\(36\) 0 0
\(37\) 6.03248 0.991733 0.495867 0.868399i \(-0.334851\pi\)
0.495867 + 0.868399i \(0.334851\pi\)
\(38\) 0 0
\(39\) 15.1972 2.43350
\(40\) 0 0
\(41\) 2.81883 0.440228 0.220114 0.975474i \(-0.429357\pi\)
0.220114 + 0.975474i \(0.429357\pi\)
\(42\) 0 0
\(43\) −11.4268 −1.74257 −0.871286 0.490775i \(-0.836714\pi\)
−0.871286 + 0.490775i \(0.836714\pi\)
\(44\) 0 0
\(45\) −10.5909 −1.57880
\(46\) 0 0
\(47\) 8.25534 1.20416 0.602082 0.798434i \(-0.294338\pi\)
0.602082 + 0.798434i \(0.294338\pi\)
\(48\) 0 0
\(49\) 1.00042 0.142918
\(50\) 0 0
\(51\) 2.56455 0.359108
\(52\) 0 0
\(53\) −4.66698 −0.641059 −0.320529 0.947239i \(-0.603861\pi\)
−0.320529 + 0.947239i \(0.603861\pi\)
\(54\) 0 0
\(55\) −11.6120 −1.56577
\(56\) 0 0
\(57\) −19.5422 −2.58843
\(58\) 0 0
\(59\) 1.78874 0.232874 0.116437 0.993198i \(-0.462853\pi\)
0.116437 + 0.993198i \(0.462853\pi\)
\(60\) 0 0
\(61\) −7.68018 −0.983346 −0.491673 0.870780i \(-0.663614\pi\)
−0.491673 + 0.870780i \(0.663614\pi\)
\(62\) 0 0
\(63\) −15.2567 −1.92217
\(64\) 0 0
\(65\) 10.2994 1.27748
\(66\) 0 0
\(67\) 2.96915 0.362739 0.181370 0.983415i \(-0.441947\pi\)
0.181370 + 0.983415i \(0.441947\pi\)
\(68\) 0 0
\(69\) 16.6097 1.99958
\(70\) 0 0
\(71\) 15.7082 1.86422 0.932109 0.362178i \(-0.117967\pi\)
0.932109 + 0.362178i \(0.117967\pi\)
\(72\) 0 0
\(73\) 10.8478 1.26964 0.634818 0.772662i \(-0.281075\pi\)
0.634818 + 0.772662i \(0.281075\pi\)
\(74\) 0 0
\(75\) 3.31643 0.382949
\(76\) 0 0
\(77\) −16.7277 −1.90629
\(78\) 0 0
\(79\) 16.2472 1.82796 0.913979 0.405761i \(-0.132994\pi\)
0.913979 + 0.405761i \(0.132994\pi\)
\(80\) 0 0
\(81\) 3.91265 0.434739
\(82\) 0 0
\(83\) 9.57081 1.05053 0.525266 0.850938i \(-0.323966\pi\)
0.525266 + 0.850938i \(0.323966\pi\)
\(84\) 0 0
\(85\) 1.73803 0.188516
\(86\) 0 0
\(87\) 28.8603 3.09414
\(88\) 0 0
\(89\) 7.66435 0.812419 0.406209 0.913780i \(-0.366850\pi\)
0.406209 + 0.913780i \(0.366850\pi\)
\(90\) 0 0
\(91\) 14.8367 1.55531
\(92\) 0 0
\(93\) 1.59138 0.165018
\(94\) 0 0
\(95\) −13.2441 −1.35881
\(96\) 0 0
\(97\) −2.26689 −0.230167 −0.115084 0.993356i \(-0.536714\pi\)
−0.115084 + 0.993356i \(0.536714\pi\)
\(98\) 0 0
\(99\) 31.8995 3.20602
\(100\) 0 0
\(101\) 3.21332 0.319737 0.159868 0.987138i \(-0.448893\pi\)
0.159868 + 0.987138i \(0.448893\pi\)
\(102\) 0 0
\(103\) 12.8095 1.26216 0.631078 0.775720i \(-0.282613\pi\)
0.631078 + 0.775720i \(0.282613\pi\)
\(104\) 0 0
\(105\) −16.0905 −1.57027
\(106\) 0 0
\(107\) −4.94467 −0.478019 −0.239009 0.971017i \(-0.576823\pi\)
−0.239009 + 0.971017i \(0.576823\pi\)
\(108\) 0 0
\(109\) 17.2598 1.65318 0.826592 0.562801i \(-0.190276\pi\)
0.826592 + 0.562801i \(0.190276\pi\)
\(110\) 0 0
\(111\) −17.4775 −1.65889
\(112\) 0 0
\(113\) 6.43103 0.604980 0.302490 0.953153i \(-0.402182\pi\)
0.302490 + 0.953153i \(0.402182\pi\)
\(114\) 0 0
\(115\) 11.2567 1.04969
\(116\) 0 0
\(117\) −28.2934 −2.61573
\(118\) 0 0
\(119\) 2.50371 0.229515
\(120\) 0 0
\(121\) 23.9750 2.17955
\(122\) 0 0
\(123\) −8.16680 −0.736376
\(124\) 0 0
\(125\) 12.0651 1.07913
\(126\) 0 0
\(127\) −16.7812 −1.48909 −0.744545 0.667572i \(-0.767334\pi\)
−0.744545 + 0.667572i \(0.767334\pi\)
\(128\) 0 0
\(129\) 33.1061 2.91483
\(130\) 0 0
\(131\) −10.2727 −0.897532 −0.448766 0.893649i \(-0.648136\pi\)
−0.448766 + 0.893649i \(0.648136\pi\)
\(132\) 0 0
\(133\) −19.0787 −1.65433
\(134\) 0 0
\(135\) 13.6183 1.17208
\(136\) 0 0
\(137\) −12.5903 −1.07566 −0.537830 0.843053i \(-0.680756\pi\)
−0.537830 + 0.843053i \(0.680756\pi\)
\(138\) 0 0
\(139\) −10.2390 −0.868458 −0.434229 0.900803i \(-0.642979\pi\)
−0.434229 + 0.900803i \(0.642979\pi\)
\(140\) 0 0
\(141\) −23.9176 −2.01422
\(142\) 0 0
\(143\) −31.0213 −2.59413
\(144\) 0 0
\(145\) 19.5590 1.62429
\(146\) 0 0
\(147\) −2.89845 −0.239060
\(148\) 0 0
\(149\) −11.9960 −0.982752 −0.491376 0.870948i \(-0.663506\pi\)
−0.491376 + 0.870948i \(0.663506\pi\)
\(150\) 0 0
\(151\) −19.2519 −1.56670 −0.783350 0.621580i \(-0.786491\pi\)
−0.783350 + 0.621580i \(0.786491\pi\)
\(152\) 0 0
\(153\) −4.77455 −0.386000
\(154\) 0 0
\(155\) 1.07850 0.0866273
\(156\) 0 0
\(157\) 7.60624 0.607044 0.303522 0.952824i \(-0.401837\pi\)
0.303522 + 0.952824i \(0.401837\pi\)
\(158\) 0 0
\(159\) 13.5213 1.07231
\(160\) 0 0
\(161\) 16.2157 1.27798
\(162\) 0 0
\(163\) 15.9299 1.24772 0.623861 0.781535i \(-0.285563\pi\)
0.623861 + 0.781535i \(0.285563\pi\)
\(164\) 0 0
\(165\) 33.6427 2.61908
\(166\) 0 0
\(167\) −1.36948 −0.105973 −0.0529867 0.998595i \(-0.516874\pi\)
−0.0529867 + 0.998595i \(0.516874\pi\)
\(168\) 0 0
\(169\) 14.5145 1.11650
\(170\) 0 0
\(171\) 36.3828 2.78226
\(172\) 0 0
\(173\) 10.3098 0.783837 0.391918 0.920000i \(-0.371812\pi\)
0.391918 + 0.920000i \(0.371812\pi\)
\(174\) 0 0
\(175\) 3.23776 0.244752
\(176\) 0 0
\(177\) −5.18239 −0.389533
\(178\) 0 0
\(179\) −3.59185 −0.268468 −0.134234 0.990950i \(-0.542857\pi\)
−0.134234 + 0.990950i \(0.542857\pi\)
\(180\) 0 0
\(181\) −12.4691 −0.926821 −0.463410 0.886144i \(-0.653374\pi\)
−0.463410 + 0.886144i \(0.653374\pi\)
\(182\) 0 0
\(183\) 22.2512 1.64486
\(184\) 0 0
\(185\) −11.8447 −0.870842
\(186\) 0 0
\(187\) −5.23488 −0.382812
\(188\) 0 0
\(189\) 19.6178 1.42698
\(190\) 0 0
\(191\) −19.7753 −1.43089 −0.715445 0.698669i \(-0.753776\pi\)
−0.715445 + 0.698669i \(0.753776\pi\)
\(192\) 0 0
\(193\) 8.12365 0.584753 0.292376 0.956303i \(-0.405554\pi\)
0.292376 + 0.956303i \(0.405554\pi\)
\(194\) 0 0
\(195\) −29.8396 −2.13686
\(196\) 0 0
\(197\) −17.6046 −1.25427 −0.627137 0.778909i \(-0.715774\pi\)
−0.627137 + 0.778909i \(0.715774\pi\)
\(198\) 0 0
\(199\) 11.7180 0.830665 0.415332 0.909670i \(-0.363665\pi\)
0.415332 + 0.909670i \(0.363665\pi\)
\(200\) 0 0
\(201\) −8.60229 −0.606759
\(202\) 0 0
\(203\) 28.1757 1.97754
\(204\) 0 0
\(205\) −5.53476 −0.386565
\(206\) 0 0
\(207\) −30.9232 −2.14931
\(208\) 0 0
\(209\) 39.8906 2.75929
\(210\) 0 0
\(211\) 15.0254 1.03439 0.517194 0.855868i \(-0.326976\pi\)
0.517194 + 0.855868i \(0.326976\pi\)
\(212\) 0 0
\(213\) −45.5102 −3.11831
\(214\) 0 0
\(215\) 22.4365 1.53015
\(216\) 0 0
\(217\) 1.55363 0.105467
\(218\) 0 0
\(219\) −31.4285 −2.12374
\(220\) 0 0
\(221\) 4.64311 0.312329
\(222\) 0 0
\(223\) 4.49435 0.300964 0.150482 0.988613i \(-0.451917\pi\)
0.150482 + 0.988613i \(0.451917\pi\)
\(224\) 0 0
\(225\) −6.17438 −0.411625
\(226\) 0 0
\(227\) 7.92460 0.525974 0.262987 0.964799i \(-0.415292\pi\)
0.262987 + 0.964799i \(0.415292\pi\)
\(228\) 0 0
\(229\) 26.8508 1.77435 0.887174 0.461434i \(-0.152665\pi\)
0.887174 + 0.461434i \(0.152665\pi\)
\(230\) 0 0
\(231\) 48.4639 3.18869
\(232\) 0 0
\(233\) 16.1047 1.05505 0.527527 0.849538i \(-0.323119\pi\)
0.527527 + 0.849538i \(0.323119\pi\)
\(234\) 0 0
\(235\) −16.2093 −1.05738
\(236\) 0 0
\(237\) −47.0720 −3.05765
\(238\) 0 0
\(239\) 0.556383 0.0359894 0.0179947 0.999838i \(-0.494272\pi\)
0.0179947 + 0.999838i \(0.494272\pi\)
\(240\) 0 0
\(241\) −23.7226 −1.52811 −0.764055 0.645151i \(-0.776794\pi\)
−0.764055 + 0.645151i \(0.776794\pi\)
\(242\) 0 0
\(243\) 9.47140 0.607590
\(244\) 0 0
\(245\) −1.96433 −0.125496
\(246\) 0 0
\(247\) −35.3812 −2.25125
\(248\) 0 0
\(249\) −27.7288 −1.75724
\(250\) 0 0
\(251\) −9.95962 −0.628646 −0.314323 0.949316i \(-0.601777\pi\)
−0.314323 + 0.949316i \(0.601777\pi\)
\(252\) 0 0
\(253\) −33.9046 −2.13157
\(254\) 0 0
\(255\) −5.03547 −0.315333
\(256\) 0 0
\(257\) 21.5503 1.34427 0.672136 0.740428i \(-0.265377\pi\)
0.672136 + 0.740428i \(0.265377\pi\)
\(258\) 0 0
\(259\) −17.0629 −1.06024
\(260\) 0 0
\(261\) −53.7307 −3.32585
\(262\) 0 0
\(263\) 18.8835 1.16440 0.582202 0.813044i \(-0.302191\pi\)
0.582202 + 0.813044i \(0.302191\pi\)
\(264\) 0 0
\(265\) 9.16359 0.562915
\(266\) 0 0
\(267\) −22.2053 −1.35895
\(268\) 0 0
\(269\) −19.0557 −1.16185 −0.580925 0.813957i \(-0.697309\pi\)
−0.580925 + 0.813957i \(0.697309\pi\)
\(270\) 0 0
\(271\) 24.9458 1.51535 0.757673 0.652634i \(-0.226336\pi\)
0.757673 + 0.652634i \(0.226336\pi\)
\(272\) 0 0
\(273\) −42.9853 −2.60159
\(274\) 0 0
\(275\) −6.76967 −0.408226
\(276\) 0 0
\(277\) −20.2851 −1.21881 −0.609406 0.792858i \(-0.708592\pi\)
−0.609406 + 0.792858i \(0.708592\pi\)
\(278\) 0 0
\(279\) −2.96276 −0.177376
\(280\) 0 0
\(281\) −16.5942 −0.989927 −0.494963 0.868914i \(-0.664819\pi\)
−0.494963 + 0.868914i \(0.664819\pi\)
\(282\) 0 0
\(283\) −1.44632 −0.0859745 −0.0429873 0.999076i \(-0.513687\pi\)
−0.0429873 + 0.999076i \(0.513687\pi\)
\(284\) 0 0
\(285\) 38.3710 2.27290
\(286\) 0 0
\(287\) −7.97308 −0.470636
\(288\) 0 0
\(289\) −16.2165 −0.953910
\(290\) 0 0
\(291\) 6.56768 0.385004
\(292\) 0 0
\(293\) −27.8511 −1.62708 −0.813538 0.581512i \(-0.802461\pi\)
−0.813538 + 0.581512i \(0.802461\pi\)
\(294\) 0 0
\(295\) −3.51218 −0.204487
\(296\) 0 0
\(297\) −41.0178 −2.38009
\(298\) 0 0
\(299\) 30.0719 1.73910
\(300\) 0 0
\(301\) 32.3208 1.86294
\(302\) 0 0
\(303\) −9.30970 −0.534829
\(304\) 0 0
\(305\) 15.0800 0.863477
\(306\) 0 0
\(307\) −5.60883 −0.320113 −0.160057 0.987108i \(-0.551168\pi\)
−0.160057 + 0.987108i \(0.551168\pi\)
\(308\) 0 0
\(309\) −37.1120 −2.11123
\(310\) 0 0
\(311\) 3.62958 0.205814 0.102907 0.994691i \(-0.467186\pi\)
0.102907 + 0.994691i \(0.467186\pi\)
\(312\) 0 0
\(313\) 31.3094 1.76971 0.884856 0.465865i \(-0.154257\pi\)
0.884856 + 0.465865i \(0.154257\pi\)
\(314\) 0 0
\(315\) 29.9565 1.68786
\(316\) 0 0
\(317\) −30.0319 −1.68676 −0.843379 0.537320i \(-0.819437\pi\)
−0.843379 + 0.537320i \(0.819437\pi\)
\(318\) 0 0
\(319\) −58.9110 −3.29838
\(320\) 0 0
\(321\) 14.3258 0.799589
\(322\) 0 0
\(323\) −5.97062 −0.332214
\(324\) 0 0
\(325\) 6.00439 0.333064
\(326\) 0 0
\(327\) −50.0054 −2.76531
\(328\) 0 0
\(329\) −23.3502 −1.28734
\(330\) 0 0
\(331\) −27.3224 −1.50178 −0.750888 0.660429i \(-0.770374\pi\)
−0.750888 + 0.660429i \(0.770374\pi\)
\(332\) 0 0
\(333\) 32.5387 1.78311
\(334\) 0 0
\(335\) −5.82990 −0.318522
\(336\) 0 0
\(337\) −14.0173 −0.763573 −0.381787 0.924251i \(-0.624691\pi\)
−0.381787 + 0.924251i \(0.624691\pi\)
\(338\) 0 0
\(339\) −18.6321 −1.01196
\(340\) 0 0
\(341\) −3.24840 −0.175911
\(342\) 0 0
\(343\) 16.9698 0.916284
\(344\) 0 0
\(345\) −32.6131 −1.75583
\(346\) 0 0
\(347\) 3.56304 0.191274 0.0956371 0.995416i \(-0.469511\pi\)
0.0956371 + 0.995416i \(0.469511\pi\)
\(348\) 0 0
\(349\) −4.10170 −0.219559 −0.109779 0.993956i \(-0.535014\pi\)
−0.109779 + 0.993956i \(0.535014\pi\)
\(350\) 0 0
\(351\) 36.3809 1.94187
\(352\) 0 0
\(353\) 1.81928 0.0968303 0.0484152 0.998827i \(-0.484583\pi\)
0.0484152 + 0.998827i \(0.484583\pi\)
\(354\) 0 0
\(355\) −30.8429 −1.63697
\(356\) 0 0
\(357\) −7.25382 −0.383913
\(358\) 0 0
\(359\) 17.6082 0.929326 0.464663 0.885488i \(-0.346175\pi\)
0.464663 + 0.885488i \(0.346175\pi\)
\(360\) 0 0
\(361\) 26.4970 1.39458
\(362\) 0 0
\(363\) −69.4610 −3.64576
\(364\) 0 0
\(365\) −21.2995 −1.11487
\(366\) 0 0
\(367\) −28.0930 −1.46644 −0.733220 0.679991i \(-0.761984\pi\)
−0.733220 + 0.679991i \(0.761984\pi\)
\(368\) 0 0
\(369\) 15.2046 0.791519
\(370\) 0 0
\(371\) 13.2006 0.685339
\(372\) 0 0
\(373\) −4.09615 −0.212091 −0.106045 0.994361i \(-0.533819\pi\)
−0.106045 + 0.994361i \(0.533819\pi\)
\(374\) 0 0
\(375\) −34.9552 −1.80508
\(376\) 0 0
\(377\) 52.2514 2.69109
\(378\) 0 0
\(379\) −28.3145 −1.45442 −0.727209 0.686416i \(-0.759183\pi\)
−0.727209 + 0.686416i \(0.759183\pi\)
\(380\) 0 0
\(381\) 48.6189 2.49082
\(382\) 0 0
\(383\) 4.05496 0.207199 0.103599 0.994619i \(-0.466964\pi\)
0.103599 + 0.994619i \(0.466964\pi\)
\(384\) 0 0
\(385\) 32.8447 1.67392
\(386\) 0 0
\(387\) −61.6354 −3.13310
\(388\) 0 0
\(389\) −14.4208 −0.731164 −0.365582 0.930779i \(-0.619130\pi\)
−0.365582 + 0.930779i \(0.619130\pi\)
\(390\) 0 0
\(391\) 5.07467 0.256637
\(392\) 0 0
\(393\) 29.7624 1.50131
\(394\) 0 0
\(395\) −31.9014 −1.60513
\(396\) 0 0
\(397\) −20.8229 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(398\) 0 0
\(399\) 55.2752 2.76722
\(400\) 0 0
\(401\) 8.08829 0.403910 0.201955 0.979395i \(-0.435271\pi\)
0.201955 + 0.979395i \(0.435271\pi\)
\(402\) 0 0
\(403\) 2.88119 0.143522
\(404\) 0 0
\(405\) −7.68246 −0.381745
\(406\) 0 0
\(407\) 35.6759 1.76839
\(408\) 0 0
\(409\) 31.1393 1.53974 0.769871 0.638200i \(-0.220321\pi\)
0.769871 + 0.638200i \(0.220321\pi\)
\(410\) 0 0
\(411\) 36.4769 1.79927
\(412\) 0 0
\(413\) −5.05946 −0.248960
\(414\) 0 0
\(415\) −18.7922 −0.922474
\(416\) 0 0
\(417\) 29.6646 1.45268
\(418\) 0 0
\(419\) −22.9688 −1.12210 −0.561050 0.827782i \(-0.689602\pi\)
−0.561050 + 0.827782i \(0.689602\pi\)
\(420\) 0 0
\(421\) −7.36313 −0.358857 −0.179428 0.983771i \(-0.557425\pi\)
−0.179428 + 0.983771i \(0.557425\pi\)
\(422\) 0 0
\(423\) 44.5287 2.16506
\(424\) 0 0
\(425\) 1.01325 0.0491498
\(426\) 0 0
\(427\) 21.7234 1.05127
\(428\) 0 0
\(429\) 89.8756 4.33924
\(430\) 0 0
\(431\) 2.47834 0.119378 0.0596888 0.998217i \(-0.480989\pi\)
0.0596888 + 0.998217i \(0.480989\pi\)
\(432\) 0 0
\(433\) 10.3130 0.495610 0.247805 0.968810i \(-0.420291\pi\)
0.247805 + 0.968810i \(0.420291\pi\)
\(434\) 0 0
\(435\) −56.6669 −2.71697
\(436\) 0 0
\(437\) −38.6698 −1.84983
\(438\) 0 0
\(439\) 9.99261 0.476921 0.238461 0.971152i \(-0.423357\pi\)
0.238461 + 0.971152i \(0.423357\pi\)
\(440\) 0 0
\(441\) 5.39621 0.256962
\(442\) 0 0
\(443\) 16.6060 0.788973 0.394487 0.918902i \(-0.370922\pi\)
0.394487 + 0.918902i \(0.370922\pi\)
\(444\) 0 0
\(445\) −15.0489 −0.713386
\(446\) 0 0
\(447\) 34.7552 1.64386
\(448\) 0 0
\(449\) −17.9995 −0.849448 −0.424724 0.905323i \(-0.639629\pi\)
−0.424724 + 0.905323i \(0.639629\pi\)
\(450\) 0 0
\(451\) 16.6705 0.784983
\(452\) 0 0
\(453\) 55.7772 2.62064
\(454\) 0 0
\(455\) −29.1318 −1.36572
\(456\) 0 0
\(457\) 3.86419 0.180759 0.0903797 0.995907i \(-0.471192\pi\)
0.0903797 + 0.995907i \(0.471192\pi\)
\(458\) 0 0
\(459\) 6.13933 0.286559
\(460\) 0 0
\(461\) −9.89511 −0.460861 −0.230431 0.973089i \(-0.574013\pi\)
−0.230431 + 0.973089i \(0.574013\pi\)
\(462\) 0 0
\(463\) 5.13438 0.238615 0.119307 0.992857i \(-0.461933\pi\)
0.119307 + 0.992857i \(0.461933\pi\)
\(464\) 0 0
\(465\) −3.12466 −0.144903
\(466\) 0 0
\(467\) 35.6977 1.65189 0.825947 0.563748i \(-0.190641\pi\)
0.825947 + 0.563748i \(0.190641\pi\)
\(468\) 0 0
\(469\) −8.39824 −0.387795
\(470\) 0 0
\(471\) −22.0370 −1.01541
\(472\) 0 0
\(473\) −67.5778 −3.10723
\(474\) 0 0
\(475\) −7.72112 −0.354269
\(476\) 0 0
\(477\) −25.1733 −1.15261
\(478\) 0 0
\(479\) 10.4946 0.479511 0.239756 0.970833i \(-0.422933\pi\)
0.239756 + 0.970833i \(0.422933\pi\)
\(480\) 0 0
\(481\) −31.6429 −1.44279
\(482\) 0 0
\(483\) −46.9807 −2.13769
\(484\) 0 0
\(485\) 4.45102 0.202110
\(486\) 0 0
\(487\) −4.77888 −0.216552 −0.108276 0.994121i \(-0.534533\pi\)
−0.108276 + 0.994121i \(0.534533\pi\)
\(488\) 0 0
\(489\) −46.1524 −2.08708
\(490\) 0 0
\(491\) −18.1654 −0.819792 −0.409896 0.912132i \(-0.634435\pi\)
−0.409896 + 0.912132i \(0.634435\pi\)
\(492\) 0 0
\(493\) 8.81750 0.397120
\(494\) 0 0
\(495\) −62.6345 −2.81521
\(496\) 0 0
\(497\) −44.4306 −1.99299
\(498\) 0 0
\(499\) 17.2912 0.774060 0.387030 0.922067i \(-0.373501\pi\)
0.387030 + 0.922067i \(0.373501\pi\)
\(500\) 0 0
\(501\) 3.96769 0.177263
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −6.30933 −0.280761
\(506\) 0 0
\(507\) −42.0517 −1.86758
\(508\) 0 0
\(509\) 28.1695 1.24859 0.624295 0.781188i \(-0.285386\pi\)
0.624295 + 0.781188i \(0.285386\pi\)
\(510\) 0 0
\(511\) −30.6829 −1.35733
\(512\) 0 0
\(513\) −46.7826 −2.06550
\(514\) 0 0
\(515\) −25.1513 −1.10830
\(516\) 0 0
\(517\) 48.8218 2.14718
\(518\) 0 0
\(519\) −29.8697 −1.31114
\(520\) 0 0
\(521\) 29.9674 1.31290 0.656448 0.754371i \(-0.272058\pi\)
0.656448 + 0.754371i \(0.272058\pi\)
\(522\) 0 0
\(523\) −34.3252 −1.50093 −0.750467 0.660907i \(-0.770172\pi\)
−0.750467 + 0.660907i \(0.770172\pi\)
\(524\) 0 0
\(525\) −9.38053 −0.409400
\(526\) 0 0
\(527\) 0.486205 0.0211794
\(528\) 0 0
\(529\) 9.86701 0.429001
\(530\) 0 0
\(531\) 9.64834 0.418702
\(532\) 0 0
\(533\) −14.7860 −0.640452
\(534\) 0 0
\(535\) 9.70882 0.419749
\(536\) 0 0
\(537\) 10.4064 0.449070
\(538\) 0 0
\(539\) 5.91647 0.254840
\(540\) 0 0
\(541\) 20.1364 0.865732 0.432866 0.901458i \(-0.357502\pi\)
0.432866 + 0.901458i \(0.357502\pi\)
\(542\) 0 0
\(543\) 36.1258 1.55031
\(544\) 0 0
\(545\) −33.8894 −1.45166
\(546\) 0 0
\(547\) −15.2845 −0.653518 −0.326759 0.945108i \(-0.605957\pi\)
−0.326759 + 0.945108i \(0.605957\pi\)
\(548\) 0 0
\(549\) −41.4263 −1.76803
\(550\) 0 0
\(551\) −67.1907 −2.86242
\(552\) 0 0
\(553\) −45.9554 −1.95422
\(554\) 0 0
\(555\) 34.3169 1.45667
\(556\) 0 0
\(557\) −12.8257 −0.543443 −0.271721 0.962376i \(-0.587593\pi\)
−0.271721 + 0.962376i \(0.587593\pi\)
\(558\) 0 0
\(559\) 59.9385 2.53513
\(560\) 0 0
\(561\) 15.1666 0.640336
\(562\) 0 0
\(563\) 4.61580 0.194533 0.0972664 0.995258i \(-0.468990\pi\)
0.0972664 + 0.995258i \(0.468990\pi\)
\(564\) 0 0
\(565\) −12.6273 −0.531234
\(566\) 0 0
\(567\) −11.0669 −0.464768
\(568\) 0 0
\(569\) 4.53204 0.189993 0.0949965 0.995478i \(-0.469716\pi\)
0.0949965 + 0.995478i \(0.469716\pi\)
\(570\) 0 0
\(571\) 1.28024 0.0535763 0.0267882 0.999641i \(-0.491472\pi\)
0.0267882 + 0.999641i \(0.491472\pi\)
\(572\) 0 0
\(573\) 57.2935 2.39347
\(574\) 0 0
\(575\) 6.56249 0.273675
\(576\) 0 0
\(577\) −12.4646 −0.518909 −0.259455 0.965755i \(-0.583543\pi\)
−0.259455 + 0.965755i \(0.583543\pi\)
\(578\) 0 0
\(579\) −23.5360 −0.978125
\(580\) 0 0
\(581\) −27.0710 −1.12310
\(582\) 0 0
\(583\) −27.6004 −1.14309
\(584\) 0 0
\(585\) 55.5540 2.29687
\(586\) 0 0
\(587\) −23.2510 −0.959670 −0.479835 0.877359i \(-0.659303\pi\)
−0.479835 + 0.877359i \(0.659303\pi\)
\(588\) 0 0
\(589\) −3.70495 −0.152660
\(590\) 0 0
\(591\) 51.0045 2.09804
\(592\) 0 0
\(593\) 18.5175 0.760421 0.380210 0.924900i \(-0.375852\pi\)
0.380210 + 0.924900i \(0.375852\pi\)
\(594\) 0 0
\(595\) −4.91602 −0.201537
\(596\) 0 0
\(597\) −33.9496 −1.38946
\(598\) 0 0
\(599\) 41.6620 1.70227 0.851133 0.524951i \(-0.175916\pi\)
0.851133 + 0.524951i \(0.175916\pi\)
\(600\) 0 0
\(601\) −5.47016 −0.223132 −0.111566 0.993757i \(-0.535587\pi\)
−0.111566 + 0.993757i \(0.535587\pi\)
\(602\) 0 0
\(603\) 16.0154 0.652196
\(604\) 0 0
\(605\) −47.0748 −1.91386
\(606\) 0 0
\(607\) −5.25588 −0.213330 −0.106665 0.994295i \(-0.534017\pi\)
−0.106665 + 0.994295i \(0.534017\pi\)
\(608\) 0 0
\(609\) −81.6313 −3.30787
\(610\) 0 0
\(611\) −43.3027 −1.75184
\(612\) 0 0
\(613\) 32.8948 1.32861 0.664303 0.747463i \(-0.268728\pi\)
0.664303 + 0.747463i \(0.268728\pi\)
\(614\) 0 0
\(615\) 16.0355 0.646612
\(616\) 0 0
\(617\) −6.66495 −0.268321 −0.134160 0.990960i \(-0.542834\pi\)
−0.134160 + 0.990960i \(0.542834\pi\)
\(618\) 0 0
\(619\) −34.5637 −1.38923 −0.694617 0.719380i \(-0.744426\pi\)
−0.694617 + 0.719380i \(0.744426\pi\)
\(620\) 0 0
\(621\) 39.7625 1.59561
\(622\) 0 0
\(623\) −21.6786 −0.868535
\(624\) 0 0
\(625\) −17.9662 −0.718649
\(626\) 0 0
\(627\) −115.572 −4.61550
\(628\) 0 0
\(629\) −5.33978 −0.212911
\(630\) 0 0
\(631\) −5.68292 −0.226233 −0.113117 0.993582i \(-0.536083\pi\)
−0.113117 + 0.993582i \(0.536083\pi\)
\(632\) 0 0
\(633\) −43.5319 −1.73024
\(634\) 0 0
\(635\) 32.9498 1.30757
\(636\) 0 0
\(637\) −5.24765 −0.207919
\(638\) 0 0
\(639\) 84.7288 3.35182
\(640\) 0 0
\(641\) −24.3525 −0.961865 −0.480932 0.876758i \(-0.659702\pi\)
−0.480932 + 0.876758i \(0.659702\pi\)
\(642\) 0 0
\(643\) −14.4231 −0.568790 −0.284395 0.958707i \(-0.591793\pi\)
−0.284395 + 0.958707i \(0.591793\pi\)
\(644\) 0 0
\(645\) −65.0036 −2.55951
\(646\) 0 0
\(647\) −41.0850 −1.61522 −0.807608 0.589719i \(-0.799238\pi\)
−0.807608 + 0.589719i \(0.799238\pi\)
\(648\) 0 0
\(649\) 10.5786 0.415245
\(650\) 0 0
\(651\) −4.50122 −0.176417
\(652\) 0 0
\(653\) −32.6034 −1.27587 −0.637935 0.770090i \(-0.720211\pi\)
−0.637935 + 0.770090i \(0.720211\pi\)
\(654\) 0 0
\(655\) 20.1704 0.788124
\(656\) 0 0
\(657\) 58.5121 2.28277
\(658\) 0 0
\(659\) 26.2682 1.02326 0.511631 0.859205i \(-0.329041\pi\)
0.511631 + 0.859205i \(0.329041\pi\)
\(660\) 0 0
\(661\) −21.7102 −0.844430 −0.422215 0.906496i \(-0.638747\pi\)
−0.422215 + 0.906496i \(0.638747\pi\)
\(662\) 0 0
\(663\) −13.4521 −0.522437
\(664\) 0 0
\(665\) 37.4608 1.45267
\(666\) 0 0
\(667\) 57.1081 2.21123
\(668\) 0 0
\(669\) −13.0211 −0.503426
\(670\) 0 0
\(671\) −45.4203 −1.75343
\(672\) 0 0
\(673\) −15.6069 −0.601600 −0.300800 0.953687i \(-0.597254\pi\)
−0.300800 + 0.953687i \(0.597254\pi\)
\(674\) 0 0
\(675\) 7.93929 0.305583
\(676\) 0 0
\(677\) 18.6421 0.716474 0.358237 0.933631i \(-0.383378\pi\)
0.358237 + 0.933631i \(0.383378\pi\)
\(678\) 0 0
\(679\) 6.41189 0.246066
\(680\) 0 0
\(681\) −22.9594 −0.879805
\(682\) 0 0
\(683\) 12.2022 0.466903 0.233451 0.972368i \(-0.424998\pi\)
0.233451 + 0.972368i \(0.424998\pi\)
\(684\) 0 0
\(685\) 24.7209 0.944538
\(686\) 0 0
\(687\) −77.7928 −2.96798
\(688\) 0 0
\(689\) 24.4803 0.932625
\(690\) 0 0
\(691\) −23.6452 −0.899506 −0.449753 0.893153i \(-0.648488\pi\)
−0.449753 + 0.893153i \(0.648488\pi\)
\(692\) 0 0
\(693\) −90.2278 −3.42747
\(694\) 0 0
\(695\) 20.1042 0.762594
\(696\) 0 0
\(697\) −2.49515 −0.0945107
\(698\) 0 0
\(699\) −46.6590 −1.76480
\(700\) 0 0
\(701\) 19.0573 0.719785 0.359893 0.932994i \(-0.382813\pi\)
0.359893 + 0.932994i \(0.382813\pi\)
\(702\) 0 0
\(703\) 40.6900 1.53465
\(704\) 0 0
\(705\) 46.9620 1.76869
\(706\) 0 0
\(707\) −9.08887 −0.341822
\(708\) 0 0
\(709\) 22.1610 0.832274 0.416137 0.909302i \(-0.363384\pi\)
0.416137 + 0.909302i \(0.363384\pi\)
\(710\) 0 0
\(711\) 87.6364 3.28662
\(712\) 0 0
\(713\) 3.14899 0.117931
\(714\) 0 0
\(715\) 60.9101 2.27791
\(716\) 0 0
\(717\) −1.61197 −0.0602000
\(718\) 0 0
\(719\) 3.65057 0.136143 0.0680716 0.997680i \(-0.478315\pi\)
0.0680716 + 0.997680i \(0.478315\pi\)
\(720\) 0 0
\(721\) −36.2316 −1.34934
\(722\) 0 0
\(723\) 68.7299 2.55609
\(724\) 0 0
\(725\) 11.4027 0.423484
\(726\) 0 0
\(727\) −14.6398 −0.542960 −0.271480 0.962444i \(-0.587513\pi\)
−0.271480 + 0.962444i \(0.587513\pi\)
\(728\) 0 0
\(729\) −39.1787 −1.45106
\(730\) 0 0
\(731\) 10.1147 0.374106
\(732\) 0 0
\(733\) −45.7076 −1.68825 −0.844125 0.536146i \(-0.819880\pi\)
−0.844125 + 0.536146i \(0.819880\pi\)
\(734\) 0 0
\(735\) 5.69110 0.209919
\(736\) 0 0
\(737\) 17.5594 0.646810
\(738\) 0 0
\(739\) 27.6620 1.01756 0.508781 0.860896i \(-0.330096\pi\)
0.508781 + 0.860896i \(0.330096\pi\)
\(740\) 0 0
\(741\) 102.507 3.76570
\(742\) 0 0
\(743\) −15.1666 −0.556410 −0.278205 0.960522i \(-0.589739\pi\)
−0.278205 + 0.960522i \(0.589739\pi\)
\(744\) 0 0
\(745\) 23.5541 0.862956
\(746\) 0 0
\(747\) 51.6242 1.88883
\(748\) 0 0
\(749\) 13.9860 0.511037
\(750\) 0 0
\(751\) −29.3066 −1.06941 −0.534707 0.845038i \(-0.679578\pi\)
−0.534707 + 0.845038i \(0.679578\pi\)
\(752\) 0 0
\(753\) 28.8553 1.05155
\(754\) 0 0
\(755\) 37.8011 1.37572
\(756\) 0 0
\(757\) 20.8165 0.756589 0.378295 0.925685i \(-0.376511\pi\)
0.378295 + 0.925685i \(0.376511\pi\)
\(758\) 0 0
\(759\) 98.2294 3.56550
\(760\) 0 0
\(761\) −31.3601 −1.13680 −0.568401 0.822752i \(-0.692438\pi\)
−0.568401 + 0.822752i \(0.692438\pi\)
\(762\) 0 0
\(763\) −48.8192 −1.76738
\(764\) 0 0
\(765\) 9.37481 0.338947
\(766\) 0 0
\(767\) −9.38271 −0.338790
\(768\) 0 0
\(769\) 0.137445 0.00495640 0.00247820 0.999997i \(-0.499211\pi\)
0.00247820 + 0.999997i \(0.499211\pi\)
\(770\) 0 0
\(771\) −62.4361 −2.24858
\(772\) 0 0
\(773\) −30.1120 −1.08305 −0.541526 0.840684i \(-0.682153\pi\)
−0.541526 + 0.840684i \(0.682153\pi\)
\(774\) 0 0
\(775\) 0.628752 0.0225855
\(776\) 0 0
\(777\) 49.4350 1.77347
\(778\) 0 0
\(779\) 19.0135 0.681228
\(780\) 0 0
\(781\) 92.8977 3.32414
\(782\) 0 0
\(783\) 69.0893 2.46905
\(784\) 0 0
\(785\) −14.9348 −0.533046
\(786\) 0 0
\(787\) 29.4682 1.05043 0.525214 0.850970i \(-0.323985\pi\)
0.525214 + 0.850970i \(0.323985\pi\)
\(788\) 0 0
\(789\) −54.7097 −1.94772
\(790\) 0 0
\(791\) −18.1902 −0.646768
\(792\) 0 0
\(793\) 40.2858 1.43059
\(794\) 0 0
\(795\) −26.5490 −0.941596
\(796\) 0 0
\(797\) 28.9883 1.02682 0.513408 0.858144i \(-0.328383\pi\)
0.513408 + 0.858144i \(0.328383\pi\)
\(798\) 0 0
\(799\) −7.30740 −0.258517
\(800\) 0 0
\(801\) 41.3409 1.46071
\(802\) 0 0
\(803\) 64.1534 2.26392
\(804\) 0 0
\(805\) −31.8395 −1.12219
\(806\) 0 0
\(807\) 55.2088 1.94344
\(808\) 0 0
\(809\) −36.8567 −1.29581 −0.647907 0.761720i \(-0.724355\pi\)
−0.647907 + 0.761720i \(0.724355\pi\)
\(810\) 0 0
\(811\) 34.4827 1.21085 0.605425 0.795902i \(-0.293003\pi\)
0.605425 + 0.795902i \(0.293003\pi\)
\(812\) 0 0
\(813\) −72.2735 −2.53474
\(814\) 0 0
\(815\) −31.2782 −1.09563
\(816\) 0 0
\(817\) −77.0755 −2.69653
\(818\) 0 0
\(819\) 80.0280 2.79640
\(820\) 0 0
\(821\) 18.0859 0.631204 0.315602 0.948892i \(-0.397794\pi\)
0.315602 + 0.948892i \(0.397794\pi\)
\(822\) 0 0
\(823\) −6.44917 −0.224804 −0.112402 0.993663i \(-0.535854\pi\)
−0.112402 + 0.993663i \(0.535854\pi\)
\(824\) 0 0
\(825\) 19.6133 0.682846
\(826\) 0 0
\(827\) 2.33358 0.0811466 0.0405733 0.999177i \(-0.487082\pi\)
0.0405733 + 0.999177i \(0.487082\pi\)
\(828\) 0 0
\(829\) −27.4949 −0.954938 −0.477469 0.878649i \(-0.658446\pi\)
−0.477469 + 0.878649i \(0.658446\pi\)
\(830\) 0 0
\(831\) 58.7705 2.03872
\(832\) 0 0
\(833\) −0.885547 −0.0306824
\(834\) 0 0
\(835\) 2.68896 0.0930553
\(836\) 0 0
\(837\) 3.80964 0.131680
\(838\) 0 0
\(839\) −39.0866 −1.34942 −0.674710 0.738083i \(-0.735731\pi\)
−0.674710 + 0.738083i \(0.735731\pi\)
\(840\) 0 0
\(841\) 70.2282 2.42166
\(842\) 0 0
\(843\) 48.0772 1.65587
\(844\) 0 0
\(845\) −28.4991 −0.980398
\(846\) 0 0
\(847\) −67.8133 −2.33009
\(848\) 0 0
\(849\) 4.19030 0.143811
\(850\) 0 0
\(851\) −34.5840 −1.18553
\(852\) 0 0
\(853\) 10.4262 0.356988 0.178494 0.983941i \(-0.442878\pi\)
0.178494 + 0.983941i \(0.442878\pi\)
\(854\) 0 0
\(855\) −71.4375 −2.44311
\(856\) 0 0
\(857\) −30.8938 −1.05531 −0.527656 0.849458i \(-0.676929\pi\)
−0.527656 + 0.849458i \(0.676929\pi\)
\(858\) 0 0
\(859\) −44.6266 −1.52264 −0.761320 0.648377i \(-0.775448\pi\)
−0.761320 + 0.648377i \(0.775448\pi\)
\(860\) 0 0
\(861\) 23.0998 0.787240
\(862\) 0 0
\(863\) −2.60527 −0.0886844 −0.0443422 0.999016i \(-0.514119\pi\)
−0.0443422 + 0.999016i \(0.514119\pi\)
\(864\) 0 0
\(865\) −20.2432 −0.688288
\(866\) 0 0
\(867\) 46.9828 1.59562
\(868\) 0 0
\(869\) 96.0857 3.25948
\(870\) 0 0
\(871\) −15.5744 −0.527720
\(872\) 0 0
\(873\) −12.2274 −0.413835
\(874\) 0 0
\(875\) −34.1261 −1.15367
\(876\) 0 0
\(877\) −36.1095 −1.21933 −0.609666 0.792658i \(-0.708697\pi\)
−0.609666 + 0.792658i \(0.708697\pi\)
\(878\) 0 0
\(879\) 80.6908 2.72163
\(880\) 0 0
\(881\) −26.9625 −0.908390 −0.454195 0.890902i \(-0.650073\pi\)
−0.454195 + 0.890902i \(0.650073\pi\)
\(882\) 0 0
\(883\) 11.6289 0.391345 0.195672 0.980669i \(-0.437311\pi\)
0.195672 + 0.980669i \(0.437311\pi\)
\(884\) 0 0
\(885\) 10.1756 0.342049
\(886\) 0 0
\(887\) 16.3652 0.549491 0.274746 0.961517i \(-0.411406\pi\)
0.274746 + 0.961517i \(0.411406\pi\)
\(888\) 0 0
\(889\) 47.4657 1.59195
\(890\) 0 0
\(891\) 23.1393 0.775195
\(892\) 0 0
\(893\) 55.6835 1.86338
\(894\) 0 0
\(895\) 7.05258 0.235742
\(896\) 0 0
\(897\) −87.1251 −2.90902
\(898\) 0 0
\(899\) 5.47153 0.182486
\(900\) 0 0
\(901\) 4.13108 0.137626
\(902\) 0 0
\(903\) −93.6406 −3.11616
\(904\) 0 0
\(905\) 24.4830 0.813843
\(906\) 0 0
\(907\) 9.36503 0.310961 0.155480 0.987839i \(-0.450307\pi\)
0.155480 + 0.987839i \(0.450307\pi\)
\(908\) 0 0
\(909\) 17.3324 0.574879
\(910\) 0 0
\(911\) −48.0428 −1.59173 −0.795864 0.605475i \(-0.792983\pi\)
−0.795864 + 0.605475i \(0.792983\pi\)
\(912\) 0 0
\(913\) 56.6014 1.87323
\(914\) 0 0
\(915\) −43.6901 −1.44435
\(916\) 0 0
\(917\) 29.0564 0.959527
\(918\) 0 0
\(919\) 33.6245 1.10917 0.554585 0.832127i \(-0.312877\pi\)
0.554585 + 0.832127i \(0.312877\pi\)
\(920\) 0 0
\(921\) 16.2501 0.535458
\(922\) 0 0
\(923\) −82.3961 −2.71210
\(924\) 0 0
\(925\) −6.90533 −0.227046
\(926\) 0 0
\(927\) 69.0934 2.26932
\(928\) 0 0
\(929\) −26.4329 −0.867235 −0.433618 0.901097i \(-0.642763\pi\)
−0.433618 + 0.901097i \(0.642763\pi\)
\(930\) 0 0
\(931\) 6.74801 0.221157
\(932\) 0 0
\(933\) −10.5157 −0.344269
\(934\) 0 0
\(935\) 10.2787 0.336148
\(936\) 0 0
\(937\) 5.70987 0.186533 0.0932666 0.995641i \(-0.470269\pi\)
0.0932666 + 0.995641i \(0.470269\pi\)
\(938\) 0 0
\(939\) −90.7104 −2.96022
\(940\) 0 0
\(941\) 33.9969 1.10827 0.554134 0.832427i \(-0.313049\pi\)
0.554134 + 0.832427i \(0.313049\pi\)
\(942\) 0 0
\(943\) −16.1603 −0.526252
\(944\) 0 0
\(945\) −38.5194 −1.25303
\(946\) 0 0
\(947\) −47.1654 −1.53267 −0.766334 0.642442i \(-0.777921\pi\)
−0.766334 + 0.642442i \(0.777921\pi\)
\(948\) 0 0
\(949\) −56.9012 −1.84709
\(950\) 0 0
\(951\) 87.0091 2.82146
\(952\) 0 0
\(953\) 5.07255 0.164316 0.0821581 0.996619i \(-0.473819\pi\)
0.0821581 + 0.996619i \(0.473819\pi\)
\(954\) 0 0
\(955\) 38.8287 1.25647
\(956\) 0 0
\(957\) 170.679 5.51726
\(958\) 0 0
\(959\) 35.6116 1.14996
\(960\) 0 0
\(961\) −30.6983 −0.990268
\(962\) 0 0
\(963\) −26.6712 −0.859466
\(964\) 0 0
\(965\) −15.9507 −0.513472
\(966\) 0 0
\(967\) 6.30261 0.202678 0.101339 0.994852i \(-0.467687\pi\)
0.101339 + 0.994852i \(0.467687\pi\)
\(968\) 0 0
\(969\) 17.2982 0.555700
\(970\) 0 0
\(971\) 0.764960 0.0245487 0.0122744 0.999925i \(-0.496093\pi\)
0.0122744 + 0.999925i \(0.496093\pi\)
\(972\) 0 0
\(973\) 28.9609 0.928445
\(974\) 0 0
\(975\) −17.3961 −0.557121
\(976\) 0 0
\(977\) −57.2135 −1.83042 −0.915211 0.402974i \(-0.867976\pi\)
−0.915211 + 0.402974i \(0.867976\pi\)
\(978\) 0 0
\(979\) 45.3267 1.44865
\(980\) 0 0
\(981\) 93.0978 2.97238
\(982\) 0 0
\(983\) −21.2431 −0.677548 −0.338774 0.940868i \(-0.610012\pi\)
−0.338774 + 0.940868i \(0.610012\pi\)
\(984\) 0 0
\(985\) 34.5665 1.10138
\(986\) 0 0
\(987\) 67.6509 2.15335
\(988\) 0 0
\(989\) 65.5096 2.08309
\(990\) 0 0
\(991\) −1.70053 −0.0540193 −0.0270096 0.999635i \(-0.508598\pi\)
−0.0270096 + 0.999635i \(0.508598\pi\)
\(992\) 0 0
\(993\) 79.1593 2.51204
\(994\) 0 0
\(995\) −23.0082 −0.729408
\(996\) 0 0
\(997\) −32.3205 −1.02360 −0.511800 0.859104i \(-0.671021\pi\)
−0.511800 + 0.859104i \(0.671021\pi\)
\(998\) 0 0
\(999\) −41.8397 −1.32375
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 \(a_p\))