Properties

Label 8024.2.a.y.1.7
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.61430 q^{3}\) \(-1.23431 q^{5}\) \(+4.85046 q^{7}\) \(-0.394052 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.61430 q^{3}\) \(-1.23431 q^{5}\) \(+4.85046 q^{7}\) \(-0.394052 q^{9}\) \(-1.78231 q^{11}\) \(-5.69601 q^{13}\) \(+1.99254 q^{15}\) \(-1.00000 q^{17}\) \(+2.51169 q^{19}\) \(-7.83007 q^{21}\) \(+6.91882 q^{23}\) \(-3.47648 q^{25}\) \(+5.47900 q^{27}\) \(-7.19652 q^{29}\) \(+5.87284 q^{31}\) \(+2.87718 q^{33}\) \(-5.98697 q^{35}\) \(+3.49518 q^{37}\) \(+9.19504 q^{39}\) \(-1.25490 q^{41}\) \(+1.45306 q^{43}\) \(+0.486382 q^{45}\) \(+2.43142 q^{47}\) \(+16.5270 q^{49}\) \(+1.61430 q^{51}\) \(+2.66779 q^{53}\) \(+2.19993 q^{55}\) \(-4.05460 q^{57}\) \(-1.00000 q^{59}\) \(-8.88620 q^{61}\) \(-1.91133 q^{63}\) \(+7.03064 q^{65}\) \(-3.95895 q^{67}\) \(-11.1690 q^{69}\) \(-2.75208 q^{71}\) \(-9.97414 q^{73}\) \(+5.61206 q^{75}\) \(-8.64504 q^{77}\) \(+1.01525 q^{79}\) \(-7.66257 q^{81}\) \(-2.01954 q^{83}\) \(+1.23431 q^{85}\) \(+11.6173 q^{87}\) \(+11.9291 q^{89}\) \(-27.6283 q^{91}\) \(-9.48050 q^{93}\) \(-3.10020 q^{95}\) \(-3.33104 q^{97}\) \(+0.702323 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.61430 −0.932014 −0.466007 0.884781i \(-0.654308\pi\)
−0.466007 + 0.884781i \(0.654308\pi\)
\(4\) 0 0
\(5\) −1.23431 −0.552000 −0.276000 0.961158i \(-0.589009\pi\)
−0.276000 + 0.961158i \(0.589009\pi\)
\(6\) 0 0
\(7\) 4.85046 1.83330 0.916651 0.399689i \(-0.130882\pi\)
0.916651 + 0.399689i \(0.130882\pi\)
\(8\) 0 0
\(9\) −0.394052 −0.131351
\(10\) 0 0
\(11\) −1.78231 −0.537388 −0.268694 0.963226i \(-0.586592\pi\)
−0.268694 + 0.963226i \(0.586592\pi\)
\(12\) 0 0
\(13\) −5.69601 −1.57979 −0.789894 0.613243i \(-0.789865\pi\)
−0.789894 + 0.613243i \(0.789865\pi\)
\(14\) 0 0
\(15\) 1.99254 0.514472
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 2.51169 0.576221 0.288110 0.957597i \(-0.406973\pi\)
0.288110 + 0.957597i \(0.406973\pi\)
\(20\) 0 0
\(21\) −7.83007 −1.70866
\(22\) 0 0
\(23\) 6.91882 1.44267 0.721337 0.692584i \(-0.243528\pi\)
0.721337 + 0.692584i \(0.243528\pi\)
\(24\) 0 0
\(25\) −3.47648 −0.695296
\(26\) 0 0
\(27\) 5.47900 1.05443
\(28\) 0 0
\(29\) −7.19652 −1.33636 −0.668180 0.743999i \(-0.732926\pi\)
−0.668180 + 0.743999i \(0.732926\pi\)
\(30\) 0 0
\(31\) 5.87284 1.05479 0.527397 0.849619i \(-0.323168\pi\)
0.527397 + 0.849619i \(0.323168\pi\)
\(32\) 0 0
\(33\) 2.87718 0.500853
\(34\) 0 0
\(35\) −5.98697 −1.01198
\(36\) 0 0
\(37\) 3.49518 0.574604 0.287302 0.957840i \(-0.407242\pi\)
0.287302 + 0.957840i \(0.407242\pi\)
\(38\) 0 0
\(39\) 9.19504 1.47238
\(40\) 0 0
\(41\) −1.25490 −0.195982 −0.0979909 0.995187i \(-0.531242\pi\)
−0.0979909 + 0.995187i \(0.531242\pi\)
\(42\) 0 0
\(43\) 1.45306 0.221590 0.110795 0.993843i \(-0.464660\pi\)
0.110795 + 0.993843i \(0.464660\pi\)
\(44\) 0 0
\(45\) 0.486382 0.0725055
\(46\) 0 0
\(47\) 2.43142 0.354659 0.177330 0.984151i \(-0.443254\pi\)
0.177330 + 0.984151i \(0.443254\pi\)
\(48\) 0 0
\(49\) 16.5270 2.36100
\(50\) 0 0
\(51\) 1.61430 0.226047
\(52\) 0 0
\(53\) 2.66779 0.366450 0.183225 0.983071i \(-0.441346\pi\)
0.183225 + 0.983071i \(0.441346\pi\)
\(54\) 0 0
\(55\) 2.19993 0.296638
\(56\) 0 0
\(57\) −4.05460 −0.537045
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −8.88620 −1.13776 −0.568881 0.822420i \(-0.692623\pi\)
−0.568881 + 0.822420i \(0.692623\pi\)
\(62\) 0 0
\(63\) −1.91133 −0.240805
\(64\) 0 0
\(65\) 7.03064 0.872043
\(66\) 0 0
\(67\) −3.95895 −0.483663 −0.241831 0.970318i \(-0.577748\pi\)
−0.241831 + 0.970318i \(0.577748\pi\)
\(68\) 0 0
\(69\) −11.1690 −1.34459
\(70\) 0 0
\(71\) −2.75208 −0.326611 −0.163306 0.986576i \(-0.552216\pi\)
−0.163306 + 0.986576i \(0.552216\pi\)
\(72\) 0 0
\(73\) −9.97414 −1.16739 −0.583693 0.811975i \(-0.698393\pi\)
−0.583693 + 0.811975i \(0.698393\pi\)
\(74\) 0 0
\(75\) 5.61206 0.648025
\(76\) 0 0
\(77\) −8.64504 −0.985194
\(78\) 0 0
\(79\) 1.01525 0.114224 0.0571120 0.998368i \(-0.481811\pi\)
0.0571120 + 0.998368i \(0.481811\pi\)
\(80\) 0 0
\(81\) −7.66257 −0.851396
\(82\) 0 0
\(83\) −2.01954 −0.221673 −0.110836 0.993839i \(-0.535353\pi\)
−0.110836 + 0.993839i \(0.535353\pi\)
\(84\) 0 0
\(85\) 1.23431 0.133880
\(86\) 0 0
\(87\) 11.6173 1.24551
\(88\) 0 0
\(89\) 11.9291 1.26448 0.632242 0.774771i \(-0.282135\pi\)
0.632242 + 0.774771i \(0.282135\pi\)
\(90\) 0 0
\(91\) −27.6283 −2.89623
\(92\) 0 0
\(93\) −9.48050 −0.983082
\(94\) 0 0
\(95\) −3.10020 −0.318074
\(96\) 0 0
\(97\) −3.33104 −0.338216 −0.169108 0.985598i \(-0.554089\pi\)
−0.169108 + 0.985598i \(0.554089\pi\)
\(98\) 0 0
\(99\) 0.702323 0.0705861
\(100\) 0 0
\(101\) 20.0483 1.99488 0.997438 0.0715347i \(-0.0227897\pi\)
0.997438 + 0.0715347i \(0.0227897\pi\)
\(102\) 0 0
\(103\) −7.51221 −0.740201 −0.370100 0.928992i \(-0.620677\pi\)
−0.370100 + 0.928992i \(0.620677\pi\)
\(104\) 0 0
\(105\) 9.66474 0.943182
\(106\) 0 0
\(107\) 9.87323 0.954481 0.477241 0.878773i \(-0.341637\pi\)
0.477241 + 0.878773i \(0.341637\pi\)
\(108\) 0 0
\(109\) −17.6636 −1.69187 −0.845934 0.533287i \(-0.820957\pi\)
−0.845934 + 0.533287i \(0.820957\pi\)
\(110\) 0 0
\(111\) −5.64225 −0.535539
\(112\) 0 0
\(113\) −16.4550 −1.54796 −0.773979 0.633211i \(-0.781737\pi\)
−0.773979 + 0.633211i \(0.781737\pi\)
\(114\) 0 0
\(115\) −8.53997 −0.796356
\(116\) 0 0
\(117\) 2.24452 0.207506
\(118\) 0 0
\(119\) −4.85046 −0.444641
\(120\) 0 0
\(121\) −7.82336 −0.711215
\(122\) 0 0
\(123\) 2.02577 0.182658
\(124\) 0 0
\(125\) 10.4626 0.935803
\(126\) 0 0
\(127\) −14.7641 −1.31011 −0.655053 0.755583i \(-0.727354\pi\)
−0.655053 + 0.755583i \(0.727354\pi\)
\(128\) 0 0
\(129\) −2.34567 −0.206525
\(130\) 0 0
\(131\) 14.3236 1.25146 0.625731 0.780039i \(-0.284801\pi\)
0.625731 + 0.780039i \(0.284801\pi\)
\(132\) 0 0
\(133\) 12.1828 1.05639
\(134\) 0 0
\(135\) −6.76278 −0.582048
\(136\) 0 0
\(137\) 19.3455 1.65280 0.826398 0.563086i \(-0.190386\pi\)
0.826398 + 0.563086i \(0.190386\pi\)
\(138\) 0 0
\(139\) −9.81724 −0.832687 −0.416344 0.909207i \(-0.636689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(140\) 0 0
\(141\) −3.92503 −0.330547
\(142\) 0 0
\(143\) 10.1521 0.848959
\(144\) 0 0
\(145\) 8.88273 0.737671
\(146\) 0 0
\(147\) −26.6794 −2.20048
\(148\) 0 0
\(149\) −11.7655 −0.963871 −0.481936 0.876207i \(-0.660066\pi\)
−0.481936 + 0.876207i \(0.660066\pi\)
\(150\) 0 0
\(151\) 19.1626 1.55943 0.779713 0.626137i \(-0.215365\pi\)
0.779713 + 0.626137i \(0.215365\pi\)
\(152\) 0 0
\(153\) 0.394052 0.0318572
\(154\) 0 0
\(155\) −7.24891 −0.582246
\(156\) 0 0
\(157\) −5.26747 −0.420390 −0.210195 0.977659i \(-0.567410\pi\)
−0.210195 + 0.977659i \(0.567410\pi\)
\(158\) 0 0
\(159\) −4.30661 −0.341536
\(160\) 0 0
\(161\) 33.5595 2.64486
\(162\) 0 0
\(163\) −21.1836 −1.65923 −0.829615 0.558335i \(-0.811440\pi\)
−0.829615 + 0.558335i \(0.811440\pi\)
\(164\) 0 0
\(165\) −3.55133 −0.276471
\(166\) 0 0
\(167\) 22.8657 1.76940 0.884702 0.466157i \(-0.154362\pi\)
0.884702 + 0.466157i \(0.154362\pi\)
\(168\) 0 0
\(169\) 19.4445 1.49573
\(170\) 0 0
\(171\) −0.989735 −0.0756869
\(172\) 0 0
\(173\) 0.613113 0.0466141 0.0233071 0.999728i \(-0.492580\pi\)
0.0233071 + 0.999728i \(0.492580\pi\)
\(174\) 0 0
\(175\) −16.8625 −1.27469
\(176\) 0 0
\(177\) 1.61430 0.121338
\(178\) 0 0
\(179\) −7.90303 −0.590700 −0.295350 0.955389i \(-0.595436\pi\)
−0.295350 + 0.955389i \(0.595436\pi\)
\(180\) 0 0
\(181\) −2.58128 −0.191865 −0.0959327 0.995388i \(-0.530583\pi\)
−0.0959327 + 0.995388i \(0.530583\pi\)
\(182\) 0 0
\(183\) 14.3449 1.06041
\(184\) 0 0
\(185\) −4.31414 −0.317182
\(186\) 0 0
\(187\) 1.78231 0.130336
\(188\) 0 0
\(189\) 26.5757 1.93310
\(190\) 0 0
\(191\) 21.9845 1.59074 0.795372 0.606122i \(-0.207276\pi\)
0.795372 + 0.606122i \(0.207276\pi\)
\(192\) 0 0
\(193\) 6.87376 0.494784 0.247392 0.968915i \(-0.420426\pi\)
0.247392 + 0.968915i \(0.420426\pi\)
\(194\) 0 0
\(195\) −11.3495 −0.812756
\(196\) 0 0
\(197\) −4.58120 −0.326397 −0.163198 0.986593i \(-0.552181\pi\)
−0.163198 + 0.986593i \(0.552181\pi\)
\(198\) 0 0
\(199\) −0.266704 −0.0189061 −0.00945307 0.999955i \(-0.503009\pi\)
−0.00945307 + 0.999955i \(0.503009\pi\)
\(200\) 0 0
\(201\) 6.39091 0.450780
\(202\) 0 0
\(203\) −34.9064 −2.44995
\(204\) 0 0
\(205\) 1.54893 0.108182
\(206\) 0 0
\(207\) −2.72637 −0.189496
\(208\) 0 0
\(209\) −4.47661 −0.309654
\(210\) 0 0
\(211\) −20.0898 −1.38304 −0.691518 0.722359i \(-0.743058\pi\)
−0.691518 + 0.722359i \(0.743058\pi\)
\(212\) 0 0
\(213\) 4.44266 0.304406
\(214\) 0 0
\(215\) −1.79353 −0.122318
\(216\) 0 0
\(217\) 28.4860 1.93376
\(218\) 0 0
\(219\) 16.1012 1.08802
\(220\) 0 0
\(221\) 5.69601 0.383155
\(222\) 0 0
\(223\) −28.2922 −1.89459 −0.947293 0.320369i \(-0.896193\pi\)
−0.947293 + 0.320369i \(0.896193\pi\)
\(224\) 0 0
\(225\) 1.36991 0.0913275
\(226\) 0 0
\(227\) 7.16434 0.475514 0.237757 0.971325i \(-0.423588\pi\)
0.237757 + 0.971325i \(0.423588\pi\)
\(228\) 0 0
\(229\) −6.92016 −0.457297 −0.228649 0.973509i \(-0.573431\pi\)
−0.228649 + 0.973509i \(0.573431\pi\)
\(230\) 0 0
\(231\) 13.9556 0.918214
\(232\) 0 0
\(233\) −14.6107 −0.957177 −0.478589 0.878039i \(-0.658851\pi\)
−0.478589 + 0.878039i \(0.658851\pi\)
\(234\) 0 0
\(235\) −3.00113 −0.195772
\(236\) 0 0
\(237\) −1.63891 −0.106458
\(238\) 0 0
\(239\) 12.7951 0.827643 0.413822 0.910358i \(-0.364194\pi\)
0.413822 + 0.910358i \(0.364194\pi\)
\(240\) 0 0
\(241\) −19.1401 −1.23292 −0.616460 0.787387i \(-0.711434\pi\)
−0.616460 + 0.787387i \(0.711434\pi\)
\(242\) 0 0
\(243\) −4.06736 −0.260921
\(244\) 0 0
\(245\) −20.3994 −1.30327
\(246\) 0 0
\(247\) −14.3066 −0.910307
\(248\) 0 0
\(249\) 3.26013 0.206602
\(250\) 0 0
\(251\) −3.57492 −0.225647 −0.112824 0.993615i \(-0.535989\pi\)
−0.112824 + 0.993615i \(0.535989\pi\)
\(252\) 0 0
\(253\) −12.3315 −0.775275
\(254\) 0 0
\(255\) −1.99254 −0.124778
\(256\) 0 0
\(257\) 0.666916 0.0416011 0.0208005 0.999784i \(-0.493379\pi\)
0.0208005 + 0.999784i \(0.493379\pi\)
\(258\) 0 0
\(259\) 16.9532 1.05342
\(260\) 0 0
\(261\) 2.83580 0.175532
\(262\) 0 0
\(263\) −22.7227 −1.40114 −0.700570 0.713584i \(-0.747071\pi\)
−0.700570 + 0.713584i \(0.747071\pi\)
\(264\) 0 0
\(265\) −3.29288 −0.202280
\(266\) 0 0
\(267\) −19.2571 −1.17852
\(268\) 0 0
\(269\) 1.26415 0.0770764 0.0385382 0.999257i \(-0.487730\pi\)
0.0385382 + 0.999257i \(0.487730\pi\)
\(270\) 0 0
\(271\) 11.8640 0.720687 0.360344 0.932820i \(-0.382659\pi\)
0.360344 + 0.932820i \(0.382659\pi\)
\(272\) 0 0
\(273\) 44.6002 2.69933
\(274\) 0 0
\(275\) 6.19617 0.373643
\(276\) 0 0
\(277\) 30.7805 1.84942 0.924709 0.380674i \(-0.124308\pi\)
0.924709 + 0.380674i \(0.124308\pi\)
\(278\) 0 0
\(279\) −2.31420 −0.138548
\(280\) 0 0
\(281\) −27.4165 −1.63553 −0.817766 0.575552i \(-0.804787\pi\)
−0.817766 + 0.575552i \(0.804787\pi\)
\(282\) 0 0
\(283\) 11.1308 0.661658 0.330829 0.943691i \(-0.392672\pi\)
0.330829 + 0.943691i \(0.392672\pi\)
\(284\) 0 0
\(285\) 5.00464 0.296449
\(286\) 0 0
\(287\) −6.08682 −0.359294
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 5.37728 0.315222
\(292\) 0 0
\(293\) −7.52573 −0.439658 −0.219829 0.975538i \(-0.570550\pi\)
−0.219829 + 0.975538i \(0.570550\pi\)
\(294\) 0 0
\(295\) 1.23431 0.0718643
\(296\) 0 0
\(297\) −9.76529 −0.566640
\(298\) 0 0
\(299\) −39.4097 −2.27912
\(300\) 0 0
\(301\) 7.04803 0.406242
\(302\) 0 0
\(303\) −32.3638 −1.85925
\(304\) 0 0
\(305\) 10.9683 0.628044
\(306\) 0 0
\(307\) 3.24046 0.184943 0.0924713 0.995715i \(-0.470523\pi\)
0.0924713 + 0.995715i \(0.470523\pi\)
\(308\) 0 0
\(309\) 12.1269 0.689877
\(310\) 0 0
\(311\) 2.79100 0.158263 0.0791316 0.996864i \(-0.474785\pi\)
0.0791316 + 0.996864i \(0.474785\pi\)
\(312\) 0 0
\(313\) −19.8043 −1.11941 −0.559703 0.828693i \(-0.689085\pi\)
−0.559703 + 0.828693i \(0.689085\pi\)
\(314\) 0 0
\(315\) 2.35918 0.132924
\(316\) 0 0
\(317\) −27.4278 −1.54050 −0.770250 0.637742i \(-0.779869\pi\)
−0.770250 + 0.637742i \(0.779869\pi\)
\(318\) 0 0
\(319\) 12.8265 0.718143
\(320\) 0 0
\(321\) −15.9383 −0.889590
\(322\) 0 0
\(323\) −2.51169 −0.139754
\(324\) 0 0
\(325\) 19.8021 1.09842
\(326\) 0 0
\(327\) 28.5143 1.57684
\(328\) 0 0
\(329\) 11.7935 0.650198
\(330\) 0 0
\(331\) 0.729561 0.0401003 0.0200501 0.999799i \(-0.493617\pi\)
0.0200501 + 0.999799i \(0.493617\pi\)
\(332\) 0 0
\(333\) −1.37728 −0.0754746
\(334\) 0 0
\(335\) 4.88657 0.266982
\(336\) 0 0
\(337\) −23.1846 −1.26294 −0.631472 0.775399i \(-0.717549\pi\)
−0.631472 + 0.775399i \(0.717549\pi\)
\(338\) 0 0
\(339\) 26.5633 1.44272
\(340\) 0 0
\(341\) −10.4672 −0.566833
\(342\) 0 0
\(343\) 46.2102 2.49512
\(344\) 0 0
\(345\) 13.7860 0.742215
\(346\) 0 0
\(347\) 26.6414 1.43018 0.715092 0.699031i \(-0.246385\pi\)
0.715092 + 0.699031i \(0.246385\pi\)
\(348\) 0 0
\(349\) −21.5689 −1.15456 −0.577278 0.816548i \(-0.695885\pi\)
−0.577278 + 0.816548i \(0.695885\pi\)
\(350\) 0 0
\(351\) −31.2084 −1.66578
\(352\) 0 0
\(353\) −18.7378 −0.997314 −0.498657 0.866799i \(-0.666173\pi\)
−0.498657 + 0.866799i \(0.666173\pi\)
\(354\) 0 0
\(355\) 3.39691 0.180289
\(356\) 0 0
\(357\) 7.83007 0.414412
\(358\) 0 0
\(359\) 9.27611 0.489574 0.244787 0.969577i \(-0.421282\pi\)
0.244787 + 0.969577i \(0.421282\pi\)
\(360\) 0 0
\(361\) −12.6914 −0.667970
\(362\) 0 0
\(363\) 12.6292 0.662862
\(364\) 0 0
\(365\) 12.3112 0.644397
\(366\) 0 0
\(367\) −17.8028 −0.929298 −0.464649 0.885495i \(-0.653819\pi\)
−0.464649 + 0.885495i \(0.653819\pi\)
\(368\) 0 0
\(369\) 0.494494 0.0257423
\(370\) 0 0
\(371\) 12.9400 0.671813
\(372\) 0 0
\(373\) −2.76975 −0.143412 −0.0717060 0.997426i \(-0.522844\pi\)
−0.0717060 + 0.997426i \(0.522844\pi\)
\(374\) 0 0
\(375\) −16.8897 −0.872182
\(376\) 0 0
\(377\) 40.9914 2.11117
\(378\) 0 0
\(379\) 19.8785 1.02109 0.510546 0.859851i \(-0.329443\pi\)
0.510546 + 0.859851i \(0.329443\pi\)
\(380\) 0 0
\(381\) 23.8337 1.22104
\(382\) 0 0
\(383\) −23.5542 −1.20357 −0.601783 0.798660i \(-0.705543\pi\)
−0.601783 + 0.798660i \(0.705543\pi\)
\(384\) 0 0
\(385\) 10.6707 0.543827
\(386\) 0 0
\(387\) −0.572582 −0.0291060
\(388\) 0 0
\(389\) −3.68939 −0.187060 −0.0935298 0.995616i \(-0.529815\pi\)
−0.0935298 + 0.995616i \(0.529815\pi\)
\(390\) 0 0
\(391\) −6.91882 −0.349900
\(392\) 0 0
\(393\) −23.1226 −1.16638
\(394\) 0 0
\(395\) −1.25313 −0.0630517
\(396\) 0 0
\(397\) −27.3140 −1.37085 −0.685425 0.728143i \(-0.740384\pi\)
−0.685425 + 0.728143i \(0.740384\pi\)
\(398\) 0 0
\(399\) −19.6667 −0.984566
\(400\) 0 0
\(401\) 9.50420 0.474617 0.237309 0.971434i \(-0.423735\pi\)
0.237309 + 0.971434i \(0.423735\pi\)
\(402\) 0 0
\(403\) −33.4518 −1.66635
\(404\) 0 0
\(405\) 9.45798 0.469971
\(406\) 0 0
\(407\) −6.22951 −0.308785
\(408\) 0 0
\(409\) −24.4497 −1.20896 −0.604479 0.796621i \(-0.706619\pi\)
−0.604479 + 0.796621i \(0.706619\pi\)
\(410\) 0 0
\(411\) −31.2293 −1.54043
\(412\) 0 0
\(413\) −4.85046 −0.238676
\(414\) 0 0
\(415\) 2.49273 0.122363
\(416\) 0 0
\(417\) 15.8479 0.776076
\(418\) 0 0
\(419\) −20.1650 −0.985126 −0.492563 0.870277i \(-0.663940\pi\)
−0.492563 + 0.870277i \(0.663940\pi\)
\(420\) 0 0
\(421\) 28.7819 1.40274 0.701372 0.712796i \(-0.252571\pi\)
0.701372 + 0.712796i \(0.252571\pi\)
\(422\) 0 0
\(423\) −0.958106 −0.0465847
\(424\) 0 0
\(425\) 3.47648 0.168634
\(426\) 0 0
\(427\) −43.1022 −2.08586
\(428\) 0 0
\(429\) −16.3884 −0.791241
\(430\) 0 0
\(431\) 19.0386 0.917059 0.458529 0.888679i \(-0.348376\pi\)
0.458529 + 0.888679i \(0.348376\pi\)
\(432\) 0 0
\(433\) 19.1501 0.920297 0.460148 0.887842i \(-0.347796\pi\)
0.460148 + 0.887842i \(0.347796\pi\)
\(434\) 0 0
\(435\) −14.3394 −0.687519
\(436\) 0 0
\(437\) 17.3779 0.831299
\(438\) 0 0
\(439\) −23.0343 −1.09937 −0.549684 0.835372i \(-0.685252\pi\)
−0.549684 + 0.835372i \(0.685252\pi\)
\(440\) 0 0
\(441\) −6.51248 −0.310118
\(442\) 0 0
\(443\) −28.1446 −1.33719 −0.668595 0.743626i \(-0.733104\pi\)
−0.668595 + 0.743626i \(0.733104\pi\)
\(444\) 0 0
\(445\) −14.7242 −0.697995
\(446\) 0 0
\(447\) 18.9931 0.898341
\(448\) 0 0
\(449\) −23.2186 −1.09576 −0.547878 0.836558i \(-0.684564\pi\)
−0.547878 + 0.836558i \(0.684564\pi\)
\(450\) 0 0
\(451\) 2.23662 0.105318
\(452\) 0 0
\(453\) −30.9340 −1.45341
\(454\) 0 0
\(455\) 34.1018 1.59872
\(456\) 0 0
\(457\) 39.7866 1.86114 0.930569 0.366115i \(-0.119312\pi\)
0.930569 + 0.366115i \(0.119312\pi\)
\(458\) 0 0
\(459\) −5.47900 −0.255738
\(460\) 0 0
\(461\) −23.5524 −1.09694 −0.548471 0.836169i \(-0.684790\pi\)
−0.548471 + 0.836169i \(0.684790\pi\)
\(462\) 0 0
\(463\) 17.2771 0.802937 0.401469 0.915873i \(-0.368500\pi\)
0.401469 + 0.915873i \(0.368500\pi\)
\(464\) 0 0
\(465\) 11.7019 0.542662
\(466\) 0 0
\(467\) −11.6604 −0.539577 −0.269789 0.962920i \(-0.586954\pi\)
−0.269789 + 0.962920i \(0.586954\pi\)
\(468\) 0 0
\(469\) −19.2027 −0.886700
\(470\) 0 0
\(471\) 8.50326 0.391809
\(472\) 0 0
\(473\) −2.58981 −0.119080
\(474\) 0 0
\(475\) −8.73183 −0.400644
\(476\) 0 0
\(477\) −1.05125 −0.0481334
\(478\) 0 0
\(479\) −13.7278 −0.627240 −0.313620 0.949549i \(-0.601542\pi\)
−0.313620 + 0.949549i \(0.601542\pi\)
\(480\) 0 0
\(481\) −19.9086 −0.907753
\(482\) 0 0
\(483\) −54.1749 −2.46504
\(484\) 0 0
\(485\) 4.11153 0.186695
\(486\) 0 0
\(487\) −8.37770 −0.379630 −0.189815 0.981820i \(-0.560789\pi\)
−0.189815 + 0.981820i \(0.560789\pi\)
\(488\) 0 0
\(489\) 34.1966 1.54643
\(490\) 0 0
\(491\) −10.1742 −0.459154 −0.229577 0.973290i \(-0.573734\pi\)
−0.229577 + 0.973290i \(0.573734\pi\)
\(492\) 0 0
\(493\) 7.19652 0.324115
\(494\) 0 0
\(495\) −0.866884 −0.0389636
\(496\) 0 0
\(497\) −13.3488 −0.598777
\(498\) 0 0
\(499\) 6.06056 0.271308 0.135654 0.990756i \(-0.456686\pi\)
0.135654 + 0.990756i \(0.456686\pi\)
\(500\) 0 0
\(501\) −36.9121 −1.64911
\(502\) 0 0
\(503\) −3.10211 −0.138316 −0.0691581 0.997606i \(-0.522031\pi\)
−0.0691581 + 0.997606i \(0.522031\pi\)
\(504\) 0 0
\(505\) −24.7458 −1.10117
\(506\) 0 0
\(507\) −31.3892 −1.39404
\(508\) 0 0
\(509\) −33.8803 −1.50172 −0.750859 0.660462i \(-0.770360\pi\)
−0.750859 + 0.660462i \(0.770360\pi\)
\(510\) 0 0
\(511\) −48.3792 −2.14017
\(512\) 0 0
\(513\) 13.7615 0.607587
\(514\) 0 0
\(515\) 9.27240 0.408591
\(516\) 0 0
\(517\) −4.33356 −0.190590
\(518\) 0 0
\(519\) −0.989745 −0.0434450
\(520\) 0 0
\(521\) −10.0899 −0.442046 −0.221023 0.975269i \(-0.570940\pi\)
−0.221023 + 0.975269i \(0.570940\pi\)
\(522\) 0 0
\(523\) 3.78130 0.165345 0.0826723 0.996577i \(-0.473655\pi\)
0.0826723 + 0.996577i \(0.473655\pi\)
\(524\) 0 0
\(525\) 27.2211 1.18803
\(526\) 0 0
\(527\) −5.87284 −0.255825
\(528\) 0 0
\(529\) 24.8701 1.08131
\(530\) 0 0
\(531\) 0.394052 0.0171004
\(532\) 0 0
\(533\) 7.14790 0.309610
\(534\) 0 0
\(535\) −12.1866 −0.526874
\(536\) 0 0
\(537\) 12.7578 0.550541
\(538\) 0 0
\(539\) −29.4562 −1.26877
\(540\) 0 0
\(541\) 36.8884 1.58596 0.792979 0.609249i \(-0.208529\pi\)
0.792979 + 0.609249i \(0.208529\pi\)
\(542\) 0 0
\(543\) 4.16695 0.178821
\(544\) 0 0
\(545\) 21.8024 0.933911
\(546\) 0 0
\(547\) 13.3980 0.572855 0.286428 0.958102i \(-0.407532\pi\)
0.286428 + 0.958102i \(0.407532\pi\)
\(548\) 0 0
\(549\) 3.50162 0.149446
\(550\) 0 0
\(551\) −18.0754 −0.770038
\(552\) 0 0
\(553\) 4.92441 0.209407
\(554\) 0 0
\(555\) 6.96429 0.295618
\(556\) 0 0
\(557\) 36.2789 1.53719 0.768594 0.639737i \(-0.220957\pi\)
0.768594 + 0.639737i \(0.220957\pi\)
\(558\) 0 0
\(559\) −8.27666 −0.350065
\(560\) 0 0
\(561\) −2.87718 −0.121475
\(562\) 0 0
\(563\) −20.1913 −0.850964 −0.425482 0.904967i \(-0.639895\pi\)
−0.425482 + 0.904967i \(0.639895\pi\)
\(564\) 0 0
\(565\) 20.3106 0.854473
\(566\) 0 0
\(567\) −37.1670 −1.56087
\(568\) 0 0
\(569\) 2.37441 0.0995405 0.0497702 0.998761i \(-0.484151\pi\)
0.0497702 + 0.998761i \(0.484151\pi\)
\(570\) 0 0
\(571\) −33.7880 −1.41398 −0.706991 0.707222i \(-0.749948\pi\)
−0.706991 + 0.707222i \(0.749948\pi\)
\(572\) 0 0
\(573\) −35.4895 −1.48260
\(574\) 0 0
\(575\) −24.0531 −1.00309
\(576\) 0 0
\(577\) −33.9418 −1.41302 −0.706509 0.707704i \(-0.749731\pi\)
−0.706509 + 0.707704i \(0.749731\pi\)
\(578\) 0 0
\(579\) −11.0963 −0.461146
\(580\) 0 0
\(581\) −9.79568 −0.406393
\(582\) 0 0
\(583\) −4.75484 −0.196926
\(584\) 0 0
\(585\) −2.77043 −0.114543
\(586\) 0 0
\(587\) −37.8512 −1.56229 −0.781143 0.624353i \(-0.785363\pi\)
−0.781143 + 0.624353i \(0.785363\pi\)
\(588\) 0 0
\(589\) 14.7507 0.607794
\(590\) 0 0
\(591\) 7.39540 0.304206
\(592\) 0 0
\(593\) 29.3239 1.20419 0.602094 0.798425i \(-0.294333\pi\)
0.602094 + 0.798425i \(0.294333\pi\)
\(594\) 0 0
\(595\) 5.98697 0.245442
\(596\) 0 0
\(597\) 0.430539 0.0176208
\(598\) 0 0
\(599\) 14.0944 0.575882 0.287941 0.957648i \(-0.407029\pi\)
0.287941 + 0.957648i \(0.407029\pi\)
\(600\) 0 0
\(601\) −36.5380 −1.49042 −0.745208 0.666832i \(-0.767650\pi\)
−0.745208 + 0.666832i \(0.767650\pi\)
\(602\) 0 0
\(603\) 1.56003 0.0635294
\(604\) 0 0
\(605\) 9.65645 0.392590
\(606\) 0 0
\(607\) −14.9790 −0.607977 −0.303988 0.952676i \(-0.598318\pi\)
−0.303988 + 0.952676i \(0.598318\pi\)
\(608\) 0 0
\(609\) 56.3493 2.28339
\(610\) 0 0
\(611\) −13.8494 −0.560287
\(612\) 0 0
\(613\) −40.9844 −1.65534 −0.827672 0.561212i \(-0.810335\pi\)
−0.827672 + 0.561212i \(0.810335\pi\)
\(614\) 0 0
\(615\) −2.50043 −0.100827
\(616\) 0 0
\(617\) −28.9541 −1.16565 −0.582824 0.812599i \(-0.698052\pi\)
−0.582824 + 0.812599i \(0.698052\pi\)
\(618\) 0 0
\(619\) −26.1513 −1.05111 −0.525554 0.850760i \(-0.676142\pi\)
−0.525554 + 0.850760i \(0.676142\pi\)
\(620\) 0 0
\(621\) 37.9082 1.52121
\(622\) 0 0
\(623\) 57.8617 2.31818
\(624\) 0 0
\(625\) 4.46831 0.178733
\(626\) 0 0
\(627\) 7.22657 0.288602
\(628\) 0 0
\(629\) −3.49518 −0.139362
\(630\) 0 0
\(631\) 4.46223 0.177638 0.0888192 0.996048i \(-0.471691\pi\)
0.0888192 + 0.996048i \(0.471691\pi\)
\(632\) 0 0
\(633\) 32.4308 1.28901
\(634\) 0 0
\(635\) 18.2235 0.723179
\(636\) 0 0
\(637\) −94.1378 −3.72987
\(638\) 0 0
\(639\) 1.08446 0.0429006
\(640\) 0 0
\(641\) −37.7471 −1.49092 −0.745460 0.666551i \(-0.767770\pi\)
−0.745460 + 0.666551i \(0.767770\pi\)
\(642\) 0 0
\(643\) 10.0647 0.396914 0.198457 0.980110i \(-0.436407\pi\)
0.198457 + 0.980110i \(0.436407\pi\)
\(644\) 0 0
\(645\) 2.89529 0.114002
\(646\) 0 0
\(647\) 1.36824 0.0537909 0.0268954 0.999638i \(-0.491438\pi\)
0.0268954 + 0.999638i \(0.491438\pi\)
\(648\) 0 0
\(649\) 1.78231 0.0699619
\(650\) 0 0
\(651\) −45.9848 −1.80229
\(652\) 0 0
\(653\) −38.3956 −1.50254 −0.751269 0.659996i \(-0.770558\pi\)
−0.751269 + 0.659996i \(0.770558\pi\)
\(654\) 0 0
\(655\) −17.6798 −0.690807
\(656\) 0 0
\(657\) 3.93033 0.153337
\(658\) 0 0
\(659\) 25.3253 0.986533 0.493266 0.869878i \(-0.335803\pi\)
0.493266 + 0.869878i \(0.335803\pi\)
\(660\) 0 0
\(661\) −5.39400 −0.209802 −0.104901 0.994483i \(-0.533453\pi\)
−0.104901 + 0.994483i \(0.533453\pi\)
\(662\) 0 0
\(663\) −9.19504 −0.357106
\(664\) 0 0
\(665\) −15.0374 −0.583125
\(666\) 0 0
\(667\) −49.7915 −1.92793
\(668\) 0 0
\(669\) 45.6720 1.76578
\(670\) 0 0
\(671\) 15.8380 0.611419
\(672\) 0 0
\(673\) 18.9020 0.728620 0.364310 0.931278i \(-0.381305\pi\)
0.364310 + 0.931278i \(0.381305\pi\)
\(674\) 0 0
\(675\) −19.0476 −0.733144
\(676\) 0 0
\(677\) −25.4561 −0.978356 −0.489178 0.872184i \(-0.662703\pi\)
−0.489178 + 0.872184i \(0.662703\pi\)
\(678\) 0 0
\(679\) −16.1571 −0.620051
\(680\) 0 0
\(681\) −11.5654 −0.443186
\(682\) 0 0
\(683\) −0.245640 −0.00939916 −0.00469958 0.999989i \(-0.501496\pi\)
−0.00469958 + 0.999989i \(0.501496\pi\)
\(684\) 0 0
\(685\) −23.8783 −0.912344
\(686\) 0 0
\(687\) 11.1712 0.426207
\(688\) 0 0
\(689\) −15.1958 −0.578913
\(690\) 0 0
\(691\) −42.1558 −1.60368 −0.801840 0.597538i \(-0.796146\pi\)
−0.801840 + 0.597538i \(0.796146\pi\)
\(692\) 0 0
\(693\) 3.40659 0.129406
\(694\) 0 0
\(695\) 12.1175 0.459643
\(696\) 0 0
\(697\) 1.25490 0.0475326
\(698\) 0 0
\(699\) 23.5859 0.892102
\(700\) 0 0
\(701\) −24.5288 −0.926442 −0.463221 0.886243i \(-0.653306\pi\)
−0.463221 + 0.886243i \(0.653306\pi\)
\(702\) 0 0
\(703\) 8.77880 0.331099
\(704\) 0 0
\(705\) 4.84471 0.182462
\(706\) 0 0
\(707\) 97.2433 3.65721
\(708\) 0 0
\(709\) 46.2949 1.73864 0.869321 0.494249i \(-0.164557\pi\)
0.869321 + 0.494249i \(0.164557\pi\)
\(710\) 0 0
\(711\) −0.400059 −0.0150034
\(712\) 0 0
\(713\) 40.6332 1.52172
\(714\) 0 0
\(715\) −12.5308 −0.468625
\(716\) 0 0
\(717\) −20.6550 −0.771375
\(718\) 0 0
\(719\) 39.5347 1.47440 0.737198 0.675676i \(-0.236148\pi\)
0.737198 + 0.675676i \(0.236148\pi\)
\(720\) 0 0
\(721\) −36.4377 −1.35701
\(722\) 0 0
\(723\) 30.8977 1.14910
\(724\) 0 0
\(725\) 25.0186 0.929166
\(726\) 0 0
\(727\) −21.5557 −0.799456 −0.399728 0.916634i \(-0.630895\pi\)
−0.399728 + 0.916634i \(0.630895\pi\)
\(728\) 0 0
\(729\) 29.5536 1.09458
\(730\) 0 0
\(731\) −1.45306 −0.0537435
\(732\) 0 0
\(733\) −2.88456 −0.106544 −0.0532719 0.998580i \(-0.516965\pi\)
−0.0532719 + 0.998580i \(0.516965\pi\)
\(734\) 0 0
\(735\) 32.9306 1.21467
\(736\) 0 0
\(737\) 7.05609 0.259914
\(738\) 0 0
\(739\) −24.7043 −0.908761 −0.454380 0.890808i \(-0.650139\pi\)
−0.454380 + 0.890808i \(0.650139\pi\)
\(740\) 0 0
\(741\) 23.0951 0.848418
\(742\) 0 0
\(743\) −34.5812 −1.26866 −0.634331 0.773061i \(-0.718725\pi\)
−0.634331 + 0.773061i \(0.718725\pi\)
\(744\) 0 0
\(745\) 14.5223 0.532057
\(746\) 0 0
\(747\) 0.795801 0.0291169
\(748\) 0 0
\(749\) 47.8897 1.74985
\(750\) 0 0
\(751\) −5.19955 −0.189734 −0.0948672 0.995490i \(-0.530243\pi\)
−0.0948672 + 0.995490i \(0.530243\pi\)
\(752\) 0 0
\(753\) 5.77098 0.210306
\(754\) 0 0
\(755\) −23.6525 −0.860804
\(756\) 0 0
\(757\) −26.1870 −0.951783 −0.475892 0.879504i \(-0.657875\pi\)
−0.475892 + 0.879504i \(0.657875\pi\)
\(758\) 0 0
\(759\) 19.9067 0.722567
\(760\) 0 0
\(761\) −14.4960 −0.525480 −0.262740 0.964867i \(-0.584626\pi\)
−0.262740 + 0.964867i \(0.584626\pi\)
\(762\) 0 0
\(763\) −85.6767 −3.10171
\(764\) 0 0
\(765\) −0.486382 −0.0175852
\(766\) 0 0
\(767\) 5.69601 0.205671
\(768\) 0 0
\(769\) −39.3720 −1.41979 −0.709895 0.704308i \(-0.751257\pi\)
−0.709895 + 0.704308i \(0.751257\pi\)
\(770\) 0 0
\(771\) −1.07660 −0.0387728
\(772\) 0 0
\(773\) 5.98155 0.215141 0.107571 0.994197i \(-0.465693\pi\)
0.107571 + 0.994197i \(0.465693\pi\)
\(774\) 0 0
\(775\) −20.4168 −0.733394
\(776\) 0 0
\(777\) −27.3675 −0.981805
\(778\) 0 0
\(779\) −3.15191 −0.112929
\(780\) 0 0
\(781\) 4.90506 0.175517
\(782\) 0 0
\(783\) −39.4297 −1.40910
\(784\) 0 0
\(785\) 6.50169 0.232055
\(786\) 0 0
\(787\) −7.77371 −0.277103 −0.138551 0.990355i \(-0.544245\pi\)
−0.138551 + 0.990355i \(0.544245\pi\)
\(788\) 0 0
\(789\) 36.6811 1.30588
\(790\) 0 0
\(791\) −79.8145 −2.83788
\(792\) 0 0
\(793\) 50.6159 1.79742
\(794\) 0 0
\(795\) 5.31569 0.188528
\(796\) 0 0
\(797\) −26.2899 −0.931237 −0.465619 0.884985i \(-0.654168\pi\)
−0.465619 + 0.884985i \(0.654168\pi\)
\(798\) 0 0
\(799\) −2.43142 −0.0860175
\(800\) 0 0
\(801\) −4.70069 −0.166091
\(802\) 0 0
\(803\) 17.7770 0.627338
\(804\) 0 0
\(805\) −41.4228 −1.45996
\(806\) 0 0
\(807\) −2.04071 −0.0718362
\(808\) 0 0
\(809\) −4.73126 −0.166342 −0.0831711 0.996535i \(-0.526505\pi\)
−0.0831711 + 0.996535i \(0.526505\pi\)
\(810\) 0 0
\(811\) 12.4726 0.437973 0.218987 0.975728i \(-0.429725\pi\)
0.218987 + 0.975728i \(0.429725\pi\)
\(812\) 0 0
\(813\) −19.1520 −0.671690
\(814\) 0 0
\(815\) 26.1472 0.915895
\(816\) 0 0
\(817\) 3.64964 0.127685
\(818\) 0 0
\(819\) 10.8870 0.380421
\(820\) 0 0
\(821\) 48.1030 1.67881 0.839404 0.543509i \(-0.182904\pi\)
0.839404 + 0.543509i \(0.182904\pi\)
\(822\) 0 0
\(823\) 19.3001 0.672761 0.336380 0.941726i \(-0.390797\pi\)
0.336380 + 0.941726i \(0.390797\pi\)
\(824\) 0 0
\(825\) −10.0025 −0.348241
\(826\) 0 0
\(827\) 13.4333 0.467120 0.233560 0.972342i \(-0.424962\pi\)
0.233560 + 0.972342i \(0.424962\pi\)
\(828\) 0 0
\(829\) 7.72366 0.268254 0.134127 0.990964i \(-0.457177\pi\)
0.134127 + 0.990964i \(0.457177\pi\)
\(830\) 0 0
\(831\) −49.6887 −1.72368
\(832\) 0 0
\(833\) −16.5270 −0.572626
\(834\) 0 0
\(835\) −28.2234 −0.976711
\(836\) 0 0
\(837\) 32.1773 1.11221
\(838\) 0 0
\(839\) −42.3323 −1.46147 −0.730737 0.682659i \(-0.760823\pi\)
−0.730737 + 0.682659i \(0.760823\pi\)
\(840\) 0 0
\(841\) 22.7899 0.785859
\(842\) 0 0
\(843\) 44.2583 1.52434
\(844\) 0 0
\(845\) −24.0006 −0.825644
\(846\) 0 0
\(847\) −37.9469 −1.30387
\(848\) 0 0
\(849\) −17.9684 −0.616674
\(850\) 0 0
\(851\) 24.1825 0.828967
\(852\) 0 0
\(853\) 50.1307 1.71644 0.858221 0.513281i \(-0.171570\pi\)
0.858221 + 0.513281i \(0.171570\pi\)
\(854\) 0 0
\(855\) 1.22164 0.0417792
\(856\) 0 0
\(857\) −32.9976 −1.12718 −0.563588 0.826056i \(-0.690580\pi\)
−0.563588 + 0.826056i \(0.690580\pi\)
\(858\) 0 0
\(859\) 54.0597 1.84449 0.922246 0.386604i \(-0.126352\pi\)
0.922246 + 0.386604i \(0.126352\pi\)
\(860\) 0 0
\(861\) 9.82593 0.334867
\(862\) 0 0
\(863\) −14.7938 −0.503587 −0.251794 0.967781i \(-0.581020\pi\)
−0.251794 + 0.967781i \(0.581020\pi\)
\(864\) 0 0
\(865\) −0.756771 −0.0257310
\(866\) 0 0
\(867\) −1.61430 −0.0548243
\(868\) 0 0
\(869\) −1.80949 −0.0613826
\(870\) 0 0
\(871\) 22.5502 0.764085
\(872\) 0 0
\(873\) 1.31260 0.0444248
\(874\) 0 0
\(875\) 50.7484 1.71561
\(876\) 0 0
\(877\) 23.0894 0.779673 0.389837 0.920884i \(-0.372531\pi\)
0.389837 + 0.920884i \(0.372531\pi\)
\(878\) 0 0
\(879\) 12.1487 0.409767
\(880\) 0 0
\(881\) 34.0516 1.14723 0.573613 0.819126i \(-0.305541\pi\)
0.573613 + 0.819126i \(0.305541\pi\)
\(882\) 0 0
\(883\) −27.0301 −0.909634 −0.454817 0.890585i \(-0.650295\pi\)
−0.454817 + 0.890585i \(0.650295\pi\)
\(884\) 0 0
\(885\) −1.99254 −0.0669785
\(886\) 0 0
\(887\) 56.0157 1.88082 0.940412 0.340037i \(-0.110440\pi\)
0.940412 + 0.340037i \(0.110440\pi\)
\(888\) 0 0
\(889\) −71.6129 −2.40182
\(890\) 0 0
\(891\) 13.6571 0.457530
\(892\) 0 0
\(893\) 6.10697 0.204362
\(894\) 0 0
\(895\) 9.75479 0.326067
\(896\) 0 0
\(897\) 63.6188 2.12417
\(898\) 0 0
\(899\) −42.2641 −1.40959
\(900\) 0 0
\(901\) −2.66779 −0.0888771
\(902\) 0 0
\(903\) −11.3776 −0.378623
\(904\) 0 0
\(905\) 3.18610 0.105910
\(906\) 0 0
\(907\) 39.2412 1.30298 0.651491 0.758656i \(-0.274144\pi\)
0.651491 + 0.758656i \(0.274144\pi\)
\(908\) 0 0
\(909\) −7.90005 −0.262028
\(910\) 0 0
\(911\) 34.2943 1.13622 0.568110 0.822952i \(-0.307675\pi\)
0.568110 + 0.822952i \(0.307675\pi\)
\(912\) 0 0
\(913\) 3.59944 0.119124
\(914\) 0 0
\(915\) −17.7061 −0.585346
\(916\) 0 0
\(917\) 69.4762 2.29431
\(918\) 0 0
\(919\) −18.1283 −0.597998 −0.298999 0.954253i \(-0.596653\pi\)
−0.298999 + 0.954253i \(0.596653\pi\)
\(920\) 0 0
\(921\) −5.23105 −0.172369
\(922\) 0 0
\(923\) 15.6758 0.515977
\(924\) 0 0
\(925\) −12.1509 −0.399520
\(926\) 0 0
\(927\) 2.96020 0.0972257
\(928\) 0 0
\(929\) 5.79273 0.190053 0.0950266 0.995475i \(-0.469706\pi\)
0.0950266 + 0.995475i \(0.469706\pi\)
\(930\) 0 0
\(931\) 41.5106 1.36045
\(932\) 0 0
\(933\) −4.50550 −0.147503
\(934\) 0 0
\(935\) −2.19993 −0.0719453
\(936\) 0 0
\(937\) −11.4079 −0.372679 −0.186339 0.982485i \(-0.559662\pi\)
−0.186339 + 0.982485i \(0.559662\pi\)
\(938\) 0 0
\(939\) 31.9700 1.04330
\(940\) 0 0
\(941\) 15.6788 0.511114 0.255557 0.966794i \(-0.417741\pi\)
0.255557 + 0.966794i \(0.417741\pi\)
\(942\) 0 0
\(943\) −8.68240 −0.282738
\(944\) 0 0
\(945\) −32.8026 −1.06707
\(946\) 0 0
\(947\) −46.9839 −1.52677 −0.763386 0.645943i \(-0.776464\pi\)
−0.763386 + 0.645943i \(0.776464\pi\)
\(948\) 0 0
\(949\) 56.8128 1.84422
\(950\) 0 0
\(951\) 44.2766 1.43577
\(952\) 0 0
\(953\) −6.19866 −0.200794 −0.100397 0.994947i \(-0.532011\pi\)
−0.100397 + 0.994947i \(0.532011\pi\)
\(954\) 0 0
\(955\) −27.1357 −0.878091
\(956\) 0 0
\(957\) −20.7057 −0.669319
\(958\) 0 0
\(959\) 93.8345 3.03007
\(960\) 0 0
\(961\) 3.49031 0.112590
\(962\) 0 0
\(963\) −3.89056 −0.125372
\(964\) 0 0
\(965\) −8.48435 −0.273121
\(966\) 0 0
\(967\) 37.6246 1.20992 0.604962 0.796254i \(-0.293188\pi\)
0.604962 + 0.796254i \(0.293188\pi\)
\(968\) 0 0
\(969\) 4.05460 0.130253
\(970\) 0 0
\(971\) −33.8081 −1.08495 −0.542477 0.840070i \(-0.682514\pi\)
−0.542477 + 0.840070i \(0.682514\pi\)
\(972\) 0 0
\(973\) −47.6181 −1.52657
\(974\) 0 0
\(975\) −31.9664 −1.02374
\(976\) 0 0
\(977\) 11.4683 0.366903 0.183451 0.983029i \(-0.441273\pi\)
0.183451 + 0.983029i \(0.441273\pi\)
\(978\) 0 0
\(979\) −21.2614 −0.679518
\(980\) 0 0
\(981\) 6.96038 0.222228
\(982\) 0 0
\(983\) 15.5235 0.495124 0.247562 0.968872i \(-0.420371\pi\)
0.247562 + 0.968872i \(0.420371\pi\)
\(984\) 0 0
\(985\) 5.65461 0.180171
\(986\) 0 0
\(987\) −19.0382 −0.605993
\(988\) 0 0
\(989\) 10.0535 0.319682
\(990\) 0 0
\(991\) 57.8531 1.83776 0.918881 0.394534i \(-0.129094\pi\)
0.918881 + 0.394534i \(0.129094\pi\)
\(992\) 0 0
\(993\) −1.17773 −0.0373740
\(994\) 0 0
\(995\) 0.329195 0.0104362
\(996\) 0 0
\(997\) 0.537065 0.0170090 0.00850452 0.999964i \(-0.497293\pi\)
0.00850452 + 0.999964i \(0.497293\pi\)
\(998\) 0 0
\(999\) 19.1501 0.605882
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 \(a_p\))