Properties

Label 6008.2.a.e.1.7
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 1.7
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56656 q^{3}\) \(-2.44840 q^{5}\) \(-1.80922 q^{7}\) \(+3.58725 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56656 q^{3}\) \(-2.44840 q^{5}\) \(-1.80922 q^{7}\) \(+3.58725 q^{9}\) \(-2.13745 q^{11}\) \(+4.47684 q^{13}\) \(+6.28398 q^{15}\) \(-0.551102 q^{17}\) \(+1.19678 q^{19}\) \(+4.64349 q^{21}\) \(+0.789962 q^{23}\) \(+0.994664 q^{25}\) \(-1.50722 q^{27}\) \(-4.78818 q^{29}\) \(-4.84032 q^{31}\) \(+5.48590 q^{33}\) \(+4.42970 q^{35}\) \(-0.0175611 q^{37}\) \(-11.4901 q^{39}\) \(+6.24195 q^{41}\) \(-2.48027 q^{43}\) \(-8.78303 q^{45}\) \(-13.2993 q^{47}\) \(-3.72671 q^{49}\) \(+1.41444 q^{51}\) \(+4.32069 q^{53}\) \(+5.23333 q^{55}\) \(-3.07162 q^{57}\) \(-1.86061 q^{59}\) \(+1.93449 q^{61}\) \(-6.49014 q^{63}\) \(-10.9611 q^{65}\) \(-5.88481 q^{67}\) \(-2.02749 q^{69}\) \(-13.3726 q^{71}\) \(-7.69380 q^{73}\) \(-2.55287 q^{75}\) \(+3.86712 q^{77}\) \(+14.1962 q^{79}\) \(-6.89337 q^{81}\) \(-10.0132 q^{83}\) \(+1.34932 q^{85}\) \(+12.2892 q^{87}\) \(-0.170246 q^{89}\) \(-8.09959 q^{91}\) \(+12.4230 q^{93}\) \(-2.93020 q^{95}\) \(-2.90425 q^{97}\) \(-7.66757 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.56656 −1.48181 −0.740903 0.671612i \(-0.765602\pi\)
−0.740903 + 0.671612i \(0.765602\pi\)
\(4\) 0 0
\(5\) −2.44840 −1.09496 −0.547479 0.836819i \(-0.684412\pi\)
−0.547479 + 0.836819i \(0.684412\pi\)
\(6\) 0 0
\(7\) −1.80922 −0.683822 −0.341911 0.939732i \(-0.611074\pi\)
−0.341911 + 0.939732i \(0.611074\pi\)
\(8\) 0 0
\(9\) 3.58725 1.19575
\(10\) 0 0
\(11\) −2.13745 −0.644465 −0.322232 0.946661i \(-0.604433\pi\)
−0.322232 + 0.946661i \(0.604433\pi\)
\(12\) 0 0
\(13\) 4.47684 1.24165 0.620826 0.783949i \(-0.286798\pi\)
0.620826 + 0.783949i \(0.286798\pi\)
\(14\) 0 0
\(15\) 6.28398 1.62252
\(16\) 0 0
\(17\) −0.551102 −0.133662 −0.0668309 0.997764i \(-0.521289\pi\)
−0.0668309 + 0.997764i \(0.521289\pi\)
\(18\) 0 0
\(19\) 1.19678 0.274560 0.137280 0.990532i \(-0.456164\pi\)
0.137280 + 0.990532i \(0.456164\pi\)
\(20\) 0 0
\(21\) 4.64349 1.01329
\(22\) 0 0
\(23\) 0.789962 0.164718 0.0823592 0.996603i \(-0.473755\pi\)
0.0823592 + 0.996603i \(0.473755\pi\)
\(24\) 0 0
\(25\) 0.994664 0.198933
\(26\) 0 0
\(27\) −1.50722 −0.290065
\(28\) 0 0
\(29\) −4.78818 −0.889143 −0.444571 0.895743i \(-0.646644\pi\)
−0.444571 + 0.895743i \(0.646644\pi\)
\(30\) 0 0
\(31\) −4.84032 −0.869347 −0.434674 0.900588i \(-0.643136\pi\)
−0.434674 + 0.900588i \(0.643136\pi\)
\(32\) 0 0
\(33\) 5.48590 0.954972
\(34\) 0 0
\(35\) 4.42970 0.748756
\(36\) 0 0
\(37\) −0.0175611 −0.00288703 −0.00144352 0.999999i \(-0.500459\pi\)
−0.00144352 + 0.999999i \(0.500459\pi\)
\(38\) 0 0
\(39\) −11.4901 −1.83989
\(40\) 0 0
\(41\) 6.24195 0.974829 0.487415 0.873171i \(-0.337940\pi\)
0.487415 + 0.873171i \(0.337940\pi\)
\(42\) 0 0
\(43\) −2.48027 −0.378237 −0.189119 0.981954i \(-0.560563\pi\)
−0.189119 + 0.981954i \(0.560563\pi\)
\(44\) 0 0
\(45\) −8.78303 −1.30930
\(46\) 0 0
\(47\) −13.2993 −1.93990 −0.969950 0.243303i \(-0.921769\pi\)
−0.969950 + 0.243303i \(0.921769\pi\)
\(48\) 0 0
\(49\) −3.72671 −0.532388
\(50\) 0 0
\(51\) 1.41444 0.198061
\(52\) 0 0
\(53\) 4.32069 0.593493 0.296746 0.954956i \(-0.404098\pi\)
0.296746 + 0.954956i \(0.404098\pi\)
\(54\) 0 0
\(55\) 5.23333 0.705662
\(56\) 0 0
\(57\) −3.07162 −0.406846
\(58\) 0 0
\(59\) −1.86061 −0.242231 −0.121116 0.992638i \(-0.538647\pi\)
−0.121116 + 0.992638i \(0.538647\pi\)
\(60\) 0 0
\(61\) 1.93449 0.247686 0.123843 0.992302i \(-0.460478\pi\)
0.123843 + 0.992302i \(0.460478\pi\)
\(62\) 0 0
\(63\) −6.49014 −0.817681
\(64\) 0 0
\(65\) −10.9611 −1.35956
\(66\) 0 0
\(67\) −5.88481 −0.718943 −0.359472 0.933156i \(-0.617043\pi\)
−0.359472 + 0.933156i \(0.617043\pi\)
\(68\) 0 0
\(69\) −2.02749 −0.244081
\(70\) 0 0
\(71\) −13.3726 −1.58703 −0.793517 0.608548i \(-0.791752\pi\)
−0.793517 + 0.608548i \(0.791752\pi\)
\(72\) 0 0
\(73\) −7.69380 −0.900491 −0.450246 0.892905i \(-0.648664\pi\)
−0.450246 + 0.892905i \(0.648664\pi\)
\(74\) 0 0
\(75\) −2.55287 −0.294780
\(76\) 0 0
\(77\) 3.86712 0.440699
\(78\) 0 0
\(79\) 14.1962 1.59720 0.798601 0.601861i \(-0.205574\pi\)
0.798601 + 0.601861i \(0.205574\pi\)
\(80\) 0 0
\(81\) −6.89337 −0.765931
\(82\) 0 0
\(83\) −10.0132 −1.09910 −0.549548 0.835462i \(-0.685200\pi\)
−0.549548 + 0.835462i \(0.685200\pi\)
\(84\) 0 0
\(85\) 1.34932 0.146354
\(86\) 0 0
\(87\) 12.2892 1.31754
\(88\) 0 0
\(89\) −0.170246 −0.0180460 −0.00902300 0.999959i \(-0.502872\pi\)
−0.00902300 + 0.999959i \(0.502872\pi\)
\(90\) 0 0
\(91\) −8.09959 −0.849068
\(92\) 0 0
\(93\) 12.4230 1.28820
\(94\) 0 0
\(95\) −2.93020 −0.300632
\(96\) 0 0
\(97\) −2.90425 −0.294882 −0.147441 0.989071i \(-0.547104\pi\)
−0.147441 + 0.989071i \(0.547104\pi\)
\(98\) 0 0
\(99\) −7.66757 −0.770620
\(100\) 0 0
\(101\) −12.3985 −1.23370 −0.616851 0.787080i \(-0.711592\pi\)
−0.616851 + 0.787080i \(0.711592\pi\)
\(102\) 0 0
\(103\) −3.18406 −0.313734 −0.156867 0.987620i \(-0.550139\pi\)
−0.156867 + 0.987620i \(0.550139\pi\)
\(104\) 0 0
\(105\) −11.3691 −1.10951
\(106\) 0 0
\(107\) −2.91941 −0.282230 −0.141115 0.989993i \(-0.545069\pi\)
−0.141115 + 0.989993i \(0.545069\pi\)
\(108\) 0 0
\(109\) 13.5046 1.29350 0.646751 0.762701i \(-0.276127\pi\)
0.646751 + 0.762701i \(0.276127\pi\)
\(110\) 0 0
\(111\) 0.0450718 0.00427802
\(112\) 0 0
\(113\) −6.91487 −0.650496 −0.325248 0.945629i \(-0.605448\pi\)
−0.325248 + 0.945629i \(0.605448\pi\)
\(114\) 0 0
\(115\) −1.93414 −0.180360
\(116\) 0 0
\(117\) 16.0595 1.48471
\(118\) 0 0
\(119\) 0.997066 0.0914009
\(120\) 0 0
\(121\) −6.43131 −0.584665
\(122\) 0 0
\(123\) −16.0204 −1.44451
\(124\) 0 0
\(125\) 9.80667 0.877135
\(126\) 0 0
\(127\) 0.0250628 0.00222396 0.00111198 0.999999i \(-0.499646\pi\)
0.00111198 + 0.999999i \(0.499646\pi\)
\(128\) 0 0
\(129\) 6.36577 0.560475
\(130\) 0 0
\(131\) 9.54951 0.834345 0.417172 0.908827i \(-0.363021\pi\)
0.417172 + 0.908827i \(0.363021\pi\)
\(132\) 0 0
\(133\) −2.16524 −0.187750
\(134\) 0 0
\(135\) 3.69028 0.317609
\(136\) 0 0
\(137\) 10.5953 0.905217 0.452608 0.891709i \(-0.350494\pi\)
0.452608 + 0.891709i \(0.350494\pi\)
\(138\) 0 0
\(139\) −11.1313 −0.944148 −0.472074 0.881559i \(-0.656494\pi\)
−0.472074 + 0.881559i \(0.656494\pi\)
\(140\) 0 0
\(141\) 34.1335 2.87456
\(142\) 0 0
\(143\) −9.56901 −0.800201
\(144\) 0 0
\(145\) 11.7234 0.973574
\(146\) 0 0
\(147\) 9.56485 0.788896
\(148\) 0 0
\(149\) −4.00331 −0.327964 −0.163982 0.986463i \(-0.552434\pi\)
−0.163982 + 0.986463i \(0.552434\pi\)
\(150\) 0 0
\(151\) −6.73538 −0.548117 −0.274059 0.961713i \(-0.588366\pi\)
−0.274059 + 0.961713i \(0.588366\pi\)
\(152\) 0 0
\(153\) −1.97694 −0.159826
\(154\) 0 0
\(155\) 11.8510 0.951899
\(156\) 0 0
\(157\) −8.88782 −0.709325 −0.354663 0.934994i \(-0.615404\pi\)
−0.354663 + 0.934994i \(0.615404\pi\)
\(158\) 0 0
\(159\) −11.0893 −0.879442
\(160\) 0 0
\(161\) −1.42922 −0.112638
\(162\) 0 0
\(163\) 10.2920 0.806131 0.403065 0.915171i \(-0.367945\pi\)
0.403065 + 0.915171i \(0.367945\pi\)
\(164\) 0 0
\(165\) −13.4317 −1.04565
\(166\) 0 0
\(167\) −6.87682 −0.532144 −0.266072 0.963953i \(-0.585726\pi\)
−0.266072 + 0.963953i \(0.585726\pi\)
\(168\) 0 0
\(169\) 7.04207 0.541697
\(170\) 0 0
\(171\) 4.29316 0.328306
\(172\) 0 0
\(173\) 16.6398 1.26510 0.632551 0.774519i \(-0.282008\pi\)
0.632551 + 0.774519i \(0.282008\pi\)
\(174\) 0 0
\(175\) −1.79957 −0.136035
\(176\) 0 0
\(177\) 4.77539 0.358940
\(178\) 0 0
\(179\) 6.32228 0.472549 0.236275 0.971686i \(-0.424074\pi\)
0.236275 + 0.971686i \(0.424074\pi\)
\(180\) 0 0
\(181\) 5.48762 0.407892 0.203946 0.978982i \(-0.434623\pi\)
0.203946 + 0.978982i \(0.434623\pi\)
\(182\) 0 0
\(183\) −4.96500 −0.367023
\(184\) 0 0
\(185\) 0.0429967 0.00316118
\(186\) 0 0
\(187\) 1.17795 0.0861404
\(188\) 0 0
\(189\) 2.72690 0.198353
\(190\) 0 0
\(191\) −12.7759 −0.924431 −0.462215 0.886768i \(-0.652945\pi\)
−0.462215 + 0.886768i \(0.652945\pi\)
\(192\) 0 0
\(193\) 13.8704 0.998410 0.499205 0.866484i \(-0.333625\pi\)
0.499205 + 0.866484i \(0.333625\pi\)
\(194\) 0 0
\(195\) 28.1323 2.01460
\(196\) 0 0
\(197\) 0.261964 0.0186641 0.00933207 0.999956i \(-0.497029\pi\)
0.00933207 + 0.999956i \(0.497029\pi\)
\(198\) 0 0
\(199\) 14.9729 1.06140 0.530700 0.847560i \(-0.321929\pi\)
0.530700 + 0.847560i \(0.321929\pi\)
\(200\) 0 0
\(201\) 15.1037 1.06534
\(202\) 0 0
\(203\) 8.66288 0.608015
\(204\) 0 0
\(205\) −15.2828 −1.06740
\(206\) 0 0
\(207\) 2.83379 0.196962
\(208\) 0 0
\(209\) −2.55806 −0.176945
\(210\) 0 0
\(211\) −12.6792 −0.872873 −0.436436 0.899735i \(-0.643760\pi\)
−0.436436 + 0.899735i \(0.643760\pi\)
\(212\) 0 0
\(213\) 34.3216 2.35168
\(214\) 0 0
\(215\) 6.07269 0.414154
\(216\) 0 0
\(217\) 8.75722 0.594479
\(218\) 0 0
\(219\) 19.7466 1.33435
\(220\) 0 0
\(221\) −2.46719 −0.165961
\(222\) 0 0
\(223\) −4.99647 −0.334589 −0.167294 0.985907i \(-0.553503\pi\)
−0.167294 + 0.985907i \(0.553503\pi\)
\(224\) 0 0
\(225\) 3.56811 0.237874
\(226\) 0 0
\(227\) −1.31456 −0.0872503 −0.0436251 0.999048i \(-0.513891\pi\)
−0.0436251 + 0.999048i \(0.513891\pi\)
\(228\) 0 0
\(229\) 25.2575 1.66906 0.834532 0.550959i \(-0.185738\pi\)
0.834532 + 0.550959i \(0.185738\pi\)
\(230\) 0 0
\(231\) −9.92521 −0.653031
\(232\) 0 0
\(233\) 17.0040 1.11397 0.556986 0.830522i \(-0.311958\pi\)
0.556986 + 0.830522i \(0.311958\pi\)
\(234\) 0 0
\(235\) 32.5620 2.12411
\(236\) 0 0
\(237\) −36.4356 −2.36674
\(238\) 0 0
\(239\) −8.51611 −0.550861 −0.275431 0.961321i \(-0.588820\pi\)
−0.275431 + 0.961321i \(0.588820\pi\)
\(240\) 0 0
\(241\) −19.8423 −1.27815 −0.639077 0.769143i \(-0.720684\pi\)
−0.639077 + 0.769143i \(0.720684\pi\)
\(242\) 0 0
\(243\) 22.2140 1.42503
\(244\) 0 0
\(245\) 9.12449 0.582942
\(246\) 0 0
\(247\) 5.35779 0.340908
\(248\) 0 0
\(249\) 25.6996 1.62865
\(250\) 0 0
\(251\) 2.93072 0.184985 0.0924926 0.995713i \(-0.470517\pi\)
0.0924926 + 0.995713i \(0.470517\pi\)
\(252\) 0 0
\(253\) −1.68850 −0.106155
\(254\) 0 0
\(255\) −3.46311 −0.216868
\(256\) 0 0
\(257\) −0.485551 −0.0302878 −0.0151439 0.999885i \(-0.504821\pi\)
−0.0151439 + 0.999885i \(0.504821\pi\)
\(258\) 0 0
\(259\) 0.0317720 0.00197422
\(260\) 0 0
\(261\) −17.1764 −1.06319
\(262\) 0 0
\(263\) −25.5434 −1.57507 −0.787535 0.616270i \(-0.788643\pi\)
−0.787535 + 0.616270i \(0.788643\pi\)
\(264\) 0 0
\(265\) −10.5788 −0.649850
\(266\) 0 0
\(267\) 0.436946 0.0267407
\(268\) 0 0
\(269\) −9.54689 −0.582084 −0.291042 0.956710i \(-0.594002\pi\)
−0.291042 + 0.956710i \(0.594002\pi\)
\(270\) 0 0
\(271\) 13.3008 0.807963 0.403982 0.914767i \(-0.367626\pi\)
0.403982 + 0.914767i \(0.367626\pi\)
\(272\) 0 0
\(273\) 20.7881 1.25815
\(274\) 0 0
\(275\) −2.12604 −0.128205
\(276\) 0 0
\(277\) 26.0988 1.56813 0.784063 0.620682i \(-0.213144\pi\)
0.784063 + 0.620682i \(0.213144\pi\)
\(278\) 0 0
\(279\) −17.3635 −1.03952
\(280\) 0 0
\(281\) 2.77521 0.165555 0.0827775 0.996568i \(-0.473621\pi\)
0.0827775 + 0.996568i \(0.473621\pi\)
\(282\) 0 0
\(283\) 22.0868 1.31292 0.656461 0.754360i \(-0.272052\pi\)
0.656461 + 0.754360i \(0.272052\pi\)
\(284\) 0 0
\(285\) 7.52055 0.445479
\(286\) 0 0
\(287\) −11.2931 −0.666610
\(288\) 0 0
\(289\) −16.6963 −0.982135
\(290\) 0 0
\(291\) 7.45395 0.436958
\(292\) 0 0
\(293\) 12.6610 0.739664 0.369832 0.929099i \(-0.379415\pi\)
0.369832 + 0.929099i \(0.379415\pi\)
\(294\) 0 0
\(295\) 4.55553 0.265233
\(296\) 0 0
\(297\) 3.22161 0.186937
\(298\) 0 0
\(299\) 3.53653 0.204523
\(300\) 0 0
\(301\) 4.48736 0.258647
\(302\) 0 0
\(303\) 31.8217 1.82811
\(304\) 0 0
\(305\) −4.73641 −0.271206
\(306\) 0 0
\(307\) −4.31977 −0.246543 −0.123271 0.992373i \(-0.539339\pi\)
−0.123271 + 0.992373i \(0.539339\pi\)
\(308\) 0 0
\(309\) 8.17209 0.464894
\(310\) 0 0
\(311\) −18.5351 −1.05103 −0.525515 0.850785i \(-0.676127\pi\)
−0.525515 + 0.850785i \(0.676127\pi\)
\(312\) 0 0
\(313\) 27.5380 1.55654 0.778271 0.627929i \(-0.216097\pi\)
0.778271 + 0.627929i \(0.216097\pi\)
\(314\) 0 0
\(315\) 15.8905 0.895326
\(316\) 0 0
\(317\) −16.1722 −0.908323 −0.454161 0.890919i \(-0.650061\pi\)
−0.454161 + 0.890919i \(0.650061\pi\)
\(318\) 0 0
\(319\) 10.2345 0.573021
\(320\) 0 0
\(321\) 7.49284 0.418210
\(322\) 0 0
\(323\) −0.659549 −0.0366983
\(324\) 0 0
\(325\) 4.45295 0.247005
\(326\) 0 0
\(327\) −34.6603 −1.91672
\(328\) 0 0
\(329\) 24.0614 1.32655
\(330\) 0 0
\(331\) 22.2357 1.22219 0.611093 0.791559i \(-0.290730\pi\)
0.611093 + 0.791559i \(0.290730\pi\)
\(332\) 0 0
\(333\) −0.0629962 −0.00345217
\(334\) 0 0
\(335\) 14.4084 0.787213
\(336\) 0 0
\(337\) −22.7884 −1.24137 −0.620683 0.784062i \(-0.713144\pi\)
−0.620683 + 0.784062i \(0.713144\pi\)
\(338\) 0 0
\(339\) 17.7475 0.963909
\(340\) 0 0
\(341\) 10.3459 0.560264
\(342\) 0 0
\(343\) 19.4070 1.04788
\(344\) 0 0
\(345\) 4.96410 0.267258
\(346\) 0 0
\(347\) −8.23593 −0.442128 −0.221064 0.975259i \(-0.570953\pi\)
−0.221064 + 0.975259i \(0.570953\pi\)
\(348\) 0 0
\(349\) 9.43094 0.504827 0.252413 0.967619i \(-0.418776\pi\)
0.252413 + 0.967619i \(0.418776\pi\)
\(350\) 0 0
\(351\) −6.74759 −0.360160
\(352\) 0 0
\(353\) −7.12121 −0.379024 −0.189512 0.981878i \(-0.560691\pi\)
−0.189512 + 0.981878i \(0.560691\pi\)
\(354\) 0 0
\(355\) 32.7415 1.73774
\(356\) 0 0
\(357\) −2.55903 −0.135438
\(358\) 0 0
\(359\) −16.0196 −0.845483 −0.422741 0.906250i \(-0.638932\pi\)
−0.422741 + 0.906250i \(0.638932\pi\)
\(360\) 0 0
\(361\) −17.5677 −0.924617
\(362\) 0 0
\(363\) 16.5064 0.866360
\(364\) 0 0
\(365\) 18.8375 0.986000
\(366\) 0 0
\(367\) 12.0338 0.628162 0.314081 0.949396i \(-0.398304\pi\)
0.314081 + 0.949396i \(0.398304\pi\)
\(368\) 0 0
\(369\) 22.3915 1.16565
\(370\) 0 0
\(371\) −7.81710 −0.405843
\(372\) 0 0
\(373\) 1.19675 0.0619654 0.0309827 0.999520i \(-0.490136\pi\)
0.0309827 + 0.999520i \(0.490136\pi\)
\(374\) 0 0
\(375\) −25.1694 −1.29974
\(376\) 0 0
\(377\) −21.4359 −1.10401
\(378\) 0 0
\(379\) 21.7608 1.11778 0.558889 0.829242i \(-0.311228\pi\)
0.558889 + 0.829242i \(0.311228\pi\)
\(380\) 0 0
\(381\) −0.0643252 −0.00329548
\(382\) 0 0
\(383\) 5.83140 0.297970 0.148985 0.988839i \(-0.452399\pi\)
0.148985 + 0.988839i \(0.452399\pi\)
\(384\) 0 0
\(385\) −9.46826 −0.482547
\(386\) 0 0
\(387\) −8.89735 −0.452278
\(388\) 0 0
\(389\) 6.18027 0.313352 0.156676 0.987650i \(-0.449922\pi\)
0.156676 + 0.987650i \(0.449922\pi\)
\(390\) 0 0
\(391\) −0.435350 −0.0220166
\(392\) 0 0
\(393\) −24.5094 −1.23634
\(394\) 0 0
\(395\) −34.7581 −1.74887
\(396\) 0 0
\(397\) 14.7733 0.741449 0.370725 0.928743i \(-0.379109\pi\)
0.370725 + 0.928743i \(0.379109\pi\)
\(398\) 0 0
\(399\) 5.55724 0.278210
\(400\) 0 0
\(401\) 7.17765 0.358435 0.179217 0.983810i \(-0.442643\pi\)
0.179217 + 0.983810i \(0.442643\pi\)
\(402\) 0 0
\(403\) −21.6693 −1.07943
\(404\) 0 0
\(405\) 16.8777 0.838662
\(406\) 0 0
\(407\) 0.0375360 0.00186059
\(408\) 0 0
\(409\) −18.8648 −0.932806 −0.466403 0.884572i \(-0.654450\pi\)
−0.466403 + 0.884572i \(0.654450\pi\)
\(410\) 0 0
\(411\) −27.1935 −1.34136
\(412\) 0 0
\(413\) 3.36626 0.165643
\(414\) 0 0
\(415\) 24.5164 1.20346
\(416\) 0 0
\(417\) 28.5693 1.39904
\(418\) 0 0
\(419\) −5.31234 −0.259525 −0.129762 0.991545i \(-0.541421\pi\)
−0.129762 + 0.991545i \(0.541421\pi\)
\(420\) 0 0
\(421\) −22.6664 −1.10469 −0.552345 0.833615i \(-0.686267\pi\)
−0.552345 + 0.833615i \(0.686267\pi\)
\(422\) 0 0
\(423\) −47.7079 −2.31964
\(424\) 0 0
\(425\) −0.548161 −0.0265897
\(426\) 0 0
\(427\) −3.49993 −0.169373
\(428\) 0 0
\(429\) 24.5595 1.18574
\(430\) 0 0
\(431\) 26.5731 1.27998 0.639991 0.768382i \(-0.278938\pi\)
0.639991 + 0.768382i \(0.278938\pi\)
\(432\) 0 0
\(433\) 8.85714 0.425647 0.212824 0.977091i \(-0.431734\pi\)
0.212824 + 0.977091i \(0.431734\pi\)
\(434\) 0 0
\(435\) −30.0888 −1.44265
\(436\) 0 0
\(437\) 0.945412 0.0452252
\(438\) 0 0
\(439\) 27.3431 1.30502 0.652508 0.757782i \(-0.273717\pi\)
0.652508 + 0.757782i \(0.273717\pi\)
\(440\) 0 0
\(441\) −13.3687 −0.636603
\(442\) 0 0
\(443\) −29.5210 −1.40258 −0.701292 0.712874i \(-0.747393\pi\)
−0.701292 + 0.712874i \(0.747393\pi\)
\(444\) 0 0
\(445\) 0.416829 0.0197596
\(446\) 0 0
\(447\) 10.2748 0.485979
\(448\) 0 0
\(449\) 3.54195 0.167155 0.0835775 0.996501i \(-0.473365\pi\)
0.0835775 + 0.996501i \(0.473365\pi\)
\(450\) 0 0
\(451\) −13.3419 −0.628243
\(452\) 0 0
\(453\) 17.2868 0.812204
\(454\) 0 0
\(455\) 19.8310 0.929694
\(456\) 0 0
\(457\) 30.2661 1.41579 0.707894 0.706319i \(-0.249645\pi\)
0.707894 + 0.706319i \(0.249645\pi\)
\(458\) 0 0
\(459\) 0.830633 0.0387706
\(460\) 0 0
\(461\) 12.2656 0.571266 0.285633 0.958339i \(-0.407796\pi\)
0.285633 + 0.958339i \(0.407796\pi\)
\(462\) 0 0
\(463\) −32.7651 −1.52272 −0.761362 0.648326i \(-0.775469\pi\)
−0.761362 + 0.648326i \(0.775469\pi\)
\(464\) 0 0
\(465\) −30.4165 −1.41053
\(466\) 0 0
\(467\) 16.5828 0.767360 0.383680 0.923466i \(-0.374657\pi\)
0.383680 + 0.923466i \(0.374657\pi\)
\(468\) 0 0
\(469\) 10.6469 0.491629
\(470\) 0 0
\(471\) 22.8112 1.05108
\(472\) 0 0
\(473\) 5.30144 0.243761
\(474\) 0 0
\(475\) 1.19040 0.0546191
\(476\) 0 0
\(477\) 15.4994 0.709670
\(478\) 0 0
\(479\) −3.49906 −0.159876 −0.0799382 0.996800i \(-0.525472\pi\)
−0.0799382 + 0.996800i \(0.525472\pi\)
\(480\) 0 0
\(481\) −0.0786183 −0.00358469
\(482\) 0 0
\(483\) 3.66818 0.166908
\(484\) 0 0
\(485\) 7.11077 0.322883
\(486\) 0 0
\(487\) 31.9812 1.44921 0.724604 0.689165i \(-0.242023\pi\)
0.724604 + 0.689165i \(0.242023\pi\)
\(488\) 0 0
\(489\) −26.4150 −1.19453
\(490\) 0 0
\(491\) −10.0324 −0.452757 −0.226379 0.974039i \(-0.572689\pi\)
−0.226379 + 0.974039i \(0.572689\pi\)
\(492\) 0 0
\(493\) 2.63878 0.118844
\(494\) 0 0
\(495\) 18.7733 0.843796
\(496\) 0 0
\(497\) 24.1940 1.08525
\(498\) 0 0
\(499\) −27.0449 −1.21070 −0.605349 0.795960i \(-0.706966\pi\)
−0.605349 + 0.795960i \(0.706966\pi\)
\(500\) 0 0
\(501\) 17.6498 0.788535
\(502\) 0 0
\(503\) −14.7974 −0.659783 −0.329892 0.944019i \(-0.607012\pi\)
−0.329892 + 0.944019i \(0.607012\pi\)
\(504\) 0 0
\(505\) 30.3566 1.35085
\(506\) 0 0
\(507\) −18.0739 −0.802691
\(508\) 0 0
\(509\) −13.9989 −0.620490 −0.310245 0.950657i \(-0.600411\pi\)
−0.310245 + 0.950657i \(0.600411\pi\)
\(510\) 0 0
\(511\) 13.9198 0.615775
\(512\) 0 0
\(513\) −1.80382 −0.0796404
\(514\) 0 0
\(515\) 7.79585 0.343526
\(516\) 0 0
\(517\) 28.4265 1.25020
\(518\) 0 0
\(519\) −42.7071 −1.87464
\(520\) 0 0
\(521\) 15.8170 0.692955 0.346478 0.938058i \(-0.387378\pi\)
0.346478 + 0.938058i \(0.387378\pi\)
\(522\) 0 0
\(523\) 33.9050 1.48256 0.741282 0.671194i \(-0.234218\pi\)
0.741282 + 0.671194i \(0.234218\pi\)
\(524\) 0 0
\(525\) 4.61871 0.201577
\(526\) 0 0
\(527\) 2.66751 0.116199
\(528\) 0 0
\(529\) −22.3760 −0.972868
\(530\) 0 0
\(531\) −6.67449 −0.289648
\(532\) 0 0
\(533\) 27.9442 1.21040
\(534\) 0 0
\(535\) 7.14787 0.309029
\(536\) 0 0
\(537\) −16.2265 −0.700226
\(538\) 0 0
\(539\) 7.96566 0.343105
\(540\) 0 0
\(541\) 35.8456 1.54112 0.770562 0.637365i \(-0.219976\pi\)
0.770562 + 0.637365i \(0.219976\pi\)
\(542\) 0 0
\(543\) −14.0843 −0.604417
\(544\) 0 0
\(545\) −33.0646 −1.41633
\(546\) 0 0
\(547\) 43.3775 1.85469 0.927344 0.374210i \(-0.122086\pi\)
0.927344 + 0.374210i \(0.122086\pi\)
\(548\) 0 0
\(549\) 6.93951 0.296171
\(550\) 0 0
\(551\) −5.73040 −0.244123
\(552\) 0 0
\(553\) −25.6841 −1.09220
\(554\) 0 0
\(555\) −0.110354 −0.00468426
\(556\) 0 0
\(557\) 13.2163 0.559993 0.279996 0.960001i \(-0.409667\pi\)
0.279996 + 0.960001i \(0.409667\pi\)
\(558\) 0 0
\(559\) −11.1038 −0.469639
\(560\) 0 0
\(561\) −3.02329 −0.127643
\(562\) 0 0
\(563\) 36.4127 1.53461 0.767307 0.641280i \(-0.221596\pi\)
0.767307 + 0.641280i \(0.221596\pi\)
\(564\) 0 0
\(565\) 16.9304 0.712266
\(566\) 0 0
\(567\) 12.4716 0.523760
\(568\) 0 0
\(569\) 2.52668 0.105924 0.0529621 0.998597i \(-0.483134\pi\)
0.0529621 + 0.998597i \(0.483134\pi\)
\(570\) 0 0
\(571\) −11.4886 −0.480783 −0.240391 0.970676i \(-0.577276\pi\)
−0.240391 + 0.970676i \(0.577276\pi\)
\(572\) 0 0
\(573\) 32.7901 1.36983
\(574\) 0 0
\(575\) 0.785747 0.0327679
\(576\) 0 0
\(577\) 24.7983 1.03237 0.516183 0.856479i \(-0.327353\pi\)
0.516183 + 0.856479i \(0.327353\pi\)
\(578\) 0 0
\(579\) −35.5992 −1.47945
\(580\) 0 0
\(581\) 18.1162 0.751585
\(582\) 0 0
\(583\) −9.23526 −0.382485
\(584\) 0 0
\(585\) −39.3202 −1.62569
\(586\) 0 0
\(587\) −1.36183 −0.0562089 −0.0281044 0.999605i \(-0.508947\pi\)
−0.0281044 + 0.999605i \(0.508947\pi\)
\(588\) 0 0
\(589\) −5.79281 −0.238688
\(590\) 0 0
\(591\) −0.672347 −0.0276567
\(592\) 0 0
\(593\) 23.6352 0.970582 0.485291 0.874353i \(-0.338714\pi\)
0.485291 + 0.874353i \(0.338714\pi\)
\(594\) 0 0
\(595\) −2.44122 −0.100080
\(596\) 0 0
\(597\) −38.4289 −1.57279
\(598\) 0 0
\(599\) 3.86457 0.157902 0.0789510 0.996879i \(-0.474843\pi\)
0.0789510 + 0.996879i \(0.474843\pi\)
\(600\) 0 0
\(601\) −14.1137 −0.575708 −0.287854 0.957674i \(-0.592942\pi\)
−0.287854 + 0.957674i \(0.592942\pi\)
\(602\) 0 0
\(603\) −21.1103 −0.859677
\(604\) 0 0
\(605\) 15.7464 0.640184
\(606\) 0 0
\(607\) −21.0746 −0.855390 −0.427695 0.903923i \(-0.640674\pi\)
−0.427695 + 0.903923i \(0.640674\pi\)
\(608\) 0 0
\(609\) −22.2338 −0.900961
\(610\) 0 0
\(611\) −59.5387 −2.40868
\(612\) 0 0
\(613\) −26.5072 −1.07062 −0.535308 0.844657i \(-0.679804\pi\)
−0.535308 + 0.844657i \(0.679804\pi\)
\(614\) 0 0
\(615\) 39.2243 1.58168
\(616\) 0 0
\(617\) 33.8798 1.36395 0.681975 0.731376i \(-0.261121\pi\)
0.681975 + 0.731376i \(0.261121\pi\)
\(618\) 0 0
\(619\) −17.5460 −0.705232 −0.352616 0.935768i \(-0.614708\pi\)
−0.352616 + 0.935768i \(0.614708\pi\)
\(620\) 0 0
\(621\) −1.19065 −0.0477791
\(622\) 0 0
\(623\) 0.308012 0.0123402
\(624\) 0 0
\(625\) −28.9840 −1.15936
\(626\) 0 0
\(627\) 6.56542 0.262198
\(628\) 0 0
\(629\) 0.00967798 0.000385886 0
\(630\) 0 0
\(631\) −0.165749 −0.00659837 −0.00329919 0.999995i \(-0.501050\pi\)
−0.00329919 + 0.999995i \(0.501050\pi\)
\(632\) 0 0
\(633\) 32.5420 1.29343
\(634\) 0 0
\(635\) −0.0613637 −0.00243514
\(636\) 0 0
\(637\) −16.6839 −0.661040
\(638\) 0 0
\(639\) −47.9709 −1.89770
\(640\) 0 0
\(641\) −18.8972 −0.746395 −0.373198 0.927752i \(-0.621739\pi\)
−0.373198 + 0.927752i \(0.621739\pi\)
\(642\) 0 0
\(643\) −18.7468 −0.739302 −0.369651 0.929171i \(-0.620523\pi\)
−0.369651 + 0.929171i \(0.620523\pi\)
\(644\) 0 0
\(645\) −15.5859 −0.613696
\(646\) 0 0
\(647\) 25.0230 0.983756 0.491878 0.870664i \(-0.336311\pi\)
0.491878 + 0.870664i \(0.336311\pi\)
\(648\) 0 0
\(649\) 3.97697 0.156110
\(650\) 0 0
\(651\) −22.4760 −0.880903
\(652\) 0 0
\(653\) −12.2712 −0.480210 −0.240105 0.970747i \(-0.577182\pi\)
−0.240105 + 0.970747i \(0.577182\pi\)
\(654\) 0 0
\(655\) −23.3810 −0.913573
\(656\) 0 0
\(657\) −27.5996 −1.07676
\(658\) 0 0
\(659\) −20.6594 −0.804776 −0.402388 0.915469i \(-0.631820\pi\)
−0.402388 + 0.915469i \(0.631820\pi\)
\(660\) 0 0
\(661\) 23.4286 0.911268 0.455634 0.890167i \(-0.349413\pi\)
0.455634 + 0.890167i \(0.349413\pi\)
\(662\) 0 0
\(663\) 6.33221 0.245923
\(664\) 0 0
\(665\) 5.30138 0.205579
\(666\) 0 0
\(667\) −3.78248 −0.146458
\(668\) 0 0
\(669\) 12.8238 0.495796
\(670\) 0 0
\(671\) −4.13488 −0.159625
\(672\) 0 0
\(673\) −13.9682 −0.538435 −0.269217 0.963079i \(-0.586765\pi\)
−0.269217 + 0.963079i \(0.586765\pi\)
\(674\) 0 0
\(675\) −1.49918 −0.0577035
\(676\) 0 0
\(677\) −3.98635 −0.153208 −0.0766039 0.997062i \(-0.524408\pi\)
−0.0766039 + 0.997062i \(0.524408\pi\)
\(678\) 0 0
\(679\) 5.25444 0.201647
\(680\) 0 0
\(681\) 3.37390 0.129288
\(682\) 0 0
\(683\) −20.0896 −0.768707 −0.384353 0.923186i \(-0.625576\pi\)
−0.384353 + 0.923186i \(0.625576\pi\)
\(684\) 0 0
\(685\) −25.9415 −0.991174
\(686\) 0 0
\(687\) −64.8251 −2.47323
\(688\) 0 0
\(689\) 19.3430 0.736911
\(690\) 0 0
\(691\) −8.92252 −0.339429 −0.169714 0.985493i \(-0.554285\pi\)
−0.169714 + 0.985493i \(0.554285\pi\)
\(692\) 0 0
\(693\) 13.8723 0.526966
\(694\) 0 0
\(695\) 27.2540 1.03380
\(696\) 0 0
\(697\) −3.43995 −0.130298
\(698\) 0 0
\(699\) −43.6420 −1.65069
\(700\) 0 0
\(701\) 16.1113 0.608515 0.304258 0.952590i \(-0.401592\pi\)
0.304258 + 0.952590i \(0.401592\pi\)
\(702\) 0 0
\(703\) −0.0210168 −0.000792665 0
\(704\) 0 0
\(705\) −83.5724 −3.14752
\(706\) 0 0
\(707\) 22.4317 0.843632
\(708\) 0 0
\(709\) 18.6515 0.700472 0.350236 0.936662i \(-0.386101\pi\)
0.350236 + 0.936662i \(0.386101\pi\)
\(710\) 0 0
\(711\) 50.9255 1.90986
\(712\) 0 0
\(713\) −3.82367 −0.143198
\(714\) 0 0
\(715\) 23.4288 0.876186
\(716\) 0 0
\(717\) 21.8571 0.816270
\(718\) 0 0
\(719\) −25.0236 −0.933221 −0.466611 0.884463i \(-0.654525\pi\)
−0.466611 + 0.884463i \(0.654525\pi\)
\(720\) 0 0
\(721\) 5.76067 0.214538
\(722\) 0 0
\(723\) 50.9265 1.89398
\(724\) 0 0
\(725\) −4.76263 −0.176880
\(726\) 0 0
\(727\) −2.39703 −0.0889009 −0.0444504 0.999012i \(-0.514154\pi\)
−0.0444504 + 0.999012i \(0.514154\pi\)
\(728\) 0 0
\(729\) −36.3334 −1.34568
\(730\) 0 0
\(731\) 1.36688 0.0505559
\(732\) 0 0
\(733\) 37.8646 1.39856 0.699280 0.714848i \(-0.253504\pi\)
0.699280 + 0.714848i \(0.253504\pi\)
\(734\) 0 0
\(735\) −23.4186 −0.863808
\(736\) 0 0
\(737\) 12.5785 0.463334
\(738\) 0 0
\(739\) 37.6414 1.38466 0.692331 0.721580i \(-0.256584\pi\)
0.692331 + 0.721580i \(0.256584\pi\)
\(740\) 0 0
\(741\) −13.7511 −0.505160
\(742\) 0 0
\(743\) −6.18272 −0.226822 −0.113411 0.993548i \(-0.536178\pi\)
−0.113411 + 0.993548i \(0.536178\pi\)
\(744\) 0 0
\(745\) 9.80171 0.359107
\(746\) 0 0
\(747\) −35.9200 −1.31424
\(748\) 0 0
\(749\) 5.28185 0.192995
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −7.52187 −0.274112
\(754\) 0 0
\(755\) 16.4909 0.600165
\(756\) 0 0
\(757\) 26.2362 0.953571 0.476786 0.879020i \(-0.341802\pi\)
0.476786 + 0.879020i \(0.341802\pi\)
\(758\) 0 0
\(759\) 4.33365 0.157302
\(760\) 0 0
\(761\) 7.56611 0.274271 0.137136 0.990552i \(-0.456210\pi\)
0.137136 + 0.990552i \(0.456210\pi\)
\(762\) 0 0
\(763\) −24.4327 −0.884525
\(764\) 0 0
\(765\) 4.84035 0.175003
\(766\) 0 0
\(767\) −8.32966 −0.300767
\(768\) 0 0
\(769\) −20.8995 −0.753656 −0.376828 0.926283i \(-0.622985\pi\)
−0.376828 + 0.926283i \(0.622985\pi\)
\(770\) 0 0
\(771\) 1.24620 0.0448807
\(772\) 0 0
\(773\) −18.5994 −0.668976 −0.334488 0.942400i \(-0.608563\pi\)
−0.334488 + 0.942400i \(0.608563\pi\)
\(774\) 0 0
\(775\) −4.81450 −0.172942
\(776\) 0 0
\(777\) −0.0815449 −0.00292541
\(778\) 0 0
\(779\) 7.47025 0.267650
\(780\) 0 0
\(781\) 28.5832 1.02279
\(782\) 0 0
\(783\) 7.21685 0.257909
\(784\) 0 0
\(785\) 21.7609 0.776682
\(786\) 0 0
\(787\) 9.57855 0.341439 0.170719 0.985320i \(-0.445391\pi\)
0.170719 + 0.985320i \(0.445391\pi\)
\(788\) 0 0
\(789\) 65.5587 2.33395
\(790\) 0 0
\(791\) 12.5105 0.444823
\(792\) 0 0
\(793\) 8.66041 0.307540
\(794\) 0 0
\(795\) 27.1511 0.962952
\(796\) 0 0
\(797\) −34.6861 −1.22864 −0.614322 0.789056i \(-0.710570\pi\)
−0.614322 + 0.789056i \(0.710570\pi\)
\(798\) 0 0
\(799\) 7.32926 0.259291
\(800\) 0 0
\(801\) −0.610714 −0.0215785
\(802\) 0 0
\(803\) 16.4451 0.580335
\(804\) 0 0
\(805\) 3.49929 0.123334
\(806\) 0 0
\(807\) 24.5027 0.862537
\(808\) 0 0
\(809\) −20.6387 −0.725618 −0.362809 0.931864i \(-0.618182\pi\)
−0.362809 + 0.931864i \(0.618182\pi\)
\(810\) 0 0
\(811\) 9.69768 0.340532 0.170266 0.985398i \(-0.445537\pi\)
0.170266 + 0.985398i \(0.445537\pi\)
\(812\) 0 0
\(813\) −34.1372 −1.19725
\(814\) 0 0
\(815\) −25.1989 −0.882679
\(816\) 0 0
\(817\) −2.96834 −0.103849
\(818\) 0 0
\(819\) −29.0553 −1.01527
\(820\) 0 0
\(821\) 51.8540 1.80972 0.904859 0.425712i \(-0.139976\pi\)
0.904859 + 0.425712i \(0.139976\pi\)
\(822\) 0 0
\(823\) −24.1171 −0.840668 −0.420334 0.907370i \(-0.638087\pi\)
−0.420334 + 0.907370i \(0.638087\pi\)
\(824\) 0 0
\(825\) 5.45663 0.189975
\(826\) 0 0
\(827\) −6.30011 −0.219076 −0.109538 0.993983i \(-0.534937\pi\)
−0.109538 + 0.993983i \(0.534937\pi\)
\(828\) 0 0
\(829\) −26.2665 −0.912272 −0.456136 0.889910i \(-0.650767\pi\)
−0.456136 + 0.889910i \(0.650767\pi\)
\(830\) 0 0
\(831\) −66.9843 −2.32366
\(832\) 0 0
\(833\) 2.05380 0.0711599
\(834\) 0 0
\(835\) 16.8372 0.582676
\(836\) 0 0
\(837\) 7.29544 0.252167
\(838\) 0 0
\(839\) 17.4493 0.602416 0.301208 0.953558i \(-0.402610\pi\)
0.301208 + 0.953558i \(0.402610\pi\)
\(840\) 0 0
\(841\) −6.07333 −0.209425
\(842\) 0 0
\(843\) −7.12275 −0.245320
\(844\) 0 0
\(845\) −17.2418 −0.593136
\(846\) 0 0
\(847\) 11.6357 0.399807
\(848\) 0 0
\(849\) −56.6872 −1.94550
\(850\) 0 0
\(851\) −0.0138726 −0.000475548 0
\(852\) 0 0
\(853\) 40.2108 1.37679 0.688395 0.725336i \(-0.258316\pi\)
0.688395 + 0.725336i \(0.258316\pi\)
\(854\) 0 0
\(855\) −10.5114 −0.359481
\(856\) 0 0
\(857\) −16.1566 −0.551900 −0.275950 0.961172i \(-0.588992\pi\)
−0.275950 + 0.961172i \(0.588992\pi\)
\(858\) 0 0
\(859\) 24.5604 0.837989 0.418994 0.907989i \(-0.362383\pi\)
0.418994 + 0.907989i \(0.362383\pi\)
\(860\) 0 0
\(861\) 28.9844 0.987786
\(862\) 0 0
\(863\) 9.08012 0.309091 0.154546 0.987986i \(-0.450609\pi\)
0.154546 + 0.987986i \(0.450609\pi\)
\(864\) 0 0
\(865\) −40.7409 −1.38523
\(866\) 0 0
\(867\) 42.8521 1.45533
\(868\) 0 0
\(869\) −30.3437 −1.02934
\(870\) 0 0
\(871\) −26.3453 −0.892677
\(872\) 0 0
\(873\) −10.4183 −0.352606
\(874\) 0 0
\(875\) −17.7424 −0.599804
\(876\) 0 0
\(877\) 15.5446 0.524903 0.262451 0.964945i \(-0.415469\pi\)
0.262451 + 0.964945i \(0.415469\pi\)
\(878\) 0 0
\(879\) −32.4953 −1.09604
\(880\) 0 0
\(881\) 28.6291 0.964537 0.482269 0.876023i \(-0.339813\pi\)
0.482269 + 0.876023i \(0.339813\pi\)
\(882\) 0 0
\(883\) −45.7876 −1.54088 −0.770438 0.637515i \(-0.779962\pi\)
−0.770438 + 0.637515i \(0.779962\pi\)
\(884\) 0 0
\(885\) −11.6921 −0.393024
\(886\) 0 0
\(887\) 29.4477 0.988758 0.494379 0.869247i \(-0.335396\pi\)
0.494379 + 0.869247i \(0.335396\pi\)
\(888\) 0 0
\(889\) −0.0453441 −0.00152079
\(890\) 0 0
\(891\) 14.7342 0.493615
\(892\) 0 0
\(893\) −15.9163 −0.532620
\(894\) 0 0
\(895\) −15.4795 −0.517421
\(896\) 0 0
\(897\) −9.07673 −0.303063
\(898\) 0 0
\(899\) 23.1763 0.772974
\(900\) 0 0
\(901\) −2.38114 −0.0793274
\(902\) 0 0
\(903\) −11.5171 −0.383265
\(904\) 0 0
\(905\) −13.4359 −0.446624
\(906\) 0 0
\(907\) −32.1041 −1.06600 −0.532999 0.846116i \(-0.678935\pi\)
−0.532999 + 0.846116i \(0.678935\pi\)
\(908\) 0 0
\(909\) −44.4767 −1.47520
\(910\) 0 0
\(911\) 20.6539 0.684293 0.342147 0.939647i \(-0.388846\pi\)
0.342147 + 0.939647i \(0.388846\pi\)
\(912\) 0 0
\(913\) 21.4028 0.708328
\(914\) 0 0
\(915\) 12.1563 0.401875
\(916\) 0 0
\(917\) −17.2772 −0.570543
\(918\) 0 0
\(919\) −25.0690 −0.826949 −0.413475 0.910516i \(-0.635685\pi\)
−0.413475 + 0.910516i \(0.635685\pi\)
\(920\) 0 0
\(921\) 11.0870 0.365328
\(922\) 0 0
\(923\) −59.8669 −1.97054
\(924\) 0 0
\(925\) −0.0174674 −0.000574326 0
\(926\) 0 0
\(927\) −11.4220 −0.375148
\(928\) 0 0
\(929\) 38.5762 1.26564 0.632822 0.774297i \(-0.281897\pi\)
0.632822 + 0.774297i \(0.281897\pi\)
\(930\) 0 0
\(931\) −4.46006 −0.146173
\(932\) 0 0
\(933\) 47.5715 1.55742
\(934\) 0 0
\(935\) −2.88410 −0.0943201
\(936\) 0 0
\(937\) 21.3586 0.697754 0.348877 0.937169i \(-0.386563\pi\)
0.348877 + 0.937169i \(0.386563\pi\)
\(938\) 0 0
\(939\) −70.6781 −2.30649
\(940\) 0 0
\(941\) −19.1208 −0.623319 −0.311659 0.950194i \(-0.600885\pi\)
−0.311659 + 0.950194i \(0.600885\pi\)
\(942\) 0 0
\(943\) 4.93091 0.160572
\(944\) 0 0
\(945\) −6.67655 −0.217188
\(946\) 0 0
\(947\) 18.2197 0.592061 0.296031 0.955178i \(-0.404337\pi\)
0.296031 + 0.955178i \(0.404337\pi\)
\(948\) 0 0
\(949\) −34.4439 −1.11810
\(950\) 0 0
\(951\) 41.5071 1.34596
\(952\) 0 0
\(953\) 0.670277 0.0217124 0.0108562 0.999941i \(-0.496544\pi\)
0.0108562 + 0.999941i \(0.496544\pi\)
\(954\) 0 0
\(955\) 31.2805 1.01221
\(956\) 0 0
\(957\) −26.2675 −0.849107
\(958\) 0 0
\(959\) −19.1692 −0.619007
\(960\) 0 0
\(961\) −7.57128 −0.244235
\(962\) 0 0
\(963\) −10.4726 −0.337476
\(964\) 0 0
\(965\) −33.9602 −1.09322
\(966\) 0 0
\(967\) 45.3619 1.45874 0.729370 0.684120i \(-0.239813\pi\)
0.729370 + 0.684120i \(0.239813\pi\)
\(968\) 0 0
\(969\) 1.69277 0.0543797
\(970\) 0 0
\(971\) 6.02577 0.193376 0.0966882 0.995315i \(-0.469175\pi\)
0.0966882 + 0.995315i \(0.469175\pi\)
\(972\) 0 0
\(973\) 20.1391 0.645629
\(974\) 0 0
\(975\) −11.4288 −0.366014
\(976\) 0 0
\(977\) −35.8636 −1.14738 −0.573688 0.819074i \(-0.694488\pi\)
−0.573688 + 0.819074i \(0.694488\pi\)
\(978\) 0 0
\(979\) 0.363891 0.0116300
\(980\) 0 0
\(981\) 48.4443 1.54671
\(982\) 0 0
\(983\) 12.2172 0.389669 0.194835 0.980836i \(-0.437583\pi\)
0.194835 + 0.980836i \(0.437583\pi\)
\(984\) 0 0
\(985\) −0.641392 −0.0204365
\(986\) 0 0
\(987\) −61.7551 −1.96569
\(988\) 0 0
\(989\) −1.95932 −0.0623027
\(990\) 0 0
\(991\) 3.99614 0.126942 0.0634708 0.997984i \(-0.479783\pi\)
0.0634708 + 0.997984i \(0.479783\pi\)
\(992\) 0 0
\(993\) −57.0694 −1.81104
\(994\) 0 0
\(995\) −36.6596 −1.16219
\(996\) 0 0
\(997\) −11.8256 −0.374519 −0.187260 0.982310i \(-0.559961\pi\)
−0.187260 + 0.982310i \(0.559961\pi\)
\(998\) 0 0
\(999\) 0.0264685 0.000837428 0
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 \(a_p\))