Properties

Label 8036.2.a.t.1.1
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.15720\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.15720 q^{3}\) \(+2.22019 q^{5}\) \(+6.96793 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.15720 q^{3}\) \(+2.22019 q^{5}\) \(+6.96793 q^{9}\) \(-4.12500 q^{11}\) \(+2.30989 q^{13}\) \(-7.00960 q^{15}\) \(-2.24833 q^{17}\) \(+1.92368 q^{19}\) \(-2.59856 q^{23}\) \(-0.0707440 q^{25}\) \(-12.5275 q^{27}\) \(+4.54657 q^{29}\) \(+0.881932 q^{31}\) \(+13.0235 q^{33}\) \(+7.08817 q^{37}\) \(-7.29279 q^{39}\) \(-1.00000 q^{41}\) \(-12.1276 q^{43}\) \(+15.4701 q^{45}\) \(-5.83253 q^{47}\) \(+7.09843 q^{51}\) \(-8.01354 q^{53}\) \(-9.15830 q^{55}\) \(-6.07345 q^{57}\) \(+11.7512 q^{59}\) \(+7.46459 q^{61}\) \(+5.12840 q^{65}\) \(+1.58808 q^{67}\) \(+8.20417 q^{69}\) \(+8.75853 q^{71}\) \(+2.18255 q^{73}\) \(+0.223353 q^{75}\) \(-0.403174 q^{79}\) \(+18.6482 q^{81}\) \(+5.26975 q^{83}\) \(-4.99173 q^{85}\) \(-14.3544 q^{87}\) \(+13.2977 q^{89}\) \(-2.78444 q^{93}\) \(+4.27095 q^{95}\) \(+3.49549 q^{97}\) \(-28.7427 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.15720 −1.82281 −0.911406 0.411509i \(-0.865002\pi\)
−0.911406 + 0.411509i \(0.865002\pi\)
\(4\) 0 0
\(5\) 2.22019 0.992900 0.496450 0.868065i \(-0.334637\pi\)
0.496450 + 0.868065i \(0.334637\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 6.96793 2.32264
\(10\) 0 0
\(11\) −4.12500 −1.24374 −0.621868 0.783122i \(-0.713626\pi\)
−0.621868 + 0.783122i \(0.713626\pi\)
\(12\) 0 0
\(13\) 2.30989 0.640649 0.320324 0.947308i \(-0.396208\pi\)
0.320324 + 0.947308i \(0.396208\pi\)
\(14\) 0 0
\(15\) −7.00960 −1.80987
\(16\) 0 0
\(17\) −2.24833 −0.545300 −0.272650 0.962113i \(-0.587900\pi\)
−0.272650 + 0.962113i \(0.587900\pi\)
\(18\) 0 0
\(19\) 1.92368 0.441323 0.220661 0.975350i \(-0.429178\pi\)
0.220661 + 0.975350i \(0.429178\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.59856 −0.541837 −0.270918 0.962602i \(-0.587327\pi\)
−0.270918 + 0.962602i \(0.587327\pi\)
\(24\) 0 0
\(25\) −0.0707440 −0.0141488
\(26\) 0 0
\(27\) −12.5275 −2.41093
\(28\) 0 0
\(29\) 4.54657 0.844277 0.422138 0.906531i \(-0.361280\pi\)
0.422138 + 0.906531i \(0.361280\pi\)
\(30\) 0 0
\(31\) 0.881932 0.158400 0.0791998 0.996859i \(-0.474763\pi\)
0.0791998 + 0.996859i \(0.474763\pi\)
\(32\) 0 0
\(33\) 13.0235 2.26709
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.08817 1.16529 0.582644 0.812727i \(-0.302018\pi\)
0.582644 + 0.812727i \(0.302018\pi\)
\(38\) 0 0
\(39\) −7.29279 −1.16778
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −12.1276 −1.84945 −0.924724 0.380637i \(-0.875705\pi\)
−0.924724 + 0.380637i \(0.875705\pi\)
\(44\) 0 0
\(45\) 15.4701 2.30615
\(46\) 0 0
\(47\) −5.83253 −0.850763 −0.425381 0.905014i \(-0.639860\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.09843 0.993980
\(52\) 0 0
\(53\) −8.01354 −1.10074 −0.550372 0.834920i \(-0.685514\pi\)
−0.550372 + 0.834920i \(0.685514\pi\)
\(54\) 0 0
\(55\) −9.15830 −1.23491
\(56\) 0 0
\(57\) −6.07345 −0.804449
\(58\) 0 0
\(59\) 11.7512 1.52988 0.764939 0.644103i \(-0.222769\pi\)
0.764939 + 0.644103i \(0.222769\pi\)
\(60\) 0 0
\(61\) 7.46459 0.955743 0.477872 0.878430i \(-0.341408\pi\)
0.477872 + 0.878430i \(0.341408\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.12840 0.636100
\(66\) 0 0
\(67\) 1.58808 0.194014 0.0970072 0.995284i \(-0.469073\pi\)
0.0970072 + 0.995284i \(0.469073\pi\)
\(68\) 0 0
\(69\) 8.20417 0.987666
\(70\) 0 0
\(71\) 8.75853 1.03945 0.519723 0.854335i \(-0.326035\pi\)
0.519723 + 0.854335i \(0.326035\pi\)
\(72\) 0 0
\(73\) 2.18255 0.255448 0.127724 0.991810i \(-0.459233\pi\)
0.127724 + 0.991810i \(0.459233\pi\)
\(74\) 0 0
\(75\) 0.223353 0.0257906
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.403174 −0.0453606 −0.0226803 0.999743i \(-0.507220\pi\)
−0.0226803 + 0.999743i \(0.507220\pi\)
\(80\) 0 0
\(81\) 18.6482 2.07202
\(82\) 0 0
\(83\) 5.26975 0.578430 0.289215 0.957264i \(-0.406606\pi\)
0.289215 + 0.957264i \(0.406606\pi\)
\(84\) 0 0
\(85\) −4.99173 −0.541429
\(86\) 0 0
\(87\) −14.3544 −1.53896
\(88\) 0 0
\(89\) 13.2977 1.40956 0.704778 0.709428i \(-0.251047\pi\)
0.704778 + 0.709428i \(0.251047\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.78444 −0.288733
\(94\) 0 0
\(95\) 4.27095 0.438190
\(96\) 0 0
\(97\) 3.49549 0.354913 0.177457 0.984129i \(-0.443213\pi\)
0.177457 + 0.984129i \(0.443213\pi\)
\(98\) 0 0
\(99\) −28.7427 −2.88875
\(100\) 0 0
\(101\) −2.26651 −0.225526 −0.112763 0.993622i \(-0.535970\pi\)
−0.112763 + 0.993622i \(0.535970\pi\)
\(102\) 0 0
\(103\) 10.2779 1.01271 0.506355 0.862325i \(-0.330993\pi\)
0.506355 + 0.862325i \(0.330993\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.6855 −1.12968 −0.564839 0.825201i \(-0.691062\pi\)
−0.564839 + 0.825201i \(0.691062\pi\)
\(108\) 0 0
\(109\) −14.5791 −1.39642 −0.698212 0.715891i \(-0.746021\pi\)
−0.698212 + 0.715891i \(0.746021\pi\)
\(110\) 0 0
\(111\) −22.3788 −2.12410
\(112\) 0 0
\(113\) 4.30076 0.404582 0.202291 0.979326i \(-0.435161\pi\)
0.202291 + 0.979326i \(0.435161\pi\)
\(114\) 0 0
\(115\) −5.76930 −0.537990
\(116\) 0 0
\(117\) 16.0952 1.48800
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 6.01565 0.546877
\(122\) 0 0
\(123\) 3.15720 0.284675
\(124\) 0 0
\(125\) −11.2580 −1.00695
\(126\) 0 0
\(127\) 17.3254 1.53738 0.768688 0.639623i \(-0.220910\pi\)
0.768688 + 0.639623i \(0.220910\pi\)
\(128\) 0 0
\(129\) 38.2894 3.37120
\(130\) 0 0
\(131\) 8.51120 0.743627 0.371814 0.928307i \(-0.378736\pi\)
0.371814 + 0.928307i \(0.378736\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −27.8136 −2.39381
\(136\) 0 0
\(137\) −19.7219 −1.68495 −0.842477 0.538732i \(-0.818903\pi\)
−0.842477 + 0.538732i \(0.818903\pi\)
\(138\) 0 0
\(139\) −2.78918 −0.236575 −0.118288 0.992979i \(-0.537740\pi\)
−0.118288 + 0.992979i \(0.537740\pi\)
\(140\) 0 0
\(141\) 18.4145 1.55078
\(142\) 0 0
\(143\) −9.52831 −0.796797
\(144\) 0 0
\(145\) 10.0943 0.838283
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.5417 −1.60092 −0.800458 0.599389i \(-0.795410\pi\)
−0.800458 + 0.599389i \(0.795410\pi\)
\(150\) 0 0
\(151\) 5.15883 0.419820 0.209910 0.977721i \(-0.432683\pi\)
0.209910 + 0.977721i \(0.432683\pi\)
\(152\) 0 0
\(153\) −15.6662 −1.26654
\(154\) 0 0
\(155\) 1.95806 0.157275
\(156\) 0 0
\(157\) 18.7616 1.49734 0.748670 0.662943i \(-0.230693\pi\)
0.748670 + 0.662943i \(0.230693\pi\)
\(158\) 0 0
\(159\) 25.3004 2.00645
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −20.9239 −1.63888 −0.819442 0.573163i \(-0.805716\pi\)
−0.819442 + 0.573163i \(0.805716\pi\)
\(164\) 0 0
\(165\) 28.9146 2.25100
\(166\) 0 0
\(167\) −11.9531 −0.924957 −0.462479 0.886630i \(-0.653040\pi\)
−0.462479 + 0.886630i \(0.653040\pi\)
\(168\) 0 0
\(169\) −7.66440 −0.589569
\(170\) 0 0
\(171\) 13.4041 1.02504
\(172\) 0 0
\(173\) 5.88830 0.447679 0.223840 0.974626i \(-0.428141\pi\)
0.223840 + 0.974626i \(0.428141\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −37.1010 −2.78868
\(178\) 0 0
\(179\) 11.1919 0.836524 0.418262 0.908326i \(-0.362639\pi\)
0.418262 + 0.908326i \(0.362639\pi\)
\(180\) 0 0
\(181\) 14.6950 1.09227 0.546134 0.837698i \(-0.316099\pi\)
0.546134 + 0.837698i \(0.316099\pi\)
\(182\) 0 0
\(183\) −23.5672 −1.74214
\(184\) 0 0
\(185\) 15.7371 1.15702
\(186\) 0 0
\(187\) 9.27437 0.678209
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.75392 0.126909 0.0634547 0.997985i \(-0.479788\pi\)
0.0634547 + 0.997985i \(0.479788\pi\)
\(192\) 0 0
\(193\) 10.3137 0.742398 0.371199 0.928553i \(-0.378947\pi\)
0.371199 + 0.928553i \(0.378947\pi\)
\(194\) 0 0
\(195\) −16.1914 −1.15949
\(196\) 0 0
\(197\) −6.69132 −0.476737 −0.238368 0.971175i \(-0.576613\pi\)
−0.238368 + 0.971175i \(0.576613\pi\)
\(198\) 0 0
\(199\) −12.1873 −0.863932 −0.431966 0.901890i \(-0.642180\pi\)
−0.431966 + 0.901890i \(0.642180\pi\)
\(200\) 0 0
\(201\) −5.01388 −0.353652
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.22019 −0.155065
\(206\) 0 0
\(207\) −18.1066 −1.25849
\(208\) 0 0
\(209\) −7.93519 −0.548889
\(210\) 0 0
\(211\) 18.7973 1.29406 0.647028 0.762466i \(-0.276012\pi\)
0.647028 + 0.762466i \(0.276012\pi\)
\(212\) 0 0
\(213\) −27.6525 −1.89472
\(214\) 0 0
\(215\) −26.9257 −1.83632
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −6.89074 −0.465633
\(220\) 0 0
\(221\) −5.19340 −0.349346
\(222\) 0 0
\(223\) 9.36899 0.627394 0.313697 0.949523i \(-0.398432\pi\)
0.313697 + 0.949523i \(0.398432\pi\)
\(224\) 0 0
\(225\) −0.492939 −0.0328626
\(226\) 0 0
\(227\) 5.87731 0.390091 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(228\) 0 0
\(229\) −12.4528 −0.822903 −0.411452 0.911432i \(-0.634978\pi\)
−0.411452 + 0.911432i \(0.634978\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.5448 −0.887350 −0.443675 0.896188i \(-0.646325\pi\)
−0.443675 + 0.896188i \(0.646325\pi\)
\(234\) 0 0
\(235\) −12.9493 −0.844722
\(236\) 0 0
\(237\) 1.27290 0.0826838
\(238\) 0 0
\(239\) 7.28427 0.471180 0.235590 0.971853i \(-0.424298\pi\)
0.235590 + 0.971853i \(0.424298\pi\)
\(240\) 0 0
\(241\) 3.31710 0.213673 0.106837 0.994277i \(-0.465928\pi\)
0.106837 + 0.994277i \(0.465928\pi\)
\(242\) 0 0
\(243\) −21.2935 −1.36598
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.44350 0.282733
\(248\) 0 0
\(249\) −16.6377 −1.05437
\(250\) 0 0
\(251\) −14.3120 −0.903367 −0.451683 0.892178i \(-0.649176\pi\)
−0.451683 + 0.892178i \(0.649176\pi\)
\(252\) 0 0
\(253\) 10.7191 0.673901
\(254\) 0 0
\(255\) 15.7599 0.986923
\(256\) 0 0
\(257\) −29.6916 −1.85211 −0.926056 0.377387i \(-0.876823\pi\)
−0.926056 + 0.377387i \(0.876823\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 31.6802 1.96095
\(262\) 0 0
\(263\) 11.9460 0.736624 0.368312 0.929702i \(-0.379936\pi\)
0.368312 + 0.929702i \(0.379936\pi\)
\(264\) 0 0
\(265\) −17.7916 −1.09293
\(266\) 0 0
\(267\) −41.9836 −2.56936
\(268\) 0 0
\(269\) 8.76168 0.534209 0.267105 0.963668i \(-0.413933\pi\)
0.267105 + 0.963668i \(0.413933\pi\)
\(270\) 0 0
\(271\) 9.34066 0.567405 0.283702 0.958912i \(-0.408437\pi\)
0.283702 + 0.958912i \(0.408437\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.291819 0.0175974
\(276\) 0 0
\(277\) 32.2328 1.93668 0.968340 0.249635i \(-0.0803106\pi\)
0.968340 + 0.249635i \(0.0803106\pi\)
\(278\) 0 0
\(279\) 6.14524 0.367906
\(280\) 0 0
\(281\) −11.0271 −0.657822 −0.328911 0.944361i \(-0.606682\pi\)
−0.328911 + 0.944361i \(0.606682\pi\)
\(282\) 0 0
\(283\) −7.96162 −0.473269 −0.236635 0.971599i \(-0.576044\pi\)
−0.236635 + 0.971599i \(0.576044\pi\)
\(284\) 0 0
\(285\) −13.4842 −0.798737
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −11.9450 −0.702648
\(290\) 0 0
\(291\) −11.0360 −0.646940
\(292\) 0 0
\(293\) −17.5374 −1.02455 −0.512273 0.858823i \(-0.671196\pi\)
−0.512273 + 0.858823i \(0.671196\pi\)
\(294\) 0 0
\(295\) 26.0900 1.51902
\(296\) 0 0
\(297\) 51.6761 2.99855
\(298\) 0 0
\(299\) −6.00239 −0.347127
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7.15582 0.411091
\(304\) 0 0
\(305\) 16.5728 0.948958
\(306\) 0 0
\(307\) 28.8642 1.64737 0.823683 0.567051i \(-0.191916\pi\)
0.823683 + 0.567051i \(0.191916\pi\)
\(308\) 0 0
\(309\) −32.4493 −1.84598
\(310\) 0 0
\(311\) −12.3112 −0.698106 −0.349053 0.937103i \(-0.613497\pi\)
−0.349053 + 0.937103i \(0.613497\pi\)
\(312\) 0 0
\(313\) −12.6368 −0.714273 −0.357136 0.934052i \(-0.616247\pi\)
−0.357136 + 0.934052i \(0.616247\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.6687 1.66636 0.833181 0.553000i \(-0.186517\pi\)
0.833181 + 0.553000i \(0.186517\pi\)
\(318\) 0 0
\(319\) −18.7546 −1.05006
\(320\) 0 0
\(321\) 36.8934 2.05919
\(322\) 0 0
\(323\) −4.32507 −0.240654
\(324\) 0 0
\(325\) −0.163411 −0.00906441
\(326\) 0 0
\(327\) 46.0292 2.54542
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.94401 −0.161817 −0.0809087 0.996722i \(-0.525782\pi\)
−0.0809087 + 0.996722i \(0.525782\pi\)
\(332\) 0 0
\(333\) 49.3899 2.70655
\(334\) 0 0
\(335\) 3.52584 0.192637
\(336\) 0 0
\(337\) 21.3836 1.16484 0.582418 0.812889i \(-0.302107\pi\)
0.582418 + 0.812889i \(0.302107\pi\)
\(338\) 0 0
\(339\) −13.5784 −0.737476
\(340\) 0 0
\(341\) −3.63797 −0.197007
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 18.2148 0.980654
\(346\) 0 0
\(347\) 25.3614 1.36147 0.680736 0.732529i \(-0.261660\pi\)
0.680736 + 0.732529i \(0.261660\pi\)
\(348\) 0 0
\(349\) 6.63010 0.354901 0.177451 0.984130i \(-0.443215\pi\)
0.177451 + 0.984130i \(0.443215\pi\)
\(350\) 0 0
\(351\) −28.9373 −1.54456
\(352\) 0 0
\(353\) 27.0903 1.44187 0.720936 0.693001i \(-0.243712\pi\)
0.720936 + 0.693001i \(0.243712\pi\)
\(354\) 0 0
\(355\) 19.4456 1.03207
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.6399 0.983774 0.491887 0.870659i \(-0.336307\pi\)
0.491887 + 0.870659i \(0.336307\pi\)
\(360\) 0 0
\(361\) −15.2994 −0.805234
\(362\) 0 0
\(363\) −18.9926 −0.996853
\(364\) 0 0
\(365\) 4.84567 0.253634
\(366\) 0 0
\(367\) −1.23109 −0.0642624 −0.0321312 0.999484i \(-0.510229\pi\)
−0.0321312 + 0.999484i \(0.510229\pi\)
\(368\) 0 0
\(369\) −6.96793 −0.362736
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 13.7085 0.709798 0.354899 0.934905i \(-0.384515\pi\)
0.354899 + 0.934905i \(0.384515\pi\)
\(374\) 0 0
\(375\) 35.5439 1.83548
\(376\) 0 0
\(377\) 10.5021 0.540885
\(378\) 0 0
\(379\) −2.85583 −0.146694 −0.0733471 0.997306i \(-0.523368\pi\)
−0.0733471 + 0.997306i \(0.523368\pi\)
\(380\) 0 0
\(381\) −54.6997 −2.80235
\(382\) 0 0
\(383\) 10.5276 0.537938 0.268969 0.963149i \(-0.413317\pi\)
0.268969 + 0.963149i \(0.413317\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −84.5045 −4.29561
\(388\) 0 0
\(389\) −10.5333 −0.534060 −0.267030 0.963688i \(-0.586042\pi\)
−0.267030 + 0.963688i \(0.586042\pi\)
\(390\) 0 0
\(391\) 5.84242 0.295464
\(392\) 0 0
\(393\) −26.8716 −1.35549
\(394\) 0 0
\(395\) −0.895123 −0.0450385
\(396\) 0 0
\(397\) 14.0280 0.704043 0.352022 0.935992i \(-0.385494\pi\)
0.352022 + 0.935992i \(0.385494\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 25.8036 1.28857 0.644286 0.764785i \(-0.277155\pi\)
0.644286 + 0.764785i \(0.277155\pi\)
\(402\) 0 0
\(403\) 2.03717 0.101479
\(404\) 0 0
\(405\) 41.4026 2.05731
\(406\) 0 0
\(407\) −29.2387 −1.44931
\(408\) 0 0
\(409\) 34.9885 1.73007 0.865036 0.501710i \(-0.167296\pi\)
0.865036 + 0.501710i \(0.167296\pi\)
\(410\) 0 0
\(411\) 62.2660 3.07135
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 11.6999 0.574324
\(416\) 0 0
\(417\) 8.80600 0.431232
\(418\) 0 0
\(419\) −11.9556 −0.584068 −0.292034 0.956408i \(-0.594332\pi\)
−0.292034 + 0.956408i \(0.594332\pi\)
\(420\) 0 0
\(421\) 9.73209 0.474313 0.237157 0.971471i \(-0.423785\pi\)
0.237157 + 0.971471i \(0.423785\pi\)
\(422\) 0 0
\(423\) −40.6407 −1.97602
\(424\) 0 0
\(425\) 0.159056 0.00771534
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 30.0828 1.45241
\(430\) 0 0
\(431\) −10.4751 −0.504570 −0.252285 0.967653i \(-0.581182\pi\)
−0.252285 + 0.967653i \(0.581182\pi\)
\(432\) 0 0
\(433\) 14.7632 0.709476 0.354738 0.934966i \(-0.384570\pi\)
0.354738 + 0.934966i \(0.384570\pi\)
\(434\) 0 0
\(435\) −31.8696 −1.52803
\(436\) 0 0
\(437\) −4.99880 −0.239125
\(438\) 0 0
\(439\) −25.1915 −1.20232 −0.601161 0.799128i \(-0.705295\pi\)
−0.601161 + 0.799128i \(0.705295\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.308041 0.0146355 0.00731774 0.999973i \(-0.497671\pi\)
0.00731774 + 0.999973i \(0.497671\pi\)
\(444\) 0 0
\(445\) 29.5235 1.39955
\(446\) 0 0
\(447\) 61.6970 2.91817
\(448\) 0 0
\(449\) 36.1781 1.70735 0.853676 0.520804i \(-0.174368\pi\)
0.853676 + 0.520804i \(0.174368\pi\)
\(450\) 0 0
\(451\) 4.12500 0.194239
\(452\) 0 0
\(453\) −16.2875 −0.765252
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −24.1807 −1.13113 −0.565563 0.824705i \(-0.691341\pi\)
−0.565563 + 0.824705i \(0.691341\pi\)
\(458\) 0 0
\(459\) 28.1661 1.31468
\(460\) 0 0
\(461\) 15.3173 0.713398 0.356699 0.934219i \(-0.383902\pi\)
0.356699 + 0.934219i \(0.383902\pi\)
\(462\) 0 0
\(463\) 4.79929 0.223042 0.111521 0.993762i \(-0.464428\pi\)
0.111521 + 0.993762i \(0.464428\pi\)
\(464\) 0 0
\(465\) −6.18199 −0.286683
\(466\) 0 0
\(467\) 22.3349 1.03353 0.516767 0.856126i \(-0.327135\pi\)
0.516767 + 0.856126i \(0.327135\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −59.2342 −2.72937
\(472\) 0 0
\(473\) 50.0266 2.30022
\(474\) 0 0
\(475\) −0.136089 −0.00624419
\(476\) 0 0
\(477\) −55.8377 −2.55663
\(478\) 0 0
\(479\) 22.1981 1.01426 0.507128 0.861871i \(-0.330707\pi\)
0.507128 + 0.861871i \(0.330707\pi\)
\(480\) 0 0
\(481\) 16.3729 0.746540
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.76066 0.352393
\(486\) 0 0
\(487\) −33.4536 −1.51593 −0.757963 0.652297i \(-0.773805\pi\)
−0.757963 + 0.652297i \(0.773805\pi\)
\(488\) 0 0
\(489\) 66.0609 2.98738
\(490\) 0 0
\(491\) 36.3600 1.64090 0.820451 0.571717i \(-0.193722\pi\)
0.820451 + 0.571717i \(0.193722\pi\)
\(492\) 0 0
\(493\) −10.2222 −0.460384
\(494\) 0 0
\(495\) −63.8144 −2.86824
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.134195 0.00600738 0.00300369 0.999995i \(-0.499044\pi\)
0.00300369 + 0.999995i \(0.499044\pi\)
\(500\) 0 0
\(501\) 37.7383 1.68602
\(502\) 0 0
\(503\) 4.13202 0.184238 0.0921189 0.995748i \(-0.470636\pi\)
0.0921189 + 0.995748i \(0.470636\pi\)
\(504\) 0 0
\(505\) −5.03208 −0.223925
\(506\) 0 0
\(507\) 24.1981 1.07467
\(508\) 0 0
\(509\) 42.7673 1.89563 0.947815 0.318822i \(-0.103287\pi\)
0.947815 + 0.318822i \(0.103287\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −24.0990 −1.06400
\(514\) 0 0
\(515\) 22.8189 1.00552
\(516\) 0 0
\(517\) 24.0592 1.05812
\(518\) 0 0
\(519\) −18.5906 −0.816035
\(520\) 0 0
\(521\) −2.13363 −0.0934762 −0.0467381 0.998907i \(-0.514883\pi\)
−0.0467381 + 0.998907i \(0.514883\pi\)
\(522\) 0 0
\(523\) 43.5611 1.90479 0.952396 0.304863i \(-0.0986108\pi\)
0.952396 + 0.304863i \(0.0986108\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.98287 −0.0863754
\(528\) 0 0
\(529\) −16.2475 −0.706413
\(530\) 0 0
\(531\) 81.8816 3.55336
\(532\) 0 0
\(533\) −2.30989 −0.100053
\(534\) 0 0
\(535\) −25.9440 −1.12166
\(536\) 0 0
\(537\) −35.3352 −1.52483
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 40.0196 1.72058 0.860289 0.509806i \(-0.170283\pi\)
0.860289 + 0.509806i \(0.170283\pi\)
\(542\) 0 0
\(543\) −46.3950 −1.99100
\(544\) 0 0
\(545\) −32.3684 −1.38651
\(546\) 0 0
\(547\) 23.5014 1.00485 0.502423 0.864622i \(-0.332442\pi\)
0.502423 + 0.864622i \(0.332442\pi\)
\(548\) 0 0
\(549\) 52.0127 2.21985
\(550\) 0 0
\(551\) 8.74615 0.372599
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −49.6852 −2.10902
\(556\) 0 0
\(557\) 33.9635 1.43908 0.719539 0.694452i \(-0.244353\pi\)
0.719539 + 0.694452i \(0.244353\pi\)
\(558\) 0 0
\(559\) −28.0135 −1.18485
\(560\) 0 0
\(561\) −29.2811 −1.23625
\(562\) 0 0
\(563\) −45.3615 −1.91176 −0.955880 0.293757i \(-0.905094\pi\)
−0.955880 + 0.293757i \(0.905094\pi\)
\(564\) 0 0
\(565\) 9.54852 0.401709
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.7354 0.827350 0.413675 0.910425i \(-0.364245\pi\)
0.413675 + 0.910425i \(0.364245\pi\)
\(570\) 0 0
\(571\) 20.8619 0.873043 0.436522 0.899694i \(-0.356210\pi\)
0.436522 + 0.899694i \(0.356210\pi\)
\(572\) 0 0
\(573\) −5.53749 −0.231332
\(574\) 0 0
\(575\) 0.183832 0.00766634
\(576\) 0 0
\(577\) −11.1897 −0.465832 −0.232916 0.972497i \(-0.574827\pi\)
−0.232916 + 0.972497i \(0.574827\pi\)
\(578\) 0 0
\(579\) −32.5625 −1.35325
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 33.0559 1.36903
\(584\) 0 0
\(585\) 35.7343 1.47743
\(586\) 0 0
\(587\) 2.93067 0.120962 0.0604808 0.998169i \(-0.480737\pi\)
0.0604808 + 0.998169i \(0.480737\pi\)
\(588\) 0 0
\(589\) 1.69656 0.0699054
\(590\) 0 0
\(591\) 21.1258 0.869001
\(592\) 0 0
\(593\) −38.4675 −1.57967 −0.789835 0.613320i \(-0.789834\pi\)
−0.789835 + 0.613320i \(0.789834\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 38.4777 1.57479
\(598\) 0 0
\(599\) 34.8868 1.42544 0.712719 0.701450i \(-0.247464\pi\)
0.712719 + 0.701450i \(0.247464\pi\)
\(600\) 0 0
\(601\) 21.5920 0.880757 0.440379 0.897812i \(-0.354844\pi\)
0.440379 + 0.897812i \(0.354844\pi\)
\(602\) 0 0
\(603\) 11.0656 0.450626
\(604\) 0 0
\(605\) 13.3559 0.542994
\(606\) 0 0
\(607\) −31.5921 −1.28228 −0.641142 0.767422i \(-0.721539\pi\)
−0.641142 + 0.767422i \(0.721539\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13.4725 −0.545040
\(612\) 0 0
\(613\) −18.7893 −0.758894 −0.379447 0.925213i \(-0.623886\pi\)
−0.379447 + 0.925213i \(0.623886\pi\)
\(614\) 0 0
\(615\) 7.00960 0.282654
\(616\) 0 0
\(617\) 15.4135 0.620526 0.310263 0.950651i \(-0.399583\pi\)
0.310263 + 0.950651i \(0.399583\pi\)
\(618\) 0 0
\(619\) 3.61805 0.145422 0.0727108 0.997353i \(-0.476835\pi\)
0.0727108 + 0.997353i \(0.476835\pi\)
\(620\) 0 0
\(621\) 32.5535 1.30633
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −24.6413 −0.985651
\(626\) 0 0
\(627\) 25.0530 1.00052
\(628\) 0 0
\(629\) −15.9366 −0.635432
\(630\) 0 0
\(631\) 35.0390 1.39488 0.697441 0.716642i \(-0.254322\pi\)
0.697441 + 0.716642i \(0.254322\pi\)
\(632\) 0 0
\(633\) −59.3467 −2.35882
\(634\) 0 0
\(635\) 38.4656 1.52646
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 61.0288 2.41426
\(640\) 0 0
\(641\) 1.26732 0.0500562 0.0250281 0.999687i \(-0.492032\pi\)
0.0250281 + 0.999687i \(0.492032\pi\)
\(642\) 0 0
\(643\) −3.98105 −0.156997 −0.0784986 0.996914i \(-0.525013\pi\)
−0.0784986 + 0.996914i \(0.525013\pi\)
\(644\) 0 0
\(645\) 85.0099 3.34726
\(646\) 0 0
\(647\) 24.0142 0.944097 0.472049 0.881573i \(-0.343515\pi\)
0.472049 + 0.881573i \(0.343515\pi\)
\(648\) 0 0
\(649\) −48.4738 −1.90276
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25.6864 1.00518 0.502592 0.864523i \(-0.332380\pi\)
0.502592 + 0.864523i \(0.332380\pi\)
\(654\) 0 0
\(655\) 18.8965 0.738348
\(656\) 0 0
\(657\) 15.2078 0.593313
\(658\) 0 0
\(659\) 17.4949 0.681505 0.340753 0.940153i \(-0.389318\pi\)
0.340753 + 0.940153i \(0.389318\pi\)
\(660\) 0 0
\(661\) 32.6256 1.26899 0.634494 0.772928i \(-0.281209\pi\)
0.634494 + 0.772928i \(0.281209\pi\)
\(662\) 0 0
\(663\) 16.3966 0.636792
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −11.8145 −0.457460
\(668\) 0 0
\(669\) −29.5798 −1.14362
\(670\) 0 0
\(671\) −30.7915 −1.18869
\(672\) 0 0
\(673\) −7.92133 −0.305345 −0.152672 0.988277i \(-0.548788\pi\)
−0.152672 + 0.988277i \(0.548788\pi\)
\(674\) 0 0
\(675\) 0.886248 0.0341117
\(676\) 0 0
\(677\) 30.1753 1.15973 0.579866 0.814712i \(-0.303105\pi\)
0.579866 + 0.814712i \(0.303105\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −18.5558 −0.711062
\(682\) 0 0
\(683\) −16.4402 −0.629066 −0.314533 0.949247i \(-0.601848\pi\)
−0.314533 + 0.949247i \(0.601848\pi\)
\(684\) 0 0
\(685\) −43.7864 −1.67299
\(686\) 0 0
\(687\) 39.3160 1.50000
\(688\) 0 0
\(689\) −18.5104 −0.705190
\(690\) 0 0
\(691\) 51.1349 1.94526 0.972631 0.232354i \(-0.0746428\pi\)
0.972631 + 0.232354i \(0.0746428\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.19252 −0.234896
\(696\) 0 0
\(697\) 2.24833 0.0851616
\(698\) 0 0
\(699\) 42.7637 1.61747
\(700\) 0 0
\(701\) 7.11382 0.268685 0.134343 0.990935i \(-0.457108\pi\)
0.134343 + 0.990935i \(0.457108\pi\)
\(702\) 0 0
\(703\) 13.6354 0.514268
\(704\) 0 0
\(705\) 40.8837 1.53977
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 29.9782 1.12585 0.562927 0.826507i \(-0.309675\pi\)
0.562927 + 0.826507i \(0.309675\pi\)
\(710\) 0 0
\(711\) −2.80928 −0.105356
\(712\) 0 0
\(713\) −2.29175 −0.0858267
\(714\) 0 0
\(715\) −21.1547 −0.791140
\(716\) 0 0
\(717\) −22.9979 −0.858872
\(718\) 0 0
\(719\) −20.9726 −0.782147 −0.391074 0.920359i \(-0.627896\pi\)
−0.391074 + 0.920359i \(0.627896\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −10.4728 −0.389486
\(724\) 0 0
\(725\) −0.321642 −0.0119455
\(726\) 0 0
\(727\) 26.7303 0.991372 0.495686 0.868502i \(-0.334917\pi\)
0.495686 + 0.868502i \(0.334917\pi\)
\(728\) 0 0
\(729\) 11.2834 0.417903
\(730\) 0 0
\(731\) 27.2670 1.00850
\(732\) 0 0
\(733\) 20.1849 0.745545 0.372772 0.927923i \(-0.378407\pi\)
0.372772 + 0.927923i \(0.378407\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.55082 −0.241303
\(738\) 0 0
\(739\) −47.8248 −1.75926 −0.879632 0.475655i \(-0.842211\pi\)
−0.879632 + 0.475655i \(0.842211\pi\)
\(740\) 0 0
\(741\) −14.0290 −0.515369
\(742\) 0 0
\(743\) −42.2673 −1.55064 −0.775318 0.631571i \(-0.782411\pi\)
−0.775318 + 0.631571i \(0.782411\pi\)
\(744\) 0 0
\(745\) −43.3863 −1.58955
\(746\) 0 0
\(747\) 36.7192 1.34349
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −29.6944 −1.08357 −0.541783 0.840519i \(-0.682250\pi\)
−0.541783 + 0.840519i \(0.682250\pi\)
\(752\) 0 0
\(753\) 45.1859 1.64667
\(754\) 0 0
\(755\) 11.4536 0.416839
\(756\) 0 0
\(757\) 7.17713 0.260857 0.130429 0.991458i \(-0.458365\pi\)
0.130429 + 0.991458i \(0.458365\pi\)
\(758\) 0 0
\(759\) −33.8422 −1.22840
\(760\) 0 0
\(761\) −26.3861 −0.956496 −0.478248 0.878225i \(-0.658728\pi\)
−0.478248 + 0.878225i \(0.658728\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −34.7820 −1.25755
\(766\) 0 0
\(767\) 27.1440 0.980114
\(768\) 0 0
\(769\) −41.9486 −1.51270 −0.756352 0.654164i \(-0.773020\pi\)
−0.756352 + 0.654164i \(0.773020\pi\)
\(770\) 0 0
\(771\) 93.7424 3.37605
\(772\) 0 0
\(773\) −22.6024 −0.812951 −0.406476 0.913662i \(-0.633242\pi\)
−0.406476 + 0.913662i \(0.633242\pi\)
\(774\) 0 0
\(775\) −0.0623914 −0.00224116
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.92368 −0.0689231
\(780\) 0 0
\(781\) −36.1290 −1.29280
\(782\) 0 0
\(783\) −56.9573 −2.03549
\(784\) 0 0
\(785\) 41.6544 1.48671
\(786\) 0 0
\(787\) 7.45290 0.265667 0.132834 0.991138i \(-0.457592\pi\)
0.132834 + 0.991138i \(0.457592\pi\)
\(788\) 0 0
\(789\) −37.7161 −1.34273
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 17.2424 0.612296
\(794\) 0 0
\(795\) 56.1717 1.99220
\(796\) 0 0
\(797\) −38.3124 −1.35710 −0.678548 0.734556i \(-0.737391\pi\)
−0.678548 + 0.734556i \(0.737391\pi\)
\(798\) 0 0
\(799\) 13.1135 0.463921
\(800\) 0 0
\(801\) 92.6576 3.27389
\(802\) 0 0
\(803\) −9.00300 −0.317709
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −27.6624 −0.973762
\(808\) 0 0
\(809\) −13.5594 −0.476723 −0.238362 0.971176i \(-0.576610\pi\)
−0.238362 + 0.971176i \(0.576610\pi\)
\(810\) 0 0
\(811\) 10.3823 0.364572 0.182286 0.983246i \(-0.441650\pi\)
0.182286 + 0.983246i \(0.441650\pi\)
\(812\) 0 0
\(813\) −29.4904 −1.03427
\(814\) 0 0
\(815\) −46.4550 −1.62725
\(816\) 0 0
\(817\) −23.3297 −0.816204
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −23.4003 −0.816675 −0.408337 0.912831i \(-0.633891\pi\)
−0.408337 + 0.912831i \(0.633891\pi\)
\(822\) 0 0
\(823\) −1.66810 −0.0581465 −0.0290732 0.999577i \(-0.509256\pi\)
−0.0290732 + 0.999577i \(0.509256\pi\)
\(824\) 0 0
\(825\) −0.921332 −0.0320767
\(826\) 0 0
\(827\) −13.7281 −0.477373 −0.238686 0.971097i \(-0.576717\pi\)
−0.238686 + 0.971097i \(0.576717\pi\)
\(828\) 0 0
\(829\) −17.6716 −0.613761 −0.306880 0.951748i \(-0.599285\pi\)
−0.306880 + 0.951748i \(0.599285\pi\)
\(830\) 0 0
\(831\) −101.765 −3.53020
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −26.5381 −0.918390
\(836\) 0 0
\(837\) −11.0484 −0.381890
\(838\) 0 0
\(839\) 7.26376 0.250773 0.125386 0.992108i \(-0.459983\pi\)
0.125386 + 0.992108i \(0.459983\pi\)
\(840\) 0 0
\(841\) −8.32871 −0.287197
\(842\) 0 0
\(843\) 34.8148 1.19908
\(844\) 0 0
\(845\) −17.0164 −0.585384
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 25.1365 0.862681
\(850\) 0 0
\(851\) −18.4190 −0.631396
\(852\) 0 0
\(853\) 44.2376 1.51467 0.757333 0.653029i \(-0.226502\pi\)
0.757333 + 0.653029i \(0.226502\pi\)
\(854\) 0 0
\(855\) 29.7596 1.01776
\(856\) 0 0
\(857\) −44.7732 −1.52942 −0.764711 0.644373i \(-0.777119\pi\)
−0.764711 + 0.644373i \(0.777119\pi\)
\(858\) 0 0
\(859\) 32.7417 1.11713 0.558567 0.829460i \(-0.311351\pi\)
0.558567 + 0.829460i \(0.311351\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0.500831 0.0170485 0.00852424 0.999964i \(-0.497287\pi\)
0.00852424 + 0.999964i \(0.497287\pi\)
\(864\) 0 0
\(865\) 13.0732 0.444501
\(866\) 0 0
\(867\) 37.7128 1.28079
\(868\) 0 0
\(869\) 1.66309 0.0564165
\(870\) 0 0
\(871\) 3.66829 0.124295
\(872\) 0 0
\(873\) 24.3563 0.824336
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 37.6696 1.27201 0.636006 0.771684i \(-0.280585\pi\)
0.636006 + 0.771684i \(0.280585\pi\)
\(878\) 0 0
\(879\) 55.3691 1.86755
\(880\) 0 0
\(881\) −27.4049 −0.923293 −0.461647 0.887064i \(-0.652741\pi\)
−0.461647 + 0.887064i \(0.652741\pi\)
\(882\) 0 0
\(883\) −19.0131 −0.639842 −0.319921 0.947444i \(-0.603656\pi\)
−0.319921 + 0.947444i \(0.603656\pi\)
\(884\) 0 0
\(885\) −82.3713 −2.76888
\(886\) 0 0
\(887\) −27.3297 −0.917643 −0.458821 0.888529i \(-0.651728\pi\)
−0.458821 + 0.888529i \(0.651728\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −76.9239 −2.57705
\(892\) 0 0
\(893\) −11.2199 −0.375461
\(894\) 0 0
\(895\) 24.8482 0.830585
\(896\) 0 0
\(897\) 18.9507 0.632747
\(898\) 0 0
\(899\) 4.00976 0.133733
\(900\) 0 0
\(901\) 18.0171 0.600236
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 32.6257 1.08451
\(906\) 0 0
\(907\) 52.7038 1.75000 0.875001 0.484121i \(-0.160860\pi\)
0.875001 + 0.484121i \(0.160860\pi\)
\(908\) 0 0
\(909\) −15.7929 −0.523816
\(910\) 0 0
\(911\) 55.8154 1.84925 0.924623 0.380883i \(-0.124380\pi\)
0.924623 + 0.380883i \(0.124380\pi\)
\(912\) 0 0
\(913\) −21.7377 −0.719414
\(914\) 0 0
\(915\) −52.3238 −1.72977
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −56.6479 −1.86864 −0.934321 0.356434i \(-0.883992\pi\)
−0.934321 + 0.356434i \(0.883992\pi\)
\(920\) 0 0
\(921\) −91.1300 −3.00284
\(922\) 0 0
\(923\) 20.2313 0.665920
\(924\) 0 0
\(925\) −0.501445 −0.0164874
\(926\) 0 0
\(927\) 71.6155 2.35216
\(928\) 0 0
\(929\) −27.9807 −0.918016 −0.459008 0.888432i \(-0.651795\pi\)
−0.459008 + 0.888432i \(0.651795\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 38.8691 1.27252
\(934\) 0 0
\(935\) 20.5909 0.673394
\(936\) 0 0
\(937\) −17.6255 −0.575799 −0.287900 0.957661i \(-0.592957\pi\)
−0.287900 + 0.957661i \(0.592957\pi\)
\(938\) 0 0
\(939\) 39.8969 1.30198
\(940\) 0 0
\(941\) −5.16930 −0.168514 −0.0842572 0.996444i \(-0.526852\pi\)
−0.0842572 + 0.996444i \(0.526852\pi\)
\(942\) 0 0
\(943\) 2.59856 0.0846207
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 20.1393 0.654441 0.327220 0.944948i \(-0.393888\pi\)
0.327220 + 0.944948i \(0.393888\pi\)
\(948\) 0 0
\(949\) 5.04144 0.163652
\(950\) 0 0
\(951\) −93.6702 −3.03747
\(952\) 0 0
\(953\) −44.3472 −1.43655 −0.718273 0.695761i \(-0.755067\pi\)
−0.718273 + 0.695761i \(0.755067\pi\)
\(954\) 0 0
\(955\) 3.89405 0.126008
\(956\) 0 0
\(957\) 59.2121 1.91406
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.2222 −0.974910
\(962\) 0 0
\(963\) −81.4235 −2.62384
\(964\) 0 0
\(965\) 22.8985 0.737128
\(966\) 0 0
\(967\) 60.6168 1.94931 0.974653 0.223722i \(-0.0718208\pi\)
0.974653 + 0.223722i \(0.0718208\pi\)
\(968\) 0 0
\(969\) 13.6551 0.438666
\(970\) 0 0
\(971\) 22.0331 0.707075 0.353538 0.935420i \(-0.384979\pi\)
0.353538 + 0.935420i \(0.384979\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0.515921 0.0165227
\(976\) 0 0
\(977\) −33.2759 −1.06459 −0.532296 0.846558i \(-0.678671\pi\)
−0.532296 + 0.846558i \(0.678671\pi\)
\(978\) 0 0
\(979\) −54.8532 −1.75311
\(980\) 0 0
\(981\) −101.586 −3.24339
\(982\) 0 0
\(983\) −61.0791 −1.94812 −0.974061 0.226285i \(-0.927342\pi\)
−0.974061 + 0.226285i \(0.927342\pi\)
\(984\) 0 0
\(985\) −14.8560 −0.473352
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 31.5144 1.00210
\(990\) 0 0
\(991\) 31.0442 0.986151 0.493075 0.869987i \(-0.335873\pi\)
0.493075 + 0.869987i \(0.335873\pi\)
\(992\) 0 0
\(993\) 9.29483 0.294963
\(994\) 0 0
\(995\) −27.0581 −0.857799
\(996\) 0 0
\(997\) 26.4932 0.839049 0.419525 0.907744i \(-0.362197\pi\)
0.419525 + 0.907744i \(0.362197\pi\)
\(998\) 0 0
\(999\) −88.7974 −2.80942
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 \(a_p\))