Properties

Label 6036.2.a.g.1.3
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.61011\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.61011 q^{5}\) \(+0.982804 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.61011 q^{5}\) \(+0.982804 q^{7}\) \(+1.00000 q^{9}\) \(-3.24397 q^{11}\) \(+2.88731 q^{13}\) \(-3.61011 q^{15}\) \(-0.659840 q^{17}\) \(+2.91239 q^{19}\) \(+0.982804 q^{21}\) \(-1.79366 q^{23}\) \(+8.03288 q^{25}\) \(+1.00000 q^{27}\) \(+4.94801 q^{29}\) \(+1.83768 q^{31}\) \(-3.24397 q^{33}\) \(-3.54803 q^{35}\) \(-11.7471 q^{37}\) \(+2.88731 q^{39}\) \(-3.21052 q^{41}\) \(-7.99865 q^{43}\) \(-3.61011 q^{45}\) \(+6.45741 q^{47}\) \(-6.03410 q^{49}\) \(-0.659840 q^{51}\) \(+1.47583 q^{53}\) \(+11.7111 q^{55}\) \(+2.91239 q^{57}\) \(-0.809188 q^{59}\) \(+9.89425 q^{61}\) \(+0.982804 q^{63}\) \(-10.4235 q^{65}\) \(+7.49893 q^{67}\) \(-1.79366 q^{69}\) \(-11.1492 q^{71}\) \(+10.6862 q^{73}\) \(+8.03288 q^{75}\) \(-3.18818 q^{77}\) \(+5.03225 q^{79}\) \(+1.00000 q^{81}\) \(+3.32413 q^{83}\) \(+2.38209 q^{85}\) \(+4.94801 q^{87}\) \(-7.58863 q^{89}\) \(+2.83766 q^{91}\) \(+1.83768 q^{93}\) \(-10.5140 q^{95}\) \(-2.87712 q^{97}\) \(-3.24397 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −3.61011 −1.61449 −0.807245 0.590217i \(-0.799042\pi\)
−0.807245 + 0.590217i \(0.799042\pi\)
\(6\) 0 0
\(7\) 0.982804 0.371465 0.185732 0.982600i \(-0.440534\pi\)
0.185732 + 0.982600i \(0.440534\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.24397 −0.978093 −0.489047 0.872258i \(-0.662655\pi\)
−0.489047 + 0.872258i \(0.662655\pi\)
\(12\) 0 0
\(13\) 2.88731 0.800797 0.400398 0.916341i \(-0.368872\pi\)
0.400398 + 0.916341i \(0.368872\pi\)
\(14\) 0 0
\(15\) −3.61011 −0.932126
\(16\) 0 0
\(17\) −0.659840 −0.160035 −0.0800173 0.996793i \(-0.525498\pi\)
−0.0800173 + 0.996793i \(0.525498\pi\)
\(18\) 0 0
\(19\) 2.91239 0.668147 0.334074 0.942547i \(-0.391577\pi\)
0.334074 + 0.942547i \(0.391577\pi\)
\(20\) 0 0
\(21\) 0.982804 0.214465
\(22\) 0 0
\(23\) −1.79366 −0.374003 −0.187002 0.982360i \(-0.559877\pi\)
−0.187002 + 0.982360i \(0.559877\pi\)
\(24\) 0 0
\(25\) 8.03288 1.60658
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.94801 0.918822 0.459411 0.888224i \(-0.348061\pi\)
0.459411 + 0.888224i \(0.348061\pi\)
\(30\) 0 0
\(31\) 1.83768 0.330057 0.165029 0.986289i \(-0.447228\pi\)
0.165029 + 0.986289i \(0.447228\pi\)
\(32\) 0 0
\(33\) −3.24397 −0.564702
\(34\) 0 0
\(35\) −3.54803 −0.599726
\(36\) 0 0
\(37\) −11.7471 −1.93122 −0.965609 0.260000i \(-0.916277\pi\)
−0.965609 + 0.260000i \(0.916277\pi\)
\(38\) 0 0
\(39\) 2.88731 0.462340
\(40\) 0 0
\(41\) −3.21052 −0.501398 −0.250699 0.968065i \(-0.580661\pi\)
−0.250699 + 0.968065i \(0.580661\pi\)
\(42\) 0 0
\(43\) −7.99865 −1.21978 −0.609891 0.792485i \(-0.708787\pi\)
−0.609891 + 0.792485i \(0.708787\pi\)
\(44\) 0 0
\(45\) −3.61011 −0.538163
\(46\) 0 0
\(47\) 6.45741 0.941910 0.470955 0.882157i \(-0.343910\pi\)
0.470955 + 0.882157i \(0.343910\pi\)
\(48\) 0 0
\(49\) −6.03410 −0.862014
\(50\) 0 0
\(51\) −0.659840 −0.0923960
\(52\) 0 0
\(53\) 1.47583 0.202721 0.101360 0.994850i \(-0.467681\pi\)
0.101360 + 0.994850i \(0.467681\pi\)
\(54\) 0 0
\(55\) 11.7111 1.57912
\(56\) 0 0
\(57\) 2.91239 0.385755
\(58\) 0 0
\(59\) −0.809188 −0.105347 −0.0526737 0.998612i \(-0.516774\pi\)
−0.0526737 + 0.998612i \(0.516774\pi\)
\(60\) 0 0
\(61\) 9.89425 1.26683 0.633414 0.773813i \(-0.281653\pi\)
0.633414 + 0.773813i \(0.281653\pi\)
\(62\) 0 0
\(63\) 0.982804 0.123822
\(64\) 0 0
\(65\) −10.4235 −1.29288
\(66\) 0 0
\(67\) 7.49893 0.916140 0.458070 0.888916i \(-0.348541\pi\)
0.458070 + 0.888916i \(0.348541\pi\)
\(68\) 0 0
\(69\) −1.79366 −0.215931
\(70\) 0 0
\(71\) −11.1492 −1.32316 −0.661582 0.749873i \(-0.730115\pi\)
−0.661582 + 0.749873i \(0.730115\pi\)
\(72\) 0 0
\(73\) 10.6862 1.25072 0.625362 0.780335i \(-0.284951\pi\)
0.625362 + 0.780335i \(0.284951\pi\)
\(74\) 0 0
\(75\) 8.03288 0.927557
\(76\) 0 0
\(77\) −3.18818 −0.363327
\(78\) 0 0
\(79\) 5.03225 0.566172 0.283086 0.959094i \(-0.408642\pi\)
0.283086 + 0.959094i \(0.408642\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.32413 0.364871 0.182435 0.983218i \(-0.441602\pi\)
0.182435 + 0.983218i \(0.441602\pi\)
\(84\) 0 0
\(85\) 2.38209 0.258374
\(86\) 0 0
\(87\) 4.94801 0.530482
\(88\) 0 0
\(89\) −7.58863 −0.804394 −0.402197 0.915553i \(-0.631753\pi\)
−0.402197 + 0.915553i \(0.631753\pi\)
\(90\) 0 0
\(91\) 2.83766 0.297468
\(92\) 0 0
\(93\) 1.83768 0.190559
\(94\) 0 0
\(95\) −10.5140 −1.07872
\(96\) 0 0
\(97\) −2.87712 −0.292127 −0.146064 0.989275i \(-0.546660\pi\)
−0.146064 + 0.989275i \(0.546660\pi\)
\(98\) 0 0
\(99\) −3.24397 −0.326031
\(100\) 0 0
\(101\) −16.3446 −1.62635 −0.813174 0.582021i \(-0.802262\pi\)
−0.813174 + 0.582021i \(0.802262\pi\)
\(102\) 0 0
\(103\) 2.54509 0.250775 0.125388 0.992108i \(-0.459983\pi\)
0.125388 + 0.992108i \(0.459983\pi\)
\(104\) 0 0
\(105\) −3.54803 −0.346252
\(106\) 0 0
\(107\) −4.87320 −0.471110 −0.235555 0.971861i \(-0.575691\pi\)
−0.235555 + 0.971861i \(0.575691\pi\)
\(108\) 0 0
\(109\) 7.63845 0.731631 0.365816 0.930687i \(-0.380790\pi\)
0.365816 + 0.930687i \(0.380790\pi\)
\(110\) 0 0
\(111\) −11.7471 −1.11499
\(112\) 0 0
\(113\) −5.11980 −0.481630 −0.240815 0.970571i \(-0.577415\pi\)
−0.240815 + 0.970571i \(0.577415\pi\)
\(114\) 0 0
\(115\) 6.47529 0.603824
\(116\) 0 0
\(117\) 2.88731 0.266932
\(118\) 0 0
\(119\) −0.648493 −0.0594472
\(120\) 0 0
\(121\) −0.476671 −0.0433337
\(122\) 0 0
\(123\) −3.21052 −0.289483
\(124\) 0 0
\(125\) −10.9490 −0.979309
\(126\) 0 0
\(127\) −17.6475 −1.56596 −0.782979 0.622048i \(-0.786301\pi\)
−0.782979 + 0.622048i \(0.786301\pi\)
\(128\) 0 0
\(129\) −7.99865 −0.704242
\(130\) 0 0
\(131\) 1.70788 0.149218 0.0746090 0.997213i \(-0.476229\pi\)
0.0746090 + 0.997213i \(0.476229\pi\)
\(132\) 0 0
\(133\) 2.86231 0.248193
\(134\) 0 0
\(135\) −3.61011 −0.310709
\(136\) 0 0
\(137\) −18.5861 −1.58792 −0.793959 0.607971i \(-0.791984\pi\)
−0.793959 + 0.607971i \(0.791984\pi\)
\(138\) 0 0
\(139\) 3.89774 0.330602 0.165301 0.986243i \(-0.447140\pi\)
0.165301 + 0.986243i \(0.447140\pi\)
\(140\) 0 0
\(141\) 6.45741 0.543812
\(142\) 0 0
\(143\) −9.36636 −0.783254
\(144\) 0 0
\(145\) −17.8628 −1.48343
\(146\) 0 0
\(147\) −6.03410 −0.497684
\(148\) 0 0
\(149\) 4.10505 0.336299 0.168149 0.985762i \(-0.446221\pi\)
0.168149 + 0.985762i \(0.446221\pi\)
\(150\) 0 0
\(151\) −14.4204 −1.17351 −0.586757 0.809763i \(-0.699596\pi\)
−0.586757 + 0.809763i \(0.699596\pi\)
\(152\) 0 0
\(153\) −0.659840 −0.0533449
\(154\) 0 0
\(155\) −6.63422 −0.532874
\(156\) 0 0
\(157\) 4.50079 0.359202 0.179601 0.983740i \(-0.442519\pi\)
0.179601 + 0.983740i \(0.442519\pi\)
\(158\) 0 0
\(159\) 1.47583 0.117041
\(160\) 0 0
\(161\) −1.76281 −0.138929
\(162\) 0 0
\(163\) 13.2204 1.03550 0.517749 0.855532i \(-0.326770\pi\)
0.517749 + 0.855532i \(0.326770\pi\)
\(164\) 0 0
\(165\) 11.7111 0.911706
\(166\) 0 0
\(167\) −24.6872 −1.91035 −0.955176 0.296038i \(-0.904334\pi\)
−0.955176 + 0.296038i \(0.904334\pi\)
\(168\) 0 0
\(169\) −4.66342 −0.358724
\(170\) 0 0
\(171\) 2.91239 0.222716
\(172\) 0 0
\(173\) −15.0619 −1.14513 −0.572566 0.819859i \(-0.694052\pi\)
−0.572566 + 0.819859i \(0.694052\pi\)
\(174\) 0 0
\(175\) 7.89474 0.596786
\(176\) 0 0
\(177\) −0.809188 −0.0608223
\(178\) 0 0
\(179\) −21.9460 −1.64032 −0.820161 0.572134i \(-0.806116\pi\)
−0.820161 + 0.572134i \(0.806116\pi\)
\(180\) 0 0
\(181\) −20.3387 −1.51176 −0.755882 0.654708i \(-0.772792\pi\)
−0.755882 + 0.654708i \(0.772792\pi\)
\(182\) 0 0
\(183\) 9.89425 0.731404
\(184\) 0 0
\(185\) 42.4084 3.11793
\(186\) 0 0
\(187\) 2.14050 0.156529
\(188\) 0 0
\(189\) 0.982804 0.0714885
\(190\) 0 0
\(191\) 5.04043 0.364713 0.182356 0.983233i \(-0.441628\pi\)
0.182356 + 0.983233i \(0.441628\pi\)
\(192\) 0 0
\(193\) 1.77910 0.128062 0.0640311 0.997948i \(-0.479604\pi\)
0.0640311 + 0.997948i \(0.479604\pi\)
\(194\) 0 0
\(195\) −10.4235 −0.746443
\(196\) 0 0
\(197\) 3.17972 0.226546 0.113273 0.993564i \(-0.463867\pi\)
0.113273 + 0.993564i \(0.463867\pi\)
\(198\) 0 0
\(199\) −12.0516 −0.854312 −0.427156 0.904178i \(-0.640485\pi\)
−0.427156 + 0.904178i \(0.640485\pi\)
\(200\) 0 0
\(201\) 7.49893 0.528934
\(202\) 0 0
\(203\) 4.86292 0.341310
\(204\) 0 0
\(205\) 11.5903 0.809502
\(206\) 0 0
\(207\) −1.79366 −0.124668
\(208\) 0 0
\(209\) −9.44769 −0.653510
\(210\) 0 0
\(211\) −6.06555 −0.417570 −0.208785 0.977962i \(-0.566951\pi\)
−0.208785 + 0.977962i \(0.566951\pi\)
\(212\) 0 0
\(213\) −11.1492 −0.763929
\(214\) 0 0
\(215\) 28.8760 1.96933
\(216\) 0 0
\(217\) 1.80608 0.122605
\(218\) 0 0
\(219\) 10.6862 0.722105
\(220\) 0 0
\(221\) −1.90516 −0.128155
\(222\) 0 0
\(223\) −27.4945 −1.84117 −0.920583 0.390547i \(-0.872286\pi\)
−0.920583 + 0.390547i \(0.872286\pi\)
\(224\) 0 0
\(225\) 8.03288 0.535525
\(226\) 0 0
\(227\) −0.283813 −0.0188373 −0.00941867 0.999956i \(-0.502998\pi\)
−0.00941867 + 0.999956i \(0.502998\pi\)
\(228\) 0 0
\(229\) 17.0508 1.12675 0.563375 0.826201i \(-0.309503\pi\)
0.563375 + 0.826201i \(0.309503\pi\)
\(230\) 0 0
\(231\) −3.18818 −0.209767
\(232\) 0 0
\(233\) 2.24231 0.146899 0.0734494 0.997299i \(-0.476599\pi\)
0.0734494 + 0.997299i \(0.476599\pi\)
\(234\) 0 0
\(235\) −23.3119 −1.52070
\(236\) 0 0
\(237\) 5.03225 0.326880
\(238\) 0 0
\(239\) −3.40186 −0.220048 −0.110024 0.993929i \(-0.535093\pi\)
−0.110024 + 0.993929i \(0.535093\pi\)
\(240\) 0 0
\(241\) −17.0872 −1.10069 −0.550343 0.834939i \(-0.685503\pi\)
−0.550343 + 0.834939i \(0.685503\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 21.7837 1.39171
\(246\) 0 0
\(247\) 8.40898 0.535050
\(248\) 0 0
\(249\) 3.32413 0.210658
\(250\) 0 0
\(251\) 30.1261 1.90154 0.950771 0.309894i \(-0.100293\pi\)
0.950771 + 0.309894i \(0.100293\pi\)
\(252\) 0 0
\(253\) 5.81857 0.365810
\(254\) 0 0
\(255\) 2.38209 0.149172
\(256\) 0 0
\(257\) −12.5832 −0.784919 −0.392459 0.919769i \(-0.628376\pi\)
−0.392459 + 0.919769i \(0.628376\pi\)
\(258\) 0 0
\(259\) −11.5451 −0.717380
\(260\) 0 0
\(261\) 4.94801 0.306274
\(262\) 0 0
\(263\) −30.6752 −1.89151 −0.945755 0.324879i \(-0.894676\pi\)
−0.945755 + 0.324879i \(0.894676\pi\)
\(264\) 0 0
\(265\) −5.32790 −0.327290
\(266\) 0 0
\(267\) −7.58863 −0.464417
\(268\) 0 0
\(269\) −19.8127 −1.20800 −0.604002 0.796983i \(-0.706428\pi\)
−0.604002 + 0.796983i \(0.706428\pi\)
\(270\) 0 0
\(271\) −4.89053 −0.297078 −0.148539 0.988907i \(-0.547457\pi\)
−0.148539 + 0.988907i \(0.547457\pi\)
\(272\) 0 0
\(273\) 2.83766 0.171743
\(274\) 0 0
\(275\) −26.0584 −1.57138
\(276\) 0 0
\(277\) 4.15322 0.249543 0.124771 0.992186i \(-0.460180\pi\)
0.124771 + 0.992186i \(0.460180\pi\)
\(278\) 0 0
\(279\) 1.83768 0.110019
\(280\) 0 0
\(281\) 31.7832 1.89603 0.948014 0.318229i \(-0.103088\pi\)
0.948014 + 0.318229i \(0.103088\pi\)
\(282\) 0 0
\(283\) 11.6889 0.694832 0.347416 0.937711i \(-0.387059\pi\)
0.347416 + 0.937711i \(0.387059\pi\)
\(284\) 0 0
\(285\) −10.5140 −0.622797
\(286\) 0 0
\(287\) −3.15531 −0.186252
\(288\) 0 0
\(289\) −16.5646 −0.974389
\(290\) 0 0
\(291\) −2.87712 −0.168660
\(292\) 0 0
\(293\) 29.6797 1.73391 0.866954 0.498389i \(-0.166075\pi\)
0.866954 + 0.498389i \(0.166075\pi\)
\(294\) 0 0
\(295\) 2.92126 0.170082
\(296\) 0 0
\(297\) −3.24397 −0.188234
\(298\) 0 0
\(299\) −5.17885 −0.299501
\(300\) 0 0
\(301\) −7.86110 −0.453106
\(302\) 0 0
\(303\) −16.3446 −0.938972
\(304\) 0 0
\(305\) −35.7193 −2.04528
\(306\) 0 0
\(307\) 8.25970 0.471406 0.235703 0.971825i \(-0.424261\pi\)
0.235703 + 0.971825i \(0.424261\pi\)
\(308\) 0 0
\(309\) 2.54509 0.144785
\(310\) 0 0
\(311\) −22.6765 −1.28587 −0.642934 0.765921i \(-0.722283\pi\)
−0.642934 + 0.765921i \(0.722283\pi\)
\(312\) 0 0
\(313\) 18.6755 1.05560 0.527800 0.849369i \(-0.323017\pi\)
0.527800 + 0.849369i \(0.323017\pi\)
\(314\) 0 0
\(315\) −3.54803 −0.199909
\(316\) 0 0
\(317\) −10.1281 −0.568849 −0.284425 0.958698i \(-0.591803\pi\)
−0.284425 + 0.958698i \(0.591803\pi\)
\(318\) 0 0
\(319\) −16.0512 −0.898693
\(320\) 0 0
\(321\) −4.87320 −0.271995
\(322\) 0 0
\(323\) −1.92171 −0.106927
\(324\) 0 0
\(325\) 23.1934 1.28654
\(326\) 0 0
\(327\) 7.63845 0.422407
\(328\) 0 0
\(329\) 6.34636 0.349886
\(330\) 0 0
\(331\) −26.0075 −1.42950 −0.714752 0.699378i \(-0.753460\pi\)
−0.714752 + 0.699378i \(0.753460\pi\)
\(332\) 0 0
\(333\) −11.7471 −0.643739
\(334\) 0 0
\(335\) −27.0719 −1.47910
\(336\) 0 0
\(337\) −5.94577 −0.323887 −0.161943 0.986800i \(-0.551776\pi\)
−0.161943 + 0.986800i \(0.551776\pi\)
\(338\) 0 0
\(339\) −5.11980 −0.278069
\(340\) 0 0
\(341\) −5.96138 −0.322827
\(342\) 0 0
\(343\) −12.8100 −0.691673
\(344\) 0 0
\(345\) 6.47529 0.348618
\(346\) 0 0
\(347\) −17.2019 −0.923446 −0.461723 0.887024i \(-0.652769\pi\)
−0.461723 + 0.887024i \(0.652769\pi\)
\(348\) 0 0
\(349\) −24.9725 −1.33675 −0.668373 0.743826i \(-0.733009\pi\)
−0.668373 + 0.743826i \(0.733009\pi\)
\(350\) 0 0
\(351\) 2.88731 0.154113
\(352\) 0 0
\(353\) 19.7066 1.04888 0.524439 0.851448i \(-0.324275\pi\)
0.524439 + 0.851448i \(0.324275\pi\)
\(354\) 0 0
\(355\) 40.2497 2.13623
\(356\) 0 0
\(357\) −0.648493 −0.0343219
\(358\) 0 0
\(359\) −28.4459 −1.50132 −0.750659 0.660690i \(-0.770264\pi\)
−0.750659 + 0.660690i \(0.770264\pi\)
\(360\) 0 0
\(361\) −10.5180 −0.553579
\(362\) 0 0
\(363\) −0.476671 −0.0250187
\(364\) 0 0
\(365\) −38.5783 −2.01928
\(366\) 0 0
\(367\) −6.27326 −0.327461 −0.163731 0.986505i \(-0.552353\pi\)
−0.163731 + 0.986505i \(0.552353\pi\)
\(368\) 0 0
\(369\) −3.21052 −0.167133
\(370\) 0 0
\(371\) 1.45045 0.0753036
\(372\) 0 0
\(373\) −12.2395 −0.633739 −0.316869 0.948469i \(-0.602632\pi\)
−0.316869 + 0.948469i \(0.602632\pi\)
\(374\) 0 0
\(375\) −10.9490 −0.565404
\(376\) 0 0
\(377\) 14.2865 0.735790
\(378\) 0 0
\(379\) 35.1898 1.80758 0.903791 0.427975i \(-0.140773\pi\)
0.903791 + 0.427975i \(0.140773\pi\)
\(380\) 0 0
\(381\) −17.6475 −0.904107
\(382\) 0 0
\(383\) −17.5142 −0.894933 −0.447466 0.894301i \(-0.647674\pi\)
−0.447466 + 0.894301i \(0.647674\pi\)
\(384\) 0 0
\(385\) 11.5097 0.586588
\(386\) 0 0
\(387\) −7.99865 −0.406594
\(388\) 0 0
\(389\) −20.0155 −1.01482 −0.507412 0.861703i \(-0.669398\pi\)
−0.507412 + 0.861703i \(0.669398\pi\)
\(390\) 0 0
\(391\) 1.18353 0.0598535
\(392\) 0 0
\(393\) 1.70788 0.0861511
\(394\) 0 0
\(395\) −18.1670 −0.914079
\(396\) 0 0
\(397\) 10.1966 0.511754 0.255877 0.966709i \(-0.417636\pi\)
0.255877 + 0.966709i \(0.417636\pi\)
\(398\) 0 0
\(399\) 2.86231 0.143294
\(400\) 0 0
\(401\) 35.4700 1.77129 0.885644 0.464365i \(-0.153718\pi\)
0.885644 + 0.464365i \(0.153718\pi\)
\(402\) 0 0
\(403\) 5.30596 0.264309
\(404\) 0 0
\(405\) −3.61011 −0.179388
\(406\) 0 0
\(407\) 38.1073 1.88891
\(408\) 0 0
\(409\) 0.916877 0.0453367 0.0226683 0.999743i \(-0.492784\pi\)
0.0226683 + 0.999743i \(0.492784\pi\)
\(410\) 0 0
\(411\) −18.5861 −0.916785
\(412\) 0 0
\(413\) −0.795273 −0.0391328
\(414\) 0 0
\(415\) −12.0005 −0.589080
\(416\) 0 0
\(417\) 3.89774 0.190873
\(418\) 0 0
\(419\) 12.3084 0.601306 0.300653 0.953734i \(-0.402795\pi\)
0.300653 + 0.953734i \(0.402795\pi\)
\(420\) 0 0
\(421\) −19.6876 −0.959513 −0.479756 0.877402i \(-0.659275\pi\)
−0.479756 + 0.877402i \(0.659275\pi\)
\(422\) 0 0
\(423\) 6.45741 0.313970
\(424\) 0 0
\(425\) −5.30041 −0.257108
\(426\) 0 0
\(427\) 9.72410 0.470582
\(428\) 0 0
\(429\) −9.36636 −0.452212
\(430\) 0 0
\(431\) −13.5878 −0.654502 −0.327251 0.944937i \(-0.606122\pi\)
−0.327251 + 0.944937i \(0.606122\pi\)
\(432\) 0 0
\(433\) 31.3972 1.50886 0.754428 0.656383i \(-0.227915\pi\)
0.754428 + 0.656383i \(0.227915\pi\)
\(434\) 0 0
\(435\) −17.8628 −0.856458
\(436\) 0 0
\(437\) −5.22382 −0.249889
\(438\) 0 0
\(439\) 39.8580 1.90232 0.951159 0.308702i \(-0.0998946\pi\)
0.951159 + 0.308702i \(0.0998946\pi\)
\(440\) 0 0
\(441\) −6.03410 −0.287338
\(442\) 0 0
\(443\) 10.2583 0.487388 0.243694 0.969852i \(-0.421641\pi\)
0.243694 + 0.969852i \(0.421641\pi\)
\(444\) 0 0
\(445\) 27.3958 1.29868
\(446\) 0 0
\(447\) 4.10505 0.194162
\(448\) 0 0
\(449\) 16.6778 0.787076 0.393538 0.919308i \(-0.371251\pi\)
0.393538 + 0.919308i \(0.371251\pi\)
\(450\) 0 0
\(451\) 10.4148 0.490414
\(452\) 0 0
\(453\) −14.4204 −0.677529
\(454\) 0 0
\(455\) −10.2443 −0.480259
\(456\) 0 0
\(457\) −5.16028 −0.241388 −0.120694 0.992690i \(-0.538512\pi\)
−0.120694 + 0.992690i \(0.538512\pi\)
\(458\) 0 0
\(459\) −0.659840 −0.0307987
\(460\) 0 0
\(461\) 26.8986 1.25279 0.626397 0.779504i \(-0.284529\pi\)
0.626397 + 0.779504i \(0.284529\pi\)
\(462\) 0 0
\(463\) 19.9121 0.925394 0.462697 0.886516i \(-0.346882\pi\)
0.462697 + 0.886516i \(0.346882\pi\)
\(464\) 0 0
\(465\) −6.63422 −0.307655
\(466\) 0 0
\(467\) −18.8936 −0.874291 −0.437145 0.899391i \(-0.644010\pi\)
−0.437145 + 0.899391i \(0.644010\pi\)
\(468\) 0 0
\(469\) 7.36998 0.340314
\(470\) 0 0
\(471\) 4.50079 0.207385
\(472\) 0 0
\(473\) 25.9474 1.19306
\(474\) 0 0
\(475\) 23.3948 1.07343
\(476\) 0 0
\(477\) 1.47583 0.0675735
\(478\) 0 0
\(479\) 16.4848 0.753208 0.376604 0.926374i \(-0.377092\pi\)
0.376604 + 0.926374i \(0.377092\pi\)
\(480\) 0 0
\(481\) −33.9177 −1.54651
\(482\) 0 0
\(483\) −1.76281 −0.0802108
\(484\) 0 0
\(485\) 10.3867 0.471636
\(486\) 0 0
\(487\) 8.18003 0.370672 0.185336 0.982675i \(-0.440663\pi\)
0.185336 + 0.982675i \(0.440663\pi\)
\(488\) 0 0
\(489\) 13.2204 0.597845
\(490\) 0 0
\(491\) −6.85552 −0.309385 −0.154693 0.987963i \(-0.549439\pi\)
−0.154693 + 0.987963i \(0.549439\pi\)
\(492\) 0 0
\(493\) −3.26489 −0.147043
\(494\) 0 0
\(495\) 11.7111 0.526374
\(496\) 0 0
\(497\) −10.9575 −0.491509
\(498\) 0 0
\(499\) 14.7738 0.661366 0.330683 0.943742i \(-0.392721\pi\)
0.330683 + 0.943742i \(0.392721\pi\)
\(500\) 0 0
\(501\) −24.6872 −1.10294
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 59.0057 2.62572
\(506\) 0 0
\(507\) −4.66342 −0.207110
\(508\) 0 0
\(509\) −17.5415 −0.777513 −0.388756 0.921341i \(-0.627095\pi\)
−0.388756 + 0.921341i \(0.627095\pi\)
\(510\) 0 0
\(511\) 10.5024 0.464600
\(512\) 0 0
\(513\) 2.91239 0.128585
\(514\) 0 0
\(515\) −9.18806 −0.404874
\(516\) 0 0
\(517\) −20.9476 −0.921275
\(518\) 0 0
\(519\) −15.0619 −0.661142
\(520\) 0 0
\(521\) 15.1933 0.665629 0.332815 0.942992i \(-0.392002\pi\)
0.332815 + 0.942992i \(0.392002\pi\)
\(522\) 0 0
\(523\) 11.1425 0.487227 0.243613 0.969872i \(-0.421667\pi\)
0.243613 + 0.969872i \(0.421667\pi\)
\(524\) 0 0
\(525\) 7.89474 0.344555
\(526\) 0 0
\(527\) −1.21257 −0.0528205
\(528\) 0 0
\(529\) −19.7828 −0.860122
\(530\) 0 0
\(531\) −0.809188 −0.0351158
\(532\) 0 0
\(533\) −9.26977 −0.401518
\(534\) 0 0
\(535\) 17.5928 0.760602
\(536\) 0 0
\(537\) −21.9460 −0.947040
\(538\) 0 0
\(539\) 19.5744 0.843130
\(540\) 0 0
\(541\) −37.2768 −1.60265 −0.801327 0.598227i \(-0.795872\pi\)
−0.801327 + 0.598227i \(0.795872\pi\)
\(542\) 0 0
\(543\) −20.3387 −0.872817
\(544\) 0 0
\(545\) −27.5756 −1.18121
\(546\) 0 0
\(547\) −4.50714 −0.192711 −0.0963556 0.995347i \(-0.530719\pi\)
−0.0963556 + 0.995347i \(0.530719\pi\)
\(548\) 0 0
\(549\) 9.89425 0.422276
\(550\) 0 0
\(551\) 14.4105 0.613909
\(552\) 0 0
\(553\) 4.94571 0.210313
\(554\) 0 0
\(555\) 42.4084 1.80014
\(556\) 0 0
\(557\) 8.53654 0.361705 0.180852 0.983510i \(-0.442114\pi\)
0.180852 + 0.983510i \(0.442114\pi\)
\(558\) 0 0
\(559\) −23.0946 −0.976798
\(560\) 0 0
\(561\) 2.14050 0.0903719
\(562\) 0 0
\(563\) −9.17805 −0.386809 −0.193404 0.981119i \(-0.561953\pi\)
−0.193404 + 0.981119i \(0.561953\pi\)
\(564\) 0 0
\(565\) 18.4830 0.777586
\(566\) 0 0
\(567\) 0.982804 0.0412739
\(568\) 0 0
\(569\) 4.61067 0.193289 0.0966447 0.995319i \(-0.469189\pi\)
0.0966447 + 0.995319i \(0.469189\pi\)
\(570\) 0 0
\(571\) −42.0793 −1.76097 −0.880483 0.474078i \(-0.842781\pi\)
−0.880483 + 0.474078i \(0.842781\pi\)
\(572\) 0 0
\(573\) 5.04043 0.210567
\(574\) 0 0
\(575\) −14.4082 −0.600864
\(576\) 0 0
\(577\) −18.7259 −0.779568 −0.389784 0.920906i \(-0.627450\pi\)
−0.389784 + 0.920906i \(0.627450\pi\)
\(578\) 0 0
\(579\) 1.77910 0.0739368
\(580\) 0 0
\(581\) 3.26697 0.135537
\(582\) 0 0
\(583\) −4.78754 −0.198280
\(584\) 0 0
\(585\) −10.4235 −0.430959
\(586\) 0 0
\(587\) 17.3897 0.717751 0.358875 0.933386i \(-0.383160\pi\)
0.358875 + 0.933386i \(0.383160\pi\)
\(588\) 0 0
\(589\) 5.35204 0.220527
\(590\) 0 0
\(591\) 3.17972 0.130796
\(592\) 0 0
\(593\) −12.8250 −0.526659 −0.263329 0.964706i \(-0.584821\pi\)
−0.263329 + 0.964706i \(0.584821\pi\)
\(594\) 0 0
\(595\) 2.34113 0.0959769
\(596\) 0 0
\(597\) −12.0516 −0.493238
\(598\) 0 0
\(599\) 39.8287 1.62736 0.813679 0.581314i \(-0.197461\pi\)
0.813679 + 0.581314i \(0.197461\pi\)
\(600\) 0 0
\(601\) −14.5019 −0.591544 −0.295772 0.955259i \(-0.595577\pi\)
−0.295772 + 0.955259i \(0.595577\pi\)
\(602\) 0 0
\(603\) 7.49893 0.305380
\(604\) 0 0
\(605\) 1.72083 0.0699619
\(606\) 0 0
\(607\) 40.7344 1.65336 0.826679 0.562674i \(-0.190227\pi\)
0.826679 + 0.562674i \(0.190227\pi\)
\(608\) 0 0
\(609\) 4.86292 0.197055
\(610\) 0 0
\(611\) 18.6446 0.754278
\(612\) 0 0
\(613\) 10.7028 0.432283 0.216142 0.976362i \(-0.430653\pi\)
0.216142 + 0.976362i \(0.430653\pi\)
\(614\) 0 0
\(615\) 11.5903 0.467366
\(616\) 0 0
\(617\) 16.7939 0.676097 0.338048 0.941129i \(-0.390233\pi\)
0.338048 + 0.941129i \(0.390233\pi\)
\(618\) 0 0
\(619\) 16.2650 0.653747 0.326874 0.945068i \(-0.394005\pi\)
0.326874 + 0.945068i \(0.394005\pi\)
\(620\) 0 0
\(621\) −1.79366 −0.0719770
\(622\) 0 0
\(623\) −7.45814 −0.298804
\(624\) 0 0
\(625\) −0.637277 −0.0254911
\(626\) 0 0
\(627\) −9.44769 −0.377304
\(628\) 0 0
\(629\) 7.75122 0.309062
\(630\) 0 0
\(631\) −4.68508 −0.186510 −0.0932550 0.995642i \(-0.529727\pi\)
−0.0932550 + 0.995642i \(0.529727\pi\)
\(632\) 0 0
\(633\) −6.06555 −0.241084
\(634\) 0 0
\(635\) 63.7092 2.52822
\(636\) 0 0
\(637\) −17.4223 −0.690298
\(638\) 0 0
\(639\) −11.1492 −0.441055
\(640\) 0 0
\(641\) 28.2973 1.11768 0.558838 0.829277i \(-0.311247\pi\)
0.558838 + 0.829277i \(0.311247\pi\)
\(642\) 0 0
\(643\) −10.0424 −0.396034 −0.198017 0.980199i \(-0.563450\pi\)
−0.198017 + 0.980199i \(0.563450\pi\)
\(644\) 0 0
\(645\) 28.8760 1.13699
\(646\) 0 0
\(647\) −1.03715 −0.0407745 −0.0203872 0.999792i \(-0.506490\pi\)
−0.0203872 + 0.999792i \(0.506490\pi\)
\(648\) 0 0
\(649\) 2.62498 0.103040
\(650\) 0 0
\(651\) 1.80608 0.0707858
\(652\) 0 0
\(653\) 13.4029 0.524497 0.262249 0.965000i \(-0.415536\pi\)
0.262249 + 0.965000i \(0.415536\pi\)
\(654\) 0 0
\(655\) −6.16562 −0.240911
\(656\) 0 0
\(657\) 10.6862 0.416908
\(658\) 0 0
\(659\) 24.5472 0.956222 0.478111 0.878300i \(-0.341322\pi\)
0.478111 + 0.878300i \(0.341322\pi\)
\(660\) 0 0
\(661\) −20.5544 −0.799474 −0.399737 0.916630i \(-0.630899\pi\)
−0.399737 + 0.916630i \(0.630899\pi\)
\(662\) 0 0
\(663\) −1.90516 −0.0739904
\(664\) 0 0
\(665\) −10.3332 −0.400705
\(666\) 0 0
\(667\) −8.87503 −0.343642
\(668\) 0 0
\(669\) −27.4945 −1.06300
\(670\) 0 0
\(671\) −32.0966 −1.23908
\(672\) 0 0
\(673\) −26.8226 −1.03394 −0.516968 0.856004i \(-0.672940\pi\)
−0.516968 + 0.856004i \(0.672940\pi\)
\(674\) 0 0
\(675\) 8.03288 0.309186
\(676\) 0 0
\(677\) −14.8612 −0.571164 −0.285582 0.958354i \(-0.592187\pi\)
−0.285582 + 0.958354i \(0.592187\pi\)
\(678\) 0 0
\(679\) −2.82764 −0.108515
\(680\) 0 0
\(681\) −0.283813 −0.0108757
\(682\) 0 0
\(683\) 25.4164 0.972531 0.486266 0.873811i \(-0.338359\pi\)
0.486266 + 0.873811i \(0.338359\pi\)
\(684\) 0 0
\(685\) 67.0979 2.56368
\(686\) 0 0
\(687\) 17.0508 0.650529
\(688\) 0 0
\(689\) 4.26118 0.162338
\(690\) 0 0
\(691\) 17.5592 0.667985 0.333993 0.942576i \(-0.391604\pi\)
0.333993 + 0.942576i \(0.391604\pi\)
\(692\) 0 0
\(693\) −3.18818 −0.121109
\(694\) 0 0
\(695\) −14.0713 −0.533753
\(696\) 0 0
\(697\) 2.11843 0.0802411
\(698\) 0 0
\(699\) 2.24231 0.0848121
\(700\) 0 0
\(701\) −8.15151 −0.307878 −0.153939 0.988080i \(-0.549196\pi\)
−0.153939 + 0.988080i \(0.549196\pi\)
\(702\) 0 0
\(703\) −34.2122 −1.29034
\(704\) 0 0
\(705\) −23.3119 −0.877978
\(706\) 0 0
\(707\) −16.0635 −0.604131
\(708\) 0 0
\(709\) 6.77253 0.254348 0.127174 0.991880i \(-0.459409\pi\)
0.127174 + 0.991880i \(0.459409\pi\)
\(710\) 0 0
\(711\) 5.03225 0.188724
\(712\) 0 0
\(713\) −3.29617 −0.123442
\(714\) 0 0
\(715\) 33.8136 1.26456
\(716\) 0 0
\(717\) −3.40186 −0.127045
\(718\) 0 0
\(719\) 18.3219 0.683293 0.341646 0.939829i \(-0.389015\pi\)
0.341646 + 0.939829i \(0.389015\pi\)
\(720\) 0 0
\(721\) 2.50133 0.0931543
\(722\) 0 0
\(723\) −17.0872 −0.635481
\(724\) 0 0
\(725\) 39.7467 1.47616
\(726\) 0 0
\(727\) −13.7886 −0.511393 −0.255696 0.966757i \(-0.582305\pi\)
−0.255696 + 0.966757i \(0.582305\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 5.27782 0.195207
\(732\) 0 0
\(733\) −21.1474 −0.781098 −0.390549 0.920582i \(-0.627715\pi\)
−0.390549 + 0.920582i \(0.627715\pi\)
\(734\) 0 0
\(735\) 21.7837 0.803505
\(736\) 0 0
\(737\) −24.3263 −0.896070
\(738\) 0 0
\(739\) 16.3081 0.599903 0.299951 0.953954i \(-0.403030\pi\)
0.299951 + 0.953954i \(0.403030\pi\)
\(740\) 0 0
\(741\) 8.40898 0.308911
\(742\) 0 0
\(743\) −8.49786 −0.311756 −0.155878 0.987776i \(-0.549821\pi\)
−0.155878 + 0.987776i \(0.549821\pi\)
\(744\) 0 0
\(745\) −14.8197 −0.542950
\(746\) 0 0
\(747\) 3.32413 0.121624
\(748\) 0 0
\(749\) −4.78940 −0.175001
\(750\) 0 0
\(751\) −4.21411 −0.153775 −0.0768876 0.997040i \(-0.524498\pi\)
−0.0768876 + 0.997040i \(0.524498\pi\)
\(752\) 0 0
\(753\) 30.1261 1.09786
\(754\) 0 0
\(755\) 52.0591 1.89463
\(756\) 0 0
\(757\) −32.1650 −1.16906 −0.584529 0.811373i \(-0.698721\pi\)
−0.584529 + 0.811373i \(0.698721\pi\)
\(758\) 0 0
\(759\) 5.81857 0.211201
\(760\) 0 0
\(761\) −19.2414 −0.697500 −0.348750 0.937216i \(-0.613394\pi\)
−0.348750 + 0.937216i \(0.613394\pi\)
\(762\) 0 0
\(763\) 7.50710 0.271775
\(764\) 0 0
\(765\) 2.38209 0.0861247
\(766\) 0 0
\(767\) −2.33638 −0.0843618
\(768\) 0 0
\(769\) 19.1211 0.689525 0.344762 0.938690i \(-0.387959\pi\)
0.344762 + 0.938690i \(0.387959\pi\)
\(770\) 0 0
\(771\) −12.5832 −0.453173
\(772\) 0 0
\(773\) −18.6237 −0.669849 −0.334924 0.942245i \(-0.608711\pi\)
−0.334924 + 0.942245i \(0.608711\pi\)
\(774\) 0 0
\(775\) 14.7619 0.530262
\(776\) 0 0
\(777\) −11.5451 −0.414179
\(778\) 0 0
\(779\) −9.35027 −0.335008
\(780\) 0 0
\(781\) 36.1676 1.29418
\(782\) 0 0
\(783\) 4.94801 0.176827
\(784\) 0 0
\(785\) −16.2483 −0.579928
\(786\) 0 0
\(787\) 47.1489 1.68068 0.840339 0.542062i \(-0.182356\pi\)
0.840339 + 0.542062i \(0.182356\pi\)
\(788\) 0 0
\(789\) −30.6752 −1.09206
\(790\) 0 0
\(791\) −5.03175 −0.178909
\(792\) 0 0
\(793\) 28.5678 1.01447
\(794\) 0 0
\(795\) −5.32790 −0.188961
\(796\) 0 0
\(797\) 10.7918 0.382267 0.191133 0.981564i \(-0.438784\pi\)
0.191133 + 0.981564i \(0.438784\pi\)
\(798\) 0 0
\(799\) −4.26085 −0.150738
\(800\) 0 0
\(801\) −7.58863 −0.268131
\(802\) 0 0
\(803\) −34.6656 −1.22332
\(804\) 0 0
\(805\) 6.36394 0.224300
\(806\) 0 0
\(807\) −19.8127 −0.697441
\(808\) 0 0
\(809\) 19.5806 0.688416 0.344208 0.938893i \(-0.388147\pi\)
0.344208 + 0.938893i \(0.388147\pi\)
\(810\) 0 0
\(811\) 7.14317 0.250831 0.125415 0.992104i \(-0.459974\pi\)
0.125415 + 0.992104i \(0.459974\pi\)
\(812\) 0 0
\(813\) −4.89053 −0.171518
\(814\) 0 0
\(815\) −47.7269 −1.67180
\(816\) 0 0
\(817\) −23.2952 −0.814994
\(818\) 0 0
\(819\) 2.83766 0.0991560
\(820\) 0 0
\(821\) 20.0758 0.700649 0.350325 0.936628i \(-0.386071\pi\)
0.350325 + 0.936628i \(0.386071\pi\)
\(822\) 0 0
\(823\) −37.7764 −1.31680 −0.658401 0.752667i \(-0.728767\pi\)
−0.658401 + 0.752667i \(0.728767\pi\)
\(824\) 0 0
\(825\) −26.0584 −0.907237
\(826\) 0 0
\(827\) 16.1818 0.562696 0.281348 0.959606i \(-0.409218\pi\)
0.281348 + 0.959606i \(0.409218\pi\)
\(828\) 0 0
\(829\) −3.75821 −0.130528 −0.0652641 0.997868i \(-0.520789\pi\)
−0.0652641 + 0.997868i \(0.520789\pi\)
\(830\) 0 0
\(831\) 4.15322 0.144074
\(832\) 0 0
\(833\) 3.98154 0.137952
\(834\) 0 0
\(835\) 89.1234 3.08424
\(836\) 0 0
\(837\) 1.83768 0.0635195
\(838\) 0 0
\(839\) 20.2261 0.698284 0.349142 0.937070i \(-0.386473\pi\)
0.349142 + 0.937070i \(0.386473\pi\)
\(840\) 0 0
\(841\) −4.51722 −0.155766
\(842\) 0 0
\(843\) 31.7832 1.09467
\(844\) 0 0
\(845\) 16.8354 0.579156
\(846\) 0 0
\(847\) −0.468474 −0.0160970
\(848\) 0 0
\(849\) 11.6889 0.401161
\(850\) 0 0
\(851\) 21.0703 0.722282
\(852\) 0 0
\(853\) −11.1132 −0.380508 −0.190254 0.981735i \(-0.560931\pi\)
−0.190254 + 0.981735i \(0.560931\pi\)
\(854\) 0 0
\(855\) −10.5140 −0.359572
\(856\) 0 0
\(857\) −32.1874 −1.09950 −0.549750 0.835329i \(-0.685277\pi\)
−0.549750 + 0.835329i \(0.685277\pi\)
\(858\) 0 0
\(859\) −9.71379 −0.331430 −0.165715 0.986174i \(-0.552993\pi\)
−0.165715 + 0.986174i \(0.552993\pi\)
\(860\) 0 0
\(861\) −3.15531 −0.107533
\(862\) 0 0
\(863\) −12.5958 −0.428765 −0.214383 0.976750i \(-0.568774\pi\)
−0.214383 + 0.976750i \(0.568774\pi\)
\(864\) 0 0
\(865\) 54.3749 1.84880
\(866\) 0 0
\(867\) −16.5646 −0.562564
\(868\) 0 0
\(869\) −16.3245 −0.553769
\(870\) 0 0
\(871\) 21.6518 0.733642
\(872\) 0 0
\(873\) −2.87712 −0.0973757
\(874\) 0 0
\(875\) −10.7607 −0.363779
\(876\) 0 0
\(877\) 43.7071 1.47588 0.737942 0.674865i \(-0.235798\pi\)
0.737942 + 0.674865i \(0.235798\pi\)
\(878\) 0 0
\(879\) 29.6797 1.00107
\(880\) 0 0
\(881\) −14.6184 −0.492507 −0.246253 0.969205i \(-0.579200\pi\)
−0.246253 + 0.969205i \(0.579200\pi\)
\(882\) 0 0
\(883\) −14.2901 −0.480899 −0.240450 0.970662i \(-0.577295\pi\)
−0.240450 + 0.970662i \(0.577295\pi\)
\(884\) 0 0
\(885\) 2.92126 0.0981970
\(886\) 0 0
\(887\) −29.5310 −0.991554 −0.495777 0.868450i \(-0.665117\pi\)
−0.495777 + 0.868450i \(0.665117\pi\)
\(888\) 0 0
\(889\) −17.3440 −0.581699
\(890\) 0 0
\(891\) −3.24397 −0.108677
\(892\) 0 0
\(893\) 18.8065 0.629334
\(894\) 0 0
\(895\) 79.2274 2.64828
\(896\) 0 0
\(897\) −5.17885 −0.172917
\(898\) 0 0
\(899\) 9.09285 0.303264
\(900\) 0 0
\(901\) −0.973810 −0.0324423
\(902\) 0 0
\(903\) −7.86110 −0.261601
\(904\) 0 0
\(905\) 73.4249 2.44073
\(906\) 0 0
\(907\) 7.87205 0.261387 0.130694 0.991423i \(-0.458280\pi\)
0.130694 + 0.991423i \(0.458280\pi\)
\(908\) 0 0
\(909\) −16.3446 −0.542116
\(910\) 0 0
\(911\) −25.6372 −0.849398 −0.424699 0.905335i \(-0.639620\pi\)
−0.424699 + 0.905335i \(0.639620\pi\)
\(912\) 0 0
\(913\) −10.7834 −0.356877
\(914\) 0 0
\(915\) −35.7193 −1.18084
\(916\) 0 0
\(917\) 1.67851 0.0554293
\(918\) 0 0
\(919\) 47.6491 1.57180 0.785900 0.618354i \(-0.212200\pi\)
0.785900 + 0.618354i \(0.212200\pi\)
\(920\) 0 0
\(921\) 8.25970 0.272166
\(922\) 0 0
\(923\) −32.1912 −1.05959
\(924\) 0 0
\(925\) −94.3633 −3.10265
\(926\) 0 0
\(927\) 2.54509 0.0835918
\(928\) 0 0
\(929\) −40.1854 −1.31844 −0.659221 0.751949i \(-0.729114\pi\)
−0.659221 + 0.751949i \(0.729114\pi\)
\(930\) 0 0
\(931\) −17.5736 −0.575952
\(932\) 0 0
\(933\) −22.6765 −0.742397
\(934\) 0 0
\(935\) −7.72743 −0.252714
\(936\) 0 0
\(937\) 0.331054 0.0108151 0.00540753 0.999985i \(-0.498279\pi\)
0.00540753 + 0.999985i \(0.498279\pi\)
\(938\) 0 0
\(939\) 18.6755 0.609451
\(940\) 0 0
\(941\) 44.4168 1.44795 0.723973 0.689828i \(-0.242314\pi\)
0.723973 + 0.689828i \(0.242314\pi\)
\(942\) 0 0
\(943\) 5.75857 0.187525
\(944\) 0 0
\(945\) −3.54803 −0.115417
\(946\) 0 0
\(947\) 52.5325 1.70708 0.853538 0.521030i \(-0.174452\pi\)
0.853538 + 0.521030i \(0.174452\pi\)
\(948\) 0 0
\(949\) 30.8544 1.00158
\(950\) 0 0
\(951\) −10.1281 −0.328425
\(952\) 0 0
\(953\) 32.3105 1.04664 0.523320 0.852136i \(-0.324693\pi\)
0.523320 + 0.852136i \(0.324693\pi\)
\(954\) 0 0
\(955\) −18.1965 −0.588825
\(956\) 0 0
\(957\) −16.0512 −0.518861
\(958\) 0 0
\(959\) −18.2665 −0.589856
\(960\) 0 0
\(961\) −27.6229 −0.891062
\(962\) 0 0
\(963\) −4.87320 −0.157037
\(964\) 0 0
\(965\) −6.42274 −0.206755
\(966\) 0 0
\(967\) 28.4425 0.914648 0.457324 0.889300i \(-0.348808\pi\)
0.457324 + 0.889300i \(0.348808\pi\)
\(968\) 0 0
\(969\) −1.92171 −0.0617342
\(970\) 0 0
\(971\) −29.2913 −0.940004 −0.470002 0.882665i \(-0.655747\pi\)
−0.470002 + 0.882665i \(0.655747\pi\)
\(972\) 0 0
\(973\) 3.83071 0.122807
\(974\) 0 0
\(975\) 23.1934 0.742785
\(976\) 0 0
\(977\) −22.6562 −0.724835 −0.362417 0.932016i \(-0.618048\pi\)
−0.362417 + 0.932016i \(0.618048\pi\)
\(978\) 0 0
\(979\) 24.6173 0.786772
\(980\) 0 0
\(981\) 7.63845 0.243877
\(982\) 0 0
\(983\) −16.2148 −0.517173 −0.258587 0.965988i \(-0.583257\pi\)
−0.258587 + 0.965988i \(0.583257\pi\)
\(984\) 0 0
\(985\) −11.4791 −0.365755
\(986\) 0 0
\(987\) 6.34636 0.202007
\(988\) 0 0
\(989\) 14.3468 0.456203
\(990\) 0 0
\(991\) 49.9491 1.58669 0.793343 0.608774i \(-0.208339\pi\)
0.793343 + 0.608774i \(0.208339\pi\)
\(992\) 0 0
\(993\) −26.0075 −0.825324
\(994\) 0 0
\(995\) 43.5074 1.37928
\(996\) 0 0
\(997\) −58.5213 −1.85339 −0.926694 0.375818i \(-0.877362\pi\)
−0.926694 + 0.375818i \(0.877362\pi\)
\(998\) 0 0
\(999\) −11.7471 −0.371663
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 \(a_p\))