Properties

Label 6008.2.a.e.1.6
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 1.6
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58697 q^{3} +0.0890087 q^{5} +4.21791 q^{7} +3.69244 q^{9} +O(q^{10})\) \(q-2.58697 q^{3} +0.0890087 q^{5} +4.21791 q^{7} +3.69244 q^{9} -5.56038 q^{11} +5.65898 q^{13} -0.230263 q^{15} +4.66419 q^{17} +5.92080 q^{19} -10.9116 q^{21} -2.98182 q^{23} -4.99208 q^{25} -1.79132 q^{27} +6.14670 q^{29} -0.725876 q^{31} +14.3846 q^{33} +0.375431 q^{35} +11.8046 q^{37} -14.6396 q^{39} -3.43975 q^{41} +4.18359 q^{43} +0.328659 q^{45} -5.47405 q^{47} +10.7908 q^{49} -12.0662 q^{51} +2.96430 q^{53} -0.494922 q^{55} -15.3170 q^{57} +3.19404 q^{59} +2.66626 q^{61} +15.5744 q^{63} +0.503698 q^{65} -2.11614 q^{67} +7.71389 q^{69} +12.6906 q^{71} -5.71725 q^{73} +12.9144 q^{75} -23.4532 q^{77} +7.85668 q^{79} -6.44322 q^{81} -2.69956 q^{83} +0.415154 q^{85} -15.9013 q^{87} -12.3442 q^{89} +23.8691 q^{91} +1.87782 q^{93} +0.527003 q^{95} -4.06463 q^{97} -20.5314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.58697 −1.49359 −0.746795 0.665054i \(-0.768408\pi\)
−0.746795 + 0.665054i \(0.768408\pi\)
\(4\) 0 0
\(5\) 0.0890087 0.0398059 0.0199029 0.999802i \(-0.493664\pi\)
0.0199029 + 0.999802i \(0.493664\pi\)
\(6\) 0 0
\(7\) 4.21791 1.59422 0.797111 0.603833i \(-0.206361\pi\)
0.797111 + 0.603833i \(0.206361\pi\)
\(8\) 0 0
\(9\) 3.69244 1.23081
\(10\) 0 0
\(11\) −5.56038 −1.67652 −0.838260 0.545271i \(-0.816427\pi\)
−0.838260 + 0.545271i \(0.816427\pi\)
\(12\) 0 0
\(13\) 5.65898 1.56952 0.784759 0.619801i \(-0.212787\pi\)
0.784759 + 0.619801i \(0.212787\pi\)
\(14\) 0 0
\(15\) −0.230263 −0.0594537
\(16\) 0 0
\(17\) 4.66419 1.13123 0.565617 0.824668i \(-0.308638\pi\)
0.565617 + 0.824668i \(0.308638\pi\)
\(18\) 0 0
\(19\) 5.92080 1.35833 0.679163 0.733988i \(-0.262343\pi\)
0.679163 + 0.733988i \(0.262343\pi\)
\(20\) 0 0
\(21\) −10.9116 −2.38111
\(22\) 0 0
\(23\) −2.98182 −0.621752 −0.310876 0.950450i \(-0.600622\pi\)
−0.310876 + 0.950450i \(0.600622\pi\)
\(24\) 0 0
\(25\) −4.99208 −0.998415
\(26\) 0 0
\(27\) −1.79132 −0.344739
\(28\) 0 0
\(29\) 6.14670 1.14141 0.570707 0.821154i \(-0.306669\pi\)
0.570707 + 0.821154i \(0.306669\pi\)
\(30\) 0 0
\(31\) −0.725876 −0.130371 −0.0651856 0.997873i \(-0.520764\pi\)
−0.0651856 + 0.997873i \(0.520764\pi\)
\(32\) 0 0
\(33\) 14.3846 2.50403
\(34\) 0 0
\(35\) 0.375431 0.0634594
\(36\) 0 0
\(37\) 11.8046 1.94067 0.970334 0.241770i \(-0.0777279\pi\)
0.970334 + 0.241770i \(0.0777279\pi\)
\(38\) 0 0
\(39\) −14.6396 −2.34422
\(40\) 0 0
\(41\) −3.43975 −0.537199 −0.268600 0.963252i \(-0.586561\pi\)
−0.268600 + 0.963252i \(0.586561\pi\)
\(42\) 0 0
\(43\) 4.18359 0.637991 0.318995 0.947756i \(-0.396655\pi\)
0.318995 + 0.947756i \(0.396655\pi\)
\(44\) 0 0
\(45\) 0.328659 0.0489936
\(46\) 0 0
\(47\) −5.47405 −0.798472 −0.399236 0.916848i \(-0.630725\pi\)
−0.399236 + 0.916848i \(0.630725\pi\)
\(48\) 0 0
\(49\) 10.7908 1.54154
\(50\) 0 0
\(51\) −12.0662 −1.68960
\(52\) 0 0
\(53\) 2.96430 0.407178 0.203589 0.979056i \(-0.434739\pi\)
0.203589 + 0.979056i \(0.434739\pi\)
\(54\) 0 0
\(55\) −0.494922 −0.0667353
\(56\) 0 0
\(57\) −15.3170 −2.02878
\(58\) 0 0
\(59\) 3.19404 0.415828 0.207914 0.978147i \(-0.433333\pi\)
0.207914 + 0.978147i \(0.433333\pi\)
\(60\) 0 0
\(61\) 2.66626 0.341379 0.170690 0.985325i \(-0.445400\pi\)
0.170690 + 0.985325i \(0.445400\pi\)
\(62\) 0 0
\(63\) 15.5744 1.96219
\(64\) 0 0
\(65\) 0.503698 0.0624760
\(66\) 0 0
\(67\) −2.11614 −0.258528 −0.129264 0.991610i \(-0.541261\pi\)
−0.129264 + 0.991610i \(0.541261\pi\)
\(68\) 0 0
\(69\) 7.71389 0.928643
\(70\) 0 0
\(71\) 12.6906 1.50609 0.753046 0.657968i \(-0.228584\pi\)
0.753046 + 0.657968i \(0.228584\pi\)
\(72\) 0 0
\(73\) −5.71725 −0.669153 −0.334577 0.942369i \(-0.608593\pi\)
−0.334577 + 0.942369i \(0.608593\pi\)
\(74\) 0 0
\(75\) 12.9144 1.49122
\(76\) 0 0
\(77\) −23.4532 −2.67274
\(78\) 0 0
\(79\) 7.85668 0.883945 0.441973 0.897029i \(-0.354279\pi\)
0.441973 + 0.897029i \(0.354279\pi\)
\(80\) 0 0
\(81\) −6.44322 −0.715913
\(82\) 0 0
\(83\) −2.69956 −0.296315 −0.148158 0.988964i \(-0.547334\pi\)
−0.148158 + 0.988964i \(0.547334\pi\)
\(84\) 0 0
\(85\) 0.415154 0.0450297
\(86\) 0 0
\(87\) −15.9013 −1.70480
\(88\) 0 0
\(89\) −12.3442 −1.30848 −0.654241 0.756286i \(-0.727012\pi\)
−0.654241 + 0.756286i \(0.727012\pi\)
\(90\) 0 0
\(91\) 23.8691 2.50216
\(92\) 0 0
\(93\) 1.87782 0.194721
\(94\) 0 0
\(95\) 0.527003 0.0540693
\(96\) 0 0
\(97\) −4.06463 −0.412701 −0.206350 0.978478i \(-0.566159\pi\)
−0.206350 + 0.978478i \(0.566159\pi\)
\(98\) 0 0
\(99\) −20.5314 −2.06348
\(100\) 0 0
\(101\) 18.9006 1.88068 0.940340 0.340236i \(-0.110507\pi\)
0.940340 + 0.340236i \(0.110507\pi\)
\(102\) 0 0
\(103\) −14.8998 −1.46812 −0.734062 0.679083i \(-0.762378\pi\)
−0.734062 + 0.679083i \(0.762378\pi\)
\(104\) 0 0
\(105\) −0.971230 −0.0947823
\(106\) 0 0
\(107\) −9.90443 −0.957498 −0.478749 0.877952i \(-0.658910\pi\)
−0.478749 + 0.877952i \(0.658910\pi\)
\(108\) 0 0
\(109\) −16.0205 −1.53448 −0.767241 0.641359i \(-0.778371\pi\)
−0.767241 + 0.641359i \(0.778371\pi\)
\(110\) 0 0
\(111\) −30.5382 −2.89856
\(112\) 0 0
\(113\) 8.17961 0.769473 0.384737 0.923026i \(-0.374292\pi\)
0.384737 + 0.923026i \(0.374292\pi\)
\(114\) 0 0
\(115\) −0.265408 −0.0247494
\(116\) 0 0
\(117\) 20.8954 1.93178
\(118\) 0 0
\(119\) 19.6732 1.80344
\(120\) 0 0
\(121\) 19.9179 1.81072
\(122\) 0 0
\(123\) 8.89855 0.802355
\(124\) 0 0
\(125\) −0.889382 −0.0795487
\(126\) 0 0
\(127\) −9.32495 −0.827455 −0.413728 0.910401i \(-0.635773\pi\)
−0.413728 + 0.910401i \(0.635773\pi\)
\(128\) 0 0
\(129\) −10.8228 −0.952897
\(130\) 0 0
\(131\) 5.34175 0.466711 0.233355 0.972392i \(-0.425029\pi\)
0.233355 + 0.972392i \(0.425029\pi\)
\(132\) 0 0
\(133\) 24.9734 2.16547
\(134\) 0 0
\(135\) −0.159443 −0.0137226
\(136\) 0 0
\(137\) −15.0180 −1.28307 −0.641537 0.767092i \(-0.721703\pi\)
−0.641537 + 0.767092i \(0.721703\pi\)
\(138\) 0 0
\(139\) 1.35192 0.114669 0.0573344 0.998355i \(-0.481740\pi\)
0.0573344 + 0.998355i \(0.481740\pi\)
\(140\) 0 0
\(141\) 14.1612 1.19259
\(142\) 0 0
\(143\) −31.4661 −2.63133
\(144\) 0 0
\(145\) 0.547109 0.0454350
\(146\) 0 0
\(147\) −27.9155 −2.30243
\(148\) 0 0
\(149\) −10.8113 −0.885699 −0.442850 0.896596i \(-0.646032\pi\)
−0.442850 + 0.896596i \(0.646032\pi\)
\(150\) 0 0
\(151\) −4.91695 −0.400136 −0.200068 0.979782i \(-0.564116\pi\)
−0.200068 + 0.979782i \(0.564116\pi\)
\(152\) 0 0
\(153\) 17.2222 1.39234
\(154\) 0 0
\(155\) −0.0646092 −0.00518954
\(156\) 0 0
\(157\) 20.8790 1.66632 0.833162 0.553029i \(-0.186528\pi\)
0.833162 + 0.553029i \(0.186528\pi\)
\(158\) 0 0
\(159\) −7.66858 −0.608158
\(160\) 0 0
\(161\) −12.5770 −0.991210
\(162\) 0 0
\(163\) −1.79156 −0.140326 −0.0701631 0.997536i \(-0.522352\pi\)
−0.0701631 + 0.997536i \(0.522352\pi\)
\(164\) 0 0
\(165\) 1.28035 0.0996752
\(166\) 0 0
\(167\) −10.7548 −0.832231 −0.416116 0.909312i \(-0.636609\pi\)
−0.416116 + 0.909312i \(0.636609\pi\)
\(168\) 0 0
\(169\) 19.0240 1.46338
\(170\) 0 0
\(171\) 21.8622 1.67184
\(172\) 0 0
\(173\) −19.0997 −1.45212 −0.726061 0.687630i \(-0.758651\pi\)
−0.726061 + 0.687630i \(0.758651\pi\)
\(174\) 0 0
\(175\) −21.0561 −1.59170
\(176\) 0 0
\(177\) −8.26290 −0.621077
\(178\) 0 0
\(179\) −16.9659 −1.26809 −0.634045 0.773296i \(-0.718607\pi\)
−0.634045 + 0.773296i \(0.718607\pi\)
\(180\) 0 0
\(181\) 8.82509 0.655964 0.327982 0.944684i \(-0.393631\pi\)
0.327982 + 0.944684i \(0.393631\pi\)
\(182\) 0 0
\(183\) −6.89754 −0.509880
\(184\) 0 0
\(185\) 1.05071 0.0772500
\(186\) 0 0
\(187\) −25.9347 −1.89653
\(188\) 0 0
\(189\) −7.55562 −0.549591
\(190\) 0 0
\(191\) 14.0977 1.02007 0.510036 0.860153i \(-0.329632\pi\)
0.510036 + 0.860153i \(0.329632\pi\)
\(192\) 0 0
\(193\) 12.2396 0.881028 0.440514 0.897746i \(-0.354796\pi\)
0.440514 + 0.897746i \(0.354796\pi\)
\(194\) 0 0
\(195\) −1.30305 −0.0933136
\(196\) 0 0
\(197\) 17.3032 1.23280 0.616401 0.787432i \(-0.288590\pi\)
0.616401 + 0.787432i \(0.288590\pi\)
\(198\) 0 0
\(199\) 7.97358 0.565232 0.282616 0.959233i \(-0.408798\pi\)
0.282616 + 0.959233i \(0.408798\pi\)
\(200\) 0 0
\(201\) 5.47440 0.386134
\(202\) 0 0
\(203\) 25.9262 1.81967
\(204\) 0 0
\(205\) −0.306168 −0.0213837
\(206\) 0 0
\(207\) −11.0102 −0.765260
\(208\) 0 0
\(209\) −32.9219 −2.27726
\(210\) 0 0
\(211\) 1.21487 0.0836348 0.0418174 0.999125i \(-0.486685\pi\)
0.0418174 + 0.999125i \(0.486685\pi\)
\(212\) 0 0
\(213\) −32.8301 −2.24948
\(214\) 0 0
\(215\) 0.372375 0.0253958
\(216\) 0 0
\(217\) −3.06168 −0.207840
\(218\) 0 0
\(219\) 14.7904 0.999441
\(220\) 0 0
\(221\) 26.3946 1.77549
\(222\) 0 0
\(223\) −7.75290 −0.519172 −0.259586 0.965720i \(-0.583586\pi\)
−0.259586 + 0.965720i \(0.583586\pi\)
\(224\) 0 0
\(225\) −18.4329 −1.22886
\(226\) 0 0
\(227\) −17.9480 −1.19125 −0.595626 0.803262i \(-0.703096\pi\)
−0.595626 + 0.803262i \(0.703096\pi\)
\(228\) 0 0
\(229\) 11.2040 0.740383 0.370192 0.928955i \(-0.379292\pi\)
0.370192 + 0.928955i \(0.379292\pi\)
\(230\) 0 0
\(231\) 60.6729 3.99198
\(232\) 0 0
\(233\) 24.8767 1.62973 0.814864 0.579653i \(-0.196812\pi\)
0.814864 + 0.579653i \(0.196812\pi\)
\(234\) 0 0
\(235\) −0.487238 −0.0317839
\(236\) 0 0
\(237\) −20.3250 −1.32025
\(238\) 0 0
\(239\) −2.12353 −0.137360 −0.0686798 0.997639i \(-0.521879\pi\)
−0.0686798 + 0.997639i \(0.521879\pi\)
\(240\) 0 0
\(241\) 19.9586 1.28565 0.642823 0.766015i \(-0.277763\pi\)
0.642823 + 0.766015i \(0.277763\pi\)
\(242\) 0 0
\(243\) 22.0424 1.41402
\(244\) 0 0
\(245\) 0.960474 0.0613624
\(246\) 0 0
\(247\) 33.5057 2.13191
\(248\) 0 0
\(249\) 6.98370 0.442574
\(250\) 0 0
\(251\) 19.5092 1.23141 0.615706 0.787976i \(-0.288871\pi\)
0.615706 + 0.787976i \(0.288871\pi\)
\(252\) 0 0
\(253\) 16.5801 1.04238
\(254\) 0 0
\(255\) −1.07399 −0.0672560
\(256\) 0 0
\(257\) 8.20677 0.511924 0.255962 0.966687i \(-0.417608\pi\)
0.255962 + 0.966687i \(0.417608\pi\)
\(258\) 0 0
\(259\) 49.7909 3.09385
\(260\) 0 0
\(261\) 22.6963 1.40487
\(262\) 0 0
\(263\) 12.5489 0.773801 0.386901 0.922121i \(-0.373546\pi\)
0.386901 + 0.922121i \(0.373546\pi\)
\(264\) 0 0
\(265\) 0.263849 0.0162081
\(266\) 0 0
\(267\) 31.9341 1.95434
\(268\) 0 0
\(269\) −21.4017 −1.30489 −0.652443 0.757837i \(-0.726256\pi\)
−0.652443 + 0.757837i \(0.726256\pi\)
\(270\) 0 0
\(271\) −30.0583 −1.82591 −0.912955 0.408060i \(-0.866206\pi\)
−0.912955 + 0.408060i \(0.866206\pi\)
\(272\) 0 0
\(273\) −61.7487 −3.73720
\(274\) 0 0
\(275\) 27.7579 1.67386
\(276\) 0 0
\(277\) −2.25631 −0.135568 −0.0677842 0.997700i \(-0.521593\pi\)
−0.0677842 + 0.997700i \(0.521593\pi\)
\(278\) 0 0
\(279\) −2.68025 −0.160462
\(280\) 0 0
\(281\) 23.4142 1.39677 0.698387 0.715720i \(-0.253901\pi\)
0.698387 + 0.715720i \(0.253901\pi\)
\(282\) 0 0
\(283\) 4.89680 0.291084 0.145542 0.989352i \(-0.453507\pi\)
0.145542 + 0.989352i \(0.453507\pi\)
\(284\) 0 0
\(285\) −1.36334 −0.0807574
\(286\) 0 0
\(287\) −14.5086 −0.856414
\(288\) 0 0
\(289\) 4.75471 0.279689
\(290\) 0 0
\(291\) 10.5151 0.616406
\(292\) 0 0
\(293\) −30.9491 −1.80806 −0.904032 0.427465i \(-0.859407\pi\)
−0.904032 + 0.427465i \(0.859407\pi\)
\(294\) 0 0
\(295\) 0.284297 0.0165524
\(296\) 0 0
\(297\) 9.96041 0.577962
\(298\) 0 0
\(299\) −16.8740 −0.975850
\(300\) 0 0
\(301\) 17.6460 1.01710
\(302\) 0 0
\(303\) −48.8954 −2.80897
\(304\) 0 0
\(305\) 0.237320 0.0135889
\(306\) 0 0
\(307\) 23.2317 1.32590 0.662951 0.748663i \(-0.269304\pi\)
0.662951 + 0.748663i \(0.269304\pi\)
\(308\) 0 0
\(309\) 38.5455 2.19278
\(310\) 0 0
\(311\) −21.8622 −1.23969 −0.619847 0.784723i \(-0.712805\pi\)
−0.619847 + 0.784723i \(0.712805\pi\)
\(312\) 0 0
\(313\) −13.2754 −0.750369 −0.375184 0.926950i \(-0.622421\pi\)
−0.375184 + 0.926950i \(0.622421\pi\)
\(314\) 0 0
\(315\) 1.38625 0.0781066
\(316\) 0 0
\(317\) 25.0392 1.40634 0.703172 0.711020i \(-0.251766\pi\)
0.703172 + 0.711020i \(0.251766\pi\)
\(318\) 0 0
\(319\) −34.1780 −1.91360
\(320\) 0 0
\(321\) 25.6225 1.43011
\(322\) 0 0
\(323\) 27.6158 1.53658
\(324\) 0 0
\(325\) −28.2500 −1.56703
\(326\) 0 0
\(327\) 41.4445 2.29189
\(328\) 0 0
\(329\) −23.0891 −1.27294
\(330\) 0 0
\(331\) 17.9055 0.984174 0.492087 0.870546i \(-0.336234\pi\)
0.492087 + 0.870546i \(0.336234\pi\)
\(332\) 0 0
\(333\) 43.5878 2.38860
\(334\) 0 0
\(335\) −0.188355 −0.0102909
\(336\) 0 0
\(337\) 7.72574 0.420848 0.210424 0.977610i \(-0.432516\pi\)
0.210424 + 0.977610i \(0.432516\pi\)
\(338\) 0 0
\(339\) −21.1604 −1.14928
\(340\) 0 0
\(341\) 4.03615 0.218570
\(342\) 0 0
\(343\) 15.9892 0.863337
\(344\) 0 0
\(345\) 0.686603 0.0369654
\(346\) 0 0
\(347\) −4.90582 −0.263358 −0.131679 0.991292i \(-0.542037\pi\)
−0.131679 + 0.991292i \(0.542037\pi\)
\(348\) 0 0
\(349\) −0.611795 −0.0327487 −0.0163743 0.999866i \(-0.505212\pi\)
−0.0163743 + 0.999866i \(0.505212\pi\)
\(350\) 0 0
\(351\) −10.1370 −0.541074
\(352\) 0 0
\(353\) 10.5794 0.563083 0.281542 0.959549i \(-0.409154\pi\)
0.281542 + 0.959549i \(0.409154\pi\)
\(354\) 0 0
\(355\) 1.12957 0.0599513
\(356\) 0 0
\(357\) −50.8940 −2.69359
\(358\) 0 0
\(359\) −1.20906 −0.0638119 −0.0319060 0.999491i \(-0.510158\pi\)
−0.0319060 + 0.999491i \(0.510158\pi\)
\(360\) 0 0
\(361\) 16.0559 0.845047
\(362\) 0 0
\(363\) −51.5270 −2.70447
\(364\) 0 0
\(365\) −0.508884 −0.0266362
\(366\) 0 0
\(367\) −26.1402 −1.36451 −0.682254 0.731116i \(-0.739000\pi\)
−0.682254 + 0.731116i \(0.739000\pi\)
\(368\) 0 0
\(369\) −12.7011 −0.661191
\(370\) 0 0
\(371\) 12.5032 0.649132
\(372\) 0 0
\(373\) 27.0290 1.39951 0.699755 0.714383i \(-0.253292\pi\)
0.699755 + 0.714383i \(0.253292\pi\)
\(374\) 0 0
\(375\) 2.30081 0.118813
\(376\) 0 0
\(377\) 34.7840 1.79147
\(378\) 0 0
\(379\) 16.1069 0.827357 0.413679 0.910423i \(-0.364244\pi\)
0.413679 + 0.910423i \(0.364244\pi\)
\(380\) 0 0
\(381\) 24.1234 1.23588
\(382\) 0 0
\(383\) 0.795719 0.0406594 0.0203297 0.999793i \(-0.493528\pi\)
0.0203297 + 0.999793i \(0.493528\pi\)
\(384\) 0 0
\(385\) −2.08754 −0.106391
\(386\) 0 0
\(387\) 15.4476 0.785247
\(388\) 0 0
\(389\) −28.1735 −1.42845 −0.714226 0.699915i \(-0.753221\pi\)
−0.714226 + 0.699915i \(0.753221\pi\)
\(390\) 0 0
\(391\) −13.9078 −0.703346
\(392\) 0 0
\(393\) −13.8190 −0.697075
\(394\) 0 0
\(395\) 0.699312 0.0351862
\(396\) 0 0
\(397\) 12.0999 0.607276 0.303638 0.952787i \(-0.401799\pi\)
0.303638 + 0.952787i \(0.401799\pi\)
\(398\) 0 0
\(399\) −64.6056 −3.23433
\(400\) 0 0
\(401\) 36.2367 1.80958 0.904788 0.425863i \(-0.140029\pi\)
0.904788 + 0.425863i \(0.140029\pi\)
\(402\) 0 0
\(403\) −4.10771 −0.204620
\(404\) 0 0
\(405\) −0.573502 −0.0284976
\(406\) 0 0
\(407\) −65.6382 −3.25357
\(408\) 0 0
\(409\) 10.6678 0.527490 0.263745 0.964592i \(-0.415042\pi\)
0.263745 + 0.964592i \(0.415042\pi\)
\(410\) 0 0
\(411\) 38.8512 1.91639
\(412\) 0 0
\(413\) 13.4722 0.662922
\(414\) 0 0
\(415\) −0.240284 −0.0117951
\(416\) 0 0
\(417\) −3.49739 −0.171268
\(418\) 0 0
\(419\) 23.2757 1.13709 0.568546 0.822651i \(-0.307506\pi\)
0.568546 + 0.822651i \(0.307506\pi\)
\(420\) 0 0
\(421\) 11.9908 0.584395 0.292197 0.956358i \(-0.405614\pi\)
0.292197 + 0.956358i \(0.405614\pi\)
\(422\) 0 0
\(423\) −20.2126 −0.982769
\(424\) 0 0
\(425\) −23.2840 −1.12944
\(426\) 0 0
\(427\) 11.2460 0.544234
\(428\) 0 0
\(429\) 81.4019 3.93012
\(430\) 0 0
\(431\) 3.76114 0.181168 0.0905840 0.995889i \(-0.471127\pi\)
0.0905840 + 0.995889i \(0.471127\pi\)
\(432\) 0 0
\(433\) 4.30609 0.206937 0.103469 0.994633i \(-0.467006\pi\)
0.103469 + 0.994633i \(0.467006\pi\)
\(434\) 0 0
\(435\) −1.41536 −0.0678612
\(436\) 0 0
\(437\) −17.6547 −0.844541
\(438\) 0 0
\(439\) −3.06838 −0.146446 −0.0732230 0.997316i \(-0.523328\pi\)
−0.0732230 + 0.997316i \(0.523328\pi\)
\(440\) 0 0
\(441\) 39.8443 1.89735
\(442\) 0 0
\(443\) −3.96278 −0.188277 −0.0941387 0.995559i \(-0.530010\pi\)
−0.0941387 + 0.995559i \(0.530010\pi\)
\(444\) 0 0
\(445\) −1.09874 −0.0520853
\(446\) 0 0
\(447\) 27.9687 1.32287
\(448\) 0 0
\(449\) −28.6478 −1.35197 −0.675986 0.736914i \(-0.736282\pi\)
−0.675986 + 0.736914i \(0.736282\pi\)
\(450\) 0 0
\(451\) 19.1263 0.900624
\(452\) 0 0
\(453\) 12.7200 0.597639
\(454\) 0 0
\(455\) 2.12455 0.0996006
\(456\) 0 0
\(457\) 8.32907 0.389618 0.194809 0.980841i \(-0.437591\pi\)
0.194809 + 0.980841i \(0.437591\pi\)
\(458\) 0 0
\(459\) −8.35505 −0.389980
\(460\) 0 0
\(461\) −37.6682 −1.75438 −0.877192 0.480139i \(-0.840586\pi\)
−0.877192 + 0.480139i \(0.840586\pi\)
\(462\) 0 0
\(463\) 32.1495 1.49411 0.747057 0.664760i \(-0.231466\pi\)
0.747057 + 0.664760i \(0.231466\pi\)
\(464\) 0 0
\(465\) 0.167142 0.00775104
\(466\) 0 0
\(467\) 35.6401 1.64923 0.824614 0.565695i \(-0.191392\pi\)
0.824614 + 0.565695i \(0.191392\pi\)
\(468\) 0 0
\(469\) −8.92569 −0.412150
\(470\) 0 0
\(471\) −54.0134 −2.48881
\(472\) 0 0
\(473\) −23.2623 −1.06960
\(474\) 0 0
\(475\) −29.5571 −1.35617
\(476\) 0 0
\(477\) 10.9455 0.501160
\(478\) 0 0
\(479\) 27.3687 1.25051 0.625254 0.780421i \(-0.284995\pi\)
0.625254 + 0.780421i \(0.284995\pi\)
\(480\) 0 0
\(481\) 66.8020 3.04591
\(482\) 0 0
\(483\) 32.5365 1.48046
\(484\) 0 0
\(485\) −0.361787 −0.0164279
\(486\) 0 0
\(487\) −11.6603 −0.528378 −0.264189 0.964471i \(-0.585104\pi\)
−0.264189 + 0.964471i \(0.585104\pi\)
\(488\) 0 0
\(489\) 4.63473 0.209590
\(490\) 0 0
\(491\) −17.2858 −0.780097 −0.390048 0.920794i \(-0.627542\pi\)
−0.390048 + 0.920794i \(0.627542\pi\)
\(492\) 0 0
\(493\) 28.6694 1.29120
\(494\) 0 0
\(495\) −1.82747 −0.0821387
\(496\) 0 0
\(497\) 53.5277 2.40104
\(498\) 0 0
\(499\) 38.9749 1.74476 0.872378 0.488832i \(-0.162577\pi\)
0.872378 + 0.488832i \(0.162577\pi\)
\(500\) 0 0
\(501\) 27.8224 1.24301
\(502\) 0 0
\(503\) 32.0605 1.42951 0.714753 0.699377i \(-0.246539\pi\)
0.714753 + 0.699377i \(0.246539\pi\)
\(504\) 0 0
\(505\) 1.68232 0.0748621
\(506\) 0 0
\(507\) −49.2146 −2.18570
\(508\) 0 0
\(509\) 18.1814 0.805877 0.402939 0.915227i \(-0.367989\pi\)
0.402939 + 0.915227i \(0.367989\pi\)
\(510\) 0 0
\(511\) −24.1148 −1.06678
\(512\) 0 0
\(513\) −10.6060 −0.468268
\(514\) 0 0
\(515\) −1.32621 −0.0584400
\(516\) 0 0
\(517\) 30.4378 1.33865
\(518\) 0 0
\(519\) 49.4104 2.16888
\(520\) 0 0
\(521\) 35.9460 1.57482 0.787412 0.616427i \(-0.211420\pi\)
0.787412 + 0.616427i \(0.211420\pi\)
\(522\) 0 0
\(523\) 28.4882 1.24570 0.622850 0.782341i \(-0.285975\pi\)
0.622850 + 0.782341i \(0.285975\pi\)
\(524\) 0 0
\(525\) 54.4717 2.37734
\(526\) 0 0
\(527\) −3.38562 −0.147480
\(528\) 0 0
\(529\) −14.1088 −0.613425
\(530\) 0 0
\(531\) 11.7938 0.511807
\(532\) 0 0
\(533\) −19.4655 −0.843143
\(534\) 0 0
\(535\) −0.881580 −0.0381140
\(536\) 0 0
\(537\) 43.8904 1.89401
\(538\) 0 0
\(539\) −60.0010 −2.58442
\(540\) 0 0
\(541\) 30.4441 1.30889 0.654447 0.756108i \(-0.272902\pi\)
0.654447 + 0.756108i \(0.272902\pi\)
\(542\) 0 0
\(543\) −22.8303 −0.979741
\(544\) 0 0
\(545\) −1.42596 −0.0610814
\(546\) 0 0
\(547\) −38.5946 −1.65018 −0.825092 0.564998i \(-0.808877\pi\)
−0.825092 + 0.564998i \(0.808877\pi\)
\(548\) 0 0
\(549\) 9.84498 0.420174
\(550\) 0 0
\(551\) 36.3934 1.55041
\(552\) 0 0
\(553\) 33.1388 1.40920
\(554\) 0 0
\(555\) −2.71817 −0.115380
\(556\) 0 0
\(557\) −36.2175 −1.53459 −0.767293 0.641297i \(-0.778397\pi\)
−0.767293 + 0.641297i \(0.778397\pi\)
\(558\) 0 0
\(559\) 23.6748 1.00134
\(560\) 0 0
\(561\) 67.0924 2.83265
\(562\) 0 0
\(563\) −21.6524 −0.912540 −0.456270 0.889841i \(-0.650815\pi\)
−0.456270 + 0.889841i \(0.650815\pi\)
\(564\) 0 0
\(565\) 0.728056 0.0306296
\(566\) 0 0
\(567\) −27.1769 −1.14132
\(568\) 0 0
\(569\) 5.26799 0.220846 0.110423 0.993885i \(-0.464779\pi\)
0.110423 + 0.993885i \(0.464779\pi\)
\(570\) 0 0
\(571\) −18.9409 −0.792654 −0.396327 0.918109i \(-0.629715\pi\)
−0.396327 + 0.918109i \(0.629715\pi\)
\(572\) 0 0
\(573\) −36.4703 −1.52357
\(574\) 0 0
\(575\) 14.8855 0.620767
\(576\) 0 0
\(577\) 31.8242 1.32486 0.662429 0.749125i \(-0.269526\pi\)
0.662429 + 0.749125i \(0.269526\pi\)
\(578\) 0 0
\(579\) −31.6636 −1.31590
\(580\) 0 0
\(581\) −11.3865 −0.472392
\(582\) 0 0
\(583\) −16.4827 −0.682642
\(584\) 0 0
\(585\) 1.85987 0.0768963
\(586\) 0 0
\(587\) 27.8655 1.15013 0.575066 0.818107i \(-0.304977\pi\)
0.575066 + 0.818107i \(0.304977\pi\)
\(588\) 0 0
\(589\) −4.29777 −0.177086
\(590\) 0 0
\(591\) −44.7629 −1.84130
\(592\) 0 0
\(593\) 7.37337 0.302788 0.151394 0.988473i \(-0.451624\pi\)
0.151394 + 0.988473i \(0.451624\pi\)
\(594\) 0 0
\(595\) 1.75108 0.0717874
\(596\) 0 0
\(597\) −20.6274 −0.844225
\(598\) 0 0
\(599\) 14.1996 0.580181 0.290090 0.956999i \(-0.406315\pi\)
0.290090 + 0.956999i \(0.406315\pi\)
\(600\) 0 0
\(601\) −18.3842 −0.749906 −0.374953 0.927044i \(-0.622341\pi\)
−0.374953 + 0.927044i \(0.622341\pi\)
\(602\) 0 0
\(603\) −7.81371 −0.318199
\(604\) 0 0
\(605\) 1.77286 0.0720772
\(606\) 0 0
\(607\) −37.9474 −1.54024 −0.770119 0.637900i \(-0.779803\pi\)
−0.770119 + 0.637900i \(0.779803\pi\)
\(608\) 0 0
\(609\) −67.0705 −2.71783
\(610\) 0 0
\(611\) −30.9775 −1.25322
\(612\) 0 0
\(613\) 31.9514 1.29050 0.645252 0.763970i \(-0.276752\pi\)
0.645252 + 0.763970i \(0.276752\pi\)
\(614\) 0 0
\(615\) 0.792048 0.0319385
\(616\) 0 0
\(617\) −17.2855 −0.695887 −0.347943 0.937516i \(-0.613120\pi\)
−0.347943 + 0.937516i \(0.613120\pi\)
\(618\) 0 0
\(619\) 31.9095 1.28255 0.641276 0.767311i \(-0.278406\pi\)
0.641276 + 0.767311i \(0.278406\pi\)
\(620\) 0 0
\(621\) 5.34138 0.214342
\(622\) 0 0
\(623\) −52.0667 −2.08601
\(624\) 0 0
\(625\) 24.8812 0.995249
\(626\) 0 0
\(627\) 85.1682 3.40129
\(628\) 0 0
\(629\) 55.0590 2.19535
\(630\) 0 0
\(631\) 30.6529 1.22027 0.610136 0.792296i \(-0.291115\pi\)
0.610136 + 0.792296i \(0.291115\pi\)
\(632\) 0 0
\(633\) −3.14283 −0.124916
\(634\) 0 0
\(635\) −0.830001 −0.0329376
\(636\) 0 0
\(637\) 61.0648 2.41948
\(638\) 0 0
\(639\) 46.8591 1.85372
\(640\) 0 0
\(641\) −38.1552 −1.50704 −0.753521 0.657424i \(-0.771646\pi\)
−0.753521 + 0.657424i \(0.771646\pi\)
\(642\) 0 0
\(643\) 12.8788 0.507890 0.253945 0.967219i \(-0.418272\pi\)
0.253945 + 0.967219i \(0.418272\pi\)
\(644\) 0 0
\(645\) −0.963326 −0.0379309
\(646\) 0 0
\(647\) 35.2593 1.38619 0.693093 0.720849i \(-0.256248\pi\)
0.693093 + 0.720849i \(0.256248\pi\)
\(648\) 0 0
\(649\) −17.7601 −0.697144
\(650\) 0 0
\(651\) 7.92049 0.310428
\(652\) 0 0
\(653\) −31.0639 −1.21563 −0.607813 0.794080i \(-0.707953\pi\)
−0.607813 + 0.794080i \(0.707953\pi\)
\(654\) 0 0
\(655\) 0.475462 0.0185778
\(656\) 0 0
\(657\) −21.1106 −0.823602
\(658\) 0 0
\(659\) −5.31684 −0.207115 −0.103557 0.994623i \(-0.533023\pi\)
−0.103557 + 0.994623i \(0.533023\pi\)
\(660\) 0 0
\(661\) 7.89945 0.307253 0.153627 0.988129i \(-0.450905\pi\)
0.153627 + 0.988129i \(0.450905\pi\)
\(662\) 0 0
\(663\) −68.2821 −2.65186
\(664\) 0 0
\(665\) 2.22285 0.0861985
\(666\) 0 0
\(667\) −18.3283 −0.709676
\(668\) 0 0
\(669\) 20.0565 0.775431
\(670\) 0 0
\(671\) −14.8254 −0.572328
\(672\) 0 0
\(673\) −26.0511 −1.00420 −0.502099 0.864810i \(-0.667439\pi\)
−0.502099 + 0.864810i \(0.667439\pi\)
\(674\) 0 0
\(675\) 8.94240 0.344193
\(676\) 0 0
\(677\) 36.7302 1.41166 0.705829 0.708383i \(-0.250575\pi\)
0.705829 + 0.708383i \(0.250575\pi\)
\(678\) 0 0
\(679\) −17.1443 −0.657936
\(680\) 0 0
\(681\) 46.4311 1.77924
\(682\) 0 0
\(683\) 15.9340 0.609696 0.304848 0.952401i \(-0.401394\pi\)
0.304848 + 0.952401i \(0.401394\pi\)
\(684\) 0 0
\(685\) −1.33673 −0.0510739
\(686\) 0 0
\(687\) −28.9845 −1.10583
\(688\) 0 0
\(689\) 16.7749 0.639073
\(690\) 0 0
\(691\) 29.3833 1.11779 0.558896 0.829237i \(-0.311225\pi\)
0.558896 + 0.829237i \(0.311225\pi\)
\(692\) 0 0
\(693\) −86.5995 −3.28964
\(694\) 0 0
\(695\) 0.120333 0.00456449
\(696\) 0 0
\(697\) −16.0437 −0.607697
\(698\) 0 0
\(699\) −64.3554 −2.43415
\(700\) 0 0
\(701\) 28.0036 1.05768 0.528841 0.848721i \(-0.322627\pi\)
0.528841 + 0.848721i \(0.322627\pi\)
\(702\) 0 0
\(703\) 69.8928 2.63606
\(704\) 0 0
\(705\) 1.26047 0.0474721
\(706\) 0 0
\(707\) 79.7211 2.99822
\(708\) 0 0
\(709\) −22.3354 −0.838824 −0.419412 0.907796i \(-0.637764\pi\)
−0.419412 + 0.907796i \(0.637764\pi\)
\(710\) 0 0
\(711\) 29.0103 1.08797
\(712\) 0 0
\(713\) 2.16443 0.0810585
\(714\) 0 0
\(715\) −2.80075 −0.104742
\(716\) 0 0
\(717\) 5.49351 0.205159
\(718\) 0 0
\(719\) −27.0098 −1.00729 −0.503647 0.863910i \(-0.668009\pi\)
−0.503647 + 0.863910i \(0.668009\pi\)
\(720\) 0 0
\(721\) −62.8462 −2.34051
\(722\) 0 0
\(723\) −51.6323 −1.92023
\(724\) 0 0
\(725\) −30.6848 −1.13960
\(726\) 0 0
\(727\) −14.5021 −0.537853 −0.268926 0.963161i \(-0.586669\pi\)
−0.268926 + 0.963161i \(0.586669\pi\)
\(728\) 0 0
\(729\) −37.6935 −1.39605
\(730\) 0 0
\(731\) 19.5131 0.721716
\(732\) 0 0
\(733\) −53.3408 −1.97019 −0.985094 0.172019i \(-0.944971\pi\)
−0.985094 + 0.172019i \(0.944971\pi\)
\(734\) 0 0
\(735\) −2.48472 −0.0916503
\(736\) 0 0
\(737\) 11.7665 0.433426
\(738\) 0 0
\(739\) −38.1112 −1.40194 −0.700971 0.713190i \(-0.747250\pi\)
−0.700971 + 0.713190i \(0.747250\pi\)
\(740\) 0 0
\(741\) −86.6783 −3.18421
\(742\) 0 0
\(743\) −6.84011 −0.250939 −0.125470 0.992097i \(-0.540044\pi\)
−0.125470 + 0.992097i \(0.540044\pi\)
\(744\) 0 0
\(745\) −0.962303 −0.0352560
\(746\) 0 0
\(747\) −9.96796 −0.364709
\(748\) 0 0
\(749\) −41.7760 −1.52646
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −50.4699 −1.83923
\(754\) 0 0
\(755\) −0.437651 −0.0159278
\(756\) 0 0
\(757\) −0.408020 −0.0148297 −0.00741486 0.999973i \(-0.502360\pi\)
−0.00741486 + 0.999973i \(0.502360\pi\)
\(758\) 0 0
\(759\) −42.8922 −1.55689
\(760\) 0 0
\(761\) 4.96730 0.180065 0.0900323 0.995939i \(-0.471303\pi\)
0.0900323 + 0.995939i \(0.471303\pi\)
\(762\) 0 0
\(763\) −67.5729 −2.44630
\(764\) 0 0
\(765\) 1.53293 0.0554232
\(766\) 0 0
\(767\) 18.0750 0.652650
\(768\) 0 0
\(769\) −49.6772 −1.79141 −0.895703 0.444654i \(-0.853327\pi\)
−0.895703 + 0.444654i \(0.853327\pi\)
\(770\) 0 0
\(771\) −21.2307 −0.764605
\(772\) 0 0
\(773\) −17.0274 −0.612434 −0.306217 0.951962i \(-0.599063\pi\)
−0.306217 + 0.951962i \(0.599063\pi\)
\(774\) 0 0
\(775\) 3.62363 0.130165
\(776\) 0 0
\(777\) −128.808 −4.62095
\(778\) 0 0
\(779\) −20.3661 −0.729691
\(780\) 0 0
\(781\) −70.5644 −2.52499
\(782\) 0 0
\(783\) −11.0107 −0.393490
\(784\) 0 0
\(785\) 1.85841 0.0663295
\(786\) 0 0
\(787\) −47.6401 −1.69819 −0.849094 0.528242i \(-0.822851\pi\)
−0.849094 + 0.528242i \(0.822851\pi\)
\(788\) 0 0
\(789\) −32.4638 −1.15574
\(790\) 0 0
\(791\) 34.5009 1.22671
\(792\) 0 0
\(793\) 15.0883 0.535800
\(794\) 0 0
\(795\) −0.682570 −0.0242083
\(796\) 0 0
\(797\) 12.1881 0.431724 0.215862 0.976424i \(-0.430744\pi\)
0.215862 + 0.976424i \(0.430744\pi\)
\(798\) 0 0
\(799\) −25.5320 −0.903258
\(800\) 0 0
\(801\) −45.5802 −1.61050
\(802\) 0 0
\(803\) 31.7901 1.12185
\(804\) 0 0
\(805\) −1.11947 −0.0394560
\(806\) 0 0
\(807\) 55.3657 1.94897
\(808\) 0 0
\(809\) −11.2380 −0.395105 −0.197553 0.980292i \(-0.563299\pi\)
−0.197553 + 0.980292i \(0.563299\pi\)
\(810\) 0 0
\(811\) −21.0646 −0.739679 −0.369840 0.929096i \(-0.620587\pi\)
−0.369840 + 0.929096i \(0.620587\pi\)
\(812\) 0 0
\(813\) 77.7600 2.72716
\(814\) 0 0
\(815\) −0.159465 −0.00558581
\(816\) 0 0
\(817\) 24.7702 0.866599
\(818\) 0 0
\(819\) 88.1350 3.07969
\(820\) 0 0
\(821\) −34.1236 −1.19092 −0.595460 0.803385i \(-0.703030\pi\)
−0.595460 + 0.803385i \(0.703030\pi\)
\(822\) 0 0
\(823\) 40.9583 1.42772 0.713858 0.700290i \(-0.246946\pi\)
0.713858 + 0.700290i \(0.246946\pi\)
\(824\) 0 0
\(825\) −71.8089 −2.50007
\(826\) 0 0
\(827\) −39.1072 −1.35989 −0.679945 0.733263i \(-0.737997\pi\)
−0.679945 + 0.733263i \(0.737997\pi\)
\(828\) 0 0
\(829\) 2.04428 0.0710008 0.0355004 0.999370i \(-0.488698\pi\)
0.0355004 + 0.999370i \(0.488698\pi\)
\(830\) 0 0
\(831\) 5.83701 0.202484
\(832\) 0 0
\(833\) 50.3303 1.74384
\(834\) 0 0
\(835\) −0.957270 −0.0331277
\(836\) 0 0
\(837\) 1.30027 0.0449440
\(838\) 0 0
\(839\) −19.4503 −0.671500 −0.335750 0.941951i \(-0.608990\pi\)
−0.335750 + 0.941951i \(0.608990\pi\)
\(840\) 0 0
\(841\) 8.78189 0.302824
\(842\) 0 0
\(843\) −60.5720 −2.08621
\(844\) 0 0
\(845\) 1.69330 0.0582513
\(846\) 0 0
\(847\) 84.0119 2.88668
\(848\) 0 0
\(849\) −12.6679 −0.434761
\(850\) 0 0
\(851\) −35.1992 −1.20661
\(852\) 0 0
\(853\) −6.54966 −0.224256 −0.112128 0.993694i \(-0.535767\pi\)
−0.112128 + 0.993694i \(0.535767\pi\)
\(854\) 0 0
\(855\) 1.94592 0.0665492
\(856\) 0 0
\(857\) 1.39320 0.0475908 0.0237954 0.999717i \(-0.492425\pi\)
0.0237954 + 0.999717i \(0.492425\pi\)
\(858\) 0 0
\(859\) −33.8037 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(860\) 0 0
\(861\) 37.5333 1.27913
\(862\) 0 0
\(863\) 0.551415 0.0187704 0.00938520 0.999956i \(-0.497013\pi\)
0.00938520 + 0.999956i \(0.497013\pi\)
\(864\) 0 0
\(865\) −1.70004 −0.0578030
\(866\) 0 0
\(867\) −12.3003 −0.417740
\(868\) 0 0
\(869\) −43.6861 −1.48195
\(870\) 0 0
\(871\) −11.9752 −0.405764
\(872\) 0 0
\(873\) −15.0084 −0.507957
\(874\) 0 0
\(875\) −3.75133 −0.126818
\(876\) 0 0
\(877\) −18.0494 −0.609486 −0.304743 0.952435i \(-0.598571\pi\)
−0.304743 + 0.952435i \(0.598571\pi\)
\(878\) 0 0
\(879\) 80.0645 2.70051
\(880\) 0 0
\(881\) 7.82956 0.263785 0.131892 0.991264i \(-0.457895\pi\)
0.131892 + 0.991264i \(0.457895\pi\)
\(882\) 0 0
\(883\) −1.21190 −0.0407836 −0.0203918 0.999792i \(-0.506491\pi\)
−0.0203918 + 0.999792i \(0.506491\pi\)
\(884\) 0 0
\(885\) −0.735469 −0.0247225
\(886\) 0 0
\(887\) −6.09078 −0.204508 −0.102254 0.994758i \(-0.532605\pi\)
−0.102254 + 0.994758i \(0.532605\pi\)
\(888\) 0 0
\(889\) −39.3318 −1.31915
\(890\) 0 0
\(891\) 35.8268 1.20024
\(892\) 0 0
\(893\) −32.4108 −1.08458
\(894\) 0 0
\(895\) −1.51011 −0.0504775
\(896\) 0 0
\(897\) 43.6527 1.45752
\(898\) 0 0
\(899\) −4.46174 −0.148807
\(900\) 0 0
\(901\) 13.8261 0.460614
\(902\) 0 0
\(903\) −45.6498 −1.51913
\(904\) 0 0
\(905\) 0.785510 0.0261112
\(906\) 0 0
\(907\) −17.1667 −0.570012 −0.285006 0.958526i \(-0.591996\pi\)
−0.285006 + 0.958526i \(0.591996\pi\)
\(908\) 0 0
\(909\) 69.7893 2.31476
\(910\) 0 0
\(911\) 14.3889 0.476725 0.238363 0.971176i \(-0.423389\pi\)
0.238363 + 0.971176i \(0.423389\pi\)
\(912\) 0 0
\(913\) 15.0106 0.496778
\(914\) 0 0
\(915\) −0.613940 −0.0202962
\(916\) 0 0
\(917\) 22.5310 0.744040
\(918\) 0 0
\(919\) 43.1639 1.42384 0.711922 0.702258i \(-0.247825\pi\)
0.711922 + 0.702258i \(0.247825\pi\)
\(920\) 0 0
\(921\) −60.0997 −1.98035
\(922\) 0 0
\(923\) 71.8155 2.36384
\(924\) 0 0
\(925\) −58.9296 −1.93759
\(926\) 0 0
\(927\) −55.0167 −1.80698
\(928\) 0 0
\(929\) −7.22440 −0.237025 −0.118512 0.992953i \(-0.537813\pi\)
−0.118512 + 0.992953i \(0.537813\pi\)
\(930\) 0 0
\(931\) 63.8901 2.09391
\(932\) 0 0
\(933\) 56.5570 1.85159
\(934\) 0 0
\(935\) −2.30841 −0.0754932
\(936\) 0 0
\(937\) −40.6497 −1.32797 −0.663984 0.747747i \(-0.731136\pi\)
−0.663984 + 0.747747i \(0.731136\pi\)
\(938\) 0 0
\(939\) 34.3431 1.12074
\(940\) 0 0
\(941\) −14.8638 −0.484547 −0.242274 0.970208i \(-0.577893\pi\)
−0.242274 + 0.970208i \(0.577893\pi\)
\(942\) 0 0
\(943\) 10.2567 0.334005
\(944\) 0 0
\(945\) −0.672516 −0.0218769
\(946\) 0 0
\(947\) −32.4110 −1.05322 −0.526608 0.850109i \(-0.676536\pi\)
−0.526608 + 0.850109i \(0.676536\pi\)
\(948\) 0 0
\(949\) −32.3538 −1.05025
\(950\) 0 0
\(951\) −64.7759 −2.10050
\(952\) 0 0
\(953\) 40.2154 1.30270 0.651352 0.758776i \(-0.274202\pi\)
0.651352 + 0.758776i \(0.274202\pi\)
\(954\) 0 0
\(955\) 1.25482 0.0406049
\(956\) 0 0
\(957\) 88.4176 2.85814
\(958\) 0 0
\(959\) −63.3446 −2.04551
\(960\) 0 0
\(961\) −30.4731 −0.983003
\(962\) 0 0
\(963\) −36.5715 −1.17850
\(964\) 0 0
\(965\) 1.08943 0.0350701
\(966\) 0 0
\(967\) 48.2295 1.55096 0.775478 0.631374i \(-0.217509\pi\)
0.775478 + 0.631374i \(0.217509\pi\)
\(968\) 0 0
\(969\) −71.4413 −2.29502
\(970\) 0 0
\(971\) −11.2576 −0.361272 −0.180636 0.983550i \(-0.557816\pi\)
−0.180636 + 0.983550i \(0.557816\pi\)
\(972\) 0 0
\(973\) 5.70230 0.182807
\(974\) 0 0
\(975\) 73.0821 2.34050
\(976\) 0 0
\(977\) 27.2631 0.872223 0.436111 0.899893i \(-0.356355\pi\)
0.436111 + 0.899893i \(0.356355\pi\)
\(978\) 0 0
\(979\) 68.6385 2.19369
\(980\) 0 0
\(981\) −59.1546 −1.88866
\(982\) 0 0
\(983\) 13.0263 0.415475 0.207737 0.978185i \(-0.433390\pi\)
0.207737 + 0.978185i \(0.433390\pi\)
\(984\) 0 0
\(985\) 1.54013 0.0490728
\(986\) 0 0
\(987\) 59.7308 1.90125
\(988\) 0 0
\(989\) −12.4747 −0.396672
\(990\) 0 0
\(991\) 51.8539 1.64719 0.823597 0.567175i \(-0.191964\pi\)
0.823597 + 0.567175i \(0.191964\pi\)
\(992\) 0 0
\(993\) −46.3210 −1.46995
\(994\) 0 0
\(995\) 0.709718 0.0224996
\(996\) 0 0
\(997\) −22.0678 −0.698895 −0.349448 0.936956i \(-0.613631\pi\)
−0.349448 + 0.936956i \(0.613631\pi\)
\(998\) 0 0
\(999\) −21.1458 −0.669024
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 \(a_p\))