Properties

Label 4028.2.a.d.1.8
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.01911\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.01911 q^{3} +3.39604 q^{5} -2.78127 q^{7} -1.96142 q^{9} +O(q^{10})\) \(q-1.01911 q^{3} +3.39604 q^{5} -2.78127 q^{7} -1.96142 q^{9} +1.42621 q^{11} -5.82753 q^{13} -3.46093 q^{15} +0.730044 q^{17} -1.00000 q^{19} +2.83442 q^{21} +2.62707 q^{23} +6.53310 q^{25} +5.05622 q^{27} +9.98145 q^{29} +8.88856 q^{31} -1.45346 q^{33} -9.44531 q^{35} -1.61419 q^{37} +5.93889 q^{39} +0.419992 q^{41} -9.18535 q^{43} -6.66106 q^{45} -7.19973 q^{47} +0.735466 q^{49} -0.743994 q^{51} +1.00000 q^{53} +4.84346 q^{55} +1.01911 q^{57} -11.5341 q^{59} +0.616251 q^{61} +5.45523 q^{63} -19.7905 q^{65} -12.1943 q^{67} -2.67727 q^{69} -8.09796 q^{71} +1.60322 q^{73} -6.65794 q^{75} -3.96667 q^{77} -3.28668 q^{79} +0.731414 q^{81} -13.0549 q^{83} +2.47926 q^{85} -10.1722 q^{87} +1.73855 q^{89} +16.2079 q^{91} -9.05841 q^{93} -3.39604 q^{95} -12.9515 q^{97} -2.79739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) −1.01911 −0.588383 −0.294191 0.955747i \(-0.595050\pi\)
−0.294191 + 0.955747i \(0.595050\pi\)
\(4\) 0 0
\(5\) 3.39604 1.51876 0.759378 0.650650i \(-0.225503\pi\)
0.759378 + 0.650650i \(0.225503\pi\)
\(6\) 0 0
\(7\) −2.78127 −1.05122 −0.525611 0.850725i \(-0.676163\pi\)
−0.525611 + 0.850725i \(0.676163\pi\)
\(8\) 0 0
\(9\) −1.96142 −0.653806
\(10\) 0 0
\(11\) 1.42621 0.430018 0.215009 0.976612i \(-0.431022\pi\)
0.215009 + 0.976612i \(0.431022\pi\)
\(12\) 0 0
\(13\) −5.82753 −1.61627 −0.808133 0.589000i \(-0.799522\pi\)
−0.808133 + 0.589000i \(0.799522\pi\)
\(14\) 0 0
\(15\) −3.46093 −0.893610
\(16\) 0 0
\(17\) 0.730044 0.177062 0.0885308 0.996073i \(-0.471783\pi\)
0.0885308 + 0.996073i \(0.471783\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.83442 0.618520
\(22\) 0 0
\(23\) 2.62707 0.547782 0.273891 0.961761i \(-0.411689\pi\)
0.273891 + 0.961761i \(0.411689\pi\)
\(24\) 0 0
\(25\) 6.53310 1.30662
\(26\) 0 0
\(27\) 5.05622 0.973071
\(28\) 0 0
\(29\) 9.98145 1.85351 0.926754 0.375669i \(-0.122587\pi\)
0.926754 + 0.375669i \(0.122587\pi\)
\(30\) 0 0
\(31\) 8.88856 1.59643 0.798217 0.602371i \(-0.205777\pi\)
0.798217 + 0.602371i \(0.205777\pi\)
\(32\) 0 0
\(33\) −1.45346 −0.253015
\(34\) 0 0
\(35\) −9.44531 −1.59655
\(36\) 0 0
\(37\) −1.61419 −0.265370 −0.132685 0.991158i \(-0.542360\pi\)
−0.132685 + 0.991158i \(0.542360\pi\)
\(38\) 0 0
\(39\) 5.93889 0.950983
\(40\) 0 0
\(41\) 0.419992 0.0655917 0.0327959 0.999462i \(-0.489559\pi\)
0.0327959 + 0.999462i \(0.489559\pi\)
\(42\) 0 0
\(43\) −9.18535 −1.40075 −0.700376 0.713774i \(-0.746984\pi\)
−0.700376 + 0.713774i \(0.746984\pi\)
\(44\) 0 0
\(45\) −6.66106 −0.992972
\(46\) 0 0
\(47\) −7.19973 −1.05019 −0.525094 0.851044i \(-0.675970\pi\)
−0.525094 + 0.851044i \(0.675970\pi\)
\(48\) 0 0
\(49\) 0.735466 0.105067
\(50\) 0 0
\(51\) −0.743994 −0.104180
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 4.84346 0.653092
\(56\) 0 0
\(57\) 1.01911 0.134984
\(58\) 0 0
\(59\) −11.5341 −1.50161 −0.750806 0.660522i \(-0.770335\pi\)
−0.750806 + 0.660522i \(0.770335\pi\)
\(60\) 0 0
\(61\) 0.616251 0.0789029 0.0394514 0.999221i \(-0.487439\pi\)
0.0394514 + 0.999221i \(0.487439\pi\)
\(62\) 0 0
\(63\) 5.45523 0.687295
\(64\) 0 0
\(65\) −19.7905 −2.45471
\(66\) 0 0
\(67\) −12.1943 −1.48978 −0.744888 0.667189i \(-0.767497\pi\)
−0.744888 + 0.667189i \(0.767497\pi\)
\(68\) 0 0
\(69\) −2.67727 −0.322306
\(70\) 0 0
\(71\) −8.09796 −0.961051 −0.480525 0.876981i \(-0.659554\pi\)
−0.480525 + 0.876981i \(0.659554\pi\)
\(72\) 0 0
\(73\) 1.60322 0.187643 0.0938216 0.995589i \(-0.470092\pi\)
0.0938216 + 0.995589i \(0.470092\pi\)
\(74\) 0 0
\(75\) −6.65794 −0.768792
\(76\) 0 0
\(77\) −3.96667 −0.452044
\(78\) 0 0
\(79\) −3.28668 −0.369781 −0.184890 0.982759i \(-0.559193\pi\)
−0.184890 + 0.982759i \(0.559193\pi\)
\(80\) 0 0
\(81\) 0.731414 0.0812683
\(82\) 0 0
\(83\) −13.0549 −1.43296 −0.716482 0.697606i \(-0.754249\pi\)
−0.716482 + 0.697606i \(0.754249\pi\)
\(84\) 0 0
\(85\) 2.47926 0.268913
\(86\) 0 0
\(87\) −10.1722 −1.09057
\(88\) 0 0
\(89\) 1.73855 0.184286 0.0921428 0.995746i \(-0.470628\pi\)
0.0921428 + 0.995746i \(0.470628\pi\)
\(90\) 0 0
\(91\) 16.2079 1.69905
\(92\) 0 0
\(93\) −9.05841 −0.939313
\(94\) 0 0
\(95\) −3.39604 −0.348427
\(96\) 0 0
\(97\) −12.9515 −1.31503 −0.657514 0.753442i \(-0.728392\pi\)
−0.657514 + 0.753442i \(0.728392\pi\)
\(98\) 0 0
\(99\) −2.79739 −0.281148
\(100\) 0 0
\(101\) 0.977436 0.0972585 0.0486292 0.998817i \(-0.484515\pi\)
0.0486292 + 0.998817i \(0.484515\pi\)
\(102\) 0 0
\(103\) −0.0403488 −0.00397568 −0.00198784 0.999998i \(-0.500633\pi\)
−0.00198784 + 0.999998i \(0.500633\pi\)
\(104\) 0 0
\(105\) 9.62580 0.939382
\(106\) 0 0
\(107\) −12.4248 −1.20115 −0.600576 0.799568i \(-0.705062\pi\)
−0.600576 + 0.799568i \(0.705062\pi\)
\(108\) 0 0
\(109\) 19.3523 1.85362 0.926809 0.375534i \(-0.122541\pi\)
0.926809 + 0.375534i \(0.122541\pi\)
\(110\) 0 0
\(111\) 1.64503 0.156139
\(112\) 0 0
\(113\) −14.3330 −1.34834 −0.674168 0.738578i \(-0.735498\pi\)
−0.674168 + 0.738578i \(0.735498\pi\)
\(114\) 0 0
\(115\) 8.92164 0.831948
\(116\) 0 0
\(117\) 11.4302 1.05672
\(118\) 0 0
\(119\) −2.03045 −0.186131
\(120\) 0 0
\(121\) −8.96593 −0.815085
\(122\) 0 0
\(123\) −0.428017 −0.0385930
\(124\) 0 0
\(125\) 5.20647 0.465681
\(126\) 0 0
\(127\) −18.8326 −1.67112 −0.835562 0.549395i \(-0.814858\pi\)
−0.835562 + 0.549395i \(0.814858\pi\)
\(128\) 0 0
\(129\) 9.36086 0.824178
\(130\) 0 0
\(131\) −6.91591 −0.604246 −0.302123 0.953269i \(-0.597695\pi\)
−0.302123 + 0.953269i \(0.597695\pi\)
\(132\) 0 0
\(133\) 2.78127 0.241167
\(134\) 0 0
\(135\) 17.1711 1.47786
\(136\) 0 0
\(137\) 11.4324 0.976733 0.488366 0.872639i \(-0.337593\pi\)
0.488366 + 0.872639i \(0.337593\pi\)
\(138\) 0 0
\(139\) −4.18394 −0.354877 −0.177439 0.984132i \(-0.556781\pi\)
−0.177439 + 0.984132i \(0.556781\pi\)
\(140\) 0 0
\(141\) 7.33730 0.617912
\(142\) 0 0
\(143\) −8.31127 −0.695023
\(144\) 0 0
\(145\) 33.8974 2.81503
\(146\) 0 0
\(147\) −0.749520 −0.0618193
\(148\) 0 0
\(149\) −12.9467 −1.06063 −0.530315 0.847800i \(-0.677927\pi\)
−0.530315 + 0.847800i \(0.677927\pi\)
\(150\) 0 0
\(151\) 20.5029 1.66850 0.834251 0.551384i \(-0.185900\pi\)
0.834251 + 0.551384i \(0.185900\pi\)
\(152\) 0 0
\(153\) −1.43192 −0.115764
\(154\) 0 0
\(155\) 30.1859 2.42459
\(156\) 0 0
\(157\) −19.3543 −1.54464 −0.772320 0.635233i \(-0.780904\pi\)
−0.772320 + 0.635233i \(0.780904\pi\)
\(158\) 0 0
\(159\) −1.01911 −0.0808206
\(160\) 0 0
\(161\) −7.30660 −0.575840
\(162\) 0 0
\(163\) 16.8234 1.31771 0.658855 0.752270i \(-0.271041\pi\)
0.658855 + 0.752270i \(0.271041\pi\)
\(164\) 0 0
\(165\) −4.93601 −0.384268
\(166\) 0 0
\(167\) −5.34045 −0.413256 −0.206628 0.978420i \(-0.566249\pi\)
−0.206628 + 0.978420i \(0.566249\pi\)
\(168\) 0 0
\(169\) 20.9601 1.61232
\(170\) 0 0
\(171\) 1.96142 0.149993
\(172\) 0 0
\(173\) 21.5842 1.64102 0.820509 0.571634i \(-0.193690\pi\)
0.820509 + 0.571634i \(0.193690\pi\)
\(174\) 0 0
\(175\) −18.1703 −1.37355
\(176\) 0 0
\(177\) 11.7545 0.883523
\(178\) 0 0
\(179\) −21.7623 −1.62659 −0.813297 0.581849i \(-0.802329\pi\)
−0.813297 + 0.581849i \(0.802329\pi\)
\(180\) 0 0
\(181\) −13.4511 −0.999816 −0.499908 0.866079i \(-0.666633\pi\)
−0.499908 + 0.866079i \(0.666633\pi\)
\(182\) 0 0
\(183\) −0.628027 −0.0464251
\(184\) 0 0
\(185\) −5.48184 −0.403033
\(186\) 0 0
\(187\) 1.04119 0.0761396
\(188\) 0 0
\(189\) −14.0627 −1.02291
\(190\) 0 0
\(191\) −14.5835 −1.05523 −0.527614 0.849484i \(-0.676913\pi\)
−0.527614 + 0.849484i \(0.676913\pi\)
\(192\) 0 0
\(193\) 15.0472 1.08312 0.541562 0.840661i \(-0.317833\pi\)
0.541562 + 0.840661i \(0.317833\pi\)
\(194\) 0 0
\(195\) 20.1687 1.44431
\(196\) 0 0
\(197\) −8.55539 −0.609547 −0.304773 0.952425i \(-0.598581\pi\)
−0.304773 + 0.952425i \(0.598581\pi\)
\(198\) 0 0
\(199\) −3.84835 −0.272802 −0.136401 0.990654i \(-0.543554\pi\)
−0.136401 + 0.990654i \(0.543554\pi\)
\(200\) 0 0
\(201\) 12.4274 0.876558
\(202\) 0 0
\(203\) −27.7611 −1.94845
\(204\) 0 0
\(205\) 1.42631 0.0996178
\(206\) 0 0
\(207\) −5.15279 −0.358143
\(208\) 0 0
\(209\) −1.42621 −0.0986528
\(210\) 0 0
\(211\) −12.3323 −0.848990 −0.424495 0.905430i \(-0.639548\pi\)
−0.424495 + 0.905430i \(0.639548\pi\)
\(212\) 0 0
\(213\) 8.25270 0.565465
\(214\) 0 0
\(215\) −31.1938 −2.12740
\(216\) 0 0
\(217\) −24.7215 −1.67820
\(218\) 0 0
\(219\) −1.63386 −0.110406
\(220\) 0 0
\(221\) −4.25435 −0.286179
\(222\) 0 0
\(223\) −16.3464 −1.09464 −0.547318 0.836925i \(-0.684351\pi\)
−0.547318 + 0.836925i \(0.684351\pi\)
\(224\) 0 0
\(225\) −12.8141 −0.854276
\(226\) 0 0
\(227\) 13.2943 0.882374 0.441187 0.897415i \(-0.354558\pi\)
0.441187 + 0.897415i \(0.354558\pi\)
\(228\) 0 0
\(229\) 21.9953 1.45349 0.726747 0.686905i \(-0.241031\pi\)
0.726747 + 0.686905i \(0.241031\pi\)
\(230\) 0 0
\(231\) 4.04246 0.265975
\(232\) 0 0
\(233\) 8.43894 0.552853 0.276427 0.961035i \(-0.410850\pi\)
0.276427 + 0.961035i \(0.410850\pi\)
\(234\) 0 0
\(235\) −24.4506 −1.59498
\(236\) 0 0
\(237\) 3.34949 0.217573
\(238\) 0 0
\(239\) −26.2390 −1.69726 −0.848631 0.528985i \(-0.822573\pi\)
−0.848631 + 0.528985i \(0.822573\pi\)
\(240\) 0 0
\(241\) 2.68226 0.172780 0.0863898 0.996261i \(-0.472467\pi\)
0.0863898 + 0.996261i \(0.472467\pi\)
\(242\) 0 0
\(243\) −15.9141 −1.02089
\(244\) 0 0
\(245\) 2.49767 0.159571
\(246\) 0 0
\(247\) 5.82753 0.370797
\(248\) 0 0
\(249\) 13.3044 0.843131
\(250\) 0 0
\(251\) 1.61739 0.102089 0.0510443 0.998696i \(-0.483745\pi\)
0.0510443 + 0.998696i \(0.483745\pi\)
\(252\) 0 0
\(253\) 3.74675 0.235556
\(254\) 0 0
\(255\) −2.52663 −0.158224
\(256\) 0 0
\(257\) −8.49474 −0.529887 −0.264944 0.964264i \(-0.585353\pi\)
−0.264944 + 0.964264i \(0.585353\pi\)
\(258\) 0 0
\(259\) 4.48949 0.278963
\(260\) 0 0
\(261\) −19.5778 −1.21183
\(262\) 0 0
\(263\) 14.0296 0.865102 0.432551 0.901609i \(-0.357614\pi\)
0.432551 + 0.901609i \(0.357614\pi\)
\(264\) 0 0
\(265\) 3.39604 0.208617
\(266\) 0 0
\(267\) −1.77177 −0.108430
\(268\) 0 0
\(269\) 20.2241 1.23309 0.616544 0.787321i \(-0.288532\pi\)
0.616544 + 0.787321i \(0.288532\pi\)
\(270\) 0 0
\(271\) 4.56823 0.277500 0.138750 0.990327i \(-0.455692\pi\)
0.138750 + 0.990327i \(0.455692\pi\)
\(272\) 0 0
\(273\) −16.5177 −0.999694
\(274\) 0 0
\(275\) 9.31755 0.561870
\(276\) 0 0
\(277\) −20.9886 −1.26108 −0.630542 0.776155i \(-0.717167\pi\)
−0.630542 + 0.776155i \(0.717167\pi\)
\(278\) 0 0
\(279\) −17.4342 −1.04376
\(280\) 0 0
\(281\) −7.48708 −0.446642 −0.223321 0.974745i \(-0.571690\pi\)
−0.223321 + 0.974745i \(0.571690\pi\)
\(282\) 0 0
\(283\) 25.8026 1.53381 0.766903 0.641763i \(-0.221797\pi\)
0.766903 + 0.641763i \(0.221797\pi\)
\(284\) 0 0
\(285\) 3.46093 0.205008
\(286\) 0 0
\(287\) −1.16811 −0.0689514
\(288\) 0 0
\(289\) −16.4670 −0.968649
\(290\) 0 0
\(291\) 13.1990 0.773739
\(292\) 0 0
\(293\) 21.4452 1.25284 0.626420 0.779486i \(-0.284519\pi\)
0.626420 + 0.779486i \(0.284519\pi\)
\(294\) 0 0
\(295\) −39.1703 −2.28058
\(296\) 0 0
\(297\) 7.21122 0.418438
\(298\) 0 0
\(299\) −15.3093 −0.885362
\(300\) 0 0
\(301\) 25.5469 1.47250
\(302\) 0 0
\(303\) −0.996113 −0.0572252
\(304\) 0 0
\(305\) 2.09282 0.119834
\(306\) 0 0
\(307\) 17.7094 1.01073 0.505366 0.862905i \(-0.331358\pi\)
0.505366 + 0.862905i \(0.331358\pi\)
\(308\) 0 0
\(309\) 0.0411198 0.00233922
\(310\) 0 0
\(311\) 0.565422 0.0320622 0.0160311 0.999871i \(-0.494897\pi\)
0.0160311 + 0.999871i \(0.494897\pi\)
\(312\) 0 0
\(313\) −11.9488 −0.675389 −0.337694 0.941256i \(-0.609647\pi\)
−0.337694 + 0.941256i \(0.609647\pi\)
\(314\) 0 0
\(315\) 18.5262 1.04383
\(316\) 0 0
\(317\) 21.0263 1.18095 0.590477 0.807054i \(-0.298940\pi\)
0.590477 + 0.807054i \(0.298940\pi\)
\(318\) 0 0
\(319\) 14.2356 0.797041
\(320\) 0 0
\(321\) 12.6622 0.706737
\(322\) 0 0
\(323\) −0.730044 −0.0406207
\(324\) 0 0
\(325\) −38.0718 −2.11185
\(326\) 0 0
\(327\) −19.7221 −1.09064
\(328\) 0 0
\(329\) 20.0244 1.10398
\(330\) 0 0
\(331\) 9.00189 0.494788 0.247394 0.968915i \(-0.420426\pi\)
0.247394 + 0.968915i \(0.420426\pi\)
\(332\) 0 0
\(333\) 3.16609 0.173501
\(334\) 0 0
\(335\) −41.4125 −2.26261
\(336\) 0 0
\(337\) 30.7720 1.67626 0.838129 0.545473i \(-0.183650\pi\)
0.838129 + 0.545473i \(0.183650\pi\)
\(338\) 0 0
\(339\) 14.6069 0.793337
\(340\) 0 0
\(341\) 12.6769 0.686494
\(342\) 0 0
\(343\) 17.4234 0.940773
\(344\) 0 0
\(345\) −9.09212 −0.489503
\(346\) 0 0
\(347\) −25.4367 −1.36551 −0.682757 0.730646i \(-0.739219\pi\)
−0.682757 + 0.730646i \(0.739219\pi\)
\(348\) 0 0
\(349\) −5.58602 −0.299013 −0.149506 0.988761i \(-0.547768\pi\)
−0.149506 + 0.988761i \(0.547768\pi\)
\(350\) 0 0
\(351\) −29.4653 −1.57274
\(352\) 0 0
\(353\) −5.47919 −0.291628 −0.145814 0.989312i \(-0.546580\pi\)
−0.145814 + 0.989312i \(0.546580\pi\)
\(354\) 0 0
\(355\) −27.5010 −1.45960
\(356\) 0 0
\(357\) 2.06925 0.109516
\(358\) 0 0
\(359\) −17.0132 −0.897921 −0.448960 0.893552i \(-0.648206\pi\)
−0.448960 + 0.893552i \(0.648206\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 9.13726 0.479582
\(364\) 0 0
\(365\) 5.44462 0.284984
\(366\) 0 0
\(367\) −9.20559 −0.480528 −0.240264 0.970708i \(-0.577234\pi\)
−0.240264 + 0.970708i \(0.577234\pi\)
\(368\) 0 0
\(369\) −0.823780 −0.0428843
\(370\) 0 0
\(371\) −2.78127 −0.144396
\(372\) 0 0
\(373\) 6.86681 0.355550 0.177775 0.984071i \(-0.443110\pi\)
0.177775 + 0.984071i \(0.443110\pi\)
\(374\) 0 0
\(375\) −5.30596 −0.273998
\(376\) 0 0
\(377\) −58.1672 −2.99576
\(378\) 0 0
\(379\) 20.2855 1.04200 0.520998 0.853558i \(-0.325560\pi\)
0.520998 + 0.853558i \(0.325560\pi\)
\(380\) 0 0
\(381\) 19.1925 0.983261
\(382\) 0 0
\(383\) 4.26966 0.218169 0.109085 0.994032i \(-0.465208\pi\)
0.109085 + 0.994032i \(0.465208\pi\)
\(384\) 0 0
\(385\) −13.4710 −0.686544
\(386\) 0 0
\(387\) 18.0163 0.915820
\(388\) 0 0
\(389\) 2.56158 0.129877 0.0649386 0.997889i \(-0.479315\pi\)
0.0649386 + 0.997889i \(0.479315\pi\)
\(390\) 0 0
\(391\) 1.91788 0.0969912
\(392\) 0 0
\(393\) 7.04806 0.355528
\(394\) 0 0
\(395\) −11.1617 −0.561607
\(396\) 0 0
\(397\) −26.6743 −1.33875 −0.669373 0.742926i \(-0.733437\pi\)
−0.669373 + 0.742926i \(0.733437\pi\)
\(398\) 0 0
\(399\) −2.83442 −0.141898
\(400\) 0 0
\(401\) −1.32390 −0.0661122 −0.0330561 0.999453i \(-0.510524\pi\)
−0.0330561 + 0.999453i \(0.510524\pi\)
\(402\) 0 0
\(403\) −51.7984 −2.58026
\(404\) 0 0
\(405\) 2.48391 0.123427
\(406\) 0 0
\(407\) −2.30216 −0.114114
\(408\) 0 0
\(409\) 20.5225 1.01477 0.507385 0.861719i \(-0.330612\pi\)
0.507385 + 0.861719i \(0.330612\pi\)
\(410\) 0 0
\(411\) −11.6508 −0.574692
\(412\) 0 0
\(413\) 32.0795 1.57853
\(414\) 0 0
\(415\) −44.3351 −2.17632
\(416\) 0 0
\(417\) 4.26389 0.208804
\(418\) 0 0
\(419\) 12.6355 0.617283 0.308642 0.951178i \(-0.400126\pi\)
0.308642 + 0.951178i \(0.400126\pi\)
\(420\) 0 0
\(421\) 32.4459 1.58131 0.790657 0.612259i \(-0.209739\pi\)
0.790657 + 0.612259i \(0.209739\pi\)
\(422\) 0 0
\(423\) 14.1217 0.686619
\(424\) 0 0
\(425\) 4.76945 0.231352
\(426\) 0 0
\(427\) −1.71396 −0.0829444
\(428\) 0 0
\(429\) 8.47008 0.408939
\(430\) 0 0
\(431\) 19.8630 0.956767 0.478384 0.878151i \(-0.341223\pi\)
0.478384 + 0.878151i \(0.341223\pi\)
\(432\) 0 0
\(433\) −6.54023 −0.314304 −0.157152 0.987574i \(-0.550231\pi\)
−0.157152 + 0.987574i \(0.550231\pi\)
\(434\) 0 0
\(435\) −34.5451 −1.65631
\(436\) 0 0
\(437\) −2.62707 −0.125670
\(438\) 0 0
\(439\) 19.8488 0.947332 0.473666 0.880705i \(-0.342930\pi\)
0.473666 + 0.880705i \(0.342930\pi\)
\(440\) 0 0
\(441\) −1.44256 −0.0686932
\(442\) 0 0
\(443\) −18.0623 −0.858165 −0.429083 0.903265i \(-0.641163\pi\)
−0.429083 + 0.903265i \(0.641163\pi\)
\(444\) 0 0
\(445\) 5.90418 0.279885
\(446\) 0 0
\(447\) 13.1940 0.624057
\(448\) 0 0
\(449\) −41.5384 −1.96032 −0.980159 0.198215i \(-0.936486\pi\)
−0.980159 + 0.198215i \(0.936486\pi\)
\(450\) 0 0
\(451\) 0.598996 0.0282056
\(452\) 0 0
\(453\) −20.8947 −0.981718
\(454\) 0 0
\(455\) 55.0428 2.58045
\(456\) 0 0
\(457\) 5.17840 0.242235 0.121118 0.992638i \(-0.461352\pi\)
0.121118 + 0.992638i \(0.461352\pi\)
\(458\) 0 0
\(459\) 3.69126 0.172293
\(460\) 0 0
\(461\) −29.3335 −1.36620 −0.683099 0.730326i \(-0.739368\pi\)
−0.683099 + 0.730326i \(0.739368\pi\)
\(462\) 0 0
\(463\) 4.72241 0.219469 0.109735 0.993961i \(-0.465000\pi\)
0.109735 + 0.993961i \(0.465000\pi\)
\(464\) 0 0
\(465\) −30.7627 −1.42659
\(466\) 0 0
\(467\) 35.6441 1.64941 0.824705 0.565563i \(-0.191341\pi\)
0.824705 + 0.565563i \(0.191341\pi\)
\(468\) 0 0
\(469\) 33.9158 1.56608
\(470\) 0 0
\(471\) 19.7241 0.908840
\(472\) 0 0
\(473\) −13.1002 −0.602348
\(474\) 0 0
\(475\) −6.53310 −0.299759
\(476\) 0 0
\(477\) −1.96142 −0.0898072
\(478\) 0 0
\(479\) −11.3863 −0.520252 −0.260126 0.965575i \(-0.583764\pi\)
−0.260126 + 0.965575i \(0.583764\pi\)
\(480\) 0 0
\(481\) 9.40672 0.428909
\(482\) 0 0
\(483\) 7.44621 0.338814
\(484\) 0 0
\(485\) −43.9839 −1.99721
\(486\) 0 0
\(487\) −36.2347 −1.64195 −0.820975 0.570965i \(-0.806569\pi\)
−0.820975 + 0.570965i \(0.806569\pi\)
\(488\) 0 0
\(489\) −17.1449 −0.775318
\(490\) 0 0
\(491\) 32.8337 1.48176 0.740881 0.671636i \(-0.234408\pi\)
0.740881 + 0.671636i \(0.234408\pi\)
\(492\) 0 0
\(493\) 7.28689 0.328185
\(494\) 0 0
\(495\) −9.50005 −0.426995
\(496\) 0 0
\(497\) 22.5226 1.01028
\(498\) 0 0
\(499\) 7.14536 0.319870 0.159935 0.987128i \(-0.448871\pi\)
0.159935 + 0.987128i \(0.448871\pi\)
\(500\) 0 0
\(501\) 5.44249 0.243153
\(502\) 0 0
\(503\) −24.7089 −1.10171 −0.550857 0.834600i \(-0.685699\pi\)
−0.550857 + 0.834600i \(0.685699\pi\)
\(504\) 0 0
\(505\) 3.31941 0.147712
\(506\) 0 0
\(507\) −21.3606 −0.948659
\(508\) 0 0
\(509\) −4.90294 −0.217319 −0.108659 0.994079i \(-0.534656\pi\)
−0.108659 + 0.994079i \(0.534656\pi\)
\(510\) 0 0
\(511\) −4.45900 −0.197255
\(512\) 0 0
\(513\) −5.05622 −0.223238
\(514\) 0 0
\(515\) −0.137026 −0.00603809
\(516\) 0 0
\(517\) −10.2683 −0.451600
\(518\) 0 0
\(519\) −21.9967 −0.965546
\(520\) 0 0
\(521\) 24.6977 1.08203 0.541013 0.841014i \(-0.318041\pi\)
0.541013 + 0.841014i \(0.318041\pi\)
\(522\) 0 0
\(523\) −3.18909 −0.139449 −0.0697246 0.997566i \(-0.522212\pi\)
−0.0697246 + 0.997566i \(0.522212\pi\)
\(524\) 0 0
\(525\) 18.5175 0.808171
\(526\) 0 0
\(527\) 6.48904 0.282667
\(528\) 0 0
\(529\) −16.0985 −0.699935
\(530\) 0 0
\(531\) 22.6232 0.981763
\(532\) 0 0
\(533\) −2.44752 −0.106014
\(534\) 0 0
\(535\) −42.1952 −1.82426
\(536\) 0 0
\(537\) 22.1782 0.957059
\(538\) 0 0
\(539\) 1.04893 0.0451805
\(540\) 0 0
\(541\) −44.6386 −1.91916 −0.959582 0.281429i \(-0.909192\pi\)
−0.959582 + 0.281429i \(0.909192\pi\)
\(542\) 0 0
\(543\) 13.7082 0.588274
\(544\) 0 0
\(545\) 65.7213 2.81519
\(546\) 0 0
\(547\) 1.60025 0.0684216 0.0342108 0.999415i \(-0.489108\pi\)
0.0342108 + 0.999415i \(0.489108\pi\)
\(548\) 0 0
\(549\) −1.20873 −0.0515872
\(550\) 0 0
\(551\) −9.98145 −0.425224
\(552\) 0 0
\(553\) 9.14116 0.388722
\(554\) 0 0
\(555\) 5.58659 0.237138
\(556\) 0 0
\(557\) −21.2700 −0.901240 −0.450620 0.892716i \(-0.648797\pi\)
−0.450620 + 0.892716i \(0.648797\pi\)
\(558\) 0 0
\(559\) 53.5279 2.26399
\(560\) 0 0
\(561\) −1.06109 −0.0447992
\(562\) 0 0
\(563\) 3.10740 0.130961 0.0654806 0.997854i \(-0.479142\pi\)
0.0654806 + 0.997854i \(0.479142\pi\)
\(564\) 0 0
\(565\) −48.6755 −2.04779
\(566\) 0 0
\(567\) −2.03426 −0.0854309
\(568\) 0 0
\(569\) −38.5197 −1.61483 −0.807415 0.589984i \(-0.799134\pi\)
−0.807415 + 0.589984i \(0.799134\pi\)
\(570\) 0 0
\(571\) −14.9193 −0.624354 −0.312177 0.950024i \(-0.601058\pi\)
−0.312177 + 0.950024i \(0.601058\pi\)
\(572\) 0 0
\(573\) 14.8622 0.620877
\(574\) 0 0
\(575\) 17.1629 0.715743
\(576\) 0 0
\(577\) −25.9795 −1.08154 −0.540769 0.841171i \(-0.681867\pi\)
−0.540769 + 0.841171i \(0.681867\pi\)
\(578\) 0 0
\(579\) −15.3348 −0.637291
\(580\) 0 0
\(581\) 36.3093 1.50636
\(582\) 0 0
\(583\) 1.42621 0.0590675
\(584\) 0 0
\(585\) 38.8175 1.60491
\(586\) 0 0
\(587\) −2.61947 −0.108117 −0.0540585 0.998538i \(-0.517216\pi\)
−0.0540585 + 0.998538i \(0.517216\pi\)
\(588\) 0 0
\(589\) −8.88856 −0.366247
\(590\) 0 0
\(591\) 8.71887 0.358647
\(592\) 0 0
\(593\) 43.8237 1.79962 0.899811 0.436280i \(-0.143704\pi\)
0.899811 + 0.436280i \(0.143704\pi\)
\(594\) 0 0
\(595\) −6.89549 −0.282687
\(596\) 0 0
\(597\) 3.92188 0.160512
\(598\) 0 0
\(599\) 33.5441 1.37057 0.685287 0.728273i \(-0.259677\pi\)
0.685287 + 0.728273i \(0.259677\pi\)
\(600\) 0 0
\(601\) 12.7561 0.520331 0.260166 0.965564i \(-0.416223\pi\)
0.260166 + 0.965564i \(0.416223\pi\)
\(602\) 0 0
\(603\) 23.9182 0.974025
\(604\) 0 0
\(605\) −30.4487 −1.23791
\(606\) 0 0
\(607\) 28.2396 1.14621 0.573104 0.819482i \(-0.305739\pi\)
0.573104 + 0.819482i \(0.305739\pi\)
\(608\) 0 0
\(609\) 28.2916 1.14643
\(610\) 0 0
\(611\) 41.9566 1.69738
\(612\) 0 0
\(613\) 12.6800 0.512142 0.256071 0.966658i \(-0.417572\pi\)
0.256071 + 0.966658i \(0.417572\pi\)
\(614\) 0 0
\(615\) −1.45357 −0.0586134
\(616\) 0 0
\(617\) −34.0381 −1.37032 −0.685161 0.728392i \(-0.740268\pi\)
−0.685161 + 0.728392i \(0.740268\pi\)
\(618\) 0 0
\(619\) −13.7758 −0.553696 −0.276848 0.960914i \(-0.589290\pi\)
−0.276848 + 0.960914i \(0.589290\pi\)
\(620\) 0 0
\(621\) 13.2831 0.533031
\(622\) 0 0
\(623\) −4.83537 −0.193725
\(624\) 0 0
\(625\) −14.9841 −0.599364
\(626\) 0 0
\(627\) 1.45346 0.0580456
\(628\) 0 0
\(629\) −1.17843 −0.0469869
\(630\) 0 0
\(631\) −2.85691 −0.113732 −0.0568658 0.998382i \(-0.518111\pi\)
−0.0568658 + 0.998382i \(0.518111\pi\)
\(632\) 0 0
\(633\) 12.5679 0.499531
\(634\) 0 0
\(635\) −63.9564 −2.53803
\(636\) 0 0
\(637\) −4.28595 −0.169816
\(638\) 0 0
\(639\) 15.8835 0.628341
\(640\) 0 0
\(641\) 21.2565 0.839580 0.419790 0.907621i \(-0.362104\pi\)
0.419790 + 0.907621i \(0.362104\pi\)
\(642\) 0 0
\(643\) 9.56151 0.377069 0.188535 0.982067i \(-0.439626\pi\)
0.188535 + 0.982067i \(0.439626\pi\)
\(644\) 0 0
\(645\) 31.7899 1.25173
\(646\) 0 0
\(647\) 3.52419 0.138550 0.0692752 0.997598i \(-0.477931\pi\)
0.0692752 + 0.997598i \(0.477931\pi\)
\(648\) 0 0
\(649\) −16.4500 −0.645720
\(650\) 0 0
\(651\) 25.1939 0.987426
\(652\) 0 0
\(653\) −17.8690 −0.699269 −0.349634 0.936886i \(-0.613694\pi\)
−0.349634 + 0.936886i \(0.613694\pi\)
\(654\) 0 0
\(655\) −23.4867 −0.917702
\(656\) 0 0
\(657\) −3.14459 −0.122682
\(658\) 0 0
\(659\) 9.89031 0.385272 0.192636 0.981270i \(-0.438296\pi\)
0.192636 + 0.981270i \(0.438296\pi\)
\(660\) 0 0
\(661\) −28.7023 −1.11639 −0.558195 0.829710i \(-0.688506\pi\)
−0.558195 + 0.829710i \(0.688506\pi\)
\(662\) 0 0
\(663\) 4.33565 0.168383
\(664\) 0 0
\(665\) 9.44531 0.366273
\(666\) 0 0
\(667\) 26.2220 1.01532
\(668\) 0 0
\(669\) 16.6588 0.644065
\(670\) 0 0
\(671\) 0.878902 0.0339296
\(672\) 0 0
\(673\) −10.4268 −0.401924 −0.200962 0.979599i \(-0.564407\pi\)
−0.200962 + 0.979599i \(0.564407\pi\)
\(674\) 0 0
\(675\) 33.0328 1.27143
\(676\) 0 0
\(677\) 0.489847 0.0188263 0.00941317 0.999956i \(-0.497004\pi\)
0.00941317 + 0.999956i \(0.497004\pi\)
\(678\) 0 0
\(679\) 36.0217 1.38239
\(680\) 0 0
\(681\) −13.5483 −0.519173
\(682\) 0 0
\(683\) −30.6974 −1.17460 −0.587301 0.809369i \(-0.699809\pi\)
−0.587301 + 0.809369i \(0.699809\pi\)
\(684\) 0 0
\(685\) 38.8248 1.48342
\(686\) 0 0
\(687\) −22.4156 −0.855210
\(688\) 0 0
\(689\) −5.82753 −0.222011
\(690\) 0 0
\(691\) 29.7021 1.12992 0.564961 0.825117i \(-0.308891\pi\)
0.564961 + 0.825117i \(0.308891\pi\)
\(692\) 0 0
\(693\) 7.78029 0.295549
\(694\) 0 0
\(695\) −14.2088 −0.538972
\(696\) 0 0
\(697\) 0.306612 0.0116138
\(698\) 0 0
\(699\) −8.60019 −0.325289
\(700\) 0 0
\(701\) 8.93178 0.337349 0.168674 0.985672i \(-0.446051\pi\)
0.168674 + 0.985672i \(0.446051\pi\)
\(702\) 0 0
\(703\) 1.61419 0.0608802
\(704\) 0 0
\(705\) 24.9178 0.938458
\(706\) 0 0
\(707\) −2.71851 −0.102240
\(708\) 0 0
\(709\) −25.8038 −0.969081 −0.484540 0.874769i \(-0.661013\pi\)
−0.484540 + 0.874769i \(0.661013\pi\)
\(710\) 0 0
\(711\) 6.44656 0.241765
\(712\) 0 0
\(713\) 23.3509 0.874498
\(714\) 0 0
\(715\) −28.2254 −1.05557
\(716\) 0 0
\(717\) 26.7404 0.998640
\(718\) 0 0
\(719\) −2.11153 −0.0787468 −0.0393734 0.999225i \(-0.512536\pi\)
−0.0393734 + 0.999225i \(0.512536\pi\)
\(720\) 0 0
\(721\) 0.112221 0.00417932
\(722\) 0 0
\(723\) −2.73352 −0.101661
\(724\) 0 0
\(725\) 65.2098 2.42183
\(726\) 0 0
\(727\) 43.9116 1.62859 0.814295 0.580452i \(-0.197124\pi\)
0.814295 + 0.580452i \(0.197124\pi\)
\(728\) 0 0
\(729\) 14.0239 0.519404
\(730\) 0 0
\(731\) −6.70570 −0.248019
\(732\) 0 0
\(733\) −27.2957 −1.00819 −0.504094 0.863649i \(-0.668174\pi\)
−0.504094 + 0.863649i \(0.668174\pi\)
\(734\) 0 0
\(735\) −2.54540 −0.0938885
\(736\) 0 0
\(737\) −17.3917 −0.640630
\(738\) 0 0
\(739\) 6.39207 0.235136 0.117568 0.993065i \(-0.462490\pi\)
0.117568 + 0.993065i \(0.462490\pi\)
\(740\) 0 0
\(741\) −5.93889 −0.218170
\(742\) 0 0
\(743\) 47.9311 1.75842 0.879211 0.476433i \(-0.158070\pi\)
0.879211 + 0.476433i \(0.158070\pi\)
\(744\) 0 0
\(745\) −43.9674 −1.61084
\(746\) 0 0
\(747\) 25.6062 0.936880
\(748\) 0 0
\(749\) 34.5568 1.26268
\(750\) 0 0
\(751\) −12.8524 −0.468989 −0.234495 0.972117i \(-0.575344\pi\)
−0.234495 + 0.972117i \(0.575344\pi\)
\(752\) 0 0
\(753\) −1.64829 −0.0600671
\(754\) 0 0
\(755\) 69.6287 2.53405
\(756\) 0 0
\(757\) 4.52334 0.164404 0.0822018 0.996616i \(-0.473805\pi\)
0.0822018 + 0.996616i \(0.473805\pi\)
\(758\) 0 0
\(759\) −3.81834 −0.138597
\(760\) 0 0
\(761\) −33.3495 −1.20892 −0.604459 0.796636i \(-0.706611\pi\)
−0.604459 + 0.796636i \(0.706611\pi\)
\(762\) 0 0
\(763\) −53.8241 −1.94856
\(764\) 0 0
\(765\) −4.86286 −0.175817
\(766\) 0 0
\(767\) 67.2154 2.42701
\(768\) 0 0
\(769\) −39.6251 −1.42892 −0.714458 0.699678i \(-0.753327\pi\)
−0.714458 + 0.699678i \(0.753327\pi\)
\(770\) 0 0
\(771\) 8.65706 0.311776
\(772\) 0 0
\(773\) −32.6481 −1.17427 −0.587135 0.809489i \(-0.699744\pi\)
−0.587135 + 0.809489i \(0.699744\pi\)
\(774\) 0 0
\(775\) 58.0699 2.08593
\(776\) 0 0
\(777\) −4.57527 −0.164137
\(778\) 0 0
\(779\) −0.419992 −0.0150478
\(780\) 0 0
\(781\) −11.5494 −0.413269
\(782\) 0 0
\(783\) 50.4684 1.80359
\(784\) 0 0
\(785\) −65.7280 −2.34593
\(786\) 0 0
\(787\) −31.2473 −1.11384 −0.556922 0.830564i \(-0.688018\pi\)
−0.556922 + 0.830564i \(0.688018\pi\)
\(788\) 0 0
\(789\) −14.2977 −0.509011
\(790\) 0 0
\(791\) 39.8640 1.41740
\(792\) 0 0
\(793\) −3.59122 −0.127528
\(794\) 0 0
\(795\) −3.46093 −0.122747
\(796\) 0 0
\(797\) 30.2469 1.07140 0.535701 0.844408i \(-0.320047\pi\)
0.535701 + 0.844408i \(0.320047\pi\)
\(798\) 0 0
\(799\) −5.25612 −0.185948
\(800\) 0 0
\(801\) −3.41002 −0.120487
\(802\) 0 0
\(803\) 2.28653 0.0806899
\(804\) 0 0
\(805\) −24.8135 −0.874561
\(806\) 0 0
\(807\) −20.6106 −0.725527
\(808\) 0 0
\(809\) 17.1619 0.603380 0.301690 0.953406i \(-0.402449\pi\)
0.301690 + 0.953406i \(0.402449\pi\)
\(810\) 0 0
\(811\) 35.2236 1.23687 0.618433 0.785837i \(-0.287768\pi\)
0.618433 + 0.785837i \(0.287768\pi\)
\(812\) 0 0
\(813\) −4.65552 −0.163276
\(814\) 0 0
\(815\) 57.1330 2.00128
\(816\) 0 0
\(817\) 9.18535 0.321355
\(818\) 0 0
\(819\) −31.7905 −1.11085
\(820\) 0 0
\(821\) 42.9186 1.49787 0.748935 0.662643i \(-0.230565\pi\)
0.748935 + 0.662643i \(0.230565\pi\)
\(822\) 0 0
\(823\) 37.9507 1.32288 0.661439 0.749999i \(-0.269946\pi\)
0.661439 + 0.749999i \(0.269946\pi\)
\(824\) 0 0
\(825\) −9.49560 −0.330594
\(826\) 0 0
\(827\) −13.9293 −0.484368 −0.242184 0.970230i \(-0.577864\pi\)
−0.242184 + 0.970230i \(0.577864\pi\)
\(828\) 0 0
\(829\) −30.6787 −1.06551 −0.532757 0.846268i \(-0.678844\pi\)
−0.532757 + 0.846268i \(0.678844\pi\)
\(830\) 0 0
\(831\) 21.3897 0.742000
\(832\) 0 0
\(833\) 0.536922 0.0186033
\(834\) 0 0
\(835\) −18.1364 −0.627635
\(836\) 0 0
\(837\) 44.9426 1.55344
\(838\) 0 0
\(839\) 3.81625 0.131751 0.0658757 0.997828i \(-0.479016\pi\)
0.0658757 + 0.997828i \(0.479016\pi\)
\(840\) 0 0
\(841\) 70.6293 2.43549
\(842\) 0 0
\(843\) 7.63014 0.262796
\(844\) 0 0
\(845\) 71.1814 2.44872
\(846\) 0 0
\(847\) 24.9367 0.856835
\(848\) 0 0
\(849\) −26.2956 −0.902464
\(850\) 0 0
\(851\) −4.24058 −0.145365
\(852\) 0 0
\(853\) 3.74924 0.128372 0.0641858 0.997938i \(-0.479555\pi\)
0.0641858 + 0.997938i \(0.479555\pi\)
\(854\) 0 0
\(855\) 6.66106 0.227803
\(856\) 0 0
\(857\) 48.2740 1.64901 0.824505 0.565855i \(-0.191454\pi\)
0.824505 + 0.565855i \(0.191454\pi\)
\(858\) 0 0
\(859\) 8.73850 0.298154 0.149077 0.988826i \(-0.452370\pi\)
0.149077 + 0.988826i \(0.452370\pi\)
\(860\) 0 0
\(861\) 1.19043 0.0405698
\(862\) 0 0
\(863\) 18.1458 0.617691 0.308845 0.951112i \(-0.400057\pi\)
0.308845 + 0.951112i \(0.400057\pi\)
\(864\) 0 0
\(865\) 73.3009 2.49230
\(866\) 0 0
\(867\) 16.7817 0.569936
\(868\) 0 0
\(869\) −4.68749 −0.159012
\(870\) 0 0
\(871\) 71.0629 2.40788
\(872\) 0 0
\(873\) 25.4033 0.859773
\(874\) 0 0
\(875\) −14.4806 −0.489534
\(876\) 0 0
\(877\) 44.1816 1.49191 0.745954 0.665997i \(-0.231994\pi\)
0.745954 + 0.665997i \(0.231994\pi\)
\(878\) 0 0
\(879\) −21.8550 −0.737149
\(880\) 0 0
\(881\) −49.5363 −1.66892 −0.834461 0.551067i \(-0.814221\pi\)
−0.834461 + 0.551067i \(0.814221\pi\)
\(882\) 0 0
\(883\) 8.87871 0.298793 0.149396 0.988777i \(-0.452267\pi\)
0.149396 + 0.988777i \(0.452267\pi\)
\(884\) 0 0
\(885\) 39.9188 1.34186
\(886\) 0 0
\(887\) −35.7254 −1.19954 −0.599770 0.800172i \(-0.704741\pi\)
−0.599770 + 0.800172i \(0.704741\pi\)
\(888\) 0 0
\(889\) 52.3786 1.75672
\(890\) 0 0
\(891\) 1.04315 0.0349468
\(892\) 0 0
\(893\) 7.19973 0.240930
\(894\) 0 0
\(895\) −73.9058 −2.47040
\(896\) 0 0
\(897\) 15.6019 0.520932
\(898\) 0 0
\(899\) 88.7207 2.95900
\(900\) 0 0
\(901\) 0.730044 0.0243213
\(902\) 0 0
\(903\) −26.0351 −0.866394
\(904\) 0 0
\(905\) −45.6807 −1.51848
\(906\) 0 0
\(907\) −26.4802 −0.879262 −0.439631 0.898179i \(-0.644891\pi\)
−0.439631 + 0.898179i \(0.644891\pi\)
\(908\) 0 0
\(909\) −1.91716 −0.0635882
\(910\) 0 0
\(911\) 46.1495 1.52900 0.764500 0.644624i \(-0.222986\pi\)
0.764500 + 0.644624i \(0.222986\pi\)
\(912\) 0 0
\(913\) −18.6190 −0.616200
\(914\) 0 0
\(915\) −2.13281 −0.0705084
\(916\) 0 0
\(917\) 19.2350 0.635196
\(918\) 0 0
\(919\) −53.2141 −1.75537 −0.877686 0.479236i \(-0.840914\pi\)
−0.877686 + 0.479236i \(0.840914\pi\)
\(920\) 0 0
\(921\) −18.0478 −0.594697
\(922\) 0 0
\(923\) 47.1911 1.55331
\(924\) 0 0
\(925\) −10.5456 −0.346738
\(926\) 0 0
\(927\) 0.0791408 0.00259933
\(928\) 0 0
\(929\) −3.69906 −0.121362 −0.0606812 0.998157i \(-0.519327\pi\)
−0.0606812 + 0.998157i \(0.519327\pi\)
\(930\) 0 0
\(931\) −0.735466 −0.0241039
\(932\) 0 0
\(933\) −0.576227 −0.0188648
\(934\) 0 0
\(935\) 3.53594 0.115637
\(936\) 0 0
\(937\) 45.8161 1.49675 0.748373 0.663278i \(-0.230835\pi\)
0.748373 + 0.663278i \(0.230835\pi\)
\(938\) 0 0
\(939\) 12.1772 0.397387
\(940\) 0 0
\(941\) 0.237646 0.00774705 0.00387352 0.999992i \(-0.498767\pi\)
0.00387352 + 0.999992i \(0.498767\pi\)
\(942\) 0 0
\(943\) 1.10335 0.0359300
\(944\) 0 0
\(945\) −47.7576 −1.55355
\(946\) 0 0
\(947\) 23.8032 0.773501 0.386750 0.922184i \(-0.373598\pi\)
0.386750 + 0.922184i \(0.373598\pi\)
\(948\) 0 0
\(949\) −9.34284 −0.303281
\(950\) 0 0
\(951\) −21.4281 −0.694853
\(952\) 0 0
\(953\) 13.9035 0.450380 0.225190 0.974315i \(-0.427700\pi\)
0.225190 + 0.974315i \(0.427700\pi\)
\(954\) 0 0
\(955\) −49.5263 −1.60263
\(956\) 0 0
\(957\) −14.5076 −0.468965
\(958\) 0 0
\(959\) −31.7965 −1.02676
\(960\) 0 0
\(961\) 48.0066 1.54860
\(962\) 0 0
\(963\) 24.3702 0.785320
\(964\) 0 0
\(965\) 51.1010 1.64500
\(966\) 0 0
\(967\) 34.3772 1.10550 0.552749 0.833348i \(-0.313579\pi\)
0.552749 + 0.833348i \(0.313579\pi\)
\(968\) 0 0
\(969\) 0.743994 0.0239005
\(970\) 0 0
\(971\) 21.5727 0.692301 0.346151 0.938179i \(-0.387489\pi\)
0.346151 + 0.938179i \(0.387489\pi\)
\(972\) 0 0
\(973\) 11.6367 0.373055
\(974\) 0 0
\(975\) 38.7993 1.24257
\(976\) 0 0
\(977\) −19.5939 −0.626866 −0.313433 0.949610i \(-0.601479\pi\)
−0.313433 + 0.949610i \(0.601479\pi\)
\(978\) 0 0
\(979\) 2.47953 0.0792460
\(980\) 0 0
\(981\) −37.9580 −1.21191
\(982\) 0 0
\(983\) −20.2487 −0.645832 −0.322916 0.946428i \(-0.604663\pi\)
−0.322916 + 0.946428i \(0.604663\pi\)
\(984\) 0 0
\(985\) −29.0545 −0.925753
\(986\) 0 0
\(987\) −20.4070 −0.649563
\(988\) 0 0
\(989\) −24.1306 −0.767307
\(990\) 0 0
\(991\) −32.4481 −1.03075 −0.515373 0.856966i \(-0.672347\pi\)
−0.515373 + 0.856966i \(0.672347\pi\)
\(992\) 0 0
\(993\) −9.17390 −0.291125
\(994\) 0 0
\(995\) −13.0691 −0.414320
\(996\) 0 0
\(997\) −32.2942 −1.02277 −0.511384 0.859353i \(-0.670867\pi\)
−0.511384 + 0.859353i \(0.670867\pi\)
\(998\) 0 0
\(999\) −8.16168 −0.258224
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 \(a_p\))