Properties

Label 8048.2.a.v.1.9
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.59308 q^{3} +2.75433 q^{5} -1.46360 q^{7} -0.462108 q^{9} +O(q^{10})\) \(q-1.59308 q^{3} +2.75433 q^{5} -1.46360 q^{7} -0.462108 q^{9} +5.86989 q^{11} -6.69840 q^{13} -4.38785 q^{15} -6.07288 q^{17} +1.48446 q^{19} +2.33163 q^{21} -4.40969 q^{23} +2.58632 q^{25} +5.51540 q^{27} +8.17517 q^{29} +8.84800 q^{31} -9.35119 q^{33} -4.03123 q^{35} -7.89315 q^{37} +10.6711 q^{39} +5.35916 q^{41} +8.36082 q^{43} -1.27280 q^{45} -9.07330 q^{47} -4.85788 q^{49} +9.67456 q^{51} +12.3433 q^{53} +16.1676 q^{55} -2.36485 q^{57} +2.57315 q^{59} +3.03940 q^{61} +0.676342 q^{63} -18.4496 q^{65} -1.68264 q^{67} +7.02497 q^{69} -4.21882 q^{71} -12.5331 q^{73} -4.12021 q^{75} -8.59118 q^{77} -14.2617 q^{79} -7.40013 q^{81} +17.2574 q^{83} -16.7267 q^{85} -13.0237 q^{87} -8.75945 q^{89} +9.80378 q^{91} -14.0955 q^{93} +4.08868 q^{95} +2.54144 q^{97} -2.71253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) −1.59308 −0.919763 −0.459881 0.887980i \(-0.652108\pi\)
−0.459881 + 0.887980i \(0.652108\pi\)
\(4\) 0 0
\(5\) 2.75433 1.23177 0.615886 0.787835i \(-0.288798\pi\)
0.615886 + 0.787835i \(0.288798\pi\)
\(6\) 0 0
\(7\) −1.46360 −0.553189 −0.276594 0.960987i \(-0.589206\pi\)
−0.276594 + 0.960987i \(0.589206\pi\)
\(8\) 0 0
\(9\) −0.462108 −0.154036
\(10\) 0 0
\(11\) 5.86989 1.76984 0.884920 0.465743i \(-0.154213\pi\)
0.884920 + 0.465743i \(0.154213\pi\)
\(12\) 0 0
\(13\) −6.69840 −1.85780 −0.928901 0.370328i \(-0.879245\pi\)
−0.928901 + 0.370328i \(0.879245\pi\)
\(14\) 0 0
\(15\) −4.38785 −1.13294
\(16\) 0 0
\(17\) −6.07288 −1.47289 −0.736445 0.676497i \(-0.763497\pi\)
−0.736445 + 0.676497i \(0.763497\pi\)
\(18\) 0 0
\(19\) 1.48446 0.340558 0.170279 0.985396i \(-0.445533\pi\)
0.170279 + 0.985396i \(0.445533\pi\)
\(20\) 0 0
\(21\) 2.33163 0.508802
\(22\) 0 0
\(23\) −4.40969 −0.919483 −0.459742 0.888053i \(-0.652058\pi\)
−0.459742 + 0.888053i \(0.652058\pi\)
\(24\) 0 0
\(25\) 2.58632 0.517264
\(26\) 0 0
\(27\) 5.51540 1.06144
\(28\) 0 0
\(29\) 8.17517 1.51809 0.759045 0.651038i \(-0.225666\pi\)
0.759045 + 0.651038i \(0.225666\pi\)
\(30\) 0 0
\(31\) 8.84800 1.58915 0.794574 0.607168i \(-0.207694\pi\)
0.794574 + 0.607168i \(0.207694\pi\)
\(32\) 0 0
\(33\) −9.35119 −1.62783
\(34\) 0 0
\(35\) −4.03123 −0.681403
\(36\) 0 0
\(37\) −7.89315 −1.29763 −0.648813 0.760948i \(-0.724734\pi\)
−0.648813 + 0.760948i \(0.724734\pi\)
\(38\) 0 0
\(39\) 10.6711 1.70874
\(40\) 0 0
\(41\) 5.35916 0.836961 0.418480 0.908226i \(-0.362563\pi\)
0.418480 + 0.908226i \(0.362563\pi\)
\(42\) 0 0
\(43\) 8.36082 1.27501 0.637507 0.770445i \(-0.279966\pi\)
0.637507 + 0.770445i \(0.279966\pi\)
\(44\) 0 0
\(45\) −1.27280 −0.189738
\(46\) 0 0
\(47\) −9.07330 −1.32348 −0.661739 0.749735i \(-0.730181\pi\)
−0.661739 + 0.749735i \(0.730181\pi\)
\(48\) 0 0
\(49\) −4.85788 −0.693982
\(50\) 0 0
\(51\) 9.67456 1.35471
\(52\) 0 0
\(53\) 12.3433 1.69549 0.847743 0.530406i \(-0.177961\pi\)
0.847743 + 0.530406i \(0.177961\pi\)
\(54\) 0 0
\(55\) 16.1676 2.18004
\(56\) 0 0
\(57\) −2.36485 −0.313232
\(58\) 0 0
\(59\) 2.57315 0.334996 0.167498 0.985872i \(-0.446431\pi\)
0.167498 + 0.985872i \(0.446431\pi\)
\(60\) 0 0
\(61\) 3.03940 0.389156 0.194578 0.980887i \(-0.437666\pi\)
0.194578 + 0.980887i \(0.437666\pi\)
\(62\) 0 0
\(63\) 0.676342 0.0852110
\(64\) 0 0
\(65\) −18.4496 −2.28839
\(66\) 0 0
\(67\) −1.68264 −0.205568 −0.102784 0.994704i \(-0.532775\pi\)
−0.102784 + 0.994704i \(0.532775\pi\)
\(68\) 0 0
\(69\) 7.02497 0.845707
\(70\) 0 0
\(71\) −4.21882 −0.500681 −0.250341 0.968158i \(-0.580543\pi\)
−0.250341 + 0.968158i \(0.580543\pi\)
\(72\) 0 0
\(73\) −12.5331 −1.46689 −0.733445 0.679749i \(-0.762089\pi\)
−0.733445 + 0.679749i \(0.762089\pi\)
\(74\) 0 0
\(75\) −4.12021 −0.475761
\(76\) 0 0
\(77\) −8.59118 −0.979055
\(78\) 0 0
\(79\) −14.2617 −1.60457 −0.802284 0.596943i \(-0.796382\pi\)
−0.802284 + 0.596943i \(0.796382\pi\)
\(80\) 0 0
\(81\) −7.40013 −0.822237
\(82\) 0 0
\(83\) 17.2574 1.89425 0.947124 0.320868i \(-0.103975\pi\)
0.947124 + 0.320868i \(0.103975\pi\)
\(84\) 0 0
\(85\) −16.7267 −1.81427
\(86\) 0 0
\(87\) −13.0237 −1.39628
\(88\) 0 0
\(89\) −8.75945 −0.928500 −0.464250 0.885704i \(-0.653676\pi\)
−0.464250 + 0.885704i \(0.653676\pi\)
\(90\) 0 0
\(91\) 9.80378 1.02772
\(92\) 0 0
\(93\) −14.0955 −1.46164
\(94\) 0 0
\(95\) 4.08868 0.419490
\(96\) 0 0
\(97\) 2.54144 0.258044 0.129022 0.991642i \(-0.458816\pi\)
0.129022 + 0.991642i \(0.458816\pi\)
\(98\) 0 0
\(99\) −2.71253 −0.272619
\(100\) 0 0
\(101\) −11.5172 −1.14600 −0.573001 0.819554i \(-0.694221\pi\)
−0.573001 + 0.819554i \(0.694221\pi\)
\(102\) 0 0
\(103\) −1.61935 −0.159559 −0.0797797 0.996813i \(-0.525422\pi\)
−0.0797797 + 0.996813i \(0.525422\pi\)
\(104\) 0 0
\(105\) 6.42206 0.626729
\(106\) 0 0
\(107\) −4.13438 −0.399685 −0.199843 0.979828i \(-0.564043\pi\)
−0.199843 + 0.979828i \(0.564043\pi\)
\(108\) 0 0
\(109\) −18.4290 −1.76518 −0.882588 0.470147i \(-0.844201\pi\)
−0.882588 + 0.470147i \(0.844201\pi\)
\(110\) 0 0
\(111\) 12.5744 1.19351
\(112\) 0 0
\(113\) 6.13298 0.576943 0.288471 0.957489i \(-0.406853\pi\)
0.288471 + 0.957489i \(0.406853\pi\)
\(114\) 0 0
\(115\) −12.1457 −1.13259
\(116\) 0 0
\(117\) 3.09539 0.286169
\(118\) 0 0
\(119\) 8.88827 0.814786
\(120\) 0 0
\(121\) 23.4557 2.13233
\(122\) 0 0
\(123\) −8.53756 −0.769806
\(124\) 0 0
\(125\) −6.64806 −0.594621
\(126\) 0 0
\(127\) −17.1025 −1.51760 −0.758802 0.651322i \(-0.774215\pi\)
−0.758802 + 0.651322i \(0.774215\pi\)
\(128\) 0 0
\(129\) −13.3194 −1.17271
\(130\) 0 0
\(131\) −12.3670 −1.08051 −0.540256 0.841500i \(-0.681673\pi\)
−0.540256 + 0.841500i \(0.681673\pi\)
\(132\) 0 0
\(133\) −2.17265 −0.188393
\(134\) 0 0
\(135\) 15.1912 1.30745
\(136\) 0 0
\(137\) 1.35637 0.115882 0.0579411 0.998320i \(-0.481546\pi\)
0.0579411 + 0.998320i \(0.481546\pi\)
\(138\) 0 0
\(139\) 9.42003 0.798996 0.399498 0.916734i \(-0.369184\pi\)
0.399498 + 0.916734i \(0.369184\pi\)
\(140\) 0 0
\(141\) 14.4545 1.21729
\(142\) 0 0
\(143\) −39.3189 −3.28801
\(144\) 0 0
\(145\) 22.5171 1.86994
\(146\) 0 0
\(147\) 7.73897 0.638299
\(148\) 0 0
\(149\) −14.0620 −1.15201 −0.576003 0.817448i \(-0.695388\pi\)
−0.576003 + 0.817448i \(0.695388\pi\)
\(150\) 0 0
\(151\) 9.72194 0.791161 0.395580 0.918431i \(-0.370543\pi\)
0.395580 + 0.918431i \(0.370543\pi\)
\(152\) 0 0
\(153\) 2.80633 0.226878
\(154\) 0 0
\(155\) 24.3703 1.95747
\(156\) 0 0
\(157\) 20.3959 1.62777 0.813886 0.581025i \(-0.197348\pi\)
0.813886 + 0.581025i \(0.197348\pi\)
\(158\) 0 0
\(159\) −19.6639 −1.55945
\(160\) 0 0
\(161\) 6.45402 0.508648
\(162\) 0 0
\(163\) −6.02566 −0.471966 −0.235983 0.971757i \(-0.575831\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(164\) 0 0
\(165\) −25.7562 −2.00512
\(166\) 0 0
\(167\) 4.04988 0.313389 0.156695 0.987647i \(-0.449916\pi\)
0.156695 + 0.987647i \(0.449916\pi\)
\(168\) 0 0
\(169\) 31.8686 2.45143
\(170\) 0 0
\(171\) −0.685979 −0.0524582
\(172\) 0 0
\(173\) 9.38104 0.713227 0.356614 0.934252i \(-0.383931\pi\)
0.356614 + 0.934252i \(0.383931\pi\)
\(174\) 0 0
\(175\) −3.78534 −0.286145
\(176\) 0 0
\(177\) −4.09923 −0.308117
\(178\) 0 0
\(179\) −9.00076 −0.672748 −0.336374 0.941728i \(-0.609201\pi\)
−0.336374 + 0.941728i \(0.609201\pi\)
\(180\) 0 0
\(181\) 5.30418 0.394257 0.197128 0.980378i \(-0.436838\pi\)
0.197128 + 0.980378i \(0.436838\pi\)
\(182\) 0 0
\(183\) −4.84200 −0.357931
\(184\) 0 0
\(185\) −21.7403 −1.59838
\(186\) 0 0
\(187\) −35.6472 −2.60678
\(188\) 0 0
\(189\) −8.07234 −0.587176
\(190\) 0 0
\(191\) −14.5843 −1.05529 −0.527643 0.849466i \(-0.676924\pi\)
−0.527643 + 0.849466i \(0.676924\pi\)
\(192\) 0 0
\(193\) −1.26930 −0.0913665 −0.0456833 0.998956i \(-0.514546\pi\)
−0.0456833 + 0.998956i \(0.514546\pi\)
\(194\) 0 0
\(195\) 29.3916 2.10478
\(196\) 0 0
\(197\) −13.7100 −0.976795 −0.488397 0.872621i \(-0.662418\pi\)
−0.488397 + 0.872621i \(0.662418\pi\)
\(198\) 0 0
\(199\) −18.2227 −1.29177 −0.645887 0.763433i \(-0.723512\pi\)
−0.645887 + 0.763433i \(0.723512\pi\)
\(200\) 0 0
\(201\) 2.68058 0.189074
\(202\) 0 0
\(203\) −11.9652 −0.839790
\(204\) 0 0
\(205\) 14.7609 1.03095
\(206\) 0 0
\(207\) 2.03775 0.141634
\(208\) 0 0
\(209\) 8.71360 0.602732
\(210\) 0 0
\(211\) 10.1444 0.698373 0.349186 0.937053i \(-0.386458\pi\)
0.349186 + 0.937053i \(0.386458\pi\)
\(212\) 0 0
\(213\) 6.72090 0.460508
\(214\) 0 0
\(215\) 23.0284 1.57053
\(216\) 0 0
\(217\) −12.9499 −0.879098
\(218\) 0 0
\(219\) 19.9662 1.34919
\(220\) 0 0
\(221\) 40.6786 2.73634
\(222\) 0 0
\(223\) −9.35840 −0.626685 −0.313342 0.949640i \(-0.601449\pi\)
−0.313342 + 0.949640i \(0.601449\pi\)
\(224\) 0 0
\(225\) −1.19516 −0.0796774
\(226\) 0 0
\(227\) −13.4970 −0.895825 −0.447913 0.894077i \(-0.647832\pi\)
−0.447913 + 0.894077i \(0.647832\pi\)
\(228\) 0 0
\(229\) 3.85673 0.254860 0.127430 0.991848i \(-0.459327\pi\)
0.127430 + 0.991848i \(0.459327\pi\)
\(230\) 0 0
\(231\) 13.6864 0.900499
\(232\) 0 0
\(233\) −26.6606 −1.74659 −0.873296 0.487190i \(-0.838022\pi\)
−0.873296 + 0.487190i \(0.838022\pi\)
\(234\) 0 0
\(235\) −24.9908 −1.63022
\(236\) 0 0
\(237\) 22.7200 1.47582
\(238\) 0 0
\(239\) 10.6255 0.687304 0.343652 0.939097i \(-0.388336\pi\)
0.343652 + 0.939097i \(0.388336\pi\)
\(240\) 0 0
\(241\) −21.2402 −1.36820 −0.684102 0.729387i \(-0.739806\pi\)
−0.684102 + 0.729387i \(0.739806\pi\)
\(242\) 0 0
\(243\) −4.75724 −0.305177
\(244\) 0 0
\(245\) −13.3802 −0.854828
\(246\) 0 0
\(247\) −9.94348 −0.632688
\(248\) 0 0
\(249\) −27.4924 −1.74226
\(250\) 0 0
\(251\) 19.6652 1.24126 0.620629 0.784105i \(-0.286878\pi\)
0.620629 + 0.784105i \(0.286878\pi\)
\(252\) 0 0
\(253\) −25.8844 −1.62734
\(254\) 0 0
\(255\) 26.6469 1.66869
\(256\) 0 0
\(257\) −23.6914 −1.47783 −0.738916 0.673798i \(-0.764662\pi\)
−0.738916 + 0.673798i \(0.764662\pi\)
\(258\) 0 0
\(259\) 11.5524 0.717832
\(260\) 0 0
\(261\) −3.77781 −0.233841
\(262\) 0 0
\(263\) 1.08534 0.0669247 0.0334624 0.999440i \(-0.489347\pi\)
0.0334624 + 0.999440i \(0.489347\pi\)
\(264\) 0 0
\(265\) 33.9976 2.08845
\(266\) 0 0
\(267\) 13.9545 0.854000
\(268\) 0 0
\(269\) 8.92937 0.544433 0.272217 0.962236i \(-0.412243\pi\)
0.272217 + 0.962236i \(0.412243\pi\)
\(270\) 0 0
\(271\) −8.03612 −0.488160 −0.244080 0.969755i \(-0.578486\pi\)
−0.244080 + 0.969755i \(0.578486\pi\)
\(272\) 0 0
\(273\) −15.6182 −0.945254
\(274\) 0 0
\(275\) 15.1814 0.915475
\(276\) 0 0
\(277\) 10.7093 0.643458 0.321729 0.946832i \(-0.395736\pi\)
0.321729 + 0.946832i \(0.395736\pi\)
\(278\) 0 0
\(279\) −4.08873 −0.244786
\(280\) 0 0
\(281\) −10.6054 −0.632663 −0.316332 0.948649i \(-0.602451\pi\)
−0.316332 + 0.948649i \(0.602451\pi\)
\(282\) 0 0
\(283\) −2.63639 −0.156717 −0.0783586 0.996925i \(-0.524968\pi\)
−0.0783586 + 0.996925i \(0.524968\pi\)
\(284\) 0 0
\(285\) −6.51358 −0.385831
\(286\) 0 0
\(287\) −7.84367 −0.462997
\(288\) 0 0
\(289\) 19.8799 1.16941
\(290\) 0 0
\(291\) −4.04870 −0.237339
\(292\) 0 0
\(293\) 7.32611 0.427996 0.213998 0.976834i \(-0.431351\pi\)
0.213998 + 0.976834i \(0.431351\pi\)
\(294\) 0 0
\(295\) 7.08731 0.412639
\(296\) 0 0
\(297\) 32.3748 1.87858
\(298\) 0 0
\(299\) 29.5379 1.70822
\(300\) 0 0
\(301\) −12.2369 −0.705323
\(302\) 0 0
\(303\) 18.3477 1.05405
\(304\) 0 0
\(305\) 8.37152 0.479352
\(306\) 0 0
\(307\) 13.2865 0.758301 0.379151 0.925335i \(-0.376216\pi\)
0.379151 + 0.925335i \(0.376216\pi\)
\(308\) 0 0
\(309\) 2.57975 0.146757
\(310\) 0 0
\(311\) −22.6292 −1.28318 −0.641591 0.767047i \(-0.721725\pi\)
−0.641591 + 0.767047i \(0.721725\pi\)
\(312\) 0 0
\(313\) 2.01120 0.113680 0.0568399 0.998383i \(-0.481898\pi\)
0.0568399 + 0.998383i \(0.481898\pi\)
\(314\) 0 0
\(315\) 1.86287 0.104961
\(316\) 0 0
\(317\) −30.4277 −1.70899 −0.854495 0.519460i \(-0.826133\pi\)
−0.854495 + 0.519460i \(0.826133\pi\)
\(318\) 0 0
\(319\) 47.9874 2.68678
\(320\) 0 0
\(321\) 6.58638 0.367616
\(322\) 0 0
\(323\) −9.01493 −0.501604
\(324\) 0 0
\(325\) −17.3242 −0.960975
\(326\) 0 0
\(327\) 29.3588 1.62354
\(328\) 0 0
\(329\) 13.2797 0.732133
\(330\) 0 0
\(331\) −0.921540 −0.0506524 −0.0253262 0.999679i \(-0.508062\pi\)
−0.0253262 + 0.999679i \(0.508062\pi\)
\(332\) 0 0
\(333\) 3.64749 0.199881
\(334\) 0 0
\(335\) −4.63455 −0.253213
\(336\) 0 0
\(337\) 2.03118 0.110646 0.0553228 0.998469i \(-0.482381\pi\)
0.0553228 + 0.998469i \(0.482381\pi\)
\(338\) 0 0
\(339\) −9.77031 −0.530650
\(340\) 0 0
\(341\) 51.9368 2.81254
\(342\) 0 0
\(343\) 17.3552 0.937092
\(344\) 0 0
\(345\) 19.3491 1.04172
\(346\) 0 0
\(347\) −11.1452 −0.598305 −0.299152 0.954205i \(-0.596704\pi\)
−0.299152 + 0.954205i \(0.596704\pi\)
\(348\) 0 0
\(349\) 29.5827 1.58352 0.791762 0.610829i \(-0.209164\pi\)
0.791762 + 0.610829i \(0.209164\pi\)
\(350\) 0 0
\(351\) −36.9444 −1.97194
\(352\) 0 0
\(353\) −0.527017 −0.0280503 −0.0140251 0.999902i \(-0.504464\pi\)
−0.0140251 + 0.999902i \(0.504464\pi\)
\(354\) 0 0
\(355\) −11.6200 −0.616726
\(356\) 0 0
\(357\) −14.1597 −0.749410
\(358\) 0 0
\(359\) 0.171064 0.00902843 0.00451422 0.999990i \(-0.498563\pi\)
0.00451422 + 0.999990i \(0.498563\pi\)
\(360\) 0 0
\(361\) −16.7964 −0.884021
\(362\) 0 0
\(363\) −37.3667 −1.96124
\(364\) 0 0
\(365\) −34.5203 −1.80687
\(366\) 0 0
\(367\) −3.35445 −0.175101 −0.0875506 0.996160i \(-0.527904\pi\)
−0.0875506 + 0.996160i \(0.527904\pi\)
\(368\) 0 0
\(369\) −2.47651 −0.128922
\(370\) 0 0
\(371\) −18.0657 −0.937924
\(372\) 0 0
\(373\) −23.2102 −1.20178 −0.600890 0.799332i \(-0.705187\pi\)
−0.600890 + 0.799332i \(0.705187\pi\)
\(374\) 0 0
\(375\) 10.5909 0.546910
\(376\) 0 0
\(377\) −54.7605 −2.82031
\(378\) 0 0
\(379\) 25.0589 1.28719 0.643594 0.765367i \(-0.277442\pi\)
0.643594 + 0.765367i \(0.277442\pi\)
\(380\) 0 0
\(381\) 27.2456 1.39584
\(382\) 0 0
\(383\) 13.5652 0.693148 0.346574 0.938023i \(-0.387345\pi\)
0.346574 + 0.938023i \(0.387345\pi\)
\(384\) 0 0
\(385\) −23.6629 −1.20597
\(386\) 0 0
\(387\) −3.86361 −0.196398
\(388\) 0 0
\(389\) −24.9073 −1.26285 −0.631424 0.775438i \(-0.717529\pi\)
−0.631424 + 0.775438i \(0.717529\pi\)
\(390\) 0 0
\(391\) 26.7795 1.35430
\(392\) 0 0
\(393\) 19.7016 0.993816
\(394\) 0 0
\(395\) −39.2814 −1.97646
\(396\) 0 0
\(397\) −23.8957 −1.19929 −0.599647 0.800265i \(-0.704692\pi\)
−0.599647 + 0.800265i \(0.704692\pi\)
\(398\) 0 0
\(399\) 3.46120 0.173277
\(400\) 0 0
\(401\) −26.2689 −1.31181 −0.655903 0.754845i \(-0.727712\pi\)
−0.655903 + 0.754845i \(0.727712\pi\)
\(402\) 0 0
\(403\) −59.2674 −2.95232
\(404\) 0 0
\(405\) −20.3824 −1.01281
\(406\) 0 0
\(407\) −46.3320 −2.29659
\(408\) 0 0
\(409\) 15.9584 0.789093 0.394546 0.918876i \(-0.370902\pi\)
0.394546 + 0.918876i \(0.370902\pi\)
\(410\) 0 0
\(411\) −2.16079 −0.106584
\(412\) 0 0
\(413\) −3.76607 −0.185316
\(414\) 0 0
\(415\) 47.5326 2.33328
\(416\) 0 0
\(417\) −15.0068 −0.734887
\(418\) 0 0
\(419\) 5.96030 0.291180 0.145590 0.989345i \(-0.453492\pi\)
0.145590 + 0.989345i \(0.453492\pi\)
\(420\) 0 0
\(421\) −21.1846 −1.03247 −0.516236 0.856446i \(-0.672667\pi\)
−0.516236 + 0.856446i \(0.672667\pi\)
\(422\) 0 0
\(423\) 4.19285 0.203863
\(424\) 0 0
\(425\) −15.7064 −0.761874
\(426\) 0 0
\(427\) −4.44847 −0.215277
\(428\) 0 0
\(429\) 62.6380 3.02419
\(430\) 0 0
\(431\) −2.38874 −0.115062 −0.0575309 0.998344i \(-0.518323\pi\)
−0.0575309 + 0.998344i \(0.518323\pi\)
\(432\) 0 0
\(433\) 3.90143 0.187491 0.0937455 0.995596i \(-0.470116\pi\)
0.0937455 + 0.995596i \(0.470116\pi\)
\(434\) 0 0
\(435\) −35.8714 −1.71990
\(436\) 0 0
\(437\) −6.54599 −0.313137
\(438\) 0 0
\(439\) 5.34917 0.255302 0.127651 0.991819i \(-0.459256\pi\)
0.127651 + 0.991819i \(0.459256\pi\)
\(440\) 0 0
\(441\) 2.24487 0.106898
\(442\) 0 0
\(443\) −22.8298 −1.08467 −0.542337 0.840161i \(-0.682461\pi\)
−0.542337 + 0.840161i \(0.682461\pi\)
\(444\) 0 0
\(445\) −24.1264 −1.14370
\(446\) 0 0
\(447\) 22.4019 1.05957
\(448\) 0 0
\(449\) −31.5053 −1.48683 −0.743413 0.668833i \(-0.766794\pi\)
−0.743413 + 0.668833i \(0.766794\pi\)
\(450\) 0 0
\(451\) 31.4577 1.48129
\(452\) 0 0
\(453\) −15.4878 −0.727680
\(454\) 0 0
\(455\) 27.0028 1.26591
\(456\) 0 0
\(457\) 16.1928 0.757469 0.378734 0.925505i \(-0.376359\pi\)
0.378734 + 0.925505i \(0.376359\pi\)
\(458\) 0 0
\(459\) −33.4944 −1.56338
\(460\) 0 0
\(461\) −25.9691 −1.20950 −0.604751 0.796415i \(-0.706727\pi\)
−0.604751 + 0.796415i \(0.706727\pi\)
\(462\) 0 0
\(463\) 22.1706 1.03036 0.515179 0.857083i \(-0.327726\pi\)
0.515179 + 0.857083i \(0.327726\pi\)
\(464\) 0 0
\(465\) −38.8237 −1.80041
\(466\) 0 0
\(467\) −29.5908 −1.36930 −0.684649 0.728873i \(-0.740044\pi\)
−0.684649 + 0.728873i \(0.740044\pi\)
\(468\) 0 0
\(469\) 2.46272 0.113718
\(470\) 0 0
\(471\) −32.4923 −1.49716
\(472\) 0 0
\(473\) 49.0772 2.25657
\(474\) 0 0
\(475\) 3.83928 0.176158
\(476\) 0 0
\(477\) −5.70396 −0.261166
\(478\) 0 0
\(479\) −25.2331 −1.15293 −0.576465 0.817122i \(-0.695568\pi\)
−0.576465 + 0.817122i \(0.695568\pi\)
\(480\) 0 0
\(481\) 52.8715 2.41073
\(482\) 0 0
\(483\) −10.2817 −0.467835
\(484\) 0 0
\(485\) 6.99995 0.317851
\(486\) 0 0
\(487\) 19.4539 0.881542 0.440771 0.897620i \(-0.354705\pi\)
0.440771 + 0.897620i \(0.354705\pi\)
\(488\) 0 0
\(489\) 9.59934 0.434097
\(490\) 0 0
\(491\) 4.65848 0.210234 0.105117 0.994460i \(-0.466478\pi\)
0.105117 + 0.994460i \(0.466478\pi\)
\(492\) 0 0
\(493\) −49.6468 −2.23598
\(494\) 0 0
\(495\) −7.47119 −0.335805
\(496\) 0 0
\(497\) 6.17466 0.276971
\(498\) 0 0
\(499\) 9.16907 0.410464 0.205232 0.978713i \(-0.434205\pi\)
0.205232 + 0.978713i \(0.434205\pi\)
\(500\) 0 0
\(501\) −6.45177 −0.288244
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −31.7221 −1.41161
\(506\) 0 0
\(507\) −50.7691 −2.25473
\(508\) 0 0
\(509\) 11.6477 0.516275 0.258137 0.966108i \(-0.416891\pi\)
0.258137 + 0.966108i \(0.416891\pi\)
\(510\) 0 0
\(511\) 18.3435 0.811467
\(512\) 0 0
\(513\) 8.18737 0.361481
\(514\) 0 0
\(515\) −4.46023 −0.196541
\(516\) 0 0
\(517\) −53.2593 −2.34234
\(518\) 0 0
\(519\) −14.9447 −0.656000
\(520\) 0 0
\(521\) 16.4805 0.722024 0.361012 0.932561i \(-0.382431\pi\)
0.361012 + 0.932561i \(0.382431\pi\)
\(522\) 0 0
\(523\) −8.75352 −0.382765 −0.191382 0.981516i \(-0.561297\pi\)
−0.191382 + 0.981516i \(0.561297\pi\)
\(524\) 0 0
\(525\) 6.03033 0.263185
\(526\) 0 0
\(527\) −53.7328 −2.34064
\(528\) 0 0
\(529\) −3.55465 −0.154550
\(530\) 0 0
\(531\) −1.18908 −0.0516015
\(532\) 0 0
\(533\) −35.8978 −1.55491
\(534\) 0 0
\(535\) −11.3874 −0.492321
\(536\) 0 0
\(537\) 14.3389 0.618769
\(538\) 0 0
\(539\) −28.5152 −1.22824
\(540\) 0 0
\(541\) 22.3348 0.960248 0.480124 0.877201i \(-0.340592\pi\)
0.480124 + 0.877201i \(0.340592\pi\)
\(542\) 0 0
\(543\) −8.44997 −0.362623
\(544\) 0 0
\(545\) −50.7595 −2.17430
\(546\) 0 0
\(547\) −12.9067 −0.551849 −0.275925 0.961179i \(-0.588984\pi\)
−0.275925 + 0.961179i \(0.588984\pi\)
\(548\) 0 0
\(549\) −1.40453 −0.0599441
\(550\) 0 0
\(551\) 12.1357 0.516997
\(552\) 0 0
\(553\) 20.8734 0.887629
\(554\) 0 0
\(555\) 34.6340 1.47013
\(556\) 0 0
\(557\) −3.56576 −0.151086 −0.0755430 0.997143i \(-0.524069\pi\)
−0.0755430 + 0.997143i \(0.524069\pi\)
\(558\) 0 0
\(559\) −56.0041 −2.36872
\(560\) 0 0
\(561\) 56.7887 2.39762
\(562\) 0 0
\(563\) 35.6331 1.50176 0.750878 0.660441i \(-0.229631\pi\)
0.750878 + 0.660441i \(0.229631\pi\)
\(564\) 0 0
\(565\) 16.8922 0.710662
\(566\) 0 0
\(567\) 10.8308 0.454852
\(568\) 0 0
\(569\) −11.2523 −0.471721 −0.235861 0.971787i \(-0.575791\pi\)
−0.235861 + 0.971787i \(0.575791\pi\)
\(570\) 0 0
\(571\) 12.2326 0.511918 0.255959 0.966688i \(-0.417609\pi\)
0.255959 + 0.966688i \(0.417609\pi\)
\(572\) 0 0
\(573\) 23.2340 0.970613
\(574\) 0 0
\(575\) −11.4049 −0.475616
\(576\) 0 0
\(577\) −14.9930 −0.624167 −0.312083 0.950055i \(-0.601027\pi\)
−0.312083 + 0.950055i \(0.601027\pi\)
\(578\) 0 0
\(579\) 2.02210 0.0840355
\(580\) 0 0
\(581\) −25.2580 −1.04788
\(582\) 0 0
\(583\) 72.4541 3.00074
\(584\) 0 0
\(585\) 8.52571 0.352495
\(586\) 0 0
\(587\) −45.7141 −1.88682 −0.943412 0.331622i \(-0.892404\pi\)
−0.943412 + 0.331622i \(0.892404\pi\)
\(588\) 0 0
\(589\) 13.1345 0.541196
\(590\) 0 0
\(591\) 21.8410 0.898419
\(592\) 0 0
\(593\) 26.8233 1.10150 0.550750 0.834670i \(-0.314342\pi\)
0.550750 + 0.834670i \(0.314342\pi\)
\(594\) 0 0
\(595\) 24.4812 1.00363
\(596\) 0 0
\(597\) 29.0302 1.18813
\(598\) 0 0
\(599\) 13.0654 0.533837 0.266918 0.963719i \(-0.413995\pi\)
0.266918 + 0.963719i \(0.413995\pi\)
\(600\) 0 0
\(601\) 8.45943 0.345068 0.172534 0.985004i \(-0.444805\pi\)
0.172534 + 0.985004i \(0.444805\pi\)
\(602\) 0 0
\(603\) 0.777564 0.0316648
\(604\) 0 0
\(605\) 64.6046 2.62655
\(606\) 0 0
\(607\) −31.3103 −1.27085 −0.635423 0.772164i \(-0.719174\pi\)
−0.635423 + 0.772164i \(0.719174\pi\)
\(608\) 0 0
\(609\) 19.0614 0.772408
\(610\) 0 0
\(611\) 60.7766 2.45876
\(612\) 0 0
\(613\) −13.9304 −0.562642 −0.281321 0.959614i \(-0.590773\pi\)
−0.281321 + 0.959614i \(0.590773\pi\)
\(614\) 0 0
\(615\) −23.5152 −0.948226
\(616\) 0 0
\(617\) −47.0125 −1.89265 −0.946325 0.323215i \(-0.895236\pi\)
−0.946325 + 0.323215i \(0.895236\pi\)
\(618\) 0 0
\(619\) −33.3762 −1.34150 −0.670751 0.741682i \(-0.734028\pi\)
−0.670751 + 0.741682i \(0.734028\pi\)
\(620\) 0 0
\(621\) −24.3212 −0.975976
\(622\) 0 0
\(623\) 12.8203 0.513636
\(624\) 0 0
\(625\) −31.2425 −1.24970
\(626\) 0 0
\(627\) −13.8814 −0.554371
\(628\) 0 0
\(629\) 47.9342 1.91126
\(630\) 0 0
\(631\) −3.74341 −0.149023 −0.0745114 0.997220i \(-0.523740\pi\)
−0.0745114 + 0.997220i \(0.523740\pi\)
\(632\) 0 0
\(633\) −16.1609 −0.642337
\(634\) 0 0
\(635\) −47.1059 −1.86934
\(636\) 0 0
\(637\) 32.5400 1.28928
\(638\) 0 0
\(639\) 1.94955 0.0771230
\(640\) 0 0
\(641\) −1.81336 −0.0716234 −0.0358117 0.999359i \(-0.511402\pi\)
−0.0358117 + 0.999359i \(0.511402\pi\)
\(642\) 0 0
\(643\) 13.6210 0.537160 0.268580 0.963257i \(-0.413446\pi\)
0.268580 + 0.963257i \(0.413446\pi\)
\(644\) 0 0
\(645\) −36.6861 −1.44451
\(646\) 0 0
\(647\) 16.6018 0.652685 0.326342 0.945252i \(-0.394184\pi\)
0.326342 + 0.945252i \(0.394184\pi\)
\(648\) 0 0
\(649\) 15.1041 0.592889
\(650\) 0 0
\(651\) 20.6302 0.808562
\(652\) 0 0
\(653\) −5.76542 −0.225618 −0.112809 0.993617i \(-0.535985\pi\)
−0.112809 + 0.993617i \(0.535985\pi\)
\(654\) 0 0
\(655\) −34.0629 −1.33095
\(656\) 0 0
\(657\) 5.79166 0.225954
\(658\) 0 0
\(659\) 19.3602 0.754168 0.377084 0.926179i \(-0.376927\pi\)
0.377084 + 0.926179i \(0.376927\pi\)
\(660\) 0 0
\(661\) −5.17780 −0.201393 −0.100697 0.994917i \(-0.532107\pi\)
−0.100697 + 0.994917i \(0.532107\pi\)
\(662\) 0 0
\(663\) −64.8041 −2.51678
\(664\) 0 0
\(665\) −5.98419 −0.232057
\(666\) 0 0
\(667\) −36.0499 −1.39586
\(668\) 0 0
\(669\) 14.9086 0.576401
\(670\) 0 0
\(671\) 17.8410 0.688744
\(672\) 0 0
\(673\) 2.58114 0.0994958 0.0497479 0.998762i \(-0.484158\pi\)
0.0497479 + 0.998762i \(0.484158\pi\)
\(674\) 0 0
\(675\) 14.2646 0.549045
\(676\) 0 0
\(677\) 43.2830 1.66350 0.831751 0.555149i \(-0.187339\pi\)
0.831751 + 0.555149i \(0.187339\pi\)
\(678\) 0 0
\(679\) −3.71965 −0.142747
\(680\) 0 0
\(681\) 21.5017 0.823947
\(682\) 0 0
\(683\) 14.8597 0.568590 0.284295 0.958737i \(-0.408240\pi\)
0.284295 + 0.958737i \(0.408240\pi\)
\(684\) 0 0
\(685\) 3.73588 0.142741
\(686\) 0 0
\(687\) −6.14406 −0.234411
\(688\) 0 0
\(689\) −82.6806 −3.14988
\(690\) 0 0
\(691\) −34.7070 −1.32032 −0.660158 0.751127i \(-0.729511\pi\)
−0.660158 + 0.751127i \(0.729511\pi\)
\(692\) 0 0
\(693\) 3.97005 0.150810
\(694\) 0 0
\(695\) 25.9458 0.984182
\(696\) 0 0
\(697\) −32.5456 −1.23275
\(698\) 0 0
\(699\) 42.4723 1.60645
\(700\) 0 0
\(701\) 12.6514 0.477838 0.238919 0.971040i \(-0.423207\pi\)
0.238919 + 0.971040i \(0.423207\pi\)
\(702\) 0 0
\(703\) −11.7170 −0.441917
\(704\) 0 0
\(705\) 39.8123 1.49942
\(706\) 0 0
\(707\) 16.8565 0.633956
\(708\) 0 0
\(709\) −0.358275 −0.0134553 −0.00672765 0.999977i \(-0.502141\pi\)
−0.00672765 + 0.999977i \(0.502141\pi\)
\(710\) 0 0
\(711\) 6.59046 0.247161
\(712\) 0 0
\(713\) −39.0169 −1.46119
\(714\) 0 0
\(715\) −108.297 −4.05008
\(716\) 0 0
\(717\) −16.9272 −0.632157
\(718\) 0 0
\(719\) 23.9993 0.895024 0.447512 0.894278i \(-0.352310\pi\)
0.447512 + 0.894278i \(0.352310\pi\)
\(720\) 0 0
\(721\) 2.37008 0.0882665
\(722\) 0 0
\(723\) 33.8373 1.25842
\(724\) 0 0
\(725\) 21.1436 0.785254
\(726\) 0 0
\(727\) 38.0953 1.41288 0.706438 0.707775i \(-0.250301\pi\)
0.706438 + 0.707775i \(0.250301\pi\)
\(728\) 0 0
\(729\) 29.7790 1.10293
\(730\) 0 0
\(731\) −50.7743 −1.87796
\(732\) 0 0
\(733\) 50.7757 1.87544 0.937721 0.347388i \(-0.112931\pi\)
0.937721 + 0.347388i \(0.112931\pi\)
\(734\) 0 0
\(735\) 21.3156 0.786240
\(736\) 0 0
\(737\) −9.87694 −0.363822
\(738\) 0 0
\(739\) −30.7456 −1.13099 −0.565497 0.824750i \(-0.691316\pi\)
−0.565497 + 0.824750i \(0.691316\pi\)
\(740\) 0 0
\(741\) 15.8407 0.581923
\(742\) 0 0
\(743\) 17.3272 0.635673 0.317837 0.948146i \(-0.397044\pi\)
0.317837 + 0.948146i \(0.397044\pi\)
\(744\) 0 0
\(745\) −38.7314 −1.41901
\(746\) 0 0
\(747\) −7.97480 −0.291783
\(748\) 0 0
\(749\) 6.05107 0.221101
\(750\) 0 0
\(751\) −33.6584 −1.22821 −0.614106 0.789224i \(-0.710483\pi\)
−0.614106 + 0.789224i \(0.710483\pi\)
\(752\) 0 0
\(753\) −31.3282 −1.14166
\(754\) 0 0
\(755\) 26.7774 0.974530
\(756\) 0 0
\(757\) −34.1538 −1.24134 −0.620671 0.784071i \(-0.713140\pi\)
−0.620671 + 0.784071i \(0.713140\pi\)
\(758\) 0 0
\(759\) 41.2358 1.49677
\(760\) 0 0
\(761\) 14.3681 0.520842 0.260421 0.965495i \(-0.416139\pi\)
0.260421 + 0.965495i \(0.416139\pi\)
\(762\) 0 0
\(763\) 26.9727 0.976476
\(764\) 0 0
\(765\) 7.72955 0.279463
\(766\) 0 0
\(767\) −17.2360 −0.622356
\(768\) 0 0
\(769\) 27.4962 0.991537 0.495768 0.868455i \(-0.334887\pi\)
0.495768 + 0.868455i \(0.334887\pi\)
\(770\) 0 0
\(771\) 37.7423 1.35925
\(772\) 0 0
\(773\) −7.75525 −0.278937 −0.139469 0.990226i \(-0.544539\pi\)
−0.139469 + 0.990226i \(0.544539\pi\)
\(774\) 0 0
\(775\) 22.8838 0.822009
\(776\) 0 0
\(777\) −18.4039 −0.660236
\(778\) 0 0
\(779\) 7.95544 0.285033
\(780\) 0 0
\(781\) −24.7640 −0.886126
\(782\) 0 0
\(783\) 45.0893 1.61136
\(784\) 0 0
\(785\) 56.1770 2.00504
\(786\) 0 0
\(787\) 19.6903 0.701885 0.350942 0.936397i \(-0.385861\pi\)
0.350942 + 0.936397i \(0.385861\pi\)
\(788\) 0 0
\(789\) −1.72902 −0.0615549
\(790\) 0 0
\(791\) −8.97623 −0.319158
\(792\) 0 0
\(793\) −20.3591 −0.722975
\(794\) 0 0
\(795\) −54.1607 −1.92088
\(796\) 0 0
\(797\) −21.9546 −0.777671 −0.388835 0.921307i \(-0.627123\pi\)
−0.388835 + 0.921307i \(0.627123\pi\)
\(798\) 0 0
\(799\) 55.1011 1.94934
\(800\) 0 0
\(801\) 4.04782 0.143023
\(802\) 0 0
\(803\) −73.5680 −2.59616
\(804\) 0 0
\(805\) 17.7765 0.626539
\(806\) 0 0
\(807\) −14.2252 −0.500750
\(808\) 0 0
\(809\) −10.3431 −0.363644 −0.181822 0.983331i \(-0.558199\pi\)
−0.181822 + 0.983331i \(0.558199\pi\)
\(810\) 0 0
\(811\) 32.4712 1.14022 0.570109 0.821569i \(-0.306901\pi\)
0.570109 + 0.821569i \(0.306901\pi\)
\(812\) 0 0
\(813\) 12.8022 0.448991
\(814\) 0 0
\(815\) −16.5967 −0.581355
\(816\) 0 0
\(817\) 12.4113 0.434215
\(818\) 0 0
\(819\) −4.53041 −0.158305
\(820\) 0 0
\(821\) −54.2464 −1.89321 −0.946606 0.322394i \(-0.895513\pi\)
−0.946606 + 0.322394i \(0.895513\pi\)
\(822\) 0 0
\(823\) −49.1896 −1.71464 −0.857322 0.514781i \(-0.827873\pi\)
−0.857322 + 0.514781i \(0.827873\pi\)
\(824\) 0 0
\(825\) −24.1852 −0.842020
\(826\) 0 0
\(827\) −42.9413 −1.49322 −0.746608 0.665265i \(-0.768319\pi\)
−0.746608 + 0.665265i \(0.768319\pi\)
\(828\) 0 0
\(829\) −21.5437 −0.748245 −0.374122 0.927379i \(-0.622056\pi\)
−0.374122 + 0.927379i \(0.622056\pi\)
\(830\) 0 0
\(831\) −17.0607 −0.591829
\(832\) 0 0
\(833\) 29.5013 1.02216
\(834\) 0 0
\(835\) 11.1547 0.386025
\(836\) 0 0
\(837\) 48.8003 1.68678
\(838\) 0 0
\(839\) −18.6657 −0.644410 −0.322205 0.946670i \(-0.604424\pi\)
−0.322205 + 0.946670i \(0.604424\pi\)
\(840\) 0 0
\(841\) 37.8333 1.30460
\(842\) 0 0
\(843\) 16.8952 0.581900
\(844\) 0 0
\(845\) 87.7765 3.01960
\(846\) 0 0
\(847\) −34.3297 −1.17958
\(848\) 0 0
\(849\) 4.19997 0.144143
\(850\) 0 0
\(851\) 34.8063 1.19315
\(852\) 0 0
\(853\) −29.7303 −1.01795 −0.508974 0.860782i \(-0.669975\pi\)
−0.508974 + 0.860782i \(0.669975\pi\)
\(854\) 0 0
\(855\) −1.88941 −0.0646165
\(856\) 0 0
\(857\) −22.9356 −0.783465 −0.391733 0.920079i \(-0.628124\pi\)
−0.391733 + 0.920079i \(0.628124\pi\)
\(858\) 0 0
\(859\) −21.3777 −0.729397 −0.364698 0.931126i \(-0.618828\pi\)
−0.364698 + 0.931126i \(0.618828\pi\)
\(860\) 0 0
\(861\) 12.4956 0.425848
\(862\) 0 0
\(863\) 54.1528 1.84338 0.921692 0.387922i \(-0.126807\pi\)
0.921692 + 0.387922i \(0.126807\pi\)
\(864\) 0 0
\(865\) 25.8385 0.878534
\(866\) 0 0
\(867\) −31.6702 −1.07558
\(868\) 0 0
\(869\) −83.7147 −2.83983
\(870\) 0 0
\(871\) 11.2710 0.381904
\(872\) 0 0
\(873\) −1.17442 −0.0397481
\(874\) 0 0
\(875\) 9.73010 0.328937
\(876\) 0 0
\(877\) −30.5204 −1.03060 −0.515300 0.857010i \(-0.672319\pi\)
−0.515300 + 0.857010i \(0.672319\pi\)
\(878\) 0 0
\(879\) −11.6711 −0.393655
\(880\) 0 0
\(881\) 3.55114 0.119641 0.0598205 0.998209i \(-0.480947\pi\)
0.0598205 + 0.998209i \(0.480947\pi\)
\(882\) 0 0
\(883\) 26.5969 0.895056 0.447528 0.894270i \(-0.352305\pi\)
0.447528 + 0.894270i \(0.352305\pi\)
\(884\) 0 0
\(885\) −11.2906 −0.379530
\(886\) 0 0
\(887\) 47.2877 1.58776 0.793882 0.608071i \(-0.208057\pi\)
0.793882 + 0.608071i \(0.208057\pi\)
\(888\) 0 0
\(889\) 25.0312 0.839521
\(890\) 0 0
\(891\) −43.4380 −1.45523
\(892\) 0 0
\(893\) −13.4689 −0.450720
\(894\) 0 0
\(895\) −24.7910 −0.828673
\(896\) 0 0
\(897\) −47.0561 −1.57116
\(898\) 0 0
\(899\) 72.3339 2.41247
\(900\) 0 0
\(901\) −74.9596 −2.49727
\(902\) 0 0
\(903\) 19.4943 0.648730
\(904\) 0 0
\(905\) 14.6095 0.485635
\(906\) 0 0
\(907\) −5.29369 −0.175774 −0.0878870 0.996130i \(-0.528011\pi\)
−0.0878870 + 0.996130i \(0.528011\pi\)
\(908\) 0 0
\(909\) 5.32219 0.176526
\(910\) 0 0
\(911\) 14.4595 0.479064 0.239532 0.970888i \(-0.423006\pi\)
0.239532 + 0.970888i \(0.423006\pi\)
\(912\) 0 0
\(913\) 101.299 3.35252
\(914\) 0 0
\(915\) −13.3365 −0.440890
\(916\) 0 0
\(917\) 18.1004 0.597727
\(918\) 0 0
\(919\) −3.00395 −0.0990911 −0.0495456 0.998772i \(-0.515777\pi\)
−0.0495456 + 0.998772i \(0.515777\pi\)
\(920\) 0 0
\(921\) −21.1664 −0.697457
\(922\) 0 0
\(923\) 28.2593 0.930167
\(924\) 0 0
\(925\) −20.4142 −0.671216
\(926\) 0 0
\(927\) 0.748316 0.0245779
\(928\) 0 0
\(929\) 13.1686 0.432047 0.216023 0.976388i \(-0.430691\pi\)
0.216023 + 0.976388i \(0.430691\pi\)
\(930\) 0 0
\(931\) −7.21130 −0.236341
\(932\) 0 0
\(933\) 36.0500 1.18022
\(934\) 0 0
\(935\) −98.1840 −3.21096
\(936\) 0 0
\(937\) 7.66519 0.250411 0.125205 0.992131i \(-0.460041\pi\)
0.125205 + 0.992131i \(0.460041\pi\)
\(938\) 0 0
\(939\) −3.20400 −0.104559
\(940\) 0 0
\(941\) −31.8108 −1.03700 −0.518501 0.855077i \(-0.673510\pi\)
−0.518501 + 0.855077i \(0.673510\pi\)
\(942\) 0 0
\(943\) −23.6322 −0.769572
\(944\) 0 0
\(945\) −22.2339 −0.723268
\(946\) 0 0
\(947\) 20.1008 0.653189 0.326595 0.945165i \(-0.394099\pi\)
0.326595 + 0.945165i \(0.394099\pi\)
\(948\) 0 0
\(949\) 83.9518 2.72519
\(950\) 0 0
\(951\) 48.4736 1.57187
\(952\) 0 0
\(953\) 2.24603 0.0727560 0.0363780 0.999338i \(-0.488418\pi\)
0.0363780 + 0.999338i \(0.488418\pi\)
\(954\) 0 0
\(955\) −40.1701 −1.29987
\(956\) 0 0
\(957\) −76.4475 −2.47120
\(958\) 0 0
\(959\) −1.98518 −0.0641047
\(960\) 0 0
\(961\) 47.2871 1.52539
\(962\) 0 0
\(963\) 1.91053 0.0615660
\(964\) 0 0
\(965\) −3.49608 −0.112543
\(966\) 0 0
\(967\) 25.4322 0.817843 0.408921 0.912570i \(-0.365905\pi\)
0.408921 + 0.912570i \(0.365905\pi\)
\(968\) 0 0
\(969\) 14.3615 0.461357
\(970\) 0 0
\(971\) −10.2958 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(972\) 0 0
\(973\) −13.7872 −0.441996
\(974\) 0 0
\(975\) 27.5988 0.883869
\(976\) 0 0
\(977\) −2.26590 −0.0724925 −0.0362462 0.999343i \(-0.511540\pi\)
−0.0362462 + 0.999343i \(0.511540\pi\)
\(978\) 0 0
\(979\) −51.4170 −1.64330
\(980\) 0 0
\(981\) 8.51619 0.271901
\(982\) 0 0
\(983\) −19.6737 −0.627492 −0.313746 0.949507i \(-0.601584\pi\)
−0.313746 + 0.949507i \(0.601584\pi\)
\(984\) 0 0
\(985\) −37.7617 −1.20319
\(986\) 0 0
\(987\) −21.1555 −0.673388
\(988\) 0 0
\(989\) −36.8686 −1.17235
\(990\) 0 0
\(991\) −48.1094 −1.52825 −0.764123 0.645070i \(-0.776828\pi\)
−0.764123 + 0.645070i \(0.776828\pi\)
\(992\) 0 0
\(993\) 1.46808 0.0465882
\(994\) 0 0
\(995\) −50.1914 −1.59117
\(996\) 0 0
\(997\) −1.90282 −0.0602629 −0.0301315 0.999546i \(-0.509593\pi\)
−0.0301315 + 0.999546i \(0.509593\pi\)
\(998\) 0 0
\(999\) −43.5339 −1.37735
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 \(a_p\))