Properties

Label 6027.2.a.bn.1.22
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +9.97400 q^{10} +3.81355 q^{11} -4.56633 q^{12} -6.39406 q^{13} -3.89232 q^{15} +7.71874 q^{16} -1.70351 q^{17} +2.56249 q^{18} +6.47548 q^{19} +17.7736 q^{20} +9.77216 q^{22} +3.51424 q^{23} -6.57620 q^{24} +10.1501 q^{25} -16.3847 q^{26} -1.00000 q^{27} -8.65494 q^{29} -9.97400 q^{30} -0.432523 q^{31} +6.62678 q^{32} -3.81355 q^{33} -4.36521 q^{34} +4.56633 q^{36} +7.97403 q^{37} +16.5933 q^{38} +6.39406 q^{39} +25.5966 q^{40} +1.00000 q^{41} -6.41643 q^{43} +17.4139 q^{44} +3.89232 q^{45} +9.00520 q^{46} -3.72691 q^{47} -7.71874 q^{48} +26.0095 q^{50} +1.70351 q^{51} -29.1974 q^{52} +14.2446 q^{53} -2.56249 q^{54} +14.8435 q^{55} -6.47548 q^{57} -22.1782 q^{58} -3.38894 q^{59} -17.7736 q^{60} +4.40630 q^{61} -1.10833 q^{62} +1.54354 q^{64} -24.8877 q^{65} -9.77216 q^{66} +3.61186 q^{67} -7.77878 q^{68} -3.51424 q^{69} -0.619870 q^{71} +6.57620 q^{72} -2.71814 q^{73} +20.4334 q^{74} -10.1501 q^{75} +29.5692 q^{76} +16.3847 q^{78} +11.5546 q^{79} +30.0438 q^{80} +1.00000 q^{81} +2.56249 q^{82} -5.74873 q^{83} -6.63058 q^{85} -16.4420 q^{86} +8.65494 q^{87} +25.0786 q^{88} -16.4936 q^{89} +9.97400 q^{90} +16.0472 q^{92} +0.432523 q^{93} -9.55015 q^{94} +25.2046 q^{95} -6.62678 q^{96} -2.81728 q^{97} +3.81355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56249 1.81195 0.905976 0.423330i \(-0.139139\pi\)
0.905976 + 0.423330i \(0.139139\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.56633 2.28317
\(5\) 3.89232 1.74070 0.870348 0.492437i \(-0.163894\pi\)
0.870348 + 0.492437i \(0.163894\pi\)
\(6\) −2.56249 −1.04613
\(7\) 0 0
\(8\) 6.57620 2.32504
\(9\) 1.00000 0.333333
\(10\) 9.97400 3.15406
\(11\) 3.81355 1.14983 0.574914 0.818214i \(-0.305035\pi\)
0.574914 + 0.818214i \(0.305035\pi\)
\(12\) −4.56633 −1.31819
\(13\) −6.39406 −1.77339 −0.886697 0.462351i \(-0.847006\pi\)
−0.886697 + 0.462351i \(0.847006\pi\)
\(14\) 0 0
\(15\) −3.89232 −1.00499
\(16\) 7.71874 1.92969
\(17\) −1.70351 −0.413161 −0.206580 0.978430i \(-0.566233\pi\)
−0.206580 + 0.978430i \(0.566233\pi\)
\(18\) 2.56249 0.603984
\(19\) 6.47548 1.48558 0.742789 0.669526i \(-0.233503\pi\)
0.742789 + 0.669526i \(0.233503\pi\)
\(20\) 17.7736 3.97430
\(21\) 0 0
\(22\) 9.77216 2.08343
\(23\) 3.51424 0.732771 0.366385 0.930463i \(-0.380595\pi\)
0.366385 + 0.930463i \(0.380595\pi\)
\(24\) −6.57620 −1.34236
\(25\) 10.1501 2.03002
\(26\) −16.3847 −3.21330
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.65494 −1.60718 −0.803591 0.595182i \(-0.797080\pi\)
−0.803591 + 0.595182i \(0.797080\pi\)
\(30\) −9.97400 −1.82100
\(31\) −0.432523 −0.0776834 −0.0388417 0.999245i \(-0.512367\pi\)
−0.0388417 + 0.999245i \(0.512367\pi\)
\(32\) 6.62678 1.17146
\(33\) −3.81355 −0.663854
\(34\) −4.36521 −0.748627
\(35\) 0 0
\(36\) 4.56633 0.761056
\(37\) 7.97403 1.31092 0.655462 0.755229i \(-0.272474\pi\)
0.655462 + 0.755229i \(0.272474\pi\)
\(38\) 16.5933 2.69179
\(39\) 6.39406 1.02387
\(40\) 25.5966 4.04718
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −6.41643 −0.978496 −0.489248 0.872145i \(-0.662729\pi\)
−0.489248 + 0.872145i \(0.662729\pi\)
\(44\) 17.4139 2.62525
\(45\) 3.89232 0.580232
\(46\) 9.00520 1.32774
\(47\) −3.72691 −0.543625 −0.271813 0.962350i \(-0.587623\pi\)
−0.271813 + 0.962350i \(0.587623\pi\)
\(48\) −7.71874 −1.11410
\(49\) 0 0
\(50\) 26.0095 3.67830
\(51\) 1.70351 0.238538
\(52\) −29.1974 −4.04896
\(53\) 14.2446 1.95665 0.978323 0.207085i \(-0.0663977\pi\)
0.978323 + 0.207085i \(0.0663977\pi\)
\(54\) −2.56249 −0.348710
\(55\) 14.8435 2.00150
\(56\) 0 0
\(57\) −6.47548 −0.857699
\(58\) −22.1782 −2.91213
\(59\) −3.38894 −0.441203 −0.220601 0.975364i \(-0.570802\pi\)
−0.220601 + 0.975364i \(0.570802\pi\)
\(60\) −17.7736 −2.29456
\(61\) 4.40630 0.564169 0.282084 0.959390i \(-0.408974\pi\)
0.282084 + 0.959390i \(0.408974\pi\)
\(62\) −1.10833 −0.140759
\(63\) 0 0
\(64\) 1.54354 0.192943
\(65\) −24.8877 −3.08694
\(66\) −9.77216 −1.20287
\(67\) 3.61186 0.441259 0.220630 0.975358i \(-0.429189\pi\)
0.220630 + 0.975358i \(0.429189\pi\)
\(68\) −7.77878 −0.943315
\(69\) −3.51424 −0.423065
\(70\) 0 0
\(71\) −0.619870 −0.0735650 −0.0367825 0.999323i \(-0.511711\pi\)
−0.0367825 + 0.999323i \(0.511711\pi\)
\(72\) 6.57620 0.775012
\(73\) −2.71814 −0.318134 −0.159067 0.987268i \(-0.550849\pi\)
−0.159067 + 0.987268i \(0.550849\pi\)
\(74\) 20.4334 2.37533
\(75\) −10.1501 −1.17204
\(76\) 29.5692 3.39182
\(77\) 0 0
\(78\) 16.3847 1.85520
\(79\) 11.5546 1.29999 0.649995 0.759939i \(-0.274771\pi\)
0.649995 + 0.759939i \(0.274771\pi\)
\(80\) 30.0438 3.35900
\(81\) 1.00000 0.111111
\(82\) 2.56249 0.282979
\(83\) −5.74873 −0.631005 −0.315502 0.948925i \(-0.602173\pi\)
−0.315502 + 0.948925i \(0.602173\pi\)
\(84\) 0 0
\(85\) −6.63058 −0.719188
\(86\) −16.4420 −1.77299
\(87\) 8.65494 0.927907
\(88\) 25.0786 2.67339
\(89\) −16.4936 −1.74831 −0.874157 0.485644i \(-0.838585\pi\)
−0.874157 + 0.485644i \(0.838585\pi\)
\(90\) 9.97400 1.05135
\(91\) 0 0
\(92\) 16.0472 1.67304
\(93\) 0.432523 0.0448505
\(94\) −9.55015 −0.985022
\(95\) 25.2046 2.58594
\(96\) −6.62678 −0.676343
\(97\) −2.81728 −0.286051 −0.143026 0.989719i \(-0.545683\pi\)
−0.143026 + 0.989719i \(0.545683\pi\)
\(98\) 0 0
\(99\) 3.81355 0.383276
\(100\) 46.3489 4.63489
\(101\) −9.17978 −0.913422 −0.456711 0.889615i \(-0.650973\pi\)
−0.456711 + 0.889615i \(0.650973\pi\)
\(102\) 4.36521 0.432220
\(103\) 12.7010 1.25147 0.625734 0.780036i \(-0.284799\pi\)
0.625734 + 0.780036i \(0.284799\pi\)
\(104\) −42.0486 −4.12321
\(105\) 0 0
\(106\) 36.5016 3.54535
\(107\) 9.75066 0.942632 0.471316 0.881964i \(-0.343779\pi\)
0.471316 + 0.881964i \(0.343779\pi\)
\(108\) −4.56633 −0.439396
\(109\) −15.4367 −1.47856 −0.739282 0.673396i \(-0.764835\pi\)
−0.739282 + 0.673396i \(0.764835\pi\)
\(110\) 38.0363 3.62662
\(111\) −7.97403 −0.756862
\(112\) 0 0
\(113\) 16.0865 1.51329 0.756646 0.653825i \(-0.226837\pi\)
0.756646 + 0.653825i \(0.226837\pi\)
\(114\) −16.5933 −1.55411
\(115\) 13.6786 1.27553
\(116\) −39.5213 −3.66946
\(117\) −6.39406 −0.591131
\(118\) −8.68412 −0.799438
\(119\) 0 0
\(120\) −25.5966 −2.33664
\(121\) 3.54315 0.322105
\(122\) 11.2911 1.02225
\(123\) −1.00000 −0.0901670
\(124\) −1.97504 −0.177364
\(125\) 20.0459 1.79296
\(126\) 0 0
\(127\) −13.4222 −1.19103 −0.595515 0.803344i \(-0.703052\pi\)
−0.595515 + 0.803344i \(0.703052\pi\)
\(128\) −9.29825 −0.821857
\(129\) 6.41643 0.564935
\(130\) −63.7744 −5.59339
\(131\) 3.10894 0.271630 0.135815 0.990734i \(-0.456635\pi\)
0.135815 + 0.990734i \(0.456635\pi\)
\(132\) −17.4139 −1.51569
\(133\) 0 0
\(134\) 9.25535 0.799540
\(135\) −3.89232 −0.334997
\(136\) −11.2026 −0.960614
\(137\) −12.3063 −1.05140 −0.525700 0.850670i \(-0.676196\pi\)
−0.525700 + 0.850670i \(0.676196\pi\)
\(138\) −9.00520 −0.766574
\(139\) −10.9403 −0.927944 −0.463972 0.885850i \(-0.653576\pi\)
−0.463972 + 0.885850i \(0.653576\pi\)
\(140\) 0 0
\(141\) 3.72691 0.313862
\(142\) −1.58841 −0.133296
\(143\) −24.3841 −2.03910
\(144\) 7.71874 0.643229
\(145\) −33.6877 −2.79762
\(146\) −6.96519 −0.576443
\(147\) 0 0
\(148\) 36.4121 2.99306
\(149\) 10.0711 0.825057 0.412529 0.910945i \(-0.364646\pi\)
0.412529 + 0.910945i \(0.364646\pi\)
\(150\) −26.0095 −2.12367
\(151\) −17.6807 −1.43883 −0.719416 0.694579i \(-0.755590\pi\)
−0.719416 + 0.694579i \(0.755590\pi\)
\(152\) 42.5841 3.45402
\(153\) −1.70351 −0.137720
\(154\) 0 0
\(155\) −1.68352 −0.135223
\(156\) 29.1974 2.33767
\(157\) −9.27189 −0.739977 −0.369989 0.929036i \(-0.620638\pi\)
−0.369989 + 0.929036i \(0.620638\pi\)
\(158\) 29.6084 2.35552
\(159\) −14.2446 −1.12967
\(160\) 25.7935 2.03916
\(161\) 0 0
\(162\) 2.56249 0.201328
\(163\) −21.2183 −1.66195 −0.830974 0.556312i \(-0.812216\pi\)
−0.830974 + 0.556312i \(0.812216\pi\)
\(164\) 4.56633 0.356571
\(165\) −14.8435 −1.15557
\(166\) −14.7310 −1.14335
\(167\) 15.0869 1.16746 0.583731 0.811947i \(-0.301592\pi\)
0.583731 + 0.811947i \(0.301592\pi\)
\(168\) 0 0
\(169\) 27.8841 2.14493
\(170\) −16.9908 −1.30313
\(171\) 6.47548 0.495193
\(172\) −29.2996 −2.23407
\(173\) 3.21775 0.244641 0.122320 0.992491i \(-0.460966\pi\)
0.122320 + 0.992491i \(0.460966\pi\)
\(174\) 22.1782 1.68132
\(175\) 0 0
\(176\) 29.4358 2.21881
\(177\) 3.38894 0.254729
\(178\) −42.2645 −3.16786
\(179\) −3.09693 −0.231475 −0.115738 0.993280i \(-0.536923\pi\)
−0.115738 + 0.993280i \(0.536923\pi\)
\(180\) 17.7736 1.32477
\(181\) 0.106111 0.00788716 0.00394358 0.999992i \(-0.498745\pi\)
0.00394358 + 0.999992i \(0.498745\pi\)
\(182\) 0 0
\(183\) −4.40630 −0.325723
\(184\) 23.1104 1.70372
\(185\) 31.0375 2.28192
\(186\) 1.10833 0.0812670
\(187\) −6.49640 −0.475064
\(188\) −17.0183 −1.24119
\(189\) 0 0
\(190\) 64.5865 4.68560
\(191\) −11.2353 −0.812957 −0.406478 0.913660i \(-0.633243\pi\)
−0.406478 + 0.913660i \(0.633243\pi\)
\(192\) −1.54354 −0.111396
\(193\) −8.99177 −0.647242 −0.323621 0.946187i \(-0.604900\pi\)
−0.323621 + 0.946187i \(0.604900\pi\)
\(194\) −7.21924 −0.518311
\(195\) 24.8877 1.78225
\(196\) 0 0
\(197\) 0.416020 0.0296402 0.0148201 0.999890i \(-0.495282\pi\)
0.0148201 + 0.999890i \(0.495282\pi\)
\(198\) 9.77216 0.694477
\(199\) 7.21407 0.511392 0.255696 0.966757i \(-0.417695\pi\)
0.255696 + 0.966757i \(0.417695\pi\)
\(200\) 66.7492 4.71988
\(201\) −3.61186 −0.254761
\(202\) −23.5231 −1.65508
\(203\) 0 0
\(204\) 7.77878 0.544623
\(205\) 3.89232 0.271851
\(206\) 32.5462 2.26760
\(207\) 3.51424 0.244257
\(208\) −49.3541 −3.42209
\(209\) 24.6946 1.70816
\(210\) 0 0
\(211\) −11.7020 −0.805599 −0.402800 0.915288i \(-0.631963\pi\)
−0.402800 + 0.915288i \(0.631963\pi\)
\(212\) 65.0456 4.46735
\(213\) 0.619870 0.0424728
\(214\) 24.9859 1.70800
\(215\) −24.9748 −1.70327
\(216\) −6.57620 −0.447454
\(217\) 0 0
\(218\) −39.5562 −2.67909
\(219\) 2.71814 0.183675
\(220\) 67.7805 4.56976
\(221\) 10.8923 0.732697
\(222\) −20.4334 −1.37140
\(223\) 8.90948 0.596623 0.298311 0.954469i \(-0.403577\pi\)
0.298311 + 0.954469i \(0.403577\pi\)
\(224\) 0 0
\(225\) 10.1501 0.676675
\(226\) 41.2215 2.74201
\(227\) 14.3864 0.954861 0.477431 0.878669i \(-0.341568\pi\)
0.477431 + 0.878669i \(0.341568\pi\)
\(228\) −29.5692 −1.95827
\(229\) 4.19714 0.277355 0.138677 0.990338i \(-0.455715\pi\)
0.138677 + 0.990338i \(0.455715\pi\)
\(230\) 35.0511 2.31120
\(231\) 0 0
\(232\) −56.9166 −3.73676
\(233\) −4.56437 −0.299022 −0.149511 0.988760i \(-0.547770\pi\)
−0.149511 + 0.988760i \(0.547770\pi\)
\(234\) −16.3847 −1.07110
\(235\) −14.5063 −0.946287
\(236\) −15.4750 −1.00734
\(237\) −11.5546 −0.750549
\(238\) 0 0
\(239\) −26.7068 −1.72752 −0.863761 0.503902i \(-0.831897\pi\)
−0.863761 + 0.503902i \(0.831897\pi\)
\(240\) −30.0438 −1.93932
\(241\) −10.9960 −0.708316 −0.354158 0.935186i \(-0.615233\pi\)
−0.354158 + 0.935186i \(0.615233\pi\)
\(242\) 9.07927 0.583638
\(243\) −1.00000 −0.0641500
\(244\) 20.1206 1.28809
\(245\) 0 0
\(246\) −2.56249 −0.163378
\(247\) −41.4047 −2.63452
\(248\) −2.84436 −0.180617
\(249\) 5.74873 0.364311
\(250\) 51.3673 3.24876
\(251\) 19.7095 1.24405 0.622026 0.782997i \(-0.286310\pi\)
0.622026 + 0.782997i \(0.286310\pi\)
\(252\) 0 0
\(253\) 13.4017 0.842560
\(254\) −34.3943 −2.15809
\(255\) 6.63058 0.415223
\(256\) −26.9137 −1.68211
\(257\) 31.9263 1.99151 0.995754 0.0920522i \(-0.0293427\pi\)
0.995754 + 0.0920522i \(0.0293427\pi\)
\(258\) 16.4420 1.02363
\(259\) 0 0
\(260\) −113.646 −7.04800
\(261\) −8.65494 −0.535727
\(262\) 7.96662 0.492180
\(263\) 17.2241 1.06208 0.531042 0.847345i \(-0.321801\pi\)
0.531042 + 0.847345i \(0.321801\pi\)
\(264\) −25.0786 −1.54348
\(265\) 55.4445 3.40593
\(266\) 0 0
\(267\) 16.4936 1.00939
\(268\) 16.4930 1.00747
\(269\) −10.3538 −0.631282 −0.315641 0.948879i \(-0.602220\pi\)
−0.315641 + 0.948879i \(0.602220\pi\)
\(270\) −9.97400 −0.606999
\(271\) −27.4283 −1.66615 −0.833076 0.553158i \(-0.813423\pi\)
−0.833076 + 0.553158i \(0.813423\pi\)
\(272\) −13.1489 −0.797271
\(273\) 0 0
\(274\) −31.5348 −1.90508
\(275\) 38.7080 2.33418
\(276\) −16.0472 −0.965929
\(277\) 11.9690 0.719149 0.359574 0.933116i \(-0.382922\pi\)
0.359574 + 0.933116i \(0.382922\pi\)
\(278\) −28.0344 −1.68139
\(279\) −0.432523 −0.0258945
\(280\) 0 0
\(281\) 10.1762 0.607063 0.303531 0.952821i \(-0.401834\pi\)
0.303531 + 0.952821i \(0.401834\pi\)
\(282\) 9.55015 0.568703
\(283\) 6.37817 0.379143 0.189572 0.981867i \(-0.439290\pi\)
0.189572 + 0.981867i \(0.439290\pi\)
\(284\) −2.83053 −0.167961
\(285\) −25.2046 −1.49299
\(286\) −62.4838 −3.69475
\(287\) 0 0
\(288\) 6.62678 0.390487
\(289\) −14.0981 −0.829298
\(290\) −86.3244 −5.06914
\(291\) 2.81728 0.165152
\(292\) −12.4119 −0.726353
\(293\) −31.5877 −1.84537 −0.922687 0.385550i \(-0.874012\pi\)
−0.922687 + 0.385550i \(0.874012\pi\)
\(294\) 0 0
\(295\) −13.1908 −0.768000
\(296\) 52.4388 3.04794
\(297\) −3.81355 −0.221285
\(298\) 25.8071 1.49496
\(299\) −22.4703 −1.29949
\(300\) −46.3489 −2.67595
\(301\) 0 0
\(302\) −45.3065 −2.60709
\(303\) 9.17978 0.527364
\(304\) 49.9826 2.86670
\(305\) 17.1507 0.982046
\(306\) −4.36521 −0.249542
\(307\) 4.13968 0.236264 0.118132 0.992998i \(-0.462309\pi\)
0.118132 + 0.992998i \(0.462309\pi\)
\(308\) 0 0
\(309\) −12.7010 −0.722536
\(310\) −4.31398 −0.245018
\(311\) −14.6828 −0.832587 −0.416293 0.909230i \(-0.636671\pi\)
−0.416293 + 0.909230i \(0.636671\pi\)
\(312\) 42.0486 2.38053
\(313\) 32.5963 1.84245 0.921225 0.389031i \(-0.127190\pi\)
0.921225 + 0.389031i \(0.127190\pi\)
\(314\) −23.7591 −1.34080
\(315\) 0 0
\(316\) 52.7620 2.96809
\(317\) −0.374845 −0.0210534 −0.0105267 0.999945i \(-0.503351\pi\)
−0.0105267 + 0.999945i \(0.503351\pi\)
\(318\) −36.5016 −2.04691
\(319\) −33.0060 −1.84798
\(320\) 6.00795 0.335855
\(321\) −9.75066 −0.544229
\(322\) 0 0
\(323\) −11.0310 −0.613782
\(324\) 4.56633 0.253685
\(325\) −64.9005 −3.60003
\(326\) −54.3717 −3.01137
\(327\) 15.4367 0.853650
\(328\) 6.57620 0.363110
\(329\) 0 0
\(330\) −38.0363 −2.09383
\(331\) −2.42663 −0.133379 −0.0666897 0.997774i \(-0.521244\pi\)
−0.0666897 + 0.997774i \(0.521244\pi\)
\(332\) −26.2506 −1.44069
\(333\) 7.97403 0.436974
\(334\) 38.6601 2.11539
\(335\) 14.0585 0.768098
\(336\) 0 0
\(337\) −22.6106 −1.23168 −0.615840 0.787871i \(-0.711183\pi\)
−0.615840 + 0.787871i \(0.711183\pi\)
\(338\) 71.4525 3.88650
\(339\) −16.0865 −0.873699
\(340\) −30.2775 −1.64203
\(341\) −1.64945 −0.0893225
\(342\) 16.5933 0.897265
\(343\) 0 0
\(344\) −42.1957 −2.27504
\(345\) −13.6786 −0.736428
\(346\) 8.24544 0.443277
\(347\) −32.2232 −1.72983 −0.864916 0.501916i \(-0.832629\pi\)
−0.864916 + 0.501916i \(0.832629\pi\)
\(348\) 39.5213 2.11857
\(349\) −9.93257 −0.531678 −0.265839 0.964017i \(-0.585649\pi\)
−0.265839 + 0.964017i \(0.585649\pi\)
\(350\) 0 0
\(351\) 6.39406 0.341290
\(352\) 25.2715 1.34698
\(353\) −0.470477 −0.0250410 −0.0125205 0.999922i \(-0.503985\pi\)
−0.0125205 + 0.999922i \(0.503985\pi\)
\(354\) 8.68412 0.461556
\(355\) −2.41273 −0.128054
\(356\) −75.3151 −3.99169
\(357\) 0 0
\(358\) −7.93584 −0.419422
\(359\) −3.78654 −0.199846 −0.0999230 0.994995i \(-0.531860\pi\)
−0.0999230 + 0.994995i \(0.531860\pi\)
\(360\) 25.5966 1.34906
\(361\) 22.9319 1.20694
\(362\) 0.271908 0.0142912
\(363\) −3.54315 −0.185967
\(364\) 0 0
\(365\) −10.5799 −0.553775
\(366\) −11.2911 −0.590194
\(367\) 5.50525 0.287372 0.143686 0.989623i \(-0.454105\pi\)
0.143686 + 0.989623i \(0.454105\pi\)
\(368\) 27.1256 1.41402
\(369\) 1.00000 0.0520579
\(370\) 79.5331 4.13473
\(371\) 0 0
\(372\) 1.97504 0.102401
\(373\) 18.8594 0.976505 0.488252 0.872703i \(-0.337635\pi\)
0.488252 + 0.872703i \(0.337635\pi\)
\(374\) −16.6469 −0.860793
\(375\) −20.0459 −1.03517
\(376\) −24.5089 −1.26395
\(377\) 55.3402 2.85017
\(378\) 0 0
\(379\) 4.70498 0.241678 0.120839 0.992672i \(-0.461441\pi\)
0.120839 + 0.992672i \(0.461441\pi\)
\(380\) 115.093 5.90413
\(381\) 13.4222 0.687642
\(382\) −28.7903 −1.47304
\(383\) −9.31366 −0.475906 −0.237953 0.971277i \(-0.576476\pi\)
−0.237953 + 0.971277i \(0.576476\pi\)
\(384\) 9.29825 0.474500
\(385\) 0 0
\(386\) −23.0413 −1.17277
\(387\) −6.41643 −0.326165
\(388\) −12.8646 −0.653103
\(389\) 11.8547 0.601056 0.300528 0.953773i \(-0.402837\pi\)
0.300528 + 0.953773i \(0.402837\pi\)
\(390\) 63.7744 3.22934
\(391\) −5.98654 −0.302752
\(392\) 0 0
\(393\) −3.10894 −0.156825
\(394\) 1.06605 0.0537066
\(395\) 44.9740 2.26289
\(396\) 17.4139 0.875083
\(397\) 24.0952 1.20930 0.604652 0.796490i \(-0.293312\pi\)
0.604652 + 0.796490i \(0.293312\pi\)
\(398\) 18.4860 0.926617
\(399\) 0 0
\(400\) 78.3462 3.91731
\(401\) 28.0444 1.40047 0.700234 0.713913i \(-0.253079\pi\)
0.700234 + 0.713913i \(0.253079\pi\)
\(402\) −9.25535 −0.461615
\(403\) 2.76558 0.137763
\(404\) −41.9179 −2.08550
\(405\) 3.89232 0.193411
\(406\) 0 0
\(407\) 30.4094 1.50734
\(408\) 11.2026 0.554611
\(409\) 17.0017 0.840682 0.420341 0.907366i \(-0.361911\pi\)
0.420341 + 0.907366i \(0.361911\pi\)
\(410\) 9.97400 0.492581
\(411\) 12.3063 0.607026
\(412\) 57.9971 2.85731
\(413\) 0 0
\(414\) 9.00520 0.442582
\(415\) −22.3759 −1.09839
\(416\) −42.3721 −2.07746
\(417\) 10.9403 0.535749
\(418\) 63.2795 3.09510
\(419\) 34.5411 1.68744 0.843722 0.536781i \(-0.180360\pi\)
0.843722 + 0.536781i \(0.180360\pi\)
\(420\) 0 0
\(421\) −7.26526 −0.354087 −0.177044 0.984203i \(-0.556653\pi\)
−0.177044 + 0.984203i \(0.556653\pi\)
\(422\) −29.9862 −1.45971
\(423\) −3.72691 −0.181208
\(424\) 93.6753 4.54927
\(425\) −17.2908 −0.838726
\(426\) 1.58841 0.0769586
\(427\) 0 0
\(428\) 44.5248 2.15219
\(429\) 24.3841 1.17727
\(430\) −63.9975 −3.08623
\(431\) −8.73640 −0.420818 −0.210409 0.977613i \(-0.567480\pi\)
−0.210409 + 0.977613i \(0.567480\pi\)
\(432\) −7.71874 −0.371368
\(433\) −25.5753 −1.22907 −0.614534 0.788890i \(-0.710656\pi\)
−0.614534 + 0.788890i \(0.710656\pi\)
\(434\) 0 0
\(435\) 33.6877 1.61520
\(436\) −70.4890 −3.37581
\(437\) 22.7564 1.08859
\(438\) 6.96519 0.332810
\(439\) 30.0329 1.43339 0.716697 0.697385i \(-0.245653\pi\)
0.716697 + 0.697385i \(0.245653\pi\)
\(440\) 97.6140 4.65357
\(441\) 0 0
\(442\) 27.9114 1.32761
\(443\) 11.8190 0.561538 0.280769 0.959775i \(-0.409411\pi\)
0.280769 + 0.959775i \(0.409411\pi\)
\(444\) −36.4121 −1.72804
\(445\) −64.1981 −3.04328
\(446\) 22.8304 1.08105
\(447\) −10.0711 −0.476347
\(448\) 0 0
\(449\) 4.74219 0.223798 0.111899 0.993720i \(-0.464307\pi\)
0.111899 + 0.993720i \(0.464307\pi\)
\(450\) 26.0095 1.22610
\(451\) 3.81355 0.179573
\(452\) 73.4564 3.45510
\(453\) 17.6807 0.830710
\(454\) 36.8650 1.73016
\(455\) 0 0
\(456\) −42.5841 −1.99418
\(457\) −4.79322 −0.224217 −0.112109 0.993696i \(-0.535760\pi\)
−0.112109 + 0.993696i \(0.535760\pi\)
\(458\) 10.7551 0.502553
\(459\) 1.70351 0.0795128
\(460\) 62.4608 2.91225
\(461\) −0.478050 −0.0222650 −0.0111325 0.999938i \(-0.503544\pi\)
−0.0111325 + 0.999938i \(0.503544\pi\)
\(462\) 0 0
\(463\) −4.36341 −0.202785 −0.101392 0.994847i \(-0.532330\pi\)
−0.101392 + 0.994847i \(0.532330\pi\)
\(464\) −66.8052 −3.10136
\(465\) 1.68352 0.0780711
\(466\) −11.6961 −0.541813
\(467\) −34.5418 −1.59841 −0.799203 0.601062i \(-0.794745\pi\)
−0.799203 + 0.601062i \(0.794745\pi\)
\(468\) −29.1974 −1.34965
\(469\) 0 0
\(470\) −37.1722 −1.71463
\(471\) 9.27189 0.427226
\(472\) −22.2864 −1.02581
\(473\) −24.4694 −1.12510
\(474\) −29.6084 −1.35996
\(475\) 65.7269 3.01576
\(476\) 0 0
\(477\) 14.2446 0.652215
\(478\) −68.4359 −3.13018
\(479\) −41.9564 −1.91704 −0.958518 0.285032i \(-0.907996\pi\)
−0.958518 + 0.285032i \(0.907996\pi\)
\(480\) −25.7935 −1.17731
\(481\) −50.9865 −2.32478
\(482\) −28.1772 −1.28343
\(483\) 0 0
\(484\) 16.1792 0.735419
\(485\) −10.9657 −0.497929
\(486\) −2.56249 −0.116237
\(487\) 12.9603 0.587287 0.293644 0.955915i \(-0.405132\pi\)
0.293644 + 0.955915i \(0.405132\pi\)
\(488\) 28.9767 1.31171
\(489\) 21.2183 0.959526
\(490\) 0 0
\(491\) −29.3306 −1.32367 −0.661835 0.749650i \(-0.730222\pi\)
−0.661835 + 0.749650i \(0.730222\pi\)
\(492\) −4.56633 −0.205866
\(493\) 14.7437 0.664024
\(494\) −106.099 −4.77361
\(495\) 14.8435 0.667167
\(496\) −3.33853 −0.149905
\(497\) 0 0
\(498\) 14.7310 0.660114
\(499\) 29.3644 1.31453 0.657265 0.753659i \(-0.271713\pi\)
0.657265 + 0.753659i \(0.271713\pi\)
\(500\) 91.5363 4.09363
\(501\) −15.0869 −0.674035
\(502\) 50.5053 2.25416
\(503\) 14.3799 0.641166 0.320583 0.947220i \(-0.396121\pi\)
0.320583 + 0.947220i \(0.396121\pi\)
\(504\) 0 0
\(505\) −35.7306 −1.58999
\(506\) 34.3418 1.52668
\(507\) −27.8841 −1.23837
\(508\) −61.2904 −2.71932
\(509\) 22.5208 0.998216 0.499108 0.866540i \(-0.333661\pi\)
0.499108 + 0.866540i \(0.333661\pi\)
\(510\) 16.9908 0.752364
\(511\) 0 0
\(512\) −50.3696 −2.22604
\(513\) −6.47548 −0.285900
\(514\) 81.8107 3.60852
\(515\) 49.4364 2.17843
\(516\) 29.2996 1.28984
\(517\) −14.2127 −0.625076
\(518\) 0 0
\(519\) −3.21775 −0.141243
\(520\) −163.667 −7.17725
\(521\) 19.3136 0.846144 0.423072 0.906096i \(-0.360952\pi\)
0.423072 + 0.906096i \(0.360952\pi\)
\(522\) −22.1782 −0.970712
\(523\) 2.22956 0.0974918 0.0487459 0.998811i \(-0.484478\pi\)
0.0487459 + 0.998811i \(0.484478\pi\)
\(524\) 14.1965 0.620176
\(525\) 0 0
\(526\) 44.1366 1.92445
\(527\) 0.736805 0.0320957
\(528\) −29.4358 −1.28103
\(529\) −10.6501 −0.463047
\(530\) 142.076 6.17137
\(531\) −3.38894 −0.147068
\(532\) 0 0
\(533\) −6.39406 −0.276958
\(534\) 42.2645 1.82896
\(535\) 37.9527 1.64084
\(536\) 23.7523 1.02594
\(537\) 3.09693 0.133642
\(538\) −26.5315 −1.14385
\(539\) 0 0
\(540\) −17.7736 −0.764855
\(541\) −22.6192 −0.972473 −0.486237 0.873827i \(-0.661631\pi\)
−0.486237 + 0.873827i \(0.661631\pi\)
\(542\) −70.2847 −3.01899
\(543\) −0.106111 −0.00455366
\(544\) −11.2888 −0.484001
\(545\) −60.0844 −2.57373
\(546\) 0 0
\(547\) −30.0174 −1.28345 −0.641725 0.766935i \(-0.721781\pi\)
−0.641725 + 0.766935i \(0.721781\pi\)
\(548\) −56.1947 −2.40052
\(549\) 4.40630 0.188056
\(550\) 99.1887 4.22942
\(551\) −56.0449 −2.38759
\(552\) −23.1104 −0.983643
\(553\) 0 0
\(554\) 30.6705 1.30306
\(555\) −31.0375 −1.31747
\(556\) −49.9571 −2.11865
\(557\) 7.24842 0.307125 0.153563 0.988139i \(-0.450925\pi\)
0.153563 + 0.988139i \(0.450925\pi\)
\(558\) −1.10833 −0.0469195
\(559\) 41.0271 1.73526
\(560\) 0 0
\(561\) 6.49640 0.274278
\(562\) 26.0764 1.09997
\(563\) −22.1704 −0.934372 −0.467186 0.884159i \(-0.654732\pi\)
−0.467186 + 0.884159i \(0.654732\pi\)
\(564\) 17.0183 0.716600
\(565\) 62.6138 2.63418
\(566\) 16.3440 0.686989
\(567\) 0 0
\(568\) −4.07639 −0.171041
\(569\) −31.1263 −1.30488 −0.652440 0.757840i \(-0.726255\pi\)
−0.652440 + 0.757840i \(0.726255\pi\)
\(570\) −64.5865 −2.70523
\(571\) −18.3057 −0.766068 −0.383034 0.923734i \(-0.625121\pi\)
−0.383034 + 0.923734i \(0.625121\pi\)
\(572\) −111.346 −4.65560
\(573\) 11.2353 0.469361
\(574\) 0 0
\(575\) 35.6700 1.48754
\(576\) 1.54354 0.0643143
\(577\) 4.86103 0.202367 0.101184 0.994868i \(-0.467737\pi\)
0.101184 + 0.994868i \(0.467737\pi\)
\(578\) −36.1261 −1.50265
\(579\) 8.99177 0.373685
\(580\) −153.830 −6.38742
\(581\) 0 0
\(582\) 7.21924 0.299247
\(583\) 54.3225 2.24981
\(584\) −17.8750 −0.739673
\(585\) −24.8877 −1.02898
\(586\) −80.9431 −3.34373
\(587\) 28.6682 1.18326 0.591632 0.806208i \(-0.298484\pi\)
0.591632 + 0.806208i \(0.298484\pi\)
\(588\) 0 0
\(589\) −2.80079 −0.115405
\(590\) −33.8013 −1.39158
\(591\) −0.416020 −0.0171128
\(592\) 61.5495 2.52967
\(593\) 21.9738 0.902354 0.451177 0.892434i \(-0.351004\pi\)
0.451177 + 0.892434i \(0.351004\pi\)
\(594\) −9.77216 −0.400957
\(595\) 0 0
\(596\) 45.9881 1.88374
\(597\) −7.21407 −0.295252
\(598\) −57.5799 −2.35462
\(599\) 31.3230 1.27982 0.639911 0.768449i \(-0.278971\pi\)
0.639911 + 0.768449i \(0.278971\pi\)
\(600\) −66.7492 −2.72502
\(601\) 6.15788 0.251185 0.125593 0.992082i \(-0.459917\pi\)
0.125593 + 0.992082i \(0.459917\pi\)
\(602\) 0 0
\(603\) 3.61186 0.147086
\(604\) −80.7358 −3.28509
\(605\) 13.7911 0.560686
\(606\) 23.5231 0.955559
\(607\) 12.7567 0.517779 0.258889 0.965907i \(-0.416643\pi\)
0.258889 + 0.965907i \(0.416643\pi\)
\(608\) 42.9116 1.74029
\(609\) 0 0
\(610\) 43.9484 1.77942
\(611\) 23.8301 0.964062
\(612\) −7.77878 −0.314438
\(613\) −43.0140 −1.73732 −0.868659 0.495410i \(-0.835018\pi\)
−0.868659 + 0.495410i \(0.835018\pi\)
\(614\) 10.6079 0.428099
\(615\) −3.89232 −0.156953
\(616\) 0 0
\(617\) −34.6914 −1.39662 −0.698312 0.715793i \(-0.746065\pi\)
−0.698312 + 0.715793i \(0.746065\pi\)
\(618\) −32.5462 −1.30920
\(619\) −3.93932 −0.158335 −0.0791673 0.996861i \(-0.525226\pi\)
−0.0791673 + 0.996861i \(0.525226\pi\)
\(620\) −7.68749 −0.308737
\(621\) −3.51424 −0.141022
\(622\) −37.6246 −1.50861
\(623\) 0 0
\(624\) 49.3541 1.97575
\(625\) 27.2744 1.09097
\(626\) 83.5275 3.33843
\(627\) −24.6946 −0.986206
\(628\) −42.3385 −1.68949
\(629\) −13.5838 −0.541622
\(630\) 0 0
\(631\) 1.68087 0.0669144 0.0334572 0.999440i \(-0.489348\pi\)
0.0334572 + 0.999440i \(0.489348\pi\)
\(632\) 75.9850 3.02252
\(633\) 11.7020 0.465113
\(634\) −0.960534 −0.0381477
\(635\) −52.2436 −2.07322
\(636\) −65.0456 −2.57923
\(637\) 0 0
\(638\) −84.5775 −3.34845
\(639\) −0.619870 −0.0245217
\(640\) −36.1917 −1.43060
\(641\) 21.8935 0.864740 0.432370 0.901696i \(-0.357678\pi\)
0.432370 + 0.901696i \(0.357678\pi\)
\(642\) −24.9859 −0.986116
\(643\) −47.8257 −1.88606 −0.943031 0.332705i \(-0.892039\pi\)
−0.943031 + 0.332705i \(0.892039\pi\)
\(644\) 0 0
\(645\) 24.9748 0.983381
\(646\) −28.2668 −1.11214
\(647\) −13.4095 −0.527181 −0.263591 0.964635i \(-0.584907\pi\)
−0.263591 + 0.964635i \(0.584907\pi\)
\(648\) 6.57620 0.258337
\(649\) −12.9239 −0.507307
\(650\) −166.307 −6.52309
\(651\) 0 0
\(652\) −96.8900 −3.79450
\(653\) 4.31746 0.168955 0.0844775 0.996425i \(-0.473078\pi\)
0.0844775 + 0.996425i \(0.473078\pi\)
\(654\) 39.5562 1.54677
\(655\) 12.1010 0.472825
\(656\) 7.71874 0.301366
\(657\) −2.71814 −0.106045
\(658\) 0 0
\(659\) 27.7187 1.07977 0.539883 0.841740i \(-0.318468\pi\)
0.539883 + 0.841740i \(0.318468\pi\)
\(660\) −67.7805 −2.63835
\(661\) 24.2825 0.944481 0.472241 0.881470i \(-0.343445\pi\)
0.472241 + 0.881470i \(0.343445\pi\)
\(662\) −6.21820 −0.241677
\(663\) −10.8923 −0.423023
\(664\) −37.8048 −1.46711
\(665\) 0 0
\(666\) 20.4334 0.791776
\(667\) −30.4156 −1.17770
\(668\) 68.8920 2.66551
\(669\) −8.90948 −0.344460
\(670\) 36.0247 1.39176
\(671\) 16.8036 0.648697
\(672\) 0 0
\(673\) 16.8664 0.650152 0.325076 0.945688i \(-0.394610\pi\)
0.325076 + 0.945688i \(0.394610\pi\)
\(674\) −57.9395 −2.23174
\(675\) −10.1501 −0.390678
\(676\) 127.328 4.89723
\(677\) 36.5414 1.40440 0.702200 0.711980i \(-0.252201\pi\)
0.702200 + 0.711980i \(0.252201\pi\)
\(678\) −41.2215 −1.58310
\(679\) 0 0
\(680\) −43.6040 −1.67214
\(681\) −14.3864 −0.551289
\(682\) −4.22668 −0.161848
\(683\) −19.6855 −0.753244 −0.376622 0.926367i \(-0.622914\pi\)
−0.376622 + 0.926367i \(0.622914\pi\)
\(684\) 29.5692 1.13061
\(685\) −47.9001 −1.83017
\(686\) 0 0
\(687\) −4.19714 −0.160131
\(688\) −49.5268 −1.88819
\(689\) −91.0809 −3.46990
\(690\) −35.0511 −1.33437
\(691\) 11.0941 0.422041 0.211020 0.977482i \(-0.432321\pi\)
0.211020 + 0.977482i \(0.432321\pi\)
\(692\) 14.6933 0.558556
\(693\) 0 0
\(694\) −82.5715 −3.13437
\(695\) −42.5831 −1.61527
\(696\) 56.9166 2.15742
\(697\) −1.70351 −0.0645249
\(698\) −25.4521 −0.963375
\(699\) 4.56437 0.172640
\(700\) 0 0
\(701\) 29.7923 1.12524 0.562620 0.826716i \(-0.309794\pi\)
0.562620 + 0.826716i \(0.309794\pi\)
\(702\) 16.3847 0.618401
\(703\) 51.6357 1.94748
\(704\) 5.88637 0.221851
\(705\) 14.5063 0.546339
\(706\) −1.20559 −0.0453730
\(707\) 0 0
\(708\) 15.4750 0.581588
\(709\) 36.5747 1.37359 0.686795 0.726851i \(-0.259017\pi\)
0.686795 + 0.726851i \(0.259017\pi\)
\(710\) −6.18258 −0.232028
\(711\) 11.5546 0.433330
\(712\) −108.465 −4.06489
\(713\) −1.51999 −0.0569241
\(714\) 0 0
\(715\) −94.9105 −3.54945
\(716\) −14.1416 −0.528497
\(717\) 26.7068 0.997385
\(718\) −9.70296 −0.362111
\(719\) −34.8891 −1.30114 −0.650572 0.759444i \(-0.725471\pi\)
−0.650572 + 0.759444i \(0.725471\pi\)
\(720\) 30.0438 1.11967
\(721\) 0 0
\(722\) 58.7626 2.18692
\(723\) 10.9960 0.408947
\(724\) 0.484538 0.0180077
\(725\) −87.8487 −3.26262
\(726\) −9.07927 −0.336963
\(727\) 5.29173 0.196259 0.0981296 0.995174i \(-0.468714\pi\)
0.0981296 + 0.995174i \(0.468714\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −27.1107 −1.00341
\(731\) 10.9304 0.404276
\(732\) −20.1206 −0.743680
\(733\) −10.9375 −0.403986 −0.201993 0.979387i \(-0.564742\pi\)
−0.201993 + 0.979387i \(0.564742\pi\)
\(734\) 14.1071 0.520703
\(735\) 0 0
\(736\) 23.2881 0.858412
\(737\) 13.7740 0.507372
\(738\) 2.56249 0.0943264
\(739\) 14.0490 0.516802 0.258401 0.966038i \(-0.416805\pi\)
0.258401 + 0.966038i \(0.416805\pi\)
\(740\) 141.727 5.21000
\(741\) 41.4047 1.52104
\(742\) 0 0
\(743\) −47.8936 −1.75704 −0.878522 0.477701i \(-0.841470\pi\)
−0.878522 + 0.477701i \(0.841470\pi\)
\(744\) 2.84436 0.104279
\(745\) 39.1999 1.43617
\(746\) 48.3270 1.76938
\(747\) −5.74873 −0.210335
\(748\) −29.6647 −1.08465
\(749\) 0 0
\(750\) −51.3673 −1.87567
\(751\) −30.9737 −1.13025 −0.565124 0.825006i \(-0.691172\pi\)
−0.565124 + 0.825006i \(0.691172\pi\)
\(752\) −28.7670 −1.04903
\(753\) −19.7095 −0.718254
\(754\) 141.809 5.16436
\(755\) −68.8187 −2.50457
\(756\) 0 0
\(757\) 20.1123 0.730995 0.365497 0.930812i \(-0.380899\pi\)
0.365497 + 0.930812i \(0.380899\pi\)
\(758\) 12.0564 0.437909
\(759\) −13.4017 −0.486452
\(760\) 165.751 6.01240
\(761\) −13.6838 −0.496038 −0.248019 0.968755i \(-0.579780\pi\)
−0.248019 + 0.968755i \(0.579780\pi\)
\(762\) 34.3943 1.24597
\(763\) 0 0
\(764\) −51.3041 −1.85612
\(765\) −6.63058 −0.239729
\(766\) −23.8661 −0.862318
\(767\) 21.6691 0.782427
\(768\) 26.9137 0.971166
\(769\) 1.06746 0.0384937 0.0192468 0.999815i \(-0.493873\pi\)
0.0192468 + 0.999815i \(0.493873\pi\)
\(770\) 0 0
\(771\) −31.9263 −1.14980
\(772\) −41.0594 −1.47776
\(773\) 2.94940 0.106082 0.0530412 0.998592i \(-0.483109\pi\)
0.0530412 + 0.998592i \(0.483109\pi\)
\(774\) −16.4420 −0.590996
\(775\) −4.39016 −0.157699
\(776\) −18.5270 −0.665080
\(777\) 0 0
\(778\) 30.3774 1.08908
\(779\) 6.47548 0.232008
\(780\) 113.646 4.06917
\(781\) −2.36390 −0.0845871
\(782\) −15.3404 −0.548572
\(783\) 8.65494 0.309302
\(784\) 0 0
\(785\) −36.0891 −1.28808
\(786\) −7.96662 −0.284160
\(787\) 0.0995646 0.00354910 0.00177455 0.999998i \(-0.499435\pi\)
0.00177455 + 0.999998i \(0.499435\pi\)
\(788\) 1.89969 0.0676735
\(789\) −17.2241 −0.613195
\(790\) 115.245 4.10024
\(791\) 0 0
\(792\) 25.0786 0.891131
\(793\) −28.1741 −1.00049
\(794\) 61.7437 2.19120
\(795\) −55.4445 −1.96641
\(796\) 32.9419 1.16759
\(797\) 18.5859 0.658346 0.329173 0.944270i \(-0.393230\pi\)
0.329173 + 0.944270i \(0.393230\pi\)
\(798\) 0 0
\(799\) 6.34881 0.224605
\(800\) 67.2626 2.37809
\(801\) −16.4936 −0.582771
\(802\) 71.8633 2.53758
\(803\) −10.3657 −0.365799
\(804\) −16.4930 −0.581662
\(805\) 0 0
\(806\) 7.08676 0.249620
\(807\) 10.3538 0.364471
\(808\) −60.3680 −2.12374
\(809\) −37.1832 −1.30729 −0.653645 0.756801i \(-0.726761\pi\)
−0.653645 + 0.756801i \(0.726761\pi\)
\(810\) 9.97400 0.350451
\(811\) −15.1429 −0.531738 −0.265869 0.964009i \(-0.585659\pi\)
−0.265869 + 0.964009i \(0.585659\pi\)
\(812\) 0 0
\(813\) 27.4283 0.961954
\(814\) 77.9236 2.73122
\(815\) −82.5884 −2.89295
\(816\) 13.1489 0.460304
\(817\) −41.5495 −1.45363
\(818\) 43.5667 1.52327
\(819\) 0 0
\(820\) 17.7736 0.620682
\(821\) −9.35104 −0.326354 −0.163177 0.986597i \(-0.552174\pi\)
−0.163177 + 0.986597i \(0.552174\pi\)
\(822\) 31.5348 1.09990
\(823\) 4.99218 0.174017 0.0870083 0.996208i \(-0.472269\pi\)
0.0870083 + 0.996208i \(0.472269\pi\)
\(824\) 83.5244 2.90971
\(825\) −38.7080 −1.34764
\(826\) 0 0
\(827\) 6.42913 0.223563 0.111781 0.993733i \(-0.464344\pi\)
0.111781 + 0.993733i \(0.464344\pi\)
\(828\) 16.0472 0.557679
\(829\) −18.3653 −0.637853 −0.318926 0.947779i \(-0.603322\pi\)
−0.318926 + 0.947779i \(0.603322\pi\)
\(830\) −57.3378 −1.99023
\(831\) −11.9690 −0.415201
\(832\) −9.86951 −0.342164
\(833\) 0 0
\(834\) 28.0344 0.970750
\(835\) 58.7231 2.03220
\(836\) 112.764 3.90001
\(837\) 0.432523 0.0149502
\(838\) 88.5111 3.05756
\(839\) −54.3366 −1.87591 −0.937954 0.346760i \(-0.887282\pi\)
−0.937954 + 0.346760i \(0.887282\pi\)
\(840\) 0 0
\(841\) 45.9079 1.58303
\(842\) −18.6171 −0.641589
\(843\) −10.1762 −0.350488
\(844\) −53.4353 −1.83932
\(845\) 108.534 3.73367
\(846\) −9.55015 −0.328341
\(847\) 0 0
\(848\) 109.950 3.77571
\(849\) −6.37817 −0.218898
\(850\) −44.3074 −1.51973
\(851\) 28.0227 0.960606
\(852\) 2.83053 0.0969725
\(853\) 23.5896 0.807692 0.403846 0.914827i \(-0.367673\pi\)
0.403846 + 0.914827i \(0.367673\pi\)
\(854\) 0 0
\(855\) 25.2046 0.861980
\(856\) 64.1223 2.19165
\(857\) 45.5365 1.55550 0.777749 0.628575i \(-0.216362\pi\)
0.777749 + 0.628575i \(0.216362\pi\)
\(858\) 62.4838 2.13316
\(859\) −46.3999 −1.58314 −0.791572 0.611075i \(-0.790737\pi\)
−0.791572 + 0.611075i \(0.790737\pi\)
\(860\) −114.043 −3.88884
\(861\) 0 0
\(862\) −22.3869 −0.762501
\(863\) −28.2733 −0.962433 −0.481217 0.876602i \(-0.659805\pi\)
−0.481217 + 0.876602i \(0.659805\pi\)
\(864\) −6.62678 −0.225448
\(865\) 12.5245 0.425846
\(866\) −65.5362 −2.22701
\(867\) 14.0981 0.478796
\(868\) 0 0
\(869\) 44.0639 1.49476
\(870\) 86.3244 2.92667
\(871\) −23.0945 −0.782527
\(872\) −101.515 −3.43772
\(873\) −2.81728 −0.0953504
\(874\) 58.3130 1.97247
\(875\) 0 0
\(876\) 12.4119 0.419360
\(877\) 25.1433 0.849030 0.424515 0.905421i \(-0.360445\pi\)
0.424515 + 0.905421i \(0.360445\pi\)
\(878\) 76.9590 2.59724
\(879\) 31.5877 1.06543
\(880\) 114.573 3.86227
\(881\) −25.6604 −0.864519 −0.432260 0.901749i \(-0.642284\pi\)
−0.432260 + 0.901749i \(0.642284\pi\)
\(882\) 0 0
\(883\) −50.6683 −1.70512 −0.852562 0.522627i \(-0.824952\pi\)
−0.852562 + 0.522627i \(0.824952\pi\)
\(884\) 49.7380 1.67287
\(885\) 13.1908 0.443405
\(886\) 30.2860 1.01748
\(887\) 23.1852 0.778483 0.389242 0.921136i \(-0.372737\pi\)
0.389242 + 0.921136i \(0.372737\pi\)
\(888\) −52.4388 −1.75973
\(889\) 0 0
\(890\) −164.507 −5.51428
\(891\) 3.81355 0.127759
\(892\) 40.6836 1.36219
\(893\) −24.1335 −0.807598
\(894\) −25.8071 −0.863118
\(895\) −12.0542 −0.402928
\(896\) 0 0
\(897\) 22.4703 0.750262
\(898\) 12.1518 0.405511
\(899\) 3.74346 0.124851
\(900\) 46.3489 1.54496
\(901\) −24.2658 −0.808409
\(902\) 9.77216 0.325377
\(903\) 0 0
\(904\) 105.788 3.51846
\(905\) 0.413017 0.0137292
\(906\) 45.3065 1.50521
\(907\) 33.2474 1.10396 0.551981 0.833856i \(-0.313872\pi\)
0.551981 + 0.833856i \(0.313872\pi\)
\(908\) 65.6933 2.18011
\(909\) −9.17978 −0.304474
\(910\) 0 0
\(911\) 15.5992 0.516825 0.258412 0.966035i \(-0.416801\pi\)
0.258412 + 0.966035i \(0.416801\pi\)
\(912\) −49.9826 −1.65509
\(913\) −21.9231 −0.725547
\(914\) −12.2826 −0.406271
\(915\) −17.1507 −0.566985
\(916\) 19.1655 0.633247
\(917\) 0 0
\(918\) 4.36521 0.144073
\(919\) −4.50305 −0.148542 −0.0742709 0.997238i \(-0.523663\pi\)
−0.0742709 + 0.997238i \(0.523663\pi\)
\(920\) 89.9528 2.96566
\(921\) −4.13968 −0.136407
\(922\) −1.22500 −0.0403431
\(923\) 3.96349 0.130460
\(924\) 0 0
\(925\) 80.9374 2.66121
\(926\) −11.1812 −0.367437
\(927\) 12.7010 0.417156
\(928\) −57.3544 −1.88275
\(929\) 4.26219 0.139838 0.0699190 0.997553i \(-0.477726\pi\)
0.0699190 + 0.997553i \(0.477726\pi\)
\(930\) 4.31398 0.141461
\(931\) 0 0
\(932\) −20.8424 −0.682717
\(933\) 14.6828 0.480694
\(934\) −88.5130 −2.89623
\(935\) −25.2860 −0.826942
\(936\) −42.0486 −1.37440
\(937\) 25.6728 0.838695 0.419347 0.907826i \(-0.362259\pi\)
0.419347 + 0.907826i \(0.362259\pi\)
\(938\) 0 0
\(939\) −32.5963 −1.06374
\(940\) −66.2406 −2.16053
\(941\) −25.1298 −0.819210 −0.409605 0.912263i \(-0.634333\pi\)
−0.409605 + 0.912263i \(0.634333\pi\)
\(942\) 23.7591 0.774113
\(943\) 3.51424 0.114440
\(944\) −26.1584 −0.851383
\(945\) 0 0
\(946\) −62.7024 −2.03863
\(947\) 1.84065 0.0598131 0.0299065 0.999553i \(-0.490479\pi\)
0.0299065 + 0.999553i \(0.490479\pi\)
\(948\) −52.7620 −1.71363
\(949\) 17.3799 0.564177
\(950\) 168.424 5.46441
\(951\) 0.374845 0.0121552
\(952\) 0 0
\(953\) −25.9038 −0.839107 −0.419554 0.907731i \(-0.637813\pi\)
−0.419554 + 0.907731i \(0.637813\pi\)
\(954\) 36.5016 1.18178
\(955\) −43.7313 −1.41511
\(956\) −121.952 −3.94422
\(957\) 33.0060 1.06693
\(958\) −107.513 −3.47358
\(959\) 0 0
\(960\) −6.00795 −0.193906
\(961\) −30.8129 −0.993965
\(962\) −130.652 −4.21240
\(963\) 9.75066 0.314211
\(964\) −50.2115 −1.61720
\(965\) −34.9988 −1.12665
\(966\) 0 0
\(967\) −17.7879 −0.572019 −0.286009 0.958227i \(-0.592329\pi\)
−0.286009 + 0.958227i \(0.592329\pi\)
\(968\) 23.3005 0.748905
\(969\) 11.0310 0.354367
\(970\) −28.0996 −0.902222
\(971\) −53.5532 −1.71860 −0.859302 0.511468i \(-0.829102\pi\)
−0.859302 + 0.511468i \(0.829102\pi\)
\(972\) −4.56633 −0.146465
\(973\) 0 0
\(974\) 33.2106 1.06414
\(975\) 64.9005 2.07848
\(976\) 34.0111 1.08867
\(977\) 31.9422 1.02192 0.510961 0.859604i \(-0.329290\pi\)
0.510961 + 0.859604i \(0.329290\pi\)
\(978\) 54.3717 1.73861
\(979\) −62.8990 −2.01026
\(980\) 0 0
\(981\) −15.4367 −0.492855
\(982\) −75.1591 −2.39842
\(983\) −26.2569 −0.837466 −0.418733 0.908109i \(-0.637526\pi\)
−0.418733 + 0.908109i \(0.637526\pi\)
\(984\) −6.57620 −0.209642
\(985\) 1.61928 0.0515946
\(986\) 37.7806 1.20318
\(987\) 0 0
\(988\) −189.068 −6.01504
\(989\) −22.5489 −0.717014
\(990\) 38.0363 1.20887
\(991\) −59.4449 −1.88833 −0.944164 0.329475i \(-0.893128\pi\)
−0.944164 + 0.329475i \(0.893128\pi\)
\(992\) −2.86623 −0.0910030
\(993\) 2.42663 0.0770066
\(994\) 0 0
\(995\) 28.0794 0.890178
\(996\) 26.2506 0.831783
\(997\) 6.34221 0.200860 0.100430 0.994944i \(-0.467978\pi\)
0.100430 + 0.994944i \(0.467978\pi\)
\(998\) 75.2458 2.38187
\(999\) −7.97403 −0.252287
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 \(a_p\))