Properties

Label 8023.2.a.c.1.2
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +O(q^{10})\) \(q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +3.77538 q^{10} -2.32075 q^{11} -16.2445 q^{12} +0.925145 q^{13} -12.6992 q^{14} +3.84982 q^{15} +17.3712 q^{16} +6.55335 q^{17} -14.0060 q^{18} +3.74303 q^{19} -7.78066 q^{20} -12.9496 q^{21} +6.45229 q^{22} -3.65314 q^{23} +29.3993 q^{24} -3.15604 q^{25} -2.57214 q^{26} -5.77690 q^{27} +26.1718 q^{28} +6.80696 q^{29} -10.7035 q^{30} +0.567710 q^{31} -27.5566 q^{32} +6.57951 q^{33} -18.2200 q^{34} -6.20253 q^{35} +28.8648 q^{36} -0.527535 q^{37} -10.4066 q^{38} -2.62285 q^{39} +14.0815 q^{40} -10.2683 q^{41} +36.0033 q^{42} +2.28995 q^{43} -13.2975 q^{44} -6.84076 q^{45} +10.1567 q^{46} +6.93053 q^{47} -49.2486 q^{48} +13.8635 q^{49} +8.77459 q^{50} -18.5793 q^{51} +5.30091 q^{52} -6.32497 q^{53} +16.0613 q^{54} +3.15141 q^{55} -47.3659 q^{56} -10.6118 q^{57} -18.9251 q^{58} +4.25528 q^{59} +22.0588 q^{60} +13.6294 q^{61} -1.57838 q^{62} +23.0103 q^{63} +41.8720 q^{64} -1.25628 q^{65} -18.2927 q^{66} +0.248824 q^{67} +37.5495 q^{68} +10.3569 q^{69} +17.2446 q^{70} -1.00000 q^{71} -52.2397 q^{72} -4.69109 q^{73} +1.46668 q^{74} +8.94761 q^{75} +21.4469 q^{76} -10.6004 q^{77} +7.29220 q^{78} -10.4399 q^{79} -23.5887 q^{80} +1.26500 q^{81} +28.5486 q^{82} -12.1304 q^{83} -74.1991 q^{84} -8.89896 q^{85} -6.36666 q^{86} -19.2982 q^{87} +24.0659 q^{88} -11.0175 q^{89} +19.0190 q^{90} +4.22574 q^{91} -20.9318 q^{92} -1.60950 q^{93} -19.2686 q^{94} -5.08275 q^{95} +78.1250 q^{96} -11.9944 q^{97} -38.5440 q^{98} -11.6912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 158q - 24q^{2} - 23q^{3} + 158q^{4} - 31q^{5} - 17q^{6} - 2q^{7} - 69q^{8} + 135q^{9} + O(q^{10}) \) \( 158q - 24q^{2} - 23q^{3} + 158q^{4} - 31q^{5} - 17q^{6} - 2q^{7} - 69q^{8} + 135q^{9} - 10q^{10} - 10q^{11} - 46q^{12} - 28q^{13} - 27q^{14} - 41q^{15} + 150q^{16} - 137q^{17} - 67q^{18} - 42q^{19} - 66q^{20} - 46q^{21} - 8q^{22} - 26q^{23} - 48q^{24} + 129q^{25} - 67q^{26} - 89q^{27} - 21q^{28} - 79q^{29} - 11q^{30} + 7q^{31} - 147q^{32} - 112q^{33} - 28q^{34} - 53q^{35} + 141q^{36} - 60q^{37} - 53q^{38} - 3q^{39} - 48q^{40} - 128q^{41} + 32q^{42} - 63q^{43} - 88q^{45} - 2q^{46} - 92q^{47} - 131q^{48} + 122q^{49} - 116q^{50} - 12q^{51} - 89q^{52} - 94q^{53} - 71q^{54} - 12q^{55} - 104q^{56} - 93q^{57} - 65q^{58} - 54q^{59} - 12q^{60} + 17q^{61} - 97q^{62} - 28q^{63} + 163q^{64} - 163q^{65} - 65q^{66} - 35q^{67} - 217q^{68} - 46q^{69} - 79q^{70} - 158q^{71} - 99q^{72} - 165q^{73} - 94q^{75} - 93q^{76} - 140q^{77} + 25q^{78} - 61q^{79} - 134q^{80} + 114q^{81} + 10q^{82} - 158q^{83} - 160q^{84} + 23q^{85} - 122q^{86} - 71q^{87} - 14q^{88} - 251q^{89} - 6q^{90} - 57q^{91} - 58q^{92} - 52q^{93} - 64q^{94} - 84q^{95} - 98q^{96} - 48q^{97} - 84q^{98} + 85q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78025 −1.96594 −0.982969 0.183774i \(-0.941169\pi\)
−0.982969 + 0.183774i \(0.941169\pi\)
\(3\) −2.83508 −1.63683 −0.818416 0.574626i \(-0.805147\pi\)
−0.818416 + 0.574626i \(0.805147\pi\)
\(4\) 5.72982 2.86491
\(5\) −1.35792 −0.607283 −0.303641 0.952786i \(-0.598202\pi\)
−0.303641 + 0.952786i \(0.598202\pi\)
\(6\) 7.88223 3.21791
\(7\) 4.56765 1.72641 0.863206 0.504853i \(-0.168453\pi\)
0.863206 + 0.504853i \(0.168453\pi\)
\(8\) −10.3698 −3.66629
\(9\) 5.03765 1.67922
\(10\) 3.77538 1.19388
\(11\) −2.32075 −0.699734 −0.349867 0.936799i \(-0.613773\pi\)
−0.349867 + 0.936799i \(0.613773\pi\)
\(12\) −16.2445 −4.68937
\(13\) 0.925145 0.256589 0.128294 0.991736i \(-0.459050\pi\)
0.128294 + 0.991736i \(0.459050\pi\)
\(14\) −12.6992 −3.39402
\(15\) 3.84982 0.994019
\(16\) 17.3712 4.34279
\(17\) 6.55335 1.58942 0.794711 0.606988i \(-0.207623\pi\)
0.794711 + 0.606988i \(0.207623\pi\)
\(18\) −14.0060 −3.30124
\(19\) 3.74303 0.858709 0.429355 0.903136i \(-0.358741\pi\)
0.429355 + 0.903136i \(0.358741\pi\)
\(20\) −7.78066 −1.73981
\(21\) −12.9496 −2.82584
\(22\) 6.45229 1.37563
\(23\) −3.65314 −0.761732 −0.380866 0.924630i \(-0.624374\pi\)
−0.380866 + 0.924630i \(0.624374\pi\)
\(24\) 29.3993 6.00110
\(25\) −3.15604 −0.631208
\(26\) −2.57214 −0.504438
\(27\) −5.77690 −1.11177
\(28\) 26.1718 4.94601
\(29\) 6.80696 1.26402 0.632010 0.774960i \(-0.282230\pi\)
0.632010 + 0.774960i \(0.282230\pi\)
\(30\) −10.7035 −1.95418
\(31\) 0.567710 0.101964 0.0509819 0.998700i \(-0.483765\pi\)
0.0509819 + 0.998700i \(0.483765\pi\)
\(32\) −27.5566 −4.87136
\(33\) 6.57951 1.14535
\(34\) −18.2200 −3.12470
\(35\) −6.20253 −1.04842
\(36\) 28.8648 4.81081
\(37\) −0.527535 −0.0867262 −0.0433631 0.999059i \(-0.513807\pi\)
−0.0433631 + 0.999059i \(0.513807\pi\)
\(38\) −10.4066 −1.68817
\(39\) −2.62285 −0.419993
\(40\) 14.0815 2.22648
\(41\) −10.2683 −1.60364 −0.801821 0.597564i \(-0.796135\pi\)
−0.801821 + 0.597564i \(0.796135\pi\)
\(42\) 36.0033 5.55543
\(43\) 2.28995 0.349215 0.174607 0.984638i \(-0.444134\pi\)
0.174607 + 0.984638i \(0.444134\pi\)
\(44\) −13.2975 −2.00467
\(45\) −6.84076 −1.01976
\(46\) 10.1567 1.49752
\(47\) 6.93053 1.01092 0.505461 0.862850i \(-0.331323\pi\)
0.505461 + 0.862850i \(0.331323\pi\)
\(48\) −49.2486 −7.10842
\(49\) 13.8635 1.98050
\(50\) 8.77459 1.24092
\(51\) −18.5793 −2.60162
\(52\) 5.30091 0.735104
\(53\) −6.32497 −0.868802 −0.434401 0.900720i \(-0.643040\pi\)
−0.434401 + 0.900720i \(0.643040\pi\)
\(54\) 16.0613 2.18566
\(55\) 3.15141 0.424936
\(56\) −47.3659 −6.32953
\(57\) −10.6118 −1.40556
\(58\) −18.9251 −2.48498
\(59\) 4.25528 0.553990 0.276995 0.960871i \(-0.410661\pi\)
0.276995 + 0.960871i \(0.410661\pi\)
\(60\) 22.0588 2.84777
\(61\) 13.6294 1.74506 0.872532 0.488557i \(-0.162477\pi\)
0.872532 + 0.488557i \(0.162477\pi\)
\(62\) −1.57838 −0.200454
\(63\) 23.0103 2.89902
\(64\) 41.8720 5.23400
\(65\) −1.25628 −0.155822
\(66\) −18.2927 −2.25168
\(67\) 0.248824 0.0303986 0.0151993 0.999884i \(-0.495162\pi\)
0.0151993 + 0.999884i \(0.495162\pi\)
\(68\) 37.5495 4.55355
\(69\) 10.3569 1.24683
\(70\) 17.2446 2.06113
\(71\) −1.00000 −0.118678
\(72\) −52.2397 −6.15650
\(73\) −4.69109 −0.549050 −0.274525 0.961580i \(-0.588521\pi\)
−0.274525 + 0.961580i \(0.588521\pi\)
\(74\) 1.46668 0.170498
\(75\) 8.94761 1.03318
\(76\) 21.4469 2.46012
\(77\) −10.6004 −1.20803
\(78\) 7.29220 0.825680
\(79\) −10.4399 −1.17458 −0.587292 0.809375i \(-0.699806\pi\)
−0.587292 + 0.809375i \(0.699806\pi\)
\(80\) −23.5887 −2.63730
\(81\) 1.26500 0.140555
\(82\) 28.5486 3.15266
\(83\) −12.1304 −1.33148 −0.665741 0.746183i \(-0.731884\pi\)
−0.665741 + 0.746183i \(0.731884\pi\)
\(84\) −74.1991 −8.09579
\(85\) −8.89896 −0.965228
\(86\) −6.36666 −0.686534
\(87\) −19.2982 −2.06899
\(88\) 24.0659 2.56543
\(89\) −11.0175 −1.16785 −0.583927 0.811806i \(-0.698484\pi\)
−0.583927 + 0.811806i \(0.698484\pi\)
\(90\) 19.0190 2.00478
\(91\) 4.22574 0.442978
\(92\) −20.9318 −2.18229
\(93\) −1.60950 −0.166898
\(94\) −19.2686 −1.98741
\(95\) −5.08275 −0.521479
\(96\) 78.1250 7.97360
\(97\) −11.9944 −1.21784 −0.608922 0.793230i \(-0.708398\pi\)
−0.608922 + 0.793230i \(0.708398\pi\)
\(98\) −38.5440 −3.89353
\(99\) −11.6912 −1.17501
\(100\) −18.0835 −1.80835
\(101\) 1.99744 0.198753 0.0993765 0.995050i \(-0.468315\pi\)
0.0993765 + 0.995050i \(0.468315\pi\)
\(102\) 51.6551 5.11461
\(103\) −13.4220 −1.32251 −0.661253 0.750163i \(-0.729975\pi\)
−0.661253 + 0.750163i \(0.729975\pi\)
\(104\) −9.59360 −0.940730
\(105\) 17.5846 1.71609
\(106\) 17.5850 1.70801
\(107\) 9.86660 0.953840 0.476920 0.878947i \(-0.341753\pi\)
0.476920 + 0.878947i \(0.341753\pi\)
\(108\) −33.1006 −3.18511
\(109\) 2.21647 0.212299 0.106149 0.994350i \(-0.466148\pi\)
0.106149 + 0.994350i \(0.466148\pi\)
\(110\) −8.76172 −0.835397
\(111\) 1.49560 0.141956
\(112\) 79.3455 7.49744
\(113\) −1.00000 −0.0940721
\(114\) 29.5034 2.76325
\(115\) 4.96069 0.462587
\(116\) 39.0026 3.62130
\(117\) 4.66056 0.430869
\(118\) −11.8308 −1.08911
\(119\) 29.9334 2.74399
\(120\) −39.9220 −3.64437
\(121\) −5.61410 −0.510373
\(122\) −37.8932 −3.43068
\(123\) 29.1115 2.62489
\(124\) 3.25288 0.292117
\(125\) 11.0753 0.990604
\(126\) −63.9744 −5.69929
\(127\) −22.0617 −1.95766 −0.978828 0.204686i \(-0.934383\pi\)
−0.978828 + 0.204686i \(0.934383\pi\)
\(128\) −61.3017 −5.41835
\(129\) −6.49219 −0.571606
\(130\) 3.49277 0.306336
\(131\) −4.10331 −0.358508 −0.179254 0.983803i \(-0.557368\pi\)
−0.179254 + 0.983803i \(0.557368\pi\)
\(132\) 37.6994 3.28131
\(133\) 17.0969 1.48249
\(134\) −0.691793 −0.0597618
\(135\) 7.84460 0.675156
\(136\) −67.9572 −5.82728
\(137\) −11.1980 −0.956713 −0.478357 0.878166i \(-0.658767\pi\)
−0.478357 + 0.878166i \(0.658767\pi\)
\(138\) −28.7949 −2.45118
\(139\) 1.30155 0.110396 0.0551980 0.998475i \(-0.482421\pi\)
0.0551980 + 0.998475i \(0.482421\pi\)
\(140\) −35.5394 −3.00363
\(141\) −19.6486 −1.65471
\(142\) 2.78025 0.233314
\(143\) −2.14703 −0.179544
\(144\) 87.5099 7.29249
\(145\) −9.24334 −0.767617
\(146\) 13.0424 1.07940
\(147\) −39.3040 −3.24174
\(148\) −3.02268 −0.248463
\(149\) −5.33309 −0.436904 −0.218452 0.975848i \(-0.570101\pi\)
−0.218452 + 0.975848i \(0.570101\pi\)
\(150\) −24.8766 −2.03117
\(151\) −2.88788 −0.235013 −0.117506 0.993072i \(-0.537490\pi\)
−0.117506 + 0.993072i \(0.537490\pi\)
\(152\) −38.8146 −3.14828
\(153\) 33.0135 2.66899
\(154\) 29.4718 2.37491
\(155\) −0.770908 −0.0619208
\(156\) −15.0285 −1.20324
\(157\) −16.0035 −1.27722 −0.638608 0.769532i \(-0.720490\pi\)
−0.638608 + 0.769532i \(0.720490\pi\)
\(158\) 29.0257 2.30916
\(159\) 17.9318 1.42208
\(160\) 37.4198 2.95829
\(161\) −16.6863 −1.31506
\(162\) −3.51702 −0.276323
\(163\) −23.6542 −1.85274 −0.926371 0.376612i \(-0.877089\pi\)
−0.926371 + 0.376612i \(0.877089\pi\)
\(164\) −58.8356 −4.59429
\(165\) −8.93449 −0.695549
\(166\) 33.7255 2.61761
\(167\) −8.49400 −0.657285 −0.328643 0.944454i \(-0.606591\pi\)
−0.328643 + 0.944454i \(0.606591\pi\)
\(168\) 134.286 10.3604
\(169\) −12.1441 −0.934162
\(170\) 24.7414 1.89758
\(171\) 18.8561 1.44196
\(172\) 13.1210 1.00047
\(173\) −1.96994 −0.149772 −0.0748859 0.997192i \(-0.523859\pi\)
−0.0748859 + 0.997192i \(0.523859\pi\)
\(174\) 53.6540 4.06750
\(175\) −14.4157 −1.08972
\(176\) −40.3142 −3.03880
\(177\) −12.0640 −0.906789
\(178\) 30.6315 2.29593
\(179\) 3.32473 0.248502 0.124251 0.992251i \(-0.460347\pi\)
0.124251 + 0.992251i \(0.460347\pi\)
\(180\) −39.1963 −2.92152
\(181\) −9.24568 −0.687226 −0.343613 0.939111i \(-0.611651\pi\)
−0.343613 + 0.939111i \(0.611651\pi\)
\(182\) −11.7486 −0.870867
\(183\) −38.6403 −2.85638
\(184\) 37.8825 2.79273
\(185\) 0.716353 0.0526673
\(186\) 4.47482 0.328110
\(187\) −15.2087 −1.11217
\(188\) 39.7107 2.89620
\(189\) −26.3869 −1.91936
\(190\) 14.1313 1.02520
\(191\) 4.13653 0.299309 0.149655 0.988738i \(-0.452184\pi\)
0.149655 + 0.988738i \(0.452184\pi\)
\(192\) −118.710 −8.56718
\(193\) −2.78974 −0.200810 −0.100405 0.994947i \(-0.532014\pi\)
−0.100405 + 0.994947i \(0.532014\pi\)
\(194\) 33.3474 2.39420
\(195\) 3.56164 0.255054
\(196\) 79.4351 5.67394
\(197\) −21.1019 −1.50345 −0.751726 0.659476i \(-0.770778\pi\)
−0.751726 + 0.659476i \(0.770778\pi\)
\(198\) 32.5044 2.30999
\(199\) 6.71402 0.475944 0.237972 0.971272i \(-0.423517\pi\)
0.237972 + 0.971272i \(0.423517\pi\)
\(200\) 32.7276 2.31419
\(201\) −0.705434 −0.0497574
\(202\) −5.55340 −0.390736
\(203\) 31.0918 2.18222
\(204\) −106.456 −7.45339
\(205\) 13.9436 0.973864
\(206\) 37.3165 2.59996
\(207\) −18.4033 −1.27911
\(208\) 16.0708 1.11431
\(209\) −8.68664 −0.600868
\(210\) −48.8898 −3.37372
\(211\) −10.2201 −0.703580 −0.351790 0.936079i \(-0.614427\pi\)
−0.351790 + 0.936079i \(0.614427\pi\)
\(212\) −36.2409 −2.48904
\(213\) 2.83508 0.194256
\(214\) −27.4317 −1.87519
\(215\) −3.10959 −0.212072
\(216\) 59.9056 4.07606
\(217\) 2.59310 0.176031
\(218\) −6.16234 −0.417366
\(219\) 13.2996 0.898702
\(220\) 18.0570 1.21740
\(221\) 6.06280 0.407828
\(222\) −4.15815 −0.279077
\(223\) 1.64166 0.109933 0.0549667 0.998488i \(-0.482495\pi\)
0.0549667 + 0.998488i \(0.482495\pi\)
\(224\) −125.869 −8.40997
\(225\) −15.8990 −1.05994
\(226\) 2.78025 0.184940
\(227\) 14.4635 0.959977 0.479988 0.877275i \(-0.340641\pi\)
0.479988 + 0.877275i \(0.340641\pi\)
\(228\) −60.8035 −4.02681
\(229\) 17.4257 1.15152 0.575760 0.817619i \(-0.304706\pi\)
0.575760 + 0.817619i \(0.304706\pi\)
\(230\) −13.7920 −0.909416
\(231\) 30.0529 1.97734
\(232\) −70.5871 −4.63427
\(233\) −9.64829 −0.632081 −0.316040 0.948746i \(-0.602354\pi\)
−0.316040 + 0.948746i \(0.602354\pi\)
\(234\) −12.9575 −0.847061
\(235\) −9.41114 −0.613915
\(236\) 24.3820 1.58713
\(237\) 29.5980 1.92260
\(238\) −83.2226 −5.39452
\(239\) 12.4640 0.806232 0.403116 0.915149i \(-0.367927\pi\)
0.403116 + 0.915149i \(0.367927\pi\)
\(240\) 66.8759 4.31682
\(241\) −20.0926 −1.29428 −0.647139 0.762372i \(-0.724035\pi\)
−0.647139 + 0.762372i \(0.724035\pi\)
\(242\) 15.6086 1.00336
\(243\) 13.7443 0.881700
\(244\) 78.0939 4.99945
\(245\) −18.8255 −1.20272
\(246\) −80.9373 −5.16037
\(247\) 3.46284 0.220335
\(248\) −5.88706 −0.373829
\(249\) 34.3905 2.17941
\(250\) −30.7921 −1.94747
\(251\) 9.05151 0.571327 0.285663 0.958330i \(-0.407786\pi\)
0.285663 + 0.958330i \(0.407786\pi\)
\(252\) 131.845 8.30543
\(253\) 8.47804 0.533010
\(254\) 61.3370 3.84863
\(255\) 25.2292 1.57992
\(256\) 86.6903 5.41814
\(257\) 7.75143 0.483521 0.241761 0.970336i \(-0.422275\pi\)
0.241761 + 0.970336i \(0.422275\pi\)
\(258\) 18.0500 1.12374
\(259\) −2.40960 −0.149725
\(260\) −7.19824 −0.446416
\(261\) 34.2911 2.12257
\(262\) 11.4083 0.704804
\(263\) −7.97762 −0.491921 −0.245961 0.969280i \(-0.579103\pi\)
−0.245961 + 0.969280i \(0.579103\pi\)
\(264\) −68.2285 −4.19917
\(265\) 8.58884 0.527608
\(266\) −47.5336 −2.91447
\(267\) 31.2355 1.91158
\(268\) 1.42571 0.0870893
\(269\) 9.21856 0.562065 0.281033 0.959698i \(-0.409323\pi\)
0.281033 + 0.959698i \(0.409323\pi\)
\(270\) −21.8100 −1.32731
\(271\) 13.6676 0.830246 0.415123 0.909765i \(-0.363739\pi\)
0.415123 + 0.909765i \(0.363739\pi\)
\(272\) 113.839 6.90253
\(273\) −11.9803 −0.725080
\(274\) 31.1334 1.88084
\(275\) 7.32439 0.441677
\(276\) 59.3433 3.57205
\(277\) 20.2242 1.21515 0.607576 0.794262i \(-0.292142\pi\)
0.607576 + 0.794262i \(0.292142\pi\)
\(278\) −3.61864 −0.217032
\(279\) 2.85993 0.171219
\(280\) 64.3193 3.84381
\(281\) 30.7000 1.83141 0.915705 0.401851i \(-0.131633\pi\)
0.915705 + 0.401851i \(0.131633\pi\)
\(282\) 54.6280 3.25305
\(283\) 32.8524 1.95287 0.976436 0.215805i \(-0.0692377\pi\)
0.976436 + 0.215805i \(0.0692377\pi\)
\(284\) −5.72982 −0.340002
\(285\) 14.4100 0.853574
\(286\) 5.96930 0.352972
\(287\) −46.9021 −2.76855
\(288\) −138.821 −8.18008
\(289\) 25.9464 1.52626
\(290\) 25.6988 1.50909
\(291\) 34.0049 1.99341
\(292\) −26.8791 −1.57298
\(293\) −24.4695 −1.42952 −0.714761 0.699369i \(-0.753464\pi\)
−0.714761 + 0.699369i \(0.753464\pi\)
\(294\) 109.275 6.37305
\(295\) −5.77835 −0.336429
\(296\) 5.47045 0.317964
\(297\) 13.4068 0.777940
\(298\) 14.8274 0.858926
\(299\) −3.37968 −0.195452
\(300\) 51.2682 2.95997
\(301\) 10.4597 0.602888
\(302\) 8.02905 0.462020
\(303\) −5.66290 −0.325325
\(304\) 65.0207 3.72920
\(305\) −18.5077 −1.05975
\(306\) −91.7860 −5.24706
\(307\) −5.00753 −0.285795 −0.142897 0.989738i \(-0.545642\pi\)
−0.142897 + 0.989738i \(0.545642\pi\)
\(308\) −60.7384 −3.46089
\(309\) 38.0523 2.16472
\(310\) 2.14332 0.121732
\(311\) 13.2735 0.752669 0.376334 0.926484i \(-0.377184\pi\)
0.376334 + 0.926484i \(0.377184\pi\)
\(312\) 27.1986 1.53982
\(313\) −13.5598 −0.766445 −0.383222 0.923656i \(-0.625186\pi\)
−0.383222 + 0.923656i \(0.625186\pi\)
\(314\) 44.4937 2.51093
\(315\) −31.2462 −1.76052
\(316\) −59.8189 −3.36507
\(317\) −18.2361 −1.02424 −0.512121 0.858913i \(-0.671140\pi\)
−0.512121 + 0.858913i \(0.671140\pi\)
\(318\) −49.8549 −2.79572
\(319\) −15.7973 −0.884478
\(320\) −56.8590 −3.17852
\(321\) −27.9726 −1.56128
\(322\) 46.3921 2.58533
\(323\) 24.5294 1.36485
\(324\) 7.24820 0.402678
\(325\) −2.91979 −0.161961
\(326\) 65.7648 3.64237
\(327\) −6.28385 −0.347498
\(328\) 106.481 5.87942
\(329\) 31.6563 1.74527
\(330\) 24.8401 1.36741
\(331\) −14.7073 −0.808387 −0.404193 0.914674i \(-0.632448\pi\)
−0.404193 + 0.914674i \(0.632448\pi\)
\(332\) −69.5048 −3.81457
\(333\) −2.65754 −0.145632
\(334\) 23.6155 1.29218
\(335\) −0.337884 −0.0184606
\(336\) −224.950 −12.2721
\(337\) 32.8557 1.78977 0.894883 0.446300i \(-0.147259\pi\)
0.894883 + 0.446300i \(0.147259\pi\)
\(338\) 33.7637 1.83650
\(339\) 2.83508 0.153980
\(340\) −50.9894 −2.76529
\(341\) −1.31752 −0.0713475
\(342\) −52.4247 −2.83480
\(343\) 31.3499 1.69274
\(344\) −23.7465 −1.28032
\(345\) −14.0639 −0.757177
\(346\) 5.47694 0.294442
\(347\) 35.1785 1.88848 0.944240 0.329258i \(-0.106799\pi\)
0.944240 + 0.329258i \(0.106799\pi\)
\(348\) −110.575 −5.92746
\(349\) 30.8581 1.65180 0.825898 0.563820i \(-0.190669\pi\)
0.825898 + 0.563820i \(0.190669\pi\)
\(350\) 40.0793 2.14233
\(351\) −5.34447 −0.285267
\(352\) 63.9521 3.40866
\(353\) 19.6728 1.04708 0.523538 0.852003i \(-0.324612\pi\)
0.523538 + 0.852003i \(0.324612\pi\)
\(354\) 33.5411 1.78269
\(355\) 1.35792 0.0720712
\(356\) −63.1283 −3.34579
\(357\) −84.8636 −4.49146
\(358\) −9.24360 −0.488539
\(359\) −25.3106 −1.33584 −0.667921 0.744232i \(-0.732816\pi\)
−0.667921 + 0.744232i \(0.732816\pi\)
\(360\) 70.9376 3.73874
\(361\) −4.98975 −0.262618
\(362\) 25.7053 1.35104
\(363\) 15.9164 0.835394
\(364\) 24.2127 1.26909
\(365\) 6.37014 0.333428
\(366\) 107.430 5.61545
\(367\) −32.0745 −1.67427 −0.837137 0.546994i \(-0.815772\pi\)
−0.837137 + 0.546994i \(0.815772\pi\)
\(368\) −63.4593 −3.30804
\(369\) −51.7283 −2.69287
\(370\) −1.99164 −0.103541
\(371\) −28.8903 −1.49991
\(372\) −9.22215 −0.478146
\(373\) −18.1022 −0.937298 −0.468649 0.883384i \(-0.655259\pi\)
−0.468649 + 0.883384i \(0.655259\pi\)
\(374\) 42.2841 2.18646
\(375\) −31.3993 −1.62145
\(376\) −71.8685 −3.70633
\(377\) 6.29742 0.324334
\(378\) 73.3623 3.77335
\(379\) −17.8823 −0.918553 −0.459276 0.888293i \(-0.651891\pi\)
−0.459276 + 0.888293i \(0.651891\pi\)
\(380\) −29.1232 −1.49399
\(381\) 62.5465 3.20435
\(382\) −11.5006 −0.588423
\(383\) 30.5204 1.55952 0.779759 0.626080i \(-0.215342\pi\)
0.779759 + 0.626080i \(0.215342\pi\)
\(384\) 173.795 8.86893
\(385\) 14.3946 0.733614
\(386\) 7.75620 0.394780
\(387\) 11.5360 0.586408
\(388\) −68.7255 −3.48901
\(389\) −34.2585 −1.73697 −0.868486 0.495713i \(-0.834907\pi\)
−0.868486 + 0.495713i \(0.834907\pi\)
\(390\) −9.90227 −0.501421
\(391\) −23.9403 −1.21071
\(392\) −143.762 −7.26107
\(393\) 11.6332 0.586817
\(394\) 58.6688 2.95569
\(395\) 14.1766 0.713304
\(396\) −66.9882 −3.36628
\(397\) −30.0695 −1.50915 −0.754573 0.656216i \(-0.772156\pi\)
−0.754573 + 0.656216i \(0.772156\pi\)
\(398\) −18.6667 −0.935677
\(399\) −48.4709 −2.42658
\(400\) −54.8241 −2.74120
\(401\) −27.4334 −1.36996 −0.684980 0.728562i \(-0.740189\pi\)
−0.684980 + 0.728562i \(0.740189\pi\)
\(402\) 1.96129 0.0978200
\(403\) 0.525214 0.0261628
\(404\) 11.4450 0.569409
\(405\) −1.71777 −0.0853568
\(406\) −86.4432 −4.29010
\(407\) 1.22428 0.0606852
\(408\) 192.664 9.53828
\(409\) 10.2227 0.505481 0.252740 0.967534i \(-0.418668\pi\)
0.252740 + 0.967534i \(0.418668\pi\)
\(410\) −38.7668 −1.91456
\(411\) 31.7473 1.56598
\(412\) −76.9054 −3.78886
\(413\) 19.4366 0.956415
\(414\) 51.1657 2.51466
\(415\) 16.4721 0.808586
\(416\) −25.4938 −1.24994
\(417\) −3.68999 −0.180700
\(418\) 24.1511 1.18127
\(419\) −36.6206 −1.78903 −0.894516 0.447036i \(-0.852480\pi\)
−0.894516 + 0.447036i \(0.852480\pi\)
\(420\) 100.757 4.91643
\(421\) 26.5902 1.29593 0.647965 0.761670i \(-0.275620\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(422\) 28.4145 1.38319
\(423\) 34.9136 1.69756
\(424\) 65.5890 3.18528
\(425\) −20.6826 −1.00326
\(426\) −7.88223 −0.381895
\(427\) 62.2543 3.01270
\(428\) 56.5338 2.73267
\(429\) 6.08700 0.293883
\(430\) 8.64544 0.416920
\(431\) −20.4152 −0.983367 −0.491684 0.870774i \(-0.663618\pi\)
−0.491684 + 0.870774i \(0.663618\pi\)
\(432\) −100.352 −4.82817
\(433\) −24.3286 −1.16916 −0.584578 0.811337i \(-0.698740\pi\)
−0.584578 + 0.811337i \(0.698740\pi\)
\(434\) −7.20949 −0.346067
\(435\) 26.2056 1.25646
\(436\) 12.6999 0.608217
\(437\) −13.6738 −0.654107
\(438\) −36.9762 −1.76679
\(439\) 14.7695 0.704909 0.352454 0.935829i \(-0.385347\pi\)
0.352454 + 0.935829i \(0.385347\pi\)
\(440\) −32.6796 −1.55794
\(441\) 69.8393 3.32568
\(442\) −16.8561 −0.801764
\(443\) −9.08687 −0.431730 −0.215865 0.976423i \(-0.569257\pi\)
−0.215865 + 0.976423i \(0.569257\pi\)
\(444\) 8.56952 0.406692
\(445\) 14.9609 0.709217
\(446\) −4.56422 −0.216122
\(447\) 15.1197 0.715138
\(448\) 191.257 9.03604
\(449\) −25.8193 −1.21849 −0.609245 0.792982i \(-0.708527\pi\)
−0.609245 + 0.792982i \(0.708527\pi\)
\(450\) 44.2034 2.08377
\(451\) 23.8302 1.12212
\(452\) −5.72982 −0.269508
\(453\) 8.18736 0.384676
\(454\) −40.2122 −1.88725
\(455\) −5.73824 −0.269013
\(456\) 110.042 5.15320
\(457\) −28.4982 −1.33309 −0.666545 0.745465i \(-0.732227\pi\)
−0.666545 + 0.745465i \(0.732227\pi\)
\(458\) −48.4478 −2.26382
\(459\) −37.8581 −1.76706
\(460\) 28.4238 1.32527
\(461\) 16.1738 0.753288 0.376644 0.926358i \(-0.377078\pi\)
0.376644 + 0.926358i \(0.377078\pi\)
\(462\) −83.5548 −3.88732
\(463\) 3.84579 0.178729 0.0893646 0.995999i \(-0.471516\pi\)
0.0893646 + 0.995999i \(0.471516\pi\)
\(464\) 118.245 5.48938
\(465\) 2.18558 0.101354
\(466\) 26.8247 1.24263
\(467\) −19.6041 −0.907170 −0.453585 0.891213i \(-0.649855\pi\)
−0.453585 + 0.891213i \(0.649855\pi\)
\(468\) 26.7041 1.23440
\(469\) 1.13654 0.0524805
\(470\) 26.1654 1.20692
\(471\) 45.3711 2.09059
\(472\) −44.1266 −2.03109
\(473\) −5.31442 −0.244357
\(474\) −82.2899 −3.77970
\(475\) −11.8131 −0.542024
\(476\) 171.513 7.86129
\(477\) −31.8630 −1.45891
\(478\) −34.6532 −1.58500
\(479\) −19.6463 −0.897663 −0.448832 0.893616i \(-0.648160\pi\)
−0.448832 + 0.893616i \(0.648160\pi\)
\(480\) −106.088 −4.84223
\(481\) −0.488046 −0.0222530
\(482\) 55.8625 2.54447
\(483\) 47.3069 2.15254
\(484\) −32.1678 −1.46217
\(485\) 16.2875 0.739575
\(486\) −38.2128 −1.73337
\(487\) −8.52740 −0.386413 −0.193207 0.981158i \(-0.561889\pi\)
−0.193207 + 0.981158i \(0.561889\pi\)
\(488\) −141.335 −6.39791
\(489\) 67.0615 3.03263
\(490\) 52.3398 2.36447
\(491\) 40.5401 1.82955 0.914774 0.403965i \(-0.132368\pi\)
0.914774 + 0.403965i \(0.132368\pi\)
\(492\) 166.803 7.52008
\(493\) 44.6084 2.00906
\(494\) −9.62758 −0.433165
\(495\) 15.8757 0.713560
\(496\) 9.86179 0.442807
\(497\) −4.56765 −0.204887
\(498\) −95.6145 −4.28459
\(499\) 11.9027 0.532837 0.266419 0.963857i \(-0.414160\pi\)
0.266419 + 0.963857i \(0.414160\pi\)
\(500\) 63.4594 2.83799
\(501\) 24.0811 1.07587
\(502\) −25.1655 −1.12319
\(503\) 13.4961 0.601763 0.300882 0.953662i \(-0.402719\pi\)
0.300882 + 0.953662i \(0.402719\pi\)
\(504\) −238.613 −10.6287
\(505\) −2.71238 −0.120699
\(506\) −23.5711 −1.04786
\(507\) 34.4295 1.52907
\(508\) −126.409 −5.60850
\(509\) 41.5708 1.84259 0.921296 0.388862i \(-0.127132\pi\)
0.921296 + 0.388862i \(0.127132\pi\)
\(510\) −70.1437 −3.10601
\(511\) −21.4273 −0.947886
\(512\) −118.418 −5.23337
\(513\) −21.6231 −0.954683
\(514\) −21.5510 −0.950572
\(515\) 18.2260 0.803135
\(516\) −37.1991 −1.63760
\(517\) −16.0841 −0.707376
\(518\) 6.69929 0.294350
\(519\) 5.58493 0.245151
\(520\) 13.0274 0.571289
\(521\) 16.4250 0.719593 0.359797 0.933031i \(-0.382846\pi\)
0.359797 + 0.933031i \(0.382846\pi\)
\(522\) −95.3380 −4.17283
\(523\) −8.56429 −0.374490 −0.187245 0.982313i \(-0.559956\pi\)
−0.187245 + 0.982313i \(0.559956\pi\)
\(524\) −23.5112 −1.02709
\(525\) 40.8696 1.78370
\(526\) 22.1798 0.967086
\(527\) 3.72041 0.162063
\(528\) 114.294 4.97400
\(529\) −9.65457 −0.419764
\(530\) −23.8792 −1.03724
\(531\) 21.4366 0.930270
\(532\) 97.9618 4.24718
\(533\) −9.49968 −0.411477
\(534\) −86.8425 −3.75804
\(535\) −13.3981 −0.579251
\(536\) −2.58026 −0.111450
\(537\) −9.42586 −0.406756
\(538\) −25.6299 −1.10499
\(539\) −32.1737 −1.38582
\(540\) 44.9481 1.93426
\(541\) 19.5921 0.842331 0.421165 0.906984i \(-0.361621\pi\)
0.421165 + 0.906984i \(0.361621\pi\)
\(542\) −37.9993 −1.63221
\(543\) 26.2122 1.12487
\(544\) −180.588 −7.74265
\(545\) −3.00979 −0.128925
\(546\) 33.3083 1.42546
\(547\) 31.2971 1.33817 0.669084 0.743187i \(-0.266687\pi\)
0.669084 + 0.743187i \(0.266687\pi\)
\(548\) −64.1627 −2.74090
\(549\) 68.6601 2.93034
\(550\) −20.3637 −0.868310
\(551\) 25.4786 1.08543
\(552\) −107.400 −4.57123
\(553\) −47.6860 −2.02781
\(554\) −56.2283 −2.38891
\(555\) −2.03091 −0.0862075
\(556\) 7.45764 0.316274
\(557\) −38.7702 −1.64274 −0.821372 0.570393i \(-0.806791\pi\)
−0.821372 + 0.570393i \(0.806791\pi\)
\(558\) −7.95133 −0.336607
\(559\) 2.11854 0.0896046
\(560\) −107.745 −4.55307
\(561\) 43.1179 1.82044
\(562\) −85.3539 −3.60044
\(563\) −18.9163 −0.797228 −0.398614 0.917119i \(-0.630509\pi\)
−0.398614 + 0.917119i \(0.630509\pi\)
\(564\) −112.583 −4.74059
\(565\) 1.35792 0.0571283
\(566\) −91.3381 −3.83923
\(567\) 5.77807 0.242656
\(568\) 10.3698 0.435109
\(569\) 43.1626 1.80947 0.904736 0.425974i \(-0.140068\pi\)
0.904736 + 0.425974i \(0.140068\pi\)
\(570\) −40.0634 −1.67807
\(571\) 18.6071 0.778682 0.389341 0.921094i \(-0.372703\pi\)
0.389341 + 0.921094i \(0.372703\pi\)
\(572\) −12.3021 −0.514377
\(573\) −11.7274 −0.489918
\(574\) 130.400 5.44279
\(575\) 11.5295 0.480811
\(576\) 210.937 8.78903
\(577\) −8.60942 −0.358415 −0.179207 0.983811i \(-0.557353\pi\)
−0.179207 + 0.983811i \(0.557353\pi\)
\(578\) −72.1377 −3.00053
\(579\) 7.90913 0.328692
\(580\) −52.9626 −2.19915
\(581\) −55.4074 −2.29869
\(582\) −94.5424 −3.91891
\(583\) 14.6787 0.607930
\(584\) 48.6458 2.01298
\(585\) −6.32869 −0.261659
\(586\) 68.0314 2.81035
\(587\) −8.58617 −0.354389 −0.177195 0.984176i \(-0.556702\pi\)
−0.177195 + 0.984176i \(0.556702\pi\)
\(588\) −225.205 −9.28728
\(589\) 2.12495 0.0875572
\(590\) 16.0653 0.661397
\(591\) 59.8256 2.46090
\(592\) −9.16390 −0.376634
\(593\) −15.3209 −0.629152 −0.314576 0.949232i \(-0.601862\pi\)
−0.314576 + 0.949232i \(0.601862\pi\)
\(594\) −37.2742 −1.52938
\(595\) −40.6474 −1.66638
\(596\) −30.5577 −1.25169
\(597\) −19.0348 −0.779041
\(598\) 9.39638 0.384246
\(599\) −12.4253 −0.507682 −0.253841 0.967246i \(-0.581694\pi\)
−0.253841 + 0.967246i \(0.581694\pi\)
\(600\) −92.7853 −3.78794
\(601\) 34.8496 1.42154 0.710771 0.703423i \(-0.248346\pi\)
0.710771 + 0.703423i \(0.248346\pi\)
\(602\) −29.0807 −1.18524
\(603\) 1.25349 0.0510459
\(604\) −16.5470 −0.673289
\(605\) 7.62353 0.309940
\(606\) 15.7443 0.639569
\(607\) −19.7067 −0.799872 −0.399936 0.916543i \(-0.630968\pi\)
−0.399936 + 0.916543i \(0.630968\pi\)
\(608\) −103.145 −4.18308
\(609\) −88.1477 −3.57192
\(610\) 51.4561 2.08340
\(611\) 6.41174 0.259391
\(612\) 189.161 7.64640
\(613\) 14.5960 0.589525 0.294763 0.955571i \(-0.404759\pi\)
0.294763 + 0.955571i \(0.404759\pi\)
\(614\) 13.9222 0.561854
\(615\) −39.5312 −1.59405
\(616\) 109.924 4.42898
\(617\) 3.43056 0.138109 0.0690545 0.997613i \(-0.478002\pi\)
0.0690545 + 0.997613i \(0.478002\pi\)
\(618\) −105.795 −4.25570
\(619\) −35.7460 −1.43675 −0.718376 0.695655i \(-0.755114\pi\)
−0.718376 + 0.695655i \(0.755114\pi\)
\(620\) −4.41716 −0.177397
\(621\) 21.1038 0.846868
\(622\) −36.9036 −1.47970
\(623\) −50.3242 −2.01619
\(624\) −45.5621 −1.82394
\(625\) 0.740785 0.0296314
\(626\) 37.6997 1.50678
\(627\) 24.6273 0.983519
\(628\) −91.6970 −3.65911
\(629\) −3.45712 −0.137844
\(630\) 86.8724 3.46108
\(631\) 4.08984 0.162814 0.0814069 0.996681i \(-0.474059\pi\)
0.0814069 + 0.996681i \(0.474059\pi\)
\(632\) 108.260 4.30637
\(633\) 28.9747 1.15164
\(634\) 50.7011 2.01360
\(635\) 29.9581 1.18885
\(636\) 102.746 4.07414
\(637\) 12.8257 0.508173
\(638\) 43.9204 1.73883
\(639\) −5.03765 −0.199287
\(640\) 83.2431 3.29047
\(641\) 12.1121 0.478398 0.239199 0.970971i \(-0.423115\pi\)
0.239199 + 0.970971i \(0.423115\pi\)
\(642\) 77.7709 3.06937
\(643\) 35.7414 1.40950 0.704752 0.709453i \(-0.251058\pi\)
0.704752 + 0.709453i \(0.251058\pi\)
\(644\) −95.6093 −3.76754
\(645\) 8.81591 0.347126
\(646\) −68.1979 −2.68321
\(647\) 5.27768 0.207487 0.103743 0.994604i \(-0.466918\pi\)
0.103743 + 0.994604i \(0.466918\pi\)
\(648\) −13.1178 −0.515317
\(649\) −9.87546 −0.387646
\(650\) 8.11777 0.318405
\(651\) −7.35165 −0.288134
\(652\) −135.534 −5.30794
\(653\) −20.9329 −0.819166 −0.409583 0.912273i \(-0.634326\pi\)
−0.409583 + 0.912273i \(0.634326\pi\)
\(654\) 17.4707 0.683158
\(655\) 5.57199 0.217716
\(656\) −178.373 −6.96429
\(657\) −23.6321 −0.921975
\(658\) −88.0125 −3.43108
\(659\) −22.1436 −0.862594 −0.431297 0.902210i \(-0.641944\pi\)
−0.431297 + 0.902210i \(0.641944\pi\)
\(660\) −51.1930 −1.99268
\(661\) −13.7208 −0.533679 −0.266839 0.963741i \(-0.585979\pi\)
−0.266839 + 0.963741i \(0.585979\pi\)
\(662\) 40.8901 1.58924
\(663\) −17.1885 −0.667546
\(664\) 125.790 4.88160
\(665\) −23.2162 −0.900287
\(666\) 7.38863 0.286304
\(667\) −24.8668 −0.962845
\(668\) −48.6691 −1.88306
\(669\) −4.65422 −0.179943
\(670\) 0.939403 0.0362923
\(671\) −31.6304 −1.22108
\(672\) 356.848 13.7657
\(673\) 12.8606 0.495739 0.247870 0.968793i \(-0.420270\pi\)
0.247870 + 0.968793i \(0.420270\pi\)
\(674\) −91.3474 −3.51857
\(675\) 18.2321 0.701755
\(676\) −69.5835 −2.67629
\(677\) −26.5452 −1.02022 −0.510108 0.860111i \(-0.670394\pi\)
−0.510108 + 0.860111i \(0.670394\pi\)
\(678\) −7.88223 −0.302715
\(679\) −54.7861 −2.10250
\(680\) 92.2808 3.53881
\(681\) −41.0051 −1.57132
\(682\) 3.66303 0.140265
\(683\) 33.0229 1.26359 0.631793 0.775137i \(-0.282319\pi\)
0.631793 + 0.775137i \(0.282319\pi\)
\(684\) 108.042 4.13108
\(685\) 15.2061 0.580995
\(686\) −87.1608 −3.32782
\(687\) −49.4031 −1.88485
\(688\) 39.7792 1.51657
\(689\) −5.85151 −0.222925
\(690\) 39.1013 1.48856
\(691\) −13.5117 −0.514011 −0.257005 0.966410i \(-0.582736\pi\)
−0.257005 + 0.966410i \(0.582736\pi\)
\(692\) −11.2874 −0.429083
\(693\) −53.4012 −2.02854
\(694\) −97.8052 −3.71263
\(695\) −1.76741 −0.0670415
\(696\) 200.120 7.58552
\(697\) −67.2919 −2.54886
\(698\) −85.7933 −3.24733
\(699\) 27.3536 1.03461
\(700\) −82.5993 −3.12196
\(701\) 6.34428 0.239620 0.119810 0.992797i \(-0.461771\pi\)
0.119810 + 0.992797i \(0.461771\pi\)
\(702\) 14.8590 0.560817
\(703\) −1.97458 −0.0744726
\(704\) −97.1746 −3.66241
\(705\) 26.6813 1.00488
\(706\) −54.6953 −2.05848
\(707\) 9.12363 0.343129
\(708\) −69.1247 −2.59787
\(709\) −6.33194 −0.237801 −0.118900 0.992906i \(-0.537937\pi\)
−0.118900 + 0.992906i \(0.537937\pi\)
\(710\) −3.77538 −0.141687
\(711\) −52.5927 −1.97238
\(712\) 114.250 4.28169
\(713\) −2.07392 −0.0776691
\(714\) 235.942 8.82992
\(715\) 2.91551 0.109034
\(716\) 19.0501 0.711936
\(717\) −35.3365 −1.31967
\(718\) 70.3699 2.62618
\(719\) −12.5088 −0.466499 −0.233250 0.972417i \(-0.574936\pi\)
−0.233250 + 0.972417i \(0.574936\pi\)
\(720\) −118.832 −4.42860
\(721\) −61.3069 −2.28319
\(722\) 13.8728 0.516291
\(723\) 56.9640 2.11852
\(724\) −52.9761 −1.96884
\(725\) −21.4830 −0.797860
\(726\) −44.2516 −1.64233
\(727\) 42.7515 1.58557 0.792783 0.609504i \(-0.208631\pi\)
0.792783 + 0.609504i \(0.208631\pi\)
\(728\) −43.8203 −1.62409
\(729\) −42.7613 −1.58375
\(730\) −17.7106 −0.655499
\(731\) 15.0069 0.555049
\(732\) −221.402 −8.18325
\(733\) 15.8530 0.585543 0.292772 0.956182i \(-0.405422\pi\)
0.292772 + 0.956182i \(0.405422\pi\)
\(734\) 89.1752 3.29152
\(735\) 53.3718 1.96865
\(736\) 100.668 3.71067
\(737\) −0.577458 −0.0212709
\(738\) 143.818 5.29400
\(739\) 25.2962 0.930535 0.465268 0.885170i \(-0.345958\pi\)
0.465268 + 0.885170i \(0.345958\pi\)
\(740\) 4.10457 0.150887
\(741\) −9.81742 −0.360652
\(742\) 80.3224 2.94873
\(743\) 22.9640 0.842467 0.421233 0.906952i \(-0.361597\pi\)
0.421233 + 0.906952i \(0.361597\pi\)
\(744\) 16.6903 0.611895
\(745\) 7.24194 0.265324
\(746\) 50.3288 1.84267
\(747\) −61.1086 −2.23585
\(748\) −87.1432 −3.18627
\(749\) 45.0672 1.64672
\(750\) 87.2980 3.18767
\(751\) −0.0225246 −0.000821935 0 −0.000410967 1.00000i \(-0.500131\pi\)
−0.000410967 1.00000i \(0.500131\pi\)
\(752\) 120.391 4.39022
\(753\) −25.6617 −0.935165
\(754\) −17.5084 −0.637619
\(755\) 3.92153 0.142719
\(756\) −151.192 −5.49880
\(757\) −13.9006 −0.505227 −0.252613 0.967567i \(-0.581290\pi\)
−0.252613 + 0.967567i \(0.581290\pi\)
\(758\) 49.7174 1.80582
\(759\) −24.0359 −0.872447
\(760\) 52.7073 1.91189
\(761\) 28.5594 1.03528 0.517639 0.855599i \(-0.326811\pi\)
0.517639 + 0.855599i \(0.326811\pi\)
\(762\) −173.895 −6.29956
\(763\) 10.1240 0.366515
\(764\) 23.7016 0.857493
\(765\) −44.8299 −1.62083
\(766\) −84.8544 −3.06591
\(767\) 3.93675 0.142148
\(768\) −245.773 −8.86858
\(769\) −16.7698 −0.604736 −0.302368 0.953191i \(-0.597777\pi\)
−0.302368 + 0.953191i \(0.597777\pi\)
\(770\) −40.0205 −1.44224
\(771\) −21.9759 −0.791443
\(772\) −15.9847 −0.575303
\(773\) −47.5970 −1.71195 −0.855973 0.517020i \(-0.827041\pi\)
−0.855973 + 0.517020i \(0.827041\pi\)
\(774\) −32.0730 −1.15284
\(775\) −1.79172 −0.0643603
\(776\) 124.380 4.46497
\(777\) 6.83139 0.245075
\(778\) 95.2472 3.41478
\(779\) −38.4346 −1.37706
\(780\) 20.4075 0.730707
\(781\) 2.32075 0.0830431
\(782\) 66.5602 2.38019
\(783\) −39.3231 −1.40529
\(784\) 240.825 8.60088
\(785\) 21.7315 0.775631
\(786\) −32.3433 −1.15365
\(787\) −14.7359 −0.525276 −0.262638 0.964894i \(-0.584593\pi\)
−0.262638 + 0.964894i \(0.584593\pi\)
\(788\) −120.910 −4.30725
\(789\) 22.6172 0.805192
\(790\) −39.4147 −1.40231
\(791\) −4.56765 −0.162407
\(792\) 121.235 4.30791
\(793\) 12.6091 0.447764
\(794\) 83.6009 2.96689
\(795\) −24.3500 −0.863606
\(796\) 38.4701 1.36354
\(797\) 40.4274 1.43201 0.716007 0.698093i \(-0.245968\pi\)
0.716007 + 0.698093i \(0.245968\pi\)
\(798\) 134.761 4.77050
\(799\) 45.4182 1.60678
\(800\) 86.9697 3.07484
\(801\) −55.5024 −1.96108
\(802\) 76.2719 2.69325
\(803\) 10.8869 0.384189
\(804\) −4.04201 −0.142551
\(805\) 22.6587 0.798615
\(806\) −1.46023 −0.0514344
\(807\) −26.1353 −0.920007
\(808\) −20.7132 −0.728687
\(809\) 9.41337 0.330956 0.165478 0.986213i \(-0.447083\pi\)
0.165478 + 0.986213i \(0.447083\pi\)
\(810\) 4.77584 0.167806
\(811\) −12.6653 −0.444739 −0.222369 0.974962i \(-0.571379\pi\)
−0.222369 + 0.974962i \(0.571379\pi\)
\(812\) 178.150 6.25186
\(813\) −38.7486 −1.35897
\(814\) −3.40381 −0.119303
\(815\) 32.1207 1.12514
\(816\) −322.743 −11.2983
\(817\) 8.57136 0.299874
\(818\) −28.4217 −0.993743
\(819\) 21.2878 0.743857
\(820\) 79.8943 2.79003
\(821\) −10.3521 −0.361291 −0.180646 0.983548i \(-0.557819\pi\)
−0.180646 + 0.983548i \(0.557819\pi\)
\(822\) −88.2656 −3.07862
\(823\) −39.6681 −1.38274 −0.691371 0.722500i \(-0.742993\pi\)
−0.691371 + 0.722500i \(0.742993\pi\)
\(824\) 139.184 4.84869
\(825\) −20.7652 −0.722952
\(826\) −54.0388 −1.88025
\(827\) −26.4575 −0.920018 −0.460009 0.887914i \(-0.652154\pi\)
−0.460009 + 0.887914i \(0.652154\pi\)
\(828\) −105.447 −3.66455
\(829\) −15.9603 −0.554322 −0.277161 0.960823i \(-0.589394\pi\)
−0.277161 + 0.960823i \(0.589394\pi\)
\(830\) −45.7968 −1.58963
\(831\) −57.3370 −1.98900
\(832\) 38.7377 1.34299
\(833\) 90.8522 3.14784
\(834\) 10.2591 0.355244
\(835\) 11.5342 0.399158
\(836\) −49.7729 −1.72143
\(837\) −3.27961 −0.113360
\(838\) 101.815 3.51712
\(839\) 30.8623 1.06548 0.532742 0.846278i \(-0.321162\pi\)
0.532742 + 0.846278i \(0.321162\pi\)
\(840\) −182.350 −6.29167
\(841\) 17.3347 0.597747
\(842\) −73.9276 −2.54772
\(843\) −87.0369 −2.99771
\(844\) −58.5593 −2.01569
\(845\) 16.4908 0.567300
\(846\) −97.0687 −3.33729
\(847\) −25.6433 −0.881113
\(848\) −109.872 −3.77303
\(849\) −93.1391 −3.19652
\(850\) 57.5030 1.97234
\(851\) 1.92716 0.0660621
\(852\) 16.2445 0.556526
\(853\) 53.2145 1.82203 0.911015 0.412373i \(-0.135300\pi\)
0.911015 + 0.412373i \(0.135300\pi\)
\(854\) −173.083 −5.92277
\(855\) −25.6051 −0.875677
\(856\) −102.315 −3.49706
\(857\) −8.79570 −0.300455 −0.150228 0.988651i \(-0.548001\pi\)
−0.150228 + 0.988651i \(0.548001\pi\)
\(858\) −16.9234 −0.577756
\(859\) −33.0621 −1.12806 −0.564032 0.825753i \(-0.690750\pi\)
−0.564032 + 0.825753i \(0.690750\pi\)
\(860\) −17.8174 −0.607567
\(861\) 132.971 4.53164
\(862\) 56.7596 1.93324
\(863\) 24.2564 0.825697 0.412849 0.910800i \(-0.364534\pi\)
0.412849 + 0.910800i \(0.364534\pi\)
\(864\) 159.192 5.41581
\(865\) 2.67503 0.0909538
\(866\) 67.6396 2.29849
\(867\) −73.5601 −2.49823
\(868\) 14.8580 0.504314
\(869\) 24.2285 0.821896
\(870\) −72.8581 −2.47012
\(871\) 0.230198 0.00779995
\(872\) −22.9844 −0.778350
\(873\) −60.4235 −2.04503
\(874\) 38.0166 1.28593
\(875\) 50.5881 1.71019
\(876\) 76.2042 2.57470
\(877\) −6.35434 −0.214571 −0.107285 0.994228i \(-0.534216\pi\)
−0.107285 + 0.994228i \(0.534216\pi\)
\(878\) −41.0629 −1.38581
\(879\) 69.3728 2.33989
\(880\) 54.7437 1.84541
\(881\) 5.62464 0.189499 0.0947495 0.995501i \(-0.469795\pi\)
0.0947495 + 0.995501i \(0.469795\pi\)
\(882\) −194.171 −6.53808
\(883\) −25.9219 −0.872341 −0.436170 0.899864i \(-0.643665\pi\)
−0.436170 + 0.899864i \(0.643665\pi\)
\(884\) 34.7387 1.16839
\(885\) 16.3821 0.550677
\(886\) 25.2638 0.848754
\(887\) −20.1048 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(888\) −15.5091 −0.520453
\(889\) −100.770 −3.37972
\(890\) −41.5952 −1.39428
\(891\) −2.93575 −0.0983513
\(892\) 9.40639 0.314949
\(893\) 25.9412 0.868088
\(894\) −42.0367 −1.40592
\(895\) −4.51473 −0.150911
\(896\) −280.005 −9.35431
\(897\) 9.58165 0.319922
\(898\) 71.7843 2.39547
\(899\) 3.86438 0.128884
\(900\) −91.0986 −3.03662
\(901\) −41.4498 −1.38089
\(902\) −66.2542 −2.20602
\(903\) −29.6541 −0.986827
\(904\) 10.3698 0.344896
\(905\) 12.5549 0.417340
\(906\) −22.7630 −0.756249
\(907\) 33.1419 1.10046 0.550229 0.835014i \(-0.314540\pi\)
0.550229 + 0.835014i \(0.314540\pi\)
\(908\) 82.8732 2.75025
\(909\) 10.0624 0.333750
\(910\) 15.9538 0.528862
\(911\) −50.2957 −1.66637 −0.833185 0.552994i \(-0.813485\pi\)
−0.833185 + 0.552994i \(0.813485\pi\)
\(912\) −184.339 −6.10407
\(913\) 28.1516 0.931683
\(914\) 79.2323 2.62077
\(915\) 52.4707 1.73463
\(916\) 99.8459 3.29900
\(917\) −18.7425 −0.618932
\(918\) 105.255 3.47394
\(919\) −17.9589 −0.592410 −0.296205 0.955124i \(-0.595721\pi\)
−0.296205 + 0.955124i \(0.595721\pi\)
\(920\) −51.4416 −1.69598
\(921\) 14.1967 0.467798
\(922\) −44.9672 −1.48092
\(923\) −0.925145 −0.0304515
\(924\) 172.198 5.66489
\(925\) 1.66492 0.0547423
\(926\) −10.6923 −0.351370
\(927\) −67.6152 −2.22078
\(928\) −187.577 −6.15750
\(929\) 5.28059 0.173251 0.0866253 0.996241i \(-0.472392\pi\)
0.0866253 + 0.996241i \(0.472392\pi\)
\(930\) −6.07648 −0.199255
\(931\) 51.8913 1.70067
\(932\) −55.2830 −1.81085
\(933\) −37.6313 −1.23199
\(934\) 54.5044 1.78344
\(935\) 20.6523 0.675402
\(936\) −48.3293 −1.57969
\(937\) −13.4700 −0.440045 −0.220023 0.975495i \(-0.570613\pi\)
−0.220023 + 0.975495i \(0.570613\pi\)
\(938\) −3.15987 −0.103173
\(939\) 38.4430 1.25454
\(940\) −53.9241 −1.75881
\(941\) −17.2245 −0.561502 −0.280751 0.959781i \(-0.590583\pi\)
−0.280751 + 0.959781i \(0.590583\pi\)
\(942\) −126.143 −4.10996
\(943\) 37.5116 1.22155
\(944\) 73.9192 2.40586
\(945\) 35.8314 1.16560
\(946\) 14.7754 0.480391
\(947\) −12.2776 −0.398968 −0.199484 0.979901i \(-0.563927\pi\)
−0.199484 + 0.979901i \(0.563927\pi\)
\(948\) 169.591 5.50806
\(949\) −4.33993 −0.140880
\(950\) 32.8435 1.06559
\(951\) 51.7008 1.67651
\(952\) −310.405 −10.0603
\(953\) 51.1836 1.65800 0.828999 0.559250i \(-0.188911\pi\)
0.828999 + 0.559250i \(0.188911\pi\)
\(954\) 88.5873 2.86812
\(955\) −5.61710 −0.181765
\(956\) 71.4167 2.30978
\(957\) 44.7865 1.44774
\(958\) 54.6218 1.76475
\(959\) −51.1488 −1.65168
\(960\) 161.200 5.20270
\(961\) −30.6777 −0.989603
\(962\) 1.35689 0.0437480
\(963\) 49.7045 1.60171
\(964\) −115.127 −3.70799
\(965\) 3.78826 0.121948
\(966\) −131.525 −4.23175
\(967\) −27.4749 −0.883534 −0.441767 0.897130i \(-0.645648\pi\)
−0.441767 + 0.897130i \(0.645648\pi\)
\(968\) 58.2173 1.87118
\(969\) −69.5426 −2.23403
\(970\) −45.2833 −1.45396
\(971\) 41.9208 1.34530 0.672651 0.739960i \(-0.265156\pi\)
0.672651 + 0.739960i \(0.265156\pi\)
\(972\) 78.7526 2.52599
\(973\) 5.94503 0.190589
\(974\) 23.7084 0.759665
\(975\) 8.27783 0.265103
\(976\) 236.758 7.57845
\(977\) −41.6747 −1.33329 −0.666646 0.745375i \(-0.732271\pi\)
−0.666646 + 0.745375i \(0.732271\pi\)
\(978\) −186.448 −5.96195
\(979\) 25.5689 0.817186
\(980\) −107.867 −3.44568
\(981\) 11.1658 0.356496
\(982\) −112.712 −3.59678
\(983\) −20.9423 −0.667955 −0.333977 0.942581i \(-0.608391\pi\)
−0.333977 + 0.942581i \(0.608391\pi\)
\(984\) −301.881 −9.62363
\(985\) 28.6549 0.913020
\(986\) −124.023 −3.94969
\(987\) −89.7479 −2.85671
\(988\) 19.8414 0.631240
\(989\) −8.36552 −0.266008
\(990\) −44.1385 −1.40281
\(991\) −30.0934 −0.955950 −0.477975 0.878374i \(-0.658629\pi\)
−0.477975 + 0.878374i \(0.658629\pi\)
\(992\) −15.6442 −0.496703
\(993\) 41.6963 1.32319
\(994\) 12.6992 0.402796
\(995\) −9.11714 −0.289033
\(996\) 197.051 6.24382
\(997\) −43.6776 −1.38328 −0.691642 0.722241i \(-0.743112\pi\)
−0.691642 + 0.722241i \(0.743112\pi\)
\(998\) −33.0925 −1.04752
\(999\) 3.04752 0.0964192
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 \(a_p\))