Properties

Label 4003.2.a.b.1.6
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.70039 q^{2} +3.13054 q^{3} +5.29213 q^{4} -0.910228 q^{5} -8.45368 q^{6} +0.335007 q^{7} -8.89004 q^{8} +6.80026 q^{9} +O(q^{10})\) \(q-2.70039 q^{2} +3.13054 q^{3} +5.29213 q^{4} -0.910228 q^{5} -8.45368 q^{6} +0.335007 q^{7} -8.89004 q^{8} +6.80026 q^{9} +2.45797 q^{10} -2.87116 q^{11} +16.5672 q^{12} +1.35841 q^{13} -0.904652 q^{14} -2.84950 q^{15} +13.4224 q^{16} -1.80293 q^{17} -18.3634 q^{18} +6.84396 q^{19} -4.81704 q^{20} +1.04875 q^{21} +7.75327 q^{22} -6.94339 q^{23} -27.8306 q^{24} -4.17148 q^{25} -3.66824 q^{26} +11.8969 q^{27} +1.77290 q^{28} -7.95760 q^{29} +7.69478 q^{30} +0.990375 q^{31} -18.4656 q^{32} -8.98828 q^{33} +4.86862 q^{34} -0.304933 q^{35} +35.9879 q^{36} -9.83248 q^{37} -18.4814 q^{38} +4.25255 q^{39} +8.09197 q^{40} -5.45758 q^{41} -2.83205 q^{42} -12.1971 q^{43} -15.1946 q^{44} -6.18979 q^{45} +18.7499 q^{46} -11.1117 q^{47} +42.0192 q^{48} -6.88777 q^{49} +11.2647 q^{50} -5.64414 q^{51} +7.18888 q^{52} -10.4892 q^{53} -32.1262 q^{54} +2.61341 q^{55} -2.97823 q^{56} +21.4253 q^{57} +21.4887 q^{58} +8.31097 q^{59} -15.0799 q^{60} +7.42467 q^{61} -2.67440 q^{62} +2.27814 q^{63} +23.0196 q^{64} -1.23646 q^{65} +24.2719 q^{66} +1.37216 q^{67} -9.54134 q^{68} -21.7365 q^{69} +0.823440 q^{70} +2.67864 q^{71} -60.4546 q^{72} -3.12188 q^{73} +26.5516 q^{74} -13.0590 q^{75} +36.2191 q^{76} -0.961861 q^{77} -11.4836 q^{78} -14.0008 q^{79} -12.2174 q^{80} +16.8428 q^{81} +14.7376 q^{82} +17.8567 q^{83} +5.55014 q^{84} +1.64108 q^{85} +32.9371 q^{86} -24.9116 q^{87} +25.5248 q^{88} +2.60497 q^{89} +16.7149 q^{90} +0.455077 q^{91} -36.7453 q^{92} +3.10041 q^{93} +30.0059 q^{94} -6.22957 q^{95} -57.8071 q^{96} +10.7020 q^{97} +18.5997 q^{98} -19.5247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70039 −1.90947 −0.954733 0.297463i \(-0.903860\pi\)
−0.954733 + 0.297463i \(0.903860\pi\)
\(3\) 3.13054 1.80742 0.903708 0.428149i \(-0.140834\pi\)
0.903708 + 0.428149i \(0.140834\pi\)
\(4\) 5.29213 2.64606
\(5\) −0.910228 −0.407066 −0.203533 0.979068i \(-0.565242\pi\)
−0.203533 + 0.979068i \(0.565242\pi\)
\(6\) −8.45368 −3.45120
\(7\) 0.335007 0.126621 0.0633104 0.997994i \(-0.479834\pi\)
0.0633104 + 0.997994i \(0.479834\pi\)
\(8\) −8.89004 −3.14310
\(9\) 6.80026 2.26675
\(10\) 2.45797 0.777280
\(11\) −2.87116 −0.865688 −0.432844 0.901469i \(-0.642490\pi\)
−0.432844 + 0.901469i \(0.642490\pi\)
\(12\) 16.5672 4.78254
\(13\) 1.35841 0.376755 0.188378 0.982097i \(-0.439677\pi\)
0.188378 + 0.982097i \(0.439677\pi\)
\(14\) −0.904652 −0.241778
\(15\) −2.84950 −0.735739
\(16\) 13.4224 3.35559
\(17\) −1.80293 −0.437275 −0.218637 0.975806i \(-0.570161\pi\)
−0.218637 + 0.975806i \(0.570161\pi\)
\(18\) −18.3634 −4.32829
\(19\) 6.84396 1.57011 0.785057 0.619424i \(-0.212634\pi\)
0.785057 + 0.619424i \(0.212634\pi\)
\(20\) −4.81704 −1.07712
\(21\) 1.04875 0.228857
\(22\) 7.75327 1.65300
\(23\) −6.94339 −1.44780 −0.723899 0.689906i \(-0.757652\pi\)
−0.723899 + 0.689906i \(0.757652\pi\)
\(24\) −27.8306 −5.68090
\(25\) −4.17148 −0.834297
\(26\) −3.66824 −0.719401
\(27\) 11.8969 2.28955
\(28\) 1.77290 0.335047
\(29\) −7.95760 −1.47769 −0.738845 0.673876i \(-0.764628\pi\)
−0.738845 + 0.673876i \(0.764628\pi\)
\(30\) 7.69478 1.40487
\(31\) 0.990375 0.177877 0.0889383 0.996037i \(-0.471653\pi\)
0.0889383 + 0.996037i \(0.471653\pi\)
\(32\) −18.4656 −3.26428
\(33\) −8.98828 −1.56466
\(34\) 4.86862 0.834962
\(35\) −0.304933 −0.0515431
\(36\) 35.9879 5.99798
\(37\) −9.83248 −1.61645 −0.808225 0.588874i \(-0.799571\pi\)
−0.808225 + 0.588874i \(0.799571\pi\)
\(38\) −18.4814 −2.99808
\(39\) 4.25255 0.680954
\(40\) 8.09197 1.27945
\(41\) −5.45758 −0.852331 −0.426165 0.904645i \(-0.640136\pi\)
−0.426165 + 0.904645i \(0.640136\pi\)
\(42\) −2.83205 −0.436994
\(43\) −12.1971 −1.86005 −0.930023 0.367501i \(-0.880213\pi\)
−0.930023 + 0.367501i \(0.880213\pi\)
\(44\) −15.1946 −2.29067
\(45\) −6.18979 −0.922720
\(46\) 18.7499 2.76452
\(47\) −11.1117 −1.62081 −0.810403 0.585873i \(-0.800752\pi\)
−0.810403 + 0.585873i \(0.800752\pi\)
\(48\) 42.0192 6.06495
\(49\) −6.88777 −0.983967
\(50\) 11.2647 1.59306
\(51\) −5.64414 −0.790338
\(52\) 7.18888 0.996918
\(53\) −10.4892 −1.44080 −0.720402 0.693557i \(-0.756043\pi\)
−0.720402 + 0.693557i \(0.756043\pi\)
\(54\) −32.1262 −4.37183
\(55\) 2.61341 0.352393
\(56\) −2.97823 −0.397983
\(57\) 21.4253 2.83785
\(58\) 21.4887 2.82160
\(59\) 8.31097 1.08200 0.540998 0.841024i \(-0.318047\pi\)
0.540998 + 0.841024i \(0.318047\pi\)
\(60\) −15.0799 −1.94681
\(61\) 7.42467 0.950632 0.475316 0.879815i \(-0.342334\pi\)
0.475316 + 0.879815i \(0.342334\pi\)
\(62\) −2.67440 −0.339649
\(63\) 2.27814 0.287018
\(64\) 23.0196 2.87745
\(65\) −1.23646 −0.153364
\(66\) 24.2719 2.98766
\(67\) 1.37216 0.167636 0.0838182 0.996481i \(-0.473288\pi\)
0.0838182 + 0.996481i \(0.473288\pi\)
\(68\) −9.54134 −1.15706
\(69\) −21.7365 −2.61677
\(70\) 0.823440 0.0984199
\(71\) 2.67864 0.317897 0.158948 0.987287i \(-0.449190\pi\)
0.158948 + 0.987287i \(0.449190\pi\)
\(72\) −60.4546 −7.12464
\(73\) −3.12188 −0.365388 −0.182694 0.983170i \(-0.558482\pi\)
−0.182694 + 0.983170i \(0.558482\pi\)
\(74\) 26.5516 3.08656
\(75\) −13.0590 −1.50792
\(76\) 36.2191 4.15462
\(77\) −0.961861 −0.109614
\(78\) −11.4836 −1.30026
\(79\) −14.0008 −1.57522 −0.787609 0.616175i \(-0.788681\pi\)
−0.787609 + 0.616175i \(0.788681\pi\)
\(80\) −12.2174 −1.36595
\(81\) 16.8428 1.87142
\(82\) 14.7376 1.62750
\(83\) 17.8567 1.96003 0.980016 0.198917i \(-0.0637423\pi\)
0.980016 + 0.198917i \(0.0637423\pi\)
\(84\) 5.55014 0.605569
\(85\) 1.64108 0.178000
\(86\) 32.9371 3.55170
\(87\) −24.9116 −2.67080
\(88\) 25.5248 2.72095
\(89\) 2.60497 0.276127 0.138063 0.990423i \(-0.455912\pi\)
0.138063 + 0.990423i \(0.455912\pi\)
\(90\) 16.7149 1.76190
\(91\) 0.455077 0.0477051
\(92\) −36.7453 −3.83096
\(93\) 3.10041 0.321497
\(94\) 30.0059 3.09488
\(95\) −6.22957 −0.639140
\(96\) −57.8071 −5.89992
\(97\) 10.7020 1.08662 0.543310 0.839532i \(-0.317171\pi\)
0.543310 + 0.839532i \(0.317171\pi\)
\(98\) 18.5997 1.87885
\(99\) −19.5247 −1.96230
\(100\) −22.0760 −2.20760
\(101\) 17.7598 1.76717 0.883584 0.468274i \(-0.155124\pi\)
0.883584 + 0.468274i \(0.155124\pi\)
\(102\) 15.2414 1.50912
\(103\) −16.6991 −1.64541 −0.822705 0.568468i \(-0.807536\pi\)
−0.822705 + 0.568468i \(0.807536\pi\)
\(104\) −12.0763 −1.18418
\(105\) −0.954605 −0.0931599
\(106\) 28.3250 2.75117
\(107\) 3.37830 0.326593 0.163296 0.986577i \(-0.447787\pi\)
0.163296 + 0.986577i \(0.447787\pi\)
\(108\) 62.9597 6.05830
\(109\) 18.3509 1.75770 0.878851 0.477097i \(-0.158311\pi\)
0.878851 + 0.477097i \(0.158311\pi\)
\(110\) −7.05725 −0.672882
\(111\) −30.7809 −2.92160
\(112\) 4.49659 0.424888
\(113\) 4.33945 0.408221 0.204110 0.978948i \(-0.434570\pi\)
0.204110 + 0.978948i \(0.434570\pi\)
\(114\) −57.8567 −5.41878
\(115\) 6.32007 0.589350
\(116\) −42.1126 −3.91006
\(117\) 9.23755 0.854011
\(118\) −22.4429 −2.06604
\(119\) −0.603995 −0.0553681
\(120\) 25.3322 2.31250
\(121\) −2.75642 −0.250584
\(122\) −20.0495 −1.81520
\(123\) −17.0852 −1.54052
\(124\) 5.24119 0.470673
\(125\) 8.34814 0.746681
\(126\) −6.15187 −0.548052
\(127\) −0.610893 −0.0542080 −0.0271040 0.999633i \(-0.508629\pi\)
−0.0271040 + 0.999633i \(0.508629\pi\)
\(128\) −25.2308 −2.23011
\(129\) −38.1836 −3.36188
\(130\) 3.33894 0.292844
\(131\) 1.12138 0.0979759 0.0489879 0.998799i \(-0.484400\pi\)
0.0489879 + 0.998799i \(0.484400\pi\)
\(132\) −47.5671 −4.14019
\(133\) 2.29278 0.198809
\(134\) −3.70538 −0.320096
\(135\) −10.8289 −0.932000
\(136\) 16.0281 1.37440
\(137\) −5.91022 −0.504944 −0.252472 0.967604i \(-0.581244\pi\)
−0.252472 + 0.967604i \(0.581244\pi\)
\(138\) 58.6972 4.99664
\(139\) −7.92180 −0.671918 −0.335959 0.941877i \(-0.609060\pi\)
−0.335959 + 0.941877i \(0.609060\pi\)
\(140\) −1.61375 −0.136386
\(141\) −34.7855 −2.92947
\(142\) −7.23339 −0.607013
\(143\) −3.90022 −0.326152
\(144\) 91.2756 7.60630
\(145\) 7.24323 0.601518
\(146\) 8.43030 0.697697
\(147\) −21.5624 −1.77844
\(148\) −52.0347 −4.27723
\(149\) 14.3922 1.17906 0.589529 0.807748i \(-0.299314\pi\)
0.589529 + 0.807748i \(0.299314\pi\)
\(150\) 35.2644 2.87933
\(151\) −3.75370 −0.305472 −0.152736 0.988267i \(-0.548808\pi\)
−0.152736 + 0.988267i \(0.548808\pi\)
\(152\) −60.8431 −4.93503
\(153\) −12.2604 −0.991195
\(154\) 2.59740 0.209305
\(155\) −0.901467 −0.0724076
\(156\) 22.5051 1.80185
\(157\) 3.81315 0.304322 0.152161 0.988356i \(-0.451377\pi\)
0.152161 + 0.988356i \(0.451377\pi\)
\(158\) 37.8078 3.00783
\(159\) −32.8369 −2.60413
\(160\) 16.8079 1.32878
\(161\) −2.32609 −0.183321
\(162\) −45.4822 −3.57342
\(163\) 9.08991 0.711977 0.355988 0.934490i \(-0.384144\pi\)
0.355988 + 0.934490i \(0.384144\pi\)
\(164\) −28.8822 −2.25532
\(165\) 8.18139 0.636920
\(166\) −48.2203 −3.74262
\(167\) −23.6192 −1.82771 −0.913853 0.406045i \(-0.866908\pi\)
−0.913853 + 0.406045i \(0.866908\pi\)
\(168\) −9.32346 −0.719320
\(169\) −11.1547 −0.858056
\(170\) −4.43156 −0.339885
\(171\) 46.5408 3.55906
\(172\) −64.5488 −4.92180
\(173\) 23.6533 1.79832 0.899162 0.437616i \(-0.144177\pi\)
0.899162 + 0.437616i \(0.144177\pi\)
\(174\) 67.2710 5.09980
\(175\) −1.39748 −0.105639
\(176\) −38.5378 −2.90489
\(177\) 26.0178 1.95562
\(178\) −7.03445 −0.527254
\(179\) −3.66446 −0.273895 −0.136947 0.990578i \(-0.543729\pi\)
−0.136947 + 0.990578i \(0.543729\pi\)
\(180\) −32.7572 −2.44157
\(181\) −23.5154 −1.74789 −0.873944 0.486027i \(-0.838446\pi\)
−0.873944 + 0.486027i \(0.838446\pi\)
\(182\) −1.22889 −0.0910913
\(183\) 23.2432 1.71819
\(184\) 61.7270 4.55058
\(185\) 8.94980 0.658002
\(186\) −8.37232 −0.613888
\(187\) 5.17651 0.378544
\(188\) −58.8045 −4.28876
\(189\) 3.98554 0.289905
\(190\) 16.8223 1.22042
\(191\) 22.6385 1.63807 0.819034 0.573745i \(-0.194510\pi\)
0.819034 + 0.573745i \(0.194510\pi\)
\(192\) 72.0637 5.20075
\(193\) 5.06900 0.364875 0.182437 0.983217i \(-0.441601\pi\)
0.182437 + 0.983217i \(0.441601\pi\)
\(194\) −28.8995 −2.07486
\(195\) −3.87079 −0.277193
\(196\) −36.4510 −2.60364
\(197\) −23.1746 −1.65112 −0.825559 0.564316i \(-0.809140\pi\)
−0.825559 + 0.564316i \(0.809140\pi\)
\(198\) 52.7243 3.74695
\(199\) 4.50709 0.319499 0.159749 0.987158i \(-0.448931\pi\)
0.159749 + 0.987158i \(0.448931\pi\)
\(200\) 37.0847 2.62228
\(201\) 4.29561 0.302989
\(202\) −47.9585 −3.37435
\(203\) −2.66586 −0.187106
\(204\) −29.8695 −2.09128
\(205\) 4.96764 0.346955
\(206\) 45.0941 3.14186
\(207\) −47.2169 −3.28180
\(208\) 18.2331 1.26424
\(209\) −19.6501 −1.35923
\(210\) 2.57781 0.177886
\(211\) 4.34279 0.298970 0.149485 0.988764i \(-0.452238\pi\)
0.149485 + 0.988764i \(0.452238\pi\)
\(212\) −55.5103 −3.81246
\(213\) 8.38559 0.574571
\(214\) −9.12274 −0.623618
\(215\) 11.1022 0.757162
\(216\) −105.764 −7.19630
\(217\) 0.331783 0.0225229
\(218\) −49.5548 −3.35627
\(219\) −9.77316 −0.660409
\(220\) 13.8305 0.932453
\(221\) −2.44912 −0.164746
\(222\) 83.1207 5.57869
\(223\) −2.56579 −0.171818 −0.0859090 0.996303i \(-0.527379\pi\)
−0.0859090 + 0.996303i \(0.527379\pi\)
\(224\) −6.18610 −0.413326
\(225\) −28.3672 −1.89115
\(226\) −11.7182 −0.779484
\(227\) 8.46916 0.562118 0.281059 0.959691i \(-0.409314\pi\)
0.281059 + 0.959691i \(0.409314\pi\)
\(228\) 113.385 7.50913
\(229\) 4.27224 0.282317 0.141159 0.989987i \(-0.454917\pi\)
0.141159 + 0.989987i \(0.454917\pi\)
\(230\) −17.0667 −1.12534
\(231\) −3.01114 −0.198119
\(232\) 70.7434 4.64453
\(233\) −30.2017 −1.97858 −0.989290 0.145965i \(-0.953371\pi\)
−0.989290 + 0.145965i \(0.953371\pi\)
\(234\) −24.9450 −1.63071
\(235\) 10.1142 0.659776
\(236\) 43.9827 2.86303
\(237\) −43.8302 −2.84707
\(238\) 1.63102 0.105724
\(239\) 12.7096 0.822115 0.411057 0.911609i \(-0.365160\pi\)
0.411057 + 0.911609i \(0.365160\pi\)
\(240\) −38.2470 −2.46884
\(241\) 9.18172 0.591447 0.295723 0.955274i \(-0.404439\pi\)
0.295723 + 0.955274i \(0.404439\pi\)
\(242\) 7.44343 0.478482
\(243\) 17.0364 1.09288
\(244\) 39.2923 2.51543
\(245\) 6.26944 0.400540
\(246\) 46.1367 2.94157
\(247\) 9.29691 0.591548
\(248\) −8.80447 −0.559085
\(249\) 55.9012 3.54260
\(250\) −22.5433 −1.42576
\(251\) 12.7925 0.807456 0.403728 0.914879i \(-0.367714\pi\)
0.403728 + 0.914879i \(0.367714\pi\)
\(252\) 12.0562 0.759469
\(253\) 19.9356 1.25334
\(254\) 1.64965 0.103508
\(255\) 5.13746 0.321720
\(256\) 22.0940 1.38088
\(257\) 10.8812 0.678749 0.339375 0.940651i \(-0.389785\pi\)
0.339375 + 0.940651i \(0.389785\pi\)
\(258\) 103.111 6.41939
\(259\) −3.29395 −0.204676
\(260\) −6.54352 −0.405812
\(261\) −54.1138 −3.34956
\(262\) −3.02818 −0.187082
\(263\) 12.9874 0.800837 0.400419 0.916332i \(-0.368865\pi\)
0.400419 + 0.916332i \(0.368865\pi\)
\(264\) 79.9062 4.91789
\(265\) 9.54758 0.586503
\(266\) −6.19141 −0.379619
\(267\) 8.15496 0.499076
\(268\) 7.26166 0.443577
\(269\) −14.5566 −0.887534 −0.443767 0.896142i \(-0.646358\pi\)
−0.443767 + 0.896142i \(0.646358\pi\)
\(270\) 29.2422 1.77962
\(271\) −9.36239 −0.568725 −0.284362 0.958717i \(-0.591782\pi\)
−0.284362 + 0.958717i \(0.591782\pi\)
\(272\) −24.1996 −1.46731
\(273\) 1.42464 0.0862229
\(274\) 15.9599 0.964174
\(275\) 11.9770 0.722241
\(276\) −115.033 −6.92415
\(277\) 9.79051 0.588254 0.294127 0.955766i \(-0.404971\pi\)
0.294127 + 0.955766i \(0.404971\pi\)
\(278\) 21.3920 1.28301
\(279\) 6.73481 0.403203
\(280\) 2.71087 0.162005
\(281\) 19.6930 1.17478 0.587392 0.809303i \(-0.300155\pi\)
0.587392 + 0.809303i \(0.300155\pi\)
\(282\) 93.9347 5.59373
\(283\) 14.1195 0.839317 0.419658 0.907682i \(-0.362150\pi\)
0.419658 + 0.907682i \(0.362150\pi\)
\(284\) 14.1757 0.841174
\(285\) −19.5019 −1.15519
\(286\) 10.5321 0.622777
\(287\) −1.82833 −0.107923
\(288\) −125.571 −7.39933
\(289\) −13.7494 −0.808791
\(290\) −19.5596 −1.14858
\(291\) 33.5029 1.96397
\(292\) −16.5214 −0.966841
\(293\) 23.7634 1.38827 0.694137 0.719843i \(-0.255786\pi\)
0.694137 + 0.719843i \(0.255786\pi\)
\(294\) 58.2270 3.39587
\(295\) −7.56488 −0.440444
\(296\) 87.4111 5.08067
\(297\) −34.1578 −1.98204
\(298\) −38.8647 −2.25137
\(299\) −9.43197 −0.545465
\(300\) −69.1098 −3.99006
\(301\) −4.08613 −0.235521
\(302\) 10.1365 0.583288
\(303\) 55.5977 3.19401
\(304\) 91.8621 5.26865
\(305\) −6.75815 −0.386970
\(306\) 33.1079 1.89265
\(307\) 4.23632 0.241780 0.120890 0.992666i \(-0.461425\pi\)
0.120890 + 0.992666i \(0.461425\pi\)
\(308\) −5.09029 −0.290046
\(309\) −52.2771 −2.97394
\(310\) 2.43432 0.138260
\(311\) −20.6468 −1.17077 −0.585386 0.810755i \(-0.699057\pi\)
−0.585386 + 0.810755i \(0.699057\pi\)
\(312\) −37.8054 −2.14031
\(313\) 11.5386 0.652202 0.326101 0.945335i \(-0.394265\pi\)
0.326101 + 0.945335i \(0.394265\pi\)
\(314\) −10.2970 −0.581093
\(315\) −2.07363 −0.116836
\(316\) −74.0942 −4.16813
\(317\) 12.4923 0.701637 0.350819 0.936443i \(-0.385903\pi\)
0.350819 + 0.936443i \(0.385903\pi\)
\(318\) 88.6725 4.97251
\(319\) 22.8476 1.27922
\(320\) −20.9531 −1.17131
\(321\) 10.5759 0.590289
\(322\) 6.28135 0.350046
\(323\) −12.3392 −0.686571
\(324\) 89.1342 4.95190
\(325\) −5.66659 −0.314326
\(326\) −24.5463 −1.35950
\(327\) 57.4483 3.17690
\(328\) 48.5181 2.67896
\(329\) −3.72250 −0.205228
\(330\) −22.0930 −1.21618
\(331\) −19.8172 −1.08925 −0.544626 0.838679i \(-0.683328\pi\)
−0.544626 + 0.838679i \(0.683328\pi\)
\(332\) 94.5002 5.18637
\(333\) −66.8634 −3.66409
\(334\) 63.7811 3.48994
\(335\) −1.24898 −0.0682392
\(336\) 14.0767 0.767949
\(337\) −9.54812 −0.520119 −0.260060 0.965593i \(-0.583742\pi\)
−0.260060 + 0.965593i \(0.583742\pi\)
\(338\) 30.1221 1.63843
\(339\) 13.5848 0.737825
\(340\) 8.68479 0.470999
\(341\) −2.84353 −0.153986
\(342\) −125.678 −6.79591
\(343\) −4.65251 −0.251212
\(344\) 108.433 5.84632
\(345\) 19.7852 1.06520
\(346\) −63.8731 −3.43384
\(347\) −7.57674 −0.406741 −0.203370 0.979102i \(-0.565190\pi\)
−0.203370 + 0.979102i \(0.565190\pi\)
\(348\) −131.835 −7.06711
\(349\) −18.8040 −1.00656 −0.503278 0.864125i \(-0.667873\pi\)
−0.503278 + 0.864125i \(0.667873\pi\)
\(350\) 3.77374 0.201715
\(351\) 16.1608 0.862601
\(352\) 53.0177 2.82585
\(353\) 6.75816 0.359701 0.179850 0.983694i \(-0.442439\pi\)
0.179850 + 0.983694i \(0.442439\pi\)
\(354\) −70.2583 −3.73419
\(355\) −2.43818 −0.129405
\(356\) 13.7858 0.730648
\(357\) −1.89083 −0.100073
\(358\) 9.89549 0.522993
\(359\) −35.6097 −1.87941 −0.939705 0.341987i \(-0.888900\pi\)
−0.939705 + 0.341987i \(0.888900\pi\)
\(360\) 55.0275 2.90020
\(361\) 27.8398 1.46526
\(362\) 63.5009 3.33753
\(363\) −8.62909 −0.452910
\(364\) 2.40833 0.126231
\(365\) 2.84162 0.148737
\(366\) −62.7658 −3.28082
\(367\) −13.5997 −0.709896 −0.354948 0.934886i \(-0.615501\pi\)
−0.354948 + 0.934886i \(0.615501\pi\)
\(368\) −93.1967 −4.85821
\(369\) −37.1130 −1.93202
\(370\) −24.1680 −1.25643
\(371\) −3.51396 −0.182436
\(372\) 16.4077 0.850702
\(373\) 7.69833 0.398604 0.199302 0.979938i \(-0.436132\pi\)
0.199302 + 0.979938i \(0.436132\pi\)
\(374\) −13.9786 −0.722817
\(375\) 26.1342 1.34956
\(376\) 98.7833 5.09436
\(377\) −10.8097 −0.556727
\(378\) −10.7625 −0.553564
\(379\) −1.36932 −0.0703374 −0.0351687 0.999381i \(-0.511197\pi\)
−0.0351687 + 0.999381i \(0.511197\pi\)
\(380\) −32.9677 −1.69121
\(381\) −1.91242 −0.0979764
\(382\) −61.1330 −3.12784
\(383\) −25.2003 −1.28767 −0.643837 0.765162i \(-0.722659\pi\)
−0.643837 + 0.765162i \(0.722659\pi\)
\(384\) −78.9861 −4.03074
\(385\) 0.875513 0.0446203
\(386\) −13.6883 −0.696716
\(387\) −82.9437 −4.21627
\(388\) 56.6362 2.87527
\(389\) −15.1749 −0.769399 −0.384700 0.923042i \(-0.625695\pi\)
−0.384700 + 0.923042i \(0.625695\pi\)
\(390\) 10.4527 0.529291
\(391\) 12.5185 0.633085
\(392\) 61.2326 3.09271
\(393\) 3.51054 0.177083
\(394\) 62.5804 3.15276
\(395\) 12.7440 0.641218
\(396\) −103.327 −5.19238
\(397\) 3.34796 0.168029 0.0840147 0.996465i \(-0.473226\pi\)
0.0840147 + 0.996465i \(0.473226\pi\)
\(398\) −12.1709 −0.610073
\(399\) 7.17763 0.359331
\(400\) −55.9911 −2.79956
\(401\) −28.3491 −1.41569 −0.707844 0.706368i \(-0.750332\pi\)
−0.707844 + 0.706368i \(0.750332\pi\)
\(402\) −11.5998 −0.578547
\(403\) 1.34534 0.0670159
\(404\) 93.9872 4.67604
\(405\) −15.3308 −0.761793
\(406\) 7.19886 0.357273
\(407\) 28.2307 1.39934
\(408\) 50.1766 2.48411
\(409\) −2.86642 −0.141735 −0.0708677 0.997486i \(-0.522577\pi\)
−0.0708677 + 0.997486i \(0.522577\pi\)
\(410\) −13.4146 −0.662500
\(411\) −18.5022 −0.912644
\(412\) −88.3737 −4.35386
\(413\) 2.78424 0.137003
\(414\) 127.504 6.26649
\(415\) −16.2537 −0.797864
\(416\) −25.0838 −1.22984
\(417\) −24.7995 −1.21444
\(418\) 53.0631 2.59540
\(419\) −10.1437 −0.495554 −0.247777 0.968817i \(-0.579700\pi\)
−0.247777 + 0.968817i \(0.579700\pi\)
\(420\) −5.05189 −0.246507
\(421\) 2.11469 0.103064 0.0515320 0.998671i \(-0.483590\pi\)
0.0515320 + 0.998671i \(0.483590\pi\)
\(422\) −11.7272 −0.570873
\(423\) −75.5624 −3.67397
\(424\) 93.2495 4.52860
\(425\) 7.52090 0.364817
\(426\) −22.6444 −1.09713
\(427\) 2.48732 0.120370
\(428\) 17.8784 0.864185
\(429\) −12.2098 −0.589493
\(430\) −29.9803 −1.44578
\(431\) −18.2324 −0.878225 −0.439112 0.898432i \(-0.644707\pi\)
−0.439112 + 0.898432i \(0.644707\pi\)
\(432\) 159.684 7.68280
\(433\) −0.816044 −0.0392166 −0.0196083 0.999808i \(-0.506242\pi\)
−0.0196083 + 0.999808i \(0.506242\pi\)
\(434\) −0.895945 −0.0430067
\(435\) 22.6752 1.08719
\(436\) 97.1155 4.65099
\(437\) −47.5203 −2.27321
\(438\) 26.3914 1.26103
\(439\) 23.2143 1.10796 0.553979 0.832530i \(-0.313109\pi\)
0.553979 + 0.832530i \(0.313109\pi\)
\(440\) −23.2334 −1.10761
\(441\) −46.8386 −2.23041
\(442\) 6.61359 0.314576
\(443\) −0.339021 −0.0161074 −0.00805368 0.999968i \(-0.502564\pi\)
−0.00805368 + 0.999968i \(0.502564\pi\)
\(444\) −162.897 −7.73073
\(445\) −2.37112 −0.112402
\(446\) 6.92864 0.328081
\(447\) 45.0554 2.13105
\(448\) 7.71173 0.364345
\(449\) 11.8952 0.561367 0.280684 0.959800i \(-0.409439\pi\)
0.280684 + 0.959800i \(0.409439\pi\)
\(450\) 76.6026 3.61108
\(451\) 15.6696 0.737853
\(452\) 22.9649 1.08018
\(453\) −11.7511 −0.552114
\(454\) −22.8701 −1.07334
\(455\) −0.414224 −0.0194191
\(456\) −190.472 −8.91965
\(457\) −23.6878 −1.10807 −0.554034 0.832494i \(-0.686912\pi\)
−0.554034 + 0.832494i \(0.686912\pi\)
\(458\) −11.5367 −0.539076
\(459\) −21.4492 −1.00116
\(460\) 33.4466 1.55946
\(461\) −33.7049 −1.56980 −0.784898 0.619626i \(-0.787284\pi\)
−0.784898 + 0.619626i \(0.787284\pi\)
\(462\) 8.13127 0.378301
\(463\) −15.6462 −0.727141 −0.363570 0.931567i \(-0.618442\pi\)
−0.363570 + 0.931567i \(0.618442\pi\)
\(464\) −106.810 −4.95852
\(465\) −2.82208 −0.130871
\(466\) 81.5565 3.77803
\(467\) −7.48433 −0.346334 −0.173167 0.984893i \(-0.555400\pi\)
−0.173167 + 0.984893i \(0.555400\pi\)
\(468\) 48.8863 2.25977
\(469\) 0.459685 0.0212263
\(470\) −27.3122 −1.25982
\(471\) 11.9372 0.550037
\(472\) −73.8849 −3.40083
\(473\) 35.0200 1.61022
\(474\) 118.359 5.43640
\(475\) −28.5495 −1.30994
\(476\) −3.19642 −0.146508
\(477\) −71.3294 −3.26595
\(478\) −34.3209 −1.56980
\(479\) −11.1305 −0.508567 −0.254284 0.967130i \(-0.581840\pi\)
−0.254284 + 0.967130i \(0.581840\pi\)
\(480\) 52.6177 2.40166
\(481\) −13.3565 −0.609006
\(482\) −24.7943 −1.12935
\(483\) −7.28190 −0.331338
\(484\) −14.5873 −0.663061
\(485\) −9.74123 −0.442326
\(486\) −46.0049 −2.08683
\(487\) −36.4684 −1.65254 −0.826271 0.563273i \(-0.809542\pi\)
−0.826271 + 0.563273i \(0.809542\pi\)
\(488\) −66.0056 −2.98793
\(489\) 28.4563 1.28684
\(490\) −16.9300 −0.764818
\(491\) 24.3289 1.09795 0.548974 0.835840i \(-0.315019\pi\)
0.548974 + 0.835840i \(0.315019\pi\)
\(492\) −90.4168 −4.07631
\(493\) 14.3470 0.646156
\(494\) −25.1053 −1.12954
\(495\) 17.7719 0.798787
\(496\) 13.2932 0.596881
\(497\) 0.897365 0.0402523
\(498\) −150.955 −6.76447
\(499\) 32.9844 1.47659 0.738293 0.674480i \(-0.235632\pi\)
0.738293 + 0.674480i \(0.235632\pi\)
\(500\) 44.1794 1.97576
\(501\) −73.9407 −3.30343
\(502\) −34.5448 −1.54181
\(503\) 14.0983 0.628610 0.314305 0.949322i \(-0.398229\pi\)
0.314305 + 0.949322i \(0.398229\pi\)
\(504\) −20.2527 −0.902129
\(505\) −16.1655 −0.719354
\(506\) −53.8340 −2.39321
\(507\) −34.9203 −1.55086
\(508\) −3.23292 −0.143438
\(509\) 25.1707 1.11567 0.557836 0.829951i \(-0.311632\pi\)
0.557836 + 0.829951i \(0.311632\pi\)
\(510\) −13.8732 −0.614314
\(511\) −1.04585 −0.0462658
\(512\) −9.20085 −0.406624
\(513\) 81.4217 3.59486
\(514\) −29.3835 −1.29605
\(515\) 15.2000 0.669791
\(516\) −202.072 −8.89574
\(517\) 31.9035 1.40311
\(518\) 8.89497 0.390823
\(519\) 74.0474 3.25032
\(520\) 10.9922 0.482040
\(521\) 8.71454 0.381791 0.190895 0.981610i \(-0.438861\pi\)
0.190895 + 0.981610i \(0.438861\pi\)
\(522\) 146.129 6.39587
\(523\) 8.00491 0.350030 0.175015 0.984566i \(-0.444003\pi\)
0.175015 + 0.984566i \(0.444003\pi\)
\(524\) 5.93451 0.259250
\(525\) −4.37486 −0.190934
\(526\) −35.0711 −1.52917
\(527\) −1.78558 −0.0777810
\(528\) −120.644 −5.25035
\(529\) 25.2107 1.09612
\(530\) −25.7822 −1.11991
\(531\) 56.5168 2.45262
\(532\) 12.1337 0.526062
\(533\) −7.41363 −0.321120
\(534\) −22.0216 −0.952968
\(535\) −3.07502 −0.132945
\(536\) −12.1986 −0.526899
\(537\) −11.4717 −0.495042
\(538\) 39.3086 1.69472
\(539\) 19.7759 0.851809
\(540\) −57.3077 −2.46613
\(541\) 21.6603 0.931251 0.465625 0.884982i \(-0.345829\pi\)
0.465625 + 0.884982i \(0.345829\pi\)
\(542\) 25.2821 1.08596
\(543\) −73.6159 −3.15916
\(544\) 33.2921 1.42739
\(545\) −16.7035 −0.715501
\(546\) −3.84708 −0.164640
\(547\) 8.63899 0.369377 0.184688 0.982797i \(-0.440872\pi\)
0.184688 + 0.982797i \(0.440872\pi\)
\(548\) −31.2776 −1.33611
\(549\) 50.4897 2.15485
\(550\) −32.3426 −1.37910
\(551\) −54.4615 −2.32014
\(552\) 193.239 8.22479
\(553\) −4.69039 −0.199456
\(554\) −26.4382 −1.12325
\(555\) 28.0177 1.18928
\(556\) −41.9232 −1.77794
\(557\) 25.3346 1.07346 0.536731 0.843753i \(-0.319659\pi\)
0.536731 + 0.843753i \(0.319659\pi\)
\(558\) −18.1866 −0.769902
\(559\) −16.5687 −0.700782
\(560\) −4.09292 −0.172958
\(561\) 16.2052 0.684186
\(562\) −53.1788 −2.24321
\(563\) −28.0295 −1.18130 −0.590652 0.806927i \(-0.701129\pi\)
−0.590652 + 0.806927i \(0.701129\pi\)
\(564\) −184.090 −7.75157
\(565\) −3.94989 −0.166173
\(566\) −38.1282 −1.60265
\(567\) 5.64246 0.236961
\(568\) −23.8132 −0.999182
\(569\) −2.93774 −0.123156 −0.0615782 0.998102i \(-0.519613\pi\)
−0.0615782 + 0.998102i \(0.519613\pi\)
\(570\) 52.6628 2.20580
\(571\) 30.7347 1.28621 0.643104 0.765779i \(-0.277646\pi\)
0.643104 + 0.765779i \(0.277646\pi\)
\(572\) −20.6404 −0.863020
\(573\) 70.8708 2.96067
\(574\) 4.93721 0.206075
\(575\) 28.9642 1.20789
\(576\) 156.539 6.52247
\(577\) −12.7311 −0.530001 −0.265001 0.964248i \(-0.585372\pi\)
−0.265001 + 0.964248i \(0.585372\pi\)
\(578\) 37.1289 1.54436
\(579\) 15.8687 0.659481
\(580\) 38.3321 1.59165
\(581\) 5.98214 0.248181
\(582\) −90.4710 −3.75014
\(583\) 30.1162 1.24729
\(584\) 27.7536 1.14845
\(585\) −8.40828 −0.347639
\(586\) −64.1706 −2.65086
\(587\) 18.0016 0.743007 0.371503 0.928432i \(-0.378842\pi\)
0.371503 + 0.928432i \(0.378842\pi\)
\(588\) −114.111 −4.70586
\(589\) 6.77809 0.279286
\(590\) 20.4282 0.841014
\(591\) −72.5488 −2.98426
\(592\) −131.975 −5.42414
\(593\) 32.6429 1.34048 0.670242 0.742142i \(-0.266190\pi\)
0.670242 + 0.742142i \(0.266190\pi\)
\(594\) 92.2396 3.78464
\(595\) 0.549773 0.0225385
\(596\) 76.1655 3.11986
\(597\) 14.1096 0.577468
\(598\) 25.4700 1.04155
\(599\) −5.01090 −0.204740 −0.102370 0.994746i \(-0.532643\pi\)
−0.102370 + 0.994746i \(0.532643\pi\)
\(600\) 116.095 4.73956
\(601\) 14.7232 0.600573 0.300286 0.953849i \(-0.402918\pi\)
0.300286 + 0.953849i \(0.402918\pi\)
\(602\) 11.0342 0.449719
\(603\) 9.33107 0.379991
\(604\) −19.8650 −0.808297
\(605\) 2.50897 0.102004
\(606\) −150.136 −6.09885
\(607\) 4.37686 0.177651 0.0888257 0.996047i \(-0.471689\pi\)
0.0888257 + 0.996047i \(0.471689\pi\)
\(608\) −126.378 −5.12529
\(609\) −8.34556 −0.338179
\(610\) 18.2497 0.738907
\(611\) −15.0942 −0.610647
\(612\) −64.8836 −2.62276
\(613\) −30.8178 −1.24472 −0.622360 0.782731i \(-0.713826\pi\)
−0.622360 + 0.782731i \(0.713826\pi\)
\(614\) −11.4397 −0.461670
\(615\) 15.5514 0.627093
\(616\) 8.55098 0.344529
\(617\) −25.4753 −1.02560 −0.512799 0.858509i \(-0.671391\pi\)
−0.512799 + 0.858509i \(0.671391\pi\)
\(618\) 141.169 5.67864
\(619\) 1.08134 0.0434629 0.0217315 0.999764i \(-0.493082\pi\)
0.0217315 + 0.999764i \(0.493082\pi\)
\(620\) −4.77068 −0.191595
\(621\) −82.6046 −3.31481
\(622\) 55.7545 2.23555
\(623\) 0.872685 0.0349634
\(624\) 57.0793 2.28500
\(625\) 13.2587 0.530348
\(626\) −31.1589 −1.24536
\(627\) −61.5155 −2.45669
\(628\) 20.1797 0.805256
\(629\) 17.7273 0.706833
\(630\) 5.59961 0.223094
\(631\) −24.3293 −0.968534 −0.484267 0.874920i \(-0.660914\pi\)
−0.484267 + 0.874920i \(0.660914\pi\)
\(632\) 124.468 4.95107
\(633\) 13.5953 0.540363
\(634\) −33.7341 −1.33975
\(635\) 0.556052 0.0220663
\(636\) −173.777 −6.89070
\(637\) −9.35642 −0.370715
\(638\) −61.6974 −2.44262
\(639\) 18.2155 0.720593
\(640\) 22.9658 0.907804
\(641\) −21.8901 −0.864608 −0.432304 0.901728i \(-0.642299\pi\)
−0.432304 + 0.901728i \(0.642299\pi\)
\(642\) −28.5591 −1.12714
\(643\) −18.8332 −0.742708 −0.371354 0.928491i \(-0.621106\pi\)
−0.371354 + 0.928491i \(0.621106\pi\)
\(644\) −12.3100 −0.485080
\(645\) 34.7558 1.36851
\(646\) 33.3207 1.31098
\(647\) 7.15482 0.281285 0.140643 0.990060i \(-0.455083\pi\)
0.140643 + 0.990060i \(0.455083\pi\)
\(648\) −149.733 −5.88207
\(649\) −23.8622 −0.936672
\(650\) 15.3020 0.600194
\(651\) 1.03866 0.0407083
\(652\) 48.1050 1.88394
\(653\) 36.9824 1.44723 0.723617 0.690202i \(-0.242478\pi\)
0.723617 + 0.690202i \(0.242478\pi\)
\(654\) −155.133 −6.06618
\(655\) −1.02072 −0.0398827
\(656\) −73.2536 −2.86007
\(657\) −21.2296 −0.828245
\(658\) 10.0522 0.391876
\(659\) −15.9092 −0.619734 −0.309867 0.950780i \(-0.600285\pi\)
−0.309867 + 0.950780i \(0.600285\pi\)
\(660\) 43.2969 1.68533
\(661\) 31.2122 1.21401 0.607007 0.794696i \(-0.292370\pi\)
0.607007 + 0.794696i \(0.292370\pi\)
\(662\) 53.5143 2.07989
\(663\) −7.66706 −0.297764
\(664\) −158.747 −6.16059
\(665\) −2.08695 −0.0809285
\(666\) 180.558 6.99647
\(667\) 55.2527 2.13939
\(668\) −124.996 −4.83623
\(669\) −8.03230 −0.310547
\(670\) 3.37274 0.130300
\(671\) −21.3174 −0.822951
\(672\) −19.3658 −0.747053
\(673\) 16.2384 0.625945 0.312972 0.949762i \(-0.398675\pi\)
0.312972 + 0.949762i \(0.398675\pi\)
\(674\) 25.7837 0.993150
\(675\) −49.6276 −1.91017
\(676\) −59.0322 −2.27047
\(677\) −28.6766 −1.10213 −0.551065 0.834462i \(-0.685778\pi\)
−0.551065 + 0.834462i \(0.685778\pi\)
\(678\) −36.6843 −1.40885
\(679\) 3.58524 0.137589
\(680\) −14.5893 −0.559472
\(681\) 26.5130 1.01598
\(682\) 7.67865 0.294031
\(683\) −22.9001 −0.876248 −0.438124 0.898915i \(-0.644357\pi\)
−0.438124 + 0.898915i \(0.644357\pi\)
\(684\) 246.300 9.41750
\(685\) 5.37965 0.205546
\(686\) 12.5636 0.479680
\(687\) 13.3744 0.510265
\(688\) −163.714 −6.24155
\(689\) −14.2487 −0.542830
\(690\) −53.4279 −2.03396
\(691\) 14.9114 0.567258 0.283629 0.958934i \(-0.408462\pi\)
0.283629 + 0.958934i \(0.408462\pi\)
\(692\) 125.176 4.75848
\(693\) −6.54091 −0.248469
\(694\) 20.4602 0.776658
\(695\) 7.21064 0.273515
\(696\) 221.465 8.39460
\(697\) 9.83964 0.372703
\(698\) 50.7782 1.92198
\(699\) −94.5476 −3.57612
\(700\) −7.39563 −0.279529
\(701\) −13.6159 −0.514265 −0.257133 0.966376i \(-0.582778\pi\)
−0.257133 + 0.966376i \(0.582778\pi\)
\(702\) −43.6406 −1.64711
\(703\) −67.2931 −2.53801
\(704\) −66.0930 −2.49097
\(705\) 31.6628 1.19249
\(706\) −18.2497 −0.686837
\(707\) 5.94967 0.223760
\(708\) 137.690 5.17469
\(709\) 15.4987 0.582065 0.291033 0.956713i \(-0.406001\pi\)
0.291033 + 0.956713i \(0.406001\pi\)
\(710\) 6.58404 0.247095
\(711\) −95.2094 −3.57063
\(712\) −23.1583 −0.867894
\(713\) −6.87656 −0.257529
\(714\) 5.10598 0.191087
\(715\) 3.55009 0.132766
\(716\) −19.3928 −0.724743
\(717\) 39.7878 1.48590
\(718\) 96.1603 3.58867
\(719\) −9.46399 −0.352947 −0.176474 0.984305i \(-0.556469\pi\)
−0.176474 + 0.984305i \(0.556469\pi\)
\(720\) −83.0816 −3.09627
\(721\) −5.59432 −0.208343
\(722\) −75.1786 −2.79786
\(723\) 28.7437 1.06899
\(724\) −124.447 −4.62502
\(725\) 33.1950 1.23283
\(726\) 23.3019 0.864816
\(727\) 5.49675 0.203863 0.101932 0.994791i \(-0.467498\pi\)
0.101932 + 0.994791i \(0.467498\pi\)
\(728\) −4.04566 −0.149942
\(729\) 2.80467 0.103877
\(730\) −7.67350 −0.284009
\(731\) 21.9906 0.813351
\(732\) 123.006 4.54643
\(733\) 22.8811 0.845132 0.422566 0.906332i \(-0.361130\pi\)
0.422566 + 0.906332i \(0.361130\pi\)
\(734\) 36.7244 1.35552
\(735\) 19.6267 0.723943
\(736\) 128.214 4.72602
\(737\) −3.93971 −0.145121
\(738\) 100.220 3.68914
\(739\) −0.823815 −0.0303045 −0.0151523 0.999885i \(-0.504823\pi\)
−0.0151523 + 0.999885i \(0.504823\pi\)
\(740\) 47.3635 1.74112
\(741\) 29.1043 1.06917
\(742\) 9.48909 0.348355
\(743\) 47.1711 1.73054 0.865270 0.501307i \(-0.167147\pi\)
0.865270 + 0.501307i \(0.167147\pi\)
\(744\) −27.5627 −1.01050
\(745\) −13.1002 −0.479955
\(746\) −20.7885 −0.761122
\(747\) 121.431 4.44291
\(748\) 27.3947 1.00165
\(749\) 1.13176 0.0413534
\(750\) −70.5726 −2.57695
\(751\) −3.46166 −0.126318 −0.0631589 0.998003i \(-0.520117\pi\)
−0.0631589 + 0.998003i \(0.520117\pi\)
\(752\) −149.145 −5.43876
\(753\) 40.0474 1.45941
\(754\) 29.1904 1.06305
\(755\) 3.41672 0.124347
\(756\) 21.0920 0.767108
\(757\) −7.10101 −0.258091 −0.129045 0.991639i \(-0.541191\pi\)
−0.129045 + 0.991639i \(0.541191\pi\)
\(758\) 3.69771 0.134307
\(759\) 62.4092 2.26531
\(760\) 55.3811 2.00888
\(761\) 9.27484 0.336213 0.168106 0.985769i \(-0.446235\pi\)
0.168106 + 0.985769i \(0.446235\pi\)
\(762\) 5.16430 0.187083
\(763\) 6.14770 0.222562
\(764\) 119.806 4.33443
\(765\) 11.1598 0.403482
\(766\) 68.0507 2.45877
\(767\) 11.2897 0.407648
\(768\) 69.1661 2.49582
\(769\) −11.6503 −0.420121 −0.210060 0.977688i \(-0.567366\pi\)
−0.210060 + 0.977688i \(0.567366\pi\)
\(770\) −2.36423 −0.0852009
\(771\) 34.0639 1.22678
\(772\) 26.8258 0.965482
\(773\) −39.6441 −1.42590 −0.712949 0.701216i \(-0.752641\pi\)
−0.712949 + 0.701216i \(0.752641\pi\)
\(774\) 223.981 8.05082
\(775\) −4.13133 −0.148402
\(776\) −95.1409 −3.41536
\(777\) −10.3118 −0.369935
\(778\) 40.9783 1.46914
\(779\) −37.3515 −1.33826
\(780\) −20.4847 −0.733471
\(781\) −7.69082 −0.275199
\(782\) −33.8047 −1.20886
\(783\) −94.6705 −3.38325
\(784\) −92.4501 −3.30179
\(785\) −3.47084 −0.123879
\(786\) −9.47983 −0.338134
\(787\) 43.0250 1.53368 0.766838 0.641841i \(-0.221829\pi\)
0.766838 + 0.641841i \(0.221829\pi\)
\(788\) −122.643 −4.36896
\(789\) 40.6575 1.44745
\(790\) −34.4137 −1.22439
\(791\) 1.45375 0.0516893
\(792\) 173.575 6.16772
\(793\) 10.0857 0.358155
\(794\) −9.04082 −0.320847
\(795\) 29.8891 1.06006
\(796\) 23.8521 0.845414
\(797\) −4.95566 −0.175538 −0.0877692 0.996141i \(-0.527974\pi\)
−0.0877692 + 0.996141i \(0.527974\pi\)
\(798\) −19.3824 −0.686130
\(799\) 20.0336 0.708738
\(800\) 77.0288 2.72338
\(801\) 17.7145 0.625911
\(802\) 76.5539 2.70321
\(803\) 8.96342 0.316312
\(804\) 22.7329 0.801728
\(805\) 2.11727 0.0746240
\(806\) −3.63294 −0.127965
\(807\) −45.5701 −1.60414
\(808\) −157.885 −5.55439
\(809\) 2.39932 0.0843556 0.0421778 0.999110i \(-0.486570\pi\)
0.0421778 + 0.999110i \(0.486570\pi\)
\(810\) 41.3992 1.45462
\(811\) −38.7064 −1.35916 −0.679582 0.733599i \(-0.737839\pi\)
−0.679582 + 0.733599i \(0.737839\pi\)
\(812\) −14.1080 −0.495095
\(813\) −29.3093 −1.02792
\(814\) −76.2339 −2.67200
\(815\) −8.27390 −0.289822
\(816\) −75.7577 −2.65205
\(817\) −83.4768 −2.92048
\(818\) 7.74047 0.270639
\(819\) 3.09465 0.108136
\(820\) 26.2894 0.918066
\(821\) 42.9669 1.49956 0.749778 0.661689i \(-0.230160\pi\)
0.749778 + 0.661689i \(0.230160\pi\)
\(822\) 49.9631 1.74266
\(823\) −34.8172 −1.21365 −0.606825 0.794835i \(-0.707557\pi\)
−0.606825 + 0.794835i \(0.707557\pi\)
\(824\) 148.456 5.17170
\(825\) 37.4945 1.30539
\(826\) −7.51854 −0.261603
\(827\) −42.0406 −1.46189 −0.730947 0.682435i \(-0.760921\pi\)
−0.730947 + 0.682435i \(0.760921\pi\)
\(828\) −249.878 −8.68385
\(829\) 3.43424 0.119276 0.0596381 0.998220i \(-0.481005\pi\)
0.0596381 + 0.998220i \(0.481005\pi\)
\(830\) 43.8914 1.52349
\(831\) 30.6495 1.06322
\(832\) 31.2700 1.08409
\(833\) 12.4182 0.430264
\(834\) 66.9684 2.31892
\(835\) 21.4988 0.743998
\(836\) −103.991 −3.59660
\(837\) 11.7824 0.407258
\(838\) 27.3921 0.946244
\(839\) −4.22085 −0.145720 −0.0728599 0.997342i \(-0.523213\pi\)
−0.0728599 + 0.997342i \(0.523213\pi\)
\(840\) 8.48647 0.292811
\(841\) 34.3234 1.18357
\(842\) −5.71051 −0.196797
\(843\) 61.6496 2.12332
\(844\) 22.9826 0.791093
\(845\) 10.1533 0.349286
\(846\) 204.048 7.01532
\(847\) −0.923422 −0.0317292
\(848\) −140.790 −4.83475
\(849\) 44.2016 1.51700
\(850\) −20.3094 −0.696606
\(851\) 68.2707 2.34029
\(852\) 44.3776 1.52035
\(853\) −24.5056 −0.839054 −0.419527 0.907743i \(-0.637804\pi\)
−0.419527 + 0.907743i \(0.637804\pi\)
\(854\) −6.71674 −0.229842
\(855\) −42.3627 −1.44877
\(856\) −30.0332 −1.02651
\(857\) −24.2650 −0.828875 −0.414438 0.910078i \(-0.636022\pi\)
−0.414438 + 0.910078i \(0.636022\pi\)
\(858\) 32.9712 1.12562
\(859\) 47.5984 1.62404 0.812018 0.583633i \(-0.198369\pi\)
0.812018 + 0.583633i \(0.198369\pi\)
\(860\) 58.7541 2.00350
\(861\) −5.72365 −0.195062
\(862\) 49.2347 1.67694
\(863\) 2.13895 0.0728105 0.0364053 0.999337i \(-0.488409\pi\)
0.0364053 + 0.999337i \(0.488409\pi\)
\(864\) −219.682 −7.47375
\(865\) −21.5299 −0.732037
\(866\) 2.20364 0.0748828
\(867\) −43.0431 −1.46182
\(868\) 1.75584 0.0595970
\(869\) 40.1987 1.36365
\(870\) −61.2320 −2.07596
\(871\) 1.86396 0.0631579
\(872\) −163.141 −5.52464
\(873\) 72.7762 2.46310
\(874\) 128.324 4.34061
\(875\) 2.79669 0.0945454
\(876\) −51.7208 −1.74748
\(877\) −45.5524 −1.53820 −0.769098 0.639131i \(-0.779294\pi\)
−0.769098 + 0.639131i \(0.779294\pi\)
\(878\) −62.6878 −2.11561
\(879\) 74.3923 2.50919
\(880\) 35.0782 1.18248
\(881\) −37.3643 −1.25883 −0.629417 0.777067i \(-0.716706\pi\)
−0.629417 + 0.777067i \(0.716706\pi\)
\(882\) 126.483 4.25890
\(883\) −26.1137 −0.878795 −0.439397 0.898293i \(-0.644808\pi\)
−0.439397 + 0.898293i \(0.644808\pi\)
\(884\) −12.9610 −0.435927
\(885\) −23.6821 −0.796067
\(886\) 0.915490 0.0307565
\(887\) 44.5924 1.49727 0.748633 0.662985i \(-0.230711\pi\)
0.748633 + 0.662985i \(0.230711\pi\)
\(888\) 273.644 9.18289
\(889\) −0.204654 −0.00686387
\(890\) 6.40296 0.214628
\(891\) −48.3584 −1.62007
\(892\) −13.5785 −0.454641
\(893\) −76.0480 −2.54485
\(894\) −121.667 −4.06916
\(895\) 3.33550 0.111493
\(896\) −8.45252 −0.282379
\(897\) −29.5271 −0.985882
\(898\) −32.1216 −1.07191
\(899\) −7.88101 −0.262846
\(900\) −150.123 −5.00409
\(901\) 18.9113 0.630028
\(902\) −42.3141 −1.40891
\(903\) −12.7918 −0.425684
\(904\) −38.5778 −1.28308
\(905\) 21.4044 0.711506
\(906\) 31.7326 1.05424
\(907\) 20.4550 0.679197 0.339599 0.940570i \(-0.389709\pi\)
0.339599 + 0.940570i \(0.389709\pi\)
\(908\) 44.8198 1.48740
\(909\) 120.771 4.00573
\(910\) 1.11857 0.0370802
\(911\) 50.7054 1.67994 0.839972 0.542629i \(-0.182571\pi\)
0.839972 + 0.542629i \(0.182571\pi\)
\(912\) 287.578 9.52265
\(913\) −51.2696 −1.69678
\(914\) 63.9663 2.11582
\(915\) −21.1566 −0.699417
\(916\) 22.6092 0.747030
\(917\) 0.375672 0.0124058
\(918\) 57.9213 1.91169
\(919\) −17.3347 −0.571818 −0.285909 0.958257i \(-0.592295\pi\)
−0.285909 + 0.958257i \(0.592295\pi\)
\(920\) −56.1857 −1.85239
\(921\) 13.2620 0.436997
\(922\) 91.0166 2.99747
\(923\) 3.63870 0.119769
\(924\) −15.9353 −0.524234
\(925\) 41.0160 1.34860
\(926\) 42.2509 1.38845
\(927\) −113.558 −3.72974
\(928\) 146.942 4.82359
\(929\) −16.1779 −0.530779 −0.265389 0.964141i \(-0.585501\pi\)
−0.265389 + 0.964141i \(0.585501\pi\)
\(930\) 7.62072 0.249893
\(931\) −47.1397 −1.54494
\(932\) −159.831 −5.23545
\(933\) −64.6356 −2.11607
\(934\) 20.2106 0.661312
\(935\) −4.71180 −0.154092
\(936\) −82.1222 −2.68425
\(937\) −41.2823 −1.34863 −0.674317 0.738442i \(-0.735562\pi\)
−0.674317 + 0.738442i \(0.735562\pi\)
\(938\) −1.24133 −0.0405309
\(939\) 36.1221 1.17880
\(940\) 53.5255 1.74581
\(941\) 25.0114 0.815350 0.407675 0.913127i \(-0.366340\pi\)
0.407675 + 0.913127i \(0.366340\pi\)
\(942\) −32.2351 −1.05028
\(943\) 37.8941 1.23400
\(944\) 111.553 3.63074
\(945\) −3.62775 −0.118011
\(946\) −94.5677 −3.07466
\(947\) 44.7324 1.45361 0.726803 0.686846i \(-0.241005\pi\)
0.726803 + 0.686846i \(0.241005\pi\)
\(948\) −231.955 −7.53354
\(949\) −4.24079 −0.137662
\(950\) 77.0949 2.50129
\(951\) 39.1076 1.26815
\(952\) 5.36954 0.174028
\(953\) −25.3381 −0.820781 −0.410391 0.911910i \(-0.634608\pi\)
−0.410391 + 0.911910i \(0.634608\pi\)
\(954\) 192.618 6.23622
\(955\) −20.6062 −0.666802
\(956\) 67.2608 2.17537
\(957\) 71.5252 2.31208
\(958\) 30.0568 0.971092
\(959\) −1.97997 −0.0639365
\(960\) −65.5944 −2.11705
\(961\) −30.0192 −0.968360
\(962\) 36.0679 1.16288
\(963\) 22.9733 0.740305
\(964\) 48.5909 1.56501
\(965\) −4.61395 −0.148528
\(966\) 19.6640 0.632679
\(967\) 53.4439 1.71864 0.859321 0.511437i \(-0.170887\pi\)
0.859321 + 0.511437i \(0.170887\pi\)
\(968\) 24.5047 0.787611
\(969\) −38.6283 −1.24092
\(970\) 26.3052 0.844608
\(971\) −43.0730 −1.38228 −0.691140 0.722721i \(-0.742891\pi\)
−0.691140 + 0.722721i \(0.742891\pi\)
\(972\) 90.1587 2.89184
\(973\) −2.65386 −0.0850789
\(974\) 98.4791 3.15547
\(975\) −17.7395 −0.568117
\(976\) 99.6566 3.18993
\(977\) 6.05349 0.193668 0.0968342 0.995301i \(-0.469128\pi\)
0.0968342 + 0.995301i \(0.469128\pi\)
\(978\) −76.8433 −2.45718
\(979\) −7.47930 −0.239039
\(980\) 33.1787 1.05985
\(981\) 124.791 3.98428
\(982\) −65.6976 −2.09649
\(983\) 27.8820 0.889297 0.444648 0.895705i \(-0.353329\pi\)
0.444648 + 0.895705i \(0.353329\pi\)
\(984\) 151.888 4.84200
\(985\) 21.0941 0.672115
\(986\) −38.7426 −1.23381
\(987\) −11.6534 −0.370932
\(988\) 49.2004 1.56527
\(989\) 84.6895 2.69297
\(990\) −47.9911 −1.52526
\(991\) 52.9405 1.68171 0.840854 0.541261i \(-0.182053\pi\)
0.840854 + 0.541261i \(0.182053\pi\)
\(992\) −18.2878 −0.580639
\(993\) −62.0385 −1.96873
\(994\) −2.42324 −0.0768605
\(995\) −4.10248 −0.130057
\(996\) 295.836 9.37393
\(997\) 16.2377 0.514253 0.257127 0.966378i \(-0.417224\pi\)
0.257127 + 0.966378i \(0.417224\pi\)
\(998\) −89.0710 −2.81949
\(999\) −116.976 −3.70095
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 \(a_p\))