Properties

Label 6003.2.a.t.1.7
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35991 q^{2} -0.150655 q^{4} +4.20064 q^{5} +0.870260 q^{7} +2.92469 q^{8} +O(q^{10})\) \(q-1.35991 q^{2} -0.150655 q^{4} +4.20064 q^{5} +0.870260 q^{7} +2.92469 q^{8} -5.71248 q^{10} -3.24281 q^{11} -1.60184 q^{13} -1.18347 q^{14} -3.67599 q^{16} -7.96215 q^{17} -1.89212 q^{19} -0.632848 q^{20} +4.40992 q^{22} +1.00000 q^{23} +12.6454 q^{25} +2.17835 q^{26} -0.131109 q^{28} +1.00000 q^{29} -6.87026 q^{31} -0.850373 q^{32} +10.8278 q^{34} +3.65565 q^{35} +5.65195 q^{37} +2.57310 q^{38} +12.2856 q^{40} +5.17129 q^{41} +12.5424 q^{43} +0.488546 q^{44} -1.35991 q^{46} +4.23722 q^{47} -6.24265 q^{49} -17.1965 q^{50} +0.241325 q^{52} -6.69371 q^{53} -13.6219 q^{55} +2.54524 q^{56} -1.35991 q^{58} +1.30032 q^{59} -14.9100 q^{61} +9.34291 q^{62} +8.50841 q^{64} -6.72875 q^{65} -0.0645202 q^{67} +1.19954 q^{68} -4.97134 q^{70} -7.40240 q^{71} -4.96764 q^{73} -7.68612 q^{74} +0.285057 q^{76} -2.82209 q^{77} -3.28830 q^{79} -15.4415 q^{80} -7.03247 q^{82} -2.68133 q^{83} -33.4461 q^{85} -17.0565 q^{86} -9.48422 q^{88} -11.1742 q^{89} -1.39402 q^{91} -0.150655 q^{92} -5.76222 q^{94} -7.94809 q^{95} +1.63869 q^{97} +8.48942 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35991 −0.961599 −0.480799 0.876831i \(-0.659653\pi\)
−0.480799 + 0.876831i \(0.659653\pi\)
\(3\) 0 0
\(4\) −0.150655 −0.0753275
\(5\) 4.20064 1.87858 0.939291 0.343120i \(-0.111484\pi\)
0.939291 + 0.343120i \(0.111484\pi\)
\(6\) 0 0
\(7\) 0.870260 0.328927 0.164464 0.986383i \(-0.447411\pi\)
0.164464 + 0.986383i \(0.447411\pi\)
\(8\) 2.92469 1.03403
\(9\) 0 0
\(10\) −5.71248 −1.80644
\(11\) −3.24281 −0.977745 −0.488872 0.872355i \(-0.662592\pi\)
−0.488872 + 0.872355i \(0.662592\pi\)
\(12\) 0 0
\(13\) −1.60184 −0.444270 −0.222135 0.975016i \(-0.571303\pi\)
−0.222135 + 0.975016i \(0.571303\pi\)
\(14\) −1.18347 −0.316296
\(15\) 0 0
\(16\) −3.67599 −0.918998
\(17\) −7.96215 −1.93110 −0.965552 0.260210i \(-0.916208\pi\)
−0.965552 + 0.260210i \(0.916208\pi\)
\(18\) 0 0
\(19\) −1.89212 −0.434081 −0.217040 0.976163i \(-0.569640\pi\)
−0.217040 + 0.976163i \(0.569640\pi\)
\(20\) −0.632848 −0.141509
\(21\) 0 0
\(22\) 4.40992 0.940198
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 12.6454 2.52907
\(26\) 2.17835 0.427210
\(27\) 0 0
\(28\) −0.131109 −0.0247773
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −6.87026 −1.23394 −0.616968 0.786988i \(-0.711639\pi\)
−0.616968 + 0.786988i \(0.711639\pi\)
\(32\) −0.850373 −0.150326
\(33\) 0 0
\(34\) 10.8278 1.85695
\(35\) 3.65565 0.617917
\(36\) 0 0
\(37\) 5.65195 0.929175 0.464587 0.885527i \(-0.346203\pi\)
0.464587 + 0.885527i \(0.346203\pi\)
\(38\) 2.57310 0.417412
\(39\) 0 0
\(40\) 12.2856 1.94252
\(41\) 5.17129 0.807620 0.403810 0.914843i \(-0.367686\pi\)
0.403810 + 0.914843i \(0.367686\pi\)
\(42\) 0 0
\(43\) 12.5424 1.91269 0.956347 0.292232i \(-0.0943980\pi\)
0.956347 + 0.292232i \(0.0943980\pi\)
\(44\) 0.488546 0.0736511
\(45\) 0 0
\(46\) −1.35991 −0.200507
\(47\) 4.23722 0.618062 0.309031 0.951052i \(-0.399995\pi\)
0.309031 + 0.951052i \(0.399995\pi\)
\(48\) 0 0
\(49\) −6.24265 −0.891807
\(50\) −17.1965 −2.43195
\(51\) 0 0
\(52\) 0.241325 0.0334658
\(53\) −6.69371 −0.919452 −0.459726 0.888061i \(-0.652052\pi\)
−0.459726 + 0.888061i \(0.652052\pi\)
\(54\) 0 0
\(55\) −13.6219 −1.83677
\(56\) 2.54524 0.340122
\(57\) 0 0
\(58\) −1.35991 −0.178564
\(59\) 1.30032 0.169287 0.0846435 0.996411i \(-0.473025\pi\)
0.0846435 + 0.996411i \(0.473025\pi\)
\(60\) 0 0
\(61\) −14.9100 −1.90902 −0.954512 0.298172i \(-0.903623\pi\)
−0.954512 + 0.298172i \(0.903623\pi\)
\(62\) 9.34291 1.18655
\(63\) 0 0
\(64\) 8.50841 1.06355
\(65\) −6.72875 −0.834598
\(66\) 0 0
\(67\) −0.0645202 −0.00788240 −0.00394120 0.999992i \(-0.501255\pi\)
−0.00394120 + 0.999992i \(0.501255\pi\)
\(68\) 1.19954 0.145465
\(69\) 0 0
\(70\) −4.97134 −0.594188
\(71\) −7.40240 −0.878503 −0.439251 0.898364i \(-0.644756\pi\)
−0.439251 + 0.898364i \(0.644756\pi\)
\(72\) 0 0
\(73\) −4.96764 −0.581419 −0.290709 0.956811i \(-0.593891\pi\)
−0.290709 + 0.956811i \(0.593891\pi\)
\(74\) −7.68612 −0.893493
\(75\) 0 0
\(76\) 0.285057 0.0326983
\(77\) −2.82209 −0.321607
\(78\) 0 0
\(79\) −3.28830 −0.369962 −0.184981 0.982742i \(-0.559222\pi\)
−0.184981 + 0.982742i \(0.559222\pi\)
\(80\) −15.4415 −1.72641
\(81\) 0 0
\(82\) −7.03247 −0.776606
\(83\) −2.68133 −0.294314 −0.147157 0.989113i \(-0.547012\pi\)
−0.147157 + 0.989113i \(0.547012\pi\)
\(84\) 0 0
\(85\) −33.4461 −3.62774
\(86\) −17.0565 −1.83925
\(87\) 0 0
\(88\) −9.48422 −1.01102
\(89\) −11.1742 −1.18446 −0.592232 0.805767i \(-0.701753\pi\)
−0.592232 + 0.805767i \(0.701753\pi\)
\(90\) 0 0
\(91\) −1.39402 −0.146133
\(92\) −0.150655 −0.0157069
\(93\) 0 0
\(94\) −5.76222 −0.594328
\(95\) −7.94809 −0.815457
\(96\) 0 0
\(97\) 1.63869 0.166384 0.0831918 0.996534i \(-0.473489\pi\)
0.0831918 + 0.996534i \(0.473489\pi\)
\(98\) 8.48942 0.857561
\(99\) 0 0
\(100\) −1.90509 −0.190509
\(101\) 15.1598 1.50846 0.754230 0.656610i \(-0.228010\pi\)
0.754230 + 0.656610i \(0.228010\pi\)
\(102\) 0 0
\(103\) −13.6519 −1.34516 −0.672579 0.740026i \(-0.734813\pi\)
−0.672579 + 0.740026i \(0.734813\pi\)
\(104\) −4.68488 −0.459390
\(105\) 0 0
\(106\) 9.10282 0.884144
\(107\) 13.7576 1.33000 0.664999 0.746844i \(-0.268432\pi\)
0.664999 + 0.746844i \(0.268432\pi\)
\(108\) 0 0
\(109\) −6.63576 −0.635591 −0.317795 0.948159i \(-0.602943\pi\)
−0.317795 + 0.948159i \(0.602943\pi\)
\(110\) 18.5245 1.76624
\(111\) 0 0
\(112\) −3.19907 −0.302284
\(113\) 4.37941 0.411981 0.205990 0.978554i \(-0.433958\pi\)
0.205990 + 0.978554i \(0.433958\pi\)
\(114\) 0 0
\(115\) 4.20064 0.391712
\(116\) −0.150655 −0.0139880
\(117\) 0 0
\(118\) −1.76831 −0.162786
\(119\) −6.92913 −0.635193
\(120\) 0 0
\(121\) −0.484172 −0.0440156
\(122\) 20.2761 1.83572
\(123\) 0 0
\(124\) 1.03504 0.0929493
\(125\) 32.1154 2.87249
\(126\) 0 0
\(127\) −9.03976 −0.802149 −0.401075 0.916045i \(-0.631363\pi\)
−0.401075 + 0.916045i \(0.631363\pi\)
\(128\) −9.86990 −0.872384
\(129\) 0 0
\(130\) 9.15047 0.802549
\(131\) −3.26008 −0.284834 −0.142417 0.989807i \(-0.545487\pi\)
−0.142417 + 0.989807i \(0.545487\pi\)
\(132\) 0 0
\(133\) −1.64663 −0.142781
\(134\) 0.0877414 0.00757970
\(135\) 0 0
\(136\) −23.2868 −1.99683
\(137\) −15.5938 −1.33227 −0.666133 0.745833i \(-0.732052\pi\)
−0.666133 + 0.745833i \(0.732052\pi\)
\(138\) 0 0
\(139\) 9.27779 0.786932 0.393466 0.919339i \(-0.371276\pi\)
0.393466 + 0.919339i \(0.371276\pi\)
\(140\) −0.550742 −0.0465462
\(141\) 0 0
\(142\) 10.0666 0.844767
\(143\) 5.19446 0.434383
\(144\) 0 0
\(145\) 4.20064 0.348844
\(146\) 6.75553 0.559091
\(147\) 0 0
\(148\) −0.851495 −0.0699924
\(149\) 6.92426 0.567257 0.283629 0.958934i \(-0.408462\pi\)
0.283629 + 0.958934i \(0.408462\pi\)
\(150\) 0 0
\(151\) −22.0062 −1.79084 −0.895419 0.445224i \(-0.853124\pi\)
−0.895419 + 0.445224i \(0.853124\pi\)
\(152\) −5.53385 −0.448854
\(153\) 0 0
\(154\) 3.83778 0.309257
\(155\) −28.8595 −2.31805
\(156\) 0 0
\(157\) −20.5974 −1.64385 −0.821926 0.569594i \(-0.807100\pi\)
−0.821926 + 0.569594i \(0.807100\pi\)
\(158\) 4.47178 0.355755
\(159\) 0 0
\(160\) −3.57211 −0.282400
\(161\) 0.870260 0.0685861
\(162\) 0 0
\(163\) 8.65285 0.677743 0.338872 0.940833i \(-0.389955\pi\)
0.338872 + 0.940833i \(0.389955\pi\)
\(164\) −0.779081 −0.0608360
\(165\) 0 0
\(166\) 3.64635 0.283012
\(167\) 5.82700 0.450907 0.225453 0.974254i \(-0.427614\pi\)
0.225453 + 0.974254i \(0.427614\pi\)
\(168\) 0 0
\(169\) −10.4341 −0.802624
\(170\) 45.4836 3.48843
\(171\) 0 0
\(172\) −1.88957 −0.144079
\(173\) −4.42101 −0.336123 −0.168061 0.985777i \(-0.553751\pi\)
−0.168061 + 0.985777i \(0.553751\pi\)
\(174\) 0 0
\(175\) 11.0048 0.831881
\(176\) 11.9206 0.898546
\(177\) 0 0
\(178\) 15.1959 1.13898
\(179\) 18.9842 1.41895 0.709474 0.704732i \(-0.248933\pi\)
0.709474 + 0.704732i \(0.248933\pi\)
\(180\) 0 0
\(181\) −9.20077 −0.683888 −0.341944 0.939720i \(-0.611085\pi\)
−0.341944 + 0.939720i \(0.611085\pi\)
\(182\) 1.89573 0.140521
\(183\) 0 0
\(184\) 2.92469 0.215611
\(185\) 23.7418 1.74553
\(186\) 0 0
\(187\) 25.8197 1.88813
\(188\) −0.638359 −0.0465571
\(189\) 0 0
\(190\) 10.8087 0.784143
\(191\) −22.0536 −1.59574 −0.797871 0.602828i \(-0.794041\pi\)
−0.797871 + 0.602828i \(0.794041\pi\)
\(192\) 0 0
\(193\) −1.88602 −0.135759 −0.0678793 0.997694i \(-0.521623\pi\)
−0.0678793 + 0.997694i \(0.521623\pi\)
\(194\) −2.22846 −0.159994
\(195\) 0 0
\(196\) 0.940487 0.0671776
\(197\) 9.88749 0.704455 0.352227 0.935914i \(-0.385424\pi\)
0.352227 + 0.935914i \(0.385424\pi\)
\(198\) 0 0
\(199\) −0.824714 −0.0584624 −0.0292312 0.999573i \(-0.509306\pi\)
−0.0292312 + 0.999573i \(0.509306\pi\)
\(200\) 36.9838 2.61515
\(201\) 0 0
\(202\) −20.6160 −1.45053
\(203\) 0.870260 0.0610803
\(204\) 0 0
\(205\) 21.7227 1.51718
\(206\) 18.5652 1.29350
\(207\) 0 0
\(208\) 5.88835 0.408284
\(209\) 6.13577 0.424420
\(210\) 0 0
\(211\) −19.7545 −1.35995 −0.679977 0.733234i \(-0.738010\pi\)
−0.679977 + 0.733234i \(0.738010\pi\)
\(212\) 1.00844 0.0692601
\(213\) 0 0
\(214\) −18.7091 −1.27892
\(215\) 52.6860 3.59316
\(216\) 0 0
\(217\) −5.97891 −0.405875
\(218\) 9.02402 0.611183
\(219\) 0 0
\(220\) 2.05221 0.138360
\(221\) 12.7541 0.857932
\(222\) 0 0
\(223\) 6.70935 0.449291 0.224646 0.974441i \(-0.427878\pi\)
0.224646 + 0.974441i \(0.427878\pi\)
\(224\) −0.740045 −0.0494463
\(225\) 0 0
\(226\) −5.95559 −0.396160
\(227\) 3.30901 0.219626 0.109813 0.993952i \(-0.464975\pi\)
0.109813 + 0.993952i \(0.464975\pi\)
\(228\) 0 0
\(229\) −22.9262 −1.51501 −0.757503 0.652832i \(-0.773581\pi\)
−0.757503 + 0.652832i \(0.773581\pi\)
\(230\) −5.71248 −0.376669
\(231\) 0 0
\(232\) 2.92469 0.192015
\(233\) −15.0316 −0.984752 −0.492376 0.870383i \(-0.663871\pi\)
−0.492376 + 0.870383i \(0.663871\pi\)
\(234\) 0 0
\(235\) 17.7990 1.16108
\(236\) −0.195899 −0.0127520
\(237\) 0 0
\(238\) 9.42297 0.610801
\(239\) −3.77404 −0.244122 −0.122061 0.992523i \(-0.538950\pi\)
−0.122061 + 0.992523i \(0.538950\pi\)
\(240\) 0 0
\(241\) 15.9280 1.02602 0.513008 0.858384i \(-0.328531\pi\)
0.513008 + 0.858384i \(0.328531\pi\)
\(242\) 0.658428 0.0423254
\(243\) 0 0
\(244\) 2.24626 0.143802
\(245\) −26.2231 −1.67533
\(246\) 0 0
\(247\) 3.03086 0.192849
\(248\) −20.0934 −1.27593
\(249\) 0 0
\(250\) −43.6740 −2.76219
\(251\) 20.6886 1.30585 0.652925 0.757423i \(-0.273542\pi\)
0.652925 + 0.757423i \(0.273542\pi\)
\(252\) 0 0
\(253\) −3.24281 −0.203874
\(254\) 12.2932 0.771346
\(255\) 0 0
\(256\) −3.59469 −0.224668
\(257\) −0.653474 −0.0407626 −0.0203813 0.999792i \(-0.506488\pi\)
−0.0203813 + 0.999792i \(0.506488\pi\)
\(258\) 0 0
\(259\) 4.91866 0.305631
\(260\) 1.01372 0.0628682
\(261\) 0 0
\(262\) 4.43340 0.273896
\(263\) −12.3265 −0.760082 −0.380041 0.924970i \(-0.624090\pi\)
−0.380041 + 0.924970i \(0.624090\pi\)
\(264\) 0 0
\(265\) −28.1179 −1.72727
\(266\) 2.23926 0.137298
\(267\) 0 0
\(268\) 0.00972029 0.000593761 0
\(269\) −12.2201 −0.745071 −0.372536 0.928018i \(-0.621512\pi\)
−0.372536 + 0.928018i \(0.621512\pi\)
\(270\) 0 0
\(271\) −25.7038 −1.56140 −0.780698 0.624909i \(-0.785136\pi\)
−0.780698 + 0.624909i \(0.785136\pi\)
\(272\) 29.2688 1.77468
\(273\) 0 0
\(274\) 21.2061 1.28111
\(275\) −41.0066 −2.47279
\(276\) 0 0
\(277\) −31.0715 −1.86691 −0.933453 0.358700i \(-0.883220\pi\)
−0.933453 + 0.358700i \(0.883220\pi\)
\(278\) −12.6169 −0.756713
\(279\) 0 0
\(280\) 10.6916 0.638947
\(281\) 15.1309 0.902635 0.451317 0.892363i \(-0.350954\pi\)
0.451317 + 0.892363i \(0.350954\pi\)
\(282\) 0 0
\(283\) 11.2893 0.671078 0.335539 0.942026i \(-0.391082\pi\)
0.335539 + 0.942026i \(0.391082\pi\)
\(284\) 1.11521 0.0661754
\(285\) 0 0
\(286\) −7.06398 −0.417702
\(287\) 4.50036 0.265648
\(288\) 0 0
\(289\) 46.3958 2.72916
\(290\) −5.71248 −0.335448
\(291\) 0 0
\(292\) 0.748400 0.0437968
\(293\) −15.7003 −0.917219 −0.458609 0.888638i \(-0.651652\pi\)
−0.458609 + 0.888638i \(0.651652\pi\)
\(294\) 0 0
\(295\) 5.46217 0.318020
\(296\) 16.5302 0.960798
\(297\) 0 0
\(298\) −9.41634 −0.545474
\(299\) −1.60184 −0.0926367
\(300\) 0 0
\(301\) 10.9151 0.629137
\(302\) 29.9263 1.72207
\(303\) 0 0
\(304\) 6.95540 0.398920
\(305\) −62.6314 −3.58626
\(306\) 0 0
\(307\) 23.2734 1.32828 0.664141 0.747607i \(-0.268797\pi\)
0.664141 + 0.747607i \(0.268797\pi\)
\(308\) 0.425162 0.0242258
\(309\) 0 0
\(310\) 39.2462 2.22903
\(311\) −4.08567 −0.231677 −0.115839 0.993268i \(-0.536956\pi\)
−0.115839 + 0.993268i \(0.536956\pi\)
\(312\) 0 0
\(313\) −19.8880 −1.12414 −0.562068 0.827091i \(-0.689994\pi\)
−0.562068 + 0.827091i \(0.689994\pi\)
\(314\) 28.0105 1.58073
\(315\) 0 0
\(316\) 0.495399 0.0278683
\(317\) −26.3501 −1.47997 −0.739984 0.672624i \(-0.765167\pi\)
−0.739984 + 0.672624i \(0.765167\pi\)
\(318\) 0 0
\(319\) −3.24281 −0.181563
\(320\) 35.7408 1.99797
\(321\) 0 0
\(322\) −1.18347 −0.0659523
\(323\) 15.0653 0.838256
\(324\) 0 0
\(325\) −20.2558 −1.12359
\(326\) −11.7671 −0.651717
\(327\) 0 0
\(328\) 15.1244 0.835106
\(329\) 3.68748 0.203297
\(330\) 0 0
\(331\) 6.24238 0.343112 0.171556 0.985174i \(-0.445120\pi\)
0.171556 + 0.985174i \(0.445120\pi\)
\(332\) 0.403956 0.0221699
\(333\) 0 0
\(334\) −7.92417 −0.433591
\(335\) −0.271026 −0.0148077
\(336\) 0 0
\(337\) 20.7024 1.12773 0.563866 0.825866i \(-0.309313\pi\)
0.563866 + 0.825866i \(0.309313\pi\)
\(338\) 14.1894 0.771802
\(339\) 0 0
\(340\) 5.03882 0.273269
\(341\) 22.2790 1.20647
\(342\) 0 0
\(343\) −11.5245 −0.622267
\(344\) 36.6826 1.97779
\(345\) 0 0
\(346\) 6.01216 0.323215
\(347\) 2.61804 0.140544 0.0702719 0.997528i \(-0.477613\pi\)
0.0702719 + 0.997528i \(0.477613\pi\)
\(348\) 0 0
\(349\) −22.4939 −1.20407 −0.602036 0.798469i \(-0.705644\pi\)
−0.602036 + 0.798469i \(0.705644\pi\)
\(350\) −14.9654 −0.799936
\(351\) 0 0
\(352\) 2.75760 0.146981
\(353\) −20.1237 −1.07108 −0.535539 0.844511i \(-0.679891\pi\)
−0.535539 + 0.844511i \(0.679891\pi\)
\(354\) 0 0
\(355\) −31.0948 −1.65034
\(356\) 1.68345 0.0892228
\(357\) 0 0
\(358\) −25.8168 −1.36446
\(359\) 9.07923 0.479183 0.239592 0.970874i \(-0.422986\pi\)
0.239592 + 0.970874i \(0.422986\pi\)
\(360\) 0 0
\(361\) −15.4199 −0.811574
\(362\) 12.5122 0.657625
\(363\) 0 0
\(364\) 0.210016 0.0110078
\(365\) −20.8673 −1.09224
\(366\) 0 0
\(367\) 14.8257 0.773896 0.386948 0.922102i \(-0.373529\pi\)
0.386948 + 0.922102i \(0.373529\pi\)
\(368\) −3.67599 −0.191624
\(369\) 0 0
\(370\) −32.2866 −1.67850
\(371\) −5.82527 −0.302433
\(372\) 0 0
\(373\) 25.9963 1.34604 0.673018 0.739627i \(-0.264998\pi\)
0.673018 + 0.739627i \(0.264998\pi\)
\(374\) −35.1124 −1.81562
\(375\) 0 0
\(376\) 12.3925 0.639097
\(377\) −1.60184 −0.0824989
\(378\) 0 0
\(379\) −4.07417 −0.209276 −0.104638 0.994510i \(-0.533368\pi\)
−0.104638 + 0.994510i \(0.533368\pi\)
\(380\) 1.19742 0.0614264
\(381\) 0 0
\(382\) 29.9908 1.53446
\(383\) −8.15209 −0.416552 −0.208276 0.978070i \(-0.566785\pi\)
−0.208276 + 0.978070i \(0.566785\pi\)
\(384\) 0 0
\(385\) −11.8546 −0.604165
\(386\) 2.56481 0.130545
\(387\) 0 0
\(388\) −0.246877 −0.0125333
\(389\) −6.48252 −0.328677 −0.164338 0.986404i \(-0.552549\pi\)
−0.164338 + 0.986404i \(0.552549\pi\)
\(390\) 0 0
\(391\) −7.96215 −0.402663
\(392\) −18.2578 −0.922158
\(393\) 0 0
\(394\) −13.4461 −0.677403
\(395\) −13.8129 −0.695005
\(396\) 0 0
\(397\) 23.1797 1.16335 0.581677 0.813420i \(-0.302397\pi\)
0.581677 + 0.813420i \(0.302397\pi\)
\(398\) 1.12153 0.0562174
\(399\) 0 0
\(400\) −46.4843 −2.32421
\(401\) 19.8688 0.992201 0.496100 0.868265i \(-0.334765\pi\)
0.496100 + 0.868265i \(0.334765\pi\)
\(402\) 0 0
\(403\) 11.0051 0.548201
\(404\) −2.28391 −0.113629
\(405\) 0 0
\(406\) −1.18347 −0.0587347
\(407\) −18.3282 −0.908495
\(408\) 0 0
\(409\) −14.3957 −0.711822 −0.355911 0.934520i \(-0.615829\pi\)
−0.355911 + 0.934520i \(0.615829\pi\)
\(410\) −29.5409 −1.45892
\(411\) 0 0
\(412\) 2.05672 0.101327
\(413\) 1.13161 0.0556831
\(414\) 0 0
\(415\) −11.2633 −0.552893
\(416\) 1.36216 0.0667854
\(417\) 0 0
\(418\) −8.34408 −0.408122
\(419\) 37.9245 1.85273 0.926367 0.376623i \(-0.122915\pi\)
0.926367 + 0.376623i \(0.122915\pi\)
\(420\) 0 0
\(421\) −25.7114 −1.25310 −0.626548 0.779382i \(-0.715533\pi\)
−0.626548 + 0.779382i \(0.715533\pi\)
\(422\) 26.8642 1.30773
\(423\) 0 0
\(424\) −19.5770 −0.950745
\(425\) −100.684 −4.88390
\(426\) 0 0
\(427\) −12.9755 −0.627930
\(428\) −2.07265 −0.100185
\(429\) 0 0
\(430\) −71.6480 −3.45517
\(431\) −4.24671 −0.204557 −0.102278 0.994756i \(-0.532613\pi\)
−0.102278 + 0.994756i \(0.532613\pi\)
\(432\) 0 0
\(433\) −14.0188 −0.673699 −0.336849 0.941559i \(-0.609361\pi\)
−0.336849 + 0.941559i \(0.609361\pi\)
\(434\) 8.13076 0.390289
\(435\) 0 0
\(436\) 0.999711 0.0478775
\(437\) −1.89212 −0.0905121
\(438\) 0 0
\(439\) 3.32357 0.158626 0.0793128 0.996850i \(-0.474727\pi\)
0.0793128 + 0.996850i \(0.474727\pi\)
\(440\) −39.8398 −1.89929
\(441\) 0 0
\(442\) −17.3443 −0.824987
\(443\) 15.7380 0.747735 0.373868 0.927482i \(-0.378031\pi\)
0.373868 + 0.927482i \(0.378031\pi\)
\(444\) 0 0
\(445\) −46.9388 −2.22511
\(446\) −9.12409 −0.432038
\(447\) 0 0
\(448\) 7.40453 0.349831
\(449\) −19.6901 −0.929232 −0.464616 0.885512i \(-0.653808\pi\)
−0.464616 + 0.885512i \(0.653808\pi\)
\(450\) 0 0
\(451\) −16.7695 −0.789646
\(452\) −0.659781 −0.0310335
\(453\) 0 0
\(454\) −4.49994 −0.211193
\(455\) −5.85576 −0.274522
\(456\) 0 0
\(457\) 3.06929 0.143576 0.0717878 0.997420i \(-0.477130\pi\)
0.0717878 + 0.997420i \(0.477130\pi\)
\(458\) 31.1775 1.45683
\(459\) 0 0
\(460\) −0.632848 −0.0295067
\(461\) 28.8928 1.34567 0.672836 0.739792i \(-0.265076\pi\)
0.672836 + 0.739792i \(0.265076\pi\)
\(462\) 0 0
\(463\) −0.754421 −0.0350609 −0.0175305 0.999846i \(-0.505580\pi\)
−0.0175305 + 0.999846i \(0.505580\pi\)
\(464\) −3.67599 −0.170654
\(465\) 0 0
\(466\) 20.4415 0.946936
\(467\) 32.5794 1.50759 0.753796 0.657108i \(-0.228220\pi\)
0.753796 + 0.657108i \(0.228220\pi\)
\(468\) 0 0
\(469\) −0.0561493 −0.00259273
\(470\) −24.2050 −1.11649
\(471\) 0 0
\(472\) 3.80303 0.175048
\(473\) −40.6726 −1.87013
\(474\) 0 0
\(475\) −23.9265 −1.09782
\(476\) 1.04391 0.0478475
\(477\) 0 0
\(478\) 5.13234 0.234748
\(479\) −38.6620 −1.76651 −0.883255 0.468893i \(-0.844653\pi\)
−0.883255 + 0.468893i \(0.844653\pi\)
\(480\) 0 0
\(481\) −9.05351 −0.412805
\(482\) −21.6606 −0.986615
\(483\) 0 0
\(484\) 0.0729429 0.00331559
\(485\) 6.88354 0.312565
\(486\) 0 0
\(487\) 12.2269 0.554051 0.277026 0.960862i \(-0.410651\pi\)
0.277026 + 0.960862i \(0.410651\pi\)
\(488\) −43.6070 −1.97400
\(489\) 0 0
\(490\) 35.6610 1.61100
\(491\) −13.6997 −0.618258 −0.309129 0.951020i \(-0.600037\pi\)
−0.309129 + 0.951020i \(0.600037\pi\)
\(492\) 0 0
\(493\) −7.96215 −0.358597
\(494\) −4.12169 −0.185444
\(495\) 0 0
\(496\) 25.2550 1.13398
\(497\) −6.44201 −0.288963
\(498\) 0 0
\(499\) −4.31795 −0.193298 −0.0966489 0.995319i \(-0.530812\pi\)
−0.0966489 + 0.995319i \(0.530812\pi\)
\(500\) −4.83835 −0.216378
\(501\) 0 0
\(502\) −28.1345 −1.25570
\(503\) −25.5037 −1.13716 −0.568578 0.822629i \(-0.692506\pi\)
−0.568578 + 0.822629i \(0.692506\pi\)
\(504\) 0 0
\(505\) 63.6810 2.83377
\(506\) 4.40992 0.196045
\(507\) 0 0
\(508\) 1.36189 0.0604239
\(509\) −11.1100 −0.492444 −0.246222 0.969213i \(-0.579189\pi\)
−0.246222 + 0.969213i \(0.579189\pi\)
\(510\) 0 0
\(511\) −4.32314 −0.191244
\(512\) 24.6282 1.08842
\(513\) 0 0
\(514\) 0.888664 0.0391973
\(515\) −57.3465 −2.52699
\(516\) 0 0
\(517\) −13.7405 −0.604307
\(518\) −6.68892 −0.293894
\(519\) 0 0
\(520\) −19.6795 −0.863003
\(521\) 15.0317 0.658550 0.329275 0.944234i \(-0.393196\pi\)
0.329275 + 0.944234i \(0.393196\pi\)
\(522\) 0 0
\(523\) 39.8498 1.74251 0.871255 0.490830i \(-0.163307\pi\)
0.871255 + 0.490830i \(0.163307\pi\)
\(524\) 0.491147 0.0214559
\(525\) 0 0
\(526\) 16.7628 0.730894
\(527\) 54.7020 2.38286
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 38.2377 1.66094
\(531\) 0 0
\(532\) 0.248073 0.0107553
\(533\) −8.28357 −0.358801
\(534\) 0 0
\(535\) 57.7907 2.49851
\(536\) −0.188702 −0.00815066
\(537\) 0 0
\(538\) 16.6182 0.716460
\(539\) 20.2437 0.871959
\(540\) 0 0
\(541\) 23.8204 1.02412 0.512059 0.858950i \(-0.328883\pi\)
0.512059 + 0.858950i \(0.328883\pi\)
\(542\) 34.9548 1.50144
\(543\) 0 0
\(544\) 6.77079 0.290295
\(545\) −27.8744 −1.19401
\(546\) 0 0
\(547\) −6.98119 −0.298494 −0.149247 0.988800i \(-0.547685\pi\)
−0.149247 + 0.988800i \(0.547685\pi\)
\(548\) 2.34928 0.100356
\(549\) 0 0
\(550\) 55.7651 2.37783
\(551\) −1.89212 −0.0806068
\(552\) 0 0
\(553\) −2.86167 −0.121691
\(554\) 42.2543 1.79521
\(555\) 0 0
\(556\) −1.39775 −0.0592776
\(557\) 26.5781 1.12615 0.563074 0.826406i \(-0.309618\pi\)
0.563074 + 0.826406i \(0.309618\pi\)
\(558\) 0 0
\(559\) −20.0909 −0.849753
\(560\) −13.4381 −0.567865
\(561\) 0 0
\(562\) −20.5766 −0.867973
\(563\) 12.0275 0.506898 0.253449 0.967349i \(-0.418435\pi\)
0.253449 + 0.967349i \(0.418435\pi\)
\(564\) 0 0
\(565\) 18.3963 0.773940
\(566\) −15.3524 −0.645308
\(567\) 0 0
\(568\) −21.6497 −0.908402
\(569\) 15.0935 0.632752 0.316376 0.948634i \(-0.397534\pi\)
0.316376 + 0.948634i \(0.397534\pi\)
\(570\) 0 0
\(571\) −31.3282 −1.31105 −0.655523 0.755176i \(-0.727552\pi\)
−0.655523 + 0.755176i \(0.727552\pi\)
\(572\) −0.782572 −0.0327210
\(573\) 0 0
\(574\) −6.12007 −0.255447
\(575\) 12.6454 0.527348
\(576\) 0 0
\(577\) −13.9233 −0.579637 −0.289818 0.957082i \(-0.593595\pi\)
−0.289818 + 0.957082i \(0.593595\pi\)
\(578\) −63.0939 −2.62436
\(579\) 0 0
\(580\) −0.632848 −0.0262776
\(581\) −2.33345 −0.0968079
\(582\) 0 0
\(583\) 21.7065 0.898989
\(584\) −14.5288 −0.601206
\(585\) 0 0
\(586\) 21.3509 0.881997
\(587\) 33.5235 1.38366 0.691831 0.722060i \(-0.256804\pi\)
0.691831 + 0.722060i \(0.256804\pi\)
\(588\) 0 0
\(589\) 12.9993 0.535628
\(590\) −7.42803 −0.305807
\(591\) 0 0
\(592\) −20.7765 −0.853910
\(593\) −5.89456 −0.242061 −0.121030 0.992649i \(-0.538620\pi\)
−0.121030 + 0.992649i \(0.538620\pi\)
\(594\) 0 0
\(595\) −29.1068 −1.19326
\(596\) −1.04317 −0.0427301
\(597\) 0 0
\(598\) 2.17835 0.0890794
\(599\) −33.5549 −1.37101 −0.685507 0.728066i \(-0.740420\pi\)
−0.685507 + 0.728066i \(0.740420\pi\)
\(600\) 0 0
\(601\) −29.2001 −1.19110 −0.595549 0.803319i \(-0.703065\pi\)
−0.595549 + 0.803319i \(0.703065\pi\)
\(602\) −14.8435 −0.604978
\(603\) 0 0
\(604\) 3.31534 0.134899
\(605\) −2.03383 −0.0826870
\(606\) 0 0
\(607\) −47.1693 −1.91454 −0.957272 0.289188i \(-0.906615\pi\)
−0.957272 + 0.289188i \(0.906615\pi\)
\(608\) 1.60900 0.0652537
\(609\) 0 0
\(610\) 85.1728 3.44854
\(611\) −6.78734 −0.274587
\(612\) 0 0
\(613\) 42.5400 1.71818 0.859088 0.511829i \(-0.171032\pi\)
0.859088 + 0.511829i \(0.171032\pi\)
\(614\) −31.6496 −1.27727
\(615\) 0 0
\(616\) −8.25373 −0.332552
\(617\) 44.3717 1.78634 0.893169 0.449722i \(-0.148477\pi\)
0.893169 + 0.449722i \(0.148477\pi\)
\(618\) 0 0
\(619\) −18.8365 −0.757102 −0.378551 0.925580i \(-0.623578\pi\)
−0.378551 + 0.925580i \(0.623578\pi\)
\(620\) 4.34783 0.174613
\(621\) 0 0
\(622\) 5.55613 0.222780
\(623\) −9.72447 −0.389603
\(624\) 0 0
\(625\) 71.6785 2.86714
\(626\) 27.0458 1.08097
\(627\) 0 0
\(628\) 3.10310 0.123827
\(629\) −45.0016 −1.79433
\(630\) 0 0
\(631\) −37.2650 −1.48350 −0.741749 0.670678i \(-0.766003\pi\)
−0.741749 + 0.670678i \(0.766003\pi\)
\(632\) −9.61725 −0.382554
\(633\) 0 0
\(634\) 35.8337 1.42314
\(635\) −37.9728 −1.50690
\(636\) 0 0
\(637\) 9.99972 0.396203
\(638\) 4.40992 0.174590
\(639\) 0 0
\(640\) −41.4599 −1.63885
\(641\) −8.03569 −0.317391 −0.158695 0.987328i \(-0.550729\pi\)
−0.158695 + 0.987328i \(0.550729\pi\)
\(642\) 0 0
\(643\) −39.4899 −1.55733 −0.778664 0.627441i \(-0.784103\pi\)
−0.778664 + 0.627441i \(0.784103\pi\)
\(644\) −0.131109 −0.00516642
\(645\) 0 0
\(646\) −20.4874 −0.806066
\(647\) −3.52753 −0.138681 −0.0693407 0.997593i \(-0.522090\pi\)
−0.0693407 + 0.997593i \(0.522090\pi\)
\(648\) 0 0
\(649\) −4.21669 −0.165519
\(650\) 27.5461 1.08045
\(651\) 0 0
\(652\) −1.30360 −0.0510527
\(653\) −30.9353 −1.21059 −0.605295 0.796001i \(-0.706945\pi\)
−0.605295 + 0.796001i \(0.706945\pi\)
\(654\) 0 0
\(655\) −13.6944 −0.535085
\(656\) −19.0096 −0.742201
\(657\) 0 0
\(658\) −5.01463 −0.195491
\(659\) 35.1637 1.36978 0.684891 0.728646i \(-0.259850\pi\)
0.684891 + 0.728646i \(0.259850\pi\)
\(660\) 0 0
\(661\) 18.4718 0.718468 0.359234 0.933248i \(-0.383038\pi\)
0.359234 + 0.933248i \(0.383038\pi\)
\(662\) −8.48905 −0.329936
\(663\) 0 0
\(664\) −7.84205 −0.304331
\(665\) −6.91690 −0.268226
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −0.877867 −0.0339657
\(669\) 0 0
\(670\) 0.368570 0.0142391
\(671\) 48.3502 1.86654
\(672\) 0 0
\(673\) 37.6630 1.45180 0.725902 0.687798i \(-0.241423\pi\)
0.725902 + 0.687798i \(0.241423\pi\)
\(674\) −28.1534 −1.08443
\(675\) 0 0
\(676\) 1.57195 0.0604597
\(677\) −49.9213 −1.91863 −0.959315 0.282338i \(-0.908890\pi\)
−0.959315 + 0.282338i \(0.908890\pi\)
\(678\) 0 0
\(679\) 1.42608 0.0547281
\(680\) −97.8195 −3.75120
\(681\) 0 0
\(682\) −30.2973 −1.16014
\(683\) −14.1168 −0.540165 −0.270083 0.962837i \(-0.587051\pi\)
−0.270083 + 0.962837i \(0.587051\pi\)
\(684\) 0 0
\(685\) −65.5038 −2.50277
\(686\) 15.6723 0.598371
\(687\) 0 0
\(688\) −46.1057 −1.75776
\(689\) 10.7223 0.408485
\(690\) 0 0
\(691\) 42.4830 1.61613 0.808064 0.589095i \(-0.200516\pi\)
0.808064 + 0.589095i \(0.200516\pi\)
\(692\) 0.666047 0.0253193
\(693\) 0 0
\(694\) −3.56029 −0.135147
\(695\) 38.9726 1.47832
\(696\) 0 0
\(697\) −41.1746 −1.55960
\(698\) 30.5896 1.15783
\(699\) 0 0
\(700\) −1.65792 −0.0626636
\(701\) 4.16302 0.157235 0.0786175 0.996905i \(-0.474949\pi\)
0.0786175 + 0.996905i \(0.474949\pi\)
\(702\) 0 0
\(703\) −10.6941 −0.403337
\(704\) −27.5912 −1.03988
\(705\) 0 0
\(706\) 27.3664 1.02995
\(707\) 13.1930 0.496174
\(708\) 0 0
\(709\) 22.4150 0.841812 0.420906 0.907104i \(-0.361712\pi\)
0.420906 + 0.907104i \(0.361712\pi\)
\(710\) 42.2860 1.58697
\(711\) 0 0
\(712\) −32.6811 −1.22478
\(713\) −6.87026 −0.257293
\(714\) 0 0
\(715\) 21.8201 0.816024
\(716\) −2.86007 −0.106886
\(717\) 0 0
\(718\) −12.3469 −0.460782
\(719\) 6.23578 0.232555 0.116278 0.993217i \(-0.462904\pi\)
0.116278 + 0.993217i \(0.462904\pi\)
\(720\) 0 0
\(721\) −11.8807 −0.442459
\(722\) 20.9696 0.780408
\(723\) 0 0
\(724\) 1.38614 0.0515156
\(725\) 12.6454 0.469637
\(726\) 0 0
\(727\) 2.68791 0.0996891 0.0498446 0.998757i \(-0.484127\pi\)
0.0498446 + 0.998757i \(0.484127\pi\)
\(728\) −4.07706 −0.151106
\(729\) 0 0
\(730\) 28.3775 1.05030
\(731\) −99.8642 −3.69361
\(732\) 0 0
\(733\) −10.3347 −0.381720 −0.190860 0.981617i \(-0.561128\pi\)
−0.190860 + 0.981617i \(0.561128\pi\)
\(734\) −20.1616 −0.744178
\(735\) 0 0
\(736\) −0.850373 −0.0313452
\(737\) 0.209227 0.00770697
\(738\) 0 0
\(739\) −7.45273 −0.274153 −0.137077 0.990560i \(-0.543771\pi\)
−0.137077 + 0.990560i \(0.543771\pi\)
\(740\) −3.57682 −0.131487
\(741\) 0 0
\(742\) 7.92182 0.290819
\(743\) 17.7690 0.651882 0.325941 0.945390i \(-0.394319\pi\)
0.325941 + 0.945390i \(0.394319\pi\)
\(744\) 0 0
\(745\) 29.0863 1.06564
\(746\) −35.3525 −1.29435
\(747\) 0 0
\(748\) −3.88987 −0.142228
\(749\) 11.9727 0.437473
\(750\) 0 0
\(751\) 20.0716 0.732424 0.366212 0.930531i \(-0.380654\pi\)
0.366212 + 0.930531i \(0.380654\pi\)
\(752\) −15.5760 −0.567998
\(753\) 0 0
\(754\) 2.17835 0.0793309
\(755\) −92.4400 −3.36424
\(756\) 0 0
\(757\) −37.4069 −1.35958 −0.679788 0.733409i \(-0.737928\pi\)
−0.679788 + 0.733409i \(0.737928\pi\)
\(758\) 5.54049 0.201240
\(759\) 0 0
\(760\) −23.2457 −0.843210
\(761\) 26.5113 0.961033 0.480516 0.876986i \(-0.340449\pi\)
0.480516 + 0.876986i \(0.340449\pi\)
\(762\) 0 0
\(763\) −5.77484 −0.209063
\(764\) 3.32249 0.120203
\(765\) 0 0
\(766\) 11.0861 0.400556
\(767\) −2.08290 −0.0752092
\(768\) 0 0
\(769\) 25.5111 0.919955 0.459978 0.887931i \(-0.347857\pi\)
0.459978 + 0.887931i \(0.347857\pi\)
\(770\) 16.1211 0.580964
\(771\) 0 0
\(772\) 0.284138 0.0102264
\(773\) 0.0409421 0.00147259 0.000736293 1.00000i \(-0.499766\pi\)
0.000736293 1.00000i \(0.499766\pi\)
\(774\) 0 0
\(775\) −86.8770 −3.12071
\(776\) 4.79265 0.172046
\(777\) 0 0
\(778\) 8.81562 0.316055
\(779\) −9.78467 −0.350572
\(780\) 0 0
\(781\) 24.0046 0.858951
\(782\) 10.8278 0.387200
\(783\) 0 0
\(784\) 22.9479 0.819569
\(785\) −86.5223 −3.08811
\(786\) 0 0
\(787\) 33.4211 1.19133 0.595666 0.803232i \(-0.296888\pi\)
0.595666 + 0.803232i \(0.296888\pi\)
\(788\) −1.48960 −0.0530648
\(789\) 0 0
\(790\) 18.7843 0.668316
\(791\) 3.81123 0.135512
\(792\) 0 0
\(793\) 23.8834 0.848123
\(794\) −31.5222 −1.11868
\(795\) 0 0
\(796\) 0.124247 0.00440383
\(797\) −47.4657 −1.68132 −0.840661 0.541562i \(-0.817833\pi\)
−0.840661 + 0.541562i \(0.817833\pi\)
\(798\) 0 0
\(799\) −33.7374 −1.19354
\(800\) −10.7533 −0.380186
\(801\) 0 0
\(802\) −27.0197 −0.954099
\(803\) 16.1091 0.568479
\(804\) 0 0
\(805\) 3.65565 0.128845
\(806\) −14.9658 −0.527149
\(807\) 0 0
\(808\) 44.3378 1.55980
\(809\) 45.6804 1.60604 0.803019 0.595953i \(-0.203225\pi\)
0.803019 + 0.595953i \(0.203225\pi\)
\(810\) 0 0
\(811\) 12.6623 0.444633 0.222316 0.974975i \(-0.428638\pi\)
0.222316 + 0.974975i \(0.428638\pi\)
\(812\) −0.131109 −0.00460103
\(813\) 0 0
\(814\) 24.9246 0.873608
\(815\) 36.3475 1.27320
\(816\) 0 0
\(817\) −23.7316 −0.830264
\(818\) 19.5768 0.684488
\(819\) 0 0
\(820\) −3.27264 −0.114285
\(821\) 15.1497 0.528727 0.264363 0.964423i \(-0.414838\pi\)
0.264363 + 0.964423i \(0.414838\pi\)
\(822\) 0 0
\(823\) −33.7831 −1.17761 −0.588803 0.808276i \(-0.700401\pi\)
−0.588803 + 0.808276i \(0.700401\pi\)
\(824\) −39.9274 −1.39094
\(825\) 0 0
\(826\) −1.53889 −0.0535448
\(827\) 35.9126 1.24880 0.624402 0.781103i \(-0.285343\pi\)
0.624402 + 0.781103i \(0.285343\pi\)
\(828\) 0 0
\(829\) −23.8358 −0.827853 −0.413927 0.910310i \(-0.635843\pi\)
−0.413927 + 0.910310i \(0.635843\pi\)
\(830\) 15.3170 0.531661
\(831\) 0 0
\(832\) −13.6291 −0.472504
\(833\) 49.7049 1.72217
\(834\) 0 0
\(835\) 24.4771 0.847065
\(836\) −0.924385 −0.0319705
\(837\) 0 0
\(838\) −51.5738 −1.78159
\(839\) 39.5267 1.36461 0.682307 0.731066i \(-0.260977\pi\)
0.682307 + 0.731066i \(0.260977\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 34.9651 1.20498
\(843\) 0 0
\(844\) 2.97611 0.102442
\(845\) −43.8299 −1.50780
\(846\) 0 0
\(847\) −0.421355 −0.0144779
\(848\) 24.6060 0.844975
\(849\) 0 0
\(850\) 136.921 4.69636
\(851\) 5.65195 0.193746
\(852\) 0 0
\(853\) −10.7801 −0.369105 −0.184552 0.982823i \(-0.559084\pi\)
−0.184552 + 0.982823i \(0.559084\pi\)
\(854\) 17.6455 0.603817
\(855\) 0 0
\(856\) 40.2367 1.37526
\(857\) 34.2748 1.17081 0.585403 0.810743i \(-0.300936\pi\)
0.585403 + 0.810743i \(0.300936\pi\)
\(858\) 0 0
\(859\) −5.67545 −0.193644 −0.0968220 0.995302i \(-0.530868\pi\)
−0.0968220 + 0.995302i \(0.530868\pi\)
\(860\) −7.93741 −0.270664
\(861\) 0 0
\(862\) 5.77513 0.196702
\(863\) −2.77819 −0.0945708 −0.0472854 0.998881i \(-0.515057\pi\)
−0.0472854 + 0.998881i \(0.515057\pi\)
\(864\) 0 0
\(865\) −18.5711 −0.631435
\(866\) 19.0642 0.647828
\(867\) 0 0
\(868\) 0.900753 0.0305736
\(869\) 10.6633 0.361729
\(870\) 0 0
\(871\) 0.103351 0.00350191
\(872\) −19.4075 −0.657222
\(873\) 0 0
\(874\) 2.57310 0.0870364
\(875\) 27.9488 0.944841
\(876\) 0 0
\(877\) 28.3972 0.958906 0.479453 0.877567i \(-0.340835\pi\)
0.479453 + 0.877567i \(0.340835\pi\)
\(878\) −4.51975 −0.152534
\(879\) 0 0
\(880\) 50.0739 1.68799
\(881\) −32.6430 −1.09977 −0.549886 0.835240i \(-0.685329\pi\)
−0.549886 + 0.835240i \(0.685329\pi\)
\(882\) 0 0
\(883\) −32.7949 −1.10363 −0.551817 0.833965i \(-0.686065\pi\)
−0.551817 + 0.833965i \(0.686065\pi\)
\(884\) −1.92147 −0.0646259
\(885\) 0 0
\(886\) −21.4022 −0.719022
\(887\) −21.1685 −0.710769 −0.355384 0.934720i \(-0.615650\pi\)
−0.355384 + 0.934720i \(0.615650\pi\)
\(888\) 0 0
\(889\) −7.86694 −0.263849
\(890\) 63.8324 2.13967
\(891\) 0 0
\(892\) −1.01080 −0.0338440
\(893\) −8.01731 −0.268289
\(894\) 0 0
\(895\) 79.7459 2.66561
\(896\) −8.58937 −0.286951
\(897\) 0 0
\(898\) 26.7766 0.893548
\(899\) −6.87026 −0.229136
\(900\) 0 0
\(901\) 53.2963 1.77556
\(902\) 22.8050 0.759322
\(903\) 0 0
\(904\) 12.8084 0.426002
\(905\) −38.6491 −1.28474
\(906\) 0 0
\(907\) −46.1813 −1.53343 −0.766713 0.641990i \(-0.778109\pi\)
−0.766713 + 0.641990i \(0.778109\pi\)
\(908\) −0.498518 −0.0165439
\(909\) 0 0
\(910\) 7.96328 0.263980
\(911\) 13.8496 0.458857 0.229429 0.973325i \(-0.426314\pi\)
0.229429 + 0.973325i \(0.426314\pi\)
\(912\) 0 0
\(913\) 8.69504 0.287764
\(914\) −4.17395 −0.138062
\(915\) 0 0
\(916\) 3.45395 0.114122
\(917\) −2.83711 −0.0936897
\(918\) 0 0
\(919\) 31.9148 1.05277 0.526386 0.850246i \(-0.323547\pi\)
0.526386 + 0.850246i \(0.323547\pi\)
\(920\) 12.2856 0.405043
\(921\) 0 0
\(922\) −39.2915 −1.29400
\(923\) 11.8574 0.390293
\(924\) 0 0
\(925\) 71.4710 2.34995
\(926\) 1.02594 0.0337146
\(927\) 0 0
\(928\) −0.850373 −0.0279149
\(929\) −35.3248 −1.15897 −0.579485 0.814983i \(-0.696746\pi\)
−0.579485 + 0.814983i \(0.696746\pi\)
\(930\) 0 0
\(931\) 11.8118 0.387116
\(932\) 2.26458 0.0741789
\(933\) 0 0
\(934\) −44.3049 −1.44970
\(935\) 108.459 3.54700
\(936\) 0 0
\(937\) 9.47258 0.309456 0.154728 0.987957i \(-0.450550\pi\)
0.154728 + 0.987957i \(0.450550\pi\)
\(938\) 0.0763578 0.00249317
\(939\) 0 0
\(940\) −2.68151 −0.0874613
\(941\) −36.1900 −1.17976 −0.589880 0.807491i \(-0.700825\pi\)
−0.589880 + 0.807491i \(0.700825\pi\)
\(942\) 0 0
\(943\) 5.17129 0.168400
\(944\) −4.77996 −0.155574
\(945\) 0 0
\(946\) 55.3109 1.79831
\(947\) −20.6534 −0.671146 −0.335573 0.942014i \(-0.608930\pi\)
−0.335573 + 0.942014i \(0.608930\pi\)
\(948\) 0 0
\(949\) 7.95736 0.258307
\(950\) 32.5378 1.05567
\(951\) 0 0
\(952\) −20.2656 −0.656811
\(953\) −10.0858 −0.326710 −0.163355 0.986567i \(-0.552232\pi\)
−0.163355 + 0.986567i \(0.552232\pi\)
\(954\) 0 0
\(955\) −92.6392 −2.99774
\(956\) 0.568578 0.0183891
\(957\) 0 0
\(958\) 52.5766 1.69867
\(959\) −13.5706 −0.438219
\(960\) 0 0
\(961\) 16.2005 0.522597
\(962\) 12.3119 0.396952
\(963\) 0 0
\(964\) −2.39964 −0.0772872
\(965\) −7.92248 −0.255034
\(966\) 0 0
\(967\) 38.0671 1.22416 0.612078 0.790798i \(-0.290334\pi\)
0.612078 + 0.790798i \(0.290334\pi\)
\(968\) −1.41605 −0.0455136
\(969\) 0 0
\(970\) −9.36096 −0.300562
\(971\) 32.0663 1.02906 0.514528 0.857473i \(-0.327967\pi\)
0.514528 + 0.857473i \(0.327967\pi\)
\(972\) 0 0
\(973\) 8.07408 0.258843
\(974\) −16.6274 −0.532775
\(975\) 0 0
\(976\) 54.8089 1.75439
\(977\) 10.9317 0.349737 0.174868 0.984592i \(-0.444050\pi\)
0.174868 + 0.984592i \(0.444050\pi\)
\(978\) 0 0
\(979\) 36.2359 1.15810
\(980\) 3.95064 0.126199
\(981\) 0 0
\(982\) 18.6303 0.594516
\(983\) 46.5709 1.48538 0.742690 0.669635i \(-0.233550\pi\)
0.742690 + 0.669635i \(0.233550\pi\)
\(984\) 0 0
\(985\) 41.5338 1.32338
\(986\) 10.8278 0.344827
\(987\) 0 0
\(988\) −0.456615 −0.0145269
\(989\) 12.5424 0.398824
\(990\) 0 0
\(991\) −4.69862 −0.149257 −0.0746283 0.997211i \(-0.523777\pi\)
−0.0746283 + 0.997211i \(0.523777\pi\)
\(992\) 5.84228 0.185493
\(993\) 0 0
\(994\) 8.76053 0.277867
\(995\) −3.46433 −0.109827
\(996\) 0 0
\(997\) −12.7393 −0.403458 −0.201729 0.979441i \(-0.564656\pi\)
−0.201729 + 0.979441i \(0.564656\pi\)
\(998\) 5.87200 0.185875
\(999\) 0 0
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 \(a_p\))