Properties

Label 8018.2.a.j.1.10
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} -1.79399 q^{10} -1.56812 q^{11} -2.00763 q^{12} -4.34066 q^{13} -2.43862 q^{14} +3.60167 q^{15} +1.00000 q^{16} -2.98642 q^{17} +1.03060 q^{18} -1.00000 q^{19} -1.79399 q^{20} +4.89585 q^{21} -1.56812 q^{22} +1.92268 q^{23} -2.00763 q^{24} -1.78161 q^{25} -4.34066 q^{26} +3.95384 q^{27} -2.43862 q^{28} +0.562491 q^{29} +3.60167 q^{30} -4.85429 q^{31} +1.00000 q^{32} +3.14822 q^{33} -2.98642 q^{34} +4.37484 q^{35} +1.03060 q^{36} -3.93975 q^{37} -1.00000 q^{38} +8.71445 q^{39} -1.79399 q^{40} -11.0744 q^{41} +4.89585 q^{42} -8.43678 q^{43} -1.56812 q^{44} -1.84888 q^{45} +1.92268 q^{46} -6.03573 q^{47} -2.00763 q^{48} -1.05316 q^{49} -1.78161 q^{50} +5.99564 q^{51} -4.34066 q^{52} -4.46382 q^{53} +3.95384 q^{54} +2.81319 q^{55} -2.43862 q^{56} +2.00763 q^{57} +0.562491 q^{58} +14.3798 q^{59} +3.60167 q^{60} -12.9806 q^{61} -4.85429 q^{62} -2.51323 q^{63} +1.00000 q^{64} +7.78708 q^{65} +3.14822 q^{66} -15.9394 q^{67} -2.98642 q^{68} -3.86004 q^{69} +4.37484 q^{70} +8.05400 q^{71} +1.03060 q^{72} +2.43690 q^{73} -3.93975 q^{74} +3.57683 q^{75} -1.00000 q^{76} +3.82405 q^{77} +8.71445 q^{78} -2.99978 q^{79} -1.79399 q^{80} -11.0297 q^{81} -11.0744 q^{82} +9.69270 q^{83} +4.89585 q^{84} +5.35760 q^{85} -8.43678 q^{86} -1.12928 q^{87} -1.56812 q^{88} -11.2633 q^{89} -1.84888 q^{90} +10.5852 q^{91} +1.92268 q^{92} +9.74564 q^{93} -6.03573 q^{94} +1.79399 q^{95} -2.00763 q^{96} +3.44243 q^{97} -1.05316 q^{98} -1.61610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.00763 −1.15911 −0.579554 0.814934i \(-0.696773\pi\)
−0.579554 + 0.814934i \(0.696773\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.79399 −0.802295 −0.401147 0.916013i \(-0.631389\pi\)
−0.401147 + 0.916013i \(0.631389\pi\)
\(6\) −2.00763 −0.819614
\(7\) −2.43862 −0.921710 −0.460855 0.887475i \(-0.652457\pi\)
−0.460855 + 0.887475i \(0.652457\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.03060 0.343533
\(10\) −1.79399 −0.567308
\(11\) −1.56812 −0.472807 −0.236403 0.971655i \(-0.575969\pi\)
−0.236403 + 0.971655i \(0.575969\pi\)
\(12\) −2.00763 −0.579554
\(13\) −4.34066 −1.20388 −0.601941 0.798541i \(-0.705606\pi\)
−0.601941 + 0.798541i \(0.705606\pi\)
\(14\) −2.43862 −0.651747
\(15\) 3.60167 0.929947
\(16\) 1.00000 0.250000
\(17\) −2.98642 −0.724313 −0.362157 0.932117i \(-0.617959\pi\)
−0.362157 + 0.932117i \(0.617959\pi\)
\(18\) 1.03060 0.242914
\(19\) −1.00000 −0.229416
\(20\) −1.79399 −0.401147
\(21\) 4.89585 1.06836
\(22\) −1.56812 −0.334325
\(23\) 1.92268 0.400906 0.200453 0.979703i \(-0.435759\pi\)
0.200453 + 0.979703i \(0.435759\pi\)
\(24\) −2.00763 −0.409807
\(25\) −1.78161 −0.356323
\(26\) −4.34066 −0.851273
\(27\) 3.95384 0.760917
\(28\) −2.43862 −0.460855
\(29\) 0.562491 0.104452 0.0522260 0.998635i \(-0.483368\pi\)
0.0522260 + 0.998635i \(0.483368\pi\)
\(30\) 3.60167 0.657572
\(31\) −4.85429 −0.871856 −0.435928 0.899982i \(-0.643580\pi\)
−0.435928 + 0.899982i \(0.643580\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.14822 0.548034
\(34\) −2.98642 −0.512167
\(35\) 4.37484 0.739483
\(36\) 1.03060 0.171766
\(37\) −3.93975 −0.647691 −0.323846 0.946110i \(-0.604976\pi\)
−0.323846 + 0.946110i \(0.604976\pi\)
\(38\) −1.00000 −0.162221
\(39\) 8.71445 1.39543
\(40\) −1.79399 −0.283654
\(41\) −11.0744 −1.72954 −0.864768 0.502172i \(-0.832534\pi\)
−0.864768 + 0.502172i \(0.832534\pi\)
\(42\) 4.89585 0.755446
\(43\) −8.43678 −1.28660 −0.643298 0.765616i \(-0.722434\pi\)
−0.643298 + 0.765616i \(0.722434\pi\)
\(44\) −1.56812 −0.236403
\(45\) −1.84888 −0.275615
\(46\) 1.92268 0.283484
\(47\) −6.03573 −0.880401 −0.440201 0.897899i \(-0.645093\pi\)
−0.440201 + 0.897899i \(0.645093\pi\)
\(48\) −2.00763 −0.289777
\(49\) −1.05316 −0.150451
\(50\) −1.78161 −0.251958
\(51\) 5.99564 0.839558
\(52\) −4.34066 −0.601941
\(53\) −4.46382 −0.613153 −0.306577 0.951846i \(-0.599184\pi\)
−0.306577 + 0.951846i \(0.599184\pi\)
\(54\) 3.95384 0.538049
\(55\) 2.81319 0.379331
\(56\) −2.43862 −0.325874
\(57\) 2.00763 0.265918
\(58\) 0.562491 0.0738587
\(59\) 14.3798 1.87209 0.936043 0.351886i \(-0.114459\pi\)
0.936043 + 0.351886i \(0.114459\pi\)
\(60\) 3.60167 0.464974
\(61\) −12.9806 −1.66200 −0.830998 0.556275i \(-0.812230\pi\)
−0.830998 + 0.556275i \(0.812230\pi\)
\(62\) −4.85429 −0.616495
\(63\) −2.51323 −0.316638
\(64\) 1.00000 0.125000
\(65\) 7.78708 0.965868
\(66\) 3.14822 0.387519
\(67\) −15.9394 −1.94731 −0.973656 0.228020i \(-0.926775\pi\)
−0.973656 + 0.228020i \(0.926775\pi\)
\(68\) −2.98642 −0.362157
\(69\) −3.86004 −0.464694
\(70\) 4.37484 0.522894
\(71\) 8.05400 0.955834 0.477917 0.878405i \(-0.341392\pi\)
0.477917 + 0.878405i \(0.341392\pi\)
\(72\) 1.03060 0.121457
\(73\) 2.43690 0.285217 0.142609 0.989779i \(-0.454451\pi\)
0.142609 + 0.989779i \(0.454451\pi\)
\(74\) −3.93975 −0.457987
\(75\) 3.57683 0.413017
\(76\) −1.00000 −0.114708
\(77\) 3.82405 0.435791
\(78\) 8.71445 0.986718
\(79\) −2.99978 −0.337502 −0.168751 0.985659i \(-0.553973\pi\)
−0.168751 + 0.985659i \(0.553973\pi\)
\(80\) −1.79399 −0.200574
\(81\) −11.0297 −1.22552
\(82\) −11.0744 −1.22297
\(83\) 9.69270 1.06391 0.531956 0.846772i \(-0.321457\pi\)
0.531956 + 0.846772i \(0.321457\pi\)
\(84\) 4.89585 0.534181
\(85\) 5.35760 0.581113
\(86\) −8.43678 −0.909761
\(87\) −1.12928 −0.121071
\(88\) −1.56812 −0.167162
\(89\) −11.2633 −1.19390 −0.596951 0.802277i \(-0.703621\pi\)
−0.596951 + 0.802277i \(0.703621\pi\)
\(90\) −1.84888 −0.194889
\(91\) 10.5852 1.10963
\(92\) 1.92268 0.200453
\(93\) 9.74564 1.01058
\(94\) −6.03573 −0.622538
\(95\) 1.79399 0.184059
\(96\) −2.00763 −0.204903
\(97\) 3.44243 0.349526 0.174763 0.984611i \(-0.444084\pi\)
0.174763 + 0.984611i \(0.444084\pi\)
\(98\) −1.05316 −0.106385
\(99\) −1.61610 −0.162425
\(100\) −1.78161 −0.178161
\(101\) 15.0221 1.49475 0.747376 0.664402i \(-0.231314\pi\)
0.747376 + 0.664402i \(0.231314\pi\)
\(102\) 5.99564 0.593657
\(103\) 1.88560 0.185793 0.0928967 0.995676i \(-0.470387\pi\)
0.0928967 + 0.995676i \(0.470387\pi\)
\(104\) −4.34066 −0.425636
\(105\) −8.78309 −0.857141
\(106\) −4.46382 −0.433565
\(107\) −15.1780 −1.46731 −0.733655 0.679522i \(-0.762187\pi\)
−0.733655 + 0.679522i \(0.762187\pi\)
\(108\) 3.95384 0.380458
\(109\) −6.18520 −0.592434 −0.296217 0.955121i \(-0.595725\pi\)
−0.296217 + 0.955121i \(0.595725\pi\)
\(110\) 2.81319 0.268227
\(111\) 7.90958 0.750744
\(112\) −2.43862 −0.230427
\(113\) 6.58029 0.619022 0.309511 0.950896i \(-0.399835\pi\)
0.309511 + 0.950896i \(0.399835\pi\)
\(114\) 2.00763 0.188032
\(115\) −3.44926 −0.321645
\(116\) 0.562491 0.0522260
\(117\) −4.47347 −0.413573
\(118\) 14.3798 1.32376
\(119\) 7.28273 0.667607
\(120\) 3.60167 0.328786
\(121\) −8.54099 −0.776454
\(122\) −12.9806 −1.17521
\(123\) 22.2334 2.00472
\(124\) −4.85429 −0.435928
\(125\) 12.1661 1.08817
\(126\) −2.51323 −0.223897
\(127\) 5.64488 0.500902 0.250451 0.968129i \(-0.419421\pi\)
0.250451 + 0.968129i \(0.419421\pi\)
\(128\) 1.00000 0.0883883
\(129\) 16.9380 1.49131
\(130\) 7.78708 0.682972
\(131\) −22.2737 −1.94606 −0.973030 0.230679i \(-0.925905\pi\)
−0.973030 + 0.230679i \(0.925905\pi\)
\(132\) 3.14822 0.274017
\(133\) 2.43862 0.211455
\(134\) −15.9394 −1.37696
\(135\) −7.09313 −0.610480
\(136\) −2.98642 −0.256083
\(137\) 16.4778 1.40780 0.703899 0.710301i \(-0.251441\pi\)
0.703899 + 0.710301i \(0.251441\pi\)
\(138\) −3.86004 −0.328588
\(139\) −11.6853 −0.991134 −0.495567 0.868570i \(-0.665040\pi\)
−0.495567 + 0.868570i \(0.665040\pi\)
\(140\) 4.37484 0.369742
\(141\) 12.1175 1.02048
\(142\) 8.05400 0.675877
\(143\) 6.80668 0.569203
\(144\) 1.03060 0.0858832
\(145\) −1.00910 −0.0838013
\(146\) 2.43690 0.201679
\(147\) 2.11435 0.174389
\(148\) −3.93975 −0.323846
\(149\) 8.74140 0.716123 0.358062 0.933698i \(-0.383438\pi\)
0.358062 + 0.933698i \(0.383438\pi\)
\(150\) 3.57683 0.292047
\(151\) 1.07980 0.0878725 0.0439362 0.999034i \(-0.486010\pi\)
0.0439362 + 0.999034i \(0.486010\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −3.07780 −0.248825
\(154\) 3.82405 0.308151
\(155\) 8.70853 0.699486
\(156\) 8.71445 0.697715
\(157\) −2.01582 −0.160880 −0.0804402 0.996759i \(-0.525633\pi\)
−0.0804402 + 0.996759i \(0.525633\pi\)
\(158\) −2.99978 −0.238650
\(159\) 8.96173 0.710711
\(160\) −1.79399 −0.141827
\(161\) −4.68867 −0.369519
\(162\) −11.0297 −0.866572
\(163\) 21.8879 1.71439 0.857197 0.514988i \(-0.172204\pi\)
0.857197 + 0.514988i \(0.172204\pi\)
\(164\) −11.0744 −0.864768
\(165\) −5.64786 −0.439685
\(166\) 9.69270 0.752300
\(167\) −4.09048 −0.316530 −0.158265 0.987397i \(-0.550590\pi\)
−0.158265 + 0.987397i \(0.550590\pi\)
\(168\) 4.89585 0.377723
\(169\) 5.84130 0.449331
\(170\) 5.35760 0.410909
\(171\) −1.03060 −0.0788118
\(172\) −8.43678 −0.643298
\(173\) 8.61177 0.654741 0.327370 0.944896i \(-0.393838\pi\)
0.327370 + 0.944896i \(0.393838\pi\)
\(174\) −1.12928 −0.0856103
\(175\) 4.34467 0.328426
\(176\) −1.56812 −0.118202
\(177\) −28.8693 −2.16995
\(178\) −11.2633 −0.844217
\(179\) 16.8064 1.25617 0.628085 0.778145i \(-0.283839\pi\)
0.628085 + 0.778145i \(0.283839\pi\)
\(180\) −1.84888 −0.137807
\(181\) 6.55162 0.486978 0.243489 0.969904i \(-0.421708\pi\)
0.243489 + 0.969904i \(0.421708\pi\)
\(182\) 10.5852 0.784627
\(183\) 26.0603 1.92643
\(184\) 1.92268 0.141742
\(185\) 7.06786 0.519639
\(186\) 9.74564 0.714585
\(187\) 4.68307 0.342460
\(188\) −6.03573 −0.440201
\(189\) −9.64189 −0.701345
\(190\) 1.79399 0.130149
\(191\) −22.4079 −1.62138 −0.810688 0.585478i \(-0.800907\pi\)
−0.810688 + 0.585478i \(0.800907\pi\)
\(192\) −2.00763 −0.144889
\(193\) 21.0583 1.51581 0.757904 0.652366i \(-0.226224\pi\)
0.757904 + 0.652366i \(0.226224\pi\)
\(194\) 3.44243 0.247152
\(195\) −15.6336 −1.11955
\(196\) −1.05316 −0.0752254
\(197\) 17.7540 1.26492 0.632461 0.774592i \(-0.282045\pi\)
0.632461 + 0.774592i \(0.282045\pi\)
\(198\) −1.61610 −0.114852
\(199\) 10.1854 0.722023 0.361012 0.932561i \(-0.382432\pi\)
0.361012 + 0.932561i \(0.382432\pi\)
\(200\) −1.78161 −0.125979
\(201\) 32.0006 2.25715
\(202\) 15.0221 1.05695
\(203\) −1.37170 −0.0962744
\(204\) 5.99564 0.419779
\(205\) 19.8674 1.38760
\(206\) 1.88560 0.131376
\(207\) 1.98151 0.137724
\(208\) −4.34066 −0.300970
\(209\) 1.56812 0.108469
\(210\) −8.78309 −0.606090
\(211\) −1.00000 −0.0688428
\(212\) −4.46382 −0.306577
\(213\) −16.1695 −1.10792
\(214\) −15.1780 −1.03754
\(215\) 15.1355 1.03223
\(216\) 3.95384 0.269025
\(217\) 11.8377 0.803598
\(218\) −6.18520 −0.418914
\(219\) −4.89240 −0.330598
\(220\) 2.81319 0.189665
\(221\) 12.9630 0.871987
\(222\) 7.90958 0.530856
\(223\) −18.5493 −1.24215 −0.621076 0.783750i \(-0.713304\pi\)
−0.621076 + 0.783750i \(0.713304\pi\)
\(224\) −2.43862 −0.162937
\(225\) −1.83613 −0.122409
\(226\) 6.58029 0.437715
\(227\) −17.7495 −1.17807 −0.589036 0.808107i \(-0.700493\pi\)
−0.589036 + 0.808107i \(0.700493\pi\)
\(228\) 2.00763 0.132959
\(229\) −5.45582 −0.360531 −0.180265 0.983618i \(-0.557696\pi\)
−0.180265 + 0.983618i \(0.557696\pi\)
\(230\) −3.44926 −0.227437
\(231\) −7.67729 −0.505129
\(232\) 0.562491 0.0369294
\(233\) 7.59030 0.497257 0.248629 0.968599i \(-0.420020\pi\)
0.248629 + 0.968599i \(0.420020\pi\)
\(234\) −4.47347 −0.292440
\(235\) 10.8280 0.706341
\(236\) 14.3798 0.936043
\(237\) 6.02247 0.391201
\(238\) 7.28273 0.472069
\(239\) −21.3228 −1.37926 −0.689630 0.724162i \(-0.742227\pi\)
−0.689630 + 0.724162i \(0.742227\pi\)
\(240\) 3.60167 0.232487
\(241\) 0.738320 0.0475594 0.0237797 0.999717i \(-0.492430\pi\)
0.0237797 + 0.999717i \(0.492430\pi\)
\(242\) −8.54099 −0.549036
\(243\) 10.2820 0.659592
\(244\) −12.9806 −0.830998
\(245\) 1.88935 0.120706
\(246\) 22.2334 1.41755
\(247\) 4.34066 0.276189
\(248\) −4.85429 −0.308248
\(249\) −19.4594 −1.23319
\(250\) 12.1661 0.769453
\(251\) −27.1705 −1.71499 −0.857494 0.514494i \(-0.827980\pi\)
−0.857494 + 0.514494i \(0.827980\pi\)
\(252\) −2.51323 −0.158319
\(253\) −3.01500 −0.189551
\(254\) 5.64488 0.354191
\(255\) −10.7561 −0.673573
\(256\) 1.00000 0.0625000
\(257\) 3.47591 0.216821 0.108411 0.994106i \(-0.465424\pi\)
0.108411 + 0.994106i \(0.465424\pi\)
\(258\) 16.9380 1.05451
\(259\) 9.60754 0.596983
\(260\) 7.78708 0.482934
\(261\) 0.579702 0.0358827
\(262\) −22.2737 −1.37607
\(263\) 15.5129 0.956569 0.478285 0.878205i \(-0.341259\pi\)
0.478285 + 0.878205i \(0.341259\pi\)
\(264\) 3.14822 0.193759
\(265\) 8.00804 0.491930
\(266\) 2.43862 0.149521
\(267\) 22.6125 1.38386
\(268\) −15.9394 −0.973656
\(269\) −6.93004 −0.422532 −0.211266 0.977429i \(-0.567759\pi\)
−0.211266 + 0.977429i \(0.567759\pi\)
\(270\) −7.09313 −0.431674
\(271\) 14.8948 0.904793 0.452397 0.891817i \(-0.350569\pi\)
0.452397 + 0.891817i \(0.350569\pi\)
\(272\) −2.98642 −0.181078
\(273\) −21.2512 −1.28618
\(274\) 16.4778 0.995463
\(275\) 2.79379 0.168472
\(276\) −3.86004 −0.232347
\(277\) 21.9705 1.32008 0.660040 0.751230i \(-0.270539\pi\)
0.660040 + 0.751230i \(0.270539\pi\)
\(278\) −11.6853 −0.700838
\(279\) −5.00282 −0.299511
\(280\) 4.37484 0.261447
\(281\) 4.45825 0.265957 0.132979 0.991119i \(-0.457546\pi\)
0.132979 + 0.991119i \(0.457546\pi\)
\(282\) 12.1175 0.721589
\(283\) −5.52346 −0.328335 −0.164168 0.986432i \(-0.552494\pi\)
−0.164168 + 0.986432i \(0.552494\pi\)
\(284\) 8.05400 0.477917
\(285\) −3.60167 −0.213344
\(286\) 6.80668 0.402488
\(287\) 27.0063 1.59413
\(288\) 1.03060 0.0607286
\(289\) −8.08130 −0.475370
\(290\) −1.00910 −0.0592565
\(291\) −6.91115 −0.405139
\(292\) 2.43690 0.142609
\(293\) −19.8393 −1.15903 −0.579513 0.814963i \(-0.696757\pi\)
−0.579513 + 0.814963i \(0.696757\pi\)
\(294\) 2.11435 0.123312
\(295\) −25.7971 −1.50197
\(296\) −3.93975 −0.228993
\(297\) −6.20011 −0.359767
\(298\) 8.74140 0.506376
\(299\) −8.34569 −0.482644
\(300\) 3.57683 0.206508
\(301\) 20.5741 1.18587
\(302\) 1.07980 0.0621352
\(303\) −30.1588 −1.73258
\(304\) −1.00000 −0.0573539
\(305\) 23.2870 1.33341
\(306\) −3.07780 −0.175946
\(307\) 4.65577 0.265719 0.132859 0.991135i \(-0.457584\pi\)
0.132859 + 0.991135i \(0.457584\pi\)
\(308\) 3.82405 0.217895
\(309\) −3.78559 −0.215355
\(310\) 8.70853 0.494611
\(311\) −24.6145 −1.39576 −0.697879 0.716215i \(-0.745873\pi\)
−0.697879 + 0.716215i \(0.745873\pi\)
\(312\) 8.71445 0.493359
\(313\) 3.34650 0.189155 0.0945777 0.995517i \(-0.469850\pi\)
0.0945777 + 0.995517i \(0.469850\pi\)
\(314\) −2.01582 −0.113760
\(315\) 4.50870 0.254037
\(316\) −2.99978 −0.168751
\(317\) 5.15681 0.289636 0.144818 0.989458i \(-0.453740\pi\)
0.144818 + 0.989458i \(0.453740\pi\)
\(318\) 8.96173 0.502549
\(319\) −0.882055 −0.0493856
\(320\) −1.79399 −0.100287
\(321\) 30.4718 1.70077
\(322\) −4.68867 −0.261290
\(323\) 2.98642 0.166169
\(324\) −11.0297 −0.612759
\(325\) 7.73337 0.428970
\(326\) 21.8879 1.21226
\(327\) 12.4176 0.686696
\(328\) −11.0744 −0.611483
\(329\) 14.7188 0.811474
\(330\) −5.64786 −0.310904
\(331\) −25.8264 −1.41955 −0.709774 0.704430i \(-0.751203\pi\)
−0.709774 + 0.704430i \(0.751203\pi\)
\(332\) 9.69270 0.531956
\(333\) −4.06030 −0.222503
\(334\) −4.09048 −0.223821
\(335\) 28.5951 1.56232
\(336\) 4.89585 0.267090
\(337\) 19.1488 1.04310 0.521550 0.853221i \(-0.325354\pi\)
0.521550 + 0.853221i \(0.325354\pi\)
\(338\) 5.84130 0.317725
\(339\) −13.2108 −0.717514
\(340\) 5.35760 0.290556
\(341\) 7.61212 0.412219
\(342\) −1.03060 −0.0557284
\(343\) 19.6385 1.06038
\(344\) −8.43678 −0.454881
\(345\) 6.92485 0.372822
\(346\) 8.61177 0.462972
\(347\) 17.9943 0.965984 0.482992 0.875625i \(-0.339550\pi\)
0.482992 + 0.875625i \(0.339550\pi\)
\(348\) −1.12928 −0.0605356
\(349\) −13.2057 −0.706884 −0.353442 0.935456i \(-0.614989\pi\)
−0.353442 + 0.935456i \(0.614989\pi\)
\(350\) 4.34467 0.232232
\(351\) −17.1623 −0.916054
\(352\) −1.56812 −0.0835812
\(353\) −30.3089 −1.61318 −0.806591 0.591110i \(-0.798690\pi\)
−0.806591 + 0.591110i \(0.798690\pi\)
\(354\) −28.8693 −1.53439
\(355\) −14.4488 −0.766861
\(356\) −11.2633 −0.596951
\(357\) −14.6211 −0.773829
\(358\) 16.8064 0.888246
\(359\) 21.6062 1.14033 0.570165 0.821530i \(-0.306879\pi\)
0.570165 + 0.821530i \(0.306879\pi\)
\(360\) −1.84888 −0.0974445
\(361\) 1.00000 0.0526316
\(362\) 6.55162 0.344346
\(363\) 17.1472 0.899994
\(364\) 10.5852 0.554815
\(365\) −4.37176 −0.228829
\(366\) 26.0603 1.36219
\(367\) −9.98272 −0.521094 −0.260547 0.965461i \(-0.583903\pi\)
−0.260547 + 0.965461i \(0.583903\pi\)
\(368\) 1.92268 0.100227
\(369\) −11.4133 −0.594152
\(370\) 7.06786 0.367441
\(371\) 10.8855 0.565149
\(372\) 9.74564 0.505288
\(373\) −27.0164 −1.39885 −0.699427 0.714704i \(-0.746561\pi\)
−0.699427 + 0.714704i \(0.746561\pi\)
\(374\) 4.68307 0.242156
\(375\) −24.4251 −1.26131
\(376\) −6.03573 −0.311269
\(377\) −2.44158 −0.125748
\(378\) −9.64189 −0.495926
\(379\) 0.972204 0.0499388 0.0249694 0.999688i \(-0.492051\pi\)
0.0249694 + 0.999688i \(0.492051\pi\)
\(380\) 1.79399 0.0920295
\(381\) −11.3329 −0.580600
\(382\) −22.4079 −1.14649
\(383\) −18.3603 −0.938167 −0.469084 0.883154i \(-0.655416\pi\)
−0.469084 + 0.883154i \(0.655416\pi\)
\(384\) −2.00763 −0.102452
\(385\) −6.86029 −0.349633
\(386\) 21.0583 1.07184
\(387\) −8.69493 −0.441988
\(388\) 3.44243 0.174763
\(389\) 17.7954 0.902264 0.451132 0.892457i \(-0.351020\pi\)
0.451132 + 0.892457i \(0.351020\pi\)
\(390\) −15.6336 −0.791639
\(391\) −5.74193 −0.290382
\(392\) −1.05316 −0.0531924
\(393\) 44.7174 2.25569
\(394\) 17.7540 0.894435
\(395\) 5.38157 0.270776
\(396\) −1.61610 −0.0812123
\(397\) 34.8852 1.75084 0.875420 0.483364i \(-0.160585\pi\)
0.875420 + 0.483364i \(0.160585\pi\)
\(398\) 10.1854 0.510547
\(399\) −4.89585 −0.245099
\(400\) −1.78161 −0.0890807
\(401\) 11.6845 0.583494 0.291747 0.956496i \(-0.405764\pi\)
0.291747 + 0.956496i \(0.405764\pi\)
\(402\) 32.0006 1.59604
\(403\) 21.0708 1.04961
\(404\) 15.0221 0.747376
\(405\) 19.7871 0.983227
\(406\) −1.37170 −0.0680763
\(407\) 6.17801 0.306233
\(408\) 5.99564 0.296828
\(409\) −16.5589 −0.818783 −0.409391 0.912359i \(-0.634259\pi\)
−0.409391 + 0.912359i \(0.634259\pi\)
\(410\) 19.8674 0.981180
\(411\) −33.0815 −1.63179
\(412\) 1.88560 0.0928967
\(413\) −35.0667 −1.72552
\(414\) 1.98151 0.0973859
\(415\) −17.3886 −0.853571
\(416\) −4.34066 −0.212818
\(417\) 23.4598 1.14883
\(418\) 1.56812 0.0766994
\(419\) 7.52769 0.367751 0.183876 0.982949i \(-0.441136\pi\)
0.183876 + 0.982949i \(0.441136\pi\)
\(420\) −8.78309 −0.428571
\(421\) −3.34379 −0.162967 −0.0814833 0.996675i \(-0.525966\pi\)
−0.0814833 + 0.996675i \(0.525966\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −6.22041 −0.302447
\(424\) −4.46382 −0.216782
\(425\) 5.32065 0.258089
\(426\) −16.1695 −0.783414
\(427\) 31.6547 1.53188
\(428\) −15.1780 −0.733655
\(429\) −13.6653 −0.659769
\(430\) 15.1355 0.729897
\(431\) −36.7080 −1.76816 −0.884080 0.467335i \(-0.845214\pi\)
−0.884080 + 0.467335i \(0.845214\pi\)
\(432\) 3.95384 0.190229
\(433\) 35.4441 1.70333 0.851667 0.524084i \(-0.175592\pi\)
0.851667 + 0.524084i \(0.175592\pi\)
\(434\) 11.8377 0.568230
\(435\) 2.02591 0.0971348
\(436\) −6.18520 −0.296217
\(437\) −1.92268 −0.0919742
\(438\) −4.89240 −0.233768
\(439\) 25.0169 1.19399 0.596995 0.802245i \(-0.296361\pi\)
0.596995 + 0.802245i \(0.296361\pi\)
\(440\) 2.81319 0.134114
\(441\) −1.08538 −0.0516848
\(442\) 12.9630 0.616588
\(443\) 20.7863 0.987587 0.493794 0.869579i \(-0.335610\pi\)
0.493794 + 0.869579i \(0.335610\pi\)
\(444\) 7.90958 0.375372
\(445\) 20.2061 0.957862
\(446\) −18.5493 −0.878335
\(447\) −17.5495 −0.830065
\(448\) −2.43862 −0.115214
\(449\) −2.12952 −0.100498 −0.0502492 0.998737i \(-0.516002\pi\)
−0.0502492 + 0.998737i \(0.516002\pi\)
\(450\) −1.83613 −0.0865559
\(451\) 17.3661 0.817736
\(452\) 6.58029 0.309511
\(453\) −2.16783 −0.101854
\(454\) −17.7495 −0.833023
\(455\) −18.9897 −0.890250
\(456\) 2.00763 0.0940161
\(457\) 8.37829 0.391920 0.195960 0.980612i \(-0.437218\pi\)
0.195960 + 0.980612i \(0.437218\pi\)
\(458\) −5.45582 −0.254934
\(459\) −11.8078 −0.551142
\(460\) −3.44926 −0.160823
\(461\) −26.4321 −1.23106 −0.615532 0.788112i \(-0.711059\pi\)
−0.615532 + 0.788112i \(0.711059\pi\)
\(462\) −7.67729 −0.357180
\(463\) 7.76656 0.360943 0.180471 0.983580i \(-0.442238\pi\)
0.180471 + 0.983580i \(0.442238\pi\)
\(464\) 0.562491 0.0261130
\(465\) −17.4835 −0.810780
\(466\) 7.59030 0.351614
\(467\) 8.58514 0.397273 0.198636 0.980073i \(-0.436349\pi\)
0.198636 + 0.980073i \(0.436349\pi\)
\(468\) −4.47347 −0.206786
\(469\) 38.8702 1.79486
\(470\) 10.8280 0.499459
\(471\) 4.04704 0.186478
\(472\) 14.3798 0.661882
\(473\) 13.2299 0.608312
\(474\) 6.02247 0.276621
\(475\) 1.78161 0.0817460
\(476\) 7.28273 0.333803
\(477\) −4.60041 −0.210638
\(478\) −21.3228 −0.975284
\(479\) −26.8403 −1.22636 −0.613182 0.789942i \(-0.710111\pi\)
−0.613182 + 0.789942i \(0.710111\pi\)
\(480\) 3.60167 0.164393
\(481\) 17.1011 0.779743
\(482\) 0.738320 0.0336296
\(483\) 9.41315 0.428313
\(484\) −8.54099 −0.388227
\(485\) −6.17567 −0.280423
\(486\) 10.2820 0.466402
\(487\) −2.04309 −0.0925810 −0.0462905 0.998928i \(-0.514740\pi\)
−0.0462905 + 0.998928i \(0.514740\pi\)
\(488\) −12.9806 −0.587605
\(489\) −43.9430 −1.98717
\(490\) 1.88935 0.0853520
\(491\) 27.0638 1.22137 0.610685 0.791873i \(-0.290894\pi\)
0.610685 + 0.791873i \(0.290894\pi\)
\(492\) 22.2334 1.00236
\(493\) −1.67983 −0.0756560
\(494\) 4.34066 0.195295
\(495\) 2.89927 0.130312
\(496\) −4.85429 −0.217964
\(497\) −19.6406 −0.881001
\(498\) −19.4594 −0.871997
\(499\) −15.2351 −0.682015 −0.341008 0.940061i \(-0.610768\pi\)
−0.341008 + 0.940061i \(0.610768\pi\)
\(500\) 12.1661 0.544085
\(501\) 8.21218 0.366893
\(502\) −27.1705 −1.21268
\(503\) −39.1190 −1.74423 −0.872115 0.489302i \(-0.837252\pi\)
−0.872115 + 0.489302i \(0.837252\pi\)
\(504\) −2.51323 −0.111948
\(505\) −26.9494 −1.19923
\(506\) −3.01500 −0.134033
\(507\) −11.7272 −0.520823
\(508\) 5.64488 0.250451
\(509\) 19.3701 0.858564 0.429282 0.903171i \(-0.358767\pi\)
0.429282 + 0.903171i \(0.358767\pi\)
\(510\) −10.7561 −0.476288
\(511\) −5.94266 −0.262888
\(512\) 1.00000 0.0441942
\(513\) −3.95384 −0.174566
\(514\) 3.47591 0.153316
\(515\) −3.38274 −0.149061
\(516\) 16.9380 0.745653
\(517\) 9.46476 0.416260
\(518\) 9.60754 0.422131
\(519\) −17.2893 −0.758916
\(520\) 7.78708 0.341486
\(521\) 11.8930 0.521042 0.260521 0.965468i \(-0.416106\pi\)
0.260521 + 0.965468i \(0.416106\pi\)
\(522\) 0.579702 0.0253729
\(523\) 14.1575 0.619066 0.309533 0.950889i \(-0.399827\pi\)
0.309533 + 0.950889i \(0.399827\pi\)
\(524\) −22.2737 −0.973030
\(525\) −8.72251 −0.380682
\(526\) 15.5129 0.676397
\(527\) 14.4969 0.631497
\(528\) 3.14822 0.137009
\(529\) −19.3033 −0.839274
\(530\) 8.00804 0.347847
\(531\) 14.8198 0.643123
\(532\) 2.43862 0.105727
\(533\) 48.0703 2.08216
\(534\) 22.6125 0.978539
\(535\) 27.2291 1.17721
\(536\) −15.9394 −0.688479
\(537\) −33.7411 −1.45604
\(538\) −6.93004 −0.298775
\(539\) 1.65148 0.0711342
\(540\) −7.09313 −0.305240
\(541\) −0.952493 −0.0409509 −0.0204754 0.999790i \(-0.506518\pi\)
−0.0204754 + 0.999790i \(0.506518\pi\)
\(542\) 14.8948 0.639786
\(543\) −13.1533 −0.564461
\(544\) −2.98642 −0.128042
\(545\) 11.0962 0.475307
\(546\) −21.2512 −0.909467
\(547\) 4.26440 0.182333 0.0911664 0.995836i \(-0.470941\pi\)
0.0911664 + 0.995836i \(0.470941\pi\)
\(548\) 16.4778 0.703899
\(549\) −13.3778 −0.570950
\(550\) 2.79379 0.119128
\(551\) −0.562491 −0.0239629
\(552\) −3.86004 −0.164294
\(553\) 7.31531 0.311079
\(554\) 21.9705 0.933438
\(555\) −14.1897 −0.602318
\(556\) −11.6853 −0.495567
\(557\) 43.2644 1.83317 0.916586 0.399837i \(-0.130933\pi\)
0.916586 + 0.399837i \(0.130933\pi\)
\(558\) −5.00282 −0.211786
\(559\) 36.6212 1.54891
\(560\) 4.37484 0.184871
\(561\) −9.40190 −0.396949
\(562\) 4.45825 0.188060
\(563\) −5.26828 −0.222032 −0.111016 0.993819i \(-0.535410\pi\)
−0.111016 + 0.993819i \(0.535410\pi\)
\(564\) 12.1175 0.510240
\(565\) −11.8050 −0.496638
\(566\) −5.52346 −0.232168
\(567\) 26.8971 1.12957
\(568\) 8.05400 0.337938
\(569\) −25.8701 −1.08453 −0.542265 0.840207i \(-0.682433\pi\)
−0.542265 + 0.840207i \(0.682433\pi\)
\(570\) −3.60167 −0.150857
\(571\) 22.2409 0.930753 0.465377 0.885113i \(-0.345919\pi\)
0.465377 + 0.885113i \(0.345919\pi\)
\(572\) 6.80668 0.284602
\(573\) 44.9868 1.87935
\(574\) 27.0063 1.12722
\(575\) −3.42547 −0.142852
\(576\) 1.03060 0.0429416
\(577\) −13.5623 −0.564606 −0.282303 0.959325i \(-0.591098\pi\)
−0.282303 + 0.959325i \(0.591098\pi\)
\(578\) −8.08130 −0.336138
\(579\) −42.2773 −1.75699
\(580\) −1.00910 −0.0419007
\(581\) −23.6368 −0.980618
\(582\) −6.91115 −0.286476
\(583\) 6.99982 0.289903
\(584\) 2.43690 0.100840
\(585\) 8.02535 0.331807
\(586\) −19.8393 −0.819555
\(587\) −23.9666 −0.989208 −0.494604 0.869118i \(-0.664687\pi\)
−0.494604 + 0.869118i \(0.664687\pi\)
\(588\) 2.11435 0.0871945
\(589\) 4.85429 0.200017
\(590\) −25.7971 −1.06205
\(591\) −35.6436 −1.46618
\(592\) −3.93975 −0.161923
\(593\) 45.1261 1.85311 0.926553 0.376164i \(-0.122757\pi\)
0.926553 + 0.376164i \(0.122757\pi\)
\(594\) −6.20011 −0.254393
\(595\) −13.0651 −0.535617
\(596\) 8.74140 0.358062
\(597\) −20.4485 −0.836903
\(598\) −8.34569 −0.341281
\(599\) 42.9732 1.75584 0.877918 0.478810i \(-0.158932\pi\)
0.877918 + 0.478810i \(0.158932\pi\)
\(600\) 3.57683 0.146023
\(601\) −17.6388 −0.719501 −0.359751 0.933049i \(-0.617138\pi\)
−0.359751 + 0.933049i \(0.617138\pi\)
\(602\) 20.5741 0.838536
\(603\) −16.4272 −0.668966
\(604\) 1.07980 0.0439362
\(605\) 15.3224 0.622945
\(606\) −30.1588 −1.22512
\(607\) −24.9758 −1.01374 −0.506868 0.862024i \(-0.669197\pi\)
−0.506868 + 0.862024i \(0.669197\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 2.75387 0.111593
\(610\) 23.2870 0.942864
\(611\) 26.1990 1.05990
\(612\) −3.07780 −0.124413
\(613\) −41.6642 −1.68280 −0.841401 0.540411i \(-0.818269\pi\)
−0.841401 + 0.540411i \(0.818269\pi\)
\(614\) 4.65577 0.187891
\(615\) −39.8864 −1.60838
\(616\) 3.82405 0.154075
\(617\) −24.4712 −0.985173 −0.492587 0.870263i \(-0.663949\pi\)
−0.492587 + 0.870263i \(0.663949\pi\)
\(618\) −3.78559 −0.152279
\(619\) −2.64664 −0.106377 −0.0531887 0.998584i \(-0.516938\pi\)
−0.0531887 + 0.998584i \(0.516938\pi\)
\(620\) 8.70853 0.349743
\(621\) 7.60197 0.305056
\(622\) −24.6145 −0.986950
\(623\) 27.4667 1.10043
\(624\) 8.71445 0.348857
\(625\) −12.9178 −0.516711
\(626\) 3.34650 0.133753
\(627\) −3.14822 −0.125728
\(628\) −2.01582 −0.0804402
\(629\) 11.7658 0.469131
\(630\) 4.50870 0.179631
\(631\) 7.39706 0.294472 0.147236 0.989101i \(-0.452962\pi\)
0.147236 + 0.989101i \(0.452962\pi\)
\(632\) −2.99978 −0.119325
\(633\) 2.00763 0.0797963
\(634\) 5.15681 0.204803
\(635\) −10.1268 −0.401871
\(636\) 8.96173 0.355356
\(637\) 4.57139 0.181125
\(638\) −0.882055 −0.0349209
\(639\) 8.30044 0.328360
\(640\) −1.79399 −0.0709135
\(641\) 40.8577 1.61378 0.806892 0.590700i \(-0.201148\pi\)
0.806892 + 0.590700i \(0.201148\pi\)
\(642\) 30.4718 1.20263
\(643\) 21.0525 0.830230 0.415115 0.909769i \(-0.363741\pi\)
0.415115 + 0.909769i \(0.363741\pi\)
\(644\) −4.68867 −0.184760
\(645\) −30.3865 −1.19647
\(646\) 2.98642 0.117499
\(647\) −11.4788 −0.451277 −0.225638 0.974211i \(-0.572447\pi\)
−0.225638 + 0.974211i \(0.572447\pi\)
\(648\) −11.0297 −0.433286
\(649\) −22.5492 −0.885135
\(650\) 7.73337 0.303328
\(651\) −23.7659 −0.931458
\(652\) 21.8879 0.857197
\(653\) 31.3640 1.22737 0.613685 0.789551i \(-0.289687\pi\)
0.613685 + 0.789551i \(0.289687\pi\)
\(654\) 12.4176 0.485567
\(655\) 39.9587 1.56131
\(656\) −11.0744 −0.432384
\(657\) 2.51146 0.0979815
\(658\) 14.7188 0.573799
\(659\) 2.78257 0.108393 0.0541967 0.998530i \(-0.482740\pi\)
0.0541967 + 0.998530i \(0.482740\pi\)
\(660\) −5.64786 −0.219843
\(661\) 39.1029 1.52093 0.760464 0.649380i \(-0.224972\pi\)
0.760464 + 0.649380i \(0.224972\pi\)
\(662\) −25.8264 −1.00377
\(663\) −26.0250 −1.01073
\(664\) 9.69270 0.376150
\(665\) −4.37484 −0.169649
\(666\) −4.06030 −0.157333
\(667\) 1.08149 0.0418755
\(668\) −4.09048 −0.158265
\(669\) 37.2402 1.43979
\(670\) 28.5951 1.10473
\(671\) 20.3552 0.785803
\(672\) 4.89585 0.188861
\(673\) −47.2618 −1.82181 −0.910905 0.412616i \(-0.864615\pi\)
−0.910905 + 0.412616i \(0.864615\pi\)
\(674\) 19.1488 0.737583
\(675\) −7.04422 −0.271132
\(676\) 5.84130 0.224665
\(677\) −37.7782 −1.45194 −0.725968 0.687729i \(-0.758608\pi\)
−0.725968 + 0.687729i \(0.758608\pi\)
\(678\) −13.2108 −0.507359
\(679\) −8.39477 −0.322162
\(680\) 5.35760 0.205454
\(681\) 35.6344 1.36551
\(682\) 7.61212 0.291483
\(683\) 14.2962 0.547029 0.273515 0.961868i \(-0.411814\pi\)
0.273515 + 0.961868i \(0.411814\pi\)
\(684\) −1.03060 −0.0394059
\(685\) −29.5610 −1.12947
\(686\) 19.6385 0.749803
\(687\) 10.9533 0.417894
\(688\) −8.43678 −0.321649
\(689\) 19.3759 0.738164
\(690\) 6.92485 0.263625
\(691\) 38.5441 1.46629 0.733144 0.680073i \(-0.238052\pi\)
0.733144 + 0.680073i \(0.238052\pi\)
\(692\) 8.61177 0.327370
\(693\) 3.94106 0.149708
\(694\) 17.9943 0.683054
\(695\) 20.9633 0.795182
\(696\) −1.12928 −0.0428051
\(697\) 33.0729 1.25273
\(698\) −13.2057 −0.499842
\(699\) −15.2386 −0.576375
\(700\) 4.34467 0.164213
\(701\) −24.8451 −0.938387 −0.469194 0.883095i \(-0.655455\pi\)
−0.469194 + 0.883095i \(0.655455\pi\)
\(702\) −17.1623 −0.647748
\(703\) 3.93975 0.148591
\(704\) −1.56812 −0.0591009
\(705\) −21.7387 −0.818726
\(706\) −30.3089 −1.14069
\(707\) −36.6330 −1.37773
\(708\) −28.8693 −1.08498
\(709\) −12.8176 −0.481376 −0.240688 0.970603i \(-0.577373\pi\)
−0.240688 + 0.970603i \(0.577373\pi\)
\(710\) −14.4488 −0.542252
\(711\) −3.09157 −0.115943
\(712\) −11.2633 −0.422108
\(713\) −9.33324 −0.349533
\(714\) −14.6211 −0.547179
\(715\) −12.2111 −0.456669
\(716\) 16.8064 0.628085
\(717\) 42.8085 1.59871
\(718\) 21.6062 0.806336
\(719\) −20.0904 −0.749245 −0.374623 0.927177i \(-0.622228\pi\)
−0.374623 + 0.927177i \(0.622228\pi\)
\(720\) −1.84888 −0.0689036
\(721\) −4.59825 −0.171248
\(722\) 1.00000 0.0372161
\(723\) −1.48228 −0.0551265
\(724\) 6.55162 0.243489
\(725\) −1.00214 −0.0372186
\(726\) 17.1472 0.636392
\(727\) −7.51975 −0.278892 −0.139446 0.990230i \(-0.544532\pi\)
−0.139446 + 0.990230i \(0.544532\pi\)
\(728\) 10.5852 0.392313
\(729\) 12.4465 0.460980
\(730\) −4.37176 −0.161806
\(731\) 25.1958 0.931899
\(732\) 26.0603 0.963217
\(733\) 17.4972 0.646274 0.323137 0.946352i \(-0.395263\pi\)
0.323137 + 0.946352i \(0.395263\pi\)
\(734\) −9.98272 −0.368469
\(735\) −3.79312 −0.139911
\(736\) 1.92268 0.0708709
\(737\) 24.9950 0.920703
\(738\) −11.4133 −0.420129
\(739\) −27.4871 −1.01113 −0.505565 0.862789i \(-0.668716\pi\)
−0.505565 + 0.862789i \(0.668716\pi\)
\(740\) 7.06786 0.259820
\(741\) −8.71445 −0.320133
\(742\) 10.8855 0.399621
\(743\) −44.5321 −1.63373 −0.816863 0.576832i \(-0.804289\pi\)
−0.816863 + 0.576832i \(0.804289\pi\)
\(744\) 9.74564 0.357292
\(745\) −15.6820 −0.574542
\(746\) −27.0164 −0.989139
\(747\) 9.98928 0.365489
\(748\) 4.68307 0.171230
\(749\) 37.0132 1.35243
\(750\) −24.4251 −0.891880
\(751\) 25.6955 0.937644 0.468822 0.883293i \(-0.344679\pi\)
0.468822 + 0.883293i \(0.344679\pi\)
\(752\) −6.03573 −0.220100
\(753\) 54.5485 1.98786
\(754\) −2.44158 −0.0889171
\(755\) −1.93714 −0.0704996
\(756\) −9.64189 −0.350672
\(757\) 18.4588 0.670895 0.335447 0.942059i \(-0.391113\pi\)
0.335447 + 0.942059i \(0.391113\pi\)
\(758\) 0.972204 0.0353120
\(759\) 6.05301 0.219710
\(760\) 1.79399 0.0650747
\(761\) 18.1033 0.656243 0.328121 0.944636i \(-0.393584\pi\)
0.328121 + 0.944636i \(0.393584\pi\)
\(762\) −11.3329 −0.410546
\(763\) 15.0833 0.546053
\(764\) −22.4079 −0.810688
\(765\) 5.52153 0.199631
\(766\) −18.3603 −0.663385
\(767\) −62.4176 −2.25377
\(768\) −2.00763 −0.0724443
\(769\) −45.5260 −1.64171 −0.820855 0.571137i \(-0.806503\pi\)
−0.820855 + 0.571137i \(0.806503\pi\)
\(770\) −6.86029 −0.247228
\(771\) −6.97836 −0.251320
\(772\) 21.0583 0.757904
\(773\) −22.0175 −0.791913 −0.395956 0.918269i \(-0.629587\pi\)
−0.395956 + 0.918269i \(0.629587\pi\)
\(774\) −8.69493 −0.312533
\(775\) 8.64847 0.310662
\(776\) 3.44243 0.123576
\(777\) −19.2884 −0.691969
\(778\) 17.7954 0.637997
\(779\) 11.0744 0.396783
\(780\) −15.6336 −0.559773
\(781\) −12.6297 −0.451925
\(782\) −5.74193 −0.205331
\(783\) 2.22400 0.0794793
\(784\) −1.05316 −0.0376127
\(785\) 3.61636 0.129073
\(786\) 44.7174 1.59502
\(787\) −28.0918 −1.00137 −0.500683 0.865631i \(-0.666918\pi\)
−0.500683 + 0.865631i \(0.666918\pi\)
\(788\) 17.7540 0.632461
\(789\) −31.1443 −1.10877
\(790\) 5.38157 0.191468
\(791\) −16.0468 −0.570559
\(792\) −1.61610 −0.0574258
\(793\) 56.3444 2.00085
\(794\) 34.8852 1.23803
\(795\) −16.0772 −0.570200
\(796\) 10.1854 0.361012
\(797\) −9.55800 −0.338562 −0.169281 0.985568i \(-0.554144\pi\)
−0.169281 + 0.985568i \(0.554144\pi\)
\(798\) −4.89585 −0.173311
\(799\) 18.0252 0.637686
\(800\) −1.78161 −0.0629896
\(801\) −11.6079 −0.410145
\(802\) 11.6845 0.412592
\(803\) −3.82136 −0.134853
\(804\) 32.0006 1.12857
\(805\) 8.41142 0.296463
\(806\) 21.0708 0.742187
\(807\) 13.9130 0.489760
\(808\) 15.0221 0.528474
\(809\) 3.15214 0.110823 0.0554116 0.998464i \(-0.482353\pi\)
0.0554116 + 0.998464i \(0.482353\pi\)
\(810\) 19.7871 0.695246
\(811\) −42.8175 −1.50353 −0.751763 0.659433i \(-0.770796\pi\)
−0.751763 + 0.659433i \(0.770796\pi\)
\(812\) −1.37170 −0.0481372
\(813\) −29.9033 −1.04875
\(814\) 6.17801 0.216539
\(815\) −39.2666 −1.37545
\(816\) 5.99564 0.209889
\(817\) 8.43678 0.295165
\(818\) −16.5589 −0.578967
\(819\) 10.9091 0.381194
\(820\) 19.8674 0.693799
\(821\) −5.54040 −0.193361 −0.0966807 0.995315i \(-0.530823\pi\)
−0.0966807 + 0.995315i \(0.530823\pi\)
\(822\) −33.0815 −1.15385
\(823\) −10.4057 −0.362718 −0.181359 0.983417i \(-0.558050\pi\)
−0.181359 + 0.983417i \(0.558050\pi\)
\(824\) 1.88560 0.0656879
\(825\) −5.60891 −0.195277
\(826\) −35.0667 −1.22013
\(827\) −55.2056 −1.91969 −0.959843 0.280538i \(-0.909487\pi\)
−0.959843 + 0.280538i \(0.909487\pi\)
\(828\) 1.98151 0.0688622
\(829\) −43.3892 −1.50697 −0.753484 0.657466i \(-0.771628\pi\)
−0.753484 + 0.657466i \(0.771628\pi\)
\(830\) −17.3886 −0.603566
\(831\) −44.1088 −1.53012
\(832\) −4.34066 −0.150485
\(833\) 3.14517 0.108974
\(834\) 23.4598 0.812347
\(835\) 7.33826 0.253951
\(836\) 1.56812 0.0542347
\(837\) −19.1931 −0.663410
\(838\) 7.52769 0.260040
\(839\) −43.8812 −1.51495 −0.757474 0.652865i \(-0.773567\pi\)
−0.757474 + 0.652865i \(0.773567\pi\)
\(840\) −8.78309 −0.303045
\(841\) −28.6836 −0.989090
\(842\) −3.34379 −0.115235
\(843\) −8.95055 −0.308273
\(844\) −1.00000 −0.0344214
\(845\) −10.4792 −0.360496
\(846\) −6.22041 −0.213862
\(847\) 20.8282 0.715665
\(848\) −4.46382 −0.153288
\(849\) 11.0891 0.380576
\(850\) 5.32065 0.182497
\(851\) −7.57488 −0.259663
\(852\) −16.1695 −0.553958
\(853\) −6.94606 −0.237829 −0.118914 0.992905i \(-0.537941\pi\)
−0.118914 + 0.992905i \(0.537941\pi\)
\(854\) 31.6547 1.08320
\(855\) 1.84888 0.0632303
\(856\) −15.1780 −0.518772
\(857\) −3.03688 −0.103738 −0.0518690 0.998654i \(-0.516518\pi\)
−0.0518690 + 0.998654i \(0.516518\pi\)
\(858\) −13.6653 −0.466527
\(859\) −12.6581 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(860\) 15.1355 0.516115
\(861\) −54.2187 −1.84777
\(862\) −36.7080 −1.25028
\(863\) −14.4476 −0.491803 −0.245902 0.969295i \(-0.579084\pi\)
−0.245902 + 0.969295i \(0.579084\pi\)
\(864\) 3.95384 0.134512
\(865\) −15.4494 −0.525295
\(866\) 35.4441 1.20444
\(867\) 16.2243 0.551006
\(868\) 11.8377 0.401799
\(869\) 4.70403 0.159573
\(870\) 2.02591 0.0686847
\(871\) 69.1877 2.34433
\(872\) −6.18520 −0.209457
\(873\) 3.54776 0.120074
\(874\) −1.92268 −0.0650356
\(875\) −29.6685 −1.00298
\(876\) −4.89240 −0.165299
\(877\) 21.0284 0.710080 0.355040 0.934851i \(-0.384467\pi\)
0.355040 + 0.934851i \(0.384467\pi\)
\(878\) 25.0169 0.844278
\(879\) 39.8301 1.34344
\(880\) 2.81319 0.0948326
\(881\) −43.6644 −1.47109 −0.735546 0.677474i \(-0.763074\pi\)
−0.735546 + 0.677474i \(0.763074\pi\)
\(882\) −1.08538 −0.0365467
\(883\) −17.7562 −0.597543 −0.298771 0.954325i \(-0.596577\pi\)
−0.298771 + 0.954325i \(0.596577\pi\)
\(884\) 12.9630 0.435994
\(885\) 51.7912 1.74094
\(886\) 20.7863 0.698330
\(887\) −37.3649 −1.25459 −0.627295 0.778782i \(-0.715838\pi\)
−0.627295 + 0.778782i \(0.715838\pi\)
\(888\) 7.90958 0.265428
\(889\) −13.7657 −0.461687
\(890\) 20.2061 0.677311
\(891\) 17.2959 0.579433
\(892\) −18.5493 −0.621076
\(893\) 6.03573 0.201978
\(894\) −17.5495 −0.586944
\(895\) −30.1505 −1.00782
\(896\) −2.43862 −0.0814684
\(897\) 16.7551 0.559437
\(898\) −2.12952 −0.0710631
\(899\) −2.73049 −0.0910671
\(900\) −1.83613 −0.0612043
\(901\) 13.3309 0.444115
\(902\) 17.3661 0.578227
\(903\) −41.3052 −1.37455
\(904\) 6.58029 0.218857
\(905\) −11.7535 −0.390700
\(906\) −2.16783 −0.0720215
\(907\) −35.1732 −1.16791 −0.583953 0.811787i \(-0.698495\pi\)
−0.583953 + 0.811787i \(0.698495\pi\)
\(908\) −17.7495 −0.589036
\(909\) 15.4817 0.513496
\(910\) −18.9897 −0.629502
\(911\) −38.8799 −1.28815 −0.644075 0.764962i \(-0.722758\pi\)
−0.644075 + 0.764962i \(0.722758\pi\)
\(912\) 2.00763 0.0664794
\(913\) −15.1993 −0.503025
\(914\) 8.37829 0.277129
\(915\) −46.7519 −1.54557
\(916\) −5.45582 −0.180265
\(917\) 54.3169 1.79370
\(918\) −11.8078 −0.389716
\(919\) 10.4829 0.345798 0.172899 0.984940i \(-0.444687\pi\)
0.172899 + 0.984940i \(0.444687\pi\)
\(920\) −3.44926 −0.113719
\(921\) −9.34708 −0.307997
\(922\) −26.4321 −0.870493
\(923\) −34.9596 −1.15071
\(924\) −7.67729 −0.252564
\(925\) 7.01912 0.230787
\(926\) 7.76656 0.255225
\(927\) 1.94329 0.0638261
\(928\) 0.562491 0.0184647
\(929\) −21.2402 −0.696869 −0.348434 0.937333i \(-0.613287\pi\)
−0.348434 + 0.937333i \(0.613287\pi\)
\(930\) −17.4835 −0.573308
\(931\) 1.05316 0.0345158
\(932\) 7.59030 0.248629
\(933\) 49.4169 1.61784
\(934\) 8.58514 0.280914
\(935\) −8.40137 −0.274754
\(936\) −4.47347 −0.146220
\(937\) −24.8936 −0.813239 −0.406620 0.913598i \(-0.633293\pi\)
−0.406620 + 0.913598i \(0.633293\pi\)
\(938\) 38.8702 1.26916
\(939\) −6.71855 −0.219252
\(940\) 10.8280 0.353171
\(941\) 8.16223 0.266081 0.133041 0.991111i \(-0.457526\pi\)
0.133041 + 0.991111i \(0.457526\pi\)
\(942\) 4.04704 0.131860
\(943\) −21.2926 −0.693382
\(944\) 14.3798 0.468021
\(945\) 17.2974 0.562685
\(946\) 13.2299 0.430141
\(947\) 44.4251 1.44362 0.721811 0.692090i \(-0.243310\pi\)
0.721811 + 0.692090i \(0.243310\pi\)
\(948\) 6.02247 0.195601
\(949\) −10.5777 −0.343368
\(950\) 1.78161 0.0578032
\(951\) −10.3530 −0.335719
\(952\) 7.28273 0.236035
\(953\) 8.42769 0.273000 0.136500 0.990640i \(-0.456415\pi\)
0.136500 + 0.990640i \(0.456415\pi\)
\(954\) −4.60041 −0.148944
\(955\) 40.1994 1.30082
\(956\) −21.3228 −0.689630
\(957\) 1.77084 0.0572433
\(958\) −26.8403 −0.867170
\(959\) −40.1831 −1.29758
\(960\) 3.60167 0.116243
\(961\) −7.43588 −0.239867
\(962\) 17.1011 0.551362
\(963\) −15.6424 −0.504069
\(964\) 0.738320 0.0237797
\(965\) −37.7783 −1.21613
\(966\) 9.41315 0.302863
\(967\) 17.6656 0.568086 0.284043 0.958812i \(-0.408324\pi\)
0.284043 + 0.958812i \(0.408324\pi\)
\(968\) −8.54099 −0.274518
\(969\) −5.99564 −0.192608
\(970\) −6.17567 −0.198289
\(971\) 52.1695 1.67420 0.837099 0.547051i \(-0.184250\pi\)
0.837099 + 0.547051i \(0.184250\pi\)
\(972\) 10.2820 0.329796
\(973\) 28.4960 0.913538
\(974\) −2.04309 −0.0654647
\(975\) −15.5258 −0.497223
\(976\) −12.9806 −0.415499
\(977\) −22.8120 −0.729819 −0.364909 0.931043i \(-0.618900\pi\)
−0.364909 + 0.931043i \(0.618900\pi\)
\(978\) −43.9430 −1.40514
\(979\) 17.6622 0.564485
\(980\) 1.88935 0.0603530
\(981\) −6.37445 −0.203521
\(982\) 27.0638 0.863640
\(983\) −14.4751 −0.461682 −0.230841 0.972991i \(-0.574148\pi\)
−0.230841 + 0.972991i \(0.574148\pi\)
\(984\) 22.2334 0.708775
\(985\) −31.8505 −1.01484
\(986\) −1.67983 −0.0534968
\(987\) −29.5500 −0.940587
\(988\) 4.34066 0.138095
\(989\) −16.2212 −0.515805
\(990\) 2.89927 0.0921448
\(991\) −29.6521 −0.941929 −0.470964 0.882152i \(-0.656094\pi\)
−0.470964 + 0.882152i \(0.656094\pi\)
\(992\) −4.85429 −0.154124
\(993\) 51.8500 1.64541
\(994\) −19.6406 −0.622962
\(995\) −18.2724 −0.579275
\(996\) −19.4594 −0.616595
\(997\) −21.5565 −0.682700 −0.341350 0.939936i \(-0.610884\pi\)
−0.341350 + 0.939936i \(0.610884\pi\)
\(998\) −15.2351 −0.482257
\(999\) −15.5771 −0.492839
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 \(a_p\))