Properties

Label 8047.2.a.a.1.1
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 0
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\)
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} +0.236068 q^{6} -2.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\) \(q-0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} +3.23607 q^{5} +0.236068 q^{6} -2.61803 q^{7} +2.23607 q^{8} -2.85410 q^{9} -2.00000 q^{10} +5.00000 q^{11} +0.618034 q^{12} -1.00000 q^{13} +1.61803 q^{14} -1.23607 q^{15} +1.85410 q^{16} +4.23607 q^{17} +1.76393 q^{18} -8.23607 q^{19} -5.23607 q^{20} +1.00000 q^{21} -3.09017 q^{22} -4.00000 q^{23} -0.854102 q^{24} +5.47214 q^{25} +0.618034 q^{26} +2.23607 q^{27} +4.23607 q^{28} +7.23607 q^{29} +0.763932 q^{30} -6.23607 q^{31} -5.61803 q^{32} -1.90983 q^{33} -2.61803 q^{34} -8.47214 q^{35} +4.61803 q^{36} -2.47214 q^{37} +5.09017 q^{38} +0.381966 q^{39} +7.23607 q^{40} +4.23607 q^{41} -0.618034 q^{42} -9.23607 q^{43} -8.09017 q^{44} -9.23607 q^{45} +2.47214 q^{46} +5.14590 q^{47} -0.708204 q^{48} -0.145898 q^{49} -3.38197 q^{50} -1.61803 q^{51} +1.61803 q^{52} +5.70820 q^{53} -1.38197 q^{54} +16.1803 q^{55} -5.85410 q^{56} +3.14590 q^{57} -4.47214 q^{58} +11.0902 q^{59} +2.00000 q^{60} +11.9443 q^{61} +3.85410 q^{62} +7.47214 q^{63} -0.236068 q^{64} -3.23607 q^{65} +1.18034 q^{66} -6.70820 q^{67} -6.85410 q^{68} +1.52786 q^{69} +5.23607 q^{70} +9.18034 q^{71} -6.38197 q^{72} +13.4164 q^{73} +1.52786 q^{74} -2.09017 q^{75} +13.3262 q^{76} -13.0902 q^{77} -0.236068 q^{78} -9.47214 q^{79} +6.00000 q^{80} +7.70820 q^{81} -2.61803 q^{82} -1.76393 q^{83} -1.61803 q^{84} +13.7082 q^{85} +5.70820 q^{86} -2.76393 q^{87} +11.1803 q^{88} +0.145898 q^{89} +5.70820 q^{90} +2.61803 q^{91} +6.47214 q^{92} +2.38197 q^{93} -3.18034 q^{94} -26.6525 q^{95} +2.14590 q^{96} +3.90983 q^{97} +0.0901699 q^{98} -14.2705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - 3q^{3} - q^{4} + 2q^{5} - 4q^{6} - 3q^{7} + q^{9} + O(q^{10}) \) \( 2q + q^{2} - 3q^{3} - q^{4} + 2q^{5} - 4q^{6} - 3q^{7} + q^{9} - 4q^{10} + 10q^{11} - q^{12} - 2q^{13} + q^{14} + 2q^{15} - 3q^{16} + 4q^{17} + 8q^{18} - 12q^{19} - 6q^{20} + 2q^{21} + 5q^{22} - 8q^{23} + 5q^{24} + 2q^{25} - q^{26} + 4q^{28} + 10q^{29} + 6q^{30} - 8q^{31} - 9q^{32} - 15q^{33} - 3q^{34} - 8q^{35} + 7q^{36} + 4q^{37} - q^{38} + 3q^{39} + 10q^{40} + 4q^{41} + q^{42} - 14q^{43} - 5q^{44} - 14q^{45} - 4q^{46} + 17q^{47} + 12q^{48} - 7q^{49} - 9q^{50} - q^{51} + q^{52} - 2q^{53} - 5q^{54} + 10q^{55} - 5q^{56} + 13q^{57} + 11q^{59} + 4q^{60} + 6q^{61} + q^{62} + 6q^{63} + 4q^{64} - 2q^{65} - 20q^{66} - 7q^{68} + 12q^{69} + 6q^{70} - 4q^{71} - 15q^{72} + 12q^{74} + 7q^{75} + 11q^{76} - 15q^{77} + 4q^{78} - 10q^{79} + 12q^{80} + 2q^{81} - 3q^{82} - 8q^{83} - q^{84} + 14q^{85} - 2q^{86} - 10q^{87} + 7q^{89} - 2q^{90} + 3q^{91} + 4q^{92} + 7q^{93} + 16q^{94} - 22q^{95} + 11q^{96} + 19q^{97} - 11q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.618034 −0.437016 −0.218508 0.975835i \(-0.570119\pi\)
−0.218508 + 0.975835i \(0.570119\pi\)
\(3\) −0.381966 −0.220528 −0.110264 0.993902i \(-0.535170\pi\)
−0.110264 + 0.993902i \(0.535170\pi\)
\(4\) −1.61803 −0.809017
\(5\) 3.23607 1.44721 0.723607 0.690212i \(-0.242483\pi\)
0.723607 + 0.690212i \(0.242483\pi\)
\(6\) 0.236068 0.0963743
\(7\) −2.61803 −0.989524 −0.494762 0.869029i \(-0.664745\pi\)
−0.494762 + 0.869029i \(0.664745\pi\)
\(8\) 2.23607 0.790569
\(9\) −2.85410 −0.951367
\(10\) −2.00000 −0.632456
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0.618034 0.178411
\(13\) −1.00000 −0.277350
\(14\) 1.61803 0.432438
\(15\) −1.23607 −0.319151
\(16\) 1.85410 0.463525
\(17\) 4.23607 1.02740 0.513699 0.857971i \(-0.328275\pi\)
0.513699 + 0.857971i \(0.328275\pi\)
\(18\) 1.76393 0.415763
\(19\) −8.23607 −1.88948 −0.944742 0.327815i \(-0.893688\pi\)
−0.944742 + 0.327815i \(0.893688\pi\)
\(20\) −5.23607 −1.17082
\(21\) 1.00000 0.218218
\(22\) −3.09017 −0.658826
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −0.854102 −0.174343
\(25\) 5.47214 1.09443
\(26\) 0.618034 0.121206
\(27\) 2.23607 0.430331
\(28\) 4.23607 0.800542
\(29\) 7.23607 1.34370 0.671852 0.740685i \(-0.265499\pi\)
0.671852 + 0.740685i \(0.265499\pi\)
\(30\) 0.763932 0.139474
\(31\) −6.23607 −1.12003 −0.560015 0.828482i \(-0.689205\pi\)
−0.560015 + 0.828482i \(0.689205\pi\)
\(32\) −5.61803 −0.993137
\(33\) −1.90983 −0.332459
\(34\) −2.61803 −0.448989
\(35\) −8.47214 −1.43205
\(36\) 4.61803 0.769672
\(37\) −2.47214 −0.406417 −0.203208 0.979136i \(-0.565137\pi\)
−0.203208 + 0.979136i \(0.565137\pi\)
\(38\) 5.09017 0.825735
\(39\) 0.381966 0.0611635
\(40\) 7.23607 1.14412
\(41\) 4.23607 0.661563 0.330781 0.943707i \(-0.392688\pi\)
0.330781 + 0.943707i \(0.392688\pi\)
\(42\) −0.618034 −0.0953647
\(43\) −9.23607 −1.40849 −0.704244 0.709958i \(-0.748714\pi\)
−0.704244 + 0.709958i \(0.748714\pi\)
\(44\) −8.09017 −1.21964
\(45\) −9.23607 −1.37683
\(46\) 2.47214 0.364497
\(47\) 5.14590 0.750606 0.375303 0.926902i \(-0.377539\pi\)
0.375303 + 0.926902i \(0.377539\pi\)
\(48\) −0.708204 −0.102220
\(49\) −0.145898 −0.0208426
\(50\) −3.38197 −0.478282
\(51\) −1.61803 −0.226570
\(52\) 1.61803 0.224381
\(53\) 5.70820 0.784082 0.392041 0.919948i \(-0.371769\pi\)
0.392041 + 0.919948i \(0.371769\pi\)
\(54\) −1.38197 −0.188062
\(55\) 16.1803 2.18176
\(56\) −5.85410 −0.782287
\(57\) 3.14590 0.416684
\(58\) −4.47214 −0.587220
\(59\) 11.0902 1.44382 0.721909 0.691988i \(-0.243265\pi\)
0.721909 + 0.691988i \(0.243265\pi\)
\(60\) 2.00000 0.258199
\(61\) 11.9443 1.52931 0.764654 0.644441i \(-0.222910\pi\)
0.764654 + 0.644441i \(0.222910\pi\)
\(62\) 3.85410 0.489471
\(63\) 7.47214 0.941401
\(64\) −0.236068 −0.0295085
\(65\) −3.23607 −0.401385
\(66\) 1.18034 0.145290
\(67\) −6.70820 −0.819538 −0.409769 0.912189i \(-0.634391\pi\)
−0.409769 + 0.912189i \(0.634391\pi\)
\(68\) −6.85410 −0.831182
\(69\) 1.52786 0.183933
\(70\) 5.23607 0.625830
\(71\) 9.18034 1.08951 0.544753 0.838597i \(-0.316623\pi\)
0.544753 + 0.838597i \(0.316623\pi\)
\(72\) −6.38197 −0.752122
\(73\) 13.4164 1.57027 0.785136 0.619324i \(-0.212593\pi\)
0.785136 + 0.619324i \(0.212593\pi\)
\(74\) 1.52786 0.177611
\(75\) −2.09017 −0.241352
\(76\) 13.3262 1.52862
\(77\) −13.0902 −1.49176
\(78\) −0.236068 −0.0267294
\(79\) −9.47214 −1.06570 −0.532849 0.846210i \(-0.678879\pi\)
−0.532849 + 0.846210i \(0.678879\pi\)
\(80\) 6.00000 0.670820
\(81\) 7.70820 0.856467
\(82\) −2.61803 −0.289113
\(83\) −1.76393 −0.193617 −0.0968083 0.995303i \(-0.530863\pi\)
−0.0968083 + 0.995303i \(0.530863\pi\)
\(84\) −1.61803 −0.176542
\(85\) 13.7082 1.48686
\(86\) 5.70820 0.615531
\(87\) −2.76393 −0.296325
\(88\) 11.1803 1.19183
\(89\) 0.145898 0.0154652 0.00773258 0.999970i \(-0.497539\pi\)
0.00773258 + 0.999970i \(0.497539\pi\)
\(90\) 5.70820 0.601698
\(91\) 2.61803 0.274445
\(92\) 6.47214 0.674767
\(93\) 2.38197 0.246998
\(94\) −3.18034 −0.328027
\(95\) −26.6525 −2.73449
\(96\) 2.14590 0.219015
\(97\) 3.90983 0.396983 0.198492 0.980103i \(-0.436396\pi\)
0.198492 + 0.980103i \(0.436396\pi\)
\(98\) 0.0901699 0.00910854
\(99\) −14.2705 −1.43424
\(100\) −8.85410 −0.885410
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 1.00000 0.0990148
\(103\) −13.7984 −1.35959 −0.679797 0.733400i \(-0.737932\pi\)
−0.679797 + 0.733400i \(0.737932\pi\)
\(104\) −2.23607 −0.219265
\(105\) 3.23607 0.315808
\(106\) −3.52786 −0.342656
\(107\) −11.0000 −1.06341 −0.531705 0.846930i \(-0.678449\pi\)
−0.531705 + 0.846930i \(0.678449\pi\)
\(108\) −3.61803 −0.348145
\(109\) −18.7082 −1.79192 −0.895960 0.444134i \(-0.853511\pi\)
−0.895960 + 0.444134i \(0.853511\pi\)
\(110\) −10.0000 −0.953463
\(111\) 0.944272 0.0896263
\(112\) −4.85410 −0.458670
\(113\) 6.09017 0.572915 0.286457 0.958093i \(-0.407522\pi\)
0.286457 + 0.958093i \(0.407522\pi\)
\(114\) −1.94427 −0.182098
\(115\) −12.9443 −1.20706
\(116\) −11.7082 −1.08708
\(117\) 2.85410 0.263862
\(118\) −6.85410 −0.630971
\(119\) −11.0902 −1.01663
\(120\) −2.76393 −0.252311
\(121\) 14.0000 1.27273
\(122\) −7.38197 −0.668332
\(123\) −1.61803 −0.145893
\(124\) 10.0902 0.906124
\(125\) 1.52786 0.136656
\(126\) −4.61803 −0.411407
\(127\) 19.7984 1.75682 0.878411 0.477906i \(-0.158604\pi\)
0.878411 + 0.477906i \(0.158604\pi\)
\(128\) 11.3820 1.00603
\(129\) 3.52786 0.310611
\(130\) 2.00000 0.175412
\(131\) −16.4164 −1.43431 −0.717154 0.696915i \(-0.754556\pi\)
−0.717154 + 0.696915i \(0.754556\pi\)
\(132\) 3.09017 0.268965
\(133\) 21.5623 1.86969
\(134\) 4.14590 0.358151
\(135\) 7.23607 0.622782
\(136\) 9.47214 0.812229
\(137\) 13.7082 1.17117 0.585585 0.810611i \(-0.300865\pi\)
0.585585 + 0.810611i \(0.300865\pi\)
\(138\) −0.944272 −0.0803818
\(139\) 3.23607 0.274480 0.137240 0.990538i \(-0.456177\pi\)
0.137240 + 0.990538i \(0.456177\pi\)
\(140\) 13.7082 1.15855
\(141\) −1.96556 −0.165530
\(142\) −5.67376 −0.476132
\(143\) −5.00000 −0.418121
\(144\) −5.29180 −0.440983
\(145\) 23.4164 1.94463
\(146\) −8.29180 −0.686234
\(147\) 0.0557281 0.00459638
\(148\) 4.00000 0.328798
\(149\) −16.6180 −1.36140 −0.680701 0.732561i \(-0.738325\pi\)
−0.680701 + 0.732561i \(0.738325\pi\)
\(150\) 1.29180 0.105475
\(151\) 3.05573 0.248672 0.124336 0.992240i \(-0.460320\pi\)
0.124336 + 0.992240i \(0.460320\pi\)
\(152\) −18.4164 −1.49377
\(153\) −12.0902 −0.977432
\(154\) 8.09017 0.651924
\(155\) −20.1803 −1.62092
\(156\) −0.618034 −0.0494823
\(157\) −0.944272 −0.0753611 −0.0376806 0.999290i \(-0.511997\pi\)
−0.0376806 + 0.999290i \(0.511997\pi\)
\(158\) 5.85410 0.465727
\(159\) −2.18034 −0.172912
\(160\) −18.1803 −1.43728
\(161\) 10.4721 0.825320
\(162\) −4.76393 −0.374290
\(163\) 0.708204 0.0554708 0.0277354 0.999615i \(-0.491170\pi\)
0.0277354 + 0.999615i \(0.491170\pi\)
\(164\) −6.85410 −0.535215
\(165\) −6.18034 −0.481139
\(166\) 1.09017 0.0846136
\(167\) 20.9443 1.62072 0.810358 0.585935i \(-0.199273\pi\)
0.810358 + 0.585935i \(0.199273\pi\)
\(168\) 2.23607 0.172516
\(169\) 1.00000 0.0769231
\(170\) −8.47214 −0.649783
\(171\) 23.5066 1.79759
\(172\) 14.9443 1.13949
\(173\) 3.29180 0.250271 0.125135 0.992140i \(-0.460064\pi\)
0.125135 + 0.992140i \(0.460064\pi\)
\(174\) 1.70820 0.129499
\(175\) −14.3262 −1.08296
\(176\) 9.27051 0.698791
\(177\) −4.23607 −0.318402
\(178\) −0.0901699 −0.00675852
\(179\) 22.7082 1.69729 0.848645 0.528962i \(-0.177419\pi\)
0.848645 + 0.528962i \(0.177419\pi\)
\(180\) 14.9443 1.11388
\(181\) 18.2361 1.35548 0.677738 0.735303i \(-0.262960\pi\)
0.677738 + 0.735303i \(0.262960\pi\)
\(182\) −1.61803 −0.119937
\(183\) −4.56231 −0.337255
\(184\) −8.94427 −0.659380
\(185\) −8.00000 −0.588172
\(186\) −1.47214 −0.107942
\(187\) 21.1803 1.54886
\(188\) −8.32624 −0.607253
\(189\) −5.85410 −0.425823
\(190\) 16.4721 1.19501
\(191\) 1.79837 0.130126 0.0650629 0.997881i \(-0.479275\pi\)
0.0650629 + 0.997881i \(0.479275\pi\)
\(192\) 0.0901699 0.00650746
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −2.41641 −0.173488
\(195\) 1.23607 0.0885167
\(196\) 0.236068 0.0168620
\(197\) 12.5623 0.895027 0.447514 0.894277i \(-0.352310\pi\)
0.447514 + 0.894277i \(0.352310\pi\)
\(198\) 8.81966 0.626786
\(199\) −2.61803 −0.185588 −0.0927938 0.995685i \(-0.529580\pi\)
−0.0927938 + 0.995685i \(0.529580\pi\)
\(200\) 12.2361 0.865221
\(201\) 2.56231 0.180731
\(202\) 3.70820 0.260908
\(203\) −18.9443 −1.32963
\(204\) 2.61803 0.183299
\(205\) 13.7082 0.957422
\(206\) 8.52786 0.594164
\(207\) 11.4164 0.793495
\(208\) −1.85410 −0.128559
\(209\) −41.1803 −2.84850
\(210\) −2.00000 −0.138013
\(211\) −19.2705 −1.32664 −0.663318 0.748337i \(-0.730852\pi\)
−0.663318 + 0.748337i \(0.730852\pi\)
\(212\) −9.23607 −0.634336
\(213\) −3.50658 −0.240267
\(214\) 6.79837 0.464727
\(215\) −29.8885 −2.03838
\(216\) 5.00000 0.340207
\(217\) 16.3262 1.10830
\(218\) 11.5623 0.783098
\(219\) −5.12461 −0.346289
\(220\) −26.1803 −1.76508
\(221\) −4.23607 −0.284949
\(222\) −0.583592 −0.0391681
\(223\) 19.0902 1.27837 0.639186 0.769052i \(-0.279271\pi\)
0.639186 + 0.769052i \(0.279271\pi\)
\(224\) 14.7082 0.982733
\(225\) −15.6180 −1.04120
\(226\) −3.76393 −0.250373
\(227\) −20.4164 −1.35508 −0.677542 0.735484i \(-0.736955\pi\)
−0.677542 + 0.735484i \(0.736955\pi\)
\(228\) −5.09017 −0.337105
\(229\) −9.41641 −0.622254 −0.311127 0.950368i \(-0.600706\pi\)
−0.311127 + 0.950368i \(0.600706\pi\)
\(230\) 8.00000 0.527504
\(231\) 5.00000 0.328976
\(232\) 16.1803 1.06229
\(233\) −4.56231 −0.298887 −0.149443 0.988770i \(-0.547748\pi\)
−0.149443 + 0.988770i \(0.547748\pi\)
\(234\) −1.76393 −0.115312
\(235\) 16.6525 1.08629
\(236\) −17.9443 −1.16807
\(237\) 3.61803 0.235017
\(238\) 6.85410 0.444285
\(239\) 15.7082 1.01608 0.508040 0.861334i \(-0.330370\pi\)
0.508040 + 0.861334i \(0.330370\pi\)
\(240\) −2.29180 −0.147935
\(241\) −10.8885 −0.701393 −0.350696 0.936489i \(-0.614055\pi\)
−0.350696 + 0.936489i \(0.614055\pi\)
\(242\) −8.65248 −0.556202
\(243\) −9.65248 −0.619207
\(244\) −19.3262 −1.23724
\(245\) −0.472136 −0.0301637
\(246\) 1.00000 0.0637577
\(247\) 8.23607 0.524048
\(248\) −13.9443 −0.885462
\(249\) 0.673762 0.0426979
\(250\) −0.944272 −0.0597210
\(251\) 19.4721 1.22907 0.614535 0.788889i \(-0.289344\pi\)
0.614535 + 0.788889i \(0.289344\pi\)
\(252\) −12.0902 −0.761609
\(253\) −20.0000 −1.25739
\(254\) −12.2361 −0.767759
\(255\) −5.23607 −0.327895
\(256\) −6.56231 −0.410144
\(257\) 0.819660 0.0511290 0.0255645 0.999673i \(-0.491862\pi\)
0.0255645 + 0.999673i \(0.491862\pi\)
\(258\) −2.18034 −0.135742
\(259\) 6.47214 0.402159
\(260\) 5.23607 0.324727
\(261\) −20.6525 −1.27836
\(262\) 10.1459 0.626816
\(263\) 18.2361 1.12448 0.562242 0.826973i \(-0.309939\pi\)
0.562242 + 0.826973i \(0.309939\pi\)
\(264\) −4.27051 −0.262832
\(265\) 18.4721 1.13473
\(266\) −13.3262 −0.817084
\(267\) −0.0557281 −0.00341050
\(268\) 10.8541 0.663020
\(269\) 15.2361 0.928959 0.464480 0.885584i \(-0.346241\pi\)
0.464480 + 0.885584i \(0.346241\pi\)
\(270\) −4.47214 −0.272166
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 7.85410 0.476225
\(273\) −1.00000 −0.0605228
\(274\) −8.47214 −0.511820
\(275\) 27.3607 1.64991
\(276\) −2.47214 −0.148805
\(277\) −22.0344 −1.32392 −0.661961 0.749539i \(-0.730275\pi\)
−0.661961 + 0.749539i \(0.730275\pi\)
\(278\) −2.00000 −0.119952
\(279\) 17.7984 1.06556
\(280\) −18.9443 −1.13214
\(281\) 26.7082 1.59328 0.796639 0.604455i \(-0.206609\pi\)
0.796639 + 0.604455i \(0.206609\pi\)
\(282\) 1.21478 0.0723392
\(283\) 7.29180 0.433452 0.216726 0.976232i \(-0.430462\pi\)
0.216726 + 0.976232i \(0.430462\pi\)
\(284\) −14.8541 −0.881429
\(285\) 10.1803 0.603031
\(286\) 3.09017 0.182726
\(287\) −11.0902 −0.654632
\(288\) 16.0344 0.944839
\(289\) 0.944272 0.0555454
\(290\) −14.4721 −0.849833
\(291\) −1.49342 −0.0875460
\(292\) −21.7082 −1.27038
\(293\) −22.7426 −1.32864 −0.664320 0.747448i \(-0.731279\pi\)
−0.664320 + 0.747448i \(0.731279\pi\)
\(294\) −0.0344419 −0.00200869
\(295\) 35.8885 2.08951
\(296\) −5.52786 −0.321301
\(297\) 11.1803 0.648749
\(298\) 10.2705 0.594955
\(299\) 4.00000 0.231326
\(300\) 3.38197 0.195258
\(301\) 24.1803 1.39373
\(302\) −1.88854 −0.108673
\(303\) 2.29180 0.131660
\(304\) −15.2705 −0.875824
\(305\) 38.6525 2.21323
\(306\) 7.47214 0.427154
\(307\) 4.14590 0.236619 0.118309 0.992977i \(-0.462253\pi\)
0.118309 + 0.992977i \(0.462253\pi\)
\(308\) 21.1803 1.20686
\(309\) 5.27051 0.299829
\(310\) 12.4721 0.708370
\(311\) −11.2918 −0.640299 −0.320150 0.947367i \(-0.603733\pi\)
−0.320150 + 0.947367i \(0.603733\pi\)
\(312\) 0.854102 0.0483540
\(313\) 18.0000 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 0.583592 0.0329340
\(315\) 24.1803 1.36241
\(316\) 15.3262 0.862168
\(317\) 14.8885 0.836224 0.418112 0.908395i \(-0.362692\pi\)
0.418112 + 0.908395i \(0.362692\pi\)
\(318\) 1.34752 0.0755654
\(319\) 36.1803 2.02571
\(320\) −0.763932 −0.0427051
\(321\) 4.20163 0.234512
\(322\) −6.47214 −0.360678
\(323\) −34.8885 −1.94125
\(324\) −12.4721 −0.692896
\(325\) −5.47214 −0.303539
\(326\) −0.437694 −0.0242416
\(327\) 7.14590 0.395169
\(328\) 9.47214 0.523011
\(329\) −13.4721 −0.742743
\(330\) 3.81966 0.210265
\(331\) −7.03444 −0.386648 −0.193324 0.981135i \(-0.561927\pi\)
−0.193324 + 0.981135i \(0.561927\pi\)
\(332\) 2.85410 0.156639
\(333\) 7.05573 0.386652
\(334\) −12.9443 −0.708279
\(335\) −21.7082 −1.18605
\(336\) 1.85410 0.101150
\(337\) 8.67376 0.472490 0.236245 0.971694i \(-0.424083\pi\)
0.236245 + 0.971694i \(0.424083\pi\)
\(338\) −0.618034 −0.0336166
\(339\) −2.32624 −0.126344
\(340\) −22.1803 −1.20290
\(341\) −31.1803 −1.68851
\(342\) −14.5279 −0.785577
\(343\) 18.7082 1.01015
\(344\) −20.6525 −1.11351
\(345\) 4.94427 0.266191
\(346\) −2.03444 −0.109372
\(347\) −5.23607 −0.281087 −0.140543 0.990075i \(-0.544885\pi\)
−0.140543 + 0.990075i \(0.544885\pi\)
\(348\) 4.47214 0.239732
\(349\) −2.52786 −0.135313 −0.0676567 0.997709i \(-0.521552\pi\)
−0.0676567 + 0.997709i \(0.521552\pi\)
\(350\) 8.85410 0.473272
\(351\) −2.23607 −0.119352
\(352\) −28.0902 −1.49721
\(353\) 11.6525 0.620199 0.310099 0.950704i \(-0.399638\pi\)
0.310099 + 0.950704i \(0.399638\pi\)
\(354\) 2.61803 0.139147
\(355\) 29.7082 1.57675
\(356\) −0.236068 −0.0125116
\(357\) 4.23607 0.224196
\(358\) −14.0344 −0.741743
\(359\) −5.47214 −0.288808 −0.144404 0.989519i \(-0.546127\pi\)
−0.144404 + 0.989519i \(0.546127\pi\)
\(360\) −20.6525 −1.08848
\(361\) 48.8328 2.57015
\(362\) −11.2705 −0.592365
\(363\) −5.34752 −0.280672
\(364\) −4.23607 −0.222030
\(365\) 43.4164 2.27252
\(366\) 2.81966 0.147386
\(367\) 1.43769 0.0750470 0.0375235 0.999296i \(-0.488053\pi\)
0.0375235 + 0.999296i \(0.488053\pi\)
\(368\) −7.41641 −0.386607
\(369\) −12.0902 −0.629389
\(370\) 4.94427 0.257040
\(371\) −14.9443 −0.775868
\(372\) −3.85410 −0.199826
\(373\) 4.85410 0.251336 0.125668 0.992072i \(-0.459893\pi\)
0.125668 + 0.992072i \(0.459893\pi\)
\(374\) −13.0902 −0.676877
\(375\) −0.583592 −0.0301366
\(376\) 11.5066 0.593406
\(377\) −7.23607 −0.372676
\(378\) 3.61803 0.186092
\(379\) 13.1246 0.674166 0.337083 0.941475i \(-0.390560\pi\)
0.337083 + 0.941475i \(0.390560\pi\)
\(380\) 43.1246 2.21225
\(381\) −7.56231 −0.387429
\(382\) −1.11146 −0.0568670
\(383\) −12.2918 −0.628081 −0.314041 0.949410i \(-0.601683\pi\)
−0.314041 + 0.949410i \(0.601683\pi\)
\(384\) −4.34752 −0.221859
\(385\) −42.3607 −2.15890
\(386\) −3.70820 −0.188743
\(387\) 26.3607 1.33999
\(388\) −6.32624 −0.321166
\(389\) −1.41641 −0.0718147 −0.0359074 0.999355i \(-0.511432\pi\)
−0.0359074 + 0.999355i \(0.511432\pi\)
\(390\) −0.763932 −0.0386832
\(391\) −16.9443 −0.856909
\(392\) −0.326238 −0.0164775
\(393\) 6.27051 0.316305
\(394\) −7.76393 −0.391141
\(395\) −30.6525 −1.54229
\(396\) 23.0902 1.16032
\(397\) −8.05573 −0.404305 −0.202153 0.979354i \(-0.564794\pi\)
−0.202153 + 0.979354i \(0.564794\pi\)
\(398\) 1.61803 0.0811047
\(399\) −8.23607 −0.412319
\(400\) 10.1459 0.507295
\(401\) 6.52786 0.325986 0.162993 0.986627i \(-0.447885\pi\)
0.162993 + 0.986627i \(0.447885\pi\)
\(402\) −1.58359 −0.0789824
\(403\) 6.23607 0.310641
\(404\) 9.70820 0.483001
\(405\) 24.9443 1.23949
\(406\) 11.7082 0.581068
\(407\) −12.3607 −0.612696
\(408\) −3.61803 −0.179119
\(409\) −29.2705 −1.44733 −0.723667 0.690150i \(-0.757545\pi\)
−0.723667 + 0.690150i \(0.757545\pi\)
\(410\) −8.47214 −0.418409
\(411\) −5.23607 −0.258276
\(412\) 22.3262 1.09993
\(413\) −29.0344 −1.42869
\(414\) −7.05573 −0.346770
\(415\) −5.70820 −0.280205
\(416\) 5.61803 0.275447
\(417\) −1.23607 −0.0605305
\(418\) 25.4508 1.24484
\(419\) −15.6525 −0.764673 −0.382337 0.924023i \(-0.624881\pi\)
−0.382337 + 0.924023i \(0.624881\pi\)
\(420\) −5.23607 −0.255494
\(421\) 17.5279 0.854256 0.427128 0.904191i \(-0.359525\pi\)
0.427128 + 0.904191i \(0.359525\pi\)
\(422\) 11.9098 0.579761
\(423\) −14.6869 −0.714102
\(424\) 12.7639 0.619871
\(425\) 23.1803 1.12441
\(426\) 2.16718 0.105000
\(427\) −31.2705 −1.51329
\(428\) 17.7984 0.860317
\(429\) 1.90983 0.0922075
\(430\) 18.4721 0.890805
\(431\) −0.416408 −0.0200577 −0.0100288 0.999950i \(-0.503192\pi\)
−0.0100288 + 0.999950i \(0.503192\pi\)
\(432\) 4.14590 0.199470
\(433\) 25.5623 1.22845 0.614223 0.789132i \(-0.289470\pi\)
0.614223 + 0.789132i \(0.289470\pi\)
\(434\) −10.0902 −0.484344
\(435\) −8.94427 −0.428845
\(436\) 30.2705 1.44969
\(437\) 32.9443 1.57594
\(438\) 3.16718 0.151334
\(439\) 40.9443 1.95416 0.977082 0.212864i \(-0.0682793\pi\)
0.977082 + 0.212864i \(0.0682793\pi\)
\(440\) 36.1803 1.72483
\(441\) 0.416408 0.0198289
\(442\) 2.61803 0.124527
\(443\) −21.8541 −1.03832 −0.519160 0.854677i \(-0.673755\pi\)
−0.519160 + 0.854677i \(0.673755\pi\)
\(444\) −1.52786 −0.0725092
\(445\) 0.472136 0.0223814
\(446\) −11.7984 −0.558669
\(447\) 6.34752 0.300228
\(448\) 0.618034 0.0291994
\(449\) 34.1246 1.61044 0.805220 0.592976i \(-0.202047\pi\)
0.805220 + 0.592976i \(0.202047\pi\)
\(450\) 9.65248 0.455022
\(451\) 21.1803 0.997343
\(452\) −9.85410 −0.463498
\(453\) −1.16718 −0.0548391
\(454\) 12.6180 0.592194
\(455\) 8.47214 0.397180
\(456\) 7.03444 0.329418
\(457\) 8.23607 0.385267 0.192634 0.981271i \(-0.438297\pi\)
0.192634 + 0.981271i \(0.438297\pi\)
\(458\) 5.81966 0.271935
\(459\) 9.47214 0.442121
\(460\) 20.9443 0.976532
\(461\) 11.0902 0.516521 0.258260 0.966075i \(-0.416851\pi\)
0.258260 + 0.966075i \(0.416851\pi\)
\(462\) −3.09017 −0.143768
\(463\) 6.12461 0.284635 0.142317 0.989821i \(-0.454545\pi\)
0.142317 + 0.989821i \(0.454545\pi\)
\(464\) 13.4164 0.622841
\(465\) 7.70820 0.357459
\(466\) 2.81966 0.130618
\(467\) 8.29180 0.383699 0.191849 0.981424i \(-0.438552\pi\)
0.191849 + 0.981424i \(0.438552\pi\)
\(468\) −4.61803 −0.213469
\(469\) 17.5623 0.810952
\(470\) −10.2918 −0.474725
\(471\) 0.360680 0.0166192
\(472\) 24.7984 1.14144
\(473\) −46.1803 −2.12337
\(474\) −2.23607 −0.102706
\(475\) −45.0689 −2.06790
\(476\) 17.9443 0.822474
\(477\) −16.2918 −0.745950
\(478\) −9.70820 −0.444043
\(479\) 19.3607 0.884612 0.442306 0.896864i \(-0.354161\pi\)
0.442306 + 0.896864i \(0.354161\pi\)
\(480\) 6.94427 0.316961
\(481\) 2.47214 0.112720
\(482\) 6.72949 0.306520
\(483\) −4.00000 −0.182006
\(484\) −22.6525 −1.02966
\(485\) 12.6525 0.574519
\(486\) 5.96556 0.270603
\(487\) 43.6869 1.97964 0.989822 0.142314i \(-0.0454542\pi\)
0.989822 + 0.142314i \(0.0454542\pi\)
\(488\) 26.7082 1.20902
\(489\) −0.270510 −0.0122329
\(490\) 0.291796 0.0131820
\(491\) 2.76393 0.124735 0.0623673 0.998053i \(-0.480135\pi\)
0.0623673 + 0.998053i \(0.480135\pi\)
\(492\) 2.61803 0.118030
\(493\) 30.6525 1.38052
\(494\) −5.09017 −0.229018
\(495\) −46.1803 −2.07565
\(496\) −11.5623 −0.519163
\(497\) −24.0344 −1.07809
\(498\) −0.416408 −0.0186597
\(499\) 19.9787 0.894370 0.447185 0.894441i \(-0.352427\pi\)
0.447185 + 0.894441i \(0.352427\pi\)
\(500\) −2.47214 −0.110557
\(501\) −8.00000 −0.357414
\(502\) −12.0344 −0.537123
\(503\) 32.5410 1.45093 0.725466 0.688258i \(-0.241624\pi\)
0.725466 + 0.688258i \(0.241624\pi\)
\(504\) 16.7082 0.744243
\(505\) −19.4164 −0.864019
\(506\) 12.3607 0.549499
\(507\) −0.381966 −0.0169637
\(508\) −32.0344 −1.42130
\(509\) −4.85410 −0.215154 −0.107577 0.994197i \(-0.534309\pi\)
−0.107577 + 0.994197i \(0.534309\pi\)
\(510\) 3.23607 0.143295
\(511\) −35.1246 −1.55382
\(512\) −18.7082 −0.826794
\(513\) −18.4164 −0.813104
\(514\) −0.506578 −0.0223442
\(515\) −44.6525 −1.96762
\(516\) −5.70820 −0.251290
\(517\) 25.7295 1.13158
\(518\) −4.00000 −0.175750
\(519\) −1.25735 −0.0551917
\(520\) −7.23607 −0.317323
\(521\) 13.2148 0.578950 0.289475 0.957186i \(-0.406519\pi\)
0.289475 + 0.957186i \(0.406519\pi\)
\(522\) 12.7639 0.558662
\(523\) 11.3475 0.496193 0.248096 0.968735i \(-0.420195\pi\)
0.248096 + 0.968735i \(0.420195\pi\)
\(524\) 26.5623 1.16038
\(525\) 5.47214 0.238824
\(526\) −11.2705 −0.491418
\(527\) −26.4164 −1.15072
\(528\) −3.54102 −0.154103
\(529\) −7.00000 −0.304348
\(530\) −11.4164 −0.495897
\(531\) −31.6525 −1.37360
\(532\) −34.8885 −1.51261
\(533\) −4.23607 −0.183484
\(534\) 0.0344419 0.00149044
\(535\) −35.5967 −1.53898
\(536\) −15.0000 −0.647901
\(537\) −8.67376 −0.374300
\(538\) −9.41641 −0.405970
\(539\) −0.729490 −0.0314214
\(540\) −11.7082 −0.503841
\(541\) 11.9443 0.513524 0.256762 0.966475i \(-0.417344\pi\)
0.256762 + 0.966475i \(0.417344\pi\)
\(542\) 8.03444 0.345109
\(543\) −6.96556 −0.298921
\(544\) −23.7984 −1.02035
\(545\) −60.5410 −2.59329
\(546\) 0.618034 0.0264494
\(547\) 13.8197 0.590886 0.295443 0.955360i \(-0.404533\pi\)
0.295443 + 0.955360i \(0.404533\pi\)
\(548\) −22.1803 −0.947497
\(549\) −34.0902 −1.45493
\(550\) −16.9098 −0.721038
\(551\) −59.5967 −2.53891
\(552\) 3.41641 0.145412
\(553\) 24.7984 1.05453
\(554\) 13.6180 0.578575
\(555\) 3.05573 0.129708
\(556\) −5.23607 −0.222059
\(557\) −9.38197 −0.397527 −0.198763 0.980048i \(-0.563693\pi\)
−0.198763 + 0.980048i \(0.563693\pi\)
\(558\) −11.0000 −0.465667
\(559\) 9.23607 0.390644
\(560\) −15.7082 −0.663793
\(561\) −8.09017 −0.341567
\(562\) −16.5066 −0.696288
\(563\) 9.09017 0.383105 0.191552 0.981482i \(-0.438648\pi\)
0.191552 + 0.981482i \(0.438648\pi\)
\(564\) 3.18034 0.133916
\(565\) 19.7082 0.829130
\(566\) −4.50658 −0.189426
\(567\) −20.1803 −0.847495
\(568\) 20.5279 0.861330
\(569\) 17.9098 0.750819 0.375410 0.926859i \(-0.377502\pi\)
0.375410 + 0.926859i \(0.377502\pi\)
\(570\) −6.29180 −0.263534
\(571\) 32.7771 1.37168 0.685839 0.727753i \(-0.259435\pi\)
0.685839 + 0.727753i \(0.259435\pi\)
\(572\) 8.09017 0.338267
\(573\) −0.686918 −0.0286964
\(574\) 6.85410 0.286085
\(575\) −21.8885 −0.912815
\(576\) 0.673762 0.0280734
\(577\) −23.1246 −0.962690 −0.481345 0.876531i \(-0.659852\pi\)
−0.481345 + 0.876531i \(0.659852\pi\)
\(578\) −0.583592 −0.0242742
\(579\) −2.29180 −0.0952438
\(580\) −37.8885 −1.57324
\(581\) 4.61803 0.191588
\(582\) 0.922986 0.0382590
\(583\) 28.5410 1.18205
\(584\) 30.0000 1.24141
\(585\) 9.23607 0.381864
\(586\) 14.0557 0.580637
\(587\) −36.7984 −1.51883 −0.759416 0.650606i \(-0.774515\pi\)
−0.759416 + 0.650606i \(0.774515\pi\)
\(588\) −0.0901699 −0.00371855
\(589\) 51.3607 2.11628
\(590\) −22.1803 −0.913150
\(591\) −4.79837 −0.197379
\(592\) −4.58359 −0.188384
\(593\) 21.0344 0.863781 0.431890 0.901926i \(-0.357847\pi\)
0.431890 + 0.901926i \(0.357847\pi\)
\(594\) −6.90983 −0.283514
\(595\) −35.8885 −1.47129
\(596\) 26.8885 1.10140
\(597\) 1.00000 0.0409273
\(598\) −2.47214 −0.101093
\(599\) −2.12461 −0.0868093 −0.0434046 0.999058i \(-0.513820\pi\)
−0.0434046 + 0.999058i \(0.513820\pi\)
\(600\) −4.67376 −0.190806
\(601\) 38.2705 1.56109 0.780543 0.625102i \(-0.214943\pi\)
0.780543 + 0.625102i \(0.214943\pi\)
\(602\) −14.9443 −0.609083
\(603\) 19.1459 0.779681
\(604\) −4.94427 −0.201180
\(605\) 45.3050 1.84191
\(606\) −1.41641 −0.0575376
\(607\) 19.3607 0.785826 0.392913 0.919576i \(-0.371467\pi\)
0.392913 + 0.919576i \(0.371467\pi\)
\(608\) 46.2705 1.87652
\(609\) 7.23607 0.293220
\(610\) −23.8885 −0.967219
\(611\) −5.14590 −0.208181
\(612\) 19.5623 0.790759
\(613\) 12.0344 0.486067 0.243033 0.970018i \(-0.421858\pi\)
0.243033 + 0.970018i \(0.421858\pi\)
\(614\) −2.56231 −0.103406
\(615\) −5.23607 −0.211139
\(616\) −29.2705 −1.17934
\(617\) 38.6525 1.55609 0.778045 0.628208i \(-0.216212\pi\)
0.778045 + 0.628208i \(0.216212\pi\)
\(618\) −3.25735 −0.131030
\(619\) 1.00000 0.0401934
\(620\) 32.6525 1.31135
\(621\) −8.94427 −0.358921
\(622\) 6.97871 0.279821
\(623\) −0.381966 −0.0153031
\(624\) 0.708204 0.0283508
\(625\) −22.4164 −0.896656
\(626\) −11.1246 −0.444629
\(627\) 15.7295 0.628175
\(628\) 1.52786 0.0609684
\(629\) −10.4721 −0.417551
\(630\) −14.9443 −0.595394
\(631\) −30.2148 −1.20283 −0.601416 0.798936i \(-0.705396\pi\)
−0.601416 + 0.798936i \(0.705396\pi\)
\(632\) −21.1803 −0.842509
\(633\) 7.36068 0.292561
\(634\) −9.20163 −0.365443
\(635\) 64.0689 2.54250
\(636\) 3.52786 0.139889
\(637\) 0.145898 0.00578069
\(638\) −22.3607 −0.885268
\(639\) −26.2016 −1.03652
\(640\) 36.8328 1.45594
\(641\) 24.0000 0.947943 0.473972 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) −2.59675 −0.102485
\(643\) 12.4164 0.489655 0.244828 0.969567i \(-0.421269\pi\)
0.244828 + 0.969567i \(0.421269\pi\)
\(644\) −16.9443 −0.667698
\(645\) 11.4164 0.449521
\(646\) 21.5623 0.848358
\(647\) −4.87539 −0.191671 −0.0958356 0.995397i \(-0.530552\pi\)
−0.0958356 + 0.995397i \(0.530552\pi\)
\(648\) 17.2361 0.677097
\(649\) 55.4508 2.17664
\(650\) 3.38197 0.132652
\(651\) −6.23607 −0.244411
\(652\) −1.14590 −0.0448768
\(653\) 1.00000 0.0391330 0.0195665 0.999809i \(-0.493771\pi\)
0.0195665 + 0.999809i \(0.493771\pi\)
\(654\) −4.41641 −0.172695
\(655\) −53.1246 −2.07575
\(656\) 7.85410 0.306651
\(657\) −38.2918 −1.49391
\(658\) 8.32624 0.324591
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 10.0000 0.389249
\(661\) −20.7082 −0.805456 −0.402728 0.915320i \(-0.631938\pi\)
−0.402728 + 0.915320i \(0.631938\pi\)
\(662\) 4.34752 0.168971
\(663\) 1.61803 0.0628392
\(664\) −3.94427 −0.153067
\(665\) 69.7771 2.70584
\(666\) −4.36068 −0.168973
\(667\) −28.9443 −1.12073
\(668\) −33.8885 −1.31119
\(669\) −7.29180 −0.281917
\(670\) 13.4164 0.518321
\(671\) 59.7214 2.30552
\(672\) −5.61803 −0.216720
\(673\) −26.5623 −1.02390 −0.511951 0.859015i \(-0.671077\pi\)
−0.511951 + 0.859015i \(0.671077\pi\)
\(674\) −5.36068 −0.206486
\(675\) 12.2361 0.470966
\(676\) −1.61803 −0.0622321
\(677\) −11.2918 −0.433979 −0.216989 0.976174i \(-0.569624\pi\)
−0.216989 + 0.976174i \(0.569624\pi\)
\(678\) 1.43769 0.0552143
\(679\) −10.2361 −0.392824
\(680\) 30.6525 1.17547
\(681\) 7.79837 0.298834
\(682\) 19.2705 0.737906
\(683\) −29.5623 −1.13117 −0.565585 0.824690i \(-0.691350\pi\)
−0.565585 + 0.824690i \(0.691350\pi\)
\(684\) −38.0344 −1.45428
\(685\) 44.3607 1.69493
\(686\) −11.5623 −0.441451
\(687\) 3.59675 0.137224
\(688\) −17.1246 −0.652870
\(689\) −5.70820 −0.217465
\(690\) −3.05573 −0.116330
\(691\) 35.8328 1.36314 0.681572 0.731751i \(-0.261297\pi\)
0.681572 + 0.731751i \(0.261297\pi\)
\(692\) −5.32624 −0.202473
\(693\) 37.3607 1.41921
\(694\) 3.23607 0.122839
\(695\) 10.4721 0.397231
\(696\) −6.18034 −0.234265
\(697\) 17.9443 0.679688
\(698\) 1.56231 0.0591342
\(699\) 1.74265 0.0659129
\(700\) 23.1803 0.876134
\(701\) 30.2361 1.14200 0.571000 0.820950i \(-0.306556\pi\)
0.571000 + 0.820950i \(0.306556\pi\)
\(702\) 1.38197 0.0521589
\(703\) 20.3607 0.767918
\(704\) −1.18034 −0.0444857
\(705\) −6.36068 −0.239557
\(706\) −7.20163 −0.271037
\(707\) 15.7082 0.590768
\(708\) 6.85410 0.257593
\(709\) −47.1246 −1.76980 −0.884901 0.465779i \(-0.845774\pi\)
−0.884901 + 0.465779i \(0.845774\pi\)
\(710\) −18.3607 −0.689064
\(711\) 27.0344 1.01387
\(712\) 0.326238 0.0122263
\(713\) 24.9443 0.934170
\(714\) −2.61803 −0.0979775
\(715\) −16.1803 −0.605110
\(716\) −36.7426 −1.37314
\(717\) −6.00000 −0.224074
\(718\) 3.38197 0.126214
\(719\) 32.2918 1.20428 0.602140 0.798390i \(-0.294315\pi\)
0.602140 + 0.798390i \(0.294315\pi\)
\(720\) −17.1246 −0.638197
\(721\) 36.1246 1.34535
\(722\) −30.1803 −1.12320
\(723\) 4.15905 0.154677
\(724\) −29.5066 −1.09660
\(725\) 39.5967 1.47059
\(726\) 3.30495 0.122658
\(727\) 44.1803 1.63856 0.819279 0.573395i \(-0.194374\pi\)
0.819279 + 0.573395i \(0.194374\pi\)
\(728\) 5.85410 0.216967
\(729\) −19.4377 −0.719915
\(730\) −26.8328 −0.993127
\(731\) −39.1246 −1.44708
\(732\) 7.38197 0.272845
\(733\) 20.5836 0.760272 0.380136 0.924931i \(-0.375877\pi\)
0.380136 + 0.924931i \(0.375877\pi\)
\(734\) −0.888544 −0.0327968
\(735\) 0.180340 0.00665194
\(736\) 22.4721 0.828334
\(737\) −33.5410 −1.23550
\(738\) 7.47214 0.275053
\(739\) 18.1803 0.668775 0.334387 0.942436i \(-0.391471\pi\)
0.334387 + 0.942436i \(0.391471\pi\)
\(740\) 12.9443 0.475841
\(741\) −3.14590 −0.115567
\(742\) 9.23607 0.339067
\(743\) −10.8541 −0.398198 −0.199099 0.979979i \(-0.563802\pi\)
−0.199099 + 0.979979i \(0.563802\pi\)
\(744\) 5.32624 0.195269
\(745\) −53.7771 −1.97024
\(746\) −3.00000 −0.109838
\(747\) 5.03444 0.184201
\(748\) −34.2705 −1.25305
\(749\) 28.7984 1.05227
\(750\) 0.360680 0.0131702
\(751\) 44.2148 1.61342 0.806710 0.590947i \(-0.201246\pi\)
0.806710 + 0.590947i \(0.201246\pi\)
\(752\) 9.54102 0.347925
\(753\) −7.43769 −0.271045
\(754\) 4.47214 0.162866
\(755\) 9.88854 0.359881
\(756\) 9.47214 0.344498
\(757\) −21.3820 −0.777141 −0.388570 0.921419i \(-0.627031\pi\)
−0.388570 + 0.921419i \(0.627031\pi\)
\(758\) −8.11146 −0.294621
\(759\) 7.63932 0.277290
\(760\) −59.5967 −2.16180
\(761\) −12.9098 −0.467981 −0.233990 0.972239i \(-0.575178\pi\)
−0.233990 + 0.972239i \(0.575178\pi\)
\(762\) 4.67376 0.169313
\(763\) 48.9787 1.77315
\(764\) −2.90983 −0.105274
\(765\) −39.1246 −1.41455
\(766\) 7.59675 0.274482
\(767\) −11.0902 −0.400443
\(768\) 2.50658 0.0904483
\(769\) −4.02129 −0.145011 −0.0725056 0.997368i \(-0.523100\pi\)
−0.0725056 + 0.997368i \(0.523100\pi\)
\(770\) 26.1803 0.943474
\(771\) −0.313082 −0.0112754
\(772\) −9.70820 −0.349406
\(773\) −29.7426 −1.06977 −0.534884 0.844925i \(-0.679645\pi\)
−0.534884 + 0.844925i \(0.679645\pi\)
\(774\) −16.2918 −0.585597
\(775\) −34.1246 −1.22579
\(776\) 8.74265 0.313843
\(777\) −2.47214 −0.0886874
\(778\) 0.875388 0.0313842
\(779\) −34.8885 −1.25001
\(780\) −2.00000 −0.0716115
\(781\) 45.9017 1.64249
\(782\) 10.4721 0.374483
\(783\) 16.1803 0.578238
\(784\) −0.270510 −0.00966107
\(785\) −3.05573 −0.109064
\(786\) −3.87539 −0.138231
\(787\) 43.0000 1.53278 0.766392 0.642373i \(-0.222050\pi\)
0.766392 + 0.642373i \(0.222050\pi\)
\(788\) −20.3262 −0.724092
\(789\) −6.96556 −0.247980
\(790\) 18.9443 0.674007
\(791\) −15.9443 −0.566913
\(792\) −31.9098 −1.13387
\(793\) −11.9443 −0.424154
\(794\) 4.97871 0.176688
\(795\) −7.05573 −0.250241
\(796\) 4.23607 0.150143
\(797\) −44.8328 −1.58806 −0.794030 0.607879i \(-0.792021\pi\)
−0.794030 + 0.607879i \(0.792021\pi\)
\(798\) 5.09017 0.180190
\(799\) 21.7984 0.771171
\(800\) −30.7426 −1.08692
\(801\) −0.416408 −0.0147130
\(802\) −4.03444 −0.142461
\(803\) 67.0820 2.36727
\(804\) −4.14590 −0.146215
\(805\) 33.8885 1.19441
\(806\) −3.85410 −0.135755
\(807\) −5.81966 −0.204862
\(808\) −13.4164 −0.471988
\(809\) 38.7426 1.36212 0.681059 0.732228i \(-0.261520\pi\)
0.681059 + 0.732228i \(0.261520\pi\)
\(810\) −15.4164 −0.541677
\(811\) −37.9443 −1.33240 −0.666202 0.745772i \(-0.732081\pi\)
−0.666202 + 0.745772i \(0.732081\pi\)
\(812\) 30.6525 1.07569
\(813\) 4.96556 0.174150
\(814\) 7.63932 0.267758
\(815\) 2.29180 0.0802781
\(816\) −3.00000 −0.105021
\(817\) 76.0689 2.66131
\(818\) 18.0902 0.632508
\(819\) −7.47214 −0.261098
\(820\) −22.1803 −0.774571
\(821\) 7.76393 0.270963 0.135482 0.990780i \(-0.456742\pi\)
0.135482 + 0.990780i \(0.456742\pi\)
\(822\) 3.23607 0.112871
\(823\) 21.7639 0.758643 0.379321 0.925265i \(-0.376157\pi\)
0.379321 + 0.925265i \(0.376157\pi\)
\(824\) −30.8541 −1.07485
\(825\) −10.4508 −0.363852
\(826\) 17.9443 0.624361
\(827\) 39.9574 1.38946 0.694728 0.719273i \(-0.255525\pi\)
0.694728 + 0.719273i \(0.255525\pi\)
\(828\) −18.4721 −0.641951
\(829\) −29.7984 −1.03494 −0.517470 0.855701i \(-0.673126\pi\)
−0.517470 + 0.855701i \(0.673126\pi\)
\(830\) 3.52786 0.122454
\(831\) 8.41641 0.291962
\(832\) 0.236068 0.00818418
\(833\) −0.618034 −0.0214136
\(834\) 0.763932 0.0264528
\(835\) 67.7771 2.34552
\(836\) 66.6312 2.30449
\(837\) −13.9443 −0.481985
\(838\) 9.67376 0.334175
\(839\) 12.0344 0.415475 0.207738 0.978185i \(-0.433390\pi\)
0.207738 + 0.978185i \(0.433390\pi\)
\(840\) 7.23607 0.249668
\(841\) 23.3607 0.805541
\(842\) −10.8328 −0.373323
\(843\) −10.2016 −0.351363
\(844\) 31.1803 1.07327
\(845\) 3.23607 0.111324
\(846\) 9.07701 0.312074
\(847\) −36.6525 −1.25939
\(848\) 10.5836 0.363442
\(849\) −2.78522 −0.0955884
\(850\) −14.3262 −0.491386
\(851\) 9.88854 0.338975
\(852\) 5.67376 0.194380
\(853\) 16.5279 0.565903 0.282952 0.959134i \(-0.408686\pi\)
0.282952 + 0.959134i \(0.408686\pi\)
\(854\) 19.3262 0.661330
\(855\) 76.0689 2.60150
\(856\) −24.5967 −0.840700
\(857\) 36.9230 1.26127 0.630633 0.776082i \(-0.282796\pi\)
0.630633 + 0.776082i \(0.282796\pi\)
\(858\) −1.18034 −0.0402961
\(859\) 5.45085 0.185981 0.0929903 0.995667i \(-0.470357\pi\)
0.0929903 + 0.995667i \(0.470357\pi\)
\(860\) 48.3607 1.64909
\(861\) 4.23607 0.144365
\(862\) 0.257354 0.00876552
\(863\) −5.21478 −0.177513 −0.0887566 0.996053i \(-0.528289\pi\)
−0.0887566 + 0.996053i \(0.528289\pi\)
\(864\) −12.5623 −0.427378
\(865\) 10.6525 0.362195
\(866\) −15.7984 −0.536851
\(867\) −0.360680 −0.0122493
\(868\) −26.4164 −0.896631
\(869\) −47.3607 −1.60660
\(870\) 5.52786 0.187412
\(871\) 6.70820 0.227299
\(872\) −41.8328 −1.41664
\(873\) −11.1591 −0.377677
\(874\) −20.3607 −0.688710
\(875\) −4.00000 −0.135225
\(876\) 8.29180 0.280154
\(877\) −17.8328 −0.602171 −0.301086 0.953597i \(-0.597349\pi\)
−0.301086 + 0.953597i \(0.597349\pi\)
\(878\) −25.3050 −0.854001
\(879\) 8.68692 0.293002
\(880\) 30.0000 1.01130
\(881\) −30.2148 −1.01796 −0.508981 0.860778i \(-0.669978\pi\)
−0.508981 + 0.860778i \(0.669978\pi\)
\(882\) −0.257354 −0.00866557
\(883\) 7.21478 0.242797 0.121398 0.992604i \(-0.461262\pi\)
0.121398 + 0.992604i \(0.461262\pi\)
\(884\) 6.85410 0.230528
\(885\) −13.7082 −0.460796
\(886\) 13.5066 0.453762
\(887\) 3.67376 0.123353 0.0616764 0.998096i \(-0.480355\pi\)
0.0616764 + 0.998096i \(0.480355\pi\)
\(888\) 2.11146 0.0708558
\(889\) −51.8328 −1.73842
\(890\) −0.291796 −0.00978103
\(891\) 38.5410 1.29117
\(892\) −30.8885 −1.03422
\(893\) −42.3820 −1.41826
\(894\) −3.92299 −0.131204
\(895\) 73.4853 2.45634
\(896\) −29.7984 −0.995494
\(897\) −1.52786 −0.0510139
\(898\) −21.0902 −0.703788
\(899\) −45.1246 −1.50499
\(900\) 25.2705 0.842350
\(901\) 24.1803 0.805564
\(902\) −13.0902 −0.435855
\(903\) −9.23607 −0.307357
\(904\) 13.6180 0.452929
\(905\) 59.0132 1.96166
\(906\) 0.721360 0.0239656
\(907\) −40.9230 −1.35883 −0.679413 0.733756i \(-0.737765\pi\)
−0.679413 + 0.733756i \(0.737765\pi\)
\(908\) 33.0344 1.09629
\(909\) 17.1246 0.567988
\(910\) −5.23607 −0.173574
\(911\) 48.5623 1.60894 0.804470 0.593993i \(-0.202449\pi\)
0.804470 + 0.593993i \(0.202449\pi\)
\(912\) 5.83282 0.193144
\(913\) −8.81966 −0.291888
\(914\) −5.09017 −0.168368
\(915\) −14.7639 −0.488081
\(916\) 15.2361 0.503414
\(917\) 42.9787 1.41928
\(918\) −5.85410 −0.193214
\(919\) 22.4164 0.739449 0.369725 0.929141i \(-0.379452\pi\)
0.369725 + 0.929141i \(0.379452\pi\)
\(920\) −28.9443 −0.954264
\(921\) −1.58359 −0.0521811
\(922\) −6.85410 −0.225728
\(923\) −9.18034 −0.302175
\(924\) −8.09017 −0.266147
\(925\) −13.5279 −0.444793
\(926\) −3.78522 −0.124390
\(927\) 39.3820 1.29347
\(928\) −40.6525 −1.33448
\(929\) 29.3607 0.963293 0.481646 0.876366i \(-0.340039\pi\)
0.481646 + 0.876366i \(0.340039\pi\)
\(930\) −4.76393 −0.156215
\(931\) 1.20163 0.0393817
\(932\) 7.38197 0.241804
\(933\) 4.31308 0.141204
\(934\) −5.12461 −0.167682
\(935\) 68.5410 2.24153
\(936\) 6.38197 0.208601
\(937\) 13.3475 0.436045 0.218022 0.975944i \(-0.430039\pi\)
0.218022 + 0.975944i \(0.430039\pi\)
\(938\) −10.8541 −0.354399
\(939\) −6.87539 −0.224370
\(940\) −26.9443 −0.878825
\(941\) 36.2705 1.18238 0.591192 0.806531i \(-0.298657\pi\)
0.591192 + 0.806531i \(0.298657\pi\)
\(942\) −0.222912 −0.00726288
\(943\) −16.9443 −0.551781
\(944\) 20.5623 0.669246
\(945\) −18.9443 −0.616257
\(946\) 28.5410 0.927949
\(947\) −25.5410 −0.829972 −0.414986 0.909828i \(-0.636213\pi\)
−0.414986 + 0.909828i \(0.636213\pi\)
\(948\) −5.85410 −0.190132
\(949\) −13.4164 −0.435515
\(950\) 27.8541 0.903706
\(951\) −5.68692 −0.184411
\(952\) −24.7984 −0.803720
\(953\) −26.7771 −0.867395 −0.433697 0.901059i \(-0.642791\pi\)
−0.433697 + 0.901059i \(0.642791\pi\)
\(954\) 10.0689 0.325992
\(955\) 5.81966 0.188320
\(956\) −25.4164 −0.822025
\(957\) −13.8197 −0.446726
\(958\) −11.9656 −0.386590
\(959\) −35.8885 −1.15890
\(960\) 0.291796 0.00941768
\(961\) 7.88854 0.254469
\(962\) −1.52786 −0.0492603
\(963\) 31.3951 1.01169
\(964\) 17.6180 0.567439
\(965\) 19.4164 0.625036
\(966\) 2.47214 0.0795397
\(967\) −16.3951 −0.527232 −0.263616 0.964628i \(-0.584915\pi\)
−0.263616 + 0.964628i \(0.584915\pi\)
\(968\) 31.3050 1.00618
\(969\) 13.3262 0.428100
\(970\) −7.81966 −0.251074
\(971\) −18.1246 −0.581646 −0.290823 0.956777i \(-0.593929\pi\)
−0.290823 + 0.956777i \(0.593929\pi\)
\(972\) 15.6180 0.500949
\(973\) −8.47214 −0.271604
\(974\) −27.0000 −0.865136
\(975\) 2.09017 0.0669390
\(976\) 22.1459 0.708873
\(977\) 32.6738 1.04533 0.522663 0.852539i \(-0.324939\pi\)
0.522663 + 0.852539i \(0.324939\pi\)
\(978\) 0.167184 0.00534596
\(979\) 0.729490 0.0233146
\(980\) 0.763932 0.0244029
\(981\) 53.3951 1.70478
\(982\) −1.70820 −0.0545110
\(983\) −54.7771 −1.74712 −0.873559 0.486718i \(-0.838194\pi\)
−0.873559 + 0.486718i \(0.838194\pi\)
\(984\) −3.61803 −0.115339
\(985\) 40.6525 1.29530
\(986\) −18.9443 −0.603309
\(987\) 5.14590 0.163796
\(988\) −13.3262 −0.423964
\(989\) 36.9443 1.17476
\(990\) 28.5410 0.907093
\(991\) 49.3050 1.56622 0.783112 0.621881i \(-0.213631\pi\)
0.783112 + 0.621881i \(0.213631\pi\)
\(992\) 35.0344 1.11234
\(993\) 2.68692 0.0852668
\(994\) 14.8541 0.471144
\(995\) −8.47214 −0.268585
\(996\) −1.09017 −0.0345434
\(997\) −23.4508 −0.742696 −0.371348 0.928494i \(-0.621104\pi\)
−0.371348 + 0.928494i \(0.621104\pi\)
\(998\) −12.3475 −0.390854
\(999\) −5.52786 −0.174894
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 \(a_p\))