Properties

Label 8042.2.a.c.1.5
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +4.36753 q^{10} -3.11755 q^{11} -2.78277 q^{12} +2.74460 q^{13} +3.26500 q^{14} +12.1538 q^{15} +1.00000 q^{16} -0.733217 q^{17} -4.74379 q^{18} +3.29698 q^{19} -4.36753 q^{20} +9.08573 q^{21} +3.11755 q^{22} -3.92947 q^{23} +2.78277 q^{24} +14.0753 q^{25} -2.74460 q^{26} -4.85257 q^{27} -3.26500 q^{28} -0.134478 q^{29} -12.1538 q^{30} -0.0430877 q^{31} -1.00000 q^{32} +8.67541 q^{33} +0.733217 q^{34} +14.2600 q^{35} +4.74379 q^{36} +5.10334 q^{37} -3.29698 q^{38} -7.63758 q^{39} +4.36753 q^{40} -7.00654 q^{41} -9.08573 q^{42} +6.34974 q^{43} -3.11755 q^{44} -20.7187 q^{45} +3.92947 q^{46} +3.45793 q^{47} -2.78277 q^{48} +3.66020 q^{49} -14.0753 q^{50} +2.04037 q^{51} +2.74460 q^{52} -9.77167 q^{53} +4.85257 q^{54} +13.6160 q^{55} +3.26500 q^{56} -9.17474 q^{57} +0.134478 q^{58} -0.605095 q^{59} +12.1538 q^{60} -9.60040 q^{61} +0.0430877 q^{62} -15.4885 q^{63} +1.00000 q^{64} -11.9871 q^{65} -8.67541 q^{66} +2.80505 q^{67} -0.733217 q^{68} +10.9348 q^{69} -14.2600 q^{70} -1.07101 q^{71} -4.74379 q^{72} +10.9618 q^{73} -5.10334 q^{74} -39.1683 q^{75} +3.29698 q^{76} +10.1788 q^{77} +7.63758 q^{78} -4.01696 q^{79} -4.36753 q^{80} -0.727798 q^{81} +7.00654 q^{82} +3.72621 q^{83} +9.08573 q^{84} +3.20234 q^{85} -6.34974 q^{86} +0.374222 q^{87} +3.11755 q^{88} -3.02088 q^{89} +20.7187 q^{90} -8.96111 q^{91} -3.92947 q^{92} +0.119903 q^{93} -3.45793 q^{94} -14.3997 q^{95} +2.78277 q^{96} -15.4949 q^{97} -3.66020 q^{98} -14.7890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

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
\(3\) −2.78277 −1.60663 −0.803316 0.595553i \(-0.796933\pi\)
−0.803316 + 0.595553i \(0.796933\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.36753 −1.95322 −0.976609 0.215024i \(-0.931017\pi\)
−0.976609 + 0.215024i \(0.931017\pi\)
\(6\) 2.78277 1.13606
\(7\) −3.26500 −1.23405 −0.617026 0.786942i \(-0.711663\pi\)
−0.617026 + 0.786942i \(0.711663\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.74379 1.58126
\(10\) 4.36753 1.38113
\(11\) −3.11755 −0.939976 −0.469988 0.882673i \(-0.655742\pi\)
−0.469988 + 0.882673i \(0.655742\pi\)
\(12\) −2.78277 −0.803316
\(13\) 2.74460 0.761215 0.380607 0.924737i \(-0.375715\pi\)
0.380607 + 0.924737i \(0.375715\pi\)
\(14\) 3.26500 0.872607
\(15\) 12.1538 3.13810
\(16\) 1.00000 0.250000
\(17\) −0.733217 −0.177831 −0.0889156 0.996039i \(-0.528340\pi\)
−0.0889156 + 0.996039i \(0.528340\pi\)
\(18\) −4.74379 −1.11812
\(19\) 3.29698 0.756380 0.378190 0.925728i \(-0.376547\pi\)
0.378190 + 0.925728i \(0.376547\pi\)
\(20\) −4.36753 −0.976609
\(21\) 9.08573 1.98267
\(22\) 3.11755 0.664664
\(23\) −3.92947 −0.819352 −0.409676 0.912231i \(-0.634358\pi\)
−0.409676 + 0.912231i \(0.634358\pi\)
\(24\) 2.78277 0.568030
\(25\) 14.0753 2.81506
\(26\) −2.74460 −0.538260
\(27\) −4.85257 −0.933878
\(28\) −3.26500 −0.617026
\(29\) −0.134478 −0.0249720 −0.0124860 0.999922i \(-0.503975\pi\)
−0.0124860 + 0.999922i \(0.503975\pi\)
\(30\) −12.1538 −2.21897
\(31\) −0.0430877 −0.00773878 −0.00386939 0.999993i \(-0.501232\pi\)
−0.00386939 + 0.999993i \(0.501232\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.67541 1.51020
\(34\) 0.733217 0.125746
\(35\) 14.2600 2.41037
\(36\) 4.74379 0.790632
\(37\) 5.10334 0.838983 0.419492 0.907759i \(-0.362208\pi\)
0.419492 + 0.907759i \(0.362208\pi\)
\(38\) −3.29698 −0.534841
\(39\) −7.63758 −1.22299
\(40\) 4.36753 0.690567
\(41\) −7.00654 −1.09424 −0.547119 0.837055i \(-0.684275\pi\)
−0.547119 + 0.837055i \(0.684275\pi\)
\(42\) −9.08573 −1.40196
\(43\) 6.34974 0.968326 0.484163 0.874978i \(-0.339124\pi\)
0.484163 + 0.874978i \(0.339124\pi\)
\(44\) −3.11755 −0.469988
\(45\) −20.7187 −3.08855
\(46\) 3.92947 0.579369
\(47\) 3.45793 0.504392 0.252196 0.967676i \(-0.418847\pi\)
0.252196 + 0.967676i \(0.418847\pi\)
\(48\) −2.78277 −0.401658
\(49\) 3.66020 0.522886
\(50\) −14.0753 −1.99055
\(51\) 2.04037 0.285709
\(52\) 2.74460 0.380607
\(53\) −9.77167 −1.34224 −0.671121 0.741348i \(-0.734187\pi\)
−0.671121 + 0.741348i \(0.734187\pi\)
\(54\) 4.85257 0.660352
\(55\) 13.6160 1.83598
\(56\) 3.26500 0.436304
\(57\) −9.17474 −1.21522
\(58\) 0.134478 0.0176579
\(59\) −0.605095 −0.0787767 −0.0393883 0.999224i \(-0.512541\pi\)
−0.0393883 + 0.999224i \(0.512541\pi\)
\(60\) 12.1538 1.56905
\(61\) −9.60040 −1.22921 −0.614603 0.788837i \(-0.710684\pi\)
−0.614603 + 0.788837i \(0.710684\pi\)
\(62\) 0.0430877 0.00547214
\(63\) −15.4885 −1.95136
\(64\) 1.00000 0.125000
\(65\) −11.9871 −1.48682
\(66\) −8.67541 −1.06787
\(67\) 2.80505 0.342692 0.171346 0.985211i \(-0.445188\pi\)
0.171346 + 0.985211i \(0.445188\pi\)
\(68\) −0.733217 −0.0889156
\(69\) 10.9348 1.31640
\(70\) −14.2600 −1.70439
\(71\) −1.07101 −0.127106 −0.0635529 0.997978i \(-0.520243\pi\)
−0.0635529 + 0.997978i \(0.520243\pi\)
\(72\) −4.74379 −0.559062
\(73\) 10.9618 1.28299 0.641493 0.767129i \(-0.278315\pi\)
0.641493 + 0.767129i \(0.278315\pi\)
\(74\) −5.10334 −0.593251
\(75\) −39.1683 −4.52276
\(76\) 3.29698 0.378190
\(77\) 10.1788 1.15998
\(78\) 7.63758 0.864786
\(79\) −4.01696 −0.451943 −0.225971 0.974134i \(-0.572556\pi\)
−0.225971 + 0.974134i \(0.572556\pi\)
\(80\) −4.36753 −0.488304
\(81\) −0.727798 −0.0808665
\(82\) 7.00654 0.773743
\(83\) 3.72621 0.409004 0.204502 0.978866i \(-0.434442\pi\)
0.204502 + 0.978866i \(0.434442\pi\)
\(84\) 9.08573 0.991334
\(85\) 3.20234 0.347343
\(86\) −6.34974 −0.684710
\(87\) 0.374222 0.0401208
\(88\) 3.11755 0.332332
\(89\) −3.02088 −0.320212 −0.160106 0.987100i \(-0.551184\pi\)
−0.160106 + 0.987100i \(0.551184\pi\)
\(90\) 20.7187 2.18394
\(91\) −8.96111 −0.939379
\(92\) −3.92947 −0.409676
\(93\) 0.119903 0.0124334
\(94\) −3.45793 −0.356659
\(95\) −14.3997 −1.47737
\(96\) 2.78277 0.284015
\(97\) −15.4949 −1.57327 −0.786633 0.617421i \(-0.788177\pi\)
−0.786633 + 0.617421i \(0.788177\pi\)
\(98\) −3.66020 −0.369736
\(99\) −14.7890 −1.48635
\(100\) 14.0753 1.40753
\(101\) −15.2192 −1.51436 −0.757181 0.653205i \(-0.773424\pi\)
−0.757181 + 0.653205i \(0.773424\pi\)
\(102\) −2.04037 −0.202027
\(103\) 4.49261 0.442670 0.221335 0.975198i \(-0.428959\pi\)
0.221335 + 0.975198i \(0.428959\pi\)
\(104\) −2.74460 −0.269130
\(105\) −39.6822 −3.87258
\(106\) 9.77167 0.949108
\(107\) 15.0718 1.45704 0.728522 0.685022i \(-0.240207\pi\)
0.728522 + 0.685022i \(0.240207\pi\)
\(108\) −4.85257 −0.466939
\(109\) −10.3524 −0.991580 −0.495790 0.868442i \(-0.665121\pi\)
−0.495790 + 0.868442i \(0.665121\pi\)
\(110\) −13.6160 −1.29823
\(111\) −14.2014 −1.34794
\(112\) −3.26500 −0.308513
\(113\) −8.10425 −0.762384 −0.381192 0.924496i \(-0.624486\pi\)
−0.381192 + 0.924496i \(0.624486\pi\)
\(114\) 9.17474 0.859293
\(115\) 17.1621 1.60037
\(116\) −0.134478 −0.0124860
\(117\) 13.0198 1.20368
\(118\) 0.605095 0.0557035
\(119\) 2.39395 0.219453
\(120\) −12.1538 −1.10949
\(121\) −1.28089 −0.116444
\(122\) 9.60040 0.869180
\(123\) 19.4976 1.75804
\(124\) −0.0430877 −0.00386939
\(125\) −39.6366 −3.54521
\(126\) 15.4885 1.37982
\(127\) 5.29846 0.470162 0.235081 0.971976i \(-0.424464\pi\)
0.235081 + 0.971976i \(0.424464\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −17.6699 −1.55574
\(130\) 11.9871 1.05134
\(131\) −1.68600 −0.147307 −0.0736533 0.997284i \(-0.523466\pi\)
−0.0736533 + 0.997284i \(0.523466\pi\)
\(132\) 8.67541 0.755098
\(133\) −10.7646 −0.933413
\(134\) −2.80505 −0.242320
\(135\) 21.1938 1.82407
\(136\) 0.733217 0.0628728
\(137\) −4.54990 −0.388724 −0.194362 0.980930i \(-0.562264\pi\)
−0.194362 + 0.980930i \(0.562264\pi\)
\(138\) −10.9348 −0.930833
\(139\) −3.78163 −0.320753 −0.160377 0.987056i \(-0.551271\pi\)
−0.160377 + 0.987056i \(0.551271\pi\)
\(140\) 14.2600 1.20519
\(141\) −9.62263 −0.810371
\(142\) 1.07101 0.0898774
\(143\) −8.55642 −0.715524
\(144\) 4.74379 0.395316
\(145\) 0.587338 0.0487757
\(146\) −10.9618 −0.907208
\(147\) −10.1855 −0.840085
\(148\) 5.10334 0.419492
\(149\) −3.03435 −0.248583 −0.124292 0.992246i \(-0.539666\pi\)
−0.124292 + 0.992246i \(0.539666\pi\)
\(150\) 39.1683 3.19808
\(151\) −11.0635 −0.900338 −0.450169 0.892943i \(-0.648636\pi\)
−0.450169 + 0.892943i \(0.648636\pi\)
\(152\) −3.29698 −0.267421
\(153\) −3.47823 −0.281198
\(154\) −10.1788 −0.820230
\(155\) 0.188187 0.0151155
\(156\) −7.63758 −0.611496
\(157\) −11.2183 −0.895320 −0.447660 0.894204i \(-0.647743\pi\)
−0.447660 + 0.894204i \(0.647743\pi\)
\(158\) 4.01696 0.319572
\(159\) 27.1923 2.15649
\(160\) 4.36753 0.345283
\(161\) 12.8297 1.01112
\(162\) 0.727798 0.0571812
\(163\) 17.9514 1.40606 0.703029 0.711161i \(-0.251830\pi\)
0.703029 + 0.711161i \(0.251830\pi\)
\(164\) −7.00654 −0.547119
\(165\) −37.8901 −2.94974
\(166\) −3.72621 −0.289210
\(167\) 17.7999 1.37739 0.688697 0.725049i \(-0.258183\pi\)
0.688697 + 0.725049i \(0.258183\pi\)
\(168\) −9.08573 −0.700979
\(169\) −5.46717 −0.420552
\(170\) −3.20234 −0.245609
\(171\) 15.6402 1.19604
\(172\) 6.34974 0.484163
\(173\) 3.92053 0.298072 0.149036 0.988832i \(-0.452383\pi\)
0.149036 + 0.988832i \(0.452383\pi\)
\(174\) −0.374222 −0.0283697
\(175\) −45.9558 −3.47393
\(176\) −3.11755 −0.234994
\(177\) 1.68384 0.126565
\(178\) 3.02088 0.226424
\(179\) 2.73828 0.204668 0.102334 0.994750i \(-0.467369\pi\)
0.102334 + 0.994750i \(0.467369\pi\)
\(180\) −20.7187 −1.54428
\(181\) 7.17351 0.533203 0.266601 0.963807i \(-0.414099\pi\)
0.266601 + 0.963807i \(0.414099\pi\)
\(182\) 8.96111 0.664242
\(183\) 26.7157 1.97488
\(184\) 3.92947 0.289685
\(185\) −22.2890 −1.63872
\(186\) −0.119903 −0.00879172
\(187\) 2.28584 0.167157
\(188\) 3.45793 0.252196
\(189\) 15.8436 1.15246
\(190\) 14.3997 1.04466
\(191\) −17.7616 −1.28519 −0.642593 0.766208i \(-0.722141\pi\)
−0.642593 + 0.766208i \(0.722141\pi\)
\(192\) −2.78277 −0.200829
\(193\) −12.3999 −0.892568 −0.446284 0.894891i \(-0.647253\pi\)
−0.446284 + 0.894891i \(0.647253\pi\)
\(194\) 15.4949 1.11247
\(195\) 33.3573 2.38877
\(196\) 3.66020 0.261443
\(197\) −7.82326 −0.557384 −0.278692 0.960380i \(-0.589901\pi\)
−0.278692 + 0.960380i \(0.589901\pi\)
\(198\) 14.7890 1.05101
\(199\) −7.84733 −0.556283 −0.278141 0.960540i \(-0.589718\pi\)
−0.278141 + 0.960540i \(0.589718\pi\)
\(200\) −14.0753 −0.995274
\(201\) −7.80581 −0.550579
\(202\) 15.2192 1.07082
\(203\) 0.439071 0.0308168
\(204\) 2.04037 0.142855
\(205\) 30.6013 2.13729
\(206\) −4.49261 −0.313015
\(207\) −18.6406 −1.29561
\(208\) 2.74460 0.190304
\(209\) −10.2785 −0.710979
\(210\) 39.6822 2.73833
\(211\) −17.0065 −1.17078 −0.585388 0.810753i \(-0.699058\pi\)
−0.585388 + 0.810753i \(0.699058\pi\)
\(212\) −9.77167 −0.671121
\(213\) 2.98038 0.204212
\(214\) −15.0718 −1.03029
\(215\) −27.7327 −1.89135
\(216\) 4.85257 0.330176
\(217\) 0.140681 0.00955006
\(218\) 10.3524 0.701153
\(219\) −30.5042 −2.06128
\(220\) 13.6160 0.917989
\(221\) −2.01239 −0.135368
\(222\) 14.2014 0.953135
\(223\) −8.08309 −0.541283 −0.270642 0.962680i \(-0.587236\pi\)
−0.270642 + 0.962680i \(0.587236\pi\)
\(224\) 3.26500 0.218152
\(225\) 66.7703 4.45135
\(226\) 8.10425 0.539087
\(227\) −11.9799 −0.795133 −0.397566 0.917573i \(-0.630145\pi\)
−0.397566 + 0.917573i \(0.630145\pi\)
\(228\) −9.17474 −0.607612
\(229\) 3.60531 0.238246 0.119123 0.992880i \(-0.461992\pi\)
0.119123 + 0.992880i \(0.461992\pi\)
\(230\) −17.1621 −1.13163
\(231\) −28.3252 −1.86366
\(232\) 0.134478 0.00882893
\(233\) −15.7848 −1.03409 −0.517047 0.855957i \(-0.672969\pi\)
−0.517047 + 0.855957i \(0.672969\pi\)
\(234\) −13.0198 −0.851132
\(235\) −15.1026 −0.985186
\(236\) −0.605095 −0.0393883
\(237\) 11.1783 0.726106
\(238\) −2.39395 −0.155177
\(239\) 23.8660 1.54376 0.771881 0.635767i \(-0.219316\pi\)
0.771881 + 0.635767i \(0.219316\pi\)
\(240\) 12.1538 0.784525
\(241\) −10.1267 −0.652321 −0.326160 0.945314i \(-0.605755\pi\)
−0.326160 + 0.945314i \(0.605755\pi\)
\(242\) 1.28089 0.0823385
\(243\) 16.5830 1.06380
\(244\) −9.60040 −0.614603
\(245\) −15.9860 −1.02131
\(246\) −19.4976 −1.24312
\(247\) 9.04890 0.575768
\(248\) 0.0430877 0.00273607
\(249\) −10.3692 −0.657119
\(250\) 39.6366 2.50684
\(251\) 14.6540 0.924955 0.462478 0.886631i \(-0.346961\pi\)
0.462478 + 0.886631i \(0.346961\pi\)
\(252\) −15.4885 −0.975682
\(253\) 12.2503 0.770172
\(254\) −5.29846 −0.332455
\(255\) −8.91138 −0.558052
\(256\) 1.00000 0.0625000
\(257\) 17.8500 1.11345 0.556727 0.830696i \(-0.312057\pi\)
0.556727 + 0.830696i \(0.312057\pi\)
\(258\) 17.6699 1.10008
\(259\) −16.6624 −1.03535
\(260\) −11.9871 −0.743409
\(261\) −0.637938 −0.0394873
\(262\) 1.68600 0.104161
\(263\) 12.8351 0.791448 0.395724 0.918369i \(-0.370494\pi\)
0.395724 + 0.918369i \(0.370494\pi\)
\(264\) −8.67541 −0.533935
\(265\) 42.6780 2.62169
\(266\) 10.7646 0.660022
\(267\) 8.40640 0.514463
\(268\) 2.80505 0.171346
\(269\) 3.38381 0.206315 0.103157 0.994665i \(-0.467105\pi\)
0.103157 + 0.994665i \(0.467105\pi\)
\(270\) −21.1938 −1.28981
\(271\) −28.7294 −1.74519 −0.872594 0.488447i \(-0.837564\pi\)
−0.872594 + 0.488447i \(0.837564\pi\)
\(272\) −0.733217 −0.0444578
\(273\) 24.9367 1.50924
\(274\) 4.54990 0.274870
\(275\) −43.8804 −2.64609
\(276\) 10.9348 0.658198
\(277\) 31.1705 1.87285 0.936426 0.350865i \(-0.114112\pi\)
0.936426 + 0.350865i \(0.114112\pi\)
\(278\) 3.78163 0.226807
\(279\) −0.204399 −0.0122371
\(280\) −14.2600 −0.852196
\(281\) 10.2220 0.609796 0.304898 0.952385i \(-0.401378\pi\)
0.304898 + 0.952385i \(0.401378\pi\)
\(282\) 9.62263 0.573019
\(283\) −15.6991 −0.933214 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(284\) −1.07101 −0.0635529
\(285\) 40.0709 2.37360
\(286\) 8.55642 0.505952
\(287\) 22.8763 1.35035
\(288\) −4.74379 −0.279531
\(289\) −16.4624 −0.968376
\(290\) −0.587338 −0.0344897
\(291\) 43.1186 2.52766
\(292\) 10.9618 0.641493
\(293\) −12.3158 −0.719495 −0.359748 0.933050i \(-0.617137\pi\)
−0.359748 + 0.933050i \(0.617137\pi\)
\(294\) 10.1855 0.594030
\(295\) 2.64277 0.153868
\(296\) −5.10334 −0.296625
\(297\) 15.1281 0.877824
\(298\) 3.03435 0.175775
\(299\) −10.7848 −0.623703
\(300\) −39.1683 −2.26138
\(301\) −20.7319 −1.19497
\(302\) 11.0635 0.636635
\(303\) 42.3514 2.43302
\(304\) 3.29698 0.189095
\(305\) 41.9300 2.40091
\(306\) 3.47823 0.198837
\(307\) −1.13457 −0.0647535 −0.0323767 0.999476i \(-0.510308\pi\)
−0.0323767 + 0.999476i \(0.510308\pi\)
\(308\) 10.1788 0.579990
\(309\) −12.5019 −0.711208
\(310\) −0.188187 −0.0106883
\(311\) −17.2736 −0.979494 −0.489747 0.871865i \(-0.662911\pi\)
−0.489747 + 0.871865i \(0.662911\pi\)
\(312\) 7.63758 0.432393
\(313\) −11.3761 −0.643015 −0.321507 0.946907i \(-0.604189\pi\)
−0.321507 + 0.946907i \(0.604189\pi\)
\(314\) 11.2183 0.633087
\(315\) 67.6463 3.81144
\(316\) −4.01696 −0.225971
\(317\) 1.16065 0.0651884 0.0325942 0.999469i \(-0.489623\pi\)
0.0325942 + 0.999469i \(0.489623\pi\)
\(318\) −27.1923 −1.52487
\(319\) 0.419243 0.0234731
\(320\) −4.36753 −0.244152
\(321\) −41.9413 −2.34093
\(322\) −12.8297 −0.714972
\(323\) −2.41740 −0.134508
\(324\) −0.727798 −0.0404332
\(325\) 38.6311 2.14287
\(326\) −17.9514 −0.994234
\(327\) 28.8083 1.59310
\(328\) 7.00654 0.386872
\(329\) −11.2901 −0.622446
\(330\) 37.8901 2.08578
\(331\) 18.7672 1.03154 0.515769 0.856728i \(-0.327506\pi\)
0.515769 + 0.856728i \(0.327506\pi\)
\(332\) 3.72621 0.204502
\(333\) 24.2092 1.32665
\(334\) −17.7999 −0.973965
\(335\) −12.2511 −0.669351
\(336\) 9.08573 0.495667
\(337\) −18.2617 −0.994781 −0.497390 0.867527i \(-0.665708\pi\)
−0.497390 + 0.867527i \(0.665708\pi\)
\(338\) 5.46717 0.297375
\(339\) 22.5522 1.22487
\(340\) 3.20234 0.173671
\(341\) 0.134328 0.00727427
\(342\) −15.6402 −0.845726
\(343\) 10.9044 0.588784
\(344\) −6.34974 −0.342355
\(345\) −47.7581 −2.57121
\(346\) −3.92053 −0.210769
\(347\) −0.263336 −0.0141366 −0.00706831 0.999975i \(-0.502250\pi\)
−0.00706831 + 0.999975i \(0.502250\pi\)
\(348\) 0.374222 0.0200604
\(349\) 1.19989 0.0642287 0.0321144 0.999484i \(-0.489776\pi\)
0.0321144 + 0.999484i \(0.489776\pi\)
\(350\) 45.9558 2.45644
\(351\) −13.3184 −0.710882
\(352\) 3.11755 0.166166
\(353\) 5.56876 0.296395 0.148198 0.988958i \(-0.452653\pi\)
0.148198 + 0.988958i \(0.452653\pi\)
\(354\) −1.68384 −0.0894951
\(355\) 4.67768 0.248265
\(356\) −3.02088 −0.160106
\(357\) −6.66180 −0.352580
\(358\) −2.73828 −0.144722
\(359\) 8.04904 0.424812 0.212406 0.977182i \(-0.431870\pi\)
0.212406 + 0.977182i \(0.431870\pi\)
\(360\) 20.7187 1.09197
\(361\) −8.12990 −0.427890
\(362\) −7.17351 −0.377031
\(363\) 3.56441 0.187083
\(364\) −8.96111 −0.469690
\(365\) −47.8761 −2.50595
\(366\) −26.7157 −1.39645
\(367\) −22.6472 −1.18218 −0.591088 0.806607i \(-0.701301\pi\)
−0.591088 + 0.806607i \(0.701301\pi\)
\(368\) −3.92947 −0.204838
\(369\) −33.2376 −1.73028
\(370\) 22.2890 1.15875
\(371\) 31.9045 1.65640
\(372\) 0.119903 0.00621668
\(373\) −17.7569 −0.919415 −0.459708 0.888070i \(-0.652046\pi\)
−0.459708 + 0.888070i \(0.652046\pi\)
\(374\) −2.28584 −0.118198
\(375\) 110.299 5.69584
\(376\) −3.45793 −0.178329
\(377\) −0.369089 −0.0190091
\(378\) −15.8436 −0.814909
\(379\) 37.0912 1.90525 0.952623 0.304154i \(-0.0983737\pi\)
0.952623 + 0.304154i \(0.0983737\pi\)
\(380\) −14.3997 −0.738687
\(381\) −14.7444 −0.755377
\(382\) 17.7616 0.908763
\(383\) −6.53919 −0.334137 −0.167069 0.985945i \(-0.553430\pi\)
−0.167069 + 0.985945i \(0.553430\pi\)
\(384\) 2.78277 0.142008
\(385\) −44.4561 −2.26569
\(386\) 12.3999 0.631141
\(387\) 30.1219 1.53118
\(388\) −15.4949 −0.786633
\(389\) 2.35711 0.119510 0.0597552 0.998213i \(-0.480968\pi\)
0.0597552 + 0.998213i \(0.480968\pi\)
\(390\) −33.3573 −1.68911
\(391\) 2.88116 0.145706
\(392\) −3.66020 −0.184868
\(393\) 4.69175 0.236667
\(394\) 7.82326 0.394130
\(395\) 17.5442 0.882743
\(396\) −14.7890 −0.743176
\(397\) −13.4473 −0.674901 −0.337450 0.941343i \(-0.609564\pi\)
−0.337450 + 0.941343i \(0.609564\pi\)
\(398\) 7.84733 0.393351
\(399\) 29.9555 1.49965
\(400\) 14.0753 0.703765
\(401\) 26.5582 1.32626 0.663128 0.748506i \(-0.269229\pi\)
0.663128 + 0.748506i \(0.269229\pi\)
\(402\) 7.80581 0.389318
\(403\) −0.118258 −0.00589087
\(404\) −15.2192 −0.757181
\(405\) 3.17868 0.157950
\(406\) −0.439071 −0.0217907
\(407\) −15.9099 −0.788625
\(408\) −2.04037 −0.101013
\(409\) 20.6602 1.02158 0.510790 0.859706i \(-0.329353\pi\)
0.510790 + 0.859706i \(0.329353\pi\)
\(410\) −30.6013 −1.51129
\(411\) 12.6613 0.624537
\(412\) 4.49261 0.221335
\(413\) 1.97563 0.0972146
\(414\) 18.6406 0.916136
\(415\) −16.2743 −0.798875
\(416\) −2.74460 −0.134565
\(417\) 10.5234 0.515333
\(418\) 10.2785 0.502738
\(419\) −26.8045 −1.30949 −0.654743 0.755851i \(-0.727223\pi\)
−0.654743 + 0.755851i \(0.727223\pi\)
\(420\) −39.6822 −1.93629
\(421\) −6.85131 −0.333912 −0.166956 0.985964i \(-0.553394\pi\)
−0.166956 + 0.985964i \(0.553394\pi\)
\(422\) 17.0065 0.827864
\(423\) 16.4037 0.797577
\(424\) 9.77167 0.474554
\(425\) −10.3202 −0.500605
\(426\) −2.98038 −0.144400
\(427\) 31.3453 1.51690
\(428\) 15.0718 0.728522
\(429\) 23.8105 1.14958
\(430\) 27.7327 1.33739
\(431\) −5.53959 −0.266832 −0.133416 0.991060i \(-0.542595\pi\)
−0.133416 + 0.991060i \(0.542595\pi\)
\(432\) −4.85257 −0.233470
\(433\) 5.11384 0.245755 0.122878 0.992422i \(-0.460788\pi\)
0.122878 + 0.992422i \(0.460788\pi\)
\(434\) −0.140681 −0.00675291
\(435\) −1.63442 −0.0783647
\(436\) −10.3524 −0.495790
\(437\) −12.9554 −0.619741
\(438\) 30.5042 1.45755
\(439\) 8.98166 0.428671 0.214336 0.976760i \(-0.431241\pi\)
0.214336 + 0.976760i \(0.431241\pi\)
\(440\) −13.6160 −0.649116
\(441\) 17.3633 0.826822
\(442\) 2.01239 0.0957194
\(443\) 5.64420 0.268164 0.134082 0.990970i \(-0.457191\pi\)
0.134082 + 0.990970i \(0.457191\pi\)
\(444\) −14.2014 −0.673969
\(445\) 13.1938 0.625445
\(446\) 8.08309 0.382745
\(447\) 8.44388 0.399382
\(448\) −3.26500 −0.154257
\(449\) −23.5286 −1.11038 −0.555191 0.831723i \(-0.687355\pi\)
−0.555191 + 0.831723i \(0.687355\pi\)
\(450\) −66.7703 −3.14758
\(451\) 21.8432 1.02856
\(452\) −8.10425 −0.381192
\(453\) 30.7873 1.44651
\(454\) 11.9799 0.562244
\(455\) 39.1379 1.83481
\(456\) 9.17474 0.429646
\(457\) 38.0044 1.77777 0.888885 0.458131i \(-0.151481\pi\)
0.888885 + 0.458131i \(0.151481\pi\)
\(458\) −3.60531 −0.168465
\(459\) 3.55799 0.166073
\(460\) 17.1621 0.800186
\(461\) −32.4326 −1.51054 −0.755268 0.655416i \(-0.772493\pi\)
−0.755268 + 0.655416i \(0.772493\pi\)
\(462\) 28.3252 1.31781
\(463\) −33.2441 −1.54499 −0.772493 0.635024i \(-0.780990\pi\)
−0.772493 + 0.635024i \(0.780990\pi\)
\(464\) −0.134478 −0.00624300
\(465\) −0.523680 −0.0242851
\(466\) 15.7848 0.731215
\(467\) 17.4265 0.806401 0.403200 0.915112i \(-0.367898\pi\)
0.403200 + 0.915112i \(0.367898\pi\)
\(468\) 13.0198 0.601841
\(469\) −9.15848 −0.422900
\(470\) 15.1026 0.696632
\(471\) 31.2180 1.43845
\(472\) 0.605095 0.0278518
\(473\) −19.7956 −0.910204
\(474\) −11.1783 −0.513434
\(475\) 46.4060 2.12925
\(476\) 2.39395 0.109726
\(477\) −46.3548 −2.12244
\(478\) −23.8660 −1.09160
\(479\) −39.9799 −1.82673 −0.913363 0.407146i \(-0.866524\pi\)
−0.913363 + 0.407146i \(0.866524\pi\)
\(480\) −12.1538 −0.554743
\(481\) 14.0066 0.638647
\(482\) 10.1267 0.461260
\(483\) −35.7021 −1.62450
\(484\) −1.28089 −0.0582221
\(485\) 67.6743 3.07293
\(486\) −16.5830 −0.752221
\(487\) −25.2224 −1.14294 −0.571468 0.820624i \(-0.693626\pi\)
−0.571468 + 0.820624i \(0.693626\pi\)
\(488\) 9.60040 0.434590
\(489\) −49.9544 −2.25902
\(490\) 15.9860 0.722176
\(491\) 14.3680 0.648421 0.324211 0.945985i \(-0.394901\pi\)
0.324211 + 0.945985i \(0.394901\pi\)
\(492\) 19.4976 0.879019
\(493\) 0.0986017 0.00444080
\(494\) −9.04890 −0.407129
\(495\) 64.5914 2.90317
\(496\) −0.0430877 −0.00193469
\(497\) 3.49685 0.156855
\(498\) 10.3692 0.464654
\(499\) 24.4553 1.09477 0.547384 0.836882i \(-0.315624\pi\)
0.547384 + 0.836882i \(0.315624\pi\)
\(500\) −39.6366 −1.77260
\(501\) −49.5329 −2.21296
\(502\) −14.6540 −0.654042
\(503\) −4.69182 −0.209198 −0.104599 0.994514i \(-0.533356\pi\)
−0.104599 + 0.994514i \(0.533356\pi\)
\(504\) 15.4885 0.689911
\(505\) 66.4701 2.95788
\(506\) −12.2503 −0.544594
\(507\) 15.2139 0.675672
\(508\) 5.29846 0.235081
\(509\) 22.5963 1.00157 0.500783 0.865573i \(-0.333046\pi\)
0.500783 + 0.865573i \(0.333046\pi\)
\(510\) 8.91138 0.394602
\(511\) −35.7903 −1.58327
\(512\) −1.00000 −0.0441942
\(513\) −15.9989 −0.706367
\(514\) −17.8500 −0.787331
\(515\) −19.6216 −0.864631
\(516\) −17.6699 −0.777872
\(517\) −10.7803 −0.474116
\(518\) 16.6624 0.732103
\(519\) −10.9099 −0.478892
\(520\) 11.9871 0.525670
\(521\) −4.89976 −0.214663 −0.107331 0.994223i \(-0.534231\pi\)
−0.107331 + 0.994223i \(0.534231\pi\)
\(522\) 0.637938 0.0279218
\(523\) −22.3032 −0.975249 −0.487624 0.873054i \(-0.662136\pi\)
−0.487624 + 0.873054i \(0.662136\pi\)
\(524\) −1.68600 −0.0736533
\(525\) 127.884 5.58133
\(526\) −12.8351 −0.559638
\(527\) 0.0315926 0.00137620
\(528\) 8.67541 0.377549
\(529\) −7.55924 −0.328662
\(530\) −42.6780 −1.85381
\(531\) −2.87045 −0.124567
\(532\) −10.7646 −0.466706
\(533\) −19.2302 −0.832950
\(534\) −8.40640 −0.363781
\(535\) −65.8265 −2.84593
\(536\) −2.80505 −0.121160
\(537\) −7.61999 −0.328827
\(538\) −3.38381 −0.145886
\(539\) −11.4109 −0.491501
\(540\) 21.1938 0.912034
\(541\) 4.81851 0.207164 0.103582 0.994621i \(-0.466970\pi\)
0.103582 + 0.994621i \(0.466970\pi\)
\(542\) 28.7294 1.23403
\(543\) −19.9622 −0.856661
\(544\) 0.733217 0.0314364
\(545\) 45.2144 1.93677
\(546\) −24.9367 −1.06719
\(547\) −28.8973 −1.23556 −0.617780 0.786351i \(-0.711968\pi\)
−0.617780 + 0.786351i \(0.711968\pi\)
\(548\) −4.54990 −0.194362
\(549\) −45.5423 −1.94370
\(550\) 43.8804 1.87107
\(551\) −0.443373 −0.0188883
\(552\) −10.9348 −0.465416
\(553\) 13.1154 0.557721
\(554\) −31.1705 −1.32431
\(555\) 62.0250 2.63281
\(556\) −3.78163 −0.160377
\(557\) 16.9780 0.719380 0.359690 0.933072i \(-0.382882\pi\)
0.359690 + 0.933072i \(0.382882\pi\)
\(558\) 0.204399 0.00865291
\(559\) 17.4275 0.737105
\(560\) 14.2600 0.602593
\(561\) −6.36096 −0.268560
\(562\) −10.2220 −0.431191
\(563\) 5.42232 0.228524 0.114262 0.993451i \(-0.463550\pi\)
0.114262 + 0.993451i \(0.463550\pi\)
\(564\) −9.62263 −0.405186
\(565\) 35.3955 1.48910
\(566\) 15.6991 0.659882
\(567\) 2.37626 0.0997935
\(568\) 1.07101 0.0449387
\(569\) −36.6814 −1.53776 −0.768881 0.639391i \(-0.779186\pi\)
−0.768881 + 0.639391i \(0.779186\pi\)
\(570\) −40.0709 −1.67839
\(571\) 8.07612 0.337975 0.168988 0.985618i \(-0.445950\pi\)
0.168988 + 0.985618i \(0.445950\pi\)
\(572\) −8.55642 −0.357762
\(573\) 49.4264 2.06482
\(574\) −22.8763 −0.954840
\(575\) −55.3085 −2.30652
\(576\) 4.74379 0.197658
\(577\) −13.2727 −0.552551 −0.276276 0.961078i \(-0.589100\pi\)
−0.276276 + 0.961078i \(0.589100\pi\)
\(578\) 16.4624 0.684745
\(579\) 34.5062 1.43403
\(580\) 0.587338 0.0243879
\(581\) −12.1661 −0.504733
\(582\) −43.1186 −1.78732
\(583\) 30.4637 1.26168
\(584\) −10.9618 −0.453604
\(585\) −56.8644 −2.35105
\(586\) 12.3158 0.508760
\(587\) 29.3679 1.21214 0.606071 0.795411i \(-0.292745\pi\)
0.606071 + 0.795411i \(0.292745\pi\)
\(588\) −10.1855 −0.420043
\(589\) −0.142059 −0.00585346
\(590\) −2.64277 −0.108801
\(591\) 21.7703 0.895511
\(592\) 5.10334 0.209746
\(593\) −24.5766 −1.00924 −0.504619 0.863342i \(-0.668367\pi\)
−0.504619 + 0.863342i \(0.668367\pi\)
\(594\) −15.1281 −0.620715
\(595\) −10.4556 −0.428639
\(596\) −3.03435 −0.124292
\(597\) 21.8373 0.893741
\(598\) 10.7848 0.441025
\(599\) 11.6195 0.474759 0.237380 0.971417i \(-0.423711\pi\)
0.237380 + 0.971417i \(0.423711\pi\)
\(600\) 39.1683 1.59904
\(601\) −37.8896 −1.54555 −0.772775 0.634680i \(-0.781132\pi\)
−0.772775 + 0.634680i \(0.781132\pi\)
\(602\) 20.7319 0.844969
\(603\) 13.3066 0.541886
\(604\) −11.0635 −0.450169
\(605\) 5.59431 0.227441
\(606\) −42.3514 −1.72041
\(607\) −19.7543 −0.801801 −0.400901 0.916122i \(-0.631303\pi\)
−0.400901 + 0.916122i \(0.631303\pi\)
\(608\) −3.29698 −0.133710
\(609\) −1.22183 −0.0495112
\(610\) −41.9300 −1.69770
\(611\) 9.49064 0.383950
\(612\) −3.47823 −0.140599
\(613\) −1.06042 −0.0428302 −0.0214151 0.999771i \(-0.506817\pi\)
−0.0214151 + 0.999771i \(0.506817\pi\)
\(614\) 1.13457 0.0457876
\(615\) −85.1562 −3.43383
\(616\) −10.1788 −0.410115
\(617\) 34.5568 1.39120 0.695602 0.718428i \(-0.255138\pi\)
0.695602 + 0.718428i \(0.255138\pi\)
\(618\) 12.5019 0.502900
\(619\) −20.9560 −0.842293 −0.421147 0.906993i \(-0.638372\pi\)
−0.421147 + 0.906993i \(0.638372\pi\)
\(620\) 0.188187 0.00755776
\(621\) 19.0681 0.765175
\(622\) 17.2736 0.692607
\(623\) 9.86316 0.395159
\(624\) −7.63758 −0.305748
\(625\) 102.737 4.10950
\(626\) 11.3761 0.454680
\(627\) 28.6027 1.14228
\(628\) −11.2183 −0.447660
\(629\) −3.74185 −0.149197
\(630\) −67.6463 −2.69509
\(631\) −44.2350 −1.76097 −0.880483 0.474078i \(-0.842781\pi\)
−0.880483 + 0.474078i \(0.842781\pi\)
\(632\) 4.01696 0.159786
\(633\) 47.3252 1.88101
\(634\) −1.16065 −0.0460951
\(635\) −23.1412 −0.918329
\(636\) 27.1923 1.07824
\(637\) 10.0458 0.398029
\(638\) −0.419243 −0.0165980
\(639\) −5.08067 −0.200988
\(640\) 4.36753 0.172642
\(641\) 33.6782 1.33021 0.665105 0.746749i \(-0.268387\pi\)
0.665105 + 0.746749i \(0.268387\pi\)
\(642\) 41.9413 1.65529
\(643\) −46.0220 −1.81493 −0.907464 0.420129i \(-0.861985\pi\)
−0.907464 + 0.420129i \(0.861985\pi\)
\(644\) 12.8297 0.505562
\(645\) 77.1736 3.03871
\(646\) 2.41740 0.0951114
\(647\) −1.36238 −0.0535607 −0.0267803 0.999641i \(-0.508525\pi\)
−0.0267803 + 0.999641i \(0.508525\pi\)
\(648\) 0.727798 0.0285906
\(649\) 1.88641 0.0740482
\(650\) −38.6311 −1.51523
\(651\) −0.391483 −0.0153434
\(652\) 17.9514 0.703029
\(653\) −5.64681 −0.220977 −0.110488 0.993877i \(-0.535242\pi\)
−0.110488 + 0.993877i \(0.535242\pi\)
\(654\) −28.8083 −1.12649
\(655\) 7.36365 0.287722
\(656\) −7.00654 −0.273560
\(657\) 52.0007 2.02874
\(658\) 11.2901 0.440136
\(659\) 10.4139 0.405668 0.202834 0.979213i \(-0.434985\pi\)
0.202834 + 0.979213i \(0.434985\pi\)
\(660\) −37.8901 −1.47487
\(661\) −50.4412 −1.96193 −0.980967 0.194176i \(-0.937797\pi\)
−0.980967 + 0.194176i \(0.937797\pi\)
\(662\) −18.7672 −0.729407
\(663\) 5.60000 0.217486
\(664\) −3.72621 −0.144605
\(665\) 47.0149 1.82316
\(666\) −24.2092 −0.938087
\(667\) 0.528429 0.0204609
\(668\) 17.7999 0.688697
\(669\) 22.4933 0.869643
\(670\) 12.2511 0.473303
\(671\) 29.9297 1.15542
\(672\) −9.08573 −0.350490
\(673\) 28.6209 1.10326 0.551628 0.834090i \(-0.314007\pi\)
0.551628 + 0.834090i \(0.314007\pi\)
\(674\) 18.2617 0.703416
\(675\) −68.3014 −2.62892
\(676\) −5.46717 −0.210276
\(677\) 28.3191 1.08839 0.544195 0.838959i \(-0.316835\pi\)
0.544195 + 0.838959i \(0.316835\pi\)
\(678\) −22.5522 −0.866114
\(679\) 50.5907 1.94149
\(680\) −3.20234 −0.122804
\(681\) 33.3372 1.27749
\(682\) −0.134328 −0.00514369
\(683\) 15.8235 0.605469 0.302734 0.953075i \(-0.402100\pi\)
0.302734 + 0.953075i \(0.402100\pi\)
\(684\) 15.6402 0.598018
\(685\) 19.8718 0.759263
\(686\) −10.9044 −0.416333
\(687\) −10.0327 −0.382773
\(688\) 6.34974 0.242082
\(689\) −26.8193 −1.02173
\(690\) 47.7581 1.81812
\(691\) −4.54799 −0.173014 −0.0865069 0.996251i \(-0.527570\pi\)
−0.0865069 + 0.996251i \(0.527570\pi\)
\(692\) 3.92053 0.149036
\(693\) 48.2861 1.83424
\(694\) 0.263336 0.00999610
\(695\) 16.5164 0.626501
\(696\) −0.374222 −0.0141848
\(697\) 5.13731 0.194590
\(698\) −1.19989 −0.0454166
\(699\) 43.9253 1.66141
\(700\) −45.9558 −1.73697
\(701\) 28.3323 1.07010 0.535048 0.844822i \(-0.320294\pi\)
0.535048 + 0.844822i \(0.320294\pi\)
\(702\) 13.3184 0.502670
\(703\) 16.8256 0.634590
\(704\) −3.11755 −0.117497
\(705\) 42.0271 1.58283
\(706\) −5.56876 −0.209583
\(707\) 49.6905 1.86880
\(708\) 1.68384 0.0632826
\(709\) 36.9052 1.38601 0.693003 0.720935i \(-0.256287\pi\)
0.693003 + 0.720935i \(0.256287\pi\)
\(710\) −4.67768 −0.175550
\(711\) −19.0556 −0.714642
\(712\) 3.02088 0.113212
\(713\) 0.169312 0.00634078
\(714\) 6.66180 0.249312
\(715\) 37.3704 1.39757
\(716\) 2.73828 0.102334
\(717\) −66.4135 −2.48026
\(718\) −8.04904 −0.300387
\(719\) −8.35437 −0.311566 −0.155783 0.987791i \(-0.549790\pi\)
−0.155783 + 0.987791i \(0.549790\pi\)
\(720\) −20.7187 −0.772139
\(721\) −14.6684 −0.546278
\(722\) 8.12990 0.302564
\(723\) 28.1804 1.04804
\(724\) 7.17351 0.266601
\(725\) −1.89282 −0.0702977
\(726\) −3.56441 −0.132288
\(727\) 11.5600 0.428738 0.214369 0.976753i \(-0.431230\pi\)
0.214369 + 0.976753i \(0.431230\pi\)
\(728\) 8.96111 0.332121
\(729\) −43.9633 −1.62827
\(730\) 47.8761 1.77197
\(731\) −4.65574 −0.172199
\(732\) 26.7157 0.987440
\(733\) 3.06519 0.113216 0.0566078 0.998396i \(-0.481972\pi\)
0.0566078 + 0.998396i \(0.481972\pi\)
\(734\) 22.6472 0.835925
\(735\) 44.4854 1.64087
\(736\) 3.92947 0.144842
\(737\) −8.74489 −0.322122
\(738\) 33.2376 1.22349
\(739\) 25.0419 0.921180 0.460590 0.887613i \(-0.347638\pi\)
0.460590 + 0.887613i \(0.347638\pi\)
\(740\) −22.2890 −0.819359
\(741\) −25.1810 −0.925046
\(742\) −31.9045 −1.17125
\(743\) 14.6721 0.538269 0.269134 0.963103i \(-0.413262\pi\)
0.269134 + 0.963103i \(0.413262\pi\)
\(744\) −0.119903 −0.00439586
\(745\) 13.2526 0.485537
\(746\) 17.7569 0.650125
\(747\) 17.6764 0.646744
\(748\) 2.28584 0.0835785
\(749\) −49.2093 −1.79807
\(750\) −110.299 −4.02757
\(751\) 24.2778 0.885911 0.442955 0.896544i \(-0.353930\pi\)
0.442955 + 0.896544i \(0.353930\pi\)
\(752\) 3.45793 0.126098
\(753\) −40.7788 −1.48606
\(754\) 0.369089 0.0134414
\(755\) 48.3203 1.75856
\(756\) 15.8436 0.576228
\(757\) −12.3709 −0.449627 −0.224813 0.974402i \(-0.572177\pi\)
−0.224813 + 0.974402i \(0.572177\pi\)
\(758\) −37.0912 −1.34721
\(759\) −34.0898 −1.23738
\(760\) 14.3997 0.522331
\(761\) −31.8090 −1.15307 −0.576537 0.817071i \(-0.695596\pi\)
−0.576537 + 0.817071i \(0.695596\pi\)
\(762\) 14.7444 0.534132
\(763\) 33.8006 1.22366
\(764\) −17.7616 −0.642593
\(765\) 15.1913 0.549241
\(766\) 6.53919 0.236271
\(767\) −1.66074 −0.0599660
\(768\) −2.78277 −0.100414
\(769\) 32.4092 1.16871 0.584353 0.811500i \(-0.301348\pi\)
0.584353 + 0.811500i \(0.301348\pi\)
\(770\) 44.4561 1.60209
\(771\) −49.6725 −1.78891
\(772\) −12.3999 −0.446284
\(773\) 26.2329 0.943533 0.471767 0.881723i \(-0.343616\pi\)
0.471767 + 0.881723i \(0.343616\pi\)
\(774\) −30.1219 −1.08271
\(775\) −0.606472 −0.0217851
\(776\) 15.4949 0.556233
\(777\) 46.3675 1.66343
\(778\) −2.35711 −0.0845066
\(779\) −23.1005 −0.827660
\(780\) 33.3573 1.19438
\(781\) 3.33894 0.119477
\(782\) −2.88116 −0.103030
\(783\) 0.652566 0.0233208
\(784\) 3.66020 0.130722
\(785\) 48.9964 1.74875
\(786\) −4.69175 −0.167349
\(787\) 29.7366 1.06000 0.529998 0.847999i \(-0.322193\pi\)
0.529998 + 0.847999i \(0.322193\pi\)
\(788\) −7.82326 −0.278692
\(789\) −35.7172 −1.27157
\(790\) −17.5442 −0.624194
\(791\) 26.4604 0.940822
\(792\) 14.7890 0.525505
\(793\) −26.3493 −0.935690
\(794\) 13.4473 0.477227
\(795\) −118.763 −4.21209
\(796\) −7.84733 −0.278141
\(797\) −33.4836 −1.18605 −0.593025 0.805184i \(-0.702066\pi\)
−0.593025 + 0.805184i \(0.702066\pi\)
\(798\) −29.9555 −1.06041
\(799\) −2.53541 −0.0896965
\(800\) −14.0753 −0.497637
\(801\) −14.3304 −0.506341
\(802\) −26.5582 −0.937804
\(803\) −34.1740 −1.20598
\(804\) −7.80581 −0.275290
\(805\) −56.0342 −1.97494
\(806\) 0.118258 0.00416548
\(807\) −9.41636 −0.331472
\(808\) 15.2192 0.535408
\(809\) −21.9896 −0.773114 −0.386557 0.922265i \(-0.626336\pi\)
−0.386557 + 0.922265i \(0.626336\pi\)
\(810\) −3.17868 −0.111687
\(811\) 45.8776 1.61098 0.805490 0.592610i \(-0.201902\pi\)
0.805490 + 0.592610i \(0.201902\pi\)
\(812\) 0.439071 0.0154084
\(813\) 79.9473 2.80387
\(814\) 15.9099 0.557642
\(815\) −78.4030 −2.74634
\(816\) 2.04037 0.0714273
\(817\) 20.9350 0.732423
\(818\) −20.6602 −0.722366
\(819\) −42.5097 −1.48541
\(820\) 30.6013 1.06864
\(821\) −45.1300 −1.57505 −0.787523 0.616285i \(-0.788637\pi\)
−0.787523 + 0.616285i \(0.788637\pi\)
\(822\) −12.6613 −0.441614
\(823\) −29.7704 −1.03773 −0.518866 0.854856i \(-0.673646\pi\)
−0.518866 + 0.854856i \(0.673646\pi\)
\(824\) −4.49261 −0.156508
\(825\) 122.109 4.25129
\(826\) −1.97563 −0.0687411
\(827\) −26.0286 −0.905103 −0.452551 0.891738i \(-0.649486\pi\)
−0.452551 + 0.891738i \(0.649486\pi\)
\(828\) −18.6406 −0.647806
\(829\) 39.7301 1.37988 0.689942 0.723865i \(-0.257636\pi\)
0.689942 + 0.723865i \(0.257636\pi\)
\(830\) 16.2743 0.564890
\(831\) −86.7402 −3.00898
\(832\) 2.74460 0.0951519
\(833\) −2.68372 −0.0929855
\(834\) −10.5234 −0.364395
\(835\) −77.7414 −2.69035
\(836\) −10.2785 −0.355490
\(837\) 0.209086 0.00722708
\(838\) 26.8045 0.925947
\(839\) −11.1615 −0.385339 −0.192669 0.981264i \(-0.561715\pi\)
−0.192669 + 0.981264i \(0.561715\pi\)
\(840\) 39.6822 1.36916
\(841\) −28.9819 −0.999376
\(842\) 6.85131 0.236112
\(843\) −28.4456 −0.979718
\(844\) −17.0065 −0.585388
\(845\) 23.8780 0.821429
\(846\) −16.4037 −0.563972
\(847\) 4.18209 0.143698
\(848\) −9.77167 −0.335560
\(849\) 43.6869 1.49933
\(850\) 10.3202 0.353981
\(851\) −20.0534 −0.687423
\(852\) 2.98038 0.102106
\(853\) −18.9199 −0.647804 −0.323902 0.946091i \(-0.604995\pi\)
−0.323902 + 0.946091i \(0.604995\pi\)
\(854\) −31.3453 −1.07261
\(855\) −68.3090 −2.33612
\(856\) −15.0718 −0.515143
\(857\) −48.6070 −1.66038 −0.830191 0.557479i \(-0.811769\pi\)
−0.830191 + 0.557479i \(0.811769\pi\)
\(858\) −23.8105 −0.812878
\(859\) 9.09030 0.310157 0.155079 0.987902i \(-0.450437\pi\)
0.155079 + 0.987902i \(0.450437\pi\)
\(860\) −27.7327 −0.945676
\(861\) −63.6595 −2.16951
\(862\) 5.53959 0.188679
\(863\) 34.9258 1.18889 0.594444 0.804137i \(-0.297372\pi\)
0.594444 + 0.804137i \(0.297372\pi\)
\(864\) 4.85257 0.165088
\(865\) −17.1230 −0.582200
\(866\) −5.11384 −0.173775
\(867\) 45.8110 1.55582
\(868\) 0.140681 0.00477503
\(869\) 12.5231 0.424816
\(870\) 1.63442 0.0554122
\(871\) 7.69874 0.260862
\(872\) 10.3524 0.350577
\(873\) −73.5045 −2.48775
\(874\) 12.9554 0.438223
\(875\) 129.413 4.37497
\(876\) −30.5042 −1.03064
\(877\) 33.2890 1.12409 0.562046 0.827106i \(-0.310015\pi\)
0.562046 + 0.827106i \(0.310015\pi\)
\(878\) −8.98166 −0.303116
\(879\) 34.2719 1.15596
\(880\) 13.6160 0.458995
\(881\) 40.1397 1.35234 0.676170 0.736745i \(-0.263638\pi\)
0.676170 + 0.736745i \(0.263638\pi\)
\(882\) −17.3633 −0.584651
\(883\) −11.4338 −0.384779 −0.192390 0.981319i \(-0.561624\pi\)
−0.192390 + 0.981319i \(0.561624\pi\)
\(884\) −2.01239 −0.0676839
\(885\) −7.35421 −0.247209
\(886\) −5.64420 −0.189621
\(887\) −45.1721 −1.51673 −0.758365 0.651830i \(-0.774001\pi\)
−0.758365 + 0.651830i \(0.774001\pi\)
\(888\) 14.2014 0.476568
\(889\) −17.2995 −0.580205
\(890\) −13.1938 −0.442256
\(891\) 2.26895 0.0760126
\(892\) −8.08309 −0.270642
\(893\) 11.4008 0.381512
\(894\) −8.44388 −0.282406
\(895\) −11.9595 −0.399762
\(896\) 3.26500 0.109076
\(897\) 30.0117 1.00206
\(898\) 23.5286 0.785158
\(899\) 0.00579436 0.000193253 0
\(900\) 66.7703 2.22568
\(901\) 7.16475 0.238692
\(902\) −21.8432 −0.727300
\(903\) 57.6920 1.91987
\(904\) 8.10425 0.269543
\(905\) −31.3305 −1.04146
\(906\) −30.7873 −1.02284
\(907\) −20.0238 −0.664879 −0.332439 0.943125i \(-0.607872\pi\)
−0.332439 + 0.943125i \(0.607872\pi\)
\(908\) −11.9799 −0.397566
\(909\) −72.1965 −2.39461
\(910\) −39.1379 −1.29741
\(911\) −3.09739 −0.102621 −0.0513106 0.998683i \(-0.516340\pi\)
−0.0513106 + 0.998683i \(0.516340\pi\)
\(912\) −9.17474 −0.303806
\(913\) −11.6166 −0.384455
\(914\) −38.0044 −1.25707
\(915\) −116.681 −3.85737
\(916\) 3.60531 0.119123
\(917\) 5.50479 0.181784
\(918\) −3.55799 −0.117431
\(919\) 21.8272 0.720012 0.360006 0.932950i \(-0.382775\pi\)
0.360006 + 0.932950i \(0.382775\pi\)
\(920\) −17.1621 −0.565817
\(921\) 3.15725 0.104035
\(922\) 32.4326 1.06811
\(923\) −2.93950 −0.0967549
\(924\) −28.3252 −0.931831
\(925\) 71.8310 2.36179
\(926\) 33.2441 1.09247
\(927\) 21.3120 0.699979
\(928\) 0.134478 0.00441447
\(929\) 27.9214 0.916072 0.458036 0.888934i \(-0.348553\pi\)
0.458036 + 0.888934i \(0.348553\pi\)
\(930\) 0.523680 0.0171721
\(931\) 12.0676 0.395501
\(932\) −15.7848 −0.517047
\(933\) 48.0683 1.57369
\(934\) −17.4265 −0.570211
\(935\) −9.98346 −0.326494
\(936\) −13.0198 −0.425566
\(937\) 11.4017 0.372477 0.186238 0.982505i \(-0.440370\pi\)
0.186238 + 0.982505i \(0.440370\pi\)
\(938\) 9.15848 0.299035
\(939\) 31.6570 1.03309
\(940\) −15.1026 −0.492593
\(941\) 21.0014 0.684625 0.342312 0.939586i \(-0.388790\pi\)
0.342312 + 0.939586i \(0.388790\pi\)
\(942\) −31.2180 −1.01714
\(943\) 27.5320 0.896566
\(944\) −0.605095 −0.0196942
\(945\) −69.1975 −2.25100
\(946\) 19.7956 0.643611
\(947\) −3.80613 −0.123683 −0.0618413 0.998086i \(-0.519697\pi\)
−0.0618413 + 0.998086i \(0.519697\pi\)
\(948\) 11.1783 0.363053
\(949\) 30.0858 0.976628
\(950\) −46.4060 −1.50561
\(951\) −3.22981 −0.104734
\(952\) −2.39395 −0.0775884
\(953\) 1.64783 0.0533784 0.0266892 0.999644i \(-0.491504\pi\)
0.0266892 + 0.999644i \(0.491504\pi\)
\(954\) 46.3548 1.50079
\(955\) 77.5743 2.51025
\(956\) 23.8660 0.771881
\(957\) −1.16666 −0.0377126
\(958\) 39.9799 1.29169
\(959\) 14.8554 0.479706
\(960\) 12.1538 0.392263
\(961\) −30.9981 −0.999940
\(962\) −14.0066 −0.451591
\(963\) 71.4975 2.30397
\(964\) −10.1267 −0.326160
\(965\) 54.1571 1.74338
\(966\) 35.7021 1.14870
\(967\) 47.0385 1.51266 0.756328 0.654192i \(-0.226991\pi\)
0.756328 + 0.654192i \(0.226991\pi\)
\(968\) 1.28089 0.0411693
\(969\) 6.72707 0.216105
\(970\) −67.6743 −2.17289
\(971\) 8.15072 0.261569 0.130785 0.991411i \(-0.458250\pi\)
0.130785 + 0.991411i \(0.458250\pi\)
\(972\) 16.5830 0.531900
\(973\) 12.3470 0.395827
\(974\) 25.2224 0.808178
\(975\) −107.501 −3.44279
\(976\) −9.60040 −0.307301
\(977\) −30.0991 −0.962957 −0.481478 0.876458i \(-0.659900\pi\)
−0.481478 + 0.876458i \(0.659900\pi\)
\(978\) 49.9544 1.59737
\(979\) 9.41774 0.300992
\(980\) −15.9860 −0.510655
\(981\) −49.1097 −1.56795
\(982\) −14.3680 −0.458503
\(983\) −28.1701 −0.898487 −0.449243 0.893409i \(-0.648306\pi\)
−0.449243 + 0.893409i \(0.648306\pi\)
\(984\) −19.4976 −0.621560
\(985\) 34.1683 1.08869
\(986\) −0.0986017 −0.00314012
\(987\) 31.4178 1.00004
\(988\) 9.04890 0.287884
\(989\) −24.9511 −0.793400
\(990\) −64.5914 −2.05285
\(991\) 45.2685 1.43800 0.719001 0.695009i \(-0.244600\pi\)
0.719001 + 0.695009i \(0.244600\pi\)
\(992\) 0.0430877 0.00136804
\(993\) −52.2247 −1.65730
\(994\) −3.49685 −0.110913
\(995\) 34.2734 1.08654
\(996\) −10.3692 −0.328560
\(997\) −12.6222 −0.399750 −0.199875 0.979821i \(-0.564054\pi\)
−0.199875 + 0.979821i \(0.564054\pi\)
\(998\) −24.4553 −0.774118
\(999\) −24.7643 −0.783508
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 \(a_p\))