Properties

Label 8015.2.a.l.1.58
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.58
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} +O(q^{10})\) \(q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} -2.53639 q^{10} +0.694118 q^{11} +13.8046 q^{12} +6.89482 q^{13} -2.53639 q^{14} -3.11385 q^{15} +6.78751 q^{16} -1.07371 q^{17} +16.9839 q^{18} -6.93839 q^{19} -4.43329 q^{20} -3.11385 q^{21} +1.76056 q^{22} -6.40773 q^{23} +19.2180 q^{24} +1.00000 q^{25} +17.4880 q^{26} +11.5090 q^{27} -4.43329 q^{28} +8.17452 q^{29} -7.89795 q^{30} -3.45726 q^{31} +4.87221 q^{32} +2.16138 q^{33} -2.72336 q^{34} +1.00000 q^{35} +29.6857 q^{36} +3.20904 q^{37} -17.5985 q^{38} +21.4694 q^{39} -6.17179 q^{40} +12.4117 q^{41} -7.89795 q^{42} +3.20569 q^{43} +3.07723 q^{44} -6.69607 q^{45} -16.2525 q^{46} -7.35044 q^{47} +21.1353 q^{48} +1.00000 q^{49} +2.53639 q^{50} -3.34339 q^{51} +30.5667 q^{52} -4.64026 q^{53} +29.1914 q^{54} -0.694118 q^{55} -6.17179 q^{56} -21.6051 q^{57} +20.7338 q^{58} +4.98998 q^{59} -13.8046 q^{60} +8.72134 q^{61} -8.76897 q^{62} -6.69607 q^{63} -1.21717 q^{64} -6.89482 q^{65} +5.48211 q^{66} +1.23346 q^{67} -4.76009 q^{68} -19.9527 q^{69} +2.53639 q^{70} -6.96428 q^{71} +41.3268 q^{72} -0.707397 q^{73} +8.13938 q^{74} +3.11385 q^{75} -30.7599 q^{76} -0.694118 q^{77} +54.4549 q^{78} -10.5072 q^{79} -6.78751 q^{80} +15.7492 q^{81} +31.4809 q^{82} +4.46033 q^{83} -13.8046 q^{84} +1.07371 q^{85} +8.13089 q^{86} +25.4543 q^{87} +4.28395 q^{88} -10.6281 q^{89} -16.9839 q^{90} -6.89482 q^{91} -28.4074 q^{92} -10.7654 q^{93} -18.6436 q^{94} +6.93839 q^{95} +15.1713 q^{96} +16.7029 q^{97} +2.53639 q^{98} +4.64786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.53639 1.79350 0.896751 0.442536i \(-0.145921\pi\)
0.896751 + 0.442536i \(0.145921\pi\)
\(3\) 3.11385 1.79778 0.898892 0.438171i \(-0.144374\pi\)
0.898892 + 0.438171i \(0.144374\pi\)
\(4\) 4.43329 2.21665
\(5\) −1.00000 −0.447214
\(6\) 7.89795 3.22433
\(7\) −1.00000 −0.377964
\(8\) 6.17179 2.18206
\(9\) 6.69607 2.23202
\(10\) −2.53639 −0.802078
\(11\) 0.694118 0.209284 0.104642 0.994510i \(-0.466630\pi\)
0.104642 + 0.994510i \(0.466630\pi\)
\(12\) 13.8046 3.98505
\(13\) 6.89482 1.91228 0.956139 0.292914i \(-0.0946249\pi\)
0.956139 + 0.292914i \(0.0946249\pi\)
\(14\) −2.53639 −0.677880
\(15\) −3.11385 −0.803993
\(16\) 6.78751 1.69688
\(17\) −1.07371 −0.260414 −0.130207 0.991487i \(-0.541564\pi\)
−0.130207 + 0.991487i \(0.541564\pi\)
\(18\) 16.9839 4.00314
\(19\) −6.93839 −1.59178 −0.795888 0.605444i \(-0.792996\pi\)
−0.795888 + 0.605444i \(0.792996\pi\)
\(20\) −4.43329 −0.991315
\(21\) −3.11385 −0.679498
\(22\) 1.76056 0.375352
\(23\) −6.40773 −1.33610 −0.668052 0.744115i \(-0.732872\pi\)
−0.668052 + 0.744115i \(0.732872\pi\)
\(24\) 19.2180 3.92287
\(25\) 1.00000 0.200000
\(26\) 17.4880 3.42967
\(27\) 11.5090 2.21491
\(28\) −4.43329 −0.837814
\(29\) 8.17452 1.51797 0.758986 0.651107i \(-0.225695\pi\)
0.758986 + 0.651107i \(0.225695\pi\)
\(30\) −7.89795 −1.44196
\(31\) −3.45726 −0.620942 −0.310471 0.950583i \(-0.600487\pi\)
−0.310471 + 0.950583i \(0.600487\pi\)
\(32\) 4.87221 0.861294
\(33\) 2.16138 0.376248
\(34\) −2.72336 −0.467053
\(35\) 1.00000 0.169031
\(36\) 29.6857 4.94761
\(37\) 3.20904 0.527562 0.263781 0.964583i \(-0.415030\pi\)
0.263781 + 0.964583i \(0.415030\pi\)
\(38\) −17.5985 −2.85485
\(39\) 21.4694 3.43786
\(40\) −6.17179 −0.975846
\(41\) 12.4117 1.93838 0.969189 0.246317i \(-0.0792204\pi\)
0.969189 + 0.246317i \(0.0792204\pi\)
\(42\) −7.89795 −1.21868
\(43\) 3.20569 0.488863 0.244431 0.969667i \(-0.421399\pi\)
0.244431 + 0.969667i \(0.421399\pi\)
\(44\) 3.07723 0.463909
\(45\) −6.69607 −0.998192
\(46\) −16.2525 −2.39630
\(47\) −7.35044 −1.07217 −0.536086 0.844163i \(-0.680098\pi\)
−0.536086 + 0.844163i \(0.680098\pi\)
\(48\) 21.1353 3.05062
\(49\) 1.00000 0.142857
\(50\) 2.53639 0.358700
\(51\) −3.34339 −0.468168
\(52\) 30.5667 4.23885
\(53\) −4.64026 −0.637388 −0.318694 0.947858i \(-0.603244\pi\)
−0.318694 + 0.947858i \(0.603244\pi\)
\(54\) 29.1914 3.97245
\(55\) −0.694118 −0.0935948
\(56\) −6.17179 −0.824741
\(57\) −21.6051 −2.86167
\(58\) 20.7338 2.72248
\(59\) 4.98998 0.649640 0.324820 0.945776i \(-0.394696\pi\)
0.324820 + 0.945776i \(0.394696\pi\)
\(60\) −13.8046 −1.78217
\(61\) 8.72134 1.11665 0.558326 0.829621i \(-0.311444\pi\)
0.558326 + 0.829621i \(0.311444\pi\)
\(62\) −8.76897 −1.11366
\(63\) −6.69607 −0.843626
\(64\) −1.21717 −0.152146
\(65\) −6.89482 −0.855197
\(66\) 5.48211 0.674801
\(67\) 1.23346 0.150692 0.0753458 0.997157i \(-0.475994\pi\)
0.0753458 + 0.997157i \(0.475994\pi\)
\(68\) −4.76009 −0.577246
\(69\) −19.9527 −2.40203
\(70\) 2.53639 0.303157
\(71\) −6.96428 −0.826508 −0.413254 0.910616i \(-0.635608\pi\)
−0.413254 + 0.910616i \(0.635608\pi\)
\(72\) 41.3268 4.87041
\(73\) −0.707397 −0.0827946 −0.0413973 0.999143i \(-0.513181\pi\)
−0.0413973 + 0.999143i \(0.513181\pi\)
\(74\) 8.13938 0.946184
\(75\) 3.11385 0.359557
\(76\) −30.7599 −3.52841
\(77\) −0.694118 −0.0791020
\(78\) 54.4549 6.16581
\(79\) −10.5072 −1.18215 −0.591075 0.806616i \(-0.701296\pi\)
−0.591075 + 0.806616i \(0.701296\pi\)
\(80\) −6.78751 −0.758867
\(81\) 15.7492 1.74991
\(82\) 31.4809 3.47648
\(83\) 4.46033 0.489584 0.244792 0.969576i \(-0.421280\pi\)
0.244792 + 0.969576i \(0.421280\pi\)
\(84\) −13.8046 −1.50621
\(85\) 1.07371 0.116461
\(86\) 8.13089 0.876776
\(87\) 25.4543 2.72898
\(88\) 4.28395 0.456671
\(89\) −10.6281 −1.12657 −0.563287 0.826261i \(-0.690464\pi\)
−0.563287 + 0.826261i \(0.690464\pi\)
\(90\) −16.9839 −1.79026
\(91\) −6.89482 −0.722773
\(92\) −28.4074 −2.96167
\(93\) −10.7654 −1.11632
\(94\) −18.6436 −1.92294
\(95\) 6.93839 0.711864
\(96\) 15.1713 1.54842
\(97\) 16.7029 1.69592 0.847961 0.530059i \(-0.177830\pi\)
0.847961 + 0.530059i \(0.177830\pi\)
\(98\) 2.53639 0.256214
\(99\) 4.64786 0.467128
\(100\) 4.43329 0.443329
\(101\) −19.0840 −1.89893 −0.949465 0.313874i \(-0.898373\pi\)
−0.949465 + 0.313874i \(0.898373\pi\)
\(102\) −8.48015 −0.839660
\(103\) −3.71668 −0.366215 −0.183108 0.983093i \(-0.558616\pi\)
−0.183108 + 0.983093i \(0.558616\pi\)
\(104\) 42.5534 4.17270
\(105\) 3.11385 0.303881
\(106\) −11.7695 −1.14316
\(107\) −13.6558 −1.32015 −0.660077 0.751198i \(-0.729476\pi\)
−0.660077 + 0.751198i \(0.729476\pi\)
\(108\) 51.0229 4.90968
\(109\) 0.0225205 0.00215707 0.00107853 0.999999i \(-0.499657\pi\)
0.00107853 + 0.999999i \(0.499657\pi\)
\(110\) −1.76056 −0.167862
\(111\) 9.99246 0.948443
\(112\) −6.78751 −0.641359
\(113\) −9.15269 −0.861013 −0.430506 0.902588i \(-0.641665\pi\)
−0.430506 + 0.902588i \(0.641665\pi\)
\(114\) −54.7991 −5.13241
\(115\) 6.40773 0.597524
\(116\) 36.2401 3.36481
\(117\) 46.1682 4.26825
\(118\) 12.6566 1.16513
\(119\) 1.07371 0.0984272
\(120\) −19.2180 −1.75436
\(121\) −10.5182 −0.956200
\(122\) 22.1207 2.00272
\(123\) 38.6481 3.48478
\(124\) −15.3270 −1.37641
\(125\) −1.00000 −0.0894427
\(126\) −16.9839 −1.51304
\(127\) 7.14187 0.633738 0.316869 0.948469i \(-0.397368\pi\)
0.316869 + 0.948469i \(0.397368\pi\)
\(128\) −12.8316 −1.13417
\(129\) 9.98204 0.878869
\(130\) −17.4880 −1.53380
\(131\) −2.62484 −0.229333 −0.114667 0.993404i \(-0.536580\pi\)
−0.114667 + 0.993404i \(0.536580\pi\)
\(132\) 9.58203 0.834009
\(133\) 6.93839 0.601635
\(134\) 3.12855 0.270265
\(135\) −11.5090 −0.990539
\(136\) −6.62674 −0.568238
\(137\) −3.40028 −0.290506 −0.145253 0.989395i \(-0.546400\pi\)
−0.145253 + 0.989395i \(0.546400\pi\)
\(138\) −50.6080 −4.30804
\(139\) 15.1275 1.28310 0.641548 0.767083i \(-0.278292\pi\)
0.641548 + 0.767083i \(0.278292\pi\)
\(140\) 4.43329 0.374682
\(141\) −22.8882 −1.92753
\(142\) −17.6642 −1.48234
\(143\) 4.78581 0.400210
\(144\) 45.4497 3.78747
\(145\) −8.17452 −0.678857
\(146\) −1.79424 −0.148492
\(147\) 3.11385 0.256826
\(148\) 14.2266 1.16942
\(149\) 2.39105 0.195883 0.0979414 0.995192i \(-0.468774\pi\)
0.0979414 + 0.995192i \(0.468774\pi\)
\(150\) 7.89795 0.644865
\(151\) 13.7810 1.12148 0.560742 0.827991i \(-0.310516\pi\)
0.560742 + 0.827991i \(0.310516\pi\)
\(152\) −42.8223 −3.47335
\(153\) −7.18967 −0.581250
\(154\) −1.76056 −0.141870
\(155\) 3.45726 0.277694
\(156\) 95.1803 7.62052
\(157\) −14.4724 −1.15503 −0.577513 0.816382i \(-0.695977\pi\)
−0.577513 + 0.816382i \(0.695977\pi\)
\(158\) −26.6504 −2.12019
\(159\) −14.4491 −1.14589
\(160\) −4.87221 −0.385182
\(161\) 6.40773 0.505000
\(162\) 39.9461 3.13846
\(163\) −11.3530 −0.889236 −0.444618 0.895720i \(-0.646661\pi\)
−0.444618 + 0.895720i \(0.646661\pi\)
\(164\) 55.0246 4.29670
\(165\) −2.16138 −0.168263
\(166\) 11.3131 0.878070
\(167\) −23.9335 −1.85203 −0.926014 0.377489i \(-0.876788\pi\)
−0.926014 + 0.377489i \(0.876788\pi\)
\(168\) −19.2180 −1.48270
\(169\) 34.5385 2.65681
\(170\) 2.72336 0.208872
\(171\) −46.4600 −3.55288
\(172\) 14.2118 1.08364
\(173\) 22.1259 1.68220 0.841101 0.540879i \(-0.181908\pi\)
0.841101 + 0.540879i \(0.181908\pi\)
\(174\) 64.5620 4.89443
\(175\) −1.00000 −0.0755929
\(176\) 4.71133 0.355130
\(177\) 15.5381 1.16791
\(178\) −26.9570 −2.02051
\(179\) −13.2390 −0.989526 −0.494763 0.869028i \(-0.664745\pi\)
−0.494763 + 0.869028i \(0.664745\pi\)
\(180\) −29.6857 −2.21264
\(181\) −24.5051 −1.82145 −0.910724 0.413015i \(-0.864476\pi\)
−0.910724 + 0.413015i \(0.864476\pi\)
\(182\) −17.4880 −1.29629
\(183\) 27.1569 2.00750
\(184\) −39.5472 −2.91546
\(185\) −3.20904 −0.235933
\(186\) −27.3053 −2.00212
\(187\) −0.745284 −0.0545006
\(188\) −32.5867 −2.37663
\(189\) −11.5090 −0.837158
\(190\) 17.5985 1.27673
\(191\) −6.29692 −0.455629 −0.227814 0.973705i \(-0.573158\pi\)
−0.227814 + 0.973705i \(0.573158\pi\)
\(192\) −3.79008 −0.273526
\(193\) 9.76342 0.702787 0.351393 0.936228i \(-0.385708\pi\)
0.351393 + 0.936228i \(0.385708\pi\)
\(194\) 42.3651 3.04164
\(195\) −21.4694 −1.53746
\(196\) 4.43329 0.316664
\(197\) 9.83007 0.700364 0.350182 0.936682i \(-0.386120\pi\)
0.350182 + 0.936682i \(0.386120\pi\)
\(198\) 11.7888 0.837794
\(199\) 11.5793 0.820836 0.410418 0.911898i \(-0.365383\pi\)
0.410418 + 0.911898i \(0.365383\pi\)
\(200\) 6.17179 0.436412
\(201\) 3.84082 0.270911
\(202\) −48.4045 −3.40573
\(203\) −8.17452 −0.573739
\(204\) −14.8222 −1.03776
\(205\) −12.4117 −0.866869
\(206\) −9.42696 −0.656807
\(207\) −42.9066 −2.98222
\(208\) 46.7986 3.24490
\(209\) −4.81606 −0.333134
\(210\) 7.89795 0.545011
\(211\) −28.9280 −1.99149 −0.995744 0.0921609i \(-0.970623\pi\)
−0.995744 + 0.0921609i \(0.970623\pi\)
\(212\) −20.5716 −1.41286
\(213\) −21.6857 −1.48588
\(214\) −34.6364 −2.36770
\(215\) −3.20569 −0.218626
\(216\) 71.0313 4.83307
\(217\) 3.45726 0.234694
\(218\) 0.0571207 0.00386870
\(219\) −2.20273 −0.148847
\(220\) −3.07723 −0.207467
\(221\) −7.40306 −0.497984
\(222\) 25.3448 1.70103
\(223\) −16.2888 −1.09078 −0.545389 0.838183i \(-0.683618\pi\)
−0.545389 + 0.838183i \(0.683618\pi\)
\(224\) −4.87221 −0.325538
\(225\) 6.69607 0.446405
\(226\) −23.2148 −1.54423
\(227\) 9.63959 0.639802 0.319901 0.947451i \(-0.396350\pi\)
0.319901 + 0.947451i \(0.396350\pi\)
\(228\) −95.7819 −6.34331
\(229\) 1.00000 0.0660819
\(230\) 16.2525 1.07166
\(231\) −2.16138 −0.142208
\(232\) 50.4515 3.31230
\(233\) 8.65226 0.566829 0.283414 0.958998i \(-0.408533\pi\)
0.283414 + 0.958998i \(0.408533\pi\)
\(234\) 117.101 7.65511
\(235\) 7.35044 0.479490
\(236\) 22.1221 1.44002
\(237\) −32.7178 −2.12525
\(238\) 2.72336 0.176529
\(239\) 20.5627 1.33009 0.665046 0.746803i \(-0.268412\pi\)
0.665046 + 0.746803i \(0.268412\pi\)
\(240\) −21.1353 −1.36428
\(241\) 0.271703 0.0175019 0.00875096 0.999962i \(-0.497214\pi\)
0.00875096 + 0.999962i \(0.497214\pi\)
\(242\) −26.6783 −1.71495
\(243\) 14.5135 0.931042
\(244\) 38.6643 2.47523
\(245\) −1.00000 −0.0638877
\(246\) 98.0269 6.24997
\(247\) −47.8389 −3.04392
\(248\) −21.3375 −1.35493
\(249\) 13.8888 0.880167
\(250\) −2.53639 −0.160416
\(251\) −9.97546 −0.629646 −0.314823 0.949150i \(-0.601945\pi\)
−0.314823 + 0.949150i \(0.601945\pi\)
\(252\) −29.6857 −1.87002
\(253\) −4.44772 −0.279626
\(254\) 18.1146 1.13661
\(255\) 3.34339 0.209371
\(256\) −30.1118 −1.88199
\(257\) 4.57395 0.285315 0.142657 0.989772i \(-0.454435\pi\)
0.142657 + 0.989772i \(0.454435\pi\)
\(258\) 25.3184 1.57625
\(259\) −3.20904 −0.199400
\(260\) −30.5667 −1.89567
\(261\) 54.7372 3.38815
\(262\) −6.65763 −0.411310
\(263\) −4.40317 −0.271511 −0.135755 0.990742i \(-0.543346\pi\)
−0.135755 + 0.990742i \(0.543346\pi\)
\(264\) 13.3396 0.820995
\(265\) 4.64026 0.285049
\(266\) 17.5985 1.07903
\(267\) −33.0943 −2.02534
\(268\) 5.46831 0.334030
\(269\) 29.2799 1.78523 0.892613 0.450824i \(-0.148870\pi\)
0.892613 + 0.450824i \(0.148870\pi\)
\(270\) −29.1914 −1.77653
\(271\) −14.4079 −0.875219 −0.437610 0.899165i \(-0.644175\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(272\) −7.28785 −0.441891
\(273\) −21.4694 −1.29939
\(274\) −8.62446 −0.521023
\(275\) 0.694118 0.0418569
\(276\) −88.4563 −5.32444
\(277\) 16.4969 0.991202 0.495601 0.868550i \(-0.334948\pi\)
0.495601 + 0.868550i \(0.334948\pi\)
\(278\) 38.3693 2.30124
\(279\) −23.1501 −1.38596
\(280\) 6.17179 0.368835
\(281\) −19.2992 −1.15129 −0.575647 0.817698i \(-0.695250\pi\)
−0.575647 + 0.817698i \(0.695250\pi\)
\(282\) −58.0535 −3.45703
\(283\) 4.38026 0.260380 0.130190 0.991489i \(-0.458441\pi\)
0.130190 + 0.991489i \(0.458441\pi\)
\(284\) −30.8747 −1.83208
\(285\) 21.6051 1.27978
\(286\) 12.1387 0.717777
\(287\) −12.4117 −0.732638
\(288\) 32.6247 1.92243
\(289\) −15.8471 −0.932185
\(290\) −20.7338 −1.21753
\(291\) 52.0103 3.04890
\(292\) −3.13610 −0.183526
\(293\) −9.28530 −0.542453 −0.271227 0.962516i \(-0.587429\pi\)
−0.271227 + 0.962516i \(0.587429\pi\)
\(294\) 7.89795 0.460618
\(295\) −4.98998 −0.290528
\(296\) 19.8055 1.15117
\(297\) 7.98861 0.463546
\(298\) 6.06466 0.351316
\(299\) −44.1801 −2.55500
\(300\) 13.8046 0.797010
\(301\) −3.20569 −0.184773
\(302\) 34.9541 2.01138
\(303\) −59.4248 −3.41386
\(304\) −47.0944 −2.70105
\(305\) −8.72134 −0.499382
\(306\) −18.2358 −1.04247
\(307\) 11.9072 0.679580 0.339790 0.940501i \(-0.389644\pi\)
0.339790 + 0.940501i \(0.389644\pi\)
\(308\) −3.07723 −0.175341
\(309\) −11.5732 −0.658375
\(310\) 8.76897 0.498044
\(311\) 9.34999 0.530189 0.265095 0.964222i \(-0.414597\pi\)
0.265095 + 0.964222i \(0.414597\pi\)
\(312\) 132.505 7.50161
\(313\) −3.30987 −0.187085 −0.0935423 0.995615i \(-0.529819\pi\)
−0.0935423 + 0.995615i \(0.529819\pi\)
\(314\) −36.7078 −2.07154
\(315\) 6.69607 0.377281
\(316\) −46.5814 −2.62041
\(317\) −0.410312 −0.0230454 −0.0115227 0.999934i \(-0.503668\pi\)
−0.0115227 + 0.999934i \(0.503668\pi\)
\(318\) −36.6485 −2.05515
\(319\) 5.67408 0.317688
\(320\) 1.21717 0.0680418
\(321\) −42.5221 −2.37335
\(322\) 16.2525 0.905718
\(323\) 7.44985 0.414521
\(324\) 69.8207 3.87893
\(325\) 6.89482 0.382456
\(326\) −28.7957 −1.59485
\(327\) 0.0701253 0.00387794
\(328\) 76.6023 4.22966
\(329\) 7.35044 0.405243
\(330\) −5.48211 −0.301780
\(331\) 3.36690 0.185061 0.0925307 0.995710i \(-0.470504\pi\)
0.0925307 + 0.995710i \(0.470504\pi\)
\(332\) 19.7739 1.08524
\(333\) 21.4879 1.17753
\(334\) −60.7047 −3.32162
\(335\) −1.23346 −0.0673913
\(336\) −21.1353 −1.15303
\(337\) −18.9603 −1.03283 −0.516415 0.856338i \(-0.672734\pi\)
−0.516415 + 0.856338i \(0.672734\pi\)
\(338\) 87.6032 4.76499
\(339\) −28.5001 −1.54791
\(340\) 4.76009 0.258152
\(341\) −2.39974 −0.129953
\(342\) −117.841 −6.37210
\(343\) −1.00000 −0.0539949
\(344\) 19.7848 1.06673
\(345\) 19.9527 1.07422
\(346\) 56.1200 3.01703
\(347\) 2.04321 0.109685 0.0548427 0.998495i \(-0.482534\pi\)
0.0548427 + 0.998495i \(0.482534\pi\)
\(348\) 112.846 6.04919
\(349\) −17.4134 −0.932116 −0.466058 0.884754i \(-0.654326\pi\)
−0.466058 + 0.884754i \(0.654326\pi\)
\(350\) −2.53639 −0.135576
\(351\) 79.3526 4.23553
\(352\) 3.38189 0.180255
\(353\) 16.3755 0.871578 0.435789 0.900049i \(-0.356469\pi\)
0.435789 + 0.900049i \(0.356469\pi\)
\(354\) 39.4107 2.09465
\(355\) 6.96428 0.369626
\(356\) −47.1174 −2.49722
\(357\) 3.34339 0.176951
\(358\) −33.5792 −1.77472
\(359\) 18.7159 0.987789 0.493894 0.869522i \(-0.335573\pi\)
0.493894 + 0.869522i \(0.335573\pi\)
\(360\) −41.3268 −2.17811
\(361\) 29.1413 1.53375
\(362\) −62.1546 −3.26677
\(363\) −32.7521 −1.71904
\(364\) −30.5667 −1.60213
\(365\) 0.707397 0.0370269
\(366\) 68.8807 3.60045
\(367\) 7.13403 0.372394 0.186197 0.982512i \(-0.440384\pi\)
0.186197 + 0.982512i \(0.440384\pi\)
\(368\) −43.4925 −2.26720
\(369\) 83.1095 4.32651
\(370\) −8.13938 −0.423146
\(371\) 4.64026 0.240910
\(372\) −47.7262 −2.47449
\(373\) −10.4582 −0.541504 −0.270752 0.962649i \(-0.587272\pi\)
−0.270752 + 0.962649i \(0.587272\pi\)
\(374\) −1.89033 −0.0977468
\(375\) −3.11385 −0.160799
\(376\) −45.3654 −2.33954
\(377\) 56.3618 2.90278
\(378\) −29.1914 −1.50144
\(379\) −10.0073 −0.514042 −0.257021 0.966406i \(-0.582741\pi\)
−0.257021 + 0.966406i \(0.582741\pi\)
\(380\) 30.7599 1.57795
\(381\) 22.2387 1.13932
\(382\) −15.9715 −0.817171
\(383\) −12.0370 −0.615061 −0.307531 0.951538i \(-0.599503\pi\)
−0.307531 + 0.951538i \(0.599503\pi\)
\(384\) −39.9558 −2.03899
\(385\) 0.694118 0.0353755
\(386\) 24.7639 1.26045
\(387\) 21.4655 1.09115
\(388\) 74.0488 3.75926
\(389\) 6.24817 0.316795 0.158397 0.987375i \(-0.449367\pi\)
0.158397 + 0.987375i \(0.449367\pi\)
\(390\) −54.4549 −2.75743
\(391\) 6.88007 0.347940
\(392\) 6.17179 0.311723
\(393\) −8.17336 −0.412292
\(394\) 24.9329 1.25610
\(395\) 10.5072 0.528674
\(396\) 20.6053 1.03546
\(397\) 23.2972 1.16925 0.584626 0.811303i \(-0.301241\pi\)
0.584626 + 0.811303i \(0.301241\pi\)
\(398\) 29.3697 1.47217
\(399\) 21.6051 1.08161
\(400\) 6.78751 0.339375
\(401\) −12.8957 −0.643980 −0.321990 0.946743i \(-0.604352\pi\)
−0.321990 + 0.946743i \(0.604352\pi\)
\(402\) 9.74184 0.485879
\(403\) −23.8372 −1.18741
\(404\) −84.6050 −4.20926
\(405\) −15.7492 −0.782583
\(406\) −20.7338 −1.02900
\(407\) 2.22745 0.110411
\(408\) −20.6347 −1.02157
\(409\) 12.4018 0.613230 0.306615 0.951834i \(-0.400804\pi\)
0.306615 + 0.951834i \(0.400804\pi\)
\(410\) −31.4809 −1.55473
\(411\) −10.5880 −0.522267
\(412\) −16.4771 −0.811770
\(413\) −4.98998 −0.245541
\(414\) −108.828 −5.34861
\(415\) −4.46033 −0.218949
\(416\) 33.5930 1.64703
\(417\) 47.1048 2.30673
\(418\) −12.2154 −0.597476
\(419\) 25.4805 1.24481 0.622403 0.782697i \(-0.286156\pi\)
0.622403 + 0.782697i \(0.286156\pi\)
\(420\) 13.8046 0.673597
\(421\) 15.8522 0.772591 0.386296 0.922375i \(-0.373754\pi\)
0.386296 + 0.922375i \(0.373754\pi\)
\(422\) −73.3729 −3.57174
\(423\) −49.2191 −2.39311
\(424\) −28.6387 −1.39082
\(425\) −1.07371 −0.0520828
\(426\) −55.0036 −2.66493
\(427\) −8.72134 −0.422055
\(428\) −60.5401 −2.92631
\(429\) 14.9023 0.719490
\(430\) −8.13089 −0.392106
\(431\) 27.1499 1.30776 0.653881 0.756597i \(-0.273140\pi\)
0.653881 + 0.756597i \(0.273140\pi\)
\(432\) 78.1176 3.75843
\(433\) 37.4869 1.80150 0.900752 0.434335i \(-0.143016\pi\)
0.900752 + 0.434335i \(0.143016\pi\)
\(434\) 8.76897 0.420924
\(435\) −25.4543 −1.22044
\(436\) 0.0998398 0.00478146
\(437\) 44.4593 2.12678
\(438\) −5.58699 −0.266957
\(439\) 27.6510 1.31971 0.659855 0.751393i \(-0.270618\pi\)
0.659855 + 0.751393i \(0.270618\pi\)
\(440\) −4.28395 −0.204229
\(441\) 6.69607 0.318861
\(442\) −18.7771 −0.893135
\(443\) 16.4609 0.782080 0.391040 0.920374i \(-0.372115\pi\)
0.391040 + 0.920374i \(0.372115\pi\)
\(444\) 44.2995 2.10236
\(445\) 10.6281 0.503819
\(446\) −41.3148 −1.95631
\(447\) 7.44539 0.352155
\(448\) 1.21717 0.0575058
\(449\) −33.9770 −1.60347 −0.801737 0.597677i \(-0.796091\pi\)
−0.801737 + 0.597677i \(0.796091\pi\)
\(450\) 16.9839 0.800628
\(451\) 8.61516 0.405672
\(452\) −40.5766 −1.90856
\(453\) 42.9121 2.01619
\(454\) 24.4498 1.14749
\(455\) 6.89482 0.323234
\(456\) −133.342 −6.24433
\(457\) 8.90711 0.416657 0.208328 0.978059i \(-0.433198\pi\)
0.208328 + 0.978059i \(0.433198\pi\)
\(458\) 2.53639 0.118518
\(459\) −12.3574 −0.576794
\(460\) 28.4074 1.32450
\(461\) 0.253730 0.0118174 0.00590870 0.999983i \(-0.498119\pi\)
0.00590870 + 0.999983i \(0.498119\pi\)
\(462\) −5.48211 −0.255051
\(463\) −22.3456 −1.03849 −0.519244 0.854626i \(-0.673786\pi\)
−0.519244 + 0.854626i \(0.673786\pi\)
\(464\) 55.4847 2.57581
\(465\) 10.7654 0.499233
\(466\) 21.9456 1.01661
\(467\) 35.9456 1.66337 0.831683 0.555251i \(-0.187378\pi\)
0.831683 + 0.555251i \(0.187378\pi\)
\(468\) 204.677 9.46120
\(469\) −1.23346 −0.0569560
\(470\) 18.6436 0.859966
\(471\) −45.0650 −2.07649
\(472\) 30.7971 1.41755
\(473\) 2.22512 0.102311
\(474\) −82.9853 −3.81164
\(475\) −6.93839 −0.318355
\(476\) 4.76009 0.218178
\(477\) −31.0715 −1.42267
\(478\) 52.1552 2.38552
\(479\) −14.2792 −0.652434 −0.326217 0.945295i \(-0.605774\pi\)
−0.326217 + 0.945295i \(0.605774\pi\)
\(480\) −15.1713 −0.692474
\(481\) 22.1257 1.00885
\(482\) 0.689145 0.0313897
\(483\) 19.9527 0.907880
\(484\) −46.6303 −2.11956
\(485\) −16.7029 −0.758439
\(486\) 36.8120 1.66983
\(487\) −2.74442 −0.124361 −0.0621807 0.998065i \(-0.519805\pi\)
−0.0621807 + 0.998065i \(0.519805\pi\)
\(488\) 53.8263 2.43660
\(489\) −35.3516 −1.59865
\(490\) −2.53639 −0.114583
\(491\) −9.75967 −0.440448 −0.220224 0.975449i \(-0.570679\pi\)
−0.220224 + 0.975449i \(0.570679\pi\)
\(492\) 171.339 7.72454
\(493\) −8.77710 −0.395301
\(494\) −121.338 −5.45927
\(495\) −4.64786 −0.208906
\(496\) −23.4662 −1.05366
\(497\) 6.96428 0.312391
\(498\) 35.2275 1.57858
\(499\) −13.3965 −0.599709 −0.299854 0.953985i \(-0.596938\pi\)
−0.299854 + 0.953985i \(0.596938\pi\)
\(500\) −4.43329 −0.198263
\(501\) −74.5253 −3.32955
\(502\) −25.3017 −1.12927
\(503\) −38.5846 −1.72040 −0.860201 0.509954i \(-0.829662\pi\)
−0.860201 + 0.509954i \(0.829662\pi\)
\(504\) −41.3268 −1.84084
\(505\) 19.0840 0.849227
\(506\) −11.2812 −0.501509
\(507\) 107.548 4.77636
\(508\) 31.6620 1.40477
\(509\) 22.6354 1.00329 0.501647 0.865072i \(-0.332728\pi\)
0.501647 + 0.865072i \(0.332728\pi\)
\(510\) 8.48015 0.375507
\(511\) 0.707397 0.0312934
\(512\) −50.7120 −2.24118
\(513\) −79.8541 −3.52564
\(514\) 11.6013 0.511713
\(515\) 3.71668 0.163776
\(516\) 44.2533 1.94814
\(517\) −5.10207 −0.224389
\(518\) −8.13938 −0.357624
\(519\) 68.8968 3.02423
\(520\) −42.5534 −1.86609
\(521\) 13.9472 0.611037 0.305518 0.952186i \(-0.401170\pi\)
0.305518 + 0.952186i \(0.401170\pi\)
\(522\) 138.835 6.07665
\(523\) 5.46489 0.238963 0.119482 0.992836i \(-0.461877\pi\)
0.119482 + 0.992836i \(0.461877\pi\)
\(524\) −11.6367 −0.508351
\(525\) −3.11385 −0.135900
\(526\) −11.1682 −0.486955
\(527\) 3.71211 0.161702
\(528\) 14.6704 0.638446
\(529\) 18.0590 0.785174
\(530\) 11.7695 0.511235
\(531\) 33.4133 1.45001
\(532\) 30.7599 1.33361
\(533\) 85.5762 3.70672
\(534\) −83.9401 −3.63244
\(535\) 13.6558 0.590391
\(536\) 7.61268 0.328818
\(537\) −41.2242 −1.77895
\(538\) 74.2653 3.20181
\(539\) 0.694118 0.0298978
\(540\) −51.0229 −2.19568
\(541\) 12.4275 0.534300 0.267150 0.963655i \(-0.413918\pi\)
0.267150 + 0.963655i \(0.413918\pi\)
\(542\) −36.5442 −1.56971
\(543\) −76.3052 −3.27457
\(544\) −5.23136 −0.224293
\(545\) −0.0225205 −0.000964670 0
\(546\) −54.4549 −2.33046
\(547\) −26.3836 −1.12808 −0.564040 0.825748i \(-0.690754\pi\)
−0.564040 + 0.825748i \(0.690754\pi\)
\(548\) −15.0745 −0.643949
\(549\) 58.3987 2.49240
\(550\) 1.76056 0.0750703
\(551\) −56.7180 −2.41627
\(552\) −123.144 −5.24136
\(553\) 10.5072 0.446811
\(554\) 41.8426 1.77772
\(555\) −9.99246 −0.424156
\(556\) 67.0646 2.84417
\(557\) −35.8380 −1.51850 −0.759252 0.650797i \(-0.774435\pi\)
−0.759252 + 0.650797i \(0.774435\pi\)
\(558\) −58.7177 −2.48572
\(559\) 22.1026 0.934841
\(560\) 6.78751 0.286825
\(561\) −2.32070 −0.0979802
\(562\) −48.9504 −2.06485
\(563\) 28.7783 1.21286 0.606430 0.795137i \(-0.292601\pi\)
0.606430 + 0.795137i \(0.292601\pi\)
\(564\) −101.470 −4.27266
\(565\) 9.15269 0.385057
\(566\) 11.1101 0.466991
\(567\) −15.7492 −0.661403
\(568\) −42.9821 −1.80349
\(569\) 19.2339 0.806327 0.403164 0.915128i \(-0.367911\pi\)
0.403164 + 0.915128i \(0.367911\pi\)
\(570\) 54.7991 2.29528
\(571\) 4.18337 0.175068 0.0875342 0.996162i \(-0.472101\pi\)
0.0875342 + 0.996162i \(0.472101\pi\)
\(572\) 21.2169 0.887124
\(573\) −19.6077 −0.819122
\(574\) −31.4809 −1.31399
\(575\) −6.40773 −0.267221
\(576\) −8.15025 −0.339594
\(577\) 23.3122 0.970501 0.485251 0.874375i \(-0.338728\pi\)
0.485251 + 0.874375i \(0.338728\pi\)
\(578\) −40.1946 −1.67187
\(579\) 30.4019 1.26346
\(580\) −36.2401 −1.50479
\(581\) −4.46033 −0.185046
\(582\) 131.919 5.46820
\(583\) −3.22088 −0.133395
\(584\) −4.36591 −0.180663
\(585\) −46.1682 −1.90882
\(586\) −23.5512 −0.972891
\(587\) 7.83786 0.323503 0.161752 0.986832i \(-0.448286\pi\)
0.161752 + 0.986832i \(0.448286\pi\)
\(588\) 13.8046 0.569293
\(589\) 23.9878 0.988401
\(590\) −12.6566 −0.521062
\(591\) 30.6094 1.25910
\(592\) 21.7814 0.895209
\(593\) −34.7711 −1.42788 −0.713939 0.700208i \(-0.753091\pi\)
−0.713939 + 0.700208i \(0.753091\pi\)
\(594\) 20.2623 0.831371
\(595\) −1.07371 −0.0440180
\(596\) 10.6002 0.434203
\(597\) 36.0563 1.47569
\(598\) −112.058 −4.58240
\(599\) −45.6310 −1.86443 −0.932217 0.361900i \(-0.882128\pi\)
−0.932217 + 0.361900i \(0.882128\pi\)
\(600\) 19.2180 0.784574
\(601\) −31.1708 −1.27148 −0.635742 0.771902i \(-0.719306\pi\)
−0.635742 + 0.771902i \(0.719306\pi\)
\(602\) −8.13089 −0.331390
\(603\) 8.25936 0.336347
\(604\) 61.0954 2.48593
\(605\) 10.5182 0.427626
\(606\) −150.725 −6.12277
\(607\) −22.3766 −0.908237 −0.454119 0.890941i \(-0.650046\pi\)
−0.454119 + 0.890941i \(0.650046\pi\)
\(608\) −33.8053 −1.37099
\(609\) −25.4543 −1.03146
\(610\) −22.1207 −0.895643
\(611\) −50.6799 −2.05029
\(612\) −31.8739 −1.28843
\(613\) 39.7573 1.60578 0.802891 0.596126i \(-0.203294\pi\)
0.802891 + 0.596126i \(0.203294\pi\)
\(614\) 30.2013 1.21883
\(615\) −38.6481 −1.55844
\(616\) −4.28395 −0.172605
\(617\) −34.8823 −1.40431 −0.702155 0.712024i \(-0.747779\pi\)
−0.702155 + 0.712024i \(0.747779\pi\)
\(618\) −29.3541 −1.18080
\(619\) −16.6609 −0.669659 −0.334829 0.942279i \(-0.608679\pi\)
−0.334829 + 0.942279i \(0.608679\pi\)
\(620\) 15.3270 0.615549
\(621\) −73.7467 −2.95935
\(622\) 23.7153 0.950895
\(623\) 10.6281 0.425805
\(624\) 145.724 5.83363
\(625\) 1.00000 0.0400000
\(626\) −8.39512 −0.335537
\(627\) −14.9965 −0.598902
\(628\) −64.1605 −2.56028
\(629\) −3.44559 −0.137385
\(630\) 16.9839 0.676654
\(631\) 36.1944 1.44088 0.720438 0.693519i \(-0.243941\pi\)
0.720438 + 0.693519i \(0.243941\pi\)
\(632\) −64.8482 −2.57952
\(633\) −90.0776 −3.58026
\(634\) −1.04071 −0.0413320
\(635\) −7.14187 −0.283416
\(636\) −64.0570 −2.54002
\(637\) 6.89482 0.273183
\(638\) 14.3917 0.569773
\(639\) −46.6333 −1.84479
\(640\) 12.8316 0.507215
\(641\) −41.5036 −1.63929 −0.819647 0.572869i \(-0.805830\pi\)
−0.819647 + 0.572869i \(0.805830\pi\)
\(642\) −107.853 −4.25661
\(643\) 10.9258 0.430873 0.215436 0.976518i \(-0.430883\pi\)
0.215436 + 0.976518i \(0.430883\pi\)
\(644\) 28.4074 1.11941
\(645\) −9.98204 −0.393042
\(646\) 18.8958 0.743443
\(647\) −24.0338 −0.944866 −0.472433 0.881367i \(-0.656624\pi\)
−0.472433 + 0.881367i \(0.656624\pi\)
\(648\) 97.2006 3.81840
\(649\) 3.46363 0.135960
\(650\) 17.4880 0.685935
\(651\) 10.7654 0.421929
\(652\) −50.3312 −1.97112
\(653\) −44.6154 −1.74594 −0.872968 0.487778i \(-0.837807\pi\)
−0.872968 + 0.487778i \(0.837807\pi\)
\(654\) 0.177866 0.00695509
\(655\) 2.62484 0.102561
\(656\) 84.2444 3.28919
\(657\) −4.73678 −0.184799
\(658\) 18.6436 0.726804
\(659\) 32.1860 1.25379 0.626894 0.779105i \(-0.284326\pi\)
0.626894 + 0.779105i \(0.284326\pi\)
\(660\) −9.58203 −0.372980
\(661\) −26.9824 −1.04949 −0.524747 0.851258i \(-0.675840\pi\)
−0.524747 + 0.851258i \(0.675840\pi\)
\(662\) 8.53978 0.331908
\(663\) −23.0520 −0.895267
\(664\) 27.5282 1.06830
\(665\) −6.93839 −0.269059
\(666\) 54.5019 2.11190
\(667\) −52.3801 −2.02817
\(668\) −106.104 −4.10529
\(669\) −50.7209 −1.96098
\(670\) −3.12855 −0.120866
\(671\) 6.05363 0.233698
\(672\) −15.1713 −0.585247
\(673\) 33.5732 1.29415 0.647076 0.762426i \(-0.275992\pi\)
0.647076 + 0.762426i \(0.275992\pi\)
\(674\) −48.0907 −1.85238
\(675\) 11.5090 0.442982
\(676\) 153.119 5.88920
\(677\) 28.8307 1.10805 0.554026 0.832499i \(-0.313091\pi\)
0.554026 + 0.832499i \(0.313091\pi\)
\(678\) −72.2875 −2.77619
\(679\) −16.7029 −0.640998
\(680\) 6.62674 0.254124
\(681\) 30.0162 1.15022
\(682\) −6.08670 −0.233072
\(683\) 10.7047 0.409602 0.204801 0.978804i \(-0.434345\pi\)
0.204801 + 0.978804i \(0.434345\pi\)
\(684\) −205.971 −7.87549
\(685\) 3.40028 0.129918
\(686\) −2.53639 −0.0968400
\(687\) 3.11385 0.118801
\(688\) 21.7586 0.829540
\(689\) −31.9937 −1.21886
\(690\) 50.6080 1.92661
\(691\) −6.28528 −0.239103 −0.119552 0.992828i \(-0.538146\pi\)
−0.119552 + 0.992828i \(0.538146\pi\)
\(692\) 98.0906 3.72885
\(693\) −4.64786 −0.176558
\(694\) 5.18239 0.196721
\(695\) −15.1275 −0.573818
\(696\) 157.098 5.95480
\(697\) −13.3266 −0.504781
\(698\) −44.1671 −1.67175
\(699\) 26.9419 1.01904
\(700\) −4.43329 −0.167563
\(701\) 45.0514 1.70157 0.850783 0.525516i \(-0.176128\pi\)
0.850783 + 0.525516i \(0.176128\pi\)
\(702\) 201.269 7.59642
\(703\) −22.2655 −0.839761
\(704\) −0.844858 −0.0318418
\(705\) 22.8882 0.862019
\(706\) 41.5346 1.56318
\(707\) 19.0840 0.717728
\(708\) 68.8848 2.58885
\(709\) 14.3281 0.538104 0.269052 0.963126i \(-0.413290\pi\)
0.269052 + 0.963126i \(0.413290\pi\)
\(710\) 17.6642 0.662924
\(711\) −70.3569 −2.63859
\(712\) −65.5943 −2.45825
\(713\) 22.1532 0.829643
\(714\) 8.48015 0.317362
\(715\) −4.78581 −0.178979
\(716\) −58.6922 −2.19343
\(717\) 64.0293 2.39122
\(718\) 47.4710 1.77160
\(719\) −32.2886 −1.20416 −0.602081 0.798435i \(-0.705662\pi\)
−0.602081 + 0.798435i \(0.705662\pi\)
\(720\) −45.4497 −1.69381
\(721\) 3.71668 0.138416
\(722\) 73.9137 2.75078
\(723\) 0.846042 0.0314647
\(724\) −108.638 −4.03751
\(725\) 8.17452 0.303594
\(726\) −83.0723 −3.08310
\(727\) 14.2026 0.526744 0.263372 0.964694i \(-0.415165\pi\)
0.263372 + 0.964694i \(0.415165\pi\)
\(728\) −42.5534 −1.57713
\(729\) −2.05458 −0.0760954
\(730\) 1.79424 0.0664077
\(731\) −3.44199 −0.127307
\(732\) 120.395 4.44992
\(733\) −2.19744 −0.0811642 −0.0405821 0.999176i \(-0.512921\pi\)
−0.0405821 + 0.999176i \(0.512921\pi\)
\(734\) 18.0947 0.667888
\(735\) −3.11385 −0.114856
\(736\) −31.2198 −1.15078
\(737\) 0.856168 0.0315374
\(738\) 210.798 7.75960
\(739\) −25.9961 −0.956283 −0.478141 0.878283i \(-0.658689\pi\)
−0.478141 + 0.878283i \(0.658689\pi\)
\(740\) −14.2266 −0.522980
\(741\) −148.963 −5.47230
\(742\) 11.7695 0.432073
\(743\) −8.73693 −0.320527 −0.160263 0.987074i \(-0.551234\pi\)
−0.160263 + 0.987074i \(0.551234\pi\)
\(744\) −66.4418 −2.43587
\(745\) −2.39105 −0.0876014
\(746\) −26.5261 −0.971189
\(747\) 29.8667 1.09276
\(748\) −3.30406 −0.120808
\(749\) 13.6558 0.498971
\(750\) −7.89795 −0.288393
\(751\) 31.8729 1.16306 0.581530 0.813525i \(-0.302454\pi\)
0.581530 + 0.813525i \(0.302454\pi\)
\(752\) −49.8912 −1.81934
\(753\) −31.0621 −1.13197
\(754\) 142.956 5.20614
\(755\) −13.7810 −0.501543
\(756\) −51.0229 −1.85568
\(757\) −27.4187 −0.996548 −0.498274 0.867020i \(-0.666033\pi\)
−0.498274 + 0.867020i \(0.666033\pi\)
\(758\) −25.3825 −0.921934
\(759\) −13.8495 −0.502706
\(760\) 42.8223 1.55333
\(761\) 2.80527 0.101691 0.0508455 0.998707i \(-0.483808\pi\)
0.0508455 + 0.998707i \(0.483808\pi\)
\(762\) 56.4061 2.04338
\(763\) −0.0225205 −0.000815295 0
\(764\) −27.9161 −1.00997
\(765\) 7.18967 0.259943
\(766\) −30.5305 −1.10311
\(767\) 34.4050 1.24229
\(768\) −93.7636 −3.38340
\(769\) 35.1929 1.26909 0.634544 0.772886i \(-0.281188\pi\)
0.634544 + 0.772886i \(0.281188\pi\)
\(770\) 1.76056 0.0634460
\(771\) 14.2426 0.512934
\(772\) 43.2841 1.55783
\(773\) −41.9774 −1.50982 −0.754910 0.655828i \(-0.772320\pi\)
−0.754910 + 0.655828i \(0.772320\pi\)
\(774\) 54.4450 1.95699
\(775\) −3.45726 −0.124188
\(776\) 103.087 3.70060
\(777\) −9.99246 −0.358478
\(778\) 15.8478 0.568172
\(779\) −86.1171 −3.08546
\(780\) −95.1803 −3.40800
\(781\) −4.83403 −0.172975
\(782\) 17.4506 0.624031
\(783\) 94.0808 3.36217
\(784\) 6.78751 0.242411
\(785\) 14.4724 0.516543
\(786\) −20.7309 −0.739445
\(787\) 19.3395 0.689377 0.344689 0.938717i \(-0.387985\pi\)
0.344689 + 0.938717i \(0.387985\pi\)
\(788\) 43.5796 1.55246
\(789\) −13.7108 −0.488118
\(790\) 26.6504 0.948177
\(791\) 9.15269 0.325432
\(792\) 28.6856 1.01930
\(793\) 60.1320 2.13535
\(794\) 59.0908 2.09706
\(795\) 14.4491 0.512456
\(796\) 51.3345 1.81950
\(797\) 28.6379 1.01441 0.507203 0.861827i \(-0.330680\pi\)
0.507203 + 0.861827i \(0.330680\pi\)
\(798\) 54.7991 1.93987
\(799\) 7.89227 0.279209
\(800\) 4.87221 0.172259
\(801\) −71.1664 −2.51454
\(802\) −32.7086 −1.15498
\(803\) −0.491017 −0.0173276
\(804\) 17.0275 0.600513
\(805\) −6.40773 −0.225843
\(806\) −60.4604 −2.12963
\(807\) 91.1732 3.20945
\(808\) −117.783 −4.14357
\(809\) 51.2405 1.80152 0.900760 0.434317i \(-0.143010\pi\)
0.900760 + 0.434317i \(0.143010\pi\)
\(810\) −39.9461 −1.40356
\(811\) −21.6619 −0.760652 −0.380326 0.924852i \(-0.624188\pi\)
−0.380326 + 0.924852i \(0.624188\pi\)
\(812\) −36.2401 −1.27178
\(813\) −44.8642 −1.57345
\(814\) 5.64969 0.198021
\(815\) 11.3530 0.397678
\(816\) −22.6933 −0.794423
\(817\) −22.2423 −0.778160
\(818\) 31.4559 1.09983
\(819\) −46.1682 −1.61325
\(820\) −55.0246 −1.92154
\(821\) 44.4385 1.55091 0.775457 0.631400i \(-0.217520\pi\)
0.775457 + 0.631400i \(0.217520\pi\)
\(822\) −26.8553 −0.936686
\(823\) −45.4173 −1.58315 −0.791574 0.611073i \(-0.790738\pi\)
−0.791574 + 0.611073i \(0.790738\pi\)
\(824\) −22.9386 −0.799103
\(825\) 2.16138 0.0752496
\(826\) −12.6566 −0.440378
\(827\) 5.27897 0.183568 0.0917840 0.995779i \(-0.470743\pi\)
0.0917840 + 0.995779i \(0.470743\pi\)
\(828\) −190.218 −6.61052
\(829\) −5.27399 −0.183173 −0.0915866 0.995797i \(-0.529194\pi\)
−0.0915866 + 0.995797i \(0.529194\pi\)
\(830\) −11.3131 −0.392685
\(831\) 51.3688 1.78197
\(832\) −8.39215 −0.290945
\(833\) −1.07371 −0.0372020
\(834\) 119.476 4.13712
\(835\) 23.9335 0.828252
\(836\) −21.3510 −0.738440
\(837\) −39.7897 −1.37533
\(838\) 64.6287 2.23256
\(839\) −9.41643 −0.325091 −0.162546 0.986701i \(-0.551970\pi\)
−0.162546 + 0.986701i \(0.551970\pi\)
\(840\) 19.2180 0.663086
\(841\) 37.8228 1.30424
\(842\) 40.2075 1.38564
\(843\) −60.0949 −2.06978
\(844\) −128.247 −4.41443
\(845\) −34.5385 −1.18816
\(846\) −124.839 −4.29205
\(847\) 10.5182 0.361410
\(848\) −31.4958 −1.08157
\(849\) 13.6395 0.468106
\(850\) −2.72336 −0.0934106
\(851\) −20.5626 −0.704878
\(852\) −96.1392 −3.29368
\(853\) 25.9727 0.889287 0.444643 0.895708i \(-0.353330\pi\)
0.444643 + 0.895708i \(0.353330\pi\)
\(854\) −22.1207 −0.756956
\(855\) 46.4600 1.58890
\(856\) −84.2806 −2.88065
\(857\) 36.0150 1.23025 0.615125 0.788429i \(-0.289105\pi\)
0.615125 + 0.788429i \(0.289105\pi\)
\(858\) 37.7981 1.29041
\(859\) 5.11809 0.174627 0.0873134 0.996181i \(-0.472172\pi\)
0.0873134 + 0.996181i \(0.472172\pi\)
\(860\) −14.2118 −0.484617
\(861\) −38.6481 −1.31712
\(862\) 68.8627 2.34547
\(863\) −30.1432 −1.02609 −0.513043 0.858363i \(-0.671482\pi\)
−0.513043 + 0.858363i \(0.671482\pi\)
\(864\) 56.0744 1.90769
\(865\) −22.1259 −0.752303
\(866\) 95.0814 3.23100
\(867\) −49.3456 −1.67587
\(868\) 15.3270 0.520234
\(869\) −7.29322 −0.247406
\(870\) −64.5620 −2.18886
\(871\) 8.50450 0.288164
\(872\) 0.138992 0.00470685
\(873\) 111.844 3.78534
\(874\) 112.766 3.81438
\(875\) 1.00000 0.0338062
\(876\) −9.76535 −0.329941
\(877\) −4.50267 −0.152044 −0.0760221 0.997106i \(-0.524222\pi\)
−0.0760221 + 0.997106i \(0.524222\pi\)
\(878\) 70.1338 2.36690
\(879\) −28.9131 −0.975213
\(880\) −4.71133 −0.158819
\(881\) −5.48375 −0.184752 −0.0923761 0.995724i \(-0.529446\pi\)
−0.0923761 + 0.995724i \(0.529446\pi\)
\(882\) 16.9839 0.571877
\(883\) −1.62232 −0.0545954 −0.0272977 0.999627i \(-0.508690\pi\)
−0.0272977 + 0.999627i \(0.508690\pi\)
\(884\) −32.8200 −1.10385
\(885\) −15.5381 −0.522306
\(886\) 41.7513 1.40266
\(887\) 3.13140 0.105142 0.0525710 0.998617i \(-0.483258\pi\)
0.0525710 + 0.998617i \(0.483258\pi\)
\(888\) 61.6714 2.06956
\(889\) −7.14187 −0.239531
\(890\) 26.9570 0.903601
\(891\) 10.9318 0.366228
\(892\) −72.2130 −2.41787
\(893\) 51.0002 1.70666
\(894\) 18.8844 0.631590
\(895\) 13.2390 0.442530
\(896\) 12.8316 0.428675
\(897\) −137.570 −4.59334
\(898\) −86.1791 −2.87583
\(899\) −28.2614 −0.942572
\(900\) 29.6857 0.989522
\(901\) 4.98231 0.165985
\(902\) 21.8515 0.727574
\(903\) −9.98204 −0.332181
\(904\) −56.4885 −1.87878
\(905\) 24.5051 0.814577
\(906\) 108.842 3.61603
\(907\) 41.6263 1.38218 0.691090 0.722769i \(-0.257131\pi\)
0.691090 + 0.722769i \(0.257131\pi\)
\(908\) 42.7351 1.41821
\(909\) −127.788 −4.23846
\(910\) 17.4880 0.579721
\(911\) −19.8906 −0.659004 −0.329502 0.944155i \(-0.606881\pi\)
−0.329502 + 0.944155i \(0.606881\pi\)
\(912\) −146.645 −4.85590
\(913\) 3.09599 0.102462
\(914\) 22.5919 0.747275
\(915\) −27.1569 −0.897781
\(916\) 4.43329 0.146480
\(917\) 2.62484 0.0866798
\(918\) −31.3432 −1.03448
\(919\) −43.0877 −1.42133 −0.710667 0.703529i \(-0.751607\pi\)
−0.710667 + 0.703529i \(0.751607\pi\)
\(920\) 39.5472 1.30383
\(921\) 37.0773 1.22174
\(922\) 0.643560 0.0211945
\(923\) −48.0174 −1.58051
\(924\) −9.58203 −0.315226
\(925\) 3.20904 0.105512
\(926\) −56.6772 −1.86253
\(927\) −24.8871 −0.817401
\(928\) 39.8280 1.30742
\(929\) −20.6800 −0.678490 −0.339245 0.940698i \(-0.610172\pi\)
−0.339245 + 0.940698i \(0.610172\pi\)
\(930\) 27.3053 0.895375
\(931\) −6.93839 −0.227397
\(932\) 38.3580 1.25646
\(933\) 29.1145 0.953166
\(934\) 91.1723 2.98325
\(935\) 0.745284 0.0243734
\(936\) 284.940 9.31357
\(937\) 35.2520 1.15163 0.575816 0.817579i \(-0.304684\pi\)
0.575816 + 0.817579i \(0.304684\pi\)
\(938\) −3.12855 −0.102151
\(939\) −10.3064 −0.336338
\(940\) 32.5867 1.06286
\(941\) 38.6480 1.25989 0.629945 0.776640i \(-0.283077\pi\)
0.629945 + 0.776640i \(0.283077\pi\)
\(942\) −114.303 −3.72418
\(943\) −79.5307 −2.58988
\(944\) 33.8696 1.10236
\(945\) 11.5090 0.374389
\(946\) 5.64379 0.183495
\(947\) 49.5153 1.60903 0.804516 0.593932i \(-0.202425\pi\)
0.804516 + 0.593932i \(0.202425\pi\)
\(948\) −145.048 −4.71093
\(949\) −4.87737 −0.158326
\(950\) −17.5985 −0.570970
\(951\) −1.27765 −0.0414306
\(952\) 6.62674 0.214774
\(953\) 28.4065 0.920176 0.460088 0.887873i \(-0.347818\pi\)
0.460088 + 0.887873i \(0.347818\pi\)
\(954\) −78.8096 −2.55155
\(955\) 6.29692 0.203763
\(956\) 91.1606 2.94834
\(957\) 17.6682 0.571133
\(958\) −36.2177 −1.17014
\(959\) 3.40028 0.109801
\(960\) 3.79008 0.122324
\(961\) −19.0474 −0.614431
\(962\) 56.1195 1.80937
\(963\) −91.4401 −2.94661
\(964\) 1.20454 0.0387956
\(965\) −9.76342 −0.314296
\(966\) 50.6080 1.62828
\(967\) 0.0613950 0.00197433 0.000987166 1.00000i \(-0.499686\pi\)
0.000987166 1.00000i \(0.499686\pi\)
\(968\) −64.9162 −2.08648
\(969\) 23.1977 0.745218
\(970\) −42.3651 −1.36026
\(971\) −3.13614 −0.100643 −0.0503217 0.998733i \(-0.516025\pi\)
−0.0503217 + 0.998733i \(0.516025\pi\)
\(972\) 64.3427 2.06379
\(973\) −15.1275 −0.484965
\(974\) −6.96092 −0.223042
\(975\) 21.4694 0.687572
\(976\) 59.1962 1.89482
\(977\) −58.3101 −1.86551 −0.932753 0.360517i \(-0.882600\pi\)
−0.932753 + 0.360517i \(0.882600\pi\)
\(978\) −89.6655 −2.86719
\(979\) −7.37714 −0.235774
\(980\) −4.43329 −0.141616
\(981\) 0.150799 0.00481463
\(982\) −24.7544 −0.789944
\(983\) 6.56017 0.209237 0.104618 0.994512i \(-0.466638\pi\)
0.104618 + 0.994512i \(0.466638\pi\)
\(984\) 238.528 7.60400
\(985\) −9.83007 −0.313212
\(986\) −22.2622 −0.708973
\(987\) 22.8882 0.728539
\(988\) −212.084 −6.74729
\(989\) −20.5412 −0.653172
\(990\) −11.7888 −0.374673
\(991\) −43.4062 −1.37884 −0.689422 0.724360i \(-0.742135\pi\)
−0.689422 + 0.724360i \(0.742135\pi\)
\(992\) −16.8445 −0.534813
\(993\) 10.4840 0.332700
\(994\) 17.6642 0.560273
\(995\) −11.5793 −0.367089
\(996\) 61.5731 1.95102
\(997\) −27.4582 −0.869611 −0.434805 0.900524i \(-0.643183\pi\)
−0.434805 + 0.900524i \(0.643183\pi\)
\(998\) −33.9787 −1.07558
\(999\) 36.9329 1.16850
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 \(a_p\))