Properties

Label 8015.2.a.l.1.6
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 1.6
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +O(q^{10})\) \(q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +2.35302 q^{10} -5.71770 q^{11} +5.02848 q^{12} -2.54493 q^{13} +2.35302 q^{14} -1.42181 q^{15} +1.43477 q^{16} -3.84787 q^{17} +2.30235 q^{18} +4.40419 q^{19} -3.53669 q^{20} -1.42181 q^{21} +13.4538 q^{22} -5.65179 q^{23} -5.14103 q^{24} +1.00000 q^{25} +5.98827 q^{26} -5.65661 q^{27} -3.53669 q^{28} -6.59897 q^{29} +3.34553 q^{30} -1.55208 q^{31} +3.85565 q^{32} -8.12947 q^{33} +9.05410 q^{34} +1.00000 q^{35} -3.46053 q^{36} -1.11540 q^{37} -10.3631 q^{38} -3.61840 q^{39} +3.61585 q^{40} -6.51642 q^{41} +3.34553 q^{42} +8.12476 q^{43} -20.2217 q^{44} +0.978466 q^{45} +13.2988 q^{46} -7.20728 q^{47} +2.03997 q^{48} +1.00000 q^{49} -2.35302 q^{50} -5.47093 q^{51} -9.00062 q^{52} +1.36357 q^{53} +13.3101 q^{54} +5.71770 q^{55} +3.61585 q^{56} +6.26191 q^{57} +15.5275 q^{58} -3.51950 q^{59} -5.02848 q^{60} +9.88504 q^{61} +3.65208 q^{62} +0.978466 q^{63} -11.9419 q^{64} +2.54493 q^{65} +19.1288 q^{66} +9.52626 q^{67} -13.6087 q^{68} -8.03576 q^{69} -2.35302 q^{70} -6.37994 q^{71} +3.53798 q^{72} -14.6405 q^{73} +2.62456 q^{74} +1.42181 q^{75} +15.5762 q^{76} +5.71770 q^{77} +8.51416 q^{78} -15.9245 q^{79} -1.43477 q^{80} -5.10721 q^{81} +15.3332 q^{82} -5.46210 q^{83} -5.02848 q^{84} +3.84787 q^{85} -19.1177 q^{86} -9.38247 q^{87} +20.6743 q^{88} -1.58947 q^{89} -2.30235 q^{90} +2.54493 q^{91} -19.9886 q^{92} -2.20676 q^{93} +16.9588 q^{94} -4.40419 q^{95} +5.48198 q^{96} +14.6538 q^{97} -2.35302 q^{98} +5.59458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35302 −1.66383 −0.831917 0.554900i \(-0.812756\pi\)
−0.831917 + 0.554900i \(0.812756\pi\)
\(3\) 1.42181 0.820880 0.410440 0.911888i \(-0.365375\pi\)
0.410440 + 0.911888i \(0.365375\pi\)
\(4\) 3.53669 1.76834
\(5\) −1.00000 −0.447214
\(6\) −3.34553 −1.36581
\(7\) −1.00000 −0.377964
\(8\) −3.61585 −1.27839
\(9\) −0.978466 −0.326155
\(10\) 2.35302 0.744089
\(11\) −5.71770 −1.72395 −0.861976 0.506949i \(-0.830773\pi\)
−0.861976 + 0.506949i \(0.830773\pi\)
\(12\) 5.02848 1.45160
\(13\) −2.54493 −0.705837 −0.352919 0.935654i \(-0.614811\pi\)
−0.352919 + 0.935654i \(0.614811\pi\)
\(14\) 2.35302 0.628870
\(15\) −1.42181 −0.367109
\(16\) 1.43477 0.358693
\(17\) −3.84787 −0.933246 −0.466623 0.884456i \(-0.654529\pi\)
−0.466623 + 0.884456i \(0.654529\pi\)
\(18\) 2.30235 0.542668
\(19\) 4.40419 1.01039 0.505195 0.863005i \(-0.331420\pi\)
0.505195 + 0.863005i \(0.331420\pi\)
\(20\) −3.53669 −0.790827
\(21\) −1.42181 −0.310264
\(22\) 13.4538 2.86837
\(23\) −5.65179 −1.17848 −0.589240 0.807958i \(-0.700573\pi\)
−0.589240 + 0.807958i \(0.700573\pi\)
\(24\) −5.14103 −1.04941
\(25\) 1.00000 0.200000
\(26\) 5.98827 1.17440
\(27\) −5.65661 −1.08861
\(28\) −3.53669 −0.668371
\(29\) −6.59897 −1.22540 −0.612699 0.790316i \(-0.709916\pi\)
−0.612699 + 0.790316i \(0.709916\pi\)
\(30\) 3.34553 0.610808
\(31\) −1.55208 −0.278762 −0.139381 0.990239i \(-0.544511\pi\)
−0.139381 + 0.990239i \(0.544511\pi\)
\(32\) 3.85565 0.681589
\(33\) −8.12947 −1.41516
\(34\) 9.05410 1.55277
\(35\) 1.00000 0.169031
\(36\) −3.46053 −0.576754
\(37\) −1.11540 −0.183371 −0.0916854 0.995788i \(-0.529225\pi\)
−0.0916854 + 0.995788i \(0.529225\pi\)
\(38\) −10.3631 −1.68112
\(39\) −3.61840 −0.579408
\(40\) 3.61585 0.571715
\(41\) −6.51642 −1.01769 −0.508847 0.860857i \(-0.669928\pi\)
−0.508847 + 0.860857i \(0.669928\pi\)
\(42\) 3.34553 0.516227
\(43\) 8.12476 1.23901 0.619507 0.784991i \(-0.287333\pi\)
0.619507 + 0.784991i \(0.287333\pi\)
\(44\) −20.2217 −3.04854
\(45\) 0.978466 0.145861
\(46\) 13.2988 1.96080
\(47\) −7.20728 −1.05129 −0.525645 0.850704i \(-0.676176\pi\)
−0.525645 + 0.850704i \(0.676176\pi\)
\(48\) 2.03997 0.294444
\(49\) 1.00000 0.142857
\(50\) −2.35302 −0.332767
\(51\) −5.47093 −0.766083
\(52\) −9.00062 −1.24816
\(53\) 1.36357 0.187301 0.0936506 0.995605i \(-0.470146\pi\)
0.0936506 + 0.995605i \(0.470146\pi\)
\(54\) 13.3101 1.81127
\(55\) 5.71770 0.770975
\(56\) 3.61585 0.483188
\(57\) 6.26191 0.829410
\(58\) 15.5275 2.03886
\(59\) −3.51950 −0.458200 −0.229100 0.973403i \(-0.573578\pi\)
−0.229100 + 0.973403i \(0.573578\pi\)
\(60\) −5.02848 −0.649174
\(61\) 9.88504 1.26565 0.632825 0.774295i \(-0.281895\pi\)
0.632825 + 0.774295i \(0.281895\pi\)
\(62\) 3.65208 0.463814
\(63\) 0.978466 0.123275
\(64\) −11.9419 −1.49274
\(65\) 2.54493 0.315660
\(66\) 19.1288 2.35459
\(67\) 9.52626 1.16382 0.581909 0.813254i \(-0.302306\pi\)
0.581909 + 0.813254i \(0.302306\pi\)
\(68\) −13.6087 −1.65030
\(69\) −8.03576 −0.967391
\(70\) −2.35302 −0.281239
\(71\) −6.37994 −0.757160 −0.378580 0.925569i \(-0.623587\pi\)
−0.378580 + 0.925569i \(0.623587\pi\)
\(72\) 3.53798 0.416955
\(73\) −14.6405 −1.71354 −0.856771 0.515698i \(-0.827533\pi\)
−0.856771 + 0.515698i \(0.827533\pi\)
\(74\) 2.62456 0.305098
\(75\) 1.42181 0.164176
\(76\) 15.5762 1.78672
\(77\) 5.71770 0.651593
\(78\) 8.51416 0.964038
\(79\) −15.9245 −1.79165 −0.895825 0.444408i \(-0.853414\pi\)
−0.895825 + 0.444408i \(0.853414\pi\)
\(80\) −1.43477 −0.160413
\(81\) −5.10721 −0.567467
\(82\) 15.3332 1.69327
\(83\) −5.46210 −0.599543 −0.299772 0.954011i \(-0.596910\pi\)
−0.299772 + 0.954011i \(0.596910\pi\)
\(84\) −5.02848 −0.548652
\(85\) 3.84787 0.417360
\(86\) −19.1177 −2.06151
\(87\) −9.38247 −1.00591
\(88\) 20.6743 2.20389
\(89\) −1.58947 −0.168484 −0.0842419 0.996445i \(-0.526847\pi\)
−0.0842419 + 0.996445i \(0.526847\pi\)
\(90\) −2.30235 −0.242689
\(91\) 2.54493 0.266781
\(92\) −19.9886 −2.08396
\(93\) −2.20676 −0.228831
\(94\) 16.9588 1.74917
\(95\) −4.40419 −0.451860
\(96\) 5.48198 0.559503
\(97\) 14.6538 1.48787 0.743935 0.668252i \(-0.232957\pi\)
0.743935 + 0.668252i \(0.232957\pi\)
\(98\) −2.35302 −0.237691
\(99\) 5.59458 0.562276
\(100\) 3.53669 0.353669
\(101\) −8.32577 −0.828446 −0.414223 0.910176i \(-0.635947\pi\)
−0.414223 + 0.910176i \(0.635947\pi\)
\(102\) 12.8732 1.27463
\(103\) −6.89805 −0.679685 −0.339843 0.940482i \(-0.610374\pi\)
−0.339843 + 0.940482i \(0.610374\pi\)
\(104\) 9.20208 0.902338
\(105\) 1.42181 0.138754
\(106\) −3.20851 −0.311638
\(107\) −2.48737 −0.240463 −0.120232 0.992746i \(-0.538364\pi\)
−0.120232 + 0.992746i \(0.538364\pi\)
\(108\) −20.0056 −1.92504
\(109\) −16.3311 −1.56423 −0.782116 0.623132i \(-0.785860\pi\)
−0.782116 + 0.623132i \(0.785860\pi\)
\(110\) −13.4538 −1.28277
\(111\) −1.58588 −0.150525
\(112\) −1.43477 −0.135573
\(113\) −2.75707 −0.259363 −0.129681 0.991556i \(-0.541395\pi\)
−0.129681 + 0.991556i \(0.541395\pi\)
\(114\) −14.7344 −1.38000
\(115\) 5.65179 0.527032
\(116\) −23.3385 −2.16693
\(117\) 2.49013 0.230212
\(118\) 8.28145 0.762369
\(119\) 3.84787 0.352734
\(120\) 5.14103 0.469310
\(121\) 21.6921 1.97201
\(122\) −23.2597 −2.10583
\(123\) −9.26509 −0.835405
\(124\) −5.48923 −0.492948
\(125\) −1.00000 −0.0894427
\(126\) −2.30235 −0.205109
\(127\) −15.9007 −1.41096 −0.705478 0.708732i \(-0.749268\pi\)
−0.705478 + 0.708732i \(0.749268\pi\)
\(128\) 20.3883 1.80209
\(129\) 11.5518 1.01708
\(130\) −5.98827 −0.525206
\(131\) 12.6377 1.10416 0.552081 0.833790i \(-0.313834\pi\)
0.552081 + 0.833790i \(0.313834\pi\)
\(132\) −28.7514 −2.50249
\(133\) −4.40419 −0.381892
\(134\) −22.4154 −1.93640
\(135\) 5.65661 0.486843
\(136\) 13.9133 1.19306
\(137\) 8.89677 0.760102 0.380051 0.924965i \(-0.375906\pi\)
0.380051 + 0.924965i \(0.375906\pi\)
\(138\) 18.9083 1.60958
\(139\) −4.34004 −0.368117 −0.184059 0.982915i \(-0.558924\pi\)
−0.184059 + 0.982915i \(0.558924\pi\)
\(140\) 3.53669 0.298904
\(141\) −10.2474 −0.862983
\(142\) 15.0121 1.25979
\(143\) 14.5512 1.21683
\(144\) −1.40388 −0.116990
\(145\) 6.59897 0.548015
\(146\) 34.4493 2.85105
\(147\) 1.42181 0.117269
\(148\) −3.94482 −0.324262
\(149\) 15.8215 1.29615 0.648075 0.761576i \(-0.275574\pi\)
0.648075 + 0.761576i \(0.275574\pi\)
\(150\) −3.34553 −0.273162
\(151\) 4.10427 0.334001 0.167000 0.985957i \(-0.446592\pi\)
0.167000 + 0.985957i \(0.446592\pi\)
\(152\) −15.9249 −1.29168
\(153\) 3.76501 0.304383
\(154\) −13.4538 −1.08414
\(155\) 1.55208 0.124666
\(156\) −12.7971 −1.02459
\(157\) −22.0419 −1.75913 −0.879567 0.475776i \(-0.842167\pi\)
−0.879567 + 0.475776i \(0.842167\pi\)
\(158\) 37.4707 2.98101
\(159\) 1.93874 0.153752
\(160\) −3.85565 −0.304816
\(161\) 5.65179 0.445424
\(162\) 12.0173 0.944171
\(163\) −9.71053 −0.760588 −0.380294 0.924866i \(-0.624177\pi\)
−0.380294 + 0.924866i \(0.624177\pi\)
\(164\) −23.0465 −1.79963
\(165\) 8.12947 0.632878
\(166\) 12.8524 0.997540
\(167\) 20.9784 1.62335 0.811677 0.584107i \(-0.198555\pi\)
0.811677 + 0.584107i \(0.198555\pi\)
\(168\) 5.14103 0.396639
\(169\) −6.52332 −0.501794
\(170\) −9.05410 −0.694418
\(171\) −4.30935 −0.329544
\(172\) 28.7347 2.19100
\(173\) 22.0835 1.67898 0.839488 0.543378i \(-0.182855\pi\)
0.839488 + 0.543378i \(0.182855\pi\)
\(174\) 22.0771 1.67366
\(175\) −1.00000 −0.0755929
\(176\) −8.20361 −0.618370
\(177\) −5.00405 −0.376128
\(178\) 3.74005 0.280329
\(179\) −6.35822 −0.475236 −0.237618 0.971359i \(-0.576367\pi\)
−0.237618 + 0.971359i \(0.576367\pi\)
\(180\) 3.46053 0.257932
\(181\) −12.5770 −0.934843 −0.467422 0.884035i \(-0.654817\pi\)
−0.467422 + 0.884035i \(0.654817\pi\)
\(182\) −5.98827 −0.443880
\(183\) 14.0546 1.03895
\(184\) 20.4360 1.50656
\(185\) 1.11540 0.0820059
\(186\) 5.19255 0.380736
\(187\) 22.0010 1.60887
\(188\) −25.4899 −1.85904
\(189\) 5.65661 0.411458
\(190\) 10.3631 0.751821
\(191\) 20.8789 1.51075 0.755374 0.655294i \(-0.227455\pi\)
0.755374 + 0.655294i \(0.227455\pi\)
\(192\) −16.9791 −1.22536
\(193\) −21.2875 −1.53231 −0.766155 0.642656i \(-0.777832\pi\)
−0.766155 + 0.642656i \(0.777832\pi\)
\(194\) −34.4807 −2.47557
\(195\) 3.61840 0.259119
\(196\) 3.53669 0.252620
\(197\) −11.1750 −0.796186 −0.398093 0.917345i \(-0.630328\pi\)
−0.398093 + 0.917345i \(0.630328\pi\)
\(198\) −13.1641 −0.935534
\(199\) 11.3928 0.807612 0.403806 0.914845i \(-0.367687\pi\)
0.403806 + 0.914845i \(0.367687\pi\)
\(200\) −3.61585 −0.255679
\(201\) 13.5445 0.955355
\(202\) 19.5907 1.37840
\(203\) 6.59897 0.463157
\(204\) −19.3489 −1.35470
\(205\) 6.51642 0.455127
\(206\) 16.2312 1.13088
\(207\) 5.53009 0.384368
\(208\) −3.65140 −0.253179
\(209\) −25.1818 −1.74186
\(210\) −3.34553 −0.230864
\(211\) −7.59717 −0.523011 −0.261505 0.965202i \(-0.584219\pi\)
−0.261505 + 0.965202i \(0.584219\pi\)
\(212\) 4.82253 0.331213
\(213\) −9.07104 −0.621538
\(214\) 5.85282 0.400091
\(215\) −8.12476 −0.554104
\(216\) 20.4534 1.39168
\(217\) 1.55208 0.105362
\(218\) 38.4273 2.60262
\(219\) −20.8160 −1.40661
\(220\) 20.2217 1.36335
\(221\) 9.79257 0.658719
\(222\) 3.73161 0.250449
\(223\) 12.1671 0.814768 0.407384 0.913257i \(-0.366441\pi\)
0.407384 + 0.913257i \(0.366441\pi\)
\(224\) −3.85565 −0.257616
\(225\) −0.978466 −0.0652311
\(226\) 6.48742 0.431537
\(227\) 3.05345 0.202664 0.101332 0.994853i \(-0.467689\pi\)
0.101332 + 0.994853i \(0.467689\pi\)
\(228\) 22.1464 1.46668
\(229\) 1.00000 0.0660819
\(230\) −13.2988 −0.876894
\(231\) 8.12947 0.534880
\(232\) 23.8609 1.56654
\(233\) 14.9295 0.978063 0.489031 0.872266i \(-0.337350\pi\)
0.489031 + 0.872266i \(0.337350\pi\)
\(234\) −5.85931 −0.383035
\(235\) 7.20728 0.470151
\(236\) −12.4474 −0.810255
\(237\) −22.6416 −1.47073
\(238\) −9.05410 −0.586890
\(239\) −25.6759 −1.66083 −0.830416 0.557143i \(-0.811897\pi\)
−0.830416 + 0.557143i \(0.811897\pi\)
\(240\) −2.03997 −0.131680
\(241\) 22.0544 1.42065 0.710325 0.703874i \(-0.248548\pi\)
0.710325 + 0.703874i \(0.248548\pi\)
\(242\) −51.0419 −3.28110
\(243\) 9.70837 0.622792
\(244\) 34.9603 2.23810
\(245\) −1.00000 −0.0638877
\(246\) 21.8009 1.38998
\(247\) −11.2084 −0.713171
\(248\) 5.61210 0.356368
\(249\) −7.76605 −0.492153
\(250\) 2.35302 0.148818
\(251\) −2.36970 −0.149574 −0.0747871 0.997200i \(-0.523828\pi\)
−0.0747871 + 0.997200i \(0.523828\pi\)
\(252\) 3.46053 0.217993
\(253\) 32.3153 2.03164
\(254\) 37.4145 2.34760
\(255\) 5.47093 0.342603
\(256\) −24.0901 −1.50563
\(257\) 15.3174 0.955474 0.477737 0.878503i \(-0.341457\pi\)
0.477737 + 0.878503i \(0.341457\pi\)
\(258\) −27.1817 −1.69226
\(259\) 1.11540 0.0693076
\(260\) 9.00062 0.558195
\(261\) 6.45687 0.399670
\(262\) −29.7368 −1.83714
\(263\) 11.0808 0.683272 0.341636 0.939832i \(-0.389019\pi\)
0.341636 + 0.939832i \(0.389019\pi\)
\(264\) 29.3949 1.80913
\(265\) −1.36357 −0.0837637
\(266\) 10.3631 0.635404
\(267\) −2.25992 −0.138305
\(268\) 33.6914 2.05803
\(269\) 7.39826 0.451080 0.225540 0.974234i \(-0.427585\pi\)
0.225540 + 0.974234i \(0.427585\pi\)
\(270\) −13.3101 −0.810026
\(271\) 12.4457 0.756021 0.378011 0.925801i \(-0.376608\pi\)
0.378011 + 0.925801i \(0.376608\pi\)
\(272\) −5.52082 −0.334749
\(273\) 3.61840 0.218996
\(274\) −20.9342 −1.26468
\(275\) −5.71770 −0.344790
\(276\) −28.4199 −1.71068
\(277\) 12.9875 0.780344 0.390172 0.920742i \(-0.372416\pi\)
0.390172 + 0.920742i \(0.372416\pi\)
\(278\) 10.2122 0.612486
\(279\) 1.51866 0.0909199
\(280\) −3.61585 −0.216088
\(281\) 1.98709 0.118540 0.0592700 0.998242i \(-0.481123\pi\)
0.0592700 + 0.998242i \(0.481123\pi\)
\(282\) 24.1122 1.43586
\(283\) 8.87945 0.527829 0.263914 0.964546i \(-0.414986\pi\)
0.263914 + 0.964546i \(0.414986\pi\)
\(284\) −22.5638 −1.33892
\(285\) −6.26191 −0.370923
\(286\) −34.2391 −2.02460
\(287\) 6.51642 0.384652
\(288\) −3.77262 −0.222304
\(289\) −2.19390 −0.129053
\(290\) −15.5275 −0.911806
\(291\) 20.8349 1.22136
\(292\) −51.7789 −3.03013
\(293\) −23.7539 −1.38772 −0.693858 0.720112i \(-0.744091\pi\)
−0.693858 + 0.720112i \(0.744091\pi\)
\(294\) −3.34553 −0.195116
\(295\) 3.51950 0.204913
\(296\) 4.03312 0.234420
\(297\) 32.3428 1.87672
\(298\) −37.2283 −2.15658
\(299\) 14.3834 0.831815
\(300\) 5.02848 0.290320
\(301\) −8.12476 −0.468303
\(302\) −9.65742 −0.555722
\(303\) −11.8376 −0.680055
\(304\) 6.31902 0.362420
\(305\) −9.88504 −0.566016
\(306\) −8.85913 −0.506443
\(307\) 19.5236 1.11427 0.557135 0.830422i \(-0.311901\pi\)
0.557135 + 0.830422i \(0.311901\pi\)
\(308\) 20.2217 1.15224
\(309\) −9.80770 −0.557940
\(310\) −3.65208 −0.207424
\(311\) −17.4531 −0.989674 −0.494837 0.868986i \(-0.664772\pi\)
−0.494837 + 0.868986i \(0.664772\pi\)
\(312\) 13.0836 0.740712
\(313\) −26.3918 −1.49175 −0.745875 0.666086i \(-0.767969\pi\)
−0.745875 + 0.666086i \(0.767969\pi\)
\(314\) 51.8649 2.92691
\(315\) −0.978466 −0.0551303
\(316\) −56.3201 −3.16825
\(317\) 24.7068 1.38767 0.693836 0.720133i \(-0.255919\pi\)
0.693836 + 0.720133i \(0.255919\pi\)
\(318\) −4.56188 −0.255818
\(319\) 37.7310 2.11253
\(320\) 11.9419 0.667575
\(321\) −3.53656 −0.197391
\(322\) −13.2988 −0.741111
\(323\) −16.9468 −0.942943
\(324\) −18.0626 −1.00348
\(325\) −2.54493 −0.141167
\(326\) 22.8490 1.26549
\(327\) −23.2196 −1.28405
\(328\) 23.5624 1.30101
\(329\) 7.20728 0.397350
\(330\) −19.1288 −1.05300
\(331\) 23.6227 1.29842 0.649211 0.760608i \(-0.275099\pi\)
0.649211 + 0.760608i \(0.275099\pi\)
\(332\) −19.3177 −1.06020
\(333\) 1.09138 0.0598073
\(334\) −49.3624 −2.70099
\(335\) −9.52626 −0.520475
\(336\) −2.03997 −0.111290
\(337\) 20.8674 1.13672 0.568361 0.822779i \(-0.307578\pi\)
0.568361 + 0.822779i \(0.307578\pi\)
\(338\) 15.3495 0.834902
\(339\) −3.92001 −0.212906
\(340\) 13.6087 0.738036
\(341\) 8.87435 0.480573
\(342\) 10.1400 0.548307
\(343\) −1.00000 −0.0539949
\(344\) −29.3779 −1.58395
\(345\) 8.03576 0.432631
\(346\) −51.9628 −2.79354
\(347\) −8.85186 −0.475193 −0.237596 0.971364i \(-0.576360\pi\)
−0.237596 + 0.971364i \(0.576360\pi\)
\(348\) −33.1828 −1.77879
\(349\) 2.85712 0.152938 0.0764691 0.997072i \(-0.475635\pi\)
0.0764691 + 0.997072i \(0.475635\pi\)
\(350\) 2.35302 0.125774
\(351\) 14.3957 0.768385
\(352\) −22.0454 −1.17503
\(353\) −16.7454 −0.891268 −0.445634 0.895215i \(-0.647022\pi\)
−0.445634 + 0.895215i \(0.647022\pi\)
\(354\) 11.7746 0.625814
\(355\) 6.37994 0.338612
\(356\) −5.62146 −0.297937
\(357\) 5.47093 0.289552
\(358\) 14.9610 0.790713
\(359\) 8.93988 0.471829 0.235915 0.971774i \(-0.424191\pi\)
0.235915 + 0.971774i \(0.424191\pi\)
\(360\) −3.53798 −0.186468
\(361\) 0.396895 0.0208892
\(362\) 29.5940 1.55542
\(363\) 30.8420 1.61878
\(364\) 9.00062 0.471761
\(365\) 14.6405 0.766319
\(366\) −33.0708 −1.72864
\(367\) −13.2877 −0.693611 −0.346806 0.937937i \(-0.612734\pi\)
−0.346806 + 0.937937i \(0.612734\pi\)
\(368\) −8.10904 −0.422713
\(369\) 6.37610 0.331926
\(370\) −2.62456 −0.136444
\(371\) −1.36357 −0.0707932
\(372\) −7.80463 −0.404651
\(373\) 12.0371 0.623260 0.311630 0.950204i \(-0.399125\pi\)
0.311630 + 0.950204i \(0.399125\pi\)
\(374\) −51.7686 −2.67689
\(375\) −1.42181 −0.0734218
\(376\) 26.0604 1.34396
\(377\) 16.7939 0.864932
\(378\) −13.3101 −0.684597
\(379\) 35.3434 1.81547 0.907733 0.419548i \(-0.137811\pi\)
0.907733 + 0.419548i \(0.137811\pi\)
\(380\) −15.5762 −0.799044
\(381\) −22.6077 −1.15823
\(382\) −49.1285 −2.51363
\(383\) −17.6583 −0.902296 −0.451148 0.892449i \(-0.648985\pi\)
−0.451148 + 0.892449i \(0.648985\pi\)
\(384\) 28.9882 1.47930
\(385\) −5.71770 −0.291401
\(386\) 50.0899 2.54951
\(387\) −7.94980 −0.404111
\(388\) 51.8259 2.63106
\(389\) −5.06377 −0.256743 −0.128372 0.991726i \(-0.540975\pi\)
−0.128372 + 0.991726i \(0.540975\pi\)
\(390\) −8.51416 −0.431131
\(391\) 21.7474 1.09981
\(392\) −3.61585 −0.182628
\(393\) 17.9684 0.906386
\(394\) 26.2950 1.32472
\(395\) 15.9245 0.801250
\(396\) 19.7863 0.994297
\(397\) 17.4344 0.875008 0.437504 0.899216i \(-0.355863\pi\)
0.437504 + 0.899216i \(0.355863\pi\)
\(398\) −26.8074 −1.34373
\(399\) −6.26191 −0.313487
\(400\) 1.43477 0.0717387
\(401\) −18.5872 −0.928203 −0.464101 0.885782i \(-0.653623\pi\)
−0.464101 + 0.885782i \(0.653623\pi\)
\(402\) −31.8704 −1.58955
\(403\) 3.94995 0.196761
\(404\) −29.4456 −1.46498
\(405\) 5.10721 0.253779
\(406\) −15.5275 −0.770617
\(407\) 6.37753 0.316122
\(408\) 19.7820 0.979356
\(409\) −21.0220 −1.03947 −0.519737 0.854327i \(-0.673970\pi\)
−0.519737 + 0.854327i \(0.673970\pi\)
\(410\) −15.3332 −0.757255
\(411\) 12.6495 0.623953
\(412\) −24.3962 −1.20192
\(413\) 3.51950 0.173183
\(414\) −13.0124 −0.639524
\(415\) 5.46210 0.268124
\(416\) −9.81236 −0.481090
\(417\) −6.17070 −0.302180
\(418\) 59.2533 2.89817
\(419\) −4.74499 −0.231808 −0.115904 0.993260i \(-0.536977\pi\)
−0.115904 + 0.993260i \(0.536977\pi\)
\(420\) 5.02848 0.245365
\(421\) −2.40152 −0.117043 −0.0585215 0.998286i \(-0.518639\pi\)
−0.0585215 + 0.998286i \(0.518639\pi\)
\(422\) 17.8763 0.870203
\(423\) 7.05208 0.342884
\(424\) −4.93047 −0.239445
\(425\) −3.84787 −0.186649
\(426\) 21.3443 1.03414
\(427\) −9.88504 −0.478371
\(428\) −8.79704 −0.425221
\(429\) 20.6889 0.998871
\(430\) 19.1177 0.921937
\(431\) −12.6907 −0.611288 −0.305644 0.952146i \(-0.598872\pi\)
−0.305644 + 0.952146i \(0.598872\pi\)
\(432\) −8.11595 −0.390479
\(433\) 34.7723 1.67105 0.835525 0.549453i \(-0.185164\pi\)
0.835525 + 0.549453i \(0.185164\pi\)
\(434\) −3.65208 −0.175305
\(435\) 9.38247 0.449855
\(436\) −57.7579 −2.76610
\(437\) −24.8916 −1.19073
\(438\) 48.9803 2.34037
\(439\) −21.5536 −1.02870 −0.514348 0.857581i \(-0.671966\pi\)
−0.514348 + 0.857581i \(0.671966\pi\)
\(440\) −20.6743 −0.985610
\(441\) −0.978466 −0.0465936
\(442\) −23.0421 −1.09600
\(443\) 39.6840 1.88544 0.942721 0.333581i \(-0.108257\pi\)
0.942721 + 0.333581i \(0.108257\pi\)
\(444\) −5.60877 −0.266181
\(445\) 1.58947 0.0753482
\(446\) −28.6293 −1.35564
\(447\) 22.4952 1.06398
\(448\) 11.9419 0.564204
\(449\) 8.75751 0.413292 0.206646 0.978416i \(-0.433745\pi\)
0.206646 + 0.978416i \(0.433745\pi\)
\(450\) 2.30235 0.108534
\(451\) 37.2590 1.75446
\(452\) −9.75087 −0.458643
\(453\) 5.83548 0.274175
\(454\) −7.18481 −0.337200
\(455\) −2.54493 −0.119308
\(456\) −22.6421 −1.06031
\(457\) −3.21350 −0.150321 −0.0751606 0.997171i \(-0.523947\pi\)
−0.0751606 + 0.997171i \(0.523947\pi\)
\(458\) −2.35302 −0.109949
\(459\) 21.7659 1.01595
\(460\) 19.9886 0.931974
\(461\) −26.7760 −1.24708 −0.623541 0.781791i \(-0.714307\pi\)
−0.623541 + 0.781791i \(0.714307\pi\)
\(462\) −19.1288 −0.889951
\(463\) 40.1114 1.86414 0.932068 0.362285i \(-0.118003\pi\)
0.932068 + 0.362285i \(0.118003\pi\)
\(464\) −9.46803 −0.439542
\(465\) 2.20676 0.102336
\(466\) −35.1293 −1.62733
\(467\) 4.97707 0.230311 0.115156 0.993347i \(-0.463263\pi\)
0.115156 + 0.993347i \(0.463263\pi\)
\(468\) 8.80680 0.407095
\(469\) −9.52626 −0.439882
\(470\) −16.9588 −0.782253
\(471\) −31.3393 −1.44404
\(472\) 12.7260 0.585761
\(473\) −46.4549 −2.13600
\(474\) 53.2761 2.44705
\(475\) 4.40419 0.202078
\(476\) 13.6087 0.623754
\(477\) −1.33421 −0.0610893
\(478\) 60.4157 2.76335
\(479\) −20.2179 −0.923778 −0.461889 0.886938i \(-0.652828\pi\)
−0.461889 + 0.886938i \(0.652828\pi\)
\(480\) −5.48198 −0.250217
\(481\) 2.83862 0.129430
\(482\) −51.8944 −2.36373
\(483\) 8.03576 0.365640
\(484\) 76.7182 3.48719
\(485\) −14.6538 −0.665396
\(486\) −22.8439 −1.03622
\(487\) −29.0197 −1.31501 −0.657503 0.753452i \(-0.728387\pi\)
−0.657503 + 0.753452i \(0.728387\pi\)
\(488\) −35.7428 −1.61800
\(489\) −13.8065 −0.624352
\(490\) 2.35302 0.106298
\(491\) −33.2928 −1.50249 −0.751243 0.660026i \(-0.770545\pi\)
−0.751243 + 0.660026i \(0.770545\pi\)
\(492\) −32.7677 −1.47728
\(493\) 25.3920 1.14360
\(494\) 26.3735 1.18660
\(495\) −5.59458 −0.251458
\(496\) −2.22689 −0.0999902
\(497\) 6.37994 0.286179
\(498\) 18.2736 0.818861
\(499\) −26.2479 −1.17502 −0.587509 0.809218i \(-0.699891\pi\)
−0.587509 + 0.809218i \(0.699891\pi\)
\(500\) −3.53669 −0.158165
\(501\) 29.8272 1.33258
\(502\) 5.57595 0.248867
\(503\) −31.1183 −1.38750 −0.693748 0.720218i \(-0.744042\pi\)
−0.693748 + 0.720218i \(0.744042\pi\)
\(504\) −3.53798 −0.157594
\(505\) 8.32577 0.370492
\(506\) −76.0384 −3.38032
\(507\) −9.27490 −0.411913
\(508\) −56.2357 −2.49505
\(509\) −36.1055 −1.60035 −0.800174 0.599768i \(-0.795259\pi\)
−0.800174 + 0.599768i \(0.795259\pi\)
\(510\) −12.8732 −0.570034
\(511\) 14.6405 0.647658
\(512\) 15.9078 0.703033
\(513\) −24.9128 −1.09993
\(514\) −36.0421 −1.58975
\(515\) 6.89805 0.303964
\(516\) 40.8552 1.79855
\(517\) 41.2091 1.81237
\(518\) −2.62456 −0.115316
\(519\) 31.3984 1.37824
\(520\) −9.20208 −0.403538
\(521\) −44.8441 −1.96466 −0.982328 0.187168i \(-0.940069\pi\)
−0.982328 + 0.187168i \(0.940069\pi\)
\(522\) −15.1931 −0.664985
\(523\) 38.2828 1.67399 0.836994 0.547212i \(-0.184311\pi\)
0.836994 + 0.547212i \(0.184311\pi\)
\(524\) 44.6956 1.95254
\(525\) −1.42181 −0.0620527
\(526\) −26.0733 −1.13685
\(527\) 5.97222 0.260154
\(528\) −11.6639 −0.507608
\(529\) 8.94276 0.388816
\(530\) 3.20851 0.139369
\(531\) 3.44371 0.149444
\(532\) −15.5762 −0.675316
\(533\) 16.5838 0.718326
\(534\) 5.31763 0.230116
\(535\) 2.48737 0.107538
\(536\) −34.4455 −1.48782
\(537\) −9.04016 −0.390112
\(538\) −17.4082 −0.750522
\(539\) −5.71770 −0.246279
\(540\) 20.0056 0.860906
\(541\) −36.4667 −1.56782 −0.783912 0.620872i \(-0.786779\pi\)
−0.783912 + 0.620872i \(0.786779\pi\)
\(542\) −29.2849 −1.25789
\(543\) −17.8821 −0.767394
\(544\) −14.8360 −0.636089
\(545\) 16.3311 0.699546
\(546\) −8.51416 −0.364372
\(547\) 1.28065 0.0547568 0.0273784 0.999625i \(-0.491284\pi\)
0.0273784 + 0.999625i \(0.491284\pi\)
\(548\) 31.4651 1.34412
\(549\) −9.67218 −0.412799
\(550\) 13.4538 0.573674
\(551\) −29.0631 −1.23813
\(552\) 29.0561 1.23671
\(553\) 15.9245 0.677180
\(554\) −30.5598 −1.29836
\(555\) 1.58588 0.0673170
\(556\) −15.3494 −0.650958
\(557\) −0.632055 −0.0267810 −0.0133905 0.999910i \(-0.504262\pi\)
−0.0133905 + 0.999910i \(0.504262\pi\)
\(558\) −3.57343 −0.151276
\(559\) −20.6770 −0.874542
\(560\) 1.43477 0.0606302
\(561\) 31.2811 1.32069
\(562\) −4.67566 −0.197231
\(563\) −4.02607 −0.169679 −0.0848394 0.996395i \(-0.527038\pi\)
−0.0848394 + 0.996395i \(0.527038\pi\)
\(564\) −36.2417 −1.52605
\(565\) 2.75707 0.115991
\(566\) −20.8935 −0.878219
\(567\) 5.10721 0.214483
\(568\) 23.0689 0.967949
\(569\) 3.42426 0.143552 0.0717761 0.997421i \(-0.477133\pi\)
0.0717761 + 0.997421i \(0.477133\pi\)
\(570\) 14.7344 0.617155
\(571\) 13.0457 0.545944 0.272972 0.962022i \(-0.411993\pi\)
0.272972 + 0.962022i \(0.411993\pi\)
\(572\) 51.4629 2.15177
\(573\) 29.6858 1.24014
\(574\) −15.3332 −0.639997
\(575\) −5.65179 −0.235696
\(576\) 11.6848 0.486866
\(577\) −14.7833 −0.615437 −0.307718 0.951478i \(-0.599565\pi\)
−0.307718 + 0.951478i \(0.599565\pi\)
\(578\) 5.16228 0.214722
\(579\) −30.2667 −1.25784
\(580\) 23.3385 0.969078
\(581\) 5.46210 0.226606
\(582\) −49.0248 −2.03215
\(583\) −7.79651 −0.322898
\(584\) 52.9378 2.19058
\(585\) −2.49013 −0.102954
\(586\) 55.8933 2.30893
\(587\) −3.05499 −0.126093 −0.0630464 0.998011i \(-0.520082\pi\)
−0.0630464 + 0.998011i \(0.520082\pi\)
\(588\) 5.02848 0.207371
\(589\) −6.83567 −0.281659
\(590\) −8.28145 −0.340942
\(591\) −15.8887 −0.653574
\(592\) −1.60035 −0.0657739
\(593\) −2.85789 −0.117359 −0.0586797 0.998277i \(-0.518689\pi\)
−0.0586797 + 0.998277i \(0.518689\pi\)
\(594\) −76.1031 −3.12255
\(595\) −3.84787 −0.157747
\(596\) 55.9558 2.29204
\(597\) 16.1983 0.662953
\(598\) −33.8444 −1.38400
\(599\) −40.1098 −1.63884 −0.819421 0.573192i \(-0.805705\pi\)
−0.819421 + 0.573192i \(0.805705\pi\)
\(600\) −5.14103 −0.209882
\(601\) −44.6240 −1.82025 −0.910126 0.414332i \(-0.864015\pi\)
−0.910126 + 0.414332i \(0.864015\pi\)
\(602\) 19.1177 0.779179
\(603\) −9.32112 −0.379585
\(604\) 14.5155 0.590628
\(605\) −21.6921 −0.881910
\(606\) 27.8542 1.13150
\(607\) 9.34012 0.379104 0.189552 0.981871i \(-0.439296\pi\)
0.189552 + 0.981871i \(0.439296\pi\)
\(608\) 16.9810 0.688671
\(609\) 9.38247 0.380197
\(610\) 23.2597 0.941757
\(611\) 18.3420 0.742039
\(612\) 13.3157 0.538253
\(613\) 36.9880 1.49393 0.746966 0.664862i \(-0.231510\pi\)
0.746966 + 0.664862i \(0.231510\pi\)
\(614\) −45.9393 −1.85396
\(615\) 9.26509 0.373605
\(616\) −20.6743 −0.832992
\(617\) 32.7294 1.31764 0.658818 0.752302i \(-0.271057\pi\)
0.658818 + 0.752302i \(0.271057\pi\)
\(618\) 23.0777 0.928320
\(619\) −17.5271 −0.704474 −0.352237 0.935911i \(-0.614579\pi\)
−0.352237 + 0.935911i \(0.614579\pi\)
\(620\) 5.48923 0.220453
\(621\) 31.9700 1.28291
\(622\) 41.0674 1.64665
\(623\) 1.58947 0.0636809
\(624\) −5.19158 −0.207830
\(625\) 1.00000 0.0400000
\(626\) 62.1002 2.48202
\(627\) −35.8037 −1.42986
\(628\) −77.9552 −3.11075
\(629\) 4.29192 0.171130
\(630\) 2.30235 0.0917277
\(631\) −3.09103 −0.123052 −0.0615259 0.998105i \(-0.519597\pi\)
−0.0615259 + 0.998105i \(0.519597\pi\)
\(632\) 57.5806 2.29044
\(633\) −10.8017 −0.429329
\(634\) −58.1355 −2.30885
\(635\) 15.9007 0.630999
\(636\) 6.85671 0.271886
\(637\) −2.54493 −0.100834
\(638\) −88.7816 −3.51490
\(639\) 6.24256 0.246952
\(640\) −20.3883 −0.805918
\(641\) 23.9906 0.947571 0.473786 0.880640i \(-0.342887\pi\)
0.473786 + 0.880640i \(0.342887\pi\)
\(642\) 8.32158 0.328427
\(643\) −3.57180 −0.140858 −0.0704290 0.997517i \(-0.522437\pi\)
−0.0704290 + 0.997517i \(0.522437\pi\)
\(644\) 19.9886 0.787662
\(645\) −11.5518 −0.454853
\(646\) 39.8760 1.56890
\(647\) −19.8919 −0.782032 −0.391016 0.920384i \(-0.627876\pi\)
−0.391016 + 0.920384i \(0.627876\pi\)
\(648\) 18.4669 0.725447
\(649\) 20.1235 0.789915
\(650\) 5.98827 0.234879
\(651\) 2.20676 0.0864899
\(652\) −34.3431 −1.34498
\(653\) 31.7591 1.24283 0.621415 0.783482i \(-0.286558\pi\)
0.621415 + 0.783482i \(0.286558\pi\)
\(654\) 54.6361 2.13644
\(655\) −12.6377 −0.493797
\(656\) −9.34959 −0.365040
\(657\) 14.3252 0.558881
\(658\) −16.9588 −0.661124
\(659\) 14.0856 0.548699 0.274349 0.961630i \(-0.411537\pi\)
0.274349 + 0.961630i \(0.411537\pi\)
\(660\) 28.7514 1.11915
\(661\) 32.8115 1.27622 0.638110 0.769945i \(-0.279716\pi\)
0.638110 + 0.769945i \(0.279716\pi\)
\(662\) −55.5846 −2.16036
\(663\) 13.9231 0.540730
\(664\) 19.7501 0.766453
\(665\) 4.40419 0.170787
\(666\) −2.56804 −0.0995095
\(667\) 37.2960 1.44411
\(668\) 74.1939 2.87065
\(669\) 17.2992 0.668827
\(670\) 22.4154 0.865984
\(671\) −56.5197 −2.18192
\(672\) −5.48198 −0.211472
\(673\) −12.4381 −0.479454 −0.239727 0.970840i \(-0.577058\pi\)
−0.239727 + 0.970840i \(0.577058\pi\)
\(674\) −49.1014 −1.89132
\(675\) −5.65661 −0.217723
\(676\) −23.0709 −0.887344
\(677\) 19.9136 0.765342 0.382671 0.923885i \(-0.375004\pi\)
0.382671 + 0.923885i \(0.375004\pi\)
\(678\) 9.22386 0.354240
\(679\) −14.6538 −0.562362
\(680\) −13.9133 −0.533551
\(681\) 4.34141 0.166363
\(682\) −20.8815 −0.799594
\(683\) 16.5389 0.632842 0.316421 0.948619i \(-0.397519\pi\)
0.316421 + 0.948619i \(0.397519\pi\)
\(684\) −15.2408 −0.582747
\(685\) −8.89677 −0.339928
\(686\) 2.35302 0.0898386
\(687\) 1.42181 0.0542453
\(688\) 11.6572 0.444426
\(689\) −3.47020 −0.132204
\(690\) −18.9083 −0.719825
\(691\) −49.4078 −1.87956 −0.939781 0.341778i \(-0.888971\pi\)
−0.939781 + 0.341778i \(0.888971\pi\)
\(692\) 78.1023 2.96901
\(693\) −5.59458 −0.212520
\(694\) 20.8286 0.790642
\(695\) 4.34004 0.164627
\(696\) 33.9256 1.28594
\(697\) 25.0743 0.949759
\(698\) −6.72285 −0.254464
\(699\) 21.2268 0.802872
\(700\) −3.53669 −0.133674
\(701\) 0.119440 0.00451118 0.00225559 0.999997i \(-0.499282\pi\)
0.00225559 + 0.999997i \(0.499282\pi\)
\(702\) −33.8733 −1.27846
\(703\) −4.91244 −0.185276
\(704\) 68.2805 2.57342
\(705\) 10.2474 0.385938
\(706\) 39.4022 1.48292
\(707\) 8.32577 0.313123
\(708\) −17.6978 −0.665123
\(709\) 23.9976 0.901247 0.450623 0.892714i \(-0.351202\pi\)
0.450623 + 0.892714i \(0.351202\pi\)
\(710\) −15.0121 −0.563394
\(711\) 15.5816 0.584356
\(712\) 5.74729 0.215389
\(713\) 8.77206 0.328516
\(714\) −12.8732 −0.481767
\(715\) −14.5512 −0.544183
\(716\) −22.4870 −0.840380
\(717\) −36.5061 −1.36335
\(718\) −21.0357 −0.785045
\(719\) −27.6193 −1.03003 −0.515013 0.857182i \(-0.672213\pi\)
−0.515013 + 0.857182i \(0.672213\pi\)
\(720\) 1.40388 0.0523194
\(721\) 6.89805 0.256897
\(722\) −0.933900 −0.0347562
\(723\) 31.3571 1.16618
\(724\) −44.4810 −1.65312
\(725\) −6.59897 −0.245080
\(726\) −72.5717 −2.69339
\(727\) −30.2129 −1.12053 −0.560266 0.828312i \(-0.689301\pi\)
−0.560266 + 0.828312i \(0.689301\pi\)
\(728\) −9.20208 −0.341052
\(729\) 29.1250 1.07871
\(730\) −34.4493 −1.27503
\(731\) −31.2630 −1.15630
\(732\) 49.7068 1.83722
\(733\) −7.84486 −0.289756 −0.144878 0.989449i \(-0.546279\pi\)
−0.144878 + 0.989449i \(0.546279\pi\)
\(734\) 31.2661 1.15405
\(735\) −1.42181 −0.0524441
\(736\) −21.7913 −0.803239
\(737\) −54.4683 −2.00637
\(738\) −15.0031 −0.552270
\(739\) −25.5113 −0.938450 −0.469225 0.883079i \(-0.655467\pi\)
−0.469225 + 0.883079i \(0.655467\pi\)
\(740\) 3.94482 0.145014
\(741\) −15.9361 −0.585428
\(742\) 3.20851 0.117788
\(743\) 32.8188 1.20401 0.602003 0.798494i \(-0.294369\pi\)
0.602003 + 0.798494i \(0.294369\pi\)
\(744\) 7.97931 0.292536
\(745\) −15.8215 −0.579656
\(746\) −28.3236 −1.03700
\(747\) 5.34448 0.195544
\(748\) 77.8105 2.84503
\(749\) 2.48737 0.0908865
\(750\) 3.34553 0.122162
\(751\) −34.5115 −1.25934 −0.629671 0.776862i \(-0.716810\pi\)
−0.629671 + 0.776862i \(0.716810\pi\)
\(752\) −10.3408 −0.377091
\(753\) −3.36926 −0.122783
\(754\) −39.5164 −1.43910
\(755\) −4.10427 −0.149370
\(756\) 20.0056 0.727598
\(757\) 35.3452 1.28464 0.642321 0.766435i \(-0.277971\pi\)
0.642321 + 0.766435i \(0.277971\pi\)
\(758\) −83.1635 −3.02063
\(759\) 45.9461 1.66774
\(760\) 15.9249 0.577656
\(761\) 16.9825 0.615613 0.307807 0.951449i \(-0.400405\pi\)
0.307807 + 0.951449i \(0.400405\pi\)
\(762\) 53.1962 1.92710
\(763\) 16.3311 0.591224
\(764\) 73.8423 2.67152
\(765\) −3.76501 −0.136124
\(766\) 41.5502 1.50127
\(767\) 8.95689 0.323415
\(768\) −34.2515 −1.23594
\(769\) −22.0900 −0.796585 −0.398292 0.917258i \(-0.630397\pi\)
−0.398292 + 0.917258i \(0.630397\pi\)
\(770\) 13.4538 0.484843
\(771\) 21.7784 0.784330
\(772\) −75.2873 −2.70965
\(773\) 5.33896 0.192029 0.0960146 0.995380i \(-0.469390\pi\)
0.0960146 + 0.995380i \(0.469390\pi\)
\(774\) 18.7060 0.672373
\(775\) −1.55208 −0.0557525
\(776\) −52.9859 −1.90208
\(777\) 1.58588 0.0568933
\(778\) 11.9151 0.427178
\(779\) −28.6996 −1.02827
\(780\) 12.7971 0.458211
\(781\) 36.4786 1.30531
\(782\) −51.1719 −1.82990
\(783\) 37.3278 1.33399
\(784\) 1.43477 0.0512419
\(785\) 22.0419 0.786708
\(786\) −42.2799 −1.50808
\(787\) 13.3199 0.474804 0.237402 0.971411i \(-0.423704\pi\)
0.237402 + 0.971411i \(0.423704\pi\)
\(788\) −39.5225 −1.40793
\(789\) 15.7548 0.560885
\(790\) −37.4707 −1.33315
\(791\) 2.75707 0.0980300
\(792\) −20.2291 −0.718811
\(793\) −25.1568 −0.893343
\(794\) −41.0235 −1.45587
\(795\) −1.93874 −0.0687599
\(796\) 40.2926 1.42813
\(797\) −16.0532 −0.568635 −0.284318 0.958730i \(-0.591767\pi\)
−0.284318 + 0.958730i \(0.591767\pi\)
\(798\) 14.7344 0.521591
\(799\) 27.7327 0.981111
\(800\) 3.85565 0.136318
\(801\) 1.55524 0.0549519
\(802\) 43.7361 1.54438
\(803\) 83.7100 2.95406
\(804\) 47.9026 1.68940
\(805\) −5.65179 −0.199200
\(806\) −9.29429 −0.327377
\(807\) 10.5189 0.370282
\(808\) 30.1047 1.05908
\(809\) −11.1320 −0.391380 −0.195690 0.980666i \(-0.562695\pi\)
−0.195690 + 0.980666i \(0.562695\pi\)
\(810\) −12.0173 −0.422246
\(811\) 45.0957 1.58352 0.791761 0.610831i \(-0.209164\pi\)
0.791761 + 0.610831i \(0.209164\pi\)
\(812\) 23.3385 0.819021
\(813\) 17.6953 0.620603
\(814\) −15.0064 −0.525975
\(815\) 9.71053 0.340145
\(816\) −7.84954 −0.274789
\(817\) 35.7830 1.25189
\(818\) 49.4652 1.72951
\(819\) −2.49013 −0.0870121
\(820\) 23.0465 0.804820
\(821\) −24.7895 −0.865158 −0.432579 0.901596i \(-0.642396\pi\)
−0.432579 + 0.901596i \(0.642396\pi\)
\(822\) −29.7644 −1.03815
\(823\) 37.6751 1.31327 0.656636 0.754207i \(-0.271979\pi\)
0.656636 + 0.754207i \(0.271979\pi\)
\(824\) 24.9423 0.868906
\(825\) −8.12947 −0.283032
\(826\) −8.28145 −0.288148
\(827\) 47.5809 1.65455 0.827275 0.561798i \(-0.189890\pi\)
0.827275 + 0.561798i \(0.189890\pi\)
\(828\) 19.5582 0.679694
\(829\) −54.5024 −1.89295 −0.946473 0.322784i \(-0.895381\pi\)
−0.946473 + 0.322784i \(0.895381\pi\)
\(830\) −12.8524 −0.446114
\(831\) 18.4657 0.640569
\(832\) 30.3914 1.05363
\(833\) −3.84787 −0.133321
\(834\) 14.5198 0.502778
\(835\) −20.9784 −0.725986
\(836\) −89.0603 −3.08021
\(837\) 8.77953 0.303465
\(838\) 11.1650 0.385690
\(839\) 45.9443 1.58617 0.793086 0.609110i \(-0.208473\pi\)
0.793086 + 0.609110i \(0.208473\pi\)
\(840\) −5.14103 −0.177383
\(841\) 14.5465 0.501602
\(842\) 5.65082 0.194740
\(843\) 2.82526 0.0973072
\(844\) −26.8688 −0.924863
\(845\) 6.52332 0.224409
\(846\) −16.5936 −0.570501
\(847\) −21.6921 −0.745350
\(848\) 1.95642 0.0671837
\(849\) 12.6249 0.433284
\(850\) 9.05410 0.310553
\(851\) 6.30401 0.216099
\(852\) −32.0814 −1.09909
\(853\) 18.1091 0.620044 0.310022 0.950729i \(-0.399664\pi\)
0.310022 + 0.950729i \(0.399664\pi\)
\(854\) 23.2597 0.795930
\(855\) 4.30935 0.147377
\(856\) 8.99394 0.307407
\(857\) 34.1013 1.16488 0.582440 0.812874i \(-0.302098\pi\)
0.582440 + 0.812874i \(0.302098\pi\)
\(858\) −48.6814 −1.66196
\(859\) 21.6599 0.739027 0.369513 0.929225i \(-0.379524\pi\)
0.369513 + 0.929225i \(0.379524\pi\)
\(860\) −28.7347 −0.979846
\(861\) 9.26509 0.315754
\(862\) 29.8614 1.01708
\(863\) 6.72174 0.228811 0.114405 0.993434i \(-0.463504\pi\)
0.114405 + 0.993434i \(0.463504\pi\)
\(864\) −21.8099 −0.741987
\(865\) −22.0835 −0.750861
\(866\) −81.8198 −2.78035
\(867\) −3.11930 −0.105937
\(868\) 5.48923 0.186317
\(869\) 91.0517 3.08872
\(870\) −22.0771 −0.748484
\(871\) −24.2437 −0.821466
\(872\) 59.0506 1.99971
\(873\) −14.3383 −0.485277
\(874\) 58.5703 1.98117
\(875\) 1.00000 0.0338062
\(876\) −73.6195 −2.48737
\(877\) 13.2343 0.446892 0.223446 0.974716i \(-0.428269\pi\)
0.223446 + 0.974716i \(0.428269\pi\)
\(878\) 50.7159 1.71158
\(879\) −33.7734 −1.13915
\(880\) 8.20361 0.276544
\(881\) −7.01602 −0.236376 −0.118188 0.992991i \(-0.537708\pi\)
−0.118188 + 0.992991i \(0.537708\pi\)
\(882\) 2.30235 0.0775240
\(883\) −0.518990 −0.0174654 −0.00873269 0.999962i \(-0.502780\pi\)
−0.00873269 + 0.999962i \(0.502780\pi\)
\(884\) 34.6332 1.16484
\(885\) 5.00405 0.168209
\(886\) −93.3770 −3.13706
\(887\) −34.7981 −1.16841 −0.584203 0.811608i \(-0.698593\pi\)
−0.584203 + 0.811608i \(0.698593\pi\)
\(888\) 5.73431 0.192431
\(889\) 15.9007 0.533291
\(890\) −3.74005 −0.125367
\(891\) 29.2015 0.978287
\(892\) 43.0311 1.44079
\(893\) −31.7422 −1.06221
\(894\) −52.9315 −1.77029
\(895\) 6.35822 0.212532
\(896\) −20.3883 −0.681125
\(897\) 20.4505 0.682821
\(898\) −20.6066 −0.687650
\(899\) 10.2422 0.341595
\(900\) −3.46053 −0.115351
\(901\) −5.24685 −0.174798
\(902\) −87.6709 −2.91912
\(903\) −11.5518 −0.384421
\(904\) 9.96912 0.331568
\(905\) 12.5770 0.418075
\(906\) −13.7310 −0.456181
\(907\) −59.1313 −1.96342 −0.981712 0.190373i \(-0.939030\pi\)
−0.981712 + 0.190373i \(0.939030\pi\)
\(908\) 10.7991 0.358380
\(909\) 8.14649 0.270202
\(910\) 5.98827 0.198509
\(911\) 14.3450 0.475272 0.237636 0.971354i \(-0.423627\pi\)
0.237636 + 0.971354i \(0.423627\pi\)
\(912\) 8.98442 0.297504
\(913\) 31.2306 1.03358
\(914\) 7.56142 0.250109
\(915\) −14.0546 −0.464631
\(916\) 3.53669 0.116855
\(917\) −12.6377 −0.417334
\(918\) −51.2155 −1.69036
\(919\) 23.2289 0.766250 0.383125 0.923697i \(-0.374848\pi\)
0.383125 + 0.923697i \(0.374848\pi\)
\(920\) −20.4360 −0.673755
\(921\) 27.7588 0.914683
\(922\) 63.0043 2.07494
\(923\) 16.2365 0.534431
\(924\) 28.7514 0.945851
\(925\) −1.11540 −0.0366741
\(926\) −94.3828 −3.10161
\(927\) 6.74951 0.221683
\(928\) −25.4433 −0.835218
\(929\) 20.0055 0.656358 0.328179 0.944615i \(-0.393565\pi\)
0.328179 + 0.944615i \(0.393565\pi\)
\(930\) −5.19255 −0.170270
\(931\) 4.40419 0.144342
\(932\) 52.8009 1.72955
\(933\) −24.8149 −0.812404
\(934\) −11.7111 −0.383200
\(935\) −22.0010 −0.719509
\(936\) −9.00392 −0.294302
\(937\) −23.2834 −0.760634 −0.380317 0.924856i \(-0.624185\pi\)
−0.380317 + 0.924856i \(0.624185\pi\)
\(938\) 22.4154 0.731890
\(939\) −37.5240 −1.22455
\(940\) 25.4899 0.831388
\(941\) −28.6143 −0.932798 −0.466399 0.884574i \(-0.654449\pi\)
−0.466399 + 0.884574i \(0.654449\pi\)
\(942\) 73.7419 2.40264
\(943\) 36.8295 1.19933
\(944\) −5.04969 −0.164353
\(945\) −5.65661 −0.184010
\(946\) 109.309 3.55395
\(947\) −4.43218 −0.144027 −0.0720133 0.997404i \(-0.522942\pi\)
−0.0720133 + 0.997404i \(0.522942\pi\)
\(948\) −80.0762 −2.60075
\(949\) 37.2591 1.20948
\(950\) −10.3631 −0.336224
\(951\) 35.1283 1.13911
\(952\) −13.9133 −0.450933
\(953\) −8.07985 −0.261732 −0.130866 0.991400i \(-0.541776\pi\)
−0.130866 + 0.991400i \(0.541776\pi\)
\(954\) 3.13942 0.101642
\(955\) −20.8789 −0.675627
\(956\) −90.8074 −2.93692
\(957\) 53.6461 1.73413
\(958\) 47.5730 1.53701
\(959\) −8.89677 −0.287292
\(960\) 16.9791 0.547999
\(961\) −28.5910 −0.922291
\(962\) −6.67931 −0.215350
\(963\) 2.43381 0.0784283
\(964\) 77.9995 2.51220
\(965\) 21.2875 0.685270
\(966\) −18.9083 −0.608363
\(967\) −53.3012 −1.71405 −0.857025 0.515274i \(-0.827690\pi\)
−0.857025 + 0.515274i \(0.827690\pi\)
\(968\) −78.4354 −2.52101
\(969\) −24.0950 −0.774043
\(970\) 34.4807 1.10711
\(971\) 15.3663 0.493127 0.246564 0.969127i \(-0.420699\pi\)
0.246564 + 0.969127i \(0.420699\pi\)
\(972\) 34.3354 1.10131
\(973\) 4.34004 0.139135
\(974\) 68.2837 2.18795
\(975\) −3.61840 −0.115882
\(976\) 14.1828 0.453980
\(977\) −8.81407 −0.281987 −0.140993 0.990011i \(-0.545030\pi\)
−0.140993 + 0.990011i \(0.545030\pi\)
\(978\) 32.4869 1.03882
\(979\) 9.08813 0.290458
\(980\) −3.53669 −0.112975
\(981\) 15.9794 0.510183
\(982\) 78.3386 2.49989
\(983\) 46.0365 1.46834 0.734168 0.678968i \(-0.237572\pi\)
0.734168 + 0.678968i \(0.237572\pi\)
\(984\) 33.5011 1.06798
\(985\) 11.1750 0.356065
\(986\) −59.7478 −1.90276
\(987\) 10.2474 0.326177
\(988\) −39.6405 −1.26113
\(989\) −45.9194 −1.46015
\(990\) 13.1641 0.418384
\(991\) −15.8978 −0.505011 −0.252506 0.967595i \(-0.581255\pi\)
−0.252506 + 0.967595i \(0.581255\pi\)
\(992\) −5.98429 −0.190001
\(993\) 33.5869 1.06585
\(994\) −15.0121 −0.476155
\(995\) −11.3928 −0.361175
\(996\) −27.4661 −0.870296
\(997\) −31.4617 −0.996403 −0.498202 0.867061i \(-0.666006\pi\)
−0.498202 + 0.867061i \(0.666006\pi\)
\(998\) 61.7618 1.95503
\(999\) 6.30938 0.199620
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 \(a_p\))