Properties

Label 8015.2.a.l.1.49
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 1.49
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} +O(q^{10})\) \(q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} -1.87567 q^{10} -3.98252 q^{11} +2.02360 q^{12} +5.96900 q^{13} -1.87567 q^{14} -1.33294 q^{15} -4.73152 q^{16} +3.59235 q^{17} -2.29448 q^{18} +4.67846 q^{19} -1.51815 q^{20} -1.33294 q^{21} -7.46991 q^{22} +3.64241 q^{23} -1.20470 q^{24} +1.00000 q^{25} +11.1959 q^{26} -5.62936 q^{27} -1.51815 q^{28} -0.721455 q^{29} -2.50015 q^{30} -8.67804 q^{31} -7.06720 q^{32} -5.30845 q^{33} +6.73808 q^{34} +1.00000 q^{35} -1.85713 q^{36} +8.84089 q^{37} +8.77527 q^{38} +7.95630 q^{39} +0.903793 q^{40} +0.649730 q^{41} -2.50015 q^{42} +11.2509 q^{43} -6.04607 q^{44} +1.22328 q^{45} +6.83197 q^{46} -9.73223 q^{47} -6.30681 q^{48} +1.00000 q^{49} +1.87567 q^{50} +4.78838 q^{51} +9.06184 q^{52} +4.65742 q^{53} -10.5588 q^{54} +3.98252 q^{55} +0.903793 q^{56} +6.23609 q^{57} -1.35321 q^{58} +9.28342 q^{59} -2.02360 q^{60} +5.14011 q^{61} -16.2772 q^{62} +1.22328 q^{63} -3.79272 q^{64} -5.96900 q^{65} -9.95691 q^{66} +10.7240 q^{67} +5.45373 q^{68} +4.85510 q^{69} +1.87567 q^{70} +10.2206 q^{71} +1.10559 q^{72} +5.45139 q^{73} +16.5826 q^{74} +1.33294 q^{75} +7.10261 q^{76} +3.98252 q^{77} +14.9234 q^{78} +1.37256 q^{79} +4.73152 q^{80} -3.83373 q^{81} +1.21868 q^{82} -1.67954 q^{83} -2.02360 q^{84} -3.59235 q^{85} +21.1030 q^{86} -0.961653 q^{87} +3.59938 q^{88} +13.5816 q^{89} +2.29448 q^{90} -5.96900 q^{91} +5.52973 q^{92} -11.5673 q^{93} -18.2545 q^{94} -4.67846 q^{95} -9.42012 q^{96} -2.51699 q^{97} +1.87567 q^{98} +4.87175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87567 1.32630 0.663151 0.748486i \(-0.269219\pi\)
0.663151 + 0.748486i \(0.269219\pi\)
\(3\) 1.33294 0.769571 0.384785 0.923006i \(-0.374275\pi\)
0.384785 + 0.923006i \(0.374275\pi\)
\(4\) 1.51815 0.759075
\(5\) −1.00000 −0.447214
\(6\) 2.50015 1.02068
\(7\) −1.00000 −0.377964
\(8\) −0.903793 −0.319539
\(9\) −1.22328 −0.407761
\(10\) −1.87567 −0.593140
\(11\) −3.98252 −1.20078 −0.600388 0.799709i \(-0.704987\pi\)
−0.600388 + 0.799709i \(0.704987\pi\)
\(12\) 2.02360 0.584162
\(13\) 5.96900 1.65550 0.827752 0.561094i \(-0.189620\pi\)
0.827752 + 0.561094i \(0.189620\pi\)
\(14\) −1.87567 −0.501295
\(15\) −1.33294 −0.344162
\(16\) −4.73152 −1.18288
\(17\) 3.59235 0.871274 0.435637 0.900122i \(-0.356523\pi\)
0.435637 + 0.900122i \(0.356523\pi\)
\(18\) −2.29448 −0.540814
\(19\) 4.67846 1.07331 0.536657 0.843801i \(-0.319687\pi\)
0.536657 + 0.843801i \(0.319687\pi\)
\(20\) −1.51815 −0.339469
\(21\) −1.33294 −0.290870
\(22\) −7.46991 −1.59259
\(23\) 3.64241 0.759495 0.379748 0.925090i \(-0.376011\pi\)
0.379748 + 0.925090i \(0.376011\pi\)
\(24\) −1.20470 −0.245908
\(25\) 1.00000 0.200000
\(26\) 11.1959 2.19570
\(27\) −5.62936 −1.08337
\(28\) −1.51815 −0.286903
\(29\) −0.721455 −0.133971 −0.0669854 0.997754i \(-0.521338\pi\)
−0.0669854 + 0.997754i \(0.521338\pi\)
\(30\) −2.50015 −0.456463
\(31\) −8.67804 −1.55862 −0.779311 0.626638i \(-0.784431\pi\)
−0.779311 + 0.626638i \(0.784431\pi\)
\(32\) −7.06720 −1.24932
\(33\) −5.30845 −0.924082
\(34\) 6.73808 1.15557
\(35\) 1.00000 0.169031
\(36\) −1.85713 −0.309521
\(37\) 8.84089 1.45343 0.726717 0.686937i \(-0.241045\pi\)
0.726717 + 0.686937i \(0.241045\pi\)
\(38\) 8.77527 1.42354
\(39\) 7.95630 1.27403
\(40\) 0.903793 0.142902
\(41\) 0.649730 0.101471 0.0507354 0.998712i \(-0.483843\pi\)
0.0507354 + 0.998712i \(0.483843\pi\)
\(42\) −2.50015 −0.385782
\(43\) 11.2509 1.71574 0.857872 0.513863i \(-0.171786\pi\)
0.857872 + 0.513863i \(0.171786\pi\)
\(44\) −6.04607 −0.911479
\(45\) 1.22328 0.182356
\(46\) 6.83197 1.00732
\(47\) −9.73223 −1.41959 −0.709796 0.704407i \(-0.751213\pi\)
−0.709796 + 0.704407i \(0.751213\pi\)
\(48\) −6.30681 −0.910310
\(49\) 1.00000 0.142857
\(50\) 1.87567 0.265260
\(51\) 4.78838 0.670507
\(52\) 9.06184 1.25665
\(53\) 4.65742 0.639746 0.319873 0.947460i \(-0.396360\pi\)
0.319873 + 0.947460i \(0.396360\pi\)
\(54\) −10.5588 −1.43688
\(55\) 3.98252 0.537003
\(56\) 0.903793 0.120774
\(57\) 6.23609 0.825991
\(58\) −1.35321 −0.177686
\(59\) 9.28342 1.20860 0.604299 0.796757i \(-0.293453\pi\)
0.604299 + 0.796757i \(0.293453\pi\)
\(60\) −2.02360 −0.261245
\(61\) 5.14011 0.658124 0.329062 0.944308i \(-0.393268\pi\)
0.329062 + 0.944308i \(0.393268\pi\)
\(62\) −16.2772 −2.06720
\(63\) 1.22328 0.154119
\(64\) −3.79272 −0.474090
\(65\) −5.96900 −0.740364
\(66\) −9.95691 −1.22561
\(67\) 10.7240 1.31014 0.655071 0.755567i \(-0.272639\pi\)
0.655071 + 0.755567i \(0.272639\pi\)
\(68\) 5.45373 0.661362
\(69\) 4.85510 0.584485
\(70\) 1.87567 0.224186
\(71\) 10.2206 1.21296 0.606481 0.795098i \(-0.292580\pi\)
0.606481 + 0.795098i \(0.292580\pi\)
\(72\) 1.10559 0.130296
\(73\) 5.45139 0.638037 0.319018 0.947749i \(-0.396647\pi\)
0.319018 + 0.947749i \(0.396647\pi\)
\(74\) 16.5826 1.92769
\(75\) 1.33294 0.153914
\(76\) 7.10261 0.814725
\(77\) 3.98252 0.453851
\(78\) 14.9234 1.68974
\(79\) 1.37256 0.154425 0.0772123 0.997015i \(-0.475398\pi\)
0.0772123 + 0.997015i \(0.475398\pi\)
\(80\) 4.73152 0.529000
\(81\) −3.83373 −0.425970
\(82\) 1.21868 0.134581
\(83\) −1.67954 −0.184353 −0.0921767 0.995743i \(-0.529382\pi\)
−0.0921767 + 0.995743i \(0.529382\pi\)
\(84\) −2.02360 −0.220792
\(85\) −3.59235 −0.389646
\(86\) 21.1030 2.27559
\(87\) −0.961653 −0.103100
\(88\) 3.59938 0.383695
\(89\) 13.5816 1.43964 0.719822 0.694159i \(-0.244224\pi\)
0.719822 + 0.694159i \(0.244224\pi\)
\(90\) 2.29448 0.241859
\(91\) −5.96900 −0.625722
\(92\) 5.52973 0.576514
\(93\) −11.5673 −1.19947
\(94\) −18.2545 −1.88281
\(95\) −4.67846 −0.480000
\(96\) −9.42012 −0.961437
\(97\) −2.51699 −0.255562 −0.127781 0.991802i \(-0.540785\pi\)
−0.127781 + 0.991802i \(0.540785\pi\)
\(98\) 1.87567 0.189472
\(99\) 4.87175 0.489630
\(100\) 1.51815 0.151815
\(101\) −8.19186 −0.815120 −0.407560 0.913178i \(-0.633620\pi\)
−0.407560 + 0.913178i \(0.633620\pi\)
\(102\) 8.98143 0.889294
\(103\) 9.58693 0.944628 0.472314 0.881430i \(-0.343419\pi\)
0.472314 + 0.881430i \(0.343419\pi\)
\(104\) −5.39474 −0.528998
\(105\) 1.33294 0.130081
\(106\) 8.73580 0.848496
\(107\) 2.59404 0.250775 0.125388 0.992108i \(-0.459983\pi\)
0.125388 + 0.992108i \(0.459983\pi\)
\(108\) −8.54622 −0.822360
\(109\) −8.95812 −0.858033 −0.429016 0.903297i \(-0.641140\pi\)
−0.429016 + 0.903297i \(0.641140\pi\)
\(110\) 7.46991 0.712228
\(111\) 11.7843 1.11852
\(112\) 4.73152 0.447087
\(113\) −4.89637 −0.460611 −0.230306 0.973118i \(-0.573973\pi\)
−0.230306 + 0.973118i \(0.573973\pi\)
\(114\) 11.6969 1.09551
\(115\) −3.64241 −0.339657
\(116\) −1.09528 −0.101694
\(117\) −7.30178 −0.675050
\(118\) 17.4127 1.60297
\(119\) −3.59235 −0.329311
\(120\) 1.20470 0.109973
\(121\) 4.86050 0.441864
\(122\) 9.64117 0.872870
\(123\) 0.866048 0.0780889
\(124\) −13.1746 −1.18311
\(125\) −1.00000 −0.0894427
\(126\) 2.29448 0.204408
\(127\) −17.1223 −1.51936 −0.759680 0.650298i \(-0.774644\pi\)
−0.759680 + 0.650298i \(0.774644\pi\)
\(128\) 7.02050 0.620531
\(129\) 14.9967 1.32039
\(130\) −11.1959 −0.981945
\(131\) 6.84606 0.598143 0.299072 0.954231i \(-0.403323\pi\)
0.299072 + 0.954231i \(0.403323\pi\)
\(132\) −8.05902 −0.701448
\(133\) −4.67846 −0.405674
\(134\) 20.1147 1.73764
\(135\) 5.62936 0.484498
\(136\) −3.24674 −0.278406
\(137\) 10.4683 0.894369 0.447184 0.894442i \(-0.352427\pi\)
0.447184 + 0.894442i \(0.352427\pi\)
\(138\) 9.10658 0.775203
\(139\) −19.3425 −1.64061 −0.820306 0.571925i \(-0.806197\pi\)
−0.820306 + 0.571925i \(0.806197\pi\)
\(140\) 1.51815 0.128307
\(141\) −12.9724 −1.09248
\(142\) 19.1705 1.60875
\(143\) −23.7717 −1.98789
\(144\) 5.78799 0.482332
\(145\) 0.721455 0.0599136
\(146\) 10.2250 0.846229
\(147\) 1.33294 0.109939
\(148\) 13.4218 1.10326
\(149\) −1.85795 −0.152209 −0.0761045 0.997100i \(-0.524248\pi\)
−0.0761045 + 0.997100i \(0.524248\pi\)
\(150\) 2.50015 0.204137
\(151\) 16.0060 1.30255 0.651274 0.758843i \(-0.274235\pi\)
0.651274 + 0.758843i \(0.274235\pi\)
\(152\) −4.22836 −0.342966
\(153\) −4.39447 −0.355272
\(154\) 7.46991 0.601943
\(155\) 8.67804 0.697037
\(156\) 12.0789 0.967082
\(157\) 19.6666 1.56957 0.784785 0.619768i \(-0.212773\pi\)
0.784785 + 0.619768i \(0.212773\pi\)
\(158\) 2.57446 0.204813
\(159\) 6.20804 0.492330
\(160\) 7.06720 0.558711
\(161\) −3.64241 −0.287062
\(162\) −7.19083 −0.564965
\(163\) 23.0762 1.80747 0.903736 0.428091i \(-0.140814\pi\)
0.903736 + 0.428091i \(0.140814\pi\)
\(164\) 0.986387 0.0770239
\(165\) 5.30845 0.413262
\(166\) −3.15027 −0.244508
\(167\) −20.4601 −1.58325 −0.791625 0.611007i \(-0.790765\pi\)
−0.791625 + 0.611007i \(0.790765\pi\)
\(168\) 1.20470 0.0929444
\(169\) 22.6290 1.74069
\(170\) −6.73808 −0.516787
\(171\) −5.72309 −0.437655
\(172\) 17.0805 1.30238
\(173\) −15.8160 −1.20247 −0.601236 0.799072i \(-0.705325\pi\)
−0.601236 + 0.799072i \(0.705325\pi\)
\(174\) −1.80375 −0.136742
\(175\) −1.00000 −0.0755929
\(176\) 18.8434 1.42037
\(177\) 12.3742 0.930102
\(178\) 25.4746 1.90940
\(179\) 9.36766 0.700172 0.350086 0.936718i \(-0.386152\pi\)
0.350086 + 0.936718i \(0.386152\pi\)
\(180\) 1.85713 0.138422
\(181\) 18.4437 1.37091 0.685455 0.728115i \(-0.259603\pi\)
0.685455 + 0.728115i \(0.259603\pi\)
\(182\) −11.1959 −0.829895
\(183\) 6.85144 0.506473
\(184\) −3.29199 −0.242688
\(185\) −8.84089 −0.649995
\(186\) −21.6964 −1.59086
\(187\) −14.3066 −1.04621
\(188\) −14.7750 −1.07758
\(189\) 5.62936 0.409476
\(190\) −8.77527 −0.636625
\(191\) −20.1710 −1.45952 −0.729762 0.683701i \(-0.760369\pi\)
−0.729762 + 0.683701i \(0.760369\pi\)
\(192\) −5.05545 −0.364846
\(193\) −12.7911 −0.920723 −0.460361 0.887732i \(-0.652280\pi\)
−0.460361 + 0.887732i \(0.652280\pi\)
\(194\) −4.72105 −0.338952
\(195\) −7.95630 −0.569762
\(196\) 1.51815 0.108439
\(197\) −8.69625 −0.619582 −0.309791 0.950805i \(-0.600259\pi\)
−0.309791 + 0.950805i \(0.600259\pi\)
\(198\) 9.13782 0.649396
\(199\) 19.3957 1.37493 0.687463 0.726219i \(-0.258724\pi\)
0.687463 + 0.726219i \(0.258724\pi\)
\(200\) −0.903793 −0.0639078
\(201\) 14.2944 1.00825
\(202\) −15.3652 −1.08109
\(203\) 0.721455 0.0506362
\(204\) 7.26948 0.508965
\(205\) −0.649730 −0.0453791
\(206\) 17.9820 1.25286
\(207\) −4.45570 −0.309692
\(208\) −28.2425 −1.95826
\(209\) −18.6321 −1.28881
\(210\) 2.50015 0.172527
\(211\) −5.43974 −0.374487 −0.187244 0.982314i \(-0.559955\pi\)
−0.187244 + 0.982314i \(0.559955\pi\)
\(212\) 7.07067 0.485615
\(213\) 13.6234 0.933461
\(214\) 4.86557 0.332604
\(215\) −11.2509 −0.767304
\(216\) 5.08778 0.346180
\(217\) 8.67804 0.589104
\(218\) −16.8025 −1.13801
\(219\) 7.26635 0.491014
\(220\) 6.04607 0.407626
\(221\) 21.4428 1.44240
\(222\) 22.1036 1.48349
\(223\) −25.2433 −1.69041 −0.845207 0.534439i \(-0.820523\pi\)
−0.845207 + 0.534439i \(0.820523\pi\)
\(224\) 7.06720 0.472197
\(225\) −1.22328 −0.0815522
\(226\) −9.18398 −0.610909
\(227\) 8.70283 0.577627 0.288814 0.957385i \(-0.406739\pi\)
0.288814 + 0.957385i \(0.406739\pi\)
\(228\) 9.46732 0.626989
\(229\) 1.00000 0.0660819
\(230\) −6.83197 −0.450487
\(231\) 5.30845 0.349270
\(232\) 0.652046 0.0428089
\(233\) −24.1356 −1.58118 −0.790588 0.612348i \(-0.790225\pi\)
−0.790588 + 0.612348i \(0.790225\pi\)
\(234\) −13.6958 −0.895319
\(235\) 9.73223 0.634861
\(236\) 14.0936 0.917417
\(237\) 1.82953 0.118841
\(238\) −6.73808 −0.436765
\(239\) 1.86403 0.120574 0.0602869 0.998181i \(-0.480798\pi\)
0.0602869 + 0.998181i \(0.480798\pi\)
\(240\) 6.30681 0.407103
\(241\) 22.3650 1.44066 0.720329 0.693632i \(-0.243991\pi\)
0.720329 + 0.693632i \(0.243991\pi\)
\(242\) 9.11671 0.586044
\(243\) 11.7780 0.755557
\(244\) 7.80346 0.499565
\(245\) −1.00000 −0.0638877
\(246\) 1.62442 0.103569
\(247\) 27.9258 1.77687
\(248\) 7.84315 0.498040
\(249\) −2.23872 −0.141873
\(250\) −1.87567 −0.118628
\(251\) −13.2019 −0.833294 −0.416647 0.909068i \(-0.636795\pi\)
−0.416647 + 0.909068i \(0.636795\pi\)
\(252\) 1.85713 0.116988
\(253\) −14.5060 −0.911984
\(254\) −32.1159 −2.01513
\(255\) −4.78838 −0.299860
\(256\) 20.7536 1.29710
\(257\) 26.4275 1.64850 0.824251 0.566224i \(-0.191596\pi\)
0.824251 + 0.566224i \(0.191596\pi\)
\(258\) 28.1289 1.75123
\(259\) −8.84089 −0.549346
\(260\) −9.06184 −0.561992
\(261\) 0.882543 0.0546281
\(262\) 12.8410 0.793318
\(263\) 8.99028 0.554364 0.277182 0.960817i \(-0.410599\pi\)
0.277182 + 0.960817i \(0.410599\pi\)
\(264\) 4.79774 0.295280
\(265\) −4.65742 −0.286103
\(266\) −8.77527 −0.538046
\(267\) 18.1034 1.10791
\(268\) 16.2806 0.994496
\(269\) 28.4526 1.73478 0.867392 0.497625i \(-0.165795\pi\)
0.867392 + 0.497625i \(0.165795\pi\)
\(270\) 10.5588 0.642591
\(271\) 3.67532 0.223260 0.111630 0.993750i \(-0.464393\pi\)
0.111630 + 0.993750i \(0.464393\pi\)
\(272\) −16.9973 −1.03061
\(273\) −7.95630 −0.481537
\(274\) 19.6351 1.18620
\(275\) −3.98252 −0.240155
\(276\) 7.37077 0.443668
\(277\) −5.23116 −0.314310 −0.157155 0.987574i \(-0.550232\pi\)
−0.157155 + 0.987574i \(0.550232\pi\)
\(278\) −36.2803 −2.17595
\(279\) 10.6157 0.635545
\(280\) −0.903793 −0.0540120
\(281\) 17.2831 1.03103 0.515513 0.856882i \(-0.327601\pi\)
0.515513 + 0.856882i \(0.327601\pi\)
\(282\) −24.3321 −1.44895
\(283\) −11.7370 −0.697693 −0.348847 0.937180i \(-0.613427\pi\)
−0.348847 + 0.937180i \(0.613427\pi\)
\(284\) 15.5164 0.920730
\(285\) −6.23609 −0.369394
\(286\) −44.5879 −2.63654
\(287\) −0.649730 −0.0383523
\(288\) 8.64519 0.509422
\(289\) −4.09499 −0.240882
\(290\) 1.35321 0.0794634
\(291\) −3.35499 −0.196673
\(292\) 8.27602 0.484318
\(293\) 20.3986 1.19170 0.595850 0.803096i \(-0.296815\pi\)
0.595850 + 0.803096i \(0.296815\pi\)
\(294\) 2.50015 0.145812
\(295\) −9.28342 −0.540502
\(296\) −7.99033 −0.464429
\(297\) 22.4191 1.30089
\(298\) −3.48490 −0.201875
\(299\) 21.7416 1.25735
\(300\) 2.02360 0.116832
\(301\) −11.2509 −0.648490
\(302\) 30.0220 1.72757
\(303\) −10.9192 −0.627293
\(304\) −22.1363 −1.26960
\(305\) −5.14011 −0.294322
\(306\) −8.24258 −0.471197
\(307\) −12.6110 −0.719750 −0.359875 0.933001i \(-0.617181\pi\)
−0.359875 + 0.933001i \(0.617181\pi\)
\(308\) 6.04607 0.344507
\(309\) 12.7788 0.726958
\(310\) 16.2772 0.924481
\(311\) −9.49597 −0.538467 −0.269234 0.963075i \(-0.586770\pi\)
−0.269234 + 0.963075i \(0.586770\pi\)
\(312\) −7.19084 −0.407101
\(313\) −6.39603 −0.361525 −0.180762 0.983527i \(-0.557856\pi\)
−0.180762 + 0.983527i \(0.557856\pi\)
\(314\) 36.8882 2.08172
\(315\) −1.22328 −0.0689242
\(316\) 2.08374 0.117220
\(317\) −13.6302 −0.765546 −0.382773 0.923842i \(-0.625031\pi\)
−0.382773 + 0.923842i \(0.625031\pi\)
\(318\) 11.6443 0.652978
\(319\) 2.87321 0.160869
\(320\) 3.79272 0.212019
\(321\) 3.45769 0.192989
\(322\) −6.83197 −0.380731
\(323\) 16.8067 0.935150
\(324\) −5.82018 −0.323343
\(325\) 5.96900 0.331101
\(326\) 43.2835 2.39725
\(327\) −11.9406 −0.660317
\(328\) −0.587221 −0.0324239
\(329\) 9.73223 0.536555
\(330\) 9.95691 0.548110
\(331\) −3.80067 −0.208904 −0.104452 0.994530i \(-0.533309\pi\)
−0.104452 + 0.994530i \(0.533309\pi\)
\(332\) −2.54979 −0.139938
\(333\) −10.8149 −0.592653
\(334\) −38.3765 −2.09987
\(335\) −10.7240 −0.585913
\(336\) 6.30681 0.344065
\(337\) 11.4549 0.623987 0.311993 0.950084i \(-0.399003\pi\)
0.311993 + 0.950084i \(0.399003\pi\)
\(338\) 42.4446 2.30868
\(339\) −6.52654 −0.354473
\(340\) −5.45373 −0.295770
\(341\) 34.5605 1.87156
\(342\) −10.7346 −0.580463
\(343\) −1.00000 −0.0539949
\(344\) −10.1685 −0.548247
\(345\) −4.85510 −0.261390
\(346\) −29.6657 −1.59484
\(347\) 15.7027 0.842967 0.421483 0.906836i \(-0.361510\pi\)
0.421483 + 0.906836i \(0.361510\pi\)
\(348\) −1.45993 −0.0782606
\(349\) 9.26458 0.495922 0.247961 0.968770i \(-0.420240\pi\)
0.247961 + 0.968770i \(0.420240\pi\)
\(350\) −1.87567 −0.100259
\(351\) −33.6017 −1.79353
\(352\) 28.1453 1.50015
\(353\) −10.0029 −0.532402 −0.266201 0.963918i \(-0.585768\pi\)
−0.266201 + 0.963918i \(0.585768\pi\)
\(354\) 23.2100 1.23360
\(355\) −10.2206 −0.542453
\(356\) 20.6189 1.09280
\(357\) −4.78838 −0.253428
\(358\) 17.5707 0.928639
\(359\) 8.78137 0.463463 0.231731 0.972780i \(-0.425561\pi\)
0.231731 + 0.972780i \(0.425561\pi\)
\(360\) −1.10559 −0.0582699
\(361\) 2.88803 0.152002
\(362\) 34.5944 1.81824
\(363\) 6.47873 0.340045
\(364\) −9.06184 −0.474970
\(365\) −5.45139 −0.285339
\(366\) 12.8511 0.671735
\(367\) 2.35664 0.123016 0.0615078 0.998107i \(-0.480409\pi\)
0.0615078 + 0.998107i \(0.480409\pi\)
\(368\) −17.2341 −0.898392
\(369\) −0.794803 −0.0413758
\(370\) −16.5826 −0.862089
\(371\) −4.65742 −0.241801
\(372\) −17.5608 −0.910487
\(373\) −7.72871 −0.400178 −0.200089 0.979778i \(-0.564123\pi\)
−0.200089 + 0.979778i \(0.564123\pi\)
\(374\) −26.8346 −1.38758
\(375\) −1.33294 −0.0688325
\(376\) 8.79592 0.453615
\(377\) −4.30637 −0.221789
\(378\) 10.5588 0.543088
\(379\) −4.60055 −0.236314 −0.118157 0.992995i \(-0.537699\pi\)
−0.118157 + 0.992995i \(0.537699\pi\)
\(380\) −7.10261 −0.364356
\(381\) −22.8229 −1.16925
\(382\) −37.8343 −1.93577
\(383\) −18.0940 −0.924559 −0.462279 0.886734i \(-0.652968\pi\)
−0.462279 + 0.886734i \(0.652968\pi\)
\(384\) 9.35788 0.477542
\(385\) −3.98252 −0.202968
\(386\) −23.9919 −1.22116
\(387\) −13.7630 −0.699613
\(388\) −3.82117 −0.193991
\(389\) 28.8310 1.46179 0.730894 0.682491i \(-0.239104\pi\)
0.730894 + 0.682491i \(0.239104\pi\)
\(390\) −14.9234 −0.755676
\(391\) 13.0848 0.661728
\(392\) −0.903793 −0.0456484
\(393\) 9.12536 0.460313
\(394\) −16.3113 −0.821753
\(395\) −1.37256 −0.0690607
\(396\) 7.39605 0.371666
\(397\) −31.5028 −1.58108 −0.790539 0.612412i \(-0.790199\pi\)
−0.790539 + 0.612412i \(0.790199\pi\)
\(398\) 36.3800 1.82357
\(399\) −6.23609 −0.312195
\(400\) −4.73152 −0.236576
\(401\) −9.95960 −0.497359 −0.248679 0.968586i \(-0.579997\pi\)
−0.248679 + 0.968586i \(0.579997\pi\)
\(402\) 26.8116 1.33724
\(403\) −51.7992 −2.58030
\(404\) −12.4365 −0.618737
\(405\) 3.83373 0.190500
\(406\) 1.35321 0.0671589
\(407\) −35.2091 −1.74525
\(408\) −4.32770 −0.214253
\(409\) 23.2826 1.15125 0.575626 0.817713i \(-0.304759\pi\)
0.575626 + 0.817713i \(0.304759\pi\)
\(410\) −1.21868 −0.0601864
\(411\) 13.9536 0.688280
\(412\) 14.5544 0.717044
\(413\) −9.28342 −0.456807
\(414\) −8.35743 −0.410745
\(415\) 1.67954 0.0824453
\(416\) −42.1841 −2.06825
\(417\) −25.7824 −1.26257
\(418\) −34.9477 −1.70935
\(419\) −6.62465 −0.323636 −0.161818 0.986821i \(-0.551736\pi\)
−0.161818 + 0.986821i \(0.551736\pi\)
\(420\) 2.02360 0.0987414
\(421\) 37.2732 1.81658 0.908292 0.418337i \(-0.137387\pi\)
0.908292 + 0.418337i \(0.137387\pi\)
\(422\) −10.2032 −0.496683
\(423\) 11.9053 0.578854
\(424\) −4.20934 −0.204424
\(425\) 3.59235 0.174255
\(426\) 25.5531 1.23805
\(427\) −5.14011 −0.248747
\(428\) 3.93814 0.190357
\(429\) −31.6861 −1.52982
\(430\) −21.1030 −1.01768
\(431\) −26.5067 −1.27678 −0.638390 0.769713i \(-0.720399\pi\)
−0.638390 + 0.769713i \(0.720399\pi\)
\(432\) 26.6354 1.28150
\(433\) −35.0450 −1.68416 −0.842079 0.539355i \(-0.818668\pi\)
−0.842079 + 0.539355i \(0.818668\pi\)
\(434\) 16.2772 0.781329
\(435\) 0.961653 0.0461077
\(436\) −13.5998 −0.651311
\(437\) 17.0409 0.815176
\(438\) 13.6293 0.651233
\(439\) −10.8227 −0.516541 −0.258270 0.966073i \(-0.583153\pi\)
−0.258270 + 0.966073i \(0.583153\pi\)
\(440\) −3.59938 −0.171594
\(441\) −1.22328 −0.0582516
\(442\) 40.2196 1.91305
\(443\) −9.85659 −0.468301 −0.234150 0.972200i \(-0.575231\pi\)
−0.234150 + 0.972200i \(0.575231\pi\)
\(444\) 17.8904 0.849040
\(445\) −13.5816 −0.643828
\(446\) −47.3481 −2.24200
\(447\) −2.47652 −0.117136
\(448\) 3.79272 0.179189
\(449\) −40.7090 −1.92118 −0.960589 0.277972i \(-0.910338\pi\)
−0.960589 + 0.277972i \(0.910338\pi\)
\(450\) −2.29448 −0.108163
\(451\) −2.58756 −0.121844
\(452\) −7.43342 −0.349639
\(453\) 21.3349 1.00240
\(454\) 16.3237 0.766107
\(455\) 5.96900 0.279831
\(456\) −5.63614 −0.263936
\(457\) −0.252709 −0.0118212 −0.00591061 0.999983i \(-0.501881\pi\)
−0.00591061 + 0.999983i \(0.501881\pi\)
\(458\) 1.87567 0.0876445
\(459\) −20.2227 −0.943914
\(460\) −5.52973 −0.257825
\(461\) −35.2872 −1.64349 −0.821745 0.569855i \(-0.806999\pi\)
−0.821745 + 0.569855i \(0.806999\pi\)
\(462\) 9.95691 0.463238
\(463\) 6.43317 0.298975 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(464\) 3.41358 0.158471
\(465\) 11.5673 0.536419
\(466\) −45.2705 −2.09712
\(467\) −7.70547 −0.356567 −0.178283 0.983979i \(-0.557054\pi\)
−0.178283 + 0.983979i \(0.557054\pi\)
\(468\) −11.0852 −0.512413
\(469\) −10.7240 −0.495187
\(470\) 18.2545 0.842017
\(471\) 26.2144 1.20789
\(472\) −8.39029 −0.386194
\(473\) −44.8069 −2.06022
\(474\) 3.43160 0.157618
\(475\) 4.67846 0.214663
\(476\) −5.45373 −0.249971
\(477\) −5.69734 −0.260863
\(478\) 3.49630 0.159917
\(479\) −27.3454 −1.24944 −0.624722 0.780847i \(-0.714788\pi\)
−0.624722 + 0.780847i \(0.714788\pi\)
\(480\) 9.42012 0.429968
\(481\) 52.7713 2.40616
\(482\) 41.9495 1.91075
\(483\) −4.85510 −0.220915
\(484\) 7.37897 0.335408
\(485\) 2.51699 0.114291
\(486\) 22.0916 1.00210
\(487\) 2.57448 0.116661 0.0583305 0.998297i \(-0.481422\pi\)
0.0583305 + 0.998297i \(0.481422\pi\)
\(488\) −4.64560 −0.210296
\(489\) 30.7592 1.39098
\(490\) −1.87567 −0.0847343
\(491\) −9.53520 −0.430318 −0.215159 0.976579i \(-0.569027\pi\)
−0.215159 + 0.976579i \(0.569027\pi\)
\(492\) 1.31479 0.0592753
\(493\) −2.59172 −0.116725
\(494\) 52.3796 2.35667
\(495\) −4.87175 −0.218969
\(496\) 41.0603 1.84366
\(497\) −10.2206 −0.458457
\(498\) −4.19910 −0.188166
\(499\) 4.30431 0.192687 0.0963436 0.995348i \(-0.469285\pi\)
0.0963436 + 0.995348i \(0.469285\pi\)
\(500\) −1.51815 −0.0678937
\(501\) −27.2720 −1.21842
\(502\) −24.7624 −1.10520
\(503\) −5.26391 −0.234706 −0.117353 0.993090i \(-0.537441\pi\)
−0.117353 + 0.993090i \(0.537441\pi\)
\(504\) −1.10559 −0.0492471
\(505\) 8.19186 0.364533
\(506\) −27.2085 −1.20957
\(507\) 30.1630 1.33959
\(508\) −25.9942 −1.15331
\(509\) 30.6866 1.36016 0.680079 0.733138i \(-0.261945\pi\)
0.680079 + 0.733138i \(0.261945\pi\)
\(510\) −8.98143 −0.397704
\(511\) −5.45139 −0.241155
\(512\) 24.8860 1.09982
\(513\) −26.3368 −1.16280
\(514\) 49.5694 2.18641
\(515\) −9.58693 −0.422451
\(516\) 22.7672 1.00227
\(517\) 38.7588 1.70461
\(518\) −16.5826 −0.728598
\(519\) −21.0818 −0.925387
\(520\) 5.39474 0.236575
\(521\) 8.23917 0.360965 0.180482 0.983578i \(-0.442234\pi\)
0.180482 + 0.983578i \(0.442234\pi\)
\(522\) 1.65536 0.0724533
\(523\) −27.1826 −1.18861 −0.594305 0.804239i \(-0.702573\pi\)
−0.594305 + 0.804239i \(0.702573\pi\)
\(524\) 10.3933 0.454035
\(525\) −1.33294 −0.0581741
\(526\) 16.8628 0.735254
\(527\) −31.1746 −1.35799
\(528\) 25.1170 1.09308
\(529\) −9.73284 −0.423167
\(530\) −8.73580 −0.379459
\(531\) −11.3563 −0.492819
\(532\) −7.10261 −0.307937
\(533\) 3.87824 0.167985
\(534\) 33.9560 1.46942
\(535\) −2.59404 −0.112150
\(536\) −9.69225 −0.418641
\(537\) 12.4865 0.538832
\(538\) 53.3677 2.30085
\(539\) −3.98252 −0.171539
\(540\) 8.54622 0.367771
\(541\) 6.27326 0.269708 0.134854 0.990865i \(-0.456943\pi\)
0.134854 + 0.990865i \(0.456943\pi\)
\(542\) 6.89371 0.296110
\(543\) 24.5843 1.05501
\(544\) −25.3879 −1.08850
\(545\) 8.95812 0.383724
\(546\) −14.9234 −0.638663
\(547\) 13.9040 0.594494 0.297247 0.954801i \(-0.403932\pi\)
0.297247 + 0.954801i \(0.403932\pi\)
\(548\) 15.8925 0.678893
\(549\) −6.28781 −0.268357
\(550\) −7.46991 −0.318518
\(551\) −3.37530 −0.143793
\(552\) −4.38800 −0.186766
\(553\) −1.37256 −0.0583670
\(554\) −9.81195 −0.416870
\(555\) −11.7843 −0.500217
\(556\) −29.3649 −1.24535
\(557\) 26.6647 1.12982 0.564910 0.825153i \(-0.308911\pi\)
0.564910 + 0.825153i \(0.308911\pi\)
\(558\) 19.9116 0.842924
\(559\) 67.1566 2.84042
\(560\) −4.73152 −0.199943
\(561\) −19.0698 −0.805129
\(562\) 32.4175 1.36745
\(563\) 44.4070 1.87153 0.935766 0.352623i \(-0.114710\pi\)
0.935766 + 0.352623i \(0.114710\pi\)
\(564\) −19.6941 −0.829271
\(565\) 4.89637 0.205992
\(566\) −22.0148 −0.925352
\(567\) 3.83373 0.161002
\(568\) −9.23731 −0.387589
\(569\) −40.6265 −1.70315 −0.851576 0.524232i \(-0.824353\pi\)
−0.851576 + 0.524232i \(0.824353\pi\)
\(570\) −11.6969 −0.489928
\(571\) −12.9453 −0.541745 −0.270872 0.962615i \(-0.587312\pi\)
−0.270872 + 0.962615i \(0.587312\pi\)
\(572\) −36.0890 −1.50896
\(573\) −26.8867 −1.12321
\(574\) −1.21868 −0.0508668
\(575\) 3.64241 0.151899
\(576\) 4.63957 0.193315
\(577\) −15.9248 −0.662957 −0.331478 0.943463i \(-0.607547\pi\)
−0.331478 + 0.943463i \(0.607547\pi\)
\(578\) −7.68086 −0.319482
\(579\) −17.0497 −0.708561
\(580\) 1.09528 0.0454789
\(581\) 1.67954 0.0696790
\(582\) −6.29286 −0.260847
\(583\) −18.5483 −0.768192
\(584\) −4.92693 −0.203878
\(585\) 7.30178 0.301891
\(586\) 38.2611 1.58055
\(587\) 48.2730 1.99244 0.996220 0.0868715i \(-0.0276870\pi\)
0.996220 + 0.0868715i \(0.0276870\pi\)
\(588\) 2.02360 0.0834517
\(589\) −40.5999 −1.67289
\(590\) −17.4127 −0.716868
\(591\) −11.5915 −0.476812
\(592\) −41.8308 −1.71924
\(593\) −20.7831 −0.853459 −0.426730 0.904379i \(-0.640334\pi\)
−0.426730 + 0.904379i \(0.640334\pi\)
\(594\) 42.0509 1.72537
\(595\) 3.59235 0.147272
\(596\) −2.82064 −0.115538
\(597\) 25.8532 1.05810
\(598\) 40.7801 1.66762
\(599\) −26.1916 −1.07016 −0.535080 0.844801i \(-0.679719\pi\)
−0.535080 + 0.844801i \(0.679719\pi\)
\(600\) −1.20470 −0.0491816
\(601\) 27.9876 1.14164 0.570819 0.821076i \(-0.306626\pi\)
0.570819 + 0.821076i \(0.306626\pi\)
\(602\) −21.1030 −0.860093
\(603\) −13.1185 −0.534225
\(604\) 24.2995 0.988731
\(605\) −4.86050 −0.197607
\(606\) −20.4809 −0.831979
\(607\) 10.0883 0.409473 0.204737 0.978817i \(-0.434366\pi\)
0.204737 + 0.978817i \(0.434366\pi\)
\(608\) −33.0636 −1.34091
\(609\) 0.961653 0.0389681
\(610\) −9.64117 −0.390359
\(611\) −58.0917 −2.35014
\(612\) −6.67146 −0.269678
\(613\) 5.68666 0.229682 0.114841 0.993384i \(-0.463364\pi\)
0.114841 + 0.993384i \(0.463364\pi\)
\(614\) −23.6542 −0.954605
\(615\) −0.866048 −0.0349224
\(616\) −3.59938 −0.145023
\(617\) 48.2983 1.94441 0.972207 0.234122i \(-0.0752215\pi\)
0.972207 + 0.234122i \(0.0752215\pi\)
\(618\) 23.9688 0.964166
\(619\) −20.3188 −0.816682 −0.408341 0.912830i \(-0.633892\pi\)
−0.408341 + 0.912830i \(0.633892\pi\)
\(620\) 13.1746 0.529103
\(621\) −20.5045 −0.822815
\(622\) −17.8113 −0.714170
\(623\) −13.5816 −0.544134
\(624\) −37.6454 −1.50702
\(625\) 1.00000 0.0400000
\(626\) −11.9969 −0.479491
\(627\) −24.8354 −0.991830
\(628\) 29.8569 1.19142
\(629\) 31.7596 1.26634
\(630\) −2.29448 −0.0914142
\(631\) −7.50510 −0.298773 −0.149387 0.988779i \(-0.547730\pi\)
−0.149387 + 0.988779i \(0.547730\pi\)
\(632\) −1.24051 −0.0493447
\(633\) −7.25082 −0.288194
\(634\) −25.5657 −1.01534
\(635\) 17.1223 0.679478
\(636\) 9.42474 0.373715
\(637\) 5.96900 0.236501
\(638\) 5.38921 0.213361
\(639\) −12.5027 −0.494599
\(640\) −7.02050 −0.277510
\(641\) −27.7754 −1.09706 −0.548532 0.836130i \(-0.684813\pi\)
−0.548532 + 0.836130i \(0.684813\pi\)
\(642\) 6.48550 0.255962
\(643\) 39.1522 1.54401 0.772006 0.635615i \(-0.219253\pi\)
0.772006 + 0.635615i \(0.219253\pi\)
\(644\) −5.52973 −0.217902
\(645\) −14.9967 −0.590495
\(646\) 31.5239 1.24029
\(647\) −20.5738 −0.808841 −0.404421 0.914573i \(-0.632527\pi\)
−0.404421 + 0.914573i \(0.632527\pi\)
\(648\) 3.46490 0.136114
\(649\) −36.9715 −1.45126
\(650\) 11.1959 0.439139
\(651\) 11.5673 0.453357
\(652\) 35.0332 1.37201
\(653\) 11.6861 0.457311 0.228655 0.973507i \(-0.426567\pi\)
0.228655 + 0.973507i \(0.426567\pi\)
\(654\) −22.3967 −0.875779
\(655\) −6.84606 −0.267498
\(656\) −3.07421 −0.120028
\(657\) −6.66859 −0.260166
\(658\) 18.2545 0.711634
\(659\) 6.77164 0.263785 0.131893 0.991264i \(-0.457895\pi\)
0.131893 + 0.991264i \(0.457895\pi\)
\(660\) 8.05902 0.313697
\(661\) 41.0778 1.59774 0.798870 0.601503i \(-0.205431\pi\)
0.798870 + 0.601503i \(0.205431\pi\)
\(662\) −7.12881 −0.277069
\(663\) 28.5818 1.11003
\(664\) 1.51796 0.0589081
\(665\) 4.67846 0.181423
\(666\) −20.2852 −0.786037
\(667\) −2.62783 −0.101750
\(668\) −31.0615 −1.20181
\(669\) −33.6477 −1.30089
\(670\) −20.1147 −0.777097
\(671\) −20.4706 −0.790259
\(672\) 9.42012 0.363389
\(673\) −11.9457 −0.460474 −0.230237 0.973135i \(-0.573950\pi\)
−0.230237 + 0.973135i \(0.573950\pi\)
\(674\) 21.4856 0.827594
\(675\) −5.62936 −0.216674
\(676\) 34.3542 1.32132
\(677\) −41.9092 −1.61070 −0.805351 0.592799i \(-0.798023\pi\)
−0.805351 + 0.592799i \(0.798023\pi\)
\(678\) −12.2417 −0.470138
\(679\) 2.51699 0.0965933
\(680\) 3.24674 0.124507
\(681\) 11.6003 0.444525
\(682\) 64.8242 2.48225
\(683\) −16.3476 −0.625522 −0.312761 0.949832i \(-0.601254\pi\)
−0.312761 + 0.949832i \(0.601254\pi\)
\(684\) −8.68850 −0.332213
\(685\) −10.4683 −0.399974
\(686\) −1.87567 −0.0716135
\(687\) 1.33294 0.0508547
\(688\) −53.2338 −2.02952
\(689\) 27.8002 1.05910
\(690\) −9.10658 −0.346682
\(691\) −15.6603 −0.595746 −0.297873 0.954605i \(-0.596277\pi\)
−0.297873 + 0.954605i \(0.596277\pi\)
\(692\) −24.0111 −0.912766
\(693\) −4.87175 −0.185063
\(694\) 29.4532 1.11803
\(695\) 19.3425 0.733704
\(696\) 0.869135 0.0329445
\(697\) 2.33406 0.0884088
\(698\) 17.3773 0.657742
\(699\) −32.1712 −1.21683
\(700\) −1.51815 −0.0573807
\(701\) −2.99269 −0.113032 −0.0565161 0.998402i \(-0.517999\pi\)
−0.0565161 + 0.998402i \(0.517999\pi\)
\(702\) −63.0258 −2.37876
\(703\) 41.3618 1.55999
\(704\) 15.1046 0.569276
\(705\) 12.9724 0.488570
\(706\) −18.7622 −0.706125
\(707\) 8.19186 0.308086
\(708\) 18.7859 0.706017
\(709\) 15.1725 0.569817 0.284908 0.958555i \(-0.408037\pi\)
0.284908 + 0.958555i \(0.408037\pi\)
\(710\) −19.1705 −0.719457
\(711\) −1.67902 −0.0629683
\(712\) −12.2749 −0.460022
\(713\) −31.6090 −1.18377
\(714\) −8.98143 −0.336122
\(715\) 23.7717 0.889011
\(716\) 14.2215 0.531483
\(717\) 2.48463 0.0927901
\(718\) 16.4710 0.614692
\(719\) 41.4674 1.54647 0.773236 0.634119i \(-0.218637\pi\)
0.773236 + 0.634119i \(0.218637\pi\)
\(720\) −5.78799 −0.215706
\(721\) −9.58693 −0.357036
\(722\) 5.41701 0.201600
\(723\) 29.8112 1.10869
\(724\) 28.0003 1.04062
\(725\) −0.721455 −0.0267942
\(726\) 12.1520 0.451002
\(727\) −37.3677 −1.38589 −0.692946 0.720989i \(-0.743688\pi\)
−0.692946 + 0.720989i \(0.743688\pi\)
\(728\) 5.39474 0.199942
\(729\) 27.2005 1.00742
\(730\) −10.2250 −0.378445
\(731\) 40.4172 1.49488
\(732\) 10.4015 0.384451
\(733\) 21.9432 0.810491 0.405245 0.914208i \(-0.367186\pi\)
0.405245 + 0.914208i \(0.367186\pi\)
\(734\) 4.42029 0.163156
\(735\) −1.33294 −0.0491661
\(736\) −25.7416 −0.948850
\(737\) −42.7085 −1.57319
\(738\) −1.49079 −0.0548768
\(739\) −46.7710 −1.72050 −0.860250 0.509872i \(-0.829693\pi\)
−0.860250 + 0.509872i \(0.829693\pi\)
\(740\) −13.4218 −0.493395
\(741\) 37.2233 1.36743
\(742\) −8.73580 −0.320701
\(743\) −43.4227 −1.59303 −0.796513 0.604622i \(-0.793324\pi\)
−0.796513 + 0.604622i \(0.793324\pi\)
\(744\) 10.4544 0.383277
\(745\) 1.85795 0.0680699
\(746\) −14.4965 −0.530756
\(747\) 2.05455 0.0751721
\(748\) −21.7196 −0.794148
\(749\) −2.59404 −0.0947842
\(750\) −2.50015 −0.0912926
\(751\) 41.2913 1.50674 0.753371 0.657596i \(-0.228426\pi\)
0.753371 + 0.657596i \(0.228426\pi\)
\(752\) 46.0482 1.67921
\(753\) −17.5972 −0.641279
\(754\) −8.07733 −0.294159
\(755\) −16.0060 −0.582517
\(756\) 8.54622 0.310823
\(757\) 50.2207 1.82530 0.912652 0.408738i \(-0.134031\pi\)
0.912652 + 0.408738i \(0.134031\pi\)
\(758\) −8.62912 −0.313424
\(759\) −19.3355 −0.701836
\(760\) 4.22836 0.153379
\(761\) −53.1491 −1.92666 −0.963328 0.268328i \(-0.913529\pi\)
−0.963328 + 0.268328i \(0.913529\pi\)
\(762\) −42.8084 −1.55078
\(763\) 8.95812 0.324306
\(764\) −30.6226 −1.10789
\(765\) 4.39447 0.158882
\(766\) −33.9384 −1.22624
\(767\) 55.4128 2.00084
\(768\) 27.6632 0.998210
\(769\) 17.9299 0.646567 0.323284 0.946302i \(-0.395213\pi\)
0.323284 + 0.946302i \(0.395213\pi\)
\(770\) −7.46991 −0.269197
\(771\) 35.2262 1.26864
\(772\) −19.4188 −0.698898
\(773\) 25.3712 0.912538 0.456269 0.889842i \(-0.349185\pi\)
0.456269 + 0.889842i \(0.349185\pi\)
\(774\) −25.8149 −0.927898
\(775\) −8.67804 −0.311724
\(776\) 2.27484 0.0816620
\(777\) −11.7843 −0.422761
\(778\) 54.0774 1.93877
\(779\) 3.03974 0.108910
\(780\) −12.0789 −0.432492
\(781\) −40.7038 −1.45650
\(782\) 24.5429 0.877651
\(783\) 4.06133 0.145140
\(784\) −4.73152 −0.168983
\(785\) −19.6666 −0.701933
\(786\) 17.1162 0.610514
\(787\) 25.1792 0.897540 0.448770 0.893647i \(-0.351862\pi\)
0.448770 + 0.893647i \(0.351862\pi\)
\(788\) −13.2022 −0.470309
\(789\) 11.9835 0.426622
\(790\) −2.57446 −0.0915953
\(791\) 4.89637 0.174095
\(792\) −4.40306 −0.156456
\(793\) 30.6813 1.08953
\(794\) −59.0889 −2.09699
\(795\) −6.20804 −0.220177
\(796\) 29.4456 1.04367
\(797\) −4.44534 −0.157462 −0.0787310 0.996896i \(-0.525087\pi\)
−0.0787310 + 0.996896i \(0.525087\pi\)
\(798\) −11.6969 −0.414065
\(799\) −34.9616 −1.23685
\(800\) −7.06720 −0.249863
\(801\) −16.6141 −0.587030
\(802\) −18.6810 −0.659648
\(803\) −21.7103 −0.766139
\(804\) 21.7010 0.765335
\(805\) 3.64241 0.128378
\(806\) −97.1584 −3.42226
\(807\) 37.9254 1.33504
\(808\) 7.40374 0.260463
\(809\) −2.05911 −0.0723945 −0.0361973 0.999345i \(-0.511524\pi\)
−0.0361973 + 0.999345i \(0.511524\pi\)
\(810\) 7.19083 0.252660
\(811\) 31.5492 1.10784 0.553921 0.832569i \(-0.313131\pi\)
0.553921 + 0.832569i \(0.313131\pi\)
\(812\) 1.09528 0.0384367
\(813\) 4.89897 0.171814
\(814\) −66.0407 −2.31472
\(815\) −23.0762 −0.808326
\(816\) −22.6563 −0.793129
\(817\) 52.6369 1.84153
\(818\) 43.6706 1.52691
\(819\) 7.30178 0.255145
\(820\) −0.986387 −0.0344461
\(821\) −16.1075 −0.562156 −0.281078 0.959685i \(-0.590692\pi\)
−0.281078 + 0.959685i \(0.590692\pi\)
\(822\) 26.1724 0.912867
\(823\) −9.34064 −0.325594 −0.162797 0.986660i \(-0.552052\pi\)
−0.162797 + 0.986660i \(0.552052\pi\)
\(824\) −8.66460 −0.301846
\(825\) −5.30845 −0.184816
\(826\) −17.4127 −0.605864
\(827\) 10.5303 0.366174 0.183087 0.983097i \(-0.441391\pi\)
0.183087 + 0.983097i \(0.441391\pi\)
\(828\) −6.76442 −0.235080
\(829\) 49.2567 1.71075 0.855377 0.518006i \(-0.173325\pi\)
0.855377 + 0.518006i \(0.173325\pi\)
\(830\) 3.15027 0.109347
\(831\) −6.97280 −0.241884
\(832\) −22.6387 −0.784857
\(833\) 3.59235 0.124468
\(834\) −48.3593 −1.67454
\(835\) 20.4601 0.708051
\(836\) −28.2863 −0.978303
\(837\) 48.8518 1.68857
\(838\) −12.4257 −0.429238
\(839\) 34.3705 1.18660 0.593300 0.804981i \(-0.297825\pi\)
0.593300 + 0.804981i \(0.297825\pi\)
\(840\) −1.20470 −0.0415660
\(841\) −28.4795 −0.982052
\(842\) 69.9123 2.40934
\(843\) 23.0373 0.793447
\(844\) −8.25834 −0.284264
\(845\) −22.6290 −0.778461
\(846\) 22.3304 0.767735
\(847\) −4.86050 −0.167009
\(848\) −22.0367 −0.756743
\(849\) −15.6447 −0.536924
\(850\) 6.73808 0.231114
\(851\) 32.2021 1.10388
\(852\) 20.6824 0.708567
\(853\) 12.3159 0.421689 0.210845 0.977520i \(-0.432379\pi\)
0.210845 + 0.977520i \(0.432379\pi\)
\(854\) −9.64117 −0.329914
\(855\) 5.72309 0.195725
\(856\) −2.34448 −0.0801326
\(857\) 6.74722 0.230481 0.115240 0.993338i \(-0.463236\pi\)
0.115240 + 0.993338i \(0.463236\pi\)
\(858\) −59.4328 −2.02900
\(859\) 42.2635 1.44201 0.721006 0.692929i \(-0.243680\pi\)
0.721006 + 0.692929i \(0.243680\pi\)
\(860\) −17.0805 −0.582441
\(861\) −0.866048 −0.0295148
\(862\) −49.7178 −1.69340
\(863\) −43.1825 −1.46995 −0.734974 0.678095i \(-0.762806\pi\)
−0.734974 + 0.678095i \(0.762806\pi\)
\(864\) 39.7838 1.35347
\(865\) 15.8160 0.537762
\(866\) −65.7331 −2.23370
\(867\) −5.45835 −0.185375
\(868\) 13.1746 0.447174
\(869\) −5.46623 −0.185429
\(870\) 1.80375 0.0611527
\(871\) 64.0114 2.16894
\(872\) 8.09629 0.274175
\(873\) 3.07899 0.104208
\(874\) 31.9631 1.08117
\(875\) 1.00000 0.0338062
\(876\) 11.0314 0.372717
\(877\) −18.3276 −0.618881 −0.309440 0.950919i \(-0.600142\pi\)
−0.309440 + 0.950919i \(0.600142\pi\)
\(878\) −20.2999 −0.685089
\(879\) 27.1900 0.917097
\(880\) −18.8434 −0.635211
\(881\) −17.9168 −0.603631 −0.301816 0.953366i \(-0.597593\pi\)
−0.301816 + 0.953366i \(0.597593\pi\)
\(882\) −2.29448 −0.0772591
\(883\) 18.5031 0.622680 0.311340 0.950299i \(-0.399222\pi\)
0.311340 + 0.950299i \(0.399222\pi\)
\(884\) 32.5534 1.09489
\(885\) −12.3742 −0.415954
\(886\) −18.4877 −0.621108
\(887\) −13.6331 −0.457754 −0.228877 0.973455i \(-0.573505\pi\)
−0.228877 + 0.973455i \(0.573505\pi\)
\(888\) −10.6506 −0.357411
\(889\) 17.1223 0.574264
\(890\) −25.4746 −0.853910
\(891\) 15.2679 0.511495
\(892\) −38.3231 −1.28315
\(893\) −45.5319 −1.52367
\(894\) −4.64515 −0.155357
\(895\) −9.36766 −0.313126
\(896\) −7.02050 −0.234538
\(897\) 28.9801 0.967617
\(898\) −76.3569 −2.54806
\(899\) 6.26081 0.208810
\(900\) −1.85713 −0.0619042
\(901\) 16.7311 0.557394
\(902\) −4.85343 −0.161601
\(903\) −14.9967 −0.499059
\(904\) 4.42530 0.147183
\(905\) −18.4437 −0.613089
\(906\) 40.0174 1.32949
\(907\) 8.76323 0.290978 0.145489 0.989360i \(-0.453524\pi\)
0.145489 + 0.989360i \(0.453524\pi\)
\(908\) 13.2122 0.438462
\(909\) 10.0210 0.332374
\(910\) 11.1959 0.371140
\(911\) 34.9953 1.15945 0.579723 0.814814i \(-0.303161\pi\)
0.579723 + 0.814814i \(0.303161\pi\)
\(912\) −29.5062 −0.977048
\(913\) 6.68881 0.221367
\(914\) −0.473999 −0.0156785
\(915\) −6.85144 −0.226501
\(916\) 1.51815 0.0501611
\(917\) −6.84606 −0.226077
\(918\) −37.9311 −1.25191
\(919\) −31.5112 −1.03946 −0.519729 0.854331i \(-0.673967\pi\)
−0.519729 + 0.854331i \(0.673967\pi\)
\(920\) 3.29199 0.108534
\(921\) −16.8097 −0.553898
\(922\) −66.1873 −2.17976
\(923\) 61.0068 2.00806
\(924\) 8.05902 0.265122
\(925\) 8.84089 0.290687
\(926\) 12.0665 0.396531
\(927\) −11.7275 −0.385183
\(928\) 5.09867 0.167372
\(929\) −23.0321 −0.755657 −0.377829 0.925876i \(-0.623329\pi\)
−0.377829 + 0.925876i \(0.623329\pi\)
\(930\) 21.6964 0.711453
\(931\) 4.67846 0.153330
\(932\) −36.6415 −1.20023
\(933\) −12.6575 −0.414389
\(934\) −14.4529 −0.472915
\(935\) 14.3066 0.467877
\(936\) 6.59930 0.215705
\(937\) −7.03558 −0.229842 −0.114921 0.993375i \(-0.536662\pi\)
−0.114921 + 0.993375i \(0.536662\pi\)
\(938\) −20.1147 −0.656767
\(939\) −8.52549 −0.278219
\(940\) 14.7750 0.481907
\(941\) −17.1579 −0.559332 −0.279666 0.960097i \(-0.590224\pi\)
−0.279666 + 0.960097i \(0.590224\pi\)
\(942\) 49.1696 1.60203
\(943\) 2.36658 0.0770665
\(944\) −43.9247 −1.42963
\(945\) −5.62936 −0.183123
\(946\) −84.0431 −2.73248
\(947\) −23.3577 −0.759024 −0.379512 0.925187i \(-0.623908\pi\)
−0.379512 + 0.925187i \(0.623908\pi\)
\(948\) 2.77750 0.0902089
\(949\) 32.5393 1.05627
\(950\) 8.77527 0.284707
\(951\) −18.1681 −0.589142
\(952\) 3.24674 0.105228
\(953\) 44.7601 1.44992 0.724961 0.688789i \(-0.241858\pi\)
0.724961 + 0.688789i \(0.241858\pi\)
\(954\) −10.6864 −0.345984
\(955\) 20.1710 0.652719
\(956\) 2.82987 0.0915246
\(957\) 3.82981 0.123800
\(958\) −51.2911 −1.65714
\(959\) −10.4683 −0.338040
\(960\) 5.05545 0.163164
\(961\) 44.3083 1.42930
\(962\) 98.9817 3.19130
\(963\) −3.17325 −0.102256
\(964\) 33.9535 1.09357
\(965\) 12.7911 0.411760
\(966\) −9.10658 −0.292999
\(967\) −8.91431 −0.286665 −0.143332 0.989675i \(-0.545782\pi\)
−0.143332 + 0.989675i \(0.545782\pi\)
\(968\) −4.39288 −0.141193
\(969\) 22.4023 0.719664
\(970\) 4.72105 0.151584
\(971\) −52.9146 −1.69811 −0.849056 0.528303i \(-0.822829\pi\)
−0.849056 + 0.528303i \(0.822829\pi\)
\(972\) 17.8807 0.573525
\(973\) 19.3425 0.620093
\(974\) 4.82889 0.154728
\(975\) 7.95630 0.254805
\(976\) −24.3205 −0.778481
\(977\) 58.9420 1.88572 0.942861 0.333186i \(-0.108124\pi\)
0.942861 + 0.333186i \(0.108124\pi\)
\(978\) 57.6941 1.84485
\(979\) −54.0889 −1.72869
\(980\) −1.51815 −0.0484955
\(981\) 10.9583 0.349872
\(982\) −17.8849 −0.570731
\(983\) 2.32910 0.0742869 0.0371434 0.999310i \(-0.488174\pi\)
0.0371434 + 0.999310i \(0.488174\pi\)
\(984\) −0.782728 −0.0249525
\(985\) 8.69625 0.277086
\(986\) −4.86122 −0.154813
\(987\) 12.9724 0.412917
\(988\) 42.3955 1.34878
\(989\) 40.9803 1.30310
\(990\) −9.13782 −0.290419
\(991\) 17.4309 0.553710 0.276855 0.960912i \(-0.410708\pi\)
0.276855 + 0.960912i \(0.410708\pi\)
\(992\) 61.3294 1.94721
\(993\) −5.06605 −0.160766
\(994\) −19.1705 −0.608052
\(995\) −19.3957 −0.614886
\(996\) −3.39871 −0.107692
\(997\) 2.64198 0.0836724 0.0418362 0.999124i \(-0.486679\pi\)
0.0418362 + 0.999124i \(0.486679\pi\)
\(998\) 8.07347 0.255561
\(999\) −49.7686 −1.57461
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 \(a_p\))