Properties

Label 8027.2.a.f.1.17
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +O(q^{10})\) \(q-2.38066 q^{2} +0.526357 q^{3} +3.66755 q^{4} -2.52733 q^{5} -1.25308 q^{6} +3.59846 q^{7} -3.96986 q^{8} -2.72295 q^{9} +6.01672 q^{10} +0.148692 q^{11} +1.93044 q^{12} -0.823438 q^{13} -8.56671 q^{14} -1.33028 q^{15} +2.11581 q^{16} -7.17794 q^{17} +6.48242 q^{18} -3.75432 q^{19} -9.26910 q^{20} +1.89408 q^{21} -0.353985 q^{22} +1.00000 q^{23} -2.08957 q^{24} +1.38740 q^{25} +1.96033 q^{26} -3.01232 q^{27} +13.1975 q^{28} -8.30713 q^{29} +3.16694 q^{30} -6.30144 q^{31} +2.90271 q^{32} +0.0782650 q^{33} +17.0882 q^{34} -9.09450 q^{35} -9.98654 q^{36} +7.50019 q^{37} +8.93776 q^{38} -0.433423 q^{39} +10.0332 q^{40} +2.30789 q^{41} -4.50915 q^{42} -7.76200 q^{43} +0.545334 q^{44} +6.88179 q^{45} -2.38066 q^{46} -12.7353 q^{47} +1.11367 q^{48} +5.94892 q^{49} -3.30292 q^{50} -3.77816 q^{51} -3.02000 q^{52} -6.43656 q^{53} +7.17130 q^{54} -0.375793 q^{55} -14.2854 q^{56} -1.97611 q^{57} +19.7765 q^{58} -5.91991 q^{59} -4.87886 q^{60} +11.6427 q^{61} +15.0016 q^{62} -9.79842 q^{63} -11.1420 q^{64} +2.08110 q^{65} -0.186322 q^{66} -8.93362 q^{67} -26.3254 q^{68} +0.526357 q^{69} +21.6509 q^{70} -11.5173 q^{71} +10.8097 q^{72} +2.53070 q^{73} -17.8554 q^{74} +0.730267 q^{75} -13.7691 q^{76} +0.535062 q^{77} +1.03183 q^{78} +8.17168 q^{79} -5.34734 q^{80} +6.58329 q^{81} -5.49431 q^{82} +0.954879 q^{83} +6.94661 q^{84} +18.1410 q^{85} +18.4787 q^{86} -4.37252 q^{87} -0.590286 q^{88} -4.90448 q^{89} -16.3832 q^{90} -2.96311 q^{91} +3.66755 q^{92} -3.31681 q^{93} +30.3184 q^{94} +9.48841 q^{95} +1.52786 q^{96} +15.3766 q^{97} -14.1624 q^{98} -0.404880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38066 −1.68338 −0.841691 0.539960i \(-0.818439\pi\)
−0.841691 + 0.539960i \(0.818439\pi\)
\(3\) 0.526357 0.303893 0.151946 0.988389i \(-0.451446\pi\)
0.151946 + 0.988389i \(0.451446\pi\)
\(4\) 3.66755 1.83377
\(5\) −2.52733 −1.13026 −0.565128 0.825003i \(-0.691173\pi\)
−0.565128 + 0.825003i \(0.691173\pi\)
\(6\) −1.25308 −0.511567
\(7\) 3.59846 1.36009 0.680045 0.733170i \(-0.261960\pi\)
0.680045 + 0.733170i \(0.261960\pi\)
\(8\) −3.96986 −1.40356
\(9\) −2.72295 −0.907649
\(10\) 6.01672 1.90265
\(11\) 0.148692 0.0448323 0.0224161 0.999749i \(-0.492864\pi\)
0.0224161 + 0.999749i \(0.492864\pi\)
\(12\) 1.93044 0.557270
\(13\) −0.823438 −0.228381 −0.114190 0.993459i \(-0.536427\pi\)
−0.114190 + 0.993459i \(0.536427\pi\)
\(14\) −8.56671 −2.28955
\(15\) −1.33028 −0.343477
\(16\) 2.11581 0.528952
\(17\) −7.17794 −1.74091 −0.870453 0.492252i \(-0.836174\pi\)
−0.870453 + 0.492252i \(0.836174\pi\)
\(18\) 6.48242 1.52792
\(19\) −3.75432 −0.861300 −0.430650 0.902519i \(-0.641716\pi\)
−0.430650 + 0.902519i \(0.641716\pi\)
\(20\) −9.26910 −2.07263
\(21\) 1.89408 0.413321
\(22\) −0.353985 −0.0754698
\(23\) 1.00000 0.208514
\(24\) −2.08957 −0.426531
\(25\) 1.38740 0.277480
\(26\) 1.96033 0.384452
\(27\) −3.01232 −0.579720
\(28\) 13.1975 2.49410
\(29\) −8.30713 −1.54260 −0.771298 0.636474i \(-0.780392\pi\)
−0.771298 + 0.636474i \(0.780392\pi\)
\(30\) 3.16694 0.578202
\(31\) −6.30144 −1.13177 −0.565886 0.824483i \(-0.691466\pi\)
−0.565886 + 0.824483i \(0.691466\pi\)
\(32\) 2.90271 0.513132
\(33\) 0.0782650 0.0136242
\(34\) 17.0882 2.93061
\(35\) −9.09450 −1.53725
\(36\) −9.98654 −1.66442
\(37\) 7.50019 1.23302 0.616512 0.787345i \(-0.288545\pi\)
0.616512 + 0.787345i \(0.288545\pi\)
\(38\) 8.93776 1.44990
\(39\) −0.433423 −0.0694032
\(40\) 10.0332 1.58638
\(41\) 2.30789 0.360433 0.180216 0.983627i \(-0.442320\pi\)
0.180216 + 0.983627i \(0.442320\pi\)
\(42\) −4.50915 −0.695777
\(43\) −7.76200 −1.18369 −0.591847 0.806051i \(-0.701601\pi\)
−0.591847 + 0.806051i \(0.701601\pi\)
\(44\) 0.545334 0.0822122
\(45\) 6.88179 1.02588
\(46\) −2.38066 −0.351009
\(47\) −12.7353 −1.85763 −0.928817 0.370539i \(-0.879173\pi\)
−0.928817 + 0.370539i \(0.879173\pi\)
\(48\) 1.11367 0.160744
\(49\) 5.94892 0.849845
\(50\) −3.30292 −0.467104
\(51\) −3.77816 −0.529048
\(52\) −3.02000 −0.418798
\(53\) −6.43656 −0.884130 −0.442065 0.896983i \(-0.645754\pi\)
−0.442065 + 0.896983i \(0.645754\pi\)
\(54\) 7.17130 0.975891
\(55\) −0.375793 −0.0506720
\(56\) −14.2854 −1.90897
\(57\) −1.97611 −0.261743
\(58\) 19.7765 2.59678
\(59\) −5.91991 −0.770707 −0.385353 0.922769i \(-0.625920\pi\)
−0.385353 + 0.922769i \(0.625920\pi\)
\(60\) −4.87886 −0.629858
\(61\) 11.6427 1.49070 0.745350 0.666673i \(-0.232282\pi\)
0.745350 + 0.666673i \(0.232282\pi\)
\(62\) 15.0016 1.90520
\(63\) −9.79842 −1.23448
\(64\) −11.1420 −1.39275
\(65\) 2.08110 0.258129
\(66\) −0.186322 −0.0229347
\(67\) −8.93362 −1.09142 −0.545708 0.837976i \(-0.683739\pi\)
−0.545708 + 0.837976i \(0.683739\pi\)
\(68\) −26.3254 −3.19243
\(69\) 0.526357 0.0633660
\(70\) 21.6509 2.58778
\(71\) −11.5173 −1.36685 −0.683427 0.730019i \(-0.739511\pi\)
−0.683427 + 0.730019i \(0.739511\pi\)
\(72\) 10.8097 1.27394
\(73\) 2.53070 0.296196 0.148098 0.988973i \(-0.452685\pi\)
0.148098 + 0.988973i \(0.452685\pi\)
\(74\) −17.8554 −2.07565
\(75\) 0.730267 0.0843240
\(76\) −13.7691 −1.57943
\(77\) 0.535062 0.0609759
\(78\) 1.03183 0.116832
\(79\) 8.17168 0.919386 0.459693 0.888078i \(-0.347959\pi\)
0.459693 + 0.888078i \(0.347959\pi\)
\(80\) −5.34734 −0.597851
\(81\) 6.58329 0.731477
\(82\) −5.49431 −0.606745
\(83\) 0.954879 0.104812 0.0524058 0.998626i \(-0.483311\pi\)
0.0524058 + 0.998626i \(0.483311\pi\)
\(84\) 6.94661 0.757938
\(85\) 18.1410 1.96767
\(86\) 18.4787 1.99261
\(87\) −4.37252 −0.468783
\(88\) −0.590286 −0.0629247
\(89\) −4.90448 −0.519873 −0.259937 0.965626i \(-0.583702\pi\)
−0.259937 + 0.965626i \(0.583702\pi\)
\(90\) −16.3832 −1.72694
\(91\) −2.96311 −0.310618
\(92\) 3.66755 0.382368
\(93\) −3.31681 −0.343937
\(94\) 30.3184 3.12711
\(95\) 9.48841 0.973490
\(96\) 1.52786 0.155937
\(97\) 15.3766 1.56126 0.780630 0.624993i \(-0.214898\pi\)
0.780630 + 0.624993i \(0.214898\pi\)
\(98\) −14.1624 −1.43061
\(99\) −0.404880 −0.0406920
\(100\) 5.08835 0.508835
\(101\) 11.3044 1.12483 0.562416 0.826855i \(-0.309872\pi\)
0.562416 + 0.826855i \(0.309872\pi\)
\(102\) 8.99452 0.890590
\(103\) −2.26848 −0.223520 −0.111760 0.993735i \(-0.535649\pi\)
−0.111760 + 0.993735i \(0.535649\pi\)
\(104\) 3.26894 0.320546
\(105\) −4.78696 −0.467159
\(106\) 15.3233 1.48833
\(107\) 15.6792 1.51577 0.757883 0.652390i \(-0.226234\pi\)
0.757883 + 0.652390i \(0.226234\pi\)
\(108\) −11.0478 −1.06308
\(109\) 11.5832 1.10947 0.554737 0.832026i \(-0.312819\pi\)
0.554737 + 0.832026i \(0.312819\pi\)
\(110\) 0.894636 0.0853002
\(111\) 3.94778 0.374707
\(112\) 7.61364 0.719422
\(113\) 1.53096 0.144021 0.0720105 0.997404i \(-0.477058\pi\)
0.0720105 + 0.997404i \(0.477058\pi\)
\(114\) 4.70446 0.440613
\(115\) −2.52733 −0.235675
\(116\) −30.4668 −2.82877
\(117\) 2.24218 0.207289
\(118\) 14.0933 1.29739
\(119\) −25.8295 −2.36779
\(120\) 5.28103 0.482090
\(121\) −10.9779 −0.997990
\(122\) −27.7174 −2.50942
\(123\) 1.21478 0.109533
\(124\) −23.1108 −2.07541
\(125\) 9.13024 0.816633
\(126\) 23.3267 2.07811
\(127\) −13.2941 −1.17966 −0.589830 0.807527i \(-0.700805\pi\)
−0.589830 + 0.807527i \(0.700805\pi\)
\(128\) 20.7199 1.83139
\(129\) −4.08558 −0.359716
\(130\) −4.95439 −0.434529
\(131\) −11.5503 −1.00916 −0.504578 0.863366i \(-0.668352\pi\)
−0.504578 + 0.863366i \(0.668352\pi\)
\(132\) 0.287041 0.0249837
\(133\) −13.5098 −1.17145
\(134\) 21.2679 1.83727
\(135\) 7.61312 0.655233
\(136\) 28.4954 2.44346
\(137\) 10.2468 0.875441 0.437720 0.899111i \(-0.355786\pi\)
0.437720 + 0.899111i \(0.355786\pi\)
\(138\) −1.25308 −0.106669
\(139\) 22.4477 1.90399 0.951996 0.306111i \(-0.0990278\pi\)
0.951996 + 0.306111i \(0.0990278\pi\)
\(140\) −33.3545 −2.81897
\(141\) −6.70332 −0.564521
\(142\) 27.4188 2.30094
\(143\) −0.122438 −0.0102388
\(144\) −5.76123 −0.480102
\(145\) 20.9949 1.74353
\(146\) −6.02474 −0.498611
\(147\) 3.13126 0.258262
\(148\) 27.5073 2.26109
\(149\) 21.7101 1.77856 0.889278 0.457366i \(-0.151207\pi\)
0.889278 + 0.457366i \(0.151207\pi\)
\(150\) −1.73852 −0.141949
\(151\) −12.4342 −1.01188 −0.505942 0.862568i \(-0.668855\pi\)
−0.505942 + 0.862568i \(0.668855\pi\)
\(152\) 14.9041 1.20889
\(153\) 19.5452 1.58013
\(154\) −1.27380 −0.102646
\(155\) 15.9258 1.27919
\(156\) −1.58960 −0.127270
\(157\) −8.42287 −0.672218 −0.336109 0.941823i \(-0.609111\pi\)
−0.336109 + 0.941823i \(0.609111\pi\)
\(158\) −19.4540 −1.54768
\(159\) −3.38793 −0.268680
\(160\) −7.33611 −0.579970
\(161\) 3.59846 0.283598
\(162\) −15.6726 −1.23135
\(163\) −18.4711 −1.44677 −0.723384 0.690445i \(-0.757415\pi\)
−0.723384 + 0.690445i \(0.757415\pi\)
\(164\) 8.46431 0.660952
\(165\) −0.197802 −0.0153988
\(166\) −2.27324 −0.176438
\(167\) 6.02480 0.466213 0.233106 0.972451i \(-0.425111\pi\)
0.233106 + 0.972451i \(0.425111\pi\)
\(168\) −7.51922 −0.580121
\(169\) −12.3220 −0.947842
\(170\) −43.1876 −3.31234
\(171\) 10.2228 0.781758
\(172\) −28.4675 −2.17063
\(173\) −5.61865 −0.427178 −0.213589 0.976924i \(-0.568515\pi\)
−0.213589 + 0.976924i \(0.568515\pi\)
\(174\) 10.4095 0.789141
\(175\) 4.99250 0.377397
\(176\) 0.314603 0.0237141
\(177\) −3.11599 −0.234212
\(178\) 11.6759 0.875145
\(179\) 10.1063 0.755378 0.377689 0.925932i \(-0.376719\pi\)
0.377689 + 0.925932i \(0.376719\pi\)
\(180\) 25.2393 1.88123
\(181\) 22.3130 1.65851 0.829256 0.558869i \(-0.188765\pi\)
0.829256 + 0.558869i \(0.188765\pi\)
\(182\) 7.05416 0.522889
\(183\) 6.12824 0.453013
\(184\) −3.96986 −0.292662
\(185\) −18.9555 −1.39363
\(186\) 7.89620 0.578977
\(187\) −1.06730 −0.0780487
\(188\) −46.7073 −3.40648
\(189\) −10.8397 −0.788472
\(190\) −22.5887 −1.63876
\(191\) 21.4075 1.54899 0.774497 0.632578i \(-0.218003\pi\)
0.774497 + 0.632578i \(0.218003\pi\)
\(192\) −5.86466 −0.423246
\(193\) 15.7581 1.13429 0.567146 0.823617i \(-0.308047\pi\)
0.567146 + 0.823617i \(0.308047\pi\)
\(194\) −36.6065 −2.62820
\(195\) 1.09540 0.0784434
\(196\) 21.8179 1.55842
\(197\) −7.96751 −0.567662 −0.283831 0.958874i \(-0.591605\pi\)
−0.283831 + 0.958874i \(0.591605\pi\)
\(198\) 0.963882 0.0685001
\(199\) 25.5094 1.80831 0.904157 0.427201i \(-0.140500\pi\)
0.904157 + 0.427201i \(0.140500\pi\)
\(200\) −5.50778 −0.389459
\(201\) −4.70228 −0.331673
\(202\) −26.9120 −1.89352
\(203\) −29.8929 −2.09807
\(204\) −13.8566 −0.970155
\(205\) −5.83281 −0.407381
\(206\) 5.40048 0.376269
\(207\) −2.72295 −0.189258
\(208\) −1.74223 −0.120802
\(209\) −0.558237 −0.0386140
\(210\) 11.3961 0.786407
\(211\) −13.4498 −0.925924 −0.462962 0.886378i \(-0.653213\pi\)
−0.462962 + 0.886378i \(0.653213\pi\)
\(212\) −23.6064 −1.62129
\(213\) −6.06222 −0.415377
\(214\) −37.3269 −2.55161
\(215\) 19.6171 1.33788
\(216\) 11.9585 0.813672
\(217\) −22.6755 −1.53931
\(218\) −27.5758 −1.86767
\(219\) 1.33205 0.0900118
\(220\) −1.37824 −0.0929209
\(221\) 5.91059 0.397589
\(222\) −9.39833 −0.630775
\(223\) −11.4991 −0.770038 −0.385019 0.922909i \(-0.625805\pi\)
−0.385019 + 0.922909i \(0.625805\pi\)
\(224\) 10.4453 0.697905
\(225\) −3.77781 −0.251854
\(226\) −3.64471 −0.242442
\(227\) −20.8312 −1.38261 −0.691307 0.722561i \(-0.742965\pi\)
−0.691307 + 0.722561i \(0.742965\pi\)
\(228\) −7.24749 −0.479977
\(229\) −16.8488 −1.11340 −0.556699 0.830714i \(-0.687932\pi\)
−0.556699 + 0.830714i \(0.687932\pi\)
\(230\) 6.01672 0.396731
\(231\) 0.281634 0.0185301
\(232\) 32.9782 2.16512
\(233\) −1.92536 −0.126134 −0.0630671 0.998009i \(-0.520088\pi\)
−0.0630671 + 0.998009i \(0.520088\pi\)
\(234\) −5.33787 −0.348947
\(235\) 32.1863 2.09960
\(236\) −21.7115 −1.41330
\(237\) 4.30122 0.279395
\(238\) 61.4913 3.98589
\(239\) 14.1583 0.915826 0.457913 0.888997i \(-0.348597\pi\)
0.457913 + 0.888997i \(0.348597\pi\)
\(240\) −2.81461 −0.181682
\(241\) −6.43629 −0.414598 −0.207299 0.978278i \(-0.566467\pi\)
−0.207299 + 0.978278i \(0.566467\pi\)
\(242\) 26.1346 1.68000
\(243\) 12.5021 0.802011
\(244\) 42.7003 2.73361
\(245\) −15.0349 −0.960543
\(246\) −2.89197 −0.184385
\(247\) 3.09145 0.196704
\(248\) 25.0159 1.58851
\(249\) 0.502608 0.0318515
\(250\) −21.7360 −1.37471
\(251\) 0.121232 0.00765208 0.00382604 0.999993i \(-0.498782\pi\)
0.00382604 + 0.999993i \(0.498782\pi\)
\(252\) −35.9362 −2.26377
\(253\) 0.148692 0.00934817
\(254\) 31.6487 1.98582
\(255\) 9.54866 0.597960
\(256\) −27.0430 −1.69019
\(257\) 21.7696 1.35795 0.678976 0.734160i \(-0.262424\pi\)
0.678976 + 0.734160i \(0.262424\pi\)
\(258\) 9.72639 0.605539
\(259\) 26.9891 1.67702
\(260\) 7.63253 0.473349
\(261\) 22.6199 1.40014
\(262\) 27.4974 1.69879
\(263\) −26.9245 −1.66024 −0.830118 0.557587i \(-0.811727\pi\)
−0.830118 + 0.557587i \(0.811727\pi\)
\(264\) −0.310701 −0.0191224
\(265\) 16.2673 0.999293
\(266\) 32.1622 1.97199
\(267\) −2.58151 −0.157986
\(268\) −32.7645 −2.00141
\(269\) −24.9459 −1.52098 −0.760489 0.649351i \(-0.775040\pi\)
−0.760489 + 0.649351i \(0.775040\pi\)
\(270\) −18.1243 −1.10301
\(271\) −4.79701 −0.291397 −0.145699 0.989329i \(-0.546543\pi\)
−0.145699 + 0.989329i \(0.546543\pi\)
\(272\) −15.1871 −0.920855
\(273\) −1.55965 −0.0943945
\(274\) −24.3941 −1.47370
\(275\) 0.206295 0.0124400
\(276\) 1.93044 0.116199
\(277\) 8.37700 0.503325 0.251663 0.967815i \(-0.419023\pi\)
0.251663 + 0.967815i \(0.419023\pi\)
\(278\) −53.4404 −3.20514
\(279\) 17.1585 1.02725
\(280\) 36.1039 2.15762
\(281\) 23.3875 1.39518 0.697591 0.716496i \(-0.254255\pi\)
0.697591 + 0.716496i \(0.254255\pi\)
\(282\) 15.9583 0.950305
\(283\) −4.00799 −0.238250 −0.119125 0.992879i \(-0.538009\pi\)
−0.119125 + 0.992879i \(0.538009\pi\)
\(284\) −42.2403 −2.50650
\(285\) 4.99429 0.295836
\(286\) 0.291484 0.0172358
\(287\) 8.30487 0.490221
\(288\) −7.90393 −0.465743
\(289\) 34.5228 2.03075
\(290\) −49.9817 −2.93502
\(291\) 8.09360 0.474455
\(292\) 9.28146 0.543156
\(293\) −14.7643 −0.862539 −0.431269 0.902223i \(-0.641934\pi\)
−0.431269 + 0.902223i \(0.641934\pi\)
\(294\) −7.45446 −0.434753
\(295\) 14.9616 0.871096
\(296\) −29.7747 −1.73062
\(297\) −0.447907 −0.0259902
\(298\) −51.6843 −2.99399
\(299\) −0.823438 −0.0476206
\(300\) 2.67829 0.154631
\(301\) −27.9312 −1.60993
\(302\) 29.6017 1.70339
\(303\) 5.95016 0.341828
\(304\) −7.94341 −0.455586
\(305\) −29.4250 −1.68487
\(306\) −46.5304 −2.65996
\(307\) 11.4218 0.651879 0.325939 0.945391i \(-0.394319\pi\)
0.325939 + 0.945391i \(0.394319\pi\)
\(308\) 1.96236 0.111816
\(309\) −1.19403 −0.0679260
\(310\) −37.9140 −2.15337
\(311\) −25.4409 −1.44262 −0.721311 0.692612i \(-0.756460\pi\)
−0.721311 + 0.692612i \(0.756460\pi\)
\(312\) 1.72063 0.0974114
\(313\) 11.3398 0.640963 0.320481 0.947255i \(-0.396155\pi\)
0.320481 + 0.947255i \(0.396155\pi\)
\(314\) 20.0520 1.13160
\(315\) 24.7638 1.39528
\(316\) 29.9700 1.68595
\(317\) −1.08207 −0.0607750 −0.0303875 0.999538i \(-0.509674\pi\)
−0.0303875 + 0.999538i \(0.509674\pi\)
\(318\) 8.06552 0.452292
\(319\) −1.23520 −0.0691581
\(320\) 28.1595 1.57416
\(321\) 8.25287 0.460630
\(322\) −8.56671 −0.477404
\(323\) 26.9483 1.49944
\(324\) 24.1445 1.34136
\(325\) −1.14244 −0.0633709
\(326\) 43.9735 2.43546
\(327\) 6.09693 0.337161
\(328\) −9.16203 −0.505888
\(329\) −45.8275 −2.52655
\(330\) 0.470898 0.0259221
\(331\) −32.8450 −1.80533 −0.902663 0.430348i \(-0.858391\pi\)
−0.902663 + 0.430348i \(0.858391\pi\)
\(332\) 3.50207 0.192201
\(333\) −20.4226 −1.11915
\(334\) −14.3430 −0.784814
\(335\) 22.5782 1.23358
\(336\) 4.00750 0.218627
\(337\) 16.1015 0.877102 0.438551 0.898706i \(-0.355492\pi\)
0.438551 + 0.898706i \(0.355492\pi\)
\(338\) 29.3344 1.59558
\(339\) 0.805835 0.0437669
\(340\) 66.5330 3.60826
\(341\) −0.936973 −0.0507399
\(342\) −24.3371 −1.31600
\(343\) −3.78228 −0.204224
\(344\) 30.8141 1.66138
\(345\) −1.33028 −0.0716198
\(346\) 13.3761 0.719104
\(347\) 27.1934 1.45982 0.729910 0.683543i \(-0.239562\pi\)
0.729910 + 0.683543i \(0.239562\pi\)
\(348\) −16.0364 −0.859642
\(349\) −1.00000 −0.0535288
\(350\) −11.8854 −0.635304
\(351\) 2.48045 0.132397
\(352\) 0.431609 0.0230048
\(353\) −5.23971 −0.278882 −0.139441 0.990230i \(-0.544530\pi\)
−0.139441 + 0.990230i \(0.544530\pi\)
\(354\) 7.41811 0.394268
\(355\) 29.1081 1.54490
\(356\) −17.9874 −0.953330
\(357\) −13.5956 −0.719553
\(358\) −24.0596 −1.27159
\(359\) −10.9081 −0.575707 −0.287854 0.957674i \(-0.592942\pi\)
−0.287854 + 0.957674i \(0.592942\pi\)
\(360\) −27.3198 −1.43988
\(361\) −4.90508 −0.258162
\(362\) −53.1197 −2.79191
\(363\) −5.77829 −0.303282
\(364\) −10.8673 −0.569603
\(365\) −6.39592 −0.334777
\(366\) −14.5893 −0.762593
\(367\) 32.1036 1.67579 0.837896 0.545830i \(-0.183786\pi\)
0.837896 + 0.545830i \(0.183786\pi\)
\(368\) 2.11581 0.110294
\(369\) −6.28428 −0.327146
\(370\) 45.1265 2.34602
\(371\) −23.1617 −1.20250
\(372\) −12.1646 −0.630703
\(373\) −19.7458 −1.02240 −0.511199 0.859463i \(-0.670798\pi\)
−0.511199 + 0.859463i \(0.670798\pi\)
\(374\) 2.54088 0.131386
\(375\) 4.80577 0.248169
\(376\) 50.5574 2.60730
\(377\) 6.84041 0.352299
\(378\) 25.8056 1.32730
\(379\) −26.2286 −1.34727 −0.673637 0.739063i \(-0.735269\pi\)
−0.673637 + 0.739063i \(0.735269\pi\)
\(380\) 34.7992 1.78516
\(381\) −6.99745 −0.358490
\(382\) −50.9640 −2.60755
\(383\) 22.6537 1.15755 0.578776 0.815487i \(-0.303531\pi\)
0.578776 + 0.815487i \(0.303531\pi\)
\(384\) 10.9061 0.556547
\(385\) −1.35228 −0.0689184
\(386\) −37.5147 −1.90945
\(387\) 21.1355 1.07438
\(388\) 56.3945 2.86300
\(389\) −32.6874 −1.65732 −0.828660 0.559753i \(-0.810896\pi\)
−0.828660 + 0.559753i \(0.810896\pi\)
\(390\) −2.60778 −0.132050
\(391\) −7.17794 −0.363004
\(392\) −23.6164 −1.19281
\(393\) −6.07959 −0.306675
\(394\) 18.9679 0.955591
\(395\) −20.6525 −1.03914
\(396\) −1.48492 −0.0746199
\(397\) −10.3538 −0.519642 −0.259821 0.965657i \(-0.583664\pi\)
−0.259821 + 0.965657i \(0.583664\pi\)
\(398\) −60.7292 −3.04408
\(399\) −7.11097 −0.355994
\(400\) 2.93547 0.146773
\(401\) 9.42277 0.470550 0.235275 0.971929i \(-0.424401\pi\)
0.235275 + 0.971929i \(0.424401\pi\)
\(402\) 11.1945 0.558332
\(403\) 5.18884 0.258475
\(404\) 41.4595 2.06269
\(405\) −16.6381 −0.826756
\(406\) 71.1648 3.53185
\(407\) 1.11522 0.0552793
\(408\) 14.9988 0.742550
\(409\) 21.3950 1.05791 0.528957 0.848648i \(-0.322583\pi\)
0.528957 + 0.848648i \(0.322583\pi\)
\(410\) 13.8859 0.685778
\(411\) 5.39346 0.266040
\(412\) −8.31975 −0.409885
\(413\) −21.3026 −1.04823
\(414\) 6.48242 0.318593
\(415\) −2.41330 −0.118464
\(416\) −2.39020 −0.117189
\(417\) 11.8155 0.578609
\(418\) 1.32897 0.0650022
\(419\) −13.6194 −0.665349 −0.332675 0.943042i \(-0.607951\pi\)
−0.332675 + 0.943042i \(0.607951\pi\)
\(420\) −17.5564 −0.856664
\(421\) 39.3604 1.91831 0.959154 0.282884i \(-0.0912911\pi\)
0.959154 + 0.282884i \(0.0912911\pi\)
\(422\) 32.0195 1.55868
\(423\) 34.6776 1.68608
\(424\) 25.5523 1.24093
\(425\) −9.95866 −0.483066
\(426\) 14.4321 0.699238
\(427\) 41.8959 2.02749
\(428\) 57.5042 2.77957
\(429\) −0.0644464 −0.00311150
\(430\) −46.7017 −2.25216
\(431\) 12.6374 0.608721 0.304360 0.952557i \(-0.401557\pi\)
0.304360 + 0.952557i \(0.401557\pi\)
\(432\) −6.37348 −0.306644
\(433\) 13.5492 0.651133 0.325567 0.945519i \(-0.394445\pi\)
0.325567 + 0.945519i \(0.394445\pi\)
\(434\) 53.9826 2.59125
\(435\) 11.0508 0.529845
\(436\) 42.4821 2.03452
\(437\) −3.75432 −0.179593
\(438\) −3.17117 −0.151524
\(439\) −29.5329 −1.40953 −0.704763 0.709442i \(-0.748947\pi\)
−0.704763 + 0.709442i \(0.748947\pi\)
\(440\) 1.49185 0.0711211
\(441\) −16.1986 −0.771361
\(442\) −14.0711 −0.669294
\(443\) −18.0063 −0.855503 −0.427752 0.903896i \(-0.640694\pi\)
−0.427752 + 0.903896i \(0.640694\pi\)
\(444\) 14.4787 0.687127
\(445\) 12.3952 0.587590
\(446\) 27.3755 1.29627
\(447\) 11.4272 0.540490
\(448\) −40.0940 −1.89426
\(449\) 1.37881 0.0650699 0.0325349 0.999471i \(-0.489642\pi\)
0.0325349 + 0.999471i \(0.489642\pi\)
\(450\) 8.99369 0.423967
\(451\) 0.343165 0.0161590
\(452\) 5.61489 0.264102
\(453\) −6.54485 −0.307504
\(454\) 49.5920 2.32747
\(455\) 7.48875 0.351078
\(456\) 7.84490 0.367371
\(457\) −10.2483 −0.479396 −0.239698 0.970848i \(-0.577048\pi\)
−0.239698 + 0.970848i \(0.577048\pi\)
\(458\) 40.1112 1.87427
\(459\) 21.6222 1.00924
\(460\) −9.26910 −0.432174
\(461\) −15.5412 −0.723825 −0.361912 0.932212i \(-0.617876\pi\)
−0.361912 + 0.932212i \(0.617876\pi\)
\(462\) −0.670474 −0.0311933
\(463\) 14.6072 0.678852 0.339426 0.940633i \(-0.389767\pi\)
0.339426 + 0.940633i \(0.389767\pi\)
\(464\) −17.5763 −0.815958
\(465\) 8.38267 0.388737
\(466\) 4.58362 0.212332
\(467\) −36.4257 −1.68558 −0.842789 0.538244i \(-0.819088\pi\)
−0.842789 + 0.538244i \(0.819088\pi\)
\(468\) 8.22329 0.380122
\(469\) −32.1473 −1.48442
\(470\) −76.6247 −3.53443
\(471\) −4.43344 −0.204282
\(472\) 23.5012 1.08173
\(473\) −1.15415 −0.0530677
\(474\) −10.2398 −0.470328
\(475\) −5.20874 −0.238993
\(476\) −94.7310 −4.34199
\(477\) 17.5264 0.802480
\(478\) −33.7062 −1.54168
\(479\) 0.704213 0.0321763 0.0160882 0.999871i \(-0.494879\pi\)
0.0160882 + 0.999871i \(0.494879\pi\)
\(480\) −3.86141 −0.176249
\(481\) −6.17594 −0.281599
\(482\) 15.3226 0.697926
\(483\) 1.89408 0.0861834
\(484\) −40.2619 −1.83009
\(485\) −38.8618 −1.76462
\(486\) −29.7633 −1.35009
\(487\) 13.0887 0.593104 0.296552 0.955017i \(-0.404163\pi\)
0.296552 + 0.955017i \(0.404163\pi\)
\(488\) −46.2201 −2.09228
\(489\) −9.72240 −0.439662
\(490\) 35.7929 1.61696
\(491\) 21.3450 0.963286 0.481643 0.876367i \(-0.340040\pi\)
0.481643 + 0.876367i \(0.340040\pi\)
\(492\) 4.45525 0.200858
\(493\) 59.6281 2.68551
\(494\) −7.35969 −0.331128
\(495\) 1.02327 0.0459924
\(496\) −13.3326 −0.598653
\(497\) −41.4446 −1.85904
\(498\) −1.19654 −0.0536182
\(499\) −3.09987 −0.138769 −0.0693846 0.997590i \(-0.522104\pi\)
−0.0693846 + 0.997590i \(0.522104\pi\)
\(500\) 33.4856 1.49752
\(501\) 3.17120 0.141679
\(502\) −0.288612 −0.0128814
\(503\) 7.56887 0.337479 0.168740 0.985661i \(-0.446030\pi\)
0.168740 + 0.985661i \(0.446030\pi\)
\(504\) 38.8984 1.73267
\(505\) −28.5700 −1.27135
\(506\) −0.353985 −0.0157365
\(507\) −6.48575 −0.288042
\(508\) −48.7567 −2.16323
\(509\) 1.98557 0.0880086 0.0440043 0.999031i \(-0.485988\pi\)
0.0440043 + 0.999031i \(0.485988\pi\)
\(510\) −22.7321 −1.00660
\(511\) 9.10662 0.402853
\(512\) 22.9405 1.01384
\(513\) 11.3092 0.499313
\(514\) −51.8261 −2.28595
\(515\) 5.73319 0.252635
\(516\) −14.9841 −0.659637
\(517\) −1.89363 −0.0832819
\(518\) −64.2520 −2.82307
\(519\) −2.95742 −0.129816
\(520\) −8.26168 −0.362299
\(521\) 35.4309 1.55226 0.776129 0.630574i \(-0.217181\pi\)
0.776129 + 0.630574i \(0.217181\pi\)
\(522\) −53.8503 −2.35696
\(523\) 6.60112 0.288647 0.144323 0.989531i \(-0.453899\pi\)
0.144323 + 0.989531i \(0.453899\pi\)
\(524\) −42.3613 −1.85056
\(525\) 2.62784 0.114688
\(526\) 64.0981 2.79481
\(527\) 45.2313 1.97031
\(528\) 0.165594 0.00720654
\(529\) 1.00000 0.0434783
\(530\) −38.7270 −1.68219
\(531\) 16.1196 0.699531
\(532\) −49.5477 −2.14817
\(533\) −1.90041 −0.0823158
\(534\) 6.14569 0.265950
\(535\) −39.6265 −1.71320
\(536\) 35.4652 1.53187
\(537\) 5.31951 0.229554
\(538\) 59.3877 2.56038
\(539\) 0.884555 0.0381005
\(540\) 27.9215 1.20155
\(541\) −13.2356 −0.569044 −0.284522 0.958670i \(-0.591835\pi\)
−0.284522 + 0.958670i \(0.591835\pi\)
\(542\) 11.4200 0.490533
\(543\) 11.7446 0.504009
\(544\) −20.8355 −0.893314
\(545\) −29.2747 −1.25399
\(546\) 3.71301 0.158902
\(547\) 24.9942 1.06867 0.534337 0.845272i \(-0.320561\pi\)
0.534337 + 0.845272i \(0.320561\pi\)
\(548\) 37.5805 1.60536
\(549\) −31.7026 −1.35303
\(550\) −0.491118 −0.0209413
\(551\) 31.1876 1.32864
\(552\) −2.08957 −0.0889379
\(553\) 29.4055 1.25045
\(554\) −19.9428 −0.847289
\(555\) −9.97735 −0.423515
\(556\) 82.3281 3.49149
\(557\) 17.1028 0.724667 0.362333 0.932049i \(-0.381980\pi\)
0.362333 + 0.932049i \(0.381980\pi\)
\(558\) −40.8486 −1.72926
\(559\) 6.39152 0.270333
\(560\) −19.2422 −0.813131
\(561\) −0.561781 −0.0237184
\(562\) −55.6777 −2.34862
\(563\) −22.3885 −0.943561 −0.471780 0.881716i \(-0.656388\pi\)
−0.471780 + 0.881716i \(0.656388\pi\)
\(564\) −24.5847 −1.03520
\(565\) −3.86925 −0.162781
\(566\) 9.54167 0.401066
\(567\) 23.6897 0.994874
\(568\) 45.7222 1.91846
\(569\) −26.7090 −1.11970 −0.559850 0.828594i \(-0.689141\pi\)
−0.559850 + 0.828594i \(0.689141\pi\)
\(570\) −11.8897 −0.498006
\(571\) −6.80257 −0.284679 −0.142339 0.989818i \(-0.545462\pi\)
−0.142339 + 0.989818i \(0.545462\pi\)
\(572\) −0.449049 −0.0187757
\(573\) 11.2680 0.470728
\(574\) −19.7711 −0.825229
\(575\) 1.38740 0.0578585
\(576\) 30.3390 1.26413
\(577\) −9.16556 −0.381567 −0.190784 0.981632i \(-0.561103\pi\)
−0.190784 + 0.981632i \(0.561103\pi\)
\(578\) −82.1871 −3.41853
\(579\) 8.29439 0.344703
\(580\) 76.9997 3.19724
\(581\) 3.43610 0.142553
\(582\) −19.2681 −0.798689
\(583\) −0.957064 −0.0396375
\(584\) −10.0465 −0.415729
\(585\) −5.66672 −0.234290
\(586\) 35.1488 1.45198
\(587\) 27.6788 1.14243 0.571214 0.820801i \(-0.306473\pi\)
0.571214 + 0.820801i \(0.306473\pi\)
\(588\) 11.4840 0.473593
\(589\) 23.6576 0.974795
\(590\) −35.6184 −1.46639
\(591\) −4.19376 −0.172508
\(592\) 15.8690 0.652210
\(593\) −5.17627 −0.212564 −0.106282 0.994336i \(-0.533895\pi\)
−0.106282 + 0.994336i \(0.533895\pi\)
\(594\) 1.06631 0.0437514
\(595\) 65.2797 2.67621
\(596\) 79.6226 3.26147
\(597\) 13.4271 0.549533
\(598\) 1.96033 0.0801637
\(599\) −32.4991 −1.32788 −0.663940 0.747786i \(-0.731117\pi\)
−0.663940 + 0.747786i \(0.731117\pi\)
\(600\) −2.89906 −0.118354
\(601\) 36.6637 1.49554 0.747772 0.663955i \(-0.231123\pi\)
0.747772 + 0.663955i \(0.231123\pi\)
\(602\) 66.4948 2.71013
\(603\) 24.3258 0.990622
\(604\) −45.6031 −1.85556
\(605\) 27.7448 1.12798
\(606\) −14.1653 −0.575427
\(607\) 9.26373 0.376003 0.188002 0.982169i \(-0.439799\pi\)
0.188002 + 0.982169i \(0.439799\pi\)
\(608\) −10.8977 −0.441960
\(609\) −15.7343 −0.637588
\(610\) 70.0511 2.83628
\(611\) 10.4867 0.424247
\(612\) 71.6828 2.89760
\(613\) −17.8512 −0.721003 −0.360501 0.932759i \(-0.617394\pi\)
−0.360501 + 0.932759i \(0.617394\pi\)
\(614\) −27.1915 −1.09736
\(615\) −3.07014 −0.123800
\(616\) −2.12412 −0.0855833
\(617\) 22.3190 0.898528 0.449264 0.893399i \(-0.351686\pi\)
0.449264 + 0.893399i \(0.351686\pi\)
\(618\) 2.84258 0.114345
\(619\) 2.02348 0.0813306 0.0406653 0.999173i \(-0.487052\pi\)
0.0406653 + 0.999173i \(0.487052\pi\)
\(620\) 58.4087 2.34575
\(621\) −3.01232 −0.120880
\(622\) 60.5662 2.42848
\(623\) −17.6486 −0.707075
\(624\) −0.917038 −0.0367109
\(625\) −30.0121 −1.20048
\(626\) −26.9962 −1.07898
\(627\) −0.293832 −0.0117345
\(628\) −30.8913 −1.23270
\(629\) −53.8359 −2.14658
\(630\) −58.9543 −2.34880
\(631\) −15.9928 −0.636661 −0.318331 0.947980i \(-0.603122\pi\)
−0.318331 + 0.947980i \(0.603122\pi\)
\(632\) −32.4405 −1.29041
\(633\) −7.07941 −0.281381
\(634\) 2.57604 0.102308
\(635\) 33.5986 1.33332
\(636\) −12.4254 −0.492699
\(637\) −4.89856 −0.194088
\(638\) 2.94060 0.116419
\(639\) 31.3611 1.24062
\(640\) −52.3659 −2.06995
\(641\) −44.3589 −1.75207 −0.876036 0.482245i \(-0.839822\pi\)
−0.876036 + 0.482245i \(0.839822\pi\)
\(642\) −19.6473 −0.775416
\(643\) −1.39985 −0.0552048 −0.0276024 0.999619i \(-0.508787\pi\)
−0.0276024 + 0.999619i \(0.508787\pi\)
\(644\) 13.1975 0.520055
\(645\) 10.3256 0.406571
\(646\) −64.1547 −2.52413
\(647\) −49.3759 −1.94117 −0.970584 0.240762i \(-0.922603\pi\)
−0.970584 + 0.240762i \(0.922603\pi\)
\(648\) −26.1348 −1.02667
\(649\) −0.880242 −0.0345525
\(650\) 2.71975 0.106677
\(651\) −11.9354 −0.467786
\(652\) −67.7437 −2.65305
\(653\) −1.24204 −0.0486047 −0.0243023 0.999705i \(-0.507736\pi\)
−0.0243023 + 0.999705i \(0.507736\pi\)
\(654\) −14.5147 −0.567570
\(655\) 29.1914 1.14060
\(656\) 4.88306 0.190651
\(657\) −6.89096 −0.268842
\(658\) 109.100 4.25315
\(659\) 21.7765 0.848291 0.424145 0.905594i \(-0.360575\pi\)
0.424145 + 0.905594i \(0.360575\pi\)
\(660\) −0.725447 −0.0282380
\(661\) −16.6446 −0.647398 −0.323699 0.946160i \(-0.604927\pi\)
−0.323699 + 0.946160i \(0.604927\pi\)
\(662\) 78.1929 3.03905
\(663\) 3.11108 0.120824
\(664\) −3.79074 −0.147109
\(665\) 34.1437 1.32403
\(666\) 48.6194 1.88396
\(667\) −8.30713 −0.321653
\(668\) 22.0962 0.854929
\(669\) −6.05265 −0.234009
\(670\) −53.7510 −2.07658
\(671\) 1.73118 0.0668315
\(672\) 5.49795 0.212088
\(673\) 21.3316 0.822272 0.411136 0.911574i \(-0.365132\pi\)
0.411136 + 0.911574i \(0.365132\pi\)
\(674\) −38.3321 −1.47650
\(675\) −4.17928 −0.160861
\(676\) −45.1913 −1.73813
\(677\) 4.54169 0.174551 0.0872757 0.996184i \(-0.472184\pi\)
0.0872757 + 0.996184i \(0.472184\pi\)
\(678\) −1.91842 −0.0736764
\(679\) 55.3322 2.12345
\(680\) −72.0174 −2.76174
\(681\) −10.9646 −0.420166
\(682\) 2.23061 0.0854146
\(683\) −24.3951 −0.933451 −0.466725 0.884402i \(-0.654566\pi\)
−0.466725 + 0.884402i \(0.654566\pi\)
\(684\) 37.4927 1.43357
\(685\) −25.8970 −0.989473
\(686\) 9.00433 0.343787
\(687\) −8.86847 −0.338353
\(688\) −16.4229 −0.626116
\(689\) 5.30011 0.201918
\(690\) 3.16694 0.120563
\(691\) −18.5155 −0.704362 −0.352181 0.935932i \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(692\) −20.6067 −0.783348
\(693\) −1.45694 −0.0553448
\(694\) −64.7383 −2.45743
\(695\) −56.7328 −2.15200
\(696\) 17.3583 0.657965
\(697\) −16.5659 −0.627479
\(698\) 2.38066 0.0901093
\(699\) −1.01343 −0.0383313
\(700\) 18.3102 0.692061
\(701\) 3.90953 0.147661 0.0738304 0.997271i \(-0.476478\pi\)
0.0738304 + 0.997271i \(0.476478\pi\)
\(702\) −5.90512 −0.222874
\(703\) −28.1581 −1.06200
\(704\) −1.65672 −0.0624400
\(705\) 16.9415 0.638054
\(706\) 12.4740 0.469464
\(707\) 40.6785 1.52987
\(708\) −11.4280 −0.429492
\(709\) 31.3969 1.17913 0.589567 0.807719i \(-0.299298\pi\)
0.589567 + 0.807719i \(0.299298\pi\)
\(710\) −69.2964 −2.60065
\(711\) −22.2511 −0.834480
\(712\) 19.4701 0.729673
\(713\) −6.30144 −0.235991
\(714\) 32.3664 1.21128
\(715\) 0.309442 0.0115725
\(716\) 37.0652 1.38519
\(717\) 7.45234 0.278313
\(718\) 25.9685 0.969135
\(719\) −8.42710 −0.314278 −0.157139 0.987576i \(-0.550227\pi\)
−0.157139 + 0.987576i \(0.550227\pi\)
\(720\) 14.5605 0.542639
\(721\) −8.16303 −0.304007
\(722\) 11.6773 0.434585
\(723\) −3.38779 −0.125993
\(724\) 81.8339 3.04133
\(725\) −11.5253 −0.428039
\(726\) 13.7562 0.510539
\(727\) −19.4107 −0.719903 −0.359951 0.932971i \(-0.617207\pi\)
−0.359951 + 0.932971i \(0.617207\pi\)
\(728\) 11.7631 0.435971
\(729\) −13.1693 −0.487751
\(730\) 15.2265 0.563558
\(731\) 55.7151 2.06070
\(732\) 22.4756 0.830723
\(733\) −11.2020 −0.413754 −0.206877 0.978367i \(-0.566330\pi\)
−0.206877 + 0.978367i \(0.566330\pi\)
\(734\) −76.4277 −2.82100
\(735\) −7.91372 −0.291902
\(736\) 2.90271 0.106995
\(737\) −1.32836 −0.0489306
\(738\) 14.9607 0.550712
\(739\) 24.5501 0.903092 0.451546 0.892248i \(-0.350873\pi\)
0.451546 + 0.892248i \(0.350873\pi\)
\(740\) −69.5200 −2.55561
\(741\) 1.62721 0.0597769
\(742\) 55.1402 2.02426
\(743\) −45.7963 −1.68010 −0.840051 0.542507i \(-0.817475\pi\)
−0.840051 + 0.542507i \(0.817475\pi\)
\(744\) 13.1673 0.482736
\(745\) −54.8685 −2.01023
\(746\) 47.0080 1.72108
\(747\) −2.60009 −0.0951322
\(748\) −3.91437 −0.143124
\(749\) 56.4210 2.06158
\(750\) −11.4409 −0.417763
\(751\) −22.4773 −0.820209 −0.410104 0.912039i \(-0.634508\pi\)
−0.410104 + 0.912039i \(0.634508\pi\)
\(752\) −26.9454 −0.982598
\(753\) 0.0638112 0.00232541
\(754\) −16.2847 −0.593053
\(755\) 31.4254 1.14369
\(756\) −39.7551 −1.44588
\(757\) −12.6804 −0.460875 −0.230438 0.973087i \(-0.574016\pi\)
−0.230438 + 0.973087i \(0.574016\pi\)
\(758\) 62.4414 2.26797
\(759\) 0.0782650 0.00284084
\(760\) −37.6677 −1.36635
\(761\) −12.7970 −0.463891 −0.231946 0.972729i \(-0.574509\pi\)
−0.231946 + 0.972729i \(0.574509\pi\)
\(762\) 16.6586 0.603476
\(763\) 41.6818 1.50898
\(764\) 78.5131 2.84050
\(765\) −49.3971 −1.78595
\(766\) −53.9309 −1.94860
\(767\) 4.87468 0.176014
\(768\) −14.2343 −0.513635
\(769\) −31.1800 −1.12438 −0.562190 0.827008i \(-0.690041\pi\)
−0.562190 + 0.827008i \(0.690041\pi\)
\(770\) 3.21931 0.116016
\(771\) 11.4586 0.412672
\(772\) 57.7935 2.08003
\(773\) 42.0824 1.51360 0.756799 0.653647i \(-0.226762\pi\)
0.756799 + 0.653647i \(0.226762\pi\)
\(774\) −50.3165 −1.80859
\(775\) −8.74261 −0.314044
\(776\) −61.0431 −2.19132
\(777\) 14.2059 0.509635
\(778\) 77.8177 2.78990
\(779\) −8.66457 −0.310441
\(780\) 4.01744 0.143847
\(781\) −1.71253 −0.0612792
\(782\) 17.0882 0.611074
\(783\) 25.0237 0.894274
\(784\) 12.5868 0.449527
\(785\) 21.2874 0.759779
\(786\) 14.4734 0.516251
\(787\) −49.7131 −1.77208 −0.886040 0.463609i \(-0.846554\pi\)
−0.886040 + 0.463609i \(0.846554\pi\)
\(788\) −29.2212 −1.04096
\(789\) −14.1719 −0.504534
\(790\) 49.1667 1.74927
\(791\) 5.50912 0.195882
\(792\) 1.60732 0.0571136
\(793\) −9.58707 −0.340447
\(794\) 24.6489 0.874756
\(795\) 8.56242 0.303678
\(796\) 93.5569 3.31604
\(797\) 7.09248 0.251228 0.125614 0.992079i \(-0.459910\pi\)
0.125614 + 0.992079i \(0.459910\pi\)
\(798\) 16.9288 0.599273
\(799\) 91.4132 3.23397
\(800\) 4.02721 0.142384
\(801\) 13.3546 0.471863
\(802\) −22.4324 −0.792116
\(803\) 0.376294 0.0132791
\(804\) −17.2458 −0.608213
\(805\) −9.09450 −0.320539
\(806\) −12.3529 −0.435112
\(807\) −13.1304 −0.462214
\(808\) −44.8770 −1.57877
\(809\) 16.4853 0.579593 0.289796 0.957088i \(-0.406412\pi\)
0.289796 + 0.957088i \(0.406412\pi\)
\(810\) 39.6098 1.39175
\(811\) 15.5992 0.547761 0.273881 0.961764i \(-0.411693\pi\)
0.273881 + 0.961764i \(0.411693\pi\)
\(812\) −109.634 −3.84738
\(813\) −2.52494 −0.0885535
\(814\) −2.65495 −0.0930561
\(815\) 46.6826 1.63522
\(816\) −7.99385 −0.279841
\(817\) 29.1410 1.01952
\(818\) −50.9342 −1.78087
\(819\) 8.06839 0.281932
\(820\) −21.3921 −0.747045
\(821\) −17.8246 −0.622084 −0.311042 0.950396i \(-0.600678\pi\)
−0.311042 + 0.950396i \(0.600678\pi\)
\(822\) −12.8400 −0.447847
\(823\) −8.12631 −0.283265 −0.141633 0.989919i \(-0.545235\pi\)
−0.141633 + 0.989919i \(0.545235\pi\)
\(824\) 9.00555 0.313723
\(825\) 0.108585 0.00378044
\(826\) 50.7142 1.76457
\(827\) 48.0760 1.67177 0.835883 0.548907i \(-0.184956\pi\)
0.835883 + 0.548907i \(0.184956\pi\)
\(828\) −9.98654 −0.347056
\(829\) 27.6879 0.961640 0.480820 0.876819i \(-0.340339\pi\)
0.480820 + 0.876819i \(0.340339\pi\)
\(830\) 5.74524 0.199420
\(831\) 4.40930 0.152957
\(832\) 9.17473 0.318076
\(833\) −42.7010 −1.47950
\(834\) −28.1288 −0.974020
\(835\) −15.2267 −0.526940
\(836\) −2.04736 −0.0708094
\(837\) 18.9819 0.656111
\(838\) 32.4231 1.12004
\(839\) −38.4127 −1.32615 −0.663077 0.748552i \(-0.730750\pi\)
−0.663077 + 0.748552i \(0.730750\pi\)
\(840\) 19.0036 0.655685
\(841\) 40.0084 1.37960
\(842\) −93.7038 −3.22924
\(843\) 12.3102 0.423985
\(844\) −49.3278 −1.69793
\(845\) 31.1416 1.07130
\(846\) −82.5555 −2.83832
\(847\) −39.5035 −1.35736
\(848\) −13.6185 −0.467662
\(849\) −2.10964 −0.0724025
\(850\) 23.7082 0.813184
\(851\) 7.50019 0.257103
\(852\) −22.2335 −0.761707
\(853\) 9.77625 0.334732 0.167366 0.985895i \(-0.446474\pi\)
0.167366 + 0.985895i \(0.446474\pi\)
\(854\) −99.7400 −3.41303
\(855\) −25.8364 −0.883588
\(856\) −62.2443 −2.12747
\(857\) −10.5722 −0.361138 −0.180569 0.983562i \(-0.557794\pi\)
−0.180569 + 0.983562i \(0.557794\pi\)
\(858\) 0.153425 0.00523784
\(859\) 39.7160 1.35509 0.677546 0.735480i \(-0.263043\pi\)
0.677546 + 0.735480i \(0.263043\pi\)
\(860\) 71.9467 2.45336
\(861\) 4.37133 0.148974
\(862\) −30.0853 −1.02471
\(863\) 25.6876 0.874415 0.437208 0.899361i \(-0.355967\pi\)
0.437208 + 0.899361i \(0.355967\pi\)
\(864\) −8.74388 −0.297473
\(865\) 14.2002 0.482821
\(866\) −32.2561 −1.09611
\(867\) 18.1713 0.617131
\(868\) −83.1634 −2.82275
\(869\) 1.21506 0.0412182
\(870\) −26.3082 −0.891932
\(871\) 7.35628 0.249258
\(872\) −45.9839 −1.55721
\(873\) −41.8698 −1.41708
\(874\) 8.93776 0.302324
\(875\) 32.8548 1.11069
\(876\) 4.88537 0.165061
\(877\) 12.9469 0.437185 0.218592 0.975816i \(-0.429853\pi\)
0.218592 + 0.975816i \(0.429853\pi\)
\(878\) 70.3077 2.37277
\(879\) −7.77129 −0.262119
\(880\) −0.795106 −0.0268030
\(881\) 48.4011 1.63068 0.815338 0.578986i \(-0.196551\pi\)
0.815338 + 0.578986i \(0.196551\pi\)
\(882\) 38.5634 1.29850
\(883\) 7.84105 0.263873 0.131936 0.991258i \(-0.457881\pi\)
0.131936 + 0.991258i \(0.457881\pi\)
\(884\) 21.6773 0.729088
\(885\) 7.87513 0.264720
\(886\) 42.8668 1.44014
\(887\) 45.4165 1.52494 0.762468 0.647026i \(-0.223987\pi\)
0.762468 + 0.647026i \(0.223987\pi\)
\(888\) −15.6722 −0.525923
\(889\) −47.8383 −1.60444
\(890\) −29.5088 −0.989138
\(891\) 0.978881 0.0327938
\(892\) −42.1736 −1.41208
\(893\) 47.8124 1.59998
\(894\) −27.2044 −0.909851
\(895\) −25.5419 −0.853771
\(896\) 74.5596 2.49086
\(897\) −0.433423 −0.0144716
\(898\) −3.28247 −0.109537
\(899\) 52.3469 1.74587
\(900\) −13.8553 −0.461844
\(901\) 46.2012 1.53919
\(902\) −0.816959 −0.0272018
\(903\) −14.7018 −0.489246
\(904\) −6.07772 −0.202142
\(905\) −56.3923 −1.87454
\(906\) 15.5811 0.517646
\(907\) 17.5644 0.583217 0.291609 0.956538i \(-0.405809\pi\)
0.291609 + 0.956538i \(0.405809\pi\)
\(908\) −76.3993 −2.53540
\(909\) −30.7813 −1.02095
\(910\) −17.8282 −0.590998
\(911\) 1.79720 0.0595440 0.0297720 0.999557i \(-0.490522\pi\)
0.0297720 + 0.999557i \(0.490522\pi\)
\(912\) −4.18107 −0.138449
\(913\) 0.141983 0.00469894
\(914\) 24.3978 0.807006
\(915\) −15.4881 −0.512020
\(916\) −61.7936 −2.04172
\(917\) −41.5633 −1.37254
\(918\) −51.4752 −1.69893
\(919\) 32.3367 1.06669 0.533344 0.845898i \(-0.320935\pi\)
0.533344 + 0.845898i \(0.320935\pi\)
\(920\) 10.0332 0.330783
\(921\) 6.01197 0.198101
\(922\) 36.9983 1.21847
\(923\) 9.48379 0.312163
\(924\) 1.03290 0.0339801
\(925\) 10.4058 0.342139
\(926\) −34.7747 −1.14277
\(927\) 6.17695 0.202878
\(928\) −24.1132 −0.791555
\(929\) 10.4570 0.343081 0.171541 0.985177i \(-0.445125\pi\)
0.171541 + 0.985177i \(0.445125\pi\)
\(930\) −19.9563 −0.654393
\(931\) −22.3341 −0.731972
\(932\) −7.06133 −0.231302
\(933\) −13.3910 −0.438402
\(934\) 86.7172 2.83747
\(935\) 2.69742 0.0882151
\(936\) −8.90114 −0.290943
\(937\) 38.6340 1.26212 0.631058 0.775735i \(-0.282621\pi\)
0.631058 + 0.775735i \(0.282621\pi\)
\(938\) 76.5317 2.49885
\(939\) 5.96878 0.194784
\(940\) 118.045 3.85020
\(941\) −1.49539 −0.0487484 −0.0243742 0.999703i \(-0.507759\pi\)
−0.0243742 + 0.999703i \(0.507759\pi\)
\(942\) 10.5545 0.343885
\(943\) 2.30789 0.0751554
\(944\) −12.5254 −0.407666
\(945\) 27.3955 0.891176
\(946\) 2.74763 0.0893331
\(947\) 14.4837 0.470659 0.235329 0.971916i \(-0.424383\pi\)
0.235329 + 0.971916i \(0.424383\pi\)
\(948\) 15.7749 0.512346
\(949\) −2.08387 −0.0676454
\(950\) 12.4002 0.402317
\(951\) −0.569555 −0.0184691
\(952\) 102.540 3.32333
\(953\) 46.5250 1.50709 0.753546 0.657395i \(-0.228342\pi\)
0.753546 + 0.657395i \(0.228342\pi\)
\(954\) −41.7245 −1.35088
\(955\) −54.1039 −1.75076
\(956\) 51.9263 1.67942
\(957\) −0.650158 −0.0210166
\(958\) −1.67649 −0.0541650
\(959\) 36.8726 1.19068
\(960\) 14.8219 0.478376
\(961\) 8.70815 0.280908
\(962\) 14.7028 0.474038
\(963\) −42.6937 −1.37578
\(964\) −23.6054 −0.760278
\(965\) −39.8259 −1.28204
\(966\) −4.50915 −0.145080
\(967\) 41.1326 1.32273 0.661367 0.750062i \(-0.269977\pi\)
0.661367 + 0.750062i \(0.269977\pi\)
\(968\) 43.5807 1.40074
\(969\) 14.1844 0.455669
\(970\) 92.5168 2.97054
\(971\) −1.39650 −0.0448158 −0.0224079 0.999749i \(-0.507133\pi\)
−0.0224079 + 0.999749i \(0.507133\pi\)
\(972\) 45.8521 1.47071
\(973\) 80.7773 2.58960
\(974\) −31.1597 −0.998421
\(975\) −0.601330 −0.0192580
\(976\) 24.6338 0.788508
\(977\) −16.7603 −0.536211 −0.268105 0.963390i \(-0.586398\pi\)
−0.268105 + 0.963390i \(0.586398\pi\)
\(978\) 23.1457 0.740119
\(979\) −0.729255 −0.0233071
\(980\) −55.1411 −1.76142
\(981\) −31.5406 −1.00701
\(982\) −50.8152 −1.62158
\(983\) 46.8166 1.49322 0.746609 0.665263i \(-0.231680\pi\)
0.746609 + 0.665263i \(0.231680\pi\)
\(984\) −4.82250 −0.153736
\(985\) 20.1365 0.641603
\(986\) −141.954 −4.52074
\(987\) −24.1216 −0.767800
\(988\) 11.3380 0.360711
\(989\) −7.76200 −0.246817
\(990\) −2.43605 −0.0774227
\(991\) −15.0694 −0.478694 −0.239347 0.970934i \(-0.576933\pi\)
−0.239347 + 0.970934i \(0.576933\pi\)
\(992\) −18.2913 −0.580748
\(993\) −17.2882 −0.548625
\(994\) 98.6656 3.12948
\(995\) −64.4707 −2.04386
\(996\) 1.84334 0.0584084
\(997\) 30.8870 0.978202 0.489101 0.872227i \(-0.337325\pi\)
0.489101 + 0.872227i \(0.337325\pi\)
\(998\) 7.37974 0.233602
\(999\) −22.5929 −0.714809
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 \(a_p\))