Properties

Label 6027.2.a.bk.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.55282\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55282 q^{2} +1.00000 q^{3} +4.51690 q^{4} -1.95019 q^{5} -2.55282 q^{6} -6.42520 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.55282 q^{2} +1.00000 q^{3} +4.51690 q^{4} -1.95019 q^{5} -2.55282 q^{6} -6.42520 q^{8} +1.00000 q^{9} +4.97848 q^{10} +5.66056 q^{11} +4.51690 q^{12} -4.68475 q^{13} -1.95019 q^{15} +7.36860 q^{16} -4.34161 q^{17} -2.55282 q^{18} +5.53739 q^{19} -8.80881 q^{20} -14.4504 q^{22} -3.74585 q^{23} -6.42520 q^{24} -1.19677 q^{25} +11.9593 q^{26} +1.00000 q^{27} -0.177428 q^{29} +4.97848 q^{30} -0.750655 q^{31} -5.96031 q^{32} +5.66056 q^{33} +11.0834 q^{34} +4.51690 q^{36} +8.28667 q^{37} -14.1360 q^{38} -4.68475 q^{39} +12.5304 q^{40} -1.00000 q^{41} +6.12975 q^{43} +25.5682 q^{44} -1.95019 q^{45} +9.56250 q^{46} -0.738793 q^{47} +7.36860 q^{48} +3.05513 q^{50} -4.34161 q^{51} -21.1605 q^{52} -13.5974 q^{53} -2.55282 q^{54} -11.0392 q^{55} +5.53739 q^{57} +0.452941 q^{58} +4.83812 q^{59} -8.80881 q^{60} -10.3042 q^{61} +1.91629 q^{62} +0.478424 q^{64} +9.13614 q^{65} -14.4504 q^{66} +13.7621 q^{67} -19.6106 q^{68} -3.74585 q^{69} -15.8518 q^{71} -6.42520 q^{72} +9.26794 q^{73} -21.1544 q^{74} -1.19677 q^{75} +25.0119 q^{76} +11.9593 q^{78} +8.55260 q^{79} -14.3701 q^{80} +1.00000 q^{81} +2.55282 q^{82} -10.1927 q^{83} +8.46696 q^{85} -15.6482 q^{86} -0.177428 q^{87} -36.3702 q^{88} -6.24247 q^{89} +4.97848 q^{90} -16.9197 q^{92} -0.750655 q^{93} +1.88601 q^{94} -10.7990 q^{95} -5.96031 q^{96} -11.0576 q^{97} +5.66056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55282 −1.80512 −0.902559 0.430566i \(-0.858314\pi\)
−0.902559 + 0.430566i \(0.858314\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.51690 2.25845
\(5\) −1.95019 −0.872151 −0.436075 0.899910i \(-0.643632\pi\)
−0.436075 + 0.899910i \(0.643632\pi\)
\(6\) −2.55282 −1.04219
\(7\) 0 0
\(8\) −6.42520 −2.27165
\(9\) 1.00000 0.333333
\(10\) 4.97848 1.57433
\(11\) 5.66056 1.70672 0.853362 0.521320i \(-0.174560\pi\)
0.853362 + 0.521320i \(0.174560\pi\)
\(12\) 4.51690 1.30392
\(13\) −4.68475 −1.29932 −0.649658 0.760227i \(-0.725088\pi\)
−0.649658 + 0.760227i \(0.725088\pi\)
\(14\) 0 0
\(15\) −1.95019 −0.503536
\(16\) 7.36860 1.84215
\(17\) −4.34161 −1.05300 −0.526498 0.850177i \(-0.676495\pi\)
−0.526498 + 0.850177i \(0.676495\pi\)
\(18\) −2.55282 −0.601706
\(19\) 5.53739 1.27037 0.635183 0.772362i \(-0.280925\pi\)
0.635183 + 0.772362i \(0.280925\pi\)
\(20\) −8.80881 −1.96971
\(21\) 0 0
\(22\) −14.4504 −3.08084
\(23\) −3.74585 −0.781064 −0.390532 0.920589i \(-0.627709\pi\)
−0.390532 + 0.920589i \(0.627709\pi\)
\(24\) −6.42520 −1.31154
\(25\) −1.19677 −0.239353
\(26\) 11.9593 2.34542
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.177428 −0.0329475 −0.0164737 0.999864i \(-0.505244\pi\)
−0.0164737 + 0.999864i \(0.505244\pi\)
\(30\) 4.97848 0.908943
\(31\) −0.750655 −0.134822 −0.0674108 0.997725i \(-0.521474\pi\)
−0.0674108 + 0.997725i \(0.521474\pi\)
\(32\) −5.96031 −1.05364
\(33\) 5.66056 0.985377
\(34\) 11.0834 1.90078
\(35\) 0 0
\(36\) 4.51690 0.752817
\(37\) 8.28667 1.36232 0.681160 0.732134i \(-0.261476\pi\)
0.681160 + 0.732134i \(0.261476\pi\)
\(38\) −14.1360 −2.29316
\(39\) −4.68475 −0.750160
\(40\) 12.5304 1.98122
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 6.12975 0.934779 0.467389 0.884052i \(-0.345195\pi\)
0.467389 + 0.884052i \(0.345195\pi\)
\(44\) 25.5682 3.85455
\(45\) −1.95019 −0.290717
\(46\) 9.56250 1.40991
\(47\) −0.738793 −0.107764 −0.0538820 0.998547i \(-0.517159\pi\)
−0.0538820 + 0.998547i \(0.517159\pi\)
\(48\) 7.36860 1.06357
\(49\) 0 0
\(50\) 3.05513 0.432061
\(51\) −4.34161 −0.607947
\(52\) −21.1605 −2.93444
\(53\) −13.5974 −1.86775 −0.933876 0.357598i \(-0.883596\pi\)
−0.933876 + 0.357598i \(0.883596\pi\)
\(54\) −2.55282 −0.347395
\(55\) −11.0392 −1.48852
\(56\) 0 0
\(57\) 5.53739 0.733446
\(58\) 0.452941 0.0594741
\(59\) 4.83812 0.629870 0.314935 0.949113i \(-0.398017\pi\)
0.314935 + 0.949113i \(0.398017\pi\)
\(60\) −8.80881 −1.13721
\(61\) −10.3042 −1.31932 −0.659662 0.751562i \(-0.729301\pi\)
−0.659662 + 0.751562i \(0.729301\pi\)
\(62\) 1.91629 0.243369
\(63\) 0 0
\(64\) 0.478424 0.0598030
\(65\) 9.13614 1.13320
\(66\) −14.4504 −1.77872
\(67\) 13.7621 1.68131 0.840655 0.541571i \(-0.182170\pi\)
0.840655 + 0.541571i \(0.182170\pi\)
\(68\) −19.6106 −2.37814
\(69\) −3.74585 −0.450948
\(70\) 0 0
\(71\) −15.8518 −1.88126 −0.940629 0.339436i \(-0.889764\pi\)
−0.940629 + 0.339436i \(0.889764\pi\)
\(72\) −6.42520 −0.757217
\(73\) 9.26794 1.08473 0.542365 0.840143i \(-0.317529\pi\)
0.542365 + 0.840143i \(0.317529\pi\)
\(74\) −21.1544 −2.45915
\(75\) −1.19677 −0.138191
\(76\) 25.0119 2.86906
\(77\) 0 0
\(78\) 11.9593 1.35413
\(79\) 8.55260 0.962242 0.481121 0.876654i \(-0.340230\pi\)
0.481121 + 0.876654i \(0.340230\pi\)
\(80\) −14.3701 −1.60663
\(81\) 1.00000 0.111111
\(82\) 2.55282 0.281912
\(83\) −10.1927 −1.11880 −0.559400 0.828898i \(-0.688968\pi\)
−0.559400 + 0.828898i \(0.688968\pi\)
\(84\) 0 0
\(85\) 8.46696 0.918371
\(86\) −15.6482 −1.68739
\(87\) −0.177428 −0.0190222
\(88\) −36.3702 −3.87708
\(89\) −6.24247 −0.661700 −0.330850 0.943683i \(-0.607335\pi\)
−0.330850 + 0.943683i \(0.607335\pi\)
\(90\) 4.97848 0.524778
\(91\) 0 0
\(92\) −16.9197 −1.76400
\(93\) −0.750655 −0.0778393
\(94\) 1.88601 0.194527
\(95\) −10.7990 −1.10795
\(96\) −5.96031 −0.608322
\(97\) −11.0576 −1.12273 −0.561364 0.827569i \(-0.689723\pi\)
−0.561364 + 0.827569i \(0.689723\pi\)
\(98\) 0 0
\(99\) 5.66056 0.568908
\(100\) −5.40567 −0.540567
\(101\) −5.94360 −0.591410 −0.295705 0.955279i \(-0.595555\pi\)
−0.295705 + 0.955279i \(0.595555\pi\)
\(102\) 11.0834 1.09742
\(103\) −9.42784 −0.928952 −0.464476 0.885586i \(-0.653757\pi\)
−0.464476 + 0.885586i \(0.653757\pi\)
\(104\) 30.1004 2.95159
\(105\) 0 0
\(106\) 34.7118 3.37151
\(107\) −4.90421 −0.474108 −0.237054 0.971496i \(-0.576182\pi\)
−0.237054 + 0.971496i \(0.576182\pi\)
\(108\) 4.51690 0.434639
\(109\) 7.10598 0.680629 0.340315 0.940312i \(-0.389466\pi\)
0.340315 + 0.940312i \(0.389466\pi\)
\(110\) 28.1810 2.68695
\(111\) 8.28667 0.786536
\(112\) 0 0
\(113\) 16.5531 1.55719 0.778594 0.627528i \(-0.215933\pi\)
0.778594 + 0.627528i \(0.215933\pi\)
\(114\) −14.1360 −1.32396
\(115\) 7.30512 0.681206
\(116\) −0.801423 −0.0744102
\(117\) −4.68475 −0.433105
\(118\) −12.3509 −1.13699
\(119\) 0 0
\(120\) 12.5304 1.14386
\(121\) 21.0419 1.91290
\(122\) 26.3049 2.38154
\(123\) −1.00000 −0.0901670
\(124\) −3.39064 −0.304488
\(125\) 12.0849 1.08090
\(126\) 0 0
\(127\) −4.96925 −0.440950 −0.220475 0.975393i \(-0.570761\pi\)
−0.220475 + 0.975393i \(0.570761\pi\)
\(128\) 10.6993 0.945693
\(129\) 6.12975 0.539695
\(130\) −23.3229 −2.04556
\(131\) 15.3014 1.33689 0.668446 0.743761i \(-0.266960\pi\)
0.668446 + 0.743761i \(0.266960\pi\)
\(132\) 25.5682 2.22543
\(133\) 0 0
\(134\) −35.1322 −3.03496
\(135\) −1.95019 −0.167845
\(136\) 27.8957 2.39204
\(137\) −11.3447 −0.969242 −0.484621 0.874724i \(-0.661042\pi\)
−0.484621 + 0.874724i \(0.661042\pi\)
\(138\) 9.56250 0.814014
\(139\) 0.201634 0.0171024 0.00855119 0.999963i \(-0.497278\pi\)
0.00855119 + 0.999963i \(0.497278\pi\)
\(140\) 0 0
\(141\) −0.738793 −0.0622176
\(142\) 40.4667 3.39589
\(143\) −26.5183 −2.21757
\(144\) 7.36860 0.614050
\(145\) 0.346017 0.0287352
\(146\) −23.6594 −1.95807
\(147\) 0 0
\(148\) 37.4301 3.07673
\(149\) −2.73172 −0.223791 −0.111896 0.993720i \(-0.535692\pi\)
−0.111896 + 0.993720i \(0.535692\pi\)
\(150\) 3.05513 0.249450
\(151\) −9.57461 −0.779171 −0.389585 0.920990i \(-0.627382\pi\)
−0.389585 + 0.920990i \(0.627382\pi\)
\(152\) −35.5789 −2.88583
\(153\) −4.34161 −0.350999
\(154\) 0 0
\(155\) 1.46392 0.117585
\(156\) −21.1605 −1.69420
\(157\) −9.56163 −0.763101 −0.381551 0.924348i \(-0.624610\pi\)
−0.381551 + 0.924348i \(0.624610\pi\)
\(158\) −21.8333 −1.73696
\(159\) −13.5974 −1.07835
\(160\) 11.6237 0.918936
\(161\) 0 0
\(162\) −2.55282 −0.200569
\(163\) 3.62324 0.283794 0.141897 0.989881i \(-0.454680\pi\)
0.141897 + 0.989881i \(0.454680\pi\)
\(164\) −4.51690 −0.352711
\(165\) −11.0392 −0.859397
\(166\) 26.0203 2.01956
\(167\) −7.01612 −0.542923 −0.271462 0.962449i \(-0.587507\pi\)
−0.271462 + 0.962449i \(0.587507\pi\)
\(168\) 0 0
\(169\) 8.94686 0.688220
\(170\) −21.6146 −1.65777
\(171\) 5.53739 0.423455
\(172\) 27.6875 2.11115
\(173\) −14.3292 −1.08943 −0.544713 0.838622i \(-0.683361\pi\)
−0.544713 + 0.838622i \(0.683361\pi\)
\(174\) 0.452941 0.0343374
\(175\) 0 0
\(176\) 41.7104 3.14404
\(177\) 4.83812 0.363656
\(178\) 15.9359 1.19445
\(179\) 5.16712 0.386208 0.193104 0.981178i \(-0.438144\pi\)
0.193104 + 0.981178i \(0.438144\pi\)
\(180\) −8.80881 −0.656570
\(181\) −12.3174 −0.915547 −0.457774 0.889069i \(-0.651353\pi\)
−0.457774 + 0.889069i \(0.651353\pi\)
\(182\) 0 0
\(183\) −10.3042 −0.761712
\(184\) 24.0679 1.77431
\(185\) −16.1606 −1.18815
\(186\) 1.91629 0.140509
\(187\) −24.5760 −1.79717
\(188\) −3.33705 −0.243380
\(189\) 0 0
\(190\) 27.5678 1.99998
\(191\) 12.5939 0.911263 0.455632 0.890168i \(-0.349413\pi\)
0.455632 + 0.890168i \(0.349413\pi\)
\(192\) 0.478424 0.0345273
\(193\) 10.3925 0.748068 0.374034 0.927415i \(-0.377974\pi\)
0.374034 + 0.927415i \(0.377974\pi\)
\(194\) 28.2281 2.02666
\(195\) 9.13614 0.654252
\(196\) 0 0
\(197\) −2.06825 −0.147357 −0.0736785 0.997282i \(-0.523474\pi\)
−0.0736785 + 0.997282i \(0.523474\pi\)
\(198\) −14.4504 −1.02695
\(199\) 1.70462 0.120837 0.0604187 0.998173i \(-0.480756\pi\)
0.0604187 + 0.998173i \(0.480756\pi\)
\(200\) 7.68946 0.543727
\(201\) 13.7621 0.970705
\(202\) 15.1729 1.06756
\(203\) 0 0
\(204\) −19.6106 −1.37302
\(205\) 1.95019 0.136207
\(206\) 24.0676 1.67687
\(207\) −3.74585 −0.260355
\(208\) −34.5200 −2.39353
\(209\) 31.3447 2.16816
\(210\) 0 0
\(211\) −13.6714 −0.941176 −0.470588 0.882353i \(-0.655958\pi\)
−0.470588 + 0.882353i \(0.655958\pi\)
\(212\) −61.4183 −4.21822
\(213\) −15.8518 −1.08615
\(214\) 12.5196 0.855821
\(215\) −11.9542 −0.815268
\(216\) −6.42520 −0.437180
\(217\) 0 0
\(218\) −18.1403 −1.22862
\(219\) 9.26794 0.626270
\(220\) −49.8628 −3.36175
\(221\) 20.3394 1.36817
\(222\) −21.1544 −1.41979
\(223\) −16.0359 −1.07384 −0.536921 0.843633i \(-0.680413\pi\)
−0.536921 + 0.843633i \(0.680413\pi\)
\(224\) 0 0
\(225\) −1.19677 −0.0797844
\(226\) −42.2572 −2.81091
\(227\) 4.13224 0.274266 0.137133 0.990553i \(-0.456211\pi\)
0.137133 + 0.990553i \(0.456211\pi\)
\(228\) 25.0119 1.65645
\(229\) 21.4431 1.41700 0.708499 0.705711i \(-0.249372\pi\)
0.708499 + 0.705711i \(0.249372\pi\)
\(230\) −18.6487 −1.22966
\(231\) 0 0
\(232\) 1.14001 0.0748452
\(233\) −24.1939 −1.58500 −0.792498 0.609874i \(-0.791220\pi\)
−0.792498 + 0.609874i \(0.791220\pi\)
\(234\) 11.9593 0.781806
\(235\) 1.44078 0.0939864
\(236\) 21.8533 1.42253
\(237\) 8.55260 0.555551
\(238\) 0 0
\(239\) −9.87757 −0.638927 −0.319463 0.947599i \(-0.603503\pi\)
−0.319463 + 0.947599i \(0.603503\pi\)
\(240\) −14.3701 −0.927589
\(241\) −12.3991 −0.798694 −0.399347 0.916800i \(-0.630763\pi\)
−0.399347 + 0.916800i \(0.630763\pi\)
\(242\) −53.7163 −3.45302
\(243\) 1.00000 0.0641500
\(244\) −46.5433 −2.97963
\(245\) 0 0
\(246\) 2.55282 0.162762
\(247\) −25.9413 −1.65060
\(248\) 4.82311 0.306268
\(249\) −10.1927 −0.645939
\(250\) −30.8505 −1.95116
\(251\) 16.8450 1.06324 0.531622 0.846981i \(-0.321583\pi\)
0.531622 + 0.846981i \(0.321583\pi\)
\(252\) 0 0
\(253\) −21.2036 −1.33306
\(254\) 12.6856 0.795966
\(255\) 8.46696 0.530222
\(256\) −28.2702 −1.76689
\(257\) −19.3000 −1.20390 −0.601950 0.798533i \(-0.705610\pi\)
−0.601950 + 0.798533i \(0.705610\pi\)
\(258\) −15.6482 −0.974213
\(259\) 0 0
\(260\) 41.2670 2.55927
\(261\) −0.177428 −0.0109825
\(262\) −39.0618 −2.41325
\(263\) −15.4752 −0.954242 −0.477121 0.878838i \(-0.658320\pi\)
−0.477121 + 0.878838i \(0.658320\pi\)
\(264\) −36.3702 −2.23843
\(265\) 26.5176 1.62896
\(266\) 0 0
\(267\) −6.24247 −0.382033
\(268\) 62.1621 3.79716
\(269\) 26.1638 1.59524 0.797618 0.603163i \(-0.206093\pi\)
0.797618 + 0.603163i \(0.206093\pi\)
\(270\) 4.97848 0.302981
\(271\) −2.15147 −0.130692 −0.0653461 0.997863i \(-0.520815\pi\)
−0.0653461 + 0.997863i \(0.520815\pi\)
\(272\) −31.9916 −1.93977
\(273\) 0 0
\(274\) 28.9610 1.74960
\(275\) −6.77437 −0.408510
\(276\) −16.9197 −1.01844
\(277\) −13.6100 −0.817744 −0.408872 0.912592i \(-0.634078\pi\)
−0.408872 + 0.912592i \(0.634078\pi\)
\(278\) −0.514736 −0.0308718
\(279\) −0.750655 −0.0449406
\(280\) 0 0
\(281\) 8.40118 0.501172 0.250586 0.968094i \(-0.419377\pi\)
0.250586 + 0.968094i \(0.419377\pi\)
\(282\) 1.88601 0.112310
\(283\) 26.5602 1.57884 0.789421 0.613853i \(-0.210381\pi\)
0.789421 + 0.613853i \(0.210381\pi\)
\(284\) −71.6009 −4.24873
\(285\) −10.7990 −0.639675
\(286\) 67.6965 4.00298
\(287\) 0 0
\(288\) −5.96031 −0.351215
\(289\) 1.84959 0.108800
\(290\) −0.883320 −0.0518703
\(291\) −11.0576 −0.648208
\(292\) 41.8624 2.44981
\(293\) −15.7692 −0.921249 −0.460624 0.887595i \(-0.652374\pi\)
−0.460624 + 0.887595i \(0.652374\pi\)
\(294\) 0 0
\(295\) −9.43525 −0.549342
\(296\) −53.2435 −3.09472
\(297\) 5.66056 0.328459
\(298\) 6.97360 0.403970
\(299\) 17.5484 1.01485
\(300\) −5.40567 −0.312097
\(301\) 0 0
\(302\) 24.4423 1.40650
\(303\) −5.94360 −0.341451
\(304\) 40.8028 2.34020
\(305\) 20.0952 1.15065
\(306\) 11.0834 0.633594
\(307\) −16.4452 −0.938577 −0.469288 0.883045i \(-0.655490\pi\)
−0.469288 + 0.883045i \(0.655490\pi\)
\(308\) 0 0
\(309\) −9.42784 −0.536331
\(310\) −3.73713 −0.212254
\(311\) −27.3350 −1.55003 −0.775013 0.631945i \(-0.782257\pi\)
−0.775013 + 0.631945i \(0.782257\pi\)
\(312\) 30.1004 1.70410
\(313\) 13.6155 0.769591 0.384795 0.923002i \(-0.374272\pi\)
0.384795 + 0.923002i \(0.374272\pi\)
\(314\) 24.4091 1.37749
\(315\) 0 0
\(316\) 38.6312 2.17318
\(317\) 19.2420 1.08074 0.540370 0.841427i \(-0.318284\pi\)
0.540370 + 0.841427i \(0.318284\pi\)
\(318\) 34.7118 1.94654
\(319\) −1.00434 −0.0562322
\(320\) −0.933016 −0.0521572
\(321\) −4.90421 −0.273727
\(322\) 0 0
\(323\) −24.0412 −1.33769
\(324\) 4.51690 0.250939
\(325\) 5.60655 0.310995
\(326\) −9.24948 −0.512282
\(327\) 7.10598 0.392961
\(328\) 6.42520 0.354772
\(329\) 0 0
\(330\) 28.1810 1.55131
\(331\) −24.5569 −1.34977 −0.674884 0.737924i \(-0.735806\pi\)
−0.674884 + 0.737924i \(0.735806\pi\)
\(332\) −46.0396 −2.52675
\(333\) 8.28667 0.454107
\(334\) 17.9109 0.980041
\(335\) −26.8387 −1.46636
\(336\) 0 0
\(337\) 2.52040 0.137295 0.0686474 0.997641i \(-0.478132\pi\)
0.0686474 + 0.997641i \(0.478132\pi\)
\(338\) −22.8397 −1.24232
\(339\) 16.5531 0.899043
\(340\) 38.2444 2.07410
\(341\) −4.24913 −0.230103
\(342\) −14.1360 −0.764386
\(343\) 0 0
\(344\) −39.3849 −2.12349
\(345\) 7.30512 0.393294
\(346\) 36.5798 1.96654
\(347\) −4.19148 −0.225010 −0.112505 0.993651i \(-0.535888\pi\)
−0.112505 + 0.993651i \(0.535888\pi\)
\(348\) −0.801423 −0.0429608
\(349\) 24.1274 1.29151 0.645756 0.763544i \(-0.276542\pi\)
0.645756 + 0.763544i \(0.276542\pi\)
\(350\) 0 0
\(351\) −4.68475 −0.250053
\(352\) −33.7387 −1.79828
\(353\) 10.5251 0.560196 0.280098 0.959971i \(-0.409633\pi\)
0.280098 + 0.959971i \(0.409633\pi\)
\(354\) −12.3509 −0.656441
\(355\) 30.9139 1.64074
\(356\) −28.1966 −1.49442
\(357\) 0 0
\(358\) −13.1907 −0.697152
\(359\) 2.78928 0.147213 0.0736064 0.997287i \(-0.476549\pi\)
0.0736064 + 0.997287i \(0.476549\pi\)
\(360\) 12.5304 0.660408
\(361\) 11.6627 0.613828
\(362\) 31.4442 1.65267
\(363\) 21.0419 1.10442
\(364\) 0 0
\(365\) −18.0742 −0.946049
\(366\) 26.3049 1.37498
\(367\) 1.55422 0.0811298 0.0405649 0.999177i \(-0.487084\pi\)
0.0405649 + 0.999177i \(0.487084\pi\)
\(368\) −27.6017 −1.43884
\(369\) −1.00000 −0.0520579
\(370\) 41.2551 2.14475
\(371\) 0 0
\(372\) −3.39064 −0.175796
\(373\) 18.7337 0.969992 0.484996 0.874516i \(-0.338821\pi\)
0.484996 + 0.874516i \(0.338821\pi\)
\(374\) 62.7380 3.24411
\(375\) 12.0849 0.624059
\(376\) 4.74689 0.244802
\(377\) 0.831203 0.0428091
\(378\) 0 0
\(379\) −7.75137 −0.398161 −0.199081 0.979983i \(-0.563796\pi\)
−0.199081 + 0.979983i \(0.563796\pi\)
\(380\) −48.7778 −2.50225
\(381\) −4.96925 −0.254582
\(382\) −32.1500 −1.64494
\(383\) 6.64806 0.339700 0.169850 0.985470i \(-0.445672\pi\)
0.169850 + 0.985470i \(0.445672\pi\)
\(384\) 10.6993 0.545996
\(385\) 0 0
\(386\) −26.5302 −1.35035
\(387\) 6.12975 0.311593
\(388\) −49.9461 −2.53563
\(389\) 17.4068 0.882561 0.441280 0.897369i \(-0.354524\pi\)
0.441280 + 0.897369i \(0.354524\pi\)
\(390\) −23.3229 −1.18100
\(391\) 16.2630 0.822457
\(392\) 0 0
\(393\) 15.3014 0.771855
\(394\) 5.27988 0.265997
\(395\) −16.6792 −0.839220
\(396\) 25.5682 1.28485
\(397\) −13.3867 −0.671860 −0.335930 0.941887i \(-0.609050\pi\)
−0.335930 + 0.941887i \(0.609050\pi\)
\(398\) −4.35160 −0.218126
\(399\) 0 0
\(400\) −8.81849 −0.440924
\(401\) 36.5410 1.82477 0.912385 0.409334i \(-0.134239\pi\)
0.912385 + 0.409334i \(0.134239\pi\)
\(402\) −35.1322 −1.75224
\(403\) 3.51663 0.175176
\(404\) −26.8466 −1.33567
\(405\) −1.95019 −0.0969056
\(406\) 0 0
\(407\) 46.9072 2.32510
\(408\) 27.8957 1.38104
\(409\) −2.65442 −0.131252 −0.0656262 0.997844i \(-0.520904\pi\)
−0.0656262 + 0.997844i \(0.520904\pi\)
\(410\) −4.97848 −0.245870
\(411\) −11.3447 −0.559592
\(412\) −42.5846 −2.09799
\(413\) 0 0
\(414\) 9.56250 0.469971
\(415\) 19.8778 0.975761
\(416\) 27.9226 1.36902
\(417\) 0.201634 0.00987407
\(418\) −80.0176 −3.91379
\(419\) −0.446259 −0.0218012 −0.0109006 0.999941i \(-0.503470\pi\)
−0.0109006 + 0.999941i \(0.503470\pi\)
\(420\) 0 0
\(421\) −10.6932 −0.521154 −0.260577 0.965453i \(-0.583913\pi\)
−0.260577 + 0.965453i \(0.583913\pi\)
\(422\) 34.9006 1.69893
\(423\) −0.738793 −0.0359213
\(424\) 87.3663 4.24288
\(425\) 5.19589 0.252038
\(426\) 40.4667 1.96062
\(427\) 0 0
\(428\) −22.1519 −1.07075
\(429\) −26.5183 −1.28032
\(430\) 30.5169 1.47165
\(431\) −21.0322 −1.01308 −0.506542 0.862215i \(-0.669077\pi\)
−0.506542 + 0.862215i \(0.669077\pi\)
\(432\) 7.36860 0.354522
\(433\) −29.5953 −1.42226 −0.711131 0.703060i \(-0.751817\pi\)
−0.711131 + 0.703060i \(0.751817\pi\)
\(434\) 0 0
\(435\) 0.346017 0.0165902
\(436\) 32.0970 1.53717
\(437\) −20.7423 −0.992237
\(438\) −23.6594 −1.13049
\(439\) −28.4888 −1.35970 −0.679849 0.733352i \(-0.737955\pi\)
−0.679849 + 0.733352i \(0.737955\pi\)
\(440\) 70.9288 3.38140
\(441\) 0 0
\(442\) −51.9228 −2.46971
\(443\) −25.4898 −1.21106 −0.605528 0.795824i \(-0.707038\pi\)
−0.605528 + 0.795824i \(0.707038\pi\)
\(444\) 37.4301 1.77635
\(445\) 12.1740 0.577102
\(446\) 40.9367 1.93841
\(447\) −2.73172 −0.129206
\(448\) 0 0
\(449\) −36.8396 −1.73857 −0.869284 0.494313i \(-0.835420\pi\)
−0.869284 + 0.494313i \(0.835420\pi\)
\(450\) 3.05513 0.144020
\(451\) −5.66056 −0.266545
\(452\) 74.7689 3.51683
\(453\) −9.57461 −0.449855
\(454\) −10.5489 −0.495083
\(455\) 0 0
\(456\) −35.5789 −1.66613
\(457\) −1.99720 −0.0934253 −0.0467126 0.998908i \(-0.514875\pi\)
−0.0467126 + 0.998908i \(0.514875\pi\)
\(458\) −54.7404 −2.55785
\(459\) −4.34161 −0.202649
\(460\) 32.9965 1.53847
\(461\) 13.9093 0.647819 0.323909 0.946088i \(-0.395003\pi\)
0.323909 + 0.946088i \(0.395003\pi\)
\(462\) 0 0
\(463\) −36.9009 −1.71493 −0.857464 0.514544i \(-0.827961\pi\)
−0.857464 + 0.514544i \(0.827961\pi\)
\(464\) −1.30739 −0.0606941
\(465\) 1.46392 0.0678876
\(466\) 61.7628 2.86111
\(467\) 17.4145 0.805847 0.402924 0.915234i \(-0.367994\pi\)
0.402924 + 0.915234i \(0.367994\pi\)
\(468\) −21.1605 −0.978146
\(469\) 0 0
\(470\) −3.67807 −0.169657
\(471\) −9.56163 −0.440577
\(472\) −31.0859 −1.43085
\(473\) 34.6978 1.59541
\(474\) −21.8333 −1.00283
\(475\) −6.62697 −0.304066
\(476\) 0 0
\(477\) −13.5974 −0.622584
\(478\) 25.2157 1.15334
\(479\) 13.7314 0.627403 0.313702 0.949522i \(-0.398431\pi\)
0.313702 + 0.949522i \(0.398431\pi\)
\(480\) 11.6237 0.530548
\(481\) −38.8210 −1.77008
\(482\) 31.6526 1.44174
\(483\) 0 0
\(484\) 95.0444 4.32020
\(485\) 21.5644 0.979189
\(486\) −2.55282 −0.115798
\(487\) −6.36380 −0.288371 −0.144186 0.989551i \(-0.546056\pi\)
−0.144186 + 0.989551i \(0.546056\pi\)
\(488\) 66.2069 2.99704
\(489\) 3.62324 0.163849
\(490\) 0 0
\(491\) −0.00639387 −0.000288551 0 −0.000144276 1.00000i \(-0.500046\pi\)
−0.000144276 1.00000i \(0.500046\pi\)
\(492\) −4.51690 −0.203638
\(493\) 0.770321 0.0346935
\(494\) 66.2235 2.97954
\(495\) −11.0392 −0.496173
\(496\) −5.53128 −0.248362
\(497\) 0 0
\(498\) 26.0203 1.16600
\(499\) −38.1651 −1.70850 −0.854252 0.519859i \(-0.825984\pi\)
−0.854252 + 0.519859i \(0.825984\pi\)
\(500\) 54.5861 2.44117
\(501\) −7.01612 −0.313457
\(502\) −43.0022 −1.91928
\(503\) −2.51350 −0.112071 −0.0560356 0.998429i \(-0.517846\pi\)
−0.0560356 + 0.998429i \(0.517846\pi\)
\(504\) 0 0
\(505\) 11.5911 0.515799
\(506\) 54.1291 2.40633
\(507\) 8.94686 0.397344
\(508\) −22.4456 −0.995863
\(509\) 12.5359 0.555643 0.277821 0.960633i \(-0.410388\pi\)
0.277821 + 0.960633i \(0.410388\pi\)
\(510\) −21.6146 −0.957113
\(511\) 0 0
\(512\) 50.7703 2.24375
\(513\) 5.53739 0.244482
\(514\) 49.2695 2.17318
\(515\) 18.3861 0.810186
\(516\) 27.6875 1.21887
\(517\) −4.18198 −0.183923
\(518\) 0 0
\(519\) −14.3292 −0.628981
\(520\) −58.7015 −2.57423
\(521\) −30.4047 −1.33206 −0.666028 0.745927i \(-0.732007\pi\)
−0.666028 + 0.745927i \(0.732007\pi\)
\(522\) 0.452941 0.0198247
\(523\) −33.7300 −1.47491 −0.737454 0.675397i \(-0.763972\pi\)
−0.737454 + 0.675397i \(0.763972\pi\)
\(524\) 69.1150 3.01930
\(525\) 0 0
\(526\) 39.5054 1.72252
\(527\) 3.25905 0.141967
\(528\) 41.7104 1.81521
\(529\) −8.96858 −0.389938
\(530\) −67.6946 −2.94047
\(531\) 4.83812 0.209957
\(532\) 0 0
\(533\) 4.68475 0.202919
\(534\) 15.9359 0.689614
\(535\) 9.56414 0.413494
\(536\) −88.4244 −3.81935
\(537\) 5.16712 0.222978
\(538\) −66.7916 −2.87959
\(539\) 0 0
\(540\) −8.80881 −0.379071
\(541\) 15.4447 0.664020 0.332010 0.943276i \(-0.392273\pi\)
0.332010 + 0.943276i \(0.392273\pi\)
\(542\) 5.49231 0.235915
\(543\) −12.3174 −0.528592
\(544\) 25.8774 1.10948
\(545\) −13.8580 −0.593611
\(546\) 0 0
\(547\) 28.4856 1.21795 0.608977 0.793188i \(-0.291580\pi\)
0.608977 + 0.793188i \(0.291580\pi\)
\(548\) −51.2428 −2.18898
\(549\) −10.3042 −0.439775
\(550\) 17.2938 0.737408
\(551\) −0.982486 −0.0418553
\(552\) 24.0679 1.02440
\(553\) 0 0
\(554\) 34.7439 1.47612
\(555\) −16.1606 −0.685978
\(556\) 0.910762 0.0386249
\(557\) 20.6469 0.874838 0.437419 0.899258i \(-0.355893\pi\)
0.437419 + 0.899258i \(0.355893\pi\)
\(558\) 1.91629 0.0811230
\(559\) −28.7164 −1.21457
\(560\) 0 0
\(561\) −24.5760 −1.03760
\(562\) −21.4467 −0.904675
\(563\) −8.58979 −0.362017 −0.181008 0.983482i \(-0.557936\pi\)
−0.181008 + 0.983482i \(0.557936\pi\)
\(564\) −3.33705 −0.140515
\(565\) −32.2817 −1.35810
\(566\) −67.8035 −2.84999
\(567\) 0 0
\(568\) 101.851 4.27356
\(569\) 26.9090 1.12809 0.564043 0.825746i \(-0.309245\pi\)
0.564043 + 0.825746i \(0.309245\pi\)
\(570\) 27.5678 1.15469
\(571\) 9.87805 0.413384 0.206692 0.978406i \(-0.433730\pi\)
0.206692 + 0.978406i \(0.433730\pi\)
\(572\) −119.781 −5.00827
\(573\) 12.5939 0.526118
\(574\) 0 0
\(575\) 4.48291 0.186950
\(576\) 0.478424 0.0199343
\(577\) −28.6511 −1.19276 −0.596380 0.802702i \(-0.703395\pi\)
−0.596380 + 0.802702i \(0.703395\pi\)
\(578\) −4.72168 −0.196396
\(579\) 10.3925 0.431897
\(580\) 1.56293 0.0648969
\(581\) 0 0
\(582\) 28.2281 1.17009
\(583\) −76.9691 −3.18773
\(584\) −59.5484 −2.46413
\(585\) 9.13614 0.377733
\(586\) 40.2561 1.66296
\(587\) −45.8713 −1.89331 −0.946656 0.322246i \(-0.895562\pi\)
−0.946656 + 0.322246i \(0.895562\pi\)
\(588\) 0 0
\(589\) −4.15667 −0.171273
\(590\) 24.0865 0.991626
\(591\) −2.06825 −0.0850766
\(592\) 61.0611 2.50960
\(593\) −20.0783 −0.824516 −0.412258 0.911067i \(-0.635260\pi\)
−0.412258 + 0.911067i \(0.635260\pi\)
\(594\) −14.4504 −0.592907
\(595\) 0 0
\(596\) −12.3389 −0.505422
\(597\) 1.70462 0.0697655
\(598\) −44.7979 −1.83192
\(599\) −5.35572 −0.218829 −0.109414 0.993996i \(-0.534898\pi\)
−0.109414 + 0.993996i \(0.534898\pi\)
\(600\) 7.68946 0.313921
\(601\) −2.39952 −0.0978785 −0.0489393 0.998802i \(-0.515584\pi\)
−0.0489393 + 0.998802i \(0.515584\pi\)
\(602\) 0 0
\(603\) 13.7621 0.560437
\(604\) −43.2476 −1.75972
\(605\) −41.0357 −1.66834
\(606\) 15.1729 0.616359
\(607\) −4.62908 −0.187889 −0.0939443 0.995577i \(-0.529948\pi\)
−0.0939443 + 0.995577i \(0.529948\pi\)
\(608\) −33.0046 −1.33851
\(609\) 0 0
\(610\) −51.2995 −2.07706
\(611\) 3.46106 0.140019
\(612\) −19.6106 −0.792713
\(613\) 36.3740 1.46913 0.734567 0.678536i \(-0.237385\pi\)
0.734567 + 0.678536i \(0.237385\pi\)
\(614\) 41.9817 1.69424
\(615\) 1.95019 0.0786392
\(616\) 0 0
\(617\) −25.3982 −1.02249 −0.511247 0.859434i \(-0.670816\pi\)
−0.511247 + 0.859434i \(0.670816\pi\)
\(618\) 24.0676 0.968140
\(619\) −46.4558 −1.86722 −0.933609 0.358294i \(-0.883359\pi\)
−0.933609 + 0.358294i \(0.883359\pi\)
\(620\) 6.61238 0.265560
\(621\) −3.74585 −0.150316
\(622\) 69.7814 2.79798
\(623\) 0 0
\(624\) −34.5200 −1.38191
\(625\) −17.5839 −0.703357
\(626\) −34.7578 −1.38920
\(627\) 31.3447 1.25179
\(628\) −43.1889 −1.72343
\(629\) −35.9775 −1.43452
\(630\) 0 0
\(631\) 38.1736 1.51967 0.759834 0.650118i \(-0.225280\pi\)
0.759834 + 0.650118i \(0.225280\pi\)
\(632\) −54.9522 −2.18588
\(633\) −13.6714 −0.543388
\(634\) −49.1215 −1.95086
\(635\) 9.69098 0.384575
\(636\) −61.4183 −2.43539
\(637\) 0 0
\(638\) 2.56390 0.101506
\(639\) −15.8518 −0.627086
\(640\) −20.8656 −0.824787
\(641\) −23.1486 −0.914314 −0.457157 0.889386i \(-0.651132\pi\)
−0.457157 + 0.889386i \(0.651132\pi\)
\(642\) 12.5196 0.494109
\(643\) −11.2230 −0.442591 −0.221296 0.975207i \(-0.571029\pi\)
−0.221296 + 0.975207i \(0.571029\pi\)
\(644\) 0 0
\(645\) −11.9542 −0.470695
\(646\) 61.3729 2.41469
\(647\) 12.6618 0.497787 0.248894 0.968531i \(-0.419933\pi\)
0.248894 + 0.968531i \(0.419933\pi\)
\(648\) −6.42520 −0.252406
\(649\) 27.3865 1.07501
\(650\) −14.3125 −0.561383
\(651\) 0 0
\(652\) 16.3658 0.640935
\(653\) 24.5628 0.961218 0.480609 0.876935i \(-0.340416\pi\)
0.480609 + 0.876935i \(0.340416\pi\)
\(654\) −18.1403 −0.709342
\(655\) −29.8407 −1.16597
\(656\) −7.36860 −0.287695
\(657\) 9.26794 0.361577
\(658\) 0 0
\(659\) −25.2897 −0.985147 −0.492573 0.870271i \(-0.663944\pi\)
−0.492573 + 0.870271i \(0.663944\pi\)
\(660\) −49.8628 −1.94091
\(661\) −14.9100 −0.579932 −0.289966 0.957037i \(-0.593644\pi\)
−0.289966 + 0.957037i \(0.593644\pi\)
\(662\) 62.6893 2.43649
\(663\) 20.3394 0.789915
\(664\) 65.4904 2.54152
\(665\) 0 0
\(666\) −21.1544 −0.819716
\(667\) 0.664618 0.0257341
\(668\) −31.6911 −1.22617
\(669\) −16.0359 −0.619983
\(670\) 68.5145 2.64694
\(671\) −58.3278 −2.25172
\(672\) 0 0
\(673\) −26.1061 −1.00632 −0.503158 0.864195i \(-0.667829\pi\)
−0.503158 + 0.864195i \(0.667829\pi\)
\(674\) −6.43413 −0.247833
\(675\) −1.19677 −0.0460635
\(676\) 40.4121 1.55431
\(677\) 29.9611 1.15150 0.575750 0.817626i \(-0.304710\pi\)
0.575750 + 0.817626i \(0.304710\pi\)
\(678\) −42.2572 −1.62288
\(679\) 0 0
\(680\) −54.4019 −2.08622
\(681\) 4.13224 0.158348
\(682\) 10.8473 0.415364
\(683\) 22.2547 0.851551 0.425776 0.904829i \(-0.360001\pi\)
0.425776 + 0.904829i \(0.360001\pi\)
\(684\) 25.0119 0.956352
\(685\) 22.1243 0.845325
\(686\) 0 0
\(687\) 21.4431 0.818105
\(688\) 45.1677 1.72200
\(689\) 63.7005 2.42680
\(690\) −18.6487 −0.709943
\(691\) −25.3537 −0.964500 −0.482250 0.876034i \(-0.660180\pi\)
−0.482250 + 0.876034i \(0.660180\pi\)
\(692\) −64.7234 −2.46042
\(693\) 0 0
\(694\) 10.7001 0.406170
\(695\) −0.393225 −0.0149159
\(696\) 1.14001 0.0432119
\(697\) 4.34161 0.164450
\(698\) −61.5931 −2.33133
\(699\) −24.1939 −0.915098
\(700\) 0 0
\(701\) 36.2025 1.36735 0.683675 0.729787i \(-0.260381\pi\)
0.683675 + 0.729787i \(0.260381\pi\)
\(702\) 11.9593 0.451376
\(703\) 45.8866 1.73064
\(704\) 2.70815 0.102067
\(705\) 1.44078 0.0542631
\(706\) −26.8688 −1.01122
\(707\) 0 0
\(708\) 21.8533 0.821298
\(709\) −45.5410 −1.71033 −0.855165 0.518356i \(-0.826544\pi\)
−0.855165 + 0.518356i \(0.826544\pi\)
\(710\) −78.9178 −2.96173
\(711\) 8.55260 0.320747
\(712\) 40.1091 1.50315
\(713\) 2.81185 0.105304
\(714\) 0 0
\(715\) 51.7157 1.93406
\(716\) 23.3394 0.872233
\(717\) −9.87757 −0.368884
\(718\) −7.12054 −0.265736
\(719\) −42.9208 −1.60067 −0.800337 0.599550i \(-0.795346\pi\)
−0.800337 + 0.599550i \(0.795346\pi\)
\(720\) −14.3701 −0.535544
\(721\) 0 0
\(722\) −29.7729 −1.10803
\(723\) −12.3991 −0.461126
\(724\) −55.6366 −2.06772
\(725\) 0.212339 0.00788608
\(726\) −53.7163 −1.99360
\(727\) −39.9954 −1.48335 −0.741673 0.670762i \(-0.765967\pi\)
−0.741673 + 0.670762i \(0.765967\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 46.1403 1.70773
\(731\) −26.6130 −0.984318
\(732\) −46.5433 −1.72029
\(733\) −9.46168 −0.349475 −0.174737 0.984615i \(-0.555908\pi\)
−0.174737 + 0.984615i \(0.555908\pi\)
\(734\) −3.96766 −0.146449
\(735\) 0 0
\(736\) 22.3265 0.822964
\(737\) 77.9013 2.86953
\(738\) 2.55282 0.0939707
\(739\) 15.2622 0.561429 0.280714 0.959791i \(-0.409429\pi\)
0.280714 + 0.959791i \(0.409429\pi\)
\(740\) −72.9957 −2.68338
\(741\) −25.9413 −0.952977
\(742\) 0 0
\(743\) −38.0213 −1.39487 −0.697433 0.716650i \(-0.745674\pi\)
−0.697433 + 0.716650i \(0.745674\pi\)
\(744\) 4.82311 0.176824
\(745\) 5.32737 0.195180
\(746\) −47.8237 −1.75095
\(747\) −10.1927 −0.372933
\(748\) −111.007 −4.05882
\(749\) 0 0
\(750\) −30.8505 −1.12650
\(751\) −12.7453 −0.465082 −0.232541 0.972587i \(-0.574704\pi\)
−0.232541 + 0.972587i \(0.574704\pi\)
\(752\) −5.44386 −0.198517
\(753\) 16.8450 0.613865
\(754\) −2.12191 −0.0772755
\(755\) 18.6723 0.679554
\(756\) 0 0
\(757\) −37.3160 −1.35627 −0.678137 0.734936i \(-0.737212\pi\)
−0.678137 + 0.734936i \(0.737212\pi\)
\(758\) 19.7879 0.718728
\(759\) −21.2036 −0.769643
\(760\) 69.3855 2.51688
\(761\) 25.7820 0.934596 0.467298 0.884100i \(-0.345227\pi\)
0.467298 + 0.884100i \(0.345227\pi\)
\(762\) 12.6856 0.459551
\(763\) 0 0
\(764\) 56.8854 2.05804
\(765\) 8.46696 0.306124
\(766\) −16.9713 −0.613199
\(767\) −22.6654 −0.818400
\(768\) −28.2702 −1.02011
\(769\) −49.9035 −1.79957 −0.899783 0.436337i \(-0.856275\pi\)
−0.899783 + 0.436337i \(0.856275\pi\)
\(770\) 0 0
\(771\) −19.3000 −0.695072
\(772\) 46.9418 1.68947
\(773\) 20.0169 0.719957 0.359978 0.932961i \(-0.382784\pi\)
0.359978 + 0.932961i \(0.382784\pi\)
\(774\) −15.6482 −0.562462
\(775\) 0.898359 0.0322700
\(776\) 71.0473 2.55045
\(777\) 0 0
\(778\) −44.4365 −1.59313
\(779\) −5.53739 −0.198398
\(780\) 41.2670 1.47760
\(781\) −89.7299 −3.21079
\(782\) −41.5167 −1.48463
\(783\) −0.177428 −0.00634074
\(784\) 0 0
\(785\) 18.6470 0.665539
\(786\) −39.0618 −1.39329
\(787\) 0.551603 0.0196625 0.00983127 0.999952i \(-0.496871\pi\)
0.00983127 + 0.999952i \(0.496871\pi\)
\(788\) −9.34210 −0.332798
\(789\) −15.4752 −0.550932
\(790\) 42.5790 1.51489
\(791\) 0 0
\(792\) −36.3702 −1.29236
\(793\) 48.2728 1.71422
\(794\) 34.1739 1.21279
\(795\) 26.5176 0.940481
\(796\) 7.69961 0.272905
\(797\) 10.0903 0.357416 0.178708 0.983902i \(-0.442808\pi\)
0.178708 + 0.983902i \(0.442808\pi\)
\(798\) 0 0
\(799\) 3.20755 0.113475
\(800\) 7.13310 0.252193
\(801\) −6.24247 −0.220567
\(802\) −93.2826 −3.29392
\(803\) 52.4617 1.85133
\(804\) 62.1621 2.19229
\(805\) 0 0
\(806\) −8.97733 −0.316213
\(807\) 26.1638 0.921010
\(808\) 38.1888 1.34348
\(809\) −26.6690 −0.937632 −0.468816 0.883296i \(-0.655319\pi\)
−0.468816 + 0.883296i \(0.655319\pi\)
\(810\) 4.97848 0.174926
\(811\) 9.19171 0.322764 0.161382 0.986892i \(-0.448405\pi\)
0.161382 + 0.986892i \(0.448405\pi\)
\(812\) 0 0
\(813\) −2.15147 −0.0754552
\(814\) −119.746 −4.19709
\(815\) −7.06600 −0.247511
\(816\) −31.9916 −1.11993
\(817\) 33.9429 1.18751
\(818\) 6.77625 0.236926
\(819\) 0 0
\(820\) 8.80881 0.307617
\(821\) −26.5679 −0.927225 −0.463613 0.886038i \(-0.653447\pi\)
−0.463613 + 0.886038i \(0.653447\pi\)
\(822\) 28.9610 1.01013
\(823\) 16.3412 0.569618 0.284809 0.958584i \(-0.408070\pi\)
0.284809 + 0.958584i \(0.408070\pi\)
\(824\) 60.5757 2.11026
\(825\) −6.77437 −0.235853
\(826\) 0 0
\(827\) −26.2489 −0.912763 −0.456382 0.889784i \(-0.650855\pi\)
−0.456382 + 0.889784i \(0.650855\pi\)
\(828\) −16.9197 −0.587999
\(829\) −29.3109 −1.01801 −0.509004 0.860764i \(-0.669986\pi\)
−0.509004 + 0.860764i \(0.669986\pi\)
\(830\) −50.7444 −1.76136
\(831\) −13.6100 −0.472125
\(832\) −2.24129 −0.0777029
\(833\) 0 0
\(834\) −0.514736 −0.0178239
\(835\) 13.6827 0.473511
\(836\) 141.581 4.89669
\(837\) −0.750655 −0.0259464
\(838\) 1.13922 0.0393537
\(839\) −19.9983 −0.690418 −0.345209 0.938526i \(-0.612192\pi\)
−0.345209 + 0.938526i \(0.612192\pi\)
\(840\) 0 0
\(841\) −28.9685 −0.998914
\(842\) 27.2978 0.940745
\(843\) 8.40118 0.289352
\(844\) −61.7522 −2.12560
\(845\) −17.4481 −0.600231
\(846\) 1.88601 0.0648422
\(847\) 0 0
\(848\) −100.194 −3.44068
\(849\) 26.5602 0.911544
\(850\) −13.2642 −0.454958
\(851\) −31.0407 −1.06406
\(852\) −71.6009 −2.45301
\(853\) 38.0278 1.30205 0.651024 0.759057i \(-0.274340\pi\)
0.651024 + 0.759057i \(0.274340\pi\)
\(854\) 0 0
\(855\) −10.7990 −0.369317
\(856\) 31.5106 1.07701
\(857\) −44.7944 −1.53015 −0.765074 0.643943i \(-0.777297\pi\)
−0.765074 + 0.643943i \(0.777297\pi\)
\(858\) 67.6965 2.31112
\(859\) 48.2166 1.64513 0.822564 0.568672i \(-0.192543\pi\)
0.822564 + 0.568672i \(0.192543\pi\)
\(860\) −53.9958 −1.84124
\(861\) 0 0
\(862\) 53.6914 1.82874
\(863\) −34.7794 −1.18391 −0.591953 0.805973i \(-0.701643\pi\)
−0.591953 + 0.805973i \(0.701643\pi\)
\(864\) −5.96031 −0.202774
\(865\) 27.9446 0.950144
\(866\) 75.5516 2.56735
\(867\) 1.84959 0.0628155
\(868\) 0 0
\(869\) 48.4125 1.64228
\(870\) −0.883320 −0.0299474
\(871\) −64.4720 −2.18455
\(872\) −45.6573 −1.54615
\(873\) −11.0576 −0.374243
\(874\) 52.9513 1.79111
\(875\) 0 0
\(876\) 41.8624 1.41440
\(877\) 35.4222 1.19612 0.598062 0.801450i \(-0.295938\pi\)
0.598062 + 0.801450i \(0.295938\pi\)
\(878\) 72.7269 2.45441
\(879\) −15.7692 −0.531883
\(880\) −81.3431 −2.74207
\(881\) −42.7231 −1.43938 −0.719689 0.694297i \(-0.755715\pi\)
−0.719689 + 0.694297i \(0.755715\pi\)
\(882\) 0 0
\(883\) 28.6770 0.965057 0.482528 0.875880i \(-0.339719\pi\)
0.482528 + 0.875880i \(0.339719\pi\)
\(884\) 91.8709 3.08995
\(885\) −9.43525 −0.317163
\(886\) 65.0709 2.18610
\(887\) −32.6181 −1.09521 −0.547604 0.836738i \(-0.684460\pi\)
−0.547604 + 0.836738i \(0.684460\pi\)
\(888\) −53.2435 −1.78674
\(889\) 0 0
\(890\) −31.0780 −1.04174
\(891\) 5.66056 0.189636
\(892\) −72.4325 −2.42522
\(893\) −4.09099 −0.136900
\(894\) 6.97360 0.233232
\(895\) −10.0769 −0.336832
\(896\) 0 0
\(897\) 17.5484 0.585923
\(898\) 94.0450 3.13832
\(899\) 0.133187 0.00444203
\(900\) −5.40567 −0.180189
\(901\) 59.0348 1.96673
\(902\) 14.4504 0.481146
\(903\) 0 0
\(904\) −106.357 −3.53739
\(905\) 24.0213 0.798495
\(906\) 24.4423 0.812040
\(907\) 19.3298 0.641836 0.320918 0.947107i \(-0.396009\pi\)
0.320918 + 0.947107i \(0.396009\pi\)
\(908\) 18.6649 0.619417
\(909\) −5.94360 −0.197137
\(910\) 0 0
\(911\) −6.54007 −0.216682 −0.108341 0.994114i \(-0.534554\pi\)
−0.108341 + 0.994114i \(0.534554\pi\)
\(912\) 40.8028 1.35112
\(913\) −57.6966 −1.90948
\(914\) 5.09851 0.168644
\(915\) 20.0952 0.664328
\(916\) 96.8563 3.20022
\(917\) 0 0
\(918\) 11.0834 0.365805
\(919\) 6.00261 0.198008 0.0990039 0.995087i \(-0.468434\pi\)
0.0990039 + 0.995087i \(0.468434\pi\)
\(920\) −46.9369 −1.54746
\(921\) −16.4452 −0.541888
\(922\) −35.5079 −1.16939
\(923\) 74.2615 2.44435
\(924\) 0 0
\(925\) −9.91721 −0.326076
\(926\) 94.2013 3.09565
\(927\) −9.42784 −0.309651
\(928\) 1.05752 0.0347149
\(929\) −1.82438 −0.0598559 −0.0299279 0.999552i \(-0.509528\pi\)
−0.0299279 + 0.999552i \(0.509528\pi\)
\(930\) −3.73713 −0.122545
\(931\) 0 0
\(932\) −109.282 −3.57964
\(933\) −27.3350 −0.894908
\(934\) −44.4561 −1.45465
\(935\) 47.9277 1.56740
\(936\) 30.1004 0.983864
\(937\) −9.00232 −0.294093 −0.147047 0.989130i \(-0.546977\pi\)
−0.147047 + 0.989130i \(0.546977\pi\)
\(938\) 0 0
\(939\) 13.6155 0.444323
\(940\) 6.50788 0.212264
\(941\) 32.6025 1.06281 0.531405 0.847118i \(-0.321664\pi\)
0.531405 + 0.847118i \(0.321664\pi\)
\(942\) 24.4091 0.795293
\(943\) 3.74585 0.121982
\(944\) 35.6502 1.16031
\(945\) 0 0
\(946\) −88.5774 −2.87990
\(947\) −50.3619 −1.63654 −0.818271 0.574833i \(-0.805067\pi\)
−0.818271 + 0.574833i \(0.805067\pi\)
\(948\) 38.6312 1.25468
\(949\) −43.4180 −1.40941
\(950\) 16.9175 0.548875
\(951\) 19.2420 0.623966
\(952\) 0 0
\(953\) 4.18696 0.135629 0.0678145 0.997698i \(-0.478397\pi\)
0.0678145 + 0.997698i \(0.478397\pi\)
\(954\) 34.7118 1.12384
\(955\) −24.5605 −0.794759
\(956\) −44.6160 −1.44298
\(957\) −1.00434 −0.0324657
\(958\) −35.0538 −1.13254
\(959\) 0 0
\(960\) −0.933016 −0.0301130
\(961\) −30.4365 −0.981823
\(962\) 99.1030 3.19521
\(963\) −4.90421 −0.158036
\(964\) −56.0053 −1.80381
\(965\) −20.2673 −0.652428
\(966\) 0 0
\(967\) 25.6993 0.826433 0.413216 0.910633i \(-0.364405\pi\)
0.413216 + 0.910633i \(0.364405\pi\)
\(968\) −135.199 −4.34545
\(969\) −24.0412 −0.772315
\(970\) −55.0501 −1.76755
\(971\) 22.0085 0.706287 0.353143 0.935569i \(-0.385113\pi\)
0.353143 + 0.935569i \(0.385113\pi\)
\(972\) 4.51690 0.144880
\(973\) 0 0
\(974\) 16.2457 0.520544
\(975\) 5.60655 0.179553
\(976\) −75.9278 −2.43039
\(977\) −23.2219 −0.742935 −0.371467 0.928446i \(-0.621145\pi\)
−0.371467 + 0.928446i \(0.621145\pi\)
\(978\) −9.24948 −0.295766
\(979\) −35.3359 −1.12934
\(980\) 0 0
\(981\) 7.10598 0.226876
\(982\) 0.0163224 0.000520869 0
\(983\) −24.3469 −0.776545 −0.388273 0.921545i \(-0.626928\pi\)
−0.388273 + 0.921545i \(0.626928\pi\)
\(984\) 6.42520 0.204828
\(985\) 4.03348 0.128517
\(986\) −1.96649 −0.0626259
\(987\) 0 0
\(988\) −117.174 −3.72781
\(989\) −22.9612 −0.730122
\(990\) 28.1810 0.895651
\(991\) −6.13977 −0.195036 −0.0975181 0.995234i \(-0.531090\pi\)
−0.0975181 + 0.995234i \(0.531090\pi\)
\(992\) 4.47414 0.142054
\(993\) −24.5569 −0.779289
\(994\) 0 0
\(995\) −3.32433 −0.105388
\(996\) −46.0396 −1.45882
\(997\) −43.0435 −1.36320 −0.681601 0.731724i \(-0.738716\pi\)
−0.681601 + 0.731724i \(0.738716\pi\)
\(998\) 97.4287 3.08405
\(999\) 8.28667 0.262179
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 \(a_p\))