Properties

Label 6027.2.a.bo.1.16
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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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: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +1.67187 q^{10} +3.74096 q^{11} +0.272577 q^{12} +4.04957 q^{13} +1.10903 q^{15} -4.47086 q^{16} -1.28562 q^{17} +1.50751 q^{18} +2.77400 q^{19} +0.302296 q^{20} +5.63953 q^{22} +8.14553 q^{23} -2.60410 q^{24} -3.77005 q^{25} +6.10476 q^{26} +1.00000 q^{27} -1.13225 q^{29} +1.67187 q^{30} +3.06661 q^{31} -1.53164 q^{32} +3.74096 q^{33} -1.93807 q^{34} +0.272577 q^{36} -8.99346 q^{37} +4.18183 q^{38} +4.04957 q^{39} -2.88803 q^{40} -1.00000 q^{41} +5.07578 q^{43} +1.01970 q^{44} +1.10903 q^{45} +12.2794 q^{46} -1.77524 q^{47} -4.47086 q^{48} -5.68338 q^{50} -1.28562 q^{51} +1.10382 q^{52} -1.43908 q^{53} +1.50751 q^{54} +4.14884 q^{55} +2.77400 q^{57} -1.70688 q^{58} -11.8133 q^{59} +0.302296 q^{60} +6.29435 q^{61} +4.62294 q^{62} +6.63275 q^{64} +4.49110 q^{65} +5.63953 q^{66} +1.53411 q^{67} -0.350429 q^{68} +8.14553 q^{69} +12.4191 q^{71} -2.60410 q^{72} +7.32700 q^{73} -13.5577 q^{74} -3.77005 q^{75} +0.756129 q^{76} +6.10476 q^{78} +3.06259 q^{79} -4.95832 q^{80} +1.00000 q^{81} -1.50751 q^{82} -10.5895 q^{83} -1.42579 q^{85} +7.65178 q^{86} -1.13225 q^{87} -9.74185 q^{88} -0.862204 q^{89} +1.67187 q^{90} +2.22028 q^{92} +3.06661 q^{93} -2.67619 q^{94} +3.07645 q^{95} -1.53164 q^{96} -2.95888 q^{97} +3.74096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50751 1.06597 0.532984 0.846125i \(-0.321071\pi\)
0.532984 + 0.846125i \(0.321071\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.272577 0.136288
\(5\) 1.10903 0.495973 0.247987 0.968763i \(-0.420231\pi\)
0.247987 + 0.968763i \(0.420231\pi\)
\(6\) 1.50751 0.615437
\(7\) 0 0
\(8\) −2.60410 −0.920689
\(9\) 1.00000 0.333333
\(10\) 1.67187 0.528692
\(11\) 3.74096 1.12794 0.563971 0.825794i \(-0.309273\pi\)
0.563971 + 0.825794i \(0.309273\pi\)
\(12\) 0.272577 0.0786862
\(13\) 4.04957 1.12315 0.561575 0.827426i \(-0.310196\pi\)
0.561575 + 0.827426i \(0.310196\pi\)
\(14\) 0 0
\(15\) 1.10903 0.286350
\(16\) −4.47086 −1.11771
\(17\) −1.28562 −0.311808 −0.155904 0.987772i \(-0.549829\pi\)
−0.155904 + 0.987772i \(0.549829\pi\)
\(18\) 1.50751 0.355323
\(19\) 2.77400 0.636400 0.318200 0.948024i \(-0.396922\pi\)
0.318200 + 0.948024i \(0.396922\pi\)
\(20\) 0.302296 0.0675955
\(21\) 0 0
\(22\) 5.63953 1.20235
\(23\) 8.14553 1.69846 0.849230 0.528023i \(-0.177067\pi\)
0.849230 + 0.528023i \(0.177067\pi\)
\(24\) −2.60410 −0.531560
\(25\) −3.77005 −0.754010
\(26\) 6.10476 1.19724
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.13225 −0.210254 −0.105127 0.994459i \(-0.533525\pi\)
−0.105127 + 0.994459i \(0.533525\pi\)
\(30\) 1.67187 0.305240
\(31\) 3.06661 0.550779 0.275390 0.961333i \(-0.411193\pi\)
0.275390 + 0.961333i \(0.411193\pi\)
\(32\) −1.53164 −0.270758
\(33\) 3.74096 0.651218
\(34\) −1.93807 −0.332377
\(35\) 0 0
\(36\) 0.272577 0.0454295
\(37\) −8.99346 −1.47852 −0.739258 0.673423i \(-0.764823\pi\)
−0.739258 + 0.673423i \(0.764823\pi\)
\(38\) 4.18183 0.678382
\(39\) 4.04957 0.648450
\(40\) −2.88803 −0.456637
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 5.07578 0.774050 0.387025 0.922069i \(-0.373503\pi\)
0.387025 + 0.922069i \(0.373503\pi\)
\(44\) 1.01970 0.153726
\(45\) 1.10903 0.165324
\(46\) 12.2794 1.81050
\(47\) −1.77524 −0.258946 −0.129473 0.991583i \(-0.541329\pi\)
−0.129473 + 0.991583i \(0.541329\pi\)
\(48\) −4.47086 −0.645312
\(49\) 0 0
\(50\) −5.68338 −0.803751
\(51\) −1.28562 −0.180022
\(52\) 1.10382 0.153072
\(53\) −1.43908 −0.197673 −0.0988365 0.995104i \(-0.531512\pi\)
−0.0988365 + 0.995104i \(0.531512\pi\)
\(54\) 1.50751 0.205146
\(55\) 4.14884 0.559430
\(56\) 0 0
\(57\) 2.77400 0.367425
\(58\) −1.70688 −0.224124
\(59\) −11.8133 −1.53796 −0.768980 0.639273i \(-0.779235\pi\)
−0.768980 + 0.639273i \(0.779235\pi\)
\(60\) 0.302296 0.0390263
\(61\) 6.29435 0.805908 0.402954 0.915220i \(-0.367983\pi\)
0.402954 + 0.915220i \(0.367983\pi\)
\(62\) 4.62294 0.587113
\(63\) 0 0
\(64\) 6.63275 0.829094
\(65\) 4.49110 0.557052
\(66\) 5.63953 0.694178
\(67\) 1.53411 0.187421 0.0937107 0.995599i \(-0.470127\pi\)
0.0937107 + 0.995599i \(0.470127\pi\)
\(68\) −0.350429 −0.0424958
\(69\) 8.14553 0.980606
\(70\) 0 0
\(71\) 12.4191 1.47388 0.736938 0.675960i \(-0.236271\pi\)
0.736938 + 0.675960i \(0.236271\pi\)
\(72\) −2.60410 −0.306896
\(73\) 7.32700 0.857561 0.428780 0.903409i \(-0.358943\pi\)
0.428780 + 0.903409i \(0.358943\pi\)
\(74\) −13.5577 −1.57605
\(75\) −3.77005 −0.435328
\(76\) 0.756129 0.0867339
\(77\) 0 0
\(78\) 6.10476 0.691228
\(79\) 3.06259 0.344568 0.172284 0.985047i \(-0.444885\pi\)
0.172284 + 0.985047i \(0.444885\pi\)
\(80\) −4.95832 −0.554356
\(81\) 1.00000 0.111111
\(82\) −1.50751 −0.166476
\(83\) −10.5895 −1.16235 −0.581175 0.813778i \(-0.697407\pi\)
−0.581175 + 0.813778i \(0.697407\pi\)
\(84\) 0 0
\(85\) −1.42579 −0.154648
\(86\) 7.65178 0.825112
\(87\) −1.13225 −0.121390
\(88\) −9.74185 −1.03848
\(89\) −0.862204 −0.0913935 −0.0456967 0.998955i \(-0.514551\pi\)
−0.0456967 + 0.998955i \(0.514551\pi\)
\(90\) 1.67187 0.176231
\(91\) 0 0
\(92\) 2.22028 0.231480
\(93\) 3.06661 0.317993
\(94\) −2.67619 −0.276028
\(95\) 3.07645 0.315637
\(96\) −1.53164 −0.156322
\(97\) −2.95888 −0.300428 −0.150214 0.988653i \(-0.547996\pi\)
−0.150214 + 0.988653i \(0.547996\pi\)
\(98\) 0 0
\(99\) 3.74096 0.375981
\(100\) −1.02763 −0.102763
\(101\) 9.78581 0.973724 0.486862 0.873479i \(-0.338141\pi\)
0.486862 + 0.873479i \(0.338141\pi\)
\(102\) −1.93807 −0.191898
\(103\) 5.64685 0.556400 0.278200 0.960523i \(-0.410262\pi\)
0.278200 + 0.960523i \(0.410262\pi\)
\(104\) −10.5455 −1.03407
\(105\) 0 0
\(106\) −2.16942 −0.210713
\(107\) 14.2514 1.37773 0.688866 0.724889i \(-0.258109\pi\)
0.688866 + 0.724889i \(0.258109\pi\)
\(108\) 0.272577 0.0262287
\(109\) −1.98301 −0.189938 −0.0949689 0.995480i \(-0.530275\pi\)
−0.0949689 + 0.995480i \(0.530275\pi\)
\(110\) 6.25441 0.596334
\(111\) −8.99346 −0.853621
\(112\) 0 0
\(113\) 1.92257 0.180860 0.0904302 0.995903i \(-0.471176\pi\)
0.0904302 + 0.995903i \(0.471176\pi\)
\(114\) 4.18183 0.391664
\(115\) 9.03364 0.842391
\(116\) −0.308626 −0.0286552
\(117\) 4.04957 0.374383
\(118\) −17.8086 −1.63942
\(119\) 0 0
\(120\) −2.88803 −0.263640
\(121\) 2.99480 0.272255
\(122\) 9.48877 0.859073
\(123\) −1.00000 −0.0901670
\(124\) 0.835887 0.0750649
\(125\) −9.72625 −0.869943
\(126\) 0 0
\(127\) 6.05248 0.537071 0.268536 0.963270i \(-0.413460\pi\)
0.268536 + 0.963270i \(0.413460\pi\)
\(128\) 13.0622 1.15455
\(129\) 5.07578 0.446898
\(130\) 6.77036 0.593800
\(131\) 10.1642 0.888055 0.444027 0.896013i \(-0.353549\pi\)
0.444027 + 0.896013i \(0.353549\pi\)
\(132\) 1.01970 0.0887535
\(133\) 0 0
\(134\) 2.31268 0.199785
\(135\) 1.10903 0.0954501
\(136\) 3.34788 0.287078
\(137\) 10.4749 0.894928 0.447464 0.894302i \(-0.352327\pi\)
0.447464 + 0.894302i \(0.352327\pi\)
\(138\) 12.2794 1.04530
\(139\) −5.03683 −0.427219 −0.213609 0.976919i \(-0.568522\pi\)
−0.213609 + 0.976919i \(0.568522\pi\)
\(140\) 0 0
\(141\) −1.77524 −0.149503
\(142\) 18.7219 1.57110
\(143\) 15.1493 1.26685
\(144\) −4.47086 −0.372571
\(145\) −1.25570 −0.104280
\(146\) 11.0455 0.914132
\(147\) 0 0
\(148\) −2.45141 −0.201505
\(149\) 12.4511 1.02003 0.510016 0.860165i \(-0.329640\pi\)
0.510016 + 0.860165i \(0.329640\pi\)
\(150\) −5.68338 −0.464046
\(151\) 1.01228 0.0823779 0.0411889 0.999151i \(-0.486885\pi\)
0.0411889 + 0.999151i \(0.486885\pi\)
\(152\) −7.22378 −0.585926
\(153\) −1.28562 −0.103936
\(154\) 0 0
\(155\) 3.40096 0.273172
\(156\) 1.10382 0.0883763
\(157\) −3.97214 −0.317011 −0.158506 0.987358i \(-0.550668\pi\)
−0.158506 + 0.987358i \(0.550668\pi\)
\(158\) 4.61688 0.367299
\(159\) −1.43908 −0.114127
\(160\) −1.69864 −0.134289
\(161\) 0 0
\(162\) 1.50751 0.118441
\(163\) 22.6056 1.77061 0.885304 0.465013i \(-0.153950\pi\)
0.885304 + 0.465013i \(0.153950\pi\)
\(164\) −0.272577 −0.0212847
\(165\) 4.14884 0.322987
\(166\) −15.9638 −1.23903
\(167\) −10.2870 −0.796035 −0.398017 0.917378i \(-0.630302\pi\)
−0.398017 + 0.917378i \(0.630302\pi\)
\(168\) 0 0
\(169\) 3.39903 0.261464
\(170\) −2.14938 −0.164850
\(171\) 2.77400 0.212133
\(172\) 1.38354 0.105494
\(173\) −8.31332 −0.632050 −0.316025 0.948751i \(-0.602348\pi\)
−0.316025 + 0.948751i \(0.602348\pi\)
\(174\) −1.70688 −0.129398
\(175\) 0 0
\(176\) −16.7253 −1.26072
\(177\) −11.8133 −0.887942
\(178\) −1.29978 −0.0974225
\(179\) 5.82288 0.435222 0.217611 0.976036i \(-0.430174\pi\)
0.217611 + 0.976036i \(0.430174\pi\)
\(180\) 0.302296 0.0225318
\(181\) −16.9447 −1.25949 −0.629746 0.776801i \(-0.716841\pi\)
−0.629746 + 0.776801i \(0.716841\pi\)
\(182\) 0 0
\(183\) 6.29435 0.465291
\(184\) −21.2118 −1.56375
\(185\) −9.97402 −0.733304
\(186\) 4.62294 0.338970
\(187\) −4.80944 −0.351701
\(188\) −0.483891 −0.0352913
\(189\) 0 0
\(190\) 4.63777 0.336459
\(191\) 12.9496 0.937001 0.468501 0.883463i \(-0.344794\pi\)
0.468501 + 0.883463i \(0.344794\pi\)
\(192\) 6.63275 0.478678
\(193\) −1.53674 −0.110617 −0.0553084 0.998469i \(-0.517614\pi\)
−0.0553084 + 0.998469i \(0.517614\pi\)
\(194\) −4.46053 −0.320247
\(195\) 4.49110 0.321614
\(196\) 0 0
\(197\) 14.6537 1.04403 0.522017 0.852935i \(-0.325180\pi\)
0.522017 + 0.852935i \(0.325180\pi\)
\(198\) 5.63953 0.400784
\(199\) −15.9626 −1.13156 −0.565780 0.824556i \(-0.691425\pi\)
−0.565780 + 0.824556i \(0.691425\pi\)
\(200\) 9.81760 0.694209
\(201\) 1.53411 0.108208
\(202\) 14.7522 1.03796
\(203\) 0 0
\(204\) −0.350429 −0.0245350
\(205\) −1.10903 −0.0774580
\(206\) 8.51266 0.593105
\(207\) 8.14553 0.566153
\(208\) −18.1050 −1.25536
\(209\) 10.3774 0.717822
\(210\) 0 0
\(211\) 23.5174 1.61901 0.809503 0.587116i \(-0.199737\pi\)
0.809503 + 0.587116i \(0.199737\pi\)
\(212\) −0.392260 −0.0269405
\(213\) 12.4191 0.850943
\(214\) 21.4840 1.46862
\(215\) 5.62920 0.383908
\(216\) −2.60410 −0.177187
\(217\) 0 0
\(218\) −2.98940 −0.202468
\(219\) 7.32700 0.495113
\(220\) 1.13088 0.0762438
\(221\) −5.20619 −0.350206
\(222\) −13.5577 −0.909933
\(223\) −22.1230 −1.48146 −0.740732 0.671801i \(-0.765521\pi\)
−0.740732 + 0.671801i \(0.765521\pi\)
\(224\) 0 0
\(225\) −3.77005 −0.251337
\(226\) 2.89829 0.192791
\(227\) 21.8654 1.45126 0.725630 0.688085i \(-0.241549\pi\)
0.725630 + 0.688085i \(0.241549\pi\)
\(228\) 0.756129 0.0500758
\(229\) −14.7855 −0.977054 −0.488527 0.872549i \(-0.662466\pi\)
−0.488527 + 0.872549i \(0.662466\pi\)
\(230\) 13.6183 0.897962
\(231\) 0 0
\(232\) 2.94850 0.193578
\(233\) −27.2105 −1.78262 −0.891310 0.453394i \(-0.850213\pi\)
−0.891310 + 0.453394i \(0.850213\pi\)
\(234\) 6.10476 0.399080
\(235\) −1.96880 −0.128430
\(236\) −3.22003 −0.209606
\(237\) 3.06259 0.198937
\(238\) 0 0
\(239\) −23.9634 −1.55006 −0.775031 0.631924i \(-0.782266\pi\)
−0.775031 + 0.631924i \(0.782266\pi\)
\(240\) −4.95832 −0.320058
\(241\) 12.9104 0.831632 0.415816 0.909449i \(-0.363496\pi\)
0.415816 + 0.909449i \(0.363496\pi\)
\(242\) 4.51468 0.290215
\(243\) 1.00000 0.0641500
\(244\) 1.71569 0.109836
\(245\) 0 0
\(246\) −1.50751 −0.0961151
\(247\) 11.2335 0.714772
\(248\) −7.98577 −0.507097
\(249\) −10.5895 −0.671083
\(250\) −14.6624 −0.927331
\(251\) −13.4903 −0.851497 −0.425749 0.904841i \(-0.639989\pi\)
−0.425749 + 0.904841i \(0.639989\pi\)
\(252\) 0 0
\(253\) 30.4721 1.91577
\(254\) 9.12416 0.572501
\(255\) −1.42579 −0.0892863
\(256\) 6.42585 0.401616
\(257\) −4.35831 −0.271864 −0.135932 0.990718i \(-0.543403\pi\)
−0.135932 + 0.990718i \(0.543403\pi\)
\(258\) 7.65178 0.476379
\(259\) 0 0
\(260\) 1.22417 0.0759198
\(261\) −1.13225 −0.0700846
\(262\) 15.3227 0.946638
\(263\) −14.2904 −0.881182 −0.440591 0.897708i \(-0.645231\pi\)
−0.440591 + 0.897708i \(0.645231\pi\)
\(264\) −9.74185 −0.599569
\(265\) −1.59598 −0.0980405
\(266\) 0 0
\(267\) −0.862204 −0.0527660
\(268\) 0.418163 0.0255434
\(269\) −20.3295 −1.23951 −0.619755 0.784795i \(-0.712768\pi\)
−0.619755 + 0.784795i \(0.712768\pi\)
\(270\) 1.67187 0.101747
\(271\) 21.1831 1.28678 0.643392 0.765537i \(-0.277527\pi\)
0.643392 + 0.765537i \(0.277527\pi\)
\(272\) 5.74780 0.348512
\(273\) 0 0
\(274\) 15.7909 0.953965
\(275\) −14.1036 −0.850480
\(276\) 2.22028 0.133645
\(277\) 3.20291 0.192444 0.0962221 0.995360i \(-0.469324\pi\)
0.0962221 + 0.995360i \(0.469324\pi\)
\(278\) −7.59306 −0.455401
\(279\) 3.06661 0.183593
\(280\) 0 0
\(281\) −16.8668 −1.00619 −0.503094 0.864231i \(-0.667805\pi\)
−0.503094 + 0.864231i \(0.667805\pi\)
\(282\) −2.67619 −0.159365
\(283\) 29.0207 1.72510 0.862551 0.505971i \(-0.168866\pi\)
0.862551 + 0.505971i \(0.168866\pi\)
\(284\) 3.38516 0.200872
\(285\) 3.07645 0.182233
\(286\) 22.8377 1.35042
\(287\) 0 0
\(288\) −1.53164 −0.0902528
\(289\) −15.3472 −0.902776
\(290\) −1.89298 −0.111160
\(291\) −2.95888 −0.173452
\(292\) 1.99717 0.116876
\(293\) −33.4645 −1.95502 −0.977509 0.210896i \(-0.932362\pi\)
−0.977509 + 0.210896i \(0.932362\pi\)
\(294\) 0 0
\(295\) −13.1013 −0.762787
\(296\) 23.4199 1.36125
\(297\) 3.74096 0.217073
\(298\) 18.7701 1.08732
\(299\) 32.9859 1.90762
\(300\) −1.02763 −0.0593302
\(301\) 0 0
\(302\) 1.52601 0.0878122
\(303\) 9.78581 0.562180
\(304\) −12.4022 −0.711313
\(305\) 6.98062 0.399709
\(306\) −1.93807 −0.110792
\(307\) −12.0971 −0.690419 −0.345209 0.938526i \(-0.612192\pi\)
−0.345209 + 0.938526i \(0.612192\pi\)
\(308\) 0 0
\(309\) 5.64685 0.321238
\(310\) 5.12698 0.291193
\(311\) −4.23825 −0.240329 −0.120165 0.992754i \(-0.538342\pi\)
−0.120165 + 0.992754i \(0.538342\pi\)
\(312\) −10.5455 −0.597021
\(313\) 23.4002 1.32266 0.661329 0.750096i \(-0.269993\pi\)
0.661329 + 0.750096i \(0.269993\pi\)
\(314\) −5.98802 −0.337924
\(315\) 0 0
\(316\) 0.834792 0.0469607
\(317\) 7.71467 0.433299 0.216650 0.976249i \(-0.430487\pi\)
0.216650 + 0.976249i \(0.430487\pi\)
\(318\) −2.16942 −0.121655
\(319\) −4.23571 −0.237154
\(320\) 7.35592 0.411209
\(321\) 14.2514 0.795434
\(322\) 0 0
\(323\) −3.56630 −0.198434
\(324\) 0.272577 0.0151432
\(325\) −15.2671 −0.846866
\(326\) 34.0781 1.88741
\(327\) −1.98301 −0.109661
\(328\) 2.60410 0.143787
\(329\) 0 0
\(330\) 6.25441 0.344294
\(331\) 0.784765 0.0431346 0.0215673 0.999767i \(-0.493134\pi\)
0.0215673 + 0.999767i \(0.493134\pi\)
\(332\) −2.88646 −0.158415
\(333\) −8.99346 −0.492838
\(334\) −15.5078 −0.848548
\(335\) 1.70138 0.0929561
\(336\) 0 0
\(337\) −11.6836 −0.636447 −0.318224 0.948016i \(-0.603086\pi\)
−0.318224 + 0.948016i \(0.603086\pi\)
\(338\) 5.12406 0.278712
\(339\) 1.92257 0.104420
\(340\) −0.388637 −0.0210768
\(341\) 11.4721 0.621248
\(342\) 4.18183 0.226127
\(343\) 0 0
\(344\) −13.2179 −0.712659
\(345\) 9.03364 0.486355
\(346\) −12.5324 −0.673745
\(347\) 1.28541 0.0690042 0.0345021 0.999405i \(-0.489015\pi\)
0.0345021 + 0.999405i \(0.489015\pi\)
\(348\) −0.308626 −0.0165441
\(349\) −30.6569 −1.64103 −0.820513 0.571628i \(-0.806312\pi\)
−0.820513 + 0.571628i \(0.806312\pi\)
\(350\) 0 0
\(351\) 4.04957 0.216150
\(352\) −5.72981 −0.305400
\(353\) −0.656222 −0.0349271 −0.0174636 0.999848i \(-0.505559\pi\)
−0.0174636 + 0.999848i \(0.505559\pi\)
\(354\) −17.8086 −0.946518
\(355\) 13.7732 0.731003
\(356\) −0.235017 −0.0124559
\(357\) 0 0
\(358\) 8.77803 0.463933
\(359\) −0.670115 −0.0353673 −0.0176837 0.999844i \(-0.505629\pi\)
−0.0176837 + 0.999844i \(0.505629\pi\)
\(360\) −2.88803 −0.152212
\(361\) −11.3049 −0.594996
\(362\) −25.5443 −1.34258
\(363\) 2.99480 0.157186
\(364\) 0 0
\(365\) 8.12587 0.425327
\(366\) 9.48877 0.495986
\(367\) −24.0081 −1.25321 −0.626607 0.779335i \(-0.715557\pi\)
−0.626607 + 0.779335i \(0.715557\pi\)
\(368\) −36.4175 −1.89839
\(369\) −1.00000 −0.0520579
\(370\) −15.0359 −0.781679
\(371\) 0 0
\(372\) 0.835887 0.0433387
\(373\) −3.48977 −0.180694 −0.0903468 0.995910i \(-0.528798\pi\)
−0.0903468 + 0.995910i \(0.528798\pi\)
\(374\) −7.25027 −0.374902
\(375\) −9.72625 −0.502262
\(376\) 4.62292 0.238409
\(377\) −4.58513 −0.236146
\(378\) 0 0
\(379\) 29.7705 1.52921 0.764603 0.644501i \(-0.222935\pi\)
0.764603 + 0.644501i \(0.222935\pi\)
\(380\) 0.838570 0.0430177
\(381\) 6.05248 0.310078
\(382\) 19.5216 0.998814
\(383\) −9.44326 −0.482528 −0.241264 0.970460i \(-0.577562\pi\)
−0.241264 + 0.970460i \(0.577562\pi\)
\(384\) 13.0622 0.666578
\(385\) 0 0
\(386\) −2.31664 −0.117914
\(387\) 5.07578 0.258017
\(388\) −0.806521 −0.0409449
\(389\) 31.9855 1.62173 0.810864 0.585235i \(-0.198998\pi\)
0.810864 + 0.585235i \(0.198998\pi\)
\(390\) 6.77036 0.342831
\(391\) −10.4720 −0.529593
\(392\) 0 0
\(393\) 10.1642 0.512719
\(394\) 22.0906 1.11291
\(395\) 3.39651 0.170897
\(396\) 1.01970 0.0512419
\(397\) −21.0779 −1.05787 −0.528934 0.848663i \(-0.677408\pi\)
−0.528934 + 0.848663i \(0.677408\pi\)
\(398\) −24.0638 −1.20621
\(399\) 0 0
\(400\) 16.8554 0.842768
\(401\) −21.5312 −1.07522 −0.537609 0.843194i \(-0.680672\pi\)
−0.537609 + 0.843194i \(0.680672\pi\)
\(402\) 2.31268 0.115346
\(403\) 12.4185 0.618607
\(404\) 2.66739 0.132707
\(405\) 1.10903 0.0551082
\(406\) 0 0
\(407\) −33.6442 −1.66768
\(408\) 3.34788 0.165745
\(409\) 35.8518 1.77276 0.886379 0.462961i \(-0.153213\pi\)
0.886379 + 0.462961i \(0.153213\pi\)
\(410\) −1.67187 −0.0825678
\(411\) 10.4749 0.516687
\(412\) 1.53920 0.0758310
\(413\) 0 0
\(414\) 12.2794 0.603501
\(415\) −11.7441 −0.576495
\(416\) −6.20249 −0.304102
\(417\) −5.03683 −0.246655
\(418\) 15.6441 0.765176
\(419\) −9.75270 −0.476451 −0.238225 0.971210i \(-0.576566\pi\)
−0.238225 + 0.971210i \(0.576566\pi\)
\(420\) 0 0
\(421\) 0.117163 0.00571015 0.00285508 0.999996i \(-0.499091\pi\)
0.00285508 + 0.999996i \(0.499091\pi\)
\(422\) 35.4527 1.72581
\(423\) −1.77524 −0.0863153
\(424\) 3.74751 0.181995
\(425\) 4.84684 0.235106
\(426\) 18.7219 0.907078
\(427\) 0 0
\(428\) 3.88459 0.187769
\(429\) 15.1493 0.731415
\(430\) 8.48605 0.409234
\(431\) 21.1818 1.02029 0.510146 0.860088i \(-0.329591\pi\)
0.510146 + 0.860088i \(0.329591\pi\)
\(432\) −4.47086 −0.215104
\(433\) −23.6911 −1.13852 −0.569260 0.822157i \(-0.692770\pi\)
−0.569260 + 0.822157i \(0.692770\pi\)
\(434\) 0 0
\(435\) −1.25570 −0.0602063
\(436\) −0.540523 −0.0258863
\(437\) 22.5957 1.08090
\(438\) 11.0455 0.527775
\(439\) −17.5444 −0.837349 −0.418675 0.908136i \(-0.637505\pi\)
−0.418675 + 0.908136i \(0.637505\pi\)
\(440\) −10.8040 −0.515061
\(441\) 0 0
\(442\) −7.84837 −0.373309
\(443\) 4.89678 0.232653 0.116327 0.993211i \(-0.462888\pi\)
0.116327 + 0.993211i \(0.462888\pi\)
\(444\) −2.45141 −0.116339
\(445\) −0.956211 −0.0453287
\(446\) −33.3505 −1.57919
\(447\) 12.4511 0.588915
\(448\) 0 0
\(449\) −25.8031 −1.21772 −0.608862 0.793276i \(-0.708374\pi\)
−0.608862 + 0.793276i \(0.708374\pi\)
\(450\) −5.68338 −0.267917
\(451\) −3.74096 −0.176155
\(452\) 0.524049 0.0246492
\(453\) 1.01228 0.0475609
\(454\) 32.9623 1.54700
\(455\) 0 0
\(456\) −7.22378 −0.338285
\(457\) −10.7604 −0.503349 −0.251675 0.967812i \(-0.580981\pi\)
−0.251675 + 0.967812i \(0.580981\pi\)
\(458\) −22.2893 −1.04151
\(459\) −1.28562 −0.0600074
\(460\) 2.46236 0.114808
\(461\) 4.73851 0.220694 0.110347 0.993893i \(-0.464804\pi\)
0.110347 + 0.993893i \(0.464804\pi\)
\(462\) 0 0
\(463\) −13.8446 −0.643413 −0.321707 0.946839i \(-0.604256\pi\)
−0.321707 + 0.946839i \(0.604256\pi\)
\(464\) 5.06213 0.235004
\(465\) 3.40096 0.157716
\(466\) −41.0200 −1.90022
\(467\) 11.5666 0.535238 0.267619 0.963525i \(-0.413763\pi\)
0.267619 + 0.963525i \(0.413763\pi\)
\(468\) 1.10382 0.0510241
\(469\) 0 0
\(470\) −2.96798 −0.136903
\(471\) −3.97214 −0.183026
\(472\) 30.7630 1.41598
\(473\) 18.9883 0.873084
\(474\) 4.61688 0.212060
\(475\) −10.4581 −0.479852
\(476\) 0 0
\(477\) −1.43908 −0.0658910
\(478\) −36.1249 −1.65232
\(479\) 11.9744 0.547123 0.273562 0.961854i \(-0.411798\pi\)
0.273562 + 0.961854i \(0.411798\pi\)
\(480\) −1.69864 −0.0775318
\(481\) −36.4196 −1.66059
\(482\) 19.4625 0.886494
\(483\) 0 0
\(484\) 0.816313 0.0371052
\(485\) −3.28148 −0.149004
\(486\) 1.50751 0.0683819
\(487\) −11.7895 −0.534235 −0.267118 0.963664i \(-0.586071\pi\)
−0.267118 + 0.963664i \(0.586071\pi\)
\(488\) −16.3911 −0.741991
\(489\) 22.6056 1.02226
\(490\) 0 0
\(491\) −41.8155 −1.88711 −0.943553 0.331222i \(-0.892539\pi\)
−0.943553 + 0.331222i \(0.892539\pi\)
\(492\) −0.272577 −0.0122887
\(493\) 1.45564 0.0655588
\(494\) 16.9346 0.761924
\(495\) 4.14884 0.186477
\(496\) −13.7104 −0.615614
\(497\) 0 0
\(498\) −15.9638 −0.715354
\(499\) −18.7923 −0.841260 −0.420630 0.907232i \(-0.638191\pi\)
−0.420630 + 0.907232i \(0.638191\pi\)
\(500\) −2.65115 −0.118563
\(501\) −10.2870 −0.459591
\(502\) −20.3367 −0.907669
\(503\) 5.66329 0.252514 0.126257 0.991998i \(-0.459704\pi\)
0.126257 + 0.991998i \(0.459704\pi\)
\(504\) 0 0
\(505\) 10.8528 0.482941
\(506\) 45.9369 2.04215
\(507\) 3.39903 0.150956
\(508\) 1.64977 0.0731966
\(509\) −16.0628 −0.711970 −0.355985 0.934492i \(-0.615855\pi\)
−0.355985 + 0.934492i \(0.615855\pi\)
\(510\) −2.14938 −0.0951763
\(511\) 0 0
\(512\) −16.4374 −0.726437
\(513\) 2.77400 0.122475
\(514\) −6.57018 −0.289798
\(515\) 6.26253 0.275960
\(516\) 1.38354 0.0609070
\(517\) −6.64112 −0.292076
\(518\) 0 0
\(519\) −8.31332 −0.364914
\(520\) −11.6953 −0.512872
\(521\) −29.4204 −1.28893 −0.644465 0.764634i \(-0.722920\pi\)
−0.644465 + 0.764634i \(0.722920\pi\)
\(522\) −1.70688 −0.0747080
\(523\) 1.46912 0.0642401 0.0321201 0.999484i \(-0.489774\pi\)
0.0321201 + 0.999484i \(0.489774\pi\)
\(524\) 2.77054 0.121032
\(525\) 0 0
\(526\) −21.5428 −0.939312
\(527\) −3.94248 −0.171737
\(528\) −16.7253 −0.727875
\(529\) 43.3496 1.88477
\(530\) −2.40596 −0.104508
\(531\) −11.8133 −0.512653
\(532\) 0 0
\(533\) −4.04957 −0.175406
\(534\) −1.29978 −0.0562469
\(535\) 15.8052 0.683318
\(536\) −3.99498 −0.172557
\(537\) 5.82288 0.251276
\(538\) −30.6468 −1.32128
\(539\) 0 0
\(540\) 0.302296 0.0130088
\(541\) 14.1541 0.608534 0.304267 0.952587i \(-0.401588\pi\)
0.304267 + 0.952587i \(0.401588\pi\)
\(542\) 31.9337 1.37167
\(543\) −16.9447 −0.727168
\(544\) 1.96910 0.0844246
\(545\) −2.19922 −0.0942042
\(546\) 0 0
\(547\) −36.1112 −1.54401 −0.772003 0.635619i \(-0.780745\pi\)
−0.772003 + 0.635619i \(0.780745\pi\)
\(548\) 2.85521 0.121968
\(549\) 6.29435 0.268636
\(550\) −21.2613 −0.906585
\(551\) −3.14087 −0.133805
\(552\) −21.2118 −0.902834
\(553\) 0 0
\(554\) 4.82841 0.205139
\(555\) −9.97402 −0.423373
\(556\) −1.37292 −0.0582250
\(557\) −28.3038 −1.19927 −0.599635 0.800274i \(-0.704687\pi\)
−0.599635 + 0.800274i \(0.704687\pi\)
\(558\) 4.62294 0.195704
\(559\) 20.5547 0.869373
\(560\) 0 0
\(561\) −4.80944 −0.203055
\(562\) −25.4268 −1.07257
\(563\) −28.6819 −1.20880 −0.604399 0.796682i \(-0.706587\pi\)
−0.604399 + 0.796682i \(0.706587\pi\)
\(564\) −0.483891 −0.0203755
\(565\) 2.13219 0.0897019
\(566\) 43.7489 1.83890
\(567\) 0 0
\(568\) −32.3406 −1.35698
\(569\) −25.3316 −1.06195 −0.530977 0.847386i \(-0.678175\pi\)
−0.530977 + 0.847386i \(0.678175\pi\)
\(570\) 4.63777 0.194255
\(571\) −44.5188 −1.86305 −0.931526 0.363674i \(-0.881522\pi\)
−0.931526 + 0.363674i \(0.881522\pi\)
\(572\) 4.12935 0.172657
\(573\) 12.9496 0.540978
\(574\) 0 0
\(575\) −30.7091 −1.28066
\(576\) 6.63275 0.276365
\(577\) 8.77810 0.365437 0.182718 0.983165i \(-0.441510\pi\)
0.182718 + 0.983165i \(0.441510\pi\)
\(578\) −23.1360 −0.962331
\(579\) −1.53674 −0.0638646
\(580\) −0.342275 −0.0142122
\(581\) 0 0
\(582\) −4.46053 −0.184895
\(583\) −5.38355 −0.222964
\(584\) −19.0803 −0.789547
\(585\) 4.49110 0.185684
\(586\) −50.4480 −2.08399
\(587\) 8.35115 0.344689 0.172344 0.985037i \(-0.444866\pi\)
0.172344 + 0.985037i \(0.444866\pi\)
\(588\) 0 0
\(589\) 8.50678 0.350516
\(590\) −19.7503 −0.813107
\(591\) 14.6537 0.602773
\(592\) 40.2084 1.65256
\(593\) 6.68553 0.274542 0.137271 0.990534i \(-0.456167\pi\)
0.137271 + 0.990534i \(0.456167\pi\)
\(594\) 5.63953 0.231393
\(595\) 0 0
\(596\) 3.39387 0.139018
\(597\) −15.9626 −0.653306
\(598\) 49.7265 2.03347
\(599\) 6.46648 0.264213 0.132107 0.991236i \(-0.457826\pi\)
0.132107 + 0.991236i \(0.457826\pi\)
\(600\) 9.81760 0.400802
\(601\) 40.0959 1.63554 0.817772 0.575542i \(-0.195209\pi\)
0.817772 + 0.575542i \(0.195209\pi\)
\(602\) 0 0
\(603\) 1.53411 0.0624738
\(604\) 0.275923 0.0112272
\(605\) 3.32132 0.135031
\(606\) 14.7522 0.599266
\(607\) 2.40461 0.0976000 0.0488000 0.998809i \(-0.484460\pi\)
0.0488000 + 0.998809i \(0.484460\pi\)
\(608\) −4.24877 −0.172311
\(609\) 0 0
\(610\) 10.5233 0.426077
\(611\) −7.18898 −0.290835
\(612\) −0.350429 −0.0141653
\(613\) −21.6500 −0.874435 −0.437218 0.899356i \(-0.644036\pi\)
−0.437218 + 0.899356i \(0.644036\pi\)
\(614\) −18.2365 −0.735964
\(615\) −1.10903 −0.0447204
\(616\) 0 0
\(617\) −5.55725 −0.223726 −0.111863 0.993724i \(-0.535682\pi\)
−0.111863 + 0.993724i \(0.535682\pi\)
\(618\) 8.51266 0.342429
\(619\) −39.3059 −1.57984 −0.789918 0.613212i \(-0.789877\pi\)
−0.789918 + 0.613212i \(0.789877\pi\)
\(620\) 0.927024 0.0372302
\(621\) 8.14553 0.326869
\(622\) −6.38920 −0.256183
\(623\) 0 0
\(624\) −18.1050 −0.724782
\(625\) 8.06355 0.322542
\(626\) 35.2760 1.40991
\(627\) 10.3774 0.414435
\(628\) −1.08271 −0.0432049
\(629\) 11.5621 0.461012
\(630\) 0 0
\(631\) −1.34175 −0.0534142 −0.0267071 0.999643i \(-0.508502\pi\)
−0.0267071 + 0.999643i \(0.508502\pi\)
\(632\) −7.97530 −0.317240
\(633\) 23.5174 0.934733
\(634\) 11.6299 0.461883
\(635\) 6.71239 0.266373
\(636\) −0.392260 −0.0155541
\(637\) 0 0
\(638\) −6.38536 −0.252799
\(639\) 12.4191 0.491292
\(640\) 14.4864 0.572624
\(641\) 21.6189 0.853894 0.426947 0.904277i \(-0.359589\pi\)
0.426947 + 0.904277i \(0.359589\pi\)
\(642\) 21.4840 0.847907
\(643\) −24.8621 −0.980465 −0.490233 0.871592i \(-0.663088\pi\)
−0.490233 + 0.871592i \(0.663088\pi\)
\(644\) 0 0
\(645\) 5.62920 0.221649
\(646\) −5.37622 −0.211525
\(647\) −29.3258 −1.15292 −0.576459 0.817126i \(-0.695566\pi\)
−0.576459 + 0.817126i \(0.695566\pi\)
\(648\) −2.60410 −0.102299
\(649\) −44.1931 −1.73473
\(650\) −23.0152 −0.902732
\(651\) 0 0
\(652\) 6.16177 0.241313
\(653\) 40.3928 1.58069 0.790346 0.612661i \(-0.209901\pi\)
0.790346 + 0.612661i \(0.209901\pi\)
\(654\) −2.98940 −0.116895
\(655\) 11.2725 0.440452
\(656\) 4.47086 0.174558
\(657\) 7.32700 0.285854
\(658\) 0 0
\(659\) 36.6015 1.42579 0.712895 0.701271i \(-0.247384\pi\)
0.712895 + 0.701271i \(0.247384\pi\)
\(660\) 1.13088 0.0440194
\(661\) 35.4309 1.37810 0.689050 0.724714i \(-0.258028\pi\)
0.689050 + 0.724714i \(0.258028\pi\)
\(662\) 1.18304 0.0459801
\(663\) −5.20619 −0.202192
\(664\) 27.5762 1.07016
\(665\) 0 0
\(666\) −13.5577 −0.525350
\(667\) −9.22279 −0.357108
\(668\) −2.80401 −0.108490
\(669\) −22.1230 −0.855323
\(670\) 2.56484 0.0990882
\(671\) 23.5469 0.909018
\(672\) 0 0
\(673\) 4.09653 0.157910 0.0789549 0.996878i \(-0.474842\pi\)
0.0789549 + 0.996878i \(0.474842\pi\)
\(674\) −17.6131 −0.678432
\(675\) −3.77005 −0.145109
\(676\) 0.926497 0.0356345
\(677\) 46.9399 1.80405 0.902023 0.431687i \(-0.142081\pi\)
0.902023 + 0.431687i \(0.142081\pi\)
\(678\) 2.89829 0.111308
\(679\) 0 0
\(680\) 3.71290 0.142383
\(681\) 21.8654 0.837885
\(682\) 17.2942 0.662230
\(683\) 43.8835 1.67916 0.839578 0.543239i \(-0.182802\pi\)
0.839578 + 0.543239i \(0.182802\pi\)
\(684\) 0.756129 0.0289113
\(685\) 11.6169 0.443861
\(686\) 0 0
\(687\) −14.7855 −0.564103
\(688\) −22.6931 −0.865166
\(689\) −5.82766 −0.222016
\(690\) 13.6183 0.518439
\(691\) 13.1815 0.501446 0.250723 0.968059i \(-0.419332\pi\)
0.250723 + 0.968059i \(0.419332\pi\)
\(692\) −2.26602 −0.0861411
\(693\) 0 0
\(694\) 1.93776 0.0735563
\(695\) −5.58600 −0.211889
\(696\) 2.94850 0.111763
\(697\) 1.28562 0.0486962
\(698\) −46.2155 −1.74928
\(699\) −27.2105 −1.02920
\(700\) 0 0
\(701\) −21.8416 −0.824945 −0.412472 0.910970i \(-0.635335\pi\)
−0.412472 + 0.910970i \(0.635335\pi\)
\(702\) 6.10476 0.230409
\(703\) −24.9479 −0.940926
\(704\) 24.8129 0.935170
\(705\) −1.96880 −0.0741493
\(706\) −0.989258 −0.0372312
\(707\) 0 0
\(708\) −3.22003 −0.121016
\(709\) −23.7312 −0.891243 −0.445622 0.895221i \(-0.647017\pi\)
−0.445622 + 0.895221i \(0.647017\pi\)
\(710\) 20.7631 0.779226
\(711\) 3.06259 0.114856
\(712\) 2.24527 0.0841450
\(713\) 24.9792 0.935477
\(714\) 0 0
\(715\) 16.8010 0.628323
\(716\) 1.58718 0.0593158
\(717\) −23.9634 −0.894928
\(718\) −1.01020 −0.0377005
\(719\) −14.4356 −0.538358 −0.269179 0.963090i \(-0.586752\pi\)
−0.269179 + 0.963090i \(0.586752\pi\)
\(720\) −4.95832 −0.184785
\(721\) 0 0
\(722\) −17.0422 −0.634246
\(723\) 12.9104 0.480143
\(724\) −4.61874 −0.171654
\(725\) 4.26865 0.158534
\(726\) 4.51468 0.167556
\(727\) −7.96786 −0.295512 −0.147756 0.989024i \(-0.547205\pi\)
−0.147756 + 0.989024i \(0.547205\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 12.2498 0.453385
\(731\) −6.52551 −0.241355
\(732\) 1.71569 0.0634138
\(733\) 33.3492 1.23178 0.615890 0.787832i \(-0.288796\pi\)
0.615890 + 0.787832i \(0.288796\pi\)
\(734\) −36.1924 −1.33589
\(735\) 0 0
\(736\) −12.4760 −0.459872
\(737\) 5.73905 0.211401
\(738\) −1.50751 −0.0554921
\(739\) −14.8315 −0.545584 −0.272792 0.962073i \(-0.587947\pi\)
−0.272792 + 0.962073i \(0.587947\pi\)
\(740\) −2.71869 −0.0999409
\(741\) 11.2335 0.412674
\(742\) 0 0
\(743\) 31.1321 1.14213 0.571063 0.820906i \(-0.306531\pi\)
0.571063 + 0.820906i \(0.306531\pi\)
\(744\) −7.98577 −0.292772
\(745\) 13.8086 0.505908
\(746\) −5.26086 −0.192614
\(747\) −10.5895 −0.387450
\(748\) −1.31094 −0.0479328
\(749\) 0 0
\(750\) −14.6624 −0.535395
\(751\) 3.96823 0.144803 0.0724014 0.997376i \(-0.476934\pi\)
0.0724014 + 0.997376i \(0.476934\pi\)
\(752\) 7.93686 0.289427
\(753\) −13.4903 −0.491612
\(754\) −6.91212 −0.251725
\(755\) 1.12265 0.0408572
\(756\) 0 0
\(757\) −28.9528 −1.05231 −0.526153 0.850390i \(-0.676366\pi\)
−0.526153 + 0.850390i \(0.676366\pi\)
\(758\) 44.8792 1.63009
\(759\) 30.4721 1.10607
\(760\) −8.01139 −0.290604
\(761\) 12.6480 0.458490 0.229245 0.973369i \(-0.426374\pi\)
0.229245 + 0.973369i \(0.426374\pi\)
\(762\) 9.12416 0.330533
\(763\) 0 0
\(764\) 3.52977 0.127702
\(765\) −1.42579 −0.0515494
\(766\) −14.2358 −0.514359
\(767\) −47.8388 −1.72736
\(768\) 6.42585 0.231873
\(769\) 22.8838 0.825210 0.412605 0.910910i \(-0.364619\pi\)
0.412605 + 0.910910i \(0.364619\pi\)
\(770\) 0 0
\(771\) −4.35831 −0.156961
\(772\) −0.418879 −0.0150758
\(773\) −0.777954 −0.0279811 −0.0139905 0.999902i \(-0.504453\pi\)
−0.0139905 + 0.999902i \(0.504453\pi\)
\(774\) 7.65178 0.275037
\(775\) −11.5613 −0.415293
\(776\) 7.70521 0.276601
\(777\) 0 0
\(778\) 48.2183 1.72871
\(779\) −2.77400 −0.0993889
\(780\) 1.22417 0.0438323
\(781\) 46.4594 1.66245
\(782\) −15.7866 −0.564529
\(783\) −1.13225 −0.0404634
\(784\) 0 0
\(785\) −4.40522 −0.157229
\(786\) 15.3227 0.546542
\(787\) −29.3699 −1.04692 −0.523462 0.852049i \(-0.675360\pi\)
−0.523462 + 0.852049i \(0.675360\pi\)
\(788\) 3.99426 0.142290
\(789\) −14.2904 −0.508751
\(790\) 5.12026 0.182171
\(791\) 0 0
\(792\) −9.74185 −0.346162
\(793\) 25.4894 0.905155
\(794\) −31.7750 −1.12765
\(795\) −1.59598 −0.0566037
\(796\) −4.35104 −0.154219
\(797\) −22.5919 −0.800247 −0.400124 0.916461i \(-0.631033\pi\)
−0.400124 + 0.916461i \(0.631033\pi\)
\(798\) 0 0
\(799\) 2.28228 0.0807413
\(800\) 5.77437 0.204155
\(801\) −0.862204 −0.0304645
\(802\) −32.4585 −1.14615
\(803\) 27.4100 0.967279
\(804\) 0.418163 0.0147475
\(805\) 0 0
\(806\) 18.7209 0.659416
\(807\) −20.3295 −0.715632
\(808\) −25.4832 −0.896497
\(809\) 31.0716 1.09242 0.546209 0.837649i \(-0.316070\pi\)
0.546209 + 0.837649i \(0.316070\pi\)
\(810\) 1.67187 0.0587436
\(811\) −32.1947 −1.13051 −0.565254 0.824917i \(-0.691222\pi\)
−0.565254 + 0.824917i \(0.691222\pi\)
\(812\) 0 0
\(813\) 21.1831 0.742925
\(814\) −50.7188 −1.77769
\(815\) 25.0703 0.878175
\(816\) 5.74780 0.201213
\(817\) 14.0802 0.492605
\(818\) 54.0468 1.88970
\(819\) 0 0
\(820\) −0.302296 −0.0105566
\(821\) −21.4757 −0.749509 −0.374754 0.927124i \(-0.622273\pi\)
−0.374754 + 0.927124i \(0.622273\pi\)
\(822\) 15.7909 0.550772
\(823\) 27.4356 0.956345 0.478172 0.878266i \(-0.341299\pi\)
0.478172 + 0.878266i \(0.341299\pi\)
\(824\) −14.7050 −0.512272
\(825\) −14.1036 −0.491025
\(826\) 0 0
\(827\) 5.26418 0.183053 0.0915267 0.995803i \(-0.470825\pi\)
0.0915267 + 0.995803i \(0.470825\pi\)
\(828\) 2.22028 0.0771602
\(829\) 36.4033 1.26434 0.632169 0.774831i \(-0.282165\pi\)
0.632169 + 0.774831i \(0.282165\pi\)
\(830\) −17.7043 −0.614525
\(831\) 3.20291 0.111108
\(832\) 26.8598 0.931196
\(833\) 0 0
\(834\) −7.59306 −0.262926
\(835\) −11.4086 −0.394812
\(836\) 2.82865 0.0978309
\(837\) 3.06661 0.105998
\(838\) −14.7023 −0.507881
\(839\) 35.5047 1.22576 0.612880 0.790176i \(-0.290011\pi\)
0.612880 + 0.790176i \(0.290011\pi\)
\(840\) 0 0
\(841\) −27.7180 −0.955793
\(842\) 0.176623 0.00608684
\(843\) −16.8668 −0.580923
\(844\) 6.41030 0.220652
\(845\) 3.76963 0.129679
\(846\) −2.67619 −0.0920094
\(847\) 0 0
\(848\) 6.43392 0.220942
\(849\) 29.0207 0.995988
\(850\) 7.30664 0.250616
\(851\) −73.2564 −2.51120
\(852\) 3.38516 0.115974
\(853\) −28.0973 −0.962035 −0.481017 0.876711i \(-0.659733\pi\)
−0.481017 + 0.876711i \(0.659733\pi\)
\(854\) 0 0
\(855\) 3.07645 0.105212
\(856\) −37.1120 −1.26846
\(857\) 45.0276 1.53811 0.769056 0.639181i \(-0.220727\pi\)
0.769056 + 0.639181i \(0.220727\pi\)
\(858\) 22.8377 0.779665
\(859\) 19.7121 0.672568 0.336284 0.941761i \(-0.390830\pi\)
0.336284 + 0.941761i \(0.390830\pi\)
\(860\) 1.53439 0.0523222
\(861\) 0 0
\(862\) 31.9317 1.08760
\(863\) −8.30927 −0.282851 −0.141425 0.989949i \(-0.545169\pi\)
−0.141425 + 0.989949i \(0.545169\pi\)
\(864\) −1.53164 −0.0521075
\(865\) −9.21972 −0.313480
\(866\) −35.7145 −1.21363
\(867\) −15.3472 −0.521218
\(868\) 0 0
\(869\) 11.4570 0.388653
\(870\) −1.89298 −0.0641780
\(871\) 6.21249 0.210502
\(872\) 5.16396 0.174874
\(873\) −2.95888 −0.100143
\(874\) 34.0632 1.15220
\(875\) 0 0
\(876\) 1.99717 0.0674782
\(877\) 36.4096 1.22947 0.614733 0.788735i \(-0.289264\pi\)
0.614733 + 0.788735i \(0.289264\pi\)
\(878\) −26.4483 −0.892588
\(879\) −33.4645 −1.12873
\(880\) −18.5489 −0.625282
\(881\) −41.2925 −1.39118 −0.695590 0.718439i \(-0.744857\pi\)
−0.695590 + 0.718439i \(0.744857\pi\)
\(882\) 0 0
\(883\) −27.7916 −0.935261 −0.467631 0.883924i \(-0.654892\pi\)
−0.467631 + 0.883924i \(0.654892\pi\)
\(884\) −1.41909 −0.0477291
\(885\) −13.1013 −0.440395
\(886\) 7.38193 0.248001
\(887\) −22.4719 −0.754534 −0.377267 0.926105i \(-0.623136\pi\)
−0.377267 + 0.926105i \(0.623136\pi\)
\(888\) 23.4199 0.785920
\(889\) 0 0
\(890\) −1.44149 −0.0483190
\(891\) 3.74096 0.125327
\(892\) −6.03021 −0.201906
\(893\) −4.92453 −0.164793
\(894\) 18.7701 0.627765
\(895\) 6.45775 0.215859
\(896\) 0 0
\(897\) 32.9859 1.10137
\(898\) −38.8984 −1.29806
\(899\) −3.47217 −0.115803
\(900\) −1.02763 −0.0342543
\(901\) 1.85010 0.0616359
\(902\) −5.63953 −0.187776
\(903\) 0 0
\(904\) −5.00657 −0.166516
\(905\) −18.7922 −0.624675
\(906\) 1.52601 0.0506984
\(907\) −48.2992 −1.60375 −0.801875 0.597492i \(-0.796164\pi\)
−0.801875 + 0.597492i \(0.796164\pi\)
\(908\) 5.96001 0.197790
\(909\) 9.78581 0.324575
\(910\) 0 0
\(911\) 37.4429 1.24054 0.620269 0.784389i \(-0.287023\pi\)
0.620269 + 0.784389i \(0.287023\pi\)
\(912\) −12.4022 −0.410677
\(913\) −39.6150 −1.31106
\(914\) −16.2213 −0.536554
\(915\) 6.98062 0.230772
\(916\) −4.03019 −0.133161
\(917\) 0 0
\(918\) −1.93807 −0.0639660
\(919\) −11.5498 −0.380992 −0.190496 0.981688i \(-0.561010\pi\)
−0.190496 + 0.981688i \(0.561010\pi\)
\(920\) −23.5245 −0.775580
\(921\) −12.0971 −0.398613
\(922\) 7.14334 0.235253
\(923\) 50.2920 1.65538
\(924\) 0 0
\(925\) 33.9058 1.11482
\(926\) −20.8708 −0.685858
\(927\) 5.64685 0.185467
\(928\) 1.73420 0.0569280
\(929\) 2.48031 0.0813764 0.0406882 0.999172i \(-0.487045\pi\)
0.0406882 + 0.999172i \(0.487045\pi\)
\(930\) 5.12698 0.168120
\(931\) 0 0
\(932\) −7.41696 −0.242951
\(933\) −4.23825 −0.138754
\(934\) 17.4367 0.570547
\(935\) −5.33382 −0.174434
\(936\) −10.5455 −0.344690
\(937\) −20.6957 −0.676098 −0.338049 0.941128i \(-0.609767\pi\)
−0.338049 + 0.941128i \(0.609767\pi\)
\(938\) 0 0
\(939\) 23.4002 0.763637
\(940\) −0.536649 −0.0175036
\(941\) −19.6088 −0.639230 −0.319615 0.947547i \(-0.603554\pi\)
−0.319615 + 0.947547i \(0.603554\pi\)
\(942\) −5.98802 −0.195100
\(943\) −8.14553 −0.265255
\(944\) 52.8155 1.71900
\(945\) 0 0
\(946\) 28.6250 0.930679
\(947\) 51.2866 1.66659 0.833296 0.552828i \(-0.186451\pi\)
0.833296 + 0.552828i \(0.186451\pi\)
\(948\) 0.834792 0.0271128
\(949\) 29.6712 0.963168
\(950\) −15.7657 −0.511507
\(951\) 7.71467 0.250165
\(952\) 0 0
\(953\) 49.5293 1.60441 0.802205 0.597048i \(-0.203660\pi\)
0.802205 + 0.597048i \(0.203660\pi\)
\(954\) −2.16942 −0.0702377
\(955\) 14.3615 0.464728
\(956\) −6.53186 −0.211255
\(957\) −4.23571 −0.136921
\(958\) 18.0515 0.583216
\(959\) 0 0
\(960\) 7.35592 0.237411
\(961\) −21.5959 −0.696642
\(962\) −54.9029 −1.77014
\(963\) 14.2514 0.459244
\(964\) 3.51908 0.113342
\(965\) −1.70429 −0.0548630
\(966\) 0 0
\(967\) −22.8164 −0.733727 −0.366863 0.930275i \(-0.619568\pi\)
−0.366863 + 0.930275i \(0.619568\pi\)
\(968\) −7.79877 −0.250662
\(969\) −3.56630 −0.114566
\(970\) −4.94686 −0.158834
\(971\) 24.2347 0.777729 0.388864 0.921295i \(-0.372867\pi\)
0.388864 + 0.921295i \(0.372867\pi\)
\(972\) 0.272577 0.00874291
\(973\) 0 0
\(974\) −17.7728 −0.569478
\(975\) −15.2671 −0.488938
\(976\) −28.1411 −0.900775
\(977\) −33.0385 −1.05700 −0.528498 0.848934i \(-0.677245\pi\)
−0.528498 + 0.848934i \(0.677245\pi\)
\(978\) 34.0781 1.08970
\(979\) −3.22547 −0.103087
\(980\) 0 0
\(981\) −1.98301 −0.0633126
\(982\) −63.0371 −2.01159
\(983\) 21.3362 0.680518 0.340259 0.940332i \(-0.389485\pi\)
0.340259 + 0.940332i \(0.389485\pi\)
\(984\) 2.60410 0.0830157
\(985\) 16.2514 0.517813
\(986\) 2.19439 0.0698836
\(987\) 0 0
\(988\) 3.06200 0.0974151
\(989\) 41.3449 1.31469
\(990\) 6.25441 0.198778
\(991\) 6.34983 0.201709 0.100854 0.994901i \(-0.467842\pi\)
0.100854 + 0.994901i \(0.467842\pi\)
\(992\) −4.69695 −0.149128
\(993\) 0.784765 0.0249038
\(994\) 0 0
\(995\) −17.7030 −0.561224
\(996\) −2.88646 −0.0914609
\(997\) −39.8519 −1.26212 −0.631061 0.775733i \(-0.717380\pi\)
−0.631061 + 0.775733i \(0.717380\pi\)
\(998\) −28.3296 −0.896757
\(999\) −8.99346 −0.284540
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 \(a_p\))