Properties

Label 6027.2.a.bo.1.10
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 1.10
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +0.277499 q^{10} +1.38960 q^{11} -1.90464 q^{12} +6.64217 q^{13} -0.898648 q^{15} +3.43696 q^{16} +6.17243 q^{17} -0.308797 q^{18} +5.46842 q^{19} +1.71160 q^{20} -0.429104 q^{22} +4.76671 q^{23} +1.20574 q^{24} -4.19243 q^{25} -2.05108 q^{26} +1.00000 q^{27} -6.78706 q^{29} +0.277499 q^{30} -6.37461 q^{31} -3.47280 q^{32} +1.38960 q^{33} -1.90603 q^{34} -1.90464 q^{36} +7.16373 q^{37} -1.68863 q^{38} +6.64217 q^{39} -1.08354 q^{40} -1.00000 q^{41} -6.00164 q^{43} -2.64669 q^{44} -0.898648 q^{45} -1.47194 q^{46} +6.21931 q^{47} +3.43696 q^{48} +1.29461 q^{50} +6.17243 q^{51} -12.6510 q^{52} +10.4055 q^{53} -0.308797 q^{54} -1.24876 q^{55} +5.46842 q^{57} +2.09582 q^{58} -4.50432 q^{59} +1.71160 q^{60} +13.3304 q^{61} +1.96846 q^{62} -5.80153 q^{64} -5.96897 q^{65} -0.429104 q^{66} -4.95916 q^{67} -11.7563 q^{68} +4.76671 q^{69} +10.9115 q^{71} +1.20574 q^{72} +4.36211 q^{73} -2.21214 q^{74} -4.19243 q^{75} -10.4154 q^{76} -2.05108 q^{78} -8.63992 q^{79} -3.08862 q^{80} +1.00000 q^{81} +0.308797 q^{82} -9.05009 q^{83} -5.54684 q^{85} +1.85329 q^{86} -6.78706 q^{87} +1.67550 q^{88} -1.29949 q^{89} +0.277499 q^{90} -9.07888 q^{92} -6.37461 q^{93} -1.92050 q^{94} -4.91418 q^{95} -3.47280 q^{96} +7.81362 q^{97} +1.38960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.308797 −0.218352 −0.109176 0.994022i \(-0.534821\pi\)
−0.109176 + 0.994022i \(0.534821\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.90464 −0.952322
\(5\) −0.898648 −0.401888 −0.200944 0.979603i \(-0.564401\pi\)
−0.200944 + 0.979603i \(0.564401\pi\)
\(6\) −0.308797 −0.126066
\(7\) 0 0
\(8\) 1.20574 0.426294
\(9\) 1.00000 0.333333
\(10\) 0.277499 0.0877530
\(11\) 1.38960 0.418980 0.209490 0.977811i \(-0.432820\pi\)
0.209490 + 0.977811i \(0.432820\pi\)
\(12\) −1.90464 −0.549824
\(13\) 6.64217 1.84221 0.921103 0.389319i \(-0.127289\pi\)
0.921103 + 0.389319i \(0.127289\pi\)
\(14\) 0 0
\(15\) −0.898648 −0.232030
\(16\) 3.43696 0.859240
\(17\) 6.17243 1.49703 0.748517 0.663115i \(-0.230766\pi\)
0.748517 + 0.663115i \(0.230766\pi\)
\(18\) −0.308797 −0.0727841
\(19\) 5.46842 1.25454 0.627271 0.778801i \(-0.284172\pi\)
0.627271 + 0.778801i \(0.284172\pi\)
\(20\) 1.71160 0.382726
\(21\) 0 0
\(22\) −0.429104 −0.0914852
\(23\) 4.76671 0.993927 0.496964 0.867771i \(-0.334448\pi\)
0.496964 + 0.867771i \(0.334448\pi\)
\(24\) 1.20574 0.246121
\(25\) −4.19243 −0.838486
\(26\) −2.05108 −0.402250
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.78706 −1.26033 −0.630163 0.776463i \(-0.717012\pi\)
−0.630163 + 0.776463i \(0.717012\pi\)
\(30\) 0.277499 0.0506642
\(31\) −6.37461 −1.14491 −0.572457 0.819935i \(-0.694009\pi\)
−0.572457 + 0.819935i \(0.694009\pi\)
\(32\) −3.47280 −0.613911
\(33\) 1.38960 0.241898
\(34\) −1.90603 −0.326881
\(35\) 0 0
\(36\) −1.90464 −0.317441
\(37\) 7.16373 1.17771 0.588855 0.808239i \(-0.299579\pi\)
0.588855 + 0.808239i \(0.299579\pi\)
\(38\) −1.68863 −0.273932
\(39\) 6.64217 1.06360
\(40\) −1.08354 −0.171322
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −6.00164 −0.915241 −0.457620 0.889148i \(-0.651298\pi\)
−0.457620 + 0.889148i \(0.651298\pi\)
\(44\) −2.64669 −0.399004
\(45\) −0.898648 −0.133963
\(46\) −1.47194 −0.217026
\(47\) 6.21931 0.907180 0.453590 0.891211i \(-0.350143\pi\)
0.453590 + 0.891211i \(0.350143\pi\)
\(48\) 3.43696 0.496082
\(49\) 0 0
\(50\) 1.29461 0.183085
\(51\) 6.17243 0.864313
\(52\) −12.6510 −1.75437
\(53\) 10.4055 1.42930 0.714650 0.699483i \(-0.246586\pi\)
0.714650 + 0.699483i \(0.246586\pi\)
\(54\) −0.308797 −0.0420219
\(55\) −1.24876 −0.168383
\(56\) 0 0
\(57\) 5.46842 0.724310
\(58\) 2.09582 0.275195
\(59\) −4.50432 −0.586413 −0.293207 0.956049i \(-0.594722\pi\)
−0.293207 + 0.956049i \(0.594722\pi\)
\(60\) 1.71160 0.220967
\(61\) 13.3304 1.70678 0.853391 0.521272i \(-0.174542\pi\)
0.853391 + 0.521272i \(0.174542\pi\)
\(62\) 1.96846 0.249994
\(63\) 0 0
\(64\) −5.80153 −0.725191
\(65\) −5.96897 −0.740360
\(66\) −0.429104 −0.0528190
\(67\) −4.95916 −0.605857 −0.302929 0.953013i \(-0.597964\pi\)
−0.302929 + 0.953013i \(0.597964\pi\)
\(68\) −11.7563 −1.42566
\(69\) 4.76671 0.573844
\(70\) 0 0
\(71\) 10.9115 1.29496 0.647481 0.762082i \(-0.275823\pi\)
0.647481 + 0.762082i \(0.275823\pi\)
\(72\) 1.20574 0.142098
\(73\) 4.36211 0.510547 0.255273 0.966869i \(-0.417835\pi\)
0.255273 + 0.966869i \(0.417835\pi\)
\(74\) −2.21214 −0.257156
\(75\) −4.19243 −0.484100
\(76\) −10.4154 −1.19473
\(77\) 0 0
\(78\) −2.05108 −0.232239
\(79\) −8.63992 −0.972067 −0.486034 0.873940i \(-0.661557\pi\)
−0.486034 + 0.873940i \(0.661557\pi\)
\(80\) −3.08862 −0.345318
\(81\) 1.00000 0.111111
\(82\) 0.308797 0.0341009
\(83\) −9.05009 −0.993376 −0.496688 0.867929i \(-0.665451\pi\)
−0.496688 + 0.867929i \(0.665451\pi\)
\(84\) 0 0
\(85\) −5.54684 −0.601640
\(86\) 1.85329 0.199845
\(87\) −6.78706 −0.727649
\(88\) 1.67550 0.178609
\(89\) −1.29949 −0.137746 −0.0688729 0.997625i \(-0.521940\pi\)
−0.0688729 + 0.997625i \(0.521940\pi\)
\(90\) 0.277499 0.0292510
\(91\) 0 0
\(92\) −9.07888 −0.946539
\(93\) −6.37461 −0.661016
\(94\) −1.92050 −0.198085
\(95\) −4.91418 −0.504184
\(96\) −3.47280 −0.354442
\(97\) 7.81362 0.793353 0.396677 0.917958i \(-0.370163\pi\)
0.396677 + 0.917958i \(0.370163\pi\)
\(98\) 0 0
\(99\) 1.38960 0.139660
\(100\) 7.98509 0.798509
\(101\) −12.5977 −1.25352 −0.626759 0.779213i \(-0.715619\pi\)
−0.626759 + 0.779213i \(0.715619\pi\)
\(102\) −1.90603 −0.188725
\(103\) −18.5097 −1.82381 −0.911906 0.410399i \(-0.865389\pi\)
−0.911906 + 0.410399i \(0.865389\pi\)
\(104\) 8.00874 0.785321
\(105\) 0 0
\(106\) −3.21317 −0.312091
\(107\) 3.77779 0.365213 0.182607 0.983186i \(-0.441547\pi\)
0.182607 + 0.983186i \(0.441547\pi\)
\(108\) −1.90464 −0.183275
\(109\) −5.31301 −0.508894 −0.254447 0.967087i \(-0.581893\pi\)
−0.254447 + 0.967087i \(0.581893\pi\)
\(110\) 0.385613 0.0367668
\(111\) 7.16373 0.679951
\(112\) 0 0
\(113\) −16.6298 −1.56440 −0.782200 0.623028i \(-0.785902\pi\)
−0.782200 + 0.623028i \(0.785902\pi\)
\(114\) −1.68863 −0.158155
\(115\) −4.28359 −0.399447
\(116\) 12.9269 1.20024
\(117\) 6.64217 0.614069
\(118\) 1.39092 0.128045
\(119\) 0 0
\(120\) −1.08354 −0.0989129
\(121\) −9.06901 −0.824456
\(122\) −4.11638 −0.372680
\(123\) −1.00000 −0.0901670
\(124\) 12.1414 1.09033
\(125\) 8.26076 0.738865
\(126\) 0 0
\(127\) −7.11991 −0.631790 −0.315895 0.948794i \(-0.602305\pi\)
−0.315895 + 0.948794i \(0.602305\pi\)
\(128\) 8.73710 0.772258
\(129\) −6.00164 −0.528415
\(130\) 1.84320 0.161659
\(131\) −1.76987 −0.154635 −0.0773173 0.997007i \(-0.524635\pi\)
−0.0773173 + 0.997007i \(0.524635\pi\)
\(132\) −2.64669 −0.230365
\(133\) 0 0
\(134\) 1.53137 0.132290
\(135\) −0.898648 −0.0773433
\(136\) 7.44236 0.638177
\(137\) 16.2543 1.38870 0.694348 0.719640i \(-0.255693\pi\)
0.694348 + 0.719640i \(0.255693\pi\)
\(138\) −1.47194 −0.125300
\(139\) 10.8156 0.917370 0.458685 0.888599i \(-0.348321\pi\)
0.458685 + 0.888599i \(0.348321\pi\)
\(140\) 0 0
\(141\) 6.21931 0.523760
\(142\) −3.36945 −0.282758
\(143\) 9.22996 0.771848
\(144\) 3.43696 0.286413
\(145\) 6.09918 0.506509
\(146\) −1.34701 −0.111479
\(147\) 0 0
\(148\) −13.6444 −1.12156
\(149\) 6.94118 0.568644 0.284322 0.958729i \(-0.408232\pi\)
0.284322 + 0.958729i \(0.408232\pi\)
\(150\) 1.29461 0.105704
\(151\) −15.9874 −1.30103 −0.650516 0.759492i \(-0.725447\pi\)
−0.650516 + 0.759492i \(0.725447\pi\)
\(152\) 6.59350 0.534803
\(153\) 6.17243 0.499012
\(154\) 0 0
\(155\) 5.72853 0.460126
\(156\) −12.6510 −1.01289
\(157\) −7.87899 −0.628812 −0.314406 0.949289i \(-0.601805\pi\)
−0.314406 + 0.949289i \(0.601805\pi\)
\(158\) 2.66798 0.212253
\(159\) 10.4055 0.825206
\(160\) 3.12083 0.246723
\(161\) 0 0
\(162\) −0.308797 −0.0242614
\(163\) 23.6380 1.85147 0.925735 0.378172i \(-0.123447\pi\)
0.925735 + 0.378172i \(0.123447\pi\)
\(164\) 1.90464 0.148728
\(165\) −1.24876 −0.0972159
\(166\) 2.79464 0.216906
\(167\) 13.3089 1.02988 0.514938 0.857227i \(-0.327815\pi\)
0.514938 + 0.857227i \(0.327815\pi\)
\(168\) 0 0
\(169\) 31.1184 2.39372
\(170\) 1.71285 0.131369
\(171\) 5.46842 0.418180
\(172\) 11.4310 0.871604
\(173\) 6.99173 0.531571 0.265786 0.964032i \(-0.414369\pi\)
0.265786 + 0.964032i \(0.414369\pi\)
\(174\) 2.09582 0.158884
\(175\) 0 0
\(176\) 4.77600 0.360004
\(177\) −4.50432 −0.338566
\(178\) 0.401279 0.0300771
\(179\) −6.32731 −0.472925 −0.236463 0.971641i \(-0.575988\pi\)
−0.236463 + 0.971641i \(0.575988\pi\)
\(180\) 1.71160 0.127575
\(181\) 6.94382 0.516130 0.258065 0.966128i \(-0.416915\pi\)
0.258065 + 0.966128i \(0.416915\pi\)
\(182\) 0 0
\(183\) 13.3304 0.985411
\(184\) 5.74742 0.423705
\(185\) −6.43767 −0.473307
\(186\) 1.96846 0.144334
\(187\) 8.57721 0.627228
\(188\) −11.8456 −0.863927
\(189\) 0 0
\(190\) 1.51748 0.110090
\(191\) 19.9797 1.44568 0.722842 0.691014i \(-0.242836\pi\)
0.722842 + 0.691014i \(0.242836\pi\)
\(192\) −5.80153 −0.418689
\(193\) 10.2929 0.740897 0.370448 0.928853i \(-0.379204\pi\)
0.370448 + 0.928853i \(0.379204\pi\)
\(194\) −2.41282 −0.173230
\(195\) −5.96897 −0.427447
\(196\) 0 0
\(197\) −27.5794 −1.96495 −0.982477 0.186383i \(-0.940323\pi\)
−0.982477 + 0.186383i \(0.940323\pi\)
\(198\) −0.429104 −0.0304951
\(199\) 15.6115 1.10667 0.553335 0.832959i \(-0.313355\pi\)
0.553335 + 0.832959i \(0.313355\pi\)
\(200\) −5.05499 −0.357442
\(201\) −4.95916 −0.349792
\(202\) 3.89013 0.273708
\(203\) 0 0
\(204\) −11.7563 −0.823105
\(205\) 0.898648 0.0627643
\(206\) 5.71573 0.398233
\(207\) 4.76671 0.331309
\(208\) 22.8289 1.58290
\(209\) 7.59891 0.525628
\(210\) 0 0
\(211\) 20.4853 1.41026 0.705132 0.709076i \(-0.250888\pi\)
0.705132 + 0.709076i \(0.250888\pi\)
\(212\) −19.8187 −1.36115
\(213\) 10.9115 0.747646
\(214\) −1.16657 −0.0797451
\(215\) 5.39336 0.367824
\(216\) 1.20574 0.0820403
\(217\) 0 0
\(218\) 1.64064 0.111118
\(219\) 4.36211 0.294764
\(220\) 2.37845 0.160355
\(221\) 40.9983 2.75785
\(222\) −2.21214 −0.148469
\(223\) −15.7327 −1.05354 −0.526771 0.850007i \(-0.676597\pi\)
−0.526771 + 0.850007i \(0.676597\pi\)
\(224\) 0 0
\(225\) −4.19243 −0.279495
\(226\) 5.13523 0.341590
\(227\) −14.8282 −0.984183 −0.492092 0.870543i \(-0.663768\pi\)
−0.492092 + 0.870543i \(0.663768\pi\)
\(228\) −10.4154 −0.689776
\(229\) −7.20918 −0.476396 −0.238198 0.971217i \(-0.576557\pi\)
−0.238198 + 0.971217i \(0.576557\pi\)
\(230\) 1.32276 0.0872201
\(231\) 0 0
\(232\) −8.18344 −0.537269
\(233\) 4.00163 0.262156 0.131078 0.991372i \(-0.458156\pi\)
0.131078 + 0.991372i \(0.458156\pi\)
\(234\) −2.05108 −0.134083
\(235\) −5.58897 −0.364584
\(236\) 8.57914 0.558454
\(237\) −8.63992 −0.561223
\(238\) 0 0
\(239\) 2.64792 0.171280 0.0856399 0.996326i \(-0.472707\pi\)
0.0856399 + 0.996326i \(0.472707\pi\)
\(240\) −3.08862 −0.199369
\(241\) 9.68840 0.624085 0.312042 0.950068i \(-0.398987\pi\)
0.312042 + 0.950068i \(0.398987\pi\)
\(242\) 2.80048 0.180022
\(243\) 1.00000 0.0641500
\(244\) −25.3897 −1.62541
\(245\) 0 0
\(246\) 0.308797 0.0196882
\(247\) 36.3222 2.31112
\(248\) −7.68613 −0.488070
\(249\) −9.05009 −0.573526
\(250\) −2.55090 −0.161333
\(251\) 21.2826 1.34335 0.671674 0.740847i \(-0.265576\pi\)
0.671674 + 0.740847i \(0.265576\pi\)
\(252\) 0 0
\(253\) 6.62381 0.416436
\(254\) 2.19861 0.137953
\(255\) −5.54684 −0.347357
\(256\) 8.90507 0.556567
\(257\) 28.2476 1.76204 0.881019 0.473081i \(-0.156858\pi\)
0.881019 + 0.473081i \(0.156858\pi\)
\(258\) 1.85329 0.115380
\(259\) 0 0
\(260\) 11.3688 0.705061
\(261\) −6.78706 −0.420109
\(262\) 0.546531 0.0337648
\(263\) −5.67723 −0.350073 −0.175036 0.984562i \(-0.556004\pi\)
−0.175036 + 0.984562i \(0.556004\pi\)
\(264\) 1.67550 0.103120
\(265\) −9.35084 −0.574418
\(266\) 0 0
\(267\) −1.29949 −0.0795276
\(268\) 9.44543 0.576971
\(269\) −0.465240 −0.0283662 −0.0141831 0.999899i \(-0.504515\pi\)
−0.0141831 + 0.999899i \(0.504515\pi\)
\(270\) 0.277499 0.0168881
\(271\) −8.51652 −0.517342 −0.258671 0.965965i \(-0.583285\pi\)
−0.258671 + 0.965965i \(0.583285\pi\)
\(272\) 21.2144 1.28631
\(273\) 0 0
\(274\) −5.01926 −0.303225
\(275\) −5.82580 −0.351309
\(276\) −9.07888 −0.546485
\(277\) −0.909276 −0.0546331 −0.0273165 0.999627i \(-0.508696\pi\)
−0.0273165 + 0.999627i \(0.508696\pi\)
\(278\) −3.33983 −0.200310
\(279\) −6.37461 −0.381638
\(280\) 0 0
\(281\) 24.6460 1.47026 0.735128 0.677928i \(-0.237122\pi\)
0.735128 + 0.677928i \(0.237122\pi\)
\(282\) −1.92050 −0.114364
\(283\) −27.0805 −1.60977 −0.804885 0.593430i \(-0.797773\pi\)
−0.804885 + 0.593430i \(0.797773\pi\)
\(284\) −20.7826 −1.23322
\(285\) −4.91418 −0.291091
\(286\) −2.85018 −0.168535
\(287\) 0 0
\(288\) −3.47280 −0.204637
\(289\) 21.0989 1.24111
\(290\) −1.88341 −0.110597
\(291\) 7.81362 0.458043
\(292\) −8.30827 −0.486205
\(293\) −31.1849 −1.82184 −0.910921 0.412581i \(-0.864627\pi\)
−0.910921 + 0.412581i \(0.864627\pi\)
\(294\) 0 0
\(295\) 4.04780 0.235672
\(296\) 8.63761 0.502051
\(297\) 1.38960 0.0806327
\(298\) −2.14341 −0.124165
\(299\) 31.6613 1.83102
\(300\) 7.98509 0.461020
\(301\) 0 0
\(302\) 4.93684 0.284083
\(303\) −12.5977 −0.723719
\(304\) 18.7947 1.07795
\(305\) −11.9793 −0.685934
\(306\) −1.90603 −0.108960
\(307\) −25.2868 −1.44319 −0.721596 0.692314i \(-0.756591\pi\)
−0.721596 + 0.692314i \(0.756591\pi\)
\(308\) 0 0
\(309\) −18.5097 −1.05298
\(310\) −1.76895 −0.100470
\(311\) −8.85487 −0.502113 −0.251057 0.967972i \(-0.580778\pi\)
−0.251057 + 0.967972i \(0.580778\pi\)
\(312\) 8.00874 0.453406
\(313\) −3.62015 −0.204623 −0.102312 0.994752i \(-0.532624\pi\)
−0.102312 + 0.994752i \(0.532624\pi\)
\(314\) 2.43301 0.137303
\(315\) 0 0
\(316\) 16.4560 0.925721
\(317\) 12.1660 0.683312 0.341656 0.939825i \(-0.389012\pi\)
0.341656 + 0.939825i \(0.389012\pi\)
\(318\) −3.21317 −0.180186
\(319\) −9.43130 −0.528051
\(320\) 5.21353 0.291445
\(321\) 3.77779 0.210856
\(322\) 0 0
\(323\) 33.7534 1.87809
\(324\) −1.90464 −0.105814
\(325\) −27.8468 −1.54466
\(326\) −7.29934 −0.404273
\(327\) −5.31301 −0.293810
\(328\) −1.20574 −0.0665759
\(329\) 0 0
\(330\) 0.385613 0.0212273
\(331\) 2.91507 0.160227 0.0801135 0.996786i \(-0.474472\pi\)
0.0801135 + 0.996786i \(0.474472\pi\)
\(332\) 17.2372 0.946014
\(333\) 7.16373 0.392570
\(334\) −4.10976 −0.224876
\(335\) 4.45654 0.243487
\(336\) 0 0
\(337\) 14.6448 0.797753 0.398877 0.917005i \(-0.369400\pi\)
0.398877 + 0.917005i \(0.369400\pi\)
\(338\) −9.60926 −0.522675
\(339\) −16.6298 −0.903207
\(340\) 10.5648 0.572955
\(341\) −8.85815 −0.479696
\(342\) −1.68863 −0.0913106
\(343\) 0 0
\(344\) −7.23642 −0.390162
\(345\) −4.28359 −0.230621
\(346\) −2.15902 −0.116070
\(347\) 26.4588 1.42039 0.710193 0.704007i \(-0.248608\pi\)
0.710193 + 0.704007i \(0.248608\pi\)
\(348\) 12.9269 0.692957
\(349\) 4.11366 0.220199 0.110099 0.993921i \(-0.464883\pi\)
0.110099 + 0.993921i \(0.464883\pi\)
\(350\) 0 0
\(351\) 6.64217 0.354533
\(352\) −4.82581 −0.257216
\(353\) −35.9977 −1.91596 −0.957982 0.286829i \(-0.907399\pi\)
−0.957982 + 0.286829i \(0.907399\pi\)
\(354\) 1.39092 0.0739266
\(355\) −9.80563 −0.520429
\(356\) 2.47507 0.131178
\(357\) 0 0
\(358\) 1.95385 0.103264
\(359\) −14.7022 −0.775951 −0.387976 0.921670i \(-0.626826\pi\)
−0.387976 + 0.921670i \(0.626826\pi\)
\(360\) −1.08354 −0.0571074
\(361\) 10.9036 0.573874
\(362\) −2.14423 −0.112698
\(363\) −9.06901 −0.476000
\(364\) 0 0
\(365\) −3.92000 −0.205182
\(366\) −4.11638 −0.215167
\(367\) 4.99355 0.260661 0.130331 0.991471i \(-0.458396\pi\)
0.130331 + 0.991471i \(0.458396\pi\)
\(368\) 16.3830 0.854022
\(369\) −1.00000 −0.0520579
\(370\) 1.98793 0.103348
\(371\) 0 0
\(372\) 12.1414 0.629500
\(373\) 26.6906 1.38199 0.690993 0.722862i \(-0.257174\pi\)
0.690993 + 0.722862i \(0.257174\pi\)
\(374\) −2.64861 −0.136957
\(375\) 8.26076 0.426584
\(376\) 7.49888 0.386725
\(377\) −45.0808 −2.32178
\(378\) 0 0
\(379\) 1.64461 0.0844778 0.0422389 0.999108i \(-0.486551\pi\)
0.0422389 + 0.999108i \(0.486551\pi\)
\(380\) 9.35977 0.480146
\(381\) −7.11991 −0.364764
\(382\) −6.16968 −0.315668
\(383\) 10.6131 0.542306 0.271153 0.962536i \(-0.412595\pi\)
0.271153 + 0.962536i \(0.412595\pi\)
\(384\) 8.73710 0.445863
\(385\) 0 0
\(386\) −3.17840 −0.161776
\(387\) −6.00164 −0.305080
\(388\) −14.8822 −0.755528
\(389\) 26.4309 1.34010 0.670049 0.742317i \(-0.266273\pi\)
0.670049 + 0.742317i \(0.266273\pi\)
\(390\) 1.84320 0.0933340
\(391\) 29.4222 1.48794
\(392\) 0 0
\(393\) −1.76987 −0.0892783
\(394\) 8.51644 0.429052
\(395\) 7.76425 0.390662
\(396\) −2.64669 −0.133001
\(397\) −14.6264 −0.734080 −0.367040 0.930205i \(-0.619629\pi\)
−0.367040 + 0.930205i \(0.619629\pi\)
\(398\) −4.82078 −0.241644
\(399\) 0 0
\(400\) −14.4092 −0.720461
\(401\) −24.7129 −1.23410 −0.617051 0.786923i \(-0.711673\pi\)
−0.617051 + 0.786923i \(0.711673\pi\)
\(402\) 1.53137 0.0763778
\(403\) −42.3412 −2.10917
\(404\) 23.9941 1.19375
\(405\) −0.898648 −0.0446542
\(406\) 0 0
\(407\) 9.95472 0.493437
\(408\) 7.44236 0.368452
\(409\) 9.79226 0.484196 0.242098 0.970252i \(-0.422164\pi\)
0.242098 + 0.970252i \(0.422164\pi\)
\(410\) −0.277499 −0.0137047
\(411\) 16.2543 0.801764
\(412\) 35.2543 1.73686
\(413\) 0 0
\(414\) −1.47194 −0.0723421
\(415\) 8.13284 0.399226
\(416\) −23.0670 −1.13095
\(417\) 10.8156 0.529644
\(418\) −2.34652 −0.114772
\(419\) 1.56318 0.0763662 0.0381831 0.999271i \(-0.487843\pi\)
0.0381831 + 0.999271i \(0.487843\pi\)
\(420\) 0 0
\(421\) −25.0323 −1.22000 −0.610000 0.792401i \(-0.708831\pi\)
−0.610000 + 0.792401i \(0.708831\pi\)
\(422\) −6.32578 −0.307934
\(423\) 6.21931 0.302393
\(424\) 12.5463 0.609302
\(425\) −25.8775 −1.25524
\(426\) −3.36945 −0.163250
\(427\) 0 0
\(428\) −7.19536 −0.347801
\(429\) 9.22996 0.445626
\(430\) −1.66545 −0.0803152
\(431\) 12.4377 0.599101 0.299550 0.954081i \(-0.403163\pi\)
0.299550 + 0.954081i \(0.403163\pi\)
\(432\) 3.43696 0.165361
\(433\) −0.0273710 −0.00131537 −0.000657683 1.00000i \(-0.500209\pi\)
−0.000657683 1.00000i \(0.500209\pi\)
\(434\) 0 0
\(435\) 6.09918 0.292433
\(436\) 10.1194 0.484631
\(437\) 26.0664 1.24692
\(438\) −1.34701 −0.0643624
\(439\) −33.9319 −1.61948 −0.809740 0.586789i \(-0.800392\pi\)
−0.809740 + 0.586789i \(0.800392\pi\)
\(440\) −1.50568 −0.0717806
\(441\) 0 0
\(442\) −12.6602 −0.602182
\(443\) 19.8639 0.943760 0.471880 0.881663i \(-0.343575\pi\)
0.471880 + 0.881663i \(0.343575\pi\)
\(444\) −13.6444 −0.647533
\(445\) 1.16779 0.0553583
\(446\) 4.85822 0.230043
\(447\) 6.94118 0.328307
\(448\) 0 0
\(449\) 14.0360 0.662399 0.331200 0.943561i \(-0.392547\pi\)
0.331200 + 0.943561i \(0.392547\pi\)
\(450\) 1.29461 0.0610285
\(451\) −1.38960 −0.0654337
\(452\) 31.6739 1.48981
\(453\) −15.9874 −0.751152
\(454\) 4.57890 0.214899
\(455\) 0 0
\(456\) 6.59350 0.308769
\(457\) 23.3867 1.09399 0.546993 0.837137i \(-0.315773\pi\)
0.546993 + 0.837137i \(0.315773\pi\)
\(458\) 2.22617 0.104022
\(459\) 6.17243 0.288104
\(460\) 8.15872 0.380402
\(461\) 23.2004 1.08055 0.540275 0.841488i \(-0.318320\pi\)
0.540275 + 0.841488i \(0.318320\pi\)
\(462\) 0 0
\(463\) −14.4318 −0.670702 −0.335351 0.942093i \(-0.608855\pi\)
−0.335351 + 0.942093i \(0.608855\pi\)
\(464\) −23.3269 −1.08292
\(465\) 5.72853 0.265654
\(466\) −1.23569 −0.0572423
\(467\) −21.6092 −0.999955 −0.499977 0.866039i \(-0.666658\pi\)
−0.499977 + 0.866039i \(0.666658\pi\)
\(468\) −12.6510 −0.584791
\(469\) 0 0
\(470\) 1.72586 0.0796078
\(471\) −7.87899 −0.363045
\(472\) −5.43105 −0.249984
\(473\) −8.33987 −0.383468
\(474\) 2.66798 0.122544
\(475\) −22.9260 −1.05192
\(476\) 0 0
\(477\) 10.4055 0.476433
\(478\) −0.817669 −0.0373993
\(479\) −6.91726 −0.316057 −0.158029 0.987435i \(-0.550514\pi\)
−0.158029 + 0.987435i \(0.550514\pi\)
\(480\) 3.12083 0.142446
\(481\) 47.5827 2.16959
\(482\) −2.99175 −0.136270
\(483\) 0 0
\(484\) 17.2732 0.785148
\(485\) −7.02169 −0.318839
\(486\) −0.308797 −0.0140073
\(487\) 15.0820 0.683430 0.341715 0.939804i \(-0.388992\pi\)
0.341715 + 0.939804i \(0.388992\pi\)
\(488\) 16.0730 0.727591
\(489\) 23.6380 1.06895
\(490\) 0 0
\(491\) 24.3627 1.09948 0.549738 0.835337i \(-0.314728\pi\)
0.549738 + 0.835337i \(0.314728\pi\)
\(492\) 1.90464 0.0858680
\(493\) −41.8927 −1.88675
\(494\) −11.2162 −0.504639
\(495\) −1.24876 −0.0561276
\(496\) −21.9093 −0.983755
\(497\) 0 0
\(498\) 2.79464 0.125231
\(499\) 1.21709 0.0544843 0.0272421 0.999629i \(-0.491327\pi\)
0.0272421 + 0.999629i \(0.491327\pi\)
\(500\) −15.7338 −0.703637
\(501\) 13.3089 0.594599
\(502\) −6.57201 −0.293323
\(503\) 37.9289 1.69117 0.845583 0.533845i \(-0.179253\pi\)
0.845583 + 0.533845i \(0.179253\pi\)
\(504\) 0 0
\(505\) 11.3209 0.503773
\(506\) −2.04541 −0.0909297
\(507\) 31.1184 1.38202
\(508\) 13.5609 0.601668
\(509\) 27.0118 1.19728 0.598638 0.801020i \(-0.295709\pi\)
0.598638 + 0.801020i \(0.295709\pi\)
\(510\) 1.71285 0.0758461
\(511\) 0 0
\(512\) −20.2241 −0.893786
\(513\) 5.46842 0.241437
\(514\) −8.72277 −0.384745
\(515\) 16.6337 0.732967
\(516\) 11.4310 0.503221
\(517\) 8.64235 0.380090
\(518\) 0 0
\(519\) 6.99173 0.306903
\(520\) −7.19704 −0.315611
\(521\) 41.0082 1.79660 0.898300 0.439383i \(-0.144803\pi\)
0.898300 + 0.439383i \(0.144803\pi\)
\(522\) 2.09582 0.0917316
\(523\) −37.2325 −1.62807 −0.814033 0.580819i \(-0.802732\pi\)
−0.814033 + 0.580819i \(0.802732\pi\)
\(524\) 3.37098 0.147262
\(525\) 0 0
\(526\) 1.75311 0.0764392
\(527\) −39.3468 −1.71397
\(528\) 4.77600 0.207849
\(529\) −0.278497 −0.0121086
\(530\) 2.88751 0.125425
\(531\) −4.50432 −0.195471
\(532\) 0 0
\(533\) −6.64217 −0.287704
\(534\) 0.401279 0.0173650
\(535\) −3.39491 −0.146775
\(536\) −5.97946 −0.258273
\(537\) −6.32731 −0.273044
\(538\) 0.143664 0.00619381
\(539\) 0 0
\(540\) 1.71160 0.0736557
\(541\) −18.6657 −0.802500 −0.401250 0.915969i \(-0.631424\pi\)
−0.401250 + 0.915969i \(0.631424\pi\)
\(542\) 2.62987 0.112963
\(543\) 6.94382 0.297988
\(544\) −21.4357 −0.919046
\(545\) 4.77452 0.204518
\(546\) 0 0
\(547\) 22.4706 0.960775 0.480388 0.877056i \(-0.340496\pi\)
0.480388 + 0.877056i \(0.340496\pi\)
\(548\) −30.9586 −1.32249
\(549\) 13.3304 0.568927
\(550\) 1.79899 0.0767091
\(551\) −37.1145 −1.58113
\(552\) 5.74742 0.244626
\(553\) 0 0
\(554\) 0.280781 0.0119293
\(555\) −6.43767 −0.273264
\(556\) −20.5999 −0.873632
\(557\) 1.44517 0.0612339 0.0306170 0.999531i \(-0.490253\pi\)
0.0306170 + 0.999531i \(0.490253\pi\)
\(558\) 1.96846 0.0833314
\(559\) −39.8639 −1.68606
\(560\) 0 0
\(561\) 8.57721 0.362130
\(562\) −7.61060 −0.321034
\(563\) −33.4355 −1.40914 −0.704568 0.709636i \(-0.748859\pi\)
−0.704568 + 0.709636i \(0.748859\pi\)
\(564\) −11.8456 −0.498789
\(565\) 14.9443 0.628713
\(566\) 8.36238 0.351497
\(567\) 0 0
\(568\) 13.1565 0.552034
\(569\) 32.2954 1.35389 0.676946 0.736033i \(-0.263303\pi\)
0.676946 + 0.736033i \(0.263303\pi\)
\(570\) 1.51748 0.0635604
\(571\) −23.7959 −0.995829 −0.497915 0.867226i \(-0.665901\pi\)
−0.497915 + 0.867226i \(0.665901\pi\)
\(572\) −17.5798 −0.735048
\(573\) 19.9797 0.834666
\(574\) 0 0
\(575\) −19.9841 −0.833394
\(576\) −5.80153 −0.241730
\(577\) 14.7145 0.612574 0.306287 0.951939i \(-0.400913\pi\)
0.306287 + 0.951939i \(0.400913\pi\)
\(578\) −6.51528 −0.271000
\(579\) 10.2929 0.427757
\(580\) −11.6168 −0.482360
\(581\) 0 0
\(582\) −2.41282 −0.100015
\(583\) 14.4594 0.598848
\(584\) 5.25958 0.217643
\(585\) −5.96897 −0.246787
\(586\) 9.62980 0.397803
\(587\) 3.04010 0.125479 0.0627393 0.998030i \(-0.480016\pi\)
0.0627393 + 0.998030i \(0.480016\pi\)
\(588\) 0 0
\(589\) −34.8590 −1.43634
\(590\) −1.24995 −0.0514595
\(591\) −27.5794 −1.13447
\(592\) 24.6215 1.01194
\(593\) −42.2287 −1.73413 −0.867063 0.498198i \(-0.833995\pi\)
−0.867063 + 0.498198i \(0.833995\pi\)
\(594\) −0.429104 −0.0176063
\(595\) 0 0
\(596\) −13.2205 −0.541532
\(597\) 15.6115 0.638936
\(598\) −9.77690 −0.399807
\(599\) −41.9943 −1.71584 −0.857920 0.513783i \(-0.828243\pi\)
−0.857920 + 0.513783i \(0.828243\pi\)
\(600\) −5.05499 −0.206369
\(601\) −29.4544 −1.20147 −0.600735 0.799448i \(-0.705125\pi\)
−0.600735 + 0.799448i \(0.705125\pi\)
\(602\) 0 0
\(603\) −4.95916 −0.201952
\(604\) 30.4502 1.23900
\(605\) 8.14985 0.331339
\(606\) 3.89013 0.158026
\(607\) 20.7083 0.840526 0.420263 0.907402i \(-0.361938\pi\)
0.420263 + 0.907402i \(0.361938\pi\)
\(608\) −18.9907 −0.770177
\(609\) 0 0
\(610\) 3.69918 0.149775
\(611\) 41.3097 1.67121
\(612\) −11.7563 −0.475220
\(613\) −41.4706 −1.67498 −0.837491 0.546451i \(-0.815978\pi\)
−0.837491 + 0.546451i \(0.815978\pi\)
\(614\) 7.80847 0.315124
\(615\) 0.898648 0.0362370
\(616\) 0 0
\(617\) 2.76644 0.111373 0.0556863 0.998448i \(-0.482265\pi\)
0.0556863 + 0.998448i \(0.482265\pi\)
\(618\) 5.71573 0.229920
\(619\) −0.990969 −0.0398304 −0.0199152 0.999802i \(-0.506340\pi\)
−0.0199152 + 0.999802i \(0.506340\pi\)
\(620\) −10.9108 −0.438189
\(621\) 4.76671 0.191281
\(622\) 2.73435 0.109638
\(623\) 0 0
\(624\) 22.8289 0.913886
\(625\) 13.5386 0.541546
\(626\) 1.11789 0.0446799
\(627\) 7.59891 0.303471
\(628\) 15.0067 0.598832
\(629\) 44.2177 1.76307
\(630\) 0 0
\(631\) −4.46880 −0.177900 −0.0889500 0.996036i \(-0.528351\pi\)
−0.0889500 + 0.996036i \(0.528351\pi\)
\(632\) −10.4175 −0.414386
\(633\) 20.4853 0.814217
\(634\) −3.75683 −0.149203
\(635\) 6.39830 0.253909
\(636\) −19.8187 −0.785862
\(637\) 0 0
\(638\) 2.91235 0.115301
\(639\) 10.9115 0.431654
\(640\) −7.85158 −0.310361
\(641\) −30.9202 −1.22127 −0.610637 0.791911i \(-0.709086\pi\)
−0.610637 + 0.791911i \(0.709086\pi\)
\(642\) −1.16657 −0.0460409
\(643\) 9.54896 0.376574 0.188287 0.982114i \(-0.439706\pi\)
0.188287 + 0.982114i \(0.439706\pi\)
\(644\) 0 0
\(645\) 5.39336 0.212363
\(646\) −10.4230 −0.410086
\(647\) 38.0623 1.49638 0.748191 0.663484i \(-0.230923\pi\)
0.748191 + 0.663484i \(0.230923\pi\)
\(648\) 1.20574 0.0473660
\(649\) −6.25921 −0.245695
\(650\) 8.59901 0.337281
\(651\) 0 0
\(652\) −45.0220 −1.76320
\(653\) 27.2830 1.06767 0.533833 0.845590i \(-0.320751\pi\)
0.533833 + 0.845590i \(0.320751\pi\)
\(654\) 1.64064 0.0641540
\(655\) 1.59049 0.0621457
\(656\) −3.43696 −0.134191
\(657\) 4.36211 0.170182
\(658\) 0 0
\(659\) −9.31532 −0.362873 −0.181437 0.983403i \(-0.558075\pi\)
−0.181437 + 0.983403i \(0.558075\pi\)
\(660\) 2.37845 0.0925809
\(661\) −14.6419 −0.569502 −0.284751 0.958601i \(-0.591911\pi\)
−0.284751 + 0.958601i \(0.591911\pi\)
\(662\) −0.900165 −0.0349859
\(663\) 40.9983 1.59224
\(664\) −10.9121 −0.423470
\(665\) 0 0
\(666\) −2.21214 −0.0857186
\(667\) −32.3519 −1.25267
\(668\) −25.3488 −0.980774
\(669\) −15.7327 −0.608263
\(670\) −1.37616 −0.0531658
\(671\) 18.5239 0.715107
\(672\) 0 0
\(673\) −28.2730 −1.08984 −0.544921 0.838487i \(-0.683441\pi\)
−0.544921 + 0.838487i \(0.683441\pi\)
\(674\) −4.52227 −0.174191
\(675\) −4.19243 −0.161367
\(676\) −59.2695 −2.27960
\(677\) −25.4582 −0.978437 −0.489218 0.872161i \(-0.662718\pi\)
−0.489218 + 0.872161i \(0.662718\pi\)
\(678\) 5.13523 0.197217
\(679\) 0 0
\(680\) −6.68806 −0.256475
\(681\) −14.8282 −0.568219
\(682\) 2.73537 0.104743
\(683\) −51.8529 −1.98410 −0.992048 0.125861i \(-0.959831\pi\)
−0.992048 + 0.125861i \(0.959831\pi\)
\(684\) −10.4154 −0.398243
\(685\) −14.6069 −0.558099
\(686\) 0 0
\(687\) −7.20918 −0.275048
\(688\) −20.6274 −0.786412
\(689\) 69.1148 2.63306
\(690\) 1.32276 0.0503566
\(691\) −47.1718 −1.79450 −0.897249 0.441524i \(-0.854438\pi\)
−0.897249 + 0.441524i \(0.854438\pi\)
\(692\) −13.3168 −0.506227
\(693\) 0 0
\(694\) −8.17040 −0.310144
\(695\) −9.71944 −0.368679
\(696\) −8.18344 −0.310193
\(697\) −6.17243 −0.233798
\(698\) −1.27028 −0.0480809
\(699\) 4.00163 0.151356
\(700\) 0 0
\(701\) 39.7588 1.50167 0.750834 0.660491i \(-0.229652\pi\)
0.750834 + 0.660491i \(0.229652\pi\)
\(702\) −2.05108 −0.0774130
\(703\) 39.1743 1.47749
\(704\) −8.06180 −0.303841
\(705\) −5.58897 −0.210493
\(706\) 11.1160 0.418355
\(707\) 0 0
\(708\) 8.57914 0.322424
\(709\) −11.4500 −0.430016 −0.215008 0.976612i \(-0.568978\pi\)
−0.215008 + 0.976612i \(0.568978\pi\)
\(710\) 3.02795 0.113637
\(711\) −8.63992 −0.324022
\(712\) −1.56685 −0.0587202
\(713\) −30.3859 −1.13796
\(714\) 0 0
\(715\) −8.29448 −0.310196
\(716\) 12.0513 0.450377
\(717\) 2.64792 0.0988884
\(718\) 4.53998 0.169431
\(719\) 42.0567 1.56845 0.784226 0.620476i \(-0.213060\pi\)
0.784226 + 0.620476i \(0.213060\pi\)
\(720\) −3.08862 −0.115106
\(721\) 0 0
\(722\) −3.36700 −0.125307
\(723\) 9.68840 0.360315
\(724\) −13.2255 −0.491522
\(725\) 28.4543 1.05677
\(726\) 2.80048 0.103936
\(727\) −24.0062 −0.890342 −0.445171 0.895446i \(-0.646857\pi\)
−0.445171 + 0.895446i \(0.646857\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.21048 0.0448020
\(731\) −37.0447 −1.37015
\(732\) −25.3897 −0.938429
\(733\) −45.8010 −1.69170 −0.845849 0.533423i \(-0.820905\pi\)
−0.845849 + 0.533423i \(0.820905\pi\)
\(734\) −1.54199 −0.0569159
\(735\) 0 0
\(736\) −16.5538 −0.610183
\(737\) −6.89124 −0.253842
\(738\) 0.308797 0.0113670
\(739\) 27.6295 1.01637 0.508184 0.861248i \(-0.330317\pi\)
0.508184 + 0.861248i \(0.330317\pi\)
\(740\) 12.2615 0.450741
\(741\) 36.3222 1.33433
\(742\) 0 0
\(743\) −5.43601 −0.199428 −0.0997139 0.995016i \(-0.531793\pi\)
−0.0997139 + 0.995016i \(0.531793\pi\)
\(744\) −7.68613 −0.281787
\(745\) −6.23768 −0.228531
\(746\) −8.24196 −0.301760
\(747\) −9.05009 −0.331125
\(748\) −16.3365 −0.597323
\(749\) 0 0
\(750\) −2.55090 −0.0931455
\(751\) 2.55797 0.0933416 0.0466708 0.998910i \(-0.485139\pi\)
0.0466708 + 0.998910i \(0.485139\pi\)
\(752\) 21.3755 0.779485
\(753\) 21.2826 0.775582
\(754\) 13.9208 0.506966
\(755\) 14.3670 0.522869
\(756\) 0 0
\(757\) 13.4360 0.488339 0.244170 0.969733i \(-0.421485\pi\)
0.244170 + 0.969733i \(0.421485\pi\)
\(758\) −0.507849 −0.0184459
\(759\) 6.62381 0.240429
\(760\) −5.92523 −0.214931
\(761\) 19.8756 0.720489 0.360245 0.932858i \(-0.382693\pi\)
0.360245 + 0.932858i \(0.382693\pi\)
\(762\) 2.19861 0.0796471
\(763\) 0 0
\(764\) −38.0543 −1.37676
\(765\) −5.54684 −0.200547
\(766\) −3.27730 −0.118414
\(767\) −29.9185 −1.08029
\(768\) 8.90507 0.321334
\(769\) −54.3254 −1.95902 −0.979512 0.201384i \(-0.935456\pi\)
−0.979512 + 0.201384i \(0.935456\pi\)
\(770\) 0 0
\(771\) 28.2476 1.01731
\(772\) −19.6043 −0.705572
\(773\) 23.4861 0.844737 0.422368 0.906424i \(-0.361199\pi\)
0.422368 + 0.906424i \(0.361199\pi\)
\(774\) 1.85329 0.0666150
\(775\) 26.7251 0.959994
\(776\) 9.42121 0.338202
\(777\) 0 0
\(778\) −8.16176 −0.292613
\(779\) −5.46842 −0.195926
\(780\) 11.3688 0.407067
\(781\) 15.1627 0.542563
\(782\) −9.08547 −0.324896
\(783\) −6.78706 −0.242550
\(784\) 0 0
\(785\) 7.08044 0.252712
\(786\) 0.546531 0.0194941
\(787\) 21.1427 0.753655 0.376828 0.926283i \(-0.377015\pi\)
0.376828 + 0.926283i \(0.377015\pi\)
\(788\) 52.5290 1.87127
\(789\) −5.67723 −0.202115
\(790\) −2.39757 −0.0853018
\(791\) 0 0
\(792\) 1.67550 0.0595362
\(793\) 88.5427 3.14424
\(794\) 4.51660 0.160288
\(795\) −9.35084 −0.331640
\(796\) −29.7343 −1.05391
\(797\) 31.1992 1.10513 0.552566 0.833469i \(-0.313649\pi\)
0.552566 + 0.833469i \(0.313649\pi\)
\(798\) 0 0
\(799\) 38.3883 1.35808
\(800\) 14.5595 0.514756
\(801\) −1.29949 −0.0459153
\(802\) 7.63126 0.269469
\(803\) 6.06159 0.213909
\(804\) 9.44543 0.333115
\(805\) 0 0
\(806\) 13.0748 0.460541
\(807\) −0.465240 −0.0163772
\(808\) −15.1896 −0.534367
\(809\) −15.7021 −0.552058 −0.276029 0.961149i \(-0.589019\pi\)
−0.276029 + 0.961149i \(0.589019\pi\)
\(810\) 0.277499 0.00975034
\(811\) 23.2522 0.816496 0.408248 0.912871i \(-0.366140\pi\)
0.408248 + 0.912871i \(0.366140\pi\)
\(812\) 0 0
\(813\) −8.51652 −0.298687
\(814\) −3.07398 −0.107743
\(815\) −21.2422 −0.744083
\(816\) 21.2144 0.742653
\(817\) −32.8195 −1.14821
\(818\) −3.02382 −0.105725
\(819\) 0 0
\(820\) −1.71160 −0.0597718
\(821\) 51.4928 1.79711 0.898555 0.438861i \(-0.144618\pi\)
0.898555 + 0.438861i \(0.144618\pi\)
\(822\) −5.01926 −0.175067
\(823\) −7.46987 −0.260383 −0.130192 0.991489i \(-0.541559\pi\)
−0.130192 + 0.991489i \(0.541559\pi\)
\(824\) −22.3179 −0.777480
\(825\) −5.82580 −0.202828
\(826\) 0 0
\(827\) −2.08519 −0.0725090 −0.0362545 0.999343i \(-0.511543\pi\)
−0.0362545 + 0.999343i \(0.511543\pi\)
\(828\) −9.07888 −0.315513
\(829\) −35.6611 −1.23856 −0.619280 0.785170i \(-0.712575\pi\)
−0.619280 + 0.785170i \(0.712575\pi\)
\(830\) −2.51140 −0.0871718
\(831\) −0.909276 −0.0315424
\(832\) −38.5347 −1.33595
\(833\) 0 0
\(834\) −3.33983 −0.115649
\(835\) −11.9600 −0.413895
\(836\) −14.4732 −0.500567
\(837\) −6.37461 −0.220339
\(838\) −0.482704 −0.0166747
\(839\) 28.7416 0.992271 0.496136 0.868245i \(-0.334752\pi\)
0.496136 + 0.868245i \(0.334752\pi\)
\(840\) 0 0
\(841\) 17.0642 0.588421
\(842\) 7.72989 0.266390
\(843\) 24.6460 0.848853
\(844\) −39.0172 −1.34303
\(845\) −27.9645 −0.962008
\(846\) −1.92050 −0.0660282
\(847\) 0 0
\(848\) 35.7631 1.22811
\(849\) −27.0805 −0.929402
\(850\) 7.99089 0.274085
\(851\) 34.1474 1.17056
\(852\) −20.7826 −0.712000
\(853\) −10.3798 −0.355399 −0.177700 0.984085i \(-0.556866\pi\)
−0.177700 + 0.984085i \(0.556866\pi\)
\(854\) 0 0
\(855\) −4.91418 −0.168061
\(856\) 4.55504 0.155688
\(857\) −17.1959 −0.587400 −0.293700 0.955898i \(-0.594887\pi\)
−0.293700 + 0.955898i \(0.594887\pi\)
\(858\) −2.85018 −0.0973035
\(859\) −20.5963 −0.702738 −0.351369 0.936237i \(-0.614284\pi\)
−0.351369 + 0.936237i \(0.614284\pi\)
\(860\) −10.2724 −0.350287
\(861\) 0 0
\(862\) −3.84071 −0.130815
\(863\) −3.01849 −0.102750 −0.0513752 0.998679i \(-0.516360\pi\)
−0.0513752 + 0.998679i \(0.516360\pi\)
\(864\) −3.47280 −0.118147
\(865\) −6.28310 −0.213632
\(866\) 0.00845207 0.000287213 0
\(867\) 21.0989 0.716557
\(868\) 0 0
\(869\) −12.0060 −0.407277
\(870\) −1.88341 −0.0638535
\(871\) −32.9396 −1.11611
\(872\) −6.40611 −0.216938
\(873\) 7.81362 0.264451
\(874\) −8.04920 −0.272268
\(875\) 0 0
\(876\) −8.30827 −0.280711
\(877\) 14.5978 0.492933 0.246466 0.969151i \(-0.420731\pi\)
0.246466 + 0.969151i \(0.420731\pi\)
\(878\) 10.4780 0.353617
\(879\) −31.1849 −1.05184
\(880\) −4.29194 −0.144681
\(881\) 8.66646 0.291981 0.145990 0.989286i \(-0.453363\pi\)
0.145990 + 0.989286i \(0.453363\pi\)
\(882\) 0 0
\(883\) −12.6380 −0.425304 −0.212652 0.977128i \(-0.568210\pi\)
−0.212652 + 0.977128i \(0.568210\pi\)
\(884\) −78.0873 −2.62636
\(885\) 4.04780 0.136065
\(886\) −6.13389 −0.206072
\(887\) 21.8225 0.732729 0.366364 0.930472i \(-0.380602\pi\)
0.366364 + 0.930472i \(0.380602\pi\)
\(888\) 8.63761 0.289859
\(889\) 0 0
\(890\) −0.360608 −0.0120876
\(891\) 1.38960 0.0465533
\(892\) 29.9653 1.00331
\(893\) 34.0098 1.13809
\(894\) −2.14341 −0.0716865
\(895\) 5.68602 0.190063
\(896\) 0 0
\(897\) 31.6613 1.05714
\(898\) −4.33427 −0.144636
\(899\) 43.2648 1.44296
\(900\) 7.98509 0.266170
\(901\) 64.2270 2.13971
\(902\) 0.429104 0.0142876
\(903\) 0 0
\(904\) −20.0512 −0.666894
\(905\) −6.24005 −0.207426
\(906\) 4.93684 0.164016
\(907\) 8.54997 0.283897 0.141949 0.989874i \(-0.454663\pi\)
0.141949 + 0.989874i \(0.454663\pi\)
\(908\) 28.2425 0.937260
\(909\) −12.5977 −0.417839
\(910\) 0 0
\(911\) −4.92067 −0.163029 −0.0815145 0.996672i \(-0.525976\pi\)
−0.0815145 + 0.996672i \(0.525976\pi\)
\(912\) 18.7947 0.622356
\(913\) −12.5760 −0.416205
\(914\) −7.22175 −0.238874
\(915\) −11.9793 −0.396024
\(916\) 13.7309 0.453683
\(917\) 0 0
\(918\) −1.90603 −0.0629083
\(919\) −54.5333 −1.79889 −0.899444 0.437037i \(-0.856028\pi\)
−0.899444 + 0.437037i \(0.856028\pi\)
\(920\) −5.16490 −0.170282
\(921\) −25.2868 −0.833228
\(922\) −7.16420 −0.235941
\(923\) 72.4763 2.38559
\(924\) 0 0
\(925\) −30.0335 −0.987494
\(926\) 4.45649 0.146449
\(927\) −18.5097 −0.607937
\(928\) 23.5701 0.773728
\(929\) 2.13381 0.0700080 0.0350040 0.999387i \(-0.488856\pi\)
0.0350040 + 0.999387i \(0.488856\pi\)
\(930\) −1.76895 −0.0580062
\(931\) 0 0
\(932\) −7.62169 −0.249657
\(933\) −8.85487 −0.289895
\(934\) 6.67285 0.218342
\(935\) −7.70789 −0.252075
\(936\) 8.00874 0.261774
\(937\) −6.22159 −0.203250 −0.101625 0.994823i \(-0.532404\pi\)
−0.101625 + 0.994823i \(0.532404\pi\)
\(938\) 0 0
\(939\) −3.62015 −0.118139
\(940\) 10.6450 0.347202
\(941\) 10.0787 0.328555 0.164278 0.986414i \(-0.447471\pi\)
0.164278 + 0.986414i \(0.447471\pi\)
\(942\) 2.43301 0.0792716
\(943\) −4.76671 −0.155225
\(944\) −15.4812 −0.503870
\(945\) 0 0
\(946\) 2.57532 0.0837310
\(947\) −46.3131 −1.50497 −0.752486 0.658608i \(-0.771146\pi\)
−0.752486 + 0.658608i \(0.771146\pi\)
\(948\) 16.4560 0.534465
\(949\) 28.9739 0.940532
\(950\) 7.07946 0.229688
\(951\) 12.1660 0.394510
\(952\) 0 0
\(953\) 20.1172 0.651659 0.325829 0.945429i \(-0.394356\pi\)
0.325829 + 0.945429i \(0.394356\pi\)
\(954\) −3.21317 −0.104030
\(955\) −17.9548 −0.581002
\(956\) −5.04335 −0.163114
\(957\) −9.43130 −0.304871
\(958\) 2.13603 0.0690119
\(959\) 0 0
\(960\) 5.21353 0.168266
\(961\) 9.63561 0.310826
\(962\) −14.6934 −0.473734
\(963\) 3.77779 0.121738
\(964\) −18.4530 −0.594330
\(965\) −9.24966 −0.297757
\(966\) 0 0
\(967\) −34.4719 −1.10854 −0.554271 0.832336i \(-0.687003\pi\)
−0.554271 + 0.832336i \(0.687003\pi\)
\(968\) −10.9349 −0.351460
\(969\) 33.7534 1.08432
\(970\) 2.16828 0.0696191
\(971\) −15.7013 −0.503880 −0.251940 0.967743i \(-0.581069\pi\)
−0.251940 + 0.967743i \(0.581069\pi\)
\(972\) −1.90464 −0.0610915
\(973\) 0 0
\(974\) −4.65727 −0.149229
\(975\) −27.8468 −0.891813
\(976\) 45.8160 1.46653
\(977\) −13.7257 −0.439123 −0.219561 0.975599i \(-0.570463\pi\)
−0.219561 + 0.975599i \(0.570463\pi\)
\(978\) −7.29934 −0.233407
\(979\) −1.80577 −0.0577127
\(980\) 0 0
\(981\) −5.31301 −0.169631
\(982\) −7.52314 −0.240073
\(983\) 31.3146 0.998781 0.499391 0.866377i \(-0.333557\pi\)
0.499391 + 0.866377i \(0.333557\pi\)
\(984\) −1.20574 −0.0384376
\(985\) 24.7842 0.789691
\(986\) 12.9363 0.411976
\(987\) 0 0
\(988\) −69.1808 −2.20093
\(989\) −28.6080 −0.909683
\(990\) 0.385613 0.0122556
\(991\) −4.10511 −0.130403 −0.0652016 0.997872i \(-0.520769\pi\)
−0.0652016 + 0.997872i \(0.520769\pi\)
\(992\) 22.1378 0.702875
\(993\) 2.91507 0.0925071
\(994\) 0 0
\(995\) −14.0292 −0.444757
\(996\) 17.2372 0.546182
\(997\) 56.9183 1.80262 0.901311 0.433173i \(-0.142606\pi\)
0.901311 + 0.433173i \(0.142606\pi\)
\(998\) −0.375832 −0.0118968
\(999\) 7.16373 0.226650
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 \(a_p\))