Properties

Label 6027.2.a.bo.1.14
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 1.14
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.11646 q^{2} +1.00000 q^{3} -0.753512 q^{4} -0.900581 q^{5} +1.11646 q^{6} -3.07419 q^{8} +1.00000 q^{9} -1.00546 q^{10} -4.69451 q^{11} -0.753512 q^{12} +1.15587 q^{13} -0.900581 q^{15} -1.92519 q^{16} +5.04891 q^{17} +1.11646 q^{18} +0.849395 q^{19} +0.678599 q^{20} -5.24124 q^{22} -1.63546 q^{23} -3.07419 q^{24} -4.18895 q^{25} +1.29048 q^{26} +1.00000 q^{27} +7.97364 q^{29} -1.00546 q^{30} +2.94278 q^{31} +3.99898 q^{32} -4.69451 q^{33} +5.63692 q^{34} -0.753512 q^{36} +3.09905 q^{37} +0.948318 q^{38} +1.15587 q^{39} +2.76856 q^{40} -1.00000 q^{41} -3.01389 q^{43} +3.53737 q^{44} -0.900581 q^{45} -1.82593 q^{46} -8.14340 q^{47} -1.92519 q^{48} -4.67681 q^{50} +5.04891 q^{51} -0.870962 q^{52} -8.01568 q^{53} +1.11646 q^{54} +4.22779 q^{55} +0.849395 q^{57} +8.90226 q^{58} -2.60113 q^{59} +0.678599 q^{60} -7.31482 q^{61} +3.28551 q^{62} +8.31510 q^{64} -1.04095 q^{65} -5.24124 q^{66} +0.796475 q^{67} -3.80442 q^{68} -1.63546 q^{69} +10.7265 q^{71} -3.07419 q^{72} +1.76040 q^{73} +3.45997 q^{74} -4.18895 q^{75} -0.640030 q^{76} +1.29048 q^{78} +13.8908 q^{79} +1.73379 q^{80} +1.00000 q^{81} -1.11646 q^{82} +10.3080 q^{83} -4.54695 q^{85} -3.36490 q^{86} +7.97364 q^{87} +14.4318 q^{88} +15.1741 q^{89} -1.00546 q^{90} +1.23234 q^{92} +2.94278 q^{93} -9.09180 q^{94} -0.764949 q^{95} +3.99898 q^{96} -0.878601 q^{97} -4.69451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.11646 0.789458 0.394729 0.918798i \(-0.370838\pi\)
0.394729 + 0.918798i \(0.370838\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.753512 −0.376756
\(5\) −0.900581 −0.402752 −0.201376 0.979514i \(-0.564541\pi\)
−0.201376 + 0.979514i \(0.564541\pi\)
\(6\) 1.11646 0.455794
\(7\) 0 0
\(8\) −3.07419 −1.08689
\(9\) 1.00000 0.333333
\(10\) −1.00546 −0.317956
\(11\) −4.69451 −1.41545 −0.707724 0.706489i \(-0.750278\pi\)
−0.707724 + 0.706489i \(0.750278\pi\)
\(12\) −0.753512 −0.217520
\(13\) 1.15587 0.320581 0.160290 0.987070i \(-0.448757\pi\)
0.160290 + 0.987070i \(0.448757\pi\)
\(14\) 0 0
\(15\) −0.900581 −0.232529
\(16\) −1.92519 −0.481299
\(17\) 5.04891 1.22454 0.612271 0.790648i \(-0.290256\pi\)
0.612271 + 0.790648i \(0.290256\pi\)
\(18\) 1.11646 0.263153
\(19\) 0.849395 0.194865 0.0974323 0.995242i \(-0.468937\pi\)
0.0974323 + 0.995242i \(0.468937\pi\)
\(20\) 0.678599 0.151739
\(21\) 0 0
\(22\) −5.24124 −1.11744
\(23\) −1.63546 −0.341016 −0.170508 0.985356i \(-0.554541\pi\)
−0.170508 + 0.985356i \(0.554541\pi\)
\(24\) −3.07419 −0.627517
\(25\) −4.18895 −0.837791
\(26\) 1.29048 0.253085
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 7.97364 1.48067 0.740334 0.672240i \(-0.234668\pi\)
0.740334 + 0.672240i \(0.234668\pi\)
\(30\) −1.00546 −0.183572
\(31\) 2.94278 0.528539 0.264270 0.964449i \(-0.414869\pi\)
0.264270 + 0.964449i \(0.414869\pi\)
\(32\) 3.99898 0.706926
\(33\) −4.69451 −0.817210
\(34\) 5.63692 0.966724
\(35\) 0 0
\(36\) −0.753512 −0.125585
\(37\) 3.09905 0.509480 0.254740 0.967010i \(-0.418010\pi\)
0.254740 + 0.967010i \(0.418010\pi\)
\(38\) 0.948318 0.153837
\(39\) 1.15587 0.185087
\(40\) 2.76856 0.437748
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.01389 −0.459614 −0.229807 0.973236i \(-0.573810\pi\)
−0.229807 + 0.973236i \(0.573810\pi\)
\(44\) 3.53737 0.533279
\(45\) −0.900581 −0.134251
\(46\) −1.82593 −0.269218
\(47\) −8.14340 −1.18784 −0.593918 0.804525i \(-0.702420\pi\)
−0.593918 + 0.804525i \(0.702420\pi\)
\(48\) −1.92519 −0.277878
\(49\) 0 0
\(50\) −4.67681 −0.661401
\(51\) 5.04891 0.706989
\(52\) −0.870962 −0.120781
\(53\) −8.01568 −1.10104 −0.550519 0.834822i \(-0.685570\pi\)
−0.550519 + 0.834822i \(0.685570\pi\)
\(54\) 1.11646 0.151931
\(55\) 4.22779 0.570075
\(56\) 0 0
\(57\) 0.849395 0.112505
\(58\) 8.90226 1.16892
\(59\) −2.60113 −0.338638 −0.169319 0.985561i \(-0.554157\pi\)
−0.169319 + 0.985561i \(0.554157\pi\)
\(60\) 0.678599 0.0876067
\(61\) −7.31482 −0.936567 −0.468283 0.883578i \(-0.655127\pi\)
−0.468283 + 0.883578i \(0.655127\pi\)
\(62\) 3.28551 0.417260
\(63\) 0 0
\(64\) 8.31510 1.03939
\(65\) −1.04095 −0.129114
\(66\) −5.24124 −0.645153
\(67\) 0.796475 0.0973049 0.0486524 0.998816i \(-0.484507\pi\)
0.0486524 + 0.998816i \(0.484507\pi\)
\(68\) −3.80442 −0.461353
\(69\) −1.63546 −0.196886
\(70\) 0 0
\(71\) 10.7265 1.27300 0.636501 0.771276i \(-0.280381\pi\)
0.636501 + 0.771276i \(0.280381\pi\)
\(72\) −3.07419 −0.362297
\(73\) 1.76040 0.206040 0.103020 0.994679i \(-0.467149\pi\)
0.103020 + 0.994679i \(0.467149\pi\)
\(74\) 3.45997 0.402213
\(75\) −4.18895 −0.483699
\(76\) −0.640030 −0.0734164
\(77\) 0 0
\(78\) 1.29048 0.146119
\(79\) 13.8908 1.56283 0.781417 0.624009i \(-0.214497\pi\)
0.781417 + 0.624009i \(0.214497\pi\)
\(80\) 1.73379 0.193844
\(81\) 1.00000 0.111111
\(82\) −1.11646 −0.123293
\(83\) 10.3080 1.13145 0.565725 0.824594i \(-0.308596\pi\)
0.565725 + 0.824594i \(0.308596\pi\)
\(84\) 0 0
\(85\) −4.54695 −0.493186
\(86\) −3.36490 −0.362846
\(87\) 7.97364 0.854864
\(88\) 14.4318 1.53844
\(89\) 15.1741 1.60846 0.804228 0.594321i \(-0.202579\pi\)
0.804228 + 0.594321i \(0.202579\pi\)
\(90\) −1.00546 −0.105985
\(91\) 0 0
\(92\) 1.23234 0.128480
\(93\) 2.94278 0.305152
\(94\) −9.09180 −0.937747
\(95\) −0.764949 −0.0784821
\(96\) 3.99898 0.408144
\(97\) −0.878601 −0.0892084 −0.0446042 0.999005i \(-0.514203\pi\)
−0.0446042 + 0.999005i \(0.514203\pi\)
\(98\) 0 0
\(99\) −4.69451 −0.471816
\(100\) 3.15643 0.315643
\(101\) 4.56591 0.454325 0.227162 0.973857i \(-0.427055\pi\)
0.227162 + 0.973857i \(0.427055\pi\)
\(102\) 5.63692 0.558138
\(103\) −0.218199 −0.0214998 −0.0107499 0.999942i \(-0.503422\pi\)
−0.0107499 + 0.999942i \(0.503422\pi\)
\(104\) −3.55336 −0.348436
\(105\) 0 0
\(106\) −8.94920 −0.869224
\(107\) 8.05109 0.778328 0.389164 0.921168i \(-0.372764\pi\)
0.389164 + 0.921168i \(0.372764\pi\)
\(108\) −0.753512 −0.0725068
\(109\) 15.5123 1.48581 0.742905 0.669397i \(-0.233448\pi\)
0.742905 + 0.669397i \(0.233448\pi\)
\(110\) 4.72016 0.450050
\(111\) 3.09905 0.294149
\(112\) 0 0
\(113\) 16.0560 1.51042 0.755211 0.655482i \(-0.227534\pi\)
0.755211 + 0.655482i \(0.227534\pi\)
\(114\) 0.948318 0.0888181
\(115\) 1.47286 0.137345
\(116\) −6.00823 −0.557850
\(117\) 1.15587 0.106860
\(118\) −2.90406 −0.267340
\(119\) 0 0
\(120\) 2.76856 0.252734
\(121\) 11.0384 1.00349
\(122\) −8.16672 −0.739380
\(123\) −1.00000 −0.0901670
\(124\) −2.21742 −0.199130
\(125\) 8.27540 0.740174
\(126\) 0 0
\(127\) 9.08915 0.806532 0.403266 0.915083i \(-0.367875\pi\)
0.403266 + 0.915083i \(0.367875\pi\)
\(128\) 1.28554 0.113626
\(129\) −3.01389 −0.265358
\(130\) −1.16219 −0.101930
\(131\) 20.4776 1.78914 0.894570 0.446928i \(-0.147482\pi\)
0.894570 + 0.446928i \(0.147482\pi\)
\(132\) 3.53737 0.307889
\(133\) 0 0
\(134\) 0.889234 0.0768181
\(135\) −0.900581 −0.0775096
\(136\) −15.5213 −1.33094
\(137\) 20.8453 1.78094 0.890468 0.455047i \(-0.150377\pi\)
0.890468 + 0.455047i \(0.150377\pi\)
\(138\) −1.82593 −0.155433
\(139\) −0.173141 −0.0146856 −0.00734280 0.999973i \(-0.502337\pi\)
−0.00734280 + 0.999973i \(0.502337\pi\)
\(140\) 0 0
\(141\) −8.14340 −0.685798
\(142\) 11.9757 1.00498
\(143\) −5.42624 −0.453765
\(144\) −1.92519 −0.160433
\(145\) −7.18090 −0.596342
\(146\) 1.96542 0.162660
\(147\) 0 0
\(148\) −2.33517 −0.191950
\(149\) 1.04440 0.0855607 0.0427803 0.999085i \(-0.486378\pi\)
0.0427803 + 0.999085i \(0.486378\pi\)
\(150\) −4.67681 −0.381860
\(151\) −11.9553 −0.972907 −0.486453 0.873707i \(-0.661710\pi\)
−0.486453 + 0.873707i \(0.661710\pi\)
\(152\) −2.61120 −0.211797
\(153\) 5.04891 0.408180
\(154\) 0 0
\(155\) −2.65021 −0.212870
\(156\) −0.870962 −0.0697328
\(157\) −4.18839 −0.334270 −0.167135 0.985934i \(-0.553452\pi\)
−0.167135 + 0.985934i \(0.553452\pi\)
\(158\) 15.5085 1.23379
\(159\) −8.01568 −0.635685
\(160\) −3.60140 −0.284716
\(161\) 0 0
\(162\) 1.11646 0.0877176
\(163\) 10.8840 0.852499 0.426250 0.904606i \(-0.359834\pi\)
0.426250 + 0.904606i \(0.359834\pi\)
\(164\) 0.753512 0.0588394
\(165\) 4.22779 0.329133
\(166\) 11.5085 0.893232
\(167\) 12.7952 0.990120 0.495060 0.868859i \(-0.335146\pi\)
0.495060 + 0.868859i \(0.335146\pi\)
\(168\) 0 0
\(169\) −11.6640 −0.897228
\(170\) −5.07650 −0.389350
\(171\) 0.849395 0.0649549
\(172\) 2.27100 0.173162
\(173\) 5.07018 0.385479 0.192739 0.981250i \(-0.438263\pi\)
0.192739 + 0.981250i \(0.438263\pi\)
\(174\) 8.90226 0.674879
\(175\) 0 0
\(176\) 9.03785 0.681253
\(177\) −2.60113 −0.195513
\(178\) 16.9414 1.26981
\(179\) 2.27988 0.170406 0.0852032 0.996364i \(-0.472846\pi\)
0.0852032 + 0.996364i \(0.472846\pi\)
\(180\) 0.678599 0.0505798
\(181\) −8.62106 −0.640798 −0.320399 0.947283i \(-0.603817\pi\)
−0.320399 + 0.947283i \(0.603817\pi\)
\(182\) 0 0
\(183\) −7.31482 −0.540727
\(184\) 5.02771 0.370648
\(185\) −2.79094 −0.205194
\(186\) 3.28551 0.240905
\(187\) −23.7022 −1.73328
\(188\) 6.13615 0.447525
\(189\) 0 0
\(190\) −0.854037 −0.0619583
\(191\) −21.2101 −1.53471 −0.767356 0.641222i \(-0.778428\pi\)
−0.767356 + 0.641222i \(0.778428\pi\)
\(192\) 8.31510 0.600090
\(193\) −11.2364 −0.808814 −0.404407 0.914579i \(-0.632522\pi\)
−0.404407 + 0.914579i \(0.632522\pi\)
\(194\) −0.980925 −0.0704263
\(195\) −1.04095 −0.0745442
\(196\) 0 0
\(197\) 20.4011 1.45352 0.726758 0.686894i \(-0.241026\pi\)
0.726758 + 0.686894i \(0.241026\pi\)
\(198\) −5.24124 −0.372479
\(199\) 1.26866 0.0899326 0.0449663 0.998989i \(-0.485682\pi\)
0.0449663 + 0.998989i \(0.485682\pi\)
\(200\) 12.8777 0.910587
\(201\) 0.796475 0.0561790
\(202\) 5.09767 0.358670
\(203\) 0 0
\(204\) −3.80442 −0.266363
\(205\) 0.900581 0.0628993
\(206\) −0.243611 −0.0169732
\(207\) −1.63546 −0.113672
\(208\) −2.22527 −0.154295
\(209\) −3.98750 −0.275821
\(210\) 0 0
\(211\) −2.25243 −0.155064 −0.0775320 0.996990i \(-0.524704\pi\)
−0.0775320 + 0.996990i \(0.524704\pi\)
\(212\) 6.03991 0.414823
\(213\) 10.7265 0.734969
\(214\) 8.98874 0.614458
\(215\) 2.71425 0.185110
\(216\) −3.07419 −0.209172
\(217\) 0 0
\(218\) 17.3189 1.17298
\(219\) 1.76040 0.118957
\(220\) −3.18569 −0.214779
\(221\) 5.83588 0.392564
\(222\) 3.45997 0.232218
\(223\) 4.43952 0.297292 0.148646 0.988890i \(-0.452509\pi\)
0.148646 + 0.988890i \(0.452509\pi\)
\(224\) 0 0
\(225\) −4.18895 −0.279264
\(226\) 17.9259 1.19241
\(227\) −20.3906 −1.35337 −0.676686 0.736271i \(-0.736585\pi\)
−0.676686 + 0.736271i \(0.736585\pi\)
\(228\) −0.640030 −0.0423870
\(229\) 20.3158 1.34251 0.671254 0.741227i \(-0.265756\pi\)
0.671254 + 0.741227i \(0.265756\pi\)
\(230\) 1.64439 0.108428
\(231\) 0 0
\(232\) −24.5125 −1.60932
\(233\) 19.5481 1.28064 0.640319 0.768109i \(-0.278802\pi\)
0.640319 + 0.768109i \(0.278802\pi\)
\(234\) 1.29048 0.0843616
\(235\) 7.33379 0.478404
\(236\) 1.95998 0.127584
\(237\) 13.8908 0.902303
\(238\) 0 0
\(239\) −2.84235 −0.183856 −0.0919280 0.995766i \(-0.529303\pi\)
−0.0919280 + 0.995766i \(0.529303\pi\)
\(240\) 1.73379 0.111916
\(241\) −27.2252 −1.75373 −0.876866 0.480735i \(-0.840370\pi\)
−0.876866 + 0.480735i \(0.840370\pi\)
\(242\) 12.3240 0.792217
\(243\) 1.00000 0.0641500
\(244\) 5.51181 0.352857
\(245\) 0 0
\(246\) −1.11646 −0.0711830
\(247\) 0.981790 0.0624698
\(248\) −9.04668 −0.574465
\(249\) 10.3080 0.653243
\(250\) 9.23917 0.584336
\(251\) 0.890691 0.0562199 0.0281100 0.999605i \(-0.491051\pi\)
0.0281100 + 0.999605i \(0.491051\pi\)
\(252\) 0 0
\(253\) 7.67767 0.482691
\(254\) 10.1477 0.636723
\(255\) −4.54695 −0.284741
\(256\) −15.1949 −0.949684
\(257\) −15.0505 −0.938822 −0.469411 0.882980i \(-0.655534\pi\)
−0.469411 + 0.882980i \(0.655534\pi\)
\(258\) −3.36490 −0.209489
\(259\) 0 0
\(260\) 0.784371 0.0486447
\(261\) 7.97364 0.493556
\(262\) 22.8625 1.41245
\(263\) −6.76685 −0.417262 −0.208631 0.977994i \(-0.566901\pi\)
−0.208631 + 0.977994i \(0.566901\pi\)
\(264\) 14.4318 0.888218
\(265\) 7.21877 0.443445
\(266\) 0 0
\(267\) 15.1741 0.928643
\(268\) −0.600153 −0.0366602
\(269\) −20.7195 −1.26329 −0.631646 0.775257i \(-0.717620\pi\)
−0.631646 + 0.775257i \(0.717620\pi\)
\(270\) −1.00546 −0.0611906
\(271\) −2.59986 −0.157930 −0.0789651 0.996877i \(-0.525162\pi\)
−0.0789651 + 0.996877i \(0.525162\pi\)
\(272\) −9.72014 −0.589370
\(273\) 0 0
\(274\) 23.2730 1.40597
\(275\) 19.6651 1.18585
\(276\) 1.23234 0.0741780
\(277\) 17.8530 1.07268 0.536342 0.844000i \(-0.319806\pi\)
0.536342 + 0.844000i \(0.319806\pi\)
\(278\) −0.193305 −0.0115937
\(279\) 2.94278 0.176180
\(280\) 0 0
\(281\) 0.0898344 0.00535907 0.00267954 0.999996i \(-0.499147\pi\)
0.00267954 + 0.999996i \(0.499147\pi\)
\(282\) −9.09180 −0.541409
\(283\) −14.7404 −0.876226 −0.438113 0.898920i \(-0.644353\pi\)
−0.438113 + 0.898920i \(0.644353\pi\)
\(284\) −8.08256 −0.479612
\(285\) −0.764949 −0.0453117
\(286\) −6.05819 −0.358229
\(287\) 0 0
\(288\) 3.99898 0.235642
\(289\) 8.49152 0.499501
\(290\) −8.01721 −0.470787
\(291\) −0.878601 −0.0515045
\(292\) −1.32649 −0.0776267
\(293\) 6.71475 0.392280 0.196140 0.980576i \(-0.437159\pi\)
0.196140 + 0.980576i \(0.437159\pi\)
\(294\) 0 0
\(295\) 2.34252 0.136387
\(296\) −9.52707 −0.553750
\(297\) −4.69451 −0.272403
\(298\) 1.16603 0.0675465
\(299\) −1.89038 −0.109323
\(300\) 3.15643 0.182236
\(301\) 0 0
\(302\) −13.3476 −0.768069
\(303\) 4.56591 0.262305
\(304\) −1.63525 −0.0937881
\(305\) 6.58758 0.377204
\(306\) 5.63692 0.322241
\(307\) 2.35297 0.134291 0.0671455 0.997743i \(-0.478611\pi\)
0.0671455 + 0.997743i \(0.478611\pi\)
\(308\) 0 0
\(309\) −0.218199 −0.0124129
\(310\) −2.95886 −0.168052
\(311\) −24.4048 −1.38387 −0.691934 0.721961i \(-0.743241\pi\)
−0.691934 + 0.721961i \(0.743241\pi\)
\(312\) −3.55336 −0.201170
\(313\) −8.88540 −0.502232 −0.251116 0.967957i \(-0.580798\pi\)
−0.251116 + 0.967957i \(0.580798\pi\)
\(314\) −4.67618 −0.263892
\(315\) 0 0
\(316\) −10.4669 −0.588808
\(317\) −0.0289702 −0.00162713 −0.000813564 1.00000i \(-0.500259\pi\)
−0.000813564 1.00000i \(0.500259\pi\)
\(318\) −8.94920 −0.501846
\(319\) −37.4323 −2.09581
\(320\) −7.48842 −0.418615
\(321\) 8.05109 0.449368
\(322\) 0 0
\(323\) 4.28852 0.238620
\(324\) −0.753512 −0.0418618
\(325\) −4.84188 −0.268579
\(326\) 12.1516 0.673012
\(327\) 15.5123 0.857832
\(328\) 3.07419 0.169744
\(329\) 0 0
\(330\) 4.72016 0.259836
\(331\) 7.32795 0.402780 0.201390 0.979511i \(-0.435454\pi\)
0.201390 + 0.979511i \(0.435454\pi\)
\(332\) −7.76720 −0.426281
\(333\) 3.09905 0.169827
\(334\) 14.2853 0.781658
\(335\) −0.717290 −0.0391897
\(336\) 0 0
\(337\) 35.0551 1.90957 0.954785 0.297296i \(-0.0960847\pi\)
0.954785 + 0.297296i \(0.0960847\pi\)
\(338\) −13.0224 −0.708324
\(339\) 16.0560 0.872042
\(340\) 3.42619 0.185811
\(341\) −13.8149 −0.748120
\(342\) 0.948318 0.0512791
\(343\) 0 0
\(344\) 9.26528 0.499550
\(345\) 1.47286 0.0792962
\(346\) 5.66067 0.304319
\(347\) −22.7234 −1.21986 −0.609929 0.792456i \(-0.708802\pi\)
−0.609929 + 0.792456i \(0.708802\pi\)
\(348\) −6.00823 −0.322075
\(349\) 7.64444 0.409197 0.204599 0.978846i \(-0.434411\pi\)
0.204599 + 0.978846i \(0.434411\pi\)
\(350\) 0 0
\(351\) 1.15587 0.0616957
\(352\) −18.7732 −1.00062
\(353\) −0.643130 −0.0342303 −0.0171152 0.999854i \(-0.505448\pi\)
−0.0171152 + 0.999854i \(0.505448\pi\)
\(354\) −2.90406 −0.154349
\(355\) −9.66009 −0.512704
\(356\) −11.4339 −0.605996
\(357\) 0 0
\(358\) 2.54540 0.134529
\(359\) −28.7366 −1.51666 −0.758330 0.651871i \(-0.773984\pi\)
−0.758330 + 0.651871i \(0.773984\pi\)
\(360\) 2.76856 0.145916
\(361\) −18.2785 −0.962028
\(362\) −9.62509 −0.505883
\(363\) 11.0384 0.579368
\(364\) 0 0
\(365\) −1.58539 −0.0829829
\(366\) −8.16672 −0.426881
\(367\) 5.33033 0.278241 0.139120 0.990275i \(-0.455573\pi\)
0.139120 + 0.990275i \(0.455573\pi\)
\(368\) 3.14857 0.164131
\(369\) −1.00000 −0.0520579
\(370\) −3.11598 −0.161992
\(371\) 0 0
\(372\) −2.21742 −0.114968
\(373\) 9.39088 0.486241 0.243121 0.969996i \(-0.421829\pi\)
0.243121 + 0.969996i \(0.421829\pi\)
\(374\) −26.4626 −1.36835
\(375\) 8.27540 0.427340
\(376\) 25.0344 1.29105
\(377\) 9.21648 0.474673
\(378\) 0 0
\(379\) −5.32747 −0.273654 −0.136827 0.990595i \(-0.543690\pi\)
−0.136827 + 0.990595i \(0.543690\pi\)
\(380\) 0.576398 0.0295686
\(381\) 9.08915 0.465651
\(382\) −23.6803 −1.21159
\(383\) −10.5597 −0.539575 −0.269788 0.962920i \(-0.586953\pi\)
−0.269788 + 0.962920i \(0.586953\pi\)
\(384\) 1.28554 0.0656022
\(385\) 0 0
\(386\) −12.5450 −0.638525
\(387\) −3.01389 −0.153205
\(388\) 0.662037 0.0336098
\(389\) 30.7591 1.55955 0.779775 0.626060i \(-0.215333\pi\)
0.779775 + 0.626060i \(0.215333\pi\)
\(390\) −1.16219 −0.0588495
\(391\) −8.25728 −0.417589
\(392\) 0 0
\(393\) 20.4776 1.03296
\(394\) 22.7770 1.14749
\(395\) −12.5098 −0.629435
\(396\) 3.53737 0.177760
\(397\) −23.3508 −1.17194 −0.585972 0.810331i \(-0.699287\pi\)
−0.585972 + 0.810331i \(0.699287\pi\)
\(398\) 1.41641 0.0709980
\(399\) 0 0
\(400\) 8.06455 0.403228
\(401\) 12.0188 0.600190 0.300095 0.953909i \(-0.402982\pi\)
0.300095 + 0.953909i \(0.402982\pi\)
\(402\) 0.889234 0.0443509
\(403\) 3.40147 0.169439
\(404\) −3.44047 −0.171170
\(405\) −0.900581 −0.0447502
\(406\) 0 0
\(407\) −14.5485 −0.721143
\(408\) −15.5213 −0.768420
\(409\) −2.07020 −0.102365 −0.0511825 0.998689i \(-0.516299\pi\)
−0.0511825 + 0.998689i \(0.516299\pi\)
\(410\) 1.00546 0.0496563
\(411\) 20.8453 1.02822
\(412\) 0.164416 0.00810018
\(413\) 0 0
\(414\) −1.82593 −0.0897394
\(415\) −9.28318 −0.455693
\(416\) 4.62230 0.226627
\(417\) −0.173141 −0.00847873
\(418\) −4.45189 −0.217749
\(419\) −37.9166 −1.85235 −0.926173 0.377099i \(-0.876922\pi\)
−0.926173 + 0.377099i \(0.876922\pi\)
\(420\) 0 0
\(421\) −9.80911 −0.478067 −0.239033 0.971011i \(-0.576831\pi\)
−0.239033 + 0.971011i \(0.576831\pi\)
\(422\) −2.51476 −0.122416
\(423\) −8.14340 −0.395946
\(424\) 24.6417 1.19671
\(425\) −21.1497 −1.02591
\(426\) 11.9757 0.580227
\(427\) 0 0
\(428\) −6.06660 −0.293240
\(429\) −5.42624 −0.261981
\(430\) 3.03036 0.146137
\(431\) −32.4424 −1.56270 −0.781348 0.624096i \(-0.785467\pi\)
−0.781348 + 0.624096i \(0.785467\pi\)
\(432\) −1.92519 −0.0926260
\(433\) −34.9870 −1.68137 −0.840683 0.541527i \(-0.817846\pi\)
−0.840683 + 0.541527i \(0.817846\pi\)
\(434\) 0 0
\(435\) −7.18090 −0.344298
\(436\) −11.6887 −0.559788
\(437\) −1.38915 −0.0664521
\(438\) 1.96542 0.0939116
\(439\) 20.0625 0.957530 0.478765 0.877943i \(-0.341085\pi\)
0.478765 + 0.877943i \(0.341085\pi\)
\(440\) −12.9970 −0.619609
\(441\) 0 0
\(442\) 6.51554 0.309913
\(443\) −12.7373 −0.605165 −0.302583 0.953123i \(-0.597849\pi\)
−0.302583 + 0.953123i \(0.597849\pi\)
\(444\) −2.33517 −0.110822
\(445\) −13.6655 −0.647809
\(446\) 4.95655 0.234699
\(447\) 1.04440 0.0493985
\(448\) 0 0
\(449\) 20.5999 0.972170 0.486085 0.873912i \(-0.338425\pi\)
0.486085 + 0.873912i \(0.338425\pi\)
\(450\) −4.67681 −0.220467
\(451\) 4.69451 0.221056
\(452\) −12.0984 −0.569061
\(453\) −11.9553 −0.561708
\(454\) −22.7653 −1.06843
\(455\) 0 0
\(456\) −2.61120 −0.122281
\(457\) 7.53127 0.352298 0.176149 0.984364i \(-0.443636\pi\)
0.176149 + 0.984364i \(0.443636\pi\)
\(458\) 22.6819 1.05985
\(459\) 5.04891 0.235663
\(460\) −1.10982 −0.0517456
\(461\) 14.5150 0.676032 0.338016 0.941140i \(-0.390244\pi\)
0.338016 + 0.941140i \(0.390244\pi\)
\(462\) 0 0
\(463\) −1.59229 −0.0739998 −0.0369999 0.999315i \(-0.511780\pi\)
−0.0369999 + 0.999315i \(0.511780\pi\)
\(464\) −15.3508 −0.712643
\(465\) −2.65021 −0.122901
\(466\) 21.8247 1.01101
\(467\) 33.8659 1.56713 0.783565 0.621310i \(-0.213399\pi\)
0.783565 + 0.621310i \(0.213399\pi\)
\(468\) −0.870962 −0.0402602
\(469\) 0 0
\(470\) 8.18790 0.377679
\(471\) −4.18839 −0.192991
\(472\) 7.99636 0.368062
\(473\) 14.1487 0.650560
\(474\) 15.5085 0.712330
\(475\) −3.55808 −0.163256
\(476\) 0 0
\(477\) −8.01568 −0.367013
\(478\) −3.17337 −0.145147
\(479\) −9.40167 −0.429573 −0.214787 0.976661i \(-0.568906\pi\)
−0.214787 + 0.976661i \(0.568906\pi\)
\(480\) −3.60140 −0.164381
\(481\) 3.58209 0.163329
\(482\) −30.3960 −1.38450
\(483\) 0 0
\(484\) −8.31760 −0.378073
\(485\) 0.791251 0.0359289
\(486\) 1.11646 0.0506438
\(487\) 24.6937 1.11898 0.559488 0.828838i \(-0.310998\pi\)
0.559488 + 0.828838i \(0.310998\pi\)
\(488\) 22.4872 1.01795
\(489\) 10.8840 0.492191
\(490\) 0 0
\(491\) 34.9667 1.57802 0.789012 0.614378i \(-0.210593\pi\)
0.789012 + 0.614378i \(0.210593\pi\)
\(492\) 0.753512 0.0339710
\(493\) 40.2582 1.81314
\(494\) 1.09613 0.0493173
\(495\) 4.22779 0.190025
\(496\) −5.66543 −0.254385
\(497\) 0 0
\(498\) 11.5085 0.515708
\(499\) 18.5443 0.830155 0.415077 0.909786i \(-0.363755\pi\)
0.415077 + 0.909786i \(0.363755\pi\)
\(500\) −6.23561 −0.278865
\(501\) 12.7952 0.571646
\(502\) 0.994423 0.0443833
\(503\) 33.0348 1.47295 0.736473 0.676466i \(-0.236490\pi\)
0.736473 + 0.676466i \(0.236490\pi\)
\(504\) 0 0
\(505\) −4.11197 −0.182980
\(506\) 8.57183 0.381064
\(507\) −11.6640 −0.518015
\(508\) −6.84879 −0.303866
\(509\) 21.5526 0.955302 0.477651 0.878550i \(-0.341488\pi\)
0.477651 + 0.878550i \(0.341488\pi\)
\(510\) −5.07650 −0.224791
\(511\) 0 0
\(512\) −19.5356 −0.863362
\(513\) 0.849395 0.0375017
\(514\) −16.8033 −0.741161
\(515\) 0.196506 0.00865908
\(516\) 2.27100 0.0999754
\(517\) 38.2293 1.68132
\(518\) 0 0
\(519\) 5.07018 0.222556
\(520\) 3.20009 0.140333
\(521\) 36.0597 1.57981 0.789903 0.613232i \(-0.210131\pi\)
0.789903 + 0.613232i \(0.210131\pi\)
\(522\) 8.90226 0.389642
\(523\) 2.02031 0.0883421 0.0441710 0.999024i \(-0.485935\pi\)
0.0441710 + 0.999024i \(0.485935\pi\)
\(524\) −15.4302 −0.674069
\(525\) 0 0
\(526\) −7.55494 −0.329411
\(527\) 14.8579 0.647218
\(528\) 9.03785 0.393322
\(529\) −20.3253 −0.883708
\(530\) 8.05948 0.350081
\(531\) −2.60113 −0.112879
\(532\) 0 0
\(533\) −1.15587 −0.0500663
\(534\) 16.9414 0.733124
\(535\) −7.25066 −0.313473
\(536\) −2.44852 −0.105760
\(537\) 2.27988 0.0983842
\(538\) −23.1326 −0.997316
\(539\) 0 0
\(540\) 0.678599 0.0292022
\(541\) 28.2526 1.21467 0.607337 0.794444i \(-0.292238\pi\)
0.607337 + 0.794444i \(0.292238\pi\)
\(542\) −2.90264 −0.124679
\(543\) −8.62106 −0.369965
\(544\) 20.1905 0.865660
\(545\) −13.9701 −0.598413
\(546\) 0 0
\(547\) −36.6219 −1.56584 −0.782919 0.622123i \(-0.786270\pi\)
−0.782919 + 0.622123i \(0.786270\pi\)
\(548\) −15.7072 −0.670978
\(549\) −7.31482 −0.312189
\(550\) 21.9553 0.936179
\(551\) 6.77277 0.288530
\(552\) 5.02771 0.213994
\(553\) 0 0
\(554\) 19.9322 0.846840
\(555\) −2.79094 −0.118469
\(556\) 0.130464 0.00553289
\(557\) −38.9992 −1.65245 −0.826224 0.563342i \(-0.809515\pi\)
−0.826224 + 0.563342i \(0.809515\pi\)
\(558\) 3.28551 0.139087
\(559\) −3.48366 −0.147343
\(560\) 0 0
\(561\) −23.7022 −1.00071
\(562\) 0.100297 0.00423076
\(563\) 27.9805 1.17924 0.589619 0.807682i \(-0.299278\pi\)
0.589619 + 0.807682i \(0.299278\pi\)
\(564\) 6.13615 0.258379
\(565\) −14.4597 −0.608325
\(566\) −16.4571 −0.691744
\(567\) 0 0
\(568\) −32.9754 −1.38362
\(569\) 9.11873 0.382277 0.191139 0.981563i \(-0.438782\pi\)
0.191139 + 0.981563i \(0.438782\pi\)
\(570\) −0.854037 −0.0357717
\(571\) 21.4215 0.896460 0.448230 0.893918i \(-0.352055\pi\)
0.448230 + 0.893918i \(0.352055\pi\)
\(572\) 4.08874 0.170959
\(573\) −21.2101 −0.886066
\(574\) 0 0
\(575\) 6.85086 0.285700
\(576\) 8.31510 0.346462
\(577\) −31.0255 −1.29161 −0.645805 0.763502i \(-0.723478\pi\)
−0.645805 + 0.763502i \(0.723478\pi\)
\(578\) 9.48047 0.394335
\(579\) −11.2364 −0.466969
\(580\) 5.41090 0.224675
\(581\) 0 0
\(582\) −0.980925 −0.0406606
\(583\) 37.6297 1.55846
\(584\) −5.41182 −0.223943
\(585\) −1.04095 −0.0430381
\(586\) 7.49677 0.309689
\(587\) −2.11563 −0.0873215 −0.0436608 0.999046i \(-0.513902\pi\)
−0.0436608 + 0.999046i \(0.513902\pi\)
\(588\) 0 0
\(589\) 2.49959 0.102994
\(590\) 2.61534 0.107672
\(591\) 20.4011 0.839187
\(592\) −5.96627 −0.245212
\(593\) 3.84915 0.158066 0.0790328 0.996872i \(-0.474817\pi\)
0.0790328 + 0.996872i \(0.474817\pi\)
\(594\) −5.24124 −0.215051
\(595\) 0 0
\(596\) −0.786969 −0.0322355
\(597\) 1.26866 0.0519226
\(598\) −2.11053 −0.0863061
\(599\) 13.0766 0.534297 0.267148 0.963655i \(-0.413919\pi\)
0.267148 + 0.963655i \(0.413919\pi\)
\(600\) 12.8777 0.525728
\(601\) 37.2633 1.52000 0.760001 0.649922i \(-0.225199\pi\)
0.760001 + 0.649922i \(0.225199\pi\)
\(602\) 0 0
\(603\) 0.796475 0.0324350
\(604\) 9.00845 0.366549
\(605\) −9.94100 −0.404159
\(606\) 5.09767 0.207078
\(607\) 6.25992 0.254082 0.127041 0.991897i \(-0.459452\pi\)
0.127041 + 0.991897i \(0.459452\pi\)
\(608\) 3.39671 0.137755
\(609\) 0 0
\(610\) 7.35479 0.297787
\(611\) −9.41270 −0.380797
\(612\) −3.80442 −0.153784
\(613\) 9.94899 0.401836 0.200918 0.979608i \(-0.435608\pi\)
0.200918 + 0.979608i \(0.435608\pi\)
\(614\) 2.62700 0.106017
\(615\) 0.900581 0.0363149
\(616\) 0 0
\(617\) 13.0271 0.524452 0.262226 0.965007i \(-0.415543\pi\)
0.262226 + 0.965007i \(0.415543\pi\)
\(618\) −0.243611 −0.00979947
\(619\) −23.8933 −0.960354 −0.480177 0.877172i \(-0.659428\pi\)
−0.480177 + 0.877172i \(0.659428\pi\)
\(620\) 1.99697 0.0802002
\(621\) −1.63546 −0.0656286
\(622\) −27.2470 −1.09251
\(623\) 0 0
\(624\) −2.22527 −0.0890822
\(625\) 13.4921 0.539684
\(626\) −9.92021 −0.396491
\(627\) −3.98750 −0.159245
\(628\) 3.15601 0.125938
\(629\) 15.6468 0.623880
\(630\) 0 0
\(631\) −27.1911 −1.08246 −0.541230 0.840875i \(-0.682041\pi\)
−0.541230 + 0.840875i \(0.682041\pi\)
\(632\) −42.7029 −1.69863
\(633\) −2.25243 −0.0895262
\(634\) −0.0323441 −0.00128455
\(635\) −8.18552 −0.324832
\(636\) 6.03991 0.239498
\(637\) 0 0
\(638\) −41.7918 −1.65455
\(639\) 10.7265 0.424334
\(640\) −1.15773 −0.0457632
\(641\) −9.85980 −0.389439 −0.194719 0.980859i \(-0.562380\pi\)
−0.194719 + 0.980859i \(0.562380\pi\)
\(642\) 8.98874 0.354757
\(643\) −15.5002 −0.611270 −0.305635 0.952149i \(-0.598869\pi\)
−0.305635 + 0.952149i \(0.598869\pi\)
\(644\) 0 0
\(645\) 2.71425 0.106874
\(646\) 4.78797 0.188380
\(647\) −39.1567 −1.53941 −0.769705 0.638400i \(-0.779596\pi\)
−0.769705 + 0.638400i \(0.779596\pi\)
\(648\) −3.07419 −0.120766
\(649\) 12.2110 0.479324
\(650\) −5.40578 −0.212032
\(651\) 0 0
\(652\) −8.20122 −0.321184
\(653\) −29.5384 −1.15593 −0.577964 0.816062i \(-0.696153\pi\)
−0.577964 + 0.816062i \(0.696153\pi\)
\(654\) 17.3189 0.677223
\(655\) −18.4418 −0.720580
\(656\) 1.92519 0.0751662
\(657\) 1.76040 0.0686799
\(658\) 0 0
\(659\) −9.39226 −0.365871 −0.182935 0.983125i \(-0.558560\pi\)
−0.182935 + 0.983125i \(0.558560\pi\)
\(660\) −3.18569 −0.124003
\(661\) −42.1189 −1.63824 −0.819118 0.573625i \(-0.805537\pi\)
−0.819118 + 0.573625i \(0.805537\pi\)
\(662\) 8.18137 0.317978
\(663\) 5.83588 0.226647
\(664\) −31.6888 −1.22976
\(665\) 0 0
\(666\) 3.45997 0.134071
\(667\) −13.0405 −0.504932
\(668\) −9.64132 −0.373034
\(669\) 4.43952 0.171642
\(670\) −0.800827 −0.0309386
\(671\) 34.3395 1.32566
\(672\) 0 0
\(673\) −2.92211 −0.112639 −0.0563195 0.998413i \(-0.517937\pi\)
−0.0563195 + 0.998413i \(0.517937\pi\)
\(674\) 39.1377 1.50753
\(675\) −4.18895 −0.161233
\(676\) 8.78894 0.338036
\(677\) 36.7706 1.41321 0.706604 0.707609i \(-0.250226\pi\)
0.706604 + 0.707609i \(0.250226\pi\)
\(678\) 17.9259 0.688441
\(679\) 0 0
\(680\) 13.9782 0.536040
\(681\) −20.3906 −0.781370
\(682\) −15.4238 −0.590609
\(683\) −8.03451 −0.307432 −0.153716 0.988115i \(-0.549124\pi\)
−0.153716 + 0.988115i \(0.549124\pi\)
\(684\) −0.640030 −0.0244721
\(685\) −18.7729 −0.717275
\(686\) 0 0
\(687\) 20.3158 0.775098
\(688\) 5.80233 0.221212
\(689\) −9.26508 −0.352971
\(690\) 1.64439 0.0626010
\(691\) 6.60782 0.251373 0.125687 0.992070i \(-0.459887\pi\)
0.125687 + 0.992070i \(0.459887\pi\)
\(692\) −3.82045 −0.145232
\(693\) 0 0
\(694\) −25.3699 −0.963027
\(695\) 0.155927 0.00591465
\(696\) −24.5125 −0.929144
\(697\) −5.04891 −0.191241
\(698\) 8.53473 0.323044
\(699\) 19.5481 0.739377
\(700\) 0 0
\(701\) 11.0961 0.419094 0.209547 0.977799i \(-0.432801\pi\)
0.209547 + 0.977799i \(0.432801\pi\)
\(702\) 1.29048 0.0487062
\(703\) 2.63232 0.0992797
\(704\) −39.0353 −1.47120
\(705\) 7.33379 0.276206
\(706\) −0.718030 −0.0270234
\(707\) 0 0
\(708\) 1.95998 0.0736606
\(709\) 8.02154 0.301255 0.150628 0.988591i \(-0.451871\pi\)
0.150628 + 0.988591i \(0.451871\pi\)
\(710\) −10.7851 −0.404759
\(711\) 13.8908 0.520945
\(712\) −46.6482 −1.74822
\(713\) −4.81280 −0.180241
\(714\) 0 0
\(715\) 4.88677 0.182755
\(716\) −1.71792 −0.0642017
\(717\) −2.84235 −0.106149
\(718\) −32.0833 −1.19734
\(719\) −26.9116 −1.00363 −0.501816 0.864974i \(-0.667335\pi\)
−0.501816 + 0.864974i \(0.667335\pi\)
\(720\) 1.73379 0.0646147
\(721\) 0 0
\(722\) −20.4073 −0.759480
\(723\) −27.2252 −1.01252
\(724\) 6.49608 0.241425
\(725\) −33.4012 −1.24049
\(726\) 12.3240 0.457386
\(727\) 3.40083 0.126130 0.0630648 0.998009i \(-0.479913\pi\)
0.0630648 + 0.998009i \(0.479913\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.77002 −0.0655115
\(731\) −15.2169 −0.562816
\(732\) 5.51181 0.203722
\(733\) −31.6864 −1.17036 −0.585181 0.810903i \(-0.698977\pi\)
−0.585181 + 0.810903i \(0.698977\pi\)
\(734\) 5.95111 0.219659
\(735\) 0 0
\(736\) −6.54016 −0.241073
\(737\) −3.73906 −0.137730
\(738\) −1.11646 −0.0410975
\(739\) 2.74615 0.101019 0.0505095 0.998724i \(-0.483915\pi\)
0.0505095 + 0.998724i \(0.483915\pi\)
\(740\) 2.10301 0.0773082
\(741\) 0.981790 0.0360670
\(742\) 0 0
\(743\) 7.91699 0.290446 0.145223 0.989399i \(-0.453610\pi\)
0.145223 + 0.989399i \(0.453610\pi\)
\(744\) −9.04668 −0.331667
\(745\) −0.940567 −0.0344597
\(746\) 10.4846 0.383867
\(747\) 10.3080 0.377150
\(748\) 17.8599 0.653022
\(749\) 0 0
\(750\) 9.23917 0.337367
\(751\) −26.8980 −0.981524 −0.490762 0.871294i \(-0.663281\pi\)
−0.490762 + 0.871294i \(0.663281\pi\)
\(752\) 15.6776 0.571704
\(753\) 0.890691 0.0324586
\(754\) 10.2899 0.374734
\(755\) 10.7667 0.391840
\(756\) 0 0
\(757\) −36.1992 −1.31568 −0.657842 0.753156i \(-0.728530\pi\)
−0.657842 + 0.753156i \(0.728530\pi\)
\(758\) −5.94792 −0.216038
\(759\) 7.67767 0.278682
\(760\) 2.35160 0.0853015
\(761\) 9.07694 0.329039 0.164519 0.986374i \(-0.447393\pi\)
0.164519 + 0.986374i \(0.447393\pi\)
\(762\) 10.1477 0.367612
\(763\) 0 0
\(764\) 15.9821 0.578212
\(765\) −4.54695 −0.164395
\(766\) −11.7895 −0.425972
\(767\) −3.00656 −0.108561
\(768\) −15.1949 −0.548300
\(769\) −19.5528 −0.705093 −0.352547 0.935794i \(-0.614684\pi\)
−0.352547 + 0.935794i \(0.614684\pi\)
\(770\) 0 0
\(771\) −15.0505 −0.542029
\(772\) 8.46677 0.304726
\(773\) 53.8122 1.93549 0.967746 0.251928i \(-0.0810646\pi\)
0.967746 + 0.251928i \(0.0810646\pi\)
\(774\) −3.36490 −0.120949
\(775\) −12.3272 −0.442805
\(776\) 2.70099 0.0969598
\(777\) 0 0
\(778\) 34.3414 1.23120
\(779\) −0.849395 −0.0304327
\(780\) 0.784371 0.0280850
\(781\) −50.3557 −1.80187
\(782\) −9.21894 −0.329669
\(783\) 7.97364 0.284955
\(784\) 0 0
\(785\) 3.77199 0.134628
\(786\) 22.8625 0.815479
\(787\) 38.1745 1.36077 0.680387 0.732853i \(-0.261812\pi\)
0.680387 + 0.732853i \(0.261812\pi\)
\(788\) −15.3724 −0.547621
\(789\) −6.76685 −0.240906
\(790\) −13.9667 −0.496912
\(791\) 0 0
\(792\) 14.4318 0.512813
\(793\) −8.45498 −0.300245
\(794\) −26.0703 −0.925200
\(795\) 7.21877 0.256023
\(796\) −0.955947 −0.0338827
\(797\) −0.638938 −0.0226323 −0.0113162 0.999936i \(-0.503602\pi\)
−0.0113162 + 0.999936i \(0.503602\pi\)
\(798\) 0 0
\(799\) −41.1153 −1.45455
\(800\) −16.7515 −0.592256
\(801\) 15.1741 0.536152
\(802\) 13.4185 0.473825
\(803\) −8.26424 −0.291639
\(804\) −0.600153 −0.0211658
\(805\) 0 0
\(806\) 3.79762 0.133765
\(807\) −20.7195 −0.729362
\(808\) −14.0365 −0.493802
\(809\) 1.14199 0.0401501 0.0200750 0.999798i \(-0.493609\pi\)
0.0200750 + 0.999798i \(0.493609\pi\)
\(810\) −1.00546 −0.0353284
\(811\) 1.96493 0.0689979 0.0344990 0.999405i \(-0.489016\pi\)
0.0344990 + 0.999405i \(0.489016\pi\)
\(812\) 0 0
\(813\) −2.59986 −0.0911811
\(814\) −16.2429 −0.569312
\(815\) −9.80191 −0.343346
\(816\) −9.72014 −0.340273
\(817\) −2.55998 −0.0895625
\(818\) −2.31131 −0.0808129
\(819\) 0 0
\(820\) −0.678599 −0.0236977
\(821\) 7.23373 0.252459 0.126230 0.992001i \(-0.459712\pi\)
0.126230 + 0.992001i \(0.459712\pi\)
\(822\) 23.2730 0.811739
\(823\) −16.6287 −0.579640 −0.289820 0.957081i \(-0.593595\pi\)
−0.289820 + 0.957081i \(0.593595\pi\)
\(824\) 0.670786 0.0233679
\(825\) 19.6651 0.684651
\(826\) 0 0
\(827\) 27.9766 0.972842 0.486421 0.873725i \(-0.338302\pi\)
0.486421 + 0.873725i \(0.338302\pi\)
\(828\) 1.23234 0.0428267
\(829\) 22.7571 0.790388 0.395194 0.918598i \(-0.370677\pi\)
0.395194 + 0.918598i \(0.370677\pi\)
\(830\) −10.3643 −0.359751
\(831\) 17.8530 0.619315
\(832\) 9.61117 0.333207
\(833\) 0 0
\(834\) −0.193305 −0.00669360
\(835\) −11.5231 −0.398773
\(836\) 3.00463 0.103917
\(837\) 2.94278 0.101717
\(838\) −42.3324 −1.46235
\(839\) 14.9814 0.517214 0.258607 0.965983i \(-0.416737\pi\)
0.258607 + 0.965983i \(0.416737\pi\)
\(840\) 0 0
\(841\) 34.5789 1.19238
\(842\) −10.9515 −0.377414
\(843\) 0.0898344 0.00309406
\(844\) 1.69724 0.0584213
\(845\) 10.5043 0.361360
\(846\) −9.09180 −0.312582
\(847\) 0 0
\(848\) 15.4317 0.529928
\(849\) −14.7404 −0.505890
\(850\) −23.6128 −0.809912
\(851\) −5.06836 −0.173741
\(852\) −8.08256 −0.276904
\(853\) −38.1171 −1.30510 −0.652552 0.757744i \(-0.726301\pi\)
−0.652552 + 0.757744i \(0.726301\pi\)
\(854\) 0 0
\(855\) −0.764949 −0.0261607
\(856\) −24.7506 −0.845958
\(857\) −29.6584 −1.01311 −0.506556 0.862207i \(-0.669082\pi\)
−0.506556 + 0.862207i \(0.669082\pi\)
\(858\) −6.05819 −0.206823
\(859\) 14.7355 0.502770 0.251385 0.967887i \(-0.419114\pi\)
0.251385 + 0.967887i \(0.419114\pi\)
\(860\) −2.04522 −0.0697415
\(861\) 0 0
\(862\) −36.2207 −1.23368
\(863\) 13.1014 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(864\) 3.99898 0.136048
\(865\) −4.56611 −0.155252
\(866\) −39.0616 −1.32737
\(867\) 8.49152 0.288387
\(868\) 0 0
\(869\) −65.2104 −2.21211
\(870\) −8.01721 −0.271809
\(871\) 0.920621 0.0311940
\(872\) −47.6878 −1.61491
\(873\) −0.878601 −0.0297361
\(874\) −1.55093 −0.0524611
\(875\) 0 0
\(876\) −1.32649 −0.0448178
\(877\) 3.85074 0.130030 0.0650152 0.997884i \(-0.479290\pi\)
0.0650152 + 0.997884i \(0.479290\pi\)
\(878\) 22.3990 0.755930
\(879\) 6.71475 0.226483
\(880\) −8.13931 −0.274376
\(881\) 31.4622 1.05999 0.529995 0.848001i \(-0.322194\pi\)
0.529995 + 0.848001i \(0.322194\pi\)
\(882\) 0 0
\(883\) −20.4706 −0.688889 −0.344445 0.938807i \(-0.611933\pi\)
−0.344445 + 0.938807i \(0.611933\pi\)
\(884\) −4.39741 −0.147901
\(885\) 2.34252 0.0787431
\(886\) −14.2207 −0.477753
\(887\) −21.2614 −0.713887 −0.356944 0.934126i \(-0.616181\pi\)
−0.356944 + 0.934126i \(0.616181\pi\)
\(888\) −9.52707 −0.319707
\(889\) 0 0
\(890\) −15.2571 −0.511418
\(891\) −4.69451 −0.157272
\(892\) −3.34523 −0.112007
\(893\) −6.91696 −0.231467
\(894\) 1.16603 0.0389980
\(895\) −2.05322 −0.0686315
\(896\) 0 0
\(897\) −1.89038 −0.0631178
\(898\) 22.9990 0.767487
\(899\) 23.4647 0.782591
\(900\) 3.15643 0.105214
\(901\) −40.4705 −1.34827
\(902\) 5.24124 0.174514
\(903\) 0 0
\(904\) −49.3592 −1.64166
\(905\) 7.76396 0.258083
\(906\) −13.3476 −0.443445
\(907\) 24.4166 0.810739 0.405370 0.914153i \(-0.367143\pi\)
0.405370 + 0.914153i \(0.367143\pi\)
\(908\) 15.3646 0.509891
\(909\) 4.56591 0.151442
\(910\) 0 0
\(911\) 31.2660 1.03589 0.517944 0.855415i \(-0.326698\pi\)
0.517944 + 0.855415i \(0.326698\pi\)
\(912\) −1.63525 −0.0541486
\(913\) −48.3910 −1.60151
\(914\) 8.40838 0.278125
\(915\) 6.58758 0.217779
\(916\) −15.3082 −0.505798
\(917\) 0 0
\(918\) 5.63692 0.186046
\(919\) 53.3081 1.75847 0.879237 0.476385i \(-0.158053\pi\)
0.879237 + 0.476385i \(0.158053\pi\)
\(920\) −4.52786 −0.149279
\(921\) 2.35297 0.0775330
\(922\) 16.2055 0.533699
\(923\) 12.3984 0.408100
\(924\) 0 0
\(925\) −12.9818 −0.426838
\(926\) −1.77773 −0.0584197
\(927\) −0.218199 −0.00716660
\(928\) 31.8864 1.04672
\(929\) 43.0707 1.41310 0.706552 0.707662i \(-0.250250\pi\)
0.706552 + 0.707662i \(0.250250\pi\)
\(930\) −2.95886 −0.0970249
\(931\) 0 0
\(932\) −14.7297 −0.482489
\(933\) −24.4048 −0.798977
\(934\) 37.8100 1.23718
\(935\) 21.3457 0.698080
\(936\) −3.55336 −0.116145
\(937\) −35.0260 −1.14425 −0.572125 0.820166i \(-0.693881\pi\)
−0.572125 + 0.820166i \(0.693881\pi\)
\(938\) 0 0
\(939\) −8.88540 −0.289964
\(940\) −5.52610 −0.180241
\(941\) 44.2501 1.44251 0.721257 0.692668i \(-0.243565\pi\)
0.721257 + 0.692668i \(0.243565\pi\)
\(942\) −4.67618 −0.152358
\(943\) 1.63546 0.0532578
\(944\) 5.00768 0.162986
\(945\) 0 0
\(946\) 15.7965 0.513590
\(947\) −3.06304 −0.0995353 −0.0497677 0.998761i \(-0.515848\pi\)
−0.0497677 + 0.998761i \(0.515848\pi\)
\(948\) −10.4669 −0.339948
\(949\) 2.03480 0.0660523
\(950\) −3.97246 −0.128884
\(951\) −0.0289702 −0.000939423 0
\(952\) 0 0
\(953\) −3.51397 −0.113829 −0.0569143 0.998379i \(-0.518126\pi\)
−0.0569143 + 0.998379i \(0.518126\pi\)
\(954\) −8.94920 −0.289741
\(955\) 19.1014 0.618108
\(956\) 2.14174 0.0692689
\(957\) −37.4323 −1.21002
\(958\) −10.4966 −0.339130
\(959\) 0 0
\(960\) −7.48842 −0.241688
\(961\) −22.3400 −0.720646
\(962\) 3.99927 0.128942
\(963\) 8.05109 0.259443
\(964\) 20.5146 0.660729
\(965\) 10.1193 0.325751
\(966\) 0 0
\(967\) −10.9509 −0.352158 −0.176079 0.984376i \(-0.556341\pi\)
−0.176079 + 0.984376i \(0.556341\pi\)
\(968\) −33.9343 −1.09069
\(969\) 4.28852 0.137767
\(970\) 0.883402 0.0283643
\(971\) 15.9606 0.512199 0.256100 0.966650i \(-0.417563\pi\)
0.256100 + 0.966650i \(0.417563\pi\)
\(972\) −0.753512 −0.0241689
\(973\) 0 0
\(974\) 27.5695 0.883385
\(975\) −4.84188 −0.155064
\(976\) 14.0825 0.450768
\(977\) 43.3664 1.38741 0.693707 0.720257i \(-0.255976\pi\)
0.693707 + 0.720257i \(0.255976\pi\)
\(978\) 12.1516 0.388564
\(979\) −71.2352 −2.27669
\(980\) 0 0
\(981\) 15.5123 0.495270
\(982\) 39.0390 1.24578
\(983\) 4.84144 0.154418 0.0772089 0.997015i \(-0.475399\pi\)
0.0772089 + 0.997015i \(0.475399\pi\)
\(984\) 3.07419 0.0980017
\(985\) −18.3728 −0.585406
\(986\) 44.9468 1.43140
\(987\) 0 0
\(988\) −0.739791 −0.0235359
\(989\) 4.92909 0.156736
\(990\) 4.72016 0.150017
\(991\) −3.88753 −0.123492 −0.0617458 0.998092i \(-0.519667\pi\)
−0.0617458 + 0.998092i \(0.519667\pi\)
\(992\) 11.7681 0.373638
\(993\) 7.32795 0.232545
\(994\) 0 0
\(995\) −1.14253 −0.0362205
\(996\) −7.76720 −0.246113
\(997\) 37.9574 1.20212 0.601062 0.799203i \(-0.294745\pi\)
0.601062 + 0.799203i \(0.294745\pi\)
\(998\) 20.7040 0.655372
\(999\) 3.09905 0.0980495
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 \(a_p\))