Properties

Label 6027.2.a.bm.1.11
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-0.819942\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.819942 q^{2} +1.00000 q^{3} -1.32769 q^{4} +0.332064 q^{5} +0.819942 q^{6} -2.72852 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.819942 q^{2} +1.00000 q^{3} -1.32769 q^{4} +0.332064 q^{5} +0.819942 q^{6} -2.72852 q^{8} +1.00000 q^{9} +0.272273 q^{10} +1.66451 q^{11} -1.32769 q^{12} +0.0164518 q^{13} +0.332064 q^{15} +0.418163 q^{16} +1.78787 q^{17} +0.819942 q^{18} -2.53514 q^{19} -0.440879 q^{20} +1.36480 q^{22} -2.87658 q^{23} -2.72852 q^{24} -4.88973 q^{25} +0.0134895 q^{26} +1.00000 q^{27} +0.605814 q^{29} +0.272273 q^{30} -7.60543 q^{31} +5.79990 q^{32} +1.66451 q^{33} +1.46595 q^{34} -1.32769 q^{36} +1.91702 q^{37} -2.07867 q^{38} +0.0164518 q^{39} -0.906041 q^{40} +1.00000 q^{41} -12.8625 q^{43} -2.20996 q^{44} +0.332064 q^{45} -2.35863 q^{46} -6.16676 q^{47} +0.418163 q^{48} -4.00930 q^{50} +1.78787 q^{51} -0.0218429 q^{52} +3.84096 q^{53} +0.819942 q^{54} +0.552722 q^{55} -2.53514 q^{57} +0.496733 q^{58} +1.41418 q^{59} -0.440879 q^{60} -4.42492 q^{61} -6.23601 q^{62} +3.91926 q^{64} +0.00546303 q^{65} +1.36480 q^{66} +4.72149 q^{67} -2.37374 q^{68} -2.87658 q^{69} +5.80768 q^{71} -2.72852 q^{72} +0.748580 q^{73} +1.57184 q^{74} -4.88973 q^{75} +3.36589 q^{76} +0.0134895 q^{78} +4.49461 q^{79} +0.138857 q^{80} +1.00000 q^{81} +0.819942 q^{82} +11.4541 q^{83} +0.593686 q^{85} -10.5465 q^{86} +0.605814 q^{87} -4.54164 q^{88} -5.00144 q^{89} +0.272273 q^{90} +3.81922 q^{92} -7.60543 q^{93} -5.05638 q^{94} -0.841828 q^{95} +5.79990 q^{96} +6.40794 q^{97} +1.66451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.819942 0.579787 0.289893 0.957059i \(-0.406380\pi\)
0.289893 + 0.957059i \(0.406380\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.32769 −0.663847
\(5\) 0.332064 0.148503 0.0742517 0.997240i \(-0.476343\pi\)
0.0742517 + 0.997240i \(0.476343\pi\)
\(6\) 0.819942 0.334740
\(7\) 0 0
\(8\) −2.72852 −0.964677
\(9\) 1.00000 0.333333
\(10\) 0.272273 0.0861003
\(11\) 1.66451 0.501868 0.250934 0.968004i \(-0.419262\pi\)
0.250934 + 0.968004i \(0.419262\pi\)
\(12\) −1.32769 −0.383272
\(13\) 0.0164518 0.00456290 0.00228145 0.999997i \(-0.499274\pi\)
0.00228145 + 0.999997i \(0.499274\pi\)
\(14\) 0 0
\(15\) 0.332064 0.0857385
\(16\) 0.418163 0.104541
\(17\) 1.78787 0.433622 0.216811 0.976214i \(-0.430435\pi\)
0.216811 + 0.976214i \(0.430435\pi\)
\(18\) 0.819942 0.193262
\(19\) −2.53514 −0.581601 −0.290801 0.956784i \(-0.593922\pi\)
−0.290801 + 0.956784i \(0.593922\pi\)
\(20\) −0.440879 −0.0985836
\(21\) 0 0
\(22\) 1.36480 0.290976
\(23\) −2.87658 −0.599809 −0.299904 0.953969i \(-0.596955\pi\)
−0.299904 + 0.953969i \(0.596955\pi\)
\(24\) −2.72852 −0.556956
\(25\) −4.88973 −0.977947
\(26\) 0.0134895 0.00264551
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.605814 0.112497 0.0562484 0.998417i \(-0.482086\pi\)
0.0562484 + 0.998417i \(0.482086\pi\)
\(30\) 0.272273 0.0497100
\(31\) −7.60543 −1.36597 −0.682987 0.730430i \(-0.739320\pi\)
−0.682987 + 0.730430i \(0.739320\pi\)
\(32\) 5.79990 1.02529
\(33\) 1.66451 0.289754
\(34\) 1.46595 0.251408
\(35\) 0 0
\(36\) −1.32769 −0.221282
\(37\) 1.91702 0.315155 0.157578 0.987507i \(-0.449632\pi\)
0.157578 + 0.987507i \(0.449632\pi\)
\(38\) −2.07867 −0.337205
\(39\) 0.0164518 0.00263439
\(40\) −0.906041 −0.143258
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −12.8625 −1.96151 −0.980753 0.195251i \(-0.937448\pi\)
−0.980753 + 0.195251i \(0.937448\pi\)
\(44\) −2.20996 −0.333164
\(45\) 0.332064 0.0495011
\(46\) −2.35863 −0.347761
\(47\) −6.16676 −0.899514 −0.449757 0.893151i \(-0.648489\pi\)
−0.449757 + 0.893151i \(0.648489\pi\)
\(48\) 0.418163 0.0603566
\(49\) 0 0
\(50\) −4.00930 −0.567001
\(51\) 1.78787 0.250351
\(52\) −0.0218429 −0.00302907
\(53\) 3.84096 0.527596 0.263798 0.964578i \(-0.415025\pi\)
0.263798 + 0.964578i \(0.415025\pi\)
\(54\) 0.819942 0.111580
\(55\) 0.552722 0.0745291
\(56\) 0 0
\(57\) −2.53514 −0.335788
\(58\) 0.496733 0.0652242
\(59\) 1.41418 0.184110 0.0920551 0.995754i \(-0.470656\pi\)
0.0920551 + 0.995754i \(0.470656\pi\)
\(60\) −0.440879 −0.0569172
\(61\) −4.42492 −0.566552 −0.283276 0.959038i \(-0.591421\pi\)
−0.283276 + 0.959038i \(0.591421\pi\)
\(62\) −6.23601 −0.791974
\(63\) 0 0
\(64\) 3.91926 0.489908
\(65\) 0.00546303 0.000677605 0
\(66\) 1.36480 0.167995
\(67\) 4.72149 0.576822 0.288411 0.957507i \(-0.406873\pi\)
0.288411 + 0.957507i \(0.406873\pi\)
\(68\) −2.37374 −0.287858
\(69\) −2.87658 −0.346300
\(70\) 0 0
\(71\) 5.80768 0.689244 0.344622 0.938741i \(-0.388007\pi\)
0.344622 + 0.938741i \(0.388007\pi\)
\(72\) −2.72852 −0.321559
\(73\) 0.748580 0.0876147 0.0438073 0.999040i \(-0.486051\pi\)
0.0438073 + 0.999040i \(0.486051\pi\)
\(74\) 1.57184 0.182723
\(75\) −4.88973 −0.564618
\(76\) 3.36589 0.386094
\(77\) 0 0
\(78\) 0.0134895 0.00152738
\(79\) 4.49461 0.505683 0.252842 0.967508i \(-0.418635\pi\)
0.252842 + 0.967508i \(0.418635\pi\)
\(80\) 0.138857 0.0155246
\(81\) 1.00000 0.111111
\(82\) 0.819942 0.0905475
\(83\) 11.4541 1.25725 0.628626 0.777707i \(-0.283617\pi\)
0.628626 + 0.777707i \(0.283617\pi\)
\(84\) 0 0
\(85\) 0.593686 0.0643943
\(86\) −10.5465 −1.13726
\(87\) 0.605814 0.0649501
\(88\) −4.54164 −0.484140
\(89\) −5.00144 −0.530152 −0.265076 0.964228i \(-0.585397\pi\)
−0.265076 + 0.964228i \(0.585397\pi\)
\(90\) 0.272273 0.0287001
\(91\) 0 0
\(92\) 3.81922 0.398181
\(93\) −7.60543 −0.788646
\(94\) −5.05638 −0.521526
\(95\) −0.841828 −0.0863697
\(96\) 5.79990 0.591950
\(97\) 6.40794 0.650628 0.325314 0.945606i \(-0.394530\pi\)
0.325314 + 0.945606i \(0.394530\pi\)
\(98\) 0 0
\(99\) 1.66451 0.167289
\(100\) 6.49207 0.649207
\(101\) −17.5942 −1.75069 −0.875344 0.483501i \(-0.839365\pi\)
−0.875344 + 0.483501i \(0.839365\pi\)
\(102\) 1.46595 0.145150
\(103\) −4.00896 −0.395015 −0.197507 0.980301i \(-0.563285\pi\)
−0.197507 + 0.980301i \(0.563285\pi\)
\(104\) −0.0448889 −0.00440172
\(105\) 0 0
\(106\) 3.14937 0.305893
\(107\) −11.8977 −1.15019 −0.575097 0.818085i \(-0.695036\pi\)
−0.575097 + 0.818085i \(0.695036\pi\)
\(108\) −1.32769 −0.127757
\(109\) −14.1105 −1.35154 −0.675772 0.737110i \(-0.736190\pi\)
−0.675772 + 0.737110i \(0.736190\pi\)
\(110\) 0.453200 0.0432110
\(111\) 1.91702 0.181955
\(112\) 0 0
\(113\) 3.58338 0.337096 0.168548 0.985693i \(-0.446092\pi\)
0.168548 + 0.985693i \(0.446092\pi\)
\(114\) −2.07867 −0.194685
\(115\) −0.955208 −0.0890736
\(116\) −0.804336 −0.0746807
\(117\) 0.0164518 0.00152097
\(118\) 1.15954 0.106745
\(119\) 0 0
\(120\) −0.906041 −0.0827099
\(121\) −8.22941 −0.748129
\(122\) −3.62818 −0.328480
\(123\) 1.00000 0.0901670
\(124\) 10.0977 0.906799
\(125\) −3.28402 −0.293732
\(126\) 0 0
\(127\) −16.6099 −1.47389 −0.736944 0.675954i \(-0.763732\pi\)
−0.736944 + 0.675954i \(0.763732\pi\)
\(128\) −8.38624 −0.741246
\(129\) −12.8625 −1.13248
\(130\) 0.00447937 0.000392867 0
\(131\) 9.60996 0.839626 0.419813 0.907611i \(-0.362096\pi\)
0.419813 + 0.907611i \(0.362096\pi\)
\(132\) −2.20996 −0.192352
\(133\) 0 0
\(134\) 3.87135 0.334434
\(135\) 0.332064 0.0285795
\(136\) −4.87823 −0.418305
\(137\) −5.93129 −0.506744 −0.253372 0.967369i \(-0.581540\pi\)
−0.253372 + 0.967369i \(0.581540\pi\)
\(138\) −2.35863 −0.200780
\(139\) 20.3689 1.72767 0.863836 0.503773i \(-0.168055\pi\)
0.863836 + 0.503773i \(0.168055\pi\)
\(140\) 0 0
\(141\) −6.16676 −0.519335
\(142\) 4.76196 0.399615
\(143\) 0.0273841 0.00228997
\(144\) 0.418163 0.0348469
\(145\) 0.201169 0.0167062
\(146\) 0.613793 0.0507978
\(147\) 0 0
\(148\) −2.54521 −0.209215
\(149\) −15.7679 −1.29176 −0.645878 0.763440i \(-0.723509\pi\)
−0.645878 + 0.763440i \(0.723509\pi\)
\(150\) −4.00930 −0.327358
\(151\) 12.4627 1.01420 0.507102 0.861886i \(-0.330717\pi\)
0.507102 + 0.861886i \(0.330717\pi\)
\(152\) 6.91718 0.561057
\(153\) 1.78787 0.144541
\(154\) 0 0
\(155\) −2.52549 −0.202852
\(156\) −0.0218429 −0.00174883
\(157\) −14.6543 −1.16954 −0.584771 0.811198i \(-0.698816\pi\)
−0.584771 + 0.811198i \(0.698816\pi\)
\(158\) 3.68532 0.293188
\(159\) 3.84096 0.304608
\(160\) 1.92594 0.152259
\(161\) 0 0
\(162\) 0.819942 0.0644207
\(163\) −10.4822 −0.821030 −0.410515 0.911854i \(-0.634651\pi\)
−0.410515 + 0.911854i \(0.634651\pi\)
\(164\) −1.32769 −0.103676
\(165\) 0.552722 0.0430294
\(166\) 9.39172 0.728939
\(167\) 9.45153 0.731381 0.365691 0.930736i \(-0.380833\pi\)
0.365691 + 0.930736i \(0.380833\pi\)
\(168\) 0 0
\(169\) −12.9997 −0.999979
\(170\) 0.486788 0.0373349
\(171\) −2.53514 −0.193867
\(172\) 17.0774 1.30214
\(173\) −9.52226 −0.723964 −0.361982 0.932185i \(-0.617900\pi\)
−0.361982 + 0.932185i \(0.617900\pi\)
\(174\) 0.496733 0.0376572
\(175\) 0 0
\(176\) 0.696035 0.0524656
\(177\) 1.41418 0.106296
\(178\) −4.10089 −0.307375
\(179\) −22.8105 −1.70494 −0.852469 0.522778i \(-0.824896\pi\)
−0.852469 + 0.522778i \(0.824896\pi\)
\(180\) −0.440879 −0.0328612
\(181\) −3.16124 −0.234973 −0.117487 0.993074i \(-0.537484\pi\)
−0.117487 + 0.993074i \(0.537484\pi\)
\(182\) 0 0
\(183\) −4.42492 −0.327099
\(184\) 7.84880 0.578621
\(185\) 0.636571 0.0468016
\(186\) −6.23601 −0.457246
\(187\) 2.97592 0.217621
\(188\) 8.18757 0.597140
\(189\) 0 0
\(190\) −0.690250 −0.0500760
\(191\) 5.66282 0.409747 0.204874 0.978788i \(-0.434322\pi\)
0.204874 + 0.978788i \(0.434322\pi\)
\(192\) 3.91926 0.282848
\(193\) −20.1887 −1.45321 −0.726606 0.687055i \(-0.758903\pi\)
−0.726606 + 0.687055i \(0.758903\pi\)
\(194\) 5.25414 0.377225
\(195\) 0.00546303 0.000391216 0
\(196\) 0 0
\(197\) 0.477679 0.0340332 0.0170166 0.999855i \(-0.494583\pi\)
0.0170166 + 0.999855i \(0.494583\pi\)
\(198\) 1.36480 0.0969921
\(199\) −3.25632 −0.230835 −0.115417 0.993317i \(-0.536821\pi\)
−0.115417 + 0.993317i \(0.536821\pi\)
\(200\) 13.3417 0.943402
\(201\) 4.72149 0.333029
\(202\) −14.4262 −1.01503
\(203\) 0 0
\(204\) −2.37374 −0.166195
\(205\) 0.332064 0.0231923
\(206\) −3.28712 −0.229024
\(207\) −2.87658 −0.199936
\(208\) 0.00687951 0.000477008 0
\(209\) −4.21976 −0.291887
\(210\) 0 0
\(211\) 0.492222 0.0338860 0.0169430 0.999856i \(-0.494607\pi\)
0.0169430 + 0.999856i \(0.494607\pi\)
\(212\) −5.09962 −0.350244
\(213\) 5.80768 0.397935
\(214\) −9.75543 −0.666868
\(215\) −4.27115 −0.291290
\(216\) −2.72852 −0.185652
\(217\) 0 0
\(218\) −11.5698 −0.783608
\(219\) 0.748580 0.0505844
\(220\) −0.733847 −0.0494759
\(221\) 0.0294136 0.00197857
\(222\) 1.57184 0.105495
\(223\) 7.15813 0.479344 0.239672 0.970854i \(-0.422960\pi\)
0.239672 + 0.970854i \(0.422960\pi\)
\(224\) 0 0
\(225\) −4.88973 −0.325982
\(226\) 2.93816 0.195444
\(227\) −7.34618 −0.487583 −0.243791 0.969828i \(-0.578391\pi\)
−0.243791 + 0.969828i \(0.578391\pi\)
\(228\) 3.36589 0.222912
\(229\) −9.96063 −0.658217 −0.329109 0.944292i \(-0.606748\pi\)
−0.329109 + 0.944292i \(0.606748\pi\)
\(230\) −0.783215 −0.0516437
\(231\) 0 0
\(232\) −1.65297 −0.108523
\(233\) −21.3065 −1.39583 −0.697917 0.716179i \(-0.745889\pi\)
−0.697917 + 0.716179i \(0.745889\pi\)
\(234\) 0.0134895 0.000881835 0
\(235\) −2.04776 −0.133581
\(236\) −1.87760 −0.122221
\(237\) 4.49461 0.291956
\(238\) 0 0
\(239\) −10.7115 −0.692868 −0.346434 0.938074i \(-0.612608\pi\)
−0.346434 + 0.938074i \(0.612608\pi\)
\(240\) 0.138857 0.00896315
\(241\) −15.3877 −0.991212 −0.495606 0.868547i \(-0.665054\pi\)
−0.495606 + 0.868547i \(0.665054\pi\)
\(242\) −6.74764 −0.433755
\(243\) 1.00000 0.0641500
\(244\) 5.87494 0.376104
\(245\) 0 0
\(246\) 0.819942 0.0522776
\(247\) −0.0417075 −0.00265379
\(248\) 20.7515 1.31772
\(249\) 11.4541 0.725875
\(250\) −2.69271 −0.170302
\(251\) −3.83734 −0.242211 −0.121105 0.992640i \(-0.538644\pi\)
−0.121105 + 0.992640i \(0.538644\pi\)
\(252\) 0 0
\(253\) −4.78809 −0.301025
\(254\) −13.6191 −0.854541
\(255\) 0.593686 0.0371780
\(256\) −14.7148 −0.919672
\(257\) 29.6461 1.84927 0.924637 0.380850i \(-0.124368\pi\)
0.924637 + 0.380850i \(0.124368\pi\)
\(258\) −10.5465 −0.656595
\(259\) 0 0
\(260\) −0.00725323 −0.000449827 0
\(261\) 0.605814 0.0374990
\(262\) 7.87961 0.486804
\(263\) −15.0006 −0.924976 −0.462488 0.886625i \(-0.653043\pi\)
−0.462488 + 0.886625i \(0.653043\pi\)
\(264\) −4.54164 −0.279518
\(265\) 1.27544 0.0783498
\(266\) 0 0
\(267\) −5.00144 −0.306083
\(268\) −6.26870 −0.382922
\(269\) −5.76098 −0.351253 −0.175627 0.984457i \(-0.556195\pi\)
−0.175627 + 0.984457i \(0.556195\pi\)
\(270\) 0.272273 0.0165700
\(271\) 5.41966 0.329221 0.164611 0.986359i \(-0.447363\pi\)
0.164611 + 0.986359i \(0.447363\pi\)
\(272\) 0.747619 0.0453311
\(273\) 0 0
\(274\) −4.86331 −0.293803
\(275\) −8.13900 −0.490800
\(276\) 3.81922 0.229890
\(277\) −20.4003 −1.22573 −0.612867 0.790186i \(-0.709984\pi\)
−0.612867 + 0.790186i \(0.709984\pi\)
\(278\) 16.7014 1.00168
\(279\) −7.60543 −0.455325
\(280\) 0 0
\(281\) 5.03670 0.300464 0.150232 0.988651i \(-0.451998\pi\)
0.150232 + 0.988651i \(0.451998\pi\)
\(282\) −5.05638 −0.301103
\(283\) 0.733053 0.0435755 0.0217877 0.999763i \(-0.493064\pi\)
0.0217877 + 0.999763i \(0.493064\pi\)
\(284\) −7.71082 −0.457553
\(285\) −0.841828 −0.0498656
\(286\) 0.0224534 0.00132769
\(287\) 0 0
\(288\) 5.79990 0.341763
\(289\) −13.8035 −0.811972
\(290\) 0.164947 0.00968601
\(291\) 6.40794 0.375640
\(292\) −0.993886 −0.0581628
\(293\) 9.92734 0.579961 0.289981 0.957033i \(-0.406351\pi\)
0.289981 + 0.957033i \(0.406351\pi\)
\(294\) 0 0
\(295\) 0.469597 0.0273410
\(296\) −5.23061 −0.304023
\(297\) 1.66451 0.0965845
\(298\) −12.9288 −0.748943
\(299\) −0.0473248 −0.00273686
\(300\) 6.49207 0.374820
\(301\) 0 0
\(302\) 10.2187 0.588022
\(303\) −17.5942 −1.01076
\(304\) −1.06010 −0.0608010
\(305\) −1.46935 −0.0841349
\(306\) 1.46595 0.0838027
\(307\) 18.0797 1.03186 0.515930 0.856631i \(-0.327446\pi\)
0.515930 + 0.856631i \(0.327446\pi\)
\(308\) 0 0
\(309\) −4.00896 −0.228062
\(310\) −2.07075 −0.117611
\(311\) 6.53524 0.370579 0.185290 0.982684i \(-0.440678\pi\)
0.185290 + 0.982684i \(0.440678\pi\)
\(312\) −0.0448889 −0.00254133
\(313\) 6.62531 0.374485 0.187242 0.982314i \(-0.440045\pi\)
0.187242 + 0.982314i \(0.440045\pi\)
\(314\) −12.0157 −0.678085
\(315\) 0 0
\(316\) −5.96747 −0.335696
\(317\) 5.00888 0.281327 0.140663 0.990057i \(-0.455077\pi\)
0.140663 + 0.990057i \(0.455077\pi\)
\(318\) 3.14937 0.176608
\(319\) 1.00838 0.0564586
\(320\) 1.30144 0.0727529
\(321\) −11.8977 −0.664065
\(322\) 0 0
\(323\) −4.53250 −0.252195
\(324\) −1.32769 −0.0737608
\(325\) −0.0804447 −0.00446227
\(326\) −8.59480 −0.476022
\(327\) −14.1105 −0.780315
\(328\) −2.72852 −0.150657
\(329\) 0 0
\(330\) 0.453200 0.0249479
\(331\) −2.06115 −0.113291 −0.0566456 0.998394i \(-0.518040\pi\)
−0.0566456 + 0.998394i \(0.518040\pi\)
\(332\) −15.2076 −0.834624
\(333\) 1.91702 0.105052
\(334\) 7.74971 0.424045
\(335\) 1.56784 0.0856600
\(336\) 0 0
\(337\) 12.5592 0.684141 0.342070 0.939674i \(-0.388872\pi\)
0.342070 + 0.939674i \(0.388872\pi\)
\(338\) −10.6590 −0.579775
\(339\) 3.58338 0.194622
\(340\) −0.788233 −0.0427480
\(341\) −12.6593 −0.685539
\(342\) −2.07867 −0.112402
\(343\) 0 0
\(344\) 35.0954 1.89222
\(345\) −0.955208 −0.0514267
\(346\) −7.80770 −0.419745
\(347\) 11.4809 0.616325 0.308163 0.951334i \(-0.400286\pi\)
0.308163 + 0.951334i \(0.400286\pi\)
\(348\) −0.804336 −0.0431169
\(349\) 15.2242 0.814931 0.407466 0.913221i \(-0.366413\pi\)
0.407466 + 0.913221i \(0.366413\pi\)
\(350\) 0 0
\(351\) 0.0164518 0.000878130 0
\(352\) 9.65398 0.514559
\(353\) 20.4119 1.08642 0.543209 0.839598i \(-0.317209\pi\)
0.543209 + 0.839598i \(0.317209\pi\)
\(354\) 1.15954 0.0616291
\(355\) 1.92852 0.102355
\(356\) 6.64039 0.351940
\(357\) 0 0
\(358\) −18.7033 −0.988501
\(359\) 30.1992 1.59385 0.796926 0.604077i \(-0.206458\pi\)
0.796926 + 0.604077i \(0.206458\pi\)
\(360\) −0.906041 −0.0477526
\(361\) −12.5731 −0.661740
\(362\) −2.59203 −0.136234
\(363\) −8.22941 −0.431932
\(364\) 0 0
\(365\) 0.248576 0.0130111
\(366\) −3.62818 −0.189648
\(367\) 5.89363 0.307645 0.153823 0.988098i \(-0.450842\pi\)
0.153823 + 0.988098i \(0.450842\pi\)
\(368\) −1.20288 −0.0627044
\(369\) 1.00000 0.0520579
\(370\) 0.521951 0.0271350
\(371\) 0 0
\(372\) 10.0977 0.523541
\(373\) 23.0679 1.19441 0.597206 0.802088i \(-0.296278\pi\)
0.597206 + 0.802088i \(0.296278\pi\)
\(374\) 2.44008 0.126174
\(375\) −3.28402 −0.169586
\(376\) 16.8261 0.867740
\(377\) 0.00996671 0.000513311 0
\(378\) 0 0
\(379\) 15.9801 0.820843 0.410421 0.911896i \(-0.365382\pi\)
0.410421 + 0.911896i \(0.365382\pi\)
\(380\) 1.11769 0.0573363
\(381\) −16.6099 −0.850950
\(382\) 4.64319 0.237566
\(383\) −28.4963 −1.45609 −0.728046 0.685529i \(-0.759571\pi\)
−0.728046 + 0.685529i \(0.759571\pi\)
\(384\) −8.38624 −0.427959
\(385\) 0 0
\(386\) −16.5535 −0.842553
\(387\) −12.8625 −0.653836
\(388\) −8.50779 −0.431918
\(389\) 4.42493 0.224353 0.112177 0.993688i \(-0.464218\pi\)
0.112177 + 0.993688i \(0.464218\pi\)
\(390\) 0.00447937 0.000226822 0
\(391\) −5.14295 −0.260090
\(392\) 0 0
\(393\) 9.60996 0.484758
\(394\) 0.391669 0.0197320
\(395\) 1.49250 0.0750956
\(396\) −2.20996 −0.111055
\(397\) 31.0599 1.55885 0.779426 0.626494i \(-0.215511\pi\)
0.779426 + 0.626494i \(0.215511\pi\)
\(398\) −2.67000 −0.133835
\(399\) 0 0
\(400\) −2.04470 −0.102235
\(401\) −2.27093 −0.113405 −0.0567025 0.998391i \(-0.518059\pi\)
−0.0567025 + 0.998391i \(0.518059\pi\)
\(402\) 3.87135 0.193086
\(403\) −0.125123 −0.00623280
\(404\) 23.3597 1.16219
\(405\) 0.332064 0.0165004
\(406\) 0 0
\(407\) 3.19089 0.158166
\(408\) −4.87823 −0.241508
\(409\) 5.31380 0.262751 0.131375 0.991333i \(-0.458061\pi\)
0.131375 + 0.991333i \(0.458061\pi\)
\(410\) 0.272273 0.0134466
\(411\) −5.93129 −0.292569
\(412\) 5.32268 0.262229
\(413\) 0 0
\(414\) −2.35863 −0.115920
\(415\) 3.80350 0.186706
\(416\) 0.0954186 0.00467828
\(417\) 20.3689 0.997472
\(418\) −3.45996 −0.169232
\(419\) 16.3430 0.798410 0.399205 0.916862i \(-0.369286\pi\)
0.399205 + 0.916862i \(0.369286\pi\)
\(420\) 0 0
\(421\) −7.54033 −0.367493 −0.183747 0.982974i \(-0.558823\pi\)
−0.183747 + 0.982974i \(0.558823\pi\)
\(422\) 0.403594 0.0196466
\(423\) −6.16676 −0.299838
\(424\) −10.4801 −0.508960
\(425\) −8.74219 −0.424059
\(426\) 4.76196 0.230718
\(427\) 0 0
\(428\) 15.7965 0.763554
\(429\) 0.0273841 0.00132212
\(430\) −3.50210 −0.168886
\(431\) 8.22298 0.396087 0.198044 0.980193i \(-0.436541\pi\)
0.198044 + 0.980193i \(0.436541\pi\)
\(432\) 0.418163 0.0201189
\(433\) 6.10083 0.293187 0.146594 0.989197i \(-0.453169\pi\)
0.146594 + 0.989197i \(0.453169\pi\)
\(434\) 0 0
\(435\) 0.201169 0.00964531
\(436\) 18.7345 0.897220
\(437\) 7.29254 0.348850
\(438\) 0.613793 0.0293281
\(439\) −16.8750 −0.805398 −0.402699 0.915333i \(-0.631928\pi\)
−0.402699 + 0.915333i \(0.631928\pi\)
\(440\) −1.50811 −0.0718965
\(441\) 0 0
\(442\) 0.0241174 0.00114715
\(443\) −24.6875 −1.17294 −0.586468 0.809972i \(-0.699482\pi\)
−0.586468 + 0.809972i \(0.699482\pi\)
\(444\) −2.54521 −0.120790
\(445\) −1.66080 −0.0787293
\(446\) 5.86925 0.277917
\(447\) −15.7679 −0.745796
\(448\) 0 0
\(449\) 1.81494 0.0856523 0.0428262 0.999083i \(-0.486364\pi\)
0.0428262 + 0.999083i \(0.486364\pi\)
\(450\) −4.00930 −0.189000
\(451\) 1.66451 0.0783786
\(452\) −4.75763 −0.223780
\(453\) 12.4627 0.585551
\(454\) −6.02344 −0.282694
\(455\) 0 0
\(456\) 6.91718 0.323927
\(457\) 28.1049 1.31469 0.657345 0.753589i \(-0.271679\pi\)
0.657345 + 0.753589i \(0.271679\pi\)
\(458\) −8.16714 −0.381625
\(459\) 1.78787 0.0834505
\(460\) 1.26822 0.0591313
\(461\) 27.5428 1.28280 0.641399 0.767207i \(-0.278354\pi\)
0.641399 + 0.767207i \(0.278354\pi\)
\(462\) 0 0
\(463\) −23.8028 −1.10621 −0.553104 0.833112i \(-0.686557\pi\)
−0.553104 + 0.833112i \(0.686557\pi\)
\(464\) 0.253329 0.0117605
\(465\) −2.52549 −0.117117
\(466\) −17.4701 −0.809286
\(467\) −4.10944 −0.190162 −0.0950811 0.995470i \(-0.530311\pi\)
−0.0950811 + 0.995470i \(0.530311\pi\)
\(468\) −0.0218429 −0.00100969
\(469\) 0 0
\(470\) −1.67904 −0.0774484
\(471\) −14.6543 −0.675235
\(472\) −3.85861 −0.177607
\(473\) −21.4097 −0.984417
\(474\) 3.68532 0.169272
\(475\) 12.3962 0.568775
\(476\) 0 0
\(477\) 3.84096 0.175865
\(478\) −8.78279 −0.401716
\(479\) 11.3384 0.518063 0.259031 0.965869i \(-0.416597\pi\)
0.259031 + 0.965869i \(0.416597\pi\)
\(480\) 1.92594 0.0879066
\(481\) 0.0315383 0.00143802
\(482\) −12.6171 −0.574692
\(483\) 0 0
\(484\) 10.9262 0.496643
\(485\) 2.12784 0.0966204
\(486\) 0.819942 0.0371933
\(487\) 9.89485 0.448378 0.224189 0.974546i \(-0.428027\pi\)
0.224189 + 0.974546i \(0.428027\pi\)
\(488\) 12.0735 0.546540
\(489\) −10.4822 −0.474022
\(490\) 0 0
\(491\) 25.2342 1.13880 0.569402 0.822059i \(-0.307175\pi\)
0.569402 + 0.822059i \(0.307175\pi\)
\(492\) −1.32769 −0.0598571
\(493\) 1.08312 0.0487811
\(494\) −0.0341978 −0.00153863
\(495\) 0.552722 0.0248430
\(496\) −3.18030 −0.142800
\(497\) 0 0
\(498\) 9.39172 0.420853
\(499\) −1.10126 −0.0492993 −0.0246497 0.999696i \(-0.507847\pi\)
−0.0246497 + 0.999696i \(0.507847\pi\)
\(500\) 4.36018 0.194993
\(501\) 9.45153 0.422263
\(502\) −3.14640 −0.140431
\(503\) −25.1272 −1.12036 −0.560182 0.828369i \(-0.689269\pi\)
−0.560182 + 0.828369i \(0.689269\pi\)
\(504\) 0 0
\(505\) −5.84239 −0.259983
\(506\) −3.92596 −0.174530
\(507\) −12.9997 −0.577338
\(508\) 22.0528 0.978437
\(509\) −7.92927 −0.351459 −0.175729 0.984439i \(-0.556228\pi\)
−0.175729 + 0.984439i \(0.556228\pi\)
\(510\) 0.486788 0.0215553
\(511\) 0 0
\(512\) 4.70723 0.208032
\(513\) −2.53514 −0.111929
\(514\) 24.3081 1.07218
\(515\) −1.33123 −0.0586610
\(516\) 17.0774 0.751791
\(517\) −10.2646 −0.451437
\(518\) 0 0
\(519\) −9.52226 −0.417981
\(520\) −0.0149060 −0.000653670 0
\(521\) −14.0312 −0.614716 −0.307358 0.951594i \(-0.599445\pi\)
−0.307358 + 0.951594i \(0.599445\pi\)
\(522\) 0.496733 0.0217414
\(523\) 19.4953 0.852469 0.426234 0.904613i \(-0.359840\pi\)
0.426234 + 0.904613i \(0.359840\pi\)
\(524\) −12.7591 −0.557384
\(525\) 0 0
\(526\) −12.2996 −0.536289
\(527\) −13.5975 −0.592316
\(528\) 0.696035 0.0302910
\(529\) −14.7253 −0.640230
\(530\) 1.04579 0.0454262
\(531\) 1.41418 0.0613701
\(532\) 0 0
\(533\) 0.0164518 0.000712605 0
\(534\) −4.10089 −0.177463
\(535\) −3.95080 −0.170808
\(536\) −12.8827 −0.556447
\(537\) −22.8105 −0.984347
\(538\) −4.72367 −0.203652
\(539\) 0 0
\(540\) −0.440879 −0.0189724
\(541\) −13.5263 −0.581541 −0.290771 0.956793i \(-0.593912\pi\)
−0.290771 + 0.956793i \(0.593912\pi\)
\(542\) 4.44381 0.190878
\(543\) −3.16124 −0.135662
\(544\) 10.3695 0.444587
\(545\) −4.68560 −0.200709
\(546\) 0 0
\(547\) 21.4272 0.916162 0.458081 0.888911i \(-0.348537\pi\)
0.458081 + 0.888911i \(0.348537\pi\)
\(548\) 7.87494 0.336401
\(549\) −4.42492 −0.188851
\(550\) −6.67351 −0.284559
\(551\) −1.53582 −0.0654283
\(552\) 7.84880 0.334067
\(553\) 0 0
\(554\) −16.7270 −0.710664
\(555\) 0.636571 0.0270209
\(556\) −27.0437 −1.14691
\(557\) −10.4798 −0.444045 −0.222022 0.975042i \(-0.571266\pi\)
−0.222022 + 0.975042i \(0.571266\pi\)
\(558\) −6.23601 −0.263991
\(559\) −0.211610 −0.00895015
\(560\) 0 0
\(561\) 2.97592 0.125643
\(562\) 4.12980 0.174205
\(563\) −31.3895 −1.32291 −0.661454 0.749986i \(-0.730060\pi\)
−0.661454 + 0.749986i \(0.730060\pi\)
\(564\) 8.18757 0.344759
\(565\) 1.18991 0.0500598
\(566\) 0.601061 0.0252645
\(567\) 0 0
\(568\) −15.8463 −0.664898
\(569\) 6.23334 0.261315 0.130658 0.991428i \(-0.458291\pi\)
0.130658 + 0.991428i \(0.458291\pi\)
\(570\) −0.690250 −0.0289114
\(571\) −23.9382 −1.00178 −0.500890 0.865511i \(-0.666994\pi\)
−0.500890 + 0.865511i \(0.666994\pi\)
\(572\) −0.0363577 −0.00152019
\(573\) 5.66282 0.236568
\(574\) 0 0
\(575\) 14.0657 0.586581
\(576\) 3.91926 0.163303
\(577\) 16.8790 0.702683 0.351341 0.936247i \(-0.385726\pi\)
0.351341 + 0.936247i \(0.385726\pi\)
\(578\) −11.3181 −0.470771
\(579\) −20.1887 −0.839012
\(580\) −0.267091 −0.0110903
\(581\) 0 0
\(582\) 5.25414 0.217791
\(583\) 6.39331 0.264784
\(584\) −2.04251 −0.0845198
\(585\) 0.00546303 0.000225868 0
\(586\) 8.13984 0.336254
\(587\) 14.5227 0.599416 0.299708 0.954031i \(-0.403111\pi\)
0.299708 + 0.954031i \(0.403111\pi\)
\(588\) 0 0
\(589\) 19.2808 0.794453
\(590\) 0.385042 0.0158519
\(591\) 0.477679 0.0196491
\(592\) 0.801624 0.0329465
\(593\) −7.13395 −0.292956 −0.146478 0.989214i \(-0.546794\pi\)
−0.146478 + 0.989214i \(0.546794\pi\)
\(594\) 1.36480 0.0559984
\(595\) 0 0
\(596\) 20.9350 0.857529
\(597\) −3.25632 −0.133272
\(598\) −0.0388036 −0.00158680
\(599\) 5.13045 0.209624 0.104812 0.994492i \(-0.466576\pi\)
0.104812 + 0.994492i \(0.466576\pi\)
\(600\) 13.3417 0.544674
\(601\) 37.6827 1.53711 0.768554 0.639785i \(-0.220977\pi\)
0.768554 + 0.639785i \(0.220977\pi\)
\(602\) 0 0
\(603\) 4.72149 0.192274
\(604\) −16.5467 −0.673276
\(605\) −2.73269 −0.111100
\(606\) −14.4262 −0.586025
\(607\) −15.7766 −0.640354 −0.320177 0.947358i \(-0.603742\pi\)
−0.320177 + 0.947358i \(0.603742\pi\)
\(608\) −14.7036 −0.596309
\(609\) 0 0
\(610\) −1.20478 −0.0487803
\(611\) −0.101454 −0.00410439
\(612\) −2.37374 −0.0959528
\(613\) 28.8922 1.16694 0.583472 0.812133i \(-0.301694\pi\)
0.583472 + 0.812133i \(0.301694\pi\)
\(614\) 14.8243 0.598259
\(615\) 0.332064 0.0133901
\(616\) 0 0
\(617\) −23.0012 −0.925993 −0.462996 0.886360i \(-0.653226\pi\)
−0.462996 + 0.886360i \(0.653226\pi\)
\(618\) −3.28712 −0.132227
\(619\) 13.3883 0.538121 0.269060 0.963123i \(-0.413287\pi\)
0.269060 + 0.963123i \(0.413287\pi\)
\(620\) 3.35307 0.134663
\(621\) −2.87658 −0.115433
\(622\) 5.35852 0.214857
\(623\) 0 0
\(624\) 0.00687951 0.000275401 0
\(625\) 23.3582 0.934327
\(626\) 5.43237 0.217121
\(627\) −4.21976 −0.168521
\(628\) 19.4565 0.776397
\(629\) 3.42737 0.136658
\(630\) 0 0
\(631\) −0.0230585 −0.000917944 0 −0.000458972 1.00000i \(-0.500146\pi\)
−0.000458972 1.00000i \(0.500146\pi\)
\(632\) −12.2636 −0.487821
\(633\) 0.492222 0.0195641
\(634\) 4.10699 0.163109
\(635\) −5.51554 −0.218877
\(636\) −5.09962 −0.202213
\(637\) 0 0
\(638\) 0.826815 0.0327339
\(639\) 5.80768 0.229748
\(640\) −2.78477 −0.110078
\(641\) −1.14808 −0.0453465 −0.0226732 0.999743i \(-0.507218\pi\)
−0.0226732 + 0.999743i \(0.507218\pi\)
\(642\) −9.75543 −0.385016
\(643\) 6.32451 0.249414 0.124707 0.992194i \(-0.460201\pi\)
0.124707 + 0.992194i \(0.460201\pi\)
\(644\) 0 0
\(645\) −4.27115 −0.168177
\(646\) −3.71639 −0.146219
\(647\) 18.0069 0.707925 0.353963 0.935260i \(-0.384834\pi\)
0.353963 + 0.935260i \(0.384834\pi\)
\(648\) −2.72852 −0.107186
\(649\) 2.35391 0.0923990
\(650\) −0.0659600 −0.00258716
\(651\) 0 0
\(652\) 13.9172 0.545038
\(653\) −1.68150 −0.0658021 −0.0329010 0.999459i \(-0.510475\pi\)
−0.0329010 + 0.999459i \(0.510475\pi\)
\(654\) −11.5698 −0.452416
\(655\) 3.19112 0.124687
\(656\) 0.418163 0.0163265
\(657\) 0.748580 0.0292049
\(658\) 0 0
\(659\) 38.1251 1.48514 0.742571 0.669767i \(-0.233606\pi\)
0.742571 + 0.669767i \(0.233606\pi\)
\(660\) −0.733847 −0.0285649
\(661\) −7.33130 −0.285154 −0.142577 0.989784i \(-0.545539\pi\)
−0.142577 + 0.989784i \(0.545539\pi\)
\(662\) −1.69002 −0.0656847
\(663\) 0.0294136 0.00114233
\(664\) −31.2528 −1.21284
\(665\) 0 0
\(666\) 1.57184 0.0609076
\(667\) −1.74267 −0.0674766
\(668\) −12.5487 −0.485526
\(669\) 7.15813 0.276749
\(670\) 1.28554 0.0496646
\(671\) −7.36530 −0.284334
\(672\) 0 0
\(673\) 11.6171 0.447806 0.223903 0.974611i \(-0.428120\pi\)
0.223903 + 0.974611i \(0.428120\pi\)
\(674\) 10.2978 0.396656
\(675\) −4.88973 −0.188206
\(676\) 17.2597 0.663834
\(677\) 33.6999 1.29519 0.647597 0.761983i \(-0.275774\pi\)
0.647597 + 0.761983i \(0.275774\pi\)
\(678\) 2.93816 0.112839
\(679\) 0 0
\(680\) −1.61988 −0.0621196
\(681\) −7.34618 −0.281506
\(682\) −10.3799 −0.397466
\(683\) 17.5803 0.672693 0.336346 0.941738i \(-0.390809\pi\)
0.336346 + 0.941738i \(0.390809\pi\)
\(684\) 3.36589 0.128698
\(685\) −1.96956 −0.0752532
\(686\) 0 0
\(687\) −9.96063 −0.380022
\(688\) −5.37860 −0.205057
\(689\) 0.0631905 0.00240737
\(690\) −0.783215 −0.0298165
\(691\) 8.94418 0.340252 0.170126 0.985422i \(-0.445582\pi\)
0.170126 + 0.985422i \(0.445582\pi\)
\(692\) 12.6427 0.480602
\(693\) 0 0
\(694\) 9.41365 0.357337
\(695\) 6.76379 0.256565
\(696\) −1.65297 −0.0626558
\(697\) 1.78787 0.0677203
\(698\) 12.4829 0.472486
\(699\) −21.3065 −0.805885
\(700\) 0 0
\(701\) 39.6138 1.49619 0.748097 0.663590i \(-0.230968\pi\)
0.748097 + 0.663590i \(0.230968\pi\)
\(702\) 0.0134895 0.000509128 0
\(703\) −4.85990 −0.183295
\(704\) 6.52364 0.245869
\(705\) −2.04776 −0.0771229
\(706\) 16.7366 0.629890
\(707\) 0 0
\(708\) −1.87760 −0.0705644
\(709\) 17.1546 0.644256 0.322128 0.946696i \(-0.395602\pi\)
0.322128 + 0.946696i \(0.395602\pi\)
\(710\) 1.58127 0.0593441
\(711\) 4.49461 0.168561
\(712\) 13.6465 0.511425
\(713\) 21.8776 0.819324
\(714\) 0 0
\(715\) 0.00909325 0.000340068 0
\(716\) 30.2854 1.13182
\(717\) −10.7115 −0.400028
\(718\) 24.7616 0.924094
\(719\) 11.0220 0.411053 0.205526 0.978652i \(-0.434109\pi\)
0.205526 + 0.978652i \(0.434109\pi\)
\(720\) 0.138857 0.00517488
\(721\) 0 0
\(722\) −10.3092 −0.383668
\(723\) −15.3877 −0.572276
\(724\) 4.19716 0.155986
\(725\) −2.96227 −0.110016
\(726\) −6.74764 −0.250429
\(727\) 25.4401 0.943520 0.471760 0.881727i \(-0.343619\pi\)
0.471760 + 0.881727i \(0.343619\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.203818 0.00754365
\(731\) −22.9964 −0.850552
\(732\) 5.87494 0.217144
\(733\) −32.5187 −1.20110 −0.600552 0.799586i \(-0.705053\pi\)
−0.600552 + 0.799586i \(0.705053\pi\)
\(734\) 4.83244 0.178369
\(735\) 0 0
\(736\) −16.6839 −0.614977
\(737\) 7.85896 0.289489
\(738\) 0.819942 0.0301825
\(739\) 19.0598 0.701126 0.350563 0.936539i \(-0.385990\pi\)
0.350563 + 0.936539i \(0.385990\pi\)
\(740\) −0.845172 −0.0310691
\(741\) −0.0417075 −0.00153216
\(742\) 0 0
\(743\) 15.1611 0.556207 0.278104 0.960551i \(-0.410294\pi\)
0.278104 + 0.960551i \(0.410294\pi\)
\(744\) 20.7515 0.760788
\(745\) −5.23594 −0.191830
\(746\) 18.9144 0.692504
\(747\) 11.4541 0.419084
\(748\) −3.95111 −0.144467
\(749\) 0 0
\(750\) −2.69271 −0.0983238
\(751\) −1.92281 −0.0701645 −0.0350822 0.999384i \(-0.511169\pi\)
−0.0350822 + 0.999384i \(0.511169\pi\)
\(752\) −2.57871 −0.0940358
\(753\) −3.83734 −0.139840
\(754\) 0.00817212 0.000297611 0
\(755\) 4.13842 0.150613
\(756\) 0 0
\(757\) −15.5738 −0.566041 −0.283021 0.959114i \(-0.591336\pi\)
−0.283021 + 0.959114i \(0.591336\pi\)
\(758\) 13.1028 0.475914
\(759\) −4.78809 −0.173797
\(760\) 2.29694 0.0833189
\(761\) −52.7733 −1.91303 −0.956515 0.291683i \(-0.905785\pi\)
−0.956515 + 0.291683i \(0.905785\pi\)
\(762\) −13.6191 −0.493369
\(763\) 0 0
\(764\) −7.51850 −0.272010
\(765\) 0.593686 0.0214648
\(766\) −23.3653 −0.844222
\(767\) 0.0232657 0.000840076 0
\(768\) −14.7148 −0.530973
\(769\) 23.4101 0.844189 0.422095 0.906552i \(-0.361295\pi\)
0.422095 + 0.906552i \(0.361295\pi\)
\(770\) 0 0
\(771\) 29.6461 1.06768
\(772\) 26.8044 0.964710
\(773\) −5.06047 −0.182012 −0.0910062 0.995850i \(-0.529008\pi\)
−0.0910062 + 0.995850i \(0.529008\pi\)
\(774\) −10.5465 −0.379085
\(775\) 37.1885 1.33585
\(776\) −17.4842 −0.627646
\(777\) 0 0
\(778\) 3.62819 0.130077
\(779\) −2.53514 −0.0908309
\(780\) −0.00725323 −0.000259707 0
\(781\) 9.66692 0.345910
\(782\) −4.21692 −0.150797
\(783\) 0.605814 0.0216500
\(784\) 0 0
\(785\) −4.86617 −0.173681
\(786\) 7.87961 0.281056
\(787\) −36.6471 −1.30633 −0.653164 0.757216i \(-0.726559\pi\)
−0.653164 + 0.757216i \(0.726559\pi\)
\(788\) −0.634211 −0.0225928
\(789\) −15.0006 −0.534035
\(790\) 1.22376 0.0435395
\(791\) 0 0
\(792\) −4.54164 −0.161380
\(793\) −0.0727976 −0.00258512
\(794\) 25.4673 0.903802
\(795\) 1.27544 0.0452353
\(796\) 4.32340 0.153239
\(797\) −2.67790 −0.0948562 −0.0474281 0.998875i \(-0.515103\pi\)
−0.0474281 + 0.998875i \(0.515103\pi\)
\(798\) 0 0
\(799\) −11.0253 −0.390049
\(800\) −28.3600 −1.00268
\(801\) −5.00144 −0.176717
\(802\) −1.86203 −0.0657507
\(803\) 1.24602 0.0439710
\(804\) −6.26870 −0.221080
\(805\) 0 0
\(806\) −0.102593 −0.00361370
\(807\) −5.76098 −0.202796
\(808\) 48.0061 1.68885
\(809\) −26.0424 −0.915603 −0.457801 0.889055i \(-0.651363\pi\)
−0.457801 + 0.889055i \(0.651363\pi\)
\(810\) 0.272273 0.00956670
\(811\) −0.407542 −0.0143108 −0.00715538 0.999974i \(-0.502278\pi\)
−0.00715538 + 0.999974i \(0.502278\pi\)
\(812\) 0 0
\(813\) 5.41966 0.190076
\(814\) 2.61634 0.0917027
\(815\) −3.48076 −0.121926
\(816\) 0.747619 0.0261719
\(817\) 32.6082 1.14081
\(818\) 4.35701 0.152339
\(819\) 0 0
\(820\) −0.440879 −0.0153962
\(821\) −38.1013 −1.32974 −0.664871 0.746958i \(-0.731514\pi\)
−0.664871 + 0.746958i \(0.731514\pi\)
\(822\) −4.86331 −0.169628
\(823\) −3.55328 −0.123860 −0.0619298 0.998081i \(-0.519725\pi\)
−0.0619298 + 0.998081i \(0.519725\pi\)
\(824\) 10.9385 0.381062
\(825\) −8.13900 −0.283364
\(826\) 0 0
\(827\) 12.3979 0.431118 0.215559 0.976491i \(-0.430843\pi\)
0.215559 + 0.976491i \(0.430843\pi\)
\(828\) 3.81922 0.132727
\(829\) 25.6106 0.889492 0.444746 0.895657i \(-0.353294\pi\)
0.444746 + 0.895657i \(0.353294\pi\)
\(830\) 3.11865 0.108250
\(831\) −20.4003 −0.707678
\(832\) 0.0644787 0.00223540
\(833\) 0 0
\(834\) 16.7014 0.578321
\(835\) 3.13851 0.108613
\(836\) 5.60256 0.193768
\(837\) −7.60543 −0.262882
\(838\) 13.4004 0.462908
\(839\) −20.2672 −0.699703 −0.349851 0.936805i \(-0.613768\pi\)
−0.349851 + 0.936805i \(0.613768\pi\)
\(840\) 0 0
\(841\) −28.6330 −0.987344
\(842\) −6.18264 −0.213068
\(843\) 5.03670 0.173473
\(844\) −0.653521 −0.0224951
\(845\) −4.31674 −0.148500
\(846\) −5.05638 −0.173842
\(847\) 0 0
\(848\) 1.60615 0.0551553
\(849\) 0.733053 0.0251583
\(850\) −7.16810 −0.245864
\(851\) −5.51445 −0.189033
\(852\) −7.71082 −0.264168
\(853\) 17.4438 0.597264 0.298632 0.954368i \(-0.403470\pi\)
0.298632 + 0.954368i \(0.403470\pi\)
\(854\) 0 0
\(855\) −0.841828 −0.0287899
\(856\) 32.4631 1.10957
\(857\) 38.4532 1.31354 0.656769 0.754092i \(-0.271923\pi\)
0.656769 + 0.754092i \(0.271923\pi\)
\(858\) 0.0224534 0.000766545 0
\(859\) −1.73122 −0.0590686 −0.0295343 0.999564i \(-0.509402\pi\)
−0.0295343 + 0.999564i \(0.509402\pi\)
\(860\) 5.67079 0.193372
\(861\) 0 0
\(862\) 6.74237 0.229646
\(863\) −22.5174 −0.766502 −0.383251 0.923644i \(-0.625196\pi\)
−0.383251 + 0.923644i \(0.625196\pi\)
\(864\) 5.79990 0.197317
\(865\) −3.16200 −0.107511
\(866\) 5.00233 0.169986
\(867\) −13.8035 −0.468792
\(868\) 0 0
\(869\) 7.48131 0.253786
\(870\) 0.164947 0.00559222
\(871\) 0.0776769 0.00263198
\(872\) 38.5009 1.30380
\(873\) 6.40794 0.216876
\(874\) 5.97946 0.202258
\(875\) 0 0
\(876\) −0.993886 −0.0335803
\(877\) −4.48494 −0.151446 −0.0757228 0.997129i \(-0.524126\pi\)
−0.0757228 + 0.997129i \(0.524126\pi\)
\(878\) −13.8365 −0.466959
\(879\) 9.92734 0.334841
\(880\) 0.231128 0.00779132
\(881\) −40.1306 −1.35203 −0.676016 0.736887i \(-0.736295\pi\)
−0.676016 + 0.736887i \(0.736295\pi\)
\(882\) 0 0
\(883\) −15.5050 −0.521784 −0.260892 0.965368i \(-0.584017\pi\)
−0.260892 + 0.965368i \(0.584017\pi\)
\(884\) −0.0390522 −0.00131347
\(885\) 0.469597 0.0157853
\(886\) −20.2423 −0.680053
\(887\) −38.3024 −1.28607 −0.643034 0.765838i \(-0.722325\pi\)
−0.643034 + 0.765838i \(0.722325\pi\)
\(888\) −5.23061 −0.175528
\(889\) 0 0
\(890\) −1.36176 −0.0456462
\(891\) 1.66451 0.0557631
\(892\) −9.50381 −0.318211
\(893\) 15.6336 0.523158
\(894\) −12.9288 −0.432403
\(895\) −7.57454 −0.253189
\(896\) 0 0
\(897\) −0.0473248 −0.00158013
\(898\) 1.48815 0.0496601
\(899\) −4.60747 −0.153668
\(900\) 6.49207 0.216402
\(901\) 6.86713 0.228777
\(902\) 1.36480 0.0454429
\(903\) 0 0
\(904\) −9.77730 −0.325188
\(905\) −1.04973 −0.0348943
\(906\) 10.2187 0.339494
\(907\) −47.6553 −1.58237 −0.791184 0.611578i \(-0.790535\pi\)
−0.791184 + 0.611578i \(0.790535\pi\)
\(908\) 9.75348 0.323681
\(909\) −17.5942 −0.583562
\(910\) 0 0
\(911\) −49.7822 −1.64936 −0.824679 0.565601i \(-0.808644\pi\)
−0.824679 + 0.565601i \(0.808644\pi\)
\(912\) −1.06010 −0.0351035
\(913\) 19.0655 0.630975
\(914\) 23.0444 0.762240
\(915\) −1.46935 −0.0485753
\(916\) 13.2247 0.436956
\(917\) 0 0
\(918\) 1.46595 0.0483835
\(919\) 58.0170 1.91381 0.956903 0.290409i \(-0.0937914\pi\)
0.956903 + 0.290409i \(0.0937914\pi\)
\(920\) 2.60630 0.0859272
\(921\) 18.0797 0.595745
\(922\) 22.5835 0.743749
\(923\) 0.0955465 0.00314495
\(924\) 0 0
\(925\) −9.37369 −0.308205
\(926\) −19.5169 −0.641365
\(927\) −4.00896 −0.131672
\(928\) 3.51366 0.115342
\(929\) 57.4678 1.88546 0.942728 0.333561i \(-0.108250\pi\)
0.942728 + 0.333561i \(0.108250\pi\)
\(930\) −2.07075 −0.0679026
\(931\) 0 0
\(932\) 28.2885 0.926620
\(933\) 6.53524 0.213954
\(934\) −3.36950 −0.110254
\(935\) 0.988194 0.0323174
\(936\) −0.0448889 −0.00146724
\(937\) −3.15232 −0.102982 −0.0514909 0.998673i \(-0.516397\pi\)
−0.0514909 + 0.998673i \(0.516397\pi\)
\(938\) 0 0
\(939\) 6.62531 0.216209
\(940\) 2.71879 0.0886773
\(941\) −6.38432 −0.208123 −0.104062 0.994571i \(-0.533184\pi\)
−0.104062 + 0.994571i \(0.533184\pi\)
\(942\) −12.0157 −0.391493
\(943\) −2.87658 −0.0936744
\(944\) 0.591356 0.0192470
\(945\) 0 0
\(946\) −17.5547 −0.570752
\(947\) 4.84026 0.157287 0.0786436 0.996903i \(-0.474941\pi\)
0.0786436 + 0.996903i \(0.474941\pi\)
\(948\) −5.96747 −0.193814
\(949\) 0.0123155 0.000399777 0
\(950\) 10.1641 0.329768
\(951\) 5.00888 0.162424
\(952\) 0 0
\(953\) −47.9739 −1.55403 −0.777014 0.629484i \(-0.783266\pi\)
−0.777014 + 0.629484i \(0.783266\pi\)
\(954\) 3.14937 0.101964
\(955\) 1.88042 0.0608488
\(956\) 14.2216 0.459959
\(957\) 1.00838 0.0325964
\(958\) 9.29680 0.300366
\(959\) 0 0
\(960\) 1.30144 0.0420039
\(961\) 26.8425 0.865887
\(962\) 0.0258596 0.000833745 0
\(963\) −11.8977 −0.383398
\(964\) 20.4302 0.658013
\(965\) −6.70392 −0.215807
\(966\) 0 0
\(967\) 5.25867 0.169107 0.0845537 0.996419i \(-0.473054\pi\)
0.0845537 + 0.996419i \(0.473054\pi\)
\(968\) 22.4541 0.721702
\(969\) −4.53250 −0.145605
\(970\) 1.74471 0.0560193
\(971\) −56.4143 −1.81042 −0.905210 0.424964i \(-0.860287\pi\)
−0.905210 + 0.424964i \(0.860287\pi\)
\(972\) −1.32769 −0.0425858
\(973\) 0 0
\(974\) 8.11320 0.259964
\(975\) −0.0804447 −0.00257629
\(976\) −1.85033 −0.0592277
\(977\) 6.39439 0.204575 0.102287 0.994755i \(-0.467384\pi\)
0.102287 + 0.994755i \(0.467384\pi\)
\(978\) −8.59480 −0.274832
\(979\) −8.32494 −0.266066
\(980\) 0 0
\(981\) −14.1105 −0.450515
\(982\) 20.6906 0.660264
\(983\) 25.9542 0.827809 0.413905 0.910320i \(-0.364165\pi\)
0.413905 + 0.910320i \(0.364165\pi\)
\(984\) −2.72852 −0.0869820
\(985\) 0.158620 0.00505404
\(986\) 0.888092 0.0282826
\(987\) 0 0
\(988\) 0.0553749 0.00176171
\(989\) 36.9999 1.17653
\(990\) 0.453200 0.0144037
\(991\) 48.0216 1.52546 0.762728 0.646719i \(-0.223859\pi\)
0.762728 + 0.646719i \(0.223859\pi\)
\(992\) −44.1107 −1.40052
\(993\) −2.06115 −0.0654086
\(994\) 0 0
\(995\) −1.08131 −0.0342797
\(996\) −15.2076 −0.481870
\(997\) 48.7312 1.54333 0.771667 0.636027i \(-0.219423\pi\)
0.771667 + 0.636027i \(0.219423\pi\)
\(998\) −0.902973 −0.0285831
\(999\) 1.91702 0.0606517
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 \(a_p\))