Properties

Label 4030.2.a.n.1.1
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.08271\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.08271 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.08271 q^{6} -2.62527 q^{7} +1.00000 q^{8} +6.50312 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.08271 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.08271 q^{6} -2.62527 q^{7} +1.00000 q^{8} +6.50312 q^{9} -1.00000 q^{10} +0.190183 q^{11} -3.08271 q^{12} -1.00000 q^{13} -2.62527 q^{14} +3.08271 q^{15} +1.00000 q^{16} -6.93705 q^{17} +6.50312 q^{18} -0.237470 q^{19} -1.00000 q^{20} +8.09297 q^{21} +0.190183 q^{22} +4.00840 q^{23} -3.08271 q^{24} +1.00000 q^{25} -1.00000 q^{26} -10.7991 q^{27} -2.62527 q^{28} +0.0461297 q^{29} +3.08271 q^{30} -1.00000 q^{31} +1.00000 q^{32} -0.586281 q^{33} -6.93705 q^{34} +2.62527 q^{35} +6.50312 q^{36} -9.02092 q^{37} -0.237470 q^{38} +3.08271 q^{39} -1.00000 q^{40} -2.50696 q^{41} +8.09297 q^{42} -2.72309 q^{43} +0.190183 q^{44} -6.50312 q^{45} +4.00840 q^{46} -10.0962 q^{47} -3.08271 q^{48} -0.107936 q^{49} +1.00000 q^{50} +21.3849 q^{51} -1.00000 q^{52} -1.99103 q^{53} -10.7991 q^{54} -0.190183 q^{55} -2.62527 q^{56} +0.732053 q^{57} +0.0461297 q^{58} +10.7728 q^{59} +3.08271 q^{60} +0.753431 q^{61} -1.00000 q^{62} -17.0725 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.586281 q^{66} +13.2211 q^{67} -6.93705 q^{68} -12.3568 q^{69} +2.62527 q^{70} +6.14349 q^{71} +6.50312 q^{72} -5.91955 q^{73} -9.02092 q^{74} -3.08271 q^{75} -0.237470 q^{76} -0.499284 q^{77} +3.08271 q^{78} +0.817179 q^{79} -1.00000 q^{80} +13.7812 q^{81} -2.50696 q^{82} +0.435097 q^{83} +8.09297 q^{84} +6.93705 q^{85} -2.72309 q^{86} -0.142205 q^{87} +0.190183 q^{88} -1.09084 q^{89} -6.50312 q^{90} +2.62527 q^{91} +4.00840 q^{92} +3.08271 q^{93} -10.0962 q^{94} +0.237470 q^{95} -3.08271 q^{96} +8.17526 q^{97} -0.107936 q^{98} +1.23679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.08271 −1.77980 −0.889902 0.456151i \(-0.849228\pi\)
−0.889902 + 0.456151i \(0.849228\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −3.08271 −1.25851
\(7\) −2.62527 −0.992260 −0.496130 0.868248i \(-0.665246\pi\)
−0.496130 + 0.868248i \(0.665246\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.50312 2.16771
\(10\) −1.00000 −0.316228
\(11\) 0.190183 0.0573425 0.0286712 0.999589i \(-0.490872\pi\)
0.0286712 + 0.999589i \(0.490872\pi\)
\(12\) −3.08271 −0.889902
\(13\) −1.00000 −0.277350
\(14\) −2.62527 −0.701634
\(15\) 3.08271 0.795953
\(16\) 1.00000 0.250000
\(17\) −6.93705 −1.68248 −0.841241 0.540660i \(-0.818174\pi\)
−0.841241 + 0.540660i \(0.818174\pi\)
\(18\) 6.50312 1.53280
\(19\) −0.237470 −0.0544794 −0.0272397 0.999629i \(-0.508672\pi\)
−0.0272397 + 0.999629i \(0.508672\pi\)
\(20\) −1.00000 −0.223607
\(21\) 8.09297 1.76603
\(22\) 0.190183 0.0405472
\(23\) 4.00840 0.835810 0.417905 0.908491i \(-0.362765\pi\)
0.417905 + 0.908491i \(0.362765\pi\)
\(24\) −3.08271 −0.629256
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) −10.7991 −2.07829
\(28\) −2.62527 −0.496130
\(29\) 0.0461297 0.00856607 0.00428303 0.999991i \(-0.498637\pi\)
0.00428303 + 0.999991i \(0.498637\pi\)
\(30\) 3.08271 0.562824
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −0.586281 −0.102058
\(34\) −6.93705 −1.18969
\(35\) 2.62527 0.443752
\(36\) 6.50312 1.08385
\(37\) −9.02092 −1.48303 −0.741515 0.670936i \(-0.765892\pi\)
−0.741515 + 0.670936i \(0.765892\pi\)
\(38\) −0.237470 −0.0385228
\(39\) 3.08271 0.493629
\(40\) −1.00000 −0.158114
\(41\) −2.50696 −0.391522 −0.195761 0.980652i \(-0.562718\pi\)
−0.195761 + 0.980652i \(0.562718\pi\)
\(42\) 8.09297 1.24877
\(43\) −2.72309 −0.415267 −0.207633 0.978207i \(-0.566576\pi\)
−0.207633 + 0.978207i \(0.566576\pi\)
\(44\) 0.190183 0.0286712
\(45\) −6.50312 −0.969427
\(46\) 4.00840 0.591007
\(47\) −10.0962 −1.47268 −0.736341 0.676611i \(-0.763448\pi\)
−0.736341 + 0.676611i \(0.763448\pi\)
\(48\) −3.08271 −0.444951
\(49\) −0.107936 −0.0154195
\(50\) 1.00000 0.141421
\(51\) 21.3849 2.99449
\(52\) −1.00000 −0.138675
\(53\) −1.99103 −0.273489 −0.136745 0.990606i \(-0.543664\pi\)
−0.136745 + 0.990606i \(0.543664\pi\)
\(54\) −10.7991 −1.46957
\(55\) −0.190183 −0.0256443
\(56\) −2.62527 −0.350817
\(57\) 0.732053 0.0969628
\(58\) 0.0461297 0.00605712
\(59\) 10.7728 1.40250 0.701248 0.712917i \(-0.252627\pi\)
0.701248 + 0.712917i \(0.252627\pi\)
\(60\) 3.08271 0.397976
\(61\) 0.753431 0.0964670 0.0482335 0.998836i \(-0.484641\pi\)
0.0482335 + 0.998836i \(0.484641\pi\)
\(62\) −1.00000 −0.127000
\(63\) −17.0725 −2.15093
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) −0.586281 −0.0721662
\(67\) 13.2211 1.61522 0.807608 0.589719i \(-0.200762\pi\)
0.807608 + 0.589719i \(0.200762\pi\)
\(68\) −6.93705 −0.841241
\(69\) −12.3568 −1.48758
\(70\) 2.62527 0.313780
\(71\) 6.14349 0.729098 0.364549 0.931184i \(-0.381223\pi\)
0.364549 + 0.931184i \(0.381223\pi\)
\(72\) 6.50312 0.766400
\(73\) −5.91955 −0.692831 −0.346415 0.938081i \(-0.612601\pi\)
−0.346415 + 0.938081i \(0.612601\pi\)
\(74\) −9.02092 −1.04866
\(75\) −3.08271 −0.355961
\(76\) −0.237470 −0.0272397
\(77\) −0.499284 −0.0568986
\(78\) 3.08271 0.349048
\(79\) 0.817179 0.0919398 0.0459699 0.998943i \(-0.485362\pi\)
0.0459699 + 0.998943i \(0.485362\pi\)
\(80\) −1.00000 −0.111803
\(81\) 13.7812 1.53124
\(82\) −2.50696 −0.276848
\(83\) 0.435097 0.0477581 0.0238791 0.999715i \(-0.492398\pi\)
0.0238791 + 0.999715i \(0.492398\pi\)
\(84\) 8.09297 0.883015
\(85\) 6.93705 0.752429
\(86\) −2.72309 −0.293638
\(87\) −0.142205 −0.0152459
\(88\) 0.190183 0.0202736
\(89\) −1.09084 −0.115629 −0.0578145 0.998327i \(-0.518413\pi\)
−0.0578145 + 0.998327i \(0.518413\pi\)
\(90\) −6.50312 −0.685489
\(91\) 2.62527 0.275203
\(92\) 4.00840 0.417905
\(93\) 3.08271 0.319662
\(94\) −10.0962 −1.04134
\(95\) 0.237470 0.0243639
\(96\) −3.08271 −0.314628
\(97\) 8.17526 0.830072 0.415036 0.909805i \(-0.363769\pi\)
0.415036 + 0.909805i \(0.363769\pi\)
\(98\) −0.107936 −0.0109032
\(99\) 1.23679 0.124302
\(100\) 1.00000 0.100000
\(101\) −5.96499 −0.593538 −0.296769 0.954949i \(-0.595909\pi\)
−0.296769 + 0.954949i \(0.595909\pi\)
\(102\) 21.3849 2.11742
\(103\) 14.3243 1.41141 0.705707 0.708504i \(-0.250629\pi\)
0.705707 + 0.708504i \(0.250629\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −8.09297 −0.789793
\(106\) −1.99103 −0.193386
\(107\) −1.30962 −0.126606 −0.0633028 0.997994i \(-0.520163\pi\)
−0.0633028 + 0.997994i \(0.520163\pi\)
\(108\) −10.7991 −1.03914
\(109\) −0.402902 −0.0385910 −0.0192955 0.999814i \(-0.506142\pi\)
−0.0192955 + 0.999814i \(0.506142\pi\)
\(110\) −0.190183 −0.0181333
\(111\) 27.8089 2.63950
\(112\) −2.62527 −0.248065
\(113\) 2.66374 0.250584 0.125292 0.992120i \(-0.460013\pi\)
0.125292 + 0.992120i \(0.460013\pi\)
\(114\) 0.732053 0.0685630
\(115\) −4.00840 −0.373786
\(116\) 0.0461297 0.00428303
\(117\) −6.50312 −0.601213
\(118\) 10.7728 0.991714
\(119\) 18.2117 1.66946
\(120\) 3.08271 0.281412
\(121\) −10.9638 −0.996712
\(122\) 0.753431 0.0682124
\(123\) 7.72824 0.696832
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −17.0725 −1.52094
\(127\) 10.3607 0.919366 0.459683 0.888083i \(-0.347963\pi\)
0.459683 + 0.888083i \(0.347963\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.39449 0.739094
\(130\) 1.00000 0.0877058
\(131\) −10.1846 −0.889836 −0.444918 0.895571i \(-0.646767\pi\)
−0.444918 + 0.895571i \(0.646767\pi\)
\(132\) −0.586281 −0.0510292
\(133\) 0.623425 0.0540578
\(134\) 13.2211 1.14213
\(135\) 10.7991 0.929439
\(136\) −6.93705 −0.594847
\(137\) 6.23374 0.532584 0.266292 0.963892i \(-0.414201\pi\)
0.266292 + 0.963892i \(0.414201\pi\)
\(138\) −12.3568 −1.05188
\(139\) 3.87231 0.328445 0.164222 0.986423i \(-0.447489\pi\)
0.164222 + 0.986423i \(0.447489\pi\)
\(140\) 2.62527 0.221876
\(141\) 31.1237 2.62109
\(142\) 6.14349 0.515550
\(143\) −0.190183 −0.0159039
\(144\) 6.50312 0.541926
\(145\) −0.0461297 −0.00383086
\(146\) −5.91955 −0.489905
\(147\) 0.332736 0.0274436
\(148\) −9.02092 −0.741515
\(149\) 15.1295 1.23946 0.619729 0.784816i \(-0.287243\pi\)
0.619729 + 0.784816i \(0.287243\pi\)
\(150\) −3.08271 −0.251702
\(151\) 8.12239 0.660991 0.330495 0.943808i \(-0.392784\pi\)
0.330495 + 0.943808i \(0.392784\pi\)
\(152\) −0.237470 −0.0192614
\(153\) −45.1124 −3.64713
\(154\) −0.499284 −0.0402334
\(155\) 1.00000 0.0803219
\(156\) 3.08271 0.246815
\(157\) 19.0833 1.52301 0.761507 0.648157i \(-0.224460\pi\)
0.761507 + 0.648157i \(0.224460\pi\)
\(158\) 0.817179 0.0650113
\(159\) 6.13778 0.486758
\(160\) −1.00000 −0.0790569
\(161\) −10.5232 −0.829341
\(162\) 13.7812 1.08275
\(163\) −4.24035 −0.332130 −0.166065 0.986115i \(-0.553106\pi\)
−0.166065 + 0.986115i \(0.553106\pi\)
\(164\) −2.50696 −0.195761
\(165\) 0.586281 0.0456419
\(166\) 0.435097 0.0337701
\(167\) 13.5092 1.04537 0.522687 0.852524i \(-0.324929\pi\)
0.522687 + 0.852524i \(0.324929\pi\)
\(168\) 8.09297 0.624386
\(169\) 1.00000 0.0769231
\(170\) 6.93705 0.532047
\(171\) −1.54430 −0.118095
\(172\) −2.72309 −0.207633
\(173\) 1.08997 0.0828688 0.0414344 0.999141i \(-0.486807\pi\)
0.0414344 + 0.999141i \(0.486807\pi\)
\(174\) −0.142205 −0.0107805
\(175\) −2.62527 −0.198452
\(176\) 0.190183 0.0143356
\(177\) −33.2094 −2.49617
\(178\) −1.09084 −0.0817620
\(179\) 12.1337 0.906915 0.453457 0.891278i \(-0.350190\pi\)
0.453457 + 0.891278i \(0.350190\pi\)
\(180\) −6.50312 −0.484714
\(181\) 3.25448 0.241904 0.120952 0.992658i \(-0.461405\pi\)
0.120952 + 0.992658i \(0.461405\pi\)
\(182\) 2.62527 0.194598
\(183\) −2.32261 −0.171692
\(184\) 4.00840 0.295503
\(185\) 9.02092 0.663231
\(186\) 3.08271 0.226035
\(187\) −1.31931 −0.0964776
\(188\) −10.0962 −0.736341
\(189\) 28.3506 2.06220
\(190\) 0.237470 0.0172279
\(191\) −10.6539 −0.770892 −0.385446 0.922730i \(-0.625952\pi\)
−0.385446 + 0.922730i \(0.625952\pi\)
\(192\) −3.08271 −0.222476
\(193\) −12.5653 −0.904472 −0.452236 0.891898i \(-0.649374\pi\)
−0.452236 + 0.891898i \(0.649374\pi\)
\(194\) 8.17526 0.586950
\(195\) −3.08271 −0.220758
\(196\) −0.107936 −0.00770973
\(197\) 9.06106 0.645574 0.322787 0.946472i \(-0.395380\pi\)
0.322787 + 0.946472i \(0.395380\pi\)
\(198\) 1.23679 0.0878945
\(199\) 25.5763 1.81305 0.906527 0.422148i \(-0.138724\pi\)
0.906527 + 0.422148i \(0.138724\pi\)
\(200\) 1.00000 0.0707107
\(201\) −40.7569 −2.87477
\(202\) −5.96499 −0.419695
\(203\) −0.121103 −0.00849977
\(204\) 21.3849 1.49724
\(205\) 2.50696 0.175094
\(206\) 14.3243 0.998021
\(207\) 26.0671 1.81179
\(208\) −1.00000 −0.0693375
\(209\) −0.0451629 −0.00312399
\(210\) −8.09297 −0.558468
\(211\) 8.79692 0.605605 0.302802 0.953053i \(-0.402078\pi\)
0.302802 + 0.953053i \(0.402078\pi\)
\(212\) −1.99103 −0.136745
\(213\) −18.9386 −1.29765
\(214\) −1.30962 −0.0895237
\(215\) 2.72309 0.185713
\(216\) −10.7991 −0.734786
\(217\) 2.62527 0.178215
\(218\) −0.402902 −0.0272880
\(219\) 18.2483 1.23310
\(220\) −0.190183 −0.0128222
\(221\) 6.93705 0.466637
\(222\) 27.8089 1.86641
\(223\) −26.7938 −1.79425 −0.897124 0.441779i \(-0.854347\pi\)
−0.897124 + 0.441779i \(0.854347\pi\)
\(224\) −2.62527 −0.175409
\(225\) 6.50312 0.433541
\(226\) 2.66374 0.177189
\(227\) 10.2446 0.679958 0.339979 0.940433i \(-0.389580\pi\)
0.339979 + 0.940433i \(0.389580\pi\)
\(228\) 0.732053 0.0484814
\(229\) −11.9399 −0.789010 −0.394505 0.918894i \(-0.629084\pi\)
−0.394505 + 0.918894i \(0.629084\pi\)
\(230\) −4.00840 −0.264306
\(231\) 1.53915 0.101268
\(232\) 0.0461297 0.00302856
\(233\) 25.8498 1.69348 0.846739 0.532008i \(-0.178562\pi\)
0.846739 + 0.532008i \(0.178562\pi\)
\(234\) −6.50312 −0.425122
\(235\) 10.0962 0.658603
\(236\) 10.7728 0.701248
\(237\) −2.51913 −0.163635
\(238\) 18.2117 1.18049
\(239\) −4.74305 −0.306802 −0.153401 0.988164i \(-0.549023\pi\)
−0.153401 + 0.988164i \(0.549023\pi\)
\(240\) 3.08271 0.198988
\(241\) −5.76720 −0.371498 −0.185749 0.982597i \(-0.559471\pi\)
−0.185749 + 0.982597i \(0.559471\pi\)
\(242\) −10.9638 −0.704782
\(243\) −10.0861 −0.647024
\(244\) 0.753431 0.0482335
\(245\) 0.107936 0.00689579
\(246\) 7.72824 0.492735
\(247\) 0.237470 0.0151099
\(248\) −1.00000 −0.0635001
\(249\) −1.34128 −0.0850001
\(250\) −1.00000 −0.0632456
\(251\) 21.6019 1.36350 0.681751 0.731584i \(-0.261219\pi\)
0.681751 + 0.731584i \(0.261219\pi\)
\(252\) −17.0725 −1.07546
\(253\) 0.762332 0.0479274
\(254\) 10.3607 0.650090
\(255\) −21.3849 −1.33918
\(256\) 1.00000 0.0625000
\(257\) 15.1584 0.945556 0.472778 0.881182i \(-0.343251\pi\)
0.472778 + 0.881182i \(0.343251\pi\)
\(258\) 8.39449 0.522618
\(259\) 23.6824 1.47155
\(260\) 1.00000 0.0620174
\(261\) 0.299987 0.0185687
\(262\) −10.1846 −0.629209
\(263\) 1.44308 0.0889843 0.0444921 0.999010i \(-0.485833\pi\)
0.0444921 + 0.999010i \(0.485833\pi\)
\(264\) −0.586281 −0.0360831
\(265\) 1.99103 0.122308
\(266\) 0.623425 0.0382246
\(267\) 3.36275 0.205797
\(268\) 13.2211 0.807608
\(269\) −9.94188 −0.606167 −0.303084 0.952964i \(-0.598016\pi\)
−0.303084 + 0.952964i \(0.598016\pi\)
\(270\) 10.7991 0.657212
\(271\) 23.9828 1.45685 0.728427 0.685124i \(-0.240252\pi\)
0.728427 + 0.685124i \(0.240252\pi\)
\(272\) −6.93705 −0.420620
\(273\) −8.09297 −0.489809
\(274\) 6.23374 0.376594
\(275\) 0.190183 0.0114685
\(276\) −12.3568 −0.743789
\(277\) −14.2200 −0.854394 −0.427197 0.904158i \(-0.640499\pi\)
−0.427197 + 0.904158i \(0.640499\pi\)
\(278\) 3.87231 0.232246
\(279\) −6.50312 −0.389331
\(280\) 2.62527 0.156890
\(281\) 15.7629 0.940339 0.470169 0.882576i \(-0.344193\pi\)
0.470169 + 0.882576i \(0.344193\pi\)
\(282\) 31.1237 1.85339
\(283\) −18.2060 −1.08223 −0.541117 0.840947i \(-0.681999\pi\)
−0.541117 + 0.840947i \(0.681999\pi\)
\(284\) 6.14349 0.364549
\(285\) −0.732053 −0.0433631
\(286\) −0.190183 −0.0112458
\(287\) 6.58146 0.388492
\(288\) 6.50312 0.383200
\(289\) 31.1227 1.83075
\(290\) −0.0461297 −0.00270883
\(291\) −25.2020 −1.47737
\(292\) −5.91955 −0.346415
\(293\) 13.6870 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(294\) 0.332736 0.0194056
\(295\) −10.7728 −0.627215
\(296\) −9.02092 −0.524330
\(297\) −2.05381 −0.119174
\(298\) 15.1295 0.876429
\(299\) −4.00840 −0.231812
\(300\) −3.08271 −0.177980
\(301\) 7.14884 0.412053
\(302\) 8.12239 0.467391
\(303\) 18.3883 1.05638
\(304\) −0.237470 −0.0136199
\(305\) −0.753431 −0.0431413
\(306\) −45.1124 −2.57891
\(307\) 20.5185 1.17105 0.585527 0.810653i \(-0.300888\pi\)
0.585527 + 0.810653i \(0.300888\pi\)
\(308\) −0.499284 −0.0284493
\(309\) −44.1577 −2.51204
\(310\) 1.00000 0.0567962
\(311\) −18.9628 −1.07528 −0.537642 0.843173i \(-0.680685\pi\)
−0.537642 + 0.843173i \(0.680685\pi\)
\(312\) 3.08271 0.174524
\(313\) −15.8179 −0.894080 −0.447040 0.894514i \(-0.647522\pi\)
−0.447040 + 0.894514i \(0.647522\pi\)
\(314\) 19.0833 1.07693
\(315\) 17.0725 0.961924
\(316\) 0.817179 0.0459699
\(317\) 31.6064 1.77519 0.887595 0.460624i \(-0.152374\pi\)
0.887595 + 0.460624i \(0.152374\pi\)
\(318\) 6.13778 0.344190
\(319\) 0.00877310 0.000491199 0
\(320\) −1.00000 −0.0559017
\(321\) 4.03718 0.225333
\(322\) −10.5232 −0.586433
\(323\) 1.64734 0.0916607
\(324\) 13.7812 0.765621
\(325\) −1.00000 −0.0554700
\(326\) −4.24035 −0.234851
\(327\) 1.24203 0.0686845
\(328\) −2.50696 −0.138424
\(329\) 26.5053 1.46128
\(330\) 0.586281 0.0322737
\(331\) 16.2940 0.895600 0.447800 0.894134i \(-0.352208\pi\)
0.447800 + 0.894134i \(0.352208\pi\)
\(332\) 0.435097 0.0238791
\(333\) −58.6641 −3.21477
\(334\) 13.5092 0.739192
\(335\) −13.2211 −0.722347
\(336\) 8.09297 0.441507
\(337\) 15.4158 0.839753 0.419876 0.907581i \(-0.362073\pi\)
0.419876 + 0.907581i \(0.362073\pi\)
\(338\) 1.00000 0.0543928
\(339\) −8.21155 −0.445990
\(340\) 6.93705 0.376214
\(341\) −0.190183 −0.0102990
\(342\) −1.54430 −0.0835061
\(343\) 18.6603 1.00756
\(344\) −2.72309 −0.146819
\(345\) 12.3568 0.665265
\(346\) 1.08997 0.0585971
\(347\) 7.68442 0.412521 0.206261 0.978497i \(-0.433871\pi\)
0.206261 + 0.978497i \(0.433871\pi\)
\(348\) −0.142205 −0.00762296
\(349\) 16.5847 0.887760 0.443880 0.896086i \(-0.353602\pi\)
0.443880 + 0.896086i \(0.353602\pi\)
\(350\) −2.62527 −0.140327
\(351\) 10.7991 0.576413
\(352\) 0.190183 0.0101368
\(353\) −33.2411 −1.76925 −0.884623 0.466307i \(-0.845584\pi\)
−0.884623 + 0.466307i \(0.845584\pi\)
\(354\) −33.2094 −1.76506
\(355\) −6.14349 −0.326063
\(356\) −1.09084 −0.0578145
\(357\) −56.1413 −2.97131
\(358\) 12.1337 0.641286
\(359\) 21.8698 1.15424 0.577121 0.816658i \(-0.304176\pi\)
0.577121 + 0.816658i \(0.304176\pi\)
\(360\) −6.50312 −0.342744
\(361\) −18.9436 −0.997032
\(362\) 3.25448 0.171052
\(363\) 33.7983 1.77395
\(364\) 2.62527 0.137602
\(365\) 5.91955 0.309843
\(366\) −2.32261 −0.121405
\(367\) −33.8742 −1.76822 −0.884108 0.467282i \(-0.845233\pi\)
−0.884108 + 0.467282i \(0.845233\pi\)
\(368\) 4.00840 0.208952
\(369\) −16.3031 −0.848704
\(370\) 9.02092 0.468975
\(371\) 5.22701 0.271373
\(372\) 3.08271 0.159831
\(373\) −15.7122 −0.813549 −0.406775 0.913529i \(-0.633347\pi\)
−0.406775 + 0.913529i \(0.633347\pi\)
\(374\) −1.31931 −0.0682200
\(375\) 3.08271 0.159191
\(376\) −10.0962 −0.520672
\(377\) −0.0461297 −0.00237580
\(378\) 28.3506 1.45820
\(379\) 4.04448 0.207751 0.103875 0.994590i \(-0.466876\pi\)
0.103875 + 0.994590i \(0.466876\pi\)
\(380\) 0.237470 0.0121820
\(381\) −31.9391 −1.63629
\(382\) −10.6539 −0.545103
\(383\) 2.70970 0.138459 0.0692296 0.997601i \(-0.477946\pi\)
0.0692296 + 0.997601i \(0.477946\pi\)
\(384\) −3.08271 −0.157314
\(385\) 0.499284 0.0254458
\(386\) −12.5653 −0.639559
\(387\) −17.7085 −0.900176
\(388\) 8.17526 0.415036
\(389\) 14.2920 0.724632 0.362316 0.932055i \(-0.381986\pi\)
0.362316 + 0.932055i \(0.381986\pi\)
\(390\) −3.08271 −0.156099
\(391\) −27.8065 −1.40624
\(392\) −0.107936 −0.00545160
\(393\) 31.3963 1.58374
\(394\) 9.06106 0.456489
\(395\) −0.817179 −0.0411167
\(396\) 1.23679 0.0621508
\(397\) −3.48803 −0.175059 −0.0875295 0.996162i \(-0.527897\pi\)
−0.0875295 + 0.996162i \(0.527897\pi\)
\(398\) 25.5763 1.28202
\(399\) −1.92184 −0.0962123
\(400\) 1.00000 0.0500000
\(401\) −20.2318 −1.01033 −0.505165 0.863023i \(-0.668568\pi\)
−0.505165 + 0.863023i \(0.668568\pi\)
\(402\) −40.7569 −2.03277
\(403\) 1.00000 0.0498135
\(404\) −5.96499 −0.296769
\(405\) −13.7812 −0.684792
\(406\) −0.121103 −0.00601024
\(407\) −1.71563 −0.0850406
\(408\) 21.3849 1.05871
\(409\) 26.7867 1.32452 0.662259 0.749275i \(-0.269598\pi\)
0.662259 + 0.749275i \(0.269598\pi\)
\(410\) 2.50696 0.123810
\(411\) −19.2168 −0.947896
\(412\) 14.3243 0.705707
\(413\) −28.2815 −1.39164
\(414\) 26.0671 1.28113
\(415\) −0.435097 −0.0213581
\(416\) −1.00000 −0.0490290
\(417\) −11.9372 −0.584568
\(418\) −0.0451629 −0.00220899
\(419\) −37.0735 −1.81116 −0.905579 0.424177i \(-0.860563\pi\)
−0.905579 + 0.424177i \(0.860563\pi\)
\(420\) −8.09297 −0.394896
\(421\) 8.02881 0.391300 0.195650 0.980674i \(-0.437318\pi\)
0.195650 + 0.980674i \(0.437318\pi\)
\(422\) 8.79692 0.428227
\(423\) −65.6567 −3.19234
\(424\) −1.99103 −0.0966931
\(425\) −6.93705 −0.336496
\(426\) −18.9386 −0.917579
\(427\) −1.97796 −0.0957203
\(428\) −1.30962 −0.0633028
\(429\) 0.586281 0.0283059
\(430\) 2.72309 0.131319
\(431\) −25.3589 −1.22149 −0.610746 0.791826i \(-0.709131\pi\)
−0.610746 + 0.791826i \(0.709131\pi\)
\(432\) −10.7991 −0.519572
\(433\) −28.3882 −1.36425 −0.682125 0.731236i \(-0.738944\pi\)
−0.682125 + 0.731236i \(0.738944\pi\)
\(434\) 2.62527 0.126017
\(435\) 0.142205 0.00681819
\(436\) −0.402902 −0.0192955
\(437\) −0.951877 −0.0455345
\(438\) 18.2483 0.871936
\(439\) −18.2165 −0.869427 −0.434713 0.900569i \(-0.643150\pi\)
−0.434713 + 0.900569i \(0.643150\pi\)
\(440\) −0.190183 −0.00906664
\(441\) −0.701922 −0.0334248
\(442\) 6.93705 0.329962
\(443\) −19.5676 −0.929683 −0.464842 0.885394i \(-0.653889\pi\)
−0.464842 + 0.885394i \(0.653889\pi\)
\(444\) 27.8089 1.31975
\(445\) 1.09084 0.0517108
\(446\) −26.7938 −1.26872
\(447\) −46.6399 −2.20599
\(448\) −2.62527 −0.124033
\(449\) −8.23469 −0.388619 −0.194310 0.980940i \(-0.562247\pi\)
−0.194310 + 0.980940i \(0.562247\pi\)
\(450\) 6.50312 0.306560
\(451\) −0.476783 −0.0224508
\(452\) 2.66374 0.125292
\(453\) −25.0390 −1.17643
\(454\) 10.2446 0.480803
\(455\) −2.62527 −0.123075
\(456\) 0.732053 0.0342815
\(457\) −24.4634 −1.14435 −0.572175 0.820131i \(-0.693900\pi\)
−0.572175 + 0.820131i \(0.693900\pi\)
\(458\) −11.9399 −0.557914
\(459\) 74.9139 3.49668
\(460\) −4.00840 −0.186893
\(461\) −8.11358 −0.377887 −0.188944 0.981988i \(-0.560506\pi\)
−0.188944 + 0.981988i \(0.560506\pi\)
\(462\) 1.53915 0.0716076
\(463\) 10.0863 0.468749 0.234375 0.972146i \(-0.424696\pi\)
0.234375 + 0.972146i \(0.424696\pi\)
\(464\) 0.0461297 0.00214152
\(465\) −3.08271 −0.142957
\(466\) 25.8498 1.19747
\(467\) 25.0000 1.15686 0.578432 0.815731i \(-0.303665\pi\)
0.578432 + 0.815731i \(0.303665\pi\)
\(468\) −6.50312 −0.300607
\(469\) −34.7091 −1.60272
\(470\) 10.0962 0.465703
\(471\) −58.8283 −2.71067
\(472\) 10.7728 0.495857
\(473\) −0.517886 −0.0238124
\(474\) −2.51913 −0.115707
\(475\) −0.237470 −0.0108959
\(476\) 18.2117 0.834730
\(477\) −12.9479 −0.592844
\(478\) −4.74305 −0.216942
\(479\) −26.5870 −1.21479 −0.607395 0.794400i \(-0.707785\pi\)
−0.607395 + 0.794400i \(0.707785\pi\)
\(480\) 3.08271 0.140706
\(481\) 9.02092 0.411319
\(482\) −5.76720 −0.262689
\(483\) 32.4399 1.47607
\(484\) −10.9638 −0.498356
\(485\) −8.17526 −0.371220
\(486\) −10.0861 −0.457515
\(487\) −6.50732 −0.294875 −0.147437 0.989071i \(-0.547103\pi\)
−0.147437 + 0.989071i \(0.547103\pi\)
\(488\) 0.753431 0.0341062
\(489\) 13.0718 0.591126
\(490\) 0.107936 0.00487606
\(491\) −30.5048 −1.37666 −0.688331 0.725397i \(-0.741656\pi\)
−0.688331 + 0.725397i \(0.741656\pi\)
\(492\) 7.72824 0.348416
\(493\) −0.320004 −0.0144123
\(494\) 0.237470 0.0106843
\(495\) −1.23679 −0.0555894
\(496\) −1.00000 −0.0449013
\(497\) −16.1284 −0.723455
\(498\) −1.34128 −0.0601042
\(499\) 12.5736 0.562873 0.281437 0.959580i \(-0.409189\pi\)
0.281437 + 0.959580i \(0.409189\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −41.6450 −1.86056
\(502\) 21.6019 0.964142
\(503\) 10.9320 0.487436 0.243718 0.969846i \(-0.421633\pi\)
0.243718 + 0.969846i \(0.421633\pi\)
\(504\) −17.0725 −0.760468
\(505\) 5.96499 0.265438
\(506\) 0.762332 0.0338898
\(507\) −3.08271 −0.136908
\(508\) 10.3607 0.459683
\(509\) 21.9412 0.972525 0.486263 0.873813i \(-0.338360\pi\)
0.486263 + 0.873813i \(0.338360\pi\)
\(510\) −21.3849 −0.946941
\(511\) 15.5404 0.687468
\(512\) 1.00000 0.0441942
\(513\) 2.56447 0.113224
\(514\) 15.1584 0.668609
\(515\) −14.3243 −0.631204
\(516\) 8.39449 0.369547
\(517\) −1.92013 −0.0844472
\(518\) 23.6824 1.04054
\(519\) −3.36006 −0.147490
\(520\) 1.00000 0.0438529
\(521\) 10.7473 0.470849 0.235424 0.971893i \(-0.424352\pi\)
0.235424 + 0.971893i \(0.424352\pi\)
\(522\) 0.299987 0.0131301
\(523\) 12.7032 0.555472 0.277736 0.960658i \(-0.410416\pi\)
0.277736 + 0.960658i \(0.410416\pi\)
\(524\) −10.1846 −0.444918
\(525\) 8.09297 0.353206
\(526\) 1.44308 0.0629214
\(527\) 6.93705 0.302183
\(528\) −0.586281 −0.0255146
\(529\) −6.93270 −0.301422
\(530\) 1.99103 0.0864849
\(531\) 70.0566 3.04020
\(532\) 0.623425 0.0270289
\(533\) 2.50696 0.108589
\(534\) 3.36275 0.145520
\(535\) 1.30962 0.0566198
\(536\) 13.2211 0.571065
\(537\) −37.4047 −1.61413
\(538\) −9.94188 −0.428625
\(539\) −0.0205277 −0.000884189 0
\(540\) 10.7991 0.464719
\(541\) 4.21317 0.181138 0.0905692 0.995890i \(-0.471131\pi\)
0.0905692 + 0.995890i \(0.471131\pi\)
\(542\) 23.9828 1.03015
\(543\) −10.0326 −0.430541
\(544\) −6.93705 −0.297424
\(545\) 0.402902 0.0172584
\(546\) −8.09297 −0.346347
\(547\) 34.7736 1.48681 0.743406 0.668841i \(-0.233209\pi\)
0.743406 + 0.668841i \(0.233209\pi\)
\(548\) 6.23374 0.266292
\(549\) 4.89965 0.209112
\(550\) 0.190183 0.00810945
\(551\) −0.0109544 −0.000466674 0
\(552\) −12.3568 −0.525938
\(553\) −2.14532 −0.0912282
\(554\) −14.2200 −0.604148
\(555\) −27.8089 −1.18042
\(556\) 3.87231 0.164222
\(557\) −28.6834 −1.21535 −0.607677 0.794184i \(-0.707899\pi\)
−0.607677 + 0.794184i \(0.707899\pi\)
\(558\) −6.50312 −0.275299
\(559\) 2.72309 0.115174
\(560\) 2.62527 0.110938
\(561\) 4.06706 0.171711
\(562\) 15.7629 0.664920
\(563\) 38.6802 1.63018 0.815089 0.579336i \(-0.196688\pi\)
0.815089 + 0.579336i \(0.196688\pi\)
\(564\) 31.1237 1.31054
\(565\) −2.66374 −0.112064
\(566\) −18.2060 −0.765256
\(567\) −36.1794 −1.51939
\(568\) 6.14349 0.257775
\(569\) −32.2884 −1.35360 −0.676801 0.736166i \(-0.736634\pi\)
−0.676801 + 0.736166i \(0.736634\pi\)
\(570\) −0.732053 −0.0306623
\(571\) 23.4429 0.981056 0.490528 0.871425i \(-0.336804\pi\)
0.490528 + 0.871425i \(0.336804\pi\)
\(572\) −0.190183 −0.00795197
\(573\) 32.8430 1.37204
\(574\) 6.58146 0.274705
\(575\) 4.00840 0.167162
\(576\) 6.50312 0.270963
\(577\) −41.4785 −1.72677 −0.863387 0.504543i \(-0.831661\pi\)
−0.863387 + 0.504543i \(0.831661\pi\)
\(578\) 31.1227 1.29453
\(579\) 38.7353 1.60978
\(580\) −0.0461297 −0.00191543
\(581\) −1.14225 −0.0473885
\(582\) −25.2020 −1.04466
\(583\) −0.378661 −0.0156825
\(584\) −5.91955 −0.244953
\(585\) 6.50312 0.268871
\(586\) 13.6870 0.565405
\(587\) 11.7320 0.484232 0.242116 0.970247i \(-0.422159\pi\)
0.242116 + 0.970247i \(0.422159\pi\)
\(588\) 0.332736 0.0137218
\(589\) 0.237470 0.00978480
\(590\) −10.7728 −0.443508
\(591\) −27.9326 −1.14900
\(592\) −9.02092 −0.370758
\(593\) 14.8281 0.608918 0.304459 0.952525i \(-0.401524\pi\)
0.304459 + 0.952525i \(0.401524\pi\)
\(594\) −2.05381 −0.0842689
\(595\) −18.2117 −0.746605
\(596\) 15.1295 0.619729
\(597\) −78.8443 −3.22688
\(598\) −4.00840 −0.163916
\(599\) −8.04349 −0.328648 −0.164324 0.986406i \(-0.552544\pi\)
−0.164324 + 0.986406i \(0.552544\pi\)
\(600\) −3.08271 −0.125851
\(601\) −10.8367 −0.442040 −0.221020 0.975269i \(-0.570939\pi\)
−0.221020 + 0.975269i \(0.570939\pi\)
\(602\) 7.14884 0.291365
\(603\) 85.9785 3.50131
\(604\) 8.12239 0.330495
\(605\) 10.9638 0.445743
\(606\) 18.3883 0.746975
\(607\) 38.2829 1.55386 0.776928 0.629589i \(-0.216777\pi\)
0.776928 + 0.629589i \(0.216777\pi\)
\(608\) −0.237470 −0.00963070
\(609\) 0.373326 0.0151279
\(610\) −0.753431 −0.0305055
\(611\) 10.0962 0.408448
\(612\) −45.1124 −1.82356
\(613\) 6.03017 0.243556 0.121778 0.992557i \(-0.461140\pi\)
0.121778 + 0.992557i \(0.461140\pi\)
\(614\) 20.5185 0.828061
\(615\) −7.72824 −0.311633
\(616\) −0.499284 −0.0201167
\(617\) 1.89394 0.0762470 0.0381235 0.999273i \(-0.487862\pi\)
0.0381235 + 0.999273i \(0.487862\pi\)
\(618\) −44.1577 −1.77628
\(619\) −24.3574 −0.979005 −0.489503 0.872002i \(-0.662822\pi\)
−0.489503 + 0.872002i \(0.662822\pi\)
\(620\) 1.00000 0.0401610
\(621\) −43.2872 −1.73705
\(622\) −18.9628 −0.760340
\(623\) 2.86376 0.114734
\(624\) 3.08271 0.123407
\(625\) 1.00000 0.0400000
\(626\) −15.8179 −0.632210
\(627\) 0.139224 0.00556008
\(628\) 19.0833 0.761507
\(629\) 62.5786 2.49517
\(630\) 17.0725 0.680183
\(631\) −6.27936 −0.249977 −0.124989 0.992158i \(-0.539889\pi\)
−0.124989 + 0.992158i \(0.539889\pi\)
\(632\) 0.817179 0.0325056
\(633\) −27.1184 −1.07786
\(634\) 31.6064 1.25525
\(635\) −10.3607 −0.411153
\(636\) 6.13778 0.243379
\(637\) 0.107936 0.00427659
\(638\) 0.00877310 0.000347330 0
\(639\) 39.9519 1.58047
\(640\) −1.00000 −0.0395285
\(641\) −42.2402 −1.66839 −0.834193 0.551472i \(-0.814066\pi\)
−0.834193 + 0.551472i \(0.814066\pi\)
\(642\) 4.03718 0.159335
\(643\) 27.9359 1.10168 0.550841 0.834610i \(-0.314307\pi\)
0.550841 + 0.834610i \(0.314307\pi\)
\(644\) −10.5232 −0.414671
\(645\) −8.39449 −0.330533
\(646\) 1.64734 0.0648139
\(647\) 13.8574 0.544791 0.272395 0.962185i \(-0.412184\pi\)
0.272395 + 0.962185i \(0.412184\pi\)
\(648\) 13.7812 0.541376
\(649\) 2.04880 0.0804226
\(650\) −1.00000 −0.0392232
\(651\) −8.09297 −0.317188
\(652\) −4.24035 −0.166065
\(653\) 9.24792 0.361899 0.180950 0.983492i \(-0.442083\pi\)
0.180950 + 0.983492i \(0.442083\pi\)
\(654\) 1.24203 0.0485673
\(655\) 10.1846 0.397947
\(656\) −2.50696 −0.0978804
\(657\) −38.4955 −1.50185
\(658\) 26.5053 1.03328
\(659\) 28.2732 1.10137 0.550685 0.834713i \(-0.314367\pi\)
0.550685 + 0.834713i \(0.314367\pi\)
\(660\) 0.586281 0.0228210
\(661\) 31.4799 1.22443 0.612213 0.790693i \(-0.290280\pi\)
0.612213 + 0.790693i \(0.290280\pi\)
\(662\) 16.2940 0.633285
\(663\) −21.3849 −0.830522
\(664\) 0.435097 0.0168850
\(665\) −0.623425 −0.0241754
\(666\) −58.6641 −2.27319
\(667\) 0.184906 0.00715960
\(668\) 13.5092 0.522687
\(669\) 82.5977 3.19341
\(670\) −13.2211 −0.510776
\(671\) 0.143290 0.00553165
\(672\) 8.09297 0.312193
\(673\) −9.55452 −0.368300 −0.184150 0.982898i \(-0.558953\pi\)
−0.184150 + 0.982898i \(0.558953\pi\)
\(674\) 15.4158 0.593795
\(675\) −10.7991 −0.415658
\(676\) 1.00000 0.0384615
\(677\) −32.0117 −1.23031 −0.615155 0.788406i \(-0.710907\pi\)
−0.615155 + 0.788406i \(0.710907\pi\)
\(678\) −8.21155 −0.315363
\(679\) −21.4623 −0.823648
\(680\) 6.93705 0.266024
\(681\) −31.5812 −1.21019
\(682\) −0.190183 −0.00728250
\(683\) −19.9713 −0.764182 −0.382091 0.924125i \(-0.624796\pi\)
−0.382091 + 0.924125i \(0.624796\pi\)
\(684\) −1.54430 −0.0590477
\(685\) −6.23374 −0.238179
\(686\) 18.6603 0.712453
\(687\) 36.8072 1.40428
\(688\) −2.72309 −0.103817
\(689\) 1.99103 0.0758523
\(690\) 12.3568 0.470414
\(691\) −20.2688 −0.771062 −0.385531 0.922695i \(-0.625982\pi\)
−0.385531 + 0.922695i \(0.625982\pi\)
\(692\) 1.08997 0.0414344
\(693\) −3.24690 −0.123340
\(694\) 7.68442 0.291696
\(695\) −3.87231 −0.146885
\(696\) −0.142205 −0.00539025
\(697\) 17.3909 0.658728
\(698\) 16.5847 0.627741
\(699\) −79.6876 −3.01406
\(700\) −2.62527 −0.0992260
\(701\) 37.6355 1.42147 0.710736 0.703458i \(-0.248362\pi\)
0.710736 + 0.703458i \(0.248362\pi\)
\(702\) 10.7991 0.407586
\(703\) 2.14220 0.0807947
\(704\) 0.190183 0.00716781
\(705\) −31.1237 −1.17219
\(706\) −33.2411 −1.25105
\(707\) 15.6597 0.588944
\(708\) −33.2094 −1.24808
\(709\) 24.3657 0.915074 0.457537 0.889191i \(-0.348732\pi\)
0.457537 + 0.889191i \(0.348732\pi\)
\(710\) −6.14349 −0.230561
\(711\) 5.31421 0.199298
\(712\) −1.09084 −0.0408810
\(713\) −4.00840 −0.150116
\(714\) −56.1413 −2.10104
\(715\) 0.190183 0.00711246
\(716\) 12.1337 0.453457
\(717\) 14.6215 0.546048
\(718\) 21.8698 0.816173
\(719\) −18.8095 −0.701475 −0.350738 0.936474i \(-0.614069\pi\)
−0.350738 + 0.936474i \(0.614069\pi\)
\(720\) −6.50312 −0.242357
\(721\) −37.6052 −1.40049
\(722\) −18.9436 −0.705008
\(723\) 17.7786 0.661194
\(724\) 3.25448 0.120952
\(725\) 0.0461297 0.00171321
\(726\) 33.7983 1.25437
\(727\) −24.4092 −0.905286 −0.452643 0.891692i \(-0.649519\pi\)
−0.452643 + 0.891692i \(0.649519\pi\)
\(728\) 2.62527 0.0972991
\(729\) −10.2510 −0.379666
\(730\) 5.91955 0.219092
\(731\) 18.8902 0.698678
\(732\) −2.32261 −0.0858462
\(733\) −1.05303 −0.0388946 −0.0194473 0.999811i \(-0.506191\pi\)
−0.0194473 + 0.999811i \(0.506191\pi\)
\(734\) −33.8742 −1.25032
\(735\) −0.332736 −0.0122732
\(736\) 4.00840 0.147752
\(737\) 2.51444 0.0926205
\(738\) −16.3031 −0.600124
\(739\) −1.40499 −0.0516834 −0.0258417 0.999666i \(-0.508227\pi\)
−0.0258417 + 0.999666i \(0.508227\pi\)
\(740\) 9.02092 0.331616
\(741\) −0.732053 −0.0268926
\(742\) 5.22701 0.191889
\(743\) −9.58396 −0.351602 −0.175801 0.984426i \(-0.556251\pi\)
−0.175801 + 0.984426i \(0.556251\pi\)
\(744\) 3.08271 0.113018
\(745\) −15.1295 −0.554302
\(746\) −15.7122 −0.575266
\(747\) 2.82949 0.103526
\(748\) −1.31931 −0.0482388
\(749\) 3.43811 0.125626
\(750\) 3.08271 0.112565
\(751\) −9.05783 −0.330525 −0.165263 0.986250i \(-0.552847\pi\)
−0.165263 + 0.986250i \(0.552847\pi\)
\(752\) −10.0962 −0.368170
\(753\) −66.5926 −2.42677
\(754\) −0.0461297 −0.00167994
\(755\) −8.12239 −0.295604
\(756\) 28.3506 1.03110
\(757\) 38.3596 1.39420 0.697101 0.716973i \(-0.254473\pi\)
0.697101 + 0.716973i \(0.254473\pi\)
\(758\) 4.04448 0.146902
\(759\) −2.35005 −0.0853014
\(760\) 0.237470 0.00861396
\(761\) 24.8063 0.899229 0.449614 0.893223i \(-0.351561\pi\)
0.449614 + 0.893223i \(0.351561\pi\)
\(762\) −31.9391 −1.15703
\(763\) 1.05773 0.0382923
\(764\) −10.6539 −0.385446
\(765\) 45.1124 1.63104
\(766\) 2.70970 0.0979055
\(767\) −10.7728 −0.388982
\(768\) −3.08271 −0.111238
\(769\) 8.41317 0.303387 0.151693 0.988428i \(-0.451527\pi\)
0.151693 + 0.988428i \(0.451527\pi\)
\(770\) 0.499284 0.0179929
\(771\) −46.7290 −1.68290
\(772\) −12.5653 −0.452236
\(773\) 31.5147 1.13350 0.566752 0.823888i \(-0.308200\pi\)
0.566752 + 0.823888i \(0.308200\pi\)
\(774\) −17.7085 −0.636520
\(775\) −1.00000 −0.0359211
\(776\) 8.17526 0.293475
\(777\) −73.0060 −2.61908
\(778\) 14.2920 0.512392
\(779\) 0.595329 0.0213299
\(780\) −3.08271 −0.110379
\(781\) 1.16839 0.0418083
\(782\) −27.8065 −0.994358
\(783\) −0.498159 −0.0178028
\(784\) −0.107936 −0.00385486
\(785\) −19.0833 −0.681112
\(786\) 31.3963 1.11987
\(787\) −35.7119 −1.27299 −0.636495 0.771281i \(-0.719616\pi\)
−0.636495 + 0.771281i \(0.719616\pi\)
\(788\) 9.06106 0.322787
\(789\) −4.44861 −0.158375
\(790\) −0.817179 −0.0290739
\(791\) −6.99305 −0.248644
\(792\) 1.23679 0.0439472
\(793\) −0.753431 −0.0267551
\(794\) −3.48803 −0.123785
\(795\) −6.13778 −0.217685
\(796\) 25.5763 0.906527
\(797\) 20.0161 0.709006 0.354503 0.935055i \(-0.384650\pi\)
0.354503 + 0.935055i \(0.384650\pi\)
\(798\) −1.92184 −0.0680324
\(799\) 70.0378 2.47776
\(800\) 1.00000 0.0353553
\(801\) −7.09387 −0.250650
\(802\) −20.2318 −0.714411
\(803\) −1.12580 −0.0397286
\(804\) −40.7569 −1.43739
\(805\) 10.5232 0.370893
\(806\) 1.00000 0.0352235
\(807\) 30.6480 1.07886
\(808\) −5.96499 −0.209847
\(809\) −14.1815 −0.498595 −0.249298 0.968427i \(-0.580200\pi\)
−0.249298 + 0.968427i \(0.580200\pi\)
\(810\) −13.7812 −0.484221
\(811\) 12.3169 0.432505 0.216253 0.976337i \(-0.430617\pi\)
0.216253 + 0.976337i \(0.430617\pi\)
\(812\) −0.121103 −0.00424988
\(813\) −73.9322 −2.59291
\(814\) −1.71563 −0.0601328
\(815\) 4.24035 0.148533
\(816\) 21.3849 0.748622
\(817\) 0.646652 0.0226235
\(818\) 26.7867 0.936576
\(819\) 17.0725 0.596560
\(820\) 2.50696 0.0875469
\(821\) 32.4098 1.13111 0.565554 0.824711i \(-0.308662\pi\)
0.565554 + 0.824711i \(0.308662\pi\)
\(822\) −19.2168 −0.670264
\(823\) −24.0884 −0.839670 −0.419835 0.907600i \(-0.637912\pi\)
−0.419835 + 0.907600i \(0.637912\pi\)
\(824\) 14.3243 0.499010
\(825\) −0.586281 −0.0204117
\(826\) −28.2815 −0.984039
\(827\) −12.6164 −0.438716 −0.219358 0.975644i \(-0.570396\pi\)
−0.219358 + 0.975644i \(0.570396\pi\)
\(828\) 26.0671 0.905895
\(829\) −39.0359 −1.35577 −0.677887 0.735166i \(-0.737104\pi\)
−0.677887 + 0.735166i \(0.737104\pi\)
\(830\) −0.435097 −0.0151024
\(831\) 43.8360 1.52066
\(832\) −1.00000 −0.0346688
\(833\) 0.748759 0.0259430
\(834\) −11.9372 −0.413352
\(835\) −13.5092 −0.467506
\(836\) −0.0451629 −0.00156199
\(837\) 10.7991 0.373272
\(838\) −37.0735 −1.28068
\(839\) 38.9273 1.34392 0.671959 0.740588i \(-0.265453\pi\)
0.671959 + 0.740588i \(0.265453\pi\)
\(840\) −8.09297 −0.279234
\(841\) −28.9979 −0.999927
\(842\) 8.02881 0.276691
\(843\) −48.5926 −1.67362
\(844\) 8.79692 0.302802
\(845\) −1.00000 −0.0344010
\(846\) −65.6567 −2.25733
\(847\) 28.7831 0.988998
\(848\) −1.99103 −0.0683723
\(849\) 56.1239 1.92617
\(850\) −6.93705 −0.237939
\(851\) −36.1595 −1.23953
\(852\) −18.9386 −0.648827
\(853\) −15.4680 −0.529615 −0.264808 0.964301i \(-0.585308\pi\)
−0.264808 + 0.964301i \(0.585308\pi\)
\(854\) −1.97796 −0.0676845
\(855\) 1.54430 0.0528139
\(856\) −1.30962 −0.0447618
\(857\) 23.9701 0.818804 0.409402 0.912354i \(-0.365737\pi\)
0.409402 + 0.912354i \(0.365737\pi\)
\(858\) 0.586281 0.0200153
\(859\) 10.2235 0.348823 0.174411 0.984673i \(-0.444198\pi\)
0.174411 + 0.984673i \(0.444198\pi\)
\(860\) 2.72309 0.0928564
\(861\) −20.2888 −0.691439
\(862\) −25.3589 −0.863726
\(863\) 21.6389 0.736598 0.368299 0.929707i \(-0.379940\pi\)
0.368299 + 0.929707i \(0.379940\pi\)
\(864\) −10.7991 −0.367393
\(865\) −1.08997 −0.0370600
\(866\) −28.3882 −0.964670
\(867\) −95.9422 −3.25837
\(868\) 2.62527 0.0891076
\(869\) 0.155414 0.00527206
\(870\) 0.142205 0.00482119
\(871\) −13.2211 −0.447980
\(872\) −0.402902 −0.0136440
\(873\) 53.1647 1.79935
\(874\) −0.951877 −0.0321977
\(875\) 2.62527 0.0887505
\(876\) 18.2483 0.616552
\(877\) 44.3224 1.49666 0.748330 0.663327i \(-0.230856\pi\)
0.748330 + 0.663327i \(0.230856\pi\)
\(878\) −18.2165 −0.614778
\(879\) −42.1931 −1.42314
\(880\) −0.190183 −0.00641108
\(881\) 43.6937 1.47208 0.736040 0.676938i \(-0.236694\pi\)
0.736040 + 0.676938i \(0.236694\pi\)
\(882\) −0.701922 −0.0236349
\(883\) 23.6293 0.795189 0.397595 0.917561i \(-0.369845\pi\)
0.397595 + 0.917561i \(0.369845\pi\)
\(884\) 6.93705 0.233318
\(885\) 33.2094 1.11632
\(886\) −19.5676 −0.657385
\(887\) −26.3809 −0.885783 −0.442891 0.896575i \(-0.646047\pi\)
−0.442891 + 0.896575i \(0.646047\pi\)
\(888\) 27.8089 0.933206
\(889\) −27.1997 −0.912250
\(890\) 1.09084 0.0365651
\(891\) 2.62095 0.0878052
\(892\) −26.7938 −0.897124
\(893\) 2.39755 0.0802309
\(894\) −46.6399 −1.55987
\(895\) −12.1337 −0.405585
\(896\) −2.62527 −0.0877043
\(897\) 12.3568 0.412580
\(898\) −8.23469 −0.274795
\(899\) −0.0461297 −0.00153851
\(900\) 6.50312 0.216771
\(901\) 13.8119 0.460141
\(902\) −0.476783 −0.0158751
\(903\) −22.0378 −0.733373
\(904\) 2.66374 0.0885947
\(905\) −3.25448 −0.108183
\(906\) −25.0390 −0.831865
\(907\) −15.9224 −0.528696 −0.264348 0.964427i \(-0.585157\pi\)
−0.264348 + 0.964427i \(0.585157\pi\)
\(908\) 10.2446 0.339979
\(909\) −38.7910 −1.28662
\(910\) −2.62527 −0.0870270
\(911\) −5.84421 −0.193627 −0.0968136 0.995303i \(-0.530865\pi\)
−0.0968136 + 0.995303i \(0.530865\pi\)
\(912\) 0.732053 0.0242407
\(913\) 0.0827483 0.00273857
\(914\) −24.4634 −0.809178
\(915\) 2.32261 0.0767832
\(916\) −11.9399 −0.394505
\(917\) 26.7375 0.882949
\(918\) 74.9139 2.47253
\(919\) −39.4296 −1.30066 −0.650331 0.759651i \(-0.725370\pi\)
−0.650331 + 0.759651i \(0.725370\pi\)
\(920\) −4.00840 −0.132153
\(921\) −63.2527 −2.08425
\(922\) −8.11358 −0.267207
\(923\) −6.14349 −0.202216
\(924\) 1.53915 0.0506342
\(925\) −9.02092 −0.296606
\(926\) 10.0863 0.331456
\(927\) 93.1526 3.05953
\(928\) 0.0461297 0.00151428
\(929\) 40.9322 1.34294 0.671471 0.741031i \(-0.265663\pi\)
0.671471 + 0.741031i \(0.265663\pi\)
\(930\) −3.08271 −0.101086
\(931\) 0.0256316 0.000840043 0
\(932\) 25.8498 0.846739
\(933\) 58.4570 1.91379
\(934\) 25.0000 0.818026
\(935\) 1.31931 0.0431461
\(936\) −6.50312 −0.212561
\(937\) 44.8535 1.46530 0.732651 0.680605i \(-0.238283\pi\)
0.732651 + 0.680605i \(0.238283\pi\)
\(938\) −34.7091 −1.13329
\(939\) 48.7620 1.59129
\(940\) 10.0962 0.329302
\(941\) 2.31410 0.0754376 0.0377188 0.999288i \(-0.487991\pi\)
0.0377188 + 0.999288i \(0.487991\pi\)
\(942\) −58.8283 −1.91673
\(943\) −10.0489 −0.327238
\(944\) 10.7728 0.350624
\(945\) −28.3506 −0.922245
\(946\) −0.517886 −0.0168379
\(947\) 9.66596 0.314102 0.157051 0.987591i \(-0.449801\pi\)
0.157051 + 0.987591i \(0.449801\pi\)
\(948\) −2.51913 −0.0818175
\(949\) 5.91955 0.192157
\(950\) −0.237470 −0.00770456
\(951\) −97.4334 −3.15949
\(952\) 18.2117 0.590243
\(953\) −37.1792 −1.20435 −0.602177 0.798363i \(-0.705700\pi\)
−0.602177 + 0.798363i \(0.705700\pi\)
\(954\) −12.9479 −0.419204
\(955\) 10.6539 0.344753
\(956\) −4.74305 −0.153401
\(957\) −0.0270449 −0.000874239 0
\(958\) −26.5870 −0.858986
\(959\) −16.3653 −0.528462
\(960\) 3.08271 0.0994941
\(961\) 1.00000 0.0322581
\(962\) 9.02092 0.290846
\(963\) −8.51660 −0.274444
\(964\) −5.76720 −0.185749
\(965\) 12.5653 0.404492
\(966\) 32.4399 1.04374
\(967\) −21.0756 −0.677744 −0.338872 0.940832i \(-0.610045\pi\)
−0.338872 + 0.940832i \(0.610045\pi\)
\(968\) −10.9638 −0.352391
\(969\) −5.07829 −0.163138
\(970\) −8.17526 −0.262492
\(971\) −23.1383 −0.742544 −0.371272 0.928524i \(-0.621078\pi\)
−0.371272 + 0.928524i \(0.621078\pi\)
\(972\) −10.0861 −0.323512
\(973\) −10.1659 −0.325903
\(974\) −6.50732 −0.208508
\(975\) 3.08271 0.0987258
\(976\) 0.753431 0.0241167
\(977\) 57.3418 1.83453 0.917264 0.398280i \(-0.130393\pi\)
0.917264 + 0.398280i \(0.130393\pi\)
\(978\) 13.0718 0.417989
\(979\) −0.207460 −0.00663045
\(980\) 0.107936 0.00344789
\(981\) −2.62012 −0.0836540
\(982\) −30.5048 −0.973447
\(983\) 30.1178 0.960610 0.480305 0.877102i \(-0.340526\pi\)
0.480305 + 0.877102i \(0.340526\pi\)
\(984\) 7.72824 0.246367
\(985\) −9.06106 −0.288709
\(986\) −0.320004 −0.0101910
\(987\) −81.7082 −2.60080
\(988\) 0.237470 0.00755494
\(989\) −10.9152 −0.347084
\(990\) −1.23679 −0.0393076
\(991\) 30.2927 0.962280 0.481140 0.876644i \(-0.340223\pi\)
0.481140 + 0.876644i \(0.340223\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −50.2298 −1.59399
\(994\) −16.1284 −0.511560
\(995\) −25.5763 −0.810822
\(996\) −1.34128 −0.0425001
\(997\) −26.1923 −0.829518 −0.414759 0.909931i \(-0.636134\pi\)
−0.414759 + 0.909931i \(0.636134\pi\)
\(998\) 12.5736 0.398012
\(999\) 97.4178 3.08216
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 \(a_p\))