Properties

Label 8007.2.a.f.1.13
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.50666 q^{2} -1.00000 q^{3} +0.270014 q^{4} -0.475693 q^{5} +1.50666 q^{6} -0.891979 q^{7} +2.60649 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.50666 q^{2} -1.00000 q^{3} +0.270014 q^{4} -0.475693 q^{5} +1.50666 q^{6} -0.891979 q^{7} +2.60649 q^{8} +1.00000 q^{9} +0.716706 q^{10} -4.53256 q^{11} -0.270014 q^{12} +1.62404 q^{13} +1.34391 q^{14} +0.475693 q^{15} -4.46712 q^{16} -1.00000 q^{17} -1.50666 q^{18} +0.833908 q^{19} -0.128444 q^{20} +0.891979 q^{21} +6.82902 q^{22} -3.25633 q^{23} -2.60649 q^{24} -4.77372 q^{25} -2.44688 q^{26} -1.00000 q^{27} -0.240847 q^{28} +4.74015 q^{29} -0.716706 q^{30} +10.3297 q^{31} +1.51743 q^{32} +4.53256 q^{33} +1.50666 q^{34} +0.424308 q^{35} +0.270014 q^{36} -4.87105 q^{37} -1.25641 q^{38} -1.62404 q^{39} -1.23989 q^{40} +4.26901 q^{41} -1.34391 q^{42} -9.65601 q^{43} -1.22386 q^{44} -0.475693 q^{45} +4.90616 q^{46} +12.1483 q^{47} +4.46712 q^{48} -6.20437 q^{49} +7.19235 q^{50} +1.00000 q^{51} +0.438515 q^{52} +0.534008 q^{53} +1.50666 q^{54} +2.15611 q^{55} -2.32494 q^{56} -0.833908 q^{57} -7.14177 q^{58} +12.6728 q^{59} +0.128444 q^{60} +0.228820 q^{61} -15.5633 q^{62} -0.891979 q^{63} +6.64800 q^{64} -0.772546 q^{65} -6.82902 q^{66} +8.20386 q^{67} -0.270014 q^{68} +3.25633 q^{69} -0.639286 q^{70} -8.50947 q^{71} +2.60649 q^{72} -6.38859 q^{73} +7.33900 q^{74} +4.77372 q^{75} +0.225167 q^{76} +4.04295 q^{77} +2.44688 q^{78} -4.83950 q^{79} +2.12498 q^{80} +1.00000 q^{81} -6.43193 q^{82} -17.0444 q^{83} +0.240847 q^{84} +0.475693 q^{85} +14.5483 q^{86} -4.74015 q^{87} -11.8141 q^{88} -1.87298 q^{89} +0.716706 q^{90} -1.44861 q^{91} -0.879254 q^{92} -10.3297 q^{93} -18.3033 q^{94} -0.396684 q^{95} -1.51743 q^{96} -8.80052 q^{97} +9.34786 q^{98} -4.53256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50666 −1.06537 −0.532684 0.846315i \(-0.678816\pi\)
−0.532684 + 0.846315i \(0.678816\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.270014 0.135007
\(5\) −0.475693 −0.212736 −0.106368 0.994327i \(-0.533922\pi\)
−0.106368 + 0.994327i \(0.533922\pi\)
\(6\) 1.50666 0.615090
\(7\) −0.891979 −0.337136 −0.168568 0.985690i \(-0.553914\pi\)
−0.168568 + 0.985690i \(0.553914\pi\)
\(8\) 2.60649 0.921535
\(9\) 1.00000 0.333333
\(10\) 0.716706 0.226642
\(11\) −4.53256 −1.36662 −0.683310 0.730129i \(-0.739460\pi\)
−0.683310 + 0.730129i \(0.739460\pi\)
\(12\) −0.270014 −0.0779464
\(13\) 1.62404 0.450429 0.225214 0.974309i \(-0.427692\pi\)
0.225214 + 0.974309i \(0.427692\pi\)
\(14\) 1.34391 0.359174
\(15\) 0.475693 0.122823
\(16\) −4.46712 −1.11678
\(17\) −1.00000 −0.242536
\(18\) −1.50666 −0.355122
\(19\) 0.833908 0.191312 0.0956558 0.995414i \(-0.469505\pi\)
0.0956558 + 0.995414i \(0.469505\pi\)
\(20\) −0.128444 −0.0287209
\(21\) 0.891979 0.194646
\(22\) 6.82902 1.45595
\(23\) −3.25633 −0.678991 −0.339495 0.940608i \(-0.610256\pi\)
−0.339495 + 0.940608i \(0.610256\pi\)
\(24\) −2.60649 −0.532048
\(25\) −4.77372 −0.954743
\(26\) −2.44688 −0.479872
\(27\) −1.00000 −0.192450
\(28\) −0.240847 −0.0455158
\(29\) 4.74015 0.880223 0.440111 0.897943i \(-0.354939\pi\)
0.440111 + 0.897943i \(0.354939\pi\)
\(30\) −0.716706 −0.130852
\(31\) 10.3297 1.85527 0.927633 0.373493i \(-0.121840\pi\)
0.927633 + 0.373493i \(0.121840\pi\)
\(32\) 1.51743 0.268246
\(33\) 4.53256 0.789018
\(34\) 1.50666 0.258389
\(35\) 0.424308 0.0717211
\(36\) 0.270014 0.0450024
\(37\) −4.87105 −0.800795 −0.400398 0.916341i \(-0.631128\pi\)
−0.400398 + 0.916341i \(0.631128\pi\)
\(38\) −1.25641 −0.203817
\(39\) −1.62404 −0.260055
\(40\) −1.23989 −0.196044
\(41\) 4.26901 0.666707 0.333353 0.942802i \(-0.391820\pi\)
0.333353 + 0.942802i \(0.391820\pi\)
\(42\) −1.34391 −0.207369
\(43\) −9.65601 −1.47253 −0.736264 0.676695i \(-0.763412\pi\)
−0.736264 + 0.676695i \(0.763412\pi\)
\(44\) −1.22386 −0.184503
\(45\) −0.475693 −0.0709121
\(46\) 4.90616 0.723374
\(47\) 12.1483 1.77201 0.886003 0.463679i \(-0.153471\pi\)
0.886003 + 0.463679i \(0.153471\pi\)
\(48\) 4.46712 0.644773
\(49\) −6.20437 −0.886339
\(50\) 7.19235 1.01715
\(51\) 1.00000 0.140028
\(52\) 0.438515 0.0608110
\(53\) 0.534008 0.0733516 0.0366758 0.999327i \(-0.488323\pi\)
0.0366758 + 0.999327i \(0.488323\pi\)
\(54\) 1.50666 0.205030
\(55\) 2.15611 0.290729
\(56\) −2.32494 −0.310683
\(57\) −0.833908 −0.110454
\(58\) −7.14177 −0.937761
\(59\) 12.6728 1.64985 0.824926 0.565241i \(-0.191217\pi\)
0.824926 + 0.565241i \(0.191217\pi\)
\(60\) 0.128444 0.0165820
\(61\) 0.228820 0.0292974 0.0146487 0.999893i \(-0.495337\pi\)
0.0146487 + 0.999893i \(0.495337\pi\)
\(62\) −15.5633 −1.97654
\(63\) −0.891979 −0.112379
\(64\) 6.64800 0.831000
\(65\) −0.772546 −0.0958225
\(66\) −6.82902 −0.840594
\(67\) 8.20386 1.00226 0.501130 0.865372i \(-0.332918\pi\)
0.501130 + 0.865372i \(0.332918\pi\)
\(68\) −0.270014 −0.0327440
\(69\) 3.25633 0.392016
\(70\) −0.639286 −0.0764093
\(71\) −8.50947 −1.00989 −0.504944 0.863152i \(-0.668487\pi\)
−0.504944 + 0.863152i \(0.668487\pi\)
\(72\) 2.60649 0.307178
\(73\) −6.38859 −0.747728 −0.373864 0.927483i \(-0.621967\pi\)
−0.373864 + 0.927483i \(0.621967\pi\)
\(74\) 7.33900 0.853141
\(75\) 4.77372 0.551221
\(76\) 0.225167 0.0258284
\(77\) 4.04295 0.460737
\(78\) 2.44688 0.277054
\(79\) −4.83950 −0.544486 −0.272243 0.962228i \(-0.587766\pi\)
−0.272243 + 0.962228i \(0.587766\pi\)
\(80\) 2.12498 0.237580
\(81\) 1.00000 0.111111
\(82\) −6.43193 −0.710288
\(83\) −17.0444 −1.87087 −0.935435 0.353499i \(-0.884992\pi\)
−0.935435 + 0.353499i \(0.884992\pi\)
\(84\) 0.240847 0.0262786
\(85\) 0.475693 0.0515961
\(86\) 14.5483 1.56878
\(87\) −4.74015 −0.508197
\(88\) −11.8141 −1.25939
\(89\) −1.87298 −0.198536 −0.0992679 0.995061i \(-0.531650\pi\)
−0.0992679 + 0.995061i \(0.531650\pi\)
\(90\) 0.716706 0.0755474
\(91\) −1.44861 −0.151856
\(92\) −0.879254 −0.0916685
\(93\) −10.3297 −1.07114
\(94\) −18.3033 −1.88784
\(95\) −0.396684 −0.0406989
\(96\) −1.51743 −0.154872
\(97\) −8.80052 −0.893558 −0.446779 0.894644i \(-0.647429\pi\)
−0.446779 + 0.894644i \(0.647429\pi\)
\(98\) 9.34786 0.944276
\(99\) −4.53256 −0.455540
\(100\) −1.28897 −0.128897
\(101\) 12.2767 1.22157 0.610787 0.791795i \(-0.290853\pi\)
0.610787 + 0.791795i \(0.290853\pi\)
\(102\) −1.50666 −0.149181
\(103\) 5.16951 0.509367 0.254684 0.967024i \(-0.418029\pi\)
0.254684 + 0.967024i \(0.418029\pi\)
\(104\) 4.23306 0.415086
\(105\) −0.424308 −0.0414082
\(106\) −0.804566 −0.0781464
\(107\) 8.96822 0.866991 0.433495 0.901156i \(-0.357280\pi\)
0.433495 + 0.901156i \(0.357280\pi\)
\(108\) −0.270014 −0.0259821
\(109\) 5.66265 0.542383 0.271192 0.962525i \(-0.412582\pi\)
0.271192 + 0.962525i \(0.412582\pi\)
\(110\) −3.24851 −0.309734
\(111\) 4.87105 0.462339
\(112\) 3.98458 0.376507
\(113\) 0.871145 0.0819504 0.0409752 0.999160i \(-0.486954\pi\)
0.0409752 + 0.999160i \(0.486954\pi\)
\(114\) 1.25641 0.117674
\(115\) 1.54901 0.144446
\(116\) 1.27991 0.118836
\(117\) 1.62404 0.150143
\(118\) −19.0935 −1.75770
\(119\) 0.891979 0.0817676
\(120\) 1.23989 0.113186
\(121\) 9.54413 0.867648
\(122\) −0.344753 −0.0312125
\(123\) −4.26901 −0.384923
\(124\) 2.78916 0.250474
\(125\) 4.64929 0.415845
\(126\) 1.34391 0.119725
\(127\) 17.9453 1.59239 0.796194 0.605041i \(-0.206843\pi\)
0.796194 + 0.605041i \(0.206843\pi\)
\(128\) −13.0511 −1.15357
\(129\) 9.65601 0.850164
\(130\) 1.16396 0.102086
\(131\) −8.71992 −0.761863 −0.380931 0.924603i \(-0.624397\pi\)
−0.380931 + 0.924603i \(0.624397\pi\)
\(132\) 1.22386 0.106523
\(133\) −0.743829 −0.0644981
\(134\) −12.3604 −1.06778
\(135\) 0.475693 0.0409411
\(136\) −2.60649 −0.223505
\(137\) 1.67736 0.143307 0.0716534 0.997430i \(-0.477172\pi\)
0.0716534 + 0.997430i \(0.477172\pi\)
\(138\) −4.90616 −0.417640
\(139\) 6.01855 0.510486 0.255243 0.966877i \(-0.417844\pi\)
0.255243 + 0.966877i \(0.417844\pi\)
\(140\) 0.114569 0.00968286
\(141\) −12.1483 −1.02307
\(142\) 12.8208 1.07590
\(143\) −7.36108 −0.615564
\(144\) −4.46712 −0.372260
\(145\) −2.25485 −0.187255
\(146\) 9.62542 0.796605
\(147\) 6.20437 0.511728
\(148\) −1.31525 −0.108113
\(149\) 15.0198 1.23047 0.615236 0.788343i \(-0.289061\pi\)
0.615236 + 0.788343i \(0.289061\pi\)
\(150\) −7.19235 −0.587253
\(151\) −8.21834 −0.668799 −0.334400 0.942431i \(-0.608534\pi\)
−0.334400 + 0.942431i \(0.608534\pi\)
\(152\) 2.17358 0.176300
\(153\) −1.00000 −0.0808452
\(154\) −6.09134 −0.490854
\(155\) −4.91375 −0.394682
\(156\) −0.438515 −0.0351093
\(157\) −1.00000 −0.0798087
\(158\) 7.29146 0.580078
\(159\) −0.534008 −0.0423496
\(160\) −0.721829 −0.0570656
\(161\) 2.90457 0.228913
\(162\) −1.50666 −0.118374
\(163\) 11.0945 0.868986 0.434493 0.900675i \(-0.356928\pi\)
0.434493 + 0.900675i \(0.356928\pi\)
\(164\) 1.15269 0.0900101
\(165\) −2.15611 −0.167853
\(166\) 25.6801 1.99316
\(167\) −21.9002 −1.69469 −0.847345 0.531043i \(-0.821800\pi\)
−0.847345 + 0.531043i \(0.821800\pi\)
\(168\) 2.32494 0.179373
\(169\) −10.3625 −0.797114
\(170\) −0.716706 −0.0549688
\(171\) 0.833908 0.0637706
\(172\) −2.60726 −0.198802
\(173\) 4.93490 0.375194 0.187597 0.982246i \(-0.439930\pi\)
0.187597 + 0.982246i \(0.439930\pi\)
\(174\) 7.14177 0.541416
\(175\) 4.25806 0.321879
\(176\) 20.2475 1.52621
\(177\) −12.6728 −0.952543
\(178\) 2.82194 0.211514
\(179\) 11.6311 0.869347 0.434673 0.900588i \(-0.356864\pi\)
0.434673 + 0.900588i \(0.356864\pi\)
\(180\) −0.128444 −0.00957363
\(181\) −5.85579 −0.435258 −0.217629 0.976032i \(-0.569832\pi\)
−0.217629 + 0.976032i \(0.569832\pi\)
\(182\) 2.18256 0.161782
\(183\) −0.228820 −0.0169149
\(184\) −8.48760 −0.625714
\(185\) 2.31712 0.170358
\(186\) 15.5633 1.14116
\(187\) 4.53256 0.331454
\(188\) 3.28020 0.239233
\(189\) 0.891979 0.0648819
\(190\) 0.597667 0.0433593
\(191\) 10.5939 0.766548 0.383274 0.923635i \(-0.374796\pi\)
0.383274 + 0.923635i \(0.374796\pi\)
\(192\) −6.64800 −0.479778
\(193\) 14.9917 1.07913 0.539564 0.841944i \(-0.318589\pi\)
0.539564 + 0.841944i \(0.318589\pi\)
\(194\) 13.2594 0.951967
\(195\) 0.772546 0.0553231
\(196\) −1.67527 −0.119662
\(197\) −1.76016 −0.125406 −0.0627032 0.998032i \(-0.519972\pi\)
−0.0627032 + 0.998032i \(0.519972\pi\)
\(198\) 6.82902 0.485317
\(199\) −5.97216 −0.423355 −0.211678 0.977340i \(-0.567893\pi\)
−0.211678 + 0.977340i \(0.567893\pi\)
\(200\) −12.4427 −0.879829
\(201\) −8.20386 −0.578655
\(202\) −18.4967 −1.30142
\(203\) −4.22811 −0.296755
\(204\) 0.270014 0.0189048
\(205\) −2.03074 −0.141833
\(206\) −7.78868 −0.542663
\(207\) −3.25633 −0.226330
\(208\) −7.25480 −0.503030
\(209\) −3.77974 −0.261450
\(210\) 0.639286 0.0441150
\(211\) 8.82507 0.607543 0.303771 0.952745i \(-0.401754\pi\)
0.303771 + 0.952745i \(0.401754\pi\)
\(212\) 0.144190 0.00990298
\(213\) 8.50947 0.583059
\(214\) −13.5120 −0.923664
\(215\) 4.59329 0.313260
\(216\) −2.60649 −0.177349
\(217\) −9.21386 −0.625478
\(218\) −8.53166 −0.577837
\(219\) 6.38859 0.431701
\(220\) 0.582179 0.0392505
\(221\) −1.62404 −0.109245
\(222\) −7.33900 −0.492561
\(223\) 11.5235 0.771669 0.385835 0.922568i \(-0.373914\pi\)
0.385835 + 0.922568i \(0.373914\pi\)
\(224\) −1.35351 −0.0904354
\(225\) −4.77372 −0.318248
\(226\) −1.31252 −0.0873072
\(227\) 5.12093 0.339888 0.169944 0.985454i \(-0.445641\pi\)
0.169944 + 0.985454i \(0.445641\pi\)
\(228\) −0.225167 −0.0149120
\(229\) −20.4102 −1.34875 −0.674373 0.738391i \(-0.735586\pi\)
−0.674373 + 0.738391i \(0.735586\pi\)
\(230\) −2.33383 −0.153888
\(231\) −4.04295 −0.266007
\(232\) 12.3552 0.811156
\(233\) −5.32447 −0.348818 −0.174409 0.984673i \(-0.555801\pi\)
−0.174409 + 0.984673i \(0.555801\pi\)
\(234\) −2.44688 −0.159957
\(235\) −5.77884 −0.376970
\(236\) 3.42182 0.222742
\(237\) 4.83950 0.314359
\(238\) −1.34391 −0.0871125
\(239\) −12.0876 −0.781881 −0.390940 0.920416i \(-0.627850\pi\)
−0.390940 + 0.920416i \(0.627850\pi\)
\(240\) −2.12498 −0.137167
\(241\) 19.7085 1.26954 0.634770 0.772701i \(-0.281095\pi\)
0.634770 + 0.772701i \(0.281095\pi\)
\(242\) −14.3797 −0.924363
\(243\) −1.00000 −0.0641500
\(244\) 0.0617846 0.00395535
\(245\) 2.95138 0.188556
\(246\) 6.43193 0.410085
\(247\) 1.35430 0.0861722
\(248\) 26.9243 1.70969
\(249\) 17.0444 1.08015
\(250\) −7.00488 −0.443027
\(251\) 1.59923 0.100942 0.0504712 0.998726i \(-0.483928\pi\)
0.0504712 + 0.998726i \(0.483928\pi\)
\(252\) −0.240847 −0.0151719
\(253\) 14.7595 0.927922
\(254\) −27.0374 −1.69648
\(255\) −0.475693 −0.0297890
\(256\) 6.36754 0.397971
\(257\) 23.6021 1.47226 0.736128 0.676842i \(-0.236652\pi\)
0.736128 + 0.676842i \(0.236652\pi\)
\(258\) −14.5483 −0.905737
\(259\) 4.34487 0.269977
\(260\) −0.208598 −0.0129367
\(261\) 4.74015 0.293408
\(262\) 13.1379 0.811663
\(263\) 29.6514 1.82839 0.914193 0.405279i \(-0.132826\pi\)
0.914193 + 0.405279i \(0.132826\pi\)
\(264\) 11.8141 0.727108
\(265\) −0.254023 −0.0156045
\(266\) 1.12069 0.0687142
\(267\) 1.87298 0.114625
\(268\) 2.21516 0.135312
\(269\) −10.9975 −0.670528 −0.335264 0.942124i \(-0.608825\pi\)
−0.335264 + 0.942124i \(0.608825\pi\)
\(270\) −0.716706 −0.0436173
\(271\) 12.6363 0.767601 0.383800 0.923416i \(-0.374615\pi\)
0.383800 + 0.923416i \(0.374615\pi\)
\(272\) 4.46712 0.270859
\(273\) 1.44861 0.0876740
\(274\) −2.52721 −0.152674
\(275\) 21.6372 1.30477
\(276\) 0.879254 0.0529249
\(277\) −31.7187 −1.90579 −0.952896 0.303297i \(-0.901913\pi\)
−0.952896 + 0.303297i \(0.901913\pi\)
\(278\) −9.06788 −0.543855
\(279\) 10.3297 0.618422
\(280\) 1.10596 0.0660935
\(281\) 24.2286 1.44536 0.722679 0.691184i \(-0.242910\pi\)
0.722679 + 0.691184i \(0.242910\pi\)
\(282\) 18.3033 1.08994
\(283\) −26.5012 −1.57533 −0.787667 0.616101i \(-0.788711\pi\)
−0.787667 + 0.616101i \(0.788711\pi\)
\(284\) −2.29768 −0.136342
\(285\) 0.396684 0.0234975
\(286\) 11.0906 0.655802
\(287\) −3.80787 −0.224771
\(288\) 1.51743 0.0894153
\(289\) 1.00000 0.0588235
\(290\) 3.39729 0.199496
\(291\) 8.80052 0.515896
\(292\) −1.72501 −0.100949
\(293\) 14.4985 0.847012 0.423506 0.905893i \(-0.360799\pi\)
0.423506 + 0.905893i \(0.360799\pi\)
\(294\) −9.34786 −0.545178
\(295\) −6.02834 −0.350983
\(296\) −12.6964 −0.737961
\(297\) 4.53256 0.263006
\(298\) −22.6297 −1.31090
\(299\) −5.28841 −0.305837
\(300\) 1.28897 0.0744188
\(301\) 8.61296 0.496443
\(302\) 12.3822 0.712517
\(303\) −12.2767 −0.705276
\(304\) −3.72517 −0.213653
\(305\) −0.108848 −0.00623261
\(306\) 1.50666 0.0861298
\(307\) 9.63388 0.549834 0.274917 0.961468i \(-0.411350\pi\)
0.274917 + 0.961468i \(0.411350\pi\)
\(308\) 1.09165 0.0622027
\(309\) −5.16951 −0.294083
\(310\) 7.40334 0.420482
\(311\) 0.353212 0.0200288 0.0100144 0.999950i \(-0.496812\pi\)
0.0100144 + 0.999950i \(0.496812\pi\)
\(312\) −4.23306 −0.239650
\(313\) −1.87195 −0.105809 −0.0529045 0.998600i \(-0.516848\pi\)
−0.0529045 + 0.998600i \(0.516848\pi\)
\(314\) 1.50666 0.0850256
\(315\) 0.424308 0.0239070
\(316\) −1.30673 −0.0735095
\(317\) −23.7694 −1.33502 −0.667512 0.744599i \(-0.732641\pi\)
−0.667512 + 0.744599i \(0.732641\pi\)
\(318\) 0.804566 0.0451178
\(319\) −21.4850 −1.20293
\(320\) −3.16240 −0.176784
\(321\) −8.96822 −0.500557
\(322\) −4.37620 −0.243876
\(323\) −0.833908 −0.0463999
\(324\) 0.270014 0.0150008
\(325\) −7.75272 −0.430044
\(326\) −16.7156 −0.925789
\(327\) −5.66265 −0.313145
\(328\) 11.1271 0.614394
\(329\) −10.8360 −0.597408
\(330\) 3.24851 0.178825
\(331\) −19.4227 −1.06757 −0.533785 0.845620i \(-0.679231\pi\)
−0.533785 + 0.845620i \(0.679231\pi\)
\(332\) −4.60224 −0.252581
\(333\) −4.87105 −0.266932
\(334\) 32.9961 1.80547
\(335\) −3.90252 −0.213217
\(336\) −3.98458 −0.217377
\(337\) 24.0399 1.30954 0.654769 0.755829i \(-0.272766\pi\)
0.654769 + 0.755829i \(0.272766\pi\)
\(338\) 15.6127 0.849219
\(339\) −0.871145 −0.0473141
\(340\) 0.128444 0.00696584
\(341\) −46.8199 −2.53544
\(342\) −1.25641 −0.0679391
\(343\) 11.7780 0.635954
\(344\) −25.1683 −1.35699
\(345\) −1.54901 −0.0833959
\(346\) −7.43520 −0.399719
\(347\) 27.7183 1.48800 0.743998 0.668182i \(-0.232927\pi\)
0.743998 + 0.668182i \(0.232927\pi\)
\(348\) −1.27991 −0.0686102
\(349\) −23.0288 −1.23270 −0.616352 0.787471i \(-0.711390\pi\)
−0.616352 + 0.787471i \(0.711390\pi\)
\(350\) −6.41543 −0.342919
\(351\) −1.62404 −0.0866850
\(352\) −6.87783 −0.366590
\(353\) 34.6520 1.84434 0.922170 0.386785i \(-0.126414\pi\)
0.922170 + 0.386785i \(0.126414\pi\)
\(354\) 19.0935 1.01481
\(355\) 4.04789 0.214840
\(356\) −0.505732 −0.0268037
\(357\) −0.891979 −0.0472085
\(358\) −17.5240 −0.926173
\(359\) −27.3200 −1.44190 −0.720948 0.692989i \(-0.756294\pi\)
−0.720948 + 0.692989i \(0.756294\pi\)
\(360\) −1.23989 −0.0653480
\(361\) −18.3046 −0.963400
\(362\) 8.82267 0.463709
\(363\) −9.54413 −0.500937
\(364\) −0.391146 −0.0205016
\(365\) 3.03901 0.159069
\(366\) 0.344753 0.0180205
\(367\) −1.74124 −0.0908922 −0.0454461 0.998967i \(-0.514471\pi\)
−0.0454461 + 0.998967i \(0.514471\pi\)
\(368\) 14.5464 0.758283
\(369\) 4.26901 0.222236
\(370\) −3.49111 −0.181494
\(371\) −0.476324 −0.0247295
\(372\) −2.78916 −0.144611
\(373\) −27.3740 −1.41737 −0.708687 0.705523i \(-0.750712\pi\)
−0.708687 + 0.705523i \(0.750712\pi\)
\(374\) −6.82902 −0.353120
\(375\) −4.64929 −0.240088
\(376\) 31.6644 1.63297
\(377\) 7.69820 0.396478
\(378\) −1.34391 −0.0691231
\(379\) 32.0482 1.64621 0.823103 0.567892i \(-0.192241\pi\)
0.823103 + 0.567892i \(0.192241\pi\)
\(380\) −0.107110 −0.00549464
\(381\) −17.9453 −0.919366
\(382\) −15.9614 −0.816655
\(383\) −12.0255 −0.614475 −0.307238 0.951633i \(-0.599405\pi\)
−0.307238 + 0.951633i \(0.599405\pi\)
\(384\) 13.0511 0.666011
\(385\) −1.92320 −0.0980155
\(386\) −22.5874 −1.14967
\(387\) −9.65601 −0.490843
\(388\) −2.37627 −0.120637
\(389\) 5.51186 0.279462 0.139731 0.990189i \(-0.455376\pi\)
0.139731 + 0.990189i \(0.455376\pi\)
\(390\) −1.16396 −0.0589395
\(391\) 3.25633 0.164679
\(392\) −16.1717 −0.816792
\(393\) 8.71992 0.439862
\(394\) 2.65196 0.133604
\(395\) 2.30212 0.115832
\(396\) −1.22386 −0.0615011
\(397\) −30.9226 −1.55196 −0.775980 0.630757i \(-0.782744\pi\)
−0.775980 + 0.630757i \(0.782744\pi\)
\(398\) 8.99800 0.451029
\(399\) 0.743829 0.0372380
\(400\) 21.3248 1.06624
\(401\) −32.0355 −1.59978 −0.799889 0.600149i \(-0.795108\pi\)
−0.799889 + 0.600149i \(0.795108\pi\)
\(402\) 12.3604 0.616480
\(403\) 16.7759 0.835665
\(404\) 3.31487 0.164921
\(405\) −0.475693 −0.0236374
\(406\) 6.37031 0.316153
\(407\) 22.0783 1.09438
\(408\) 2.60649 0.129041
\(409\) 11.3502 0.561231 0.280616 0.959820i \(-0.409461\pi\)
0.280616 + 0.959820i \(0.409461\pi\)
\(410\) 3.05962 0.151104
\(411\) −1.67736 −0.0827383
\(412\) 1.39584 0.0687682
\(413\) −11.3038 −0.556225
\(414\) 4.90616 0.241125
\(415\) 8.10791 0.398002
\(416\) 2.46437 0.120826
\(417\) −6.01855 −0.294729
\(418\) 5.69477 0.278540
\(419\) −9.03760 −0.441516 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(420\) −0.114569 −0.00559040
\(421\) −26.6087 −1.29683 −0.648415 0.761287i \(-0.724568\pi\)
−0.648415 + 0.761287i \(0.724568\pi\)
\(422\) −13.2963 −0.647256
\(423\) 12.1483 0.590669
\(424\) 1.39189 0.0675960
\(425\) 4.77372 0.231559
\(426\) −12.8208 −0.621172
\(427\) −0.204103 −0.00987721
\(428\) 2.42155 0.117050
\(429\) 7.36108 0.355396
\(430\) −6.92052 −0.333737
\(431\) 2.18676 0.105332 0.0526662 0.998612i \(-0.483228\pi\)
0.0526662 + 0.998612i \(0.483228\pi\)
\(432\) 4.46712 0.214924
\(433\) −25.5406 −1.22740 −0.613702 0.789538i \(-0.710320\pi\)
−0.613702 + 0.789538i \(0.710320\pi\)
\(434\) 13.8821 0.666363
\(435\) 2.25485 0.108112
\(436\) 1.52899 0.0732256
\(437\) −2.71548 −0.129899
\(438\) −9.62542 −0.459920
\(439\) −38.2033 −1.82334 −0.911672 0.410919i \(-0.865208\pi\)
−0.911672 + 0.410919i \(0.865208\pi\)
\(440\) 5.61988 0.267917
\(441\) −6.20437 −0.295446
\(442\) 2.44688 0.116386
\(443\) 2.13639 0.101503 0.0507515 0.998711i \(-0.483838\pi\)
0.0507515 + 0.998711i \(0.483838\pi\)
\(444\) 1.31525 0.0624191
\(445\) 0.890965 0.0422358
\(446\) −17.3619 −0.822111
\(447\) −15.0198 −0.710413
\(448\) −5.92988 −0.280160
\(449\) 23.2737 1.09835 0.549176 0.835707i \(-0.314942\pi\)
0.549176 + 0.835707i \(0.314942\pi\)
\(450\) 7.19235 0.339051
\(451\) −19.3495 −0.911134
\(452\) 0.235221 0.0110639
\(453\) 8.21834 0.386131
\(454\) −7.71548 −0.362105
\(455\) 0.689094 0.0323052
\(456\) −2.17358 −0.101787
\(457\) −36.0245 −1.68515 −0.842577 0.538576i \(-0.818962\pi\)
−0.842577 + 0.538576i \(0.818962\pi\)
\(458\) 30.7512 1.43691
\(459\) 1.00000 0.0466760
\(460\) 0.418255 0.0195012
\(461\) −38.6054 −1.79803 −0.899016 0.437916i \(-0.855717\pi\)
−0.899016 + 0.437916i \(0.855717\pi\)
\(462\) 6.09134 0.283395
\(463\) −40.6770 −1.89042 −0.945210 0.326464i \(-0.894143\pi\)
−0.945210 + 0.326464i \(0.894143\pi\)
\(464\) −21.1748 −0.983016
\(465\) 4.91375 0.227870
\(466\) 8.02215 0.371619
\(467\) −1.34897 −0.0624228 −0.0312114 0.999513i \(-0.509937\pi\)
−0.0312114 + 0.999513i \(0.509937\pi\)
\(468\) 0.438515 0.0202703
\(469\) −7.31767 −0.337899
\(470\) 8.70673 0.401612
\(471\) 1.00000 0.0460776
\(472\) 33.0315 1.52040
\(473\) 43.7665 2.01238
\(474\) −7.29146 −0.334908
\(475\) −3.98084 −0.182654
\(476\) 0.240847 0.0110392
\(477\) 0.534008 0.0244505
\(478\) 18.2118 0.832990
\(479\) 21.1557 0.966630 0.483315 0.875447i \(-0.339433\pi\)
0.483315 + 0.875447i \(0.339433\pi\)
\(480\) 0.721829 0.0329468
\(481\) −7.91079 −0.360701
\(482\) −29.6940 −1.35253
\(483\) −2.90457 −0.132163
\(484\) 2.57705 0.117139
\(485\) 4.18634 0.190092
\(486\) 1.50666 0.0683433
\(487\) −8.44142 −0.382517 −0.191259 0.981540i \(-0.561257\pi\)
−0.191259 + 0.981540i \(0.561257\pi\)
\(488\) 0.596418 0.0269986
\(489\) −11.0945 −0.501709
\(490\) −4.44671 −0.200882
\(491\) 32.0169 1.44490 0.722451 0.691423i \(-0.243016\pi\)
0.722451 + 0.691423i \(0.243016\pi\)
\(492\) −1.15269 −0.0519674
\(493\) −4.74015 −0.213485
\(494\) −2.04047 −0.0918051
\(495\) 2.15611 0.0969098
\(496\) −46.1439 −2.07192
\(497\) 7.59027 0.340470
\(498\) −25.6801 −1.15075
\(499\) 4.86839 0.217939 0.108970 0.994045i \(-0.465245\pi\)
0.108970 + 0.994045i \(0.465245\pi\)
\(500\) 1.25537 0.0561420
\(501\) 21.9002 0.978430
\(502\) −2.40949 −0.107541
\(503\) 12.6016 0.561878 0.280939 0.959726i \(-0.409354\pi\)
0.280939 + 0.959726i \(0.409354\pi\)
\(504\) −2.32494 −0.103561
\(505\) −5.83992 −0.259873
\(506\) −22.2375 −0.988577
\(507\) 10.3625 0.460214
\(508\) 4.84549 0.214984
\(509\) 40.0736 1.77623 0.888116 0.459620i \(-0.152014\pi\)
0.888116 + 0.459620i \(0.152014\pi\)
\(510\) 0.716706 0.0317363
\(511\) 5.69849 0.252086
\(512\) 16.5085 0.729580
\(513\) −0.833908 −0.0368179
\(514\) −35.5602 −1.56849
\(515\) −2.45910 −0.108361
\(516\) 2.60726 0.114778
\(517\) −55.0628 −2.42166
\(518\) −6.54623 −0.287625
\(519\) −4.93490 −0.216618
\(520\) −2.01364 −0.0883038
\(521\) −12.2478 −0.536584 −0.268292 0.963338i \(-0.586459\pi\)
−0.268292 + 0.963338i \(0.586459\pi\)
\(522\) −7.14177 −0.312587
\(523\) −16.8777 −0.738010 −0.369005 0.929427i \(-0.620302\pi\)
−0.369005 + 0.929427i \(0.620302\pi\)
\(524\) −2.35450 −0.102857
\(525\) −4.25806 −0.185837
\(526\) −44.6745 −1.94790
\(527\) −10.3297 −0.449968
\(528\) −20.2475 −0.881160
\(529\) −12.3963 −0.538971
\(530\) 0.382726 0.0166246
\(531\) 12.6728 0.549951
\(532\) −0.200844 −0.00870770
\(533\) 6.93305 0.300304
\(534\) −2.82194 −0.122117
\(535\) −4.26612 −0.184440
\(536\) 21.3833 0.923618
\(537\) −11.6311 −0.501917
\(538\) 16.5694 0.714358
\(539\) 28.1217 1.21129
\(540\) 0.128444 0.00552734
\(541\) 23.2815 1.00095 0.500474 0.865752i \(-0.333159\pi\)
0.500474 + 0.865752i \(0.333159\pi\)
\(542\) −19.0386 −0.817777
\(543\) 5.85579 0.251296
\(544\) −1.51743 −0.0650592
\(545\) −2.69368 −0.115385
\(546\) −2.18256 −0.0934050
\(547\) −8.58081 −0.366889 −0.183445 0.983030i \(-0.558725\pi\)
−0.183445 + 0.983030i \(0.558725\pi\)
\(548\) 0.452912 0.0193474
\(549\) 0.228820 0.00976579
\(550\) −32.5998 −1.39006
\(551\) 3.95285 0.168397
\(552\) 8.48760 0.361256
\(553\) 4.31673 0.183566
\(554\) 47.7892 2.03037
\(555\) −2.31712 −0.0983563
\(556\) 1.62509 0.0689193
\(557\) 11.1953 0.474362 0.237181 0.971466i \(-0.423777\pi\)
0.237181 + 0.971466i \(0.423777\pi\)
\(558\) −15.5633 −0.658846
\(559\) −15.6818 −0.663268
\(560\) −1.89543 −0.0800967
\(561\) −4.53256 −0.191365
\(562\) −36.5042 −1.53984
\(563\) 6.52292 0.274908 0.137454 0.990508i \(-0.456108\pi\)
0.137454 + 0.990508i \(0.456108\pi\)
\(564\) −3.28020 −0.138121
\(565\) −0.414397 −0.0174338
\(566\) 39.9283 1.67831
\(567\) −0.891979 −0.0374596
\(568\) −22.1799 −0.930647
\(569\) −12.3512 −0.517788 −0.258894 0.965906i \(-0.583358\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(570\) −0.597667 −0.0250335
\(571\) 20.5319 0.859234 0.429617 0.903011i \(-0.358649\pi\)
0.429617 + 0.903011i \(0.358649\pi\)
\(572\) −1.98759 −0.0831055
\(573\) −10.5939 −0.442567
\(574\) 5.73715 0.239464
\(575\) 15.5448 0.648262
\(576\) 6.64800 0.277000
\(577\) −26.7263 −1.11263 −0.556316 0.830971i \(-0.687786\pi\)
−0.556316 + 0.830971i \(0.687786\pi\)
\(578\) −1.50666 −0.0626687
\(579\) −14.9917 −0.623035
\(580\) −0.608842 −0.0252808
\(581\) 15.2033 0.630738
\(582\) −13.2594 −0.549618
\(583\) −2.42042 −0.100244
\(584\) −16.6518 −0.689058
\(585\) −0.772546 −0.0319408
\(586\) −21.8443 −0.902379
\(587\) −35.6223 −1.47029 −0.735145 0.677910i \(-0.762886\pi\)
−0.735145 + 0.677910i \(0.762886\pi\)
\(588\) 1.67527 0.0690869
\(589\) 8.61401 0.354934
\(590\) 9.08263 0.373926
\(591\) 1.76016 0.0724034
\(592\) 21.7596 0.894312
\(593\) −31.0176 −1.27374 −0.636871 0.770971i \(-0.719772\pi\)
−0.636871 + 0.770971i \(0.719772\pi\)
\(594\) −6.82902 −0.280198
\(595\) −0.424308 −0.0173949
\(596\) 4.05556 0.166122
\(597\) 5.97216 0.244424
\(598\) 7.96782 0.325829
\(599\) 40.6580 1.66124 0.830621 0.556838i \(-0.187985\pi\)
0.830621 + 0.556838i \(0.187985\pi\)
\(600\) 12.4427 0.507970
\(601\) −17.3442 −0.707484 −0.353742 0.935343i \(-0.615091\pi\)
−0.353742 + 0.935343i \(0.615091\pi\)
\(602\) −12.9768 −0.528894
\(603\) 8.20386 0.334087
\(604\) −2.21907 −0.0902926
\(605\) −4.54007 −0.184580
\(606\) 18.4967 0.751377
\(607\) −17.0943 −0.693835 −0.346917 0.937896i \(-0.612772\pi\)
−0.346917 + 0.937896i \(0.612772\pi\)
\(608\) 1.26540 0.0513185
\(609\) 4.22811 0.171332
\(610\) 0.163996 0.00664002
\(611\) 19.7293 0.798163
\(612\) −0.270014 −0.0109147
\(613\) 13.7027 0.553448 0.276724 0.960950i \(-0.410751\pi\)
0.276724 + 0.960950i \(0.410751\pi\)
\(614\) −14.5149 −0.585775
\(615\) 2.03074 0.0818872
\(616\) 10.5379 0.424585
\(617\) −36.3555 −1.46362 −0.731808 0.681511i \(-0.761323\pi\)
−0.731808 + 0.681511i \(0.761323\pi\)
\(618\) 7.78868 0.313307
\(619\) 41.6344 1.67343 0.836714 0.547640i \(-0.184474\pi\)
0.836714 + 0.547640i \(0.184474\pi\)
\(620\) −1.32678 −0.0532849
\(621\) 3.25633 0.130672
\(622\) −0.532169 −0.0213380
\(623\) 1.67066 0.0669337
\(624\) 7.25480 0.290424
\(625\) 21.6570 0.866278
\(626\) 2.82039 0.112726
\(627\) 3.77974 0.150948
\(628\) −0.270014 −0.0107747
\(629\) 4.87105 0.194221
\(630\) −0.639286 −0.0254698
\(631\) −16.5375 −0.658348 −0.329174 0.944269i \(-0.606770\pi\)
−0.329174 + 0.944269i \(0.606770\pi\)
\(632\) −12.6141 −0.501763
\(633\) −8.82507 −0.350765
\(634\) 35.8123 1.42229
\(635\) −8.53645 −0.338759
\(636\) −0.144190 −0.00571749
\(637\) −10.0762 −0.399232
\(638\) 32.3705 1.28156
\(639\) −8.50947 −0.336629
\(640\) 6.20832 0.245405
\(641\) −15.5384 −0.613730 −0.306865 0.951753i \(-0.599280\pi\)
−0.306865 + 0.951753i \(0.599280\pi\)
\(642\) 13.5120 0.533277
\(643\) −41.0163 −1.61753 −0.808763 0.588135i \(-0.799862\pi\)
−0.808763 + 0.588135i \(0.799862\pi\)
\(644\) 0.784276 0.0309048
\(645\) −4.59329 −0.180861
\(646\) 1.25641 0.0494329
\(647\) −17.9079 −0.704034 −0.352017 0.935994i \(-0.614504\pi\)
−0.352017 + 0.935994i \(0.614504\pi\)
\(648\) 2.60649 0.102393
\(649\) −57.4401 −2.25472
\(650\) 11.6807 0.458154
\(651\) 9.21386 0.361120
\(652\) 2.99566 0.117319
\(653\) 6.04928 0.236727 0.118363 0.992970i \(-0.462235\pi\)
0.118363 + 0.992970i \(0.462235\pi\)
\(654\) 8.53166 0.333614
\(655\) 4.14800 0.162076
\(656\) −19.0702 −0.744565
\(657\) −6.38859 −0.249243
\(658\) 16.3261 0.636459
\(659\) 22.8914 0.891722 0.445861 0.895102i \(-0.352898\pi\)
0.445861 + 0.895102i \(0.352898\pi\)
\(660\) −0.582179 −0.0226613
\(661\) −43.3445 −1.68590 −0.842952 0.537988i \(-0.819185\pi\)
−0.842952 + 0.537988i \(0.819185\pi\)
\(662\) 29.2634 1.13735
\(663\) 1.62404 0.0630726
\(664\) −44.4262 −1.72407
\(665\) 0.353834 0.0137211
\(666\) 7.33900 0.284380
\(667\) −15.4355 −0.597663
\(668\) −5.91337 −0.228795
\(669\) −11.5235 −0.445523
\(670\) 5.87975 0.227155
\(671\) −1.03714 −0.0400384
\(672\) 1.35351 0.0522129
\(673\) 32.4736 1.25176 0.625882 0.779918i \(-0.284739\pi\)
0.625882 + 0.779918i \(0.284739\pi\)
\(674\) −36.2199 −1.39514
\(675\) 4.77372 0.183740
\(676\) −2.79802 −0.107616
\(677\) 1.41176 0.0542582 0.0271291 0.999632i \(-0.491363\pi\)
0.0271291 + 0.999632i \(0.491363\pi\)
\(678\) 1.31252 0.0504069
\(679\) 7.84988 0.301251
\(680\) 1.23989 0.0475476
\(681\) −5.12093 −0.196234
\(682\) 70.5416 2.70118
\(683\) −23.4829 −0.898547 −0.449274 0.893394i \(-0.648317\pi\)
−0.449274 + 0.893394i \(0.648317\pi\)
\(684\) 0.225167 0.00860947
\(685\) −0.797910 −0.0304866
\(686\) −17.7454 −0.677524
\(687\) 20.4102 0.778699
\(688\) 43.1346 1.64449
\(689\) 0.867251 0.0330396
\(690\) 2.33383 0.0888473
\(691\) 42.1455 1.60329 0.801645 0.597800i \(-0.203958\pi\)
0.801645 + 0.597800i \(0.203958\pi\)
\(692\) 1.33249 0.0506538
\(693\) 4.04295 0.153579
\(694\) −41.7619 −1.58526
\(695\) −2.86298 −0.108599
\(696\) −12.3552 −0.468321
\(697\) −4.26901 −0.161700
\(698\) 34.6965 1.31328
\(699\) 5.32447 0.201390
\(700\) 1.14973 0.0434559
\(701\) −19.6202 −0.741047 −0.370523 0.928823i \(-0.620822\pi\)
−0.370523 + 0.928823i \(0.620822\pi\)
\(702\) 2.44688 0.0923514
\(703\) −4.06201 −0.153201
\(704\) −30.1325 −1.13566
\(705\) 5.77884 0.217644
\(706\) −52.2087 −1.96490
\(707\) −10.9505 −0.411837
\(708\) −3.42182 −0.128600
\(709\) −15.3331 −0.575846 −0.287923 0.957654i \(-0.592965\pi\)
−0.287923 + 0.957654i \(0.592965\pi\)
\(710\) −6.09878 −0.228883
\(711\) −4.83950 −0.181495
\(712\) −4.88192 −0.182958
\(713\) −33.6368 −1.25971
\(714\) 1.34391 0.0502944
\(715\) 3.50161 0.130953
\(716\) 3.14055 0.117368
\(717\) 12.0876 0.451419
\(718\) 41.1619 1.53615
\(719\) −23.0278 −0.858793 −0.429396 0.903116i \(-0.641274\pi\)
−0.429396 + 0.903116i \(0.641274\pi\)
\(720\) 2.12498 0.0791932
\(721\) −4.61110 −0.171726
\(722\) 27.5787 1.02637
\(723\) −19.7085 −0.732969
\(724\) −1.58115 −0.0587629
\(725\) −22.6281 −0.840387
\(726\) 14.3797 0.533681
\(727\) 32.1931 1.19398 0.596989 0.802250i \(-0.296364\pi\)
0.596989 + 0.802250i \(0.296364\pi\)
\(728\) −3.77580 −0.139941
\(729\) 1.00000 0.0370370
\(730\) −4.57874 −0.169467
\(731\) 9.65601 0.357140
\(732\) −0.0617846 −0.00228362
\(733\) −6.04021 −0.223100 −0.111550 0.993759i \(-0.535582\pi\)
−0.111550 + 0.993759i \(0.535582\pi\)
\(734\) 2.62346 0.0968336
\(735\) −2.95138 −0.108863
\(736\) −4.94124 −0.182136
\(737\) −37.1845 −1.36971
\(738\) −6.43193 −0.236763
\(739\) −31.3883 −1.15464 −0.577319 0.816519i \(-0.695901\pi\)
−0.577319 + 0.816519i \(0.695901\pi\)
\(740\) 0.625656 0.0229996
\(741\) −1.35430 −0.0497516
\(742\) 0.717656 0.0263460
\(743\) 29.7628 1.09189 0.545946 0.837820i \(-0.316170\pi\)
0.545946 + 0.837820i \(0.316170\pi\)
\(744\) −26.9243 −0.987091
\(745\) −7.14482 −0.261766
\(746\) 41.2433 1.51002
\(747\) −17.0444 −0.623623
\(748\) 1.22386 0.0447486
\(749\) −7.99947 −0.292294
\(750\) 7.00488 0.255782
\(751\) −36.6038 −1.33569 −0.667846 0.744300i \(-0.732783\pi\)
−0.667846 + 0.744300i \(0.732783\pi\)
\(752\) −54.2678 −1.97894
\(753\) −1.59923 −0.0582792
\(754\) −11.5985 −0.422394
\(755\) 3.90941 0.142278
\(756\) 0.240847 0.00875952
\(757\) −44.9897 −1.63518 −0.817588 0.575803i \(-0.804690\pi\)
−0.817588 + 0.575803i \(0.804690\pi\)
\(758\) −48.2856 −1.75381
\(759\) −14.7595 −0.535736
\(760\) −1.03395 −0.0375055
\(761\) −39.2938 −1.42440 −0.712200 0.701977i \(-0.752301\pi\)
−0.712200 + 0.701977i \(0.752301\pi\)
\(762\) 27.0374 0.979462
\(763\) −5.05096 −0.182857
\(764\) 2.86050 0.103489
\(765\) 0.475693 0.0171987
\(766\) 18.1183 0.654642
\(767\) 20.5811 0.743141
\(768\) −6.36754 −0.229769
\(769\) −45.9204 −1.65593 −0.827967 0.560777i \(-0.810503\pi\)
−0.827967 + 0.560777i \(0.810503\pi\)
\(770\) 2.89761 0.104422
\(771\) −23.6021 −0.850008
\(772\) 4.04798 0.145690
\(773\) −16.7502 −0.602465 −0.301232 0.953551i \(-0.597398\pi\)
−0.301232 + 0.953551i \(0.597398\pi\)
\(774\) 14.5483 0.522927
\(775\) −49.3110 −1.77130
\(776\) −22.9385 −0.823445
\(777\) −4.34487 −0.155871
\(778\) −8.30448 −0.297730
\(779\) 3.55996 0.127549
\(780\) 0.208598 0.00746901
\(781\) 38.5697 1.38013
\(782\) −4.90616 −0.175444
\(783\) −4.74015 −0.169399
\(784\) 27.7157 0.989846
\(785\) 0.475693 0.0169782
\(786\) −13.1379 −0.468614
\(787\) −22.4933 −0.801800 −0.400900 0.916122i \(-0.631302\pi\)
−0.400900 + 0.916122i \(0.631302\pi\)
\(788\) −0.475269 −0.0169307
\(789\) −29.6514 −1.05562
\(790\) −3.46850 −0.123404
\(791\) −0.777043 −0.0276285
\(792\) −11.8141 −0.419796
\(793\) 0.371613 0.0131964
\(794\) 46.5897 1.65341
\(795\) 0.254023 0.00900928
\(796\) −1.61257 −0.0571559
\(797\) −7.24694 −0.256700 −0.128350 0.991729i \(-0.540968\pi\)
−0.128350 + 0.991729i \(0.540968\pi\)
\(798\) −1.12069 −0.0396722
\(799\) −12.1483 −0.429775
\(800\) −7.24377 −0.256106
\(801\) −1.87298 −0.0661786
\(802\) 48.2665 1.70435
\(803\) 28.9567 1.02186
\(804\) −2.21516 −0.0781226
\(805\) −1.38168 −0.0486980
\(806\) −25.2754 −0.890290
\(807\) 10.9975 0.387129
\(808\) 31.9990 1.12572
\(809\) −25.7925 −0.906817 −0.453408 0.891303i \(-0.649792\pi\)
−0.453408 + 0.891303i \(0.649792\pi\)
\(810\) 0.716706 0.0251825
\(811\) 13.4381 0.471874 0.235937 0.971768i \(-0.424184\pi\)
0.235937 + 0.971768i \(0.424184\pi\)
\(812\) −1.14165 −0.0400640
\(813\) −12.6363 −0.443175
\(814\) −33.2645 −1.16592
\(815\) −5.27756 −0.184865
\(816\) −4.46712 −0.156380
\(817\) −8.05222 −0.281712
\(818\) −17.1009 −0.597917
\(819\) −1.44861 −0.0506186
\(820\) −0.548327 −0.0191484
\(821\) 34.9444 1.21957 0.609784 0.792568i \(-0.291256\pi\)
0.609784 + 0.792568i \(0.291256\pi\)
\(822\) 2.52721 0.0881466
\(823\) 30.7470 1.07177 0.535886 0.844290i \(-0.319978\pi\)
0.535886 + 0.844290i \(0.319978\pi\)
\(824\) 13.4743 0.469400
\(825\) −21.6372 −0.753310
\(826\) 17.0310 0.592584
\(827\) −29.6281 −1.03027 −0.515136 0.857109i \(-0.672258\pi\)
−0.515136 + 0.857109i \(0.672258\pi\)
\(828\) −0.879254 −0.0305562
\(829\) 16.4807 0.572398 0.286199 0.958170i \(-0.407608\pi\)
0.286199 + 0.958170i \(0.407608\pi\)
\(830\) −12.2158 −0.424018
\(831\) 31.7187 1.10031
\(832\) 10.7966 0.374306
\(833\) 6.20437 0.214969
\(834\) 9.06788 0.313995
\(835\) 10.4178 0.360522
\(836\) −1.02058 −0.0352976
\(837\) −10.3297 −0.357046
\(838\) 13.6166 0.470376
\(839\) −27.4110 −0.946334 −0.473167 0.880973i \(-0.656889\pi\)
−0.473167 + 0.880973i \(0.656889\pi\)
\(840\) −1.10596 −0.0381591
\(841\) −6.53102 −0.225207
\(842\) 40.0902 1.38160
\(843\) −24.2286 −0.834478
\(844\) 2.38289 0.0820225
\(845\) 4.92936 0.169575
\(846\) −18.3033 −0.629279
\(847\) −8.51316 −0.292516
\(848\) −2.38548 −0.0819176
\(849\) 26.5012 0.909520
\(850\) −7.19235 −0.246696
\(851\) 15.8617 0.543733
\(852\) 2.29768 0.0787171
\(853\) −37.3203 −1.27782 −0.638912 0.769280i \(-0.720615\pi\)
−0.638912 + 0.769280i \(0.720615\pi\)
\(854\) 0.307512 0.0105229
\(855\) −0.396684 −0.0135663
\(856\) 23.3756 0.798962
\(857\) −42.9183 −1.46606 −0.733031 0.680196i \(-0.761895\pi\)
−0.733031 + 0.680196i \(0.761895\pi\)
\(858\) −11.0906 −0.378627
\(859\) −40.9598 −1.39753 −0.698765 0.715351i \(-0.746267\pi\)
−0.698765 + 0.715351i \(0.746267\pi\)
\(860\) 1.24025 0.0422923
\(861\) 3.80787 0.129772
\(862\) −3.29469 −0.112218
\(863\) −44.9940 −1.53161 −0.765807 0.643071i \(-0.777660\pi\)
−0.765807 + 0.643071i \(0.777660\pi\)
\(864\) −1.51743 −0.0516239
\(865\) −2.34750 −0.0798173
\(866\) 38.4809 1.30764
\(867\) −1.00000 −0.0339618
\(868\) −2.48787 −0.0844439
\(869\) 21.9353 0.744105
\(870\) −3.39729 −0.115179
\(871\) 13.3234 0.451447
\(872\) 14.7597 0.499825
\(873\) −8.80052 −0.297853
\(874\) 4.09129 0.138390
\(875\) −4.14707 −0.140196
\(876\) 1.72501 0.0582827
\(877\) −26.9678 −0.910639 −0.455319 0.890328i \(-0.650475\pi\)
−0.455319 + 0.890328i \(0.650475\pi\)
\(878\) 57.5593 1.94253
\(879\) −14.4985 −0.489023
\(880\) −9.63159 −0.324681
\(881\) −2.92987 −0.0987099 −0.0493550 0.998781i \(-0.515717\pi\)
−0.0493550 + 0.998781i \(0.515717\pi\)
\(882\) 9.34786 0.314759
\(883\) 49.1624 1.65445 0.827223 0.561874i \(-0.189920\pi\)
0.827223 + 0.561874i \(0.189920\pi\)
\(884\) −0.438515 −0.0147488
\(885\) 6.02834 0.202640
\(886\) −3.21881 −0.108138
\(887\) −51.1999 −1.71912 −0.859562 0.511032i \(-0.829263\pi\)
−0.859562 + 0.511032i \(0.829263\pi\)
\(888\) 12.6964 0.426062
\(889\) −16.0068 −0.536852
\(890\) −1.34238 −0.0449966
\(891\) −4.53256 −0.151847
\(892\) 3.11150 0.104181
\(893\) 10.1305 0.339006
\(894\) 22.6297 0.756850
\(895\) −5.53281 −0.184942
\(896\) 11.6413 0.388909
\(897\) 5.28841 0.176575
\(898\) −35.0654 −1.17015
\(899\) 48.9642 1.63305
\(900\) −1.28897 −0.0429657
\(901\) −0.534008 −0.0177904
\(902\) 29.1531 0.970693
\(903\) −8.61296 −0.286621
\(904\) 2.27063 0.0755201
\(905\) 2.78556 0.0925951
\(906\) −12.3822 −0.411372
\(907\) 43.6283 1.44866 0.724328 0.689456i \(-0.242150\pi\)
0.724328 + 0.689456i \(0.242150\pi\)
\(908\) 1.38272 0.0458872
\(909\) 12.2767 0.407191
\(910\) −1.03823 −0.0344169
\(911\) −28.4003 −0.940942 −0.470471 0.882415i \(-0.655916\pi\)
−0.470471 + 0.882415i \(0.655916\pi\)
\(912\) 3.72517 0.123353
\(913\) 77.2550 2.55677
\(914\) 54.2765 1.79531
\(915\) 0.108848 0.00359840
\(916\) −5.51105 −0.182090
\(917\) 7.77798 0.256852
\(918\) −1.50666 −0.0497271
\(919\) −35.1193 −1.15848 −0.579240 0.815157i \(-0.696650\pi\)
−0.579240 + 0.815157i \(0.696650\pi\)
\(920\) 4.03749 0.133112
\(921\) −9.63388 −0.317447
\(922\) 58.1650 1.91556
\(923\) −13.8197 −0.454883
\(924\) −1.09165 −0.0359128
\(925\) 23.2530 0.764554
\(926\) 61.2862 2.01399
\(927\) 5.16951 0.169789
\(928\) 7.19283 0.236116
\(929\) −2.24445 −0.0736381 −0.0368191 0.999322i \(-0.511723\pi\)
−0.0368191 + 0.999322i \(0.511723\pi\)
\(930\) −7.40334 −0.242765
\(931\) −5.17388 −0.169567
\(932\) −1.43768 −0.0470928
\(933\) −0.353212 −0.0115636
\(934\) 2.03243 0.0665032
\(935\) −2.15611 −0.0705122
\(936\) 4.23306 0.138362
\(937\) 28.5036 0.931173 0.465586 0.885002i \(-0.345843\pi\)
0.465586 + 0.885002i \(0.345843\pi\)
\(938\) 11.0252 0.359986
\(939\) 1.87195 0.0610889
\(940\) −1.56037 −0.0508936
\(941\) 17.7126 0.577413 0.288706 0.957418i \(-0.406775\pi\)
0.288706 + 0.957418i \(0.406775\pi\)
\(942\) −1.50666 −0.0490895
\(943\) −13.9013 −0.452688
\(944\) −56.6107 −1.84252
\(945\) −0.424308 −0.0138027
\(946\) −65.9410 −2.14393
\(947\) 27.3314 0.888152 0.444076 0.895989i \(-0.353532\pi\)
0.444076 + 0.895989i \(0.353532\pi\)
\(948\) 1.30673 0.0424407
\(949\) −10.3754 −0.336798
\(950\) 5.99776 0.194593
\(951\) 23.7694 0.770776
\(952\) 2.32494 0.0753517
\(953\) 1.40686 0.0455726 0.0227863 0.999740i \(-0.492746\pi\)
0.0227863 + 0.999740i \(0.492746\pi\)
\(954\) −0.804566 −0.0260488
\(955\) −5.03944 −0.163073
\(956\) −3.26382 −0.105559
\(957\) 21.4850 0.694512
\(958\) −31.8744 −1.02982
\(959\) −1.49617 −0.0483140
\(960\) 3.16240 0.102066
\(961\) 75.7023 2.44201
\(962\) 11.9188 0.384279
\(963\) 8.96822 0.288997
\(964\) 5.32159 0.171397
\(965\) −7.13146 −0.229570
\(966\) 4.37620 0.140802
\(967\) 57.5695 1.85131 0.925655 0.378369i \(-0.123515\pi\)
0.925655 + 0.378369i \(0.123515\pi\)
\(968\) 24.8767 0.799568
\(969\) 0.833908 0.0267890
\(970\) −6.30738 −0.202518
\(971\) 21.1275 0.678012 0.339006 0.940784i \(-0.389909\pi\)
0.339006 + 0.940784i \(0.389909\pi\)
\(972\) −0.270014 −0.00866071
\(973\) −5.36842 −0.172104
\(974\) 12.7183 0.407521
\(975\) 7.75272 0.248286
\(976\) −1.02217 −0.0327187
\(977\) 0.245514 0.00785468 0.00392734 0.999992i \(-0.498750\pi\)
0.00392734 + 0.999992i \(0.498750\pi\)
\(978\) 16.7156 0.534504
\(979\) 8.48942 0.271323
\(980\) 0.796913 0.0254564
\(981\) 5.66265 0.180794
\(982\) −48.2384 −1.53935
\(983\) −14.9535 −0.476941 −0.238471 0.971150i \(-0.576646\pi\)
−0.238471 + 0.971150i \(0.576646\pi\)
\(984\) −11.1271 −0.354720
\(985\) 0.837296 0.0266785
\(986\) 7.14177 0.227440
\(987\) 10.8360 0.344914
\(988\) 0.365681 0.0116339
\(989\) 31.4431 0.999833
\(990\) −3.24851 −0.103245
\(991\) −14.0396 −0.445982 −0.222991 0.974821i \(-0.571582\pi\)
−0.222991 + 0.974821i \(0.571582\pi\)
\(992\) 15.6745 0.497667
\(993\) 19.4227 0.616362
\(994\) −11.4359 −0.362726
\(995\) 2.84091 0.0900630
\(996\) 4.60224 0.145827
\(997\) −27.1275 −0.859135 −0.429568 0.903035i \(-0.641334\pi\)
−0.429568 + 0.903035i \(0.641334\pi\)
\(998\) −7.33500 −0.232185
\(999\) 4.87105 0.154113
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 \(a_p\))