Properties

Label 8027.2.a.f.1.19
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} +O(q^{10})\) \(q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} -6.36375 q^{10} +5.81906 q^{11} -5.74553 q^{12} +4.09184 q^{13} -6.94837 q^{14} -4.59813 q^{15} +0.840077 q^{16} +1.41108 q^{17} +0.400526 q^{18} -0.843215 q^{19} +9.34213 q^{20} -5.02055 q^{21} -13.5431 q^{22} +1.00000 q^{23} +5.54436 q^{24} +2.47648 q^{25} -9.52320 q^{26} +5.33431 q^{27} +10.2004 q^{28} +7.07815 q^{29} +10.7015 q^{30} -2.42137 q^{31} +4.63884 q^{32} -9.78555 q^{33} -3.28410 q^{34} +8.16333 q^{35} -0.587981 q^{36} -5.17537 q^{37} +1.96247 q^{38} -6.88099 q^{39} -9.01505 q^{40} -1.45321 q^{41} +11.6846 q^{42} -8.03543 q^{43} +19.8815 q^{44} -0.470559 q^{45} -2.32736 q^{46} -0.879671 q^{47} -1.41271 q^{48} +1.91327 q^{49} -5.76368 q^{50} -2.37293 q^{51} +13.9803 q^{52} +0.713413 q^{53} -12.4149 q^{54} +15.9111 q^{55} -9.84324 q^{56} +1.41798 q^{57} -16.4734 q^{58} -12.5029 q^{59} -15.7101 q^{60} +8.18803 q^{61} +5.63540 q^{62} -0.513788 q^{63} -12.4764 q^{64} +11.1884 q^{65} +22.7745 q^{66} +7.32236 q^{67} +4.82114 q^{68} -1.68164 q^{69} -18.9990 q^{70} +3.98574 q^{71} +0.567395 q^{72} -12.0378 q^{73} +12.0450 q^{74} -4.16455 q^{75} -2.88095 q^{76} +17.3729 q^{77} +16.0146 q^{78} +6.86405 q^{79} +2.29704 q^{80} -8.45410 q^{81} +3.38215 q^{82} +2.00548 q^{83} -17.1533 q^{84} +3.85834 q^{85} +18.7014 q^{86} -11.9029 q^{87} -19.1855 q^{88} -6.63433 q^{89} +1.09516 q^{90} +12.2162 q^{91} +3.41663 q^{92} +4.07186 q^{93} +2.04732 q^{94} -2.30562 q^{95} -7.80085 q^{96} -7.59549 q^{97} -4.45288 q^{98} -1.00143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32736 −1.64570 −0.822848 0.568262i \(-0.807616\pi\)
−0.822848 + 0.568262i \(0.807616\pi\)
\(3\) −1.68164 −0.970894 −0.485447 0.874266i \(-0.661343\pi\)
−0.485447 + 0.874266i \(0.661343\pi\)
\(4\) 3.41663 1.70831
\(5\) 2.73432 1.22282 0.611412 0.791313i \(-0.290602\pi\)
0.611412 + 0.791313i \(0.290602\pi\)
\(6\) 3.91378 1.59780
\(7\) 2.98551 1.12842 0.564208 0.825632i \(-0.309181\pi\)
0.564208 + 0.825632i \(0.309181\pi\)
\(8\) −3.29700 −1.16567
\(9\) −0.172094 −0.0573647
\(10\) −6.36375 −2.01239
\(11\) 5.81906 1.75451 0.877256 0.480022i \(-0.159371\pi\)
0.877256 + 0.480022i \(0.159371\pi\)
\(12\) −5.74553 −1.65859
\(13\) 4.09184 1.13487 0.567436 0.823417i \(-0.307935\pi\)
0.567436 + 0.823417i \(0.307935\pi\)
\(14\) −6.94837 −1.85703
\(15\) −4.59813 −1.18723
\(16\) 0.840077 0.210019
\(17\) 1.41108 0.342238 0.171119 0.985250i \(-0.445262\pi\)
0.171119 + 0.985250i \(0.445262\pi\)
\(18\) 0.400526 0.0944048
\(19\) −0.843215 −0.193447 −0.0967234 0.995311i \(-0.530836\pi\)
−0.0967234 + 0.995311i \(0.530836\pi\)
\(20\) 9.34213 2.08896
\(21\) −5.02055 −1.09557
\(22\) −13.5431 −2.88739
\(23\) 1.00000 0.208514
\(24\) 5.54436 1.13174
\(25\) 2.47648 0.495296
\(26\) −9.52320 −1.86765
\(27\) 5.33431 1.02659
\(28\) 10.2004 1.92769
\(29\) 7.07815 1.31438 0.657189 0.753726i \(-0.271745\pi\)
0.657189 + 0.753726i \(0.271745\pi\)
\(30\) 10.7015 1.95382
\(31\) −2.42137 −0.434890 −0.217445 0.976073i \(-0.569772\pi\)
−0.217445 + 0.976073i \(0.569772\pi\)
\(32\) 4.63884 0.820039
\(33\) −9.78555 −1.70345
\(34\) −3.28410 −0.563219
\(35\) 8.16333 1.37985
\(36\) −0.587981 −0.0979968
\(37\) −5.17537 −0.850825 −0.425413 0.904999i \(-0.639871\pi\)
−0.425413 + 0.904999i \(0.639871\pi\)
\(38\) 1.96247 0.318355
\(39\) −6.88099 −1.10184
\(40\) −9.01505 −1.42540
\(41\) −1.45321 −0.226953 −0.113477 0.993541i \(-0.536199\pi\)
−0.113477 + 0.993541i \(0.536199\pi\)
\(42\) 11.6846 1.80298
\(43\) −8.03543 −1.22539 −0.612696 0.790319i \(-0.709915\pi\)
−0.612696 + 0.790319i \(0.709915\pi\)
\(44\) 19.8815 2.99726
\(45\) −0.470559 −0.0701469
\(46\) −2.32736 −0.343151
\(47\) −0.879671 −0.128313 −0.0641566 0.997940i \(-0.520436\pi\)
−0.0641566 + 0.997940i \(0.520436\pi\)
\(48\) −1.41271 −0.203906
\(49\) 1.91327 0.273324
\(50\) −5.76368 −0.815107
\(51\) −2.37293 −0.332276
\(52\) 13.9803 1.93872
\(53\) 0.713413 0.0979948 0.0489974 0.998799i \(-0.484397\pi\)
0.0489974 + 0.998799i \(0.484397\pi\)
\(54\) −12.4149 −1.68945
\(55\) 15.9111 2.14546
\(56\) −9.84324 −1.31536
\(57\) 1.41798 0.187816
\(58\) −16.4734 −2.16307
\(59\) −12.5029 −1.62774 −0.813869 0.581049i \(-0.802643\pi\)
−0.813869 + 0.581049i \(0.802643\pi\)
\(60\) −15.7101 −2.02816
\(61\) 8.18803 1.04837 0.524185 0.851605i \(-0.324370\pi\)
0.524185 + 0.851605i \(0.324370\pi\)
\(62\) 5.63540 0.715696
\(63\) −0.513788 −0.0647313
\(64\) −12.4764 −1.55955
\(65\) 11.1884 1.38775
\(66\) 22.7745 2.80335
\(67\) 7.32236 0.894568 0.447284 0.894392i \(-0.352391\pi\)
0.447284 + 0.894392i \(0.352391\pi\)
\(68\) 4.82114 0.584649
\(69\) −1.68164 −0.202445
\(70\) −18.9990 −2.27082
\(71\) 3.98574 0.473020 0.236510 0.971629i \(-0.423996\pi\)
0.236510 + 0.971629i \(0.423996\pi\)
\(72\) 0.567395 0.0668681
\(73\) −12.0378 −1.40891 −0.704457 0.709747i \(-0.748809\pi\)
−0.704457 + 0.709747i \(0.748809\pi\)
\(74\) 12.0450 1.40020
\(75\) −4.16455 −0.480880
\(76\) −2.88095 −0.330468
\(77\) 17.3729 1.97982
\(78\) 16.0146 1.81329
\(79\) 6.86405 0.772266 0.386133 0.922443i \(-0.373811\pi\)
0.386133 + 0.922443i \(0.373811\pi\)
\(80\) 2.29704 0.256816
\(81\) −8.45410 −0.939345
\(82\) 3.38215 0.373496
\(83\) 2.00548 0.220130 0.110065 0.993924i \(-0.464894\pi\)
0.110065 + 0.993924i \(0.464894\pi\)
\(84\) −17.1533 −1.87158
\(85\) 3.85834 0.418496
\(86\) 18.7014 2.01662
\(87\) −11.9029 −1.27612
\(88\) −19.1855 −2.04518
\(89\) −6.63433 −0.703238 −0.351619 0.936143i \(-0.614369\pi\)
−0.351619 + 0.936143i \(0.614369\pi\)
\(90\) 1.09516 0.115440
\(91\) 12.2162 1.28061
\(92\) 3.41663 0.356208
\(93\) 4.07186 0.422232
\(94\) 2.04732 0.211165
\(95\) −2.30562 −0.236551
\(96\) −7.80085 −0.796171
\(97\) −7.59549 −0.771205 −0.385603 0.922665i \(-0.626006\pi\)
−0.385603 + 0.922665i \(0.626006\pi\)
\(98\) −4.45288 −0.449809
\(99\) −1.00143 −0.100647
\(100\) 8.46121 0.846121
\(101\) 17.5517 1.74646 0.873231 0.487307i \(-0.162021\pi\)
0.873231 + 0.487307i \(0.162021\pi\)
\(102\) 5.52267 0.546826
\(103\) 14.1752 1.39673 0.698363 0.715744i \(-0.253912\pi\)
0.698363 + 0.715744i \(0.253912\pi\)
\(104\) −13.4908 −1.32288
\(105\) −13.7278 −1.33969
\(106\) −1.66037 −0.161270
\(107\) 1.14586 0.110775 0.0553874 0.998465i \(-0.482361\pi\)
0.0553874 + 0.998465i \(0.482361\pi\)
\(108\) 18.2253 1.75374
\(109\) 20.2886 1.94329 0.971646 0.236442i \(-0.0759815\pi\)
0.971646 + 0.236442i \(0.0759815\pi\)
\(110\) −37.0310 −3.53077
\(111\) 8.70310 0.826061
\(112\) 2.50806 0.236989
\(113\) 4.25824 0.400581 0.200291 0.979737i \(-0.435811\pi\)
0.200291 + 0.979737i \(0.435811\pi\)
\(114\) −3.30016 −0.309089
\(115\) 2.73432 0.254976
\(116\) 24.1834 2.24537
\(117\) −0.704181 −0.0651016
\(118\) 29.0988 2.67876
\(119\) 4.21280 0.386187
\(120\) 15.1600 1.38392
\(121\) 22.8615 2.07831
\(122\) −19.0565 −1.72530
\(123\) 2.44377 0.220348
\(124\) −8.27290 −0.742928
\(125\) −6.90010 −0.617163
\(126\) 1.19577 0.106528
\(127\) 1.54916 0.137466 0.0687329 0.997635i \(-0.478104\pi\)
0.0687329 + 0.997635i \(0.478104\pi\)
\(128\) 19.7595 1.74651
\(129\) 13.5127 1.18973
\(130\) −26.0394 −2.28381
\(131\) −14.8765 −1.29977 −0.649883 0.760034i \(-0.725182\pi\)
−0.649883 + 0.760034i \(0.725182\pi\)
\(132\) −33.4336 −2.91002
\(133\) −2.51743 −0.218289
\(134\) −17.0418 −1.47219
\(135\) 14.5857 1.25534
\(136\) −4.65234 −0.398935
\(137\) 15.3396 1.31055 0.655276 0.755390i \(-0.272552\pi\)
0.655276 + 0.755390i \(0.272552\pi\)
\(138\) 3.91378 0.333163
\(139\) 14.1749 1.20230 0.601151 0.799136i \(-0.294709\pi\)
0.601151 + 0.799136i \(0.294709\pi\)
\(140\) 27.8910 2.35722
\(141\) 1.47929 0.124579
\(142\) −9.27626 −0.778446
\(143\) 23.8107 1.99115
\(144\) −0.144572 −0.0120477
\(145\) 19.3539 1.60725
\(146\) 28.0163 2.31864
\(147\) −3.21743 −0.265369
\(148\) −17.6823 −1.45348
\(149\) −18.9209 −1.55006 −0.775028 0.631927i \(-0.782264\pi\)
−0.775028 + 0.631927i \(0.782264\pi\)
\(150\) 9.69242 0.791382
\(151\) 10.0386 0.816930 0.408465 0.912774i \(-0.366064\pi\)
0.408465 + 0.912774i \(0.366064\pi\)
\(152\) 2.78008 0.225495
\(153\) −0.242839 −0.0196323
\(154\) −40.4330 −3.25818
\(155\) −6.62078 −0.531794
\(156\) −23.5098 −1.88229
\(157\) −20.3741 −1.62603 −0.813014 0.582244i \(-0.802175\pi\)
−0.813014 + 0.582244i \(0.802175\pi\)
\(158\) −15.9752 −1.27091
\(159\) −1.19970 −0.0951426
\(160\) 12.6841 1.00276
\(161\) 2.98551 0.235291
\(162\) 19.6758 1.54587
\(163\) 10.2711 0.804495 0.402248 0.915531i \(-0.368229\pi\)
0.402248 + 0.915531i \(0.368229\pi\)
\(164\) −4.96507 −0.387707
\(165\) −26.7568 −2.08301
\(166\) −4.66747 −0.362266
\(167\) 7.65655 0.592482 0.296241 0.955113i \(-0.404267\pi\)
0.296241 + 0.955113i \(0.404267\pi\)
\(168\) 16.5528 1.27707
\(169\) 3.74316 0.287935
\(170\) −8.97977 −0.688717
\(171\) 0.145112 0.0110970
\(172\) −27.4540 −2.09335
\(173\) −4.81599 −0.366153 −0.183076 0.983099i \(-0.558606\pi\)
−0.183076 + 0.983099i \(0.558606\pi\)
\(174\) 27.7023 2.10011
\(175\) 7.39356 0.558901
\(176\) 4.88846 0.368481
\(177\) 21.0253 1.58036
\(178\) 15.4405 1.15731
\(179\) 2.48395 0.185659 0.0928295 0.995682i \(-0.470409\pi\)
0.0928295 + 0.995682i \(0.470409\pi\)
\(180\) −1.60773 −0.119833
\(181\) 10.7086 0.795964 0.397982 0.917393i \(-0.369711\pi\)
0.397982 + 0.917393i \(0.369711\pi\)
\(182\) −28.4316 −2.10749
\(183\) −13.7693 −1.01786
\(184\) −3.29700 −0.243058
\(185\) −14.1511 −1.04041
\(186\) −9.47670 −0.694865
\(187\) 8.21117 0.600460
\(188\) −3.00551 −0.219199
\(189\) 15.9256 1.15842
\(190\) 5.36601 0.389291
\(191\) 15.5937 1.12832 0.564160 0.825666i \(-0.309200\pi\)
0.564160 + 0.825666i \(0.309200\pi\)
\(192\) 20.9808 1.51416
\(193\) 16.5892 1.19411 0.597057 0.802199i \(-0.296337\pi\)
0.597057 + 0.802199i \(0.296337\pi\)
\(194\) 17.6775 1.26917
\(195\) −18.8148 −1.34736
\(196\) 6.53693 0.466923
\(197\) 22.6011 1.61026 0.805132 0.593095i \(-0.202094\pi\)
0.805132 + 0.593095i \(0.202094\pi\)
\(198\) 2.33068 0.165634
\(199\) −11.0208 −0.781244 −0.390622 0.920551i \(-0.627740\pi\)
−0.390622 + 0.920551i \(0.627740\pi\)
\(200\) −8.16497 −0.577350
\(201\) −12.3136 −0.868531
\(202\) −40.8493 −2.87414
\(203\) 21.1319 1.48317
\(204\) −8.10741 −0.567632
\(205\) −3.97353 −0.277524
\(206\) −32.9909 −2.29859
\(207\) −0.172094 −0.0119614
\(208\) 3.43746 0.238345
\(209\) −4.90672 −0.339405
\(210\) 31.9495 2.20472
\(211\) −15.1655 −1.04404 −0.522018 0.852934i \(-0.674821\pi\)
−0.522018 + 0.852934i \(0.674821\pi\)
\(212\) 2.43746 0.167406
\(213\) −6.70256 −0.459252
\(214\) −2.66684 −0.182301
\(215\) −21.9714 −1.49844
\(216\) −17.5872 −1.19666
\(217\) −7.22901 −0.490737
\(218\) −47.2189 −3.19806
\(219\) 20.2432 1.36791
\(220\) 54.3624 3.66511
\(221\) 5.77392 0.388396
\(222\) −20.2553 −1.35945
\(223\) −9.58028 −0.641543 −0.320772 0.947157i \(-0.603942\pi\)
−0.320772 + 0.947157i \(0.603942\pi\)
\(224\) 13.8493 0.925346
\(225\) −0.426188 −0.0284125
\(226\) −9.91047 −0.659234
\(227\) 3.21564 0.213430 0.106715 0.994290i \(-0.465967\pi\)
0.106715 + 0.994290i \(0.465967\pi\)
\(228\) 4.84472 0.320849
\(229\) 14.8115 0.978772 0.489386 0.872067i \(-0.337221\pi\)
0.489386 + 0.872067i \(0.337221\pi\)
\(230\) −6.36375 −0.419613
\(231\) −29.2149 −1.92220
\(232\) −23.3367 −1.53213
\(233\) 16.8961 1.10690 0.553451 0.832881i \(-0.313310\pi\)
0.553451 + 0.832881i \(0.313310\pi\)
\(234\) 1.63889 0.107137
\(235\) −2.40530 −0.156904
\(236\) −42.7177 −2.78069
\(237\) −11.5428 −0.749789
\(238\) −9.80472 −0.635545
\(239\) −18.1942 −1.17689 −0.588444 0.808538i \(-0.700259\pi\)
−0.588444 + 0.808538i \(0.700259\pi\)
\(240\) −3.86278 −0.249341
\(241\) 30.7883 1.98325 0.991625 0.129153i \(-0.0412258\pi\)
0.991625 + 0.129153i \(0.0412258\pi\)
\(242\) −53.2069 −3.42027
\(243\) −1.78620 −0.114585
\(244\) 27.9754 1.79094
\(245\) 5.23149 0.334227
\(246\) −5.68755 −0.362625
\(247\) −3.45030 −0.219538
\(248\) 7.98325 0.506937
\(249\) −3.37248 −0.213722
\(250\) 16.0590 1.01566
\(251\) −7.59537 −0.479416 −0.239708 0.970845i \(-0.577052\pi\)
−0.239708 + 0.970845i \(0.577052\pi\)
\(252\) −1.75542 −0.110581
\(253\) 5.81906 0.365841
\(254\) −3.60546 −0.226227
\(255\) −6.48833 −0.406315
\(256\) −21.0347 −1.31467
\(257\) −24.6502 −1.53764 −0.768819 0.639467i \(-0.779155\pi\)
−0.768819 + 0.639467i \(0.779155\pi\)
\(258\) −31.4489 −1.95792
\(259\) −15.4511 −0.960086
\(260\) 38.2265 2.37071
\(261\) −1.21811 −0.0753989
\(262\) 34.6230 2.13902
\(263\) 8.21180 0.506361 0.253181 0.967419i \(-0.418523\pi\)
0.253181 + 0.967419i \(0.418523\pi\)
\(264\) 32.2630 1.98565
\(265\) 1.95070 0.119830
\(266\) 5.85897 0.359237
\(267\) 11.1565 0.682769
\(268\) 25.0177 1.52820
\(269\) −28.6451 −1.74652 −0.873262 0.487251i \(-0.838000\pi\)
−0.873262 + 0.487251i \(0.838000\pi\)
\(270\) −33.9462 −2.06590
\(271\) 2.23336 0.135667 0.0678333 0.997697i \(-0.478391\pi\)
0.0678333 + 0.997697i \(0.478391\pi\)
\(272\) 1.18542 0.0718765
\(273\) −20.5433 −1.24334
\(274\) −35.7009 −2.15677
\(275\) 14.4108 0.869004
\(276\) −5.74553 −0.345840
\(277\) −2.57497 −0.154715 −0.0773574 0.997003i \(-0.524648\pi\)
−0.0773574 + 0.997003i \(0.524648\pi\)
\(278\) −32.9902 −1.97862
\(279\) 0.416703 0.0249473
\(280\) −26.9145 −1.60845
\(281\) −15.4368 −0.920883 −0.460442 0.887690i \(-0.652309\pi\)
−0.460442 + 0.887690i \(0.652309\pi\)
\(282\) −3.44284 −0.205018
\(283\) 13.1430 0.781269 0.390634 0.920546i \(-0.372256\pi\)
0.390634 + 0.920546i \(0.372256\pi\)
\(284\) 13.6178 0.808066
\(285\) 3.87721 0.229666
\(286\) −55.4161 −3.27682
\(287\) −4.33857 −0.256098
\(288\) −0.798317 −0.0470413
\(289\) −15.0088 −0.882873
\(290\) −45.0435 −2.64505
\(291\) 12.7729 0.748759
\(292\) −41.1285 −2.40686
\(293\) 2.65975 0.155384 0.0776920 0.996977i \(-0.475245\pi\)
0.0776920 + 0.996977i \(0.475245\pi\)
\(294\) 7.48813 0.436717
\(295\) −34.1869 −1.99044
\(296\) 17.0632 0.991779
\(297\) 31.0407 1.80116
\(298\) 44.0357 2.55092
\(299\) 4.09184 0.236637
\(300\) −14.2287 −0.821494
\(301\) −23.9899 −1.38275
\(302\) −23.3635 −1.34442
\(303\) −29.5156 −1.69563
\(304\) −0.708366 −0.0406276
\(305\) 22.3887 1.28197
\(306\) 0.565174 0.0323089
\(307\) 19.4171 1.10819 0.554097 0.832452i \(-0.313064\pi\)
0.554097 + 0.832452i \(0.313064\pi\)
\(308\) 59.3566 3.38215
\(309\) −23.8376 −1.35607
\(310\) 15.4090 0.875170
\(311\) −31.2179 −1.77021 −0.885104 0.465394i \(-0.845913\pi\)
−0.885104 + 0.465394i \(0.845913\pi\)
\(312\) 22.6867 1.28438
\(313\) 15.7129 0.888144 0.444072 0.895991i \(-0.353534\pi\)
0.444072 + 0.895991i \(0.353534\pi\)
\(314\) 47.4179 2.67595
\(315\) −1.40486 −0.0791549
\(316\) 23.4519 1.31927
\(317\) 10.2980 0.578394 0.289197 0.957270i \(-0.406612\pi\)
0.289197 + 0.957270i \(0.406612\pi\)
\(318\) 2.79214 0.156576
\(319\) 41.1882 2.30609
\(320\) −34.1145 −1.90706
\(321\) −1.92693 −0.107551
\(322\) −6.94837 −0.387218
\(323\) −1.18985 −0.0662048
\(324\) −28.8845 −1.60469
\(325\) 10.1334 0.562098
\(326\) −23.9046 −1.32395
\(327\) −34.1180 −1.88673
\(328\) 4.79124 0.264552
\(329\) −2.62627 −0.144791
\(330\) 62.2728 3.42800
\(331\) −8.49775 −0.467079 −0.233539 0.972347i \(-0.575031\pi\)
−0.233539 + 0.972347i \(0.575031\pi\)
\(332\) 6.85196 0.376050
\(333\) 0.890650 0.0488073
\(334\) −17.8196 −0.975044
\(335\) 20.0216 1.09390
\(336\) −4.21765 −0.230091
\(337\) 24.2853 1.32290 0.661452 0.749987i \(-0.269940\pi\)
0.661452 + 0.749987i \(0.269940\pi\)
\(338\) −8.71169 −0.473853
\(339\) −7.16081 −0.388922
\(340\) 13.1825 0.714922
\(341\) −14.0901 −0.763020
\(342\) −0.337729 −0.0182623
\(343\) −15.1865 −0.819993
\(344\) 26.4928 1.42840
\(345\) −4.59813 −0.247555
\(346\) 11.2086 0.602576
\(347\) 1.91315 0.102703 0.0513516 0.998681i \(-0.483647\pi\)
0.0513516 + 0.998681i \(0.483647\pi\)
\(348\) −40.6677 −2.18002
\(349\) −1.00000 −0.0535288
\(350\) −17.2075 −0.919780
\(351\) 21.8272 1.16505
\(352\) 26.9937 1.43877
\(353\) 29.5738 1.57405 0.787027 0.616919i \(-0.211619\pi\)
0.787027 + 0.616919i \(0.211619\pi\)
\(354\) −48.9336 −2.60079
\(355\) 10.8983 0.578419
\(356\) −22.6670 −1.20135
\(357\) −7.08440 −0.374946
\(358\) −5.78105 −0.305538
\(359\) −12.7981 −0.675460 −0.337730 0.941243i \(-0.609659\pi\)
−0.337730 + 0.941243i \(0.609659\pi\)
\(360\) 1.55144 0.0817678
\(361\) −18.2890 −0.962578
\(362\) −24.9228 −1.30991
\(363\) −38.4447 −2.01782
\(364\) 41.7383 2.18768
\(365\) −32.9150 −1.72285
\(366\) 32.0462 1.67508
\(367\) 3.44465 0.179809 0.0899047 0.995950i \(-0.471344\pi\)
0.0899047 + 0.995950i \(0.471344\pi\)
\(368\) 0.840077 0.0437920
\(369\) 0.250089 0.0130191
\(370\) 32.9347 1.71220
\(371\) 2.12990 0.110579
\(372\) 13.9120 0.721305
\(373\) 0.144165 0.00746457 0.00373228 0.999993i \(-0.498812\pi\)
0.00373228 + 0.999993i \(0.498812\pi\)
\(374\) −19.1104 −0.988174
\(375\) 11.6035 0.599200
\(376\) 2.90028 0.149570
\(377\) 28.9626 1.49165
\(378\) −37.0648 −1.90641
\(379\) 2.99289 0.153735 0.0768673 0.997041i \(-0.475508\pi\)
0.0768673 + 0.997041i \(0.475508\pi\)
\(380\) −7.87743 −0.404104
\(381\) −2.60513 −0.133465
\(382\) −36.2922 −1.85687
\(383\) −35.1189 −1.79449 −0.897245 0.441533i \(-0.854435\pi\)
−0.897245 + 0.441533i \(0.854435\pi\)
\(384\) −33.2283 −1.69568
\(385\) 47.5029 2.42097
\(386\) −38.6090 −1.96515
\(387\) 1.38285 0.0702942
\(388\) −25.9510 −1.31746
\(389\) −7.35037 −0.372678 −0.186339 0.982485i \(-0.559662\pi\)
−0.186339 + 0.982485i \(0.559662\pi\)
\(390\) 43.7889 2.21734
\(391\) 1.41108 0.0713615
\(392\) −6.30806 −0.318605
\(393\) 25.0169 1.26194
\(394\) −52.6011 −2.65000
\(395\) 18.7685 0.944345
\(396\) −3.42150 −0.171937
\(397\) −24.4397 −1.22659 −0.613295 0.789854i \(-0.710156\pi\)
−0.613295 + 0.789854i \(0.710156\pi\)
\(398\) 25.6494 1.28569
\(399\) 4.23340 0.211935
\(400\) 2.08044 0.104022
\(401\) −26.9732 −1.34698 −0.673488 0.739198i \(-0.735205\pi\)
−0.673488 + 0.739198i \(0.735205\pi\)
\(402\) 28.6581 1.42934
\(403\) −9.90784 −0.493545
\(404\) 59.9677 2.98350
\(405\) −23.1162 −1.14865
\(406\) −49.1816 −2.44084
\(407\) −30.1158 −1.49278
\(408\) 7.82355 0.387323
\(409\) −11.1449 −0.551078 −0.275539 0.961290i \(-0.588856\pi\)
−0.275539 + 0.961290i \(0.588856\pi\)
\(410\) 9.24786 0.456719
\(411\) −25.7957 −1.27241
\(412\) 48.4314 2.38605
\(413\) −37.3275 −1.83677
\(414\) 0.400526 0.0196848
\(415\) 5.48360 0.269179
\(416\) 18.9814 0.930639
\(417\) −23.8371 −1.16731
\(418\) 11.4197 0.558557
\(419\) −22.2672 −1.08783 −0.543913 0.839142i \(-0.683058\pi\)
−0.543913 + 0.839142i \(0.683058\pi\)
\(420\) −46.9026 −2.28861
\(421\) 9.66366 0.470978 0.235489 0.971877i \(-0.424331\pi\)
0.235489 + 0.971877i \(0.424331\pi\)
\(422\) 35.2956 1.71816
\(423\) 0.151386 0.00736065
\(424\) −2.35212 −0.114229
\(425\) 3.49452 0.169509
\(426\) 15.5993 0.755789
\(427\) 24.4454 1.18300
\(428\) 3.91498 0.189238
\(429\) −40.0409 −1.93319
\(430\) 51.1354 2.46597
\(431\) 23.3189 1.12323 0.561616 0.827398i \(-0.310180\pi\)
0.561616 + 0.827398i \(0.310180\pi\)
\(432\) 4.48123 0.215603
\(433\) −3.76269 −0.180824 −0.0904118 0.995904i \(-0.528818\pi\)
−0.0904118 + 0.995904i \(0.528818\pi\)
\(434\) 16.8245 0.807604
\(435\) −32.5462 −1.56047
\(436\) 69.3184 3.31975
\(437\) −0.843215 −0.0403365
\(438\) −47.1132 −2.25116
\(439\) 37.5563 1.79246 0.896232 0.443585i \(-0.146294\pi\)
0.896232 + 0.443585i \(0.146294\pi\)
\(440\) −52.4591 −2.50089
\(441\) −0.329262 −0.0156792
\(442\) −13.4380 −0.639181
\(443\) 25.1894 1.19679 0.598393 0.801203i \(-0.295806\pi\)
0.598393 + 0.801203i \(0.295806\pi\)
\(444\) 29.7352 1.41117
\(445\) −18.1404 −0.859935
\(446\) 22.2968 1.05578
\(447\) 31.8180 1.50494
\(448\) −37.2485 −1.75983
\(449\) 21.2411 1.00243 0.501215 0.865323i \(-0.332886\pi\)
0.501215 + 0.865323i \(0.332886\pi\)
\(450\) 0.991894 0.0467583
\(451\) −8.45632 −0.398192
\(452\) 14.5488 0.684318
\(453\) −16.8813 −0.793152
\(454\) −7.48398 −0.351240
\(455\) 33.4030 1.56596
\(456\) −4.67509 −0.218931
\(457\) −18.5327 −0.866924 −0.433462 0.901172i \(-0.642708\pi\)
−0.433462 + 0.901172i \(0.642708\pi\)
\(458\) −34.4718 −1.61076
\(459\) 7.52715 0.351337
\(460\) 9.34213 0.435579
\(461\) 23.3608 1.08802 0.544011 0.839078i \(-0.316905\pi\)
0.544011 + 0.839078i \(0.316905\pi\)
\(462\) 67.9936 3.16335
\(463\) 6.62455 0.307869 0.153935 0.988081i \(-0.450806\pi\)
0.153935 + 0.988081i \(0.450806\pi\)
\(464\) 5.94619 0.276045
\(465\) 11.1337 0.516315
\(466\) −39.3235 −1.82162
\(467\) −40.4788 −1.87314 −0.936568 0.350487i \(-0.886016\pi\)
−0.936568 + 0.350487i \(0.886016\pi\)
\(468\) −2.40592 −0.111214
\(469\) 21.8610 1.00945
\(470\) 5.59801 0.258217
\(471\) 34.2618 1.57870
\(472\) 41.2221 1.89740
\(473\) −46.7586 −2.14996
\(474\) 26.8644 1.23392
\(475\) −2.08821 −0.0958135
\(476\) 14.3936 0.659727
\(477\) −0.122774 −0.00562144
\(478\) 42.3446 1.93680
\(479\) −38.5423 −1.76104 −0.880521 0.474007i \(-0.842807\pi\)
−0.880521 + 0.474007i \(0.842807\pi\)
\(480\) −21.3300 −0.973576
\(481\) −21.1768 −0.965578
\(482\) −71.6556 −3.26382
\(483\) −5.02055 −0.228443
\(484\) 78.1090 3.55041
\(485\) −20.7685 −0.943048
\(486\) 4.15715 0.188572
\(487\) 37.0798 1.68025 0.840124 0.542395i \(-0.182482\pi\)
0.840124 + 0.542395i \(0.182482\pi\)
\(488\) −26.9959 −1.22205
\(489\) −17.2723 −0.781080
\(490\) −12.1756 −0.550036
\(491\) −16.6178 −0.749952 −0.374976 0.927034i \(-0.622349\pi\)
−0.374976 + 0.927034i \(0.622349\pi\)
\(492\) 8.34946 0.376423
\(493\) 9.98784 0.449830
\(494\) 8.03011 0.361292
\(495\) −2.73821 −0.123074
\(496\) −2.03413 −0.0913353
\(497\) 11.8995 0.533763
\(498\) 7.84900 0.351722
\(499\) 3.04495 0.136311 0.0681553 0.997675i \(-0.478289\pi\)
0.0681553 + 0.997675i \(0.478289\pi\)
\(500\) −23.5750 −1.05431
\(501\) −12.8755 −0.575237
\(502\) 17.6772 0.788972
\(503\) −12.3013 −0.548487 −0.274244 0.961660i \(-0.588427\pi\)
−0.274244 + 0.961660i \(0.588427\pi\)
\(504\) 1.69396 0.0754551
\(505\) 47.9919 2.13561
\(506\) −13.5431 −0.602063
\(507\) −6.29463 −0.279554
\(508\) 5.29290 0.234835
\(509\) −6.68287 −0.296213 −0.148106 0.988971i \(-0.547318\pi\)
−0.148106 + 0.988971i \(0.547318\pi\)
\(510\) 15.1007 0.668671
\(511\) −35.9389 −1.58984
\(512\) 9.43645 0.417036
\(513\) −4.49798 −0.198590
\(514\) 57.3700 2.53048
\(515\) 38.7595 1.70795
\(516\) 46.1678 2.03242
\(517\) −5.11886 −0.225127
\(518\) 35.9604 1.58001
\(519\) 8.09875 0.355496
\(520\) −36.8881 −1.61765
\(521\) −12.6902 −0.555966 −0.277983 0.960586i \(-0.589666\pi\)
−0.277983 + 0.960586i \(0.589666\pi\)
\(522\) 2.83498 0.124084
\(523\) −23.9052 −1.04530 −0.522650 0.852548i \(-0.675056\pi\)
−0.522650 + 0.852548i \(0.675056\pi\)
\(524\) −50.8274 −2.22041
\(525\) −12.4333 −0.542633
\(526\) −19.1119 −0.833316
\(527\) −3.41674 −0.148836
\(528\) −8.22062 −0.357756
\(529\) 1.00000 0.0434783
\(530\) −4.53998 −0.197204
\(531\) 2.15167 0.0933747
\(532\) −8.60111 −0.372905
\(533\) −5.94630 −0.257563
\(534\) −25.9653 −1.12363
\(535\) 3.13315 0.135458
\(536\) −24.1418 −1.04277
\(537\) −4.17710 −0.180255
\(538\) 66.6677 2.87425
\(539\) 11.1334 0.479551
\(540\) 49.8339 2.14451
\(541\) −28.9264 −1.24364 −0.621821 0.783159i \(-0.713607\pi\)
−0.621821 + 0.783159i \(0.713607\pi\)
\(542\) −5.19783 −0.223266
\(543\) −18.0080 −0.772797
\(544\) 6.54578 0.280648
\(545\) 55.4753 2.37630
\(546\) 47.8117 2.04615
\(547\) 2.80933 0.120118 0.0600592 0.998195i \(-0.480871\pi\)
0.0600592 + 0.998195i \(0.480871\pi\)
\(548\) 52.4097 2.23883
\(549\) −1.40911 −0.0601394
\(550\) −33.5392 −1.43012
\(551\) −5.96840 −0.254262
\(552\) 5.54436 0.235984
\(553\) 20.4927 0.871438
\(554\) 5.99289 0.254613
\(555\) 23.7970 1.01013
\(556\) 48.4304 2.05391
\(557\) 30.3427 1.28566 0.642830 0.766009i \(-0.277760\pi\)
0.642830 + 0.766009i \(0.277760\pi\)
\(558\) −0.969819 −0.0410557
\(559\) −32.8797 −1.39066
\(560\) 6.85782 0.289796
\(561\) −13.8082 −0.582983
\(562\) 35.9271 1.51549
\(563\) −1.18456 −0.0499232 −0.0249616 0.999688i \(-0.507946\pi\)
−0.0249616 + 0.999688i \(0.507946\pi\)
\(564\) 5.05418 0.212819
\(565\) 11.6434 0.489840
\(566\) −30.5885 −1.28573
\(567\) −25.2398 −1.05997
\(568\) −13.1410 −0.551383
\(569\) 38.9487 1.63282 0.816408 0.577475i \(-0.195962\pi\)
0.816408 + 0.577475i \(0.195962\pi\)
\(570\) −9.02369 −0.377961
\(571\) −13.6586 −0.571594 −0.285797 0.958290i \(-0.592258\pi\)
−0.285797 + 0.958290i \(0.592258\pi\)
\(572\) 81.3521 3.40150
\(573\) −26.2229 −1.09548
\(574\) 10.0974 0.421459
\(575\) 2.47648 0.103276
\(576\) 2.14712 0.0894633
\(577\) −4.23214 −0.176186 −0.0880931 0.996112i \(-0.528077\pi\)
−0.0880931 + 0.996112i \(0.528077\pi\)
\(578\) 34.9311 1.45294
\(579\) −27.8970 −1.15936
\(580\) 66.1250 2.74569
\(581\) 5.98737 0.248398
\(582\) −29.7271 −1.23223
\(583\) 4.15139 0.171933
\(584\) 39.6885 1.64232
\(585\) −1.92545 −0.0796077
\(586\) −6.19020 −0.255715
\(587\) −31.4840 −1.29948 −0.649742 0.760155i \(-0.725123\pi\)
−0.649742 + 0.760155i \(0.725123\pi\)
\(588\) −10.9927 −0.453333
\(589\) 2.04173 0.0841281
\(590\) 79.5653 3.27565
\(591\) −38.0069 −1.56340
\(592\) −4.34771 −0.178690
\(593\) 4.69966 0.192992 0.0964959 0.995333i \(-0.469237\pi\)
0.0964959 + 0.995333i \(0.469237\pi\)
\(594\) −72.2430 −2.96417
\(595\) 11.5191 0.472238
\(596\) −64.6455 −2.64798
\(597\) 18.5330 0.758505
\(598\) −9.52320 −0.389433
\(599\) 11.1541 0.455744 0.227872 0.973691i \(-0.426823\pi\)
0.227872 + 0.973691i \(0.426823\pi\)
\(600\) 13.7305 0.560546
\(601\) −35.5308 −1.44933 −0.724667 0.689100i \(-0.758006\pi\)
−0.724667 + 0.689100i \(0.758006\pi\)
\(602\) 55.8331 2.27559
\(603\) −1.26013 −0.0513166
\(604\) 34.2981 1.39557
\(605\) 62.5104 2.54141
\(606\) 68.6936 2.79049
\(607\) 44.2640 1.79662 0.898310 0.439363i \(-0.144796\pi\)
0.898310 + 0.439363i \(0.144796\pi\)
\(608\) −3.91154 −0.158634
\(609\) −35.5362 −1.44000
\(610\) −52.1065 −2.10973
\(611\) −3.59947 −0.145619
\(612\) −0.829689 −0.0335382
\(613\) −5.50730 −0.222438 −0.111219 0.993796i \(-0.535475\pi\)
−0.111219 + 0.993796i \(0.535475\pi\)
\(614\) −45.1907 −1.82375
\(615\) 6.68205 0.269446
\(616\) −57.2784 −2.30781
\(617\) −10.7057 −0.430995 −0.215498 0.976504i \(-0.569137\pi\)
−0.215498 + 0.976504i \(0.569137\pi\)
\(618\) 55.4788 2.23168
\(619\) −6.23190 −0.250481 −0.125241 0.992126i \(-0.539970\pi\)
−0.125241 + 0.992126i \(0.539970\pi\)
\(620\) −22.6207 −0.908470
\(621\) 5.33431 0.214059
\(622\) 72.6555 2.91322
\(623\) −19.8069 −0.793545
\(624\) −5.78056 −0.231408
\(625\) −31.2494 −1.24998
\(626\) −36.5696 −1.46161
\(627\) 8.25133 0.329526
\(628\) −69.6106 −2.77777
\(629\) −7.30287 −0.291184
\(630\) 3.26962 0.130265
\(631\) −18.1344 −0.721919 −0.360959 0.932582i \(-0.617551\pi\)
−0.360959 + 0.932582i \(0.617551\pi\)
\(632\) −22.6308 −0.900205
\(633\) 25.5029 1.01365
\(634\) −23.9672 −0.951861
\(635\) 4.23590 0.168096
\(636\) −4.09893 −0.162533
\(637\) 7.82880 0.310188
\(638\) −95.8598 −3.79513
\(639\) −0.685921 −0.0271346
\(640\) 54.0287 2.13567
\(641\) 50.5887 1.99813 0.999066 0.0432072i \(-0.0137575\pi\)
0.999066 + 0.0432072i \(0.0137575\pi\)
\(642\) 4.48466 0.176995
\(643\) 6.78845 0.267710 0.133855 0.991001i \(-0.457264\pi\)
0.133855 + 0.991001i \(0.457264\pi\)
\(644\) 10.2004 0.401951
\(645\) 36.9479 1.45482
\(646\) 2.76920 0.108953
\(647\) 41.5726 1.63439 0.817193 0.576364i \(-0.195529\pi\)
0.817193 + 0.576364i \(0.195529\pi\)
\(648\) 27.8732 1.09496
\(649\) −72.7551 −2.85589
\(650\) −23.5840 −0.925042
\(651\) 12.1566 0.476454
\(652\) 35.0925 1.37433
\(653\) −27.1592 −1.06282 −0.531411 0.847114i \(-0.678338\pi\)
−0.531411 + 0.847114i \(0.678338\pi\)
\(654\) 79.4050 3.10498
\(655\) −40.6771 −1.58938
\(656\) −1.22081 −0.0476645
\(657\) 2.07163 0.0808219
\(658\) 6.11228 0.238282
\(659\) −28.8138 −1.12242 −0.561212 0.827672i \(-0.689665\pi\)
−0.561212 + 0.827672i \(0.689665\pi\)
\(660\) −91.4179 −3.55844
\(661\) 4.26191 0.165769 0.0828846 0.996559i \(-0.473587\pi\)
0.0828846 + 0.996559i \(0.473587\pi\)
\(662\) 19.7774 0.768669
\(663\) −9.70964 −0.377091
\(664\) −6.61206 −0.256598
\(665\) −6.88344 −0.266928
\(666\) −2.07287 −0.0803220
\(667\) 7.07815 0.274067
\(668\) 26.1596 1.01214
\(669\) 16.1106 0.622870
\(670\) −46.5976 −1.80022
\(671\) 47.6466 1.83938
\(672\) −23.2895 −0.898413
\(673\) 39.6915 1.52999 0.764997 0.644034i \(-0.222741\pi\)
0.764997 + 0.644034i \(0.222741\pi\)
\(674\) −56.5207 −2.17710
\(675\) 13.2103 0.508466
\(676\) 12.7890 0.491883
\(677\) −5.65899 −0.217493 −0.108746 0.994070i \(-0.534684\pi\)
−0.108746 + 0.994070i \(0.534684\pi\)
\(678\) 16.6658 0.640047
\(679\) −22.6764 −0.870241
\(680\) −12.7210 −0.487827
\(681\) −5.40755 −0.207218
\(682\) 32.7927 1.25570
\(683\) 40.2392 1.53971 0.769855 0.638219i \(-0.220329\pi\)
0.769855 + 0.638219i \(0.220329\pi\)
\(684\) 0.495794 0.0189572
\(685\) 41.9434 1.60257
\(686\) 35.3445 1.34946
\(687\) −24.9076 −0.950284
\(688\) −6.75038 −0.257356
\(689\) 2.91917 0.111212
\(690\) 10.7015 0.407400
\(691\) −13.1813 −0.501441 −0.250720 0.968060i \(-0.580667\pi\)
−0.250720 + 0.968060i \(0.580667\pi\)
\(692\) −16.4544 −0.625503
\(693\) −2.98977 −0.113572
\(694\) −4.45260 −0.169018
\(695\) 38.7587 1.47020
\(696\) 39.2438 1.48753
\(697\) −2.05060 −0.0776719
\(698\) 2.32736 0.0880920
\(699\) −28.4132 −1.07469
\(700\) 25.2610 0.954777
\(701\) 10.4621 0.395146 0.197573 0.980288i \(-0.436694\pi\)
0.197573 + 0.980288i \(0.436694\pi\)
\(702\) −50.7998 −1.91731
\(703\) 4.36395 0.164590
\(704\) −72.6011 −2.73626
\(705\) 4.04484 0.152338
\(706\) −68.8290 −2.59041
\(707\) 52.4008 1.97074
\(708\) 71.8357 2.69975
\(709\) −26.0586 −0.978650 −0.489325 0.872101i \(-0.662757\pi\)
−0.489325 + 0.872101i \(0.662757\pi\)
\(710\) −25.3642 −0.951902
\(711\) −1.18126 −0.0443008
\(712\) 21.8734 0.819740
\(713\) −2.42137 −0.0906808
\(714\) 16.4880 0.617047
\(715\) 65.1059 2.43482
\(716\) 8.48672 0.317164
\(717\) 30.5961 1.14263
\(718\) 29.7860 1.11160
\(719\) −20.7378 −0.773391 −0.386695 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(720\) −0.395306 −0.0147322
\(721\) 42.3203 1.57609
\(722\) 42.5651 1.58411
\(723\) −51.7748 −1.92553
\(724\) 36.5873 1.35976
\(725\) 17.5289 0.651007
\(726\) 89.4748 3.32072
\(727\) 9.92499 0.368098 0.184049 0.982917i \(-0.441080\pi\)
0.184049 + 0.982917i \(0.441080\pi\)
\(728\) −40.2769 −1.49276
\(729\) 28.3661 1.05059
\(730\) 76.6053 2.83529
\(731\) −11.3386 −0.419375
\(732\) −47.0445 −1.73882
\(733\) 39.6999 1.46635 0.733175 0.680040i \(-0.238038\pi\)
0.733175 + 0.680040i \(0.238038\pi\)
\(734\) −8.01697 −0.295912
\(735\) −8.79747 −0.324499
\(736\) 4.63884 0.170990
\(737\) 42.6092 1.56953
\(738\) −0.582048 −0.0214255
\(739\) −33.4660 −1.23107 −0.615534 0.788110i \(-0.711060\pi\)
−0.615534 + 0.788110i \(0.711060\pi\)
\(740\) −48.3490 −1.77734
\(741\) 5.80216 0.213148
\(742\) −4.95706 −0.181979
\(743\) 1.61372 0.0592017 0.0296009 0.999562i \(-0.490576\pi\)
0.0296009 + 0.999562i \(0.490576\pi\)
\(744\) −13.4249 −0.492182
\(745\) −51.7356 −1.89544
\(746\) −0.335524 −0.0122844
\(747\) −0.345130 −0.0126277
\(748\) 28.0545 1.02577
\(749\) 3.42098 0.125000
\(750\) −27.0055 −0.986101
\(751\) −11.3562 −0.414395 −0.207198 0.978299i \(-0.566434\pi\)
−0.207198 + 0.978299i \(0.566434\pi\)
\(752\) −0.738992 −0.0269483
\(753\) 12.7727 0.465462
\(754\) −67.4066 −2.45480
\(755\) 27.4487 0.998960
\(756\) 54.4120 1.97894
\(757\) 21.3892 0.777404 0.388702 0.921364i \(-0.372924\pi\)
0.388702 + 0.921364i \(0.372924\pi\)
\(758\) −6.96555 −0.253000
\(759\) −9.78555 −0.355193
\(760\) 7.60163 0.275740
\(761\) 42.2649 1.53210 0.766050 0.642781i \(-0.222219\pi\)
0.766050 + 0.642781i \(0.222219\pi\)
\(762\) 6.06308 0.219642
\(763\) 60.5717 2.19284
\(764\) 53.2778 1.92752
\(765\) −0.663998 −0.0240069
\(766\) 81.7344 2.95318
\(767\) −51.1598 −1.84727
\(768\) 35.3728 1.27641
\(769\) 7.99723 0.288388 0.144194 0.989549i \(-0.453941\pi\)
0.144194 + 0.989549i \(0.453941\pi\)
\(770\) −110.557 −3.98418
\(771\) 41.4527 1.49288
\(772\) 56.6790 2.03992
\(773\) 19.4827 0.700744 0.350372 0.936611i \(-0.386055\pi\)
0.350372 + 0.936611i \(0.386055\pi\)
\(774\) −3.21839 −0.115683
\(775\) −5.99647 −0.215399
\(776\) 25.0424 0.898968
\(777\) 25.9832 0.932141
\(778\) 17.1070 0.613315
\(779\) 1.22537 0.0439034
\(780\) −64.2831 −2.30171
\(781\) 23.1932 0.829919
\(782\) −3.28410 −0.117439
\(783\) 37.7571 1.34933
\(784\) 1.60729 0.0574034
\(785\) −55.7092 −1.98835
\(786\) −58.2234 −2.07676
\(787\) 39.3136 1.40138 0.700690 0.713466i \(-0.252876\pi\)
0.700690 + 0.713466i \(0.252876\pi\)
\(788\) 77.2196 2.75083
\(789\) −13.8093 −0.491623
\(790\) −43.6811 −1.55410
\(791\) 12.7130 0.452022
\(792\) 3.30170 0.117321
\(793\) 33.5041 1.18977
\(794\) 56.8800 2.01859
\(795\) −3.28036 −0.116343
\(796\) −37.6540 −1.33461
\(797\) 19.0338 0.674213 0.337107 0.941466i \(-0.390552\pi\)
0.337107 + 0.941466i \(0.390552\pi\)
\(798\) −9.85267 −0.348781
\(799\) −1.24129 −0.0439136
\(800\) 11.4880 0.406162
\(801\) 1.14173 0.0403410
\(802\) 62.7764 2.21671
\(803\) −70.0485 −2.47196
\(804\) −42.0708 −1.48372
\(805\) 8.16333 0.287719
\(806\) 23.0592 0.812224
\(807\) 48.1707 1.69569
\(808\) −57.8681 −2.03579
\(809\) 14.8212 0.521085 0.260542 0.965462i \(-0.416099\pi\)
0.260542 + 0.965462i \(0.416099\pi\)
\(810\) 53.7998 1.89033
\(811\) 45.1684 1.58608 0.793038 0.609172i \(-0.208498\pi\)
0.793038 + 0.609172i \(0.208498\pi\)
\(812\) 72.1997 2.53371
\(813\) −3.75569 −0.131718
\(814\) 70.0904 2.45667
\(815\) 28.0845 0.983756
\(816\) −1.99344 −0.0697844
\(817\) 6.77560 0.237048
\(818\) 25.9381 0.906906
\(819\) −2.10234 −0.0734617
\(820\) −13.5761 −0.474097
\(821\) 27.9727 0.976253 0.488126 0.872773i \(-0.337680\pi\)
0.488126 + 0.872773i \(0.337680\pi\)
\(822\) 60.0360 2.09399
\(823\) 1.30171 0.0453746 0.0226873 0.999743i \(-0.492778\pi\)
0.0226873 + 0.999743i \(0.492778\pi\)
\(824\) −46.7358 −1.62812
\(825\) −24.2337 −0.843711
\(826\) 86.8747 3.02276
\(827\) 2.97183 0.103341 0.0516703 0.998664i \(-0.483546\pi\)
0.0516703 + 0.998664i \(0.483546\pi\)
\(828\) −0.587981 −0.0204337
\(829\) 6.79264 0.235918 0.117959 0.993018i \(-0.462365\pi\)
0.117959 + 0.993018i \(0.462365\pi\)
\(830\) −12.7623 −0.442987
\(831\) 4.33016 0.150212
\(832\) −51.0515 −1.76989
\(833\) 2.69978 0.0935419
\(834\) 55.4776 1.92103
\(835\) 20.9354 0.724500
\(836\) −16.7644 −0.579810
\(837\) −12.9163 −0.446453
\(838\) 51.8240 1.79023
\(839\) −18.5299 −0.639723 −0.319861 0.947464i \(-0.603636\pi\)
−0.319861 + 0.947464i \(0.603636\pi\)
\(840\) 45.2605 1.56163
\(841\) 21.1002 0.727591
\(842\) −22.4909 −0.775086
\(843\) 25.9591 0.894080
\(844\) −51.8148 −1.78354
\(845\) 10.2350 0.352094
\(846\) −0.352331 −0.0121134
\(847\) 68.2531 2.34520
\(848\) 0.599322 0.0205808
\(849\) −22.1017 −0.758529
\(850\) −8.13302 −0.278960
\(851\) −5.17537 −0.177409
\(852\) −22.9001 −0.784546
\(853\) −12.9502 −0.443407 −0.221704 0.975114i \(-0.571162\pi\)
−0.221704 + 0.975114i \(0.571162\pi\)
\(854\) −56.8934 −1.94685
\(855\) 0.396783 0.0135697
\(856\) −3.77791 −0.129126
\(857\) 42.0953 1.43795 0.718973 0.695038i \(-0.244612\pi\)
0.718973 + 0.695038i \(0.244612\pi\)
\(858\) 93.1898 3.18145
\(859\) 20.9662 0.715356 0.357678 0.933845i \(-0.383569\pi\)
0.357678 + 0.933845i \(0.383569\pi\)
\(860\) −75.0680 −2.55980
\(861\) 7.29591 0.248644
\(862\) −54.2716 −1.84850
\(863\) 47.5313 1.61798 0.808991 0.587821i \(-0.200014\pi\)
0.808991 + 0.587821i \(0.200014\pi\)
\(864\) 24.7450 0.841843
\(865\) −13.1684 −0.447740
\(866\) 8.75716 0.297580
\(867\) 25.2394 0.857177
\(868\) −24.6988 −0.838333
\(869\) 39.9423 1.35495
\(870\) 75.7469 2.56806
\(871\) 29.9619 1.01522
\(872\) −66.8914 −2.26523
\(873\) 1.30714 0.0442400
\(874\) 1.96247 0.0663815
\(875\) −20.6003 −0.696417
\(876\) 69.1633 2.33681
\(877\) 14.3308 0.483915 0.241958 0.970287i \(-0.422210\pi\)
0.241958 + 0.970287i \(0.422210\pi\)
\(878\) −87.4072 −2.94985
\(879\) −4.47273 −0.150861
\(880\) 13.3666 0.450588
\(881\) 38.5566 1.29900 0.649502 0.760360i \(-0.274977\pi\)
0.649502 + 0.760360i \(0.274977\pi\)
\(882\) 0.766314 0.0258031
\(883\) −18.3587 −0.617818 −0.308909 0.951092i \(-0.599964\pi\)
−0.308909 + 0.951092i \(0.599964\pi\)
\(884\) 19.7273 0.663502
\(885\) 57.4899 1.93250
\(886\) −58.6250 −1.96955
\(887\) −22.2031 −0.745509 −0.372754 0.927930i \(-0.621587\pi\)
−0.372754 + 0.927930i \(0.621587\pi\)
\(888\) −28.6941 −0.962912
\(889\) 4.62504 0.155119
\(890\) 42.2192 1.41519
\(891\) −49.1949 −1.64809
\(892\) −32.7322 −1.09596
\(893\) 0.741752 0.0248218
\(894\) −74.0521 −2.47667
\(895\) 6.79190 0.227028
\(896\) 58.9922 1.97079
\(897\) −6.88099 −0.229750
\(898\) −49.4358 −1.64970
\(899\) −17.1388 −0.571610
\(900\) −1.45612 −0.0485375
\(901\) 1.00668 0.0335375
\(902\) 19.6809 0.655303
\(903\) 40.3422 1.34251
\(904\) −14.0394 −0.466944
\(905\) 29.2807 0.973324
\(906\) 39.2889 1.30529
\(907\) −52.4764 −1.74245 −0.871225 0.490884i \(-0.836674\pi\)
−0.871225 + 0.490884i \(0.836674\pi\)
\(908\) 10.9867 0.364605
\(909\) −3.02055 −0.100185
\(910\) −77.7410 −2.57709
\(911\) 17.4259 0.577347 0.288674 0.957428i \(-0.406786\pi\)
0.288674 + 0.957428i \(0.406786\pi\)
\(912\) 1.19121 0.0394451
\(913\) 11.6700 0.386220
\(914\) 43.1324 1.42669
\(915\) −37.6496 −1.24466
\(916\) 50.6054 1.67205
\(917\) −44.4139 −1.46668
\(918\) −17.5184 −0.578194
\(919\) −30.2110 −0.996569 −0.498284 0.867014i \(-0.666036\pi\)
−0.498284 + 0.867014i \(0.666036\pi\)
\(920\) −9.01505 −0.297217
\(921\) −32.6526 −1.07594
\(922\) −54.3691 −1.79055
\(923\) 16.3090 0.536817
\(924\) −99.8162 −3.28371
\(925\) −12.8167 −0.421411
\(926\) −15.4177 −0.506659
\(927\) −2.43947 −0.0801228
\(928\) 32.8344 1.07784
\(929\) −39.8728 −1.30818 −0.654092 0.756415i \(-0.726949\pi\)
−0.654092 + 0.756415i \(0.726949\pi\)
\(930\) −25.9123 −0.849698
\(931\) −1.61330 −0.0528738
\(932\) 57.7278 1.89094
\(933\) 52.4973 1.71868
\(934\) 94.2089 3.08261
\(935\) 22.4519 0.734256
\(936\) 2.32169 0.0758867
\(937\) 41.9966 1.37197 0.685985 0.727616i \(-0.259372\pi\)
0.685985 + 0.727616i \(0.259372\pi\)
\(938\) −50.8784 −1.66124
\(939\) −26.4233 −0.862293
\(940\) −8.21801 −0.268042
\(941\) 36.2933 1.18313 0.591564 0.806258i \(-0.298511\pi\)
0.591564 + 0.806258i \(0.298511\pi\)
\(942\) −79.7398 −2.59806
\(943\) −1.45321 −0.0473230
\(944\) −10.5034 −0.341856
\(945\) 43.5457 1.41654
\(946\) 108.824 3.53819
\(947\) −29.4432 −0.956774 −0.478387 0.878149i \(-0.658778\pi\)
−0.478387 + 0.878149i \(0.658778\pi\)
\(948\) −39.4376 −1.28087
\(949\) −49.2566 −1.59894
\(950\) 4.86002 0.157680
\(951\) −17.3175 −0.561560
\(952\) −13.8896 −0.450165
\(953\) −25.0974 −0.812986 −0.406493 0.913654i \(-0.633248\pi\)
−0.406493 + 0.913654i \(0.633248\pi\)
\(954\) 0.285740 0.00925118
\(955\) 42.6381 1.37974
\(956\) −62.1629 −2.01049
\(957\) −69.2636 −2.23897
\(958\) 89.7019 2.89814
\(959\) 45.7966 1.47885
\(960\) 57.3682 1.85155
\(961\) −25.1370 −0.810871
\(962\) 49.2861 1.58905
\(963\) −0.197196 −0.00635456
\(964\) 105.192 3.38801
\(965\) 45.3600 1.46019
\(966\) 11.6846 0.375947
\(967\) 47.8759 1.53958 0.769792 0.638294i \(-0.220360\pi\)
0.769792 + 0.638294i \(0.220360\pi\)
\(968\) −75.3743 −2.42262
\(969\) 2.00089 0.0642778
\(970\) 48.3358 1.55197
\(971\) −21.6509 −0.694811 −0.347406 0.937715i \(-0.612937\pi\)
−0.347406 + 0.937715i \(0.612937\pi\)
\(972\) −6.10279 −0.195747
\(973\) 42.3194 1.35670
\(974\) −86.2983 −2.76517
\(975\) −17.0407 −0.545738
\(976\) 6.87857 0.220178
\(977\) −21.1515 −0.676696 −0.338348 0.941021i \(-0.609868\pi\)
−0.338348 + 0.941021i \(0.609868\pi\)
\(978\) 40.1989 1.28542
\(979\) −38.6056 −1.23384
\(980\) 17.8740 0.570965
\(981\) −3.49154 −0.111476
\(982\) 38.6758 1.23419
\(983\) −28.6150 −0.912676 −0.456338 0.889806i \(-0.650839\pi\)
−0.456338 + 0.889806i \(0.650839\pi\)
\(984\) −8.05713 −0.256852
\(985\) 61.7986 1.96907
\(986\) −23.2453 −0.740283
\(987\) 4.41643 0.140577
\(988\) −11.7884 −0.375039
\(989\) −8.03543 −0.255512
\(990\) 6.37282 0.202542
\(991\) 33.9697 1.07908 0.539541 0.841959i \(-0.318598\pi\)
0.539541 + 0.841959i \(0.318598\pi\)
\(992\) −11.2323 −0.356627
\(993\) 14.2901 0.453484
\(994\) −27.6944 −0.878412
\(995\) −30.1344 −0.955324
\(996\) −11.5225 −0.365105
\(997\) 47.1250 1.49246 0.746232 0.665686i \(-0.231861\pi\)
0.746232 + 0.665686i \(0.231861\pi\)
\(998\) −7.08670 −0.224326
\(999\) −27.6070 −0.873448
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 \(a_p\))