Properties

Label 8027.2.a.f.1.20
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 1.20
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.30965 q^{2} +1.95797 q^{3} +3.33448 q^{4} +2.21374 q^{5} -4.52222 q^{6} +4.98325 q^{7} -3.08217 q^{8} +0.833638 q^{9} +O(q^{10})\) \(q-2.30965 q^{2} +1.95797 q^{3} +3.33448 q^{4} +2.21374 q^{5} -4.52222 q^{6} +4.98325 q^{7} -3.08217 q^{8} +0.833638 q^{9} -5.11297 q^{10} -1.08947 q^{11} +6.52879 q^{12} -5.85991 q^{13} -11.5095 q^{14} +4.33444 q^{15} +0.449774 q^{16} -3.36258 q^{17} -1.92541 q^{18} +4.22259 q^{19} +7.38167 q^{20} +9.75704 q^{21} +2.51629 q^{22} +1.00000 q^{23} -6.03479 q^{24} -0.0993443 q^{25} +13.5343 q^{26} -4.24167 q^{27} +16.6165 q^{28} +8.10322 q^{29} -10.0110 q^{30} -3.99410 q^{31} +5.12552 q^{32} -2.13315 q^{33} +7.76638 q^{34} +11.0316 q^{35} +2.77974 q^{36} +7.43590 q^{37} -9.75270 q^{38} -11.4735 q^{39} -6.82313 q^{40} +4.59774 q^{41} -22.5353 q^{42} +4.59971 q^{43} -3.63281 q^{44} +1.84546 q^{45} -2.30965 q^{46} -7.01645 q^{47} +0.880643 q^{48} +17.8328 q^{49} +0.229450 q^{50} -6.58383 q^{51} -19.5397 q^{52} +0.967875 q^{53} +9.79676 q^{54} -2.41180 q^{55} -15.3592 q^{56} +8.26770 q^{57} -18.7156 q^{58} +3.35030 q^{59} +14.4531 q^{60} -4.37700 q^{61} +9.22496 q^{62} +4.15422 q^{63} -12.7377 q^{64} -12.9723 q^{65} +4.92682 q^{66} +2.31509 q^{67} -11.2125 q^{68} +1.95797 q^{69} -25.4792 q^{70} +8.97742 q^{71} -2.56941 q^{72} +12.7859 q^{73} -17.1743 q^{74} -0.194513 q^{75} +14.0801 q^{76} -5.42910 q^{77} +26.4998 q^{78} -5.32993 q^{79} +0.995684 q^{80} -10.8060 q^{81} -10.6192 q^{82} -2.60638 q^{83} +32.5346 q^{84} -7.44389 q^{85} -10.6237 q^{86} +15.8659 q^{87} +3.35793 q^{88} -9.08077 q^{89} -4.26236 q^{90} -29.2014 q^{91} +3.33448 q^{92} -7.82032 q^{93} +16.2055 q^{94} +9.34773 q^{95} +10.0356 q^{96} +2.64450 q^{97} -41.1874 q^{98} -0.908223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30965 −1.63317 −0.816584 0.577227i \(-0.804135\pi\)
−0.816584 + 0.577227i \(0.804135\pi\)
\(3\) 1.95797 1.13043 0.565217 0.824943i \(-0.308793\pi\)
0.565217 + 0.824943i \(0.308793\pi\)
\(4\) 3.33448 1.66724
\(5\) 2.21374 0.990016 0.495008 0.868888i \(-0.335165\pi\)
0.495008 + 0.868888i \(0.335165\pi\)
\(6\) −4.52222 −1.84619
\(7\) 4.98325 1.88349 0.941745 0.336327i \(-0.109185\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(8\) −3.08217 −1.08971
\(9\) 0.833638 0.277879
\(10\) −5.11297 −1.61686
\(11\) −1.08947 −0.328487 −0.164244 0.986420i \(-0.552518\pi\)
−0.164244 + 0.986420i \(0.552518\pi\)
\(12\) 6.52879 1.88470
\(13\) −5.85991 −1.62525 −0.812623 0.582790i \(-0.801961\pi\)
−0.812623 + 0.582790i \(0.801961\pi\)
\(14\) −11.5095 −3.07606
\(15\) 4.33444 1.11915
\(16\) 0.449774 0.112443
\(17\) −3.36258 −0.815546 −0.407773 0.913083i \(-0.633695\pi\)
−0.407773 + 0.913083i \(0.633695\pi\)
\(18\) −1.92541 −0.453824
\(19\) 4.22259 0.968729 0.484364 0.874866i \(-0.339051\pi\)
0.484364 + 0.874866i \(0.339051\pi\)
\(20\) 7.38167 1.65059
\(21\) 9.75704 2.12916
\(22\) 2.51629 0.536475
\(23\) 1.00000 0.208514
\(24\) −6.03479 −1.23185
\(25\) −0.0993443 −0.0198689
\(26\) 13.5343 2.65430
\(27\) −4.24167 −0.816309
\(28\) 16.6165 3.14023
\(29\) 8.10322 1.50473 0.752365 0.658746i \(-0.228913\pi\)
0.752365 + 0.658746i \(0.228913\pi\)
\(30\) −10.0110 −1.82775
\(31\) −3.99410 −0.717361 −0.358681 0.933460i \(-0.616773\pi\)
−0.358681 + 0.933460i \(0.616773\pi\)
\(32\) 5.12552 0.906072
\(33\) −2.13315 −0.371333
\(34\) 7.76638 1.33192
\(35\) 11.0316 1.86469
\(36\) 2.77974 0.463291
\(37\) 7.43590 1.22245 0.611227 0.791455i \(-0.290676\pi\)
0.611227 + 0.791455i \(0.290676\pi\)
\(38\) −9.75270 −1.58210
\(39\) −11.4735 −1.83723
\(40\) −6.82313 −1.07883
\(41\) 4.59774 0.718047 0.359023 0.933329i \(-0.383110\pi\)
0.359023 + 0.933329i \(0.383110\pi\)
\(42\) −22.5353 −3.47728
\(43\) 4.59971 0.701448 0.350724 0.936479i \(-0.385935\pi\)
0.350724 + 0.936479i \(0.385935\pi\)
\(44\) −3.63281 −0.547667
\(45\) 1.84546 0.275105
\(46\) −2.30965 −0.340539
\(47\) −7.01645 −1.02345 −0.511727 0.859148i \(-0.670994\pi\)
−0.511727 + 0.859148i \(0.670994\pi\)
\(48\) 0.880643 0.127110
\(49\) 17.8328 2.54754
\(50\) 0.229450 0.0324492
\(51\) −6.58383 −0.921921
\(52\) −19.5397 −2.70967
\(53\) 0.967875 0.132948 0.0664740 0.997788i \(-0.478825\pi\)
0.0664740 + 0.997788i \(0.478825\pi\)
\(54\) 9.79676 1.33317
\(55\) −2.41180 −0.325208
\(56\) −15.3592 −2.05246
\(57\) 8.26770 1.09508
\(58\) −18.7156 −2.45748
\(59\) 3.35030 0.436172 0.218086 0.975930i \(-0.430019\pi\)
0.218086 + 0.975930i \(0.430019\pi\)
\(60\) 14.4531 1.86588
\(61\) −4.37700 −0.560417 −0.280209 0.959939i \(-0.590404\pi\)
−0.280209 + 0.959939i \(0.590404\pi\)
\(62\) 9.22496 1.17157
\(63\) 4.15422 0.523383
\(64\) −12.7377 −1.59221
\(65\) −12.9723 −1.60902
\(66\) 4.92682 0.606449
\(67\) 2.31509 0.282833 0.141417 0.989950i \(-0.454834\pi\)
0.141417 + 0.989950i \(0.454834\pi\)
\(68\) −11.2125 −1.35971
\(69\) 1.95797 0.235712
\(70\) −25.4792 −3.04534
\(71\) 8.97742 1.06542 0.532712 0.846297i \(-0.321173\pi\)
0.532712 + 0.846297i \(0.321173\pi\)
\(72\) −2.56941 −0.302808
\(73\) 12.7859 1.49647 0.748236 0.663432i \(-0.230901\pi\)
0.748236 + 0.663432i \(0.230901\pi\)
\(74\) −17.1743 −1.99647
\(75\) −0.194513 −0.0224604
\(76\) 14.0801 1.61510
\(77\) −5.42910 −0.618703
\(78\) 26.4998 3.00051
\(79\) −5.32993 −0.599663 −0.299832 0.953992i \(-0.596931\pi\)
−0.299832 + 0.953992i \(0.596931\pi\)
\(80\) 0.995684 0.111321
\(81\) −10.8060 −1.20066
\(82\) −10.6192 −1.17269
\(83\) −2.60638 −0.286087 −0.143044 0.989716i \(-0.545689\pi\)
−0.143044 + 0.989716i \(0.545689\pi\)
\(84\) 32.5346 3.54982
\(85\) −7.44389 −0.807404
\(86\) −10.6237 −1.14558
\(87\) 15.8659 1.70100
\(88\) 3.35793 0.357956
\(89\) −9.08077 −0.962559 −0.481280 0.876567i \(-0.659828\pi\)
−0.481280 + 0.876567i \(0.659828\pi\)
\(90\) −4.26236 −0.449292
\(91\) −29.2014 −3.06113
\(92\) 3.33448 0.347643
\(93\) −7.82032 −0.810929
\(94\) 16.2055 1.67147
\(95\) 9.34773 0.959057
\(96\) 10.0356 1.02425
\(97\) 2.64450 0.268508 0.134254 0.990947i \(-0.457136\pi\)
0.134254 + 0.990947i \(0.457136\pi\)
\(98\) −41.1874 −4.16055
\(99\) −0.908223 −0.0912799
\(100\) −0.331261 −0.0331261
\(101\) 3.00941 0.299447 0.149724 0.988728i \(-0.452162\pi\)
0.149724 + 0.988728i \(0.452162\pi\)
\(102\) 15.2063 1.50565
\(103\) 13.7650 1.35631 0.678154 0.734919i \(-0.262780\pi\)
0.678154 + 0.734919i \(0.262780\pi\)
\(104\) 18.0612 1.77105
\(105\) 21.5996 2.10790
\(106\) −2.23545 −0.217126
\(107\) −7.67796 −0.742257 −0.371128 0.928582i \(-0.621029\pi\)
−0.371128 + 0.928582i \(0.621029\pi\)
\(108\) −14.1437 −1.36098
\(109\) 11.9832 1.14779 0.573893 0.818930i \(-0.305432\pi\)
0.573893 + 0.818930i \(0.305432\pi\)
\(110\) 5.57042 0.531119
\(111\) 14.5593 1.38190
\(112\) 2.24133 0.211786
\(113\) 20.3727 1.91650 0.958249 0.285935i \(-0.0923040\pi\)
0.958249 + 0.285935i \(0.0923040\pi\)
\(114\) −19.0955 −1.78845
\(115\) 2.21374 0.206433
\(116\) 27.0200 2.50874
\(117\) −4.88504 −0.451622
\(118\) −7.73801 −0.712341
\(119\) −16.7566 −1.53607
\(120\) −13.3595 −1.21955
\(121\) −9.81306 −0.892096
\(122\) 10.1093 0.915255
\(123\) 9.00223 0.811704
\(124\) −13.3182 −1.19601
\(125\) −11.2886 −1.00969
\(126\) −9.59480 −0.854772
\(127\) 12.8181 1.13742 0.568711 0.822537i \(-0.307442\pi\)
0.568711 + 0.822537i \(0.307442\pi\)
\(128\) 19.1685 1.69428
\(129\) 9.00607 0.792941
\(130\) 29.9615 2.62780
\(131\) 1.35102 0.118039 0.0590197 0.998257i \(-0.481203\pi\)
0.0590197 + 0.998257i \(0.481203\pi\)
\(132\) −7.11292 −0.619100
\(133\) 21.0422 1.82459
\(134\) −5.34705 −0.461915
\(135\) −9.38996 −0.808159
\(136\) 10.3640 0.888710
\(137\) −2.48101 −0.211967 −0.105983 0.994368i \(-0.533799\pi\)
−0.105983 + 0.994368i \(0.533799\pi\)
\(138\) −4.52222 −0.384957
\(139\) 6.35037 0.538631 0.269316 0.963052i \(-0.413203\pi\)
0.269316 + 0.963052i \(0.413203\pi\)
\(140\) 36.7847 3.10887
\(141\) −13.7380 −1.15695
\(142\) −20.7347 −1.74002
\(143\) 6.38419 0.533873
\(144\) 0.374949 0.0312457
\(145\) 17.9384 1.48971
\(146\) −29.5309 −2.44399
\(147\) 34.9160 2.87982
\(148\) 24.7948 2.03812
\(149\) 20.4077 1.67186 0.835930 0.548836i \(-0.184929\pi\)
0.835930 + 0.548836i \(0.184929\pi\)
\(150\) 0.449257 0.0366816
\(151\) 15.4653 1.25855 0.629274 0.777183i \(-0.283352\pi\)
0.629274 + 0.777183i \(0.283352\pi\)
\(152\) −13.0147 −1.05563
\(153\) −2.80318 −0.226623
\(154\) 12.5393 1.01045
\(155\) −8.84191 −0.710199
\(156\) −38.2581 −3.06310
\(157\) 22.8772 1.82580 0.912901 0.408180i \(-0.133836\pi\)
0.912901 + 0.408180i \(0.133836\pi\)
\(158\) 12.3103 0.979351
\(159\) 1.89507 0.150289
\(160\) 11.3466 0.897025
\(161\) 4.98325 0.392735
\(162\) 24.9580 1.96088
\(163\) 17.1911 1.34651 0.673257 0.739409i \(-0.264895\pi\)
0.673257 + 0.739409i \(0.264895\pi\)
\(164\) 15.3311 1.19715
\(165\) −4.72224 −0.367626
\(166\) 6.01981 0.467228
\(167\) −13.4907 −1.04394 −0.521971 0.852963i \(-0.674803\pi\)
−0.521971 + 0.852963i \(0.674803\pi\)
\(168\) −30.0728 −2.32017
\(169\) 21.3385 1.64142
\(170\) 17.1928 1.31863
\(171\) 3.52011 0.269190
\(172\) 15.3376 1.16948
\(173\) −22.0370 −1.67544 −0.837719 0.546101i \(-0.816112\pi\)
−0.837719 + 0.546101i \(0.816112\pi\)
\(174\) −36.6445 −2.77801
\(175\) −0.495057 −0.0374228
\(176\) −0.490015 −0.0369363
\(177\) 6.55977 0.493063
\(178\) 20.9734 1.57202
\(179\) −16.9790 −1.26907 −0.634535 0.772894i \(-0.718808\pi\)
−0.634535 + 0.772894i \(0.718808\pi\)
\(180\) 6.15364 0.458665
\(181\) −2.88728 −0.214610 −0.107305 0.994226i \(-0.534222\pi\)
−0.107305 + 0.994226i \(0.534222\pi\)
\(182\) 67.4449 4.99935
\(183\) −8.57002 −0.633514
\(184\) −3.08217 −0.227220
\(185\) 16.4612 1.21025
\(186\) 18.0622 1.32438
\(187\) 3.66343 0.267897
\(188\) −23.3962 −1.70634
\(189\) −21.1373 −1.53751
\(190\) −21.5900 −1.56630
\(191\) 25.3296 1.83278 0.916392 0.400283i \(-0.131088\pi\)
0.916392 + 0.400283i \(0.131088\pi\)
\(192\) −24.9400 −1.79989
\(193\) −9.75953 −0.702506 −0.351253 0.936281i \(-0.614244\pi\)
−0.351253 + 0.936281i \(0.614244\pi\)
\(194\) −6.10785 −0.438518
\(195\) −25.3994 −1.81889
\(196\) 59.4629 4.24735
\(197\) 3.71391 0.264605 0.132302 0.991209i \(-0.457763\pi\)
0.132302 + 0.991209i \(0.457763\pi\)
\(198\) 2.09768 0.149075
\(199\) −11.8445 −0.839636 −0.419818 0.907608i \(-0.637906\pi\)
−0.419818 + 0.907608i \(0.637906\pi\)
\(200\) 0.306196 0.0216513
\(201\) 4.53287 0.319724
\(202\) −6.95067 −0.489047
\(203\) 40.3804 2.83415
\(204\) −21.9536 −1.53706
\(205\) 10.1782 0.710878
\(206\) −31.7924 −2.21508
\(207\) 0.833638 0.0579418
\(208\) −2.63563 −0.182748
\(209\) −4.60038 −0.318215
\(210\) −49.8874 −3.44256
\(211\) 2.96372 0.204031 0.102015 0.994783i \(-0.467471\pi\)
0.102015 + 0.994783i \(0.467471\pi\)
\(212\) 3.22736 0.221656
\(213\) 17.5775 1.20439
\(214\) 17.7334 1.21223
\(215\) 10.1826 0.694445
\(216\) 13.0735 0.889541
\(217\) −19.9036 −1.35114
\(218\) −27.6771 −1.87453
\(219\) 25.0343 1.69166
\(220\) −8.04210 −0.542198
\(221\) 19.7044 1.32546
\(222\) −33.6268 −2.25688
\(223\) −20.5574 −1.37662 −0.688312 0.725414i \(-0.741648\pi\)
−0.688312 + 0.725414i \(0.741648\pi\)
\(224\) 25.5417 1.70658
\(225\) −0.0828172 −0.00552115
\(226\) −47.0537 −3.12996
\(227\) 12.0617 0.800563 0.400281 0.916392i \(-0.368912\pi\)
0.400281 + 0.916392i \(0.368912\pi\)
\(228\) 27.5684 1.82576
\(229\) −6.00492 −0.396816 −0.198408 0.980119i \(-0.563577\pi\)
−0.198408 + 0.980119i \(0.563577\pi\)
\(230\) −5.11297 −0.337139
\(231\) −10.6300 −0.699402
\(232\) −24.9755 −1.63972
\(233\) 20.7440 1.35899 0.679493 0.733682i \(-0.262200\pi\)
0.679493 + 0.733682i \(0.262200\pi\)
\(234\) 11.2827 0.737575
\(235\) −15.5326 −1.01324
\(236\) 11.1715 0.727202
\(237\) −10.4358 −0.677879
\(238\) 38.7018 2.50867
\(239\) −7.00811 −0.453317 −0.226658 0.973974i \(-0.572780\pi\)
−0.226658 + 0.973974i \(0.572780\pi\)
\(240\) 1.94952 0.125841
\(241\) 4.95966 0.319480 0.159740 0.987159i \(-0.448934\pi\)
0.159740 + 0.987159i \(0.448934\pi\)
\(242\) 22.6647 1.45694
\(243\) −8.43272 −0.540959
\(244\) −14.5950 −0.934348
\(245\) 39.4771 2.52210
\(246\) −20.7920 −1.32565
\(247\) −24.7440 −1.57442
\(248\) 12.3105 0.781717
\(249\) −5.10320 −0.323402
\(250\) 26.0728 1.64899
\(251\) 4.75309 0.300012 0.150006 0.988685i \(-0.452071\pi\)
0.150006 + 0.988685i \(0.452071\pi\)
\(252\) 13.8522 0.872604
\(253\) −1.08947 −0.0684944
\(254\) −29.6053 −1.85760
\(255\) −14.5749 −0.912716
\(256\) −18.7972 −1.17483
\(257\) −12.5137 −0.780584 −0.390292 0.920691i \(-0.627626\pi\)
−0.390292 + 0.920691i \(0.627626\pi\)
\(258\) −20.8009 −1.29501
\(259\) 37.0549 2.30248
\(260\) −43.2559 −2.68262
\(261\) 6.75515 0.418134
\(262\) −3.12039 −0.192778
\(263\) −3.96093 −0.244242 −0.122121 0.992515i \(-0.538970\pi\)
−0.122121 + 0.992515i \(0.538970\pi\)
\(264\) 6.57472 0.404646
\(265\) 2.14263 0.131621
\(266\) −48.6001 −2.97986
\(267\) −17.7798 −1.08811
\(268\) 7.71962 0.471551
\(269\) −12.5826 −0.767172 −0.383586 0.923505i \(-0.625311\pi\)
−0.383586 + 0.923505i \(0.625311\pi\)
\(270\) 21.6875 1.31986
\(271\) 19.3596 1.17601 0.588006 0.808857i \(-0.299913\pi\)
0.588006 + 0.808857i \(0.299913\pi\)
\(272\) −1.51240 −0.0917029
\(273\) −57.1753 −3.46041
\(274\) 5.73025 0.346177
\(275\) 0.108233 0.00652667
\(276\) 6.52879 0.392987
\(277\) 29.2090 1.75500 0.877500 0.479577i \(-0.159210\pi\)
0.877500 + 0.479577i \(0.159210\pi\)
\(278\) −14.6671 −0.879675
\(279\) −3.32963 −0.199340
\(280\) −34.0013 −2.03197
\(281\) −26.7947 −1.59844 −0.799218 0.601042i \(-0.794753\pi\)
−0.799218 + 0.601042i \(0.794753\pi\)
\(282\) 31.7299 1.88949
\(283\) −5.70733 −0.339266 −0.169633 0.985507i \(-0.554258\pi\)
−0.169633 + 0.985507i \(0.554258\pi\)
\(284\) 29.9350 1.77631
\(285\) 18.3026 1.08415
\(286\) −14.7452 −0.871904
\(287\) 22.9117 1.35243
\(288\) 4.27283 0.251779
\(289\) −5.69303 −0.334884
\(290\) −41.4315 −2.43294
\(291\) 5.17784 0.303530
\(292\) 42.6342 2.49498
\(293\) −10.2729 −0.600148 −0.300074 0.953916i \(-0.597011\pi\)
−0.300074 + 0.953916i \(0.597011\pi\)
\(294\) −80.6436 −4.70323
\(295\) 7.41670 0.431817
\(296\) −22.9187 −1.33212
\(297\) 4.62117 0.268147
\(298\) −47.1345 −2.73043
\(299\) −5.85991 −0.338887
\(300\) −0.648599 −0.0374469
\(301\) 22.9215 1.32117
\(302\) −35.7194 −2.05542
\(303\) 5.89232 0.338505
\(304\) 1.89921 0.108927
\(305\) −9.68954 −0.554822
\(306\) 6.47435 0.370114
\(307\) −17.6042 −1.00473 −0.502364 0.864656i \(-0.667536\pi\)
−0.502364 + 0.864656i \(0.667536\pi\)
\(308\) −18.1032 −1.03152
\(309\) 26.9515 1.53322
\(310\) 20.4217 1.15987
\(311\) 8.61767 0.488663 0.244332 0.969692i \(-0.421431\pi\)
0.244332 + 0.969692i \(0.421431\pi\)
\(312\) 35.3633 2.00205
\(313\) 25.1918 1.42393 0.711964 0.702216i \(-0.247806\pi\)
0.711964 + 0.702216i \(0.247806\pi\)
\(314\) −52.8384 −2.98184
\(315\) 9.19638 0.518157
\(316\) −17.7725 −0.999781
\(317\) −12.0992 −0.679558 −0.339779 0.940505i \(-0.610352\pi\)
−0.339779 + 0.940505i \(0.610352\pi\)
\(318\) −4.37694 −0.245447
\(319\) −8.82821 −0.494285
\(320\) −28.1980 −1.57631
\(321\) −15.0332 −0.839072
\(322\) −11.5095 −0.641402
\(323\) −14.1988 −0.790043
\(324\) −36.0322 −2.00179
\(325\) 0.582149 0.0322918
\(326\) −39.7055 −2.19908
\(327\) 23.4628 1.29750
\(328\) −14.1710 −0.782463
\(329\) −34.9647 −1.92767
\(330\) 10.9067 0.600394
\(331\) 30.0755 1.65310 0.826550 0.562864i \(-0.190300\pi\)
0.826550 + 0.562864i \(0.190300\pi\)
\(332\) −8.69090 −0.476975
\(333\) 6.19885 0.339695
\(334\) 31.1588 1.70493
\(335\) 5.12502 0.280010
\(336\) 4.38846 0.239410
\(337\) 34.1753 1.86164 0.930822 0.365472i \(-0.119092\pi\)
0.930822 + 0.365472i \(0.119092\pi\)
\(338\) −49.2845 −2.68072
\(339\) 39.8890 2.16647
\(340\) −24.8215 −1.34613
\(341\) 4.35145 0.235644
\(342\) −8.13022 −0.439632
\(343\) 53.9823 2.91477
\(344\) −14.1771 −0.764376
\(345\) 4.33444 0.233358
\(346\) 50.8976 2.73627
\(347\) −32.3387 −1.73603 −0.868017 0.496535i \(-0.834606\pi\)
−0.868017 + 0.496535i \(0.834606\pi\)
\(348\) 52.9043 2.83597
\(349\) −1.00000 −0.0535288
\(350\) 1.14341 0.0611177
\(351\) 24.8558 1.32670
\(352\) −5.58409 −0.297633
\(353\) 14.9319 0.794743 0.397372 0.917658i \(-0.369922\pi\)
0.397372 + 0.917658i \(0.369922\pi\)
\(354\) −15.1508 −0.805254
\(355\) 19.8737 1.05479
\(356\) −30.2796 −1.60481
\(357\) −32.8089 −1.73643
\(358\) 39.2155 2.07260
\(359\) −28.9110 −1.52586 −0.762931 0.646480i \(-0.776241\pi\)
−0.762931 + 0.646480i \(0.776241\pi\)
\(360\) −5.68802 −0.299785
\(361\) −1.16972 −0.0615644
\(362\) 6.66861 0.350494
\(363\) −19.2136 −1.00845
\(364\) −97.3712 −5.10364
\(365\) 28.3046 1.48153
\(366\) 19.7937 1.03463
\(367\) −10.1043 −0.527439 −0.263719 0.964599i \(-0.584949\pi\)
−0.263719 + 0.964599i \(0.584949\pi\)
\(368\) 0.449774 0.0234461
\(369\) 3.83285 0.199530
\(370\) −38.0195 −1.97654
\(371\) 4.82316 0.250406
\(372\) −26.0767 −1.35201
\(373\) 3.28564 0.170124 0.0850619 0.996376i \(-0.472891\pi\)
0.0850619 + 0.996376i \(0.472891\pi\)
\(374\) −8.46124 −0.437520
\(375\) −22.1028 −1.14138
\(376\) 21.6259 1.11527
\(377\) −47.4841 −2.44556
\(378\) 48.8197 2.51101
\(379\) −12.0431 −0.618612 −0.309306 0.950963i \(-0.600097\pi\)
−0.309306 + 0.950963i \(0.600097\pi\)
\(380\) 31.1698 1.59898
\(381\) 25.0974 1.28578
\(382\) −58.5024 −2.99324
\(383\) −5.39916 −0.275884 −0.137942 0.990440i \(-0.544049\pi\)
−0.137942 + 0.990440i \(0.544049\pi\)
\(384\) 37.5314 1.91527
\(385\) −12.0186 −0.612526
\(386\) 22.5411 1.14731
\(387\) 3.83449 0.194918
\(388\) 8.81800 0.447666
\(389\) −15.6298 −0.792460 −0.396230 0.918151i \(-0.629682\pi\)
−0.396230 + 0.918151i \(0.629682\pi\)
\(390\) 58.6637 2.97055
\(391\) −3.36258 −0.170053
\(392\) −54.9635 −2.77608
\(393\) 2.64526 0.133436
\(394\) −8.57782 −0.432144
\(395\) −11.7991 −0.593676
\(396\) −3.02845 −0.152185
\(397\) 8.83680 0.443506 0.221753 0.975103i \(-0.428822\pi\)
0.221753 + 0.975103i \(0.428822\pi\)
\(398\) 27.3567 1.37127
\(399\) 41.2000 2.06258
\(400\) −0.0446825 −0.00223412
\(401\) 9.63522 0.481160 0.240580 0.970629i \(-0.422662\pi\)
0.240580 + 0.970629i \(0.422662\pi\)
\(402\) −10.4693 −0.522164
\(403\) 23.4050 1.16589
\(404\) 10.0348 0.499249
\(405\) −23.9216 −1.18867
\(406\) −93.2644 −4.62864
\(407\) −8.10119 −0.401561
\(408\) 20.2925 1.00463
\(409\) 12.5750 0.621796 0.310898 0.950443i \(-0.399370\pi\)
0.310898 + 0.950443i \(0.399370\pi\)
\(410\) −23.5081 −1.16098
\(411\) −4.85773 −0.239614
\(412\) 45.8992 2.26129
\(413\) 16.6954 0.821525
\(414\) −1.92541 −0.0946288
\(415\) −5.76985 −0.283231
\(416\) −30.0351 −1.47259
\(417\) 12.4338 0.608887
\(418\) 10.6253 0.519699
\(419\) 10.8668 0.530879 0.265440 0.964127i \(-0.414483\pi\)
0.265440 + 0.964127i \(0.414483\pi\)
\(420\) 72.0232 3.51437
\(421\) 22.4441 1.09386 0.546929 0.837179i \(-0.315797\pi\)
0.546929 + 0.837179i \(0.315797\pi\)
\(422\) −6.84515 −0.333217
\(423\) −5.84918 −0.284397
\(424\) −2.98315 −0.144875
\(425\) 0.334054 0.0162040
\(426\) −40.5978 −1.96697
\(427\) −21.8117 −1.05554
\(428\) −25.6020 −1.23752
\(429\) 12.5000 0.603508
\(430\) −23.5181 −1.13415
\(431\) −4.56255 −0.219770 −0.109885 0.993944i \(-0.535048\pi\)
−0.109885 + 0.993944i \(0.535048\pi\)
\(432\) −1.90779 −0.0917886
\(433\) 6.23755 0.299758 0.149879 0.988704i \(-0.452112\pi\)
0.149879 + 0.988704i \(0.452112\pi\)
\(434\) 45.9703 2.20664
\(435\) 35.1229 1.68401
\(436\) 39.9578 1.91363
\(437\) 4.22259 0.201994
\(438\) −57.8205 −2.76277
\(439\) 6.16399 0.294191 0.147096 0.989122i \(-0.453007\pi\)
0.147096 + 0.989122i \(0.453007\pi\)
\(440\) 7.43359 0.354382
\(441\) 14.8661 0.707908
\(442\) −45.5103 −2.16470
\(443\) −4.13367 −0.196397 −0.0981983 0.995167i \(-0.531308\pi\)
−0.0981983 + 0.995167i \(0.531308\pi\)
\(444\) 48.5475 2.30396
\(445\) −20.1025 −0.952949
\(446\) 47.4803 2.24826
\(447\) 39.9575 1.88993
\(448\) −63.4750 −2.99891
\(449\) 1.92458 0.0908263 0.0454132 0.998968i \(-0.485540\pi\)
0.0454132 + 0.998968i \(0.485540\pi\)
\(450\) 0.191279 0.00901696
\(451\) −5.00910 −0.235869
\(452\) 67.9321 3.19526
\(453\) 30.2806 1.42271
\(454\) −27.8583 −1.30745
\(455\) −64.6443 −3.03057
\(456\) −25.4824 −1.19332
\(457\) −41.5873 −1.94537 −0.972686 0.232123i \(-0.925433\pi\)
−0.972686 + 0.232123i \(0.925433\pi\)
\(458\) 13.8693 0.648068
\(459\) 14.2630 0.665738
\(460\) 7.38167 0.344172
\(461\) −14.2515 −0.663758 −0.331879 0.943322i \(-0.607683\pi\)
−0.331879 + 0.943322i \(0.607683\pi\)
\(462\) 24.5515 1.14224
\(463\) −8.40781 −0.390744 −0.195372 0.980729i \(-0.562591\pi\)
−0.195372 + 0.980729i \(0.562591\pi\)
\(464\) 3.64462 0.169197
\(465\) −17.3122 −0.802833
\(466\) −47.9114 −2.21945
\(467\) −7.21854 −0.334034 −0.167017 0.985954i \(-0.553413\pi\)
−0.167017 + 0.985954i \(0.553413\pi\)
\(468\) −16.2890 −0.752961
\(469\) 11.5367 0.532714
\(470\) 35.8749 1.65478
\(471\) 44.7929 2.06395
\(472\) −10.3262 −0.475301
\(473\) −5.01124 −0.230417
\(474\) 24.1031 1.10709
\(475\) −0.419491 −0.0192475
\(476\) −55.8744 −2.56100
\(477\) 0.806858 0.0369435
\(478\) 16.1863 0.740343
\(479\) 2.29995 0.105088 0.0525438 0.998619i \(-0.483267\pi\)
0.0525438 + 0.998619i \(0.483267\pi\)
\(480\) 22.2162 1.01403
\(481\) −43.5737 −1.98679
\(482\) −11.4551 −0.521764
\(483\) 9.75704 0.443961
\(484\) −32.7214 −1.48734
\(485\) 5.85423 0.265827
\(486\) 19.4766 0.883478
\(487\) 5.42000 0.245603 0.122802 0.992431i \(-0.460812\pi\)
0.122802 + 0.992431i \(0.460812\pi\)
\(488\) 13.4906 0.610693
\(489\) 33.6597 1.52214
\(490\) −91.1783 −4.11901
\(491\) 3.66652 0.165468 0.0827338 0.996572i \(-0.473635\pi\)
0.0827338 + 0.996572i \(0.473635\pi\)
\(492\) 30.0177 1.35330
\(493\) −27.2478 −1.22718
\(494\) 57.1499 2.57130
\(495\) −2.01057 −0.0903685
\(496\) −1.79644 −0.0806626
\(497\) 44.7367 2.00671
\(498\) 11.7866 0.528170
\(499\) −12.8305 −0.574371 −0.287186 0.957875i \(-0.592720\pi\)
−0.287186 + 0.957875i \(0.592720\pi\)
\(500\) −37.6417 −1.68339
\(501\) −26.4144 −1.18011
\(502\) −10.9780 −0.489971
\(503\) −2.25672 −0.100622 −0.0503110 0.998734i \(-0.516021\pi\)
−0.0503110 + 0.998734i \(0.516021\pi\)
\(504\) −12.8040 −0.570336
\(505\) 6.66205 0.296457
\(506\) 2.51629 0.111863
\(507\) 41.7801 1.85552
\(508\) 42.7416 1.89635
\(509\) −23.0317 −1.02086 −0.510431 0.859919i \(-0.670514\pi\)
−0.510431 + 0.859919i \(0.670514\pi\)
\(510\) 33.6629 1.49062
\(511\) 63.7151 2.81859
\(512\) 5.07788 0.224413
\(513\) −17.9108 −0.790782
\(514\) 28.9023 1.27482
\(515\) 30.4722 1.34277
\(516\) 30.0305 1.32202
\(517\) 7.64421 0.336192
\(518\) −85.5839 −3.76034
\(519\) −43.1477 −1.89397
\(520\) 39.9829 1.75337
\(521\) −28.4736 −1.24745 −0.623726 0.781643i \(-0.714382\pi\)
−0.623726 + 0.781643i \(0.714382\pi\)
\(522\) −15.6020 −0.682882
\(523\) 0.652547 0.0285339 0.0142670 0.999898i \(-0.495459\pi\)
0.0142670 + 0.999898i \(0.495459\pi\)
\(524\) 4.50495 0.196800
\(525\) −0.969306 −0.0423040
\(526\) 9.14837 0.398888
\(527\) 13.4305 0.585041
\(528\) −0.959433 −0.0417540
\(529\) 1.00000 0.0434783
\(530\) −4.94871 −0.214958
\(531\) 2.79293 0.121203
\(532\) 70.1647 3.04203
\(533\) −26.9423 −1.16700
\(534\) 41.0652 1.77706
\(535\) −16.9970 −0.734846
\(536\) −7.13550 −0.308207
\(537\) −33.2443 −1.43460
\(538\) 29.0613 1.25292
\(539\) −19.4282 −0.836834
\(540\) −31.3106 −1.34739
\(541\) −23.5573 −1.01281 −0.506404 0.862296i \(-0.669025\pi\)
−0.506404 + 0.862296i \(0.669025\pi\)
\(542\) −44.7139 −1.92062
\(543\) −5.65321 −0.242602
\(544\) −17.2350 −0.738944
\(545\) 26.5278 1.13633
\(546\) 132.055 5.65143
\(547\) −27.1115 −1.15920 −0.579602 0.814899i \(-0.696792\pi\)
−0.579602 + 0.814899i \(0.696792\pi\)
\(548\) −8.27286 −0.353399
\(549\) −3.64883 −0.155728
\(550\) −0.249979 −0.0106592
\(551\) 34.2166 1.45768
\(552\) −6.03479 −0.256858
\(553\) −26.5603 −1.12946
\(554\) −67.4626 −2.86621
\(555\) 32.2304 1.36811
\(556\) 21.1751 0.898026
\(557\) −43.3501 −1.83680 −0.918401 0.395652i \(-0.870519\pi\)
−0.918401 + 0.395652i \(0.870519\pi\)
\(558\) 7.69028 0.325556
\(559\) −26.9538 −1.14003
\(560\) 4.96174 0.209672
\(561\) 7.17288 0.302839
\(562\) 61.8862 2.61051
\(563\) 40.2540 1.69650 0.848251 0.529594i \(-0.177656\pi\)
0.848251 + 0.529594i \(0.177656\pi\)
\(564\) −45.8090 −1.92891
\(565\) 45.0998 1.89736
\(566\) 13.1819 0.554078
\(567\) −53.8488 −2.26144
\(568\) −27.6699 −1.16100
\(569\) −16.2379 −0.680730 −0.340365 0.940293i \(-0.610551\pi\)
−0.340365 + 0.940293i \(0.610551\pi\)
\(570\) −42.2725 −1.77060
\(571\) −10.6855 −0.447173 −0.223586 0.974684i \(-0.571777\pi\)
−0.223586 + 0.974684i \(0.571777\pi\)
\(572\) 21.2879 0.890093
\(573\) 49.5945 2.07184
\(574\) −52.9179 −2.20875
\(575\) −0.0993443 −0.00414294
\(576\) −10.6186 −0.442443
\(577\) −5.04145 −0.209878 −0.104939 0.994479i \(-0.533465\pi\)
−0.104939 + 0.994479i \(0.533465\pi\)
\(578\) 13.1489 0.546922
\(579\) −19.1088 −0.794136
\(580\) 59.8153 2.48370
\(581\) −12.9882 −0.538842
\(582\) −11.9590 −0.495716
\(583\) −1.05447 −0.0436717
\(584\) −39.4082 −1.63072
\(585\) −10.8142 −0.447113
\(586\) 23.7267 0.980142
\(587\) 25.6438 1.05843 0.529217 0.848486i \(-0.322486\pi\)
0.529217 + 0.848486i \(0.322486\pi\)
\(588\) 116.426 4.80134
\(589\) −16.8654 −0.694929
\(590\) −17.1300 −0.705229
\(591\) 7.27171 0.299118
\(592\) 3.34447 0.137457
\(593\) −3.48479 −0.143103 −0.0715516 0.997437i \(-0.522795\pi\)
−0.0715516 + 0.997437i \(0.522795\pi\)
\(594\) −10.6733 −0.437930
\(595\) −37.0948 −1.52074
\(596\) 68.0488 2.78739
\(597\) −23.1912 −0.949153
\(598\) 13.5343 0.553460
\(599\) 39.6790 1.62124 0.810619 0.585574i \(-0.199131\pi\)
0.810619 + 0.585574i \(0.199131\pi\)
\(600\) 0.599522 0.0244754
\(601\) −37.8911 −1.54561 −0.772806 0.634643i \(-0.781147\pi\)
−0.772806 + 0.634643i \(0.781147\pi\)
\(602\) −52.9405 −2.15769
\(603\) 1.92995 0.0785936
\(604\) 51.5687 2.09830
\(605\) −21.7236 −0.883189
\(606\) −13.6092 −0.552835
\(607\) −42.5259 −1.72607 −0.863036 0.505142i \(-0.831440\pi\)
−0.863036 + 0.505142i \(0.831440\pi\)
\(608\) 21.6430 0.877738
\(609\) 79.0635 3.20381
\(610\) 22.3794 0.906117
\(611\) 41.1157 1.66336
\(612\) −9.34712 −0.377835
\(613\) −5.58104 −0.225416 −0.112708 0.993628i \(-0.535952\pi\)
−0.112708 + 0.993628i \(0.535952\pi\)
\(614\) 40.6596 1.64089
\(615\) 19.9286 0.803600
\(616\) 16.7334 0.674207
\(617\) −16.5443 −0.666050 −0.333025 0.942918i \(-0.608069\pi\)
−0.333025 + 0.942918i \(0.608069\pi\)
\(618\) −62.2485 −2.50400
\(619\) −26.3776 −1.06020 −0.530102 0.847934i \(-0.677846\pi\)
−0.530102 + 0.847934i \(0.677846\pi\)
\(620\) −29.4831 −1.18407
\(621\) −4.24167 −0.170212
\(622\) −19.9038 −0.798069
\(623\) −45.2517 −1.81297
\(624\) −5.16049 −0.206585
\(625\) −24.4934 −0.979736
\(626\) −58.1843 −2.32551
\(627\) −9.00740 −0.359721
\(628\) 76.2836 3.04405
\(629\) −25.0038 −0.996968
\(630\) −21.2404 −0.846238
\(631\) −4.24167 −0.168858 −0.0844291 0.996429i \(-0.526907\pi\)
−0.0844291 + 0.996429i \(0.526907\pi\)
\(632\) 16.4277 0.653460
\(633\) 5.80287 0.230643
\(634\) 27.9449 1.10983
\(635\) 28.3760 1.12607
\(636\) 6.31906 0.250567
\(637\) −104.498 −4.14037
\(638\) 20.3901 0.807251
\(639\) 7.48391 0.296059
\(640\) 42.4342 1.67736
\(641\) −4.60379 −0.181839 −0.0909194 0.995858i \(-0.528981\pi\)
−0.0909194 + 0.995858i \(0.528981\pi\)
\(642\) 34.7214 1.37034
\(643\) 2.06716 0.0815210 0.0407605 0.999169i \(-0.487022\pi\)
0.0407605 + 0.999169i \(0.487022\pi\)
\(644\) 16.6165 0.654782
\(645\) 19.9371 0.785024
\(646\) 32.7943 1.29027
\(647\) 5.36556 0.210942 0.105471 0.994422i \(-0.466365\pi\)
0.105471 + 0.994422i \(0.466365\pi\)
\(648\) 33.3058 1.30837
\(649\) −3.65005 −0.143277
\(650\) −1.34456 −0.0527379
\(651\) −38.9706 −1.52738
\(652\) 57.3234 2.24496
\(653\) −26.8599 −1.05111 −0.525554 0.850760i \(-0.676142\pi\)
−0.525554 + 0.850760i \(0.676142\pi\)
\(654\) −54.1908 −2.11903
\(655\) 2.99082 0.116861
\(656\) 2.06794 0.0807397
\(657\) 10.6588 0.415839
\(658\) 80.7562 3.14820
\(659\) −0.517386 −0.0201545 −0.0100773 0.999949i \(-0.503208\pi\)
−0.0100773 + 0.999949i \(0.503208\pi\)
\(660\) −15.7462 −0.612919
\(661\) 28.2255 1.09784 0.548921 0.835874i \(-0.315039\pi\)
0.548921 + 0.835874i \(0.315039\pi\)
\(662\) −69.4638 −2.69979
\(663\) 38.5806 1.49835
\(664\) 8.03329 0.311752
\(665\) 46.5820 1.80637
\(666\) −14.3172 −0.554779
\(667\) 8.10322 0.313758
\(668\) −44.9844 −1.74050
\(669\) −40.2507 −1.55618
\(670\) −11.8370 −0.457303
\(671\) 4.76860 0.184090
\(672\) 50.0099 1.92917
\(673\) −6.37316 −0.245667 −0.122834 0.992427i \(-0.539198\pi\)
−0.122834 + 0.992427i \(0.539198\pi\)
\(674\) −78.9328 −3.04038
\(675\) 0.421386 0.0162191
\(676\) 71.1527 2.73664
\(677\) 22.3795 0.860113 0.430056 0.902802i \(-0.358494\pi\)
0.430056 + 0.902802i \(0.358494\pi\)
\(678\) −92.1296 −3.53821
\(679\) 13.1782 0.505732
\(680\) 22.9433 0.879837
\(681\) 23.6164 0.904983
\(682\) −10.0503 −0.384847
\(683\) −33.0860 −1.26600 −0.633000 0.774152i \(-0.718177\pi\)
−0.633000 + 0.774152i \(0.718177\pi\)
\(684\) 11.7377 0.448803
\(685\) −5.49231 −0.209850
\(686\) −124.680 −4.76031
\(687\) −11.7574 −0.448574
\(688\) 2.06883 0.0788733
\(689\) −5.67166 −0.216073
\(690\) −10.0110 −0.381113
\(691\) 14.3979 0.547722 0.273861 0.961769i \(-0.411699\pi\)
0.273861 + 0.961769i \(0.411699\pi\)
\(692\) −73.4817 −2.79335
\(693\) −4.52590 −0.171925
\(694\) 74.6911 2.83523
\(695\) 14.0581 0.533253
\(696\) −48.9012 −1.85360
\(697\) −15.4603 −0.585600
\(698\) 2.30965 0.0874215
\(699\) 40.6161 1.53624
\(700\) −1.65076 −0.0623927
\(701\) −13.6789 −0.516643 −0.258322 0.966059i \(-0.583169\pi\)
−0.258322 + 0.966059i \(0.583169\pi\)
\(702\) −57.4081 −2.16673
\(703\) 31.3988 1.18423
\(704\) 13.8773 0.523021
\(705\) −30.4124 −1.14540
\(706\) −34.4874 −1.29795
\(707\) 14.9966 0.564006
\(708\) 21.8734 0.822053
\(709\) 24.0575 0.903500 0.451750 0.892145i \(-0.350800\pi\)
0.451750 + 0.892145i \(0.350800\pi\)
\(710\) −45.9012 −1.72264
\(711\) −4.44323 −0.166634
\(712\) 27.9884 1.04891
\(713\) −3.99410 −0.149580
\(714\) 75.7769 2.83588
\(715\) 14.1330 0.528542
\(716\) −56.6161 −2.11584
\(717\) −13.7217 −0.512445
\(718\) 66.7742 2.49199
\(719\) 4.67069 0.174187 0.0870936 0.996200i \(-0.472242\pi\)
0.0870936 + 0.996200i \(0.472242\pi\)
\(720\) 0.830040 0.0309337
\(721\) 68.5945 2.55459
\(722\) 2.70165 0.100545
\(723\) 9.71085 0.361150
\(724\) −9.62758 −0.357806
\(725\) −0.805009 −0.0298973
\(726\) 44.3768 1.64698
\(727\) 11.9978 0.444975 0.222487 0.974936i \(-0.428582\pi\)
0.222487 + 0.974936i \(0.428582\pi\)
\(728\) 90.0035 3.33575
\(729\) 15.9069 0.589144
\(730\) −65.3737 −2.41959
\(731\) −15.4669 −0.572064
\(732\) −28.5765 −1.05622
\(733\) −22.0100 −0.812956 −0.406478 0.913661i \(-0.633243\pi\)
−0.406478 + 0.913661i \(0.633243\pi\)
\(734\) 23.3373 0.861396
\(735\) 77.2949 2.85107
\(736\) 5.12552 0.188929
\(737\) −2.52222 −0.0929072
\(738\) −8.85254 −0.325867
\(739\) 15.8025 0.581306 0.290653 0.956829i \(-0.406127\pi\)
0.290653 + 0.956829i \(0.406127\pi\)
\(740\) 54.8894 2.01777
\(741\) −48.4479 −1.77978
\(742\) −11.1398 −0.408955
\(743\) 0.948804 0.0348082 0.0174041 0.999849i \(-0.494460\pi\)
0.0174041 + 0.999849i \(0.494460\pi\)
\(744\) 24.1035 0.883678
\(745\) 45.1773 1.65517
\(746\) −7.58867 −0.277841
\(747\) −2.17277 −0.0794977
\(748\) 12.2156 0.446647
\(749\) −38.2612 −1.39803
\(750\) 51.0497 1.86407
\(751\) 27.3398 0.997644 0.498822 0.866704i \(-0.333766\pi\)
0.498822 + 0.866704i \(0.333766\pi\)
\(752\) −3.15582 −0.115081
\(753\) 9.30640 0.339144
\(754\) 109.672 3.99401
\(755\) 34.2362 1.24598
\(756\) −70.4817 −2.56340
\(757\) 11.4806 0.417268 0.208634 0.977994i \(-0.433098\pi\)
0.208634 + 0.977994i \(0.433098\pi\)
\(758\) 27.8153 1.01030
\(759\) −2.13315 −0.0774283
\(760\) −28.8113 −1.04509
\(761\) 9.14340 0.331448 0.165724 0.986172i \(-0.447004\pi\)
0.165724 + 0.986172i \(0.447004\pi\)
\(762\) −57.9662 −2.09989
\(763\) 59.7155 2.16184
\(764\) 84.4608 3.05569
\(765\) −6.20551 −0.224361
\(766\) 12.4702 0.450565
\(767\) −19.6324 −0.708886
\(768\) −36.8044 −1.32806
\(769\) −44.5901 −1.60796 −0.803981 0.594656i \(-0.797288\pi\)
−0.803981 + 0.594656i \(0.797288\pi\)
\(770\) 27.7588 1.00036
\(771\) −24.5014 −0.882398
\(772\) −32.5429 −1.17124
\(773\) −46.7806 −1.68258 −0.841291 0.540582i \(-0.818204\pi\)
−0.841291 + 0.540582i \(0.818204\pi\)
\(774\) −8.85632 −0.318334
\(775\) 0.396791 0.0142532
\(776\) −8.15078 −0.292596
\(777\) 72.5524 2.60280
\(778\) 36.0992 1.29422
\(779\) 19.4144 0.695593
\(780\) −84.6936 −3.03252
\(781\) −9.78062 −0.349978
\(782\) 7.76638 0.277725
\(783\) −34.3712 −1.22833
\(784\) 8.02071 0.286454
\(785\) 50.6443 1.80757
\(786\) −6.10962 −0.217923
\(787\) 25.0934 0.894484 0.447242 0.894413i \(-0.352406\pi\)
0.447242 + 0.894413i \(0.352406\pi\)
\(788\) 12.3839 0.441159
\(789\) −7.75538 −0.276099
\(790\) 27.2517 0.969573
\(791\) 101.522 3.60971
\(792\) 2.79930 0.0994687
\(793\) 25.6488 0.910815
\(794\) −20.4099 −0.724320
\(795\) 4.19519 0.148788
\(796\) −39.4953 −1.39987
\(797\) 22.0738 0.781895 0.390948 0.920413i \(-0.372147\pi\)
0.390948 + 0.920413i \(0.372147\pi\)
\(798\) −95.1575 −3.36854
\(799\) 23.5934 0.834674
\(800\) −0.509191 −0.0180026
\(801\) −7.57007 −0.267475
\(802\) −22.2540 −0.785815
\(803\) −13.9298 −0.491572
\(804\) 15.1148 0.533056
\(805\) 11.0316 0.388814
\(806\) −54.0574 −1.90409
\(807\) −24.6362 −0.867236
\(808\) −9.27549 −0.326311
\(809\) −4.51267 −0.158657 −0.0793285 0.996849i \(-0.525278\pi\)
−0.0793285 + 0.996849i \(0.525278\pi\)
\(810\) 55.2505 1.94131
\(811\) −33.9368 −1.19168 −0.595841 0.803103i \(-0.703181\pi\)
−0.595841 + 0.803103i \(0.703181\pi\)
\(812\) 134.647 4.72519
\(813\) 37.9055 1.32940
\(814\) 18.7109 0.655816
\(815\) 38.0567 1.33307
\(816\) −2.96123 −0.103664
\(817\) 19.4227 0.679513
\(818\) −29.0439 −1.01550
\(819\) −24.3434 −0.850626
\(820\) 33.9390 1.18520
\(821\) −18.6825 −0.652025 −0.326013 0.945365i \(-0.605705\pi\)
−0.326013 + 0.945365i \(0.605705\pi\)
\(822\) 11.2197 0.391330
\(823\) −12.0677 −0.420653 −0.210327 0.977631i \(-0.567453\pi\)
−0.210327 + 0.977631i \(0.567453\pi\)
\(824\) −42.4261 −1.47798
\(825\) 0.211916 0.00737797
\(826\) −38.5604 −1.34169
\(827\) 2.21520 0.0770301 0.0385150 0.999258i \(-0.487737\pi\)
0.0385150 + 0.999258i \(0.487737\pi\)
\(828\) 2.77974 0.0966028
\(829\) −35.7236 −1.24073 −0.620365 0.784313i \(-0.713016\pi\)
−0.620365 + 0.784313i \(0.713016\pi\)
\(830\) 13.3263 0.462563
\(831\) 57.1903 1.98391
\(832\) 74.6417 2.58773
\(833\) −59.9641 −2.07763
\(834\) −28.7177 −0.994414
\(835\) −29.8650 −1.03352
\(836\) −15.3399 −0.530540
\(837\) 16.9416 0.585589
\(838\) −25.0986 −0.867015
\(839\) 47.8380 1.65155 0.825775 0.563999i \(-0.190738\pi\)
0.825775 + 0.563999i \(0.190738\pi\)
\(840\) −66.5735 −2.29700
\(841\) 36.6622 1.26421
\(842\) −51.8379 −1.78645
\(843\) −52.4631 −1.80692
\(844\) 9.88245 0.340168
\(845\) 47.2380 1.62504
\(846\) 13.5095 0.464468
\(847\) −48.9009 −1.68025
\(848\) 0.435325 0.0149491
\(849\) −11.1748 −0.383517
\(850\) −0.771546 −0.0264638
\(851\) 7.43590 0.254899
\(852\) 58.6117 2.00800
\(853\) −51.9232 −1.77782 −0.888908 0.458085i \(-0.848536\pi\)
−0.888908 + 0.458085i \(0.848536\pi\)
\(854\) 50.3773 1.72387
\(855\) 7.79262 0.266502
\(856\) 23.6648 0.808845
\(857\) −2.82859 −0.0966228 −0.0483114 0.998832i \(-0.515384\pi\)
−0.0483114 + 0.998832i \(0.515384\pi\)
\(858\) −28.8707 −0.985629
\(859\) −13.8748 −0.473403 −0.236702 0.971582i \(-0.576066\pi\)
−0.236702 + 0.971582i \(0.576066\pi\)
\(860\) 33.9535 1.15780
\(861\) 44.8603 1.52884
\(862\) 10.5379 0.358922
\(863\) −24.0921 −0.820106 −0.410053 0.912062i \(-0.634490\pi\)
−0.410053 + 0.912062i \(0.634490\pi\)
\(864\) −21.7407 −0.739635
\(865\) −48.7842 −1.65871
\(866\) −14.4065 −0.489554
\(867\) −11.1468 −0.378564
\(868\) −66.3680 −2.25268
\(869\) 5.80679 0.196982
\(870\) −81.1216 −2.75028
\(871\) −13.5662 −0.459674
\(872\) −36.9344 −1.25076
\(873\) 2.20455 0.0746128
\(874\) −9.75270 −0.329890
\(875\) −56.2541 −1.90173
\(876\) 83.4763 2.82040
\(877\) −38.3489 −1.29495 −0.647476 0.762086i \(-0.724175\pi\)
−0.647476 + 0.762086i \(0.724175\pi\)
\(878\) −14.2367 −0.480464
\(879\) −20.1140 −0.678427
\(880\) −1.08477 −0.0365675
\(881\) −4.18008 −0.140830 −0.0704152 0.997518i \(-0.522432\pi\)
−0.0704152 + 0.997518i \(0.522432\pi\)
\(882\) −34.3354 −1.15613
\(883\) 40.3284 1.35716 0.678580 0.734527i \(-0.262596\pi\)
0.678580 + 0.734527i \(0.262596\pi\)
\(884\) 65.7039 2.20986
\(885\) 14.5217 0.488140
\(886\) 9.54732 0.320749
\(887\) −25.2631 −0.848252 −0.424126 0.905603i \(-0.639419\pi\)
−0.424126 + 0.905603i \(0.639419\pi\)
\(888\) −44.8741 −1.50588
\(889\) 63.8757 2.14232
\(890\) 46.4296 1.55633
\(891\) 11.7728 0.394402
\(892\) −68.5481 −2.29516
\(893\) −29.6276 −0.991450
\(894\) −92.2878 −3.08657
\(895\) −37.5871 −1.25640
\(896\) 95.5216 3.19115
\(897\) −11.4735 −0.383089
\(898\) −4.44509 −0.148335
\(899\) −32.3651 −1.07944
\(900\) −0.276152 −0.00920506
\(901\) −3.25456 −0.108425
\(902\) 11.5693 0.385214
\(903\) 44.8795 1.49350
\(904\) −62.7919 −2.08843
\(905\) −6.39170 −0.212467
\(906\) −69.9375 −2.32352
\(907\) −8.94543 −0.297028 −0.148514 0.988910i \(-0.547449\pi\)
−0.148514 + 0.988910i \(0.547449\pi\)
\(908\) 40.2194 1.33473
\(909\) 2.50875 0.0832101
\(910\) 149.306 4.94943
\(911\) 32.1930 1.06660 0.533300 0.845926i \(-0.320952\pi\)
0.533300 + 0.845926i \(0.320952\pi\)
\(912\) 3.71859 0.123135
\(913\) 2.83957 0.0939760
\(914\) 96.0521 3.17712
\(915\) −18.9718 −0.627189
\(916\) −20.0233 −0.661587
\(917\) 6.73248 0.222326
\(918\) −32.9424 −1.08726
\(919\) 58.8113 1.94001 0.970003 0.243093i \(-0.0781621\pi\)
0.970003 + 0.243093i \(0.0781621\pi\)
\(920\) −6.82313 −0.224952
\(921\) −34.4686 −1.13578
\(922\) 32.9159 1.08403
\(923\) −52.6068 −1.73157
\(924\) −35.4455 −1.16607
\(925\) −0.738715 −0.0242888
\(926\) 19.4191 0.638151
\(927\) 11.4751 0.376890
\(928\) 41.5332 1.36339
\(929\) −25.1883 −0.826402 −0.413201 0.910640i \(-0.635589\pi\)
−0.413201 + 0.910640i \(0.635589\pi\)
\(930\) 39.9850 1.31116
\(931\) 75.3004 2.46787
\(932\) 69.1704 2.26575
\(933\) 16.8731 0.552401
\(934\) 16.6723 0.545534
\(935\) 8.10989 0.265222
\(936\) 15.0565 0.492138
\(937\) 17.6303 0.575956 0.287978 0.957637i \(-0.407017\pi\)
0.287978 + 0.957637i \(0.407017\pi\)
\(938\) −26.6457 −0.870012
\(939\) 49.3248 1.60965
\(940\) −51.7931 −1.68930
\(941\) −37.9738 −1.23791 −0.618956 0.785426i \(-0.712444\pi\)
−0.618956 + 0.785426i \(0.712444\pi\)
\(942\) −103.456 −3.37077
\(943\) 4.59774 0.149723
\(944\) 1.50688 0.0490446
\(945\) −46.7925 −1.52216
\(946\) 11.5742 0.376310
\(947\) −7.60852 −0.247244 −0.123622 0.992329i \(-0.539451\pi\)
−0.123622 + 0.992329i \(0.539451\pi\)
\(948\) −34.7980 −1.13019
\(949\) −74.9240 −2.43214
\(950\) 0.968876 0.0314345
\(951\) −23.6898 −0.768195
\(952\) 51.6466 1.67388
\(953\) 33.0983 1.07216 0.536080 0.844167i \(-0.319905\pi\)
0.536080 + 0.844167i \(0.319905\pi\)
\(954\) −1.86356 −0.0603349
\(955\) 56.0731 1.81448
\(956\) −23.3684 −0.755787
\(957\) −17.2854 −0.558756
\(958\) −5.31209 −0.171626
\(959\) −12.3635 −0.399237
\(960\) −55.2107 −1.78192
\(961\) −15.0472 −0.485393
\(962\) 100.640 3.24476
\(963\) −6.40064 −0.206258
\(964\) 16.5378 0.532648
\(965\) −21.6051 −0.695492
\(966\) −22.5353 −0.725062
\(967\) −49.4697 −1.59084 −0.795419 0.606060i \(-0.792749\pi\)
−0.795419 + 0.606060i \(0.792749\pi\)
\(968\) 30.2455 0.972127
\(969\) −27.8008 −0.893091
\(970\) −13.5212 −0.434140
\(971\) 9.15851 0.293911 0.146955 0.989143i \(-0.453053\pi\)
0.146955 + 0.989143i \(0.453053\pi\)
\(972\) −28.1187 −0.901908
\(973\) 31.6455 1.01451
\(974\) −12.5183 −0.401112
\(975\) 1.13983 0.0365037
\(976\) −1.96866 −0.0630152
\(977\) 36.1889 1.15779 0.578894 0.815403i \(-0.303485\pi\)
0.578894 + 0.815403i \(0.303485\pi\)
\(978\) −77.7420 −2.48592
\(979\) 9.89322 0.316189
\(980\) 131.635 4.20494
\(981\) 9.98969 0.318946
\(982\) −8.46837 −0.270236
\(983\) −34.6899 −1.10644 −0.553219 0.833036i \(-0.686601\pi\)
−0.553219 + 0.833036i \(0.686601\pi\)
\(984\) −27.7464 −0.884523
\(985\) 8.22163 0.261963
\(986\) 62.9327 2.00419
\(987\) −68.4598 −2.17910
\(988\) −82.5082 −2.62494
\(989\) 4.59971 0.146262
\(990\) 4.64371 0.147587
\(991\) −43.8457 −1.39280 −0.696402 0.717652i \(-0.745217\pi\)
−0.696402 + 0.717652i \(0.745217\pi\)
\(992\) −20.4718 −0.649981
\(993\) 58.8869 1.86872
\(994\) −103.326 −3.27730
\(995\) −26.2207 −0.831253
\(996\) −17.0165 −0.539188
\(997\) −31.3040 −0.991406 −0.495703 0.868492i \(-0.665090\pi\)
−0.495703 + 0.868492i \(0.665090\pi\)
\(998\) 29.6339 0.938044
\(999\) −31.5406 −0.997901
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 \(a_p\))