Properties

Label 619.2.a.b.1.6
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.67244 q^{2} -2.69736 q^{3} +0.797052 q^{4} +3.55917 q^{5} +4.51117 q^{6} +2.20002 q^{7} +2.01186 q^{8} +4.27576 q^{9} +O(q^{10})\) \(q-1.67244 q^{2} -2.69736 q^{3} +0.797052 q^{4} +3.55917 q^{5} +4.51117 q^{6} +2.20002 q^{7} +2.01186 q^{8} +4.27576 q^{9} -5.95250 q^{10} +1.00893 q^{11} -2.14994 q^{12} +1.66780 q^{13} -3.67940 q^{14} -9.60037 q^{15} -4.95881 q^{16} +0.528086 q^{17} -7.15095 q^{18} +2.00358 q^{19} +2.83685 q^{20} -5.93426 q^{21} -1.68737 q^{22} -6.13306 q^{23} -5.42671 q^{24} +7.66770 q^{25} -2.78929 q^{26} -3.44119 q^{27} +1.75353 q^{28} -3.47822 q^{29} +16.0560 q^{30} +7.58956 q^{31} +4.26960 q^{32} -2.72145 q^{33} -0.883191 q^{34} +7.83026 q^{35} +3.40801 q^{36} -0.759584 q^{37} -3.35086 q^{38} -4.49865 q^{39} +7.16054 q^{40} +10.3573 q^{41} +9.92468 q^{42} -11.1351 q^{43} +0.804169 q^{44} +15.2182 q^{45} +10.2572 q^{46} -0.631863 q^{47} +13.3757 q^{48} -2.15990 q^{49} -12.8238 q^{50} -1.42444 q^{51} +1.32932 q^{52} +12.7076 q^{53} +5.75519 q^{54} +3.59095 q^{55} +4.42613 q^{56} -5.40437 q^{57} +5.81711 q^{58} +10.3339 q^{59} -7.65200 q^{60} +4.33343 q^{61} -12.6931 q^{62} +9.40677 q^{63} +2.77698 q^{64} +5.93597 q^{65} +4.55145 q^{66} -9.29775 q^{67} +0.420912 q^{68} +16.5431 q^{69} -13.0956 q^{70} -3.23203 q^{71} +8.60222 q^{72} +0.177418 q^{73} +1.27036 q^{74} -20.6826 q^{75} +1.59696 q^{76} +2.21967 q^{77} +7.52371 q^{78} -9.62606 q^{79} -17.6493 q^{80} -3.54514 q^{81} -17.3220 q^{82} +2.48977 q^{83} -4.72991 q^{84} +1.87955 q^{85} +18.6228 q^{86} +9.38201 q^{87} +2.02982 q^{88} +3.02247 q^{89} -25.4515 q^{90} +3.66919 q^{91} -4.88837 q^{92} -20.4718 q^{93} +1.05675 q^{94} +7.13107 q^{95} -11.5167 q^{96} +3.43521 q^{97} +3.61230 q^{98} +4.31394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67244 −1.18259 −0.591297 0.806454i \(-0.701384\pi\)
−0.591297 + 0.806454i \(0.701384\pi\)
\(3\) −2.69736 −1.55732 −0.778661 0.627444i \(-0.784101\pi\)
−0.778661 + 0.627444i \(0.784101\pi\)
\(4\) 0.797052 0.398526
\(5\) 3.55917 1.59171 0.795855 0.605487i \(-0.207022\pi\)
0.795855 + 0.605487i \(0.207022\pi\)
\(6\) 4.51117 1.84168
\(7\) 2.20002 0.831530 0.415765 0.909472i \(-0.363514\pi\)
0.415765 + 0.909472i \(0.363514\pi\)
\(8\) 2.01186 0.711299
\(9\) 4.27576 1.42525
\(10\) −5.95250 −1.88234
\(11\) 1.00893 0.304204 0.152102 0.988365i \(-0.451396\pi\)
0.152102 + 0.988365i \(0.451396\pi\)
\(12\) −2.14994 −0.620634
\(13\) 1.66780 0.462563 0.231282 0.972887i \(-0.425708\pi\)
0.231282 + 0.972887i \(0.425708\pi\)
\(14\) −3.67940 −0.983362
\(15\) −9.60037 −2.47881
\(16\) −4.95881 −1.23970
\(17\) 0.528086 0.128080 0.0640398 0.997947i \(-0.479602\pi\)
0.0640398 + 0.997947i \(0.479602\pi\)
\(18\) −7.15095 −1.68550
\(19\) 2.00358 0.459652 0.229826 0.973232i \(-0.426184\pi\)
0.229826 + 0.973232i \(0.426184\pi\)
\(20\) 2.83685 0.634338
\(21\) −5.93426 −1.29496
\(22\) −1.68737 −0.359749
\(23\) −6.13306 −1.27883 −0.639416 0.768861i \(-0.720824\pi\)
−0.639416 + 0.768861i \(0.720824\pi\)
\(24\) −5.42671 −1.10772
\(25\) 7.66770 1.53354
\(26\) −2.78929 −0.547024
\(27\) −3.44119 −0.662258
\(28\) 1.75353 0.331387
\(29\) −3.47822 −0.645889 −0.322944 0.946418i \(-0.604673\pi\)
−0.322944 + 0.946418i \(0.604673\pi\)
\(30\) 16.0560 2.93142
\(31\) 7.58956 1.36313 0.681563 0.731760i \(-0.261301\pi\)
0.681563 + 0.731760i \(0.261301\pi\)
\(32\) 4.26960 0.754766
\(33\) −2.72145 −0.473743
\(34\) −0.883191 −0.151466
\(35\) 7.83026 1.32355
\(36\) 3.40801 0.568001
\(37\) −0.759584 −0.124875 −0.0624374 0.998049i \(-0.519887\pi\)
−0.0624374 + 0.998049i \(0.519887\pi\)
\(38\) −3.35086 −0.543581
\(39\) −4.49865 −0.720360
\(40\) 7.16054 1.13218
\(41\) 10.3573 1.61755 0.808773 0.588121i \(-0.200132\pi\)
0.808773 + 0.588121i \(0.200132\pi\)
\(42\) 9.92468 1.53141
\(43\) −11.1351 −1.69809 −0.849045 0.528321i \(-0.822822\pi\)
−0.849045 + 0.528321i \(0.822822\pi\)
\(44\) 0.804169 0.121233
\(45\) 15.2182 2.26859
\(46\) 10.2572 1.51234
\(47\) −0.631863 −0.0921667 −0.0460834 0.998938i \(-0.514674\pi\)
−0.0460834 + 0.998938i \(0.514674\pi\)
\(48\) 13.3757 1.93062
\(49\) −2.15990 −0.308557
\(50\) −12.8238 −1.81355
\(51\) −1.42444 −0.199461
\(52\) 1.32932 0.184344
\(53\) 12.7076 1.74553 0.872763 0.488144i \(-0.162326\pi\)
0.872763 + 0.488144i \(0.162326\pi\)
\(54\) 5.75519 0.783182
\(55\) 3.59095 0.484204
\(56\) 4.42613 0.591466
\(57\) −5.40437 −0.715827
\(58\) 5.81711 0.763824
\(59\) 10.3339 1.34536 0.672681 0.739932i \(-0.265142\pi\)
0.672681 + 0.739932i \(0.265142\pi\)
\(60\) −7.65200 −0.987869
\(61\) 4.33343 0.554838 0.277419 0.960749i \(-0.410521\pi\)
0.277419 + 0.960749i \(0.410521\pi\)
\(62\) −12.6931 −1.61202
\(63\) 9.40677 1.18514
\(64\) 2.77698 0.347123
\(65\) 5.93597 0.736266
\(66\) 4.55145 0.560245
\(67\) −9.29775 −1.13590 −0.567950 0.823063i \(-0.692264\pi\)
−0.567950 + 0.823063i \(0.692264\pi\)
\(68\) 0.420912 0.0510431
\(69\) 16.5431 1.99155
\(70\) −13.0956 −1.56523
\(71\) −3.23203 −0.383572 −0.191786 0.981437i \(-0.561428\pi\)
−0.191786 + 0.981437i \(0.561428\pi\)
\(72\) 8.60222 1.01378
\(73\) 0.177418 0.0207652 0.0103826 0.999946i \(-0.496695\pi\)
0.0103826 + 0.999946i \(0.496695\pi\)
\(74\) 1.27036 0.147676
\(75\) −20.6826 −2.38822
\(76\) 1.59696 0.183183
\(77\) 2.21967 0.252954
\(78\) 7.52371 0.851893
\(79\) −9.62606 −1.08302 −0.541508 0.840696i \(-0.682146\pi\)
−0.541508 + 0.840696i \(0.682146\pi\)
\(80\) −17.6493 −1.97325
\(81\) −3.54514 −0.393904
\(82\) −17.3220 −1.91290
\(83\) 2.48977 0.273288 0.136644 0.990620i \(-0.456368\pi\)
0.136644 + 0.990620i \(0.456368\pi\)
\(84\) −4.72991 −0.516076
\(85\) 1.87955 0.203866
\(86\) 18.6228 2.00815
\(87\) 9.38201 1.00586
\(88\) 2.02982 0.216380
\(89\) 3.02247 0.320381 0.160190 0.987086i \(-0.448789\pi\)
0.160190 + 0.987086i \(0.448789\pi\)
\(90\) −25.4515 −2.68282
\(91\) 3.66919 0.384635
\(92\) −4.88837 −0.509648
\(93\) −20.4718 −2.12283
\(94\) 1.05675 0.108996
\(95\) 7.13107 0.731633
\(96\) −11.5167 −1.17541
\(97\) 3.43521 0.348793 0.174396 0.984676i \(-0.444203\pi\)
0.174396 + 0.984676i \(0.444203\pi\)
\(98\) 3.61230 0.364898
\(99\) 4.31394 0.433567
\(100\) 6.11156 0.611156
\(101\) 17.8212 1.77327 0.886636 0.462468i \(-0.153036\pi\)
0.886636 + 0.462468i \(0.153036\pi\)
\(102\) 2.38229 0.235882
\(103\) −11.2061 −1.10417 −0.552085 0.833788i \(-0.686168\pi\)
−0.552085 + 0.833788i \(0.686168\pi\)
\(104\) 3.35536 0.329021
\(105\) −21.1210 −2.06120
\(106\) −21.2527 −2.06425
\(107\) −1.13238 −0.109472 −0.0547358 0.998501i \(-0.517432\pi\)
−0.0547358 + 0.998501i \(0.517432\pi\)
\(108\) −2.74281 −0.263927
\(109\) 15.0183 1.43849 0.719245 0.694756i \(-0.244488\pi\)
0.719245 + 0.694756i \(0.244488\pi\)
\(110\) −6.00565 −0.572616
\(111\) 2.04887 0.194470
\(112\) −10.9095 −1.03085
\(113\) 0.00360993 0.000339594 0 0.000169797 1.00000i \(-0.499946\pi\)
0.000169797 1.00000i \(0.499946\pi\)
\(114\) 9.03848 0.846532
\(115\) −21.8286 −2.03553
\(116\) −2.77232 −0.257404
\(117\) 7.13110 0.659270
\(118\) −17.2829 −1.59102
\(119\) 1.16180 0.106502
\(120\) −19.3146 −1.76317
\(121\) −9.98206 −0.907460
\(122\) −7.24739 −0.656148
\(123\) −27.9375 −2.51904
\(124\) 6.04928 0.543241
\(125\) 9.49481 0.849241
\(126\) −15.7323 −1.40154
\(127\) 3.10299 0.275346 0.137673 0.990478i \(-0.456038\pi\)
0.137673 + 0.990478i \(0.456038\pi\)
\(128\) −13.1835 −1.16527
\(129\) 30.0355 2.64447
\(130\) −9.92755 −0.870703
\(131\) 0.699910 0.0611514 0.0305757 0.999532i \(-0.490266\pi\)
0.0305757 + 0.999532i \(0.490266\pi\)
\(132\) −2.16914 −0.188799
\(133\) 4.40791 0.382215
\(134\) 15.5499 1.34331
\(135\) −12.2478 −1.05412
\(136\) 1.06243 0.0911029
\(137\) 16.8803 1.44218 0.721092 0.692839i \(-0.243640\pi\)
0.721092 + 0.692839i \(0.243640\pi\)
\(138\) −27.6673 −2.35520
\(139\) −12.2609 −1.03995 −0.519976 0.854181i \(-0.674059\pi\)
−0.519976 + 0.854181i \(0.674059\pi\)
\(140\) 6.24113 0.527471
\(141\) 1.70436 0.143533
\(142\) 5.40538 0.453609
\(143\) 1.68269 0.140713
\(144\) −21.2027 −1.76689
\(145\) −12.3796 −1.02807
\(146\) −0.296721 −0.0245568
\(147\) 5.82604 0.480524
\(148\) −0.605428 −0.0497659
\(149\) 8.43012 0.690622 0.345311 0.938488i \(-0.387773\pi\)
0.345311 + 0.938488i \(0.387773\pi\)
\(150\) 34.5903 2.82429
\(151\) 23.0642 1.87694 0.938469 0.345365i \(-0.112245\pi\)
0.938469 + 0.345365i \(0.112245\pi\)
\(152\) 4.03091 0.326950
\(153\) 2.25797 0.182546
\(154\) −3.71226 −0.299142
\(155\) 27.0125 2.16970
\(156\) −3.58566 −0.287082
\(157\) −10.7538 −0.858248 −0.429124 0.903246i \(-0.641178\pi\)
−0.429124 + 0.903246i \(0.641178\pi\)
\(158\) 16.0990 1.28077
\(159\) −34.2771 −2.71835
\(160\) 15.1962 1.20137
\(161\) −13.4929 −1.06339
\(162\) 5.92903 0.465829
\(163\) 15.7293 1.23201 0.616007 0.787740i \(-0.288749\pi\)
0.616007 + 0.787740i \(0.288749\pi\)
\(164\) 8.25535 0.644634
\(165\) −9.68610 −0.754062
\(166\) −4.16399 −0.323188
\(167\) 11.9660 0.925956 0.462978 0.886370i \(-0.346781\pi\)
0.462978 + 0.886370i \(0.346781\pi\)
\(168\) −11.9389 −0.921104
\(169\) −10.2185 −0.786035
\(170\) −3.14343 −0.241090
\(171\) 8.56682 0.655121
\(172\) −8.87528 −0.676733
\(173\) −19.8190 −1.50681 −0.753404 0.657558i \(-0.771589\pi\)
−0.753404 + 0.657558i \(0.771589\pi\)
\(174\) −15.6908 −1.18952
\(175\) 16.8691 1.27519
\(176\) −5.00309 −0.377122
\(177\) −27.8743 −2.09516
\(178\) −5.05489 −0.378880
\(179\) 19.6175 1.46628 0.733139 0.680079i \(-0.238055\pi\)
0.733139 + 0.680079i \(0.238055\pi\)
\(180\) 12.1297 0.904093
\(181\) 7.49348 0.556986 0.278493 0.960438i \(-0.410165\pi\)
0.278493 + 0.960438i \(0.410165\pi\)
\(182\) −6.13649 −0.454867
\(183\) −11.6888 −0.864063
\(184\) −12.3388 −0.909631
\(185\) −2.70349 −0.198764
\(186\) 34.2378 2.51044
\(187\) 0.532801 0.0389623
\(188\) −0.503628 −0.0367308
\(189\) −7.57071 −0.550688
\(190\) −11.9263 −0.865224
\(191\) 14.5354 1.05174 0.525872 0.850564i \(-0.323739\pi\)
0.525872 + 0.850564i \(0.323739\pi\)
\(192\) −7.49052 −0.540582
\(193\) 5.18084 0.372925 0.186462 0.982462i \(-0.440298\pi\)
0.186462 + 0.982462i \(0.440298\pi\)
\(194\) −5.74518 −0.412480
\(195\) −16.0115 −1.14660
\(196\) −1.72156 −0.122968
\(197\) −8.32183 −0.592906 −0.296453 0.955048i \(-0.595804\pi\)
−0.296453 + 0.955048i \(0.595804\pi\)
\(198\) −7.21480 −0.512734
\(199\) 23.0744 1.63570 0.817851 0.575431i \(-0.195166\pi\)
0.817851 + 0.575431i \(0.195166\pi\)
\(200\) 15.4263 1.09081
\(201\) 25.0794 1.76896
\(202\) −29.8048 −2.09706
\(203\) −7.65216 −0.537076
\(204\) −1.13535 −0.0794906
\(205\) 36.8636 2.57466
\(206\) 18.7415 1.30578
\(207\) −26.2235 −1.82266
\(208\) −8.27028 −0.573441
\(209\) 2.02147 0.139828
\(210\) 35.3236 2.43756
\(211\) −6.27214 −0.431792 −0.215896 0.976416i \(-0.569267\pi\)
−0.215896 + 0.976416i \(0.569267\pi\)
\(212\) 10.1286 0.695638
\(213\) 8.71796 0.597345
\(214\) 1.89384 0.129460
\(215\) −39.6318 −2.70287
\(216\) −6.92319 −0.471063
\(217\) 16.6972 1.13348
\(218\) −25.1172 −1.70115
\(219\) −0.478561 −0.0323382
\(220\) 2.86218 0.192968
\(221\) 0.880739 0.0592449
\(222\) −3.42662 −0.229979
\(223\) −18.7017 −1.25236 −0.626178 0.779680i \(-0.715382\pi\)
−0.626178 + 0.779680i \(0.715382\pi\)
\(224\) 9.39321 0.627610
\(225\) 32.7853 2.18568
\(226\) −0.00603739 −0.000401601 0
\(227\) −5.00818 −0.332405 −0.166202 0.986092i \(-0.553150\pi\)
−0.166202 + 0.986092i \(0.553150\pi\)
\(228\) −4.30757 −0.285276
\(229\) −1.37016 −0.0905428 −0.0452714 0.998975i \(-0.514415\pi\)
−0.0452714 + 0.998975i \(0.514415\pi\)
\(230\) 36.5070 2.40720
\(231\) −5.98724 −0.393932
\(232\) −6.99767 −0.459420
\(233\) −19.0140 −1.24565 −0.622823 0.782363i \(-0.714014\pi\)
−0.622823 + 0.782363i \(0.714014\pi\)
\(234\) −11.9263 −0.779648
\(235\) −2.24891 −0.146703
\(236\) 8.23668 0.536162
\(237\) 25.9650 1.68661
\(238\) −1.94304 −0.125949
\(239\) −23.2602 −1.50458 −0.752289 0.658833i \(-0.771050\pi\)
−0.752289 + 0.658833i \(0.771050\pi\)
\(240\) 47.6065 3.07298
\(241\) −3.75751 −0.242043 −0.121021 0.992650i \(-0.538617\pi\)
−0.121021 + 0.992650i \(0.538617\pi\)
\(242\) 16.6944 1.07316
\(243\) 19.8861 1.27569
\(244\) 3.45397 0.221118
\(245\) −7.68746 −0.491134
\(246\) 46.7238 2.97900
\(247\) 3.34156 0.212618
\(248\) 15.2691 0.969589
\(249\) −6.71581 −0.425597
\(250\) −15.8795 −1.00431
\(251\) 7.30541 0.461114 0.230557 0.973059i \(-0.425945\pi\)
0.230557 + 0.973059i \(0.425945\pi\)
\(252\) 7.49769 0.472310
\(253\) −6.18783 −0.389025
\(254\) −5.18956 −0.325622
\(255\) −5.06982 −0.317485
\(256\) 16.4947 1.03092
\(257\) 4.05578 0.252993 0.126496 0.991967i \(-0.459627\pi\)
0.126496 + 0.991967i \(0.459627\pi\)
\(258\) −50.2325 −3.12734
\(259\) −1.67110 −0.103837
\(260\) 4.73128 0.293421
\(261\) −14.8720 −0.920556
\(262\) −1.17056 −0.0723172
\(263\) −11.7636 −0.725373 −0.362686 0.931911i \(-0.618140\pi\)
−0.362686 + 0.931911i \(0.618140\pi\)
\(264\) −5.47516 −0.336973
\(265\) 45.2286 2.77837
\(266\) −7.37197 −0.452004
\(267\) −8.15269 −0.498937
\(268\) −7.41079 −0.452686
\(269\) −7.02177 −0.428125 −0.214062 0.976820i \(-0.568670\pi\)
−0.214062 + 0.976820i \(0.568670\pi\)
\(270\) 20.4837 1.24660
\(271\) −8.66657 −0.526457 −0.263228 0.964734i \(-0.584787\pi\)
−0.263228 + 0.964734i \(0.584787\pi\)
\(272\) −2.61868 −0.158781
\(273\) −9.89713 −0.599001
\(274\) −28.2313 −1.70552
\(275\) 7.73617 0.466508
\(276\) 13.1857 0.793687
\(277\) −19.8335 −1.19168 −0.595841 0.803103i \(-0.703181\pi\)
−0.595841 + 0.803103i \(0.703181\pi\)
\(278\) 20.5055 1.22984
\(279\) 32.4512 1.94280
\(280\) 15.7534 0.941443
\(281\) −0.716227 −0.0427265 −0.0213632 0.999772i \(-0.506801\pi\)
−0.0213632 + 0.999772i \(0.506801\pi\)
\(282\) −2.85044 −0.169741
\(283\) −13.4804 −0.801328 −0.400664 0.916225i \(-0.631221\pi\)
−0.400664 + 0.916225i \(0.631221\pi\)
\(284\) −2.57610 −0.152863
\(285\) −19.2351 −1.13939
\(286\) −2.81419 −0.166407
\(287\) 22.7864 1.34504
\(288\) 18.2558 1.07573
\(289\) −16.7211 −0.983596
\(290\) 20.7041 1.21579
\(291\) −9.26601 −0.543183
\(292\) 0.141412 0.00827549
\(293\) −21.5051 −1.25634 −0.628170 0.778077i \(-0.716196\pi\)
−0.628170 + 0.778077i \(0.716196\pi\)
\(294\) −9.74369 −0.568264
\(295\) 36.7802 2.14143
\(296\) −1.52817 −0.0888233
\(297\) −3.47192 −0.201461
\(298\) −14.0989 −0.816725
\(299\) −10.2287 −0.591541
\(300\) −16.4851 −0.951767
\(301\) −24.4975 −1.41201
\(302\) −38.5735 −2.21965
\(303\) −48.0701 −2.76156
\(304\) −9.93536 −0.569832
\(305\) 15.4234 0.883142
\(306\) −3.77632 −0.215878
\(307\) 21.8871 1.24917 0.624583 0.780959i \(-0.285269\pi\)
0.624583 + 0.780959i \(0.285269\pi\)
\(308\) 1.76919 0.100809
\(309\) 30.2269 1.71955
\(310\) −45.1768 −2.56587
\(311\) 20.9084 1.18561 0.592803 0.805347i \(-0.298021\pi\)
0.592803 + 0.805347i \(0.298021\pi\)
\(312\) −9.05063 −0.512391
\(313\) −3.04906 −0.172343 −0.0861717 0.996280i \(-0.527463\pi\)
−0.0861717 + 0.996280i \(0.527463\pi\)
\(314\) 17.9851 1.01496
\(315\) 33.4803 1.88640
\(316\) −7.67247 −0.431610
\(317\) 29.3965 1.65107 0.825537 0.564348i \(-0.190872\pi\)
0.825537 + 0.564348i \(0.190872\pi\)
\(318\) 57.3263 3.21470
\(319\) −3.50927 −0.196482
\(320\) 9.88375 0.552519
\(321\) 3.05445 0.170483
\(322\) 22.5660 1.25755
\(323\) 1.05806 0.0588721
\(324\) −2.82566 −0.156981
\(325\) 12.7882 0.709359
\(326\) −26.3063 −1.45697
\(327\) −40.5098 −2.24019
\(328\) 20.8375 1.15056
\(329\) −1.39011 −0.0766394
\(330\) 16.1994 0.891748
\(331\) −27.3754 −1.50469 −0.752344 0.658770i \(-0.771077\pi\)
−0.752344 + 0.658770i \(0.771077\pi\)
\(332\) 1.98448 0.108912
\(333\) −3.24780 −0.177978
\(334\) −20.0124 −1.09503
\(335\) −33.0923 −1.80802
\(336\) 29.4269 1.60537
\(337\) 14.5105 0.790440 0.395220 0.918587i \(-0.370668\pi\)
0.395220 + 0.918587i \(0.370668\pi\)
\(338\) 17.0898 0.929560
\(339\) −0.00973729 −0.000528857 0
\(340\) 1.49810 0.0812458
\(341\) 7.65733 0.414668
\(342\) −14.3275 −0.774742
\(343\) −20.1520 −1.08811
\(344\) −22.4023 −1.20785
\(345\) 58.8797 3.16998
\(346\) 33.1460 1.78194
\(347\) 13.2318 0.710322 0.355161 0.934805i \(-0.384426\pi\)
0.355161 + 0.934805i \(0.384426\pi\)
\(348\) 7.47796 0.400861
\(349\) −4.55179 −0.243652 −0.121826 0.992551i \(-0.538875\pi\)
−0.121826 + 0.992551i \(0.538875\pi\)
\(350\) −28.2126 −1.50803
\(351\) −5.73921 −0.306336
\(352\) 4.30772 0.229602
\(353\) −1.05807 −0.0563156 −0.0281578 0.999603i \(-0.508964\pi\)
−0.0281578 + 0.999603i \(0.508964\pi\)
\(354\) 46.6181 2.47773
\(355\) −11.5034 −0.610535
\(356\) 2.40907 0.127680
\(357\) −3.13380 −0.165858
\(358\) −32.8090 −1.73401
\(359\) 22.1487 1.16897 0.584483 0.811406i \(-0.301297\pi\)
0.584483 + 0.811406i \(0.301297\pi\)
\(360\) 30.6168 1.61365
\(361\) −14.9857 −0.788720
\(362\) −12.5324 −0.658688
\(363\) 26.9252 1.41321
\(364\) 2.92453 0.153287
\(365\) 0.631462 0.0330522
\(366\) 19.5488 1.02183
\(367\) −7.89793 −0.412269 −0.206134 0.978524i \(-0.566088\pi\)
−0.206134 + 0.978524i \(0.566088\pi\)
\(368\) 30.4127 1.58537
\(369\) 44.2855 2.30541
\(370\) 4.52142 0.235057
\(371\) 27.9571 1.45146
\(372\) −16.3171 −0.846002
\(373\) 32.0426 1.65910 0.829552 0.558430i \(-0.188596\pi\)
0.829552 + 0.558430i \(0.188596\pi\)
\(374\) −0.891077 −0.0460765
\(375\) −25.6109 −1.32254
\(376\) −1.27122 −0.0655581
\(377\) −5.80095 −0.298764
\(378\) 12.6615 0.651240
\(379\) 31.2188 1.60360 0.801802 0.597590i \(-0.203875\pi\)
0.801802 + 0.597590i \(0.203875\pi\)
\(380\) 5.68384 0.291575
\(381\) −8.36989 −0.428803
\(382\) −24.3096 −1.24379
\(383\) −11.9323 −0.609713 −0.304856 0.952398i \(-0.598608\pi\)
−0.304856 + 0.952398i \(0.598608\pi\)
\(384\) 35.5608 1.81470
\(385\) 7.90017 0.402630
\(386\) −8.66464 −0.441018
\(387\) −47.6111 −2.42021
\(388\) 2.73804 0.139003
\(389\) −30.4336 −1.54305 −0.771523 0.636201i \(-0.780505\pi\)
−0.771523 + 0.636201i \(0.780505\pi\)
\(390\) 26.7782 1.35597
\(391\) −3.23878 −0.163792
\(392\) −4.34541 −0.219476
\(393\) −1.88791 −0.0952325
\(394\) 13.9177 0.701166
\(395\) −34.2608 −1.72385
\(396\) 3.43844 0.172788
\(397\) −4.63951 −0.232850 −0.116425 0.993199i \(-0.537143\pi\)
−0.116425 + 0.993199i \(0.537143\pi\)
\(398\) −38.5905 −1.93437
\(399\) −11.8897 −0.595232
\(400\) −38.0227 −1.90113
\(401\) −10.2005 −0.509388 −0.254694 0.967022i \(-0.581975\pi\)
−0.254694 + 0.967022i \(0.581975\pi\)
\(402\) −41.9438 −2.09197
\(403\) 12.6578 0.630531
\(404\) 14.2044 0.706695
\(405\) −12.6178 −0.626982
\(406\) 12.7978 0.635142
\(407\) −0.766366 −0.0379874
\(408\) −2.86577 −0.141877
\(409\) 12.6749 0.626734 0.313367 0.949632i \(-0.398543\pi\)
0.313367 + 0.949632i \(0.398543\pi\)
\(410\) −61.6521 −3.04478
\(411\) −45.5324 −2.24595
\(412\) −8.93186 −0.440041
\(413\) 22.7349 1.11871
\(414\) 43.8572 2.15547
\(415\) 8.86152 0.434995
\(416\) 7.12082 0.349127
\(417\) 33.0720 1.61954
\(418\) −3.38078 −0.165359
\(419\) 30.9828 1.51361 0.756804 0.653642i \(-0.226760\pi\)
0.756804 + 0.653642i \(0.226760\pi\)
\(420\) −16.8346 −0.821443
\(421\) −36.2433 −1.76639 −0.883195 0.469005i \(-0.844613\pi\)
−0.883195 + 0.469005i \(0.844613\pi\)
\(422\) 10.4898 0.510634
\(423\) −2.70170 −0.131361
\(424\) 25.5659 1.24159
\(425\) 4.04920 0.196415
\(426\) −14.5803 −0.706416
\(427\) 9.53364 0.461365
\(428\) −0.902569 −0.0436273
\(429\) −4.53882 −0.219136
\(430\) 66.2818 3.19639
\(431\) −13.7752 −0.663528 −0.331764 0.943362i \(-0.607644\pi\)
−0.331764 + 0.943362i \(0.607644\pi\)
\(432\) 17.0642 0.821004
\(433\) −27.6647 −1.32948 −0.664741 0.747074i \(-0.731458\pi\)
−0.664741 + 0.747074i \(0.731458\pi\)
\(434\) −27.9250 −1.34045
\(435\) 33.3922 1.60103
\(436\) 11.9704 0.573276
\(437\) −12.2881 −0.587818
\(438\) 0.800364 0.0382429
\(439\) −23.6384 −1.12820 −0.564100 0.825706i \(-0.690777\pi\)
−0.564100 + 0.825706i \(0.690777\pi\)
\(440\) 7.22448 0.344414
\(441\) −9.23523 −0.439773
\(442\) −1.47298 −0.0700626
\(443\) 5.20469 0.247282 0.123641 0.992327i \(-0.460543\pi\)
0.123641 + 0.992327i \(0.460543\pi\)
\(444\) 1.63306 0.0775016
\(445\) 10.7575 0.509954
\(446\) 31.2774 1.48103
\(447\) −22.7391 −1.07552
\(448\) 6.10942 0.288643
\(449\) −24.8056 −1.17065 −0.585324 0.810800i \(-0.699032\pi\)
−0.585324 + 0.810800i \(0.699032\pi\)
\(450\) −54.8314 −2.58478
\(451\) 10.4498 0.492063
\(452\) 0.00287730 0.000135337 0
\(453\) −62.2125 −2.92300
\(454\) 8.37588 0.393100
\(455\) 13.0593 0.612228
\(456\) −10.8728 −0.509167
\(457\) 22.8513 1.06894 0.534470 0.845187i \(-0.320511\pi\)
0.534470 + 0.845187i \(0.320511\pi\)
\(458\) 2.29151 0.107075
\(459\) −1.81725 −0.0848218
\(460\) −17.3986 −0.811212
\(461\) −7.75513 −0.361192 −0.180596 0.983557i \(-0.557803\pi\)
−0.180596 + 0.983557i \(0.557803\pi\)
\(462\) 10.0133 0.465861
\(463\) −26.0269 −1.20957 −0.604786 0.796388i \(-0.706741\pi\)
−0.604786 + 0.796388i \(0.706741\pi\)
\(464\) 17.2478 0.800710
\(465\) −72.8626 −3.37892
\(466\) 31.7997 1.47309
\(467\) 34.5038 1.59665 0.798323 0.602230i \(-0.205721\pi\)
0.798323 + 0.602230i \(0.205721\pi\)
\(468\) 5.68386 0.262736
\(469\) −20.4553 −0.944536
\(470\) 3.76116 0.173490
\(471\) 29.0070 1.33657
\(472\) 20.7904 0.956955
\(473\) −11.2345 −0.516565
\(474\) −43.4248 −1.99457
\(475\) 15.3628 0.704895
\(476\) 0.926016 0.0424439
\(477\) 54.3348 2.48782
\(478\) 38.9013 1.77930
\(479\) −23.4626 −1.07203 −0.536017 0.844207i \(-0.680072\pi\)
−0.536017 + 0.844207i \(0.680072\pi\)
\(480\) −40.9897 −1.87092
\(481\) −1.26683 −0.0577625
\(482\) 6.28421 0.286238
\(483\) 36.3952 1.65604
\(484\) −7.95623 −0.361647
\(485\) 12.2265 0.555177
\(486\) −33.2583 −1.50863
\(487\) −20.4656 −0.927384 −0.463692 0.885996i \(-0.653476\pi\)
−0.463692 + 0.885996i \(0.653476\pi\)
\(488\) 8.71823 0.394656
\(489\) −42.4276 −1.91864
\(490\) 12.8568 0.580812
\(491\) 26.3027 1.18702 0.593511 0.804826i \(-0.297741\pi\)
0.593511 + 0.804826i \(0.297741\pi\)
\(492\) −22.2677 −1.00390
\(493\) −1.83680 −0.0827252
\(494\) −5.58855 −0.251441
\(495\) 15.3541 0.690114
\(496\) −37.6352 −1.68987
\(497\) −7.11054 −0.318951
\(498\) 11.2318 0.503308
\(499\) −40.3280 −1.80533 −0.902665 0.430343i \(-0.858392\pi\)
−0.902665 + 0.430343i \(0.858392\pi\)
\(500\) 7.56786 0.338445
\(501\) −32.2766 −1.44201
\(502\) −12.2179 −0.545310
\(503\) −40.5524 −1.80814 −0.904072 0.427381i \(-0.859436\pi\)
−0.904072 + 0.427381i \(0.859436\pi\)
\(504\) 18.9251 0.842990
\(505\) 63.4286 2.82253
\(506\) 10.3488 0.460059
\(507\) 27.5629 1.22411
\(508\) 2.47325 0.109733
\(509\) −24.7022 −1.09491 −0.547454 0.836836i \(-0.684403\pi\)
−0.547454 + 0.836836i \(0.684403\pi\)
\(510\) 8.47897 0.375455
\(511\) 0.390324 0.0172669
\(512\) −1.21930 −0.0538860
\(513\) −6.89470 −0.304408
\(514\) −6.78305 −0.299187
\(515\) −39.8845 −1.75752
\(516\) 23.9398 1.05389
\(517\) −0.637505 −0.0280374
\(518\) 2.79482 0.122797
\(519\) 53.4589 2.34659
\(520\) 11.9423 0.523705
\(521\) −21.9010 −0.959499 −0.479750 0.877405i \(-0.659273\pi\)
−0.479750 + 0.877405i \(0.659273\pi\)
\(522\) 24.8726 1.08864
\(523\) 23.1525 1.01239 0.506193 0.862420i \(-0.331052\pi\)
0.506193 + 0.862420i \(0.331052\pi\)
\(524\) 0.557865 0.0243704
\(525\) −45.5021 −1.98587
\(526\) 19.6739 0.857821
\(527\) 4.00794 0.174589
\(528\) 13.4951 0.587301
\(529\) 14.6145 0.635411
\(530\) −75.6421 −3.28568
\(531\) 44.1854 1.91748
\(532\) 3.51334 0.152323
\(533\) 17.2739 0.748217
\(534\) 13.6349 0.590039
\(535\) −4.03035 −0.174247
\(536\) −18.7057 −0.807965
\(537\) −52.9154 −2.28347
\(538\) 11.7435 0.506297
\(539\) −2.17919 −0.0938643
\(540\) −9.76214 −0.420096
\(541\) −20.5750 −0.884587 −0.442293 0.896870i \(-0.645835\pi\)
−0.442293 + 0.896870i \(0.645835\pi\)
\(542\) 14.4943 0.622584
\(543\) −20.2126 −0.867407
\(544\) 2.25471 0.0966701
\(545\) 53.4527 2.28966
\(546\) 16.5523 0.708375
\(547\) −14.5562 −0.622379 −0.311190 0.950348i \(-0.600727\pi\)
−0.311190 + 0.950348i \(0.600727\pi\)
\(548\) 13.4545 0.574748
\(549\) 18.5287 0.790786
\(550\) −12.9383 −0.551690
\(551\) −6.96888 −0.296884
\(552\) 33.2823 1.41659
\(553\) −21.1775 −0.900561
\(554\) 33.1704 1.40927
\(555\) 7.29229 0.309540
\(556\) −9.77254 −0.414448
\(557\) 38.7141 1.64037 0.820184 0.572101i \(-0.193871\pi\)
0.820184 + 0.572101i \(0.193871\pi\)
\(558\) −54.2726 −2.29754
\(559\) −18.5711 −0.785474
\(560\) −38.8288 −1.64082
\(561\) −1.43716 −0.0606768
\(562\) 1.19785 0.0505281
\(563\) 16.3996 0.691159 0.345579 0.938389i \(-0.387682\pi\)
0.345579 + 0.938389i \(0.387682\pi\)
\(564\) 1.35847 0.0572018
\(565\) 0.0128484 0.000540535 0
\(566\) 22.5452 0.947645
\(567\) −7.79939 −0.327543
\(568\) −6.50238 −0.272834
\(569\) −15.6729 −0.657043 −0.328522 0.944496i \(-0.606550\pi\)
−0.328522 + 0.944496i \(0.606550\pi\)
\(570\) 32.1695 1.34743
\(571\) −2.26279 −0.0946948 −0.0473474 0.998878i \(-0.515077\pi\)
−0.0473474 + 0.998878i \(0.515077\pi\)
\(572\) 1.34119 0.0560780
\(573\) −39.2072 −1.63791
\(574\) −38.1088 −1.59063
\(575\) −47.0265 −1.96114
\(576\) 11.8737 0.494738
\(577\) −41.0633 −1.70949 −0.854744 0.519050i \(-0.826286\pi\)
−0.854744 + 0.519050i \(0.826286\pi\)
\(578\) 27.9651 1.16319
\(579\) −13.9746 −0.580764
\(580\) −9.86717 −0.409712
\(581\) 5.47755 0.227247
\(582\) 15.4968 0.642364
\(583\) 12.8211 0.530995
\(584\) 0.356940 0.0147703
\(585\) 25.3808 1.04937
\(586\) 35.9659 1.48574
\(587\) −16.1494 −0.666558 −0.333279 0.942828i \(-0.608155\pi\)
−0.333279 + 0.942828i \(0.608155\pi\)
\(588\) 4.64366 0.191501
\(589\) 15.2063 0.626563
\(590\) −61.5127 −2.53244
\(591\) 22.4470 0.923345
\(592\) 3.76663 0.154808
\(593\) −29.7453 −1.22149 −0.610746 0.791827i \(-0.709130\pi\)
−0.610746 + 0.791827i \(0.709130\pi\)
\(594\) 5.80658 0.238247
\(595\) 4.13505 0.169520
\(596\) 6.71924 0.275231
\(597\) −62.2400 −2.54731
\(598\) 17.1069 0.699552
\(599\) 16.6446 0.680079 0.340039 0.940411i \(-0.389560\pi\)
0.340039 + 0.940411i \(0.389560\pi\)
\(600\) −41.6104 −1.69874
\(601\) −33.0308 −1.34736 −0.673678 0.739025i \(-0.735287\pi\)
−0.673678 + 0.739025i \(0.735287\pi\)
\(602\) 40.9706 1.66984
\(603\) −39.7550 −1.61895
\(604\) 18.3834 0.748009
\(605\) −35.5279 −1.44441
\(606\) 80.3944 3.26580
\(607\) 35.0786 1.42380 0.711898 0.702283i \(-0.247836\pi\)
0.711898 + 0.702283i \(0.247836\pi\)
\(608\) 8.55447 0.346930
\(609\) 20.6406 0.836401
\(610\) −25.7947 −1.04440
\(611\) −1.05382 −0.0426329
\(612\) 1.79972 0.0727494
\(613\) −36.3600 −1.46857 −0.734283 0.678844i \(-0.762481\pi\)
−0.734283 + 0.678844i \(0.762481\pi\)
\(614\) −36.6049 −1.47725
\(615\) −99.4344 −4.00958
\(616\) 4.46565 0.179926
\(617\) 39.1708 1.57696 0.788479 0.615062i \(-0.210869\pi\)
0.788479 + 0.615062i \(0.210869\pi\)
\(618\) −50.5527 −2.03353
\(619\) 1.00000 0.0401934
\(620\) 21.5304 0.864682
\(621\) 21.1051 0.846917
\(622\) −34.9680 −1.40209
\(623\) 6.64950 0.266406
\(624\) 22.3080 0.893033
\(625\) −4.54486 −0.181794
\(626\) 5.09937 0.203812
\(627\) −5.45263 −0.217757
\(628\) −8.57136 −0.342034
\(629\) −0.401125 −0.0159939
\(630\) −55.9938 −2.23085
\(631\) −9.49838 −0.378124 −0.189062 0.981965i \(-0.560545\pi\)
−0.189062 + 0.981965i \(0.560545\pi\)
\(632\) −19.3662 −0.770348
\(633\) 16.9182 0.672439
\(634\) −49.1639 −1.95255
\(635\) 11.0441 0.438271
\(636\) −27.3206 −1.08333
\(637\) −3.60227 −0.142727
\(638\) 5.86905 0.232358
\(639\) −13.8194 −0.546687
\(640\) −46.9224 −1.85477
\(641\) −36.0946 −1.42565 −0.712825 0.701342i \(-0.752584\pi\)
−0.712825 + 0.701342i \(0.752584\pi\)
\(642\) −5.10838 −0.201612
\(643\) 4.89032 0.192855 0.0964277 0.995340i \(-0.469258\pi\)
0.0964277 + 0.995340i \(0.469258\pi\)
\(644\) −10.7545 −0.423788
\(645\) 106.901 4.20924
\(646\) −1.76954 −0.0696217
\(647\) −19.1484 −0.752800 −0.376400 0.926457i \(-0.622838\pi\)
−0.376400 + 0.926457i \(0.622838\pi\)
\(648\) −7.13231 −0.280184
\(649\) 10.4262 0.409264
\(650\) −21.3874 −0.838883
\(651\) −45.0384 −1.76519
\(652\) 12.5371 0.490990
\(653\) 30.0659 1.17657 0.588285 0.808654i \(-0.299803\pi\)
0.588285 + 0.808654i \(0.299803\pi\)
\(654\) 67.7501 2.64924
\(655\) 2.49110 0.0973353
\(656\) −51.3601 −2.00528
\(657\) 0.758598 0.0295957
\(658\) 2.32488 0.0906332
\(659\) 3.82306 0.148925 0.0744626 0.997224i \(-0.476276\pi\)
0.0744626 + 0.997224i \(0.476276\pi\)
\(660\) −7.72033 −0.300513
\(661\) 21.8092 0.848281 0.424140 0.905596i \(-0.360576\pi\)
0.424140 + 0.905596i \(0.360576\pi\)
\(662\) 45.7837 1.77943
\(663\) −2.37567 −0.0922634
\(664\) 5.00906 0.194389
\(665\) 15.6885 0.608375
\(666\) 5.43175 0.210476
\(667\) 21.3321 0.825983
\(668\) 9.53753 0.369018
\(669\) 50.4452 1.95032
\(670\) 55.3448 2.13816
\(671\) 4.37212 0.168784
\(672\) −25.3369 −0.977392
\(673\) 43.8015 1.68842 0.844212 0.536010i \(-0.180069\pi\)
0.844212 + 0.536010i \(0.180069\pi\)
\(674\) −24.2680 −0.934769
\(675\) −26.3861 −1.01560
\(676\) −8.14465 −0.313256
\(677\) −0.249698 −0.00959667 −0.00479833 0.999988i \(-0.501527\pi\)
−0.00479833 + 0.999988i \(0.501527\pi\)
\(678\) 0.0162850 0.000625423 0
\(679\) 7.55754 0.290032
\(680\) 3.78138 0.145009
\(681\) 13.5089 0.517661
\(682\) −12.8064 −0.490383
\(683\) 27.7196 1.06066 0.530330 0.847792i \(-0.322068\pi\)
0.530330 + 0.847792i \(0.322068\pi\)
\(684\) 6.82821 0.261083
\(685\) 60.0800 2.29554
\(686\) 33.7030 1.28679
\(687\) 3.69582 0.141004
\(688\) 55.2170 2.10513
\(689\) 21.1937 0.807416
\(690\) −98.4727 −3.74879
\(691\) 25.3309 0.963631 0.481816 0.876273i \(-0.339978\pi\)
0.481816 + 0.876273i \(0.339978\pi\)
\(692\) −15.7968 −0.600502
\(693\) 9.49077 0.360524
\(694\) −22.1294 −0.840022
\(695\) −43.6385 −1.65530
\(696\) 18.8753 0.715465
\(697\) 5.46957 0.207175
\(698\) 7.61259 0.288141
\(699\) 51.2876 1.93987
\(700\) 13.4456 0.508195
\(701\) −5.69317 −0.215028 −0.107514 0.994204i \(-0.534289\pi\)
−0.107514 + 0.994204i \(0.534289\pi\)
\(702\) 9.59848 0.362271
\(703\) −1.52188 −0.0573990
\(704\) 2.80178 0.105596
\(705\) 6.06612 0.228463
\(706\) 1.76957 0.0665985
\(707\) 39.2070 1.47453
\(708\) −22.2173 −0.834978
\(709\) −10.1048 −0.379495 −0.189748 0.981833i \(-0.560767\pi\)
−0.189748 + 0.981833i \(0.560767\pi\)
\(710\) 19.2387 0.722014
\(711\) −41.1587 −1.54357
\(712\) 6.08077 0.227887
\(713\) −46.5472 −1.74321
\(714\) 5.24108 0.196143
\(715\) 5.98897 0.223975
\(716\) 15.6361 0.584350
\(717\) 62.7412 2.34311
\(718\) −37.0424 −1.38241
\(719\) 47.9008 1.78640 0.893199 0.449662i \(-0.148456\pi\)
0.893199 + 0.449662i \(0.148456\pi\)
\(720\) −75.4641 −2.81238
\(721\) −24.6537 −0.918151
\(722\) 25.0626 0.932735
\(723\) 10.1354 0.376938
\(724\) 5.97270 0.221974
\(725\) −26.6699 −0.990496
\(726\) −45.0308 −1.67125
\(727\) 24.2576 0.899664 0.449832 0.893113i \(-0.351484\pi\)
0.449832 + 0.893113i \(0.351484\pi\)
\(728\) 7.38188 0.273591
\(729\) −43.0046 −1.59276
\(730\) −1.05608 −0.0390873
\(731\) −5.88030 −0.217491
\(732\) −9.31660 −0.344352
\(733\) 47.7676 1.76434 0.882168 0.470935i \(-0.156084\pi\)
0.882168 + 0.470935i \(0.156084\pi\)
\(734\) 13.2088 0.487546
\(735\) 20.7359 0.764854
\(736\) −26.1857 −0.965218
\(737\) −9.38077 −0.345545
\(738\) −74.0649 −2.72637
\(739\) −11.3075 −0.415951 −0.207976 0.978134i \(-0.566687\pi\)
−0.207976 + 0.978134i \(0.566687\pi\)
\(740\) −2.15482 −0.0792129
\(741\) −9.01339 −0.331115
\(742\) −46.7565 −1.71648
\(743\) −26.4422 −0.970071 −0.485036 0.874494i \(-0.661193\pi\)
−0.485036 + 0.874494i \(0.661193\pi\)
\(744\) −41.1863 −1.50996
\(745\) 30.0042 1.09927
\(746\) −53.5893 −1.96204
\(747\) 10.6457 0.389505
\(748\) 0.424670 0.0155275
\(749\) −2.49127 −0.0910289
\(750\) 42.8327 1.56403
\(751\) 51.6184 1.88358 0.941791 0.336200i \(-0.109142\pi\)
0.941791 + 0.336200i \(0.109142\pi\)
\(752\) 3.13329 0.114259
\(753\) −19.7053 −0.718103
\(754\) 9.70174 0.353317
\(755\) 82.0894 2.98754
\(756\) −6.03425 −0.219464
\(757\) −17.2070 −0.625398 −0.312699 0.949852i \(-0.601233\pi\)
−0.312699 + 0.949852i \(0.601233\pi\)
\(758\) −52.2116 −1.89641
\(759\) 16.6908 0.605838
\(760\) 14.3467 0.520409
\(761\) −32.5941 −1.18154 −0.590768 0.806841i \(-0.701175\pi\)
−0.590768 + 0.806841i \(0.701175\pi\)
\(762\) 13.9981 0.507099
\(763\) 33.0406 1.19615
\(764\) 11.5855 0.419148
\(765\) 8.03650 0.290560
\(766\) 19.9561 0.721042
\(767\) 17.2349 0.622315
\(768\) −44.4921 −1.60547
\(769\) 14.6625 0.528744 0.264372 0.964421i \(-0.414835\pi\)
0.264372 + 0.964421i \(0.414835\pi\)
\(770\) −13.2126 −0.476148
\(771\) −10.9399 −0.393991
\(772\) 4.12940 0.148620
\(773\) 26.6349 0.957990 0.478995 0.877818i \(-0.341001\pi\)
0.478995 + 0.877818i \(0.341001\pi\)
\(774\) 79.6267 2.86212
\(775\) 58.1945 2.09041
\(776\) 6.91115 0.248096
\(777\) 4.50757 0.161708
\(778\) 50.8984 1.82480
\(779\) 20.7517 0.743508
\(780\) −12.7620 −0.456952
\(781\) −3.26089 −0.116684
\(782\) 5.41667 0.193700
\(783\) 11.9692 0.427745
\(784\) 10.7105 0.382520
\(785\) −38.2747 −1.36608
\(786\) 3.15742 0.112621
\(787\) −6.94747 −0.247650 −0.123825 0.992304i \(-0.539516\pi\)
−0.123825 + 0.992304i \(0.539516\pi\)
\(788\) −6.63293 −0.236288
\(789\) 31.7306 1.12964
\(790\) 57.2991 2.03861
\(791\) 0.00794193 0.000282382 0
\(792\) 8.67903 0.308396
\(793\) 7.22727 0.256648
\(794\) 7.75929 0.275367
\(795\) −121.998 −4.32682
\(796\) 18.3915 0.651870
\(797\) 19.3366 0.684939 0.342469 0.939529i \(-0.388737\pi\)
0.342469 + 0.939529i \(0.388737\pi\)
\(798\) 19.8849 0.703917
\(799\) −0.333678 −0.0118047
\(800\) 32.7380 1.15746
\(801\) 12.9234 0.456624
\(802\) 17.0597 0.602399
\(803\) 0.179002 0.00631686
\(804\) 19.9896 0.704979
\(805\) −48.0235 −1.69260
\(806\) −21.1695 −0.745662
\(807\) 18.9402 0.666728
\(808\) 35.8536 1.26133
\(809\) −6.28808 −0.221077 −0.110539 0.993872i \(-0.535258\pi\)
−0.110539 + 0.993872i \(0.535258\pi\)
\(810\) 21.1024 0.741464
\(811\) 21.2792 0.747213 0.373607 0.927587i \(-0.378121\pi\)
0.373607 + 0.927587i \(0.378121\pi\)
\(812\) −6.09917 −0.214039
\(813\) 23.3769 0.819863
\(814\) 1.28170 0.0449236
\(815\) 55.9833 1.96101
\(816\) 7.06352 0.247273
\(817\) −22.3101 −0.780531
\(818\) −21.1980 −0.741171
\(819\) 15.6886 0.548203
\(820\) 29.3822 1.02607
\(821\) 4.35685 0.152055 0.0760275 0.997106i \(-0.475776\pi\)
0.0760275 + 0.997106i \(0.475776\pi\)
\(822\) 76.1501 2.65604
\(823\) −48.0369 −1.67446 −0.837231 0.546849i \(-0.815827\pi\)
−0.837231 + 0.546849i \(0.815827\pi\)
\(824\) −22.5451 −0.785395
\(825\) −20.8672 −0.726504
\(826\) −38.0227 −1.32298
\(827\) 24.4473 0.850115 0.425057 0.905166i \(-0.360254\pi\)
0.425057 + 0.905166i \(0.360254\pi\)
\(828\) −20.9015 −0.726378
\(829\) 55.3855 1.92362 0.961810 0.273720i \(-0.0882540\pi\)
0.961810 + 0.273720i \(0.0882540\pi\)
\(830\) −14.8204 −0.514422
\(831\) 53.4982 1.85583
\(832\) 4.63144 0.160566
\(833\) −1.14061 −0.0395199
\(834\) −55.3108 −1.91526
\(835\) 42.5890 1.47385
\(836\) 1.61122 0.0557251
\(837\) −26.1172 −0.902741
\(838\) −51.8168 −1.78998
\(839\) −51.6684 −1.78379 −0.891896 0.452241i \(-0.850625\pi\)
−0.891896 + 0.452241i \(0.850625\pi\)
\(840\) −42.4925 −1.46613
\(841\) −16.9020 −0.582828
\(842\) 60.6147 2.08892
\(843\) 1.93192 0.0665389
\(844\) −4.99922 −0.172080
\(845\) −36.3692 −1.25114
\(846\) 4.51842 0.155347
\(847\) −21.9608 −0.754581
\(848\) −63.0147 −2.16393
\(849\) 36.3616 1.24793
\(850\) −6.77205 −0.232279
\(851\) 4.65858 0.159694
\(852\) 6.94867 0.238058
\(853\) 19.3279 0.661774 0.330887 0.943670i \(-0.392652\pi\)
0.330887 + 0.943670i \(0.392652\pi\)
\(854\) −15.9444 −0.545607
\(855\) 30.4908 1.04276
\(856\) −2.27819 −0.0778670
\(857\) −40.9241 −1.39794 −0.698971 0.715150i \(-0.746358\pi\)
−0.698971 + 0.715150i \(0.746358\pi\)
\(858\) 7.59089 0.259149
\(859\) −19.7555 −0.674051 −0.337025 0.941496i \(-0.609421\pi\)
−0.337025 + 0.941496i \(0.609421\pi\)
\(860\) −31.5886 −1.07716
\(861\) −61.4631 −2.09466
\(862\) 23.0382 0.784683
\(863\) −35.0793 −1.19411 −0.597057 0.802199i \(-0.703663\pi\)
−0.597057 + 0.802199i \(0.703663\pi\)
\(864\) −14.6925 −0.499850
\(865\) −70.5391 −2.39840
\(866\) 46.2676 1.57224
\(867\) 45.1029 1.53178
\(868\) 13.3085 0.451721
\(869\) −9.71201 −0.329457
\(870\) −55.8464 −1.89337
\(871\) −15.5067 −0.525426
\(872\) 30.2146 1.02320
\(873\) 14.6881 0.497119
\(874\) 20.5510 0.695149
\(875\) 20.8888 0.706170
\(876\) −0.381438 −0.0128876
\(877\) 5.59733 0.189008 0.0945042 0.995524i \(-0.469873\pi\)
0.0945042 + 0.995524i \(0.469873\pi\)
\(878\) 39.5338 1.33420
\(879\) 58.0069 1.95653
\(880\) −17.8069 −0.600269
\(881\) −40.4065 −1.36133 −0.680664 0.732595i \(-0.738309\pi\)
−0.680664 + 0.732595i \(0.738309\pi\)
\(882\) 15.4454 0.520072
\(883\) −45.4672 −1.53009 −0.765047 0.643975i \(-0.777284\pi\)
−0.765047 + 0.643975i \(0.777284\pi\)
\(884\) 0.701995 0.0236107
\(885\) −99.2096 −3.33489
\(886\) −8.70453 −0.292434
\(887\) −38.7839 −1.30224 −0.651118 0.758977i \(-0.725700\pi\)
−0.651118 + 0.758977i \(0.725700\pi\)
\(888\) 4.12204 0.138327
\(889\) 6.82665 0.228959
\(890\) −17.9912 −0.603068
\(891\) −3.57679 −0.119827
\(892\) −14.9062 −0.499097
\(893\) −1.26599 −0.0423646
\(894\) 38.0297 1.27190
\(895\) 69.8219 2.33389
\(896\) −29.0041 −0.968958
\(897\) 27.5905 0.921220
\(898\) 41.4858 1.38440
\(899\) −26.3981 −0.880427
\(900\) 26.1316 0.871053
\(901\) 6.71071 0.223566
\(902\) −17.4767 −0.581910
\(903\) 66.0787 2.19896
\(904\) 0.00726266 0.000241553 0
\(905\) 26.6706 0.886560
\(906\) 104.047 3.45672
\(907\) 23.0320 0.764765 0.382383 0.924004i \(-0.375104\pi\)
0.382383 + 0.924004i \(0.375104\pi\)
\(908\) −3.99178 −0.132472
\(909\) 76.1991 2.52736
\(910\) −21.8408 −0.724016
\(911\) 13.9133 0.460967 0.230483 0.973076i \(-0.425969\pi\)
0.230483 + 0.973076i \(0.425969\pi\)
\(912\) 26.7993 0.887413
\(913\) 2.51200 0.0831351
\(914\) −38.2175 −1.26412
\(915\) −41.6025 −1.37534
\(916\) −1.09209 −0.0360837
\(917\) 1.53982 0.0508493
\(918\) 3.03923 0.100310
\(919\) 22.8857 0.754931 0.377465 0.926024i \(-0.376796\pi\)
0.377465 + 0.926024i \(0.376796\pi\)
\(920\) −43.9161 −1.44787
\(921\) −59.0376 −1.94535
\(922\) 12.9700 0.427143
\(923\) −5.39037 −0.177426
\(924\) −4.77215 −0.156992
\(925\) −5.82426 −0.191501
\(926\) 43.5284 1.43043
\(927\) −47.9147 −1.57372
\(928\) −14.8506 −0.487495
\(929\) −6.29562 −0.206553 −0.103276 0.994653i \(-0.532933\pi\)
−0.103276 + 0.994653i \(0.532933\pi\)
\(930\) 121.858 3.99589
\(931\) −4.32753 −0.141829
\(932\) −15.1551 −0.496423
\(933\) −56.3975 −1.84637
\(934\) −57.7055 −1.88818
\(935\) 1.89633 0.0620166
\(936\) 14.3467 0.468938
\(937\) 41.7311 1.36329 0.681647 0.731681i \(-0.261264\pi\)
0.681647 + 0.731681i \(0.261264\pi\)
\(938\) 34.2102 1.11700
\(939\) 8.22443 0.268394
\(940\) −1.79250 −0.0584649
\(941\) −42.7014 −1.39203 −0.696013 0.718029i \(-0.745044\pi\)
−0.696013 + 0.718029i \(0.745044\pi\)
\(942\) −48.5124 −1.58062
\(943\) −63.5222 −2.06857
\(944\) −51.2440 −1.66785
\(945\) −26.9454 −0.876535
\(946\) 18.7891 0.610886
\(947\) 0.482351 0.0156743 0.00783715 0.999969i \(-0.497505\pi\)
0.00783715 + 0.999969i \(0.497505\pi\)
\(948\) 20.6954 0.672157
\(949\) 0.295897 0.00960523
\(950\) −25.6934 −0.833604
\(951\) −79.2931 −2.57126
\(952\) 2.33738 0.0757548
\(953\) 13.2613 0.429577 0.214788 0.976661i \(-0.431094\pi\)
0.214788 + 0.976661i \(0.431094\pi\)
\(954\) −90.8716 −2.94208
\(955\) 51.7340 1.67407
\(956\) −18.5396 −0.599614
\(957\) 9.46579 0.305985
\(958\) 39.2398 1.26778
\(959\) 37.1371 1.19922
\(960\) −26.6601 −0.860450
\(961\) 26.6014 0.858110
\(962\) 2.11870 0.0683095
\(963\) −4.84180 −0.156025
\(964\) −2.99493 −0.0964603
\(965\) 18.4395 0.593588
\(966\) −60.8687 −1.95842
\(967\) −28.7979 −0.926077 −0.463039 0.886338i \(-0.653241\pi\)
−0.463039 + 0.886338i \(0.653241\pi\)
\(968\) −20.0825 −0.645475
\(969\) −2.85397 −0.0916828
\(970\) −20.4481 −0.656548
\(971\) 30.8971 0.991535 0.495767 0.868455i \(-0.334887\pi\)
0.495767 + 0.868455i \(0.334887\pi\)
\(972\) 15.8503 0.508398
\(973\) −26.9741 −0.864751
\(974\) 34.2274 1.09672
\(975\) −34.4943 −1.10470
\(976\) −21.4887 −0.687835
\(977\) −23.6369 −0.756212 −0.378106 0.925762i \(-0.623425\pi\)
−0.378106 + 0.925762i \(0.623425\pi\)
\(978\) 70.9577 2.26898
\(979\) 3.04946 0.0974610
\(980\) −6.12731 −0.195730
\(981\) 64.2146 2.05022
\(982\) −43.9896 −1.40376
\(983\) −31.9559 −1.01923 −0.509617 0.860401i \(-0.670213\pi\)
−0.509617 + 0.860401i \(0.670213\pi\)
\(984\) −56.2063 −1.79179
\(985\) −29.6188 −0.943734
\(986\) 3.07193 0.0978302
\(987\) 3.74964 0.119352
\(988\) 2.66340 0.0847339
\(989\) 68.2924 2.17157
\(990\) −25.6787 −0.816124
\(991\) 13.3278 0.423371 0.211685 0.977338i \(-0.432105\pi\)
0.211685 + 0.977338i \(0.432105\pi\)
\(992\) 32.4044 1.02884
\(993\) 73.8414 2.34329
\(994\) 11.8919 0.377190
\(995\) 82.1258 2.60356
\(996\) −5.35286 −0.169612
\(997\) −33.6744 −1.06648 −0.533239 0.845965i \(-0.679025\pi\)
−0.533239 + 0.845965i \(0.679025\pi\)
\(998\) 67.4462 2.13497
\(999\) 2.61388 0.0826994
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 \(a_p\))