Properties

Label 8041.2.a.g.1.20
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.66399 q^{2} +1.84747 q^{3} +0.768874 q^{4} +1.24336 q^{5} -3.07417 q^{6} +0.0311850 q^{7} +2.04859 q^{8} +0.413132 q^{9} +O(q^{10})\) \(q-1.66399 q^{2} +1.84747 q^{3} +0.768874 q^{4} +1.24336 q^{5} -3.07417 q^{6} +0.0311850 q^{7} +2.04859 q^{8} +0.413132 q^{9} -2.06894 q^{10} -1.00000 q^{11} +1.42047 q^{12} +3.49994 q^{13} -0.0518916 q^{14} +2.29706 q^{15} -4.94658 q^{16} +1.00000 q^{17} -0.687449 q^{18} -5.25992 q^{19} +0.955986 q^{20} +0.0576132 q^{21} +1.66399 q^{22} -4.42189 q^{23} +3.78469 q^{24} -3.45406 q^{25} -5.82388 q^{26} -4.77915 q^{27} +0.0239773 q^{28} -2.78056 q^{29} -3.82229 q^{30} -0.289166 q^{31} +4.13391 q^{32} -1.84747 q^{33} -1.66399 q^{34} +0.0387741 q^{35} +0.317647 q^{36} +10.1101 q^{37} +8.75248 q^{38} +6.46602 q^{39} +2.54712 q^{40} +4.09151 q^{41} -0.0958679 q^{42} +1.00000 q^{43} -0.768874 q^{44} +0.513671 q^{45} +7.35799 q^{46} +13.1048 q^{47} -9.13864 q^{48} -6.99903 q^{49} +5.74754 q^{50} +1.84747 q^{51} +2.69102 q^{52} -5.95331 q^{53} +7.95248 q^{54} -1.24336 q^{55} +0.0638850 q^{56} -9.71753 q^{57} +4.62683 q^{58} +10.5664 q^{59} +1.76615 q^{60} -5.77116 q^{61} +0.481170 q^{62} +0.0128835 q^{63} +3.01437 q^{64} +4.35168 q^{65} +3.07417 q^{66} -13.2819 q^{67} +0.768874 q^{68} -8.16928 q^{69} -0.0645198 q^{70} -0.811957 q^{71} +0.846336 q^{72} -7.66046 q^{73} -16.8232 q^{74} -6.38126 q^{75} -4.04422 q^{76} -0.0311850 q^{77} -10.7594 q^{78} +3.36894 q^{79} -6.15037 q^{80} -10.0687 q^{81} -6.80825 q^{82} -0.511288 q^{83} +0.0442973 q^{84} +1.24336 q^{85} -1.66399 q^{86} -5.13699 q^{87} -2.04859 q^{88} -13.7370 q^{89} -0.854745 q^{90} +0.109146 q^{91} -3.39987 q^{92} -0.534225 q^{93} -21.8064 q^{94} -6.53996 q^{95} +7.63726 q^{96} -9.63387 q^{97} +11.6463 q^{98} -0.413132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.66399 −1.17662 −0.588311 0.808635i \(-0.700207\pi\)
−0.588311 + 0.808635i \(0.700207\pi\)
\(3\) 1.84747 1.06664 0.533318 0.845915i \(-0.320945\pi\)
0.533318 + 0.845915i \(0.320945\pi\)
\(4\) 0.768874 0.384437
\(5\) 1.24336 0.556046 0.278023 0.960574i \(-0.410321\pi\)
0.278023 + 0.960574i \(0.410321\pi\)
\(6\) −3.07417 −1.25503
\(7\) 0.0311850 0.0117868 0.00589340 0.999983i \(-0.498124\pi\)
0.00589340 + 0.999983i \(0.498124\pi\)
\(8\) 2.04859 0.724284
\(9\) 0.413132 0.137711
\(10\) −2.06894 −0.654256
\(11\) −1.00000 −0.301511
\(12\) 1.42047 0.410054
\(13\) 3.49994 0.970709 0.485355 0.874317i \(-0.338691\pi\)
0.485355 + 0.874317i \(0.338691\pi\)
\(14\) −0.0518916 −0.0138686
\(15\) 2.29706 0.593099
\(16\) −4.94658 −1.23665
\(17\) 1.00000 0.242536
\(18\) −0.687449 −0.162033
\(19\) −5.25992 −1.20671 −0.603354 0.797473i \(-0.706170\pi\)
−0.603354 + 0.797473i \(0.706170\pi\)
\(20\) 0.955986 0.213765
\(21\) 0.0576132 0.0125722
\(22\) 1.66399 0.354765
\(23\) −4.42189 −0.922027 −0.461013 0.887393i \(-0.652514\pi\)
−0.461013 + 0.887393i \(0.652514\pi\)
\(24\) 3.78469 0.772547
\(25\) −3.45406 −0.690812
\(26\) −5.82388 −1.14216
\(27\) −4.77915 −0.919748
\(28\) 0.0239773 0.00453129
\(29\) −2.78056 −0.516336 −0.258168 0.966100i \(-0.583119\pi\)
−0.258168 + 0.966100i \(0.583119\pi\)
\(30\) −3.82229 −0.697852
\(31\) −0.289166 −0.0519358 −0.0259679 0.999663i \(-0.508267\pi\)
−0.0259679 + 0.999663i \(0.508267\pi\)
\(32\) 4.13391 0.730779
\(33\) −1.84747 −0.321603
\(34\) −1.66399 −0.285373
\(35\) 0.0387741 0.00655401
\(36\) 0.317647 0.0529411
\(37\) 10.1101 1.66210 0.831049 0.556199i \(-0.187741\pi\)
0.831049 + 0.556199i \(0.187741\pi\)
\(38\) 8.75248 1.41984
\(39\) 6.46602 1.03539
\(40\) 2.54712 0.402736
\(41\) 4.09151 0.638987 0.319494 0.947588i \(-0.396487\pi\)
0.319494 + 0.947588i \(0.396487\pi\)
\(42\) −0.0958679 −0.0147927
\(43\) 1.00000 0.152499
\(44\) −0.768874 −0.115912
\(45\) 0.513671 0.0765735
\(46\) 7.35799 1.08488
\(47\) 13.1048 1.91154 0.955769 0.294118i \(-0.0950257\pi\)
0.955769 + 0.294118i \(0.0950257\pi\)
\(48\) −9.13864 −1.31905
\(49\) −6.99903 −0.999861
\(50\) 5.74754 0.812824
\(51\) 1.84747 0.258697
\(52\) 2.69102 0.373177
\(53\) −5.95331 −0.817750 −0.408875 0.912590i \(-0.634079\pi\)
−0.408875 + 0.912590i \(0.634079\pi\)
\(54\) 7.95248 1.08220
\(55\) −1.24336 −0.167654
\(56\) 0.0638850 0.00853700
\(57\) −9.71753 −1.28712
\(58\) 4.62683 0.607532
\(59\) 10.5664 1.37563 0.687815 0.725886i \(-0.258570\pi\)
0.687815 + 0.725886i \(0.258570\pi\)
\(60\) 1.76615 0.228009
\(61\) −5.77116 −0.738921 −0.369460 0.929246i \(-0.620457\pi\)
−0.369460 + 0.929246i \(0.620457\pi\)
\(62\) 0.481170 0.0611087
\(63\) 0.0128835 0.00162317
\(64\) 3.01437 0.376796
\(65\) 4.35168 0.539759
\(66\) 3.07417 0.378404
\(67\) −13.2819 −1.62264 −0.811319 0.584604i \(-0.801250\pi\)
−0.811319 + 0.584604i \(0.801250\pi\)
\(68\) 0.768874 0.0932397
\(69\) −8.16928 −0.983466
\(70\) −0.0645198 −0.00771159
\(71\) −0.811957 −0.0963616 −0.0481808 0.998839i \(-0.515342\pi\)
−0.0481808 + 0.998839i \(0.515342\pi\)
\(72\) 0.846336 0.0997416
\(73\) −7.66046 −0.896589 −0.448295 0.893886i \(-0.647968\pi\)
−0.448295 + 0.893886i \(0.647968\pi\)
\(74\) −16.8232 −1.95566
\(75\) −6.38126 −0.736845
\(76\) −4.04422 −0.463904
\(77\) −0.0311850 −0.00355386
\(78\) −10.7594 −1.21826
\(79\) 3.36894 0.379036 0.189518 0.981877i \(-0.439308\pi\)
0.189518 + 0.981877i \(0.439308\pi\)
\(80\) −6.15037 −0.687632
\(81\) −10.0687 −1.11875
\(82\) −6.80825 −0.751846
\(83\) −0.511288 −0.0561212 −0.0280606 0.999606i \(-0.508933\pi\)
−0.0280606 + 0.999606i \(0.508933\pi\)
\(84\) 0.0442973 0.00483323
\(85\) 1.24336 0.134861
\(86\) −1.66399 −0.179433
\(87\) −5.13699 −0.550743
\(88\) −2.04859 −0.218380
\(89\) −13.7370 −1.45612 −0.728061 0.685513i \(-0.759578\pi\)
−0.728061 + 0.685513i \(0.759578\pi\)
\(90\) −0.854745 −0.0900980
\(91\) 0.109146 0.0114416
\(92\) −3.39987 −0.354461
\(93\) −0.534225 −0.0553965
\(94\) −21.8064 −2.24916
\(95\) −6.53996 −0.670986
\(96\) 7.63726 0.779474
\(97\) −9.63387 −0.978171 −0.489085 0.872236i \(-0.662669\pi\)
−0.489085 + 0.872236i \(0.662669\pi\)
\(98\) 11.6463 1.17646
\(99\) −0.413132 −0.0415213
\(100\) −2.65574 −0.265574
\(101\) −17.1787 −1.70935 −0.854674 0.519166i \(-0.826243\pi\)
−0.854674 + 0.519166i \(0.826243\pi\)
\(102\) −3.07417 −0.304388
\(103\) 0.863988 0.0851313 0.0425656 0.999094i \(-0.486447\pi\)
0.0425656 + 0.999094i \(0.486447\pi\)
\(104\) 7.16993 0.703069
\(105\) 0.0716338 0.00699074
\(106\) 9.90626 0.962181
\(107\) −11.5026 −1.11199 −0.555997 0.831184i \(-0.687663\pi\)
−0.555997 + 0.831184i \(0.687663\pi\)
\(108\) −3.67457 −0.353585
\(109\) 3.39601 0.325279 0.162640 0.986686i \(-0.447999\pi\)
0.162640 + 0.986686i \(0.447999\pi\)
\(110\) 2.06894 0.197266
\(111\) 18.6782 1.77285
\(112\) −0.154259 −0.0145761
\(113\) 3.92016 0.368777 0.184389 0.982853i \(-0.440970\pi\)
0.184389 + 0.982853i \(0.440970\pi\)
\(114\) 16.1699 1.51445
\(115\) −5.49798 −0.512690
\(116\) −2.13790 −0.198499
\(117\) 1.44594 0.133677
\(118\) −17.5825 −1.61860
\(119\) 0.0311850 0.00285872
\(120\) 4.70573 0.429572
\(121\) 1.00000 0.0909091
\(122\) 9.60317 0.869430
\(123\) 7.55893 0.681566
\(124\) −0.222332 −0.0199660
\(125\) −10.5114 −0.940170
\(126\) −0.0214381 −0.00190985
\(127\) 8.57189 0.760632 0.380316 0.924857i \(-0.375815\pi\)
0.380316 + 0.924857i \(0.375815\pi\)
\(128\) −13.2837 −1.17412
\(129\) 1.84747 0.162660
\(130\) −7.24117 −0.635092
\(131\) −0.973771 −0.0850788 −0.0425394 0.999095i \(-0.513545\pi\)
−0.0425394 + 0.999095i \(0.513545\pi\)
\(132\) −1.42047 −0.123636
\(133\) −0.164030 −0.0142232
\(134\) 22.1009 1.90923
\(135\) −5.94219 −0.511423
\(136\) 2.04859 0.175665
\(137\) −2.45605 −0.209834 −0.104917 0.994481i \(-0.533458\pi\)
−0.104917 + 0.994481i \(0.533458\pi\)
\(138\) 13.5936 1.15717
\(139\) −3.68775 −0.312791 −0.156395 0.987695i \(-0.549987\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(140\) 0.0298124 0.00251961
\(141\) 24.2108 2.03891
\(142\) 1.35109 0.113381
\(143\) −3.49994 −0.292680
\(144\) −2.04359 −0.170299
\(145\) −3.45723 −0.287107
\(146\) 12.7470 1.05495
\(147\) −12.9305 −1.06649
\(148\) 7.77343 0.638972
\(149\) −9.05753 −0.742022 −0.371011 0.928628i \(-0.620989\pi\)
−0.371011 + 0.928628i \(0.620989\pi\)
\(150\) 10.6184 0.866987
\(151\) 2.13425 0.173682 0.0868412 0.996222i \(-0.472323\pi\)
0.0868412 + 0.996222i \(0.472323\pi\)
\(152\) −10.7754 −0.874000
\(153\) 0.413132 0.0333997
\(154\) 0.0518916 0.00418154
\(155\) −0.359537 −0.0288787
\(156\) 4.97156 0.398043
\(157\) 4.54706 0.362895 0.181448 0.983401i \(-0.441922\pi\)
0.181448 + 0.983401i \(0.441922\pi\)
\(158\) −5.60590 −0.445981
\(159\) −10.9985 −0.872241
\(160\) 5.13993 0.406347
\(161\) −0.137896 −0.0108678
\(162\) 16.7543 1.31634
\(163\) 23.2936 1.82449 0.912246 0.409642i \(-0.134346\pi\)
0.912246 + 0.409642i \(0.134346\pi\)
\(164\) 3.14586 0.245650
\(165\) −2.29706 −0.178826
\(166\) 0.850780 0.0660334
\(167\) 6.92118 0.535577 0.267789 0.963478i \(-0.413707\pi\)
0.267789 + 0.963478i \(0.413707\pi\)
\(168\) 0.118025 0.00910586
\(169\) −0.750407 −0.0577236
\(170\) −2.06894 −0.158680
\(171\) −2.17304 −0.166177
\(172\) 0.768874 0.0586261
\(173\) 5.14447 0.391127 0.195563 0.980691i \(-0.437346\pi\)
0.195563 + 0.980691i \(0.437346\pi\)
\(174\) 8.54791 0.648015
\(175\) −0.107715 −0.00814247
\(176\) 4.94658 0.372863
\(177\) 19.5211 1.46730
\(178\) 22.8583 1.71330
\(179\) 6.24711 0.466931 0.233466 0.972365i \(-0.424993\pi\)
0.233466 + 0.972365i \(0.424993\pi\)
\(180\) 0.394948 0.0294377
\(181\) 3.60300 0.267809 0.133904 0.990994i \(-0.457248\pi\)
0.133904 + 0.990994i \(0.457248\pi\)
\(182\) −0.181617 −0.0134624
\(183\) −10.6620 −0.788159
\(184\) −9.05861 −0.667810
\(185\) 12.5705 0.924204
\(186\) 0.888946 0.0651807
\(187\) −1.00000 −0.0731272
\(188\) 10.0760 0.734866
\(189\) −0.149038 −0.0108409
\(190\) 10.8825 0.789496
\(191\) −11.2755 −0.815868 −0.407934 0.913011i \(-0.633751\pi\)
−0.407934 + 0.913011i \(0.633751\pi\)
\(192\) 5.56894 0.401904
\(193\) −24.7900 −1.78443 −0.892213 0.451615i \(-0.850848\pi\)
−0.892213 + 0.451615i \(0.850848\pi\)
\(194\) 16.0307 1.15094
\(195\) 8.03958 0.575726
\(196\) −5.38137 −0.384384
\(197\) −14.5191 −1.03444 −0.517222 0.855851i \(-0.673034\pi\)
−0.517222 + 0.855851i \(0.673034\pi\)
\(198\) 0.687449 0.0488549
\(199\) −12.3326 −0.874234 −0.437117 0.899405i \(-0.644001\pi\)
−0.437117 + 0.899405i \(0.644001\pi\)
\(200\) −7.07594 −0.500345
\(201\) −24.5378 −1.73076
\(202\) 28.5853 2.01125
\(203\) −0.0867116 −0.00608596
\(204\) 1.42047 0.0994528
\(205\) 5.08721 0.355306
\(206\) −1.43767 −0.100167
\(207\) −1.82682 −0.126973
\(208\) −17.3127 −1.20042
\(209\) 5.25992 0.363836
\(210\) −0.119198 −0.00822545
\(211\) −26.1271 −1.79866 −0.899331 0.437269i \(-0.855946\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(212\) −4.57735 −0.314373
\(213\) −1.50006 −0.102783
\(214\) 19.1402 1.30840
\(215\) 1.24336 0.0847963
\(216\) −9.79050 −0.666159
\(217\) −0.00901763 −0.000612157 0
\(218\) −5.65094 −0.382730
\(219\) −14.1524 −0.956333
\(220\) −0.955986 −0.0644525
\(221\) 3.49994 0.235432
\(222\) −31.0803 −2.08598
\(223\) −12.1955 −0.816672 −0.408336 0.912832i \(-0.633891\pi\)
−0.408336 + 0.912832i \(0.633891\pi\)
\(224\) 0.128916 0.00861355
\(225\) −1.42698 −0.0951322
\(226\) −6.52311 −0.433911
\(227\) −13.0764 −0.867910 −0.433955 0.900935i \(-0.642882\pi\)
−0.433955 + 0.900935i \(0.642882\pi\)
\(228\) −7.47156 −0.494816
\(229\) 2.15431 0.142361 0.0711804 0.997463i \(-0.477323\pi\)
0.0711804 + 0.997463i \(0.477323\pi\)
\(230\) 9.14861 0.603242
\(231\) −0.0576132 −0.00379067
\(232\) −5.69621 −0.373974
\(233\) 5.39996 0.353763 0.176881 0.984232i \(-0.443399\pi\)
0.176881 + 0.984232i \(0.443399\pi\)
\(234\) −2.40603 −0.157287
\(235\) 16.2940 1.06290
\(236\) 8.12425 0.528844
\(237\) 6.22401 0.404293
\(238\) −0.0518916 −0.00336363
\(239\) −2.67730 −0.173180 −0.0865900 0.996244i \(-0.527597\pi\)
−0.0865900 + 0.996244i \(0.527597\pi\)
\(240\) −11.3626 −0.733453
\(241\) 26.7524 1.72327 0.861636 0.507526i \(-0.169440\pi\)
0.861636 + 0.507526i \(0.169440\pi\)
\(242\) −1.66399 −0.106966
\(243\) −4.26416 −0.273546
\(244\) −4.43729 −0.284069
\(245\) −8.70229 −0.555969
\(246\) −12.5780 −0.801945
\(247\) −18.4094 −1.17136
\(248\) −0.592381 −0.0376162
\(249\) −0.944588 −0.0598608
\(250\) 17.4909 1.10622
\(251\) −7.99065 −0.504365 −0.252183 0.967680i \(-0.581148\pi\)
−0.252183 + 0.967680i \(0.581148\pi\)
\(252\) 0.00990579 0.000624006 0
\(253\) 4.42189 0.278002
\(254\) −14.2636 −0.894976
\(255\) 2.29706 0.143848
\(256\) 16.0753 1.00470
\(257\) 0.550791 0.0343574 0.0171787 0.999852i \(-0.494532\pi\)
0.0171787 + 0.999852i \(0.494532\pi\)
\(258\) −3.07417 −0.191390
\(259\) 0.315285 0.0195908
\(260\) 3.34589 0.207504
\(261\) −1.14874 −0.0711050
\(262\) 1.62035 0.100105
\(263\) 1.17884 0.0726904 0.0363452 0.999339i \(-0.488428\pi\)
0.0363452 + 0.999339i \(0.488428\pi\)
\(264\) −3.78469 −0.232932
\(265\) −7.40209 −0.454707
\(266\) 0.272946 0.0167354
\(267\) −25.3787 −1.55315
\(268\) −10.2121 −0.623802
\(269\) 19.5036 1.18915 0.594577 0.804039i \(-0.297320\pi\)
0.594577 + 0.804039i \(0.297320\pi\)
\(270\) 9.88777 0.601751
\(271\) 30.6217 1.86013 0.930067 0.367391i \(-0.119749\pi\)
0.930067 + 0.367391i \(0.119749\pi\)
\(272\) −4.94658 −0.299931
\(273\) 0.201643 0.0122040
\(274\) 4.08685 0.246895
\(275\) 3.45406 0.208288
\(276\) −6.28115 −0.378081
\(277\) −0.644936 −0.0387504 −0.0193752 0.999812i \(-0.506168\pi\)
−0.0193752 + 0.999812i \(0.506168\pi\)
\(278\) 6.13639 0.368036
\(279\) −0.119464 −0.00715211
\(280\) 0.0794319 0.00474697
\(281\) −27.6827 −1.65141 −0.825706 0.564101i \(-0.809223\pi\)
−0.825706 + 0.564101i \(0.809223\pi\)
\(282\) −40.2866 −2.39903
\(283\) −21.6468 −1.28677 −0.643383 0.765544i \(-0.722470\pi\)
−0.643383 + 0.765544i \(0.722470\pi\)
\(284\) −0.624293 −0.0370450
\(285\) −12.0824 −0.715697
\(286\) 5.82388 0.344373
\(287\) 0.127594 0.00753162
\(288\) 1.70785 0.100636
\(289\) 1.00000 0.0588235
\(290\) 5.75280 0.337816
\(291\) −17.7982 −1.04335
\(292\) −5.88993 −0.344682
\(293\) 30.9671 1.80911 0.904557 0.426352i \(-0.140202\pi\)
0.904557 + 0.426352i \(0.140202\pi\)
\(294\) 21.5162 1.25485
\(295\) 13.1378 0.764915
\(296\) 20.7115 1.20383
\(297\) 4.77915 0.277315
\(298\) 15.0717 0.873079
\(299\) −15.4763 −0.895020
\(300\) −4.90639 −0.283271
\(301\) 0.0311850 0.00179747
\(302\) −3.55137 −0.204358
\(303\) −31.7371 −1.82325
\(304\) 26.0186 1.49227
\(305\) −7.17561 −0.410874
\(306\) −0.687449 −0.0392988
\(307\) −23.6287 −1.34856 −0.674281 0.738475i \(-0.735546\pi\)
−0.674281 + 0.738475i \(0.735546\pi\)
\(308\) −0.0239773 −0.00136623
\(309\) 1.59619 0.0908040
\(310\) 0.598267 0.0339793
\(311\) 9.27572 0.525978 0.262989 0.964799i \(-0.415292\pi\)
0.262989 + 0.964799i \(0.415292\pi\)
\(312\) 13.2462 0.749919
\(313\) −23.1126 −1.30640 −0.653202 0.757184i \(-0.726575\pi\)
−0.653202 + 0.757184i \(0.726575\pi\)
\(314\) −7.56629 −0.426990
\(315\) 0.0160188 0.000902557 0
\(316\) 2.59029 0.145715
\(317\) 24.3691 1.36870 0.684352 0.729152i \(-0.260085\pi\)
0.684352 + 0.729152i \(0.260085\pi\)
\(318\) 18.3015 1.02630
\(319\) 2.78056 0.155681
\(320\) 3.74793 0.209516
\(321\) −21.2506 −1.18609
\(322\) 0.229459 0.0127872
\(323\) −5.25992 −0.292670
\(324\) −7.74158 −0.430088
\(325\) −12.0890 −0.670578
\(326\) −38.7603 −2.14674
\(327\) 6.27402 0.346954
\(328\) 8.38181 0.462808
\(329\) 0.408674 0.0225309
\(330\) 3.82229 0.210410
\(331\) 25.7679 1.41633 0.708166 0.706046i \(-0.249523\pi\)
0.708166 + 0.706046i \(0.249523\pi\)
\(332\) −0.393116 −0.0215751
\(333\) 4.17683 0.228889
\(334\) −11.5168 −0.630171
\(335\) −16.5141 −0.902261
\(336\) −0.284988 −0.0155474
\(337\) 1.60254 0.0872959 0.0436479 0.999047i \(-0.486102\pi\)
0.0436479 + 0.999047i \(0.486102\pi\)
\(338\) 1.24867 0.0679188
\(339\) 7.24236 0.393351
\(340\) 0.955986 0.0518456
\(341\) 0.289166 0.0156592
\(342\) 3.61593 0.195527
\(343\) −0.436559 −0.0235720
\(344\) 2.04859 0.110452
\(345\) −10.1573 −0.546853
\(346\) −8.56037 −0.460208
\(347\) −36.1877 −1.94266 −0.971330 0.237735i \(-0.923595\pi\)
−0.971330 + 0.237735i \(0.923595\pi\)
\(348\) −3.94970 −0.211726
\(349\) 2.74523 0.146949 0.0734743 0.997297i \(-0.476591\pi\)
0.0734743 + 0.997297i \(0.476591\pi\)
\(350\) 0.179237 0.00958060
\(351\) −16.7268 −0.892808
\(352\) −4.13391 −0.220338
\(353\) −6.09982 −0.324661 −0.162330 0.986736i \(-0.551901\pi\)
−0.162330 + 0.986736i \(0.551901\pi\)
\(354\) −32.4830 −1.72645
\(355\) −1.00955 −0.0535815
\(356\) −10.5620 −0.559787
\(357\) 0.0576132 0.00304921
\(358\) −10.3952 −0.549401
\(359\) −14.7446 −0.778189 −0.389094 0.921198i \(-0.627212\pi\)
−0.389094 + 0.921198i \(0.627212\pi\)
\(360\) 1.05230 0.0554610
\(361\) 8.66678 0.456146
\(362\) −5.99537 −0.315110
\(363\) 1.84747 0.0969668
\(364\) 0.0839192 0.00439856
\(365\) −9.52469 −0.498545
\(366\) 17.7415 0.927364
\(367\) −28.4531 −1.48524 −0.742620 0.669713i \(-0.766417\pi\)
−0.742620 + 0.669713i \(0.766417\pi\)
\(368\) 21.8732 1.14022
\(369\) 1.69034 0.0879953
\(370\) −20.9173 −1.08744
\(371\) −0.185654 −0.00963866
\(372\) −0.410752 −0.0212965
\(373\) −4.70699 −0.243718 −0.121859 0.992547i \(-0.538886\pi\)
−0.121859 + 0.992547i \(0.538886\pi\)
\(374\) 1.66399 0.0860431
\(375\) −19.4195 −1.00282
\(376\) 26.8464 1.38450
\(377\) −9.73179 −0.501213
\(378\) 0.247998 0.0127556
\(379\) 15.9752 0.820591 0.410295 0.911953i \(-0.365426\pi\)
0.410295 + 0.911953i \(0.365426\pi\)
\(380\) −5.02841 −0.257952
\(381\) 15.8363 0.811317
\(382\) 18.7624 0.959967
\(383\) 25.7909 1.31786 0.658928 0.752206i \(-0.271010\pi\)
0.658928 + 0.752206i \(0.271010\pi\)
\(384\) −24.5412 −1.25236
\(385\) −0.0387741 −0.00197611
\(386\) 41.2505 2.09959
\(387\) 0.413132 0.0210007
\(388\) −7.40723 −0.376045
\(389\) 24.4107 1.23767 0.618836 0.785520i \(-0.287604\pi\)
0.618836 + 0.785520i \(0.287604\pi\)
\(390\) −13.3778 −0.677412
\(391\) −4.42189 −0.223624
\(392\) −14.3381 −0.724184
\(393\) −1.79901 −0.0907480
\(394\) 24.1597 1.21715
\(395\) 4.18880 0.210761
\(396\) −0.317647 −0.0159623
\(397\) −10.5607 −0.530026 −0.265013 0.964245i \(-0.585376\pi\)
−0.265013 + 0.964245i \(0.585376\pi\)
\(398\) 20.5214 1.02864
\(399\) −0.303041 −0.0151710
\(400\) 17.0858 0.854290
\(401\) 13.9064 0.694454 0.347227 0.937781i \(-0.387123\pi\)
0.347227 + 0.937781i \(0.387123\pi\)
\(402\) 40.8307 2.03645
\(403\) −1.01206 −0.0504145
\(404\) −13.2083 −0.657137
\(405\) −12.5190 −0.622075
\(406\) 0.144287 0.00716087
\(407\) −10.1101 −0.501142
\(408\) 3.78469 0.187370
\(409\) 26.4549 1.30811 0.654055 0.756447i \(-0.273066\pi\)
0.654055 + 0.756447i \(0.273066\pi\)
\(410\) −8.46509 −0.418061
\(411\) −4.53746 −0.223817
\(412\) 0.664298 0.0327276
\(413\) 0.329513 0.0162143
\(414\) 3.03982 0.149399
\(415\) −0.635714 −0.0312060
\(416\) 14.4684 0.709374
\(417\) −6.81299 −0.333634
\(418\) −8.75248 −0.428098
\(419\) −7.68294 −0.375336 −0.187668 0.982233i \(-0.560093\pi\)
−0.187668 + 0.982233i \(0.560093\pi\)
\(420\) 0.0550774 0.00268750
\(421\) 23.1835 1.12989 0.564947 0.825127i \(-0.308897\pi\)
0.564947 + 0.825127i \(0.308897\pi\)
\(422\) 43.4753 2.11634
\(423\) 5.41403 0.263239
\(424\) −12.1959 −0.592283
\(425\) −3.45406 −0.167547
\(426\) 2.49610 0.120936
\(427\) −0.179973 −0.00870952
\(428\) −8.84402 −0.427492
\(429\) −6.46602 −0.312183
\(430\) −2.06894 −0.0997731
\(431\) −22.0653 −1.06285 −0.531423 0.847107i \(-0.678343\pi\)
−0.531423 + 0.847107i \(0.678343\pi\)
\(432\) 23.6405 1.13740
\(433\) −2.73527 −0.131449 −0.0657244 0.997838i \(-0.520936\pi\)
−0.0657244 + 0.997838i \(0.520936\pi\)
\(434\) 0.0150053 0.000720276 0
\(435\) −6.38711 −0.306238
\(436\) 2.61111 0.125049
\(437\) 23.2588 1.11262
\(438\) 23.5496 1.12524
\(439\) −25.9404 −1.23807 −0.619033 0.785365i \(-0.712475\pi\)
−0.619033 + 0.785365i \(0.712475\pi\)
\(440\) −2.54712 −0.121429
\(441\) −2.89152 −0.137692
\(442\) −5.82388 −0.277014
\(443\) −32.1727 −1.52857 −0.764285 0.644878i \(-0.776908\pi\)
−0.764285 + 0.644878i \(0.776908\pi\)
\(444\) 14.3612 0.681550
\(445\) −17.0800 −0.809671
\(446\) 20.2933 0.960913
\(447\) −16.7335 −0.791467
\(448\) 0.0940029 0.00444122
\(449\) 30.9338 1.45986 0.729929 0.683523i \(-0.239553\pi\)
0.729929 + 0.683523i \(0.239553\pi\)
\(450\) 2.37449 0.111935
\(451\) −4.09151 −0.192662
\(452\) 3.01411 0.141772
\(453\) 3.94295 0.185256
\(454\) 21.7590 1.02120
\(455\) 0.135707 0.00636204
\(456\) −19.9072 −0.932239
\(457\) −26.3308 −1.23170 −0.615851 0.787863i \(-0.711188\pi\)
−0.615851 + 0.787863i \(0.711188\pi\)
\(458\) −3.58476 −0.167505
\(459\) −4.77915 −0.223072
\(460\) −4.22726 −0.197097
\(461\) −18.0636 −0.841304 −0.420652 0.907222i \(-0.638199\pi\)
−0.420652 + 0.907222i \(0.638199\pi\)
\(462\) 0.0958679 0.00446018
\(463\) 6.04264 0.280825 0.140413 0.990093i \(-0.455157\pi\)
0.140413 + 0.990093i \(0.455157\pi\)
\(464\) 13.7543 0.638525
\(465\) −0.664232 −0.0308030
\(466\) −8.98549 −0.416245
\(467\) 0.893753 0.0413579 0.0206790 0.999786i \(-0.493417\pi\)
0.0206790 + 0.999786i \(0.493417\pi\)
\(468\) 1.11174 0.0513904
\(469\) −0.414194 −0.0191257
\(470\) −27.1131 −1.25064
\(471\) 8.40055 0.387077
\(472\) 21.6462 0.996348
\(473\) −1.00000 −0.0459800
\(474\) −10.3567 −0.475700
\(475\) 18.1681 0.833609
\(476\) 0.0239773 0.00109900
\(477\) −2.45950 −0.112613
\(478\) 4.45501 0.203767
\(479\) 40.0823 1.83141 0.915703 0.401856i \(-0.131635\pi\)
0.915703 + 0.401856i \(0.131635\pi\)
\(480\) 9.49584 0.433424
\(481\) 35.3849 1.61341
\(482\) −44.5158 −2.02764
\(483\) −0.254759 −0.0115919
\(484\) 0.768874 0.0349488
\(485\) −11.9783 −0.543908
\(486\) 7.09554 0.321860
\(487\) −4.48907 −0.203419 −0.101710 0.994814i \(-0.532431\pi\)
−0.101710 + 0.994814i \(0.532431\pi\)
\(488\) −11.8227 −0.535189
\(489\) 43.0341 1.94607
\(490\) 14.4806 0.654165
\(491\) −33.8266 −1.52658 −0.763288 0.646059i \(-0.776416\pi\)
−0.763288 + 0.646059i \(0.776416\pi\)
\(492\) 5.81187 0.262019
\(493\) −2.78056 −0.125230
\(494\) 30.6332 1.37825
\(495\) −0.513671 −0.0230878
\(496\) 1.43038 0.0642261
\(497\) −0.0253209 −0.00113580
\(498\) 1.57179 0.0704335
\(499\) 18.7854 0.840949 0.420475 0.907304i \(-0.361864\pi\)
0.420475 + 0.907304i \(0.361864\pi\)
\(500\) −8.08196 −0.361436
\(501\) 12.7867 0.571266
\(502\) 13.2964 0.593447
\(503\) 3.78604 0.168811 0.0844056 0.996431i \(-0.473101\pi\)
0.0844056 + 0.996431i \(0.473101\pi\)
\(504\) 0.0263930 0.00117564
\(505\) −21.3593 −0.950476
\(506\) −7.35799 −0.327103
\(507\) −1.38635 −0.0615700
\(508\) 6.59070 0.292415
\(509\) 25.2665 1.11992 0.559960 0.828520i \(-0.310817\pi\)
0.559960 + 0.828520i \(0.310817\pi\)
\(510\) −3.82229 −0.169254
\(511\) −0.238891 −0.0105679
\(512\) −0.181728 −0.00803132
\(513\) 25.1380 1.10987
\(514\) −0.916513 −0.0404257
\(515\) 1.07425 0.0473369
\(516\) 1.42047 0.0625327
\(517\) −13.1048 −0.576351
\(518\) −0.524632 −0.0230510
\(519\) 9.50424 0.417190
\(520\) 8.91478 0.390939
\(521\) −44.2144 −1.93707 −0.968534 0.248879i \(-0.919938\pi\)
−0.968534 + 0.248879i \(0.919938\pi\)
\(522\) 1.91149 0.0836637
\(523\) 16.4916 0.721129 0.360564 0.932734i \(-0.382584\pi\)
0.360564 + 0.932734i \(0.382584\pi\)
\(524\) −0.748707 −0.0327074
\(525\) −0.198999 −0.00868505
\(526\) −1.96158 −0.0855290
\(527\) −0.289166 −0.0125963
\(528\) 9.13864 0.397708
\(529\) −3.44693 −0.149866
\(530\) 12.3170 0.535018
\(531\) 4.36533 0.189439
\(532\) −0.126119 −0.00546794
\(533\) 14.3201 0.620271
\(534\) 42.2300 1.82747
\(535\) −14.3018 −0.618320
\(536\) −27.2090 −1.17525
\(537\) 11.5413 0.498045
\(538\) −32.4538 −1.39918
\(539\) 6.99903 0.301469
\(540\) −4.56880 −0.196610
\(541\) 10.8329 0.465741 0.232871 0.972508i \(-0.425188\pi\)
0.232871 + 0.972508i \(0.425188\pi\)
\(542\) −50.9542 −2.18867
\(543\) 6.65642 0.285654
\(544\) 4.13391 0.177240
\(545\) 4.22246 0.180870
\(546\) −0.335532 −0.0143595
\(547\) −38.6904 −1.65428 −0.827141 0.561995i \(-0.810034\pi\)
−0.827141 + 0.561995i \(0.810034\pi\)
\(548\) −1.88839 −0.0806681
\(549\) −2.38425 −0.101757
\(550\) −5.74754 −0.245076
\(551\) 14.6255 0.623068
\(552\) −16.7355 −0.712309
\(553\) 0.105060 0.00446762
\(554\) 1.07317 0.0455946
\(555\) 23.2236 0.985788
\(556\) −2.83542 −0.120248
\(557\) −15.2934 −0.648004 −0.324002 0.946056i \(-0.605028\pi\)
−0.324002 + 0.946056i \(0.605028\pi\)
\(558\) 0.198787 0.00841532
\(559\) 3.49994 0.148032
\(560\) −0.191799 −0.00810499
\(561\) −1.84747 −0.0780001
\(562\) 46.0638 1.94309
\(563\) 16.8693 0.710956 0.355478 0.934685i \(-0.384318\pi\)
0.355478 + 0.934685i \(0.384318\pi\)
\(564\) 18.6150 0.783834
\(565\) 4.87415 0.205057
\(566\) 36.0201 1.51404
\(567\) −0.313993 −0.0131864
\(568\) −1.66336 −0.0697932
\(569\) −8.51834 −0.357107 −0.178554 0.983930i \(-0.557142\pi\)
−0.178554 + 0.983930i \(0.557142\pi\)
\(570\) 20.1050 0.842105
\(571\) −29.7264 −1.24401 −0.622006 0.783013i \(-0.713682\pi\)
−0.622006 + 0.783013i \(0.713682\pi\)
\(572\) −2.69102 −0.112517
\(573\) −20.8311 −0.870233
\(574\) −0.212315 −0.00886186
\(575\) 15.2735 0.636948
\(576\) 1.24533 0.0518888
\(577\) −33.1391 −1.37960 −0.689799 0.724001i \(-0.742301\pi\)
−0.689799 + 0.724001i \(0.742301\pi\)
\(578\) −1.66399 −0.0692130
\(579\) −45.7988 −1.90333
\(580\) −2.65817 −0.110375
\(581\) −0.0159445 −0.000661490 0
\(582\) 29.6162 1.22763
\(583\) 5.95331 0.246561
\(584\) −15.6931 −0.649385
\(585\) 1.79782 0.0743306
\(586\) −51.5290 −2.12864
\(587\) −34.9504 −1.44256 −0.721279 0.692645i \(-0.756445\pi\)
−0.721279 + 0.692645i \(0.756445\pi\)
\(588\) −9.94190 −0.409997
\(589\) 1.52099 0.0626713
\(590\) −21.8613 −0.900015
\(591\) −26.8236 −1.10337
\(592\) −50.0107 −2.05543
\(593\) 13.2137 0.542620 0.271310 0.962492i \(-0.412543\pi\)
0.271310 + 0.962492i \(0.412543\pi\)
\(594\) −7.95248 −0.326294
\(595\) 0.0387741 0.00158958
\(596\) −6.96411 −0.285261
\(597\) −22.7841 −0.932489
\(598\) 25.7525 1.05310
\(599\) −8.14703 −0.332879 −0.166439 0.986052i \(-0.553227\pi\)
−0.166439 + 0.986052i \(0.553227\pi\)
\(600\) −13.0726 −0.533685
\(601\) −21.6584 −0.883466 −0.441733 0.897147i \(-0.645636\pi\)
−0.441733 + 0.897147i \(0.645636\pi\)
\(602\) −0.0518916 −0.00211494
\(603\) −5.48716 −0.223454
\(604\) 1.64097 0.0667700
\(605\) 1.24336 0.0505497
\(606\) 52.8104 2.14527
\(607\) −22.1221 −0.897908 −0.448954 0.893555i \(-0.648203\pi\)
−0.448954 + 0.893555i \(0.648203\pi\)
\(608\) −21.7440 −0.881837
\(609\) −0.160197 −0.00649150
\(610\) 11.9402 0.483443
\(611\) 45.8662 1.85555
\(612\) 0.317647 0.0128401
\(613\) 34.0633 1.37580 0.687902 0.725804i \(-0.258532\pi\)
0.687902 + 0.725804i \(0.258532\pi\)
\(614\) 39.3180 1.58675
\(615\) 9.39846 0.378982
\(616\) −0.0638850 −0.00257400
\(617\) 29.6929 1.19539 0.597696 0.801723i \(-0.296083\pi\)
0.597696 + 0.801723i \(0.296083\pi\)
\(618\) −2.65605 −0.106842
\(619\) −9.46611 −0.380475 −0.190238 0.981738i \(-0.560926\pi\)
−0.190238 + 0.981738i \(0.560926\pi\)
\(620\) −0.276439 −0.0111020
\(621\) 21.1329 0.848033
\(622\) −15.4347 −0.618876
\(623\) −0.428388 −0.0171630
\(624\) −31.9847 −1.28041
\(625\) 4.20086 0.168034
\(626\) 38.4593 1.53714
\(627\) 9.71753 0.388081
\(628\) 3.49612 0.139510
\(629\) 10.1101 0.403118
\(630\) −0.0266552 −0.00106197
\(631\) −10.2705 −0.408862 −0.204431 0.978881i \(-0.565534\pi\)
−0.204431 + 0.978881i \(0.565534\pi\)
\(632\) 6.90157 0.274530
\(633\) −48.2689 −1.91852
\(634\) −40.5500 −1.61045
\(635\) 10.6579 0.422947
\(636\) −8.45649 −0.335322
\(637\) −24.4962 −0.970574
\(638\) −4.62683 −0.183178
\(639\) −0.335446 −0.0132700
\(640\) −16.5164 −0.652868
\(641\) 3.75266 0.148221 0.0741106 0.997250i \(-0.476388\pi\)
0.0741106 + 0.997250i \(0.476388\pi\)
\(642\) 35.3608 1.39558
\(643\) 6.56660 0.258962 0.129481 0.991582i \(-0.458669\pi\)
0.129481 + 0.991582i \(0.458669\pi\)
\(644\) −0.106025 −0.00417797
\(645\) 2.29706 0.0904467
\(646\) 8.75248 0.344362
\(647\) −10.3694 −0.407665 −0.203832 0.979006i \(-0.565340\pi\)
−0.203832 + 0.979006i \(0.565340\pi\)
\(648\) −20.6266 −0.810290
\(649\) −10.5664 −0.414768
\(650\) 20.1160 0.789016
\(651\) −0.0166598 −0.000652948 0
\(652\) 17.9098 0.701403
\(653\) −9.90294 −0.387532 −0.193766 0.981048i \(-0.562070\pi\)
−0.193766 + 0.981048i \(0.562070\pi\)
\(654\) −10.4399 −0.408233
\(655\) −1.21075 −0.0473077
\(656\) −20.2390 −0.790200
\(657\) −3.16478 −0.123470
\(658\) −0.680031 −0.0265104
\(659\) −39.7314 −1.54772 −0.773859 0.633359i \(-0.781676\pi\)
−0.773859 + 0.633359i \(0.781676\pi\)
\(660\) −1.76615 −0.0687473
\(661\) 18.5390 0.721085 0.360543 0.932743i \(-0.382591\pi\)
0.360543 + 0.932743i \(0.382591\pi\)
\(662\) −42.8776 −1.66649
\(663\) 6.46602 0.251120
\(664\) −1.04742 −0.0406477
\(665\) −0.203948 −0.00790878
\(666\) −6.95021 −0.269315
\(667\) 12.2953 0.476076
\(668\) 5.32152 0.205896
\(669\) −22.5308 −0.871091
\(670\) 27.4793 1.06162
\(671\) 5.77116 0.222793
\(672\) 0.238168 0.00918751
\(673\) 6.87386 0.264968 0.132484 0.991185i \(-0.457705\pi\)
0.132484 + 0.991185i \(0.457705\pi\)
\(674\) −2.66662 −0.102714
\(675\) 16.5075 0.635373
\(676\) −0.576969 −0.0221911
\(677\) −15.0860 −0.579802 −0.289901 0.957057i \(-0.593622\pi\)
−0.289901 + 0.957057i \(0.593622\pi\)
\(678\) −12.0512 −0.462825
\(679\) −0.300432 −0.0115295
\(680\) 2.54712 0.0976777
\(681\) −24.1582 −0.925743
\(682\) −0.481170 −0.0184250
\(683\) −44.1030 −1.68756 −0.843778 0.536693i \(-0.819673\pi\)
−0.843778 + 0.536693i \(0.819673\pi\)
\(684\) −1.67080 −0.0638845
\(685\) −3.05374 −0.116678
\(686\) 0.726431 0.0277353
\(687\) 3.98002 0.151847
\(688\) −4.94658 −0.188587
\(689\) −20.8362 −0.793797
\(690\) 16.9018 0.643439
\(691\) 25.6350 0.975203 0.487602 0.873066i \(-0.337872\pi\)
0.487602 + 0.873066i \(0.337872\pi\)
\(692\) 3.95545 0.150364
\(693\) −0.0128835 −0.000489404 0
\(694\) 60.2162 2.28577
\(695\) −4.58519 −0.173926
\(696\) −10.5236 −0.398894
\(697\) 4.09151 0.154977
\(698\) −4.56804 −0.172903
\(699\) 9.97624 0.377336
\(700\) −0.0828191 −0.00313027
\(701\) −37.8442 −1.42935 −0.714677 0.699454i \(-0.753426\pi\)
−0.714677 + 0.699454i \(0.753426\pi\)
\(702\) 27.8332 1.05050
\(703\) −53.1786 −2.00567
\(704\) −3.01437 −0.113608
\(705\) 30.1026 1.13373
\(706\) 10.1501 0.382003
\(707\) −0.535718 −0.0201477
\(708\) 15.0093 0.564083
\(709\) 48.5212 1.82225 0.911125 0.412129i \(-0.135215\pi\)
0.911125 + 0.412129i \(0.135215\pi\)
\(710\) 1.67989 0.0630452
\(711\) 1.39182 0.0521973
\(712\) −28.1415 −1.05465
\(713\) 1.27866 0.0478862
\(714\) −0.0958679 −0.00358777
\(715\) −4.35168 −0.162744
\(716\) 4.80324 0.179506
\(717\) −4.94622 −0.184720
\(718\) 24.5349 0.915633
\(719\) −46.0088 −1.71584 −0.857920 0.513783i \(-0.828244\pi\)
−0.857920 + 0.513783i \(0.828244\pi\)
\(720\) −2.54091 −0.0946943
\(721\) 0.0269434 0.00100343
\(722\) −14.4215 −0.536711
\(723\) 49.4241 1.83810
\(724\) 2.77026 0.102956
\(725\) 9.60422 0.356692
\(726\) −3.07417 −0.114093
\(727\) 27.4828 1.01928 0.509640 0.860388i \(-0.329778\pi\)
0.509640 + 0.860388i \(0.329778\pi\)
\(728\) 0.223594 0.00828694
\(729\) 22.3283 0.826972
\(730\) 15.8490 0.586599
\(731\) 1.00000 0.0369863
\(732\) −8.19775 −0.302998
\(733\) −11.3404 −0.418869 −0.209434 0.977823i \(-0.567162\pi\)
−0.209434 + 0.977823i \(0.567162\pi\)
\(734\) 47.3458 1.74757
\(735\) −16.0772 −0.593016
\(736\) −18.2797 −0.673798
\(737\) 13.2819 0.489243
\(738\) −2.81271 −0.103537
\(739\) 7.67521 0.282337 0.141169 0.989986i \(-0.454914\pi\)
0.141169 + 0.989986i \(0.454914\pi\)
\(740\) 9.66516 0.355298
\(741\) −34.0108 −1.24942
\(742\) 0.308926 0.0113410
\(743\) −37.7938 −1.38652 −0.693260 0.720687i \(-0.743826\pi\)
−0.693260 + 0.720687i \(0.743826\pi\)
\(744\) −1.09440 −0.0401228
\(745\) −11.2618 −0.412599
\(746\) 7.83239 0.286764
\(747\) −0.211230 −0.00772849
\(748\) −0.768874 −0.0281128
\(749\) −0.358707 −0.0131069
\(750\) 32.3139 1.17994
\(751\) 34.1652 1.24670 0.623352 0.781941i \(-0.285770\pi\)
0.623352 + 0.781941i \(0.285770\pi\)
\(752\) −64.8242 −2.36389
\(753\) −14.7625 −0.537974
\(754\) 16.1936 0.589737
\(755\) 2.65363 0.0965755
\(756\) −0.114591 −0.00416764
\(757\) 37.4914 1.36265 0.681324 0.731982i \(-0.261404\pi\)
0.681324 + 0.731982i \(0.261404\pi\)
\(758\) −26.5826 −0.965524
\(759\) 8.16928 0.296526
\(760\) −13.3977 −0.485985
\(761\) −12.5989 −0.456710 −0.228355 0.973578i \(-0.573335\pi\)
−0.228355 + 0.973578i \(0.573335\pi\)
\(762\) −26.3515 −0.954612
\(763\) 0.105905 0.00383400
\(764\) −8.66946 −0.313650
\(765\) 0.513671 0.0185718
\(766\) −42.9160 −1.55062
\(767\) 36.9819 1.33534
\(768\) 29.6985 1.07165
\(769\) −7.05586 −0.254441 −0.127220 0.991874i \(-0.540606\pi\)
−0.127220 + 0.991874i \(0.540606\pi\)
\(770\) 0.0645198 0.00232513
\(771\) 1.01757 0.0366468
\(772\) −19.0604 −0.686000
\(773\) 17.8294 0.641279 0.320640 0.947201i \(-0.396102\pi\)
0.320640 + 0.947201i \(0.396102\pi\)
\(774\) −0.687449 −0.0247098
\(775\) 0.998797 0.0358779
\(776\) −19.7358 −0.708474
\(777\) 0.582478 0.0208963
\(778\) −40.6193 −1.45627
\(779\) −21.5210 −0.771071
\(780\) 6.18143 0.221331
\(781\) 0.811957 0.0290541
\(782\) 7.35799 0.263121
\(783\) 13.2887 0.474900
\(784\) 34.6213 1.23647
\(785\) 5.65363 0.201787
\(786\) 2.99354 0.106776
\(787\) 43.9202 1.56559 0.782793 0.622282i \(-0.213794\pi\)
0.782793 + 0.622282i \(0.213794\pi\)
\(788\) −11.1634 −0.397679
\(789\) 2.17787 0.0775341
\(790\) −6.97014 −0.247986
\(791\) 0.122250 0.00434671
\(792\) −0.846336 −0.0300732
\(793\) −20.1987 −0.717277
\(794\) 17.5729 0.623640
\(795\) −13.6751 −0.485006
\(796\) −9.48221 −0.336088
\(797\) 16.7168 0.592139 0.296069 0.955166i \(-0.404324\pi\)
0.296069 + 0.955166i \(0.404324\pi\)
\(798\) 0.504258 0.0178505
\(799\) 13.1048 0.463616
\(800\) −14.2788 −0.504831
\(801\) −5.67520 −0.200523
\(802\) −23.1402 −0.817109
\(803\) 7.66046 0.270332
\(804\) −18.8665 −0.665369
\(805\) −0.171454 −0.00604297
\(806\) 1.68407 0.0593188
\(807\) 36.0322 1.26839
\(808\) −35.1921 −1.23805
\(809\) 24.4091 0.858177 0.429088 0.903262i \(-0.358835\pi\)
0.429088 + 0.903262i \(0.358835\pi\)
\(810\) 20.8316 0.731946
\(811\) 8.29677 0.291339 0.145669 0.989333i \(-0.453466\pi\)
0.145669 + 0.989333i \(0.453466\pi\)
\(812\) −0.0666703 −0.00233967
\(813\) 56.5725 1.98408
\(814\) 16.8232 0.589654
\(815\) 28.9622 1.01450
\(816\) −9.13864 −0.319916
\(817\) −5.25992 −0.184021
\(818\) −44.0208 −1.53915
\(819\) 0.0450915 0.00157562
\(820\) 3.91143 0.136593
\(821\) 44.5956 1.55640 0.778199 0.628018i \(-0.216134\pi\)
0.778199 + 0.628018i \(0.216134\pi\)
\(822\) 7.55031 0.263347
\(823\) 29.0932 1.01413 0.507063 0.861909i \(-0.330731\pi\)
0.507063 + 0.861909i \(0.330731\pi\)
\(824\) 1.76995 0.0616592
\(825\) 6.38126 0.222167
\(826\) −0.548308 −0.0190781
\(827\) −10.3349 −0.359381 −0.179690 0.983723i \(-0.557510\pi\)
−0.179690 + 0.983723i \(0.557510\pi\)
\(828\) −1.40460 −0.0488131
\(829\) −6.82387 −0.237003 −0.118501 0.992954i \(-0.537809\pi\)
−0.118501 + 0.992954i \(0.537809\pi\)
\(830\) 1.05782 0.0367176
\(831\) −1.19150 −0.0413326
\(832\) 10.5501 0.365759
\(833\) −6.99903 −0.242502
\(834\) 11.3368 0.392560
\(835\) 8.60551 0.297806
\(836\) 4.04422 0.139872
\(837\) 1.38197 0.0477678
\(838\) 12.7844 0.441628
\(839\) 41.8740 1.44565 0.722825 0.691031i \(-0.242843\pi\)
0.722825 + 0.691031i \(0.242843\pi\)
\(840\) 0.146748 0.00506328
\(841\) −21.2685 −0.733397
\(842\) −38.5772 −1.32946
\(843\) −51.1429 −1.76145
\(844\) −20.0884 −0.691472
\(845\) −0.933024 −0.0320970
\(846\) −9.00891 −0.309733
\(847\) 0.0311850 0.00107153
\(848\) 29.4485 1.01127
\(849\) −39.9917 −1.37251
\(850\) 5.74754 0.197139
\(851\) −44.7059 −1.53250
\(852\) −1.15336 −0.0395135
\(853\) 14.3131 0.490071 0.245035 0.969514i \(-0.421200\pi\)
0.245035 + 0.969514i \(0.421200\pi\)
\(854\) 0.299474 0.0102478
\(855\) −2.70187 −0.0924019
\(856\) −23.5640 −0.805400
\(857\) −36.3183 −1.24061 −0.620305 0.784360i \(-0.712991\pi\)
−0.620305 + 0.784360i \(0.712991\pi\)
\(858\) 10.7594 0.367321
\(859\) −6.63213 −0.226286 −0.113143 0.993579i \(-0.536092\pi\)
−0.113143 + 0.993579i \(0.536092\pi\)
\(860\) 0.955986 0.0325988
\(861\) 0.235725 0.00803349
\(862\) 36.7165 1.25057
\(863\) 4.38558 0.149287 0.0746434 0.997210i \(-0.476218\pi\)
0.0746434 + 0.997210i \(0.476218\pi\)
\(864\) −19.7566 −0.672132
\(865\) 6.39642 0.217485
\(866\) 4.55147 0.154665
\(867\) 1.84747 0.0627432
\(868\) −0.00693342 −0.000235336 0
\(869\) −3.36894 −0.114284
\(870\) 10.6281 0.360327
\(871\) −46.4857 −1.57511
\(872\) 6.95702 0.235594
\(873\) −3.98006 −0.134705
\(874\) −38.7024 −1.30913
\(875\) −0.327798 −0.0110816
\(876\) −10.8815 −0.367650
\(877\) 38.8413 1.31158 0.655789 0.754944i \(-0.272336\pi\)
0.655789 + 0.754944i \(0.272336\pi\)
\(878\) 43.1646 1.45673
\(879\) 57.2106 1.92967
\(880\) 6.15037 0.207329
\(881\) 32.5138 1.09542 0.547709 0.836669i \(-0.315500\pi\)
0.547709 + 0.836669i \(0.315500\pi\)
\(882\) 4.81147 0.162011
\(883\) −32.7859 −1.10333 −0.551666 0.834065i \(-0.686008\pi\)
−0.551666 + 0.834065i \(0.686008\pi\)
\(884\) 2.69102 0.0905086
\(885\) 24.2717 0.815885
\(886\) 53.5351 1.79855
\(887\) −22.5285 −0.756432 −0.378216 0.925717i \(-0.623462\pi\)
−0.378216 + 0.925717i \(0.623462\pi\)
\(888\) 38.2638 1.28405
\(889\) 0.267314 0.00896542
\(890\) 28.4211 0.952676
\(891\) 10.0687 0.337315
\(892\) −9.37682 −0.313959
\(893\) −68.9305 −2.30667
\(894\) 27.8444 0.931257
\(895\) 7.76739 0.259635
\(896\) −0.414252 −0.0138392
\(897\) −28.5920 −0.954660
\(898\) −51.4737 −1.71770
\(899\) 0.804043 0.0268163
\(900\) −1.09717 −0.0365724
\(901\) −5.95331 −0.198333
\(902\) 6.80825 0.226690
\(903\) 0.0576132 0.00191725
\(904\) 8.03077 0.267099
\(905\) 4.47982 0.148914
\(906\) −6.56104 −0.217976
\(907\) −57.6261 −1.91344 −0.956721 0.291007i \(-0.906010\pi\)
−0.956721 + 0.291007i \(0.906010\pi\)
\(908\) −10.0541 −0.333657
\(909\) −7.09708 −0.235395
\(910\) −0.225815 −0.00748571
\(911\) −12.9954 −0.430557 −0.215278 0.976553i \(-0.569066\pi\)
−0.215278 + 0.976553i \(0.569066\pi\)
\(912\) 48.0685 1.59171
\(913\) 0.511288 0.0169212
\(914\) 43.8142 1.44925
\(915\) −13.2567 −0.438253
\(916\) 1.65639 0.0547288
\(917\) −0.0303670 −0.00100281
\(918\) 7.95248 0.262471
\(919\) 45.4946 1.50073 0.750365 0.661024i \(-0.229878\pi\)
0.750365 + 0.661024i \(0.229878\pi\)
\(920\) −11.2631 −0.371333
\(921\) −43.6532 −1.43842
\(922\) 30.0577 0.989896
\(923\) −2.84180 −0.0935391
\(924\) −0.0442973 −0.00145727
\(925\) −34.9211 −1.14820
\(926\) −10.0549 −0.330425
\(927\) 0.356941 0.0117235
\(928\) −11.4946 −0.377328
\(929\) 31.0361 1.01826 0.509131 0.860689i \(-0.329967\pi\)
0.509131 + 0.860689i \(0.329967\pi\)
\(930\) 1.10528 0.0362435
\(931\) 36.8143 1.20654
\(932\) 4.15189 0.136000
\(933\) 17.1366 0.561026
\(934\) −1.48720 −0.0486626
\(935\) −1.24336 −0.0406621
\(936\) 2.96213 0.0968201
\(937\) 29.9531 0.978525 0.489262 0.872137i \(-0.337266\pi\)
0.489262 + 0.872137i \(0.337266\pi\)
\(938\) 0.689216 0.0225037
\(939\) −42.6998 −1.39346
\(940\) 12.5280 0.408620
\(941\) −16.7839 −0.547139 −0.273570 0.961852i \(-0.588204\pi\)
−0.273570 + 0.961852i \(0.588204\pi\)
\(942\) −13.9785 −0.455443
\(943\) −18.0922 −0.589163
\(944\) −52.2677 −1.70117
\(945\) −0.185307 −0.00602804
\(946\) 1.66399 0.0541011
\(947\) −16.7225 −0.543409 −0.271704 0.962381i \(-0.587587\pi\)
−0.271704 + 0.962381i \(0.587587\pi\)
\(948\) 4.78548 0.155425
\(949\) −26.8112 −0.870327
\(950\) −30.2316 −0.980842
\(951\) 45.0210 1.45991
\(952\) 0.0638850 0.00207053
\(953\) −23.2361 −0.752692 −0.376346 0.926479i \(-0.622820\pi\)
−0.376346 + 0.926479i \(0.622820\pi\)
\(954\) 4.09259 0.132503
\(955\) −14.0195 −0.453660
\(956\) −2.05851 −0.0665768
\(957\) 5.13699 0.166055
\(958\) −66.6966 −2.15487
\(959\) −0.0765917 −0.00247328
\(960\) 6.92418 0.223477
\(961\) −30.9164 −0.997303
\(962\) −58.8803 −1.89838
\(963\) −4.75207 −0.153133
\(964\) 20.5692 0.662490
\(965\) −30.8229 −0.992224
\(966\) 0.423917 0.0136393
\(967\) −43.5139 −1.39931 −0.699656 0.714479i \(-0.746664\pi\)
−0.699656 + 0.714479i \(0.746664\pi\)
\(968\) 2.04859 0.0658440
\(969\) −9.71753 −0.312172
\(970\) 19.9319 0.639974
\(971\) −13.3176 −0.427383 −0.213691 0.976901i \(-0.568549\pi\)
−0.213691 + 0.976901i \(0.568549\pi\)
\(972\) −3.27861 −0.105161
\(973\) −0.115002 −0.00368680
\(974\) 7.46979 0.239347
\(975\) −22.3341 −0.715262
\(976\) 28.5475 0.913783
\(977\) 41.2670 1.32025 0.660125 0.751156i \(-0.270503\pi\)
0.660125 + 0.751156i \(0.270503\pi\)
\(978\) −71.6084 −2.28978
\(979\) 13.7370 0.439037
\(980\) −6.69097 −0.213735
\(981\) 1.40300 0.0447944
\(982\) 56.2873 1.79620
\(983\) −28.9531 −0.923459 −0.461730 0.887021i \(-0.652771\pi\)
−0.461730 + 0.887021i \(0.652771\pi\)
\(984\) 15.4851 0.493648
\(985\) −18.0524 −0.575199
\(986\) 4.62683 0.147348
\(987\) 0.755012 0.0240323
\(988\) −14.1545 −0.450316
\(989\) −4.42189 −0.140608
\(990\) 0.854745 0.0271656
\(991\) 15.0446 0.477909 0.238954 0.971031i \(-0.423195\pi\)
0.238954 + 0.971031i \(0.423195\pi\)
\(992\) −1.19539 −0.0379535
\(993\) 47.6053 1.51071
\(994\) 0.0421337 0.00133640
\(995\) −15.3338 −0.486115
\(996\) −0.726270 −0.0230127
\(997\) −9.65579 −0.305802 −0.152901 0.988242i \(-0.548862\pi\)
−0.152901 + 0.988242i \(0.548862\pi\)
\(998\) −31.2587 −0.989478
\(999\) −48.3179 −1.52871
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 \(a_p\))