Properties

Label 8041.2.a.i.1.4
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
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: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +O(q^{10})\) \(q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +4.59358 q^{10} +1.00000 q^{11} -7.77187 q^{12} -1.76785 q^{13} +6.10628 q^{14} +2.91016 q^{15} +8.90639 q^{16} -1.00000 q^{17} +0.776190 q^{18} +4.33043 q^{19} -8.37439 q^{20} +3.86850 q^{21} -2.59406 q^{22} -1.79914 q^{23} +11.6345 q^{24} -1.86423 q^{25} +4.58590 q^{26} +5.42195 q^{27} -11.1321 q^{28} +5.71752 q^{29} -7.54912 q^{30} +0.869088 q^{31} -8.94467 q^{32} -1.64341 q^{33} +2.59406 q^{34} +4.16840 q^{35} -1.41504 q^{36} +1.69519 q^{37} -11.2334 q^{38} +2.90529 q^{39} +12.5365 q^{40} +8.84725 q^{41} -10.0351 q^{42} -1.00000 q^{43} +4.72913 q^{44} +0.529860 q^{45} +4.66707 q^{46} -5.13726 q^{47} -14.6368 q^{48} -1.45891 q^{49} +4.83591 q^{50} +1.64341 q^{51} -8.36039 q^{52} +4.78070 q^{53} -14.0649 q^{54} -1.77081 q^{55} +16.6648 q^{56} -7.11666 q^{57} -14.8316 q^{58} +0.969361 q^{59} +13.7625 q^{60} +6.54259 q^{61} -2.25446 q^{62} +0.704346 q^{63} +5.39018 q^{64} +3.13053 q^{65} +4.26309 q^{66} -4.15695 q^{67} -4.72913 q^{68} +2.95671 q^{69} -10.8131 q^{70} -3.14680 q^{71} +2.11832 q^{72} -9.63659 q^{73} -4.39743 q^{74} +3.06368 q^{75} +20.4792 q^{76} -2.35395 q^{77} -7.53650 q^{78} -9.32988 q^{79} -15.7715 q^{80} -8.01281 q^{81} -22.9503 q^{82} +10.0262 q^{83} +18.2946 q^{84} +1.77081 q^{85} +2.59406 q^{86} -9.39621 q^{87} -7.07951 q^{88} +2.23814 q^{89} -1.37449 q^{90} +4.16143 q^{91} -8.50835 q^{92} -1.42826 q^{93} +13.3263 q^{94} -7.66838 q^{95} +14.6997 q^{96} -16.1140 q^{97} +3.78451 q^{98} -0.299219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59406 −1.83427 −0.917137 0.398571i \(-0.869506\pi\)
−0.917137 + 0.398571i \(0.869506\pi\)
\(3\) −1.64341 −0.948821 −0.474410 0.880304i \(-0.657339\pi\)
−0.474410 + 0.880304i \(0.657339\pi\)
\(4\) 4.72913 2.36456
\(5\) −1.77081 −0.791931 −0.395965 0.918265i \(-0.629590\pi\)
−0.395965 + 0.918265i \(0.629590\pi\)
\(6\) 4.26309 1.74040
\(7\) −2.35395 −0.889710 −0.444855 0.895603i \(-0.646745\pi\)
−0.444855 + 0.895603i \(0.646745\pi\)
\(8\) −7.07951 −2.50299
\(9\) −0.299219 −0.0997395
\(10\) 4.59358 1.45262
\(11\) 1.00000 0.301511
\(12\) −7.77187 −2.24355
\(13\) −1.76785 −0.490313 −0.245157 0.969483i \(-0.578839\pi\)
−0.245157 + 0.969483i \(0.578839\pi\)
\(14\) 6.10628 1.63197
\(15\) 2.91016 0.751400
\(16\) 8.90639 2.22660
\(17\) −1.00000 −0.242536
\(18\) 0.776190 0.182950
\(19\) 4.33043 0.993469 0.496735 0.867902i \(-0.334532\pi\)
0.496735 + 0.867902i \(0.334532\pi\)
\(20\) −8.37439 −1.87257
\(21\) 3.86850 0.844175
\(22\) −2.59406 −0.553055
\(23\) −1.79914 −0.375146 −0.187573 0.982251i \(-0.560062\pi\)
−0.187573 + 0.982251i \(0.560062\pi\)
\(24\) 11.6345 2.37488
\(25\) −1.86423 −0.372846
\(26\) 4.58590 0.899369
\(27\) 5.42195 1.04346
\(28\) −11.1321 −2.10378
\(29\) 5.71752 1.06172 0.530859 0.847460i \(-0.321870\pi\)
0.530859 + 0.847460i \(0.321870\pi\)
\(30\) −7.54912 −1.37827
\(31\) 0.869088 0.156093 0.0780464 0.996950i \(-0.475132\pi\)
0.0780464 + 0.996950i \(0.475132\pi\)
\(32\) −8.94467 −1.58121
\(33\) −1.64341 −0.286080
\(34\) 2.59406 0.444877
\(35\) 4.16840 0.704589
\(36\) −1.41504 −0.235841
\(37\) 1.69519 0.278688 0.139344 0.990244i \(-0.455501\pi\)
0.139344 + 0.990244i \(0.455501\pi\)
\(38\) −11.2334 −1.82230
\(39\) 2.90529 0.465219
\(40\) 12.5365 1.98219
\(41\) 8.84725 1.38171 0.690854 0.722995i \(-0.257235\pi\)
0.690854 + 0.722995i \(0.257235\pi\)
\(42\) −10.0351 −1.54845
\(43\) −1.00000 −0.152499
\(44\) 4.72913 0.712943
\(45\) 0.529860 0.0789868
\(46\) 4.66707 0.688121
\(47\) −5.13726 −0.749346 −0.374673 0.927157i \(-0.622245\pi\)
−0.374673 + 0.927157i \(0.622245\pi\)
\(48\) −14.6368 −2.11264
\(49\) −1.45891 −0.208416
\(50\) 4.83591 0.683901
\(51\) 1.64341 0.230123
\(52\) −8.36039 −1.15938
\(53\) 4.78070 0.656680 0.328340 0.944560i \(-0.393511\pi\)
0.328340 + 0.944560i \(0.393511\pi\)
\(54\) −14.0649 −1.91398
\(55\) −1.77081 −0.238776
\(56\) 16.6648 2.22693
\(57\) −7.11666 −0.942624
\(58\) −14.8316 −1.94748
\(59\) 0.969361 0.126200 0.0631000 0.998007i \(-0.479901\pi\)
0.0631000 + 0.998007i \(0.479901\pi\)
\(60\) 13.7625 1.77673
\(61\) 6.54259 0.837693 0.418846 0.908057i \(-0.362435\pi\)
0.418846 + 0.908057i \(0.362435\pi\)
\(62\) −2.25446 −0.286317
\(63\) 0.704346 0.0887393
\(64\) 5.39018 0.673772
\(65\) 3.13053 0.388294
\(66\) 4.26309 0.524750
\(67\) −4.15695 −0.507852 −0.253926 0.967224i \(-0.581722\pi\)
−0.253926 + 0.967224i \(0.581722\pi\)
\(68\) −4.72913 −0.573491
\(69\) 2.95671 0.355946
\(70\) −10.8131 −1.29241
\(71\) −3.14680 −0.373457 −0.186728 0.982412i \(-0.559788\pi\)
−0.186728 + 0.982412i \(0.559788\pi\)
\(72\) 2.11832 0.249647
\(73\) −9.63659 −1.12788 −0.563939 0.825817i \(-0.690715\pi\)
−0.563939 + 0.825817i \(0.690715\pi\)
\(74\) −4.39743 −0.511191
\(75\) 3.06368 0.353764
\(76\) 20.4792 2.34912
\(77\) −2.35395 −0.268258
\(78\) −7.53650 −0.853340
\(79\) −9.32988 −1.04969 −0.524847 0.851197i \(-0.675877\pi\)
−0.524847 + 0.851197i \(0.675877\pi\)
\(80\) −15.7715 −1.76331
\(81\) −8.01281 −0.890312
\(82\) −22.9503 −2.53443
\(83\) 10.0262 1.10051 0.550257 0.834995i \(-0.314530\pi\)
0.550257 + 0.834995i \(0.314530\pi\)
\(84\) 18.2946 1.99611
\(85\) 1.77081 0.192071
\(86\) 2.59406 0.279724
\(87\) −9.39621 −1.00738
\(88\) −7.07951 −0.754678
\(89\) 2.23814 0.237242 0.118621 0.992940i \(-0.462153\pi\)
0.118621 + 0.992940i \(0.462153\pi\)
\(90\) −1.37449 −0.144884
\(91\) 4.16143 0.436237
\(92\) −8.50835 −0.887057
\(93\) −1.42826 −0.148104
\(94\) 13.3263 1.37451
\(95\) −7.66838 −0.786759
\(96\) 14.6997 1.50028
\(97\) −16.1140 −1.63613 −0.818065 0.575126i \(-0.804953\pi\)
−0.818065 + 0.575126i \(0.804953\pi\)
\(98\) 3.78451 0.382293
\(99\) −0.299219 −0.0300726
\(100\) −8.81617 −0.881617
\(101\) 16.6742 1.65915 0.829573 0.558398i \(-0.188584\pi\)
0.829573 + 0.558398i \(0.188584\pi\)
\(102\) −4.26309 −0.422108
\(103\) 16.8928 1.66450 0.832249 0.554402i \(-0.187053\pi\)
0.832249 + 0.554402i \(0.187053\pi\)
\(104\) 12.5155 1.22725
\(105\) −6.85038 −0.668528
\(106\) −12.4014 −1.20453
\(107\) −9.65261 −0.933153 −0.466577 0.884481i \(-0.654513\pi\)
−0.466577 + 0.884481i \(0.654513\pi\)
\(108\) 25.6411 2.46732
\(109\) −8.99504 −0.861569 −0.430784 0.902455i \(-0.641763\pi\)
−0.430784 + 0.902455i \(0.641763\pi\)
\(110\) 4.59358 0.437981
\(111\) −2.78589 −0.264425
\(112\) −20.9652 −1.98103
\(113\) −15.1017 −1.42065 −0.710326 0.703873i \(-0.751453\pi\)
−0.710326 + 0.703873i \(0.751453\pi\)
\(114\) 18.4610 1.72903
\(115\) 3.18593 0.297090
\(116\) 27.0389 2.51050
\(117\) 0.528974 0.0489036
\(118\) −2.51458 −0.231486
\(119\) 2.35395 0.215786
\(120\) −20.6025 −1.88074
\(121\) 1.00000 0.0909091
\(122\) −16.9718 −1.53656
\(123\) −14.5396 −1.31099
\(124\) 4.11003 0.369091
\(125\) 12.1553 1.08720
\(126\) −1.82711 −0.162772
\(127\) −13.9568 −1.23846 −0.619232 0.785208i \(-0.712556\pi\)
−0.619232 + 0.785208i \(0.712556\pi\)
\(128\) 3.90691 0.345325
\(129\) 1.64341 0.144694
\(130\) −8.12077 −0.712238
\(131\) 11.2799 0.985529 0.492764 0.870163i \(-0.335986\pi\)
0.492764 + 0.870163i \(0.335986\pi\)
\(132\) −7.77187 −0.676455
\(133\) −10.1936 −0.883900
\(134\) 10.7834 0.931540
\(135\) −9.60126 −0.826345
\(136\) 7.07951 0.607063
\(137\) 6.91902 0.591132 0.295566 0.955322i \(-0.404492\pi\)
0.295566 + 0.955322i \(0.404492\pi\)
\(138\) −7.66988 −0.652904
\(139\) −18.9516 −1.60745 −0.803726 0.595000i \(-0.797152\pi\)
−0.803726 + 0.595000i \(0.797152\pi\)
\(140\) 19.7129 1.66605
\(141\) 8.44260 0.710995
\(142\) 8.16298 0.685022
\(143\) −1.76785 −0.147835
\(144\) −2.66496 −0.222080
\(145\) −10.1247 −0.840807
\(146\) 24.9978 2.06884
\(147\) 2.39759 0.197750
\(148\) 8.01679 0.658976
\(149\) −21.1530 −1.73292 −0.866459 0.499248i \(-0.833610\pi\)
−0.866459 + 0.499248i \(0.833610\pi\)
\(150\) −7.94736 −0.648900
\(151\) −22.3134 −1.81584 −0.907919 0.419146i \(-0.862329\pi\)
−0.907919 + 0.419146i \(0.862329\pi\)
\(152\) −30.6573 −2.48664
\(153\) 0.299219 0.0241904
\(154\) 6.10628 0.492058
\(155\) −1.53899 −0.123615
\(156\) 13.7395 1.10004
\(157\) −0.508352 −0.0405709 −0.0202854 0.999794i \(-0.506458\pi\)
−0.0202854 + 0.999794i \(0.506458\pi\)
\(158\) 24.2022 1.92543
\(159\) −7.85663 −0.623071
\(160\) 15.8393 1.25221
\(161\) 4.23508 0.333771
\(162\) 20.7857 1.63308
\(163\) 21.4027 1.67639 0.838195 0.545371i \(-0.183611\pi\)
0.838195 + 0.545371i \(0.183611\pi\)
\(164\) 41.8398 3.26714
\(165\) 2.91016 0.226556
\(166\) −26.0084 −2.01864
\(167\) −3.33393 −0.257987 −0.128994 0.991645i \(-0.541175\pi\)
−0.128994 + 0.991645i \(0.541175\pi\)
\(168\) −27.3871 −2.11296
\(169\) −9.87471 −0.759593
\(170\) −4.59358 −0.352312
\(171\) −1.29575 −0.0990882
\(172\) −4.72913 −0.360593
\(173\) −21.1513 −1.60810 −0.804052 0.594560i \(-0.797326\pi\)
−0.804052 + 0.594560i \(0.797326\pi\)
\(174\) 24.3743 1.84781
\(175\) 4.38830 0.331724
\(176\) 8.90639 0.671345
\(177\) −1.59305 −0.119741
\(178\) −5.80586 −0.435167
\(179\) −11.0187 −0.823579 −0.411790 0.911279i \(-0.635096\pi\)
−0.411790 + 0.911279i \(0.635096\pi\)
\(180\) 2.50577 0.186769
\(181\) 16.7846 1.24759 0.623795 0.781588i \(-0.285590\pi\)
0.623795 + 0.781588i \(0.285590\pi\)
\(182\) −10.7950 −0.800178
\(183\) −10.7521 −0.794820
\(184\) 12.7370 0.938986
\(185\) −3.00187 −0.220702
\(186\) 3.70500 0.271664
\(187\) −1.00000 −0.0731272
\(188\) −24.2947 −1.77188
\(189\) −12.7630 −0.928373
\(190\) 19.8922 1.44313
\(191\) 16.2603 1.17656 0.588278 0.808658i \(-0.299806\pi\)
0.588278 + 0.808658i \(0.299806\pi\)
\(192\) −8.85825 −0.639289
\(193\) −4.36012 −0.313848 −0.156924 0.987611i \(-0.550158\pi\)
−0.156924 + 0.987611i \(0.550158\pi\)
\(194\) 41.8006 3.00111
\(195\) −5.14473 −0.368422
\(196\) −6.89939 −0.492814
\(197\) 11.5518 0.823031 0.411516 0.911403i \(-0.365000\pi\)
0.411516 + 0.911403i \(0.365000\pi\)
\(198\) 0.776190 0.0551614
\(199\) 15.4184 1.09298 0.546492 0.837464i \(-0.315963\pi\)
0.546492 + 0.837464i \(0.315963\pi\)
\(200\) 13.1978 0.933227
\(201\) 6.83155 0.481860
\(202\) −43.2538 −3.04333
\(203\) −13.4588 −0.944620
\(204\) 7.77187 0.544140
\(205\) −15.6668 −1.09422
\(206\) −43.8209 −3.05315
\(207\) 0.538336 0.0374169
\(208\) −15.7452 −1.09173
\(209\) 4.33043 0.299542
\(210\) 17.7703 1.22626
\(211\) 11.3624 0.782220 0.391110 0.920344i \(-0.372091\pi\)
0.391110 + 0.920344i \(0.372091\pi\)
\(212\) 22.6085 1.55276
\(213\) 5.17147 0.354343
\(214\) 25.0394 1.71166
\(215\) 1.77081 0.120768
\(216\) −38.3848 −2.61175
\(217\) −2.04579 −0.138877
\(218\) 23.3336 1.58035
\(219\) 15.8368 1.07015
\(220\) −8.37439 −0.564601
\(221\) 1.76785 0.118918
\(222\) 7.22676 0.485028
\(223\) 22.9403 1.53620 0.768098 0.640333i \(-0.221204\pi\)
0.768098 + 0.640333i \(0.221204\pi\)
\(224\) 21.0553 1.40682
\(225\) 0.557812 0.0371874
\(226\) 39.1748 2.60587
\(227\) 21.8044 1.44721 0.723603 0.690216i \(-0.242484\pi\)
0.723603 + 0.690216i \(0.242484\pi\)
\(228\) −33.6556 −2.22890
\(229\) 8.39753 0.554925 0.277462 0.960737i \(-0.410507\pi\)
0.277462 + 0.960737i \(0.410507\pi\)
\(230\) −8.26449 −0.544944
\(231\) 3.86850 0.254528
\(232\) −40.4773 −2.65746
\(233\) −10.4308 −0.683341 −0.341671 0.939820i \(-0.610993\pi\)
−0.341671 + 0.939820i \(0.610993\pi\)
\(234\) −1.37219 −0.0897027
\(235\) 9.09711 0.593430
\(236\) 4.58423 0.298408
\(237\) 15.3328 0.995971
\(238\) −6.10628 −0.395811
\(239\) −5.29141 −0.342273 −0.171137 0.985247i \(-0.554744\pi\)
−0.171137 + 0.985247i \(0.554744\pi\)
\(240\) 25.9190 1.67307
\(241\) −3.09953 −0.199658 −0.0998290 0.995005i \(-0.531830\pi\)
−0.0998290 + 0.995005i \(0.531830\pi\)
\(242\) −2.59406 −0.166752
\(243\) −3.09756 −0.198709
\(244\) 30.9407 1.98078
\(245\) 2.58346 0.165051
\(246\) 37.7166 2.40472
\(247\) −7.65556 −0.487111
\(248\) −6.15272 −0.390698
\(249\) −16.4770 −1.04419
\(250\) −31.5314 −1.99422
\(251\) −21.2617 −1.34203 −0.671015 0.741444i \(-0.734141\pi\)
−0.671015 + 0.741444i \(0.734141\pi\)
\(252\) 3.33094 0.209830
\(253\) −1.79914 −0.113111
\(254\) 36.2047 2.27168
\(255\) −2.91016 −0.182241
\(256\) −20.9151 −1.30719
\(257\) 28.2627 1.76298 0.881489 0.472204i \(-0.156541\pi\)
0.881489 + 0.472204i \(0.156541\pi\)
\(258\) −4.26309 −0.265408
\(259\) −3.99041 −0.247952
\(260\) 14.8047 0.918147
\(261\) −1.71079 −0.105895
\(262\) −29.2607 −1.80773
\(263\) −3.19795 −0.197194 −0.0985970 0.995127i \(-0.531435\pi\)
−0.0985970 + 0.995127i \(0.531435\pi\)
\(264\) 11.6345 0.716054
\(265\) −8.46572 −0.520045
\(266\) 26.4428 1.62131
\(267\) −3.67817 −0.225100
\(268\) −19.6587 −1.20085
\(269\) 10.4584 0.637662 0.318831 0.947812i \(-0.396710\pi\)
0.318831 + 0.947812i \(0.396710\pi\)
\(270\) 24.9062 1.51574
\(271\) −25.6942 −1.56081 −0.780407 0.625272i \(-0.784988\pi\)
−0.780407 + 0.625272i \(0.784988\pi\)
\(272\) −8.90639 −0.540029
\(273\) −6.83892 −0.413910
\(274\) −17.9483 −1.08430
\(275\) −1.86423 −0.112417
\(276\) 13.9827 0.841658
\(277\) −3.47693 −0.208909 −0.104454 0.994530i \(-0.533310\pi\)
−0.104454 + 0.994530i \(0.533310\pi\)
\(278\) 49.1614 2.94851
\(279\) −0.260047 −0.0155686
\(280\) −29.5103 −1.76358
\(281\) 21.7493 1.29746 0.648728 0.761020i \(-0.275301\pi\)
0.648728 + 0.761020i \(0.275301\pi\)
\(282\) −21.9006 −1.30416
\(283\) −10.7828 −0.640971 −0.320486 0.947253i \(-0.603846\pi\)
−0.320486 + 0.947253i \(0.603846\pi\)
\(284\) −14.8816 −0.883062
\(285\) 12.6023 0.746493
\(286\) 4.58590 0.271170
\(287\) −20.8260 −1.22932
\(288\) 2.67641 0.157709
\(289\) 1.00000 0.0588235
\(290\) 26.2639 1.54227
\(291\) 26.4818 1.55239
\(292\) −45.5727 −2.66694
\(293\) −22.6856 −1.32531 −0.662654 0.748926i \(-0.730570\pi\)
−0.662654 + 0.748926i \(0.730570\pi\)
\(294\) −6.21948 −0.362727
\(295\) −1.71656 −0.0999417
\(296\) −12.0011 −0.697553
\(297\) 5.42195 0.314614
\(298\) 54.8720 3.17865
\(299\) 3.18061 0.183939
\(300\) 14.4885 0.836496
\(301\) 2.35395 0.135679
\(302\) 57.8822 3.33074
\(303\) −27.4025 −1.57423
\(304\) 38.5685 2.21206
\(305\) −11.5857 −0.663395
\(306\) −0.776190 −0.0443718
\(307\) −6.99874 −0.399439 −0.199720 0.979853i \(-0.564003\pi\)
−0.199720 + 0.979853i \(0.564003\pi\)
\(308\) −11.1321 −0.634312
\(309\) −27.7617 −1.57931
\(310\) 3.99223 0.226743
\(311\) −30.2215 −1.71370 −0.856852 0.515562i \(-0.827583\pi\)
−0.856852 + 0.515562i \(0.827583\pi\)
\(312\) −20.5681 −1.16444
\(313\) −22.1100 −1.24973 −0.624865 0.780733i \(-0.714846\pi\)
−0.624865 + 0.780733i \(0.714846\pi\)
\(314\) 1.31869 0.0744182
\(315\) −1.24726 −0.0702754
\(316\) −44.1222 −2.48207
\(317\) −24.1783 −1.35799 −0.678995 0.734143i \(-0.737584\pi\)
−0.678995 + 0.734143i \(0.737584\pi\)
\(318\) 20.3805 1.14288
\(319\) 5.71752 0.320120
\(320\) −9.54499 −0.533581
\(321\) 15.8632 0.885395
\(322\) −10.9860 −0.612228
\(323\) −4.33043 −0.240952
\(324\) −37.8936 −2.10520
\(325\) 3.29567 0.182811
\(326\) −55.5198 −3.07496
\(327\) 14.7825 0.817474
\(328\) −62.6342 −3.45839
\(329\) 12.0929 0.666700
\(330\) −7.54912 −0.415565
\(331\) −19.1308 −1.05152 −0.525762 0.850632i \(-0.676220\pi\)
−0.525762 + 0.850632i \(0.676220\pi\)
\(332\) 47.4150 2.60223
\(333\) −0.507234 −0.0277962
\(334\) 8.64841 0.473220
\(335\) 7.36117 0.402184
\(336\) 34.4544 1.87964
\(337\) −4.59630 −0.250376 −0.125188 0.992133i \(-0.539953\pi\)
−0.125188 + 0.992133i \(0.539953\pi\)
\(338\) 25.6155 1.39330
\(339\) 24.8183 1.34794
\(340\) 8.37439 0.454165
\(341\) 0.869088 0.0470638
\(342\) 3.36124 0.181755
\(343\) 19.9119 1.07514
\(344\) 7.07951 0.381702
\(345\) −5.23578 −0.281885
\(346\) 54.8676 2.94970
\(347\) 3.63707 0.195248 0.0976242 0.995223i \(-0.468876\pi\)
0.0976242 + 0.995223i \(0.468876\pi\)
\(348\) −44.4359 −2.38201
\(349\) 8.60989 0.460877 0.230439 0.973087i \(-0.425984\pi\)
0.230439 + 0.973087i \(0.425984\pi\)
\(350\) −11.3835 −0.608474
\(351\) −9.58520 −0.511620
\(352\) −8.94467 −0.476752
\(353\) 1.80228 0.0959258 0.0479629 0.998849i \(-0.484727\pi\)
0.0479629 + 0.998849i \(0.484727\pi\)
\(354\) 4.13247 0.219638
\(355\) 5.57239 0.295752
\(356\) 10.5844 0.560974
\(357\) −3.86850 −0.204743
\(358\) 28.5832 1.51067
\(359\) −20.0871 −1.06016 −0.530079 0.847948i \(-0.677838\pi\)
−0.530079 + 0.847948i \(0.677838\pi\)
\(360\) −3.75115 −0.197703
\(361\) −0.247350 −0.0130184
\(362\) −43.5402 −2.28842
\(363\) −1.64341 −0.0862564
\(364\) 19.6799 1.03151
\(365\) 17.0646 0.893201
\(366\) 27.8916 1.45792
\(367\) −3.51832 −0.183655 −0.0918274 0.995775i \(-0.529271\pi\)
−0.0918274 + 0.995775i \(0.529271\pi\)
\(368\) −16.0238 −0.835300
\(369\) −2.64726 −0.137811
\(370\) 7.78702 0.404828
\(371\) −11.2535 −0.584254
\(372\) −6.75444 −0.350202
\(373\) −8.51299 −0.440786 −0.220393 0.975411i \(-0.570734\pi\)
−0.220393 + 0.975411i \(0.570734\pi\)
\(374\) 2.59406 0.134135
\(375\) −19.9760 −1.03156
\(376\) 36.3693 1.87560
\(377\) −10.1077 −0.520574
\(378\) 33.1080 1.70289
\(379\) 24.2790 1.24713 0.623565 0.781772i \(-0.285684\pi\)
0.623565 + 0.781772i \(0.285684\pi\)
\(380\) −36.2647 −1.86034
\(381\) 22.9366 1.17508
\(382\) −42.1802 −2.15813
\(383\) −26.5810 −1.35822 −0.679112 0.734035i \(-0.737635\pi\)
−0.679112 + 0.734035i \(0.737635\pi\)
\(384\) −6.42063 −0.327652
\(385\) 4.16840 0.212441
\(386\) 11.3104 0.575684
\(387\) 0.299219 0.0152101
\(388\) −76.2052 −3.86873
\(389\) 29.5823 1.49988 0.749941 0.661504i \(-0.230082\pi\)
0.749941 + 0.661504i \(0.230082\pi\)
\(390\) 13.3457 0.675786
\(391\) 1.79914 0.0909863
\(392\) 10.3284 0.521663
\(393\) −18.5374 −0.935090
\(394\) −29.9660 −1.50967
\(395\) 16.5215 0.831284
\(396\) −1.41504 −0.0711086
\(397\) 4.74354 0.238072 0.119036 0.992890i \(-0.462020\pi\)
0.119036 + 0.992890i \(0.462020\pi\)
\(398\) −39.9963 −2.00483
\(399\) 16.7523 0.838662
\(400\) −16.6035 −0.830177
\(401\) 2.65784 0.132726 0.0663631 0.997796i \(-0.478860\pi\)
0.0663631 + 0.997796i \(0.478860\pi\)
\(402\) −17.7214 −0.883864
\(403\) −1.53642 −0.0765344
\(404\) 78.8545 3.92316
\(405\) 14.1892 0.705066
\(406\) 34.9128 1.73269
\(407\) 1.69519 0.0840277
\(408\) −11.6345 −0.575994
\(409\) −19.7444 −0.976297 −0.488149 0.872761i \(-0.662328\pi\)
−0.488149 + 0.872761i \(0.662328\pi\)
\(410\) 40.6406 2.00709
\(411\) −11.3708 −0.560878
\(412\) 79.8882 3.93581
\(413\) −2.28183 −0.112281
\(414\) −1.39647 −0.0686329
\(415\) −17.7544 −0.871531
\(416\) 15.8128 0.775288
\(417\) 31.1451 1.52518
\(418\) −11.2334 −0.549443
\(419\) 27.1836 1.32801 0.664004 0.747729i \(-0.268856\pi\)
0.664004 + 0.747729i \(0.268856\pi\)
\(420\) −32.3963 −1.58078
\(421\) −10.9269 −0.532545 −0.266273 0.963898i \(-0.585792\pi\)
−0.266273 + 0.963898i \(0.585792\pi\)
\(422\) −29.4747 −1.43481
\(423\) 1.53716 0.0747394
\(424\) −33.8450 −1.64366
\(425\) 1.86423 0.0904283
\(426\) −13.4151 −0.649963
\(427\) −15.4009 −0.745304
\(428\) −45.6484 −2.20650
\(429\) 2.90529 0.140269
\(430\) −4.59358 −0.221522
\(431\) −24.3193 −1.17142 −0.585711 0.810520i \(-0.699185\pi\)
−0.585711 + 0.810520i \(0.699185\pi\)
\(432\) 48.2901 2.32336
\(433\) −17.0035 −0.817134 −0.408567 0.912728i \(-0.633971\pi\)
−0.408567 + 0.912728i \(0.633971\pi\)
\(434\) 5.30690 0.254739
\(435\) 16.6389 0.797775
\(436\) −42.5387 −2.03723
\(437\) −7.79105 −0.372696
\(438\) −41.0816 −1.96295
\(439\) −9.75346 −0.465507 −0.232754 0.972536i \(-0.574774\pi\)
−0.232754 + 0.972536i \(0.574774\pi\)
\(440\) 12.5365 0.597653
\(441\) 0.436534 0.0207873
\(442\) −4.58590 −0.218129
\(443\) 12.4883 0.593337 0.296668 0.954981i \(-0.404124\pi\)
0.296668 + 0.954981i \(0.404124\pi\)
\(444\) −13.1748 −0.625250
\(445\) −3.96332 −0.187879
\(446\) −59.5084 −2.81780
\(447\) 34.7629 1.64423
\(448\) −12.6882 −0.599462
\(449\) −32.1774 −1.51855 −0.759274 0.650771i \(-0.774446\pi\)
−0.759274 + 0.650771i \(0.774446\pi\)
\(450\) −1.44699 −0.0682120
\(451\) 8.84725 0.416601
\(452\) −71.4181 −3.35922
\(453\) 36.6699 1.72290
\(454\) −56.5618 −2.65458
\(455\) −7.36911 −0.345469
\(456\) 50.3825 2.35937
\(457\) 10.0173 0.468591 0.234296 0.972165i \(-0.424722\pi\)
0.234296 + 0.972165i \(0.424722\pi\)
\(458\) −21.7837 −1.01788
\(459\) −5.42195 −0.253075
\(460\) 15.0667 0.702488
\(461\) 20.5438 0.956821 0.478411 0.878136i \(-0.341213\pi\)
0.478411 + 0.878136i \(0.341213\pi\)
\(462\) −10.0351 −0.466875
\(463\) −24.9672 −1.16033 −0.580163 0.814500i \(-0.697011\pi\)
−0.580163 + 0.814500i \(0.697011\pi\)
\(464\) 50.9225 2.36402
\(465\) 2.52919 0.117288
\(466\) 27.0580 1.25344
\(467\) −13.7110 −0.634470 −0.317235 0.948347i \(-0.602754\pi\)
−0.317235 + 0.948347i \(0.602754\pi\)
\(468\) 2.50158 0.115636
\(469\) 9.78525 0.451841
\(470\) −23.5984 −1.08851
\(471\) 0.835428 0.0384945
\(472\) −6.86260 −0.315877
\(473\) −1.00000 −0.0459800
\(474\) −39.7741 −1.82688
\(475\) −8.07291 −0.370411
\(476\) 11.1321 0.510241
\(477\) −1.43047 −0.0654969
\(478\) 13.7262 0.627823
\(479\) 19.2584 0.879941 0.439970 0.898012i \(-0.354989\pi\)
0.439970 + 0.898012i \(0.354989\pi\)
\(480\) −26.0304 −1.18812
\(481\) −2.99685 −0.136645
\(482\) 8.04035 0.366228
\(483\) −6.95996 −0.316689
\(484\) 4.72913 0.214960
\(485\) 28.5349 1.29570
\(486\) 8.03525 0.364486
\(487\) 20.3357 0.921500 0.460750 0.887530i \(-0.347580\pi\)
0.460750 + 0.887530i \(0.347580\pi\)
\(488\) −46.3183 −2.09673
\(489\) −35.1733 −1.59059
\(490\) −6.70164 −0.302749
\(491\) −36.0798 −1.62826 −0.814128 0.580685i \(-0.802785\pi\)
−0.814128 + 0.580685i \(0.802785\pi\)
\(492\) −68.7597 −3.09993
\(493\) −5.71752 −0.257504
\(494\) 19.8589 0.893496
\(495\) 0.529860 0.0238154
\(496\) 7.74044 0.347556
\(497\) 7.40742 0.332268
\(498\) 42.7424 1.91533
\(499\) 38.0641 1.70398 0.851991 0.523557i \(-0.175395\pi\)
0.851991 + 0.523557i \(0.175395\pi\)
\(500\) 57.4837 2.57075
\(501\) 5.47900 0.244784
\(502\) 55.1542 2.46165
\(503\) −2.83444 −0.126381 −0.0631907 0.998001i \(-0.520128\pi\)
−0.0631907 + 0.998001i \(0.520128\pi\)
\(504\) −4.98643 −0.222113
\(505\) −29.5269 −1.31393
\(506\) 4.66707 0.207476
\(507\) 16.2281 0.720717
\(508\) −66.0034 −2.92843
\(509\) −36.8478 −1.63325 −0.816624 0.577170i \(-0.804157\pi\)
−0.816624 + 0.577170i \(0.804157\pi\)
\(510\) 7.54912 0.334281
\(511\) 22.6841 1.00348
\(512\) 46.4411 2.05243
\(513\) 23.4794 1.03664
\(514\) −73.3150 −3.23379
\(515\) −29.9140 −1.31817
\(516\) 7.77187 0.342138
\(517\) −5.13726 −0.225936
\(518\) 10.3513 0.454812
\(519\) 34.7602 1.52580
\(520\) −22.1626 −0.971895
\(521\) 7.62742 0.334163 0.167082 0.985943i \(-0.446566\pi\)
0.167082 + 0.985943i \(0.446566\pi\)
\(522\) 4.43788 0.194241
\(523\) −31.6745 −1.38503 −0.692515 0.721403i \(-0.743497\pi\)
−0.692515 + 0.721403i \(0.743497\pi\)
\(524\) 53.3440 2.33035
\(525\) −7.21176 −0.314747
\(526\) 8.29566 0.361708
\(527\) −0.869088 −0.0378581
\(528\) −14.6368 −0.636986
\(529\) −19.7631 −0.859265
\(530\) 21.9605 0.953905
\(531\) −0.290051 −0.0125871
\(532\) −48.2070 −2.09004
\(533\) −15.6406 −0.677470
\(534\) 9.54138 0.412896
\(535\) 17.0930 0.738993
\(536\) 29.4292 1.27115
\(537\) 18.1083 0.781429
\(538\) −27.1298 −1.16965
\(539\) −1.45891 −0.0628399
\(540\) −45.4056 −1.95394
\(541\) −36.1665 −1.55492 −0.777460 0.628933i \(-0.783492\pi\)
−0.777460 + 0.628933i \(0.783492\pi\)
\(542\) 66.6523 2.86296
\(543\) −27.5839 −1.18374
\(544\) 8.94467 0.383499
\(545\) 15.9285 0.682303
\(546\) 17.7405 0.759225
\(547\) −18.3970 −0.786598 −0.393299 0.919411i \(-0.628666\pi\)
−0.393299 + 0.919411i \(0.628666\pi\)
\(548\) 32.7209 1.39777
\(549\) −1.95767 −0.0835511
\(550\) 4.83591 0.206204
\(551\) 24.7593 1.05478
\(552\) −20.9321 −0.890929
\(553\) 21.9621 0.933922
\(554\) 9.01936 0.383196
\(555\) 4.93329 0.209406
\(556\) −89.6244 −3.80092
\(557\) 46.8486 1.98504 0.992519 0.122091i \(-0.0389600\pi\)
0.992519 + 0.122091i \(0.0389600\pi\)
\(558\) 0.674578 0.0285571
\(559\) 1.76785 0.0747721
\(560\) 37.1254 1.56884
\(561\) 1.64341 0.0693846
\(562\) −56.4190 −2.37989
\(563\) 35.9278 1.51418 0.757089 0.653312i \(-0.226621\pi\)
0.757089 + 0.653312i \(0.226621\pi\)
\(564\) 39.9261 1.68119
\(565\) 26.7423 1.12506
\(566\) 27.9712 1.17572
\(567\) 18.8618 0.792120
\(568\) 22.2778 0.934756
\(569\) 14.1740 0.594205 0.297102 0.954846i \(-0.403980\pi\)
0.297102 + 0.954846i \(0.403980\pi\)
\(570\) −32.6910 −1.36927
\(571\) −11.0064 −0.460603 −0.230302 0.973119i \(-0.573971\pi\)
−0.230302 + 0.973119i \(0.573971\pi\)
\(572\) −8.36039 −0.349565
\(573\) −26.7223 −1.11634
\(574\) 54.0238 2.25491
\(575\) 3.35400 0.139872
\(576\) −1.61284 −0.0672017
\(577\) 25.3508 1.05537 0.527684 0.849441i \(-0.323060\pi\)
0.527684 + 0.849441i \(0.323060\pi\)
\(578\) −2.59406 −0.107899
\(579\) 7.16544 0.297786
\(580\) −47.8808 −1.98814
\(581\) −23.6011 −0.979138
\(582\) −68.6954 −2.84752
\(583\) 4.78070 0.197996
\(584\) 68.2223 2.82306
\(585\) −0.936712 −0.0387283
\(586\) 58.8477 2.43098
\(587\) 37.7421 1.55778 0.778891 0.627159i \(-0.215782\pi\)
0.778891 + 0.627159i \(0.215782\pi\)
\(588\) 11.3385 0.467592
\(589\) 3.76353 0.155073
\(590\) 4.45284 0.183321
\(591\) −18.9843 −0.780909
\(592\) 15.0981 0.620527
\(593\) −31.7640 −1.30439 −0.652195 0.758051i \(-0.726152\pi\)
−0.652195 + 0.758051i \(0.726152\pi\)
\(594\) −14.0649 −0.577088
\(595\) −4.16840 −0.170888
\(596\) −100.035 −4.09760
\(597\) −25.3387 −1.03705
\(598\) −8.25067 −0.337395
\(599\) 4.36378 0.178299 0.0891497 0.996018i \(-0.471585\pi\)
0.0891497 + 0.996018i \(0.471585\pi\)
\(600\) −21.6894 −0.885465
\(601\) 40.7997 1.66425 0.832127 0.554585i \(-0.187123\pi\)
0.832127 + 0.554585i \(0.187123\pi\)
\(602\) −6.10628 −0.248873
\(603\) 1.24384 0.0506529
\(604\) −105.523 −4.29366
\(605\) −1.77081 −0.0719937
\(606\) 71.0836 2.88757
\(607\) −44.8498 −1.82040 −0.910198 0.414173i \(-0.864071\pi\)
−0.910198 + 0.414173i \(0.864071\pi\)
\(608\) −38.7343 −1.57088
\(609\) 22.1182 0.896275
\(610\) 30.0539 1.21685
\(611\) 9.08190 0.367414
\(612\) 1.41504 0.0571997
\(613\) 33.5626 1.35558 0.677790 0.735256i \(-0.262938\pi\)
0.677790 + 0.735256i \(0.262938\pi\)
\(614\) 18.1551 0.732682
\(615\) 25.7469 1.03822
\(616\) 16.6648 0.671445
\(617\) −7.63772 −0.307483 −0.153742 0.988111i \(-0.549132\pi\)
−0.153742 + 0.988111i \(0.549132\pi\)
\(618\) 72.0155 2.89689
\(619\) 23.7717 0.955467 0.477733 0.878505i \(-0.341458\pi\)
0.477733 + 0.878505i \(0.341458\pi\)
\(620\) −7.27809 −0.292295
\(621\) −9.75484 −0.391448
\(622\) 78.3963 3.14340
\(623\) −5.26847 −0.211077
\(624\) 25.8757 1.03586
\(625\) −12.2035 −0.488141
\(626\) 57.3545 2.29235
\(627\) −7.11666 −0.284212
\(628\) −2.40406 −0.0959325
\(629\) −1.69519 −0.0675918
\(630\) 3.23547 0.128904
\(631\) 7.42487 0.295579 0.147790 0.989019i \(-0.452784\pi\)
0.147790 + 0.989019i \(0.452784\pi\)
\(632\) 66.0510 2.62737
\(633\) −18.6730 −0.742187
\(634\) 62.7200 2.49093
\(635\) 24.7148 0.980777
\(636\) −37.1550 −1.47329
\(637\) 2.57914 0.102189
\(638\) −14.8316 −0.587188
\(639\) 0.941582 0.0372484
\(640\) −6.91840 −0.273474
\(641\) 26.3072 1.03907 0.519536 0.854448i \(-0.326105\pi\)
0.519536 + 0.854448i \(0.326105\pi\)
\(642\) −41.1499 −1.62406
\(643\) 12.5432 0.494657 0.247328 0.968932i \(-0.420447\pi\)
0.247328 + 0.968932i \(0.420447\pi\)
\(644\) 20.0283 0.789224
\(645\) −2.91016 −0.114587
\(646\) 11.2334 0.441972
\(647\) −30.4398 −1.19671 −0.598356 0.801231i \(-0.704179\pi\)
−0.598356 + 0.801231i \(0.704179\pi\)
\(648\) 56.7268 2.22844
\(649\) 0.969361 0.0380507
\(650\) −8.54917 −0.335326
\(651\) 3.36206 0.131770
\(652\) 101.216 3.96393
\(653\) 38.8313 1.51959 0.759793 0.650165i \(-0.225300\pi\)
0.759793 + 0.650165i \(0.225300\pi\)
\(654\) −38.3466 −1.49947
\(655\) −19.9746 −0.780470
\(656\) 78.7971 3.07651
\(657\) 2.88345 0.112494
\(658\) −31.3695 −1.22291
\(659\) 22.3417 0.870308 0.435154 0.900356i \(-0.356694\pi\)
0.435154 + 0.900356i \(0.356694\pi\)
\(660\) 13.7625 0.535705
\(661\) 9.03348 0.351362 0.175681 0.984447i \(-0.443787\pi\)
0.175681 + 0.984447i \(0.443787\pi\)
\(662\) 49.6264 1.92878
\(663\) −2.90529 −0.112832
\(664\) −70.9803 −2.75457
\(665\) 18.0510 0.699987
\(666\) 1.31579 0.0509859
\(667\) −10.2866 −0.398299
\(668\) −15.7666 −0.610028
\(669\) −37.7002 −1.45757
\(670\) −19.0953 −0.737715
\(671\) 6.54259 0.252574
\(672\) −34.6024 −1.33482
\(673\) −3.59899 −0.138731 −0.0693654 0.997591i \(-0.522097\pi\)
−0.0693654 + 0.997591i \(0.522097\pi\)
\(674\) 11.9231 0.459259
\(675\) −10.1078 −0.389048
\(676\) −46.6988 −1.79611
\(677\) 46.4096 1.78367 0.891833 0.452364i \(-0.149419\pi\)
0.891833 + 0.452364i \(0.149419\pi\)
\(678\) −64.3800 −2.47250
\(679\) 37.9316 1.45568
\(680\) −12.5365 −0.480752
\(681\) −35.8334 −1.37314
\(682\) −2.25446 −0.0863279
\(683\) 36.0032 1.37763 0.688813 0.724939i \(-0.258132\pi\)
0.688813 + 0.724939i \(0.258132\pi\)
\(684\) −6.12775 −0.234300
\(685\) −12.2523 −0.468135
\(686\) −51.6525 −1.97210
\(687\) −13.8005 −0.526524
\(688\) −8.90639 −0.339553
\(689\) −8.45156 −0.321979
\(690\) 13.5819 0.517055
\(691\) 21.2682 0.809082 0.404541 0.914520i \(-0.367431\pi\)
0.404541 + 0.914520i \(0.367431\pi\)
\(692\) −100.027 −3.80246
\(693\) 0.704346 0.0267559
\(694\) −9.43477 −0.358139
\(695\) 33.5597 1.27299
\(696\) 66.5205 2.52145
\(697\) −8.84725 −0.335113
\(698\) −22.3345 −0.845375
\(699\) 17.1420 0.648368
\(700\) 20.7528 0.784383
\(701\) 34.3275 1.29653 0.648266 0.761414i \(-0.275495\pi\)
0.648266 + 0.761414i \(0.275495\pi\)
\(702\) 24.8645 0.938452
\(703\) 7.34093 0.276868
\(704\) 5.39018 0.203150
\(705\) −14.9502 −0.563059
\(706\) −4.67522 −0.175954
\(707\) −39.2503 −1.47616
\(708\) −7.53375 −0.283136
\(709\) 29.6094 1.11200 0.556002 0.831181i \(-0.312335\pi\)
0.556002 + 0.831181i \(0.312335\pi\)
\(710\) −14.4551 −0.542490
\(711\) 2.79167 0.104696
\(712\) −15.8449 −0.593814
\(713\) −1.56361 −0.0585576
\(714\) 10.0351 0.375554
\(715\) 3.13053 0.117075
\(716\) −52.1090 −1.94741
\(717\) 8.69594 0.324756
\(718\) 52.1072 1.94462
\(719\) −15.5793 −0.581009 −0.290504 0.956874i \(-0.593823\pi\)
−0.290504 + 0.956874i \(0.593823\pi\)
\(720\) 4.71914 0.175872
\(721\) −39.7648 −1.48092
\(722\) 0.641641 0.0238794
\(723\) 5.09378 0.189440
\(724\) 79.3765 2.95000
\(725\) −10.6588 −0.395857
\(726\) 4.26309 0.158218
\(727\) −25.7451 −0.954835 −0.477417 0.878677i \(-0.658427\pi\)
−0.477417 + 0.878677i \(0.658427\pi\)
\(728\) −29.4609 −1.09189
\(729\) 29.1290 1.07885
\(730\) −44.2665 −1.63838
\(731\) 1.00000 0.0369863
\(732\) −50.8482 −1.87940
\(733\) 14.8898 0.549968 0.274984 0.961449i \(-0.411327\pi\)
0.274984 + 0.961449i \(0.411327\pi\)
\(734\) 9.12672 0.336873
\(735\) −4.24567 −0.156604
\(736\) 16.0927 0.593184
\(737\) −4.15695 −0.153123
\(738\) 6.86714 0.252783
\(739\) −0.538480 −0.0198083 −0.00990415 0.999951i \(-0.503153\pi\)
−0.00990415 + 0.999951i \(0.503153\pi\)
\(740\) −14.1962 −0.521864
\(741\) 12.5812 0.462181
\(742\) 29.1923 1.07168
\(743\) 7.30325 0.267930 0.133965 0.990986i \(-0.457229\pi\)
0.133965 + 0.990986i \(0.457229\pi\)
\(744\) 10.1114 0.370702
\(745\) 37.4579 1.37235
\(746\) 22.0832 0.808523
\(747\) −3.00001 −0.109765
\(748\) −4.72913 −0.172914
\(749\) 22.7218 0.830236
\(750\) 51.8189 1.89216
\(751\) −13.3879 −0.488530 −0.244265 0.969709i \(-0.578547\pi\)
−0.244265 + 0.969709i \(0.578547\pi\)
\(752\) −45.7544 −1.66849
\(753\) 34.9417 1.27335
\(754\) 26.2200 0.954876
\(755\) 39.5128 1.43802
\(756\) −60.3579 −2.19520
\(757\) 29.8102 1.08347 0.541736 0.840549i \(-0.317767\pi\)
0.541736 + 0.840549i \(0.317767\pi\)
\(758\) −62.9811 −2.28758
\(759\) 2.95671 0.107322
\(760\) 54.2884 1.96925
\(761\) 3.68559 0.133602 0.0668012 0.997766i \(-0.478721\pi\)
0.0668012 + 0.997766i \(0.478721\pi\)
\(762\) −59.4989 −2.15542
\(763\) 21.1739 0.766546
\(764\) 76.8972 2.78204
\(765\) −0.529860 −0.0191571
\(766\) 68.9525 2.49136
\(767\) −1.71368 −0.0618776
\(768\) 34.3720 1.24029
\(769\) 0.646832 0.0233253 0.0116627 0.999932i \(-0.496288\pi\)
0.0116627 + 0.999932i \(0.496288\pi\)
\(770\) −10.8131 −0.389676
\(771\) −46.4471 −1.67275
\(772\) −20.6196 −0.742114
\(773\) −47.1254 −1.69498 −0.847491 0.530809i \(-0.821888\pi\)
−0.847491 + 0.530809i \(0.821888\pi\)
\(774\) −0.776190 −0.0278996
\(775\) −1.62018 −0.0581985
\(776\) 114.079 4.09521
\(777\) 6.55785 0.235262
\(778\) −76.7382 −2.75120
\(779\) 38.3124 1.37268
\(780\) −24.3301 −0.871156
\(781\) −3.14680 −0.112601
\(782\) −4.66707 −0.166894
\(783\) 31.0001 1.10785
\(784\) −12.9937 −0.464059
\(785\) 0.900195 0.0321293
\(786\) 48.0871 1.71521
\(787\) 18.0132 0.642101 0.321050 0.947062i \(-0.395964\pi\)
0.321050 + 0.947062i \(0.395964\pi\)
\(788\) 54.6299 1.94611
\(789\) 5.25553 0.187102
\(790\) −42.8576 −1.52480
\(791\) 35.5488 1.26397
\(792\) 2.11832 0.0752713
\(793\) −11.5663 −0.410732
\(794\) −12.3050 −0.436689
\(795\) 13.9126 0.493429
\(796\) 72.9158 2.58443
\(797\) 54.1709 1.91883 0.959416 0.281994i \(-0.0909957\pi\)
0.959416 + 0.281994i \(0.0909957\pi\)
\(798\) −43.4563 −1.53834
\(799\) 5.13726 0.181743
\(800\) 16.6749 0.589547
\(801\) −0.669693 −0.0236624
\(802\) −6.89459 −0.243456
\(803\) −9.63659 −0.340068
\(804\) 32.3073 1.13939
\(805\) −7.49953 −0.264324
\(806\) 3.98555 0.140385
\(807\) −17.1874 −0.605027
\(808\) −118.045 −4.15282
\(809\) −37.3147 −1.31191 −0.655957 0.754798i \(-0.727735\pi\)
−0.655957 + 0.754798i \(0.727735\pi\)
\(810\) −36.8075 −1.29328
\(811\) −10.7021 −0.375802 −0.187901 0.982188i \(-0.560168\pi\)
−0.187901 + 0.982188i \(0.560168\pi\)
\(812\) −63.6482 −2.23361
\(813\) 42.2261 1.48093
\(814\) −4.39743 −0.154130
\(815\) −37.9002 −1.32758
\(816\) 14.6368 0.512391
\(817\) −4.33043 −0.151503
\(818\) 51.2181 1.79080
\(819\) −1.24518 −0.0435100
\(820\) −74.0903 −2.58735
\(821\) −30.5621 −1.06662 −0.533312 0.845919i \(-0.679053\pi\)
−0.533312 + 0.845919i \(0.679053\pi\)
\(822\) 29.4964 1.02880
\(823\) 4.44634 0.154990 0.0774949 0.996993i \(-0.475308\pi\)
0.0774949 + 0.996993i \(0.475308\pi\)
\(824\) −119.593 −4.16621
\(825\) 3.06368 0.106664
\(826\) 5.91919 0.205955
\(827\) 45.4792 1.58147 0.790734 0.612160i \(-0.209699\pi\)
0.790734 + 0.612160i \(0.209699\pi\)
\(828\) 2.54586 0.0884747
\(829\) −19.7929 −0.687435 −0.343718 0.939073i \(-0.611686\pi\)
−0.343718 + 0.939073i \(0.611686\pi\)
\(830\) 46.0560 1.59863
\(831\) 5.71401 0.198217
\(832\) −9.52903 −0.330360
\(833\) 1.45891 0.0505484
\(834\) −80.7922 −2.79760
\(835\) 5.90376 0.204308
\(836\) 20.4792 0.708287
\(837\) 4.71216 0.162876
\(838\) −70.5159 −2.43593
\(839\) 31.8806 1.10064 0.550321 0.834953i \(-0.314506\pi\)
0.550321 + 0.834953i \(0.314506\pi\)
\(840\) 48.4973 1.67332
\(841\) 3.69006 0.127243
\(842\) 28.3450 0.976834
\(843\) −35.7430 −1.23105
\(844\) 53.7343 1.84961
\(845\) 17.4862 0.601545
\(846\) −3.98749 −0.137093
\(847\) −2.35395 −0.0808827
\(848\) 42.5788 1.46216
\(849\) 17.7205 0.608167
\(850\) −4.83591 −0.165870
\(851\) −3.04989 −0.104549
\(852\) 24.4565 0.837867
\(853\) 13.5097 0.462562 0.231281 0.972887i \(-0.425708\pi\)
0.231281 + 0.972887i \(0.425708\pi\)
\(854\) 39.9509 1.36709
\(855\) 2.29452 0.0784710
\(856\) 68.3358 2.33567
\(857\) −12.4690 −0.425932 −0.212966 0.977060i \(-0.568312\pi\)
−0.212966 + 0.977060i \(0.568312\pi\)
\(858\) −7.53650 −0.257292
\(859\) −15.8552 −0.540974 −0.270487 0.962724i \(-0.587185\pi\)
−0.270487 + 0.962724i \(0.587185\pi\)
\(860\) 8.37439 0.285564
\(861\) 34.2255 1.16640
\(862\) 63.0857 2.14871
\(863\) 18.7812 0.639320 0.319660 0.947532i \(-0.396431\pi\)
0.319660 + 0.947532i \(0.396431\pi\)
\(864\) −48.4976 −1.64992
\(865\) 37.4549 1.27351
\(866\) 44.1079 1.49885
\(867\) −1.64341 −0.0558130
\(868\) −9.67481 −0.328384
\(869\) −9.32988 −0.316494
\(870\) −43.1623 −1.46334
\(871\) 7.34886 0.249007
\(872\) 63.6805 2.15649
\(873\) 4.82161 0.163187
\(874\) 20.2104 0.683628
\(875\) −28.6129 −0.967291
\(876\) 74.8943 2.53045
\(877\) −5.90719 −0.199472 −0.0997358 0.995014i \(-0.531800\pi\)
−0.0997358 + 0.995014i \(0.531800\pi\)
\(878\) 25.3010 0.853868
\(879\) 37.2816 1.25748
\(880\) −15.7715 −0.531659
\(881\) 9.71106 0.327174 0.163587 0.986529i \(-0.447694\pi\)
0.163587 + 0.986529i \(0.447694\pi\)
\(882\) −1.13239 −0.0381297
\(883\) 25.3470 0.852994 0.426497 0.904489i \(-0.359747\pi\)
0.426497 + 0.904489i \(0.359747\pi\)
\(884\) 8.36039 0.281190
\(885\) 2.82100 0.0948268
\(886\) −32.3953 −1.08834
\(887\) −30.2617 −1.01609 −0.508044 0.861331i \(-0.669631\pi\)
−0.508044 + 0.861331i \(0.669631\pi\)
\(888\) 19.7228 0.661852
\(889\) 32.8536 1.10187
\(890\) 10.2811 0.344623
\(891\) −8.01281 −0.268439
\(892\) 108.488 3.63243
\(893\) −22.2465 −0.744452
\(894\) −90.1769 −3.01597
\(895\) 19.5121 0.652218
\(896\) −9.19667 −0.307239
\(897\) −5.22703 −0.174525
\(898\) 83.4701 2.78543
\(899\) 4.96903 0.165726
\(900\) 2.63796 0.0879321
\(901\) −4.78070 −0.159268
\(902\) −22.9503 −0.764160
\(903\) −3.86850 −0.128735
\(904\) 106.913 3.55587
\(905\) −29.7223 −0.988004
\(906\) −95.1239 −3.16028
\(907\) −21.9127 −0.727598 −0.363799 0.931477i \(-0.618521\pi\)
−0.363799 + 0.931477i \(0.618521\pi\)
\(908\) 103.116 3.42201
\(909\) −4.98923 −0.165482
\(910\) 19.1159 0.633685
\(911\) 51.0713 1.69207 0.846034 0.533129i \(-0.178984\pi\)
0.846034 + 0.533129i \(0.178984\pi\)
\(912\) −63.3838 −2.09885
\(913\) 10.0262 0.331817
\(914\) −25.9855 −0.859525
\(915\) 19.0400 0.629443
\(916\) 39.7130 1.31215
\(917\) −26.5523 −0.876835
\(918\) 14.0649 0.464209
\(919\) 45.7616 1.50954 0.754769 0.655991i \(-0.227749\pi\)
0.754769 + 0.655991i \(0.227749\pi\)
\(920\) −22.5549 −0.743612
\(921\) 11.5018 0.378996
\(922\) −53.2918 −1.75507
\(923\) 5.56307 0.183111
\(924\) 18.2946 0.601849
\(925\) −3.16023 −0.103908
\(926\) 64.7664 2.12836
\(927\) −5.05464 −0.166016
\(928\) −51.1413 −1.67880
\(929\) −38.3311 −1.25760 −0.628801 0.777566i \(-0.716454\pi\)
−0.628801 + 0.777566i \(0.716454\pi\)
\(930\) −6.56085 −0.215139
\(931\) −6.31773 −0.207055
\(932\) −49.3284 −1.61580
\(933\) 49.6662 1.62600
\(934\) 35.5671 1.16379
\(935\) 1.77081 0.0579117
\(936\) −3.74487 −0.122405
\(937\) −39.5695 −1.29268 −0.646340 0.763050i \(-0.723701\pi\)
−0.646340 + 0.763050i \(0.723701\pi\)
\(938\) −25.3835 −0.828800
\(939\) 36.3357 1.18577
\(940\) 43.0214 1.40320
\(941\) 15.1877 0.495105 0.247553 0.968874i \(-0.420374\pi\)
0.247553 + 0.968874i \(0.420374\pi\)
\(942\) −2.16715 −0.0706095
\(943\) −15.9174 −0.518342
\(944\) 8.63351 0.280997
\(945\) 22.6009 0.735207
\(946\) 2.59406 0.0843400
\(947\) −28.4202 −0.923533 −0.461766 0.887002i \(-0.652784\pi\)
−0.461766 + 0.887002i \(0.652784\pi\)
\(948\) 72.5106 2.35504
\(949\) 17.0360 0.553013
\(950\) 20.9416 0.679435
\(951\) 39.7348 1.28849
\(952\) −16.6648 −0.540110
\(953\) 35.4448 1.14817 0.574084 0.818796i \(-0.305358\pi\)
0.574084 + 0.818796i \(0.305358\pi\)
\(954\) 3.71073 0.120139
\(955\) −28.7940 −0.931752
\(956\) −25.0238 −0.809327
\(957\) −9.39621 −0.303736
\(958\) −49.9575 −1.61405
\(959\) −16.2870 −0.525936
\(960\) 15.6863 0.506273
\(961\) −30.2447 −0.975635
\(962\) 7.77400 0.250644
\(963\) 2.88824 0.0930723
\(964\) −14.6581 −0.472104
\(965\) 7.72095 0.248546
\(966\) 18.0545 0.580895
\(967\) 9.20500 0.296013 0.148006 0.988986i \(-0.452714\pi\)
0.148006 + 0.988986i \(0.452714\pi\)
\(968\) −7.07951 −0.227544
\(969\) 7.11666 0.228620
\(970\) −74.0210 −2.37667
\(971\) 36.1652 1.16060 0.580299 0.814404i \(-0.302936\pi\)
0.580299 + 0.814404i \(0.302936\pi\)
\(972\) −14.6488 −0.469859
\(973\) 44.6111 1.43017
\(974\) −52.7521 −1.69028
\(975\) −5.41613 −0.173455
\(976\) 58.2709 1.86521
\(977\) 39.7847 1.27283 0.636413 0.771348i \(-0.280417\pi\)
0.636413 + 0.771348i \(0.280417\pi\)
\(978\) 91.2416 2.91758
\(979\) 2.23814 0.0715312
\(980\) 12.2175 0.390274
\(981\) 2.69148 0.0859325
\(982\) 93.5929 2.98667
\(983\) 9.58359 0.305669 0.152835 0.988252i \(-0.451160\pi\)
0.152835 + 0.988252i \(0.451160\pi\)
\(984\) 102.933 3.28139
\(985\) −20.4561 −0.651784
\(986\) 14.8316 0.472334
\(987\) −19.8735 −0.632579
\(988\) −36.2041 −1.15181
\(989\) 1.79914 0.0572093
\(990\) −1.37449 −0.0436840
\(991\) 46.2252 1.46839 0.734196 0.678938i \(-0.237559\pi\)
0.734196 + 0.678938i \(0.237559\pi\)
\(992\) −7.77370 −0.246815
\(993\) 31.4397 0.997707
\(994\) −19.2153 −0.609471
\(995\) −27.3031 −0.865568
\(996\) −77.9220 −2.46905
\(997\) −21.1554 −0.669997 −0.334999 0.942219i \(-0.608736\pi\)
−0.334999 + 0.942219i \(0.608736\pi\)
\(998\) −98.7403 −3.12557
\(999\) 9.19127 0.290799
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 \(a_p\))