Properties

Label 8041.2.a.g.1.18
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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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 1.18
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} +O(q^{10})\) \(q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} -6.44038 q^{10} -1.00000 q^{11} -2.31207 q^{12} +0.566187 q^{13} +7.00579 q^{14} -10.1734 q^{15} -4.98171 q^{16} +1.00000 q^{17} -7.02125 q^{18} -4.77018 q^{19} +3.29053 q^{20} +11.0666 q^{21} +1.69256 q^{22} -4.27889 q^{23} -5.13725 q^{24} +9.47885 q^{25} -0.958308 q^{26} -3.07012 q^{27} -3.57941 q^{28} +0.147169 q^{29} +17.2192 q^{30} +5.78533 q^{31} +4.58895 q^{32} +2.67363 q^{33} -1.69256 q^{34} -15.7500 q^{35} +3.58731 q^{36} -4.53620 q^{37} +8.07382 q^{38} -1.51378 q^{39} +7.31133 q^{40} -3.65027 q^{41} -18.7309 q^{42} +1.00000 q^{43} -0.864767 q^{44} +15.7847 q^{45} +7.24229 q^{46} +10.5702 q^{47} +13.3193 q^{48} +10.1327 q^{49} -16.0435 q^{50} -2.67363 q^{51} +0.489620 q^{52} +12.0128 q^{53} +5.19637 q^{54} -3.80511 q^{55} -7.95320 q^{56} +12.7537 q^{57} -0.249092 q^{58} -12.3631 q^{59} -8.79767 q^{60} +4.08696 q^{61} -9.79203 q^{62} -17.1705 q^{63} +2.19633 q^{64} +2.15440 q^{65} -4.52529 q^{66} -5.44219 q^{67} +0.864767 q^{68} +11.4402 q^{69} +26.6578 q^{70} +7.93867 q^{71} +7.97075 q^{72} -8.98575 q^{73} +7.67781 q^{74} -25.3429 q^{75} -4.12509 q^{76} +4.13916 q^{77} +2.56216 q^{78} -5.18424 q^{79} -18.9560 q^{80} -4.23653 q^{81} +6.17831 q^{82} +0.350834 q^{83} +9.57002 q^{84} +3.80511 q^{85} -1.69256 q^{86} -0.393475 q^{87} -1.92145 q^{88} +7.41740 q^{89} -26.7166 q^{90} -2.34354 q^{91} -3.70024 q^{92} -15.4678 q^{93} -17.8907 q^{94} -18.1510 q^{95} -12.2692 q^{96} +2.23033 q^{97} -17.1501 q^{98} -4.14830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69256 −1.19682 −0.598411 0.801189i \(-0.704201\pi\)
−0.598411 + 0.801189i \(0.704201\pi\)
\(3\) −2.67363 −1.54362 −0.771810 0.635853i \(-0.780649\pi\)
−0.771810 + 0.635853i \(0.780649\pi\)
\(4\) 0.864767 0.432384
\(5\) 3.80511 1.70170 0.850848 0.525412i \(-0.176089\pi\)
0.850848 + 0.525412i \(0.176089\pi\)
\(6\) 4.52529 1.84744
\(7\) −4.13916 −1.56446 −0.782228 0.622992i \(-0.785917\pi\)
−0.782228 + 0.622992i \(0.785917\pi\)
\(8\) 1.92145 0.679336
\(9\) 4.14830 1.38277
\(10\) −6.44038 −2.03663
\(11\) −1.00000 −0.301511
\(12\) −2.31207 −0.667437
\(13\) 0.566187 0.157032 0.0785161 0.996913i \(-0.474982\pi\)
0.0785161 + 0.996913i \(0.474982\pi\)
\(14\) 7.00579 1.87238
\(15\) −10.1734 −2.62677
\(16\) −4.98171 −1.24543
\(17\) 1.00000 0.242536
\(18\) −7.02125 −1.65492
\(19\) −4.77018 −1.09435 −0.547177 0.837017i \(-0.684297\pi\)
−0.547177 + 0.837017i \(0.684297\pi\)
\(20\) 3.29053 0.735786
\(21\) 11.0666 2.41493
\(22\) 1.69256 0.360856
\(23\) −4.27889 −0.892210 −0.446105 0.894981i \(-0.647189\pi\)
−0.446105 + 0.894981i \(0.647189\pi\)
\(24\) −5.13725 −1.04864
\(25\) 9.47885 1.89577
\(26\) −0.958308 −0.187940
\(27\) −3.07012 −0.590845
\(28\) −3.57941 −0.676445
\(29\) 0.147169 0.0273286 0.0136643 0.999907i \(-0.495650\pi\)
0.0136643 + 0.999907i \(0.495650\pi\)
\(30\) 17.2192 3.14378
\(31\) 5.78533 1.03908 0.519538 0.854447i \(-0.326104\pi\)
0.519538 + 0.854447i \(0.326104\pi\)
\(32\) 4.58895 0.811220
\(33\) 2.67363 0.465419
\(34\) −1.69256 −0.290272
\(35\) −15.7500 −2.66223
\(36\) 3.58731 0.597885
\(37\) −4.53620 −0.745747 −0.372874 0.927882i \(-0.621628\pi\)
−0.372874 + 0.927882i \(0.621628\pi\)
\(38\) 8.07382 1.30975
\(39\) −1.51378 −0.242398
\(40\) 7.31133 1.15602
\(41\) −3.65027 −0.570076 −0.285038 0.958516i \(-0.592006\pi\)
−0.285038 + 0.958516i \(0.592006\pi\)
\(42\) −18.7309 −2.89024
\(43\) 1.00000 0.152499
\(44\) −0.864767 −0.130369
\(45\) 15.7847 2.35305
\(46\) 7.24229 1.06782
\(47\) 10.5702 1.54182 0.770908 0.636946i \(-0.219803\pi\)
0.770908 + 0.636946i \(0.219803\pi\)
\(48\) 13.3193 1.92247
\(49\) 10.1327 1.44752
\(50\) −16.0435 −2.26890
\(51\) −2.67363 −0.374383
\(52\) 0.489620 0.0678981
\(53\) 12.0128 1.65008 0.825040 0.565075i \(-0.191153\pi\)
0.825040 + 0.565075i \(0.191153\pi\)
\(54\) 5.19637 0.707136
\(55\) −3.80511 −0.513081
\(56\) −7.95320 −1.06279
\(57\) 12.7537 1.68927
\(58\) −0.249092 −0.0327074
\(59\) −12.3631 −1.60953 −0.804766 0.593592i \(-0.797709\pi\)
−0.804766 + 0.593592i \(0.797709\pi\)
\(60\) −8.79767 −1.13577
\(61\) 4.08696 0.523282 0.261641 0.965165i \(-0.415736\pi\)
0.261641 + 0.965165i \(0.415736\pi\)
\(62\) −9.79203 −1.24359
\(63\) −17.1705 −2.16328
\(64\) 2.19633 0.274542
\(65\) 2.15440 0.267221
\(66\) −4.52529 −0.557024
\(67\) −5.44219 −0.664870 −0.332435 0.943126i \(-0.607870\pi\)
−0.332435 + 0.943126i \(0.607870\pi\)
\(68\) 0.864767 0.104868
\(69\) 11.4402 1.37723
\(70\) 26.6578 3.18621
\(71\) 7.93867 0.942147 0.471073 0.882094i \(-0.343867\pi\)
0.471073 + 0.882094i \(0.343867\pi\)
\(72\) 7.97075 0.939362
\(73\) −8.98575 −1.05170 −0.525851 0.850576i \(-0.676253\pi\)
−0.525851 + 0.850576i \(0.676253\pi\)
\(74\) 7.67781 0.892527
\(75\) −25.3429 −2.92635
\(76\) −4.12509 −0.473181
\(77\) 4.13916 0.471701
\(78\) 2.56216 0.290107
\(79\) −5.18424 −0.583272 −0.291636 0.956529i \(-0.594200\pi\)
−0.291636 + 0.956529i \(0.594200\pi\)
\(80\) −18.9560 −2.11934
\(81\) −4.23653 −0.470725
\(82\) 6.17831 0.682280
\(83\) 0.350834 0.0385091 0.0192545 0.999815i \(-0.493871\pi\)
0.0192545 + 0.999815i \(0.493871\pi\)
\(84\) 9.57002 1.04417
\(85\) 3.80511 0.412722
\(86\) −1.69256 −0.182514
\(87\) −0.393475 −0.0421849
\(88\) −1.92145 −0.204827
\(89\) 7.41740 0.786243 0.393121 0.919487i \(-0.371395\pi\)
0.393121 + 0.919487i \(0.371395\pi\)
\(90\) −26.7166 −2.81618
\(91\) −2.34354 −0.245670
\(92\) −3.70024 −0.385777
\(93\) −15.4678 −1.60394
\(94\) −17.8907 −1.84528
\(95\) −18.1510 −1.86226
\(96\) −12.2692 −1.25222
\(97\) 2.23033 0.226456 0.113228 0.993569i \(-0.463881\pi\)
0.113228 + 0.993569i \(0.463881\pi\)
\(98\) −17.1501 −1.73243
\(99\) −4.14830 −0.416919
\(100\) 8.19700 0.819700
\(101\) −10.5697 −1.05173 −0.525863 0.850569i \(-0.676258\pi\)
−0.525863 + 0.850569i \(0.676258\pi\)
\(102\) 4.52529 0.448070
\(103\) −12.0753 −1.18981 −0.594906 0.803795i \(-0.702811\pi\)
−0.594906 + 0.803795i \(0.702811\pi\)
\(104\) 1.08790 0.106678
\(105\) 42.1095 4.10947
\(106\) −20.3323 −1.97485
\(107\) 9.25700 0.894908 0.447454 0.894307i \(-0.352331\pi\)
0.447454 + 0.894307i \(0.352331\pi\)
\(108\) −2.65494 −0.255472
\(109\) −9.76140 −0.934973 −0.467486 0.884000i \(-0.654840\pi\)
−0.467486 + 0.884000i \(0.654840\pi\)
\(110\) 6.44038 0.614066
\(111\) 12.1281 1.15115
\(112\) 20.6201 1.94842
\(113\) 13.2203 1.24366 0.621830 0.783152i \(-0.286389\pi\)
0.621830 + 0.783152i \(0.286389\pi\)
\(114\) −21.5864 −2.02175
\(115\) −16.2816 −1.51827
\(116\) 0.127267 0.0118164
\(117\) 2.34871 0.217139
\(118\) 20.9252 1.92632
\(119\) −4.13916 −0.379436
\(120\) −19.5478 −1.78446
\(121\) 1.00000 0.0909091
\(122\) −6.91744 −0.626276
\(123\) 9.75947 0.879982
\(124\) 5.00297 0.449280
\(125\) 17.0425 1.52433
\(126\) 29.0621 2.58906
\(127\) −4.82113 −0.427807 −0.213903 0.976855i \(-0.568618\pi\)
−0.213903 + 0.976855i \(0.568618\pi\)
\(128\) −12.8953 −1.13980
\(129\) −2.67363 −0.235400
\(130\) −3.64646 −0.319816
\(131\) 14.4913 1.26611 0.633053 0.774108i \(-0.281801\pi\)
0.633053 + 0.774108i \(0.281801\pi\)
\(132\) 2.31207 0.201240
\(133\) 19.7445 1.71207
\(134\) 9.21125 0.795731
\(135\) −11.6821 −1.00544
\(136\) 1.92145 0.164763
\(137\) 21.5445 1.84067 0.920337 0.391126i \(-0.127914\pi\)
0.920337 + 0.391126i \(0.127914\pi\)
\(138\) −19.3632 −1.64830
\(139\) −0.640466 −0.0543236 −0.0271618 0.999631i \(-0.508647\pi\)
−0.0271618 + 0.999631i \(0.508647\pi\)
\(140\) −13.6200 −1.15110
\(141\) −28.2607 −2.37998
\(142\) −13.4367 −1.12758
\(143\) −0.566187 −0.0473470
\(144\) −20.6656 −1.72213
\(145\) 0.559993 0.0465049
\(146\) 15.2089 1.25870
\(147\) −27.0910 −2.23443
\(148\) −3.92276 −0.322449
\(149\) −5.74175 −0.470382 −0.235191 0.971949i \(-0.575572\pi\)
−0.235191 + 0.971949i \(0.575572\pi\)
\(150\) 42.8945 3.50232
\(151\) −13.5127 −1.09964 −0.549822 0.835282i \(-0.685305\pi\)
−0.549822 + 0.835282i \(0.685305\pi\)
\(152\) −9.16566 −0.743434
\(153\) 4.14830 0.335370
\(154\) −7.00579 −0.564542
\(155\) 22.0138 1.76819
\(156\) −1.30906 −0.104809
\(157\) 6.53418 0.521484 0.260742 0.965409i \(-0.416033\pi\)
0.260742 + 0.965409i \(0.416033\pi\)
\(158\) 8.77464 0.698073
\(159\) −32.1177 −2.54710
\(160\) 17.4615 1.38045
\(161\) 17.7110 1.39582
\(162\) 7.17059 0.563375
\(163\) −0.906761 −0.0710230 −0.0355115 0.999369i \(-0.511306\pi\)
−0.0355115 + 0.999369i \(0.511306\pi\)
\(164\) −3.15663 −0.246492
\(165\) 10.1734 0.792002
\(166\) −0.593809 −0.0460885
\(167\) 6.82474 0.528114 0.264057 0.964507i \(-0.414939\pi\)
0.264057 + 0.964507i \(0.414939\pi\)
\(168\) 21.2639 1.64055
\(169\) −12.6794 −0.975341
\(170\) −6.44038 −0.493955
\(171\) −19.7881 −1.51323
\(172\) 0.864767 0.0659379
\(173\) 3.09668 0.235436 0.117718 0.993047i \(-0.462442\pi\)
0.117718 + 0.993047i \(0.462442\pi\)
\(174\) 0.665981 0.0504879
\(175\) −39.2345 −2.96585
\(176\) 4.98171 0.375511
\(177\) 33.0542 2.48451
\(178\) −12.5544 −0.940993
\(179\) 20.5027 1.53244 0.766222 0.642577i \(-0.222135\pi\)
0.766222 + 0.642577i \(0.222135\pi\)
\(180\) 13.6501 1.01742
\(181\) −25.3729 −1.88595 −0.942976 0.332861i \(-0.891986\pi\)
−0.942976 + 0.332861i \(0.891986\pi\)
\(182\) 3.96659 0.294023
\(183\) −10.9270 −0.807749
\(184\) −8.22168 −0.606110
\(185\) −17.2607 −1.26904
\(186\) 26.1803 1.91963
\(187\) −1.00000 −0.0731272
\(188\) 9.14073 0.666656
\(189\) 12.7077 0.924350
\(190\) 30.7218 2.22879
\(191\) −27.0934 −1.96041 −0.980203 0.197994i \(-0.936557\pi\)
−0.980203 + 0.197994i \(0.936557\pi\)
\(192\) −5.87218 −0.423788
\(193\) −12.1107 −0.871747 −0.435874 0.900008i \(-0.643561\pi\)
−0.435874 + 0.900008i \(0.643561\pi\)
\(194\) −3.77497 −0.271027
\(195\) −5.76008 −0.412488
\(196\) 8.76239 0.625885
\(197\) 10.5715 0.753186 0.376593 0.926379i \(-0.377096\pi\)
0.376593 + 0.926379i \(0.377096\pi\)
\(198\) 7.02125 0.498979
\(199\) 2.32393 0.164739 0.0823696 0.996602i \(-0.473751\pi\)
0.0823696 + 0.996602i \(0.473751\pi\)
\(200\) 18.2131 1.28786
\(201\) 14.5504 1.02631
\(202\) 17.8899 1.25873
\(203\) −0.609155 −0.0427543
\(204\) −2.31207 −0.161877
\(205\) −13.8897 −0.970096
\(206\) 20.4382 1.42399
\(207\) −17.7501 −1.23372
\(208\) −2.82058 −0.195572
\(209\) 4.77018 0.329960
\(210\) −71.2730 −4.91831
\(211\) −0.312375 −0.0215047 −0.0107524 0.999942i \(-0.503423\pi\)
−0.0107524 + 0.999942i \(0.503423\pi\)
\(212\) 10.3882 0.713467
\(213\) −21.2251 −1.45432
\(214\) −15.6681 −1.07105
\(215\) 3.80511 0.259506
\(216\) −5.89909 −0.401382
\(217\) −23.9464 −1.62559
\(218\) 16.5218 1.11900
\(219\) 24.0246 1.62343
\(220\) −3.29053 −0.221848
\(221\) 0.566187 0.0380859
\(222\) −20.5276 −1.37772
\(223\) −8.77479 −0.587604 −0.293802 0.955866i \(-0.594921\pi\)
−0.293802 + 0.955866i \(0.594921\pi\)
\(224\) −18.9944 −1.26912
\(225\) 39.3211 2.62140
\(226\) −22.3762 −1.48844
\(227\) 26.6838 1.77107 0.885533 0.464577i \(-0.153794\pi\)
0.885533 + 0.464577i \(0.153794\pi\)
\(228\) 11.0290 0.730411
\(229\) 4.66016 0.307952 0.153976 0.988075i \(-0.450792\pi\)
0.153976 + 0.988075i \(0.450792\pi\)
\(230\) 27.5577 1.81710
\(231\) −11.0666 −0.728128
\(232\) 0.282778 0.0185653
\(233\) 16.0876 1.05393 0.526966 0.849887i \(-0.323330\pi\)
0.526966 + 0.849887i \(0.323330\pi\)
\(234\) −3.97534 −0.259876
\(235\) 40.2206 2.62370
\(236\) −10.6912 −0.695936
\(237\) 13.8607 0.900351
\(238\) 7.00579 0.454118
\(239\) −22.5661 −1.45968 −0.729839 0.683619i \(-0.760405\pi\)
−0.729839 + 0.683619i \(0.760405\pi\)
\(240\) 50.6812 3.27146
\(241\) 5.46713 0.352169 0.176085 0.984375i \(-0.443657\pi\)
0.176085 + 0.984375i \(0.443657\pi\)
\(242\) −1.69256 −0.108802
\(243\) 20.5373 1.31747
\(244\) 3.53427 0.226259
\(245\) 38.5558 2.46324
\(246\) −16.5185 −1.05318
\(247\) −2.70081 −0.171849
\(248\) 11.1162 0.705882
\(249\) −0.938001 −0.0594434
\(250\) −28.8455 −1.82435
\(251\) 15.7966 0.997075 0.498537 0.866868i \(-0.333871\pi\)
0.498537 + 0.866868i \(0.333871\pi\)
\(252\) −14.8485 −0.935365
\(253\) 4.27889 0.269011
\(254\) 8.16007 0.512008
\(255\) −10.1734 −0.637086
\(256\) 17.4335 1.08959
\(257\) −13.7929 −0.860375 −0.430188 0.902740i \(-0.641553\pi\)
−0.430188 + 0.902740i \(0.641553\pi\)
\(258\) 4.52529 0.281732
\(259\) 18.7761 1.16669
\(260\) 1.86306 0.115542
\(261\) 0.610500 0.0377890
\(262\) −24.5274 −1.51530
\(263\) 11.5605 0.712851 0.356425 0.934324i \(-0.383995\pi\)
0.356425 + 0.934324i \(0.383995\pi\)
\(264\) 5.13725 0.316176
\(265\) 45.7098 2.80793
\(266\) −33.4188 −2.04904
\(267\) −19.8314 −1.21366
\(268\) −4.70623 −0.287479
\(269\) 24.4717 1.49206 0.746032 0.665910i \(-0.231956\pi\)
0.746032 + 0.665910i \(0.231956\pi\)
\(270\) 19.7727 1.20333
\(271\) −12.8118 −0.778264 −0.389132 0.921182i \(-0.627225\pi\)
−0.389132 + 0.921182i \(0.627225\pi\)
\(272\) −4.98171 −0.302061
\(273\) 6.26576 0.379221
\(274\) −36.4655 −2.20296
\(275\) −9.47885 −0.571596
\(276\) 9.89308 0.595494
\(277\) −2.23587 −0.134340 −0.0671701 0.997742i \(-0.521397\pi\)
−0.0671701 + 0.997742i \(0.521397\pi\)
\(278\) 1.08403 0.0650157
\(279\) 23.9993 1.43680
\(280\) −30.2628 −1.80855
\(281\) 13.8679 0.827291 0.413645 0.910438i \(-0.364255\pi\)
0.413645 + 0.910438i \(0.364255\pi\)
\(282\) 47.8330 2.84841
\(283\) 26.6579 1.58465 0.792324 0.610100i \(-0.208871\pi\)
0.792324 + 0.610100i \(0.208871\pi\)
\(284\) 6.86510 0.407369
\(285\) 48.5291 2.87462
\(286\) 0.958308 0.0566659
\(287\) 15.1090 0.891859
\(288\) 19.0363 1.12173
\(289\) 1.00000 0.0588235
\(290\) −0.947824 −0.0556581
\(291\) −5.96308 −0.349562
\(292\) −7.77059 −0.454739
\(293\) −5.39173 −0.314988 −0.157494 0.987520i \(-0.550342\pi\)
−0.157494 + 0.987520i \(0.550342\pi\)
\(294\) 45.8531 2.67421
\(295\) −47.0428 −2.73894
\(296\) −8.71610 −0.506613
\(297\) 3.07012 0.178146
\(298\) 9.71827 0.562964
\(299\) −2.42265 −0.140106
\(300\) −21.9157 −1.26531
\(301\) −4.13916 −0.238577
\(302\) 22.8710 1.31608
\(303\) 28.2595 1.62347
\(304\) 23.7636 1.36294
\(305\) 15.5513 0.890467
\(306\) −7.02125 −0.401378
\(307\) 1.22157 0.0697187 0.0348594 0.999392i \(-0.488902\pi\)
0.0348594 + 0.999392i \(0.488902\pi\)
\(308\) 3.57941 0.203956
\(309\) 32.2848 1.83662
\(310\) −37.2597 −2.11621
\(311\) 15.3395 0.869826 0.434913 0.900473i \(-0.356779\pi\)
0.434913 + 0.900473i \(0.356779\pi\)
\(312\) −2.90865 −0.164670
\(313\) −17.9688 −1.01566 −0.507829 0.861458i \(-0.669552\pi\)
−0.507829 + 0.861458i \(0.669552\pi\)
\(314\) −11.0595 −0.624124
\(315\) −65.3355 −3.68124
\(316\) −4.48316 −0.252197
\(317\) −22.4926 −1.26331 −0.631655 0.775250i \(-0.717624\pi\)
−0.631655 + 0.775250i \(0.717624\pi\)
\(318\) 54.3612 3.04842
\(319\) −0.147169 −0.00823987
\(320\) 8.35728 0.467186
\(321\) −24.7498 −1.38140
\(322\) −29.9770 −1.67055
\(323\) −4.77018 −0.265420
\(324\) −3.66361 −0.203534
\(325\) 5.36680 0.297697
\(326\) 1.53475 0.0850019
\(327\) 26.0984 1.44324
\(328\) −7.01382 −0.387273
\(329\) −43.7516 −2.41210
\(330\) −17.2192 −0.947886
\(331\) −14.5342 −0.798874 −0.399437 0.916761i \(-0.630794\pi\)
−0.399437 + 0.916761i \(0.630794\pi\)
\(332\) 0.303390 0.0166507
\(333\) −18.8175 −1.03119
\(334\) −11.5513 −0.632059
\(335\) −20.7081 −1.13141
\(336\) −55.1305 −3.00762
\(337\) 25.9485 1.41351 0.706753 0.707460i \(-0.250159\pi\)
0.706753 + 0.707460i \(0.250159\pi\)
\(338\) 21.4607 1.16731
\(339\) −35.3462 −1.91974
\(340\) 3.29053 0.178454
\(341\) −5.78533 −0.313293
\(342\) 33.4926 1.81107
\(343\) −12.9666 −0.700128
\(344\) 1.92145 0.103598
\(345\) 43.5311 2.34363
\(346\) −5.24132 −0.281775
\(347\) 8.43818 0.452985 0.226493 0.974013i \(-0.427274\pi\)
0.226493 + 0.974013i \(0.427274\pi\)
\(348\) −0.340264 −0.0182401
\(349\) 11.7398 0.628419 0.314210 0.949354i \(-0.398261\pi\)
0.314210 + 0.949354i \(0.398261\pi\)
\(350\) 66.4068 3.54959
\(351\) −1.73826 −0.0927816
\(352\) −4.58895 −0.244592
\(353\) −13.6394 −0.725950 −0.362975 0.931799i \(-0.618239\pi\)
−0.362975 + 0.931799i \(0.618239\pi\)
\(354\) −55.9463 −2.97351
\(355\) 30.2075 1.60325
\(356\) 6.41433 0.339959
\(357\) 11.0666 0.585706
\(358\) −34.7021 −1.83406
\(359\) 31.3133 1.65265 0.826325 0.563193i \(-0.190427\pi\)
0.826325 + 0.563193i \(0.190427\pi\)
\(360\) 30.3296 1.59851
\(361\) 3.75458 0.197609
\(362\) 42.9452 2.25715
\(363\) −2.67363 −0.140329
\(364\) −2.02662 −0.106224
\(365\) −34.1918 −1.78968
\(366\) 18.4947 0.966732
\(367\) 21.0313 1.09783 0.548913 0.835880i \(-0.315042\pi\)
0.548913 + 0.835880i \(0.315042\pi\)
\(368\) 21.3162 1.11118
\(369\) −15.1424 −0.788282
\(370\) 29.2149 1.51881
\(371\) −49.7227 −2.58148
\(372\) −13.3761 −0.693517
\(373\) −30.6169 −1.58528 −0.792642 0.609687i \(-0.791295\pi\)
−0.792642 + 0.609687i \(0.791295\pi\)
\(374\) 1.69256 0.0875203
\(375\) −45.5653 −2.35298
\(376\) 20.3101 1.04741
\(377\) 0.0833251 0.00429146
\(378\) −21.5086 −1.10628
\(379\) 26.6445 1.36864 0.684319 0.729183i \(-0.260100\pi\)
0.684319 + 0.729183i \(0.260100\pi\)
\(380\) −15.6964 −0.805210
\(381\) 12.8899 0.660371
\(382\) 45.8572 2.34626
\(383\) 22.1312 1.13085 0.565426 0.824799i \(-0.308712\pi\)
0.565426 + 0.824799i \(0.308712\pi\)
\(384\) 34.4774 1.75942
\(385\) 15.7500 0.802692
\(386\) 20.4981 1.04333
\(387\) 4.14830 0.210870
\(388\) 1.92872 0.0979158
\(389\) 4.91377 0.249138 0.124569 0.992211i \(-0.460245\pi\)
0.124569 + 0.992211i \(0.460245\pi\)
\(390\) 9.74929 0.493675
\(391\) −4.27889 −0.216393
\(392\) 19.4694 0.983354
\(393\) −38.7443 −1.95439
\(394\) −17.8929 −0.901430
\(395\) −19.7266 −0.992552
\(396\) −3.58731 −0.180269
\(397\) −4.72095 −0.236937 −0.118469 0.992958i \(-0.537799\pi\)
−0.118469 + 0.992958i \(0.537799\pi\)
\(398\) −3.93340 −0.197163
\(399\) −52.7896 −2.64278
\(400\) −47.2209 −2.36104
\(401\) −19.7264 −0.985088 −0.492544 0.870287i \(-0.663933\pi\)
−0.492544 + 0.870287i \(0.663933\pi\)
\(402\) −24.6275 −1.22831
\(403\) 3.27558 0.163168
\(404\) −9.14035 −0.454749
\(405\) −16.1204 −0.801031
\(406\) 1.03103 0.0511693
\(407\) 4.53620 0.224851
\(408\) −5.13725 −0.254332
\(409\) 26.8469 1.32749 0.663746 0.747958i \(-0.268965\pi\)
0.663746 + 0.747958i \(0.268965\pi\)
\(410\) 23.5091 1.16103
\(411\) −57.6021 −2.84130
\(412\) −10.4423 −0.514456
\(413\) 51.1727 2.51804
\(414\) 30.0432 1.47654
\(415\) 1.33496 0.0655307
\(416\) 2.59821 0.127388
\(417\) 1.71237 0.0838551
\(418\) −8.07382 −0.394903
\(419\) −13.0780 −0.638902 −0.319451 0.947603i \(-0.603499\pi\)
−0.319451 + 0.947603i \(0.603499\pi\)
\(420\) 36.4150 1.77687
\(421\) 33.2758 1.62176 0.810881 0.585211i \(-0.198988\pi\)
0.810881 + 0.585211i \(0.198988\pi\)
\(422\) 0.528713 0.0257374
\(423\) 43.8482 2.13197
\(424\) 23.0819 1.12096
\(425\) 9.47885 0.459792
\(426\) 35.9247 1.74056
\(427\) −16.9166 −0.818652
\(428\) 8.00515 0.386944
\(429\) 1.51378 0.0730858
\(430\) −6.44038 −0.310583
\(431\) −18.3460 −0.883696 −0.441848 0.897090i \(-0.645677\pi\)
−0.441848 + 0.897090i \(0.645677\pi\)
\(432\) 15.2944 0.735854
\(433\) −26.5619 −1.27648 −0.638241 0.769837i \(-0.720338\pi\)
−0.638241 + 0.769837i \(0.720338\pi\)
\(434\) 40.5308 1.94554
\(435\) −1.49721 −0.0717860
\(436\) −8.44134 −0.404267
\(437\) 20.4111 0.976393
\(438\) −40.6631 −1.94296
\(439\) −2.39358 −0.114239 −0.0571196 0.998367i \(-0.518192\pi\)
−0.0571196 + 0.998367i \(0.518192\pi\)
\(440\) −7.31133 −0.348554
\(441\) 42.0332 2.00158
\(442\) −0.958308 −0.0455820
\(443\) −13.3207 −0.632887 −0.316444 0.948611i \(-0.602489\pi\)
−0.316444 + 0.948611i \(0.602489\pi\)
\(444\) 10.4880 0.497739
\(445\) 28.2240 1.33795
\(446\) 14.8519 0.703257
\(447\) 15.3513 0.726092
\(448\) −9.09097 −0.429508
\(449\) 7.24666 0.341991 0.170995 0.985272i \(-0.445302\pi\)
0.170995 + 0.985272i \(0.445302\pi\)
\(450\) −66.5534 −3.13736
\(451\) 3.65027 0.171884
\(452\) 11.4325 0.537738
\(453\) 36.1278 1.69743
\(454\) −45.1640 −2.11965
\(455\) −8.91743 −0.418055
\(456\) 24.5056 1.14758
\(457\) −20.3899 −0.953798 −0.476899 0.878958i \(-0.658239\pi\)
−0.476899 + 0.878958i \(0.658239\pi\)
\(458\) −7.88761 −0.368564
\(459\) −3.07012 −0.143301
\(460\) −14.0798 −0.656475
\(461\) −37.0798 −1.72698 −0.863488 0.504369i \(-0.831725\pi\)
−0.863488 + 0.504369i \(0.831725\pi\)
\(462\) 18.7309 0.871440
\(463\) 19.2087 0.892705 0.446352 0.894857i \(-0.352723\pi\)
0.446352 + 0.894857i \(0.352723\pi\)
\(464\) −0.733153 −0.0340358
\(465\) −58.8568 −2.72942
\(466\) −27.2292 −1.26137
\(467\) 10.2206 0.472953 0.236476 0.971637i \(-0.424007\pi\)
0.236476 + 0.971637i \(0.424007\pi\)
\(468\) 2.03109 0.0938872
\(469\) 22.5261 1.04016
\(470\) −68.0759 −3.14011
\(471\) −17.4700 −0.804974
\(472\) −23.7550 −1.09341
\(473\) −1.00000 −0.0459800
\(474\) −23.4602 −1.07756
\(475\) −45.2158 −2.07464
\(476\) −3.57941 −0.164062
\(477\) 49.8325 2.28167
\(478\) 38.1945 1.74697
\(479\) −37.7674 −1.72564 −0.862819 0.505513i \(-0.831303\pi\)
−0.862819 + 0.505513i \(0.831303\pi\)
\(480\) −46.6855 −2.13089
\(481\) −2.56834 −0.117106
\(482\) −9.25346 −0.421484
\(483\) −47.3527 −2.15462
\(484\) 0.864767 0.0393076
\(485\) 8.48665 0.385359
\(486\) −34.7606 −1.57677
\(487\) 18.0560 0.818197 0.409098 0.912490i \(-0.365843\pi\)
0.409098 + 0.912490i \(0.365843\pi\)
\(488\) 7.85290 0.355484
\(489\) 2.42434 0.109633
\(490\) −65.2582 −2.94806
\(491\) −8.50612 −0.383876 −0.191938 0.981407i \(-0.561477\pi\)
−0.191938 + 0.981407i \(0.561477\pi\)
\(492\) 8.43967 0.380490
\(493\) 0.147169 0.00662815
\(494\) 4.57130 0.205672
\(495\) −15.7847 −0.709470
\(496\) −28.8209 −1.29409
\(497\) −32.8594 −1.47395
\(498\) 1.58762 0.0711432
\(499\) −30.3669 −1.35941 −0.679704 0.733487i \(-0.737892\pi\)
−0.679704 + 0.733487i \(0.737892\pi\)
\(500\) 14.7378 0.659094
\(501\) −18.2468 −0.815209
\(502\) −26.7368 −1.19332
\(503\) −6.93629 −0.309274 −0.154637 0.987971i \(-0.549421\pi\)
−0.154637 + 0.987971i \(0.549421\pi\)
\(504\) −32.9922 −1.46959
\(505\) −40.2189 −1.78972
\(506\) −7.24229 −0.321959
\(507\) 33.9001 1.50556
\(508\) −4.16916 −0.184977
\(509\) −23.2046 −1.02853 −0.514264 0.857632i \(-0.671935\pi\)
−0.514264 + 0.857632i \(0.671935\pi\)
\(510\) 17.2192 0.762479
\(511\) 37.1935 1.64534
\(512\) −3.71661 −0.164252
\(513\) 14.6450 0.646593
\(514\) 23.3453 1.02972
\(515\) −45.9477 −2.02470
\(516\) −2.31207 −0.101783
\(517\) −10.5702 −0.464875
\(518\) −31.7797 −1.39632
\(519\) −8.27937 −0.363424
\(520\) 4.13958 0.181533
\(521\) −2.93532 −0.128599 −0.0642994 0.997931i \(-0.520481\pi\)
−0.0642994 + 0.997931i \(0.520481\pi\)
\(522\) −1.03331 −0.0452267
\(523\) −35.4971 −1.55218 −0.776091 0.630621i \(-0.782800\pi\)
−0.776091 + 0.630621i \(0.782800\pi\)
\(524\) 12.5316 0.547444
\(525\) 104.898 4.57814
\(526\) −19.5669 −0.853156
\(527\) 5.78533 0.252013
\(528\) −13.3193 −0.579646
\(529\) −4.69110 −0.203961
\(530\) −77.3668 −3.36060
\(531\) −51.2856 −2.22561
\(532\) 17.0744 0.740270
\(533\) −2.06674 −0.0895203
\(534\) 33.5659 1.45254
\(535\) 35.2239 1.52286
\(536\) −10.4569 −0.451670
\(537\) −54.8166 −2.36551
\(538\) −41.4198 −1.78574
\(539\) −10.1327 −0.436444
\(540\) −10.1023 −0.434735
\(541\) −27.5226 −1.18329 −0.591644 0.806199i \(-0.701521\pi\)
−0.591644 + 0.806199i \(0.701521\pi\)
\(542\) 21.6849 0.931444
\(543\) 67.8377 2.91119
\(544\) 4.58895 0.196750
\(545\) −37.1432 −1.59104
\(546\) −10.6052 −0.453860
\(547\) −10.3640 −0.443132 −0.221566 0.975145i \(-0.571117\pi\)
−0.221566 + 0.975145i \(0.571117\pi\)
\(548\) 18.6310 0.795878
\(549\) 16.9539 0.723576
\(550\) 16.0435 0.684099
\(551\) −0.702021 −0.0299071
\(552\) 21.9817 0.935605
\(553\) 21.4584 0.912504
\(554\) 3.78435 0.160781
\(555\) 46.1488 1.95891
\(556\) −0.553854 −0.0234887
\(557\) 11.1230 0.471298 0.235649 0.971838i \(-0.424278\pi\)
0.235649 + 0.971838i \(0.424278\pi\)
\(558\) −40.6203 −1.71959
\(559\) 0.566187 0.0239472
\(560\) 78.4617 3.31561
\(561\) 2.67363 0.112881
\(562\) −23.4723 −0.990120
\(563\) −9.52926 −0.401610 −0.200805 0.979631i \(-0.564356\pi\)
−0.200805 + 0.979631i \(0.564356\pi\)
\(564\) −24.4389 −1.02906
\(565\) 50.3046 2.11633
\(566\) −45.1202 −1.89654
\(567\) 17.5357 0.736429
\(568\) 15.2538 0.640034
\(569\) −8.59452 −0.360301 −0.180151 0.983639i \(-0.557658\pi\)
−0.180151 + 0.983639i \(0.557658\pi\)
\(570\) −82.1386 −3.44041
\(571\) −4.01146 −0.167874 −0.0839372 0.996471i \(-0.526750\pi\)
−0.0839372 + 0.996471i \(0.526750\pi\)
\(572\) −0.489620 −0.0204721
\(573\) 72.4376 3.02612
\(574\) −25.5730 −1.06740
\(575\) −40.5589 −1.69142
\(576\) 9.11104 0.379627
\(577\) −4.19319 −0.174565 −0.0872825 0.996184i \(-0.527818\pi\)
−0.0872825 + 0.996184i \(0.527818\pi\)
\(578\) −1.69256 −0.0704013
\(579\) 32.3795 1.34565
\(580\) 0.484264 0.0201080
\(581\) −1.45216 −0.0602457
\(582\) 10.0929 0.418364
\(583\) −12.0128 −0.497518
\(584\) −17.2657 −0.714460
\(585\) 8.93711 0.369504
\(586\) 9.12584 0.376985
\(587\) 3.14725 0.129901 0.0649504 0.997888i \(-0.479311\pi\)
0.0649504 + 0.997888i \(0.479311\pi\)
\(588\) −23.4274 −0.966129
\(589\) −27.5970 −1.13712
\(590\) 79.6228 3.27802
\(591\) −28.2642 −1.16263
\(592\) 22.5981 0.928775
\(593\) 8.88285 0.364775 0.182388 0.983227i \(-0.441617\pi\)
0.182388 + 0.983227i \(0.441617\pi\)
\(594\) −5.19637 −0.213210
\(595\) −15.7500 −0.645685
\(596\) −4.96528 −0.203386
\(597\) −6.21333 −0.254295
\(598\) 4.10049 0.167682
\(599\) 30.8276 1.25958 0.629790 0.776765i \(-0.283141\pi\)
0.629790 + 0.776765i \(0.283141\pi\)
\(600\) −48.6952 −1.98797
\(601\) −9.05763 −0.369468 −0.184734 0.982789i \(-0.559142\pi\)
−0.184734 + 0.982789i \(0.559142\pi\)
\(602\) 7.00579 0.285535
\(603\) −22.5758 −0.919359
\(604\) −11.6853 −0.475468
\(605\) 3.80511 0.154700
\(606\) −47.8310 −1.94300
\(607\) 4.48265 0.181945 0.0909725 0.995853i \(-0.471002\pi\)
0.0909725 + 0.995853i \(0.471002\pi\)
\(608\) −21.8901 −0.887762
\(609\) 1.62866 0.0659965
\(610\) −26.3216 −1.06573
\(611\) 5.98469 0.242115
\(612\) 3.58731 0.145008
\(613\) −35.2953 −1.42556 −0.712782 0.701385i \(-0.752565\pi\)
−0.712782 + 0.701385i \(0.752565\pi\)
\(614\) −2.06758 −0.0834409
\(615\) 37.1358 1.49746
\(616\) 7.95320 0.320444
\(617\) −19.5833 −0.788395 −0.394197 0.919026i \(-0.628977\pi\)
−0.394197 + 0.919026i \(0.628977\pi\)
\(618\) −54.6441 −2.19811
\(619\) −17.2627 −0.693846 −0.346923 0.937894i \(-0.612773\pi\)
−0.346923 + 0.937894i \(0.612773\pi\)
\(620\) 19.0368 0.764537
\(621\) 13.1367 0.527158
\(622\) −25.9631 −1.04103
\(623\) −30.7018 −1.23004
\(624\) 7.54119 0.301889
\(625\) 17.4543 0.698172
\(626\) 30.4134 1.21556
\(627\) −12.7537 −0.509333
\(628\) 5.65054 0.225481
\(629\) −4.53620 −0.180870
\(630\) 110.584 4.40579
\(631\) −37.2850 −1.48429 −0.742147 0.670238i \(-0.766192\pi\)
−0.742147 + 0.670238i \(0.766192\pi\)
\(632\) −9.96126 −0.396238
\(633\) 0.835174 0.0331952
\(634\) 38.0701 1.51196
\(635\) −18.3449 −0.727997
\(636\) −27.7743 −1.10132
\(637\) 5.73698 0.227307
\(638\) 0.249092 0.00986166
\(639\) 32.9320 1.30277
\(640\) −49.0682 −1.93959
\(641\) −10.9269 −0.431585 −0.215793 0.976439i \(-0.569234\pi\)
−0.215793 + 0.976439i \(0.569234\pi\)
\(642\) 41.8906 1.65329
\(643\) −0.342707 −0.0135150 −0.00675752 0.999977i \(-0.502151\pi\)
−0.00675752 + 0.999977i \(0.502151\pi\)
\(644\) 15.3159 0.603531
\(645\) −10.1734 −0.400579
\(646\) 8.07382 0.317660
\(647\) −8.30809 −0.326625 −0.163312 0.986574i \(-0.552218\pi\)
−0.163312 + 0.986574i \(0.552218\pi\)
\(648\) −8.14028 −0.319781
\(649\) 12.3631 0.485292
\(650\) −9.08365 −0.356290
\(651\) 64.0239 2.50929
\(652\) −0.784137 −0.0307092
\(653\) 13.2602 0.518912 0.259456 0.965755i \(-0.416457\pi\)
0.259456 + 0.965755i \(0.416457\pi\)
\(654\) −44.1731 −1.72731
\(655\) 55.1408 2.15453
\(656\) 18.1846 0.709989
\(657\) −37.2756 −1.45426
\(658\) 74.0523 2.88686
\(659\) −29.9691 −1.16743 −0.583716 0.811958i \(-0.698402\pi\)
−0.583716 + 0.811958i \(0.698402\pi\)
\(660\) 8.79767 0.342449
\(661\) 17.2139 0.669542 0.334771 0.942300i \(-0.391341\pi\)
0.334771 + 0.942300i \(0.391341\pi\)
\(662\) 24.6001 0.956111
\(663\) −1.51378 −0.0587902
\(664\) 0.674111 0.0261606
\(665\) 75.1301 2.91342
\(666\) 31.8498 1.23416
\(667\) −0.629719 −0.0243828
\(668\) 5.90182 0.228348
\(669\) 23.4605 0.907037
\(670\) 35.0498 1.35409
\(671\) −4.08696 −0.157775
\(672\) 50.7841 1.95904
\(673\) −24.7040 −0.952269 −0.476134 0.879372i \(-0.657962\pi\)
−0.476134 + 0.879372i \(0.657962\pi\)
\(674\) −43.9195 −1.69172
\(675\) −29.1012 −1.12011
\(676\) −10.9648 −0.421722
\(677\) −14.7584 −0.567212 −0.283606 0.958941i \(-0.591531\pi\)
−0.283606 + 0.958941i \(0.591531\pi\)
\(678\) 59.8256 2.29759
\(679\) −9.23170 −0.354280
\(680\) 7.31133 0.280377
\(681\) −71.3426 −2.73385
\(682\) 9.79203 0.374956
\(683\) 39.2451 1.50167 0.750835 0.660489i \(-0.229651\pi\)
0.750835 + 0.660489i \(0.229651\pi\)
\(684\) −17.1121 −0.654298
\(685\) 81.9793 3.13227
\(686\) 21.9467 0.837929
\(687\) −12.4595 −0.475361
\(688\) −4.98171 −0.189926
\(689\) 6.80147 0.259116
\(690\) −73.6791 −2.80491
\(691\) 28.5965 1.08786 0.543931 0.839130i \(-0.316935\pi\)
0.543931 + 0.839130i \(0.316935\pi\)
\(692\) 2.67791 0.101799
\(693\) 17.1705 0.652252
\(694\) −14.2822 −0.542143
\(695\) −2.43704 −0.0924423
\(696\) −0.756043 −0.0286577
\(697\) −3.65027 −0.138264
\(698\) −19.8704 −0.752106
\(699\) −43.0122 −1.62687
\(700\) −33.9287 −1.28238
\(701\) 9.85805 0.372333 0.186167 0.982518i \(-0.440394\pi\)
0.186167 + 0.982518i \(0.440394\pi\)
\(702\) 2.94212 0.111043
\(703\) 21.6385 0.816111
\(704\) −2.19633 −0.0827774
\(705\) −107.535 −4.05000
\(706\) 23.0855 0.868833
\(707\) 43.7498 1.64538
\(708\) 28.5842 1.07426
\(709\) 6.92912 0.260229 0.130114 0.991499i \(-0.458466\pi\)
0.130114 + 0.991499i \(0.458466\pi\)
\(710\) −51.1281 −1.91880
\(711\) −21.5058 −0.806529
\(712\) 14.2522 0.534123
\(713\) −24.7548 −0.927074
\(714\) −18.7309 −0.700986
\(715\) −2.15440 −0.0805702
\(716\) 17.7301 0.662603
\(717\) 60.3333 2.25319
\(718\) −52.9996 −1.97793
\(719\) −30.4056 −1.13394 −0.566969 0.823739i \(-0.691884\pi\)
−0.566969 + 0.823739i \(0.691884\pi\)
\(720\) −78.6349 −2.93055
\(721\) 49.9815 1.86141
\(722\) −6.35486 −0.236503
\(723\) −14.6171 −0.543615
\(724\) −21.9416 −0.815455
\(725\) 1.39499 0.0518087
\(726\) 4.52529 0.167949
\(727\) −38.2251 −1.41769 −0.708845 0.705364i \(-0.750783\pi\)
−0.708845 + 0.705364i \(0.750783\pi\)
\(728\) −4.50300 −0.166892
\(729\) −42.1995 −1.56294
\(730\) 57.8717 2.14193
\(731\) 1.00000 0.0369863
\(732\) −9.44934 −0.349258
\(733\) −52.1892 −1.92765 −0.963826 0.266533i \(-0.914122\pi\)
−0.963826 + 0.266533i \(0.914122\pi\)
\(734\) −35.5968 −1.31390
\(735\) −103.084 −3.80231
\(736\) −19.6356 −0.723779
\(737\) 5.44219 0.200466
\(738\) 25.6294 0.943433
\(739\) −28.4930 −1.04813 −0.524066 0.851678i \(-0.675585\pi\)
−0.524066 + 0.851678i \(0.675585\pi\)
\(740\) −14.9265 −0.548710
\(741\) 7.22098 0.265269
\(742\) 84.1589 3.08957
\(743\) −25.8450 −0.948163 −0.474081 0.880481i \(-0.657220\pi\)
−0.474081 + 0.880481i \(0.657220\pi\)
\(744\) −29.7207 −1.08961
\(745\) −21.8480 −0.800448
\(746\) 51.8211 1.89730
\(747\) 1.45536 0.0532490
\(748\) −0.864767 −0.0316190
\(749\) −38.3162 −1.40004
\(750\) 77.1221 2.81610
\(751\) −36.4527 −1.33018 −0.665089 0.746764i \(-0.731607\pi\)
−0.665089 + 0.746764i \(0.731607\pi\)
\(752\) −52.6575 −1.92022
\(753\) −42.2344 −1.53911
\(754\) −0.141033 −0.00513612
\(755\) −51.4171 −1.87126
\(756\) 10.9892 0.399674
\(757\) 47.0009 1.70828 0.854139 0.520045i \(-0.174085\pi\)
0.854139 + 0.520045i \(0.174085\pi\)
\(758\) −45.0975 −1.63802
\(759\) −11.4402 −0.415252
\(760\) −34.8763 −1.26510
\(761\) −7.62028 −0.276235 −0.138117 0.990416i \(-0.544105\pi\)
−0.138117 + 0.990416i \(0.544105\pi\)
\(762\) −21.8170 −0.790347
\(763\) 40.4040 1.46272
\(764\) −23.4295 −0.847648
\(765\) 15.7847 0.570698
\(766\) −37.4584 −1.35343
\(767\) −6.99981 −0.252748
\(768\) −46.6107 −1.68192
\(769\) −46.2315 −1.66715 −0.833575 0.552406i \(-0.813710\pi\)
−0.833575 + 0.552406i \(0.813710\pi\)
\(770\) −26.6578 −0.960680
\(771\) 36.8770 1.32809
\(772\) −10.4729 −0.376929
\(773\) −2.30865 −0.0830362 −0.0415181 0.999138i \(-0.513219\pi\)
−0.0415181 + 0.999138i \(0.513219\pi\)
\(774\) −7.02125 −0.252374
\(775\) 54.8383 1.96985
\(776\) 4.28547 0.153840
\(777\) −50.2003 −1.80092
\(778\) −8.31687 −0.298174
\(779\) 17.4124 0.623865
\(780\) −4.98113 −0.178353
\(781\) −7.93867 −0.284068
\(782\) 7.24229 0.258984
\(783\) −0.451826 −0.0161469
\(784\) −50.4780 −1.80278
\(785\) 24.8632 0.887407
\(786\) 65.5771 2.33906
\(787\) −32.8877 −1.17232 −0.586161 0.810195i \(-0.699361\pi\)
−0.586161 + 0.810195i \(0.699361\pi\)
\(788\) 9.14186 0.325665
\(789\) −30.9085 −1.10037
\(790\) 33.3885 1.18791
\(791\) −54.7209 −1.94565
\(792\) −7.97075 −0.283228
\(793\) 2.31399 0.0821721
\(794\) 7.99049 0.283572
\(795\) −122.211 −4.33439
\(796\) 2.00966 0.0712305
\(797\) 35.6790 1.26382 0.631908 0.775044i \(-0.282272\pi\)
0.631908 + 0.775044i \(0.282272\pi\)
\(798\) 89.3496 3.16294
\(799\) 10.5702 0.373945
\(800\) 43.4980 1.53789
\(801\) 30.7696 1.08719
\(802\) 33.3881 1.17898
\(803\) 8.98575 0.317100
\(804\) 12.5827 0.443758
\(805\) 67.3923 2.37527
\(806\) −5.54413 −0.195284
\(807\) −65.4282 −2.30318
\(808\) −20.3092 −0.714475
\(809\) 49.8219 1.75164 0.875822 0.482634i \(-0.160320\pi\)
0.875822 + 0.482634i \(0.160320\pi\)
\(810\) 27.2849 0.958692
\(811\) −12.7746 −0.448577 −0.224288 0.974523i \(-0.572006\pi\)
−0.224288 + 0.974523i \(0.572006\pi\)
\(812\) −0.526778 −0.0184863
\(813\) 34.2541 1.20135
\(814\) −7.67781 −0.269107
\(815\) −3.45032 −0.120860
\(816\) 13.3193 0.466267
\(817\) −4.77018 −0.166887
\(818\) −45.4400 −1.58877
\(819\) −9.72170 −0.339704
\(820\) −12.0113 −0.419454
\(821\) −19.0499 −0.664848 −0.332424 0.943130i \(-0.607866\pi\)
−0.332424 + 0.943130i \(0.607866\pi\)
\(822\) 97.4952 3.40054
\(823\) 2.10973 0.0735405 0.0367702 0.999324i \(-0.488293\pi\)
0.0367702 + 0.999324i \(0.488293\pi\)
\(824\) −23.2021 −0.808282
\(825\) 25.3429 0.882327
\(826\) −86.6129 −3.01365
\(827\) −24.6155 −0.855966 −0.427983 0.903787i \(-0.640776\pi\)
−0.427983 + 0.903787i \(0.640776\pi\)
\(828\) −15.3497 −0.533439
\(829\) −37.4251 −1.29983 −0.649914 0.760008i \(-0.725195\pi\)
−0.649914 + 0.760008i \(0.725195\pi\)
\(830\) −2.25951 −0.0784286
\(831\) 5.97788 0.207370
\(832\) 1.24354 0.0431118
\(833\) 10.1327 0.351076
\(834\) −2.89829 −0.100360
\(835\) 25.9689 0.898690
\(836\) 4.12509 0.142669
\(837\) −17.7617 −0.613933
\(838\) 22.1353 0.764653
\(839\) 32.3519 1.11691 0.558456 0.829534i \(-0.311394\pi\)
0.558456 + 0.829534i \(0.311394\pi\)
\(840\) 80.9115 2.79171
\(841\) −28.9783 −0.999253
\(842\) −56.3213 −1.94096
\(843\) −37.0777 −1.27702
\(844\) −0.270131 −0.00929830
\(845\) −48.2466 −1.65973
\(846\) −74.2157 −2.55159
\(847\) −4.13916 −0.142223
\(848\) −59.8441 −2.05506
\(849\) −71.2734 −2.44610
\(850\) −16.0435 −0.550289
\(851\) 19.4099 0.665363
\(852\) −18.3547 −0.628823
\(853\) −52.5111 −1.79795 −0.898973 0.438004i \(-0.855686\pi\)
−0.898973 + 0.438004i \(0.855686\pi\)
\(854\) 28.6324 0.979780
\(855\) −75.2959 −2.57506
\(856\) 17.7869 0.607943
\(857\) 42.6252 1.45605 0.728025 0.685551i \(-0.240439\pi\)
0.728025 + 0.685551i \(0.240439\pi\)
\(858\) −2.56216 −0.0874707
\(859\) 18.4748 0.630353 0.315176 0.949033i \(-0.397936\pi\)
0.315176 + 0.949033i \(0.397936\pi\)
\(860\) 3.29053 0.112206
\(861\) −40.3960 −1.37669
\(862\) 31.0518 1.05763
\(863\) −1.60526 −0.0546437 −0.0273218 0.999627i \(-0.508698\pi\)
−0.0273218 + 0.999627i \(0.508698\pi\)
\(864\) −14.0886 −0.479305
\(865\) 11.7832 0.400641
\(866\) 44.9576 1.52772
\(867\) −2.67363 −0.0908012
\(868\) −20.7081 −0.702878
\(869\) 5.18424 0.175863
\(870\) 2.53413 0.0859150
\(871\) −3.08130 −0.104406
\(872\) −18.7561 −0.635160
\(873\) 9.25207 0.313135
\(874\) −34.5470 −1.16857
\(875\) −70.5416 −2.38474
\(876\) 20.7757 0.701945
\(877\) 32.0271 1.08148 0.540740 0.841190i \(-0.318144\pi\)
0.540740 + 0.841190i \(0.318144\pi\)
\(878\) 4.05128 0.136724
\(879\) 14.4155 0.486223
\(880\) 18.9560 0.639005
\(881\) 15.1263 0.509618 0.254809 0.966991i \(-0.417987\pi\)
0.254809 + 0.966991i \(0.417987\pi\)
\(882\) −71.1439 −2.39554
\(883\) −10.0289 −0.337501 −0.168750 0.985659i \(-0.553973\pi\)
−0.168750 + 0.985659i \(0.553973\pi\)
\(884\) 0.489620 0.0164677
\(885\) 125.775 4.22788
\(886\) 22.5462 0.757454
\(887\) 1.73491 0.0582526 0.0291263 0.999576i \(-0.490728\pi\)
0.0291263 + 0.999576i \(0.490728\pi\)
\(888\) 23.3036 0.782018
\(889\) 19.9555 0.669284
\(890\) −47.7709 −1.60128
\(891\) 4.23653 0.141929
\(892\) −7.58816 −0.254070
\(893\) −50.4215 −1.68729
\(894\) −25.9830 −0.869003
\(895\) 78.0150 2.60775
\(896\) 53.3759 1.78316
\(897\) 6.47728 0.216270
\(898\) −12.2654 −0.409302
\(899\) 0.851420 0.0283965
\(900\) 34.0036 1.13345
\(901\) 12.0128 0.400203
\(902\) −6.17831 −0.205715
\(903\) 11.0666 0.368273
\(904\) 25.4021 0.844863
\(905\) −96.5466 −3.20932
\(906\) −61.1486 −2.03153
\(907\) −12.5807 −0.417735 −0.208868 0.977944i \(-0.566978\pi\)
−0.208868 + 0.977944i \(0.566978\pi\)
\(908\) 23.0753 0.765780
\(909\) −43.8463 −1.45429
\(910\) 15.0933 0.500338
\(911\) −28.5723 −0.946642 −0.473321 0.880890i \(-0.656945\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(912\) −63.5352 −2.10386
\(913\) −0.350834 −0.0116109
\(914\) 34.5111 1.14153
\(915\) −41.5785 −1.37454
\(916\) 4.02995 0.133153
\(917\) −59.9816 −1.98077
\(918\) 5.19637 0.171506
\(919\) −13.9540 −0.460300 −0.230150 0.973155i \(-0.573922\pi\)
−0.230150 + 0.973155i \(0.573922\pi\)
\(920\) −31.2844 −1.03142
\(921\) −3.26603 −0.107619
\(922\) 62.7598 2.06688
\(923\) 4.49477 0.147947
\(924\) −9.57002 −0.314831
\(925\) −42.9980 −1.41376
\(926\) −32.5119 −1.06841
\(927\) −50.0918 −1.64523
\(928\) 0.675351 0.0221695
\(929\) 36.2975 1.19088 0.595441 0.803399i \(-0.296977\pi\)
0.595441 + 0.803399i \(0.296977\pi\)
\(930\) 99.6188 3.26663
\(931\) −48.3345 −1.58410
\(932\) 13.9120 0.455703
\(933\) −41.0123 −1.34268
\(934\) −17.2990 −0.566040
\(935\) −3.80511 −0.124440
\(936\) 4.51294 0.147510
\(937\) 42.3398 1.38318 0.691590 0.722290i \(-0.256910\pi\)
0.691590 + 0.722290i \(0.256910\pi\)
\(938\) −38.1269 −1.24489
\(939\) 48.0420 1.56779
\(940\) 34.7815 1.13445
\(941\) −43.2293 −1.40923 −0.704617 0.709587i \(-0.748881\pi\)
−0.704617 + 0.709587i \(0.748881\pi\)
\(942\) 29.5690 0.963411
\(943\) 15.6191 0.508628
\(944\) 61.5892 2.00456
\(945\) 48.3542 1.57296
\(946\) 1.69256 0.0550299
\(947\) −54.3855 −1.76729 −0.883645 0.468157i \(-0.844918\pi\)
−0.883645 + 0.468157i \(0.844918\pi\)
\(948\) 11.9863 0.389297
\(949\) −5.08762 −0.165151
\(950\) 76.5305 2.48298
\(951\) 60.1369 1.95007
\(952\) −7.95320 −0.257765
\(953\) 27.0643 0.876700 0.438350 0.898804i \(-0.355563\pi\)
0.438350 + 0.898804i \(0.355563\pi\)
\(954\) −84.3446 −2.73076
\(955\) −103.093 −3.33602
\(956\) −19.5144 −0.631141
\(957\) 0.393475 0.0127192
\(958\) 63.9237 2.06528
\(959\) −89.1763 −2.87965
\(960\) −22.3443 −0.721158
\(961\) 2.47006 0.0796794
\(962\) 4.34708 0.140155
\(963\) 38.4008 1.23745
\(964\) 4.72780 0.152272
\(965\) −46.0825 −1.48345
\(966\) 80.1474 2.57870
\(967\) −19.2720 −0.619745 −0.309873 0.950778i \(-0.600286\pi\)
−0.309873 + 0.950778i \(0.600286\pi\)
\(968\) 1.92145 0.0617578
\(969\) 12.7537 0.409707
\(970\) −14.3642 −0.461206
\(971\) 54.4247 1.74657 0.873286 0.487208i \(-0.161985\pi\)
0.873286 + 0.487208i \(0.161985\pi\)
\(972\) 17.7600 0.569651
\(973\) 2.65099 0.0849869
\(974\) −30.5610 −0.979236
\(975\) −14.3488 −0.459531
\(976\) −20.3601 −0.651710
\(977\) −25.7976 −0.825337 −0.412668 0.910881i \(-0.635403\pi\)
−0.412668 + 0.910881i \(0.635403\pi\)
\(978\) −4.10335 −0.131211
\(979\) −7.41740 −0.237061
\(980\) 33.3418 1.06507
\(981\) −40.4932 −1.29285
\(982\) 14.3971 0.459431
\(983\) 33.0538 1.05425 0.527126 0.849787i \(-0.323270\pi\)
0.527126 + 0.849787i \(0.323270\pi\)
\(984\) 18.7523 0.597803
\(985\) 40.2256 1.28169
\(986\) −0.249092 −0.00793272
\(987\) 116.976 3.72337
\(988\) −2.33558 −0.0743046
\(989\) −4.27889 −0.136061
\(990\) 26.7166 0.849110
\(991\) −10.6244 −0.337495 −0.168748 0.985659i \(-0.553972\pi\)
−0.168748 + 0.985659i \(0.553972\pi\)
\(992\) 26.5486 0.842920
\(993\) 38.8592 1.23316
\(994\) 55.6166 1.76405
\(995\) 8.84281 0.280336
\(996\) −0.811152 −0.0257023
\(997\) −52.3704 −1.65859 −0.829294 0.558813i \(-0.811257\pi\)
−0.829294 + 0.558813i \(0.811257\pi\)
\(998\) 51.3978 1.62697
\(999\) 13.9267 0.440621
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 \(a_p\))