Properties

Label 8047.2.a.b.1.7
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65232 q^{2} +2.65488 q^{3} +5.03481 q^{4} -0.675897 q^{5} -7.04159 q^{6} -2.02772 q^{7} -8.04928 q^{8} +4.04839 q^{9} +O(q^{10})\) \(q-2.65232 q^{2} +2.65488 q^{3} +5.03481 q^{4} -0.675897 q^{5} -7.04159 q^{6} -2.02772 q^{7} -8.04928 q^{8} +4.04839 q^{9} +1.79269 q^{10} +4.17036 q^{11} +13.3668 q^{12} +1.00000 q^{13} +5.37816 q^{14} -1.79442 q^{15} +11.2797 q^{16} -7.58358 q^{17} -10.7376 q^{18} +6.75596 q^{19} -3.40301 q^{20} -5.38335 q^{21} -11.0611 q^{22} -6.60775 q^{23} -21.3699 q^{24} -4.54316 q^{25} -2.65232 q^{26} +2.78334 q^{27} -10.2092 q^{28} +1.94163 q^{29} +4.75939 q^{30} +4.58793 q^{31} -13.8187 q^{32} +11.0718 q^{33} +20.1141 q^{34} +1.37053 q^{35} +20.3828 q^{36} -5.32619 q^{37} -17.9190 q^{38} +2.65488 q^{39} +5.44048 q^{40} -3.19215 q^{41} +14.2784 q^{42} -1.32584 q^{43} +20.9970 q^{44} -2.73629 q^{45} +17.5259 q^{46} +5.32709 q^{47} +29.9461 q^{48} -2.88835 q^{49} +12.0499 q^{50} -20.1335 q^{51} +5.03481 q^{52} +0.0678960 q^{53} -7.38232 q^{54} -2.81873 q^{55} +16.3217 q^{56} +17.9363 q^{57} -5.14983 q^{58} +6.08981 q^{59} -9.03458 q^{60} +3.16482 q^{61} -12.1687 q^{62} -8.20899 q^{63} +14.0923 q^{64} -0.675897 q^{65} -29.3660 q^{66} +5.30065 q^{67} -38.1819 q^{68} -17.5428 q^{69} -3.63508 q^{70} -10.6088 q^{71} -32.5866 q^{72} +3.17585 q^{73} +14.1268 q^{74} -12.0616 q^{75} +34.0149 q^{76} -8.45632 q^{77} -7.04159 q^{78} +2.37979 q^{79} -7.62388 q^{80} -4.75572 q^{81} +8.46660 q^{82} -17.5188 q^{83} -27.1041 q^{84} +5.12572 q^{85} +3.51655 q^{86} +5.15480 q^{87} -33.5684 q^{88} -15.0412 q^{89} +7.25752 q^{90} -2.02772 q^{91} -33.2687 q^{92} +12.1804 q^{93} -14.1291 q^{94} -4.56633 q^{95} -36.6870 q^{96} -6.42427 q^{97} +7.66084 q^{98} +16.8832 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65232 −1.87547 −0.937737 0.347346i \(-0.887083\pi\)
−0.937737 + 0.347346i \(0.887083\pi\)
\(3\) 2.65488 1.53280 0.766398 0.642366i \(-0.222047\pi\)
0.766398 + 0.642366i \(0.222047\pi\)
\(4\) 5.03481 2.51740
\(5\) −0.675897 −0.302270 −0.151135 0.988513i \(-0.548293\pi\)
−0.151135 + 0.988513i \(0.548293\pi\)
\(6\) −7.04159 −2.87472
\(7\) −2.02772 −0.766406 −0.383203 0.923664i \(-0.625179\pi\)
−0.383203 + 0.923664i \(0.625179\pi\)
\(8\) −8.04928 −2.84585
\(9\) 4.04839 1.34946
\(10\) 1.79269 0.566900
\(11\) 4.17036 1.25741 0.628705 0.777644i \(-0.283585\pi\)
0.628705 + 0.777644i \(0.283585\pi\)
\(12\) 13.3668 3.85866
\(13\) 1.00000 0.277350
\(14\) 5.37816 1.43737
\(15\) −1.79442 −0.463318
\(16\) 11.2797 2.81991
\(17\) −7.58358 −1.83929 −0.919644 0.392753i \(-0.871523\pi\)
−0.919644 + 0.392753i \(0.871523\pi\)
\(18\) −10.7376 −2.53088
\(19\) 6.75596 1.54992 0.774962 0.632008i \(-0.217769\pi\)
0.774962 + 0.632008i \(0.217769\pi\)
\(20\) −3.40301 −0.760936
\(21\) −5.38335 −1.17474
\(22\) −11.0611 −2.35824
\(23\) −6.60775 −1.37781 −0.688906 0.724851i \(-0.741909\pi\)
−0.688906 + 0.724851i \(0.741909\pi\)
\(24\) −21.3699 −4.36211
\(25\) −4.54316 −0.908633
\(26\) −2.65232 −0.520163
\(27\) 2.78334 0.535655
\(28\) −10.2092 −1.92935
\(29\) 1.94163 0.360552 0.180276 0.983616i \(-0.442301\pi\)
0.180276 + 0.983616i \(0.442301\pi\)
\(30\) 4.75939 0.868941
\(31\) 4.58793 0.824016 0.412008 0.911180i \(-0.364828\pi\)
0.412008 + 0.911180i \(0.364828\pi\)
\(32\) −13.8187 −2.44283
\(33\) 11.0718 1.92735
\(34\) 20.1141 3.44954
\(35\) 1.37053 0.231662
\(36\) 20.3828 3.39714
\(37\) −5.32619 −0.875621 −0.437810 0.899067i \(-0.644246\pi\)
−0.437810 + 0.899067i \(0.644246\pi\)
\(38\) −17.9190 −2.90684
\(39\) 2.65488 0.425121
\(40\) 5.44048 0.860215
\(41\) −3.19215 −0.498529 −0.249265 0.968435i \(-0.580189\pi\)
−0.249265 + 0.968435i \(0.580189\pi\)
\(42\) 14.2784 2.20320
\(43\) −1.32584 −0.202188 −0.101094 0.994877i \(-0.532234\pi\)
−0.101094 + 0.994877i \(0.532234\pi\)
\(44\) 20.9970 3.16541
\(45\) −2.73629 −0.407902
\(46\) 17.5259 2.58405
\(47\) 5.32709 0.777036 0.388518 0.921441i \(-0.372987\pi\)
0.388518 + 0.921441i \(0.372987\pi\)
\(48\) 29.9461 4.32235
\(49\) −2.88835 −0.412622
\(50\) 12.0499 1.70412
\(51\) −20.1335 −2.81925
\(52\) 5.03481 0.698202
\(53\) 0.0678960 0.00932623 0.00466311 0.999989i \(-0.498516\pi\)
0.00466311 + 0.999989i \(0.498516\pi\)
\(54\) −7.38232 −1.00461
\(55\) −2.81873 −0.380078
\(56\) 16.3217 2.18108
\(57\) 17.9363 2.37572
\(58\) −5.14983 −0.676206
\(59\) 6.08981 0.792826 0.396413 0.918072i \(-0.370255\pi\)
0.396413 + 0.918072i \(0.370255\pi\)
\(60\) −9.03458 −1.16636
\(61\) 3.16482 0.405214 0.202607 0.979260i \(-0.435059\pi\)
0.202607 + 0.979260i \(0.435059\pi\)
\(62\) −12.1687 −1.54542
\(63\) −8.20899 −1.03424
\(64\) 14.0923 1.76154
\(65\) −0.675897 −0.0838346
\(66\) −29.3660 −3.61470
\(67\) 5.30065 0.647577 0.323789 0.946129i \(-0.395043\pi\)
0.323789 + 0.946129i \(0.395043\pi\)
\(68\) −38.1819 −4.63023
\(69\) −17.5428 −2.11190
\(70\) −3.63508 −0.434475
\(71\) −10.6088 −1.25904 −0.629519 0.776985i \(-0.716748\pi\)
−0.629519 + 0.776985i \(0.716748\pi\)
\(72\) −32.5866 −3.84037
\(73\) 3.17585 0.371705 0.185852 0.982578i \(-0.440495\pi\)
0.185852 + 0.982578i \(0.440495\pi\)
\(74\) 14.1268 1.64220
\(75\) −12.0616 −1.39275
\(76\) 34.0149 3.90178
\(77\) −8.45632 −0.963687
\(78\) −7.04159 −0.797303
\(79\) 2.37979 0.267747 0.133873 0.990998i \(-0.457258\pi\)
0.133873 + 0.990998i \(0.457258\pi\)
\(80\) −7.62388 −0.852376
\(81\) −4.75572 −0.528413
\(82\) 8.46660 0.934979
\(83\) −17.5188 −1.92294 −0.961471 0.274905i \(-0.911354\pi\)
−0.961471 + 0.274905i \(0.911354\pi\)
\(84\) −27.1041 −2.95730
\(85\) 5.12572 0.555962
\(86\) 3.51655 0.379199
\(87\) 5.15480 0.552653
\(88\) −33.5684 −3.57840
\(89\) −15.0412 −1.59436 −0.797182 0.603739i \(-0.793677\pi\)
−0.797182 + 0.603739i \(0.793677\pi\)
\(90\) 7.25752 0.765010
\(91\) −2.02772 −0.212563
\(92\) −33.2687 −3.46851
\(93\) 12.1804 1.26305
\(94\) −14.1291 −1.45731
\(95\) −4.56633 −0.468496
\(96\) −36.6870 −3.74435
\(97\) −6.42427 −0.652286 −0.326143 0.945320i \(-0.605749\pi\)
−0.326143 + 0.945320i \(0.605749\pi\)
\(98\) 7.66084 0.773862
\(99\) 16.8832 1.69683
\(100\) −22.8739 −2.28739
\(101\) 1.06135 0.105608 0.0528040 0.998605i \(-0.483184\pi\)
0.0528040 + 0.998605i \(0.483184\pi\)
\(102\) 53.4005 5.28744
\(103\) −7.78643 −0.767220 −0.383610 0.923495i \(-0.625319\pi\)
−0.383610 + 0.923495i \(0.625319\pi\)
\(104\) −8.04928 −0.789297
\(105\) 3.63859 0.355090
\(106\) −0.180082 −0.0174911
\(107\) 16.3875 1.58424 0.792118 0.610368i \(-0.208979\pi\)
0.792118 + 0.610368i \(0.208979\pi\)
\(108\) 14.0136 1.34846
\(109\) 15.2001 1.45590 0.727952 0.685628i \(-0.240472\pi\)
0.727952 + 0.685628i \(0.240472\pi\)
\(110\) 7.47618 0.712826
\(111\) −14.1404 −1.34215
\(112\) −22.8720 −2.16120
\(113\) −17.4658 −1.64304 −0.821522 0.570176i \(-0.806875\pi\)
−0.821522 + 0.570176i \(0.806875\pi\)
\(114\) −47.5727 −4.45559
\(115\) 4.46616 0.416471
\(116\) 9.77574 0.907655
\(117\) 4.04839 0.374274
\(118\) −16.1521 −1.48693
\(119\) 15.3774 1.40964
\(120\) 14.4438 1.31853
\(121\) 6.39191 0.581082
\(122\) −8.39412 −0.759968
\(123\) −8.47476 −0.764144
\(124\) 23.0993 2.07438
\(125\) 6.45019 0.576923
\(126\) 21.7729 1.93968
\(127\) −18.8641 −1.67392 −0.836959 0.547265i \(-0.815669\pi\)
−0.836959 + 0.547265i \(0.815669\pi\)
\(128\) −9.73998 −0.860901
\(129\) −3.51994 −0.309913
\(130\) 1.79269 0.157230
\(131\) −7.52297 −0.657285 −0.328643 0.944454i \(-0.606591\pi\)
−0.328643 + 0.944454i \(0.606591\pi\)
\(132\) 55.7444 4.85193
\(133\) −13.6992 −1.18787
\(134\) −14.0590 −1.21451
\(135\) −1.88125 −0.161912
\(136\) 61.0423 5.23434
\(137\) −4.44277 −0.379572 −0.189786 0.981826i \(-0.560779\pi\)
−0.189786 + 0.981826i \(0.560779\pi\)
\(138\) 46.5291 3.96082
\(139\) 10.7970 0.915793 0.457897 0.889006i \(-0.348603\pi\)
0.457897 + 0.889006i \(0.348603\pi\)
\(140\) 6.90034 0.583186
\(141\) 14.1428 1.19104
\(142\) 28.1380 2.36129
\(143\) 4.17036 0.348743
\(144\) 45.6644 3.80537
\(145\) −1.31234 −0.108984
\(146\) −8.42336 −0.697122
\(147\) −7.66823 −0.632465
\(148\) −26.8164 −2.20429
\(149\) 11.2924 0.925111 0.462556 0.886590i \(-0.346933\pi\)
0.462556 + 0.886590i \(0.346933\pi\)
\(150\) 31.9911 2.61206
\(151\) −17.7733 −1.44637 −0.723186 0.690654i \(-0.757323\pi\)
−0.723186 + 0.690654i \(0.757323\pi\)
\(152\) −54.3806 −4.41085
\(153\) −30.7013 −2.48205
\(154\) 22.4289 1.80737
\(155\) −3.10096 −0.249075
\(156\) 13.3668 1.07020
\(157\) −7.20266 −0.574835 −0.287417 0.957805i \(-0.592797\pi\)
−0.287417 + 0.957805i \(0.592797\pi\)
\(158\) −6.31196 −0.502152
\(159\) 0.180256 0.0142952
\(160\) 9.34002 0.738393
\(161\) 13.3987 1.05596
\(162\) 12.6137 0.991026
\(163\) 3.00219 0.235149 0.117575 0.993064i \(-0.462488\pi\)
0.117575 + 0.993064i \(0.462488\pi\)
\(164\) −16.0718 −1.25500
\(165\) −7.48340 −0.582582
\(166\) 46.4656 3.60643
\(167\) 18.2577 1.41283 0.706413 0.707800i \(-0.250312\pi\)
0.706413 + 0.707800i \(0.250312\pi\)
\(168\) 43.3321 3.34314
\(169\) 1.00000 0.0769231
\(170\) −13.5950 −1.04269
\(171\) 27.3507 2.09156
\(172\) −6.67533 −0.508989
\(173\) 19.5427 1.48581 0.742903 0.669399i \(-0.233448\pi\)
0.742903 + 0.669399i \(0.233448\pi\)
\(174\) −13.6722 −1.03649
\(175\) 9.21226 0.696382
\(176\) 47.0402 3.54579
\(177\) 16.1677 1.21524
\(178\) 39.8941 2.99019
\(179\) −16.0057 −1.19632 −0.598161 0.801376i \(-0.704102\pi\)
−0.598161 + 0.801376i \(0.704102\pi\)
\(180\) −13.7767 −1.02685
\(181\) −5.70087 −0.423742 −0.211871 0.977298i \(-0.567956\pi\)
−0.211871 + 0.977298i \(0.567956\pi\)
\(182\) 5.37816 0.398656
\(183\) 8.40222 0.621110
\(184\) 53.1876 3.92104
\(185\) 3.59996 0.264674
\(186\) −32.3063 −2.36881
\(187\) −31.6263 −2.31274
\(188\) 26.8209 1.95611
\(189\) −5.64384 −0.410529
\(190\) 12.1114 0.878651
\(191\) −12.7839 −0.925013 −0.462506 0.886616i \(-0.653050\pi\)
−0.462506 + 0.886616i \(0.653050\pi\)
\(192\) 37.4135 2.70008
\(193\) −4.09396 −0.294690 −0.147345 0.989085i \(-0.547073\pi\)
−0.147345 + 0.989085i \(0.547073\pi\)
\(194\) 17.0392 1.22334
\(195\) −1.79442 −0.128501
\(196\) −14.5423 −1.03874
\(197\) −5.62001 −0.400409 −0.200205 0.979754i \(-0.564161\pi\)
−0.200205 + 0.979754i \(0.564161\pi\)
\(198\) −44.7798 −3.18236
\(199\) 2.91254 0.206464 0.103232 0.994657i \(-0.467082\pi\)
0.103232 + 0.994657i \(0.467082\pi\)
\(200\) 36.5692 2.58583
\(201\) 14.0726 0.992603
\(202\) −2.81503 −0.198065
\(203\) −3.93708 −0.276329
\(204\) −101.368 −7.09720
\(205\) 2.15756 0.150691
\(206\) 20.6521 1.43890
\(207\) −26.7507 −1.85930
\(208\) 11.2797 0.782103
\(209\) 28.1748 1.94889
\(210\) −9.65070 −0.665962
\(211\) 9.23335 0.635650 0.317825 0.948149i \(-0.397048\pi\)
0.317825 + 0.948149i \(0.397048\pi\)
\(212\) 0.341843 0.0234779
\(213\) −28.1652 −1.92985
\(214\) −43.4648 −2.97119
\(215\) 0.896129 0.0611155
\(216\) −22.4039 −1.52439
\(217\) −9.30303 −0.631531
\(218\) −40.3155 −2.73051
\(219\) 8.43149 0.569747
\(220\) −14.1918 −0.956809
\(221\) −7.58358 −0.510127
\(222\) 37.5049 2.51716
\(223\) 23.3764 1.56540 0.782700 0.622399i \(-0.213842\pi\)
0.782700 + 0.622399i \(0.213842\pi\)
\(224\) 28.0205 1.87220
\(225\) −18.3925 −1.22617
\(226\) 46.3249 3.08149
\(227\) −8.21570 −0.545295 −0.272647 0.962114i \(-0.587899\pi\)
−0.272647 + 0.962114i \(0.587899\pi\)
\(228\) 90.3056 5.98063
\(229\) 8.37014 0.553114 0.276557 0.960997i \(-0.410806\pi\)
0.276557 + 0.960997i \(0.410806\pi\)
\(230\) −11.8457 −0.781081
\(231\) −22.4505 −1.47714
\(232\) −15.6287 −1.02608
\(233\) −3.23985 −0.212250 −0.106125 0.994353i \(-0.533844\pi\)
−0.106125 + 0.994353i \(0.533844\pi\)
\(234\) −10.7376 −0.701940
\(235\) −3.60056 −0.234875
\(236\) 30.6610 1.99586
\(237\) 6.31805 0.410401
\(238\) −40.7857 −2.64375
\(239\) −19.1651 −1.23969 −0.619844 0.784725i \(-0.712804\pi\)
−0.619844 + 0.784725i \(0.712804\pi\)
\(240\) −20.2405 −1.30652
\(241\) −12.3213 −0.793683 −0.396842 0.917887i \(-0.629894\pi\)
−0.396842 + 0.917887i \(0.629894\pi\)
\(242\) −16.9534 −1.08980
\(243\) −20.9759 −1.34560
\(244\) 15.9343 1.02009
\(245\) 1.95223 0.124723
\(246\) 22.4778 1.43313
\(247\) 6.75596 0.429871
\(248\) −36.9295 −2.34503
\(249\) −46.5104 −2.94748
\(250\) −17.1080 −1.08200
\(251\) −4.25886 −0.268817 −0.134409 0.990926i \(-0.542913\pi\)
−0.134409 + 0.990926i \(0.542913\pi\)
\(252\) −41.3307 −2.60359
\(253\) −27.5567 −1.73247
\(254\) 50.0336 3.13939
\(255\) 13.6082 0.852176
\(256\) −2.35112 −0.146945
\(257\) −5.69565 −0.355285 −0.177643 0.984095i \(-0.556847\pi\)
−0.177643 + 0.984095i \(0.556847\pi\)
\(258\) 9.33601 0.581235
\(259\) 10.8000 0.671081
\(260\) −3.40301 −0.211046
\(261\) 7.86048 0.486551
\(262\) 19.9533 1.23272
\(263\) −17.3913 −1.07239 −0.536196 0.844093i \(-0.680139\pi\)
−0.536196 + 0.844093i \(0.680139\pi\)
\(264\) −89.1200 −5.48496
\(265\) −0.0458907 −0.00281904
\(266\) 36.3346 2.22782
\(267\) −39.9326 −2.44383
\(268\) 26.6877 1.63021
\(269\) −10.9477 −0.667491 −0.333745 0.942663i \(-0.608313\pi\)
−0.333745 + 0.942663i \(0.608313\pi\)
\(270\) 4.98968 0.303662
\(271\) −24.4905 −1.48769 −0.743845 0.668353i \(-0.767000\pi\)
−0.743845 + 0.668353i \(0.767000\pi\)
\(272\) −85.5402 −5.18663
\(273\) −5.38335 −0.325815
\(274\) 11.7837 0.711877
\(275\) −18.9466 −1.14252
\(276\) −88.3245 −5.31651
\(277\) −4.53142 −0.272266 −0.136133 0.990691i \(-0.543468\pi\)
−0.136133 + 0.990691i \(0.543468\pi\)
\(278\) −28.6372 −1.71755
\(279\) 18.5737 1.11198
\(280\) −11.0318 −0.659274
\(281\) −10.4551 −0.623696 −0.311848 0.950132i \(-0.600948\pi\)
−0.311848 + 0.950132i \(0.600948\pi\)
\(282\) −37.5112 −2.23376
\(283\) −1.09779 −0.0652568 −0.0326284 0.999468i \(-0.510388\pi\)
−0.0326284 + 0.999468i \(0.510388\pi\)
\(284\) −53.4134 −3.16950
\(285\) −12.1231 −0.718108
\(286\) −11.0611 −0.654059
\(287\) 6.47278 0.382076
\(288\) −55.9435 −3.29650
\(289\) 40.5107 2.38298
\(290\) 3.48075 0.204397
\(291\) −17.0557 −0.999821
\(292\) 15.9898 0.935730
\(293\) −12.0396 −0.703358 −0.351679 0.936121i \(-0.614389\pi\)
−0.351679 + 0.936121i \(0.614389\pi\)
\(294\) 20.3386 1.18617
\(295\) −4.11608 −0.239648
\(296\) 42.8720 2.49189
\(297\) 11.6075 0.673538
\(298\) −29.9511 −1.73502
\(299\) −6.60775 −0.382136
\(300\) −60.7276 −3.50611
\(301\) 2.68843 0.154958
\(302\) 47.1405 2.71263
\(303\) 2.81775 0.161876
\(304\) 76.2049 4.37065
\(305\) −2.13909 −0.122484
\(306\) 81.4296 4.65502
\(307\) −25.9279 −1.47978 −0.739892 0.672726i \(-0.765123\pi\)
−0.739892 + 0.672726i \(0.765123\pi\)
\(308\) −42.5759 −2.42599
\(309\) −20.6720 −1.17599
\(310\) 8.22475 0.467134
\(311\) 25.2114 1.42961 0.714805 0.699324i \(-0.246515\pi\)
0.714805 + 0.699324i \(0.246515\pi\)
\(312\) −21.3699 −1.20983
\(313\) −19.7808 −1.11808 −0.559040 0.829141i \(-0.688830\pi\)
−0.559040 + 0.829141i \(0.688830\pi\)
\(314\) 19.1038 1.07809
\(315\) 5.54843 0.312619
\(316\) 11.9818 0.674027
\(317\) 23.6474 1.32817 0.664085 0.747657i \(-0.268821\pi\)
0.664085 + 0.747657i \(0.268821\pi\)
\(318\) −0.478096 −0.0268103
\(319\) 8.09730 0.453362
\(320\) −9.52496 −0.532462
\(321\) 43.5067 2.42831
\(322\) −35.5376 −1.98043
\(323\) −51.2344 −2.85076
\(324\) −23.9441 −1.33023
\(325\) −4.54316 −0.252009
\(326\) −7.96276 −0.441017
\(327\) 40.3544 2.23160
\(328\) 25.6945 1.41874
\(329\) −10.8018 −0.595525
\(330\) 19.8484 1.09262
\(331\) −15.4593 −0.849717 −0.424859 0.905260i \(-0.639676\pi\)
−0.424859 + 0.905260i \(0.639676\pi\)
\(332\) −88.2040 −4.84082
\(333\) −21.5625 −1.18162
\(334\) −48.4254 −2.64972
\(335\) −3.58269 −0.195743
\(336\) −60.7223 −3.31268
\(337\) 32.2627 1.75746 0.878729 0.477320i \(-0.158392\pi\)
0.878729 + 0.477320i \(0.158392\pi\)
\(338\) −2.65232 −0.144267
\(339\) −46.3696 −2.51845
\(340\) 25.8070 1.39958
\(341\) 19.1333 1.03613
\(342\) −72.5429 −3.92267
\(343\) 20.0508 1.08264
\(344\) 10.6720 0.575398
\(345\) 11.8571 0.638365
\(346\) −51.8336 −2.78659
\(347\) −12.5919 −0.675970 −0.337985 0.941152i \(-0.609745\pi\)
−0.337985 + 0.941152i \(0.609745\pi\)
\(348\) 25.9534 1.39125
\(349\) 13.2680 0.710220 0.355110 0.934824i \(-0.384443\pi\)
0.355110 + 0.934824i \(0.384443\pi\)
\(350\) −24.4339 −1.30605
\(351\) 2.78334 0.148564
\(352\) −57.6290 −3.07164
\(353\) −14.4219 −0.767598 −0.383799 0.923417i \(-0.625384\pi\)
−0.383799 + 0.923417i \(0.625384\pi\)
\(354\) −42.8820 −2.27915
\(355\) 7.17048 0.380569
\(356\) −75.7295 −4.01366
\(357\) 40.8251 2.16069
\(358\) 42.4523 2.24367
\(359\) −17.6046 −0.929137 −0.464568 0.885537i \(-0.653791\pi\)
−0.464568 + 0.885537i \(0.653791\pi\)
\(360\) 22.0252 1.16083
\(361\) 26.6430 1.40226
\(362\) 15.1205 0.794717
\(363\) 16.9697 0.890680
\(364\) −10.2092 −0.535106
\(365\) −2.14654 −0.112355
\(366\) −22.2854 −1.16488
\(367\) 18.9707 0.990263 0.495132 0.868818i \(-0.335120\pi\)
0.495132 + 0.868818i \(0.335120\pi\)
\(368\) −74.5331 −3.88531
\(369\) −12.9230 −0.672747
\(370\) −9.54824 −0.496389
\(371\) −0.137674 −0.00714768
\(372\) 61.3259 3.17960
\(373\) 27.8996 1.44459 0.722294 0.691586i \(-0.243088\pi\)
0.722294 + 0.691586i \(0.243088\pi\)
\(374\) 83.8830 4.33749
\(375\) 17.1245 0.884305
\(376\) −42.8792 −2.21133
\(377\) 1.94163 0.0999991
\(378\) 14.9693 0.769936
\(379\) −13.0842 −0.672092 −0.336046 0.941846i \(-0.609090\pi\)
−0.336046 + 0.941846i \(0.609090\pi\)
\(380\) −22.9906 −1.17939
\(381\) −50.0819 −2.56577
\(382\) 33.9071 1.73484
\(383\) −11.8640 −0.606221 −0.303110 0.952955i \(-0.598025\pi\)
−0.303110 + 0.952955i \(0.598025\pi\)
\(384\) −25.8585 −1.31958
\(385\) 5.71560 0.291294
\(386\) 10.8585 0.552683
\(387\) −5.36750 −0.272846
\(388\) −32.3449 −1.64207
\(389\) 24.6338 1.24898 0.624490 0.781032i \(-0.285307\pi\)
0.624490 + 0.781032i \(0.285307\pi\)
\(390\) 4.75939 0.241001
\(391\) 50.1104 2.53419
\(392\) 23.2492 1.17426
\(393\) −19.9726 −1.00748
\(394\) 14.9061 0.750957
\(395\) −1.60849 −0.0809319
\(396\) 85.0038 4.27160
\(397\) 23.7086 1.18990 0.594951 0.803762i \(-0.297172\pi\)
0.594951 + 0.803762i \(0.297172\pi\)
\(398\) −7.72498 −0.387218
\(399\) −36.3697 −1.82076
\(400\) −51.2453 −2.56227
\(401\) 20.8539 1.04139 0.520697 0.853742i \(-0.325672\pi\)
0.520697 + 0.853742i \(0.325672\pi\)
\(402\) −37.3250 −1.86160
\(403\) 4.58793 0.228541
\(404\) 5.34368 0.265858
\(405\) 3.21438 0.159724
\(406\) 10.4424 0.518248
\(407\) −22.2121 −1.10102
\(408\) 162.060 8.02317
\(409\) −13.6370 −0.674307 −0.337153 0.941450i \(-0.609464\pi\)
−0.337153 + 0.941450i \(0.609464\pi\)
\(410\) −5.72254 −0.282616
\(411\) −11.7950 −0.581806
\(412\) −39.2032 −1.93140
\(413\) −12.3484 −0.607627
\(414\) 70.9515 3.48708
\(415\) 11.8409 0.581248
\(416\) −13.8187 −0.677518
\(417\) 28.6648 1.40372
\(418\) −74.7286 −3.65509
\(419\) 8.05087 0.393311 0.196655 0.980473i \(-0.436992\pi\)
0.196655 + 0.980473i \(0.436992\pi\)
\(420\) 18.3196 0.893904
\(421\) 18.0995 0.882115 0.441058 0.897479i \(-0.354603\pi\)
0.441058 + 0.897479i \(0.354603\pi\)
\(422\) −24.4898 −1.19214
\(423\) 21.5661 1.04858
\(424\) −0.546514 −0.0265410
\(425\) 34.4534 1.67124
\(426\) 74.7031 3.61938
\(427\) −6.41737 −0.310558
\(428\) 82.5077 3.98816
\(429\) 11.0718 0.534552
\(430\) −2.37682 −0.114621
\(431\) −1.89215 −0.0911415 −0.0455707 0.998961i \(-0.514511\pi\)
−0.0455707 + 0.998961i \(0.514511\pi\)
\(432\) 31.3951 1.51050
\(433\) −23.6368 −1.13591 −0.567955 0.823060i \(-0.692265\pi\)
−0.567955 + 0.823060i \(0.692265\pi\)
\(434\) 24.6746 1.18442
\(435\) −3.48411 −0.167050
\(436\) 76.5295 3.66510
\(437\) −44.6417 −2.13550
\(438\) −22.3630 −1.06855
\(439\) −1.78920 −0.0853940 −0.0426970 0.999088i \(-0.513595\pi\)
−0.0426970 + 0.999088i \(0.513595\pi\)
\(440\) 22.6888 1.08164
\(441\) −11.6932 −0.556818
\(442\) 20.1141 0.956730
\(443\) −10.4222 −0.495172 −0.247586 0.968866i \(-0.579637\pi\)
−0.247586 + 0.968866i \(0.579637\pi\)
\(444\) −71.1942 −3.37873
\(445\) 10.1663 0.481929
\(446\) −62.0018 −2.93587
\(447\) 29.9800 1.41801
\(448\) −28.5753 −1.35006
\(449\) −13.2999 −0.627662 −0.313831 0.949479i \(-0.601613\pi\)
−0.313831 + 0.949479i \(0.601613\pi\)
\(450\) 48.7828 2.29964
\(451\) −13.3124 −0.626856
\(452\) −87.9369 −4.13621
\(453\) −47.1860 −2.21699
\(454\) 21.7907 1.02269
\(455\) 1.37053 0.0642514
\(456\) −144.374 −6.76093
\(457\) −5.73775 −0.268401 −0.134200 0.990954i \(-0.542847\pi\)
−0.134200 + 0.990954i \(0.542847\pi\)
\(458\) −22.2003 −1.03735
\(459\) −21.1077 −0.985223
\(460\) 22.4862 1.04843
\(461\) −23.8884 −1.11259 −0.556297 0.830983i \(-0.687778\pi\)
−0.556297 + 0.830983i \(0.687778\pi\)
\(462\) 59.5460 2.77033
\(463\) −23.1888 −1.07768 −0.538838 0.842409i \(-0.681137\pi\)
−0.538838 + 0.842409i \(0.681137\pi\)
\(464\) 21.9009 1.01673
\(465\) −8.23269 −0.381782
\(466\) 8.59313 0.398069
\(467\) −39.2218 −1.81497 −0.907484 0.420086i \(-0.862000\pi\)
−0.907484 + 0.420086i \(0.862000\pi\)
\(468\) 20.3828 0.942197
\(469\) −10.7482 −0.496307
\(470\) 9.54984 0.440501
\(471\) −19.1222 −0.881104
\(472\) −49.0186 −2.25626
\(473\) −5.52922 −0.254234
\(474\) −16.7575 −0.769697
\(475\) −30.6934 −1.40831
\(476\) 77.4221 3.54864
\(477\) 0.274869 0.0125854
\(478\) 50.8320 2.32500
\(479\) 10.4636 0.478095 0.239048 0.971008i \(-0.423165\pi\)
0.239048 + 0.971008i \(0.423165\pi\)
\(480\) 24.7966 1.13181
\(481\) −5.32619 −0.242854
\(482\) 32.6800 1.48853
\(483\) 35.5718 1.61857
\(484\) 32.1820 1.46282
\(485\) 4.34214 0.197166
\(486\) 55.6348 2.52365
\(487\) −29.8670 −1.35340 −0.676702 0.736257i \(-0.736592\pi\)
−0.676702 + 0.736257i \(0.736592\pi\)
\(488\) −25.4745 −1.15318
\(489\) 7.97045 0.360436
\(490\) −5.17794 −0.233915
\(491\) 3.61598 0.163187 0.0815934 0.996666i \(-0.473999\pi\)
0.0815934 + 0.996666i \(0.473999\pi\)
\(492\) −42.6688 −1.92366
\(493\) −14.7245 −0.663159
\(494\) −17.9190 −0.806213
\(495\) −11.4113 −0.512901
\(496\) 51.7502 2.32365
\(497\) 21.5117 0.964934
\(498\) 123.361 5.52792
\(499\) 31.9605 1.43075 0.715375 0.698741i \(-0.246256\pi\)
0.715375 + 0.698741i \(0.246256\pi\)
\(500\) 32.4755 1.45235
\(501\) 48.4721 2.16557
\(502\) 11.2959 0.504159
\(503\) 26.4512 1.17940 0.589700 0.807623i \(-0.299246\pi\)
0.589700 + 0.807623i \(0.299246\pi\)
\(504\) 66.0765 2.94328
\(505\) −0.717361 −0.0319222
\(506\) 73.0892 3.24921
\(507\) 2.65488 0.117907
\(508\) −94.9771 −4.21393
\(509\) 30.0576 1.33228 0.666141 0.745826i \(-0.267945\pi\)
0.666141 + 0.745826i \(0.267945\pi\)
\(510\) −36.0932 −1.59823
\(511\) −6.43972 −0.284877
\(512\) 25.7159 1.13649
\(513\) 18.8042 0.830224
\(514\) 15.1067 0.666328
\(515\) 5.26282 0.231908
\(516\) −17.7222 −0.780177
\(517\) 22.2159 0.977053
\(518\) −28.6451 −1.25860
\(519\) 51.8836 2.27744
\(520\) 5.44048 0.238581
\(521\) −33.9334 −1.48665 −0.743324 0.668931i \(-0.766752\pi\)
−0.743324 + 0.668931i \(0.766752\pi\)
\(522\) −20.8485 −0.912514
\(523\) −2.14534 −0.0938091 −0.0469045 0.998899i \(-0.514936\pi\)
−0.0469045 + 0.998899i \(0.514936\pi\)
\(524\) −37.8767 −1.65465
\(525\) 24.4574 1.06741
\(526\) 46.1273 2.01124
\(527\) −34.7929 −1.51560
\(528\) 124.886 5.43497
\(529\) 20.6624 0.898363
\(530\) 0.121717 0.00528704
\(531\) 24.6539 1.06989
\(532\) −68.9728 −2.99035
\(533\) −3.19215 −0.138267
\(534\) 105.914 4.58335
\(535\) −11.0762 −0.478867
\(536\) −42.6664 −1.84291
\(537\) −42.4932 −1.83372
\(538\) 29.0367 1.25186
\(539\) −12.0455 −0.518835
\(540\) −9.47174 −0.407599
\(541\) −15.9938 −0.687628 −0.343814 0.939038i \(-0.611719\pi\)
−0.343814 + 0.939038i \(0.611719\pi\)
\(542\) 64.9565 2.79012
\(543\) −15.1351 −0.649510
\(544\) 104.795 4.49306
\(545\) −10.2737 −0.440077
\(546\) 14.2784 0.611058
\(547\) 23.5127 1.00533 0.502665 0.864482i \(-0.332353\pi\)
0.502665 + 0.864482i \(0.332353\pi\)
\(548\) −22.3685 −0.955535
\(549\) 12.8124 0.546821
\(550\) 50.2525 2.14278
\(551\) 13.1176 0.558828
\(552\) 141.207 6.01016
\(553\) −4.82554 −0.205203
\(554\) 12.0188 0.510629
\(555\) 9.55745 0.405691
\(556\) 54.3610 2.30542
\(557\) 42.8701 1.81647 0.908233 0.418465i \(-0.137432\pi\)
0.908233 + 0.418465i \(0.137432\pi\)
\(558\) −49.2634 −2.08549
\(559\) −1.32584 −0.0560770
\(560\) 15.4591 0.653266
\(561\) −83.9639 −3.54496
\(562\) 27.7302 1.16973
\(563\) 1.75569 0.0739937 0.0369968 0.999315i \(-0.488221\pi\)
0.0369968 + 0.999315i \(0.488221\pi\)
\(564\) 71.2061 2.99832
\(565\) 11.8051 0.496643
\(566\) 2.91169 0.122387
\(567\) 9.64327 0.404979
\(568\) 85.3935 3.58303
\(569\) −31.6560 −1.32709 −0.663545 0.748137i \(-0.730949\pi\)
−0.663545 + 0.748137i \(0.730949\pi\)
\(570\) 32.1542 1.34679
\(571\) −33.1136 −1.38576 −0.692880 0.721053i \(-0.743659\pi\)
−0.692880 + 0.721053i \(0.743659\pi\)
\(572\) 20.9970 0.877927
\(573\) −33.9398 −1.41786
\(574\) −17.1679 −0.716573
\(575\) 30.0201 1.25192
\(576\) 57.0512 2.37713
\(577\) 5.32609 0.221728 0.110864 0.993836i \(-0.464638\pi\)
0.110864 + 0.993836i \(0.464638\pi\)
\(578\) −107.447 −4.46922
\(579\) −10.8690 −0.451699
\(580\) −6.60739 −0.274357
\(581\) 35.5233 1.47375
\(582\) 45.2371 1.87514
\(583\) 0.283151 0.0117269
\(584\) −25.5633 −1.05782
\(585\) −2.73629 −0.113132
\(586\) 31.9328 1.31913
\(587\) 6.78547 0.280066 0.140033 0.990147i \(-0.455279\pi\)
0.140033 + 0.990147i \(0.455279\pi\)
\(588\) −38.6081 −1.59217
\(589\) 30.9958 1.27716
\(590\) 10.9172 0.449453
\(591\) −14.9204 −0.613745
\(592\) −60.0776 −2.46918
\(593\) 12.3768 0.508256 0.254128 0.967171i \(-0.418212\pi\)
0.254128 + 0.967171i \(0.418212\pi\)
\(594\) −30.7869 −1.26320
\(595\) −10.3935 −0.426093
\(596\) 56.8552 2.32888
\(597\) 7.73244 0.316468
\(598\) 17.5259 0.716686
\(599\) −31.6676 −1.29390 −0.646952 0.762531i \(-0.723956\pi\)
−0.646952 + 0.762531i \(0.723956\pi\)
\(600\) 97.0868 3.96355
\(601\) 16.0706 0.655532 0.327766 0.944759i \(-0.393704\pi\)
0.327766 + 0.944759i \(0.393704\pi\)
\(602\) −7.13057 −0.290620
\(603\) 21.4591 0.873881
\(604\) −89.4851 −3.64110
\(605\) −4.32027 −0.175644
\(606\) −7.47358 −0.303593
\(607\) −11.1798 −0.453775 −0.226887 0.973921i \(-0.572855\pi\)
−0.226887 + 0.973921i \(0.572855\pi\)
\(608\) −93.3586 −3.78619
\(609\) −10.4525 −0.423556
\(610\) 5.67355 0.229716
\(611\) 5.32709 0.215511
\(612\) −154.575 −6.24832
\(613\) 11.5790 0.467672 0.233836 0.972276i \(-0.424872\pi\)
0.233836 + 0.972276i \(0.424872\pi\)
\(614\) 68.7691 2.77530
\(615\) 5.72806 0.230978
\(616\) 68.0673 2.74251
\(617\) −6.61498 −0.266309 −0.133155 0.991095i \(-0.542511\pi\)
−0.133155 + 0.991095i \(0.542511\pi\)
\(618\) 54.8289 2.20554
\(619\) 1.00000 0.0401934
\(620\) −15.6127 −0.627023
\(621\) −18.3916 −0.738031
\(622\) −66.8688 −2.68120
\(623\) 30.4993 1.22193
\(624\) 29.9461 1.19880
\(625\) 18.3562 0.734246
\(626\) 52.4651 2.09693
\(627\) 74.8007 2.98725
\(628\) −36.2640 −1.44709
\(629\) 40.3916 1.61052
\(630\) −14.7162 −0.586308
\(631\) 29.1933 1.16217 0.581083 0.813844i \(-0.302629\pi\)
0.581083 + 0.813844i \(0.302629\pi\)
\(632\) −19.1556 −0.761967
\(633\) 24.5134 0.974321
\(634\) −62.7205 −2.49095
\(635\) 12.7502 0.505975
\(636\) 0.907552 0.0359868
\(637\) −2.88835 −0.114441
\(638\) −21.4766 −0.850269
\(639\) −42.9487 −1.69902
\(640\) 6.58322 0.260225
\(641\) −44.3376 −1.75123 −0.875615 0.483009i \(-0.839544\pi\)
−0.875615 + 0.483009i \(0.839544\pi\)
\(642\) −115.394 −4.55423
\(643\) 14.9821 0.590837 0.295419 0.955368i \(-0.404541\pi\)
0.295419 + 0.955368i \(0.404541\pi\)
\(644\) 67.4597 2.65828
\(645\) 2.37912 0.0936776
\(646\) 135.890 5.34652
\(647\) −42.6475 −1.67665 −0.838324 0.545173i \(-0.816464\pi\)
−0.838324 + 0.545173i \(0.816464\pi\)
\(648\) 38.2801 1.50379
\(649\) 25.3967 0.996909
\(650\) 12.0499 0.472637
\(651\) −24.6984 −0.968008
\(652\) 15.1154 0.591966
\(653\) −43.4618 −1.70079 −0.850395 0.526144i \(-0.823637\pi\)
−0.850395 + 0.526144i \(0.823637\pi\)
\(654\) −107.033 −4.18532
\(655\) 5.08475 0.198678
\(656\) −36.0063 −1.40581
\(657\) 12.8571 0.501601
\(658\) 28.6499 1.11689
\(659\) −7.02027 −0.273471 −0.136735 0.990608i \(-0.543661\pi\)
−0.136735 + 0.990608i \(0.543661\pi\)
\(660\) −37.6774 −1.46659
\(661\) −40.1422 −1.56135 −0.780676 0.624936i \(-0.785125\pi\)
−0.780676 + 0.624936i \(0.785125\pi\)
\(662\) 41.0029 1.59362
\(663\) −20.1335 −0.781920
\(664\) 141.014 5.47241
\(665\) 9.25924 0.359058
\(666\) 57.1907 2.21609
\(667\) −12.8298 −0.496773
\(668\) 91.9241 3.55665
\(669\) 62.0616 2.39944
\(670\) 9.50244 0.367111
\(671\) 13.1984 0.509520
\(672\) 74.3910 2.86969
\(673\) 26.0043 1.00239 0.501196 0.865334i \(-0.332893\pi\)
0.501196 + 0.865334i \(0.332893\pi\)
\(674\) −85.5709 −3.29607
\(675\) −12.6452 −0.486713
\(676\) 5.03481 0.193646
\(677\) −5.85024 −0.224843 −0.112421 0.993661i \(-0.535861\pi\)
−0.112421 + 0.993661i \(0.535861\pi\)
\(678\) 122.987 4.72329
\(679\) 13.0266 0.499916
\(680\) −41.2583 −1.58218
\(681\) −21.8117 −0.835826
\(682\) −50.7477 −1.94323
\(683\) 19.6830 0.753149 0.376574 0.926386i \(-0.377102\pi\)
0.376574 + 0.926386i \(0.377102\pi\)
\(684\) 137.706 5.26531
\(685\) 3.00285 0.114733
\(686\) −53.1812 −2.03047
\(687\) 22.2217 0.847811
\(688\) −14.9550 −0.570154
\(689\) 0.0678960 0.00258663
\(690\) −31.4488 −1.19724
\(691\) −45.7830 −1.74167 −0.870833 0.491579i \(-0.836420\pi\)
−0.870833 + 0.491579i \(0.836420\pi\)
\(692\) 98.3939 3.74037
\(693\) −34.2345 −1.30046
\(694\) 33.3978 1.26776
\(695\) −7.29768 −0.276817
\(696\) −41.4924 −1.57277
\(697\) 24.2079 0.916939
\(698\) −35.1910 −1.33200
\(699\) −8.60143 −0.325336
\(700\) 46.3819 1.75307
\(701\) −5.54535 −0.209445 −0.104722 0.994501i \(-0.533395\pi\)
−0.104722 + 0.994501i \(0.533395\pi\)
\(702\) −7.38232 −0.278628
\(703\) −35.9836 −1.35715
\(704\) 58.7701 2.21498
\(705\) −9.55906 −0.360015
\(706\) 38.2514 1.43961
\(707\) −2.15212 −0.0809386
\(708\) 81.4014 3.05925
\(709\) −24.2147 −0.909402 −0.454701 0.890644i \(-0.650254\pi\)
−0.454701 + 0.890644i \(0.650254\pi\)
\(710\) −19.0184 −0.713748
\(711\) 9.63430 0.361314
\(712\) 121.071 4.53732
\(713\) −30.3159 −1.13534
\(714\) −108.281 −4.05232
\(715\) −2.81873 −0.105415
\(716\) −80.5856 −3.01163
\(717\) −50.8810 −1.90019
\(718\) 46.6931 1.74257
\(719\) −24.2294 −0.903603 −0.451802 0.892118i \(-0.649219\pi\)
−0.451802 + 0.892118i \(0.649219\pi\)
\(720\) −30.8644 −1.15025
\(721\) 15.7887 0.588002
\(722\) −70.6657 −2.62991
\(723\) −32.7115 −1.21655
\(724\) −28.7028 −1.06673
\(725\) −8.82115 −0.327609
\(726\) −45.0092 −1.67045
\(727\) −15.9663 −0.592158 −0.296079 0.955163i \(-0.595679\pi\)
−0.296079 + 0.955163i \(0.595679\pi\)
\(728\) 16.3217 0.604922
\(729\) −41.4213 −1.53412
\(730\) 5.69332 0.210719
\(731\) 10.0546 0.371883
\(732\) 42.3035 1.56358
\(733\) −2.61233 −0.0964885 −0.0482442 0.998836i \(-0.515363\pi\)
−0.0482442 + 0.998836i \(0.515363\pi\)
\(734\) −50.3164 −1.85721
\(735\) 5.18293 0.191175
\(736\) 91.3106 3.36575
\(737\) 22.1056 0.814271
\(738\) 34.2761 1.26172
\(739\) 27.8598 1.02484 0.512419 0.858735i \(-0.328749\pi\)
0.512419 + 0.858735i \(0.328749\pi\)
\(740\) 18.1251 0.666291
\(741\) 17.9363 0.658905
\(742\) 0.365156 0.0134053
\(743\) 15.9448 0.584957 0.292478 0.956272i \(-0.405520\pi\)
0.292478 + 0.956272i \(0.405520\pi\)
\(744\) −98.0434 −3.59444
\(745\) −7.63251 −0.279634
\(746\) −73.9987 −2.70929
\(747\) −70.9231 −2.59494
\(748\) −159.232 −5.82210
\(749\) −33.2292 −1.21417
\(750\) −45.4196 −1.65849
\(751\) −10.7258 −0.391391 −0.195695 0.980665i \(-0.562696\pi\)
−0.195695 + 0.980665i \(0.562696\pi\)
\(752\) 60.0877 2.19117
\(753\) −11.3068 −0.412042
\(754\) −5.14983 −0.187546
\(755\) 12.0129 0.437195
\(756\) −28.4156 −1.03347
\(757\) 16.2845 0.591871 0.295936 0.955208i \(-0.404369\pi\)
0.295936 + 0.955208i \(0.404369\pi\)
\(758\) 34.7036 1.26049
\(759\) −73.1597 −2.65553
\(760\) 36.7557 1.33327
\(761\) −38.0708 −1.38007 −0.690033 0.723778i \(-0.742404\pi\)
−0.690033 + 0.723778i \(0.742404\pi\)
\(762\) 132.833 4.81204
\(763\) −30.8215 −1.11581
\(764\) −64.3646 −2.32863
\(765\) 20.7509 0.750250
\(766\) 31.4671 1.13695
\(767\) 6.08981 0.219890
\(768\) −6.24194 −0.225237
\(769\) 32.4063 1.16860 0.584301 0.811537i \(-0.301369\pi\)
0.584301 + 0.811537i \(0.301369\pi\)
\(770\) −15.1596 −0.546314
\(771\) −15.1213 −0.544580
\(772\) −20.6123 −0.741853
\(773\) 36.3400 1.30706 0.653529 0.756902i \(-0.273288\pi\)
0.653529 + 0.756902i \(0.273288\pi\)
\(774\) 14.2363 0.511715
\(775\) −20.8437 −0.748728
\(776\) 51.7107 1.85631
\(777\) 28.6728 1.02863
\(778\) −65.3366 −2.34243
\(779\) −21.5660 −0.772682
\(780\) −9.03458 −0.323490
\(781\) −44.2427 −1.58313
\(782\) −132.909 −4.75281
\(783\) 5.40423 0.193131
\(784\) −32.5796 −1.16356
\(785\) 4.86825 0.173755
\(786\) 52.9737 1.88951
\(787\) 41.9470 1.49525 0.747625 0.664121i \(-0.231194\pi\)
0.747625 + 0.664121i \(0.231194\pi\)
\(788\) −28.2957 −1.00799
\(789\) −46.1718 −1.64376
\(790\) 4.26623 0.151786
\(791\) 35.4158 1.25924
\(792\) −135.898 −4.82892
\(793\) 3.16482 0.112386
\(794\) −62.8829 −2.23163
\(795\) −0.121834 −0.00432101
\(796\) 14.6641 0.519754
\(797\) −12.4774 −0.441971 −0.220985 0.975277i \(-0.570927\pi\)
−0.220985 + 0.975277i \(0.570927\pi\)
\(798\) 96.4641 3.41479
\(799\) −40.3984 −1.42919
\(800\) 62.7807 2.21963
\(801\) −60.8926 −2.15153
\(802\) −55.3112 −1.95311
\(803\) 13.2444 0.467385
\(804\) 70.8527 2.49878
\(805\) −9.05611 −0.319186
\(806\) −12.1687 −0.428623
\(807\) −29.0647 −1.02313
\(808\) −8.54308 −0.300545
\(809\) 3.14230 0.110477 0.0552387 0.998473i \(-0.482408\pi\)
0.0552387 + 0.998473i \(0.482408\pi\)
\(810\) −8.52555 −0.299557
\(811\) 40.3363 1.41640 0.708200 0.706012i \(-0.249508\pi\)
0.708200 + 0.706012i \(0.249508\pi\)
\(812\) −19.8225 −0.695632
\(813\) −65.0192 −2.28032
\(814\) 58.9137 2.06493
\(815\) −2.02917 −0.0710787
\(816\) −227.099 −7.95005
\(817\) −8.95730 −0.313376
\(818\) 36.1697 1.26465
\(819\) −8.20899 −0.286845
\(820\) 10.8629 0.379349
\(821\) 14.6295 0.510571 0.255286 0.966866i \(-0.417830\pi\)
0.255286 + 0.966866i \(0.417830\pi\)
\(822\) 31.2842 1.09116
\(823\) −24.9658 −0.870253 −0.435127 0.900369i \(-0.643296\pi\)
−0.435127 + 0.900369i \(0.643296\pi\)
\(824\) 62.6752 2.18339
\(825\) −50.3010 −1.75126
\(826\) 32.7520 1.13959
\(827\) −5.77869 −0.200945 −0.100472 0.994940i \(-0.532035\pi\)
−0.100472 + 0.994940i \(0.532035\pi\)
\(828\) −134.685 −4.68062
\(829\) −24.7007 −0.857892 −0.428946 0.903330i \(-0.641115\pi\)
−0.428946 + 0.903330i \(0.641115\pi\)
\(830\) −31.4059 −1.09012
\(831\) −12.0304 −0.417329
\(832\) 14.0923 0.488564
\(833\) 21.9041 0.758931
\(834\) −76.0284 −2.63265
\(835\) −12.3403 −0.427055
\(836\) 141.855 4.90614
\(837\) 12.7698 0.441388
\(838\) −21.3535 −0.737644
\(839\) −22.4046 −0.773492 −0.386746 0.922186i \(-0.626401\pi\)
−0.386746 + 0.922186i \(0.626401\pi\)
\(840\) −29.2880 −1.01053
\(841\) −25.2301 −0.870002
\(842\) −48.0057 −1.65438
\(843\) −27.7569 −0.955999
\(844\) 46.4881 1.60019
\(845\) −0.675897 −0.0232515
\(846\) −57.2003 −1.96659
\(847\) −12.9610 −0.445345
\(848\) 0.765843 0.0262992
\(849\) −2.91450 −0.100025
\(850\) −91.3816 −3.13436
\(851\) 35.1942 1.20644
\(852\) −141.806 −4.85820
\(853\) −27.3428 −0.936201 −0.468101 0.883675i \(-0.655061\pi\)
−0.468101 + 0.883675i \(0.655061\pi\)
\(854\) 17.0209 0.582444
\(855\) −18.4863 −0.632217
\(856\) −131.907 −4.50850
\(857\) −28.0922 −0.959612 −0.479806 0.877375i \(-0.659293\pi\)
−0.479806 + 0.877375i \(0.659293\pi\)
\(858\) −29.3660 −1.00254
\(859\) −44.6057 −1.52193 −0.760963 0.648795i \(-0.775273\pi\)
−0.760963 + 0.648795i \(0.775273\pi\)
\(860\) 4.51184 0.153852
\(861\) 17.1844 0.585644
\(862\) 5.01858 0.170933
\(863\) −37.2624 −1.26843 −0.634213 0.773158i \(-0.718676\pi\)
−0.634213 + 0.773158i \(0.718676\pi\)
\(864\) −38.4622 −1.30851
\(865\) −13.2089 −0.449115
\(866\) 62.6923 2.13037
\(867\) 107.551 3.65262
\(868\) −46.8389 −1.58982
\(869\) 9.92457 0.336668
\(870\) 9.24098 0.313299
\(871\) 5.30065 0.179606
\(872\) −122.350 −4.14329
\(873\) −26.0079 −0.880235
\(874\) 118.404 4.00508
\(875\) −13.0792 −0.442157
\(876\) 42.4509 1.43428
\(877\) 44.1809 1.49188 0.745942 0.666011i \(-0.231999\pi\)
0.745942 + 0.666011i \(0.231999\pi\)
\(878\) 4.74554 0.160154
\(879\) −31.9636 −1.07810
\(880\) −31.7943 −1.07179
\(881\) 0.720633 0.0242788 0.0121394 0.999926i \(-0.496136\pi\)
0.0121394 + 0.999926i \(0.496136\pi\)
\(882\) 31.0141 1.04430
\(883\) −15.3712 −0.517283 −0.258642 0.965973i \(-0.583275\pi\)
−0.258642 + 0.965973i \(0.583275\pi\)
\(884\) −38.1819 −1.28419
\(885\) −10.9277 −0.367331
\(886\) 27.6430 0.928683
\(887\) −9.82372 −0.329848 −0.164924 0.986306i \(-0.552738\pi\)
−0.164924 + 0.986306i \(0.552738\pi\)
\(888\) 113.820 3.81955
\(889\) 38.2511 1.28290
\(890\) −26.9643 −0.903845
\(891\) −19.8331 −0.664433
\(892\) 117.696 3.94074
\(893\) 35.9896 1.20435
\(894\) −79.5167 −2.65943
\(895\) 10.8182 0.361613
\(896\) 19.7499 0.659799
\(897\) −17.5428 −0.585736
\(898\) 35.2757 1.17716
\(899\) 8.90806 0.297101
\(900\) −92.6026 −3.08675
\(901\) −0.514895 −0.0171536
\(902\) 35.3088 1.17565
\(903\) 7.13745 0.237519
\(904\) 140.587 4.67586
\(905\) 3.85320 0.128085
\(906\) 125.152 4.15791
\(907\) 36.6227 1.21604 0.608019 0.793923i \(-0.291964\pi\)
0.608019 + 0.793923i \(0.291964\pi\)
\(908\) −41.3644 −1.37273
\(909\) 4.29675 0.142514
\(910\) −3.63508 −0.120502
\(911\) 20.0404 0.663968 0.331984 0.943285i \(-0.392282\pi\)
0.331984 + 0.943285i \(0.392282\pi\)
\(912\) 202.315 6.69931
\(913\) −73.0599 −2.41793
\(914\) 15.2184 0.503379
\(915\) −5.67903 −0.187743
\(916\) 42.1420 1.39241
\(917\) 15.2545 0.503747
\(918\) 55.9844 1.84776
\(919\) −10.1625 −0.335229 −0.167615 0.985853i \(-0.553606\pi\)
−0.167615 + 0.985853i \(0.553606\pi\)
\(920\) −35.9493 −1.18521
\(921\) −68.8355 −2.26821
\(922\) 63.3597 2.08664
\(923\) −10.6088 −0.349194
\(924\) −113.034 −3.71855
\(925\) 24.1978 0.795618
\(926\) 61.5042 2.02115
\(927\) −31.5225 −1.03533
\(928\) −26.8308 −0.880766
\(929\) 16.2125 0.531915 0.265958 0.963985i \(-0.414312\pi\)
0.265958 + 0.963985i \(0.414312\pi\)
\(930\) 21.8357 0.716022
\(931\) −19.5136 −0.639532
\(932\) −16.3120 −0.534319
\(933\) 66.9334 2.19130
\(934\) 104.029 3.40393
\(935\) 21.3761 0.699073
\(936\) −32.5866 −1.06513
\(937\) 25.4576 0.831664 0.415832 0.909441i \(-0.363490\pi\)
0.415832 + 0.909441i \(0.363490\pi\)
\(938\) 28.5077 0.930811
\(939\) −52.5158 −1.71379
\(940\) −18.1281 −0.591274
\(941\) 17.0178 0.554763 0.277382 0.960760i \(-0.410533\pi\)
0.277382 + 0.960760i \(0.410533\pi\)
\(942\) 50.7182 1.65249
\(943\) 21.0929 0.686879
\(944\) 68.6910 2.23570
\(945\) 3.81465 0.124091
\(946\) 14.6653 0.476809
\(947\) 34.6990 1.12757 0.563783 0.825923i \(-0.309346\pi\)
0.563783 + 0.825923i \(0.309346\pi\)
\(948\) 31.8101 1.03315
\(949\) 3.17585 0.103092
\(950\) 81.4088 2.64125
\(951\) 62.7810 2.03581
\(952\) −123.777 −4.01163
\(953\) 44.0452 1.42676 0.713382 0.700776i \(-0.247163\pi\)
0.713382 + 0.700776i \(0.247163\pi\)
\(954\) −0.729041 −0.0236036
\(955\) 8.64061 0.279604
\(956\) −96.4926 −3.12079
\(957\) 21.4974 0.694911
\(958\) −27.7529 −0.896655
\(959\) 9.00870 0.290906
\(960\) −25.2876 −0.816155
\(961\) −9.95093 −0.320998
\(962\) 14.1268 0.455466
\(963\) 66.3428 2.13787
\(964\) −62.0352 −1.99802
\(965\) 2.76710 0.0890760
\(966\) −94.3479 −3.03560
\(967\) −11.1452 −0.358405 −0.179202 0.983812i \(-0.557352\pi\)
−0.179202 + 0.983812i \(0.557352\pi\)
\(968\) −51.4502 −1.65367
\(969\) −136.021 −4.36963
\(970\) −11.5168 −0.369781
\(971\) 37.4073 1.20046 0.600229 0.799828i \(-0.295076\pi\)
0.600229 + 0.799828i \(0.295076\pi\)
\(972\) −105.610 −3.38743
\(973\) −21.8934 −0.701869
\(974\) 79.2170 2.53828
\(975\) −12.0616 −0.386279
\(976\) 35.6981 1.14267
\(977\) −49.0615 −1.56962 −0.784808 0.619739i \(-0.787239\pi\)
−0.784808 + 0.619739i \(0.787239\pi\)
\(978\) −21.1402 −0.675989
\(979\) −62.7272 −2.00477
\(980\) 9.82909 0.313979
\(981\) 61.5359 1.96469
\(982\) −9.59073 −0.306053
\(983\) 52.2865 1.66768 0.833841 0.552005i \(-0.186137\pi\)
0.833841 + 0.552005i \(0.186137\pi\)
\(984\) 68.2157 2.17464
\(985\) 3.79854 0.121032
\(986\) 39.0542 1.24374
\(987\) −28.6776 −0.912818
\(988\) 34.0149 1.08216
\(989\) 8.76080 0.278577
\(990\) 30.2665 0.961932
\(991\) −21.6858 −0.688872 −0.344436 0.938810i \(-0.611930\pi\)
−0.344436 + 0.938810i \(0.611930\pi\)
\(992\) −63.3992 −2.01293
\(993\) −41.0425 −1.30244
\(994\) −57.0561 −1.80971
\(995\) −1.96857 −0.0624080
\(996\) −234.171 −7.41999
\(997\) 23.1905 0.734450 0.367225 0.930132i \(-0.380308\pi\)
0.367225 + 0.930132i \(0.380308\pi\)
\(998\) −84.7696 −2.68333
\(999\) −14.8246 −0.469030
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 \(a_p\))