Properties

Label 8041.2.a.i.1.1
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
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: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} +O(q^{10})\) \(q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} -4.77662 q^{10} +1.00000 q^{11} +18.1596 q^{12} -1.17718 q^{13} -0.0917056 q^{14} +5.22224 q^{15} +19.0784 q^{16} -1.00000 q^{17} -18.1401 q^{18} +1.55104 q^{19} +10.0341 q^{20} +0.100261 q^{21} -2.81193 q^{22} -2.46839 q^{23} -33.7743 q^{24} -2.11443 q^{25} +3.31015 q^{26} +10.6096 q^{27} +0.192644 q^{28} +8.97486 q^{29} -14.6846 q^{30} -0.677587 q^{31} -31.6748 q^{32} +3.07426 q^{33} +2.81193 q^{34} +0.0553996 q^{35} +38.1065 q^{36} -3.61383 q^{37} -4.36143 q^{38} -3.61896 q^{39} -18.6621 q^{40} -5.83154 q^{41} -0.281927 q^{42} -1.00000 q^{43} +5.90697 q^{44} +10.9585 q^{45} +6.94094 q^{46} +9.03871 q^{47} +58.6520 q^{48} -6.99894 q^{49} +5.94565 q^{50} -3.07426 q^{51} -6.95357 q^{52} -2.98614 q^{53} -29.8335 q^{54} +1.69870 q^{55} -0.358291 q^{56} +4.76832 q^{57} -25.2367 q^{58} +9.48257 q^{59} +30.8476 q^{60} +0.450285 q^{61} +1.90533 q^{62} +0.210390 q^{63} +50.9108 q^{64} -1.99967 q^{65} -8.64463 q^{66} +6.42090 q^{67} -5.90697 q^{68} -7.58847 q^{69} -0.155780 q^{70} +10.2825 q^{71} -70.8727 q^{72} +10.9510 q^{73} +10.1619 q^{74} -6.50032 q^{75} +9.16198 q^{76} +0.0326130 q^{77} +10.1763 q^{78} -8.83713 q^{79} +32.4084 q^{80} +13.2634 q^{81} +16.3979 q^{82} +16.2738 q^{83} +0.592239 q^{84} -1.69870 q^{85} +2.81193 q^{86} +27.5911 q^{87} -10.9861 q^{88} +11.5341 q^{89} -30.8144 q^{90} -0.0383914 q^{91} -14.5807 q^{92} -2.08308 q^{93} -25.4162 q^{94} +2.63475 q^{95} -97.3768 q^{96} +2.98376 q^{97} +19.6805 q^{98} +6.45110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81193 −1.98834 −0.994169 0.107835i \(-0.965608\pi\)
−0.994169 + 0.107835i \(0.965608\pi\)
\(3\) 3.07426 1.77493 0.887464 0.460878i \(-0.152465\pi\)
0.887464 + 0.460878i \(0.152465\pi\)
\(4\) 5.90697 2.95349
\(5\) 1.69870 0.759680 0.379840 0.925052i \(-0.375979\pi\)
0.379840 + 0.925052i \(0.375979\pi\)
\(6\) −8.64463 −3.52915
\(7\) 0.0326130 0.0123266 0.00616328 0.999981i \(-0.498038\pi\)
0.00616328 + 0.999981i \(0.498038\pi\)
\(8\) −10.9861 −3.88419
\(9\) 6.45110 2.15037
\(10\) −4.77662 −1.51050
\(11\) 1.00000 0.301511
\(12\) 18.1596 5.24222
\(13\) −1.17718 −0.326491 −0.163245 0.986585i \(-0.552196\pi\)
−0.163245 + 0.986585i \(0.552196\pi\)
\(14\) −0.0917056 −0.0245094
\(15\) 5.22224 1.34838
\(16\) 19.0784 4.76959
\(17\) −1.00000 −0.242536
\(18\) −18.1401 −4.27565
\(19\) 1.55104 0.355834 0.177917 0.984045i \(-0.443064\pi\)
0.177917 + 0.984045i \(0.443064\pi\)
\(20\) 10.0341 2.24370
\(21\) 0.100261 0.0218787
\(22\) −2.81193 −0.599506
\(23\) −2.46839 −0.514694 −0.257347 0.966319i \(-0.582848\pi\)
−0.257347 + 0.966319i \(0.582848\pi\)
\(24\) −33.7743 −6.89415
\(25\) −2.11443 −0.422887
\(26\) 3.31015 0.649174
\(27\) 10.6096 2.04182
\(28\) 0.192644 0.0364063
\(29\) 8.97486 1.66659 0.833295 0.552829i \(-0.186452\pi\)
0.833295 + 0.552829i \(0.186452\pi\)
\(30\) −14.6846 −2.68103
\(31\) −0.677587 −0.121698 −0.0608492 0.998147i \(-0.519381\pi\)
−0.0608492 + 0.998147i \(0.519381\pi\)
\(32\) −31.6748 −5.59937
\(33\) 3.07426 0.535161
\(34\) 2.81193 0.482243
\(35\) 0.0553996 0.00936424
\(36\) 38.1065 6.35108
\(37\) −3.61383 −0.594111 −0.297055 0.954860i \(-0.596005\pi\)
−0.297055 + 0.954860i \(0.596005\pi\)
\(38\) −4.36143 −0.707518
\(39\) −3.61896 −0.579498
\(40\) −18.6621 −2.95074
\(41\) −5.83154 −0.910734 −0.455367 0.890304i \(-0.650492\pi\)
−0.455367 + 0.890304i \(0.650492\pi\)
\(42\) −0.281927 −0.0435023
\(43\) −1.00000 −0.152499
\(44\) 5.90697 0.890510
\(45\) 10.9585 1.63359
\(46\) 6.94094 1.02339
\(47\) 9.03871 1.31843 0.659215 0.751954i \(-0.270889\pi\)
0.659215 + 0.751954i \(0.270889\pi\)
\(48\) 58.6520 8.46568
\(49\) −6.99894 −0.999848
\(50\) 5.94565 0.840841
\(51\) −3.07426 −0.430483
\(52\) −6.95357 −0.964287
\(53\) −2.98614 −0.410178 −0.205089 0.978743i \(-0.565748\pi\)
−0.205089 + 0.978743i \(0.565748\pi\)
\(54\) −29.8335 −4.05982
\(55\) 1.69870 0.229052
\(56\) −0.358291 −0.0478787
\(57\) 4.76832 0.631579
\(58\) −25.2367 −3.31374
\(59\) 9.48257 1.23453 0.617263 0.786757i \(-0.288242\pi\)
0.617263 + 0.786757i \(0.288242\pi\)
\(60\) 30.8476 3.98241
\(61\) 0.450285 0.0576531 0.0288266 0.999584i \(-0.490823\pi\)
0.0288266 + 0.999584i \(0.490823\pi\)
\(62\) 1.90533 0.241977
\(63\) 0.210390 0.0265066
\(64\) 50.9108 6.36385
\(65\) −1.99967 −0.248029
\(66\) −8.64463 −1.06408
\(67\) 6.42090 0.784438 0.392219 0.919872i \(-0.371707\pi\)
0.392219 + 0.919872i \(0.371707\pi\)
\(68\) −5.90697 −0.716326
\(69\) −7.58847 −0.913544
\(70\) −0.155780 −0.0186193
\(71\) 10.2825 1.22031 0.610153 0.792284i \(-0.291108\pi\)
0.610153 + 0.792284i \(0.291108\pi\)
\(72\) −70.8727 −8.35243
\(73\) 10.9510 1.28172 0.640858 0.767659i \(-0.278579\pi\)
0.640858 + 0.767659i \(0.278579\pi\)
\(74\) 10.1619 1.18129
\(75\) −6.50032 −0.750593
\(76\) 9.16198 1.05095
\(77\) 0.0326130 0.00371660
\(78\) 10.1763 1.15224
\(79\) −8.83713 −0.994255 −0.497127 0.867678i \(-0.665612\pi\)
−0.497127 + 0.867678i \(0.665612\pi\)
\(80\) 32.4084 3.62336
\(81\) 13.2634 1.47371
\(82\) 16.3979 1.81085
\(83\) 16.2738 1.78628 0.893142 0.449774i \(-0.148495\pi\)
0.893142 + 0.449774i \(0.148495\pi\)
\(84\) 0.592239 0.0646186
\(85\) −1.69870 −0.184249
\(86\) 2.81193 0.303219
\(87\) 27.5911 2.95808
\(88\) −10.9861 −1.17113
\(89\) 11.5341 1.22262 0.611308 0.791392i \(-0.290643\pi\)
0.611308 + 0.791392i \(0.290643\pi\)
\(90\) −30.8144 −3.24813
\(91\) −0.0383914 −0.00402451
\(92\) −14.5807 −1.52014
\(93\) −2.08308 −0.216006
\(94\) −25.4162 −2.62149
\(95\) 2.63475 0.270320
\(96\) −97.3768 −9.93848
\(97\) 2.98376 0.302955 0.151478 0.988461i \(-0.451597\pi\)
0.151478 + 0.988461i \(0.451597\pi\)
\(98\) 19.6805 1.98804
\(99\) 6.45110 0.648360
\(100\) −12.4899 −1.24899
\(101\) 15.8751 1.57963 0.789814 0.613346i \(-0.210177\pi\)
0.789814 + 0.613346i \(0.210177\pi\)
\(102\) 8.64463 0.855946
\(103\) −2.64399 −0.260520 −0.130260 0.991480i \(-0.541581\pi\)
−0.130260 + 0.991480i \(0.541581\pi\)
\(104\) 12.9327 1.26815
\(105\) 0.170313 0.0166208
\(106\) 8.39682 0.815572
\(107\) 0.540692 0.0522707 0.0261354 0.999658i \(-0.491680\pi\)
0.0261354 + 0.999658i \(0.491680\pi\)
\(108\) 62.6705 6.03048
\(109\) 3.08817 0.295793 0.147897 0.989003i \(-0.452750\pi\)
0.147897 + 0.989003i \(0.452750\pi\)
\(110\) −4.77662 −0.455433
\(111\) −11.1099 −1.05450
\(112\) 0.622203 0.0587927
\(113\) 13.9382 1.31119 0.655596 0.755112i \(-0.272417\pi\)
0.655596 + 0.755112i \(0.272417\pi\)
\(114\) −13.4082 −1.25579
\(115\) −4.19304 −0.391003
\(116\) 53.0142 4.92225
\(117\) −7.59410 −0.702075
\(118\) −26.6644 −2.45465
\(119\) −0.0326130 −0.00298963
\(120\) −57.3723 −5.23735
\(121\) 1.00000 0.0909091
\(122\) −1.26617 −0.114634
\(123\) −17.9277 −1.61649
\(124\) −4.00249 −0.359434
\(125\) −12.0853 −1.08094
\(126\) −0.591602 −0.0527041
\(127\) −6.74189 −0.598246 −0.299123 0.954215i \(-0.596694\pi\)
−0.299123 + 0.954215i \(0.596694\pi\)
\(128\) −79.8081 −7.05411
\(129\) −3.07426 −0.270674
\(130\) 5.62294 0.493165
\(131\) −20.3984 −1.78222 −0.891108 0.453791i \(-0.850071\pi\)
−0.891108 + 0.453791i \(0.850071\pi\)
\(132\) 18.1596 1.58059
\(133\) 0.0505842 0.00438621
\(134\) −18.0552 −1.55973
\(135\) 18.0225 1.55113
\(136\) 10.9861 0.942054
\(137\) 4.73957 0.404928 0.202464 0.979290i \(-0.435105\pi\)
0.202464 + 0.979290i \(0.435105\pi\)
\(138\) 21.3383 1.81643
\(139\) 2.72694 0.231296 0.115648 0.993290i \(-0.463106\pi\)
0.115648 + 0.993290i \(0.463106\pi\)
\(140\) 0.327244 0.0276571
\(141\) 27.7874 2.34012
\(142\) −28.9136 −2.42638
\(143\) −1.17718 −0.0984407
\(144\) 123.076 10.2564
\(145\) 15.2456 1.26607
\(146\) −30.7935 −2.54848
\(147\) −21.5166 −1.77466
\(148\) −21.3468 −1.75470
\(149\) −4.21569 −0.345363 −0.172682 0.984978i \(-0.555243\pi\)
−0.172682 + 0.984978i \(0.555243\pi\)
\(150\) 18.2785 1.49243
\(151\) 6.20840 0.505232 0.252616 0.967567i \(-0.418709\pi\)
0.252616 + 0.967567i \(0.418709\pi\)
\(152\) −17.0400 −1.38213
\(153\) −6.45110 −0.521540
\(154\) −0.0917056 −0.00738985
\(155\) −1.15101 −0.0924517
\(156\) −21.3771 −1.71154
\(157\) −17.3047 −1.38106 −0.690532 0.723302i \(-0.742623\pi\)
−0.690532 + 0.723302i \(0.742623\pi\)
\(158\) 24.8494 1.97691
\(159\) −9.18018 −0.728035
\(160\) −53.8059 −4.25373
\(161\) −0.0805015 −0.00634441
\(162\) −37.2957 −2.93023
\(163\) −8.23562 −0.645064 −0.322532 0.946559i \(-0.604534\pi\)
−0.322532 + 0.946559i \(0.604534\pi\)
\(164\) −34.4468 −2.68984
\(165\) 5.22224 0.406551
\(166\) −45.7609 −3.55174
\(167\) −2.78341 −0.215387 −0.107693 0.994184i \(-0.534346\pi\)
−0.107693 + 0.994184i \(0.534346\pi\)
\(168\) −1.10148 −0.0849812
\(169\) −11.6142 −0.893404
\(170\) 4.77662 0.366350
\(171\) 10.0059 0.765173
\(172\) −5.90697 −0.450402
\(173\) 13.1682 1.00116 0.500579 0.865691i \(-0.333120\pi\)
0.500579 + 0.865691i \(0.333120\pi\)
\(174\) −77.5843 −5.88165
\(175\) −0.0689580 −0.00521274
\(176\) 19.0784 1.43809
\(177\) 29.1519 2.19119
\(178\) −32.4333 −2.43098
\(179\) −1.33522 −0.0997991 −0.0498995 0.998754i \(-0.515890\pi\)
−0.0498995 + 0.998754i \(0.515890\pi\)
\(180\) 64.7313 4.82478
\(181\) 17.2141 1.27951 0.639756 0.768578i \(-0.279035\pi\)
0.639756 + 0.768578i \(0.279035\pi\)
\(182\) 0.107954 0.00800209
\(183\) 1.38430 0.102330
\(184\) 27.1180 1.99917
\(185\) −6.13881 −0.451334
\(186\) 5.85749 0.429492
\(187\) −1.00000 −0.0731272
\(188\) 53.3914 3.89397
\(189\) 0.346011 0.0251686
\(190\) −7.40875 −0.537487
\(191\) 19.6559 1.42225 0.711125 0.703065i \(-0.248186\pi\)
0.711125 + 0.703065i \(0.248186\pi\)
\(192\) 156.513 11.2954
\(193\) 17.1004 1.23091 0.615457 0.788170i \(-0.288971\pi\)
0.615457 + 0.788170i \(0.288971\pi\)
\(194\) −8.39015 −0.602377
\(195\) −6.14751 −0.440233
\(196\) −41.3425 −2.95304
\(197\) 10.4384 0.743704 0.371852 0.928292i \(-0.378723\pi\)
0.371852 + 0.928292i \(0.378723\pi\)
\(198\) −18.1401 −1.28916
\(199\) 10.0793 0.714499 0.357250 0.934009i \(-0.383715\pi\)
0.357250 + 0.934009i \(0.383715\pi\)
\(200\) 23.2295 1.64257
\(201\) 19.7396 1.39232
\(202\) −44.6396 −3.14083
\(203\) 0.292697 0.0205433
\(204\) −18.1596 −1.27143
\(205\) −9.90602 −0.691866
\(206\) 7.43473 0.518002
\(207\) −15.9238 −1.10678
\(208\) −22.4587 −1.55723
\(209\) 1.55104 0.107288
\(210\) −0.478909 −0.0330478
\(211\) 13.2565 0.912612 0.456306 0.889823i \(-0.349172\pi\)
0.456306 + 0.889823i \(0.349172\pi\)
\(212\) −17.6390 −1.21145
\(213\) 31.6110 2.16595
\(214\) −1.52039 −0.103932
\(215\) −1.69870 −0.115850
\(216\) −116.559 −7.93080
\(217\) −0.0220982 −0.00150012
\(218\) −8.68373 −0.588136
\(219\) 33.6662 2.27495
\(220\) 10.0341 0.676502
\(221\) 1.17718 0.0791857
\(222\) 31.2403 2.09671
\(223\) 8.69610 0.582334 0.291167 0.956672i \(-0.405956\pi\)
0.291167 + 0.956672i \(0.405956\pi\)
\(224\) −1.03301 −0.0690210
\(225\) −13.6404 −0.909361
\(226\) −39.1932 −2.60709
\(227\) −26.5657 −1.76322 −0.881612 0.471974i \(-0.843541\pi\)
−0.881612 + 0.471974i \(0.843541\pi\)
\(228\) 28.1663 1.86536
\(229\) 11.8858 0.785439 0.392719 0.919658i \(-0.371534\pi\)
0.392719 + 0.919658i \(0.371534\pi\)
\(230\) 11.7905 0.777445
\(231\) 0.100261 0.00659669
\(232\) −98.5991 −6.47335
\(233\) 13.6653 0.895246 0.447623 0.894222i \(-0.352271\pi\)
0.447623 + 0.894222i \(0.352271\pi\)
\(234\) 21.3541 1.39596
\(235\) 15.3540 1.00159
\(236\) 56.0133 3.64615
\(237\) −27.1677 −1.76473
\(238\) 0.0917056 0.00594439
\(239\) 29.6433 1.91746 0.958732 0.284312i \(-0.0917652\pi\)
0.958732 + 0.284312i \(0.0917652\pi\)
\(240\) 99.6318 6.43121
\(241\) −5.38697 −0.347005 −0.173503 0.984833i \(-0.555508\pi\)
−0.173503 + 0.984833i \(0.555508\pi\)
\(242\) −2.81193 −0.180758
\(243\) 8.94636 0.573909
\(244\) 2.65982 0.170278
\(245\) −11.8891 −0.759564
\(246\) 50.4115 3.21412
\(247\) −1.82586 −0.116177
\(248\) 7.44408 0.472699
\(249\) 50.0301 3.17053
\(250\) 33.9829 2.14927
\(251\) −11.6181 −0.733328 −0.366664 0.930353i \(-0.619500\pi\)
−0.366664 + 0.930353i \(0.619500\pi\)
\(252\) 1.24277 0.0782869
\(253\) −2.46839 −0.155186
\(254\) 18.9578 1.18952
\(255\) −5.22224 −0.327029
\(256\) 122.594 7.66210
\(257\) −24.0147 −1.49799 −0.748997 0.662573i \(-0.769464\pi\)
−0.748997 + 0.662573i \(0.769464\pi\)
\(258\) 8.64463 0.538191
\(259\) −0.117858 −0.00732334
\(260\) −11.8120 −0.732549
\(261\) 57.8977 3.58378
\(262\) 57.3590 3.54365
\(263\) −12.4444 −0.767357 −0.383678 0.923467i \(-0.625343\pi\)
−0.383678 + 0.923467i \(0.625343\pi\)
\(264\) −33.7743 −2.07867
\(265\) −5.07254 −0.311604
\(266\) −0.142240 −0.00872126
\(267\) 35.4590 2.17006
\(268\) 37.9281 2.31683
\(269\) 25.4060 1.54903 0.774516 0.632554i \(-0.217993\pi\)
0.774516 + 0.632554i \(0.217993\pi\)
\(270\) −50.6780 −3.08416
\(271\) 5.23651 0.318095 0.159048 0.987271i \(-0.449158\pi\)
0.159048 + 0.987271i \(0.449158\pi\)
\(272\) −19.0784 −1.15680
\(273\) −0.118025 −0.00714321
\(274\) −13.3273 −0.805134
\(275\) −2.11443 −0.127505
\(276\) −44.8249 −2.69814
\(277\) −3.10858 −0.186776 −0.0933882 0.995630i \(-0.529770\pi\)
−0.0933882 + 0.995630i \(0.529770\pi\)
\(278\) −7.66797 −0.459894
\(279\) −4.37118 −0.261696
\(280\) −0.608628 −0.0363725
\(281\) 13.2004 0.787470 0.393735 0.919224i \(-0.371183\pi\)
0.393735 + 0.919224i \(0.371183\pi\)
\(282\) −78.1362 −4.65295
\(283\) 0.683904 0.0406539 0.0203269 0.999793i \(-0.493529\pi\)
0.0203269 + 0.999793i \(0.493529\pi\)
\(284\) 60.7383 3.60416
\(285\) 8.09992 0.479798
\(286\) 3.31015 0.195733
\(287\) −0.190184 −0.0112262
\(288\) −204.338 −12.0407
\(289\) 1.00000 0.0588235
\(290\) −42.8695 −2.51738
\(291\) 9.17288 0.537724
\(292\) 64.6872 3.78553
\(293\) 3.34223 0.195255 0.0976276 0.995223i \(-0.468875\pi\)
0.0976276 + 0.995223i \(0.468875\pi\)
\(294\) 60.5032 3.52862
\(295\) 16.1080 0.937844
\(296\) 39.7021 2.30764
\(297\) 10.6096 0.615631
\(298\) 11.8543 0.686698
\(299\) 2.90573 0.168043
\(300\) −38.3972 −2.21687
\(301\) −0.0326130 −0.00187978
\(302\) −17.4576 −1.00457
\(303\) 48.8041 2.80372
\(304\) 29.5914 1.69718
\(305\) 0.764898 0.0437979
\(306\) 18.1401 1.03700
\(307\) −32.4504 −1.85204 −0.926021 0.377473i \(-0.876793\pi\)
−0.926021 + 0.377473i \(0.876793\pi\)
\(308\) 0.192644 0.0109769
\(309\) −8.12833 −0.462405
\(310\) 3.23658 0.183825
\(311\) −25.7160 −1.45822 −0.729109 0.684398i \(-0.760065\pi\)
−0.729109 + 0.684398i \(0.760065\pi\)
\(312\) 39.7585 2.25088
\(313\) −10.3094 −0.582720 −0.291360 0.956614i \(-0.594108\pi\)
−0.291360 + 0.956614i \(0.594108\pi\)
\(314\) 48.6596 2.74602
\(315\) 0.357388 0.0201365
\(316\) −52.2007 −2.93652
\(317\) −24.9625 −1.40204 −0.701018 0.713143i \(-0.747271\pi\)
−0.701018 + 0.713143i \(0.747271\pi\)
\(318\) 25.8141 1.44758
\(319\) 8.97486 0.502496
\(320\) 86.4820 4.83449
\(321\) 1.66223 0.0927767
\(322\) 0.226365 0.0126148
\(323\) −1.55104 −0.0863024
\(324\) 78.3464 4.35258
\(325\) 2.48907 0.138069
\(326\) 23.1580 1.28260
\(327\) 9.49385 0.525011
\(328\) 64.0662 3.53746
\(329\) 0.294779 0.0162517
\(330\) −14.6846 −0.808360
\(331\) 4.43030 0.243511 0.121756 0.992560i \(-0.461148\pi\)
0.121756 + 0.992560i \(0.461148\pi\)
\(332\) 96.1291 5.27577
\(333\) −23.3132 −1.27756
\(334\) 7.82676 0.428261
\(335\) 10.9072 0.595922
\(336\) 1.91282 0.104353
\(337\) 17.5446 0.955717 0.477858 0.878437i \(-0.341413\pi\)
0.477858 + 0.878437i \(0.341413\pi\)
\(338\) 32.6585 1.77639
\(339\) 42.8496 2.32727
\(340\) −10.0341 −0.544178
\(341\) −0.677587 −0.0366934
\(342\) −28.1360 −1.52142
\(343\) −0.456547 −0.0246512
\(344\) 10.9861 0.592333
\(345\) −12.8905 −0.694001
\(346\) −37.0281 −1.99064
\(347\) −27.3480 −1.46812 −0.734060 0.679085i \(-0.762377\pi\)
−0.734060 + 0.679085i \(0.762377\pi\)
\(348\) 162.980 8.73663
\(349\) −21.4694 −1.14923 −0.574616 0.818423i \(-0.694849\pi\)
−0.574616 + 0.818423i \(0.694849\pi\)
\(350\) 0.193905 0.0103647
\(351\) −12.4894 −0.666635
\(352\) −31.6748 −1.68827
\(353\) −0.280768 −0.0149438 −0.00747189 0.999972i \(-0.502378\pi\)
−0.00747189 + 0.999972i \(0.502378\pi\)
\(354\) −81.9733 −4.35683
\(355\) 17.4668 0.927042
\(356\) 68.1319 3.61098
\(357\) −0.100261 −0.00530638
\(358\) 3.75455 0.198434
\(359\) 16.9686 0.895569 0.447785 0.894141i \(-0.352213\pi\)
0.447785 + 0.894141i \(0.352213\pi\)
\(360\) −120.391 −6.34517
\(361\) −16.5943 −0.873382
\(362\) −48.4049 −2.54410
\(363\) 3.07426 0.161357
\(364\) −0.226777 −0.0118863
\(365\) 18.6024 0.973694
\(366\) −3.89255 −0.203467
\(367\) 2.64662 0.138152 0.0690762 0.997611i \(-0.477995\pi\)
0.0690762 + 0.997611i \(0.477995\pi\)
\(368\) −47.0928 −2.45488
\(369\) −37.6199 −1.95841
\(370\) 17.2619 0.897404
\(371\) −0.0973870 −0.00505608
\(372\) −12.3047 −0.637970
\(373\) −11.7339 −0.607560 −0.303780 0.952742i \(-0.598249\pi\)
−0.303780 + 0.952742i \(0.598249\pi\)
\(374\) 2.81193 0.145402
\(375\) −37.1533 −1.91859
\(376\) −99.3006 −5.12104
\(377\) −10.5650 −0.544126
\(378\) −0.972959 −0.0500436
\(379\) −13.3780 −0.687183 −0.343592 0.939119i \(-0.611644\pi\)
−0.343592 + 0.939119i \(0.611644\pi\)
\(380\) 15.5634 0.798386
\(381\) −20.7264 −1.06184
\(382\) −55.2711 −2.82791
\(383\) 11.9949 0.612909 0.306455 0.951885i \(-0.400857\pi\)
0.306455 + 0.951885i \(0.400857\pi\)
\(384\) −245.351 −12.5205
\(385\) 0.0553996 0.00282342
\(386\) −48.0852 −2.44747
\(387\) −6.45110 −0.327928
\(388\) 17.6250 0.894774
\(389\) 13.0047 0.659364 0.329682 0.944092i \(-0.393058\pi\)
0.329682 + 0.944092i \(0.393058\pi\)
\(390\) 17.2864 0.875331
\(391\) 2.46839 0.124832
\(392\) 76.8914 3.88360
\(393\) −62.7101 −3.16330
\(394\) −29.3521 −1.47874
\(395\) −15.0116 −0.755315
\(396\) 38.1065 1.91492
\(397\) −6.23401 −0.312876 −0.156438 0.987688i \(-0.550001\pi\)
−0.156438 + 0.987688i \(0.550001\pi\)
\(398\) −28.3422 −1.42067
\(399\) 0.155509 0.00778520
\(400\) −40.3399 −2.01700
\(401\) 4.45609 0.222527 0.111263 0.993791i \(-0.464510\pi\)
0.111263 + 0.993791i \(0.464510\pi\)
\(402\) −55.5063 −2.76840
\(403\) 0.797642 0.0397334
\(404\) 93.7736 4.66541
\(405\) 22.5304 1.11955
\(406\) −0.823045 −0.0408470
\(407\) −3.61383 −0.179131
\(408\) 33.7743 1.67208
\(409\) 20.9966 1.03821 0.519107 0.854709i \(-0.326265\pi\)
0.519107 + 0.854709i \(0.326265\pi\)
\(410\) 27.8551 1.37566
\(411\) 14.5707 0.718718
\(412\) −15.6180 −0.769443
\(413\) 0.309255 0.0152174
\(414\) 44.7767 2.20065
\(415\) 27.6443 1.35700
\(416\) 37.2870 1.82814
\(417\) 8.38333 0.410533
\(418\) −4.36143 −0.213325
\(419\) −5.35864 −0.261787 −0.130893 0.991396i \(-0.541785\pi\)
−0.130893 + 0.991396i \(0.541785\pi\)
\(420\) 1.00603 0.0490894
\(421\) −25.4388 −1.23981 −0.619906 0.784676i \(-0.712829\pi\)
−0.619906 + 0.784676i \(0.712829\pi\)
\(422\) −37.2763 −1.81458
\(423\) 58.3096 2.83511
\(424\) 32.8062 1.59321
\(425\) 2.11443 0.102565
\(426\) −88.8882 −4.30665
\(427\) 0.0146852 0.000710665 0
\(428\) 3.19386 0.154381
\(429\) −3.61896 −0.174725
\(430\) 4.77662 0.230349
\(431\) −0.0597797 −0.00287949 −0.00143974 0.999999i \(-0.500458\pi\)
−0.00143974 + 0.999999i \(0.500458\pi\)
\(432\) 202.414 9.73864
\(433\) −5.52660 −0.265591 −0.132796 0.991143i \(-0.542395\pi\)
−0.132796 + 0.991143i \(0.542395\pi\)
\(434\) 0.0621386 0.00298275
\(435\) 46.8689 2.24719
\(436\) 18.2417 0.873621
\(437\) −3.82858 −0.183146
\(438\) −94.6672 −4.52337
\(439\) −18.1528 −0.866387 −0.433194 0.901301i \(-0.642613\pi\)
−0.433194 + 0.901301i \(0.642613\pi\)
\(440\) −18.6621 −0.889682
\(441\) −45.1508 −2.15004
\(442\) −3.31015 −0.157448
\(443\) −8.33141 −0.395837 −0.197919 0.980218i \(-0.563418\pi\)
−0.197919 + 0.980218i \(0.563418\pi\)
\(444\) −65.6258 −3.11446
\(445\) 19.5930 0.928797
\(446\) −24.4529 −1.15788
\(447\) −12.9602 −0.612994
\(448\) 1.66035 0.0784444
\(449\) 30.1074 1.42086 0.710428 0.703770i \(-0.248501\pi\)
0.710428 + 0.703770i \(0.248501\pi\)
\(450\) 38.3559 1.80812
\(451\) −5.83154 −0.274597
\(452\) 82.3324 3.87259
\(453\) 19.0863 0.896750
\(454\) 74.7009 3.50589
\(455\) −0.0652153 −0.00305734
\(456\) −52.3855 −2.45317
\(457\) 42.0445 1.96676 0.983378 0.181568i \(-0.0581171\pi\)
0.983378 + 0.181568i \(0.0581171\pi\)
\(458\) −33.4222 −1.56172
\(459\) −10.6096 −0.495213
\(460\) −24.7681 −1.15482
\(461\) −13.4748 −0.627586 −0.313793 0.949491i \(-0.601600\pi\)
−0.313793 + 0.949491i \(0.601600\pi\)
\(462\) −0.281927 −0.0131164
\(463\) −42.7892 −1.98858 −0.994292 0.106697i \(-0.965972\pi\)
−0.994292 + 0.106697i \(0.965972\pi\)
\(464\) 171.226 7.94896
\(465\) −3.53852 −0.164095
\(466\) −38.4260 −1.78005
\(467\) −21.0739 −0.975182 −0.487591 0.873072i \(-0.662124\pi\)
−0.487591 + 0.873072i \(0.662124\pi\)
\(468\) −44.8582 −2.07357
\(469\) 0.209405 0.00966943
\(470\) −43.1745 −1.99149
\(471\) −53.1992 −2.45129
\(472\) −104.177 −4.79513
\(473\) −1.00000 −0.0459800
\(474\) 76.3937 3.50888
\(475\) −3.27958 −0.150477
\(476\) −0.192644 −0.00882983
\(477\) −19.2639 −0.882032
\(478\) −83.3549 −3.81256
\(479\) −25.4396 −1.16237 −0.581183 0.813773i \(-0.697410\pi\)
−0.581183 + 0.813773i \(0.697410\pi\)
\(480\) −165.414 −7.55006
\(481\) 4.25413 0.193972
\(482\) 15.1478 0.689963
\(483\) −0.247483 −0.0112609
\(484\) 5.90697 0.268499
\(485\) 5.06851 0.230149
\(486\) −25.1566 −1.14113
\(487\) −11.8702 −0.537891 −0.268946 0.963155i \(-0.586675\pi\)
−0.268946 + 0.963155i \(0.586675\pi\)
\(488\) −4.94690 −0.223936
\(489\) −25.3185 −1.14494
\(490\) 33.4313 1.51027
\(491\) 0.816766 0.0368601 0.0184301 0.999830i \(-0.494133\pi\)
0.0184301 + 0.999830i \(0.494133\pi\)
\(492\) −105.898 −4.77427
\(493\) −8.97486 −0.404207
\(494\) 5.13419 0.230998
\(495\) 10.9585 0.492546
\(496\) −12.9273 −0.580452
\(497\) 0.335343 0.0150422
\(498\) −140.681 −6.30408
\(499\) 31.6757 1.41800 0.709000 0.705208i \(-0.249146\pi\)
0.709000 + 0.705208i \(0.249146\pi\)
\(500\) −71.3873 −3.19254
\(501\) −8.55693 −0.382296
\(502\) 32.6693 1.45810
\(503\) 25.7796 1.14946 0.574729 0.818344i \(-0.305108\pi\)
0.574729 + 0.818344i \(0.305108\pi\)
\(504\) −2.31137 −0.102957
\(505\) 26.9669 1.20001
\(506\) 6.94094 0.308562
\(507\) −35.7053 −1.58573
\(508\) −39.8242 −1.76691
\(509\) −4.79531 −0.212548 −0.106274 0.994337i \(-0.533892\pi\)
−0.106274 + 0.994337i \(0.533892\pi\)
\(510\) 14.6846 0.650245
\(511\) 0.357145 0.0157991
\(512\) −185.109 −8.18073
\(513\) 16.4559 0.726548
\(514\) 67.5277 2.97852
\(515\) −4.49134 −0.197912
\(516\) −18.1596 −0.799431
\(517\) 9.03871 0.397522
\(518\) 0.331409 0.0145613
\(519\) 40.4825 1.77698
\(520\) 21.9687 0.963390
\(521\) −13.8061 −0.604856 −0.302428 0.953172i \(-0.597797\pi\)
−0.302428 + 0.953172i \(0.597797\pi\)
\(522\) −162.805 −7.12576
\(523\) 8.39846 0.367239 0.183620 0.982997i \(-0.441219\pi\)
0.183620 + 0.982997i \(0.441219\pi\)
\(524\) −120.493 −5.26375
\(525\) −0.211995 −0.00925223
\(526\) 34.9929 1.52576
\(527\) 0.677587 0.0295162
\(528\) 58.6520 2.55250
\(529\) −16.9071 −0.735090
\(530\) 14.2636 0.619573
\(531\) 61.1730 2.65468
\(532\) 0.298800 0.0129546
\(533\) 6.86477 0.297346
\(534\) −99.7084 −4.31480
\(535\) 0.918472 0.0397090
\(536\) −70.5410 −3.04691
\(537\) −4.10482 −0.177136
\(538\) −71.4400 −3.08000
\(539\) −6.99894 −0.301466
\(540\) 106.458 4.58123
\(541\) 42.1260 1.81114 0.905569 0.424199i \(-0.139444\pi\)
0.905569 + 0.424199i \(0.139444\pi\)
\(542\) −14.7247 −0.632481
\(543\) 52.9206 2.27104
\(544\) 31.6748 1.35805
\(545\) 5.24586 0.224708
\(546\) 0.331879 0.0142031
\(547\) −3.75042 −0.160356 −0.0801782 0.996781i \(-0.525549\pi\)
−0.0801782 + 0.996781i \(0.525549\pi\)
\(548\) 27.9965 1.19595
\(549\) 2.90483 0.123975
\(550\) 5.94565 0.253523
\(551\) 13.9204 0.593029
\(552\) 83.3680 3.54838
\(553\) −0.288205 −0.0122557
\(554\) 8.74112 0.371374
\(555\) −18.8723 −0.801085
\(556\) 16.1079 0.683129
\(557\) −13.1217 −0.555983 −0.277991 0.960584i \(-0.589669\pi\)
−0.277991 + 0.960584i \(0.589669\pi\)
\(558\) 12.2915 0.520340
\(559\) 1.17718 0.0497894
\(560\) 1.05693 0.0446636
\(561\) −3.07426 −0.129796
\(562\) −37.1187 −1.56576
\(563\) 26.1975 1.10409 0.552046 0.833814i \(-0.313847\pi\)
0.552046 + 0.833814i \(0.313847\pi\)
\(564\) 164.139 6.91151
\(565\) 23.6767 0.996086
\(566\) −1.92309 −0.0808337
\(567\) 0.432559 0.0181658
\(568\) −112.965 −4.73990
\(569\) −37.2159 −1.56017 −0.780087 0.625672i \(-0.784825\pi\)
−0.780087 + 0.625672i \(0.784825\pi\)
\(570\) −22.7765 −0.954001
\(571\) −16.8575 −0.705464 −0.352732 0.935724i \(-0.614747\pi\)
−0.352732 + 0.935724i \(0.614747\pi\)
\(572\) −6.95357 −0.290743
\(573\) 60.4274 2.52439
\(574\) 0.534785 0.0223215
\(575\) 5.21924 0.217657
\(576\) 328.431 13.6846
\(577\) −10.6421 −0.443037 −0.221519 0.975156i \(-0.571101\pi\)
−0.221519 + 0.975156i \(0.571101\pi\)
\(578\) −2.81193 −0.116961
\(579\) 52.5712 2.18478
\(580\) 90.0551 3.73933
\(581\) 0.530739 0.0220187
\(582\) −25.7935 −1.06918
\(583\) −2.98614 −0.123673
\(584\) −120.309 −4.97843
\(585\) −12.9001 −0.533352
\(586\) −9.39814 −0.388233
\(587\) 38.2763 1.57983 0.789915 0.613216i \(-0.210124\pi\)
0.789915 + 0.613216i \(0.210124\pi\)
\(588\) −127.098 −5.24143
\(589\) −1.05097 −0.0433044
\(590\) −45.2946 −1.86475
\(591\) 32.0904 1.32002
\(592\) −68.9461 −2.83367
\(593\) −24.3197 −0.998690 −0.499345 0.866403i \(-0.666426\pi\)
−0.499345 + 0.866403i \(0.666426\pi\)
\(594\) −29.8335 −1.22408
\(595\) −0.0553996 −0.00227116
\(596\) −24.9020 −1.02002
\(597\) 30.9863 1.26818
\(598\) −8.17073 −0.334126
\(599\) −37.1737 −1.51888 −0.759439 0.650578i \(-0.774527\pi\)
−0.759439 + 0.650578i \(0.774527\pi\)
\(600\) 71.4135 2.91545
\(601\) −45.3423 −1.84955 −0.924776 0.380513i \(-0.875747\pi\)
−0.924776 + 0.380513i \(0.875747\pi\)
\(602\) 0.0917056 0.00373764
\(603\) 41.4219 1.68683
\(604\) 36.6728 1.49220
\(605\) 1.69870 0.0690618
\(606\) −137.234 −5.57475
\(607\) −23.3124 −0.946219 −0.473110 0.881004i \(-0.656869\pi\)
−0.473110 + 0.881004i \(0.656869\pi\)
\(608\) −49.1291 −1.99245
\(609\) 0.899828 0.0364629
\(610\) −2.15084 −0.0870850
\(611\) −10.6402 −0.430456
\(612\) −38.1065 −1.54036
\(613\) −12.0420 −0.486372 −0.243186 0.969980i \(-0.578193\pi\)
−0.243186 + 0.969980i \(0.578193\pi\)
\(614\) 91.2483 3.68248
\(615\) −30.4537 −1.22801
\(616\) −0.358291 −0.0144360
\(617\) 13.4782 0.542611 0.271306 0.962493i \(-0.412545\pi\)
0.271306 + 0.962493i \(0.412545\pi\)
\(618\) 22.8563 0.919416
\(619\) −9.94513 −0.399728 −0.199864 0.979824i \(-0.564050\pi\)
−0.199864 + 0.979824i \(0.564050\pi\)
\(620\) −6.79901 −0.273055
\(621\) −26.1886 −1.05091
\(622\) 72.3116 2.89943
\(623\) 0.376163 0.0150707
\(624\) −69.0439 −2.76397
\(625\) −9.95701 −0.398280
\(626\) 28.9893 1.15864
\(627\) 4.76832 0.190428
\(628\) −102.218 −4.07895
\(629\) 3.61383 0.144093
\(630\) −1.00495 −0.0400382
\(631\) −7.73143 −0.307783 −0.153892 0.988088i \(-0.549181\pi\)
−0.153892 + 0.988088i \(0.549181\pi\)
\(632\) 97.0860 3.86187
\(633\) 40.7538 1.61982
\(634\) 70.1930 2.78772
\(635\) −11.4524 −0.454476
\(636\) −54.2271 −2.15024
\(637\) 8.23901 0.326441
\(638\) −25.2367 −0.999131
\(639\) 66.3333 2.62410
\(640\) −135.570 −5.35886
\(641\) −41.8758 −1.65400 −0.826998 0.562205i \(-0.809953\pi\)
−0.826998 + 0.562205i \(0.809953\pi\)
\(642\) −4.67408 −0.184471
\(643\) −38.1218 −1.50338 −0.751688 0.659519i \(-0.770760\pi\)
−0.751688 + 0.659519i \(0.770760\pi\)
\(644\) −0.475520 −0.0187381
\(645\) −5.22224 −0.205625
\(646\) 4.36143 0.171598
\(647\) −22.9790 −0.903397 −0.451698 0.892171i \(-0.649182\pi\)
−0.451698 + 0.892171i \(0.649182\pi\)
\(648\) −145.713 −5.72416
\(649\) 9.48257 0.372223
\(650\) −6.99909 −0.274527
\(651\) −0.0679356 −0.00266261
\(652\) −48.6476 −1.90519
\(653\) −15.0408 −0.588592 −0.294296 0.955714i \(-0.595085\pi\)
−0.294296 + 0.955714i \(0.595085\pi\)
\(654\) −26.6961 −1.04390
\(655\) −34.6507 −1.35391
\(656\) −111.256 −4.34383
\(657\) 70.6459 2.75616
\(658\) −0.828900 −0.0323139
\(659\) 20.6144 0.803024 0.401512 0.915854i \(-0.368485\pi\)
0.401512 + 0.915854i \(0.368485\pi\)
\(660\) 30.8476 1.20074
\(661\) −26.2738 −1.02193 −0.510966 0.859601i \(-0.670712\pi\)
−0.510966 + 0.859601i \(0.670712\pi\)
\(662\) −12.4577 −0.484182
\(663\) 3.61896 0.140549
\(664\) −178.787 −6.93827
\(665\) 0.0859272 0.00333211
\(666\) 65.5552 2.54021
\(667\) −22.1534 −0.857784
\(668\) −16.4415 −0.636142
\(669\) 26.7341 1.03360
\(670\) −30.6702 −1.18489
\(671\) 0.450285 0.0173831
\(672\) −3.17575 −0.122507
\(673\) −0.975638 −0.0376081 −0.0188040 0.999823i \(-0.505986\pi\)
−0.0188040 + 0.999823i \(0.505986\pi\)
\(674\) −49.3343 −1.90029
\(675\) −22.4333 −0.863457
\(676\) −68.6050 −2.63866
\(677\) 40.5937 1.56014 0.780071 0.625691i \(-0.215183\pi\)
0.780071 + 0.625691i \(0.215183\pi\)
\(678\) −120.490 −4.62740
\(679\) 0.0973095 0.00373440
\(680\) 18.6621 0.715660
\(681\) −81.6698 −3.12960
\(682\) 1.90533 0.0729589
\(683\) −26.9547 −1.03139 −0.515696 0.856772i \(-0.672467\pi\)
−0.515696 + 0.856772i \(0.672467\pi\)
\(684\) 59.1048 2.25993
\(685\) 8.05108 0.307616
\(686\) 1.28378 0.0490150
\(687\) 36.5402 1.39410
\(688\) −19.0784 −0.727356
\(689\) 3.51522 0.133919
\(690\) 36.2472 1.37991
\(691\) −25.2803 −0.961709 −0.480855 0.876800i \(-0.659673\pi\)
−0.480855 + 0.876800i \(0.659673\pi\)
\(692\) 77.7841 2.95691
\(693\) 0.210390 0.00799205
\(694\) 76.9009 2.91912
\(695\) 4.63224 0.175711
\(696\) −303.120 −11.4897
\(697\) 5.83154 0.220885
\(698\) 60.3706 2.28506
\(699\) 42.0109 1.58900
\(700\) −0.407333 −0.0153957
\(701\) 26.5820 1.00399 0.501994 0.864871i \(-0.332600\pi\)
0.501994 + 0.864871i \(0.332600\pi\)
\(702\) 35.1194 1.32549
\(703\) −5.60522 −0.211405
\(704\) 50.9108 1.91877
\(705\) 47.2023 1.77774
\(706\) 0.789501 0.0297133
\(707\) 0.517734 0.0194714
\(708\) 172.200 6.47166
\(709\) −30.6910 −1.15263 −0.576313 0.817229i \(-0.695509\pi\)
−0.576313 + 0.817229i \(0.695509\pi\)
\(710\) −49.1155 −1.84327
\(711\) −57.0092 −2.13801
\(712\) −126.716 −4.74888
\(713\) 1.67255 0.0626374
\(714\) 0.281927 0.0105509
\(715\) −1.99967 −0.0747834
\(716\) −7.88711 −0.294755
\(717\) 91.1312 3.40336
\(718\) −47.7146 −1.78069
\(719\) −22.6373 −0.844229 −0.422114 0.906543i \(-0.638712\pi\)
−0.422114 + 0.906543i \(0.638712\pi\)
\(720\) 209.070 7.79156
\(721\) −0.0862286 −0.00321132
\(722\) 46.6620 1.73658
\(723\) −16.5610 −0.615909
\(724\) 101.683 3.77902
\(725\) −18.9767 −0.704778
\(726\) −8.64463 −0.320832
\(727\) −53.3661 −1.97924 −0.989619 0.143717i \(-0.954094\pi\)
−0.989619 + 0.143717i \(0.954094\pi\)
\(728\) 0.421773 0.0156320
\(729\) −12.2867 −0.455061
\(730\) −52.3087 −1.93603
\(731\) 1.00000 0.0369863
\(732\) 8.17700 0.302231
\(733\) −13.7982 −0.509648 −0.254824 0.966987i \(-0.582018\pi\)
−0.254824 + 0.966987i \(0.582018\pi\)
\(734\) −7.44212 −0.274694
\(735\) −36.5501 −1.34817
\(736\) 78.1857 2.88196
\(737\) 6.42090 0.236517
\(738\) 105.785 3.89398
\(739\) 23.3295 0.858188 0.429094 0.903260i \(-0.358833\pi\)
0.429094 + 0.903260i \(0.358833\pi\)
\(740\) −36.2618 −1.33301
\(741\) −5.61317 −0.206205
\(742\) 0.273846 0.0100532
\(743\) 15.7367 0.577323 0.288662 0.957431i \(-0.406790\pi\)
0.288662 + 0.957431i \(0.406790\pi\)
\(744\) 22.8851 0.839007
\(745\) −7.16118 −0.262365
\(746\) 32.9951 1.20803
\(747\) 104.984 3.84117
\(748\) −5.90697 −0.215980
\(749\) 0.0176336 0.000644318 0
\(750\) 104.473 3.81480
\(751\) 7.73250 0.282163 0.141081 0.989998i \(-0.454942\pi\)
0.141081 + 0.989998i \(0.454942\pi\)
\(752\) 172.444 6.28838
\(753\) −35.7171 −1.30160
\(754\) 29.7082 1.08191
\(755\) 10.5462 0.383815
\(756\) 2.04388 0.0743350
\(757\) −13.1416 −0.477638 −0.238819 0.971064i \(-0.576760\pi\)
−0.238819 + 0.971064i \(0.576760\pi\)
\(758\) 37.6181 1.36635
\(759\) −7.58847 −0.275444
\(760\) −28.9458 −1.04997
\(761\) 9.76954 0.354146 0.177073 0.984198i \(-0.443337\pi\)
0.177073 + 0.984198i \(0.443337\pi\)
\(762\) 58.2811 2.11130
\(763\) 0.100715 0.00364611
\(764\) 116.107 4.20060
\(765\) −10.9585 −0.396204
\(766\) −33.7288 −1.21867
\(767\) −11.1627 −0.403061
\(768\) 376.885 13.5997
\(769\) 18.0080 0.649385 0.324693 0.945820i \(-0.394739\pi\)
0.324693 + 0.945820i \(0.394739\pi\)
\(770\) −0.155780 −0.00561392
\(771\) −73.8275 −2.65883
\(772\) 101.012 3.63549
\(773\) 27.8734 1.00254 0.501268 0.865292i \(-0.332867\pi\)
0.501268 + 0.865292i \(0.332867\pi\)
\(774\) 18.1401 0.652031
\(775\) 1.43271 0.0514646
\(776\) −32.7801 −1.17674
\(777\) −0.362327 −0.0129984
\(778\) −36.5683 −1.31104
\(779\) −9.04498 −0.324070
\(780\) −36.3132 −1.30022
\(781\) 10.2825 0.367936
\(782\) −6.94094 −0.248207
\(783\) 95.2196 3.40287
\(784\) −133.528 −4.76887
\(785\) −29.3954 −1.04917
\(786\) 176.337 6.28972
\(787\) 37.5912 1.33998 0.669990 0.742370i \(-0.266298\pi\)
0.669990 + 0.742370i \(0.266298\pi\)
\(788\) 61.6593 2.19652
\(789\) −38.2575 −1.36200
\(790\) 42.2116 1.50182
\(791\) 0.454566 0.0161625
\(792\) −70.8727 −2.51835
\(793\) −0.530067 −0.0188232
\(794\) 17.5296 0.622103
\(795\) −15.5943 −0.553074
\(796\) 59.5379 2.11026
\(797\) −23.8503 −0.844821 −0.422411 0.906405i \(-0.638816\pi\)
−0.422411 + 0.906405i \(0.638816\pi\)
\(798\) −0.437282 −0.0154796
\(799\) −9.03871 −0.319766
\(800\) 66.9743 2.36790
\(801\) 74.4079 2.62907
\(802\) −12.5302 −0.442458
\(803\) 10.9510 0.386452
\(804\) 116.601 4.11220
\(805\) −0.136748 −0.00481972
\(806\) −2.24292 −0.0790034
\(807\) 78.1048 2.74942
\(808\) −174.406 −6.13558
\(809\) 11.2649 0.396052 0.198026 0.980197i \(-0.436547\pi\)
0.198026 + 0.980197i \(0.436547\pi\)
\(810\) −63.3541 −2.22604
\(811\) 14.6532 0.514542 0.257271 0.966339i \(-0.417177\pi\)
0.257271 + 0.966339i \(0.417177\pi\)
\(812\) 1.72895 0.0606744
\(813\) 16.0984 0.564596
\(814\) 10.1619 0.356173
\(815\) −13.9898 −0.490042
\(816\) −58.6520 −2.05323
\(817\) −1.55104 −0.0542642
\(818\) −59.0410 −2.06432
\(819\) −0.247667 −0.00865417
\(820\) −58.5146 −2.04342
\(821\) −1.75764 −0.0613420 −0.0306710 0.999530i \(-0.509764\pi\)
−0.0306710 + 0.999530i \(0.509764\pi\)
\(822\) −40.9718 −1.42905
\(823\) 42.5583 1.48349 0.741745 0.670682i \(-0.233999\pi\)
0.741745 + 0.670682i \(0.233999\pi\)
\(824\) 29.0473 1.01191
\(825\) −6.50032 −0.226312
\(826\) −0.869605 −0.0302574
\(827\) −3.52560 −0.122597 −0.0612986 0.998119i \(-0.519524\pi\)
−0.0612986 + 0.998119i \(0.519524\pi\)
\(828\) −94.0614 −3.26886
\(829\) 35.4349 1.23070 0.615352 0.788252i \(-0.289014\pi\)
0.615352 + 0.788252i \(0.289014\pi\)
\(830\) −77.7339 −2.69818
\(831\) −9.55659 −0.331514
\(832\) −59.9312 −2.07774
\(833\) 6.99894 0.242499
\(834\) −23.5734 −0.816279
\(835\) −4.72817 −0.163625
\(836\) 9.16198 0.316874
\(837\) −7.18892 −0.248486
\(838\) 15.0681 0.520520
\(839\) 38.0672 1.31423 0.657113 0.753792i \(-0.271777\pi\)
0.657113 + 0.753792i \(0.271777\pi\)
\(840\) −1.87108 −0.0645585
\(841\) 51.5481 1.77752
\(842\) 71.5322 2.46516
\(843\) 40.5815 1.39770
\(844\) 78.3055 2.69539
\(845\) −19.7291 −0.678701
\(846\) −163.963 −5.63715
\(847\) 0.0326130 0.00112060
\(848\) −56.9707 −1.95638
\(849\) 2.10250 0.0721577
\(850\) −5.94565 −0.203934
\(851\) 8.92034 0.305785
\(852\) 186.726 6.39711
\(853\) −42.4803 −1.45450 −0.727248 0.686375i \(-0.759201\pi\)
−0.727248 + 0.686375i \(0.759201\pi\)
\(854\) −0.0412937 −0.00141304
\(855\) 16.9970 0.581287
\(856\) −5.94013 −0.203029
\(857\) −42.7923 −1.46176 −0.730879 0.682507i \(-0.760890\pi\)
−0.730879 + 0.682507i \(0.760890\pi\)
\(858\) 10.1763 0.347413
\(859\) 6.92457 0.236263 0.118132 0.992998i \(-0.462310\pi\)
0.118132 + 0.992998i \(0.462310\pi\)
\(860\) −10.0341 −0.342162
\(861\) −0.584676 −0.0199257
\(862\) 0.168097 0.00572539
\(863\) 34.3960 1.17085 0.585427 0.810725i \(-0.300927\pi\)
0.585427 + 0.810725i \(0.300927\pi\)
\(864\) −336.057 −11.4329
\(865\) 22.3687 0.760560
\(866\) 15.5404 0.528085
\(867\) 3.07426 0.104407
\(868\) −0.130533 −0.00443059
\(869\) −8.83713 −0.299779
\(870\) −131.792 −4.46817
\(871\) −7.55856 −0.256112
\(872\) −33.9271 −1.14892
\(873\) 19.2486 0.651465
\(874\) 10.7657 0.364155
\(875\) −0.394137 −0.0133242
\(876\) 198.865 6.71904
\(877\) −9.57617 −0.323364 −0.161682 0.986843i \(-0.551692\pi\)
−0.161682 + 0.986843i \(0.551692\pi\)
\(878\) 51.0446 1.72267
\(879\) 10.2749 0.346564
\(880\) 32.4084 1.09249
\(881\) −5.46537 −0.184133 −0.0920664 0.995753i \(-0.529347\pi\)
−0.0920664 + 0.995753i \(0.529347\pi\)
\(882\) 126.961 4.27500
\(883\) −45.4479 −1.52944 −0.764722 0.644360i \(-0.777124\pi\)
−0.764722 + 0.644360i \(0.777124\pi\)
\(884\) 6.95357 0.233874
\(885\) 49.5202 1.66460
\(886\) 23.4274 0.787058
\(887\) −34.7881 −1.16807 −0.584035 0.811729i \(-0.698527\pi\)
−0.584035 + 0.811729i \(0.698527\pi\)
\(888\) 122.055 4.09589
\(889\) −0.219873 −0.00737432
\(890\) −55.0942 −1.84676
\(891\) 13.2634 0.444340
\(892\) 51.3676 1.71992
\(893\) 14.0194 0.469143
\(894\) 36.4431 1.21884
\(895\) −2.26813 −0.0758154
\(896\) −2.60278 −0.0869529
\(897\) 8.93299 0.298264
\(898\) −84.6600 −2.82514
\(899\) −6.08125 −0.202821
\(900\) −80.5736 −2.68579
\(901\) 2.98614 0.0994827
\(902\) 16.3979 0.545991
\(903\) −0.100261 −0.00333648
\(904\) −153.127 −5.09292
\(905\) 29.2415 0.972020
\(906\) −53.6693 −1.78304
\(907\) −17.3796 −0.577081 −0.288540 0.957468i \(-0.593170\pi\)
−0.288540 + 0.957468i \(0.593170\pi\)
\(908\) −156.923 −5.20766
\(909\) 102.412 3.39678
\(910\) 0.183381 0.00607902
\(911\) 52.8274 1.75025 0.875125 0.483898i \(-0.160779\pi\)
0.875125 + 0.483898i \(0.160779\pi\)
\(912\) 90.9718 3.01238
\(913\) 16.2738 0.538585
\(914\) −118.226 −3.91058
\(915\) 2.35150 0.0777381
\(916\) 70.2094 2.31978
\(917\) −0.665253 −0.0219686
\(918\) 29.8335 0.984651
\(919\) −55.5962 −1.83395 −0.916975 0.398944i \(-0.869377\pi\)
−0.916975 + 0.398944i \(0.869377\pi\)
\(920\) 46.0653 1.51873
\(921\) −99.7610 −3.28724
\(922\) 37.8904 1.24785
\(923\) −12.1043 −0.398419
\(924\) 0.592239 0.0194832
\(925\) 7.64121 0.251241
\(926\) 120.320 3.95397
\(927\) −17.0567 −0.560214
\(928\) −284.277 −9.33186
\(929\) −16.0534 −0.526696 −0.263348 0.964701i \(-0.584827\pi\)
−0.263348 + 0.964701i \(0.584827\pi\)
\(930\) 9.95009 0.326276
\(931\) −10.8557 −0.355780
\(932\) 80.7208 2.64410
\(933\) −79.0576 −2.58823
\(934\) 59.2583 1.93899
\(935\) −1.69870 −0.0555533
\(936\) 83.4300 2.72699
\(937\) 30.0948 0.983154 0.491577 0.870834i \(-0.336421\pi\)
0.491577 + 0.870834i \(0.336421\pi\)
\(938\) −0.588833 −0.0192261
\(939\) −31.6937 −1.03429
\(940\) 90.6957 2.95817
\(941\) −38.9713 −1.27043 −0.635214 0.772336i \(-0.719088\pi\)
−0.635214 + 0.772336i \(0.719088\pi\)
\(942\) 149.592 4.87399
\(943\) 14.3945 0.468749
\(944\) 180.912 5.88818
\(945\) 0.587767 0.0191201
\(946\) 2.81193 0.0914239
\(947\) 25.7207 0.835810 0.417905 0.908491i \(-0.362764\pi\)
0.417905 + 0.908491i \(0.362764\pi\)
\(948\) −160.479 −5.21210
\(949\) −12.8913 −0.418469
\(950\) 9.22196 0.299200
\(951\) −76.7415 −2.48851
\(952\) 0.358291 0.0116123
\(953\) −25.5181 −0.826612 −0.413306 0.910592i \(-0.635626\pi\)
−0.413306 + 0.910592i \(0.635626\pi\)
\(954\) 54.1687 1.75378
\(955\) 33.3894 1.08045
\(956\) 175.102 5.66320
\(957\) 27.5911 0.891893
\(958\) 71.5345 2.31117
\(959\) 0.154571 0.00499137
\(960\) 265.868 8.58086
\(961\) −30.5409 −0.985190
\(962\) −11.9623 −0.385681
\(963\) 3.48806 0.112401
\(964\) −31.8207 −1.02487
\(965\) 29.0484 0.935101
\(966\) 0.695905 0.0223904
\(967\) −18.0109 −0.579193 −0.289596 0.957149i \(-0.593521\pi\)
−0.289596 + 0.957149i \(0.593521\pi\)
\(968\) −10.9861 −0.353108
\(969\) −4.76832 −0.153181
\(970\) −14.2523 −0.457614
\(971\) −10.5123 −0.337354 −0.168677 0.985671i \(-0.553950\pi\)
−0.168677 + 0.985671i \(0.553950\pi\)
\(972\) 52.8459 1.69503
\(973\) 0.0889336 0.00285108
\(974\) 33.3783 1.06951
\(975\) 7.65205 0.245062
\(976\) 8.59071 0.274982
\(977\) −14.7191 −0.470907 −0.235454 0.971886i \(-0.575658\pi\)
−0.235454 + 0.971886i \(0.575658\pi\)
\(978\) 71.1939 2.27653
\(979\) 11.5341 0.368633
\(980\) −70.2284 −2.24336
\(981\) 19.9221 0.636063
\(982\) −2.29669 −0.0732904
\(983\) 33.8125 1.07845 0.539226 0.842161i \(-0.318717\pi\)
0.539226 + 0.842161i \(0.318717\pi\)
\(984\) 196.956 6.27874
\(985\) 17.7316 0.564977
\(986\) 25.2367 0.803701
\(987\) 0.906230 0.0288456
\(988\) −10.7853 −0.343126
\(989\) 2.46839 0.0784901
\(990\) −30.8144 −0.979347
\(991\) 30.6661 0.974142 0.487071 0.873362i \(-0.338065\pi\)
0.487071 + 0.873362i \(0.338065\pi\)
\(992\) 21.4625 0.681434
\(993\) 13.6199 0.432215
\(994\) −0.942961 −0.0299089
\(995\) 17.1216 0.542791
\(996\) 295.526 9.36410
\(997\) 12.6168 0.399578 0.199789 0.979839i \(-0.435974\pi\)
0.199789 + 0.979839i \(0.435974\pi\)
\(998\) −89.0701 −2.81946
\(999\) −38.3413 −1.21306
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 \(a_p\))