Properties

Label 8007.2.a.f.1.15
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.38255 q^{2} -1.00000 q^{3} -0.0885651 q^{4} +2.12725 q^{5} +1.38255 q^{6} -0.203962 q^{7} +2.88754 q^{8} +1.00000 q^{9} -2.94103 q^{10} -1.88271 q^{11} +0.0885651 q^{12} +3.56447 q^{13} +0.281986 q^{14} -2.12725 q^{15} -3.81503 q^{16} -1.00000 q^{17} -1.38255 q^{18} -0.0124475 q^{19} -0.188400 q^{20} +0.203962 q^{21} +2.60293 q^{22} +6.58314 q^{23} -2.88754 q^{24} -0.474791 q^{25} -4.92804 q^{26} -1.00000 q^{27} +0.0180639 q^{28} +0.647363 q^{29} +2.94103 q^{30} +0.398581 q^{31} -0.500626 q^{32} +1.88271 q^{33} +1.38255 q^{34} -0.433878 q^{35} -0.0885651 q^{36} +4.09354 q^{37} +0.0172092 q^{38} -3.56447 q^{39} +6.14253 q^{40} -12.2874 q^{41} -0.281986 q^{42} -8.80499 q^{43} +0.166742 q^{44} +2.12725 q^{45} -9.10150 q^{46} +5.83223 q^{47} +3.81503 q^{48} -6.95840 q^{49} +0.656421 q^{50} +1.00000 q^{51} -0.315687 q^{52} -1.05821 q^{53} +1.38255 q^{54} -4.00500 q^{55} -0.588947 q^{56} +0.0124475 q^{57} -0.895010 q^{58} -14.7742 q^{59} +0.188400 q^{60} +2.57004 q^{61} -0.551057 q^{62} -0.203962 q^{63} +8.32219 q^{64} +7.58252 q^{65} -2.60293 q^{66} +6.56955 q^{67} +0.0885651 q^{68} -6.58314 q^{69} +0.599857 q^{70} +3.69245 q^{71} +2.88754 q^{72} +0.453140 q^{73} -5.65951 q^{74} +0.474791 q^{75} +0.00110241 q^{76} +0.384001 q^{77} +4.92804 q^{78} -2.56543 q^{79} -8.11553 q^{80} +1.00000 q^{81} +16.9879 q^{82} +8.30907 q^{83} -0.0180639 q^{84} -2.12725 q^{85} +12.1733 q^{86} -0.647363 q^{87} -5.43640 q^{88} -15.5694 q^{89} -2.94103 q^{90} -0.727014 q^{91} -0.583036 q^{92} -0.398581 q^{93} -8.06333 q^{94} -0.0264789 q^{95} +0.500626 q^{96} -12.1019 q^{97} +9.62031 q^{98} -1.88271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38255 −0.977608 −0.488804 0.872394i \(-0.662567\pi\)
−0.488804 + 0.872394i \(0.662567\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.0885651 −0.0442825
\(5\) 2.12725 0.951337 0.475668 0.879625i \(-0.342206\pi\)
0.475668 + 0.879625i \(0.342206\pi\)
\(6\) 1.38255 0.564422
\(7\) −0.203962 −0.0770903 −0.0385451 0.999257i \(-0.512272\pi\)
−0.0385451 + 0.999257i \(0.512272\pi\)
\(8\) 2.88754 1.02090
\(9\) 1.00000 0.333333
\(10\) −2.94103 −0.930035
\(11\) −1.88271 −0.567658 −0.283829 0.958875i \(-0.591605\pi\)
−0.283829 + 0.958875i \(0.591605\pi\)
\(12\) 0.0885651 0.0255665
\(13\) 3.56447 0.988605 0.494302 0.869290i \(-0.335424\pi\)
0.494302 + 0.869290i \(0.335424\pi\)
\(14\) 0.281986 0.0753641
\(15\) −2.12725 −0.549255
\(16\) −3.81503 −0.953757
\(17\) −1.00000 −0.242536
\(18\) −1.38255 −0.325869
\(19\) −0.0124475 −0.00285564 −0.00142782 0.999999i \(-0.500454\pi\)
−0.00142782 + 0.999999i \(0.500454\pi\)
\(20\) −0.188400 −0.0421276
\(21\) 0.203962 0.0445081
\(22\) 2.60293 0.554947
\(23\) 6.58314 1.37268 0.686340 0.727281i \(-0.259216\pi\)
0.686340 + 0.727281i \(0.259216\pi\)
\(24\) −2.88754 −0.589416
\(25\) −0.474791 −0.0949582
\(26\) −4.92804 −0.966468
\(27\) −1.00000 −0.192450
\(28\) 0.0180639 0.00341375
\(29\) 0.647363 0.120212 0.0601062 0.998192i \(-0.480856\pi\)
0.0601062 + 0.998192i \(0.480856\pi\)
\(30\) 2.94103 0.536956
\(31\) 0.398581 0.0715873 0.0357936 0.999359i \(-0.488604\pi\)
0.0357936 + 0.999359i \(0.488604\pi\)
\(32\) −0.500626 −0.0884990
\(33\) 1.88271 0.327738
\(34\) 1.38255 0.237105
\(35\) −0.433878 −0.0733388
\(36\) −0.0885651 −0.0147608
\(37\) 4.09354 0.672974 0.336487 0.941688i \(-0.390761\pi\)
0.336487 + 0.941688i \(0.390761\pi\)
\(38\) 0.0172092 0.00279170
\(39\) −3.56447 −0.570771
\(40\) 6.14253 0.971219
\(41\) −12.2874 −1.91897 −0.959486 0.281756i \(-0.909083\pi\)
−0.959486 + 0.281756i \(0.909083\pi\)
\(42\) −0.281986 −0.0435115
\(43\) −8.80499 −1.34275 −0.671374 0.741118i \(-0.734296\pi\)
−0.671374 + 0.741118i \(0.734296\pi\)
\(44\) 0.166742 0.0251374
\(45\) 2.12725 0.317112
\(46\) −9.10150 −1.34194
\(47\) 5.83223 0.850718 0.425359 0.905025i \(-0.360148\pi\)
0.425359 + 0.905025i \(0.360148\pi\)
\(48\) 3.81503 0.550652
\(49\) −6.95840 −0.994057
\(50\) 0.656421 0.0928319
\(51\) 1.00000 0.140028
\(52\) −0.315687 −0.0437779
\(53\) −1.05821 −0.145356 −0.0726778 0.997355i \(-0.523154\pi\)
−0.0726778 + 0.997355i \(0.523154\pi\)
\(54\) 1.38255 0.188141
\(55\) −4.00500 −0.540034
\(56\) −0.588947 −0.0787014
\(57\) 0.0124475 0.00164871
\(58\) −0.895010 −0.117521
\(59\) −14.7742 −1.92344 −0.961720 0.274034i \(-0.911642\pi\)
−0.961720 + 0.274034i \(0.911642\pi\)
\(60\) 0.188400 0.0243224
\(61\) 2.57004 0.329060 0.164530 0.986372i \(-0.447389\pi\)
0.164530 + 0.986372i \(0.447389\pi\)
\(62\) −0.551057 −0.0699843
\(63\) −0.203962 −0.0256968
\(64\) 8.32219 1.04027
\(65\) 7.58252 0.940496
\(66\) −2.60293 −0.320399
\(67\) 6.56955 0.802598 0.401299 0.915947i \(-0.368559\pi\)
0.401299 + 0.915947i \(0.368559\pi\)
\(68\) 0.0885651 0.0107401
\(69\) −6.58314 −0.792517
\(70\) 0.599857 0.0716966
\(71\) 3.69245 0.438214 0.219107 0.975701i \(-0.429686\pi\)
0.219107 + 0.975701i \(0.429686\pi\)
\(72\) 2.88754 0.340300
\(73\) 0.453140 0.0530360 0.0265180 0.999648i \(-0.491558\pi\)
0.0265180 + 0.999648i \(0.491558\pi\)
\(74\) −5.65951 −0.657905
\(75\) 0.474791 0.0548241
\(76\) 0.00110241 0.000126455 0
\(77\) 0.384001 0.0437609
\(78\) 4.92804 0.557991
\(79\) −2.56543 −0.288634 −0.144317 0.989532i \(-0.546098\pi\)
−0.144317 + 0.989532i \(0.546098\pi\)
\(80\) −8.11553 −0.907344
\(81\) 1.00000 0.111111
\(82\) 16.9879 1.87600
\(83\) 8.30907 0.912039 0.456020 0.889970i \(-0.349275\pi\)
0.456020 + 0.889970i \(0.349275\pi\)
\(84\) −0.0180639 −0.00197093
\(85\) −2.12725 −0.230733
\(86\) 12.1733 1.31268
\(87\) −0.647363 −0.0694046
\(88\) −5.43640 −0.579522
\(89\) −15.5694 −1.65035 −0.825175 0.564877i \(-0.808924\pi\)
−0.825175 + 0.564877i \(0.808924\pi\)
\(90\) −2.94103 −0.310012
\(91\) −0.727014 −0.0762118
\(92\) −0.583036 −0.0607857
\(93\) −0.398581 −0.0413309
\(94\) −8.06333 −0.831669
\(95\) −0.0264789 −0.00271668
\(96\) 0.500626 0.0510949
\(97\) −12.1019 −1.22876 −0.614380 0.789010i \(-0.710594\pi\)
−0.614380 + 0.789010i \(0.710594\pi\)
\(98\) 9.62031 0.971798
\(99\) −1.88271 −0.189219
\(100\) 0.0420499 0.00420499
\(101\) −3.19743 −0.318157 −0.159078 0.987266i \(-0.550852\pi\)
−0.159078 + 0.987266i \(0.550852\pi\)
\(102\) −1.38255 −0.136893
\(103\) 10.5170 1.03628 0.518138 0.855297i \(-0.326625\pi\)
0.518138 + 0.855297i \(0.326625\pi\)
\(104\) 10.2925 1.00927
\(105\) 0.433878 0.0423422
\(106\) 1.46302 0.142101
\(107\) −1.18955 −0.114998 −0.0574988 0.998346i \(-0.518313\pi\)
−0.0574988 + 0.998346i \(0.518313\pi\)
\(108\) 0.0885651 0.00852218
\(109\) −0.401268 −0.0384345 −0.0192173 0.999815i \(-0.506117\pi\)
−0.0192173 + 0.999815i \(0.506117\pi\)
\(110\) 5.53710 0.527942
\(111\) −4.09354 −0.388542
\(112\) 0.778119 0.0735253
\(113\) 2.21505 0.208375 0.104187 0.994558i \(-0.466776\pi\)
0.104187 + 0.994558i \(0.466776\pi\)
\(114\) −0.0172092 −0.00161179
\(115\) 14.0040 1.30588
\(116\) −0.0573338 −0.00532331
\(117\) 3.56447 0.329535
\(118\) 20.4260 1.88037
\(119\) 0.203962 0.0186971
\(120\) −6.14253 −0.560733
\(121\) −7.45540 −0.677764
\(122\) −3.55320 −0.321692
\(123\) 12.2874 1.10792
\(124\) −0.0353004 −0.00317007
\(125\) −11.6463 −1.04167
\(126\) 0.281986 0.0251214
\(127\) −14.0283 −1.24481 −0.622404 0.782696i \(-0.713844\pi\)
−0.622404 + 0.782696i \(0.713844\pi\)
\(128\) −10.5046 −0.928481
\(129\) 8.80499 0.775236
\(130\) −10.4832 −0.919437
\(131\) −12.8106 −1.11926 −0.559632 0.828741i \(-0.689058\pi\)
−0.559632 + 0.828741i \(0.689058\pi\)
\(132\) −0.166742 −0.0145131
\(133\) 0.00253880 0.000220142 0
\(134\) −9.08271 −0.784626
\(135\) −2.12725 −0.183085
\(136\) −2.88754 −0.247604
\(137\) −9.88512 −0.844543 −0.422272 0.906469i \(-0.638767\pi\)
−0.422272 + 0.906469i \(0.638767\pi\)
\(138\) 9.10150 0.774771
\(139\) −18.5865 −1.57649 −0.788245 0.615362i \(-0.789010\pi\)
−0.788245 + 0.615362i \(0.789010\pi\)
\(140\) 0.0384265 0.00324763
\(141\) −5.83223 −0.491162
\(142\) −5.10499 −0.428401
\(143\) −6.71086 −0.561190
\(144\) −3.81503 −0.317919
\(145\) 1.37711 0.114362
\(146\) −0.626487 −0.0518484
\(147\) 6.95840 0.573919
\(148\) −0.362545 −0.0298010
\(149\) 4.36739 0.357791 0.178895 0.983868i \(-0.442748\pi\)
0.178895 + 0.983868i \(0.442748\pi\)
\(150\) −0.656421 −0.0535965
\(151\) −3.13523 −0.255142 −0.127571 0.991829i \(-0.540718\pi\)
−0.127571 + 0.991829i \(0.540718\pi\)
\(152\) −0.0359425 −0.00291532
\(153\) −1.00000 −0.0808452
\(154\) −0.530899 −0.0427810
\(155\) 0.847883 0.0681036
\(156\) 0.315687 0.0252752
\(157\) −1.00000 −0.0798087
\(158\) 3.54683 0.282171
\(159\) 1.05821 0.0839211
\(160\) −1.06496 −0.0841923
\(161\) −1.34271 −0.105820
\(162\) −1.38255 −0.108623
\(163\) 2.29919 0.180086 0.0900432 0.995938i \(-0.471299\pi\)
0.0900432 + 0.995938i \(0.471299\pi\)
\(164\) 1.08824 0.0849770
\(165\) 4.00500 0.311789
\(166\) −11.4877 −0.891617
\(167\) 16.6030 1.28478 0.642388 0.766380i \(-0.277944\pi\)
0.642388 + 0.766380i \(0.277944\pi\)
\(168\) 0.588947 0.0454383
\(169\) −0.294584 −0.0226603
\(170\) 2.94103 0.225567
\(171\) −0.0124475 −0.000951881 0
\(172\) 0.779815 0.0594603
\(173\) −5.74478 −0.436767 −0.218384 0.975863i \(-0.570078\pi\)
−0.218384 + 0.975863i \(0.570078\pi\)
\(174\) 0.895010 0.0678505
\(175\) 0.0968392 0.00732035
\(176\) 7.18259 0.541408
\(177\) 14.7742 1.11050
\(178\) 21.5254 1.61340
\(179\) 7.63031 0.570316 0.285158 0.958480i \(-0.407954\pi\)
0.285158 + 0.958480i \(0.407954\pi\)
\(180\) −0.188400 −0.0140425
\(181\) 8.05234 0.598525 0.299263 0.954171i \(-0.403259\pi\)
0.299263 + 0.954171i \(0.403259\pi\)
\(182\) 1.00513 0.0745053
\(183\) −2.57004 −0.189983
\(184\) 19.0091 1.40137
\(185\) 8.70800 0.640225
\(186\) 0.551057 0.0404055
\(187\) 1.88271 0.137677
\(188\) −0.516532 −0.0376719
\(189\) 0.203962 0.0148360
\(190\) 0.0366083 0.00265585
\(191\) −4.14413 −0.299859 −0.149930 0.988697i \(-0.547905\pi\)
−0.149930 + 0.988697i \(0.547905\pi\)
\(192\) −8.32219 −0.600602
\(193\) 10.1962 0.733937 0.366969 0.930233i \(-0.380396\pi\)
0.366969 + 0.930233i \(0.380396\pi\)
\(194\) 16.7314 1.20125
\(195\) −7.58252 −0.542996
\(196\) 0.616271 0.0440194
\(197\) −7.93699 −0.565487 −0.282744 0.959196i \(-0.591245\pi\)
−0.282744 + 0.959196i \(0.591245\pi\)
\(198\) 2.60293 0.184982
\(199\) −1.58998 −0.112711 −0.0563553 0.998411i \(-0.517948\pi\)
−0.0563553 + 0.998411i \(0.517948\pi\)
\(200\) −1.37098 −0.0969427
\(201\) −6.56955 −0.463380
\(202\) 4.42060 0.311032
\(203\) −0.132037 −0.00926720
\(204\) −0.0885651 −0.00620080
\(205\) −26.1385 −1.82559
\(206\) −14.5403 −1.01307
\(207\) 6.58314 0.457560
\(208\) −13.5985 −0.942888
\(209\) 0.0234350 0.00162103
\(210\) −0.599857 −0.0413941
\(211\) −0.650575 −0.0447874 −0.0223937 0.999749i \(-0.507129\pi\)
−0.0223937 + 0.999749i \(0.507129\pi\)
\(212\) 0.0937200 0.00643672
\(213\) −3.69245 −0.253003
\(214\) 1.64460 0.112423
\(215\) −18.7305 −1.27741
\(216\) −2.88754 −0.196472
\(217\) −0.0812953 −0.00551868
\(218\) 0.554772 0.0375739
\(219\) −0.453140 −0.0306204
\(220\) 0.354703 0.0239141
\(221\) −3.56447 −0.239772
\(222\) 5.65951 0.379842
\(223\) −10.6846 −0.715491 −0.357745 0.933819i \(-0.616454\pi\)
−0.357745 + 0.933819i \(0.616454\pi\)
\(224\) 0.102108 0.00682241
\(225\) −0.474791 −0.0316527
\(226\) −3.06241 −0.203709
\(227\) 14.6258 0.970751 0.485375 0.874306i \(-0.338683\pi\)
0.485375 + 0.874306i \(0.338683\pi\)
\(228\) −0.00110241 −7.30089e−5 0
\(229\) 0.419946 0.0277508 0.0138754 0.999904i \(-0.495583\pi\)
0.0138754 + 0.999904i \(0.495583\pi\)
\(230\) −19.3612 −1.27664
\(231\) −0.384001 −0.0252654
\(232\) 1.86929 0.122725
\(233\) 21.0978 1.38216 0.691080 0.722778i \(-0.257135\pi\)
0.691080 + 0.722778i \(0.257135\pi\)
\(234\) −4.92804 −0.322156
\(235\) 12.4066 0.809319
\(236\) 1.30848 0.0851748
\(237\) 2.56543 0.166643
\(238\) −0.281986 −0.0182785
\(239\) 22.6592 1.46570 0.732851 0.680389i \(-0.238189\pi\)
0.732851 + 0.680389i \(0.238189\pi\)
\(240\) 8.11553 0.523855
\(241\) 25.3959 1.63590 0.817948 0.575292i \(-0.195112\pi\)
0.817948 + 0.575292i \(0.195112\pi\)
\(242\) 10.3074 0.662587
\(243\) −1.00000 −0.0641500
\(244\) −0.227616 −0.0145716
\(245\) −14.8023 −0.945683
\(246\) −16.9879 −1.08311
\(247\) −0.0443685 −0.00282310
\(248\) 1.15092 0.0730834
\(249\) −8.30907 −0.526566
\(250\) 16.1015 1.01835
\(251\) 1.76138 0.111178 0.0555888 0.998454i \(-0.482296\pi\)
0.0555888 + 0.998454i \(0.482296\pi\)
\(252\) 0.0180639 0.00113792
\(253\) −12.3941 −0.779213
\(254\) 19.3947 1.21693
\(255\) 2.12725 0.133214
\(256\) −2.12133 −0.132583
\(257\) 8.52815 0.531971 0.265986 0.963977i \(-0.414303\pi\)
0.265986 + 0.963977i \(0.414303\pi\)
\(258\) −12.1733 −0.757877
\(259\) −0.834925 −0.0518797
\(260\) −0.671547 −0.0416476
\(261\) 0.647363 0.0400708
\(262\) 17.7112 1.09420
\(263\) 9.05067 0.558088 0.279044 0.960278i \(-0.409982\pi\)
0.279044 + 0.960278i \(0.409982\pi\)
\(264\) 5.43640 0.334587
\(265\) −2.25107 −0.138282
\(266\) −0.00351001 −0.000215213 0
\(267\) 15.5694 0.952830
\(268\) −0.581832 −0.0355411
\(269\) 10.5853 0.645399 0.322699 0.946502i \(-0.395410\pi\)
0.322699 + 0.946502i \(0.395410\pi\)
\(270\) 2.94103 0.178985
\(271\) 9.18533 0.557969 0.278984 0.960296i \(-0.410002\pi\)
0.278984 + 0.960296i \(0.410002\pi\)
\(272\) 3.81503 0.231320
\(273\) 0.727014 0.0440009
\(274\) 13.6666 0.825632
\(275\) 0.893894 0.0539038
\(276\) 0.583036 0.0350947
\(277\) −4.83846 −0.290715 −0.145358 0.989379i \(-0.546433\pi\)
−0.145358 + 0.989379i \(0.546433\pi\)
\(278\) 25.6968 1.54119
\(279\) 0.398581 0.0238624
\(280\) −1.25284 −0.0748715
\(281\) −16.5815 −0.989171 −0.494585 0.869129i \(-0.664680\pi\)
−0.494585 + 0.869129i \(0.664680\pi\)
\(282\) 8.06333 0.480164
\(283\) 19.2054 1.14164 0.570820 0.821075i \(-0.306625\pi\)
0.570820 + 0.821075i \(0.306625\pi\)
\(284\) −0.327022 −0.0194052
\(285\) 0.0264789 0.00156847
\(286\) 9.27807 0.548624
\(287\) 2.50616 0.147934
\(288\) −0.500626 −0.0294997
\(289\) 1.00000 0.0588235
\(290\) −1.90391 −0.111802
\(291\) 12.1019 0.709425
\(292\) −0.0401324 −0.00234857
\(293\) −21.3155 −1.24527 −0.622633 0.782514i \(-0.713937\pi\)
−0.622633 + 0.782514i \(0.713937\pi\)
\(294\) −9.62031 −0.561068
\(295\) −31.4285 −1.82984
\(296\) 11.8203 0.687039
\(297\) 1.88271 0.109246
\(298\) −6.03812 −0.349779
\(299\) 23.4654 1.35704
\(300\) −0.0420499 −0.00242775
\(301\) 1.79588 0.103513
\(302\) 4.33461 0.249429
\(303\) 3.19743 0.183688
\(304\) 0.0474874 0.00272359
\(305\) 5.46713 0.313047
\(306\) 1.38255 0.0790349
\(307\) 16.5041 0.941939 0.470970 0.882149i \(-0.343904\pi\)
0.470970 + 0.882149i \(0.343904\pi\)
\(308\) −0.0340091 −0.00193785
\(309\) −10.5170 −0.598294
\(310\) −1.17224 −0.0665787
\(311\) 0.315638 0.0178982 0.00894909 0.999960i \(-0.497151\pi\)
0.00894909 + 0.999960i \(0.497151\pi\)
\(312\) −10.2925 −0.582700
\(313\) 30.8499 1.74374 0.871870 0.489738i \(-0.162907\pi\)
0.871870 + 0.489738i \(0.162907\pi\)
\(314\) 1.38255 0.0780216
\(315\) −0.433878 −0.0244463
\(316\) 0.227208 0.0127814
\(317\) −10.5058 −0.590066 −0.295033 0.955487i \(-0.595331\pi\)
−0.295033 + 0.955487i \(0.595331\pi\)
\(318\) −1.46302 −0.0820420
\(319\) −1.21880 −0.0682395
\(320\) 17.7034 0.989651
\(321\) 1.18955 0.0663939
\(322\) 1.85636 0.103451
\(323\) 0.0124475 0.000692595 0
\(324\) −0.0885651 −0.00492028
\(325\) −1.69238 −0.0938761
\(326\) −3.17874 −0.176054
\(327\) 0.401268 0.0221902
\(328\) −35.4804 −1.95908
\(329\) −1.18955 −0.0655821
\(330\) −5.53710 −0.304807
\(331\) −33.7794 −1.85668 −0.928342 0.371728i \(-0.878765\pi\)
−0.928342 + 0.371728i \(0.878765\pi\)
\(332\) −0.735894 −0.0403874
\(333\) 4.09354 0.224325
\(334\) −22.9544 −1.25601
\(335\) 13.9751 0.763541
\(336\) −0.778119 −0.0424499
\(337\) −35.5128 −1.93450 −0.967252 0.253819i \(-0.918313\pi\)
−0.967252 + 0.253819i \(0.918313\pi\)
\(338\) 0.407276 0.0221529
\(339\) −2.21505 −0.120305
\(340\) 0.188400 0.0102174
\(341\) −0.750413 −0.0406371
\(342\) 0.0172092 0.000930566 0
\(343\) 2.84698 0.153722
\(344\) −25.4248 −1.37081
\(345\) −14.0040 −0.753951
\(346\) 7.94242 0.426987
\(347\) 9.64863 0.517966 0.258983 0.965882i \(-0.416613\pi\)
0.258983 + 0.965882i \(0.416613\pi\)
\(348\) 0.0573338 0.00307341
\(349\) −20.8693 −1.11711 −0.558553 0.829469i \(-0.688643\pi\)
−0.558553 + 0.829469i \(0.688643\pi\)
\(350\) −0.133885 −0.00715644
\(351\) −3.56447 −0.190257
\(352\) 0.942533 0.0502372
\(353\) −18.8427 −1.00290 −0.501448 0.865188i \(-0.667199\pi\)
−0.501448 + 0.865188i \(0.667199\pi\)
\(354\) −20.4260 −1.08563
\(355\) 7.85478 0.416889
\(356\) 1.37890 0.0730817
\(357\) −0.203962 −0.0107948
\(358\) −10.5493 −0.557546
\(359\) −8.50792 −0.449031 −0.224515 0.974471i \(-0.572080\pi\)
−0.224515 + 0.974471i \(0.572080\pi\)
\(360\) 6.14253 0.323740
\(361\) −18.9998 −0.999992
\(362\) −11.1327 −0.585123
\(363\) 7.45540 0.391307
\(364\) 0.0643881 0.00337485
\(365\) 0.963943 0.0504551
\(366\) 3.55320 0.185729
\(367\) 26.1719 1.36616 0.683081 0.730343i \(-0.260640\pi\)
0.683081 + 0.730343i \(0.260640\pi\)
\(368\) −25.1149 −1.30920
\(369\) −12.2874 −0.639657
\(370\) −12.0392 −0.625889
\(371\) 0.215833 0.0112055
\(372\) 0.0353004 0.00183024
\(373\) 25.9925 1.34584 0.672921 0.739714i \(-0.265039\pi\)
0.672921 + 0.739714i \(0.265039\pi\)
\(374\) −2.60293 −0.134595
\(375\) 11.6463 0.601411
\(376\) 16.8408 0.868497
\(377\) 2.30750 0.118842
\(378\) −0.281986 −0.0145038
\(379\) −24.8000 −1.27389 −0.636944 0.770910i \(-0.719802\pi\)
−0.636944 + 0.770910i \(0.719802\pi\)
\(380\) 0.00234511 0.000120301 0
\(381\) 14.0283 0.718690
\(382\) 5.72946 0.293145
\(383\) 28.0135 1.43142 0.715712 0.698395i \(-0.246102\pi\)
0.715712 + 0.698395i \(0.246102\pi\)
\(384\) 10.5046 0.536059
\(385\) 0.816867 0.0416314
\(386\) −14.0967 −0.717503
\(387\) −8.80499 −0.447583
\(388\) 1.07180 0.0544126
\(389\) −27.4137 −1.38993 −0.694965 0.719043i \(-0.744580\pi\)
−0.694965 + 0.719043i \(0.744580\pi\)
\(390\) 10.4832 0.530837
\(391\) −6.58314 −0.332924
\(392\) −20.0926 −1.01483
\(393\) 12.8106 0.646208
\(394\) 10.9733 0.552825
\(395\) −5.45733 −0.274588
\(396\) 0.166742 0.00837912
\(397\) −31.1240 −1.56207 −0.781034 0.624489i \(-0.785307\pi\)
−0.781034 + 0.624489i \(0.785307\pi\)
\(398\) 2.19822 0.110187
\(399\) −0.00253880 −0.000127099 0
\(400\) 1.81134 0.0905670
\(401\) 37.7419 1.88474 0.942369 0.334574i \(-0.108593\pi\)
0.942369 + 0.334574i \(0.108593\pi\)
\(402\) 9.08271 0.453004
\(403\) 1.42073 0.0707716
\(404\) 0.283181 0.0140888
\(405\) 2.12725 0.105704
\(406\) 0.182548 0.00905969
\(407\) −7.70695 −0.382019
\(408\) 2.88754 0.142954
\(409\) −20.7562 −1.02633 −0.513165 0.858290i \(-0.671527\pi\)
−0.513165 + 0.858290i \(0.671527\pi\)
\(410\) 36.1376 1.78471
\(411\) 9.88512 0.487597
\(412\) −0.931443 −0.0458889
\(413\) 3.01337 0.148278
\(414\) −9.10150 −0.447314
\(415\) 17.6755 0.867656
\(416\) −1.78446 −0.0874905
\(417\) 18.5865 0.910187
\(418\) −0.0323999 −0.00158473
\(419\) −3.11619 −0.152236 −0.0761179 0.997099i \(-0.524253\pi\)
−0.0761179 + 0.997099i \(0.524253\pi\)
\(420\) −0.0384265 −0.00187502
\(421\) 10.8003 0.526374 0.263187 0.964745i \(-0.415226\pi\)
0.263187 + 0.964745i \(0.415226\pi\)
\(422\) 0.899450 0.0437846
\(423\) 5.83223 0.283573
\(424\) −3.05561 −0.148393
\(425\) 0.474791 0.0230307
\(426\) 5.10499 0.247337
\(427\) −0.524190 −0.0253673
\(428\) 0.105352 0.00509239
\(429\) 6.71086 0.324003
\(430\) 25.8957 1.24880
\(431\) 4.07885 0.196471 0.0982357 0.995163i \(-0.468680\pi\)
0.0982357 + 0.995163i \(0.468680\pi\)
\(432\) 3.81503 0.183551
\(433\) −28.1269 −1.35169 −0.675845 0.737043i \(-0.736221\pi\)
−0.675845 + 0.737043i \(0.736221\pi\)
\(434\) 0.112395 0.00539511
\(435\) −1.37711 −0.0660272
\(436\) 0.0355383 0.00170198
\(437\) −0.0819434 −0.00391988
\(438\) 0.626487 0.0299347
\(439\) −26.1788 −1.24944 −0.624722 0.780847i \(-0.714788\pi\)
−0.624722 + 0.780847i \(0.714788\pi\)
\(440\) −11.5646 −0.551321
\(441\) −6.95840 −0.331352
\(442\) 4.92804 0.234403
\(443\) −18.6227 −0.884790 −0.442395 0.896820i \(-0.645871\pi\)
−0.442395 + 0.896820i \(0.645871\pi\)
\(444\) 0.362545 0.0172056
\(445\) −33.1200 −1.57004
\(446\) 14.7719 0.699470
\(447\) −4.36739 −0.206570
\(448\) −1.69741 −0.0801950
\(449\) 16.9928 0.801941 0.400971 0.916091i \(-0.368673\pi\)
0.400971 + 0.916091i \(0.368673\pi\)
\(450\) 0.656421 0.0309440
\(451\) 23.1336 1.08932
\(452\) −0.196176 −0.00922735
\(453\) 3.13523 0.147306
\(454\) −20.2209 −0.949014
\(455\) −1.54654 −0.0725031
\(456\) 0.0359425 0.00168316
\(457\) −30.4744 −1.42553 −0.712765 0.701403i \(-0.752557\pi\)
−0.712765 + 0.701403i \(0.752557\pi\)
\(458\) −0.580596 −0.0271294
\(459\) 1.00000 0.0466760
\(460\) −1.24027 −0.0578277
\(461\) 14.7883 0.688762 0.344381 0.938830i \(-0.388089\pi\)
0.344381 + 0.938830i \(0.388089\pi\)
\(462\) 0.530899 0.0246996
\(463\) 22.7388 1.05676 0.528382 0.849007i \(-0.322799\pi\)
0.528382 + 0.849007i \(0.322799\pi\)
\(464\) −2.46971 −0.114653
\(465\) −0.847883 −0.0393197
\(466\) −29.1686 −1.35121
\(467\) 22.5443 1.04323 0.521613 0.853182i \(-0.325330\pi\)
0.521613 + 0.853182i \(0.325330\pi\)
\(468\) −0.315687 −0.0145926
\(469\) −1.33994 −0.0618725
\(470\) −17.1527 −0.791197
\(471\) 1.00000 0.0460776
\(472\) −42.6611 −1.96364
\(473\) 16.5772 0.762223
\(474\) −3.54683 −0.162911
\(475\) 0.00590994 0.000271167 0
\(476\) −0.0180639 −0.000827957 0
\(477\) −1.05821 −0.0484519
\(478\) −31.3274 −1.43288
\(479\) −16.4861 −0.753269 −0.376635 0.926362i \(-0.622919\pi\)
−0.376635 + 0.926362i \(0.622919\pi\)
\(480\) 1.06496 0.0486085
\(481\) 14.5913 0.665305
\(482\) −35.1111 −1.59927
\(483\) 1.34271 0.0610953
\(484\) 0.660288 0.0300131
\(485\) −25.7438 −1.16896
\(486\) 1.38255 0.0627136
\(487\) −38.4656 −1.74304 −0.871521 0.490357i \(-0.836866\pi\)
−0.871521 + 0.490357i \(0.836866\pi\)
\(488\) 7.42109 0.335937
\(489\) −2.29919 −0.103973
\(490\) 20.4648 0.924507
\(491\) 35.9939 1.62438 0.812191 0.583392i \(-0.198275\pi\)
0.812191 + 0.583392i \(0.198275\pi\)
\(492\) −1.08824 −0.0490615
\(493\) −0.647363 −0.0291558
\(494\) 0.0613416 0.00275989
\(495\) −4.00500 −0.180011
\(496\) −1.52060 −0.0682769
\(497\) −0.753119 −0.0337820
\(498\) 11.4877 0.514775
\(499\) −3.18705 −0.142672 −0.0713359 0.997452i \(-0.522726\pi\)
−0.0713359 + 0.997452i \(0.522726\pi\)
\(500\) 1.03145 0.0461280
\(501\) −16.6030 −0.741766
\(502\) −2.43519 −0.108688
\(503\) −34.4157 −1.53452 −0.767260 0.641336i \(-0.778380\pi\)
−0.767260 + 0.641336i \(0.778380\pi\)
\(504\) −0.588947 −0.0262338
\(505\) −6.80175 −0.302674
\(506\) 17.1355 0.761765
\(507\) 0.294584 0.0130829
\(508\) 1.24242 0.0551233
\(509\) −5.63897 −0.249943 −0.124972 0.992160i \(-0.539884\pi\)
−0.124972 + 0.992160i \(0.539884\pi\)
\(510\) −2.94103 −0.130231
\(511\) −0.0924232 −0.00408856
\(512\) 23.9420 1.05810
\(513\) 0.0124475 0.000549569 0
\(514\) −11.7906 −0.520059
\(515\) 22.3724 0.985847
\(516\) −0.779815 −0.0343294
\(517\) −10.9804 −0.482917
\(518\) 1.15432 0.0507181
\(519\) 5.74478 0.252168
\(520\) 21.8948 0.960152
\(521\) −6.52922 −0.286051 −0.143025 0.989719i \(-0.545683\pi\)
−0.143025 + 0.989719i \(0.545683\pi\)
\(522\) −0.895010 −0.0391735
\(523\) 16.4664 0.720025 0.360012 0.932948i \(-0.382772\pi\)
0.360012 + 0.932948i \(0.382772\pi\)
\(524\) 1.13457 0.0495639
\(525\) −0.0968392 −0.00422641
\(526\) −12.5130 −0.545591
\(527\) −0.398581 −0.0173625
\(528\) −7.18259 −0.312582
\(529\) 20.3377 0.884249
\(530\) 3.11221 0.135186
\(531\) −14.7742 −0.641147
\(532\) −0.000224849 0 −9.74846e−6 0
\(533\) −43.7981 −1.89711
\(534\) −21.5254 −0.931495
\(535\) −2.53046 −0.109402
\(536\) 18.9698 0.819371
\(537\) −7.63031 −0.329272
\(538\) −14.6347 −0.630947
\(539\) 13.1006 0.564285
\(540\) 0.188400 0.00810746
\(541\) −40.9238 −1.75945 −0.879726 0.475481i \(-0.842274\pi\)
−0.879726 + 0.475481i \(0.842274\pi\)
\(542\) −12.6991 −0.545475
\(543\) −8.05234 −0.345559
\(544\) 0.500626 0.0214642
\(545\) −0.853599 −0.0365642
\(546\) −1.00513 −0.0430156
\(547\) −36.0457 −1.54120 −0.770600 0.637319i \(-0.780044\pi\)
−0.770600 + 0.637319i \(0.780044\pi\)
\(548\) 0.875477 0.0373985
\(549\) 2.57004 0.109687
\(550\) −1.23585 −0.0526968
\(551\) −0.00805802 −0.000343283 0
\(552\) −19.0091 −0.809080
\(553\) 0.523250 0.0222509
\(554\) 6.68940 0.284205
\(555\) −8.70800 −0.369634
\(556\) 1.64612 0.0698110
\(557\) −1.03825 −0.0439919 −0.0219959 0.999758i \(-0.507002\pi\)
−0.0219959 + 0.999758i \(0.507002\pi\)
\(558\) −0.551057 −0.0233281
\(559\) −31.3851 −1.32745
\(560\) 1.65526 0.0699474
\(561\) −1.88271 −0.0794881
\(562\) 22.9247 0.967021
\(563\) 9.70404 0.408976 0.204488 0.978869i \(-0.434447\pi\)
0.204488 + 0.978869i \(0.434447\pi\)
\(564\) 0.516532 0.0217499
\(565\) 4.71198 0.198234
\(566\) −26.5523 −1.11608
\(567\) −0.203962 −0.00856558
\(568\) 10.6621 0.447372
\(569\) 19.6552 0.823988 0.411994 0.911187i \(-0.364832\pi\)
0.411994 + 0.911187i \(0.364832\pi\)
\(570\) −0.0366083 −0.00153335
\(571\) −11.3464 −0.474833 −0.237417 0.971408i \(-0.576301\pi\)
−0.237417 + 0.971408i \(0.576301\pi\)
\(572\) 0.594347 0.0248509
\(573\) 4.14413 0.173124
\(574\) −3.46489 −0.144622
\(575\) −3.12562 −0.130347
\(576\) 8.32219 0.346758
\(577\) −14.6785 −0.611072 −0.305536 0.952181i \(-0.598836\pi\)
−0.305536 + 0.952181i \(0.598836\pi\)
\(578\) −1.38255 −0.0575064
\(579\) −10.1962 −0.423739
\(580\) −0.121963 −0.00506426
\(581\) −1.69473 −0.0703093
\(582\) −16.7314 −0.693539
\(583\) 1.99229 0.0825124
\(584\) 1.30846 0.0541444
\(585\) 7.58252 0.313499
\(586\) 29.4697 1.21738
\(587\) 23.0412 0.951014 0.475507 0.879712i \(-0.342265\pi\)
0.475507 + 0.879712i \(0.342265\pi\)
\(588\) −0.616271 −0.0254146
\(589\) −0.00496132 −0.000204428 0
\(590\) 43.4514 1.78887
\(591\) 7.93699 0.326484
\(592\) −15.6170 −0.641853
\(593\) 13.6537 0.560689 0.280345 0.959899i \(-0.409551\pi\)
0.280345 + 0.959899i \(0.409551\pi\)
\(594\) −2.60293 −0.106800
\(595\) 0.433878 0.0177873
\(596\) −0.386798 −0.0158439
\(597\) 1.58998 0.0650735
\(598\) −32.4420 −1.32665
\(599\) −11.5452 −0.471724 −0.235862 0.971787i \(-0.575791\pi\)
−0.235862 + 0.971787i \(0.575791\pi\)
\(600\) 1.37098 0.0559699
\(601\) −3.24584 −0.132401 −0.0662003 0.997806i \(-0.521088\pi\)
−0.0662003 + 0.997806i \(0.521088\pi\)
\(602\) −2.48289 −0.101195
\(603\) 6.56955 0.267533
\(604\) 0.277672 0.0112983
\(605\) −15.8595 −0.644782
\(606\) −4.42060 −0.179575
\(607\) −31.7395 −1.28827 −0.644133 0.764913i \(-0.722782\pi\)
−0.644133 + 0.764913i \(0.722782\pi\)
\(608\) 0.00623152 0.000252721 0
\(609\) 0.132037 0.00535042
\(610\) −7.55856 −0.306037
\(611\) 20.7888 0.841024
\(612\) 0.0885651 0.00358003
\(613\) −13.0712 −0.527939 −0.263969 0.964531i \(-0.585032\pi\)
−0.263969 + 0.964531i \(0.585032\pi\)
\(614\) −22.8177 −0.920847
\(615\) 26.1385 1.05400
\(616\) 1.10882 0.0446755
\(617\) −21.2147 −0.854071 −0.427036 0.904235i \(-0.640442\pi\)
−0.427036 + 0.904235i \(0.640442\pi\)
\(618\) 14.5403 0.584897
\(619\) −48.3407 −1.94298 −0.971488 0.237090i \(-0.923806\pi\)
−0.971488 + 0.237090i \(0.923806\pi\)
\(620\) −0.0750929 −0.00301580
\(621\) −6.58314 −0.264172
\(622\) −0.436384 −0.0174974
\(623\) 3.17556 0.127226
\(624\) 13.5985 0.544377
\(625\) −22.4006 −0.896025
\(626\) −42.6514 −1.70469
\(627\) −0.0234350 −0.000935902 0
\(628\) 0.0885651 0.00353413
\(629\) −4.09354 −0.163220
\(630\) 0.599857 0.0238989
\(631\) −28.7219 −1.14340 −0.571700 0.820463i \(-0.693716\pi\)
−0.571700 + 0.820463i \(0.693716\pi\)
\(632\) −7.40779 −0.294666
\(633\) 0.650575 0.0258580
\(634\) 14.5248 0.576853
\(635\) −29.8417 −1.18423
\(636\) −0.0937200 −0.00371624
\(637\) −24.8030 −0.982730
\(638\) 1.68504 0.0667115
\(639\) 3.69245 0.146071
\(640\) −22.3459 −0.883298
\(641\) 30.4386 1.20225 0.601126 0.799154i \(-0.294719\pi\)
0.601126 + 0.799154i \(0.294719\pi\)
\(642\) −1.64460 −0.0649072
\(643\) 43.0852 1.69912 0.849558 0.527496i \(-0.176869\pi\)
0.849558 + 0.527496i \(0.176869\pi\)
\(644\) 0.118917 0.00468599
\(645\) 18.7305 0.737511
\(646\) −0.0172092 −0.000677086 0
\(647\) 1.33198 0.0523656 0.0261828 0.999657i \(-0.491665\pi\)
0.0261828 + 0.999657i \(0.491665\pi\)
\(648\) 2.88754 0.113433
\(649\) 27.8156 1.09186
\(650\) 2.33979 0.0917741
\(651\) 0.0812953 0.00318621
\(652\) −0.203628 −0.00797469
\(653\) −28.3679 −1.11012 −0.555061 0.831810i \(-0.687305\pi\)
−0.555061 + 0.831810i \(0.687305\pi\)
\(654\) −0.554772 −0.0216933
\(655\) −27.2513 −1.06480
\(656\) 46.8768 1.83023
\(657\) 0.453140 0.0176787
\(658\) 1.64461 0.0641136
\(659\) 34.9333 1.36081 0.680403 0.732838i \(-0.261805\pi\)
0.680403 + 0.732838i \(0.261805\pi\)
\(660\) −0.354703 −0.0138068
\(661\) 47.8486 1.86109 0.930547 0.366173i \(-0.119332\pi\)
0.930547 + 0.366173i \(0.119332\pi\)
\(662\) 46.7016 1.81511
\(663\) 3.56447 0.138432
\(664\) 23.9928 0.931100
\(665\) 0.00540068 0.000209429 0
\(666\) −5.65951 −0.219302
\(667\) 4.26168 0.165013
\(668\) −1.47044 −0.0568931
\(669\) 10.6846 0.413089
\(670\) −19.3212 −0.746444
\(671\) −4.83864 −0.186794
\(672\) −0.102108 −0.00393892
\(673\) −28.1217 −1.08401 −0.542007 0.840374i \(-0.682335\pi\)
−0.542007 + 0.840374i \(0.682335\pi\)
\(674\) 49.0980 1.89119
\(675\) 0.474791 0.0182747
\(676\) 0.0260899 0.00100346
\(677\) −50.6480 −1.94656 −0.973281 0.229618i \(-0.926252\pi\)
−0.973281 + 0.229618i \(0.926252\pi\)
\(678\) 3.06241 0.117611
\(679\) 2.46832 0.0947254
\(680\) −6.14253 −0.235555
\(681\) −14.6258 −0.560463
\(682\) 1.03748 0.0397272
\(683\) −26.7424 −1.02327 −0.511635 0.859203i \(-0.670960\pi\)
−0.511635 + 0.859203i \(0.670960\pi\)
\(684\) 0.00110241 4.21517e−5 0
\(685\) −21.0282 −0.803445
\(686\) −3.93608 −0.150280
\(687\) −0.419946 −0.0160220
\(688\) 33.5913 1.28066
\(689\) −3.77194 −0.143699
\(690\) 19.3612 0.737068
\(691\) −43.5596 −1.65709 −0.828543 0.559925i \(-0.810830\pi\)
−0.828543 + 0.559925i \(0.810830\pi\)
\(692\) 0.508786 0.0193412
\(693\) 0.384001 0.0145870
\(694\) −13.3397 −0.506367
\(695\) −39.5383 −1.49977
\(696\) −1.86929 −0.0708551
\(697\) 12.2874 0.465419
\(698\) 28.8527 1.09209
\(699\) −21.0978 −0.797991
\(700\) −0.00857657 −0.000324164 0
\(701\) −15.9742 −0.603337 −0.301669 0.953413i \(-0.597544\pi\)
−0.301669 + 0.953413i \(0.597544\pi\)
\(702\) 4.92804 0.185997
\(703\) −0.0509542 −0.00192177
\(704\) −15.6683 −0.590520
\(705\) −12.4066 −0.467261
\(706\) 26.0509 0.980439
\(707\) 0.652154 0.0245268
\(708\) −1.30848 −0.0491757
\(709\) −44.6106 −1.67539 −0.837693 0.546142i \(-0.816096\pi\)
−0.837693 + 0.546142i \(0.816096\pi\)
\(710\) −10.8596 −0.407554
\(711\) −2.56543 −0.0962113
\(712\) −44.9572 −1.68484
\(713\) 2.62392 0.0982664
\(714\) 0.281986 0.0105531
\(715\) −14.2757 −0.533881
\(716\) −0.675779 −0.0252551
\(717\) −22.6592 −0.846224
\(718\) 11.7626 0.438976
\(719\) −23.9914 −0.894729 −0.447365 0.894352i \(-0.647637\pi\)
−0.447365 + 0.894352i \(0.647637\pi\)
\(720\) −8.11553 −0.302448
\(721\) −2.14507 −0.0798868
\(722\) 26.2682 0.977600
\(723\) −25.3959 −0.944485
\(724\) −0.713156 −0.0265042
\(725\) −0.307362 −0.0114151
\(726\) −10.3074 −0.382545
\(727\) −27.8456 −1.03273 −0.516367 0.856367i \(-0.672716\pi\)
−0.516367 + 0.856367i \(0.672716\pi\)
\(728\) −2.09928 −0.0778046
\(729\) 1.00000 0.0370370
\(730\) −1.33270 −0.0493253
\(731\) 8.80499 0.325664
\(732\) 0.227616 0.00841292
\(733\) 36.3146 1.34131 0.670655 0.741769i \(-0.266013\pi\)
0.670655 + 0.741769i \(0.266013\pi\)
\(734\) −36.1838 −1.33557
\(735\) 14.8023 0.545990
\(736\) −3.29569 −0.121481
\(737\) −12.3686 −0.455602
\(738\) 16.9879 0.625334
\(739\) 11.2275 0.413012 0.206506 0.978445i \(-0.433791\pi\)
0.206506 + 0.978445i \(0.433791\pi\)
\(740\) −0.771225 −0.0283508
\(741\) 0.0443685 0.00162992
\(742\) −0.298400 −0.0109546
\(743\) −5.17852 −0.189982 −0.0949908 0.995478i \(-0.530282\pi\)
−0.0949908 + 0.995478i \(0.530282\pi\)
\(744\) −1.15092 −0.0421947
\(745\) 9.29055 0.340379
\(746\) −35.9359 −1.31571
\(747\) 8.30907 0.304013
\(748\) −0.166742 −0.00609670
\(749\) 0.242622 0.00886520
\(750\) −16.1015 −0.587944
\(751\) 29.4141 1.07333 0.536667 0.843794i \(-0.319683\pi\)
0.536667 + 0.843794i \(0.319683\pi\)
\(752\) −22.2501 −0.811378
\(753\) −1.76138 −0.0641884
\(754\) −3.19023 −0.116181
\(755\) −6.66944 −0.242726
\(756\) −0.0180639 −0.000656977 0
\(757\) −8.97631 −0.326249 −0.163125 0.986605i \(-0.552157\pi\)
−0.163125 + 0.986605i \(0.552157\pi\)
\(758\) 34.2871 1.24536
\(759\) 12.3941 0.449879
\(760\) −0.0764588 −0.00277345
\(761\) −22.4232 −0.812840 −0.406420 0.913686i \(-0.633223\pi\)
−0.406420 + 0.913686i \(0.633223\pi\)
\(762\) −19.3947 −0.702597
\(763\) 0.0818433 0.00296293
\(764\) 0.367026 0.0132785
\(765\) −2.12725 −0.0769110
\(766\) −38.7300 −1.39937
\(767\) −52.6622 −1.90152
\(768\) 2.12133 0.0765470
\(769\) 26.6961 0.962686 0.481343 0.876532i \(-0.340149\pi\)
0.481343 + 0.876532i \(0.340149\pi\)
\(770\) −1.12936 −0.0406992
\(771\) −8.52815 −0.307134
\(772\) −0.903026 −0.0325006
\(773\) −5.73569 −0.206298 −0.103149 0.994666i \(-0.532892\pi\)
−0.103149 + 0.994666i \(0.532892\pi\)
\(774\) 12.1733 0.437561
\(775\) −0.189243 −0.00679780
\(776\) −34.9446 −1.25444
\(777\) 0.834925 0.0299528
\(778\) 37.9007 1.35881
\(779\) 0.152947 0.00547990
\(780\) 0.671547 0.0240452
\(781\) −6.95182 −0.248756
\(782\) 9.10150 0.325469
\(783\) −0.647363 −0.0231349
\(784\) 26.5465 0.948088
\(785\) −2.12725 −0.0759249
\(786\) −17.7112 −0.631738
\(787\) 36.1386 1.28820 0.644101 0.764941i \(-0.277232\pi\)
0.644101 + 0.764941i \(0.277232\pi\)
\(788\) 0.702940 0.0250412
\(789\) −9.05067 −0.322212
\(790\) 7.54501 0.268439
\(791\) −0.451786 −0.0160636
\(792\) −5.43640 −0.193174
\(793\) 9.16082 0.325310
\(794\) 43.0304 1.52709
\(795\) 2.25107 0.0798373
\(796\) 0.140816 0.00499111
\(797\) −30.4504 −1.07861 −0.539303 0.842112i \(-0.681312\pi\)
−0.539303 + 0.842112i \(0.681312\pi\)
\(798\) 0.00351001 0.000124253 0
\(799\) −5.83223 −0.206329
\(800\) 0.237693 0.00840370
\(801\) −15.5694 −0.550117
\(802\) −52.1799 −1.84254
\(803\) −0.853131 −0.0301063
\(804\) 0.581832 0.0205196
\(805\) −2.85628 −0.100671
\(806\) −1.96422 −0.0691868
\(807\) −10.5853 −0.372621
\(808\) −9.23271 −0.324806
\(809\) 52.2120 1.83568 0.917839 0.396953i \(-0.129932\pi\)
0.917839 + 0.396953i \(0.129932\pi\)
\(810\) −2.94103 −0.103337
\(811\) −38.6079 −1.35571 −0.677854 0.735196i \(-0.737090\pi\)
−0.677854 + 0.735196i \(0.737090\pi\)
\(812\) 0.0116939 0.000410375 0
\(813\) −9.18533 −0.322144
\(814\) 10.6552 0.373465
\(815\) 4.89096 0.171323
\(816\) −3.81503 −0.133553
\(817\) 0.109600 0.00383441
\(818\) 28.6965 1.00335
\(819\) −0.727014 −0.0254039
\(820\) 2.31495 0.0808417
\(821\) −32.4910 −1.13394 −0.566972 0.823737i \(-0.691885\pi\)
−0.566972 + 0.823737i \(0.691885\pi\)
\(822\) −13.6666 −0.476679
\(823\) −30.8316 −1.07472 −0.537360 0.843353i \(-0.680579\pi\)
−0.537360 + 0.843353i \(0.680579\pi\)
\(824\) 30.3684 1.05793
\(825\) −0.893894 −0.0311214
\(826\) −4.16613 −0.144958
\(827\) 22.1948 0.771790 0.385895 0.922543i \(-0.373893\pi\)
0.385895 + 0.922543i \(0.373893\pi\)
\(828\) −0.583036 −0.0202619
\(829\) −36.2820 −1.26012 −0.630062 0.776545i \(-0.716971\pi\)
−0.630062 + 0.776545i \(0.716971\pi\)
\(830\) −24.4372 −0.848228
\(831\) 4.83846 0.167844
\(832\) 29.6642 1.02842
\(833\) 6.95840 0.241094
\(834\) −25.6968 −0.889806
\(835\) 35.3187 1.22225
\(836\) −0.00207552 −7.17833e−5 0
\(837\) −0.398581 −0.0137770
\(838\) 4.30828 0.148827
\(839\) 39.9576 1.37949 0.689744 0.724053i \(-0.257723\pi\)
0.689744 + 0.724053i \(0.257723\pi\)
\(840\) 1.25284 0.0432271
\(841\) −28.5809 −0.985549
\(842\) −14.9319 −0.514587
\(843\) 16.5815 0.571098
\(844\) 0.0576182 0.00198330
\(845\) −0.626655 −0.0215576
\(846\) −8.06333 −0.277223
\(847\) 1.52062 0.0522490
\(848\) 4.03708 0.138634
\(849\) −19.2054 −0.659126
\(850\) −0.656421 −0.0225150
\(851\) 26.9484 0.923778
\(852\) 0.327022 0.0112036
\(853\) 11.3176 0.387507 0.193753 0.981050i \(-0.437934\pi\)
0.193753 + 0.981050i \(0.437934\pi\)
\(854\) 0.724717 0.0247993
\(855\) −0.0264789 −0.000905559 0
\(856\) −3.43486 −0.117401
\(857\) 30.1121 1.02861 0.514305 0.857607i \(-0.328050\pi\)
0.514305 + 0.857607i \(0.328050\pi\)
\(858\) −9.27807 −0.316748
\(859\) −8.17691 −0.278993 −0.139496 0.990223i \(-0.544548\pi\)
−0.139496 + 0.990223i \(0.544548\pi\)
\(860\) 1.65886 0.0565668
\(861\) −2.50616 −0.0854098
\(862\) −5.63920 −0.192072
\(863\) 47.6091 1.62063 0.810317 0.585992i \(-0.199295\pi\)
0.810317 + 0.585992i \(0.199295\pi\)
\(864\) 0.500626 0.0170316
\(865\) −12.2206 −0.415513
\(866\) 38.8867 1.32142
\(867\) −1.00000 −0.0339618
\(868\) 0.00719992 0.000244381 0
\(869\) 4.82997 0.163845
\(870\) 1.90391 0.0645487
\(871\) 23.4169 0.793452
\(872\) −1.15868 −0.0392378
\(873\) −12.1019 −0.409587
\(874\) 0.113291 0.00383211
\(875\) 2.37539 0.0803029
\(876\) 0.0401324 0.00135595
\(877\) 29.2718 0.988438 0.494219 0.869338i \(-0.335454\pi\)
0.494219 + 0.869338i \(0.335454\pi\)
\(878\) 36.1934 1.22147
\(879\) 21.3155 0.718955
\(880\) 15.2792 0.515061
\(881\) −18.7555 −0.631890 −0.315945 0.948777i \(-0.602322\pi\)
−0.315945 + 0.948777i \(0.602322\pi\)
\(882\) 9.62031 0.323933
\(883\) 17.7396 0.596986 0.298493 0.954412i \(-0.403516\pi\)
0.298493 + 0.954412i \(0.403516\pi\)
\(884\) 0.315687 0.0106177
\(885\) 31.4285 1.05646
\(886\) 25.7467 0.864978
\(887\) 35.7410 1.20006 0.600032 0.799976i \(-0.295154\pi\)
0.600032 + 0.799976i \(0.295154\pi\)
\(888\) −11.8203 −0.396662
\(889\) 2.86123 0.0959626
\(890\) 45.7900 1.53488
\(891\) −1.88271 −0.0630732
\(892\) 0.946279 0.0316838
\(893\) −0.0725964 −0.00242935
\(894\) 6.03812 0.201945
\(895\) 16.2316 0.542563
\(896\) 2.14253 0.0715768
\(897\) −23.4654 −0.783486
\(898\) −23.4934 −0.783984
\(899\) 0.258027 0.00860567
\(900\) 0.0420499 0.00140166
\(901\) 1.05821 0.0352539
\(902\) −31.9833 −1.06493
\(903\) −1.79588 −0.0597632
\(904\) 6.39605 0.212729
\(905\) 17.1294 0.569399
\(906\) −4.33461 −0.144008
\(907\) −48.8728 −1.62280 −0.811398 0.584494i \(-0.801293\pi\)
−0.811398 + 0.584494i \(0.801293\pi\)
\(908\) −1.29534 −0.0429873
\(909\) −3.19743 −0.106052
\(910\) 2.13817 0.0708796
\(911\) −30.3594 −1.00585 −0.502926 0.864329i \(-0.667743\pi\)
−0.502926 + 0.864329i \(0.667743\pi\)
\(912\) −0.0474874 −0.00157246
\(913\) −15.6436 −0.517727
\(914\) 42.1322 1.39361
\(915\) −5.46713 −0.180738
\(916\) −0.0371926 −0.00122888
\(917\) 2.61287 0.0862844
\(918\) −1.38255 −0.0456308
\(919\) −39.7439 −1.31103 −0.655515 0.755182i \(-0.727548\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(920\) 40.4371 1.33317
\(921\) −16.5041 −0.543829
\(922\) −20.4456 −0.673339
\(923\) 13.1616 0.433220
\(924\) 0.0340091 0.00111882
\(925\) −1.94358 −0.0639044
\(926\) −31.4375 −1.03310
\(927\) 10.5170 0.345425
\(928\) −0.324087 −0.0106387
\(929\) −7.96176 −0.261217 −0.130608 0.991434i \(-0.541693\pi\)
−0.130608 + 0.991434i \(0.541693\pi\)
\(930\) 1.17224 0.0384392
\(931\) 0.0866144 0.00283867
\(932\) −1.86852 −0.0612056
\(933\) −0.315638 −0.0103335
\(934\) −31.1686 −1.01987
\(935\) 4.00500 0.130978
\(936\) 10.2925 0.336422
\(937\) 0.958798 0.0313226 0.0156613 0.999877i \(-0.495015\pi\)
0.0156613 + 0.999877i \(0.495015\pi\)
\(938\) 1.85252 0.0604870
\(939\) −30.8499 −1.00675
\(940\) −1.09879 −0.0358387
\(941\) −15.1533 −0.493985 −0.246992 0.969017i \(-0.579442\pi\)
−0.246992 + 0.969017i \(0.579442\pi\)
\(942\) −1.38255 −0.0450458
\(943\) −80.8898 −2.63413
\(944\) 56.3640 1.83449
\(945\) 0.433878 0.0141141
\(946\) −22.9188 −0.745155
\(947\) 7.54635 0.245223 0.122612 0.992455i \(-0.460873\pi\)
0.122612 + 0.992455i \(0.460873\pi\)
\(948\) −0.227208 −0.00737937
\(949\) 1.61520 0.0524317
\(950\) −0.00817077 −0.000265095 0
\(951\) 10.5058 0.340675
\(952\) 0.588947 0.0190879
\(953\) −21.8241 −0.706951 −0.353475 0.935444i \(-0.615000\pi\)
−0.353475 + 0.935444i \(0.615000\pi\)
\(954\) 1.46302 0.0473670
\(955\) −8.81563 −0.285267
\(956\) −2.00682 −0.0649050
\(957\) 1.21880 0.0393981
\(958\) 22.7928 0.736402
\(959\) 2.01619 0.0651061
\(960\) −17.7034 −0.571375
\(961\) −30.8411 −0.994875
\(962\) −20.1731 −0.650408
\(963\) −1.18955 −0.0383326
\(964\) −2.24919 −0.0724416
\(965\) 21.6899 0.698221
\(966\) −1.85636 −0.0597273
\(967\) −28.6063 −0.919916 −0.459958 0.887941i \(-0.652135\pi\)
−0.459958 + 0.887941i \(0.652135\pi\)
\(968\) −21.5278 −0.691928
\(969\) −0.0124475 −0.000399870 0
\(970\) 35.5920 1.14279
\(971\) −11.0532 −0.354714 −0.177357 0.984147i \(-0.556755\pi\)
−0.177357 + 0.984147i \(0.556755\pi\)
\(972\) 0.0885651 0.00284073
\(973\) 3.79094 0.121532
\(974\) 53.1805 1.70401
\(975\) 1.69238 0.0541994
\(976\) −9.80477 −0.313843
\(977\) −2.85988 −0.0914956 −0.0457478 0.998953i \(-0.514567\pi\)
−0.0457478 + 0.998953i \(0.514567\pi\)
\(978\) 3.17874 0.101645
\(979\) 29.3126 0.936835
\(980\) 1.31097 0.0418773
\(981\) −0.401268 −0.0128115
\(982\) −49.7632 −1.58801
\(983\) −12.8749 −0.410647 −0.205323 0.978694i \(-0.565825\pi\)
−0.205323 + 0.978694i \(0.565825\pi\)
\(984\) 35.4804 1.13107
\(985\) −16.8840 −0.537969
\(986\) 0.895010 0.0285029
\(987\) 1.18955 0.0378638
\(988\) 0.00392950 0.000125014 0
\(989\) −57.9645 −1.84316
\(990\) 5.53710 0.175981
\(991\) −1.74510 −0.0554349 −0.0277174 0.999616i \(-0.508824\pi\)
−0.0277174 + 0.999616i \(0.508824\pi\)
\(992\) −0.199540 −0.00633540
\(993\) 33.7794 1.07196
\(994\) 1.04122 0.0330256
\(995\) −3.38229 −0.107226
\(996\) 0.735894 0.0233177
\(997\) −3.28316 −0.103979 −0.0519894 0.998648i \(-0.516556\pi\)
−0.0519894 + 0.998648i \(0.516556\pi\)
\(998\) 4.40624 0.139477
\(999\) −4.09354 −0.129514
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 \(a_p\))