Properties

Label 8007.2.a.e.1.21
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

Related objects

Downloads

Learn more about

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: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.503095 q^{2} +1.00000 q^{3} -1.74690 q^{4} -1.55796 q^{5} -0.503095 q^{6} +2.07714 q^{7} +1.88504 q^{8} +1.00000 q^{9} +0.783803 q^{10} -2.88035 q^{11} -1.74690 q^{12} +2.62239 q^{13} -1.04500 q^{14} -1.55796 q^{15} +2.54544 q^{16} -1.00000 q^{17} -0.503095 q^{18} +5.60081 q^{19} +2.72160 q^{20} +2.07714 q^{21} +1.44909 q^{22} +0.593598 q^{23} +1.88504 q^{24} -2.57275 q^{25} -1.31931 q^{26} +1.00000 q^{27} -3.62855 q^{28} -9.84663 q^{29} +0.783803 q^{30} +2.75385 q^{31} -5.05068 q^{32} -2.88035 q^{33} +0.503095 q^{34} -3.23611 q^{35} -1.74690 q^{36} -2.67091 q^{37} -2.81774 q^{38} +2.62239 q^{39} -2.93683 q^{40} -8.19250 q^{41} -1.04500 q^{42} -4.66949 q^{43} +5.03167 q^{44} -1.55796 q^{45} -0.298636 q^{46} +11.4351 q^{47} +2.54544 q^{48} -2.68549 q^{49} +1.29434 q^{50} -1.00000 q^{51} -4.58105 q^{52} -9.27271 q^{53} -0.503095 q^{54} +4.48748 q^{55} +3.91550 q^{56} +5.60081 q^{57} +4.95379 q^{58} -7.63345 q^{59} +2.72160 q^{60} +3.42981 q^{61} -1.38545 q^{62} +2.07714 q^{63} -2.54990 q^{64} -4.08559 q^{65} +1.44909 q^{66} +14.2127 q^{67} +1.74690 q^{68} +0.593598 q^{69} +1.62807 q^{70} -2.18257 q^{71} +1.88504 q^{72} +8.60069 q^{73} +1.34372 q^{74} -2.57275 q^{75} -9.78404 q^{76} -5.98289 q^{77} -1.31931 q^{78} -4.94394 q^{79} -3.96569 q^{80} +1.00000 q^{81} +4.12160 q^{82} -11.9546 q^{83} -3.62855 q^{84} +1.55796 q^{85} +2.34920 q^{86} -9.84663 q^{87} -5.42958 q^{88} +7.90847 q^{89} +0.783803 q^{90} +5.44708 q^{91} -1.03695 q^{92} +2.75385 q^{93} -5.75296 q^{94} -8.72586 q^{95} -5.05068 q^{96} +7.71587 q^{97} +1.35105 q^{98} -2.88035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.503095 −0.355742 −0.177871 0.984054i \(-0.556921\pi\)
−0.177871 + 0.984054i \(0.556921\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.74690 −0.873448
\(5\) −1.55796 −0.696742 −0.348371 0.937357i \(-0.613265\pi\)
−0.348371 + 0.937357i \(0.613265\pi\)
\(6\) −0.503095 −0.205388
\(7\) 2.07714 0.785085 0.392543 0.919734i \(-0.371596\pi\)
0.392543 + 0.919734i \(0.371596\pi\)
\(8\) 1.88504 0.666463
\(9\) 1.00000 0.333333
\(10\) 0.783803 0.247860
\(11\) −2.88035 −0.868458 −0.434229 0.900803i \(-0.642979\pi\)
−0.434229 + 0.900803i \(0.642979\pi\)
\(12\) −1.74690 −0.504285
\(13\) 2.62239 0.727321 0.363661 0.931532i \(-0.381527\pi\)
0.363661 + 0.931532i \(0.381527\pi\)
\(14\) −1.04500 −0.279288
\(15\) −1.55796 −0.402264
\(16\) 2.54544 0.636359
\(17\) −1.00000 −0.242536
\(18\) −0.503095 −0.118581
\(19\) 5.60081 1.28491 0.642457 0.766321i \(-0.277915\pi\)
0.642457 + 0.766321i \(0.277915\pi\)
\(20\) 2.72160 0.608568
\(21\) 2.07714 0.453269
\(22\) 1.44909 0.308947
\(23\) 0.593598 0.123774 0.0618868 0.998083i \(-0.480288\pi\)
0.0618868 + 0.998083i \(0.480288\pi\)
\(24\) 1.88504 0.384783
\(25\) −2.57275 −0.514551
\(26\) −1.31931 −0.258738
\(27\) 1.00000 0.192450
\(28\) −3.62855 −0.685731
\(29\) −9.84663 −1.82847 −0.914236 0.405181i \(-0.867208\pi\)
−0.914236 + 0.405181i \(0.867208\pi\)
\(30\) 0.783803 0.143102
\(31\) 2.75385 0.494607 0.247303 0.968938i \(-0.420456\pi\)
0.247303 + 0.968938i \(0.420456\pi\)
\(32\) −5.05068 −0.892843
\(33\) −2.88035 −0.501404
\(34\) 0.503095 0.0862800
\(35\) −3.23611 −0.547002
\(36\) −1.74690 −0.291149
\(37\) −2.67091 −0.439095 −0.219548 0.975602i \(-0.570458\pi\)
−0.219548 + 0.975602i \(0.570458\pi\)
\(38\) −2.81774 −0.457098
\(39\) 2.62239 0.419919
\(40\) −2.93683 −0.464353
\(41\) −8.19250 −1.27945 −0.639727 0.768603i \(-0.720952\pi\)
−0.639727 + 0.768603i \(0.720952\pi\)
\(42\) −1.04500 −0.161247
\(43\) −4.66949 −0.712091 −0.356045 0.934469i \(-0.615875\pi\)
−0.356045 + 0.934469i \(0.615875\pi\)
\(44\) 5.03167 0.758553
\(45\) −1.55796 −0.232247
\(46\) −0.298636 −0.0440315
\(47\) 11.4351 1.66799 0.833993 0.551775i \(-0.186049\pi\)
0.833993 + 0.551775i \(0.186049\pi\)
\(48\) 2.54544 0.367402
\(49\) −2.68549 −0.383641
\(50\) 1.29434 0.183047
\(51\) −1.00000 −0.140028
\(52\) −4.58105 −0.635277
\(53\) −9.27271 −1.27370 −0.636852 0.770986i \(-0.719764\pi\)
−0.636852 + 0.770986i \(0.719764\pi\)
\(54\) −0.503095 −0.0684625
\(55\) 4.48748 0.605091
\(56\) 3.91550 0.523231
\(57\) 5.60081 0.741846
\(58\) 4.95379 0.650464
\(59\) −7.63345 −0.993791 −0.496895 0.867810i \(-0.665527\pi\)
−0.496895 + 0.867810i \(0.665527\pi\)
\(60\) 2.72160 0.351357
\(61\) 3.42981 0.439142 0.219571 0.975597i \(-0.429534\pi\)
0.219571 + 0.975597i \(0.429534\pi\)
\(62\) −1.38545 −0.175952
\(63\) 2.07714 0.261695
\(64\) −2.54990 −0.318738
\(65\) −4.08559 −0.506755
\(66\) 1.44909 0.178370
\(67\) 14.2127 1.73636 0.868182 0.496247i \(-0.165289\pi\)
0.868182 + 0.496247i \(0.165289\pi\)
\(68\) 1.74690 0.211842
\(69\) 0.593598 0.0714608
\(70\) 1.62807 0.194591
\(71\) −2.18257 −0.259023 −0.129512 0.991578i \(-0.541341\pi\)
−0.129512 + 0.991578i \(0.541341\pi\)
\(72\) 1.88504 0.222154
\(73\) 8.60069 1.00663 0.503317 0.864102i \(-0.332113\pi\)
0.503317 + 0.864102i \(0.332113\pi\)
\(74\) 1.34372 0.156205
\(75\) −2.57275 −0.297076
\(76\) −9.78404 −1.12231
\(77\) −5.98289 −0.681813
\(78\) −1.31931 −0.149383
\(79\) −4.94394 −0.556237 −0.278119 0.960547i \(-0.589711\pi\)
−0.278119 + 0.960547i \(0.589711\pi\)
\(80\) −3.96569 −0.443378
\(81\) 1.00000 0.111111
\(82\) 4.12160 0.455155
\(83\) −11.9546 −1.31218 −0.656091 0.754681i \(-0.727791\pi\)
−0.656091 + 0.754681i \(0.727791\pi\)
\(84\) −3.62855 −0.395907
\(85\) 1.55796 0.168985
\(86\) 2.34920 0.253320
\(87\) −9.84663 −1.05567
\(88\) −5.42958 −0.578795
\(89\) 7.90847 0.838296 0.419148 0.907918i \(-0.362329\pi\)
0.419148 + 0.907918i \(0.362329\pi\)
\(90\) 0.783803 0.0826201
\(91\) 5.44708 0.571009
\(92\) −1.03695 −0.108110
\(93\) 2.75385 0.285561
\(94\) −5.75296 −0.593372
\(95\) −8.72586 −0.895254
\(96\) −5.05068 −0.515483
\(97\) 7.71587 0.783428 0.391714 0.920087i \(-0.371882\pi\)
0.391714 + 0.920087i \(0.371882\pi\)
\(98\) 1.35105 0.136477
\(99\) −2.88035 −0.289486
\(100\) 4.49433 0.449433
\(101\) 3.17301 0.315726 0.157863 0.987461i \(-0.449540\pi\)
0.157863 + 0.987461i \(0.449540\pi\)
\(102\) 0.503095 0.0498138
\(103\) 4.99764 0.492432 0.246216 0.969215i \(-0.420813\pi\)
0.246216 + 0.969215i \(0.420813\pi\)
\(104\) 4.94333 0.484733
\(105\) −3.23611 −0.315812
\(106\) 4.66505 0.453110
\(107\) 16.7318 1.61753 0.808763 0.588135i \(-0.200138\pi\)
0.808763 + 0.588135i \(0.200138\pi\)
\(108\) −1.74690 −0.168095
\(109\) 10.9675 1.05049 0.525246 0.850950i \(-0.323973\pi\)
0.525246 + 0.850950i \(0.323973\pi\)
\(110\) −2.25763 −0.215256
\(111\) −2.67091 −0.253512
\(112\) 5.28723 0.499596
\(113\) 11.7341 1.10386 0.551928 0.833892i \(-0.313892\pi\)
0.551928 + 0.833892i \(0.313892\pi\)
\(114\) −2.81774 −0.263906
\(115\) −0.924803 −0.0862383
\(116\) 17.2010 1.59708
\(117\) 2.62239 0.242440
\(118\) 3.84035 0.353533
\(119\) −2.07714 −0.190411
\(120\) −2.93683 −0.268094
\(121\) −2.70359 −0.245781
\(122\) −1.72552 −0.156221
\(123\) −8.19250 −0.738693
\(124\) −4.81070 −0.432013
\(125\) 11.7981 1.05525
\(126\) −1.04500 −0.0930958
\(127\) −10.8830 −0.965714 −0.482857 0.875699i \(-0.660401\pi\)
−0.482857 + 0.875699i \(0.660401\pi\)
\(128\) 11.3842 1.00623
\(129\) −4.66949 −0.411126
\(130\) 2.05544 0.180274
\(131\) −8.77004 −0.766242 −0.383121 0.923698i \(-0.625151\pi\)
−0.383121 + 0.923698i \(0.625151\pi\)
\(132\) 5.03167 0.437951
\(133\) 11.6337 1.00877
\(134\) −7.15036 −0.617697
\(135\) −1.55796 −0.134088
\(136\) −1.88504 −0.161641
\(137\) −11.3931 −0.973376 −0.486688 0.873576i \(-0.661795\pi\)
−0.486688 + 0.873576i \(0.661795\pi\)
\(138\) −0.298636 −0.0254216
\(139\) 3.70066 0.313886 0.156943 0.987608i \(-0.449836\pi\)
0.156943 + 0.987608i \(0.449836\pi\)
\(140\) 5.65314 0.477778
\(141\) 11.4351 0.963012
\(142\) 1.09804 0.0921454
\(143\) −7.55341 −0.631648
\(144\) 2.54544 0.212120
\(145\) 15.3407 1.27397
\(146\) −4.32696 −0.358102
\(147\) −2.68549 −0.221495
\(148\) 4.66581 0.383527
\(149\) 21.4973 1.76112 0.880562 0.473930i \(-0.157165\pi\)
0.880562 + 0.473930i \(0.157165\pi\)
\(150\) 1.29434 0.105682
\(151\) −14.5312 −1.18253 −0.591264 0.806478i \(-0.701371\pi\)
−0.591264 + 0.806478i \(0.701371\pi\)
\(152\) 10.5578 0.856349
\(153\) −1.00000 −0.0808452
\(154\) 3.00996 0.242549
\(155\) −4.29040 −0.344613
\(156\) −4.58105 −0.366777
\(157\) 1.00000 0.0798087
\(158\) 2.48727 0.197877
\(159\) −9.27271 −0.735374
\(160\) 7.86877 0.622081
\(161\) 1.23299 0.0971729
\(162\) −0.503095 −0.0395269
\(163\) −11.2459 −0.880844 −0.440422 0.897791i \(-0.645171\pi\)
−0.440422 + 0.897791i \(0.645171\pi\)
\(164\) 14.3114 1.11754
\(165\) 4.48748 0.349350
\(166\) 6.01427 0.466798
\(167\) −11.9886 −0.927704 −0.463852 0.885913i \(-0.653533\pi\)
−0.463852 + 0.885913i \(0.653533\pi\)
\(168\) 3.91550 0.302087
\(169\) −6.12305 −0.471004
\(170\) −0.783803 −0.0601149
\(171\) 5.60081 0.428305
\(172\) 8.15712 0.621974
\(173\) −21.0540 −1.60071 −0.800353 0.599529i \(-0.795355\pi\)
−0.800353 + 0.599529i \(0.795355\pi\)
\(174\) 4.95379 0.375546
\(175\) −5.34397 −0.403966
\(176\) −7.33174 −0.552651
\(177\) −7.63345 −0.573765
\(178\) −3.97871 −0.298217
\(179\) −23.0346 −1.72169 −0.860844 0.508869i \(-0.830064\pi\)
−0.860844 + 0.508869i \(0.830064\pi\)
\(180\) 2.72160 0.202856
\(181\) −12.5707 −0.934372 −0.467186 0.884159i \(-0.654732\pi\)
−0.467186 + 0.884159i \(0.654732\pi\)
\(182\) −2.74040 −0.203132
\(183\) 3.42981 0.253539
\(184\) 1.11896 0.0824906
\(185\) 4.16118 0.305936
\(186\) −1.38545 −0.101586
\(187\) 2.88035 0.210632
\(188\) −19.9760 −1.45690
\(189\) 2.07714 0.151090
\(190\) 4.38993 0.318479
\(191\) −19.0475 −1.37823 −0.689113 0.724654i \(-0.742000\pi\)
−0.689113 + 0.724654i \(0.742000\pi\)
\(192\) −2.54990 −0.184023
\(193\) 2.65031 0.190774 0.0953868 0.995440i \(-0.469591\pi\)
0.0953868 + 0.995440i \(0.469591\pi\)
\(194\) −3.88181 −0.278698
\(195\) −4.08559 −0.292575
\(196\) 4.69127 0.335091
\(197\) −21.2170 −1.51165 −0.755823 0.654775i \(-0.772763\pi\)
−0.755823 + 0.654775i \(0.772763\pi\)
\(198\) 1.44909 0.102982
\(199\) −9.57360 −0.678654 −0.339327 0.940668i \(-0.610199\pi\)
−0.339327 + 0.940668i \(0.610199\pi\)
\(200\) −4.84975 −0.342929
\(201\) 14.2127 1.00249
\(202\) −1.59632 −0.112317
\(203\) −20.4528 −1.43551
\(204\) 1.74690 0.122307
\(205\) 12.7636 0.891449
\(206\) −2.51429 −0.175179
\(207\) 0.593598 0.0412579
\(208\) 6.67514 0.462837
\(209\) −16.1323 −1.11589
\(210\) 1.62807 0.112347
\(211\) −6.62775 −0.456273 −0.228137 0.973629i \(-0.573263\pi\)
−0.228137 + 0.973629i \(0.573263\pi\)
\(212\) 16.1985 1.11251
\(213\) −2.18257 −0.149547
\(214\) −8.41768 −0.575421
\(215\) 7.27490 0.496144
\(216\) 1.88504 0.128261
\(217\) 5.72014 0.388309
\(218\) −5.51767 −0.373704
\(219\) 8.60069 0.581181
\(220\) −7.83915 −0.528516
\(221\) −2.62239 −0.176401
\(222\) 1.34372 0.0901847
\(223\) −7.81608 −0.523403 −0.261702 0.965149i \(-0.584284\pi\)
−0.261702 + 0.965149i \(0.584284\pi\)
\(224\) −10.4910 −0.700958
\(225\) −2.57275 −0.171517
\(226\) −5.90339 −0.392688
\(227\) −4.26210 −0.282886 −0.141443 0.989946i \(-0.545174\pi\)
−0.141443 + 0.989946i \(0.545174\pi\)
\(228\) −9.78404 −0.647964
\(229\) −2.65238 −0.175274 −0.0876370 0.996152i \(-0.527932\pi\)
−0.0876370 + 0.996152i \(0.527932\pi\)
\(230\) 0.465263 0.0306786
\(231\) −5.98289 −0.393645
\(232\) −18.5613 −1.21861
\(233\) 24.7740 1.62300 0.811500 0.584352i \(-0.198651\pi\)
0.811500 + 0.584352i \(0.198651\pi\)
\(234\) −1.31931 −0.0862461
\(235\) −17.8155 −1.16216
\(236\) 13.3348 0.868025
\(237\) −4.94394 −0.321144
\(238\) 1.04500 0.0677372
\(239\) −26.1059 −1.68865 −0.844324 0.535833i \(-0.819998\pi\)
−0.844324 + 0.535833i \(0.819998\pi\)
\(240\) −3.96569 −0.255984
\(241\) −28.0678 −1.80801 −0.904003 0.427525i \(-0.859386\pi\)
−0.904003 + 0.427525i \(0.859386\pi\)
\(242\) 1.36016 0.0874345
\(243\) 1.00000 0.0641500
\(244\) −5.99152 −0.383568
\(245\) 4.18389 0.267299
\(246\) 4.12160 0.262784
\(247\) 14.6875 0.934546
\(248\) 5.19113 0.329637
\(249\) −11.9546 −0.757589
\(250\) −5.93554 −0.375397
\(251\) 7.18179 0.453311 0.226655 0.973975i \(-0.427221\pi\)
0.226655 + 0.973975i \(0.427221\pi\)
\(252\) −3.62855 −0.228577
\(253\) −1.70977 −0.107492
\(254\) 5.47520 0.343545
\(255\) 1.55796 0.0975634
\(256\) −0.627532 −0.0392208
\(257\) −0.0993936 −0.00620000 −0.00310000 0.999995i \(-0.500987\pi\)
−0.00310000 + 0.999995i \(0.500987\pi\)
\(258\) 2.34920 0.146255
\(259\) −5.54786 −0.344727
\(260\) 7.13710 0.442624
\(261\) −9.84663 −0.609491
\(262\) 4.41216 0.272584
\(263\) 16.9410 1.04463 0.522315 0.852753i \(-0.325069\pi\)
0.522315 + 0.852753i \(0.325069\pi\)
\(264\) −5.42958 −0.334168
\(265\) 14.4465 0.887444
\(266\) −5.85284 −0.358861
\(267\) 7.90847 0.483991
\(268\) −24.8282 −1.51662
\(269\) 20.4855 1.24902 0.624512 0.781015i \(-0.285298\pi\)
0.624512 + 0.781015i \(0.285298\pi\)
\(270\) 0.783803 0.0477007
\(271\) −9.61120 −0.583839 −0.291919 0.956443i \(-0.594294\pi\)
−0.291919 + 0.956443i \(0.594294\pi\)
\(272\) −2.54544 −0.154340
\(273\) 5.44708 0.329672
\(274\) 5.73179 0.346270
\(275\) 7.41043 0.446865
\(276\) −1.03695 −0.0624173
\(277\) 11.6939 0.702619 0.351309 0.936259i \(-0.385737\pi\)
0.351309 + 0.936259i \(0.385737\pi\)
\(278\) −1.86178 −0.111662
\(279\) 2.75385 0.164869
\(280\) −6.10020 −0.364557
\(281\) 12.4451 0.742415 0.371207 0.928550i \(-0.378944\pi\)
0.371207 + 0.928550i \(0.378944\pi\)
\(282\) −5.75296 −0.342584
\(283\) 8.85469 0.526357 0.263178 0.964747i \(-0.415229\pi\)
0.263178 + 0.964747i \(0.415229\pi\)
\(284\) 3.81272 0.226243
\(285\) −8.72586 −0.516875
\(286\) 3.80008 0.224703
\(287\) −17.0170 −1.00448
\(288\) −5.05068 −0.297614
\(289\) 1.00000 0.0588235
\(290\) −7.71781 −0.453206
\(291\) 7.71587 0.452312
\(292\) −15.0245 −0.879243
\(293\) 23.2694 1.35941 0.679705 0.733486i \(-0.262108\pi\)
0.679705 + 0.733486i \(0.262108\pi\)
\(294\) 1.35105 0.0787951
\(295\) 11.8926 0.692416
\(296\) −5.03479 −0.292641
\(297\) −2.88035 −0.167135
\(298\) −10.8152 −0.626505
\(299\) 1.55665 0.0900232
\(300\) 4.49433 0.259480
\(301\) −9.69919 −0.559052
\(302\) 7.31055 0.420675
\(303\) 3.17301 0.182285
\(304\) 14.2565 0.817667
\(305\) −5.34351 −0.305969
\(306\) 0.503095 0.0287600
\(307\) −22.8169 −1.30223 −0.651116 0.758978i \(-0.725699\pi\)
−0.651116 + 0.758978i \(0.725699\pi\)
\(308\) 10.4515 0.595529
\(309\) 4.99764 0.284306
\(310\) 2.15848 0.122593
\(311\) 11.1896 0.634504 0.317252 0.948341i \(-0.397240\pi\)
0.317252 + 0.948341i \(0.397240\pi\)
\(312\) 4.94333 0.279861
\(313\) −10.9958 −0.621519 −0.310760 0.950489i \(-0.600583\pi\)
−0.310760 + 0.950489i \(0.600583\pi\)
\(314\) −0.503095 −0.0283913
\(315\) −3.23611 −0.182334
\(316\) 8.63655 0.485844
\(317\) −0.0439860 −0.00247050 −0.00123525 0.999999i \(-0.500393\pi\)
−0.00123525 + 0.999999i \(0.500393\pi\)
\(318\) 4.66505 0.261603
\(319\) 28.3617 1.58795
\(320\) 3.97265 0.222078
\(321\) 16.7318 0.933878
\(322\) −0.620309 −0.0345684
\(323\) −5.60081 −0.311638
\(324\) −1.74690 −0.0970498
\(325\) −6.74677 −0.374243
\(326\) 5.65773 0.313353
\(327\) 10.9675 0.606502
\(328\) −15.4432 −0.852709
\(329\) 23.7524 1.30951
\(330\) −2.25763 −0.124278
\(331\) −13.4548 −0.739541 −0.369770 0.929123i \(-0.620564\pi\)
−0.369770 + 0.929123i \(0.620564\pi\)
\(332\) 20.8834 1.14612
\(333\) −2.67091 −0.146365
\(334\) 6.03139 0.330023
\(335\) −22.1429 −1.20980
\(336\) 5.28723 0.288442
\(337\) 0.544072 0.0296375 0.0148188 0.999890i \(-0.495283\pi\)
0.0148188 + 0.999890i \(0.495283\pi\)
\(338\) 3.08047 0.167556
\(339\) 11.7341 0.637312
\(340\) −2.72160 −0.147599
\(341\) −7.93206 −0.429545
\(342\) −2.81774 −0.152366
\(343\) −20.1181 −1.08628
\(344\) −8.80220 −0.474583
\(345\) −0.924803 −0.0497897
\(346\) 10.5922 0.569438
\(347\) −20.2952 −1.08950 −0.544752 0.838597i \(-0.683376\pi\)
−0.544752 + 0.838597i \(0.683376\pi\)
\(348\) 17.2010 0.922072
\(349\) −5.88048 −0.314775 −0.157387 0.987537i \(-0.550307\pi\)
−0.157387 + 0.987537i \(0.550307\pi\)
\(350\) 2.68852 0.143708
\(351\) 2.62239 0.139973
\(352\) 14.5477 0.775396
\(353\) −20.8745 −1.11104 −0.555520 0.831503i \(-0.687481\pi\)
−0.555520 + 0.831503i \(0.687481\pi\)
\(354\) 3.84035 0.204112
\(355\) 3.40036 0.180472
\(356\) −13.8153 −0.732208
\(357\) −2.07714 −0.109934
\(358\) 11.5886 0.612476
\(359\) −7.61532 −0.401921 −0.200961 0.979599i \(-0.564406\pi\)
−0.200961 + 0.979599i \(0.564406\pi\)
\(360\) −2.93683 −0.154784
\(361\) 12.3691 0.651006
\(362\) 6.32425 0.332395
\(363\) −2.70359 −0.141902
\(364\) −9.51548 −0.498747
\(365\) −13.3996 −0.701365
\(366\) −1.72552 −0.0901943
\(367\) −14.3904 −0.751173 −0.375586 0.926787i \(-0.622559\pi\)
−0.375586 + 0.926787i \(0.622559\pi\)
\(368\) 1.51096 0.0787645
\(369\) −8.19250 −0.426484
\(370\) −2.09347 −0.108834
\(371\) −19.2607 −0.999967
\(372\) −4.81070 −0.249423
\(373\) 1.66468 0.0861940 0.0430970 0.999071i \(-0.486278\pi\)
0.0430970 + 0.999071i \(0.486278\pi\)
\(374\) −1.44909 −0.0749306
\(375\) 11.7981 0.609249
\(376\) 21.5557 1.11165
\(377\) −25.8217 −1.32989
\(378\) −1.04500 −0.0537489
\(379\) −25.3244 −1.30082 −0.650412 0.759581i \(-0.725404\pi\)
−0.650412 + 0.759581i \(0.725404\pi\)
\(380\) 15.2432 0.781958
\(381\) −10.8830 −0.557555
\(382\) 9.58268 0.490292
\(383\) −32.2795 −1.64940 −0.824702 0.565567i \(-0.808657\pi\)
−0.824702 + 0.565567i \(0.808657\pi\)
\(384\) 11.3842 0.580948
\(385\) 9.32112 0.475048
\(386\) −1.33336 −0.0678661
\(387\) −4.66949 −0.237364
\(388\) −13.4788 −0.684283
\(389\) 26.1678 1.32676 0.663379 0.748283i \(-0.269122\pi\)
0.663379 + 0.748283i \(0.269122\pi\)
\(390\) 2.05544 0.104081
\(391\) −0.593598 −0.0300195
\(392\) −5.06226 −0.255683
\(393\) −8.77004 −0.442390
\(394\) 10.6741 0.537756
\(395\) 7.70248 0.387554
\(396\) 5.03167 0.252851
\(397\) −26.3583 −1.32289 −0.661443 0.749995i \(-0.730056\pi\)
−0.661443 + 0.749995i \(0.730056\pi\)
\(398\) 4.81643 0.241426
\(399\) 11.6337 0.582412
\(400\) −6.54878 −0.327439
\(401\) −12.4311 −0.620779 −0.310389 0.950609i \(-0.600459\pi\)
−0.310389 + 0.950609i \(0.600459\pi\)
\(402\) −7.15036 −0.356627
\(403\) 7.22169 0.359738
\(404\) −5.54292 −0.275770
\(405\) −1.55796 −0.0774158
\(406\) 10.2897 0.510670
\(407\) 7.69316 0.381336
\(408\) −1.88504 −0.0933236
\(409\) −15.7451 −0.778547 −0.389274 0.921122i \(-0.627274\pi\)
−0.389274 + 0.921122i \(0.627274\pi\)
\(410\) −6.42130 −0.317126
\(411\) −11.3931 −0.561979
\(412\) −8.73036 −0.430114
\(413\) −15.8558 −0.780211
\(414\) −0.298636 −0.0146772
\(415\) 18.6247 0.914253
\(416\) −13.2449 −0.649384
\(417\) 3.70066 0.181222
\(418\) 8.11607 0.396970
\(419\) 1.31712 0.0643457 0.0321729 0.999482i \(-0.489757\pi\)
0.0321729 + 0.999482i \(0.489757\pi\)
\(420\) 5.65314 0.275845
\(421\) 7.68705 0.374644 0.187322 0.982299i \(-0.440019\pi\)
0.187322 + 0.982299i \(0.440019\pi\)
\(422\) 3.33439 0.162315
\(423\) 11.4351 0.555995
\(424\) −17.4795 −0.848878
\(425\) 2.57275 0.124797
\(426\) 1.09804 0.0532002
\(427\) 7.12420 0.344764
\(428\) −29.2287 −1.41282
\(429\) −7.55341 −0.364682
\(430\) −3.65996 −0.176499
\(431\) 10.9619 0.528018 0.264009 0.964520i \(-0.414955\pi\)
0.264009 + 0.964520i \(0.414955\pi\)
\(432\) 2.54544 0.122467
\(433\) 24.0589 1.15620 0.578098 0.815967i \(-0.303795\pi\)
0.578098 + 0.815967i \(0.303795\pi\)
\(434\) −2.87777 −0.138138
\(435\) 15.3407 0.735529
\(436\) −19.1590 −0.917550
\(437\) 3.32463 0.159039
\(438\) −4.32696 −0.206750
\(439\) −15.8395 −0.755979 −0.377989 0.925810i \(-0.623384\pi\)
−0.377989 + 0.925810i \(0.623384\pi\)
\(440\) 8.45909 0.403271
\(441\) −2.68549 −0.127880
\(442\) 1.31931 0.0627533
\(443\) 17.3210 0.822945 0.411473 0.911422i \(-0.365015\pi\)
0.411473 + 0.911422i \(0.365015\pi\)
\(444\) 4.66581 0.221429
\(445\) −12.3211 −0.584076
\(446\) 3.93223 0.186196
\(447\) 21.4973 1.01679
\(448\) −5.29650 −0.250236
\(449\) −25.2040 −1.18945 −0.594725 0.803929i \(-0.702739\pi\)
−0.594725 + 0.803929i \(0.702739\pi\)
\(450\) 1.29434 0.0610157
\(451\) 23.5973 1.11115
\(452\) −20.4983 −0.964161
\(453\) −14.5312 −0.682733
\(454\) 2.14424 0.100634
\(455\) −8.48635 −0.397846
\(456\) 10.5578 0.494413
\(457\) −1.74607 −0.0816778 −0.0408389 0.999166i \(-0.513003\pi\)
−0.0408389 + 0.999166i \(0.513003\pi\)
\(458\) 1.33440 0.0623523
\(459\) −1.00000 −0.0466760
\(460\) 1.61553 0.0753247
\(461\) 30.9165 1.43993 0.719963 0.694012i \(-0.244159\pi\)
0.719963 + 0.694012i \(0.244159\pi\)
\(462\) 3.00996 0.140036
\(463\) 31.2806 1.45373 0.726865 0.686780i \(-0.240976\pi\)
0.726865 + 0.686780i \(0.240976\pi\)
\(464\) −25.0640 −1.16357
\(465\) −4.29040 −0.198963
\(466\) −12.4637 −0.577369
\(467\) 30.3699 1.40535 0.702675 0.711511i \(-0.251989\pi\)
0.702675 + 0.711511i \(0.251989\pi\)
\(468\) −4.58105 −0.211759
\(469\) 29.5219 1.36319
\(470\) 8.96289 0.413427
\(471\) 1.00000 0.0460776
\(472\) −14.3894 −0.662325
\(473\) 13.4498 0.618421
\(474\) 2.48727 0.114244
\(475\) −14.4095 −0.661154
\(476\) 3.62855 0.166314
\(477\) −9.27271 −0.424568
\(478\) 13.1337 0.600722
\(479\) −6.92807 −0.316552 −0.158276 0.987395i \(-0.550594\pi\)
−0.158276 + 0.987395i \(0.550594\pi\)
\(480\) 7.86877 0.359159
\(481\) −7.00418 −0.319363
\(482\) 14.1208 0.643183
\(483\) 1.23299 0.0561028
\(484\) 4.72289 0.214677
\(485\) −12.0210 −0.545847
\(486\) −0.503095 −0.0228208
\(487\) −3.49344 −0.158303 −0.0791515 0.996863i \(-0.525221\pi\)
−0.0791515 + 0.996863i \(0.525221\pi\)
\(488\) 6.46534 0.292672
\(489\) −11.2459 −0.508555
\(490\) −2.10489 −0.0950894
\(491\) −13.7945 −0.622537 −0.311268 0.950322i \(-0.600754\pi\)
−0.311268 + 0.950322i \(0.600754\pi\)
\(492\) 14.3114 0.645210
\(493\) 9.84663 0.443470
\(494\) −7.38922 −0.332457
\(495\) 4.48748 0.201697
\(496\) 7.00976 0.314748
\(497\) −4.53350 −0.203355
\(498\) 6.01427 0.269506
\(499\) −19.0073 −0.850881 −0.425441 0.904986i \(-0.639881\pi\)
−0.425441 + 0.904986i \(0.639881\pi\)
\(500\) −20.6100 −0.921707
\(501\) −11.9886 −0.535610
\(502\) −3.61312 −0.161262
\(503\) −30.7080 −1.36920 −0.684600 0.728919i \(-0.740023\pi\)
−0.684600 + 0.728919i \(0.740023\pi\)
\(504\) 3.91550 0.174410
\(505\) −4.94343 −0.219980
\(506\) 0.860175 0.0382395
\(507\) −6.12305 −0.271934
\(508\) 19.0115 0.843501
\(509\) −0.426399 −0.0188998 −0.00944991 0.999955i \(-0.503008\pi\)
−0.00944991 + 0.999955i \(0.503008\pi\)
\(510\) −0.783803 −0.0347074
\(511\) 17.8648 0.790294
\(512\) −22.4527 −0.992279
\(513\) 5.60081 0.247282
\(514\) 0.0500044 0.00220560
\(515\) −7.78614 −0.343098
\(516\) 8.15712 0.359097
\(517\) −32.9372 −1.44858
\(518\) 2.79110 0.122634
\(519\) −21.0540 −0.924168
\(520\) −7.70152 −0.337734
\(521\) −34.9731 −1.53220 −0.766099 0.642722i \(-0.777805\pi\)
−0.766099 + 0.642722i \(0.777805\pi\)
\(522\) 4.95379 0.216821
\(523\) 19.9792 0.873629 0.436815 0.899552i \(-0.356107\pi\)
0.436815 + 0.899552i \(0.356107\pi\)
\(524\) 15.3203 0.669272
\(525\) −5.34397 −0.233230
\(526\) −8.52295 −0.371618
\(527\) −2.75385 −0.119960
\(528\) −7.33174 −0.319073
\(529\) −22.6476 −0.984680
\(530\) −7.26798 −0.315701
\(531\) −7.63345 −0.331264
\(532\) −20.3228 −0.881106
\(533\) −21.4840 −0.930573
\(534\) −3.97871 −0.172176
\(535\) −26.0675 −1.12700
\(536\) 26.7916 1.15722
\(537\) −23.0346 −0.994017
\(538\) −10.3062 −0.444330
\(539\) 7.73514 0.333176
\(540\) 2.72160 0.117119
\(541\) −21.3330 −0.917176 −0.458588 0.888649i \(-0.651645\pi\)
−0.458588 + 0.888649i \(0.651645\pi\)
\(542\) 4.83534 0.207696
\(543\) −12.5707 −0.539460
\(544\) 5.05068 0.216546
\(545\) −17.0869 −0.731922
\(546\) −2.74040 −0.117278
\(547\) 28.3364 1.21158 0.605789 0.795625i \(-0.292858\pi\)
0.605789 + 0.795625i \(0.292858\pi\)
\(548\) 19.9025 0.850193
\(549\) 3.42981 0.146381
\(550\) −3.72815 −0.158969
\(551\) −55.1491 −2.34943
\(552\) 1.11896 0.0476260
\(553\) −10.2693 −0.436693
\(554\) −5.88314 −0.249951
\(555\) 4.16118 0.176632
\(556\) −6.46467 −0.274163
\(557\) −30.0196 −1.27197 −0.635985 0.771701i \(-0.719406\pi\)
−0.635985 + 0.771701i \(0.719406\pi\)
\(558\) −1.38545 −0.0586508
\(559\) −12.2452 −0.517919
\(560\) −8.23730 −0.348090
\(561\) 2.88035 0.121608
\(562\) −6.26108 −0.264108
\(563\) 29.7665 1.25451 0.627254 0.778815i \(-0.284179\pi\)
0.627254 + 0.778815i \(0.284179\pi\)
\(564\) −19.9760 −0.841141
\(565\) −18.2814 −0.769103
\(566\) −4.45475 −0.187247
\(567\) 2.07714 0.0872317
\(568\) −4.11424 −0.172630
\(569\) −33.3902 −1.39979 −0.699895 0.714245i \(-0.746770\pi\)
−0.699895 + 0.714245i \(0.746770\pi\)
\(570\) 4.38993 0.183874
\(571\) 2.44786 0.102440 0.0512198 0.998687i \(-0.483689\pi\)
0.0512198 + 0.998687i \(0.483689\pi\)
\(572\) 13.1950 0.551711
\(573\) −19.0475 −0.795719
\(574\) 8.56115 0.357335
\(575\) −1.52718 −0.0636878
\(576\) −2.54990 −0.106246
\(577\) 1.37179 0.0571085 0.0285543 0.999592i \(-0.490910\pi\)
0.0285543 + 0.999592i \(0.490910\pi\)
\(578\) −0.503095 −0.0209260
\(579\) 2.65031 0.110143
\(580\) −26.7986 −1.11275
\(581\) −24.8313 −1.03018
\(582\) −3.88181 −0.160906
\(583\) 26.7086 1.10616
\(584\) 16.2127 0.670885
\(585\) −4.08559 −0.168918
\(586\) −11.7067 −0.483599
\(587\) −15.2560 −0.629681 −0.314841 0.949145i \(-0.601951\pi\)
−0.314841 + 0.949145i \(0.601951\pi\)
\(588\) 4.69127 0.193465
\(589\) 15.4238 0.635528
\(590\) −5.98312 −0.246321
\(591\) −21.2170 −0.872750
\(592\) −6.79864 −0.279422
\(593\) −7.63775 −0.313645 −0.156822 0.987627i \(-0.550125\pi\)
−0.156822 + 0.987627i \(0.550125\pi\)
\(594\) 1.44909 0.0594568
\(595\) 3.23611 0.132667
\(596\) −37.5535 −1.53825
\(597\) −9.57360 −0.391821
\(598\) −0.783141 −0.0320250
\(599\) 5.05547 0.206561 0.103280 0.994652i \(-0.467066\pi\)
0.103280 + 0.994652i \(0.467066\pi\)
\(600\) −4.84975 −0.197990
\(601\) 31.3523 1.27889 0.639444 0.768838i \(-0.279165\pi\)
0.639444 + 0.768838i \(0.279165\pi\)
\(602\) 4.87961 0.198878
\(603\) 14.2127 0.578788
\(604\) 25.3844 1.03288
\(605\) 4.21209 0.171246
\(606\) −1.59632 −0.0648463
\(607\) 22.5778 0.916405 0.458203 0.888848i \(-0.348493\pi\)
0.458203 + 0.888848i \(0.348493\pi\)
\(608\) −28.2879 −1.14723
\(609\) −20.4528 −0.828790
\(610\) 2.68829 0.108846
\(611\) 29.9874 1.21316
\(612\) 1.74690 0.0706141
\(613\) 21.2044 0.856438 0.428219 0.903675i \(-0.359141\pi\)
0.428219 + 0.903675i \(0.359141\pi\)
\(614\) 11.4791 0.463258
\(615\) 12.7636 0.514678
\(616\) −11.2780 −0.454404
\(617\) 19.8455 0.798950 0.399475 0.916744i \(-0.369193\pi\)
0.399475 + 0.916744i \(0.369193\pi\)
\(618\) −2.51429 −0.101139
\(619\) 10.7616 0.432547 0.216273 0.976333i \(-0.430610\pi\)
0.216273 + 0.976333i \(0.430610\pi\)
\(620\) 7.49488 0.301002
\(621\) 0.593598 0.0238203
\(622\) −5.62943 −0.225720
\(623\) 16.4270 0.658134
\(624\) 6.67514 0.267219
\(625\) −5.51718 −0.220687
\(626\) 5.53193 0.221100
\(627\) −16.1323 −0.644262
\(628\) −1.74690 −0.0697087
\(629\) 2.67091 0.106496
\(630\) 1.62807 0.0648638
\(631\) −19.4830 −0.775604 −0.387802 0.921743i \(-0.626766\pi\)
−0.387802 + 0.921743i \(0.626766\pi\)
\(632\) −9.31955 −0.370712
\(633\) −6.62775 −0.263429
\(634\) 0.0221291 0.000878859 0
\(635\) 16.9554 0.672853
\(636\) 16.1985 0.642311
\(637\) −7.04241 −0.279030
\(638\) −14.2686 −0.564901
\(639\) −2.18257 −0.0863411
\(640\) −17.7362 −0.701084
\(641\) −11.4029 −0.450387 −0.225193 0.974314i \(-0.572301\pi\)
−0.225193 + 0.974314i \(0.572301\pi\)
\(642\) −8.41768 −0.332220
\(643\) 23.0921 0.910665 0.455333 0.890321i \(-0.349520\pi\)
0.455333 + 0.890321i \(0.349520\pi\)
\(644\) −2.15390 −0.0848754
\(645\) 7.27490 0.286449
\(646\) 2.81774 0.110862
\(647\) −14.1041 −0.554489 −0.277244 0.960799i \(-0.589421\pi\)
−0.277244 + 0.960799i \(0.589421\pi\)
\(648\) 1.88504 0.0740515
\(649\) 21.9870 0.863066
\(650\) 3.39426 0.133134
\(651\) 5.72014 0.224190
\(652\) 19.6453 0.769371
\(653\) 12.1568 0.475733 0.237866 0.971298i \(-0.423552\pi\)
0.237866 + 0.971298i \(0.423552\pi\)
\(654\) −5.51767 −0.215758
\(655\) 13.6634 0.533873
\(656\) −20.8535 −0.814192
\(657\) 8.60069 0.335545
\(658\) −11.9497 −0.465848
\(659\) −4.63902 −0.180711 −0.0903553 0.995910i \(-0.528800\pi\)
−0.0903553 + 0.995910i \(0.528800\pi\)
\(660\) −7.83915 −0.305139
\(661\) −16.4934 −0.641520 −0.320760 0.947161i \(-0.603938\pi\)
−0.320760 + 0.947161i \(0.603938\pi\)
\(662\) 6.76902 0.263085
\(663\) −2.62239 −0.101845
\(664\) −22.5349 −0.874522
\(665\) −18.1248 −0.702851
\(666\) 1.34372 0.0520682
\(667\) −5.84493 −0.226317
\(668\) 20.9428 0.810301
\(669\) −7.81608 −0.302187
\(670\) 11.1400 0.430375
\(671\) −9.87905 −0.381376
\(672\) −10.4910 −0.404698
\(673\) −12.6348 −0.487035 −0.243518 0.969896i \(-0.578301\pi\)
−0.243518 + 0.969896i \(0.578301\pi\)
\(674\) −0.273720 −0.0105433
\(675\) −2.57275 −0.0990253
\(676\) 10.6963 0.411397
\(677\) 5.05087 0.194121 0.0970603 0.995279i \(-0.469056\pi\)
0.0970603 + 0.995279i \(0.469056\pi\)
\(678\) −5.90339 −0.226718
\(679\) 16.0269 0.615057
\(680\) 2.93683 0.112622
\(681\) −4.26210 −0.163324
\(682\) 3.99058 0.152807
\(683\) −8.38588 −0.320877 −0.160438 0.987046i \(-0.551291\pi\)
−0.160438 + 0.987046i \(0.551291\pi\)
\(684\) −9.78404 −0.374102
\(685\) 17.7500 0.678192
\(686\) 10.1213 0.386434
\(687\) −2.65238 −0.101194
\(688\) −11.8859 −0.453146
\(689\) −24.3167 −0.926392
\(690\) 0.465263 0.0177123
\(691\) −45.5839 −1.73409 −0.867046 0.498227i \(-0.833984\pi\)
−0.867046 + 0.498227i \(0.833984\pi\)
\(692\) 36.7792 1.39813
\(693\) −5.98289 −0.227271
\(694\) 10.2104 0.387582
\(695\) −5.76549 −0.218698
\(696\) −18.5613 −0.703565
\(697\) 8.19250 0.310313
\(698\) 2.95844 0.111978
\(699\) 24.7740 0.937040
\(700\) 9.33536 0.352843
\(701\) 5.83362 0.220333 0.110166 0.993913i \(-0.464862\pi\)
0.110166 + 0.993913i \(0.464862\pi\)
\(702\) −1.31931 −0.0497942
\(703\) −14.9593 −0.564200
\(704\) 7.34460 0.276810
\(705\) −17.8155 −0.670971
\(706\) 10.5019 0.395243
\(707\) 6.59079 0.247872
\(708\) 13.3348 0.501154
\(709\) 24.6438 0.925517 0.462758 0.886484i \(-0.346860\pi\)
0.462758 + 0.886484i \(0.346860\pi\)
\(710\) −1.71070 −0.0642016
\(711\) −4.94394 −0.185412
\(712\) 14.9078 0.558694
\(713\) 1.63468 0.0612193
\(714\) 1.04500 0.0391081
\(715\) 11.7679 0.440096
\(716\) 40.2391 1.50380
\(717\) −26.1059 −0.974941
\(718\) 3.83123 0.142980
\(719\) 10.4581 0.390023 0.195012 0.980801i \(-0.437526\pi\)
0.195012 + 0.980801i \(0.437526\pi\)
\(720\) −3.96569 −0.147793
\(721\) 10.3808 0.386601
\(722\) −6.22284 −0.231590
\(723\) −28.0678 −1.04385
\(724\) 21.9597 0.816125
\(725\) 25.3329 0.940842
\(726\) 1.36016 0.0504803
\(727\) −15.0902 −0.559666 −0.279833 0.960049i \(-0.590279\pi\)
−0.279833 + 0.960049i \(0.590279\pi\)
\(728\) 10.2680 0.380557
\(729\) 1.00000 0.0370370
\(730\) 6.74124 0.249505
\(731\) 4.66949 0.172707
\(732\) −5.99152 −0.221453
\(733\) −4.49988 −0.166207 −0.0831035 0.996541i \(-0.526483\pi\)
−0.0831035 + 0.996541i \(0.526483\pi\)
\(734\) 7.23973 0.267223
\(735\) 4.18389 0.154325
\(736\) −2.99807 −0.110510
\(737\) −40.9377 −1.50796
\(738\) 4.12160 0.151718
\(739\) 32.6044 1.19937 0.599686 0.800235i \(-0.295292\pi\)
0.599686 + 0.800235i \(0.295292\pi\)
\(740\) −7.26915 −0.267219
\(741\) 14.6875 0.539560
\(742\) 9.68997 0.355730
\(743\) 23.8912 0.876483 0.438241 0.898857i \(-0.355602\pi\)
0.438241 + 0.898857i \(0.355602\pi\)
\(744\) 5.19113 0.190316
\(745\) −33.4919 −1.22705
\(746\) −0.837493 −0.0306628
\(747\) −11.9546 −0.437394
\(748\) −5.03167 −0.183976
\(749\) 34.7543 1.26989
\(750\) −5.93554 −0.216735
\(751\) −36.7164 −1.33980 −0.669901 0.742450i \(-0.733663\pi\)
−0.669901 + 0.742450i \(0.733663\pi\)
\(752\) 29.1074 1.06144
\(753\) 7.18179 0.261719
\(754\) 12.9908 0.473096
\(755\) 22.6390 0.823917
\(756\) −3.62855 −0.131969
\(757\) 11.4179 0.414989 0.207495 0.978236i \(-0.433469\pi\)
0.207495 + 0.978236i \(0.433469\pi\)
\(758\) 12.7405 0.462758
\(759\) −1.70977 −0.0620607
\(760\) −16.4486 −0.596654
\(761\) −3.18226 −0.115357 −0.0576784 0.998335i \(-0.518370\pi\)
−0.0576784 + 0.998335i \(0.518370\pi\)
\(762\) 5.47520 0.198346
\(763\) 22.7810 0.824726
\(764\) 33.2739 1.20381
\(765\) 1.55796 0.0563283
\(766\) 16.2396 0.586762
\(767\) −20.0179 −0.722805
\(768\) −0.627532 −0.0226441
\(769\) 4.91157 0.177116 0.0885578 0.996071i \(-0.471774\pi\)
0.0885578 + 0.996071i \(0.471774\pi\)
\(770\) −4.68940 −0.168994
\(771\) −0.0993936 −0.00357957
\(772\) −4.62982 −0.166631
\(773\) −26.7153 −0.960884 −0.480442 0.877026i \(-0.659524\pi\)
−0.480442 + 0.877026i \(0.659524\pi\)
\(774\) 2.34920 0.0844401
\(775\) −7.08499 −0.254500
\(776\) 14.5447 0.522126
\(777\) −5.54786 −0.199028
\(778\) −13.1649 −0.471983
\(779\) −45.8847 −1.64399
\(780\) 7.13710 0.255549
\(781\) 6.28656 0.224951
\(782\) 0.298636 0.0106792
\(783\) −9.84663 −0.351890
\(784\) −6.83574 −0.244134
\(785\) −1.55796 −0.0556061
\(786\) 4.41216 0.157377
\(787\) −48.5491 −1.73059 −0.865294 0.501265i \(-0.832868\pi\)
−0.865294 + 0.501265i \(0.832868\pi\)
\(788\) 37.0638 1.32034
\(789\) 16.9410 0.603117
\(790\) −3.87508 −0.137869
\(791\) 24.3735 0.866621
\(792\) −5.42958 −0.192932
\(793\) 8.99431 0.319397
\(794\) 13.2607 0.470606
\(795\) 14.4465 0.512366
\(796\) 16.7241 0.592769
\(797\) 26.6633 0.944463 0.472232 0.881475i \(-0.343449\pi\)
0.472232 + 0.881475i \(0.343449\pi\)
\(798\) −5.85284 −0.207188
\(799\) −11.4351 −0.404546
\(800\) 12.9942 0.459413
\(801\) 7.90847 0.279432
\(802\) 6.25401 0.220837
\(803\) −24.7730 −0.874220
\(804\) −24.8282 −0.875622
\(805\) −1.92095 −0.0677044
\(806\) −3.63319 −0.127974
\(807\) 20.4855 0.721125
\(808\) 5.98126 0.210420
\(809\) −13.1255 −0.461466 −0.230733 0.973017i \(-0.574112\pi\)
−0.230733 + 0.973017i \(0.574112\pi\)
\(810\) 0.783803 0.0275400
\(811\) 43.5021 1.52756 0.763782 0.645475i \(-0.223340\pi\)
0.763782 + 0.645475i \(0.223340\pi\)
\(812\) 35.7290 1.25384
\(813\) −9.61120 −0.337079
\(814\) −3.87039 −0.135657
\(815\) 17.5206 0.613721
\(816\) −2.54544 −0.0891081
\(817\) −26.1530 −0.914976
\(818\) 7.92130 0.276962
\(819\) 5.44708 0.190336
\(820\) −22.2967 −0.778634
\(821\) −36.6761 −1.28001 −0.640003 0.768372i \(-0.721067\pi\)
−0.640003 + 0.768372i \(0.721067\pi\)
\(822\) 5.73179 0.199919
\(823\) 7.32603 0.255369 0.127685 0.991815i \(-0.459245\pi\)
0.127685 + 0.991815i \(0.459245\pi\)
\(824\) 9.42077 0.328188
\(825\) 7.41043 0.257998
\(826\) 7.97695 0.277553
\(827\) 1.72713 0.0600581 0.0300290 0.999549i \(-0.490440\pi\)
0.0300290 + 0.999549i \(0.490440\pi\)
\(828\) −1.03695 −0.0360366
\(829\) −16.3117 −0.566527 −0.283264 0.959042i \(-0.591417\pi\)
−0.283264 + 0.959042i \(0.591417\pi\)
\(830\) −9.37001 −0.325238
\(831\) 11.6939 0.405657
\(832\) −6.68684 −0.231825
\(833\) 2.68549 0.0930467
\(834\) −1.86178 −0.0644683
\(835\) 18.6778 0.646371
\(836\) 28.1814 0.974676
\(837\) 2.75385 0.0951871
\(838\) −0.662638 −0.0228905
\(839\) −37.1343 −1.28202 −0.641009 0.767533i \(-0.721484\pi\)
−0.641009 + 0.767533i \(0.721484\pi\)
\(840\) −6.10020 −0.210477
\(841\) 67.9561 2.34331
\(842\) −3.86731 −0.133276
\(843\) 12.4451 0.428633
\(844\) 11.5780 0.398531
\(845\) 9.53948 0.328168
\(846\) −5.75296 −0.197791
\(847\) −5.61574 −0.192959
\(848\) −23.6031 −0.810534
\(849\) 8.85469 0.303892
\(850\) −1.29434 −0.0443954
\(851\) −1.58545 −0.0543484
\(852\) 3.81272 0.130622
\(853\) −11.1651 −0.382284 −0.191142 0.981562i \(-0.561219\pi\)
−0.191142 + 0.981562i \(0.561219\pi\)
\(854\) −3.58414 −0.122647
\(855\) −8.72586 −0.298418
\(856\) 31.5402 1.07802
\(857\) −43.7997 −1.49617 −0.748085 0.663603i \(-0.769027\pi\)
−0.748085 + 0.663603i \(0.769027\pi\)
\(858\) 3.80008 0.129733
\(859\) 14.6278 0.499095 0.249547 0.968363i \(-0.419718\pi\)
0.249547 + 0.968363i \(0.419718\pi\)
\(860\) −12.7085 −0.433356
\(861\) −17.0170 −0.579937
\(862\) −5.51489 −0.187838
\(863\) −14.5636 −0.495750 −0.247875 0.968792i \(-0.579732\pi\)
−0.247875 + 0.968792i \(0.579732\pi\)
\(864\) −5.05068 −0.171828
\(865\) 32.8014 1.11528
\(866\) −12.1039 −0.411307
\(867\) 1.00000 0.0339618
\(868\) −9.99249 −0.339167
\(869\) 14.2403 0.483068
\(870\) −7.71781 −0.261658
\(871\) 37.2714 1.26289
\(872\) 20.6741 0.700115
\(873\) 7.71587 0.261143
\(874\) −1.67260 −0.0565767
\(875\) 24.5062 0.828462
\(876\) −15.0245 −0.507631
\(877\) −46.8453 −1.58185 −0.790926 0.611912i \(-0.790401\pi\)
−0.790926 + 0.611912i \(0.790401\pi\)
\(878\) 7.96878 0.268933
\(879\) 23.2694 0.784856
\(880\) 11.4226 0.385055
\(881\) −31.3706 −1.05690 −0.528452 0.848963i \(-0.677227\pi\)
−0.528452 + 0.848963i \(0.677227\pi\)
\(882\) 1.35105 0.0454924
\(883\) 17.0836 0.574909 0.287454 0.957794i \(-0.407191\pi\)
0.287454 + 0.957794i \(0.407191\pi\)
\(884\) 4.58105 0.154077
\(885\) 11.8926 0.399767
\(886\) −8.71410 −0.292756
\(887\) −0.155587 −0.00522409 −0.00261205 0.999997i \(-0.500831\pi\)
−0.00261205 + 0.999997i \(0.500831\pi\)
\(888\) −5.03479 −0.168956
\(889\) −22.6056 −0.758168
\(890\) 6.19868 0.207780
\(891\) −2.88035 −0.0964953
\(892\) 13.6539 0.457165
\(893\) 64.0461 2.14322
\(894\) −10.8152 −0.361713
\(895\) 35.8871 1.19957
\(896\) 23.6466 0.789977
\(897\) 1.55665 0.0519749
\(898\) 12.6800 0.423137
\(899\) −27.1162 −0.904375
\(900\) 4.49433 0.149811
\(901\) 9.27271 0.308919
\(902\) −11.8717 −0.395283
\(903\) −9.69919 −0.322769
\(904\) 22.1194 0.735680
\(905\) 19.5847 0.651016
\(906\) 7.31055 0.242877
\(907\) 28.2458 0.937887 0.468943 0.883228i \(-0.344635\pi\)
0.468943 + 0.883228i \(0.344635\pi\)
\(908\) 7.44545 0.247086
\(909\) 3.17301 0.105242
\(910\) 4.26944 0.141530
\(911\) −14.0118 −0.464231 −0.232116 0.972688i \(-0.574565\pi\)
−0.232116 + 0.972688i \(0.574565\pi\)
\(912\) 14.2565 0.472080
\(913\) 34.4333 1.13958
\(914\) 0.878440 0.0290562
\(915\) −5.34351 −0.176651
\(916\) 4.63343 0.153093
\(917\) −18.2166 −0.601565
\(918\) 0.503095 0.0166046
\(919\) 38.2987 1.26336 0.631679 0.775230i \(-0.282366\pi\)
0.631679 + 0.775230i \(0.282366\pi\)
\(920\) −1.74329 −0.0574747
\(921\) −22.8169 −0.751844
\(922\) −15.5539 −0.512242
\(923\) −5.72356 −0.188393
\(924\) 10.4515 0.343829
\(925\) 6.87160 0.225937
\(926\) −15.7371 −0.517153
\(927\) 4.99764 0.164144
\(928\) 49.7322 1.63254
\(929\) −35.9691 −1.18011 −0.590054 0.807364i \(-0.700894\pi\)
−0.590054 + 0.807364i \(0.700894\pi\)
\(930\) 2.15848 0.0707793
\(931\) −15.0409 −0.492946
\(932\) −43.2776 −1.41761
\(933\) 11.1896 0.366331
\(934\) −15.2789 −0.499942
\(935\) −4.48748 −0.146756
\(936\) 4.94333 0.161578
\(937\) −10.0553 −0.328493 −0.164247 0.986419i \(-0.552519\pi\)
−0.164247 + 0.986419i \(0.552519\pi\)
\(938\) −14.8523 −0.484945
\(939\) −10.9958 −0.358834
\(940\) 31.1219 1.01508
\(941\) −19.1212 −0.623332 −0.311666 0.950192i \(-0.600887\pi\)
−0.311666 + 0.950192i \(0.600887\pi\)
\(942\) −0.503095 −0.0163917
\(943\) −4.86305 −0.158363
\(944\) −19.4305 −0.632408
\(945\) −3.23611 −0.105271
\(946\) −6.76651 −0.219998
\(947\) 42.2977 1.37449 0.687245 0.726426i \(-0.258820\pi\)
0.687245 + 0.726426i \(0.258820\pi\)
\(948\) 8.63655 0.280502
\(949\) 22.5544 0.732147
\(950\) 7.24935 0.235200
\(951\) −0.0439860 −0.00142634
\(952\) −3.91550 −0.126902
\(953\) 16.4739 0.533643 0.266822 0.963746i \(-0.414027\pi\)
0.266822 + 0.963746i \(0.414027\pi\)
\(954\) 4.66505 0.151037
\(955\) 29.6752 0.960268
\(956\) 45.6042 1.47495
\(957\) 28.3617 0.916804
\(958\) 3.48548 0.112611
\(959\) −23.6650 −0.764183
\(960\) 3.97265 0.128217
\(961\) −23.4163 −0.755364
\(962\) 3.52377 0.113611
\(963\) 16.7318 0.539175
\(964\) 49.0315 1.57920
\(965\) −4.12908 −0.132920
\(966\) −0.620309 −0.0199581
\(967\) −21.3418 −0.686305 −0.343152 0.939280i \(-0.611495\pi\)
−0.343152 + 0.939280i \(0.611495\pi\)
\(968\) −5.09638 −0.163804
\(969\) −5.60081 −0.179924
\(970\) 6.04772 0.194181
\(971\) −6.77170 −0.217314 −0.108657 0.994079i \(-0.534655\pi\)
−0.108657 + 0.994079i \(0.534655\pi\)
\(972\) −1.74690 −0.0560317
\(973\) 7.68679 0.246427
\(974\) 1.75753 0.0563150
\(975\) −6.74677 −0.216070
\(976\) 8.73036 0.279452
\(977\) 54.5680 1.74578 0.872892 0.487913i \(-0.162242\pi\)
0.872892 + 0.487913i \(0.162242\pi\)
\(978\) 5.65773 0.180914
\(979\) −22.7792 −0.728025
\(980\) −7.30882 −0.233472
\(981\) 10.9675 0.350164
\(982\) 6.93994 0.221462
\(983\) −58.4317 −1.86368 −0.931841 0.362868i \(-0.881798\pi\)
−0.931841 + 0.362868i \(0.881798\pi\)
\(984\) −15.4432 −0.492312
\(985\) 33.0553 1.05323
\(986\) −4.95379 −0.157761
\(987\) 23.7524 0.756047
\(988\) −25.6576 −0.816277
\(989\) −2.77180 −0.0881381
\(990\) −2.25763 −0.0717520
\(991\) −41.1223 −1.30629 −0.653146 0.757232i \(-0.726551\pi\)
−0.653146 + 0.757232i \(0.726551\pi\)
\(992\) −13.9088 −0.441606
\(993\) −13.4548 −0.426974
\(994\) 2.28078 0.0723420
\(995\) 14.9153 0.472847
\(996\) 20.8834 0.661715
\(997\) −39.1177 −1.23887 −0.619435 0.785048i \(-0.712638\pi\)
−0.619435 + 0.785048i \(0.712638\pi\)
\(998\) 9.56245 0.302694
\(999\) −2.67091 −0.0845039
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 \(a_p\))