Properties

Label 8007.2.a.f.1.26
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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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: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.188504 q^{2} -1.00000 q^{3} -1.96447 q^{4} +3.42459 q^{5} -0.188504 q^{6} +1.78425 q^{7} -0.747318 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.188504 q^{2} -1.00000 q^{3} -1.96447 q^{4} +3.42459 q^{5} -0.188504 q^{6} +1.78425 q^{7} -0.747318 q^{8} +1.00000 q^{9} +0.645550 q^{10} +3.14859 q^{11} +1.96447 q^{12} -5.35980 q^{13} +0.336338 q^{14} -3.42459 q^{15} +3.78806 q^{16} -1.00000 q^{17} +0.188504 q^{18} -0.832236 q^{19} -6.72750 q^{20} -1.78425 q^{21} +0.593521 q^{22} -4.73322 q^{23} +0.747318 q^{24} +6.72784 q^{25} -1.01034 q^{26} -1.00000 q^{27} -3.50509 q^{28} +1.69187 q^{29} -0.645550 q^{30} +5.10521 q^{31} +2.20870 q^{32} -3.14859 q^{33} -0.188504 q^{34} +6.11032 q^{35} -1.96447 q^{36} -3.43992 q^{37} -0.156880 q^{38} +5.35980 q^{39} -2.55926 q^{40} -6.02983 q^{41} -0.336338 q^{42} -10.8902 q^{43} -6.18529 q^{44} +3.42459 q^{45} -0.892232 q^{46} -4.41038 q^{47} -3.78806 q^{48} -3.81646 q^{49} +1.26823 q^{50} +1.00000 q^{51} +10.5291 q^{52} +8.72542 q^{53} -0.188504 q^{54} +10.7826 q^{55} -1.33340 q^{56} +0.832236 q^{57} +0.318924 q^{58} +4.56892 q^{59} +6.72750 q^{60} -1.80853 q^{61} +0.962354 q^{62} +1.78425 q^{63} -7.15977 q^{64} -18.3551 q^{65} -0.593521 q^{66} -12.6074 q^{67} +1.96447 q^{68} +4.73322 q^{69} +1.15182 q^{70} -3.53152 q^{71} -0.747318 q^{72} -9.39859 q^{73} -0.648439 q^{74} -6.72784 q^{75} +1.63490 q^{76} +5.61786 q^{77} +1.01034 q^{78} -6.65430 q^{79} +12.9726 q^{80} +1.00000 q^{81} -1.13665 q^{82} -12.3936 q^{83} +3.50509 q^{84} -3.42459 q^{85} -2.05285 q^{86} -1.69187 q^{87} -2.35300 q^{88} -11.5838 q^{89} +0.645550 q^{90} -9.56321 q^{91} +9.29825 q^{92} -5.10521 q^{93} -0.831374 q^{94} -2.85007 q^{95} -2.20870 q^{96} +6.57626 q^{97} -0.719419 q^{98} +3.14859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.188504 0.133293 0.0666463 0.997777i \(-0.478770\pi\)
0.0666463 + 0.997777i \(0.478770\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.96447 −0.982233
\(5\) 3.42459 1.53152 0.765762 0.643123i \(-0.222362\pi\)
0.765762 + 0.643123i \(0.222362\pi\)
\(6\) −0.188504 −0.0769565
\(7\) 1.78425 0.674382 0.337191 0.941436i \(-0.390523\pi\)
0.337191 + 0.941436i \(0.390523\pi\)
\(8\) −0.747318 −0.264217
\(9\) 1.00000 0.333333
\(10\) 0.645550 0.204141
\(11\) 3.14859 0.949334 0.474667 0.880165i \(-0.342568\pi\)
0.474667 + 0.880165i \(0.342568\pi\)
\(12\) 1.96447 0.567093
\(13\) −5.35980 −1.48654 −0.743271 0.668991i \(-0.766727\pi\)
−0.743271 + 0.668991i \(0.766727\pi\)
\(14\) 0.336338 0.0898901
\(15\) −3.42459 −0.884226
\(16\) 3.78806 0.947015
\(17\) −1.00000 −0.242536
\(18\) 0.188504 0.0444308
\(19\) −0.832236 −0.190928 −0.0954640 0.995433i \(-0.530433\pi\)
−0.0954640 + 0.995433i \(0.530433\pi\)
\(20\) −6.72750 −1.50431
\(21\) −1.78425 −0.389355
\(22\) 0.593521 0.126539
\(23\) −4.73322 −0.986945 −0.493472 0.869761i \(-0.664273\pi\)
−0.493472 + 0.869761i \(0.664273\pi\)
\(24\) 0.747318 0.152546
\(25\) 6.72784 1.34557
\(26\) −1.01034 −0.198145
\(27\) −1.00000 −0.192450
\(28\) −3.50509 −0.662400
\(29\) 1.69187 0.314172 0.157086 0.987585i \(-0.449790\pi\)
0.157086 + 0.987585i \(0.449790\pi\)
\(30\) −0.645550 −0.117861
\(31\) 5.10521 0.916923 0.458462 0.888714i \(-0.348401\pi\)
0.458462 + 0.888714i \(0.348401\pi\)
\(32\) 2.20870 0.390447
\(33\) −3.14859 −0.548098
\(34\) −0.188504 −0.0323282
\(35\) 6.11032 1.03283
\(36\) −1.96447 −0.327411
\(37\) −3.43992 −0.565519 −0.282760 0.959191i \(-0.591250\pi\)
−0.282760 + 0.959191i \(0.591250\pi\)
\(38\) −0.156880 −0.0254493
\(39\) 5.35980 0.858255
\(40\) −2.55926 −0.404655
\(41\) −6.02983 −0.941702 −0.470851 0.882213i \(-0.656053\pi\)
−0.470851 + 0.882213i \(0.656053\pi\)
\(42\) −0.336338 −0.0518981
\(43\) −10.8902 −1.66074 −0.830372 0.557209i \(-0.811872\pi\)
−0.830372 + 0.557209i \(0.811872\pi\)
\(44\) −6.18529 −0.932468
\(45\) 3.42459 0.510508
\(46\) −0.892232 −0.131552
\(47\) −4.41038 −0.643320 −0.321660 0.946855i \(-0.604241\pi\)
−0.321660 + 0.946855i \(0.604241\pi\)
\(48\) −3.78806 −0.546759
\(49\) −3.81646 −0.545209
\(50\) 1.26823 0.179354
\(51\) 1.00000 0.140028
\(52\) 10.5291 1.46013
\(53\) 8.72542 1.19853 0.599264 0.800551i \(-0.295460\pi\)
0.599264 + 0.800551i \(0.295460\pi\)
\(54\) −0.188504 −0.0256522
\(55\) 10.7826 1.45393
\(56\) −1.33340 −0.178183
\(57\) 0.832236 0.110232
\(58\) 0.318924 0.0418768
\(59\) 4.56892 0.594823 0.297411 0.954749i \(-0.403877\pi\)
0.297411 + 0.954749i \(0.403877\pi\)
\(60\) 6.72750 0.868516
\(61\) −1.80853 −0.231558 −0.115779 0.993275i \(-0.536936\pi\)
−0.115779 + 0.993275i \(0.536936\pi\)
\(62\) 0.962354 0.122219
\(63\) 1.78425 0.224794
\(64\) −7.15977 −0.894971
\(65\) −18.3551 −2.27668
\(66\) −0.593521 −0.0730574
\(67\) −12.6074 −1.54024 −0.770119 0.637900i \(-0.779803\pi\)
−0.770119 + 0.637900i \(0.779803\pi\)
\(68\) 1.96447 0.238227
\(69\) 4.73322 0.569813
\(70\) 1.15182 0.137669
\(71\) −3.53152 −0.419114 −0.209557 0.977796i \(-0.567202\pi\)
−0.209557 + 0.977796i \(0.567202\pi\)
\(72\) −0.747318 −0.0880723
\(73\) −9.39859 −1.10002 −0.550011 0.835158i \(-0.685376\pi\)
−0.550011 + 0.835158i \(0.685376\pi\)
\(74\) −0.648439 −0.0753795
\(75\) −6.72784 −0.776865
\(76\) 1.63490 0.187536
\(77\) 5.61786 0.640214
\(78\) 1.01034 0.114399
\(79\) −6.65430 −0.748667 −0.374334 0.927294i \(-0.622129\pi\)
−0.374334 + 0.927294i \(0.622129\pi\)
\(80\) 12.9726 1.45038
\(81\) 1.00000 0.111111
\(82\) −1.13665 −0.125522
\(83\) −12.3936 −1.36037 −0.680186 0.733040i \(-0.738101\pi\)
−0.680186 + 0.733040i \(0.738101\pi\)
\(84\) 3.50509 0.382437
\(85\) −3.42459 −0.371449
\(86\) −2.05285 −0.221365
\(87\) −1.69187 −0.181387
\(88\) −2.35300 −0.250830
\(89\) −11.5838 −1.22788 −0.613941 0.789352i \(-0.710417\pi\)
−0.613941 + 0.789352i \(0.710417\pi\)
\(90\) 0.645550 0.0680469
\(91\) −9.56321 −1.00250
\(92\) 9.29825 0.969410
\(93\) −5.10521 −0.529386
\(94\) −0.831374 −0.0857497
\(95\) −2.85007 −0.292411
\(96\) −2.20870 −0.225425
\(97\) 6.57626 0.667718 0.333859 0.942623i \(-0.391649\pi\)
0.333859 + 0.942623i \(0.391649\pi\)
\(98\) −0.719419 −0.0726723
\(99\) 3.14859 0.316445
\(100\) −13.2166 −1.32166
\(101\) 11.9878 1.19283 0.596415 0.802676i \(-0.296591\pi\)
0.596415 + 0.802676i \(0.296591\pi\)
\(102\) 0.188504 0.0186647
\(103\) 19.0602 1.87806 0.939028 0.343841i \(-0.111728\pi\)
0.939028 + 0.343841i \(0.111728\pi\)
\(104\) 4.00548 0.392769
\(105\) −6.11032 −0.596306
\(106\) 1.64478 0.159755
\(107\) −6.96116 −0.672961 −0.336481 0.941690i \(-0.609237\pi\)
−0.336481 + 0.941690i \(0.609237\pi\)
\(108\) 1.96447 0.189031
\(109\) 1.39644 0.133755 0.0668775 0.997761i \(-0.478696\pi\)
0.0668775 + 0.997761i \(0.478696\pi\)
\(110\) 2.03257 0.193798
\(111\) 3.43992 0.326503
\(112\) 6.75884 0.638650
\(113\) −7.84851 −0.738326 −0.369163 0.929365i \(-0.620356\pi\)
−0.369163 + 0.929365i \(0.620356\pi\)
\(114\) 0.156880 0.0146932
\(115\) −16.2094 −1.51153
\(116\) −3.32362 −0.308590
\(117\) −5.35980 −0.495514
\(118\) 0.861260 0.0792854
\(119\) −1.78425 −0.163562
\(120\) 2.55926 0.233628
\(121\) −1.08641 −0.0987643
\(122\) −0.340915 −0.0308649
\(123\) 6.02983 0.543692
\(124\) −10.0290 −0.900633
\(125\) 5.91716 0.529247
\(126\) 0.336338 0.0299634
\(127\) 16.7200 1.48366 0.741830 0.670588i \(-0.233958\pi\)
0.741830 + 0.670588i \(0.233958\pi\)
\(128\) −5.76705 −0.509740
\(129\) 10.8902 0.958832
\(130\) −3.46002 −0.303464
\(131\) −10.0844 −0.881081 −0.440540 0.897733i \(-0.645213\pi\)
−0.440540 + 0.897733i \(0.645213\pi\)
\(132\) 6.18529 0.538360
\(133\) −1.48492 −0.128758
\(134\) −2.37655 −0.205302
\(135\) −3.42459 −0.294742
\(136\) 0.747318 0.0640820
\(137\) 9.89827 0.845666 0.422833 0.906208i \(-0.361036\pi\)
0.422833 + 0.906208i \(0.361036\pi\)
\(138\) 0.892232 0.0759518
\(139\) 10.0127 0.849266 0.424633 0.905365i \(-0.360403\pi\)
0.424633 + 0.905365i \(0.360403\pi\)
\(140\) −12.0035 −1.01448
\(141\) 4.41038 0.371421
\(142\) −0.665706 −0.0558648
\(143\) −16.8758 −1.41122
\(144\) 3.78806 0.315672
\(145\) 5.79396 0.481162
\(146\) −1.77167 −0.146625
\(147\) 3.81646 0.314776
\(148\) 6.75760 0.555472
\(149\) −21.4950 −1.76094 −0.880471 0.474100i \(-0.842774\pi\)
−0.880471 + 0.474100i \(0.842774\pi\)
\(150\) −1.26823 −0.103550
\(151\) 6.89040 0.560733 0.280366 0.959893i \(-0.409544\pi\)
0.280366 + 0.959893i \(0.409544\pi\)
\(152\) 0.621945 0.0504464
\(153\) −1.00000 −0.0808452
\(154\) 1.05899 0.0853357
\(155\) 17.4833 1.40429
\(156\) −10.5291 −0.843007
\(157\) −1.00000 −0.0798087
\(158\) −1.25436 −0.0997917
\(159\) −8.72542 −0.691971
\(160\) 7.56390 0.597979
\(161\) −8.44524 −0.665578
\(162\) 0.188504 0.0148103
\(163\) 13.3271 1.04386 0.521931 0.852988i \(-0.325212\pi\)
0.521931 + 0.852988i \(0.325212\pi\)
\(164\) 11.8454 0.924971
\(165\) −10.7826 −0.839426
\(166\) −2.33624 −0.181327
\(167\) −21.9521 −1.69871 −0.849353 0.527825i \(-0.823008\pi\)
−0.849353 + 0.527825i \(0.823008\pi\)
\(168\) 1.33340 0.102874
\(169\) 15.7275 1.20981
\(170\) −0.645550 −0.0495114
\(171\) −0.832236 −0.0636427
\(172\) 21.3935 1.63124
\(173\) −9.46456 −0.719577 −0.359789 0.933034i \(-0.617151\pi\)
−0.359789 + 0.933034i \(0.617151\pi\)
\(174\) −0.318924 −0.0241776
\(175\) 12.0041 0.907427
\(176\) 11.9270 0.899034
\(177\) −4.56892 −0.343421
\(178\) −2.18360 −0.163667
\(179\) −6.28826 −0.470007 −0.235003 0.971995i \(-0.575510\pi\)
−0.235003 + 0.971995i \(0.575510\pi\)
\(180\) −6.72750 −0.501438
\(181\) 22.2200 1.65160 0.825799 0.563964i \(-0.190724\pi\)
0.825799 + 0.563964i \(0.190724\pi\)
\(182\) −1.80270 −0.133625
\(183\) 1.80853 0.133690
\(184\) 3.53722 0.260767
\(185\) −11.7803 −0.866107
\(186\) −0.962354 −0.0705632
\(187\) −3.14859 −0.230247
\(188\) 8.66404 0.631890
\(189\) −1.78425 −0.129785
\(190\) −0.537250 −0.0389762
\(191\) 13.2135 0.956096 0.478048 0.878334i \(-0.341345\pi\)
0.478048 + 0.878334i \(0.341345\pi\)
\(192\) 7.15977 0.516712
\(193\) −16.1579 −1.16307 −0.581536 0.813521i \(-0.697548\pi\)
−0.581536 + 0.813521i \(0.697548\pi\)
\(194\) 1.23965 0.0890018
\(195\) 18.3551 1.31444
\(196\) 7.49731 0.535522
\(197\) 22.5229 1.60469 0.802345 0.596861i \(-0.203586\pi\)
0.802345 + 0.596861i \(0.203586\pi\)
\(198\) 0.593521 0.0421797
\(199\) −14.3787 −1.01928 −0.509641 0.860387i \(-0.670222\pi\)
−0.509641 + 0.860387i \(0.670222\pi\)
\(200\) −5.02784 −0.355522
\(201\) 12.6074 0.889257
\(202\) 2.25975 0.158995
\(203\) 3.01871 0.211872
\(204\) −1.96447 −0.137540
\(205\) −20.6497 −1.44224
\(206\) 3.59292 0.250331
\(207\) −4.73322 −0.328982
\(208\) −20.3032 −1.40778
\(209\) −2.62037 −0.181255
\(210\) −1.15182 −0.0794832
\(211\) 17.9288 1.23427 0.617136 0.786856i \(-0.288293\pi\)
0.617136 + 0.786856i \(0.288293\pi\)
\(212\) −17.1408 −1.17723
\(213\) 3.53152 0.241976
\(214\) −1.31221 −0.0897007
\(215\) −37.2946 −2.54347
\(216\) 0.747318 0.0508486
\(217\) 9.10896 0.618357
\(218\) 0.263235 0.0178285
\(219\) 9.39859 0.635098
\(220\) −21.1821 −1.42810
\(221\) 5.35980 0.360539
\(222\) 0.648439 0.0435204
\(223\) −23.8723 −1.59861 −0.799304 0.600926i \(-0.794798\pi\)
−0.799304 + 0.600926i \(0.794798\pi\)
\(224\) 3.94087 0.263310
\(225\) 6.72784 0.448523
\(226\) −1.47948 −0.0984133
\(227\) 1.00897 0.0669675 0.0334837 0.999439i \(-0.489340\pi\)
0.0334837 + 0.999439i \(0.489340\pi\)
\(228\) −1.63490 −0.108274
\(229\) −22.1200 −1.46173 −0.730866 0.682521i \(-0.760884\pi\)
−0.730866 + 0.682521i \(0.760884\pi\)
\(230\) −3.05553 −0.201476
\(231\) −5.61786 −0.369628
\(232\) −1.26436 −0.0830095
\(233\) 24.2251 1.58704 0.793521 0.608543i \(-0.208246\pi\)
0.793521 + 0.608543i \(0.208246\pi\)
\(234\) −1.01034 −0.0660483
\(235\) −15.1038 −0.985260
\(236\) −8.97549 −0.584255
\(237\) 6.65430 0.432243
\(238\) −0.336338 −0.0218015
\(239\) 1.48328 0.0959451 0.0479726 0.998849i \(-0.484724\pi\)
0.0479726 + 0.998849i \(0.484724\pi\)
\(240\) −12.9726 −0.837376
\(241\) 24.7453 1.59398 0.796992 0.603989i \(-0.206423\pi\)
0.796992 + 0.603989i \(0.206423\pi\)
\(242\) −0.204792 −0.0131645
\(243\) −1.00000 −0.0641500
\(244\) 3.55279 0.227444
\(245\) −13.0698 −0.835001
\(246\) 1.13665 0.0724701
\(247\) 4.46062 0.283823
\(248\) −3.81522 −0.242267
\(249\) 12.3936 0.785411
\(250\) 1.11541 0.0705447
\(251\) −0.828587 −0.0523000 −0.0261500 0.999658i \(-0.508325\pi\)
−0.0261500 + 0.999658i \(0.508325\pi\)
\(252\) −3.50509 −0.220800
\(253\) −14.9030 −0.936941
\(254\) 3.15179 0.197761
\(255\) 3.42459 0.214456
\(256\) 13.2324 0.827027
\(257\) 1.47420 0.0919581 0.0459790 0.998942i \(-0.485359\pi\)
0.0459790 + 0.998942i \(0.485359\pi\)
\(258\) 2.05285 0.127805
\(259\) −6.13767 −0.381376
\(260\) 36.0581 2.23623
\(261\) 1.69187 0.104724
\(262\) −1.90096 −0.117441
\(263\) −10.6460 −0.656458 −0.328229 0.944598i \(-0.606452\pi\)
−0.328229 + 0.944598i \(0.606452\pi\)
\(264\) 2.35300 0.144817
\(265\) 29.8810 1.83558
\(266\) −0.279913 −0.0171625
\(267\) 11.5838 0.708918
\(268\) 24.7668 1.51287
\(269\) 13.6965 0.835093 0.417547 0.908656i \(-0.362890\pi\)
0.417547 + 0.908656i \(0.362890\pi\)
\(270\) −0.645550 −0.0392869
\(271\) 4.94456 0.300361 0.150180 0.988659i \(-0.452015\pi\)
0.150180 + 0.988659i \(0.452015\pi\)
\(272\) −3.78806 −0.229685
\(273\) 9.56321 0.578792
\(274\) 1.86586 0.112721
\(275\) 21.1832 1.27739
\(276\) −9.29825 −0.559689
\(277\) −7.90270 −0.474827 −0.237414 0.971409i \(-0.576300\pi\)
−0.237414 + 0.971409i \(0.576300\pi\)
\(278\) 1.88744 0.113201
\(279\) 5.10521 0.305641
\(280\) −4.56635 −0.272892
\(281\) −18.4923 −1.10316 −0.551579 0.834122i \(-0.685975\pi\)
−0.551579 + 0.834122i \(0.685975\pi\)
\(282\) 0.831374 0.0495076
\(283\) 31.6209 1.87967 0.939834 0.341632i \(-0.110980\pi\)
0.939834 + 0.341632i \(0.110980\pi\)
\(284\) 6.93755 0.411668
\(285\) 2.85007 0.168824
\(286\) −3.18116 −0.188106
\(287\) −10.7587 −0.635067
\(288\) 2.20870 0.130149
\(289\) 1.00000 0.0588235
\(290\) 1.09219 0.0641353
\(291\) −6.57626 −0.385507
\(292\) 18.4632 1.08048
\(293\) −24.1591 −1.41139 −0.705694 0.708517i \(-0.749365\pi\)
−0.705694 + 0.708517i \(0.749365\pi\)
\(294\) 0.719419 0.0419573
\(295\) 15.6467 0.910986
\(296\) 2.57071 0.149420
\(297\) −3.14859 −0.182699
\(298\) −4.05190 −0.234720
\(299\) 25.3691 1.46713
\(300\) 13.2166 0.763062
\(301\) −19.4309 −1.11998
\(302\) 1.29887 0.0747415
\(303\) −11.9878 −0.688681
\(304\) −3.15256 −0.180812
\(305\) −6.19347 −0.354637
\(306\) −0.188504 −0.0107761
\(307\) −29.0744 −1.65937 −0.829683 0.558235i \(-0.811479\pi\)
−0.829683 + 0.558235i \(0.811479\pi\)
\(308\) −11.0361 −0.628839
\(309\) −19.0602 −1.08430
\(310\) 3.29567 0.187182
\(311\) −2.85818 −0.162072 −0.0810361 0.996711i \(-0.525823\pi\)
−0.0810361 + 0.996711i \(0.525823\pi\)
\(312\) −4.00548 −0.226765
\(313\) −14.6211 −0.826431 −0.413215 0.910633i \(-0.635594\pi\)
−0.413215 + 0.910633i \(0.635594\pi\)
\(314\) −0.188504 −0.0106379
\(315\) 6.11032 0.344278
\(316\) 13.0721 0.735366
\(317\) −26.4706 −1.48674 −0.743368 0.668883i \(-0.766773\pi\)
−0.743368 + 0.668883i \(0.766773\pi\)
\(318\) −1.64478 −0.0922345
\(319\) 5.32699 0.298254
\(320\) −24.5193 −1.37067
\(321\) 6.96116 0.388534
\(322\) −1.59196 −0.0887166
\(323\) 0.832236 0.0463069
\(324\) −1.96447 −0.109137
\(325\) −36.0599 −2.00024
\(326\) 2.51222 0.139139
\(327\) −1.39644 −0.0772234
\(328\) 4.50620 0.248814
\(329\) −7.86920 −0.433843
\(330\) −2.03257 −0.111889
\(331\) 23.1563 1.27278 0.636391 0.771366i \(-0.280426\pi\)
0.636391 + 0.771366i \(0.280426\pi\)
\(332\) 24.3468 1.33620
\(333\) −3.43992 −0.188506
\(334\) −4.13807 −0.226425
\(335\) −43.1752 −2.35891
\(336\) −6.75884 −0.368725
\(337\) 24.3828 1.32822 0.664109 0.747636i \(-0.268811\pi\)
0.664109 + 0.747636i \(0.268811\pi\)
\(338\) 2.96469 0.161258
\(339\) 7.84851 0.426273
\(340\) 6.72750 0.364850
\(341\) 16.0742 0.870467
\(342\) −0.156880 −0.00848310
\(343\) −19.2992 −1.04206
\(344\) 8.13847 0.438797
\(345\) 16.2094 0.872683
\(346\) −1.78411 −0.0959143
\(347\) −17.2409 −0.925541 −0.462770 0.886478i \(-0.653145\pi\)
−0.462770 + 0.886478i \(0.653145\pi\)
\(348\) 3.32362 0.178165
\(349\) 28.6472 1.53345 0.766725 0.641976i \(-0.221885\pi\)
0.766725 + 0.641976i \(0.221885\pi\)
\(350\) 2.26283 0.120953
\(351\) 5.35980 0.286085
\(352\) 6.95428 0.370665
\(353\) −2.04573 −0.108883 −0.0544416 0.998517i \(-0.517338\pi\)
−0.0544416 + 0.998517i \(0.517338\pi\)
\(354\) −0.861260 −0.0457755
\(355\) −12.0940 −0.641884
\(356\) 22.7560 1.20607
\(357\) 1.78425 0.0944324
\(358\) −1.18536 −0.0626484
\(359\) 23.6854 1.25007 0.625033 0.780598i \(-0.285085\pi\)
0.625033 + 0.780598i \(0.285085\pi\)
\(360\) −2.55926 −0.134885
\(361\) −18.3074 −0.963546
\(362\) 4.18856 0.220146
\(363\) 1.08641 0.0570216
\(364\) 18.7866 0.984686
\(365\) −32.1863 −1.68471
\(366\) 0.340915 0.0178199
\(367\) −2.56356 −0.133817 −0.0669084 0.997759i \(-0.521314\pi\)
−0.0669084 + 0.997759i \(0.521314\pi\)
\(368\) −17.9297 −0.934652
\(369\) −6.02983 −0.313901
\(370\) −2.22064 −0.115446
\(371\) 15.5683 0.808266
\(372\) 10.0290 0.519980
\(373\) −35.0637 −1.81553 −0.907764 0.419482i \(-0.862212\pi\)
−0.907764 + 0.419482i \(0.862212\pi\)
\(374\) −0.593521 −0.0306903
\(375\) −5.91716 −0.305561
\(376\) 3.29595 0.169976
\(377\) −9.06808 −0.467030
\(378\) −0.336338 −0.0172994
\(379\) −11.2334 −0.577022 −0.288511 0.957477i \(-0.593160\pi\)
−0.288511 + 0.957477i \(0.593160\pi\)
\(380\) 5.59887 0.287216
\(381\) −16.7200 −0.856592
\(382\) 2.49080 0.127440
\(383\) −14.7874 −0.755603 −0.377801 0.925887i \(-0.623320\pi\)
−0.377801 + 0.925887i \(0.623320\pi\)
\(384\) 5.76705 0.294298
\(385\) 19.2389 0.980504
\(386\) −3.04583 −0.155029
\(387\) −10.8902 −0.553582
\(388\) −12.9188 −0.655855
\(389\) −36.9250 −1.87217 −0.936086 0.351772i \(-0.885579\pi\)
−0.936086 + 0.351772i \(0.885579\pi\)
\(390\) 3.46002 0.175205
\(391\) 4.73322 0.239369
\(392\) 2.85211 0.144053
\(393\) 10.0844 0.508692
\(394\) 4.24566 0.213893
\(395\) −22.7883 −1.14660
\(396\) −6.18529 −0.310823
\(397\) 4.10526 0.206037 0.103018 0.994679i \(-0.467150\pi\)
0.103018 + 0.994679i \(0.467150\pi\)
\(398\) −2.71045 −0.135863
\(399\) 1.48492 0.0743387
\(400\) 25.4855 1.27427
\(401\) −24.6512 −1.23102 −0.615510 0.788129i \(-0.711050\pi\)
−0.615510 + 0.788129i \(0.711050\pi\)
\(402\) 2.37655 0.118531
\(403\) −27.3629 −1.36304
\(404\) −23.5496 −1.17164
\(405\) 3.42459 0.170169
\(406\) 0.569039 0.0282409
\(407\) −10.8309 −0.536867
\(408\) −0.747318 −0.0369978
\(409\) −4.01280 −0.198420 −0.0992102 0.995066i \(-0.531632\pi\)
−0.0992102 + 0.995066i \(0.531632\pi\)
\(410\) −3.89256 −0.192240
\(411\) −9.89827 −0.488245
\(412\) −37.4431 −1.84469
\(413\) 8.15208 0.401138
\(414\) −0.892232 −0.0438508
\(415\) −42.4430 −2.08344
\(416\) −11.8382 −0.580415
\(417\) −10.0127 −0.490324
\(418\) −0.493950 −0.0241599
\(419\) −4.91641 −0.240182 −0.120091 0.992763i \(-0.538319\pi\)
−0.120091 + 0.992763i \(0.538319\pi\)
\(420\) 12.0035 0.585712
\(421\) −31.4007 −1.53038 −0.765189 0.643806i \(-0.777354\pi\)
−0.765189 + 0.643806i \(0.777354\pi\)
\(422\) 3.37966 0.164519
\(423\) −4.41038 −0.214440
\(424\) −6.52066 −0.316671
\(425\) −6.72784 −0.326348
\(426\) 0.665706 0.0322536
\(427\) −3.22686 −0.156159
\(428\) 13.6750 0.661005
\(429\) 16.8758 0.814771
\(430\) −7.03019 −0.339026
\(431\) 23.4265 1.12842 0.564208 0.825633i \(-0.309182\pi\)
0.564208 + 0.825633i \(0.309182\pi\)
\(432\) −3.78806 −0.182253
\(433\) −25.6687 −1.23356 −0.616781 0.787135i \(-0.711563\pi\)
−0.616781 + 0.787135i \(0.711563\pi\)
\(434\) 1.71708 0.0824223
\(435\) −5.79396 −0.277799
\(436\) −2.74326 −0.131378
\(437\) 3.93916 0.188435
\(438\) 1.77167 0.0846538
\(439\) −22.5823 −1.07779 −0.538897 0.842372i \(-0.681159\pi\)
−0.538897 + 0.842372i \(0.681159\pi\)
\(440\) −8.05805 −0.384153
\(441\) −3.81646 −0.181736
\(442\) 1.01034 0.0480572
\(443\) −19.7356 −0.937668 −0.468834 0.883286i \(-0.655326\pi\)
−0.468834 + 0.883286i \(0.655326\pi\)
\(444\) −6.75760 −0.320702
\(445\) −39.6699 −1.88053
\(446\) −4.50003 −0.213083
\(447\) 21.4950 1.01668
\(448\) −12.7748 −0.603553
\(449\) 33.9785 1.60354 0.801772 0.597630i \(-0.203891\pi\)
0.801772 + 0.597630i \(0.203891\pi\)
\(450\) 1.26823 0.0597848
\(451\) −18.9855 −0.893990
\(452\) 15.4181 0.725208
\(453\) −6.89040 −0.323739
\(454\) 0.190194 0.00892627
\(455\) −32.7501 −1.53535
\(456\) −0.621945 −0.0291253
\(457\) −5.72640 −0.267870 −0.133935 0.990990i \(-0.542761\pi\)
−0.133935 + 0.990990i \(0.542761\pi\)
\(458\) −4.16971 −0.194838
\(459\) 1.00000 0.0466760
\(460\) 31.8427 1.48468
\(461\) 13.4590 0.626847 0.313424 0.949613i \(-0.398524\pi\)
0.313424 + 0.949613i \(0.398524\pi\)
\(462\) −1.05899 −0.0492686
\(463\) 0.923415 0.0429148 0.0214574 0.999770i \(-0.493169\pi\)
0.0214574 + 0.999770i \(0.493169\pi\)
\(464\) 6.40890 0.297526
\(465\) −17.4833 −0.810768
\(466\) 4.56654 0.211541
\(467\) 30.3393 1.40394 0.701969 0.712208i \(-0.252305\pi\)
0.701969 + 0.712208i \(0.252305\pi\)
\(468\) 10.5291 0.486710
\(469\) −22.4947 −1.03871
\(470\) −2.84712 −0.131328
\(471\) 1.00000 0.0460776
\(472\) −3.41444 −0.157162
\(473\) −34.2888 −1.57660
\(474\) 1.25436 0.0576148
\(475\) −5.59916 −0.256907
\(476\) 3.50509 0.160656
\(477\) 8.72542 0.399509
\(478\) 0.279604 0.0127888
\(479\) 10.2457 0.468137 0.234069 0.972220i \(-0.424796\pi\)
0.234069 + 0.972220i \(0.424796\pi\)
\(480\) −7.56390 −0.345243
\(481\) 18.4373 0.840668
\(482\) 4.66459 0.212466
\(483\) 8.44524 0.384272
\(484\) 2.13421 0.0970095
\(485\) 22.5210 1.02263
\(486\) −0.188504 −0.00855072
\(487\) −17.2746 −0.782788 −0.391394 0.920223i \(-0.628007\pi\)
−0.391394 + 0.920223i \(0.628007\pi\)
\(488\) 1.35154 0.0611815
\(489\) −13.3271 −0.602674
\(490\) −2.46372 −0.111299
\(491\) −14.2036 −0.641000 −0.320500 0.947248i \(-0.603851\pi\)
−0.320500 + 0.947248i \(0.603851\pi\)
\(492\) −11.8454 −0.534032
\(493\) −1.69187 −0.0761979
\(494\) 0.840845 0.0378314
\(495\) 10.7826 0.484643
\(496\) 19.3389 0.868340
\(497\) −6.30111 −0.282643
\(498\) 2.33624 0.104689
\(499\) −11.8923 −0.532372 −0.266186 0.963922i \(-0.585764\pi\)
−0.266186 + 0.963922i \(0.585764\pi\)
\(500\) −11.6241 −0.519844
\(501\) 21.9521 0.980749
\(502\) −0.156192 −0.00697119
\(503\) −21.7496 −0.969765 −0.484883 0.874579i \(-0.661138\pi\)
−0.484883 + 0.874579i \(0.661138\pi\)
\(504\) −1.33340 −0.0593944
\(505\) 41.0533 1.82685
\(506\) −2.80927 −0.124887
\(507\) −15.7275 −0.698482
\(508\) −32.8459 −1.45730
\(509\) −25.2949 −1.12118 −0.560589 0.828094i \(-0.689425\pi\)
−0.560589 + 0.828094i \(0.689425\pi\)
\(510\) 0.645550 0.0285854
\(511\) −16.7694 −0.741835
\(512\) 14.0285 0.619976
\(513\) 0.832236 0.0367441
\(514\) 0.277893 0.0122573
\(515\) 65.2734 2.87629
\(516\) −21.3935 −0.941796
\(517\) −13.8865 −0.610725
\(518\) −1.15698 −0.0508346
\(519\) 9.46456 0.415448
\(520\) 13.7171 0.601536
\(521\) −2.57071 −0.112625 −0.0563124 0.998413i \(-0.517934\pi\)
−0.0563124 + 0.998413i \(0.517934\pi\)
\(522\) 0.318924 0.0139589
\(523\) 38.7582 1.69478 0.847390 0.530971i \(-0.178173\pi\)
0.847390 + 0.530971i \(0.178173\pi\)
\(524\) 19.8105 0.865427
\(525\) −12.0041 −0.523904
\(526\) −2.00681 −0.0875009
\(527\) −5.10521 −0.222387
\(528\) −11.9270 −0.519057
\(529\) −0.596618 −0.0259399
\(530\) 5.63269 0.244669
\(531\) 4.56892 0.198274
\(532\) 2.91707 0.126471
\(533\) 32.3187 1.39988
\(534\) 2.18360 0.0944935
\(535\) −23.8392 −1.03066
\(536\) 9.42174 0.406957
\(537\) 6.28826 0.271358
\(538\) 2.58185 0.111312
\(539\) −12.0165 −0.517585
\(540\) 6.72750 0.289505
\(541\) 1.12159 0.0482209 0.0241104 0.999709i \(-0.492325\pi\)
0.0241104 + 0.999709i \(0.492325\pi\)
\(542\) 0.932070 0.0400358
\(543\) −22.2200 −0.953551
\(544\) −2.20870 −0.0946973
\(545\) 4.78225 0.204849
\(546\) 1.80270 0.0771486
\(547\) −10.5264 −0.450075 −0.225037 0.974350i \(-0.572250\pi\)
−0.225037 + 0.974350i \(0.572250\pi\)
\(548\) −19.4448 −0.830641
\(549\) −1.80853 −0.0771860
\(550\) 3.99312 0.170267
\(551\) −1.40803 −0.0599843
\(552\) −3.53722 −0.150554
\(553\) −11.8729 −0.504888
\(554\) −1.48969 −0.0632909
\(555\) 11.7803 0.500047
\(556\) −19.6696 −0.834178
\(557\) −15.7987 −0.669412 −0.334706 0.942323i \(-0.608637\pi\)
−0.334706 + 0.942323i \(0.608637\pi\)
\(558\) 0.962354 0.0407397
\(559\) 58.3695 2.46877
\(560\) 23.1463 0.978108
\(561\) 3.14859 0.132933
\(562\) −3.48588 −0.147043
\(563\) 8.36938 0.352727 0.176364 0.984325i \(-0.443567\pi\)
0.176364 + 0.984325i \(0.443567\pi\)
\(564\) −8.66404 −0.364822
\(565\) −26.8780 −1.13076
\(566\) 5.96067 0.250546
\(567\) 1.78425 0.0749313
\(568\) 2.63917 0.110737
\(569\) 45.0689 1.88939 0.944693 0.327955i \(-0.106360\pi\)
0.944693 + 0.327955i \(0.106360\pi\)
\(570\) 0.537250 0.0225029
\(571\) 38.0004 1.59027 0.795135 0.606433i \(-0.207400\pi\)
0.795135 + 0.606433i \(0.207400\pi\)
\(572\) 33.1519 1.38615
\(573\) −13.2135 −0.552002
\(574\) −2.02806 −0.0846497
\(575\) −31.8444 −1.32800
\(576\) −7.15977 −0.298324
\(577\) 26.9205 1.12071 0.560357 0.828251i \(-0.310664\pi\)
0.560357 + 0.828251i \(0.310664\pi\)
\(578\) 0.188504 0.00784074
\(579\) 16.1579 0.671499
\(580\) −11.3820 −0.472613
\(581\) −22.1132 −0.917410
\(582\) −1.23965 −0.0513852
\(583\) 27.4727 1.13780
\(584\) 7.02373 0.290644
\(585\) −18.3551 −0.758892
\(586\) −4.55408 −0.188127
\(587\) −4.31654 −0.178163 −0.0890814 0.996024i \(-0.528393\pi\)
−0.0890814 + 0.996024i \(0.528393\pi\)
\(588\) −7.49731 −0.309184
\(589\) −4.24874 −0.175066
\(590\) 2.94947 0.121428
\(591\) −22.5229 −0.926468
\(592\) −13.0306 −0.535555
\(593\) 19.4764 0.799799 0.399899 0.916559i \(-0.369045\pi\)
0.399899 + 0.916559i \(0.369045\pi\)
\(594\) −0.593521 −0.0243525
\(595\) −6.11032 −0.250499
\(596\) 42.2263 1.72966
\(597\) 14.3787 0.588482
\(598\) 4.78218 0.195558
\(599\) −3.16468 −0.129305 −0.0646526 0.997908i \(-0.520594\pi\)
−0.0646526 + 0.997908i \(0.520594\pi\)
\(600\) 5.02784 0.205261
\(601\) 19.2069 0.783466 0.391733 0.920079i \(-0.371876\pi\)
0.391733 + 0.920079i \(0.371876\pi\)
\(602\) −3.66280 −0.149285
\(603\) −12.6074 −0.513413
\(604\) −13.5360 −0.550770
\(605\) −3.72050 −0.151260
\(606\) −2.25975 −0.0917960
\(607\) −0.150792 −0.00612045 −0.00306023 0.999995i \(-0.500974\pi\)
−0.00306023 + 0.999995i \(0.500974\pi\)
\(608\) −1.83816 −0.0745473
\(609\) −3.01871 −0.122324
\(610\) −1.16749 −0.0472704
\(611\) 23.6387 0.956321
\(612\) 1.96447 0.0794088
\(613\) −27.8618 −1.12533 −0.562664 0.826686i \(-0.690223\pi\)
−0.562664 + 0.826686i \(0.690223\pi\)
\(614\) −5.48065 −0.221181
\(615\) 20.6497 0.832678
\(616\) −4.19833 −0.169155
\(617\) −16.6285 −0.669439 −0.334720 0.942318i \(-0.608642\pi\)
−0.334720 + 0.942318i \(0.608642\pi\)
\(618\) −3.59292 −0.144529
\(619\) −23.0207 −0.925279 −0.462640 0.886546i \(-0.653098\pi\)
−0.462640 + 0.886546i \(0.653098\pi\)
\(620\) −34.3453 −1.37934
\(621\) 4.73322 0.189938
\(622\) −0.538778 −0.0216030
\(623\) −20.6684 −0.828062
\(624\) 20.3032 0.812780
\(625\) −13.3753 −0.535013
\(626\) −2.75613 −0.110157
\(627\) 2.62037 0.104647
\(628\) 1.96447 0.0783907
\(629\) 3.43992 0.137159
\(630\) 1.15182 0.0458896
\(631\) −27.3793 −1.08995 −0.544976 0.838452i \(-0.683461\pi\)
−0.544976 + 0.838452i \(0.683461\pi\)
\(632\) 4.97288 0.197810
\(633\) −17.9288 −0.712607
\(634\) −4.98981 −0.198171
\(635\) 57.2592 2.27226
\(636\) 17.1408 0.679677
\(637\) 20.4555 0.810476
\(638\) 1.00416 0.0397551
\(639\) −3.53152 −0.139705
\(640\) −19.7498 −0.780679
\(641\) −7.49037 −0.295852 −0.147926 0.988998i \(-0.547260\pi\)
−0.147926 + 0.988998i \(0.547260\pi\)
\(642\) 1.31221 0.0517887
\(643\) 11.1091 0.438099 0.219049 0.975714i \(-0.429704\pi\)
0.219049 + 0.975714i \(0.429704\pi\)
\(644\) 16.5904 0.653753
\(645\) 37.2946 1.46847
\(646\) 0.156880 0.00617236
\(647\) −6.63118 −0.260698 −0.130349 0.991468i \(-0.541610\pi\)
−0.130349 + 0.991468i \(0.541610\pi\)
\(648\) −0.747318 −0.0293574
\(649\) 14.3856 0.564686
\(650\) −6.79744 −0.266618
\(651\) −9.10896 −0.357008
\(652\) −26.1807 −1.02532
\(653\) −41.0044 −1.60462 −0.802312 0.596904i \(-0.796397\pi\)
−0.802312 + 0.596904i \(0.796397\pi\)
\(654\) −0.263235 −0.0102933
\(655\) −34.5351 −1.34940
\(656\) −22.8414 −0.891806
\(657\) −9.39859 −0.366674
\(658\) −1.48338 −0.0578281
\(659\) 40.5473 1.57950 0.789750 0.613429i \(-0.210210\pi\)
0.789750 + 0.613429i \(0.210210\pi\)
\(660\) 21.1821 0.824512
\(661\) −45.5368 −1.77118 −0.885588 0.464472i \(-0.846244\pi\)
−0.885588 + 0.464472i \(0.846244\pi\)
\(662\) 4.36505 0.169652
\(663\) −5.35980 −0.208157
\(664\) 9.26194 0.359433
\(665\) −5.08523 −0.197197
\(666\) −0.648439 −0.0251265
\(667\) −8.00798 −0.310070
\(668\) 43.1242 1.66853
\(669\) 23.8723 0.922957
\(670\) −8.13871 −0.314426
\(671\) −5.69430 −0.219826
\(672\) −3.94087 −0.152022
\(673\) −33.3132 −1.28413 −0.642064 0.766651i \(-0.721922\pi\)
−0.642064 + 0.766651i \(0.721922\pi\)
\(674\) 4.59626 0.177041
\(675\) −6.72784 −0.258955
\(676\) −30.8961 −1.18831
\(677\) 37.5805 1.44434 0.722168 0.691718i \(-0.243146\pi\)
0.722168 + 0.691718i \(0.243146\pi\)
\(678\) 1.47948 0.0568189
\(679\) 11.7337 0.450297
\(680\) 2.55926 0.0981432
\(681\) −1.00897 −0.0386637
\(682\) 3.03005 0.116027
\(683\) −35.3950 −1.35435 −0.677175 0.735822i \(-0.736796\pi\)
−0.677175 + 0.735822i \(0.736796\pi\)
\(684\) 1.63490 0.0625120
\(685\) 33.8975 1.29516
\(686\) −3.63799 −0.138899
\(687\) 22.1200 0.843931
\(688\) −41.2529 −1.57275
\(689\) −46.7665 −1.78166
\(690\) 3.05553 0.116322
\(691\) −46.2849 −1.76076 −0.880380 0.474270i \(-0.842712\pi\)
−0.880380 + 0.474270i \(0.842712\pi\)
\(692\) 18.5928 0.706793
\(693\) 5.61786 0.213405
\(694\) −3.24998 −0.123368
\(695\) 34.2894 1.30067
\(696\) 1.26436 0.0479256
\(697\) 6.02983 0.228396
\(698\) 5.40011 0.204397
\(699\) −24.2251 −0.916279
\(700\) −23.5817 −0.891305
\(701\) 15.6870 0.592491 0.296246 0.955112i \(-0.404265\pi\)
0.296246 + 0.955112i \(0.404265\pi\)
\(702\) 1.01034 0.0381330
\(703\) 2.86283 0.107973
\(704\) −22.5432 −0.849627
\(705\) 15.1038 0.568840
\(706\) −0.385629 −0.0145133
\(707\) 21.3892 0.804423
\(708\) 8.97549 0.337320
\(709\) 29.0503 1.09101 0.545504 0.838108i \(-0.316338\pi\)
0.545504 + 0.838108i \(0.316338\pi\)
\(710\) −2.27977 −0.0855584
\(711\) −6.65430 −0.249556
\(712\) 8.65679 0.324427
\(713\) −24.1641 −0.904953
\(714\) 0.336338 0.0125871
\(715\) −57.7927 −2.16133
\(716\) 12.3531 0.461656
\(717\) −1.48328 −0.0553939
\(718\) 4.46479 0.166625
\(719\) −1.82416 −0.0680299 −0.0340149 0.999421i \(-0.510829\pi\)
−0.0340149 + 0.999421i \(0.510829\pi\)
\(720\) 12.9726 0.483459
\(721\) 34.0081 1.26653
\(722\) −3.45102 −0.128434
\(723\) −24.7453 −0.920288
\(724\) −43.6504 −1.62225
\(725\) 11.3826 0.422740
\(726\) 0.204792 0.00760055
\(727\) 23.5960 0.875126 0.437563 0.899188i \(-0.355842\pi\)
0.437563 + 0.899188i \(0.355842\pi\)
\(728\) 7.14676 0.264877
\(729\) 1.00000 0.0370370
\(730\) −6.06726 −0.224559
\(731\) 10.8902 0.402790
\(732\) −3.55279 −0.131315
\(733\) −39.2461 −1.44959 −0.724794 0.688965i \(-0.758065\pi\)
−0.724794 + 0.688965i \(0.758065\pi\)
\(734\) −0.483242 −0.0178368
\(735\) 13.0698 0.482088
\(736\) −10.4543 −0.385350
\(737\) −39.6955 −1.46220
\(738\) −1.13665 −0.0418406
\(739\) 5.52386 0.203198 0.101599 0.994825i \(-0.467604\pi\)
0.101599 + 0.994825i \(0.467604\pi\)
\(740\) 23.1421 0.850719
\(741\) −4.46062 −0.163865
\(742\) 2.93469 0.107736
\(743\) −27.3105 −1.00193 −0.500963 0.865469i \(-0.667021\pi\)
−0.500963 + 0.865469i \(0.667021\pi\)
\(744\) 3.81522 0.139873
\(745\) −73.6118 −2.69693
\(746\) −6.60964 −0.241996
\(747\) −12.3936 −0.453457
\(748\) 6.18529 0.226157
\(749\) −12.4204 −0.453833
\(750\) −1.11541 −0.0407290
\(751\) −12.9932 −0.474128 −0.237064 0.971494i \(-0.576185\pi\)
−0.237064 + 0.971494i \(0.576185\pi\)
\(752\) −16.7068 −0.609233
\(753\) 0.828587 0.0301954
\(754\) −1.70937 −0.0622516
\(755\) 23.5968 0.858776
\(756\) 3.50509 0.127479
\(757\) 11.3433 0.412279 0.206140 0.978523i \(-0.433910\pi\)
0.206140 + 0.978523i \(0.433910\pi\)
\(758\) −2.11755 −0.0769128
\(759\) 14.9030 0.540943
\(760\) 2.12991 0.0772600
\(761\) −28.1484 −1.02038 −0.510189 0.860063i \(-0.670424\pi\)
−0.510189 + 0.860063i \(0.670424\pi\)
\(762\) −3.15179 −0.114177
\(763\) 2.49160 0.0902019
\(764\) −25.9575 −0.939109
\(765\) −3.42459 −0.123816
\(766\) −2.78749 −0.100716
\(767\) −24.4885 −0.884229
\(768\) −13.2324 −0.477484
\(769\) −38.0823 −1.37328 −0.686642 0.726996i \(-0.740916\pi\)
−0.686642 + 0.726996i \(0.740916\pi\)
\(770\) 3.62661 0.130694
\(771\) −1.47420 −0.0530920
\(772\) 31.7416 1.14241
\(773\) 42.7696 1.53832 0.769158 0.639059i \(-0.220676\pi\)
0.769158 + 0.639059i \(0.220676\pi\)
\(774\) −2.05285 −0.0737883
\(775\) 34.3471 1.23378
\(776\) −4.91456 −0.176422
\(777\) 6.13767 0.220188
\(778\) −6.96051 −0.249546
\(779\) 5.01825 0.179797
\(780\) −36.0581 −1.29109
\(781\) −11.1193 −0.397880
\(782\) 0.892232 0.0319061
\(783\) −1.69187 −0.0604624
\(784\) −14.4570 −0.516321
\(785\) −3.42459 −0.122229
\(786\) 1.90096 0.0678049
\(787\) 42.9371 1.53054 0.765271 0.643709i \(-0.222605\pi\)
0.765271 + 0.643709i \(0.222605\pi\)
\(788\) −44.2455 −1.57618
\(789\) 10.6460 0.379006
\(790\) −4.29568 −0.152834
\(791\) −14.0037 −0.497914
\(792\) −2.35300 −0.0836100
\(793\) 9.69334 0.344221
\(794\) 0.773858 0.0274632
\(795\) −29.8810 −1.05977
\(796\) 28.2465 1.00117
\(797\) −25.7429 −0.911862 −0.455931 0.890015i \(-0.650694\pi\)
−0.455931 + 0.890015i \(0.650694\pi\)
\(798\) 0.279913 0.00990880
\(799\) 4.41038 0.156028
\(800\) 14.8598 0.525373
\(801\) −11.5838 −0.409294
\(802\) −4.64685 −0.164086
\(803\) −29.5923 −1.04429
\(804\) −24.7668 −0.873458
\(805\) −28.9215 −1.01935
\(806\) −5.15802 −0.181684
\(807\) −13.6965 −0.482141
\(808\) −8.95869 −0.315166
\(809\) 31.5271 1.10843 0.554216 0.832373i \(-0.313018\pi\)
0.554216 + 0.832373i \(0.313018\pi\)
\(810\) 0.645550 0.0226823
\(811\) 52.5422 1.84501 0.922503 0.385991i \(-0.126140\pi\)
0.922503 + 0.385991i \(0.126140\pi\)
\(812\) −5.93015 −0.208108
\(813\) −4.94456 −0.173413
\(814\) −2.04167 −0.0715603
\(815\) 45.6400 1.59870
\(816\) 3.78806 0.132609
\(817\) 9.06325 0.317083
\(818\) −0.756430 −0.0264480
\(819\) −9.56321 −0.334166
\(820\) 40.5657 1.41662
\(821\) 5.39941 0.188441 0.0942203 0.995551i \(-0.469964\pi\)
0.0942203 + 0.995551i \(0.469964\pi\)
\(822\) −1.86586 −0.0650795
\(823\) 51.6915 1.80185 0.900926 0.433972i \(-0.142888\pi\)
0.900926 + 0.433972i \(0.142888\pi\)
\(824\) −14.2440 −0.496214
\(825\) −21.1832 −0.737504
\(826\) 1.53670 0.0534687
\(827\) 33.7956 1.17519 0.587594 0.809156i \(-0.300075\pi\)
0.587594 + 0.809156i \(0.300075\pi\)
\(828\) 9.29825 0.323137
\(829\) −46.8907 −1.62858 −0.814291 0.580456i \(-0.802874\pi\)
−0.814291 + 0.580456i \(0.802874\pi\)
\(830\) −8.00067 −0.277707
\(831\) 7.90270 0.274142
\(832\) 38.3749 1.33041
\(833\) 3.81646 0.132233
\(834\) −1.88744 −0.0653566
\(835\) −75.1771 −2.60161
\(836\) 5.14762 0.178034
\(837\) −5.10521 −0.176462
\(838\) −0.926763 −0.0320145
\(839\) 34.8732 1.20396 0.601978 0.798513i \(-0.294380\pi\)
0.601978 + 0.798513i \(0.294380\pi\)
\(840\) 4.56635 0.157554
\(841\) −26.1376 −0.901296
\(842\) −5.91916 −0.203988
\(843\) 18.4923 0.636909
\(844\) −35.2206 −1.21234
\(845\) 53.8602 1.85285
\(846\) −0.831374 −0.0285832
\(847\) −1.93842 −0.0666049
\(848\) 33.0524 1.13502
\(849\) −31.6209 −1.08523
\(850\) −1.26823 −0.0434998
\(851\) 16.2819 0.558136
\(852\) −6.93755 −0.237677
\(853\) 8.22003 0.281449 0.140724 0.990049i \(-0.455057\pi\)
0.140724 + 0.990049i \(0.455057\pi\)
\(854\) −0.608276 −0.0208148
\(855\) −2.85007 −0.0974704
\(856\) 5.20220 0.177808
\(857\) 1.09505 0.0374063 0.0187031 0.999825i \(-0.494046\pi\)
0.0187031 + 0.999825i \(0.494046\pi\)
\(858\) 3.18116 0.108603
\(859\) 28.4147 0.969498 0.484749 0.874653i \(-0.338911\pi\)
0.484749 + 0.874653i \(0.338911\pi\)
\(860\) 73.2640 2.49828
\(861\) 10.7587 0.366656
\(862\) 4.41599 0.150409
\(863\) −40.7980 −1.38878 −0.694389 0.719600i \(-0.744325\pi\)
−0.694389 + 0.719600i \(0.744325\pi\)
\(864\) −2.20870 −0.0751415
\(865\) −32.4123 −1.10205
\(866\) −4.83866 −0.164425
\(867\) −1.00000 −0.0339618
\(868\) −17.8943 −0.607370
\(869\) −20.9516 −0.710735
\(870\) −1.09219 −0.0370285
\(871\) 67.5731 2.28963
\(872\) −1.04359 −0.0353403
\(873\) 6.57626 0.222573
\(874\) 0.742547 0.0251170
\(875\) 10.5577 0.356915
\(876\) −18.4632 −0.623814
\(877\) 36.9166 1.24658 0.623292 0.781989i \(-0.285795\pi\)
0.623292 + 0.781989i \(0.285795\pi\)
\(878\) −4.25685 −0.143662
\(879\) 24.1591 0.814865
\(880\) 40.8452 1.37689
\(881\) −13.0274 −0.438905 −0.219452 0.975623i \(-0.570427\pi\)
−0.219452 + 0.975623i \(0.570427\pi\)
\(882\) −0.719419 −0.0242241
\(883\) 35.8333 1.20589 0.602943 0.797784i \(-0.293994\pi\)
0.602943 + 0.797784i \(0.293994\pi\)
\(884\) −10.5291 −0.354134
\(885\) −15.6467 −0.525958
\(886\) −3.72025 −0.124984
\(887\) −18.0952 −0.607576 −0.303788 0.952740i \(-0.598252\pi\)
−0.303788 + 0.952740i \(0.598252\pi\)
\(888\) −2.57071 −0.0862675
\(889\) 29.8326 1.00055
\(890\) −7.47793 −0.250661
\(891\) 3.14859 0.105482
\(892\) 46.8964 1.57021
\(893\) 3.67048 0.122828
\(894\) 4.05190 0.135516
\(895\) −21.5347 −0.719827
\(896\) −10.2898 −0.343759
\(897\) −25.3691 −0.847050
\(898\) 6.40509 0.213740
\(899\) 8.63735 0.288072
\(900\) −13.2166 −0.440554
\(901\) −8.72542 −0.290686
\(902\) −3.57884 −0.119162
\(903\) 19.4309 0.646619
\(904\) 5.86533 0.195078
\(905\) 76.0944 2.52946
\(906\) −1.29887 −0.0431520
\(907\) 8.08629 0.268501 0.134250 0.990947i \(-0.457137\pi\)
0.134250 + 0.990947i \(0.457137\pi\)
\(908\) −1.98208 −0.0657777
\(909\) 11.9878 0.397610
\(910\) −6.17353 −0.204651
\(911\) −6.91168 −0.228994 −0.114497 0.993424i \(-0.536526\pi\)
−0.114497 + 0.993424i \(0.536526\pi\)
\(912\) 3.15256 0.104392
\(913\) −39.0222 −1.29145
\(914\) −1.07945 −0.0357050
\(915\) 6.19347 0.204750
\(916\) 43.4540 1.43576
\(917\) −17.9931 −0.594185
\(918\) 0.188504 0.00622156
\(919\) −27.0744 −0.893103 −0.446552 0.894758i \(-0.647348\pi\)
−0.446552 + 0.894758i \(0.647348\pi\)
\(920\) 12.1135 0.399372
\(921\) 29.0744 0.958035
\(922\) 2.53707 0.0835541
\(923\) 18.9283 0.623031
\(924\) 11.0361 0.363061
\(925\) −23.1432 −0.760945
\(926\) 0.174068 0.00572022
\(927\) 19.0602 0.626019
\(928\) 3.73683 0.122667
\(929\) −3.69474 −0.121220 −0.0606102 0.998162i \(-0.519305\pi\)
−0.0606102 + 0.998162i \(0.519305\pi\)
\(930\) −3.29567 −0.108069
\(931\) 3.17620 0.104096
\(932\) −47.5895 −1.55884
\(933\) 2.85818 0.0935725
\(934\) 5.71909 0.187134
\(935\) −10.7826 −0.352630
\(936\) 4.00548 0.130923
\(937\) 13.7223 0.448288 0.224144 0.974556i \(-0.428041\pi\)
0.224144 + 0.974556i \(0.428041\pi\)
\(938\) −4.24035 −0.138452
\(939\) 14.6211 0.477140
\(940\) 29.6708 0.967755
\(941\) 9.84849 0.321052 0.160526 0.987032i \(-0.448681\pi\)
0.160526 + 0.987032i \(0.448681\pi\)
\(942\) 0.188504 0.00614180
\(943\) 28.5405 0.929408
\(944\) 17.3073 0.563306
\(945\) −6.11032 −0.198769
\(946\) −6.46359 −0.210149
\(947\) −4.23259 −0.137541 −0.0687704 0.997633i \(-0.521908\pi\)
−0.0687704 + 0.997633i \(0.521908\pi\)
\(948\) −13.0721 −0.424564
\(949\) 50.3746 1.63523
\(950\) −1.05546 −0.0342438
\(951\) 26.4706 0.858367
\(952\) 1.33340 0.0432158
\(953\) −19.1966 −0.621840 −0.310920 0.950436i \(-0.600637\pi\)
−0.310920 + 0.950436i \(0.600637\pi\)
\(954\) 1.64478 0.0532516
\(955\) 45.2509 1.46428
\(956\) −2.91384 −0.0942405
\(957\) −5.32699 −0.172197
\(958\) 1.93135 0.0623992
\(959\) 17.6610 0.570302
\(960\) 24.5193 0.791357
\(961\) −4.93679 −0.159251
\(962\) 3.47550 0.112055
\(963\) −6.96116 −0.224320
\(964\) −48.6113 −1.56566
\(965\) −55.3342 −1.78127
\(966\) 1.59196 0.0512205
\(967\) −7.35773 −0.236609 −0.118304 0.992977i \(-0.537746\pi\)
−0.118304 + 0.992977i \(0.537746\pi\)
\(968\) 0.811892 0.0260952
\(969\) −0.832236 −0.0267353
\(970\) 4.24530 0.136309
\(971\) 23.9232 0.767731 0.383866 0.923389i \(-0.374593\pi\)
0.383866 + 0.923389i \(0.374593\pi\)
\(972\) 1.96447 0.0630103
\(973\) 17.8651 0.572730
\(974\) −3.25634 −0.104340
\(975\) 36.0599 1.15484
\(976\) −6.85080 −0.219289
\(977\) 0.958442 0.0306633 0.0153316 0.999882i \(-0.495120\pi\)
0.0153316 + 0.999882i \(0.495120\pi\)
\(978\) −2.51222 −0.0803319
\(979\) −36.4726 −1.16567
\(980\) 25.6752 0.820166
\(981\) 1.39644 0.0445850
\(982\) −2.67744 −0.0854406
\(983\) 41.4620 1.32243 0.661216 0.750196i \(-0.270041\pi\)
0.661216 + 0.750196i \(0.270041\pi\)
\(984\) −4.50620 −0.143653
\(985\) 77.1317 2.45762
\(986\) −0.318924 −0.0101566
\(987\) 7.86920 0.250480
\(988\) −8.76274 −0.278780
\(989\) 51.5459 1.63906
\(990\) 2.03257 0.0645993
\(991\) 10.7114 0.340259 0.170130 0.985422i \(-0.445581\pi\)
0.170130 + 0.985422i \(0.445581\pi\)
\(992\) 11.2759 0.358010
\(993\) −23.1563 −0.734842
\(994\) −1.18778 −0.0376742
\(995\) −49.2413 −1.56105
\(996\) −24.3468 −0.771457
\(997\) −24.1247 −0.764037 −0.382018 0.924155i \(-0.624771\pi\)
−0.382018 + 0.924155i \(0.624771\pi\)
\(998\) −2.24175 −0.0709612
\(999\) 3.43992 0.108834
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8007.2.a.f.1.26 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.26 48 1.1 even 1 trivial