Properties

Label 6008.2.a.c.1.10
Level $6008$
Weight $2$
Character 6008.1
Self dual yes
Analytic conductor $47.974$
Analytic rank $1$
Dimension $44$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6008,2,Mod(1,6008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6008.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.08546 q^{3} -0.642029 q^{5} +1.54125 q^{7} +1.34913 q^{9} +O(q^{10})\) \(q-2.08546 q^{3} -0.642029 q^{5} +1.54125 q^{7} +1.34913 q^{9} -0.0501981 q^{11} +5.91068 q^{13} +1.33892 q^{15} +1.47527 q^{17} -1.81866 q^{19} -3.21422 q^{21} +0.0921709 q^{23} -4.58780 q^{25} +3.44283 q^{27} -10.4043 q^{29} -0.864148 q^{31} +0.104686 q^{33} -0.989531 q^{35} -7.04976 q^{37} -12.3265 q^{39} -8.73678 q^{41} -2.81571 q^{43} -0.866178 q^{45} +11.2378 q^{47} -4.62453 q^{49} -3.07661 q^{51} +5.08975 q^{53} +0.0322287 q^{55} +3.79274 q^{57} +4.28163 q^{59} +13.7408 q^{61} +2.07935 q^{63} -3.79483 q^{65} -6.92186 q^{67} -0.192218 q^{69} +6.95662 q^{71} +9.20107 q^{73} +9.56765 q^{75} -0.0773681 q^{77} -9.91915 q^{79} -11.2272 q^{81} +16.3935 q^{83} -0.947165 q^{85} +21.6977 q^{87} +1.60753 q^{89} +9.10986 q^{91} +1.80214 q^{93} +1.16764 q^{95} -3.53207 q^{97} -0.0677236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9} + 11 q^{11} - 36 q^{13} - 5 q^{15} - 10 q^{17} - 7 q^{19} - 42 q^{21} - 5 q^{23} + 29 q^{25} - 16 q^{27} - 57 q^{29} - 21 q^{31} - 32 q^{33} + 17 q^{35} - 52 q^{37} + 8 q^{39} - 16 q^{41} - 9 q^{43} - 84 q^{45} - q^{47} + 28 q^{49} - q^{51} - 52 q^{53} - 39 q^{55} - 15 q^{57} + 7 q^{59} - 85 q^{61} - 25 q^{63} - 9 q^{65} - 36 q^{67} - 72 q^{69} + 12 q^{71} - 60 q^{73} - 5 q^{75} - 81 q^{77} - 13 q^{79} + 20 q^{81} + 5 q^{83} - 72 q^{85} + 9 q^{87} - 37 q^{89} - 23 q^{91} - 60 q^{93} + 24 q^{95} - 79 q^{97} + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 0
\(3\) −2.08546 −1.20404 −0.602019 0.798482i \(-0.705637\pi\)
−0.602019 + 0.798482i \(0.705637\pi\)
\(4\) 0 0
\(5\) −0.642029 −0.287124 −0.143562 0.989641i \(-0.545856\pi\)
−0.143562 + 0.989641i \(0.545856\pi\)
\(6\) 0 0
\(7\) 1.54125 0.582540 0.291270 0.956641i \(-0.405922\pi\)
0.291270 + 0.956641i \(0.405922\pi\)
\(8\) 0 0
\(9\) 1.34913 0.449709
\(10\) 0 0
\(11\) −0.0501981 −0.0151353 −0.00756765 0.999971i \(-0.502409\pi\)
−0.00756765 + 0.999971i \(0.502409\pi\)
\(12\) 0 0
\(13\) 5.91068 1.63933 0.819664 0.572845i \(-0.194160\pi\)
0.819664 + 0.572845i \(0.194160\pi\)
\(14\) 0 0
\(15\) 1.33892 0.345709
\(16\) 0 0
\(17\) 1.47527 0.357805 0.178903 0.983867i \(-0.442745\pi\)
0.178903 + 0.983867i \(0.442745\pi\)
\(18\) 0 0
\(19\) −1.81866 −0.417230 −0.208615 0.977998i \(-0.566896\pi\)
−0.208615 + 0.977998i \(0.566896\pi\)
\(20\) 0 0
\(21\) −3.21422 −0.701400
\(22\) 0 0
\(23\) 0.0921709 0.0192190 0.00960948 0.999954i \(-0.496941\pi\)
0.00960948 + 0.999954i \(0.496941\pi\)
\(24\) 0 0
\(25\) −4.58780 −0.917560
\(26\) 0 0
\(27\) 3.44283 0.662572
\(28\) 0 0
\(29\) −10.4043 −1.93203 −0.966016 0.258481i \(-0.916778\pi\)
−0.966016 + 0.258481i \(0.916778\pi\)
\(30\) 0 0
\(31\) −0.864148 −0.155206 −0.0776028 0.996984i \(-0.524727\pi\)
−0.0776028 + 0.996984i \(0.524727\pi\)
\(32\) 0 0
\(33\) 0.104686 0.0182235
\(34\) 0 0
\(35\) −0.989531 −0.167261
\(36\) 0 0
\(37\) −7.04976 −1.15897 −0.579487 0.814982i \(-0.696747\pi\)
−0.579487 + 0.814982i \(0.696747\pi\)
\(38\) 0 0
\(39\) −12.3265 −1.97381
\(40\) 0 0
\(41\) −8.73678 −1.36446 −0.682228 0.731140i \(-0.738989\pi\)
−0.682228 + 0.731140i \(0.738989\pi\)
\(42\) 0 0
\(43\) −2.81571 −0.429392 −0.214696 0.976681i \(-0.568876\pi\)
−0.214696 + 0.976681i \(0.568876\pi\)
\(44\) 0 0
\(45\) −0.866178 −0.129122
\(46\) 0 0
\(47\) 11.2378 1.63920 0.819599 0.572938i \(-0.194197\pi\)
0.819599 + 0.572938i \(0.194197\pi\)
\(48\) 0 0
\(49\) −4.62453 −0.660648
\(50\) 0 0
\(51\) −3.07661 −0.430811
\(52\) 0 0
\(53\) 5.08975 0.699131 0.349565 0.936912i \(-0.386329\pi\)
0.349565 + 0.936912i \(0.386329\pi\)
\(54\) 0 0
\(55\) 0.0322287 0.00434571
\(56\) 0 0
\(57\) 3.79274 0.502361
\(58\) 0 0
\(59\) 4.28163 0.557421 0.278710 0.960375i \(-0.410093\pi\)
0.278710 + 0.960375i \(0.410093\pi\)
\(60\) 0 0
\(61\) 13.7408 1.75933 0.879665 0.475593i \(-0.157767\pi\)
0.879665 + 0.475593i \(0.157767\pi\)
\(62\) 0 0
\(63\) 2.07935 0.261973
\(64\) 0 0
\(65\) −3.79483 −0.470691
\(66\) 0 0
\(67\) −6.92186 −0.845640 −0.422820 0.906214i \(-0.638960\pi\)
−0.422820 + 0.906214i \(0.638960\pi\)
\(68\) 0 0
\(69\) −0.192218 −0.0231404
\(70\) 0 0
\(71\) 6.95662 0.825599 0.412799 0.910822i \(-0.364551\pi\)
0.412799 + 0.910822i \(0.364551\pi\)
\(72\) 0 0
\(73\) 9.20107 1.07690 0.538452 0.842656i \(-0.319009\pi\)
0.538452 + 0.842656i \(0.319009\pi\)
\(74\) 0 0
\(75\) 9.56765 1.10478
\(76\) 0 0
\(77\) −0.0773681 −0.00881692
\(78\) 0 0
\(79\) −9.91915 −1.11599 −0.557996 0.829844i \(-0.688429\pi\)
−0.557996 + 0.829844i \(0.688429\pi\)
\(80\) 0 0
\(81\) −11.2272 −1.24747
\(82\) 0 0
\(83\) 16.3935 1.79942 0.899711 0.436486i \(-0.143777\pi\)
0.899711 + 0.436486i \(0.143777\pi\)
\(84\) 0 0
\(85\) −0.947165 −0.102735
\(86\) 0 0
\(87\) 21.6977 2.32624
\(88\) 0 0
\(89\) 1.60753 0.170398 0.0851991 0.996364i \(-0.472847\pi\)
0.0851991 + 0.996364i \(0.472847\pi\)
\(90\) 0 0
\(91\) 9.10986 0.954973
\(92\) 0 0
\(93\) 1.80214 0.186874
\(94\) 0 0
\(95\) 1.16764 0.119797
\(96\) 0 0
\(97\) −3.53207 −0.358628 −0.179314 0.983792i \(-0.557388\pi\)
−0.179314 + 0.983792i \(0.557388\pi\)
\(98\) 0 0
\(99\) −0.0677236 −0.00680648
\(100\) 0 0
\(101\) −9.43385 −0.938704 −0.469352 0.883011i \(-0.655512\pi\)
−0.469352 + 0.883011i \(0.655512\pi\)
\(102\) 0 0
\(103\) 10.5896 1.04342 0.521712 0.853121i \(-0.325293\pi\)
0.521712 + 0.853121i \(0.325293\pi\)
\(104\) 0 0
\(105\) 2.06362 0.201389
\(106\) 0 0
\(107\) −6.37416 −0.616213 −0.308107 0.951352i \(-0.599695\pi\)
−0.308107 + 0.951352i \(0.599695\pi\)
\(108\) 0 0
\(109\) −3.85130 −0.368887 −0.184444 0.982843i \(-0.559048\pi\)
−0.184444 + 0.982843i \(0.559048\pi\)
\(110\) 0 0
\(111\) 14.7020 1.39545
\(112\) 0 0
\(113\) 4.72562 0.444549 0.222275 0.974984i \(-0.428652\pi\)
0.222275 + 0.974984i \(0.428652\pi\)
\(114\) 0 0
\(115\) −0.0591764 −0.00551823
\(116\) 0 0
\(117\) 7.97425 0.737220
\(118\) 0 0
\(119\) 2.27376 0.208436
\(120\) 0 0
\(121\) −10.9975 −0.999771
\(122\) 0 0
\(123\) 18.2202 1.64286
\(124\) 0 0
\(125\) 6.15565 0.550578
\(126\) 0 0
\(127\) 2.96695 0.263275 0.131637 0.991298i \(-0.457977\pi\)
0.131637 + 0.991298i \(0.457977\pi\)
\(128\) 0 0
\(129\) 5.87204 0.517004
\(130\) 0 0
\(131\) −11.4114 −0.997017 −0.498508 0.866885i \(-0.666119\pi\)
−0.498508 + 0.866885i \(0.666119\pi\)
\(132\) 0 0
\(133\) −2.80302 −0.243053
\(134\) 0 0
\(135\) −2.21040 −0.190241
\(136\) 0 0
\(137\) 5.41797 0.462889 0.231444 0.972848i \(-0.425655\pi\)
0.231444 + 0.972848i \(0.425655\pi\)
\(138\) 0 0
\(139\) −19.4051 −1.64592 −0.822959 0.568101i \(-0.807678\pi\)
−0.822959 + 0.568101i \(0.807678\pi\)
\(140\) 0 0
\(141\) −23.4359 −1.97366
\(142\) 0 0
\(143\) −0.296705 −0.0248117
\(144\) 0 0
\(145\) 6.67988 0.554733
\(146\) 0 0
\(147\) 9.64426 0.795445
\(148\) 0 0
\(149\) −16.0999 −1.31895 −0.659476 0.751725i \(-0.729222\pi\)
−0.659476 + 0.751725i \(0.729222\pi\)
\(150\) 0 0
\(151\) −3.26939 −0.266059 −0.133029 0.991112i \(-0.542471\pi\)
−0.133029 + 0.991112i \(0.542471\pi\)
\(152\) 0 0
\(153\) 1.99032 0.160908
\(154\) 0 0
\(155\) 0.554809 0.0445633
\(156\) 0 0
\(157\) −12.9713 −1.03522 −0.517609 0.855617i \(-0.673178\pi\)
−0.517609 + 0.855617i \(0.673178\pi\)
\(158\) 0 0
\(159\) −10.6144 −0.841780
\(160\) 0 0
\(161\) 0.142059 0.0111958
\(162\) 0 0
\(163\) −14.0026 −1.09677 −0.548385 0.836226i \(-0.684757\pi\)
−0.548385 + 0.836226i \(0.684757\pi\)
\(164\) 0 0
\(165\) −0.0672115 −0.00523241
\(166\) 0 0
\(167\) 5.00593 0.387370 0.193685 0.981064i \(-0.437956\pi\)
0.193685 + 0.981064i \(0.437956\pi\)
\(168\) 0 0
\(169\) 21.9361 1.68740
\(170\) 0 0
\(171\) −2.45361 −0.187632
\(172\) 0 0
\(173\) −8.40960 −0.639370 −0.319685 0.947524i \(-0.603577\pi\)
−0.319685 + 0.947524i \(0.603577\pi\)
\(174\) 0 0
\(175\) −7.07097 −0.534515
\(176\) 0 0
\(177\) −8.92915 −0.671156
\(178\) 0 0
\(179\) 3.34033 0.249668 0.124834 0.992178i \(-0.460160\pi\)
0.124834 + 0.992178i \(0.460160\pi\)
\(180\) 0 0
\(181\) −17.1120 −1.27192 −0.635961 0.771721i \(-0.719396\pi\)
−0.635961 + 0.771721i \(0.719396\pi\)
\(182\) 0 0
\(183\) −28.6559 −2.11830
\(184\) 0 0
\(185\) 4.52615 0.332769
\(186\) 0 0
\(187\) −0.0740557 −0.00541549
\(188\) 0 0
\(189\) 5.30627 0.385974
\(190\) 0 0
\(191\) 25.3928 1.83736 0.918678 0.395006i \(-0.129258\pi\)
0.918678 + 0.395006i \(0.129258\pi\)
\(192\) 0 0
\(193\) 0.0475098 0.00341983 0.00170992 0.999999i \(-0.499456\pi\)
0.00170992 + 0.999999i \(0.499456\pi\)
\(194\) 0 0
\(195\) 7.91395 0.566730
\(196\) 0 0
\(197\) 13.8514 0.986872 0.493436 0.869782i \(-0.335741\pi\)
0.493436 + 0.869782i \(0.335741\pi\)
\(198\) 0 0
\(199\) −3.23782 −0.229523 −0.114761 0.993393i \(-0.536610\pi\)
−0.114761 + 0.993393i \(0.536610\pi\)
\(200\) 0 0
\(201\) 14.4352 1.01818
\(202\) 0 0
\(203\) −16.0357 −1.12549
\(204\) 0 0
\(205\) 5.60927 0.391768
\(206\) 0 0
\(207\) 0.124350 0.00864293
\(208\) 0 0
\(209\) 0.0912936 0.00631491
\(210\) 0 0
\(211\) −19.4682 −1.34025 −0.670124 0.742249i \(-0.733759\pi\)
−0.670124 + 0.742249i \(0.733759\pi\)
\(212\) 0 0
\(213\) −14.5077 −0.994052
\(214\) 0 0
\(215\) 1.80777 0.123289
\(216\) 0 0
\(217\) −1.33187 −0.0904134
\(218\) 0 0
\(219\) −19.1884 −1.29663
\(220\) 0 0
\(221\) 8.71984 0.586560
\(222\) 0 0
\(223\) 2.90612 0.194608 0.0973041 0.995255i \(-0.468978\pi\)
0.0973041 + 0.995255i \(0.468978\pi\)
\(224\) 0 0
\(225\) −6.18952 −0.412634
\(226\) 0 0
\(227\) −3.03346 −0.201338 −0.100669 0.994920i \(-0.532098\pi\)
−0.100669 + 0.994920i \(0.532098\pi\)
\(228\) 0 0
\(229\) −18.8418 −1.24510 −0.622550 0.782580i \(-0.713903\pi\)
−0.622550 + 0.782580i \(0.713903\pi\)
\(230\) 0 0
\(231\) 0.161348 0.0106159
\(232\) 0 0
\(233\) −1.18903 −0.0778959 −0.0389480 0.999241i \(-0.512401\pi\)
−0.0389480 + 0.999241i \(0.512401\pi\)
\(234\) 0 0
\(235\) −7.21498 −0.470653
\(236\) 0 0
\(237\) 20.6859 1.34370
\(238\) 0 0
\(239\) −6.22584 −0.402716 −0.201358 0.979518i \(-0.564535\pi\)
−0.201358 + 0.979518i \(0.564535\pi\)
\(240\) 0 0
\(241\) 11.1906 0.720851 0.360425 0.932788i \(-0.382632\pi\)
0.360425 + 0.932788i \(0.382632\pi\)
\(242\) 0 0
\(243\) 13.0854 0.839431
\(244\) 0 0
\(245\) 2.96909 0.189688
\(246\) 0 0
\(247\) −10.7495 −0.683977
\(248\) 0 0
\(249\) −34.1880 −2.16657
\(250\) 0 0
\(251\) −4.07544 −0.257239 −0.128620 0.991694i \(-0.541055\pi\)
−0.128620 + 0.991694i \(0.541055\pi\)
\(252\) 0 0
\(253\) −0.00462681 −0.000290885 0
\(254\) 0 0
\(255\) 1.97527 0.123696
\(256\) 0 0
\(257\) −20.9796 −1.30867 −0.654334 0.756205i \(-0.727051\pi\)
−0.654334 + 0.756205i \(0.727051\pi\)
\(258\) 0 0
\(259\) −10.8655 −0.675148
\(260\) 0 0
\(261\) −14.0367 −0.868852
\(262\) 0 0
\(263\) 22.9152 1.41301 0.706507 0.707706i \(-0.250270\pi\)
0.706507 + 0.707706i \(0.250270\pi\)
\(264\) 0 0
\(265\) −3.26777 −0.200737
\(266\) 0 0
\(267\) −3.35244 −0.205166
\(268\) 0 0
\(269\) 9.45474 0.576465 0.288233 0.957560i \(-0.406932\pi\)
0.288233 + 0.957560i \(0.406932\pi\)
\(270\) 0 0
\(271\) 27.6847 1.68173 0.840863 0.541249i \(-0.182048\pi\)
0.840863 + 0.541249i \(0.182048\pi\)
\(272\) 0 0
\(273\) −18.9982 −1.14982
\(274\) 0 0
\(275\) 0.230299 0.0138875
\(276\) 0 0
\(277\) −5.57740 −0.335114 −0.167557 0.985862i \(-0.553588\pi\)
−0.167557 + 0.985862i \(0.553588\pi\)
\(278\) 0 0
\(279\) −1.16584 −0.0697973
\(280\) 0 0
\(281\) −22.1712 −1.32262 −0.661312 0.750111i \(-0.730000\pi\)
−0.661312 + 0.750111i \(0.730000\pi\)
\(282\) 0 0
\(283\) 12.9925 0.772325 0.386163 0.922431i \(-0.373800\pi\)
0.386163 + 0.922431i \(0.373800\pi\)
\(284\) 0 0
\(285\) −2.43505 −0.144240
\(286\) 0 0
\(287\) −13.4656 −0.794849
\(288\) 0 0
\(289\) −14.8236 −0.871976
\(290\) 0 0
\(291\) 7.36598 0.431802
\(292\) 0 0
\(293\) 16.0045 0.934992 0.467496 0.883995i \(-0.345156\pi\)
0.467496 + 0.883995i \(0.345156\pi\)
\(294\) 0 0
\(295\) −2.74893 −0.160049
\(296\) 0 0
\(297\) −0.172823 −0.0100282
\(298\) 0 0
\(299\) 0.544793 0.0315062
\(300\) 0 0
\(301\) −4.33973 −0.250138
\(302\) 0 0
\(303\) 19.6739 1.13024
\(304\) 0 0
\(305\) −8.82200 −0.505147
\(306\) 0 0
\(307\) −30.6056 −1.74675 −0.873377 0.487045i \(-0.838075\pi\)
−0.873377 + 0.487045i \(0.838075\pi\)
\(308\) 0 0
\(309\) −22.0842 −1.25632
\(310\) 0 0
\(311\) −1.17447 −0.0665979 −0.0332990 0.999445i \(-0.510601\pi\)
−0.0332990 + 0.999445i \(0.510601\pi\)
\(312\) 0 0
\(313\) −27.3467 −1.54573 −0.772863 0.634572i \(-0.781176\pi\)
−0.772863 + 0.634572i \(0.781176\pi\)
\(314\) 0 0
\(315\) −1.33500 −0.0752188
\(316\) 0 0
\(317\) −11.6836 −0.656219 −0.328110 0.944640i \(-0.606412\pi\)
−0.328110 + 0.944640i \(0.606412\pi\)
\(318\) 0 0
\(319\) 0.522277 0.0292419
\(320\) 0 0
\(321\) 13.2930 0.741945
\(322\) 0 0
\(323\) −2.68302 −0.149287
\(324\) 0 0
\(325\) −27.1170 −1.50418
\(326\) 0 0
\(327\) 8.03171 0.444154
\(328\) 0 0
\(329\) 17.3203 0.954897
\(330\) 0 0
\(331\) −25.9504 −1.42636 −0.713181 0.700980i \(-0.752746\pi\)
−0.713181 + 0.700980i \(0.752746\pi\)
\(332\) 0 0
\(333\) −9.51101 −0.521200
\(334\) 0 0
\(335\) 4.44404 0.242804
\(336\) 0 0
\(337\) −20.4647 −1.11478 −0.557392 0.830249i \(-0.688198\pi\)
−0.557392 + 0.830249i \(0.688198\pi\)
\(338\) 0 0
\(339\) −9.85508 −0.535254
\(340\) 0 0
\(341\) 0.0433786 0.00234908
\(342\) 0 0
\(343\) −17.9164 −0.967393
\(344\) 0 0
\(345\) 0.123410 0.00664416
\(346\) 0 0
\(347\) −5.34715 −0.287050 −0.143525 0.989647i \(-0.545844\pi\)
−0.143525 + 0.989647i \(0.545844\pi\)
\(348\) 0 0
\(349\) 28.8729 1.54553 0.772766 0.634692i \(-0.218873\pi\)
0.772766 + 0.634692i \(0.218873\pi\)
\(350\) 0 0
\(351\) 20.3494 1.08617
\(352\) 0 0
\(353\) 12.9605 0.689820 0.344910 0.938636i \(-0.387909\pi\)
0.344910 + 0.938636i \(0.387909\pi\)
\(354\) 0 0
\(355\) −4.46635 −0.237049
\(356\) 0 0
\(357\) −4.74183 −0.250964
\(358\) 0 0
\(359\) −26.1233 −1.37874 −0.689368 0.724411i \(-0.742112\pi\)
−0.689368 + 0.724411i \(0.742112\pi\)
\(360\) 0 0
\(361\) −15.6925 −0.825919
\(362\) 0 0
\(363\) 22.9348 1.20376
\(364\) 0 0
\(365\) −5.90736 −0.309205
\(366\) 0 0
\(367\) 8.97620 0.468554 0.234277 0.972170i \(-0.424728\pi\)
0.234277 + 0.972170i \(0.424728\pi\)
\(368\) 0 0
\(369\) −11.7870 −0.613607
\(370\) 0 0
\(371\) 7.84460 0.407271
\(372\) 0 0
\(373\) −14.7106 −0.761688 −0.380844 0.924639i \(-0.624367\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(374\) 0 0
\(375\) −12.8373 −0.662917
\(376\) 0 0
\(377\) −61.4966 −3.16723
\(378\) 0 0
\(379\) 23.1235 1.18777 0.593886 0.804549i \(-0.297593\pi\)
0.593886 + 0.804549i \(0.297593\pi\)
\(380\) 0 0
\(381\) −6.18745 −0.316993
\(382\) 0 0
\(383\) 8.17455 0.417700 0.208850 0.977948i \(-0.433028\pi\)
0.208850 + 0.977948i \(0.433028\pi\)
\(384\) 0 0
\(385\) 0.0496726 0.00253155
\(386\) 0 0
\(387\) −3.79875 −0.193101
\(388\) 0 0
\(389\) −10.7191 −0.543480 −0.271740 0.962371i \(-0.587599\pi\)
−0.271740 + 0.962371i \(0.587599\pi\)
\(390\) 0 0
\(391\) 0.135977 0.00687664
\(392\) 0 0
\(393\) 23.7979 1.20045
\(394\) 0 0
\(395\) 6.36838 0.320428
\(396\) 0 0
\(397\) −23.2188 −1.16532 −0.582658 0.812717i \(-0.697987\pi\)
−0.582658 + 0.812717i \(0.697987\pi\)
\(398\) 0 0
\(399\) 5.84558 0.292645
\(400\) 0 0
\(401\) 5.80075 0.289676 0.144838 0.989455i \(-0.453734\pi\)
0.144838 + 0.989455i \(0.453734\pi\)
\(402\) 0 0
\(403\) −5.10770 −0.254433
\(404\) 0 0
\(405\) 7.20822 0.358179
\(406\) 0 0
\(407\) 0.353885 0.0175414
\(408\) 0 0
\(409\) 33.4473 1.65386 0.826931 0.562304i \(-0.190085\pi\)
0.826931 + 0.562304i \(0.190085\pi\)
\(410\) 0 0
\(411\) −11.2989 −0.557336
\(412\) 0 0
\(413\) 6.59908 0.324720
\(414\) 0 0
\(415\) −10.5251 −0.516658
\(416\) 0 0
\(417\) 40.4684 1.98175
\(418\) 0 0
\(419\) 19.7263 0.963691 0.481846 0.876256i \(-0.339967\pi\)
0.481846 + 0.876256i \(0.339967\pi\)
\(420\) 0 0
\(421\) −19.8019 −0.965086 −0.482543 0.875872i \(-0.660287\pi\)
−0.482543 + 0.875872i \(0.660287\pi\)
\(422\) 0 0
\(423\) 15.1612 0.737161
\(424\) 0 0
\(425\) −6.76823 −0.328307
\(426\) 0 0
\(427\) 21.1781 1.02488
\(428\) 0 0
\(429\) 0.618765 0.0298743
\(430\) 0 0
\(431\) −2.65053 −0.127672 −0.0638358 0.997960i \(-0.520333\pi\)
−0.0638358 + 0.997960i \(0.520333\pi\)
\(432\) 0 0
\(433\) −16.1746 −0.777303 −0.388651 0.921385i \(-0.627059\pi\)
−0.388651 + 0.921385i \(0.627059\pi\)
\(434\) 0 0
\(435\) −13.9306 −0.667920
\(436\) 0 0
\(437\) −0.167628 −0.00801873
\(438\) 0 0
\(439\) 8.28436 0.395391 0.197695 0.980263i \(-0.436654\pi\)
0.197695 + 0.980263i \(0.436654\pi\)
\(440\) 0 0
\(441\) −6.23908 −0.297099
\(442\) 0 0
\(443\) −8.99960 −0.427584 −0.213792 0.976879i \(-0.568581\pi\)
−0.213792 + 0.976879i \(0.568581\pi\)
\(444\) 0 0
\(445\) −1.03208 −0.0489255
\(446\) 0 0
\(447\) 33.5756 1.58807
\(448\) 0 0
\(449\) 5.80196 0.273811 0.136906 0.990584i \(-0.456284\pi\)
0.136906 + 0.990584i \(0.456284\pi\)
\(450\) 0 0
\(451\) 0.438570 0.0206514
\(452\) 0 0
\(453\) 6.81816 0.320345
\(454\) 0 0
\(455\) −5.84880 −0.274196
\(456\) 0 0
\(457\) −12.2264 −0.571928 −0.285964 0.958240i \(-0.592314\pi\)
−0.285964 + 0.958240i \(0.592314\pi\)
\(458\) 0 0
\(459\) 5.07909 0.237072
\(460\) 0 0
\(461\) −8.32633 −0.387796 −0.193898 0.981022i \(-0.562113\pi\)
−0.193898 + 0.981022i \(0.562113\pi\)
\(462\) 0 0
\(463\) 23.7604 1.10424 0.552120 0.833765i \(-0.313819\pi\)
0.552120 + 0.833765i \(0.313819\pi\)
\(464\) 0 0
\(465\) −1.15703 −0.0536559
\(466\) 0 0
\(467\) −8.21135 −0.379976 −0.189988 0.981786i \(-0.560845\pi\)
−0.189988 + 0.981786i \(0.560845\pi\)
\(468\) 0 0
\(469\) −10.6684 −0.492619
\(470\) 0 0
\(471\) 27.0510 1.24644
\(472\) 0 0
\(473\) 0.141343 0.00649898
\(474\) 0 0
\(475\) 8.34366 0.382834
\(476\) 0 0
\(477\) 6.86671 0.314405
\(478\) 0 0
\(479\) −5.98344 −0.273390 −0.136695 0.990613i \(-0.543648\pi\)
−0.136695 + 0.990613i \(0.543648\pi\)
\(480\) 0 0
\(481\) −41.6689 −1.89994
\(482\) 0 0
\(483\) −0.296257 −0.0134802
\(484\) 0 0
\(485\) 2.26769 0.102971
\(486\) 0 0
\(487\) −24.7539 −1.12170 −0.560852 0.827916i \(-0.689526\pi\)
−0.560852 + 0.827916i \(0.689526\pi\)
\(488\) 0 0
\(489\) 29.2019 1.32055
\(490\) 0 0
\(491\) −28.2139 −1.27328 −0.636638 0.771163i \(-0.719676\pi\)
−0.636638 + 0.771163i \(0.719676\pi\)
\(492\) 0 0
\(493\) −15.3492 −0.691291
\(494\) 0 0
\(495\) 0.0434805 0.00195430
\(496\) 0 0
\(497\) 10.7219 0.480944
\(498\) 0 0
\(499\) 32.9382 1.47452 0.737258 0.675611i \(-0.236120\pi\)
0.737258 + 0.675611i \(0.236120\pi\)
\(500\) 0 0
\(501\) −10.4396 −0.466409
\(502\) 0 0
\(503\) 4.83380 0.215529 0.107764 0.994176i \(-0.465631\pi\)
0.107764 + 0.994176i \(0.465631\pi\)
\(504\) 0 0
\(505\) 6.05681 0.269525
\(506\) 0 0
\(507\) −45.7469 −2.03169
\(508\) 0 0
\(509\) −17.3878 −0.770701 −0.385350 0.922770i \(-0.625919\pi\)
−0.385350 + 0.922770i \(0.625919\pi\)
\(510\) 0 0
\(511\) 14.1812 0.627339
\(512\) 0 0
\(513\) −6.26134 −0.276445
\(514\) 0 0
\(515\) −6.79884 −0.299593
\(516\) 0 0
\(517\) −0.564115 −0.0248098
\(518\) 0 0
\(519\) 17.5378 0.769826
\(520\) 0 0
\(521\) −39.4075 −1.72647 −0.863236 0.504800i \(-0.831566\pi\)
−0.863236 + 0.504800i \(0.831566\pi\)
\(522\) 0 0
\(523\) 17.0790 0.746811 0.373406 0.927668i \(-0.378190\pi\)
0.373406 + 0.927668i \(0.378190\pi\)
\(524\) 0 0
\(525\) 14.7462 0.643576
\(526\) 0 0
\(527\) −1.27485 −0.0555334
\(528\) 0 0
\(529\) −22.9915 −0.999631
\(530\) 0 0
\(531\) 5.77645 0.250677
\(532\) 0 0
\(533\) −51.6403 −2.23679
\(534\) 0 0
\(535\) 4.09240 0.176930
\(536\) 0 0
\(537\) −6.96611 −0.300610
\(538\) 0 0
\(539\) 0.232143 0.00999911
\(540\) 0 0
\(541\) −40.5944 −1.74529 −0.872645 0.488356i \(-0.837597\pi\)
−0.872645 + 0.488356i \(0.837597\pi\)
\(542\) 0 0
\(543\) 35.6863 1.53144
\(544\) 0 0
\(545\) 2.47264 0.105916
\(546\) 0 0
\(547\) −21.9615 −0.939008 −0.469504 0.882930i \(-0.655567\pi\)
−0.469504 + 0.882930i \(0.655567\pi\)
\(548\) 0 0
\(549\) 18.5381 0.791186
\(550\) 0 0
\(551\) 18.9220 0.806102
\(552\) 0 0
\(553\) −15.2879 −0.650109
\(554\) 0 0
\(555\) −9.43909 −0.400667
\(556\) 0 0
\(557\) 40.0017 1.69493 0.847464 0.530853i \(-0.178128\pi\)
0.847464 + 0.530853i \(0.178128\pi\)
\(558\) 0 0
\(559\) −16.6428 −0.703914
\(560\) 0 0
\(561\) 0.154440 0.00652046
\(562\) 0 0
\(563\) 7.22300 0.304413 0.152206 0.988349i \(-0.451362\pi\)
0.152206 + 0.988349i \(0.451362\pi\)
\(564\) 0 0
\(565\) −3.03399 −0.127641
\(566\) 0 0
\(567\) −17.3040 −0.726701
\(568\) 0 0
\(569\) −40.0952 −1.68088 −0.840438 0.541907i \(-0.817702\pi\)
−0.840438 + 0.541907i \(0.817702\pi\)
\(570\) 0 0
\(571\) −38.3778 −1.60606 −0.803030 0.595939i \(-0.796780\pi\)
−0.803030 + 0.595939i \(0.796780\pi\)
\(572\) 0 0
\(573\) −52.9555 −2.21225
\(574\) 0 0
\(575\) −0.422861 −0.0176345
\(576\) 0 0
\(577\) 37.0470 1.54229 0.771143 0.636662i \(-0.219685\pi\)
0.771143 + 0.636662i \(0.219685\pi\)
\(578\) 0 0
\(579\) −0.0990796 −0.00411761
\(580\) 0 0
\(581\) 25.2666 1.04823
\(582\) 0 0
\(583\) −0.255496 −0.0105816
\(584\) 0 0
\(585\) −5.11970 −0.211674
\(586\) 0 0
\(587\) 11.3856 0.469935 0.234967 0.972003i \(-0.424502\pi\)
0.234967 + 0.972003i \(0.424502\pi\)
\(588\) 0 0
\(589\) 1.57160 0.0647565
\(590\) 0 0
\(591\) −28.8865 −1.18823
\(592\) 0 0
\(593\) −17.1895 −0.705890 −0.352945 0.935644i \(-0.614820\pi\)
−0.352945 + 0.935644i \(0.614820\pi\)
\(594\) 0 0
\(595\) −1.45982 −0.0598469
\(596\) 0 0
\(597\) 6.75233 0.276354
\(598\) 0 0
\(599\) 8.96812 0.366428 0.183214 0.983073i \(-0.441350\pi\)
0.183214 + 0.983073i \(0.441350\pi\)
\(600\) 0 0
\(601\) 23.4485 0.956485 0.478242 0.878228i \(-0.341274\pi\)
0.478242 + 0.878228i \(0.341274\pi\)
\(602\) 0 0
\(603\) −9.33846 −0.380292
\(604\) 0 0
\(605\) 7.06071 0.287058
\(606\) 0 0
\(607\) −10.5102 −0.426595 −0.213298 0.976987i \(-0.568420\pi\)
−0.213298 + 0.976987i \(0.568420\pi\)
\(608\) 0 0
\(609\) 33.4417 1.35513
\(610\) 0 0
\(611\) 66.4229 2.68718
\(612\) 0 0
\(613\) 9.85872 0.398190 0.199095 0.979980i \(-0.436200\pi\)
0.199095 + 0.979980i \(0.436200\pi\)
\(614\) 0 0
\(615\) −11.6979 −0.471704
\(616\) 0 0
\(617\) 14.0795 0.566819 0.283409 0.958999i \(-0.408534\pi\)
0.283409 + 0.958999i \(0.408534\pi\)
\(618\) 0 0
\(619\) 29.0924 1.16932 0.584660 0.811278i \(-0.301228\pi\)
0.584660 + 0.811278i \(0.301228\pi\)
\(620\) 0 0
\(621\) 0.317328 0.0127339
\(622\) 0 0
\(623\) 2.47762 0.0992637
\(624\) 0 0
\(625\) 18.9869 0.759475
\(626\) 0 0
\(627\) −0.190389 −0.00760339
\(628\) 0 0
\(629\) −10.4003 −0.414687
\(630\) 0 0
\(631\) −8.88008 −0.353511 −0.176755 0.984255i \(-0.556560\pi\)
−0.176755 + 0.984255i \(0.556560\pi\)
\(632\) 0 0
\(633\) 40.6001 1.61371
\(634\) 0 0
\(635\) −1.90487 −0.0755925
\(636\) 0 0
\(637\) −27.3341 −1.08302
\(638\) 0 0
\(639\) 9.38535 0.371279
\(640\) 0 0
\(641\) −26.6249 −1.05162 −0.525810 0.850602i \(-0.676238\pi\)
−0.525810 + 0.850602i \(0.676238\pi\)
\(642\) 0 0
\(643\) −24.1245 −0.951379 −0.475689 0.879613i \(-0.657801\pi\)
−0.475689 + 0.879613i \(0.657801\pi\)
\(644\) 0 0
\(645\) −3.77002 −0.148444
\(646\) 0 0
\(647\) 6.26986 0.246493 0.123247 0.992376i \(-0.460669\pi\)
0.123247 + 0.992376i \(0.460669\pi\)
\(648\) 0 0
\(649\) −0.214930 −0.00843673
\(650\) 0 0
\(651\) 2.77756 0.108861
\(652\) 0 0
\(653\) 12.8395 0.502448 0.251224 0.967929i \(-0.419167\pi\)
0.251224 + 0.967929i \(0.419167\pi\)
\(654\) 0 0
\(655\) 7.32644 0.286268
\(656\) 0 0
\(657\) 12.4134 0.484293
\(658\) 0 0
\(659\) −49.1704 −1.91541 −0.957703 0.287758i \(-0.907090\pi\)
−0.957703 + 0.287758i \(0.907090\pi\)
\(660\) 0 0
\(661\) −32.6539 −1.27009 −0.635045 0.772475i \(-0.719019\pi\)
−0.635045 + 0.772475i \(0.719019\pi\)
\(662\) 0 0
\(663\) −18.1848 −0.706241
\(664\) 0 0
\(665\) 1.79962 0.0697864
\(666\) 0 0
\(667\) −0.958975 −0.0371317
\(668\) 0 0
\(669\) −6.06058 −0.234316
\(670\) 0 0
\(671\) −0.689763 −0.0266280
\(672\) 0 0
\(673\) −31.7798 −1.22502 −0.612511 0.790462i \(-0.709840\pi\)
−0.612511 + 0.790462i \(0.709840\pi\)
\(674\) 0 0
\(675\) −15.7950 −0.607949
\(676\) 0 0
\(677\) −27.5105 −1.05732 −0.528658 0.848835i \(-0.677305\pi\)
−0.528658 + 0.848835i \(0.677305\pi\)
\(678\) 0 0
\(679\) −5.44382 −0.208915
\(680\) 0 0
\(681\) 6.32614 0.242418
\(682\) 0 0
\(683\) −31.8314 −1.21799 −0.608997 0.793173i \(-0.708428\pi\)
−0.608997 + 0.793173i \(0.708428\pi\)
\(684\) 0 0
\(685\) −3.47850 −0.132907
\(686\) 0 0
\(687\) 39.2937 1.49915
\(688\) 0 0
\(689\) 30.0839 1.14610
\(690\) 0 0
\(691\) −18.6656 −0.710074 −0.355037 0.934852i \(-0.615532\pi\)
−0.355037 + 0.934852i \(0.615532\pi\)
\(692\) 0 0
\(693\) −0.104379 −0.00396504
\(694\) 0 0
\(695\) 12.4586 0.472583
\(696\) 0 0
\(697\) −12.8891 −0.488209
\(698\) 0 0
\(699\) 2.47967 0.0937897
\(700\) 0 0
\(701\) 41.8342 1.58006 0.790029 0.613070i \(-0.210066\pi\)
0.790029 + 0.613070i \(0.210066\pi\)
\(702\) 0 0
\(703\) 12.8211 0.483559
\(704\) 0 0
\(705\) 15.0465 0.566685
\(706\) 0 0
\(707\) −14.5400 −0.546832
\(708\) 0 0
\(709\) 36.1050 1.35595 0.677976 0.735084i \(-0.262857\pi\)
0.677976 + 0.735084i \(0.262857\pi\)
\(710\) 0 0
\(711\) −13.3822 −0.501871
\(712\) 0 0
\(713\) −0.0796493 −0.00298289
\(714\) 0 0
\(715\) 0.190493 0.00712405
\(716\) 0 0
\(717\) 12.9837 0.484886
\(718\) 0 0
\(719\) −50.8607 −1.89678 −0.948392 0.317101i \(-0.897291\pi\)
−0.948392 + 0.317101i \(0.897291\pi\)
\(720\) 0 0
\(721\) 16.3213 0.607836
\(722\) 0 0
\(723\) −23.3375 −0.867932
\(724\) 0 0
\(725\) 47.7329 1.77276
\(726\) 0 0
\(727\) −7.40123 −0.274497 −0.137248 0.990537i \(-0.543826\pi\)
−0.137248 + 0.990537i \(0.543826\pi\)
\(728\) 0 0
\(729\) 6.39263 0.236764
\(730\) 0 0
\(731\) −4.15393 −0.153639
\(732\) 0 0
\(733\) −7.86308 −0.290430 −0.145215 0.989400i \(-0.546387\pi\)
−0.145215 + 0.989400i \(0.546387\pi\)
\(734\) 0 0
\(735\) −6.19190 −0.228392
\(736\) 0 0
\(737\) 0.347465 0.0127990
\(738\) 0 0
\(739\) −10.7204 −0.394357 −0.197179 0.980368i \(-0.563178\pi\)
−0.197179 + 0.980368i \(0.563178\pi\)
\(740\) 0 0
\(741\) 22.4177 0.823535
\(742\) 0 0
\(743\) 48.6548 1.78497 0.892485 0.451077i \(-0.148960\pi\)
0.892485 + 0.451077i \(0.148960\pi\)
\(744\) 0 0
\(745\) 10.3366 0.378703
\(746\) 0 0
\(747\) 22.1169 0.809216
\(748\) 0 0
\(749\) −9.82421 −0.358969
\(750\) 0 0
\(751\) 1.00000 0.0364905
\(752\) 0 0
\(753\) 8.49914 0.309726
\(754\) 0 0
\(755\) 2.09904 0.0763920
\(756\) 0 0
\(757\) −15.0966 −0.548695 −0.274347 0.961631i \(-0.588462\pi\)
−0.274347 + 0.961631i \(0.588462\pi\)
\(758\) 0 0
\(759\) 0.00964900 0.000350237 0
\(760\) 0 0
\(761\) 25.7099 0.931982 0.465991 0.884789i \(-0.345698\pi\)
0.465991 + 0.884789i \(0.345698\pi\)
\(762\) 0 0
\(763\) −5.93583 −0.214891
\(764\) 0 0
\(765\) −1.27785 −0.0462006
\(766\) 0 0
\(767\) 25.3073 0.913795
\(768\) 0 0
\(769\) 25.1074 0.905397 0.452699 0.891664i \(-0.350461\pi\)
0.452699 + 0.891664i \(0.350461\pi\)
\(770\) 0 0
\(771\) 43.7519 1.57569
\(772\) 0 0
\(773\) −21.2918 −0.765814 −0.382907 0.923787i \(-0.625077\pi\)
−0.382907 + 0.923787i \(0.625077\pi\)
\(774\) 0 0
\(775\) 3.96454 0.142410
\(776\) 0 0
\(777\) 22.6595 0.812904
\(778\) 0 0
\(779\) 15.8893 0.569292
\(780\) 0 0
\(781\) −0.349209 −0.0124957
\(782\) 0 0
\(783\) −35.8202 −1.28011
\(784\) 0 0
\(785\) 8.32792 0.297236
\(786\) 0 0
\(787\) 52.5407 1.87287 0.936436 0.350838i \(-0.114103\pi\)
0.936436 + 0.350838i \(0.114103\pi\)
\(788\) 0 0
\(789\) −47.7887 −1.70132
\(790\) 0 0
\(791\) 7.28339 0.258968
\(792\) 0 0
\(793\) 81.2175 2.88412
\(794\) 0 0
\(795\) 6.81479 0.241696
\(796\) 0 0
\(797\) 15.2143 0.538917 0.269459 0.963012i \(-0.413155\pi\)
0.269459 + 0.963012i \(0.413155\pi\)
\(798\) 0 0
\(799\) 16.5787 0.586513
\(800\) 0 0
\(801\) 2.16877 0.0766296
\(802\) 0 0
\(803\) −0.461876 −0.0162993
\(804\) 0 0
\(805\) −0.0912059 −0.00321459
\(806\) 0 0
\(807\) −19.7174 −0.694087
\(808\) 0 0
\(809\) 36.6243 1.28764 0.643822 0.765176i \(-0.277348\pi\)
0.643822 + 0.765176i \(0.277348\pi\)
\(810\) 0 0
\(811\) −27.4004 −0.962160 −0.481080 0.876677i \(-0.659755\pi\)
−0.481080 + 0.876677i \(0.659755\pi\)
\(812\) 0 0
\(813\) −57.7352 −2.02486
\(814\) 0 0
\(815\) 8.99010 0.314910
\(816\) 0 0
\(817\) 5.12083 0.179155
\(818\) 0 0
\(819\) 12.2904 0.429460
\(820\) 0 0
\(821\) −29.4789 −1.02882 −0.514411 0.857544i \(-0.671989\pi\)
−0.514411 + 0.857544i \(0.671989\pi\)
\(822\) 0 0
\(823\) −34.7350 −1.21079 −0.605393 0.795926i \(-0.706984\pi\)
−0.605393 + 0.795926i \(0.706984\pi\)
\(824\) 0 0
\(825\) −0.480278 −0.0167211
\(826\) 0 0
\(827\) 7.67951 0.267043 0.133521 0.991046i \(-0.457372\pi\)
0.133521 + 0.991046i \(0.457372\pi\)
\(828\) 0 0
\(829\) 33.3990 1.15999 0.579997 0.814618i \(-0.303054\pi\)
0.579997 + 0.814618i \(0.303054\pi\)
\(830\) 0 0
\(831\) 11.6314 0.403490
\(832\) 0 0
\(833\) −6.82243 −0.236383
\(834\) 0 0
\(835\) −3.21395 −0.111223
\(836\) 0 0
\(837\) −2.97511 −0.102835
\(838\) 0 0
\(839\) −26.4432 −0.912922 −0.456461 0.889743i \(-0.650883\pi\)
−0.456461 + 0.889743i \(0.650883\pi\)
\(840\) 0 0
\(841\) 79.2498 2.73275
\(842\) 0 0
\(843\) 46.2371 1.59249
\(844\) 0 0
\(845\) −14.0836 −0.484492
\(846\) 0 0
\(847\) −16.9499 −0.582406
\(848\) 0 0
\(849\) −27.0953 −0.929909
\(850\) 0 0
\(851\) −0.649783 −0.0222743
\(852\) 0 0
\(853\) −3.50180 −0.119899 −0.0599497 0.998201i \(-0.519094\pi\)
−0.0599497 + 0.998201i \(0.519094\pi\)
\(854\) 0 0
\(855\) 1.57529 0.0538737
\(856\) 0 0
\(857\) 27.3142 0.933037 0.466518 0.884512i \(-0.345508\pi\)
0.466518 + 0.884512i \(0.345508\pi\)
\(858\) 0 0
\(859\) −35.8721 −1.22394 −0.611970 0.790881i \(-0.709623\pi\)
−0.611970 + 0.790881i \(0.709623\pi\)
\(860\) 0 0
\(861\) 28.0819 0.957029
\(862\) 0 0
\(863\) 41.2786 1.40514 0.702570 0.711615i \(-0.252036\pi\)
0.702570 + 0.711615i \(0.252036\pi\)
\(864\) 0 0
\(865\) 5.39921 0.183579
\(866\) 0 0
\(867\) 30.9139 1.04989
\(868\) 0 0
\(869\) 0.497923 0.0168909
\(870\) 0 0
\(871\) −40.9129 −1.38628
\(872\) 0 0
\(873\) −4.76521 −0.161278
\(874\) 0 0
\(875\) 9.48742 0.320733
\(876\) 0 0
\(877\) 20.1733 0.681203 0.340602 0.940208i \(-0.389369\pi\)
0.340602 + 0.940208i \(0.389369\pi\)
\(878\) 0 0
\(879\) −33.3766 −1.12577
\(880\) 0 0
\(881\) −19.4979 −0.656901 −0.328451 0.944521i \(-0.606526\pi\)
−0.328451 + 0.944521i \(0.606526\pi\)
\(882\) 0 0
\(883\) 15.4599 0.520267 0.260133 0.965573i \(-0.416233\pi\)
0.260133 + 0.965573i \(0.416233\pi\)
\(884\) 0 0
\(885\) 5.73277 0.192705
\(886\) 0 0
\(887\) 2.30232 0.0773042 0.0386521 0.999253i \(-0.487694\pi\)
0.0386521 + 0.999253i \(0.487694\pi\)
\(888\) 0 0
\(889\) 4.57283 0.153368
\(890\) 0 0
\(891\) 0.563586 0.0188809
\(892\) 0 0
\(893\) −20.4377 −0.683923
\(894\) 0 0
\(895\) −2.14459 −0.0716857
\(896\) 0 0
\(897\) −1.13614 −0.0379346
\(898\) 0 0
\(899\) 8.99087 0.299862
\(900\) 0 0
\(901\) 7.50874 0.250153
\(902\) 0 0
\(903\) 9.05031 0.301175
\(904\) 0 0
\(905\) 10.9864 0.365200
\(906\) 0 0
\(907\) −37.0716 −1.23094 −0.615471 0.788159i \(-0.711034\pi\)
−0.615471 + 0.788159i \(0.711034\pi\)
\(908\) 0 0
\(909\) −12.7275 −0.422143
\(910\) 0 0
\(911\) 15.9981 0.530040 0.265020 0.964243i \(-0.414621\pi\)
0.265020 + 0.964243i \(0.414621\pi\)
\(912\) 0 0
\(913\) −0.822924 −0.0272348
\(914\) 0 0
\(915\) 18.3979 0.608216
\(916\) 0 0
\(917\) −17.5878 −0.580802
\(918\) 0 0
\(919\) −1.52056 −0.0501586 −0.0250793 0.999685i \(-0.507984\pi\)
−0.0250793 + 0.999685i \(0.507984\pi\)
\(920\) 0 0
\(921\) 63.8266 2.10316
\(922\) 0 0
\(923\) 41.1183 1.35343
\(924\) 0 0
\(925\) 32.3429 1.06343
\(926\) 0 0
\(927\) 14.2867 0.469237
\(928\) 0 0
\(929\) −27.7168 −0.909359 −0.454680 0.890655i \(-0.650246\pi\)
−0.454680 + 0.890655i \(0.650246\pi\)
\(930\) 0 0
\(931\) 8.41047 0.275642
\(932\) 0 0
\(933\) 2.44930 0.0801864
\(934\) 0 0
\(935\) 0.0475459 0.00155492
\(936\) 0 0
\(937\) −48.8797 −1.59683 −0.798415 0.602108i \(-0.794328\pi\)
−0.798415 + 0.602108i \(0.794328\pi\)
\(938\) 0 0
\(939\) 57.0303 1.86111
\(940\) 0 0
\(941\) −52.7097 −1.71829 −0.859144 0.511734i \(-0.829003\pi\)
−0.859144 + 0.511734i \(0.829003\pi\)
\(942\) 0 0
\(943\) −0.805276 −0.0262234
\(944\) 0 0
\(945\) −3.40678 −0.110823
\(946\) 0 0
\(947\) 39.9828 1.29927 0.649634 0.760247i \(-0.274922\pi\)
0.649634 + 0.760247i \(0.274922\pi\)
\(948\) 0 0
\(949\) 54.3846 1.76540
\(950\) 0 0
\(951\) 24.3657 0.790113
\(952\) 0 0
\(953\) 25.7459 0.833993 0.416996 0.908908i \(-0.363083\pi\)
0.416996 + 0.908908i \(0.363083\pi\)
\(954\) 0 0
\(955\) −16.3029 −0.527550
\(956\) 0 0
\(957\) −1.08919 −0.0352084
\(958\) 0 0
\(959\) 8.35048 0.269651
\(960\) 0 0
\(961\) −30.2532 −0.975911
\(962\) 0 0
\(963\) −8.59954 −0.277116
\(964\) 0 0
\(965\) −0.0305027 −0.000981916 0
\(966\) 0 0
\(967\) 4.22972 0.136019 0.0680093 0.997685i \(-0.478335\pi\)
0.0680093 + 0.997685i \(0.478335\pi\)
\(968\) 0 0
\(969\) 5.59531 0.179747
\(970\) 0 0
\(971\) −30.5328 −0.979843 −0.489922 0.871767i \(-0.662975\pi\)
−0.489922 + 0.871767i \(0.662975\pi\)
\(972\) 0 0
\(973\) −29.9082 −0.958812
\(974\) 0 0
\(975\) 56.5513 1.81109
\(976\) 0 0
\(977\) −31.0283 −0.992682 −0.496341 0.868128i \(-0.665324\pi\)
−0.496341 + 0.868128i \(0.665324\pi\)
\(978\) 0 0
\(979\) −0.0806952 −0.00257903
\(980\) 0 0
\(981\) −5.19588 −0.165892
\(982\) 0 0
\(983\) −22.0224 −0.702407 −0.351203 0.936299i \(-0.614227\pi\)
−0.351203 + 0.936299i \(0.614227\pi\)
\(984\) 0 0
\(985\) −8.89302 −0.283355
\(986\) 0 0
\(987\) −36.1206 −1.14973
\(988\) 0 0
\(989\) −0.259526 −0.00825246
\(990\) 0 0
\(991\) 4.40511 0.139933 0.0699665 0.997549i \(-0.477711\pi\)
0.0699665 + 0.997549i \(0.477711\pi\)
\(992\) 0 0
\(993\) 54.1184 1.71739
\(994\) 0 0
\(995\) 2.07877 0.0659016
\(996\) 0 0
\(997\) −10.6821 −0.338305 −0.169153 0.985590i \(-0.554103\pi\)
−0.169153 + 0.985590i \(0.554103\pi\)
\(998\) 0 0
\(999\) −24.2711 −0.767904
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 6008.2.a.c.1.10 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.c.1.10 44 1.1 even 1 trivial