Properties

Label 3800.2.a.bb.1.1
Level $3800$
Weight $2$
Character 3800.1
Self dual yes
Analytic conductor $30.343$
Analytic rank $0$
Dimension $6$
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] = [3800,2,Mod(1,3800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("3800.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.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: \(30.3431527681\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 12x^{4} + 16x^{3} + 33x^{2} - 4x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.30105\) of defining polynomial
Character \(\chi\) \(=\) 3800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.30105 q^{3} +1.63094 q^{7} +7.89694 q^{9} +O(q^{10})\) \(q-3.30105 q^{3} +1.63094 q^{7} +7.89694 q^{9} -4.67473 q^{11} -4.75288 q^{13} -1.41425 q^{17} +1.00000 q^{19} -5.38382 q^{21} -1.96494 q^{23} -16.1650 q^{27} +6.85936 q^{29} +5.08277 q^{31} +15.4315 q^{33} +10.6081 q^{37} +15.6895 q^{39} -4.52536 q^{41} -7.83425 q^{43} -10.9382 q^{47} -4.34003 q^{49} +4.66852 q^{51} -1.55831 q^{53} -3.30105 q^{57} -6.81879 q^{59} -0.109000 q^{61} +12.8794 q^{63} -10.5615 q^{67} +6.48638 q^{69} +12.7070 q^{71} +0.519837 q^{73} -7.62422 q^{77} +0.840485 q^{79} +29.6708 q^{81} +11.9407 q^{83} -22.6431 q^{87} -7.44352 q^{89} -7.75167 q^{91} -16.7785 q^{93} +8.85637 q^{97} -36.9161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} - 2 q^{7} + 10 q^{9} + 3 q^{11} + 3 q^{13} + 2 q^{17} + 6 q^{19} + 11 q^{21} - 4 q^{23} - 20 q^{27} + 7 q^{29} + 5 q^{31} + 16 q^{33} + 8 q^{39} + 11 q^{41} + 7 q^{43} - 20 q^{47} - 2 q^{49} + 13 q^{51} + 7 q^{53} - 2 q^{57} - 4 q^{59} + 13 q^{61} + q^{63} - 25 q^{67} + 7 q^{69} + 29 q^{71} + 19 q^{73} - 24 q^{77} + 28 q^{79} + 38 q^{81} + 15 q^{83} - 57 q^{87} - 12 q^{89} + 27 q^{93} + 13 q^{97} + 10 q^{99}+O(q^{100}) \) 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
\(3\) −3.30105 −1.90586 −0.952931 0.303186i \(-0.901950\pi\)
−0.952931 + 0.303186i \(0.901950\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.63094 0.616438 0.308219 0.951315i \(-0.400267\pi\)
0.308219 + 0.951315i \(0.400267\pi\)
\(8\) 0 0
\(9\) 7.89694 2.63231
\(10\) 0 0
\(11\) −4.67473 −1.40949 −0.704743 0.709463i \(-0.748938\pi\)
−0.704743 + 0.709463i \(0.748938\pi\)
\(12\) 0 0
\(13\) −4.75288 −1.31821 −0.659106 0.752050i \(-0.729065\pi\)
−0.659106 + 0.752050i \(0.729065\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.41425 −0.343007 −0.171503 0.985184i \(-0.554862\pi\)
−0.171503 + 0.985184i \(0.554862\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −5.38382 −1.17485
\(22\) 0 0
\(23\) −1.96494 −0.409719 −0.204860 0.978791i \(-0.565674\pi\)
−0.204860 + 0.978791i \(0.565674\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −16.1650 −3.11096
\(28\) 0 0
\(29\) 6.85936 1.27375 0.636876 0.770967i \(-0.280227\pi\)
0.636876 + 0.770967i \(0.280227\pi\)
\(30\) 0 0
\(31\) 5.08277 0.912893 0.456446 0.889751i \(-0.349122\pi\)
0.456446 + 0.889751i \(0.349122\pi\)
\(32\) 0 0
\(33\) 15.4315 2.68629
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.6081 1.74397 0.871983 0.489537i \(-0.162834\pi\)
0.871983 + 0.489537i \(0.162834\pi\)
\(38\) 0 0
\(39\) 15.6895 2.51233
\(40\) 0 0
\(41\) −4.52536 −0.706742 −0.353371 0.935483i \(-0.614965\pi\)
−0.353371 + 0.935483i \(0.614965\pi\)
\(42\) 0 0
\(43\) −7.83425 −1.19471 −0.597356 0.801976i \(-0.703782\pi\)
−0.597356 + 0.801976i \(0.703782\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.9382 −1.59550 −0.797751 0.602987i \(-0.793977\pi\)
−0.797751 + 0.602987i \(0.793977\pi\)
\(48\) 0 0
\(49\) −4.34003 −0.620004
\(50\) 0 0
\(51\) 4.66852 0.653723
\(52\) 0 0
\(53\) −1.55831 −0.214050 −0.107025 0.994256i \(-0.534133\pi\)
−0.107025 + 0.994256i \(0.534133\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.30105 −0.437235
\(58\) 0 0
\(59\) −6.81879 −0.887731 −0.443865 0.896093i \(-0.646393\pi\)
−0.443865 + 0.896093i \(0.646393\pi\)
\(60\) 0 0
\(61\) −0.109000 −0.0139561 −0.00697803 0.999976i \(-0.502221\pi\)
−0.00697803 + 0.999976i \(0.502221\pi\)
\(62\) 0 0
\(63\) 12.8794 1.62266
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10.5615 −1.29030 −0.645148 0.764057i \(-0.723204\pi\)
−0.645148 + 0.764057i \(0.723204\pi\)
\(68\) 0 0
\(69\) 6.48638 0.780868
\(70\) 0 0
\(71\) 12.7070 1.50804 0.754021 0.656850i \(-0.228112\pi\)
0.754021 + 0.656850i \(0.228112\pi\)
\(72\) 0 0
\(73\) 0.519837 0.0608423 0.0304211 0.999537i \(-0.490315\pi\)
0.0304211 + 0.999537i \(0.490315\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.62422 −0.868861
\(78\) 0 0
\(79\) 0.840485 0.0945620 0.0472810 0.998882i \(-0.484944\pi\)
0.0472810 + 0.998882i \(0.484944\pi\)
\(80\) 0 0
\(81\) 29.6708 3.29676
\(82\) 0 0
\(83\) 11.9407 1.31067 0.655333 0.755340i \(-0.272528\pi\)
0.655333 + 0.755340i \(0.272528\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −22.6431 −2.42759
\(88\) 0 0
\(89\) −7.44352 −0.789011 −0.394506 0.918894i \(-0.629084\pi\)
−0.394506 + 0.918894i \(0.629084\pi\)
\(90\) 0 0
\(91\) −7.75167 −0.812596
\(92\) 0 0
\(93\) −16.7785 −1.73985
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.85637 0.899228 0.449614 0.893223i \(-0.351562\pi\)
0.449614 + 0.893223i \(0.351562\pi\)
\(98\) 0 0
\(99\) −36.9161 −3.71021
\(100\) 0 0
\(101\) −12.9534 −1.28891 −0.644455 0.764642i \(-0.722916\pi\)
−0.644455 + 0.764642i \(0.722916\pi\)
\(102\) 0 0
\(103\) −3.16232 −0.311592 −0.155796 0.987789i \(-0.549794\pi\)
−0.155796 + 0.987789i \(0.549794\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.8458 −1.82189 −0.910946 0.412527i \(-0.864646\pi\)
−0.910946 + 0.412527i \(0.864646\pi\)
\(108\) 0 0
\(109\) 13.4693 1.29013 0.645063 0.764130i \(-0.276831\pi\)
0.645063 + 0.764130i \(0.276831\pi\)
\(110\) 0 0
\(111\) −35.0180 −3.32376
\(112\) 0 0
\(113\) 4.43245 0.416970 0.208485 0.978026i \(-0.433147\pi\)
0.208485 + 0.978026i \(0.433147\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −37.5332 −3.46994
\(118\) 0 0
\(119\) −2.30656 −0.211442
\(120\) 0 0
\(121\) 10.8531 0.986649
\(122\) 0 0
\(123\) 14.9384 1.34695
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −4.48637 −0.398101 −0.199051 0.979989i \(-0.563786\pi\)
−0.199051 + 0.979989i \(0.563786\pi\)
\(128\) 0 0
\(129\) 25.8613 2.27696
\(130\) 0 0
\(131\) −11.1275 −0.972211 −0.486105 0.873900i \(-0.661583\pi\)
−0.486105 + 0.873900i \(0.661583\pi\)
\(132\) 0 0
\(133\) 1.63094 0.141421
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.6851 1.68181 0.840904 0.541184i \(-0.182024\pi\)
0.840904 + 0.541184i \(0.182024\pi\)
\(138\) 0 0
\(139\) 9.15699 0.776686 0.388343 0.921515i \(-0.373048\pi\)
0.388343 + 0.921515i \(0.373048\pi\)
\(140\) 0 0
\(141\) 36.1076 3.04081
\(142\) 0 0
\(143\) 22.2185 1.85800
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 14.3267 1.18164
\(148\) 0 0
\(149\) 2.68165 0.219689 0.109845 0.993949i \(-0.464965\pi\)
0.109845 + 0.993949i \(0.464965\pi\)
\(150\) 0 0
\(151\) 18.6183 1.51513 0.757567 0.652758i \(-0.226388\pi\)
0.757567 + 0.652758i \(0.226388\pi\)
\(152\) 0 0
\(153\) −11.1683 −0.902900
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.33933 0.505934 0.252967 0.967475i \(-0.418594\pi\)
0.252967 + 0.967475i \(0.418594\pi\)
\(158\) 0 0
\(159\) 5.14406 0.407950
\(160\) 0 0
\(161\) −3.20471 −0.252566
\(162\) 0 0
\(163\) −13.4585 −1.05415 −0.527074 0.849819i \(-0.676711\pi\)
−0.527074 + 0.849819i \(0.676711\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.1325 1.01622 0.508112 0.861291i \(-0.330344\pi\)
0.508112 + 0.861291i \(0.330344\pi\)
\(168\) 0 0
\(169\) 9.58987 0.737682
\(170\) 0 0
\(171\) 7.89694 0.603894
\(172\) 0 0
\(173\) −0.857255 −0.0651759 −0.0325879 0.999469i \(-0.510375\pi\)
−0.0325879 + 0.999469i \(0.510375\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 22.5092 1.69189
\(178\) 0 0
\(179\) 8.93269 0.667661 0.333830 0.942633i \(-0.391659\pi\)
0.333830 + 0.942633i \(0.391659\pi\)
\(180\) 0 0
\(181\) −6.95157 −0.516706 −0.258353 0.966051i \(-0.583180\pi\)
−0.258353 + 0.966051i \(0.583180\pi\)
\(182\) 0 0
\(183\) 0.359816 0.0265983
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.61125 0.483463
\(188\) 0 0
\(189\) −26.3642 −1.91772
\(190\) 0 0
\(191\) 9.36170 0.677389 0.338695 0.940896i \(-0.390015\pi\)
0.338695 + 0.940896i \(0.390015\pi\)
\(192\) 0 0
\(193\) 26.7785 1.92756 0.963779 0.266703i \(-0.0859343\pi\)
0.963779 + 0.266703i \(0.0859343\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.92419 −0.279587 −0.139793 0.990181i \(-0.544644\pi\)
−0.139793 + 0.990181i \(0.544644\pi\)
\(198\) 0 0
\(199\) −7.52186 −0.533211 −0.266605 0.963806i \(-0.585902\pi\)
−0.266605 + 0.963806i \(0.585902\pi\)
\(200\) 0 0
\(201\) 34.8642 2.45913
\(202\) 0 0
\(203\) 11.1872 0.785189
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −15.5170 −1.07851
\(208\) 0 0
\(209\) −4.67473 −0.323358
\(210\) 0 0
\(211\) 9.97579 0.686761 0.343381 0.939196i \(-0.388428\pi\)
0.343381 + 0.939196i \(0.388428\pi\)
\(212\) 0 0
\(213\) −41.9464 −2.87412
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 8.28970 0.562742
\(218\) 0 0
\(219\) −1.71601 −0.115957
\(220\) 0 0
\(221\) 6.72177 0.452155
\(222\) 0 0
\(223\) 21.3953 1.43273 0.716367 0.697724i \(-0.245804\pi\)
0.716367 + 0.697724i \(0.245804\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.2964 1.34712 0.673560 0.739132i \(-0.264764\pi\)
0.673560 + 0.739132i \(0.264764\pi\)
\(228\) 0 0
\(229\) 19.9525 1.31850 0.659249 0.751925i \(-0.270874\pi\)
0.659249 + 0.751925i \(0.270874\pi\)
\(230\) 0 0
\(231\) 25.1679 1.65593
\(232\) 0 0
\(233\) −13.2102 −0.865431 −0.432715 0.901531i \(-0.642445\pi\)
−0.432715 + 0.901531i \(0.642445\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.77448 −0.180222
\(238\) 0 0
\(239\) 26.0537 1.68527 0.842636 0.538484i \(-0.181003\pi\)
0.842636 + 0.538484i \(0.181003\pi\)
\(240\) 0 0
\(241\) 2.12098 0.136624 0.0683122 0.997664i \(-0.478239\pi\)
0.0683122 + 0.997664i \(0.478239\pi\)
\(242\) 0 0
\(243\) −49.4497 −3.17220
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.75288 −0.302419
\(248\) 0 0
\(249\) −39.4170 −2.49795
\(250\) 0 0
\(251\) −14.8911 −0.939921 −0.469960 0.882688i \(-0.655732\pi\)
−0.469960 + 0.882688i \(0.655732\pi\)
\(252\) 0 0
\(253\) 9.18559 0.577493
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.91006 0.493416 0.246708 0.969090i \(-0.420651\pi\)
0.246708 + 0.969090i \(0.420651\pi\)
\(258\) 0 0
\(259\) 17.3012 1.07505
\(260\) 0 0
\(261\) 54.1679 3.35291
\(262\) 0 0
\(263\) 17.1828 1.05954 0.529768 0.848143i \(-0.322279\pi\)
0.529768 + 0.848143i \(0.322279\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 24.5714 1.50375
\(268\) 0 0
\(269\) −12.9237 −0.787972 −0.393986 0.919116i \(-0.628904\pi\)
−0.393986 + 0.919116i \(0.628904\pi\)
\(270\) 0 0
\(271\) −20.9897 −1.27503 −0.637515 0.770438i \(-0.720038\pi\)
−0.637515 + 0.770438i \(0.720038\pi\)
\(272\) 0 0
\(273\) 25.5887 1.54870
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 6.27361 0.376945 0.188472 0.982078i \(-0.439646\pi\)
0.188472 + 0.982078i \(0.439646\pi\)
\(278\) 0 0
\(279\) 40.1383 2.40302
\(280\) 0 0
\(281\) −28.7635 −1.71588 −0.857942 0.513747i \(-0.828257\pi\)
−0.857942 + 0.513747i \(0.828257\pi\)
\(282\) 0 0
\(283\) 28.0145 1.66529 0.832644 0.553808i \(-0.186826\pi\)
0.832644 + 0.553808i \(0.186826\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.38059 −0.435663
\(288\) 0 0
\(289\) −14.9999 −0.882346
\(290\) 0 0
\(291\) −29.2353 −1.71380
\(292\) 0 0
\(293\) 22.5521 1.31751 0.658753 0.752359i \(-0.271084\pi\)
0.658753 + 0.752359i \(0.271084\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 75.5673 4.38486
\(298\) 0 0
\(299\) 9.33914 0.540097
\(300\) 0 0
\(301\) −12.7772 −0.736466
\(302\) 0 0
\(303\) 42.7598 2.45649
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 14.5977 0.833137 0.416568 0.909104i \(-0.363233\pi\)
0.416568 + 0.909104i \(0.363233\pi\)
\(308\) 0 0
\(309\) 10.4390 0.593852
\(310\) 0 0
\(311\) 27.1608 1.54015 0.770074 0.637955i \(-0.220219\pi\)
0.770074 + 0.637955i \(0.220219\pi\)
\(312\) 0 0
\(313\) −28.3854 −1.60444 −0.802219 0.597030i \(-0.796347\pi\)
−0.802219 + 0.597030i \(0.796347\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.9910 1.17897 0.589485 0.807779i \(-0.299331\pi\)
0.589485 + 0.807779i \(0.299331\pi\)
\(318\) 0 0
\(319\) −32.0657 −1.79533
\(320\) 0 0
\(321\) 62.2109 3.47227
\(322\) 0 0
\(323\) −1.41425 −0.0786911
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −44.4629 −2.45880
\(328\) 0 0
\(329\) −17.8396 −0.983528
\(330\) 0 0
\(331\) −1.81631 −0.0998332 −0.0499166 0.998753i \(-0.515896\pi\)
−0.0499166 + 0.998753i \(0.515896\pi\)
\(332\) 0 0
\(333\) 83.7717 4.59066
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −25.6967 −1.39979 −0.699895 0.714245i \(-0.746770\pi\)
−0.699895 + 0.714245i \(0.746770\pi\)
\(338\) 0 0
\(339\) −14.6317 −0.794687
\(340\) 0 0
\(341\) −23.7606 −1.28671
\(342\) 0 0
\(343\) −18.4949 −0.998632
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.2851 0.605814 0.302907 0.953020i \(-0.402043\pi\)
0.302907 + 0.953020i \(0.402043\pi\)
\(348\) 0 0
\(349\) 3.62702 0.194150 0.0970750 0.995277i \(-0.469051\pi\)
0.0970750 + 0.995277i \(0.469051\pi\)
\(350\) 0 0
\(351\) 76.8305 4.10091
\(352\) 0 0
\(353\) 31.6766 1.68597 0.842987 0.537935i \(-0.180795\pi\)
0.842987 + 0.537935i \(0.180795\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.61408 0.402980
\(358\) 0 0
\(359\) −23.4772 −1.23908 −0.619539 0.784966i \(-0.712680\pi\)
−0.619539 + 0.784966i \(0.712680\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −35.8268 −1.88042
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 32.2584 1.68387 0.841937 0.539576i \(-0.181416\pi\)
0.841937 + 0.539576i \(0.181416\pi\)
\(368\) 0 0
\(369\) −35.7365 −1.86037
\(370\) 0 0
\(371\) −2.54151 −0.131949
\(372\) 0 0
\(373\) 21.5626 1.11647 0.558235 0.829683i \(-0.311479\pi\)
0.558235 + 0.829683i \(0.311479\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −32.6017 −1.67907
\(378\) 0 0
\(379\) 12.3881 0.636335 0.318168 0.948035i \(-0.396933\pi\)
0.318168 + 0.948035i \(0.396933\pi\)
\(380\) 0 0
\(381\) 14.8097 0.758726
\(382\) 0 0
\(383\) −6.64117 −0.339348 −0.169674 0.985500i \(-0.554271\pi\)
−0.169674 + 0.985500i \(0.554271\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −61.8666 −3.14485
\(388\) 0 0
\(389\) −10.0607 −0.510095 −0.255048 0.966928i \(-0.582091\pi\)
−0.255048 + 0.966928i \(0.582091\pi\)
\(390\) 0 0
\(391\) 2.77893 0.140536
\(392\) 0 0
\(393\) 36.7323 1.85290
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 6.64223 0.333364 0.166682 0.986011i \(-0.446695\pi\)
0.166682 + 0.986011i \(0.446695\pi\)
\(398\) 0 0
\(399\) −5.38382 −0.269528
\(400\) 0 0
\(401\) −16.4296 −0.820456 −0.410228 0.911983i \(-0.634551\pi\)
−0.410228 + 0.911983i \(0.634551\pi\)
\(402\) 0 0
\(403\) −24.1578 −1.20339
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −49.5902 −2.45809
\(408\) 0 0
\(409\) 32.6210 1.61300 0.806501 0.591232i \(-0.201358\pi\)
0.806501 + 0.591232i \(0.201358\pi\)
\(410\) 0 0
\(411\) −64.9814 −3.20530
\(412\) 0 0
\(413\) −11.1211 −0.547231
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −30.2277 −1.48026
\(418\) 0 0
\(419\) −17.1286 −0.836786 −0.418393 0.908266i \(-0.637406\pi\)
−0.418393 + 0.908266i \(0.637406\pi\)
\(420\) 0 0
\(421\) 18.5724 0.905162 0.452581 0.891723i \(-0.350503\pi\)
0.452581 + 0.891723i \(0.350503\pi\)
\(422\) 0 0
\(423\) −86.3783 −4.19986
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.177773 −0.00860305
\(428\) 0 0
\(429\) −73.3442 −3.54109
\(430\) 0 0
\(431\) 2.21969 0.106919 0.0534593 0.998570i \(-0.482975\pi\)
0.0534593 + 0.998570i \(0.482975\pi\)
\(432\) 0 0
\(433\) 21.0400 1.01112 0.505560 0.862791i \(-0.331286\pi\)
0.505560 + 0.862791i \(0.331286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.96494 −0.0939960
\(438\) 0 0
\(439\) 3.27039 0.156087 0.0780435 0.996950i \(-0.475133\pi\)
0.0780435 + 0.996950i \(0.475133\pi\)
\(440\) 0 0
\(441\) −34.2729 −1.63204
\(442\) 0 0
\(443\) −27.6697 −1.31463 −0.657314 0.753617i \(-0.728307\pi\)
−0.657314 + 0.753617i \(0.728307\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −8.85226 −0.418697
\(448\) 0 0
\(449\) 7.69551 0.363174 0.181587 0.983375i \(-0.441877\pi\)
0.181587 + 0.983375i \(0.441877\pi\)
\(450\) 0 0
\(451\) 21.1548 0.996143
\(452\) 0 0
\(453\) −61.4598 −2.88764
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.06460 0.377246 0.188623 0.982050i \(-0.439598\pi\)
0.188623 + 0.982050i \(0.439598\pi\)
\(458\) 0 0
\(459\) 22.8614 1.06708
\(460\) 0 0
\(461\) −3.10933 −0.144816 −0.0724079 0.997375i \(-0.523068\pi\)
−0.0724079 + 0.997375i \(0.523068\pi\)
\(462\) 0 0
\(463\) 12.4068 0.576592 0.288296 0.957541i \(-0.406911\pi\)
0.288296 + 0.957541i \(0.406911\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.63093 −0.0754706 −0.0377353 0.999288i \(-0.512014\pi\)
−0.0377353 + 0.999288i \(0.512014\pi\)
\(468\) 0 0
\(469\) −17.2252 −0.795388
\(470\) 0 0
\(471\) −20.9265 −0.964240
\(472\) 0 0
\(473\) 36.6230 1.68393
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.3059 −0.563447
\(478\) 0 0
\(479\) 15.4392 0.705433 0.352716 0.935730i \(-0.385258\pi\)
0.352716 + 0.935730i \(0.385258\pi\)
\(480\) 0 0
\(481\) −50.4192 −2.29892
\(482\) 0 0
\(483\) 10.5789 0.481357
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 38.2792 1.73460 0.867298 0.497789i \(-0.165855\pi\)
0.867298 + 0.497789i \(0.165855\pi\)
\(488\) 0 0
\(489\) 44.4271 2.00906
\(490\) 0 0
\(491\) −19.3511 −0.873301 −0.436651 0.899631i \(-0.643835\pi\)
−0.436651 + 0.899631i \(0.643835\pi\)
\(492\) 0 0
\(493\) −9.70086 −0.436905
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.7244 0.929615
\(498\) 0 0
\(499\) 18.1775 0.813738 0.406869 0.913487i \(-0.366621\pi\)
0.406869 + 0.913487i \(0.366621\pi\)
\(500\) 0 0
\(501\) −43.3511 −1.93678
\(502\) 0 0
\(503\) −19.4368 −0.866643 −0.433321 0.901240i \(-0.642658\pi\)
−0.433321 + 0.901240i \(0.642658\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −31.6566 −1.40592
\(508\) 0 0
\(509\) −0.155404 −0.00688816 −0.00344408 0.999994i \(-0.501096\pi\)
−0.00344408 + 0.999994i \(0.501096\pi\)
\(510\) 0 0
\(511\) 0.847823 0.0375055
\(512\) 0 0
\(513\) −16.1650 −0.713704
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 51.1332 2.24884
\(518\) 0 0
\(519\) 2.82984 0.124216
\(520\) 0 0
\(521\) −12.7626 −0.559140 −0.279570 0.960125i \(-0.590192\pi\)
−0.279570 + 0.960125i \(0.590192\pi\)
\(522\) 0 0
\(523\) 9.49811 0.415323 0.207662 0.978201i \(-0.433415\pi\)
0.207662 + 0.978201i \(0.433415\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.18832 −0.313128
\(528\) 0 0
\(529\) −19.1390 −0.832130
\(530\) 0 0
\(531\) −53.8476 −2.33679
\(532\) 0 0
\(533\) 21.5085 0.931636
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −29.4873 −1.27247
\(538\) 0 0
\(539\) 20.2885 0.873887
\(540\) 0 0
\(541\) −0.840655 −0.0361426 −0.0180713 0.999837i \(-0.505753\pi\)
−0.0180713 + 0.999837i \(0.505753\pi\)
\(542\) 0 0
\(543\) 22.9475 0.984771
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 30.9252 1.32227 0.661134 0.750268i \(-0.270075\pi\)
0.661134 + 0.750268i \(0.270075\pi\)
\(548\) 0 0
\(549\) −0.860769 −0.0367367
\(550\) 0 0
\(551\) 6.85936 0.292219
\(552\) 0 0
\(553\) 1.37078 0.0582916
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −25.4896 −1.08003 −0.540014 0.841656i \(-0.681581\pi\)
−0.540014 + 0.841656i \(0.681581\pi\)
\(558\) 0 0
\(559\) 37.2352 1.57488
\(560\) 0 0
\(561\) −21.8241 −0.921414
\(562\) 0 0
\(563\) 10.2674 0.432718 0.216359 0.976314i \(-0.430582\pi\)
0.216359 + 0.976314i \(0.430582\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 48.3913 2.03225
\(568\) 0 0
\(569\) 33.6002 1.40859 0.704296 0.709906i \(-0.251263\pi\)
0.704296 + 0.709906i \(0.251263\pi\)
\(570\) 0 0
\(571\) 8.89143 0.372095 0.186047 0.982541i \(-0.440432\pi\)
0.186047 + 0.982541i \(0.440432\pi\)
\(572\) 0 0
\(573\) −30.9035 −1.29101
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −31.3264 −1.30413 −0.652067 0.758161i \(-0.726098\pi\)
−0.652067 + 0.758161i \(0.726098\pi\)
\(578\) 0 0
\(579\) −88.3971 −3.67366
\(580\) 0 0
\(581\) 19.4746 0.807944
\(582\) 0 0
\(583\) 7.28468 0.301701
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 38.7544 1.59957 0.799784 0.600289i \(-0.204948\pi\)
0.799784 + 0.600289i \(0.204948\pi\)
\(588\) 0 0
\(589\) 5.08277 0.209432
\(590\) 0 0
\(591\) 12.9539 0.532854
\(592\) 0 0
\(593\) −43.7426 −1.79629 −0.898146 0.439696i \(-0.855086\pi\)
−0.898146 + 0.439696i \(0.855086\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 24.8300 1.01623
\(598\) 0 0
\(599\) 31.2288 1.27597 0.637987 0.770047i \(-0.279767\pi\)
0.637987 + 0.770047i \(0.279767\pi\)
\(600\) 0 0
\(601\) −45.1869 −1.84321 −0.921606 0.388127i \(-0.873122\pi\)
−0.921606 + 0.388127i \(0.873122\pi\)
\(602\) 0 0
\(603\) −83.4038 −3.39646
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −31.3958 −1.27432 −0.637159 0.770733i \(-0.719890\pi\)
−0.637159 + 0.770733i \(0.719890\pi\)
\(608\) 0 0
\(609\) −36.9296 −1.49646
\(610\) 0 0
\(611\) 51.9880 2.10321
\(612\) 0 0
\(613\) −20.7340 −0.837439 −0.418719 0.908116i \(-0.637521\pi\)
−0.418719 + 0.908116i \(0.637521\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10.4584 −0.421038 −0.210519 0.977590i \(-0.567515\pi\)
−0.210519 + 0.977590i \(0.567515\pi\)
\(618\) 0 0
\(619\) 13.9795 0.561883 0.280942 0.959725i \(-0.409353\pi\)
0.280942 + 0.959725i \(0.409353\pi\)
\(620\) 0 0
\(621\) 31.7634 1.27462
\(622\) 0 0
\(623\) −12.1399 −0.486377
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 15.4315 0.616276
\(628\) 0 0
\(629\) −15.0026 −0.598192
\(630\) 0 0
\(631\) 13.2899 0.529061 0.264531 0.964377i \(-0.414783\pi\)
0.264531 + 0.964377i \(0.414783\pi\)
\(632\) 0 0
\(633\) −32.9306 −1.30887
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 20.6276 0.817297
\(638\) 0 0
\(639\) 100.346 3.96964
\(640\) 0 0
\(641\) −14.8444 −0.586319 −0.293160 0.956064i \(-0.594707\pi\)
−0.293160 + 0.956064i \(0.594707\pi\)
\(642\) 0 0
\(643\) 19.8963 0.784634 0.392317 0.919830i \(-0.371674\pi\)
0.392317 + 0.919830i \(0.371674\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.90793 0.389521 0.194760 0.980851i \(-0.437607\pi\)
0.194760 + 0.980851i \(0.437607\pi\)
\(648\) 0 0
\(649\) 31.8760 1.25124
\(650\) 0 0
\(651\) −27.3647 −1.07251
\(652\) 0 0
\(653\) 5.31852 0.208130 0.104065 0.994571i \(-0.466815\pi\)
0.104065 + 0.994571i \(0.466815\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.10512 0.160156
\(658\) 0 0
\(659\) −6.86569 −0.267449 −0.133725 0.991019i \(-0.542694\pi\)
−0.133725 + 0.991019i \(0.542694\pi\)
\(660\) 0 0
\(661\) 48.7637 1.89669 0.948344 0.317243i \(-0.102757\pi\)
0.948344 + 0.317243i \(0.102757\pi\)
\(662\) 0 0
\(663\) −22.1889 −0.861746
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −13.4783 −0.521880
\(668\) 0 0
\(669\) −70.6269 −2.73059
\(670\) 0 0
\(671\) 0.509548 0.0196709
\(672\) 0 0
\(673\) −25.8294 −0.995651 −0.497825 0.867277i \(-0.665868\pi\)
−0.497825 + 0.867277i \(0.665868\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.58131 0.137641 0.0688205 0.997629i \(-0.478076\pi\)
0.0688205 + 0.997629i \(0.478076\pi\)
\(678\) 0 0
\(679\) 14.4442 0.554318
\(680\) 0 0
\(681\) −66.9995 −2.56743
\(682\) 0 0
\(683\) 36.1449 1.38304 0.691522 0.722355i \(-0.256940\pi\)
0.691522 + 0.722355i \(0.256940\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −65.8642 −2.51288
\(688\) 0 0
\(689\) 7.40645 0.282163
\(690\) 0 0
\(691\) −24.0392 −0.914493 −0.457246 0.889340i \(-0.651164\pi\)
−0.457246 + 0.889340i \(0.651164\pi\)
\(692\) 0 0
\(693\) −60.2080 −2.28711
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 6.40000 0.242417
\(698\) 0 0
\(699\) 43.6076 1.64939
\(700\) 0 0
\(701\) −14.5851 −0.550872 −0.275436 0.961319i \(-0.588822\pi\)
−0.275436 + 0.961319i \(0.588822\pi\)
\(702\) 0 0
\(703\) 10.6081 0.400093
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.1262 −0.794533
\(708\) 0 0
\(709\) 46.5636 1.74873 0.874366 0.485268i \(-0.161278\pi\)
0.874366 + 0.485268i \(0.161278\pi\)
\(710\) 0 0
\(711\) 6.63726 0.248917
\(712\) 0 0
\(713\) −9.98736 −0.374030
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −86.0045 −3.21190
\(718\) 0 0
\(719\) 4.36765 0.162886 0.0814429 0.996678i \(-0.474047\pi\)
0.0814429 + 0.996678i \(0.474047\pi\)
\(720\) 0 0
\(721\) −5.15756 −0.192077
\(722\) 0 0
\(723\) −7.00147 −0.260387
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −49.3720 −1.83111 −0.915553 0.402198i \(-0.868246\pi\)
−0.915553 + 0.402198i \(0.868246\pi\)
\(728\) 0 0
\(729\) 74.2236 2.74902
\(730\) 0 0
\(731\) 11.0796 0.409794
\(732\) 0 0
\(733\) −28.3530 −1.04724 −0.523621 0.851952i \(-0.675419\pi\)
−0.523621 + 0.851952i \(0.675419\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 49.3724 1.81865
\(738\) 0 0
\(739\) 25.4558 0.936408 0.468204 0.883620i \(-0.344901\pi\)
0.468204 + 0.883620i \(0.344901\pi\)
\(740\) 0 0
\(741\) 15.6895 0.576368
\(742\) 0 0
\(743\) −7.99036 −0.293138 −0.146569 0.989200i \(-0.546823\pi\)
−0.146569 + 0.989200i \(0.546823\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 94.2952 3.45008
\(748\) 0 0
\(749\) −30.7364 −1.12308
\(750\) 0 0
\(751\) −50.6911 −1.84974 −0.924872 0.380279i \(-0.875828\pi\)
−0.924872 + 0.380279i \(0.875828\pi\)
\(752\) 0 0
\(753\) 49.1564 1.79136
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.449092 −0.0163225 −0.00816127 0.999967i \(-0.502598\pi\)
−0.00816127 + 0.999967i \(0.502598\pi\)
\(758\) 0 0
\(759\) −30.3221 −1.10062
\(760\) 0 0
\(761\) 32.9995 1.19623 0.598115 0.801410i \(-0.295917\pi\)
0.598115 + 0.801410i \(0.295917\pi\)
\(762\) 0 0
\(763\) 21.9676 0.795282
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 32.4089 1.17022
\(768\) 0 0
\(769\) 7.87810 0.284091 0.142046 0.989860i \(-0.454632\pi\)
0.142046 + 0.989860i \(0.454632\pi\)
\(770\) 0 0
\(771\) −26.1115 −0.940383
\(772\) 0 0
\(773\) 17.7424 0.638149 0.319074 0.947730i \(-0.396628\pi\)
0.319074 + 0.947730i \(0.396628\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −57.1123 −2.04889
\(778\) 0 0
\(779\) −4.52536 −0.162138
\(780\) 0 0
\(781\) −59.4018 −2.12556
\(782\) 0 0
\(783\) −110.882 −3.96259
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −47.7349 −1.70156 −0.850782 0.525519i \(-0.823871\pi\)
−0.850782 + 0.525519i \(0.823871\pi\)
\(788\) 0 0
\(789\) −56.7213 −2.01933
\(790\) 0 0
\(791\) 7.22907 0.257036
\(792\) 0 0
\(793\) 0.518066 0.0183971
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.5233 0.620706 0.310353 0.950621i \(-0.399553\pi\)
0.310353 + 0.950621i \(0.399553\pi\)
\(798\) 0 0
\(799\) 15.4694 0.547268
\(800\) 0 0
\(801\) −58.7810 −2.07692
\(802\) 0 0
\(803\) −2.43010 −0.0857563
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 42.6618 1.50177
\(808\) 0 0
\(809\) 41.8643 1.47187 0.735936 0.677051i \(-0.236742\pi\)
0.735936 + 0.677051i \(0.236742\pi\)
\(810\) 0 0
\(811\) −29.8960 −1.04979 −0.524895 0.851167i \(-0.675895\pi\)
−0.524895 + 0.851167i \(0.675895\pi\)
\(812\) 0 0
\(813\) 69.2879 2.43003
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −7.83425 −0.274086
\(818\) 0 0
\(819\) −61.2144 −2.13901
\(820\) 0 0
\(821\) 46.3602 1.61798 0.808992 0.587820i \(-0.200014\pi\)
0.808992 + 0.587820i \(0.200014\pi\)
\(822\) 0 0
\(823\) 37.3940 1.30347 0.651737 0.758445i \(-0.274040\pi\)
0.651737 + 0.758445i \(0.274040\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.68450 0.336763 0.168382 0.985722i \(-0.446146\pi\)
0.168382 + 0.985722i \(0.446146\pi\)
\(828\) 0 0
\(829\) 16.8732 0.586031 0.293016 0.956108i \(-0.405341\pi\)
0.293016 + 0.956108i \(0.405341\pi\)
\(830\) 0 0
\(831\) −20.7095 −0.718405
\(832\) 0 0
\(833\) 6.13790 0.212665
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −82.1632 −2.83997
\(838\) 0 0
\(839\) −35.3160 −1.21924 −0.609622 0.792692i \(-0.708679\pi\)
−0.609622 + 0.792692i \(0.708679\pi\)
\(840\) 0 0
\(841\) 18.0508 0.622442
\(842\) 0 0
\(843\) 94.9496 3.27024
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 17.7008 0.608208
\(848\) 0 0
\(849\) −92.4773 −3.17381
\(850\) 0 0
\(851\) −20.8444 −0.714536
\(852\) 0 0
\(853\) 18.3492 0.628265 0.314133 0.949379i \(-0.398286\pi\)
0.314133 + 0.949379i \(0.398286\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.4209 −0.868361 −0.434181 0.900826i \(-0.642962\pi\)
−0.434181 + 0.900826i \(0.642962\pi\)
\(858\) 0 0
\(859\) 27.2820 0.930849 0.465425 0.885088i \(-0.345902\pi\)
0.465425 + 0.885088i \(0.345902\pi\)
\(860\) 0 0
\(861\) 24.3637 0.830313
\(862\) 0 0
\(863\) 3.63233 0.123646 0.0618230 0.998087i \(-0.480309\pi\)
0.0618230 + 0.998087i \(0.480309\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 49.5154 1.68163
\(868\) 0 0
\(869\) −3.92904 −0.133284
\(870\) 0 0
\(871\) 50.1977 1.70088
\(872\) 0 0
\(873\) 69.9382 2.36705
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 57.1986 1.93146 0.965731 0.259547i \(-0.0835731\pi\)
0.965731 + 0.259547i \(0.0835731\pi\)
\(878\) 0 0
\(879\) −74.4455 −2.51099
\(880\) 0 0
\(881\) −48.3846 −1.63012 −0.815059 0.579378i \(-0.803296\pi\)
−0.815059 + 0.579378i \(0.803296\pi\)
\(882\) 0 0
\(883\) 17.6993 0.595630 0.297815 0.954624i \(-0.403742\pi\)
0.297815 + 0.954624i \(0.403742\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40.1640 −1.34858 −0.674288 0.738468i \(-0.735549\pi\)
−0.674288 + 0.738468i \(0.735549\pi\)
\(888\) 0 0
\(889\) −7.31701 −0.245405
\(890\) 0 0
\(891\) −138.703 −4.64673
\(892\) 0 0
\(893\) −10.9382 −0.366033
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −30.8290 −1.02935
\(898\) 0 0
\(899\) 34.8646 1.16280
\(900\) 0 0
\(901\) 2.20384 0.0734206
\(902\) 0 0
\(903\) 42.1782 1.40360
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 12.5765 0.417596 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(908\) 0 0
\(909\) −102.292 −3.39281
\(910\) 0 0
\(911\) −29.7278 −0.984927 −0.492464 0.870333i \(-0.663904\pi\)
−0.492464 + 0.870333i \(0.663904\pi\)
\(912\) 0 0
\(913\) −55.8197 −1.84736
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −18.1482 −0.599308
\(918\) 0 0
\(919\) 22.1146 0.729492 0.364746 0.931107i \(-0.381156\pi\)
0.364746 + 0.931107i \(0.381156\pi\)
\(920\) 0 0
\(921\) −48.1879 −1.58784
\(922\) 0 0
\(923\) −60.3948 −1.98792
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −24.9726 −0.820208
\(928\) 0 0
\(929\) −23.4746 −0.770175 −0.385088 0.922880i \(-0.625829\pi\)
−0.385088 + 0.922880i \(0.625829\pi\)
\(930\) 0 0
\(931\) −4.34003 −0.142239
\(932\) 0 0
\(933\) −89.6592 −2.93531
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.29393 −0.238282 −0.119141 0.992877i \(-0.538014\pi\)
−0.119141 + 0.992877i \(0.538014\pi\)
\(938\) 0 0
\(939\) 93.7016 3.05784
\(940\) 0 0
\(941\) −36.3844 −1.18610 −0.593048 0.805167i \(-0.702076\pi\)
−0.593048 + 0.805167i \(0.702076\pi\)
\(942\) 0 0
\(943\) 8.89207 0.289566
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −6.77953 −0.220305 −0.110152 0.993915i \(-0.535134\pi\)
−0.110152 + 0.993915i \(0.535134\pi\)
\(948\) 0 0
\(949\) −2.47072 −0.0802030
\(950\) 0 0
\(951\) −69.2922 −2.24695
\(952\) 0 0
\(953\) −9.00668 −0.291755 −0.145877 0.989303i \(-0.546601\pi\)
−0.145877 + 0.989303i \(0.546601\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 105.850 3.42166
\(958\) 0 0
\(959\) 32.1052 1.03673
\(960\) 0 0
\(961\) −5.16544 −0.166627
\(962\) 0 0
\(963\) −148.824 −4.79579
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0.251168 0.00807702 0.00403851 0.999992i \(-0.498714\pi\)
0.00403851 + 0.999992i \(0.498714\pi\)
\(968\) 0 0
\(969\) 4.66852 0.149974
\(970\) 0 0
\(971\) −9.76919 −0.313508 −0.156754 0.987638i \(-0.550103\pi\)
−0.156754 + 0.987638i \(0.550103\pi\)
\(972\) 0 0
\(973\) 14.9345 0.478779
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 37.8438 1.21073 0.605365 0.795948i \(-0.293027\pi\)
0.605365 + 0.795948i \(0.293027\pi\)
\(978\) 0 0
\(979\) 34.7965 1.11210
\(980\) 0 0
\(981\) 106.366 3.39601
\(982\) 0 0
\(983\) 32.0062 1.02084 0.510420 0.859925i \(-0.329490\pi\)
0.510420 + 0.859925i \(0.329490\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 58.8894 1.87447
\(988\) 0 0
\(989\) 15.3939 0.489496
\(990\) 0 0
\(991\) −14.8408 −0.471432 −0.235716 0.971822i \(-0.575744\pi\)
−0.235716 + 0.971822i \(0.575744\pi\)
\(992\) 0 0
\(993\) 5.99572 0.190268
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −46.6666 −1.47795 −0.738973 0.673735i \(-0.764689\pi\)
−0.738973 + 0.673735i \(0.764689\pi\)
\(998\) 0 0
\(999\) −171.481 −5.42541
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 3800.2.a.bb.1.1 6
4.3 odd 2 7600.2.a.cm.1.6 6
5.2 odd 4 3800.2.d.p.3649.12 12
5.3 odd 4 3800.2.d.p.3649.1 12
5.4 even 2 3800.2.a.bd.1.6 yes 6
20.19 odd 2 7600.2.a.ci.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3800.2.a.bb.1.1 6 1.1 even 1 trivial
3800.2.a.bd.1.6 yes 6 5.4 even 2
3800.2.d.p.3649.1 12 5.3 odd 4
3800.2.d.p.3649.12 12 5.2 odd 4
7600.2.a.ci.1.1 6 20.19 odd 2
7600.2.a.cm.1.6 6 4.3 odd 2