Properties

Label 6044.2.a.b.1.14
Level $6044$
Weight $2$
Character 6044.1
Self dual yes
Analytic conductor $48.262$
Analytic rank $0$
Dimension $63$
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] = [6044,2,Mod(1,6044)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6044.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6044 = 2^{2} \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6044.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: \(48.2615829817\)
Analytic rank: \(0\)
Dimension: \(63\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6044.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.12225 q^{3} -0.499336 q^{5} -0.0909608 q^{7} +1.50393 q^{9} +O(q^{10})\) \(q-2.12225 q^{3} -0.499336 q^{5} -0.0909608 q^{7} +1.50393 q^{9} -5.99078 q^{11} -1.72950 q^{13} +1.05971 q^{15} +0.991439 q^{17} -0.171467 q^{19} +0.193041 q^{21} -8.88287 q^{23} -4.75066 q^{25} +3.17503 q^{27} -0.101836 q^{29} +3.95137 q^{31} +12.7139 q^{33} +0.0454200 q^{35} -10.2433 q^{37} +3.67042 q^{39} -8.52563 q^{41} +1.82550 q^{43} -0.750966 q^{45} +4.29537 q^{47} -6.99173 q^{49} -2.10408 q^{51} -11.1387 q^{53} +2.99141 q^{55} +0.363896 q^{57} +7.94489 q^{59} -0.282218 q^{61} -0.136799 q^{63} +0.863601 q^{65} -0.845161 q^{67} +18.8516 q^{69} -0.472422 q^{71} -1.28928 q^{73} +10.0821 q^{75} +0.544926 q^{77} -9.72295 q^{79} -11.2500 q^{81} +9.08035 q^{83} -0.495061 q^{85} +0.216121 q^{87} -6.22911 q^{89} +0.157316 q^{91} -8.38579 q^{93} +0.0856197 q^{95} -8.05618 q^{97} -9.00971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 63 q + 5 q^{3} + 5 q^{5} + 22 q^{7} + 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 63 q + 5 q^{3} + 5 q^{5} + 22 q^{7} + 62 q^{9} + 21 q^{11} + 17 q^{13} + 26 q^{15} - 5 q^{17} + 57 q^{19} + 18 q^{21} + 16 q^{23} + 60 q^{25} + 14 q^{27} + 22 q^{29} + 36 q^{31} - q^{33} + 28 q^{35} + 21 q^{37} + 69 q^{39} - 3 q^{41} + 86 q^{43} + 39 q^{45} + 23 q^{47} + 63 q^{49} + 67 q^{51} + 18 q^{53} + 67 q^{55} + 27 q^{59} + 62 q^{61} + 58 q^{63} - 13 q^{65} + 62 q^{67} + 45 q^{69} + 29 q^{71} - q^{73} + 39 q^{75} + 19 q^{77} + 132 q^{79} + 51 q^{81} + 35 q^{83} + 60 q^{85} + 55 q^{87} - 2 q^{89} + 84 q^{91} + 29 q^{93} + 53 q^{95} - 10 q^{97} + 95 q^{99}+O(q^{100}) \) 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
\(3\) −2.12225 −1.22528 −0.612640 0.790362i \(-0.709892\pi\)
−0.612640 + 0.790362i \(0.709892\pi\)
\(4\) 0 0
\(5\) −0.499336 −0.223310 −0.111655 0.993747i \(-0.535615\pi\)
−0.111655 + 0.993747i \(0.535615\pi\)
\(6\) 0 0
\(7\) −0.0909608 −0.0343799 −0.0171900 0.999852i \(-0.505472\pi\)
−0.0171900 + 0.999852i \(0.505472\pi\)
\(8\) 0 0
\(9\) 1.50393 0.501310
\(10\) 0 0
\(11\) −5.99078 −1.80629 −0.903144 0.429338i \(-0.858747\pi\)
−0.903144 + 0.429338i \(0.858747\pi\)
\(12\) 0 0
\(13\) −1.72950 −0.479677 −0.239838 0.970813i \(-0.577094\pi\)
−0.239838 + 0.970813i \(0.577094\pi\)
\(14\) 0 0
\(15\) 1.05971 0.273617
\(16\) 0 0
\(17\) 0.991439 0.240459 0.120230 0.992746i \(-0.461637\pi\)
0.120230 + 0.992746i \(0.461637\pi\)
\(18\) 0 0
\(19\) −0.171467 −0.0393373 −0.0196686 0.999807i \(-0.506261\pi\)
−0.0196686 + 0.999807i \(0.506261\pi\)
\(20\) 0 0
\(21\) 0.193041 0.0421250
\(22\) 0 0
\(23\) −8.88287 −1.85221 −0.926103 0.377270i \(-0.876863\pi\)
−0.926103 + 0.377270i \(0.876863\pi\)
\(24\) 0 0
\(25\) −4.75066 −0.950133
\(26\) 0 0
\(27\) 3.17503 0.611035
\(28\) 0 0
\(29\) −0.101836 −0.0189105 −0.00945523 0.999955i \(-0.503010\pi\)
−0.00945523 + 0.999955i \(0.503010\pi\)
\(30\) 0 0
\(31\) 3.95137 0.709688 0.354844 0.934926i \(-0.384534\pi\)
0.354844 + 0.934926i \(0.384534\pi\)
\(32\) 0 0
\(33\) 12.7139 2.21321
\(34\) 0 0
\(35\) 0.0454200 0.00767738
\(36\) 0 0
\(37\) −10.2433 −1.68399 −0.841993 0.539489i \(-0.818617\pi\)
−0.841993 + 0.539489i \(0.818617\pi\)
\(38\) 0 0
\(39\) 3.67042 0.587738
\(40\) 0 0
\(41\) −8.52563 −1.33148 −0.665740 0.746184i \(-0.731884\pi\)
−0.665740 + 0.746184i \(0.731884\pi\)
\(42\) 0 0
\(43\) 1.82550 0.278386 0.139193 0.990265i \(-0.455549\pi\)
0.139193 + 0.990265i \(0.455549\pi\)
\(44\) 0 0
\(45\) −0.750966 −0.111947
\(46\) 0 0
\(47\) 4.29537 0.626544 0.313272 0.949663i \(-0.398575\pi\)
0.313272 + 0.949663i \(0.398575\pi\)
\(48\) 0 0
\(49\) −6.99173 −0.998818
\(50\) 0 0
\(51\) −2.10408 −0.294630
\(52\) 0 0
\(53\) −11.1387 −1.53002 −0.765008 0.644020i \(-0.777265\pi\)
−0.765008 + 0.644020i \(0.777265\pi\)
\(54\) 0 0
\(55\) 2.99141 0.403362
\(56\) 0 0
\(57\) 0.363896 0.0481991
\(58\) 0 0
\(59\) 7.94489 1.03434 0.517168 0.855884i \(-0.326986\pi\)
0.517168 + 0.855884i \(0.326986\pi\)
\(60\) 0 0
\(61\) −0.282218 −0.0361344 −0.0180672 0.999837i \(-0.505751\pi\)
−0.0180672 + 0.999837i \(0.505751\pi\)
\(62\) 0 0
\(63\) −0.136799 −0.0172350
\(64\) 0 0
\(65\) 0.863601 0.107116
\(66\) 0 0
\(67\) −0.845161 −0.103253 −0.0516264 0.998666i \(-0.516441\pi\)
−0.0516264 + 0.998666i \(0.516441\pi\)
\(68\) 0 0
\(69\) 18.8516 2.26947
\(70\) 0 0
\(71\) −0.472422 −0.0560661 −0.0280331 0.999607i \(-0.508924\pi\)
−0.0280331 + 0.999607i \(0.508924\pi\)
\(72\) 0 0
\(73\) −1.28928 −0.150899 −0.0754495 0.997150i \(-0.524039\pi\)
−0.0754495 + 0.997150i \(0.524039\pi\)
\(74\) 0 0
\(75\) 10.0821 1.16418
\(76\) 0 0
\(77\) 0.544926 0.0621001
\(78\) 0 0
\(79\) −9.72295 −1.09392 −0.546959 0.837160i \(-0.684214\pi\)
−0.546959 + 0.837160i \(0.684214\pi\)
\(80\) 0 0
\(81\) −11.2500 −1.25000
\(82\) 0 0
\(83\) 9.08035 0.996698 0.498349 0.866976i \(-0.333940\pi\)
0.498349 + 0.866976i \(0.333940\pi\)
\(84\) 0 0
\(85\) −0.495061 −0.0536969
\(86\) 0 0
\(87\) 0.216121 0.0231706
\(88\) 0 0
\(89\) −6.22911 −0.660285 −0.330142 0.943931i \(-0.607097\pi\)
−0.330142 + 0.943931i \(0.607097\pi\)
\(90\) 0 0
\(91\) 0.157316 0.0164913
\(92\) 0 0
\(93\) −8.38579 −0.869566
\(94\) 0 0
\(95\) 0.0856197 0.00878440
\(96\) 0 0
\(97\) −8.05618 −0.817981 −0.408991 0.912539i \(-0.634119\pi\)
−0.408991 + 0.912539i \(0.634119\pi\)
\(98\) 0 0
\(99\) −9.00971 −0.905510
\(100\) 0 0
\(101\) 8.57036 0.852782 0.426391 0.904539i \(-0.359785\pi\)
0.426391 + 0.904539i \(0.359785\pi\)
\(102\) 0 0
\(103\) 10.9163 1.07562 0.537808 0.843067i \(-0.319252\pi\)
0.537808 + 0.843067i \(0.319252\pi\)
\(104\) 0 0
\(105\) −0.0963924 −0.00940693
\(106\) 0 0
\(107\) 12.5855 1.21668 0.608341 0.793676i \(-0.291835\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(108\) 0 0
\(109\) 7.67943 0.735556 0.367778 0.929914i \(-0.380119\pi\)
0.367778 + 0.929914i \(0.380119\pi\)
\(110\) 0 0
\(111\) 21.7388 2.06335
\(112\) 0 0
\(113\) −20.6116 −1.93897 −0.969487 0.245144i \(-0.921165\pi\)
−0.969487 + 0.245144i \(0.921165\pi\)
\(114\) 0 0
\(115\) 4.43554 0.413616
\(116\) 0 0
\(117\) −2.60104 −0.240467
\(118\) 0 0
\(119\) −0.0901820 −0.00826697
\(120\) 0 0
\(121\) 24.8894 2.26268
\(122\) 0 0
\(123\) 18.0935 1.63143
\(124\) 0 0
\(125\) 4.86886 0.435484
\(126\) 0 0
\(127\) −18.6852 −1.65804 −0.829020 0.559219i \(-0.811101\pi\)
−0.829020 + 0.559219i \(0.811101\pi\)
\(128\) 0 0
\(129\) −3.87416 −0.341101
\(130\) 0 0
\(131\) −20.7804 −1.81559 −0.907795 0.419415i \(-0.862235\pi\)
−0.907795 + 0.419415i \(0.862235\pi\)
\(132\) 0 0
\(133\) 0.0155968 0.00135241
\(134\) 0 0
\(135\) −1.58541 −0.136450
\(136\) 0 0
\(137\) −13.9678 −1.19335 −0.596676 0.802482i \(-0.703512\pi\)
−0.596676 + 0.802482i \(0.703512\pi\)
\(138\) 0 0
\(139\) 1.82195 0.154536 0.0772680 0.997010i \(-0.475380\pi\)
0.0772680 + 0.997010i \(0.475380\pi\)
\(140\) 0 0
\(141\) −9.11584 −0.767692
\(142\) 0 0
\(143\) 10.3610 0.866434
\(144\) 0 0
\(145\) 0.0508503 0.00422289
\(146\) 0 0
\(147\) 14.8382 1.22383
\(148\) 0 0
\(149\) −6.93768 −0.568357 −0.284179 0.958771i \(-0.591721\pi\)
−0.284179 + 0.958771i \(0.591721\pi\)
\(150\) 0 0
\(151\) 17.7458 1.44413 0.722066 0.691824i \(-0.243193\pi\)
0.722066 + 0.691824i \(0.243193\pi\)
\(152\) 0 0
\(153\) 1.49105 0.120545
\(154\) 0 0
\(155\) −1.97306 −0.158480
\(156\) 0 0
\(157\) 15.8906 1.26821 0.634104 0.773248i \(-0.281369\pi\)
0.634104 + 0.773248i \(0.281369\pi\)
\(158\) 0 0
\(159\) 23.6390 1.87470
\(160\) 0 0
\(161\) 0.807993 0.0636787
\(162\) 0 0
\(163\) 10.8649 0.851006 0.425503 0.904957i \(-0.360097\pi\)
0.425503 + 0.904957i \(0.360097\pi\)
\(164\) 0 0
\(165\) −6.34851 −0.494231
\(166\) 0 0
\(167\) −19.4310 −1.50361 −0.751807 0.659383i \(-0.770818\pi\)
−0.751807 + 0.659383i \(0.770818\pi\)
\(168\) 0 0
\(169\) −10.0088 −0.769910
\(170\) 0 0
\(171\) −0.257875 −0.0197202
\(172\) 0 0
\(173\) 3.46800 0.263667 0.131834 0.991272i \(-0.457914\pi\)
0.131834 + 0.991272i \(0.457914\pi\)
\(174\) 0 0
\(175\) 0.432124 0.0326655
\(176\) 0 0
\(177\) −16.8610 −1.26735
\(178\) 0 0
\(179\) −8.38527 −0.626745 −0.313372 0.949630i \(-0.601459\pi\)
−0.313372 + 0.949630i \(0.601459\pi\)
\(180\) 0 0
\(181\) −21.3824 −1.58934 −0.794671 0.607041i \(-0.792356\pi\)
−0.794671 + 0.607041i \(0.792356\pi\)
\(182\) 0 0
\(183\) 0.598937 0.0442747
\(184\) 0 0
\(185\) 5.11484 0.376050
\(186\) 0 0
\(187\) −5.93949 −0.434339
\(188\) 0 0
\(189\) −0.288803 −0.0210073
\(190\) 0 0
\(191\) 8.65612 0.626335 0.313168 0.949698i \(-0.398610\pi\)
0.313168 + 0.949698i \(0.398610\pi\)
\(192\) 0 0
\(193\) 19.3099 1.38996 0.694980 0.719029i \(-0.255413\pi\)
0.694980 + 0.719029i \(0.255413\pi\)
\(194\) 0 0
\(195\) −1.83277 −0.131248
\(196\) 0 0
\(197\) −15.5205 −1.10579 −0.552895 0.833251i \(-0.686477\pi\)
−0.552895 + 0.833251i \(0.686477\pi\)
\(198\) 0 0
\(199\) −1.72616 −0.122364 −0.0611819 0.998127i \(-0.519487\pi\)
−0.0611819 + 0.998127i \(0.519487\pi\)
\(200\) 0 0
\(201\) 1.79364 0.126514
\(202\) 0 0
\(203\) 0.00926307 0.000650140 0
\(204\) 0 0
\(205\) 4.25715 0.297332
\(206\) 0 0
\(207\) −13.3592 −0.928529
\(208\) 0 0
\(209\) 1.02722 0.0710544
\(210\) 0 0
\(211\) 11.5443 0.794744 0.397372 0.917658i \(-0.369922\pi\)
0.397372 + 0.917658i \(0.369922\pi\)
\(212\) 0 0
\(213\) 1.00260 0.0686967
\(214\) 0 0
\(215\) −0.911537 −0.0621663
\(216\) 0 0
\(217\) −0.359420 −0.0243990
\(218\) 0 0
\(219\) 2.73617 0.184893
\(220\) 0 0
\(221\) −1.71469 −0.115343
\(222\) 0 0
\(223\) 3.90655 0.261602 0.130801 0.991409i \(-0.458245\pi\)
0.130801 + 0.991409i \(0.458245\pi\)
\(224\) 0 0
\(225\) −7.14466 −0.476311
\(226\) 0 0
\(227\) −6.26878 −0.416074 −0.208037 0.978121i \(-0.566707\pi\)
−0.208037 + 0.978121i \(0.566707\pi\)
\(228\) 0 0
\(229\) 10.3543 0.684235 0.342117 0.939657i \(-0.388856\pi\)
0.342117 + 0.939657i \(0.388856\pi\)
\(230\) 0 0
\(231\) −1.15647 −0.0760899
\(232\) 0 0
\(233\) −9.63035 −0.630905 −0.315452 0.948941i \(-0.602156\pi\)
−0.315452 + 0.948941i \(0.602156\pi\)
\(234\) 0 0
\(235\) −2.14483 −0.139914
\(236\) 0 0
\(237\) 20.6345 1.34035
\(238\) 0 0
\(239\) −9.74469 −0.630331 −0.315166 0.949037i \(-0.602060\pi\)
−0.315166 + 0.949037i \(0.602060\pi\)
\(240\) 0 0
\(241\) −0.117859 −0.00759197 −0.00379598 0.999993i \(-0.501208\pi\)
−0.00379598 + 0.999993i \(0.501208\pi\)
\(242\) 0 0
\(243\) 14.3501 0.920562
\(244\) 0 0
\(245\) 3.49122 0.223046
\(246\) 0 0
\(247\) 0.296552 0.0188692
\(248\) 0 0
\(249\) −19.2707 −1.22123
\(250\) 0 0
\(251\) 13.9295 0.879221 0.439611 0.898188i \(-0.355116\pi\)
0.439611 + 0.898188i \(0.355116\pi\)
\(252\) 0 0
\(253\) 53.2153 3.34562
\(254\) 0 0
\(255\) 1.05064 0.0657937
\(256\) 0 0
\(257\) 2.18250 0.136141 0.0680704 0.997681i \(-0.478316\pi\)
0.0680704 + 0.997681i \(0.478316\pi\)
\(258\) 0 0
\(259\) 0.931737 0.0578953
\(260\) 0 0
\(261\) −0.153154 −0.00948000
\(262\) 0 0
\(263\) −8.97555 −0.553456 −0.276728 0.960948i \(-0.589250\pi\)
−0.276728 + 0.960948i \(0.589250\pi\)
\(264\) 0 0
\(265\) 5.56195 0.341668
\(266\) 0 0
\(267\) 13.2197 0.809033
\(268\) 0 0
\(269\) 18.1278 1.10527 0.552636 0.833422i \(-0.313622\pi\)
0.552636 + 0.833422i \(0.313622\pi\)
\(270\) 0 0
\(271\) −0.706196 −0.0428983 −0.0214492 0.999770i \(-0.506828\pi\)
−0.0214492 + 0.999770i \(0.506828\pi\)
\(272\) 0 0
\(273\) −0.333864 −0.0202064
\(274\) 0 0
\(275\) 28.4602 1.71621
\(276\) 0 0
\(277\) 19.3095 1.16020 0.580099 0.814546i \(-0.303014\pi\)
0.580099 + 0.814546i \(0.303014\pi\)
\(278\) 0 0
\(279\) 5.94259 0.355773
\(280\) 0 0
\(281\) 30.5129 1.82024 0.910122 0.414340i \(-0.135987\pi\)
0.910122 + 0.414340i \(0.135987\pi\)
\(282\) 0 0
\(283\) 0.0618746 0.00367806 0.00183903 0.999998i \(-0.499415\pi\)
0.00183903 + 0.999998i \(0.499415\pi\)
\(284\) 0 0
\(285\) −0.181706 −0.0107633
\(286\) 0 0
\(287\) 0.775498 0.0457762
\(288\) 0 0
\(289\) −16.0170 −0.942179
\(290\) 0 0
\(291\) 17.0972 1.00226
\(292\) 0 0
\(293\) 25.9403 1.51545 0.757723 0.652576i \(-0.226312\pi\)
0.757723 + 0.652576i \(0.226312\pi\)
\(294\) 0 0
\(295\) −3.96717 −0.230978
\(296\) 0 0
\(297\) −19.0209 −1.10370
\(298\) 0 0
\(299\) 15.3629 0.888460
\(300\) 0 0
\(301\) −0.166049 −0.00957089
\(302\) 0 0
\(303\) −18.1884 −1.04490
\(304\) 0 0
\(305\) 0.140922 0.00806916
\(306\) 0 0
\(307\) 15.1562 0.865010 0.432505 0.901631i \(-0.357630\pi\)
0.432505 + 0.901631i \(0.357630\pi\)
\(308\) 0 0
\(309\) −23.1671 −1.31793
\(310\) 0 0
\(311\) 22.4188 1.27125 0.635626 0.771997i \(-0.280742\pi\)
0.635626 + 0.771997i \(0.280742\pi\)
\(312\) 0 0
\(313\) 10.1346 0.572839 0.286420 0.958104i \(-0.407535\pi\)
0.286420 + 0.958104i \(0.407535\pi\)
\(314\) 0 0
\(315\) 0.0683084 0.00384874
\(316\) 0 0
\(317\) 0.369448 0.0207503 0.0103751 0.999946i \(-0.496697\pi\)
0.0103751 + 0.999946i \(0.496697\pi\)
\(318\) 0 0
\(319\) 0.610077 0.0341577
\(320\) 0 0
\(321\) −26.7094 −1.49078
\(322\) 0 0
\(323\) −0.169999 −0.00945901
\(324\) 0 0
\(325\) 8.21627 0.455756
\(326\) 0 0
\(327\) −16.2976 −0.901262
\(328\) 0 0
\(329\) −0.390710 −0.0215406
\(330\) 0 0
\(331\) −18.7982 −1.03324 −0.516622 0.856214i \(-0.672811\pi\)
−0.516622 + 0.856214i \(0.672811\pi\)
\(332\) 0 0
\(333\) −15.4052 −0.844198
\(334\) 0 0
\(335\) 0.422019 0.0230574
\(336\) 0 0
\(337\) −3.65923 −0.199331 −0.0996656 0.995021i \(-0.531777\pi\)
−0.0996656 + 0.995021i \(0.531777\pi\)
\(338\) 0 0
\(339\) 43.7428 2.37578
\(340\) 0 0
\(341\) −23.6718 −1.28190
\(342\) 0 0
\(343\) 1.27270 0.0687192
\(344\) 0 0
\(345\) −9.41330 −0.506795
\(346\) 0 0
\(347\) −23.2193 −1.24648 −0.623238 0.782032i \(-0.714183\pi\)
−0.623238 + 0.782032i \(0.714183\pi\)
\(348\) 0 0
\(349\) 13.6150 0.728795 0.364397 0.931244i \(-0.381275\pi\)
0.364397 + 0.931244i \(0.381275\pi\)
\(350\) 0 0
\(351\) −5.49121 −0.293099
\(352\) 0 0
\(353\) 15.0014 0.798442 0.399221 0.916855i \(-0.369281\pi\)
0.399221 + 0.916855i \(0.369281\pi\)
\(354\) 0 0
\(355\) 0.235897 0.0125201
\(356\) 0 0
\(357\) 0.191388 0.0101294
\(358\) 0 0
\(359\) −14.1671 −0.747713 −0.373856 0.927487i \(-0.621965\pi\)
−0.373856 + 0.927487i \(0.621965\pi\)
\(360\) 0 0
\(361\) −18.9706 −0.998453
\(362\) 0 0
\(363\) −52.8215 −2.77241
\(364\) 0 0
\(365\) 0.643784 0.0336972
\(366\) 0 0
\(367\) −1.12351 −0.0586470 −0.0293235 0.999570i \(-0.509335\pi\)
−0.0293235 + 0.999570i \(0.509335\pi\)
\(368\) 0 0
\(369\) −12.8219 −0.667484
\(370\) 0 0
\(371\) 1.01318 0.0526019
\(372\) 0 0
\(373\) 7.19359 0.372470 0.186235 0.982505i \(-0.440371\pi\)
0.186235 + 0.982505i \(0.440371\pi\)
\(374\) 0 0
\(375\) −10.3329 −0.533589
\(376\) 0 0
\(377\) 0.176125 0.00907090
\(378\) 0 0
\(379\) 5.91948 0.304063 0.152032 0.988376i \(-0.451418\pi\)
0.152032 + 0.988376i \(0.451418\pi\)
\(380\) 0 0
\(381\) 39.6545 2.03156
\(382\) 0 0
\(383\) 9.77174 0.499313 0.249656 0.968334i \(-0.419682\pi\)
0.249656 + 0.968334i \(0.419682\pi\)
\(384\) 0 0
\(385\) −0.272101 −0.0138676
\(386\) 0 0
\(387\) 2.74542 0.139558
\(388\) 0 0
\(389\) −14.2916 −0.724614 −0.362307 0.932059i \(-0.618011\pi\)
−0.362307 + 0.932059i \(0.618011\pi\)
\(390\) 0 0
\(391\) −8.80682 −0.445380
\(392\) 0 0
\(393\) 44.1011 2.22460
\(394\) 0 0
\(395\) 4.85502 0.244282
\(396\) 0 0
\(397\) 23.7973 1.19435 0.597175 0.802111i \(-0.296290\pi\)
0.597175 + 0.802111i \(0.296290\pi\)
\(398\) 0 0
\(399\) −0.0331002 −0.00165708
\(400\) 0 0
\(401\) −18.5586 −0.926771 −0.463386 0.886157i \(-0.653365\pi\)
−0.463386 + 0.886157i \(0.653365\pi\)
\(402\) 0 0
\(403\) −6.83390 −0.340421
\(404\) 0 0
\(405\) 5.61752 0.279137
\(406\) 0 0
\(407\) 61.3652 3.04176
\(408\) 0 0
\(409\) 38.9219 1.92457 0.962283 0.272051i \(-0.0877019\pi\)
0.962283 + 0.272051i \(0.0877019\pi\)
\(410\) 0 0
\(411\) 29.6432 1.46219
\(412\) 0 0
\(413\) −0.722673 −0.0355604
\(414\) 0 0
\(415\) −4.53415 −0.222572
\(416\) 0 0
\(417\) −3.86663 −0.189350
\(418\) 0 0
\(419\) 38.0419 1.85847 0.929235 0.369489i \(-0.120467\pi\)
0.929235 + 0.369489i \(0.120467\pi\)
\(420\) 0 0
\(421\) 8.38416 0.408619 0.204309 0.978906i \(-0.434505\pi\)
0.204309 + 0.978906i \(0.434505\pi\)
\(422\) 0 0
\(423\) 6.45994 0.314093
\(424\) 0 0
\(425\) −4.70999 −0.228468
\(426\) 0 0
\(427\) 0.0256708 0.00124230
\(428\) 0 0
\(429\) −21.9887 −1.06162
\(430\) 0 0
\(431\) −23.6362 −1.13851 −0.569257 0.822160i \(-0.692769\pi\)
−0.569257 + 0.822160i \(0.692769\pi\)
\(432\) 0 0
\(433\) 11.6966 0.562105 0.281052 0.959692i \(-0.409317\pi\)
0.281052 + 0.959692i \(0.409317\pi\)
\(434\) 0 0
\(435\) −0.107917 −0.00517422
\(436\) 0 0
\(437\) 1.52312 0.0728607
\(438\) 0 0
\(439\) −25.8022 −1.23147 −0.615736 0.787952i \(-0.711141\pi\)
−0.615736 + 0.787952i \(0.711141\pi\)
\(440\) 0 0
\(441\) −10.5151 −0.500717
\(442\) 0 0
\(443\) −28.1598 −1.33791 −0.668957 0.743301i \(-0.733259\pi\)
−0.668957 + 0.743301i \(0.733259\pi\)
\(444\) 0 0
\(445\) 3.11042 0.147448
\(446\) 0 0
\(447\) 14.7235 0.696396
\(448\) 0 0
\(449\) 21.4005 1.00995 0.504977 0.863133i \(-0.331501\pi\)
0.504977 + 0.863133i \(0.331501\pi\)
\(450\) 0 0
\(451\) 51.0751 2.40503
\(452\) 0 0
\(453\) −37.6610 −1.76947
\(454\) 0 0
\(455\) −0.0785538 −0.00368266
\(456\) 0 0
\(457\) −28.2516 −1.32155 −0.660777 0.750582i \(-0.729773\pi\)
−0.660777 + 0.750582i \(0.729773\pi\)
\(458\) 0 0
\(459\) 3.14785 0.146929
\(460\) 0 0
\(461\) −33.4176 −1.55641 −0.778206 0.628009i \(-0.783870\pi\)
−0.778206 + 0.628009i \(0.783870\pi\)
\(462\) 0 0
\(463\) 14.2409 0.661831 0.330916 0.943660i \(-0.392642\pi\)
0.330916 + 0.943660i \(0.392642\pi\)
\(464\) 0 0
\(465\) 4.18733 0.194183
\(466\) 0 0
\(467\) 37.6400 1.74177 0.870885 0.491487i \(-0.163546\pi\)
0.870885 + 0.491487i \(0.163546\pi\)
\(468\) 0 0
\(469\) 0.0768765 0.00354983
\(470\) 0 0
\(471\) −33.7238 −1.55391
\(472\) 0 0
\(473\) −10.9362 −0.502845
\(474\) 0 0
\(475\) 0.814583 0.0373756
\(476\) 0 0
\(477\) −16.7518 −0.767012
\(478\) 0 0
\(479\) 38.5608 1.76189 0.880945 0.473219i \(-0.156908\pi\)
0.880945 + 0.473219i \(0.156908\pi\)
\(480\) 0 0
\(481\) 17.7157 0.807768
\(482\) 0 0
\(483\) −1.71476 −0.0780243
\(484\) 0 0
\(485\) 4.02274 0.182663
\(486\) 0 0
\(487\) −16.9010 −0.765857 −0.382929 0.923778i \(-0.625085\pi\)
−0.382929 + 0.923778i \(0.625085\pi\)
\(488\) 0 0
\(489\) −23.0580 −1.04272
\(490\) 0 0
\(491\) 31.5936 1.42580 0.712899 0.701266i \(-0.247382\pi\)
0.712899 + 0.701266i \(0.247382\pi\)
\(492\) 0 0
\(493\) −0.100964 −0.00454719
\(494\) 0 0
\(495\) 4.49887 0.202209
\(496\) 0 0
\(497\) 0.0429718 0.00192755
\(498\) 0 0
\(499\) 14.7837 0.661810 0.330905 0.943664i \(-0.392646\pi\)
0.330905 + 0.943664i \(0.392646\pi\)
\(500\) 0 0
\(501\) 41.2373 1.84235
\(502\) 0 0
\(503\) 12.5093 0.557763 0.278881 0.960326i \(-0.410036\pi\)
0.278881 + 0.960326i \(0.410036\pi\)
\(504\) 0 0
\(505\) −4.27949 −0.190435
\(506\) 0 0
\(507\) 21.2412 0.943355
\(508\) 0 0
\(509\) −37.9373 −1.68154 −0.840772 0.541390i \(-0.817898\pi\)
−0.840772 + 0.541390i \(0.817898\pi\)
\(510\) 0 0
\(511\) 0.117274 0.00518790
\(512\) 0 0
\(513\) −0.544413 −0.0240364
\(514\) 0 0
\(515\) −5.45091 −0.240196
\(516\) 0 0
\(517\) −25.7326 −1.13172
\(518\) 0 0
\(519\) −7.35995 −0.323066
\(520\) 0 0
\(521\) 20.7642 0.909695 0.454848 0.890569i \(-0.349694\pi\)
0.454848 + 0.890569i \(0.349694\pi\)
\(522\) 0 0
\(523\) 17.8026 0.778455 0.389228 0.921142i \(-0.372742\pi\)
0.389228 + 0.921142i \(0.372742\pi\)
\(524\) 0 0
\(525\) −0.917074 −0.0400244
\(526\) 0 0
\(527\) 3.91755 0.170651
\(528\) 0 0
\(529\) 55.9054 2.43067
\(530\) 0 0
\(531\) 11.9486 0.518523
\(532\) 0 0
\(533\) 14.7451 0.638679
\(534\) 0 0
\(535\) −6.28437 −0.271697
\(536\) 0 0
\(537\) 17.7956 0.767938
\(538\) 0 0
\(539\) 41.8859 1.80415
\(540\) 0 0
\(541\) 12.2441 0.526413 0.263207 0.964739i \(-0.415220\pi\)
0.263207 + 0.964739i \(0.415220\pi\)
\(542\) 0 0
\(543\) 45.3787 1.94739
\(544\) 0 0
\(545\) −3.83461 −0.164257
\(546\) 0 0
\(547\) −34.6674 −1.48227 −0.741135 0.671357i \(-0.765712\pi\)
−0.741135 + 0.671357i \(0.765712\pi\)
\(548\) 0 0
\(549\) −0.424436 −0.0181145
\(550\) 0 0
\(551\) 0.0174615 0.000743886 0
\(552\) 0 0
\(553\) 0.884407 0.0376088
\(554\) 0 0
\(555\) −10.8549 −0.460767
\(556\) 0 0
\(557\) 1.70453 0.0722234 0.0361117 0.999348i \(-0.488503\pi\)
0.0361117 + 0.999348i \(0.488503\pi\)
\(558\) 0 0
\(559\) −3.15720 −0.133535
\(560\) 0 0
\(561\) 12.6051 0.532186
\(562\) 0 0
\(563\) −0.0501719 −0.00211449 −0.00105725 0.999999i \(-0.500337\pi\)
−0.00105725 + 0.999999i \(0.500337\pi\)
\(564\) 0 0
\(565\) 10.2921 0.432992
\(566\) 0 0
\(567\) 1.02331 0.0429749
\(568\) 0 0
\(569\) −17.8035 −0.746363 −0.373182 0.927758i \(-0.621733\pi\)
−0.373182 + 0.927758i \(0.621733\pi\)
\(570\) 0 0
\(571\) 42.8677 1.79396 0.896980 0.442072i \(-0.145756\pi\)
0.896980 + 0.442072i \(0.145756\pi\)
\(572\) 0 0
\(573\) −18.3704 −0.767436
\(574\) 0 0
\(575\) 42.1995 1.75984
\(576\) 0 0
\(577\) 31.8902 1.32761 0.663804 0.747907i \(-0.268941\pi\)
0.663804 + 0.747907i \(0.268941\pi\)
\(578\) 0 0
\(579\) −40.9805 −1.70309
\(580\) 0 0
\(581\) −0.825956 −0.0342664
\(582\) 0 0
\(583\) 66.7294 2.76365
\(584\) 0 0
\(585\) 1.29879 0.0536985
\(586\) 0 0
\(587\) −35.4373 −1.46265 −0.731326 0.682028i \(-0.761098\pi\)
−0.731326 + 0.682028i \(0.761098\pi\)
\(588\) 0 0
\(589\) −0.677531 −0.0279172
\(590\) 0 0
\(591\) 32.9383 1.35490
\(592\) 0 0
\(593\) 10.8530 0.445680 0.222840 0.974855i \(-0.428467\pi\)
0.222840 + 0.974855i \(0.428467\pi\)
\(594\) 0 0
\(595\) 0.0450311 0.00184610
\(596\) 0 0
\(597\) 3.66333 0.149930
\(598\) 0 0
\(599\) 17.8873 0.730857 0.365428 0.930839i \(-0.380923\pi\)
0.365428 + 0.930839i \(0.380923\pi\)
\(600\) 0 0
\(601\) −10.5916 −0.432040 −0.216020 0.976389i \(-0.569308\pi\)
−0.216020 + 0.976389i \(0.569308\pi\)
\(602\) 0 0
\(603\) −1.27106 −0.0517617
\(604\) 0 0
\(605\) −12.4282 −0.505278
\(606\) 0 0
\(607\) −30.2267 −1.22686 −0.613431 0.789748i \(-0.710211\pi\)
−0.613431 + 0.789748i \(0.710211\pi\)
\(608\) 0 0
\(609\) −0.0196585 −0.000796604 0
\(610\) 0 0
\(611\) −7.42884 −0.300539
\(612\) 0 0
\(613\) −16.2329 −0.655642 −0.327821 0.944740i \(-0.606314\pi\)
−0.327821 + 0.944740i \(0.606314\pi\)
\(614\) 0 0
\(615\) −9.03473 −0.364315
\(616\) 0 0
\(617\) −20.7233 −0.834287 −0.417144 0.908841i \(-0.636969\pi\)
−0.417144 + 0.908841i \(0.636969\pi\)
\(618\) 0 0
\(619\) −11.1370 −0.447636 −0.223818 0.974631i \(-0.571852\pi\)
−0.223818 + 0.974631i \(0.571852\pi\)
\(620\) 0 0
\(621\) −28.2034 −1.13176
\(622\) 0 0
\(623\) 0.566605 0.0227005
\(624\) 0 0
\(625\) 21.3221 0.852885
\(626\) 0 0
\(627\) −2.18002 −0.0870615
\(628\) 0 0
\(629\) −10.1556 −0.404930
\(630\) 0 0
\(631\) −9.97550 −0.397118 −0.198559 0.980089i \(-0.563626\pi\)
−0.198559 + 0.980089i \(0.563626\pi\)
\(632\) 0 0
\(633\) −24.4999 −0.973783
\(634\) 0 0
\(635\) 9.33017 0.370256
\(636\) 0 0
\(637\) 12.0922 0.479110
\(638\) 0 0
\(639\) −0.710489 −0.0281065
\(640\) 0 0
\(641\) −29.4343 −1.16259 −0.581293 0.813694i \(-0.697453\pi\)
−0.581293 + 0.813694i \(0.697453\pi\)
\(642\) 0 0
\(643\) 3.83020 0.151048 0.0755242 0.997144i \(-0.475937\pi\)
0.0755242 + 0.997144i \(0.475937\pi\)
\(644\) 0 0
\(645\) 1.93451 0.0761711
\(646\) 0 0
\(647\) −8.31181 −0.326771 −0.163386 0.986562i \(-0.552241\pi\)
−0.163386 + 0.986562i \(0.552241\pi\)
\(648\) 0 0
\(649\) −47.5961 −1.86831
\(650\) 0 0
\(651\) 0.762778 0.0298956
\(652\) 0 0
\(653\) 10.4205 0.407785 0.203893 0.978993i \(-0.434641\pi\)
0.203893 + 0.978993i \(0.434641\pi\)
\(654\) 0 0
\(655\) 10.3764 0.405439
\(656\) 0 0
\(657\) −1.93899 −0.0756471
\(658\) 0 0
\(659\) −9.88523 −0.385074 −0.192537 0.981290i \(-0.561672\pi\)
−0.192537 + 0.981290i \(0.561672\pi\)
\(660\) 0 0
\(661\) 34.1127 1.32683 0.663415 0.748252i \(-0.269106\pi\)
0.663415 + 0.748252i \(0.269106\pi\)
\(662\) 0 0
\(663\) 3.63900 0.141327
\(664\) 0 0
\(665\) −0.00778803 −0.000302007 0
\(666\) 0 0
\(667\) 0.904595 0.0350261
\(668\) 0 0
\(669\) −8.29066 −0.320535
\(670\) 0 0
\(671\) 1.69071 0.0652690
\(672\) 0 0
\(673\) 0.592944 0.0228563 0.0114282 0.999935i \(-0.496362\pi\)
0.0114282 + 0.999935i \(0.496362\pi\)
\(674\) 0 0
\(675\) −15.0835 −0.580564
\(676\) 0 0
\(677\) 15.2324 0.585429 0.292714 0.956200i \(-0.405441\pi\)
0.292714 + 0.956200i \(0.405441\pi\)
\(678\) 0 0
\(679\) 0.732796 0.0281221
\(680\) 0 0
\(681\) 13.3039 0.509806
\(682\) 0 0
\(683\) −26.9810 −1.03240 −0.516200 0.856468i \(-0.672654\pi\)
−0.516200 + 0.856468i \(0.672654\pi\)
\(684\) 0 0
\(685\) 6.97463 0.266487
\(686\) 0 0
\(687\) −21.9745 −0.838379
\(688\) 0 0
\(689\) 19.2643 0.733913
\(690\) 0 0
\(691\) 39.4958 1.50249 0.751246 0.660022i \(-0.229453\pi\)
0.751246 + 0.660022i \(0.229453\pi\)
\(692\) 0 0
\(693\) 0.819530 0.0311314
\(694\) 0 0
\(695\) −0.909767 −0.0345094
\(696\) 0 0
\(697\) −8.45264 −0.320166
\(698\) 0 0
\(699\) 20.4380 0.773035
\(700\) 0 0
\(701\) −41.2447 −1.55779 −0.778895 0.627154i \(-0.784219\pi\)
−0.778895 + 0.627154i \(0.784219\pi\)
\(702\) 0 0
\(703\) 1.75639 0.0662434
\(704\) 0 0
\(705\) 4.55187 0.171433
\(706\) 0 0
\(707\) −0.779566 −0.0293186
\(708\) 0 0
\(709\) −1.93993 −0.0728557 −0.0364278 0.999336i \(-0.511598\pi\)
−0.0364278 + 0.999336i \(0.511598\pi\)
\(710\) 0 0
\(711\) −14.6226 −0.548391
\(712\) 0 0
\(713\) −35.0995 −1.31449
\(714\) 0 0
\(715\) −5.17364 −0.193483
\(716\) 0 0
\(717\) 20.6806 0.772332
\(718\) 0 0
\(719\) −32.6548 −1.21782 −0.608909 0.793240i \(-0.708393\pi\)
−0.608909 + 0.793240i \(0.708393\pi\)
\(720\) 0 0
\(721\) −0.992956 −0.0369796
\(722\) 0 0
\(723\) 0.250126 0.00930228
\(724\) 0 0
\(725\) 0.483788 0.0179674
\(726\) 0 0
\(727\) −30.5702 −1.13379 −0.566893 0.823791i \(-0.691855\pi\)
−0.566893 + 0.823791i \(0.691855\pi\)
\(728\) 0 0
\(729\) 3.29541 0.122052
\(730\) 0 0
\(731\) 1.80987 0.0669405
\(732\) 0 0
\(733\) −35.8563 −1.32438 −0.662192 0.749334i \(-0.730374\pi\)
−0.662192 + 0.749334i \(0.730374\pi\)
\(734\) 0 0
\(735\) −7.40923 −0.273294
\(736\) 0 0
\(737\) 5.06317 0.186504
\(738\) 0 0
\(739\) −3.80175 −0.139850 −0.0699249 0.997552i \(-0.522276\pi\)
−0.0699249 + 0.997552i \(0.522276\pi\)
\(740\) 0 0
\(741\) −0.629357 −0.0231200
\(742\) 0 0
\(743\) −44.8001 −1.64356 −0.821778 0.569808i \(-0.807017\pi\)
−0.821778 + 0.569808i \(0.807017\pi\)
\(744\) 0 0
\(745\) 3.46423 0.126920
\(746\) 0 0
\(747\) 13.6562 0.499655
\(748\) 0 0
\(749\) −1.14478 −0.0418294
\(750\) 0 0
\(751\) −9.92611 −0.362209 −0.181104 0.983464i \(-0.557967\pi\)
−0.181104 + 0.983464i \(0.557967\pi\)
\(752\) 0 0
\(753\) −29.5618 −1.07729
\(754\) 0 0
\(755\) −8.86111 −0.322489
\(756\) 0 0
\(757\) 7.56108 0.274812 0.137406 0.990515i \(-0.456123\pi\)
0.137406 + 0.990515i \(0.456123\pi\)
\(758\) 0 0
\(759\) −112.936 −4.09932
\(760\) 0 0
\(761\) 12.3775 0.448685 0.224343 0.974510i \(-0.427976\pi\)
0.224343 + 0.974510i \(0.427976\pi\)
\(762\) 0 0
\(763\) −0.698527 −0.0252884
\(764\) 0 0
\(765\) −0.744537 −0.0269188
\(766\) 0 0
\(767\) −13.7407 −0.496147
\(768\) 0 0
\(769\) 10.7979 0.389383 0.194691 0.980865i \(-0.437629\pi\)
0.194691 + 0.980865i \(0.437629\pi\)
\(770\) 0 0
\(771\) −4.63181 −0.166811
\(772\) 0 0
\(773\) −30.0401 −1.08047 −0.540233 0.841515i \(-0.681664\pi\)
−0.540233 + 0.841515i \(0.681664\pi\)
\(774\) 0 0
\(775\) −18.7716 −0.674297
\(776\) 0 0
\(777\) −1.97737 −0.0709379
\(778\) 0 0
\(779\) 1.46187 0.0523768
\(780\) 0 0
\(781\) 2.83017 0.101272
\(782\) 0 0
\(783\) −0.323332 −0.0115550
\(784\) 0 0
\(785\) −7.93475 −0.283203
\(786\) 0 0
\(787\) −48.0365 −1.71232 −0.856158 0.516713i \(-0.827155\pi\)
−0.856158 + 0.516713i \(0.827155\pi\)
\(788\) 0 0
\(789\) 19.0483 0.678139
\(790\) 0 0
\(791\) 1.87484 0.0666618
\(792\) 0 0
\(793\) 0.488096 0.0173328
\(794\) 0 0
\(795\) −11.8038 −0.418638
\(796\) 0 0
\(797\) −28.6947 −1.01642 −0.508210 0.861233i \(-0.669693\pi\)
−0.508210 + 0.861233i \(0.669693\pi\)
\(798\) 0 0
\(799\) 4.25860 0.150658
\(800\) 0 0
\(801\) −9.36815 −0.331007
\(802\) 0 0
\(803\) 7.72380 0.272567
\(804\) 0 0
\(805\) −0.403460 −0.0142201
\(806\) 0 0
\(807\) −38.4717 −1.35427
\(808\) 0 0
\(809\) −8.06849 −0.283673 −0.141836 0.989890i \(-0.545301\pi\)
−0.141836 + 0.989890i \(0.545301\pi\)
\(810\) 0 0
\(811\) 9.74183 0.342082 0.171041 0.985264i \(-0.445287\pi\)
0.171041 + 0.985264i \(0.445287\pi\)
\(812\) 0 0
\(813\) 1.49872 0.0525625
\(814\) 0 0
\(815\) −5.42524 −0.190038
\(816\) 0 0
\(817\) −0.313013 −0.0109509
\(818\) 0 0
\(819\) 0.236593 0.00826723
\(820\) 0 0
\(821\) −36.8338 −1.28551 −0.642755 0.766072i \(-0.722209\pi\)
−0.642755 + 0.766072i \(0.722209\pi\)
\(822\) 0 0
\(823\) 9.14156 0.318655 0.159327 0.987226i \(-0.449067\pi\)
0.159327 + 0.987226i \(0.449067\pi\)
\(824\) 0 0
\(825\) −60.3995 −2.10284
\(826\) 0 0
\(827\) 20.3922 0.709105 0.354553 0.935036i \(-0.384633\pi\)
0.354553 + 0.935036i \(0.384633\pi\)
\(828\) 0 0
\(829\) 13.4389 0.466754 0.233377 0.972386i \(-0.425022\pi\)
0.233377 + 0.972386i \(0.425022\pi\)
\(830\) 0 0
\(831\) −40.9796 −1.42157
\(832\) 0 0
\(833\) −6.93187 −0.240175
\(834\) 0 0
\(835\) 9.70259 0.335772
\(836\) 0 0
\(837\) 12.5457 0.433644
\(838\) 0 0
\(839\) −36.0771 −1.24552 −0.622759 0.782414i \(-0.713988\pi\)
−0.622759 + 0.782414i \(0.713988\pi\)
\(840\) 0 0
\(841\) −28.9896 −0.999642
\(842\) 0 0
\(843\) −64.7558 −2.23031
\(844\) 0 0
\(845\) 4.99777 0.171929
\(846\) 0 0
\(847\) −2.26396 −0.0777906
\(848\) 0 0
\(849\) −0.131313 −0.00450665
\(850\) 0 0
\(851\) 90.9897 3.11909
\(852\) 0 0
\(853\) −39.6517 −1.35765 −0.678824 0.734301i \(-0.737510\pi\)
−0.678824 + 0.734301i \(0.737510\pi\)
\(854\) 0 0
\(855\) 0.128766 0.00440370
\(856\) 0 0
\(857\) 39.3706 1.34487 0.672437 0.740154i \(-0.265248\pi\)
0.672437 + 0.740154i \(0.265248\pi\)
\(858\) 0 0
\(859\) −45.8736 −1.56519 −0.782593 0.622533i \(-0.786104\pi\)
−0.782593 + 0.622533i \(0.786104\pi\)
\(860\) 0 0
\(861\) −1.64580 −0.0560886
\(862\) 0 0
\(863\) 51.7247 1.76073 0.880365 0.474296i \(-0.157297\pi\)
0.880365 + 0.474296i \(0.157297\pi\)
\(864\) 0 0
\(865\) −1.73170 −0.0588795
\(866\) 0 0
\(867\) 33.9921 1.15443
\(868\) 0 0
\(869\) 58.2480 1.97593
\(870\) 0 0
\(871\) 1.46170 0.0495280
\(872\) 0 0
\(873\) −12.1159 −0.410062
\(874\) 0 0
\(875\) −0.442875 −0.0149719
\(876\) 0 0
\(877\) 24.1286 0.814766 0.407383 0.913257i \(-0.366441\pi\)
0.407383 + 0.913257i \(0.366441\pi\)
\(878\) 0 0
\(879\) −55.0516 −1.85685
\(880\) 0 0
\(881\) −43.6777 −1.47154 −0.735770 0.677232i \(-0.763179\pi\)
−0.735770 + 0.677232i \(0.763179\pi\)
\(882\) 0 0
\(883\) 30.7644 1.03531 0.517653 0.855591i \(-0.326806\pi\)
0.517653 + 0.855591i \(0.326806\pi\)
\(884\) 0 0
\(885\) 8.41931 0.283012
\(886\) 0 0
\(887\) 8.32049 0.279375 0.139687 0.990196i \(-0.455390\pi\)
0.139687 + 0.990196i \(0.455390\pi\)
\(888\) 0 0
\(889\) 1.69962 0.0570033
\(890\) 0 0
\(891\) 67.3962 2.25786
\(892\) 0 0
\(893\) −0.736515 −0.0246465
\(894\) 0 0
\(895\) 4.18707 0.139958
\(896\) 0 0
\(897\) −32.6039 −1.08861
\(898\) 0 0
\(899\) −0.402392 −0.0134205
\(900\) 0 0
\(901\) −11.0433 −0.367907
\(902\) 0 0
\(903\) 0.352396 0.0117270
\(904\) 0 0
\(905\) 10.6770 0.354915
\(906\) 0 0
\(907\) −43.8510 −1.45605 −0.728025 0.685551i \(-0.759562\pi\)
−0.728025 + 0.685551i \(0.759562\pi\)
\(908\) 0 0
\(909\) 12.8892 0.427508
\(910\) 0 0
\(911\) 21.5806 0.714997 0.357498 0.933914i \(-0.383630\pi\)
0.357498 + 0.933914i \(0.383630\pi\)
\(912\) 0 0
\(913\) −54.3984 −1.80032
\(914\) 0 0
\(915\) −0.299071 −0.00988697
\(916\) 0 0
\(917\) 1.89020 0.0624198
\(918\) 0 0
\(919\) 5.26334 0.173621 0.0868107 0.996225i \(-0.472332\pi\)
0.0868107 + 0.996225i \(0.472332\pi\)
\(920\) 0 0
\(921\) −32.1652 −1.05988
\(922\) 0 0
\(923\) 0.817053 0.0268936
\(924\) 0 0
\(925\) 48.6624 1.60001
\(926\) 0 0
\(927\) 16.4174 0.539217
\(928\) 0 0
\(929\) 24.4477 0.802103 0.401051 0.916056i \(-0.368645\pi\)
0.401051 + 0.916056i \(0.368645\pi\)
\(930\) 0 0
\(931\) 1.19885 0.0392908
\(932\) 0 0
\(933\) −47.5781 −1.55764
\(934\) 0 0
\(935\) 2.96580 0.0969920
\(936\) 0 0
\(937\) −49.4119 −1.61422 −0.807108 0.590404i \(-0.798969\pi\)
−0.807108 + 0.590404i \(0.798969\pi\)
\(938\) 0 0
\(939\) −21.5080 −0.701888
\(940\) 0 0
\(941\) 32.1962 1.04957 0.524784 0.851236i \(-0.324146\pi\)
0.524784 + 0.851236i \(0.324146\pi\)
\(942\) 0 0
\(943\) 75.7320 2.46617
\(944\) 0 0
\(945\) 0.144210 0.00469114
\(946\) 0 0
\(947\) −23.1315 −0.751672 −0.375836 0.926686i \(-0.622644\pi\)
−0.375836 + 0.926686i \(0.622644\pi\)
\(948\) 0 0
\(949\) 2.22981 0.0723827
\(950\) 0 0
\(951\) −0.784059 −0.0254249
\(952\) 0 0
\(953\) 35.9741 1.16532 0.582658 0.812718i \(-0.302013\pi\)
0.582658 + 0.812718i \(0.302013\pi\)
\(954\) 0 0
\(955\) −4.32231 −0.139867
\(956\) 0 0
\(957\) −1.29473 −0.0418528
\(958\) 0 0
\(959\) 1.27052 0.0410273
\(960\) 0 0
\(961\) −15.3866 −0.496343
\(962\) 0 0
\(963\) 18.9276 0.609934
\(964\) 0 0
\(965\) −9.64215 −0.310392
\(966\) 0 0
\(967\) 4.67208 0.150244 0.0751220 0.997174i \(-0.476065\pi\)
0.0751220 + 0.997174i \(0.476065\pi\)
\(968\) 0 0
\(969\) 0.360780 0.0115899
\(970\) 0 0
\(971\) 24.7247 0.793454 0.396727 0.917937i \(-0.370146\pi\)
0.396727 + 0.917937i \(0.370146\pi\)
\(972\) 0 0
\(973\) −0.165726 −0.00531294
\(974\) 0 0
\(975\) −17.4369 −0.558429
\(976\) 0 0
\(977\) −56.7770 −1.81646 −0.908228 0.418476i \(-0.862564\pi\)
−0.908228 + 0.418476i \(0.862564\pi\)
\(978\) 0 0
\(979\) 37.3172 1.19266
\(980\) 0 0
\(981\) 11.5493 0.368741
\(982\) 0 0
\(983\) 6.05308 0.193063 0.0965316 0.995330i \(-0.469225\pi\)
0.0965316 + 0.995330i \(0.469225\pi\)
\(984\) 0 0
\(985\) 7.74994 0.246934
\(986\) 0 0
\(987\) 0.829184 0.0263932
\(988\) 0 0
\(989\) −16.2157 −0.515628
\(990\) 0 0
\(991\) 41.3882 1.31474 0.657369 0.753569i \(-0.271669\pi\)
0.657369 + 0.753569i \(0.271669\pi\)
\(992\) 0 0
\(993\) 39.8945 1.26601
\(994\) 0 0
\(995\) 0.861931 0.0273251
\(996\) 0 0
\(997\) −37.2892 −1.18096 −0.590480 0.807052i \(-0.701062\pi\)
−0.590480 + 0.807052i \(0.701062\pi\)
\(998\) 0 0
\(999\) −32.5227 −1.02897
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 6044.2.a.b.1.14 63
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6044.2.a.b.1.14 63 1.1 even 1 trivial