Properties

Label 2600.2.a.v.1.1
Level $2600$
Weight $2$
Character 2600.1
Self dual yes
Analytic conductor $20.761$
Analytic rank $0$
Dimension $2$
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] = [2600,2,Mod(1,2600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2600, 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("2600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2600.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: \(20.7611045255\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 520)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 2600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.732051 q^{3} -3.46410 q^{7} -2.46410 q^{9} +O(q^{10})\) \(q-0.732051 q^{3} -3.46410 q^{7} -2.46410 q^{9} +2.73205 q^{11} -1.00000 q^{13} -7.46410 q^{17} -2.73205 q^{19} +2.53590 q^{21} +0.732051 q^{23} +4.00000 q^{27} +9.46410 q^{29} -0.196152 q^{31} -2.00000 q^{33} +0.732051 q^{39} +0.535898 q^{41} +7.26795 q^{43} -4.53590 q^{47} +5.00000 q^{49} +5.46410 q^{51} +0.535898 q^{53} +2.00000 q^{57} +5.66025 q^{59} -12.3923 q^{61} +8.53590 q^{63} +12.9282 q^{67} -0.535898 q^{69} +9.26795 q^{71} +2.92820 q^{73} -9.46410 q^{77} -6.53590 q^{79} +4.46410 q^{81} +10.3923 q^{83} -6.92820 q^{87} -12.9282 q^{89} +3.46410 q^{91} +0.143594 q^{93} -15.8564 q^{97} -6.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{9} + 2 q^{11} - 2 q^{13} - 8 q^{17} - 2 q^{19} + 12 q^{21} - 2 q^{23} + 8 q^{27} + 12 q^{29} + 10 q^{31} - 4 q^{33} - 2 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{47} + 10 q^{49} + 4 q^{51} + 8 q^{53} + 4 q^{57} - 6 q^{59} - 4 q^{61} + 24 q^{63} + 12 q^{67} - 8 q^{69} + 22 q^{71} - 8 q^{73} - 12 q^{77} - 20 q^{79} + 2 q^{81} - 12 q^{89} + 28 q^{93} - 4 q^{97} - 10 q^{99}+O(q^{100}) \) 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
\(3\) −0.732051 −0.422650 −0.211325 0.977416i \(-0.567778\pi\)
−0.211325 + 0.977416i \(0.567778\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.46410 −1.30931 −0.654654 0.755929i \(-0.727186\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 0 0
\(9\) −2.46410 −0.821367
\(10\) 0 0
\(11\) 2.73205 0.823744 0.411872 0.911242i \(-0.364875\pi\)
0.411872 + 0.911242i \(0.364875\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.46410 −1.81031 −0.905155 0.425081i \(-0.860246\pi\)
−0.905155 + 0.425081i \(0.860246\pi\)
\(18\) 0 0
\(19\) −2.73205 −0.626775 −0.313388 0.949625i \(-0.601464\pi\)
−0.313388 + 0.949625i \(0.601464\pi\)
\(20\) 0 0
\(21\) 2.53590 0.553378
\(22\) 0 0
\(23\) 0.732051 0.152643 0.0763216 0.997083i \(-0.475682\pi\)
0.0763216 + 0.997083i \(0.475682\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 9.46410 1.75744 0.878720 0.477338i \(-0.158398\pi\)
0.878720 + 0.477338i \(0.158398\pi\)
\(30\) 0 0
\(31\) −0.196152 −0.0352300 −0.0176150 0.999845i \(-0.505607\pi\)
−0.0176150 + 0.999845i \(0.505607\pi\)
\(32\) 0 0
\(33\) −2.00000 −0.348155
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0.732051 0.117222
\(40\) 0 0
\(41\) 0.535898 0.0836933 0.0418466 0.999124i \(-0.486676\pi\)
0.0418466 + 0.999124i \(0.486676\pi\)
\(42\) 0 0
\(43\) 7.26795 1.10835 0.554176 0.832400i \(-0.313033\pi\)
0.554176 + 0.832400i \(0.313033\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.53590 −0.661629 −0.330814 0.943696i \(-0.607323\pi\)
−0.330814 + 0.943696i \(0.607323\pi\)
\(48\) 0 0
\(49\) 5.00000 0.714286
\(50\) 0 0
\(51\) 5.46410 0.765127
\(52\) 0 0
\(53\) 0.535898 0.0736113 0.0368057 0.999322i \(-0.488282\pi\)
0.0368057 + 0.999322i \(0.488282\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 5.66025 0.736902 0.368451 0.929647i \(-0.379888\pi\)
0.368451 + 0.929647i \(0.379888\pi\)
\(60\) 0 0
\(61\) −12.3923 −1.58667 −0.793336 0.608784i \(-0.791658\pi\)
−0.793336 + 0.608784i \(0.791658\pi\)
\(62\) 0 0
\(63\) 8.53590 1.07542
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.9282 1.57943 0.789716 0.613473i \(-0.210228\pi\)
0.789716 + 0.613473i \(0.210228\pi\)
\(68\) 0 0
\(69\) −0.535898 −0.0645146
\(70\) 0 0
\(71\) 9.26795 1.09990 0.549952 0.835197i \(-0.314646\pi\)
0.549952 + 0.835197i \(0.314646\pi\)
\(72\) 0 0
\(73\) 2.92820 0.342720 0.171360 0.985208i \(-0.445184\pi\)
0.171360 + 0.985208i \(0.445184\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.46410 −1.07853
\(78\) 0 0
\(79\) −6.53590 −0.735346 −0.367673 0.929955i \(-0.619845\pi\)
−0.367673 + 0.929955i \(0.619845\pi\)
\(80\) 0 0
\(81\) 4.46410 0.496011
\(82\) 0 0
\(83\) 10.3923 1.14070 0.570352 0.821401i \(-0.306807\pi\)
0.570352 + 0.821401i \(0.306807\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.92820 −0.742781
\(88\) 0 0
\(89\) −12.9282 −1.37039 −0.685193 0.728361i \(-0.740282\pi\)
−0.685193 + 0.728361i \(0.740282\pi\)
\(90\) 0 0
\(91\) 3.46410 0.363137
\(92\) 0 0
\(93\) 0.143594 0.0148900
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −15.8564 −1.60997 −0.804987 0.593292i \(-0.797828\pi\)
−0.804987 + 0.593292i \(0.797828\pi\)
\(98\) 0 0
\(99\) −6.73205 −0.676597
\(100\) 0 0
\(101\) 4.92820 0.490375 0.245187 0.969476i \(-0.421151\pi\)
0.245187 + 0.969476i \(0.421151\pi\)
\(102\) 0 0
\(103\) 6.19615 0.610525 0.305263 0.952268i \(-0.401256\pi\)
0.305263 + 0.952268i \(0.401256\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.0526 1.93855 0.969277 0.245972i \(-0.0791070\pi\)
0.969277 + 0.245972i \(0.0791070\pi\)
\(108\) 0 0
\(109\) 15.8564 1.51877 0.759384 0.650643i \(-0.225500\pi\)
0.759384 + 0.650643i \(0.225500\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 18.3923 1.73020 0.865101 0.501597i \(-0.167254\pi\)
0.865101 + 0.501597i \(0.167254\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.46410 0.227806
\(118\) 0 0
\(119\) 25.8564 2.37025
\(120\) 0 0
\(121\) −3.53590 −0.321445
\(122\) 0 0
\(123\) −0.392305 −0.0353729
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.80385 0.160066 0.0800328 0.996792i \(-0.474497\pi\)
0.0800328 + 0.996792i \(0.474497\pi\)
\(128\) 0 0
\(129\) −5.32051 −0.468445
\(130\) 0 0
\(131\) −2.92820 −0.255838 −0.127919 0.991785i \(-0.540830\pi\)
−0.127919 + 0.991785i \(0.540830\pi\)
\(132\) 0 0
\(133\) 9.46410 0.820642
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.92820 −0.762788 −0.381394 0.924413i \(-0.624556\pi\)
−0.381394 + 0.924413i \(0.624556\pi\)
\(138\) 0 0
\(139\) −13.4641 −1.14201 −0.571005 0.820947i \(-0.693446\pi\)
−0.571005 + 0.820947i \(0.693446\pi\)
\(140\) 0 0
\(141\) 3.32051 0.279637
\(142\) 0 0
\(143\) −2.73205 −0.228466
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.66025 −0.301893
\(148\) 0 0
\(149\) −7.85641 −0.643622 −0.321811 0.946804i \(-0.604292\pi\)
−0.321811 + 0.946804i \(0.604292\pi\)
\(150\) 0 0
\(151\) 11.8038 0.960583 0.480292 0.877109i \(-0.340531\pi\)
0.480292 + 0.877109i \(0.340531\pi\)
\(152\) 0 0
\(153\) 18.3923 1.48693
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 7.85641 0.627009 0.313505 0.949587i \(-0.398497\pi\)
0.313505 + 0.949587i \(0.398497\pi\)
\(158\) 0 0
\(159\) −0.392305 −0.0311118
\(160\) 0 0
\(161\) −2.53590 −0.199857
\(162\) 0 0
\(163\) 8.92820 0.699311 0.349655 0.936878i \(-0.386299\pi\)
0.349655 + 0.936878i \(0.386299\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.3205 1.64983 0.824915 0.565256i \(-0.191223\pi\)
0.824915 + 0.565256i \(0.191223\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 6.73205 0.514813
\(172\) 0 0
\(173\) 2.39230 0.181884 0.0909418 0.995856i \(-0.471012\pi\)
0.0909418 + 0.995856i \(0.471012\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.14359 −0.311452
\(178\) 0 0
\(179\) −21.8564 −1.63362 −0.816812 0.576904i \(-0.804261\pi\)
−0.816812 + 0.576904i \(0.804261\pi\)
\(180\) 0 0
\(181\) 6.53590 0.485810 0.242905 0.970050i \(-0.421900\pi\)
0.242905 + 0.970050i \(0.421900\pi\)
\(182\) 0 0
\(183\) 9.07180 0.670607
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −20.3923 −1.49123
\(188\) 0 0
\(189\) −13.8564 −1.00791
\(190\) 0 0
\(191\) 18.9282 1.36960 0.684798 0.728733i \(-0.259890\pi\)
0.684798 + 0.728733i \(0.259890\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.92820 −0.636108 −0.318054 0.948073i \(-0.603029\pi\)
−0.318054 + 0.948073i \(0.603029\pi\)
\(198\) 0 0
\(199\) −6.92820 −0.491127 −0.245564 0.969380i \(-0.578973\pi\)
−0.245564 + 0.969380i \(0.578973\pi\)
\(200\) 0 0
\(201\) −9.46410 −0.667546
\(202\) 0 0
\(203\) −32.7846 −2.30103
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.80385 −0.125376
\(208\) 0 0
\(209\) −7.46410 −0.516303
\(210\) 0 0
\(211\) 2.92820 0.201586 0.100793 0.994907i \(-0.467862\pi\)
0.100793 + 0.994907i \(0.467862\pi\)
\(212\) 0 0
\(213\) −6.78461 −0.464874
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.679492 0.0461269
\(218\) 0 0
\(219\) −2.14359 −0.144851
\(220\) 0 0
\(221\) 7.46410 0.502090
\(222\) 0 0
\(223\) −25.3205 −1.69559 −0.847793 0.530327i \(-0.822069\pi\)
−0.847793 + 0.530327i \(0.822069\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) 19.4641 1.28622 0.643112 0.765772i \(-0.277643\pi\)
0.643112 + 0.765772i \(0.277643\pi\)
\(230\) 0 0
\(231\) 6.92820 0.455842
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 4.78461 0.310794
\(238\) 0 0
\(239\) 25.2679 1.63445 0.817224 0.576320i \(-0.195512\pi\)
0.817224 + 0.576320i \(0.195512\pi\)
\(240\) 0 0
\(241\) 20.2487 1.30433 0.652167 0.758075i \(-0.273860\pi\)
0.652167 + 0.758075i \(0.273860\pi\)
\(242\) 0 0
\(243\) −15.2679 −0.979439
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.73205 0.173836
\(248\) 0 0
\(249\) −7.60770 −0.482118
\(250\) 0 0
\(251\) 23.3205 1.47198 0.735989 0.676994i \(-0.236718\pi\)
0.735989 + 0.676994i \(0.236718\pi\)
\(252\) 0 0
\(253\) 2.00000 0.125739
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −23.3205 −1.44350
\(262\) 0 0
\(263\) 11.6603 0.719002 0.359501 0.933145i \(-0.382947\pi\)
0.359501 + 0.933145i \(0.382947\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.46410 0.579194
\(268\) 0 0
\(269\) −0.143594 −0.00875505 −0.00437753 0.999990i \(-0.501393\pi\)
−0.00437753 + 0.999990i \(0.501393\pi\)
\(270\) 0 0
\(271\) −23.1244 −1.40470 −0.702352 0.711830i \(-0.747867\pi\)
−0.702352 + 0.711830i \(0.747867\pi\)
\(272\) 0 0
\(273\) −2.53590 −0.153480
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 21.3205 1.28103 0.640513 0.767948i \(-0.278722\pi\)
0.640513 + 0.767948i \(0.278722\pi\)
\(278\) 0 0
\(279\) 0.483340 0.0289368
\(280\) 0 0
\(281\) −4.53590 −0.270589 −0.135295 0.990805i \(-0.543198\pi\)
−0.135295 + 0.990805i \(0.543198\pi\)
\(282\) 0 0
\(283\) 24.0526 1.42978 0.714888 0.699239i \(-0.246478\pi\)
0.714888 + 0.699239i \(0.246478\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.85641 −0.109580
\(288\) 0 0
\(289\) 38.7128 2.27722
\(290\) 0 0
\(291\) 11.6077 0.680455
\(292\) 0 0
\(293\) −6.92820 −0.404750 −0.202375 0.979308i \(-0.564866\pi\)
−0.202375 + 0.979308i \(0.564866\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 10.9282 0.634119
\(298\) 0 0
\(299\) −0.732051 −0.0423356
\(300\) 0 0
\(301\) −25.1769 −1.45117
\(302\) 0 0
\(303\) −3.60770 −0.207257
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.5359 0.943754 0.471877 0.881665i \(-0.343577\pi\)
0.471877 + 0.881665i \(0.343577\pi\)
\(308\) 0 0
\(309\) −4.53590 −0.258038
\(310\) 0 0
\(311\) 31.3205 1.77602 0.888012 0.459821i \(-0.152086\pi\)
0.888012 + 0.459821i \(0.152086\pi\)
\(312\) 0 0
\(313\) −10.3923 −0.587408 −0.293704 0.955896i \(-0.594888\pi\)
−0.293704 + 0.955896i \(0.594888\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.85641 0.104266 0.0521331 0.998640i \(-0.483398\pi\)
0.0521331 + 0.998640i \(0.483398\pi\)
\(318\) 0 0
\(319\) 25.8564 1.44768
\(320\) 0 0
\(321\) −14.6795 −0.819329
\(322\) 0 0
\(323\) 20.3923 1.13466
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −11.6077 −0.641907
\(328\) 0 0
\(329\) 15.7128 0.866275
\(330\) 0 0
\(331\) −8.58846 −0.472064 −0.236032 0.971745i \(-0.575847\pi\)
−0.236032 + 0.971745i \(0.575847\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −22.3923 −1.21979 −0.609893 0.792484i \(-0.708788\pi\)
−0.609893 + 0.792484i \(0.708788\pi\)
\(338\) 0 0
\(339\) −13.4641 −0.731270
\(340\) 0 0
\(341\) −0.535898 −0.0290205
\(342\) 0 0
\(343\) 6.92820 0.374088
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.19615 −0.117896 −0.0589478 0.998261i \(-0.518775\pi\)
−0.0589478 + 0.998261i \(0.518775\pi\)
\(348\) 0 0
\(349\) 12.5359 0.671031 0.335516 0.942035i \(-0.391089\pi\)
0.335516 + 0.942035i \(0.391089\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) 6.92820 0.368751 0.184376 0.982856i \(-0.440974\pi\)
0.184376 + 0.982856i \(0.440974\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −18.9282 −1.00179
\(358\) 0 0
\(359\) 11.1244 0.587121 0.293561 0.955940i \(-0.405160\pi\)
0.293561 + 0.955940i \(0.405160\pi\)
\(360\) 0 0
\(361\) −11.5359 −0.607153
\(362\) 0 0
\(363\) 2.58846 0.135859
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.41154 0.0736819 0.0368410 0.999321i \(-0.488271\pi\)
0.0368410 + 0.999321i \(0.488271\pi\)
\(368\) 0 0
\(369\) −1.32051 −0.0687429
\(370\) 0 0
\(371\) −1.85641 −0.0963798
\(372\) 0 0
\(373\) 7.85641 0.406789 0.203395 0.979097i \(-0.434803\pi\)
0.203395 + 0.979097i \(0.434803\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.46410 −0.487426
\(378\) 0 0
\(379\) −20.1962 −1.03741 −0.518703 0.854954i \(-0.673585\pi\)
−0.518703 + 0.854954i \(0.673585\pi\)
\(380\) 0 0
\(381\) −1.32051 −0.0676517
\(382\) 0 0
\(383\) 1.60770 0.0821494 0.0410747 0.999156i \(-0.486922\pi\)
0.0410747 + 0.999156i \(0.486922\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −17.9090 −0.910364
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) −5.46410 −0.276331
\(392\) 0 0
\(393\) 2.14359 0.108130
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.07180 0.254546 0.127273 0.991868i \(-0.459378\pi\)
0.127273 + 0.991868i \(0.459378\pi\)
\(398\) 0 0
\(399\) −6.92820 −0.346844
\(400\) 0 0
\(401\) −10.7846 −0.538558 −0.269279 0.963062i \(-0.586785\pi\)
−0.269279 + 0.963062i \(0.586785\pi\)
\(402\) 0 0
\(403\) 0.196152 0.00977105
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 33.3205 1.64759 0.823797 0.566886i \(-0.191852\pi\)
0.823797 + 0.566886i \(0.191852\pi\)
\(410\) 0 0
\(411\) 6.53590 0.322392
\(412\) 0 0
\(413\) −19.6077 −0.964832
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 9.85641 0.482670
\(418\) 0 0
\(419\) −25.4641 −1.24400 −0.622001 0.783016i \(-0.713680\pi\)
−0.622001 + 0.783016i \(0.713680\pi\)
\(420\) 0 0
\(421\) −19.0718 −0.929503 −0.464751 0.885441i \(-0.653856\pi\)
−0.464751 + 0.885441i \(0.653856\pi\)
\(422\) 0 0
\(423\) 11.1769 0.543440
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 42.9282 2.07744
\(428\) 0 0
\(429\) 2.00000 0.0965609
\(430\) 0 0
\(431\) −22.0526 −1.06223 −0.531117 0.847298i \(-0.678228\pi\)
−0.531117 + 0.847298i \(0.678228\pi\)
\(432\) 0 0
\(433\) −15.0718 −0.724304 −0.362152 0.932119i \(-0.617958\pi\)
−0.362152 + 0.932119i \(0.617958\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) −13.8564 −0.661330 −0.330665 0.943748i \(-0.607273\pi\)
−0.330665 + 0.943748i \(0.607273\pi\)
\(440\) 0 0
\(441\) −12.3205 −0.586691
\(442\) 0 0
\(443\) −28.4449 −1.35146 −0.675728 0.737151i \(-0.736171\pi\)
−0.675728 + 0.737151i \(0.736171\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.75129 0.272027
\(448\) 0 0
\(449\) −14.3923 −0.679215 −0.339607 0.940567i \(-0.610294\pi\)
−0.339607 + 0.940567i \(0.610294\pi\)
\(450\) 0 0
\(451\) 1.46410 0.0689419
\(452\) 0 0
\(453\) −8.64102 −0.405990
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 30.7846 1.44004 0.720022 0.693952i \(-0.244132\pi\)
0.720022 + 0.693952i \(0.244132\pi\)
\(458\) 0 0
\(459\) −29.8564 −1.39358
\(460\) 0 0
\(461\) −12.2487 −0.570479 −0.285240 0.958456i \(-0.592073\pi\)
−0.285240 + 0.958456i \(0.592073\pi\)
\(462\) 0 0
\(463\) −27.8564 −1.29460 −0.647298 0.762237i \(-0.724101\pi\)
−0.647298 + 0.762237i \(0.724101\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.5885 −0.860171 −0.430086 0.902788i \(-0.641517\pi\)
−0.430086 + 0.902788i \(0.641517\pi\)
\(468\) 0 0
\(469\) −44.7846 −2.06796
\(470\) 0 0
\(471\) −5.75129 −0.265005
\(472\) 0 0
\(473\) 19.8564 0.912999
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.32051 −0.0604619
\(478\) 0 0
\(479\) 11.1244 0.508285 0.254142 0.967167i \(-0.418207\pi\)
0.254142 + 0.967167i \(0.418207\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 1.85641 0.0844694
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 39.8564 1.80607 0.903033 0.429571i \(-0.141335\pi\)
0.903033 + 0.429571i \(0.141335\pi\)
\(488\) 0 0
\(489\) −6.53590 −0.295564
\(490\) 0 0
\(491\) −33.4641 −1.51021 −0.755107 0.655602i \(-0.772415\pi\)
−0.755107 + 0.655602i \(0.772415\pi\)
\(492\) 0 0
\(493\) −70.6410 −3.18151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −32.1051 −1.44011
\(498\) 0 0
\(499\) 24.1962 1.08317 0.541584 0.840646i \(-0.317825\pi\)
0.541584 + 0.840646i \(0.317825\pi\)
\(500\) 0 0
\(501\) −15.6077 −0.697300
\(502\) 0 0
\(503\) 41.1244 1.83364 0.916822 0.399296i \(-0.130745\pi\)
0.916822 + 0.399296i \(0.130745\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.732051 −0.0325115
\(508\) 0 0
\(509\) −3.46410 −0.153544 −0.0767718 0.997049i \(-0.524461\pi\)
−0.0767718 + 0.997049i \(0.524461\pi\)
\(510\) 0 0
\(511\) −10.1436 −0.448726
\(512\) 0 0
\(513\) −10.9282 −0.482492
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −12.3923 −0.545013
\(518\) 0 0
\(519\) −1.75129 −0.0768730
\(520\) 0 0
\(521\) 8.39230 0.367674 0.183837 0.982957i \(-0.441148\pi\)
0.183837 + 0.982957i \(0.441148\pi\)
\(522\) 0 0
\(523\) −17.5167 −0.765950 −0.382975 0.923759i \(-0.625100\pi\)
−0.382975 + 0.923759i \(0.625100\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.46410 0.0637773
\(528\) 0 0
\(529\) −22.4641 −0.976700
\(530\) 0 0
\(531\) −13.9474 −0.605267
\(532\) 0 0
\(533\) −0.535898 −0.0232123
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.0000 0.690451
\(538\) 0 0
\(539\) 13.6603 0.588389
\(540\) 0 0
\(541\) 38.3923 1.65061 0.825307 0.564684i \(-0.191002\pi\)
0.825307 + 0.564684i \(0.191002\pi\)
\(542\) 0 0
\(543\) −4.78461 −0.205327
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.33975 0.356582 0.178291 0.983978i \(-0.442943\pi\)
0.178291 + 0.983978i \(0.442943\pi\)
\(548\) 0 0
\(549\) 30.5359 1.30324
\(550\) 0 0
\(551\) −25.8564 −1.10152
\(552\) 0 0
\(553\) 22.6410 0.962794
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −21.8564 −0.926086 −0.463043 0.886336i \(-0.653242\pi\)
−0.463043 + 0.886336i \(0.653242\pi\)
\(558\) 0 0
\(559\) −7.26795 −0.307401
\(560\) 0 0
\(561\) 14.9282 0.630269
\(562\) 0 0
\(563\) −40.7321 −1.71665 −0.858326 0.513105i \(-0.828495\pi\)
−0.858326 + 0.513105i \(0.828495\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −15.4641 −0.649431
\(568\) 0 0
\(569\) −17.4641 −0.732133 −0.366067 0.930589i \(-0.619296\pi\)
−0.366067 + 0.930589i \(0.619296\pi\)
\(570\) 0 0
\(571\) −27.3205 −1.14333 −0.571664 0.820488i \(-0.693702\pi\)
−0.571664 + 0.820488i \(0.693702\pi\)
\(572\) 0 0
\(573\) −13.8564 −0.578860
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 30.6410 1.27560 0.637801 0.770201i \(-0.279844\pi\)
0.637801 + 0.770201i \(0.279844\pi\)
\(578\) 0 0
\(579\) −1.46410 −0.0608460
\(580\) 0 0
\(581\) −36.0000 −1.49353
\(582\) 0 0
\(583\) 1.46410 0.0606369
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.21539 −0.0501645 −0.0250823 0.999685i \(-0.507985\pi\)
−0.0250823 + 0.999685i \(0.507985\pi\)
\(588\) 0 0
\(589\) 0.535898 0.0220813
\(590\) 0 0
\(591\) 6.53590 0.268851
\(592\) 0 0
\(593\) −40.6410 −1.66893 −0.834463 0.551064i \(-0.814222\pi\)
−0.834463 + 0.551064i \(0.814222\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.07180 0.207575
\(598\) 0 0
\(599\) −33.4641 −1.36731 −0.683653 0.729807i \(-0.739610\pi\)
−0.683653 + 0.729807i \(0.739610\pi\)
\(600\) 0 0
\(601\) −3.85641 −0.157306 −0.0786531 0.996902i \(-0.525062\pi\)
−0.0786531 + 0.996902i \(0.525062\pi\)
\(602\) 0 0
\(603\) −31.8564 −1.29729
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.5167 0.548624 0.274312 0.961641i \(-0.411550\pi\)
0.274312 + 0.961641i \(0.411550\pi\)
\(608\) 0 0
\(609\) 24.0000 0.972529
\(610\) 0 0
\(611\) 4.53590 0.183503
\(612\) 0 0
\(613\) 0.143594 0.00579969 0.00289984 0.999996i \(-0.499077\pi\)
0.00289984 + 0.999996i \(0.499077\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.7128 1.84033 0.920164 0.391533i \(-0.128055\pi\)
0.920164 + 0.391533i \(0.128055\pi\)
\(618\) 0 0
\(619\) −18.3397 −0.737137 −0.368568 0.929601i \(-0.620152\pi\)
−0.368568 + 0.929601i \(0.620152\pi\)
\(620\) 0 0
\(621\) 2.92820 0.117505
\(622\) 0 0
\(623\) 44.7846 1.79426
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 5.46410 0.218215
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −7.80385 −0.310666 −0.155333 0.987862i \(-0.549645\pi\)
−0.155333 + 0.987862i \(0.549645\pi\)
\(632\) 0 0
\(633\) −2.14359 −0.0852002
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.00000 −0.198107
\(638\) 0 0
\(639\) −22.8372 −0.903424
\(640\) 0 0
\(641\) −0.928203 −0.0366618 −0.0183309 0.999832i \(-0.505835\pi\)
−0.0183309 + 0.999832i \(0.505835\pi\)
\(642\) 0 0
\(643\) 9.60770 0.378891 0.189445 0.981891i \(-0.439331\pi\)
0.189445 + 0.981891i \(0.439331\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.339746 −0.0133568 −0.00667840 0.999978i \(-0.502126\pi\)
−0.00667840 + 0.999978i \(0.502126\pi\)
\(648\) 0 0
\(649\) 15.4641 0.607019
\(650\) 0 0
\(651\) −0.497423 −0.0194955
\(652\) 0 0
\(653\) 33.7128 1.31928 0.659642 0.751580i \(-0.270708\pi\)
0.659642 + 0.751580i \(0.270708\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.21539 −0.281499
\(658\) 0 0
\(659\) 39.3205 1.53171 0.765855 0.643014i \(-0.222316\pi\)
0.765855 + 0.643014i \(0.222316\pi\)
\(660\) 0 0
\(661\) 20.9282 0.814013 0.407006 0.913425i \(-0.366573\pi\)
0.407006 + 0.913425i \(0.366573\pi\)
\(662\) 0 0
\(663\) −5.46410 −0.212208
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.92820 0.268261
\(668\) 0 0
\(669\) 18.5359 0.716639
\(670\) 0 0
\(671\) −33.8564 −1.30701
\(672\) 0 0
\(673\) −28.5359 −1.09998 −0.549989 0.835172i \(-0.685368\pi\)
−0.549989 + 0.835172i \(0.685368\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.60770 −0.369254 −0.184627 0.982809i \(-0.559108\pi\)
−0.184627 + 0.982809i \(0.559108\pi\)
\(678\) 0 0
\(679\) 54.9282 2.10795
\(680\) 0 0
\(681\) 13.1769 0.504940
\(682\) 0 0
\(683\) −24.9282 −0.953851 −0.476926 0.878944i \(-0.658249\pi\)
−0.476926 + 0.878944i \(0.658249\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −14.2487 −0.543622
\(688\) 0 0
\(689\) −0.535898 −0.0204161
\(690\) 0 0
\(691\) 43.9090 1.67038 0.835188 0.549965i \(-0.185359\pi\)
0.835188 + 0.549965i \(0.185359\pi\)
\(692\) 0 0
\(693\) 23.3205 0.885873
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 0 0
\(699\) 13.1769 0.498397
\(700\) 0 0
\(701\) 29.7128 1.12224 0.561119 0.827735i \(-0.310371\pi\)
0.561119 + 0.827735i \(0.310371\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −17.0718 −0.642051
\(708\) 0 0
\(709\) 5.60770 0.210601 0.105301 0.994440i \(-0.466419\pi\)
0.105301 + 0.994440i \(0.466419\pi\)
\(710\) 0 0
\(711\) 16.1051 0.603989
\(712\) 0 0
\(713\) −0.143594 −0.00537762
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −18.4974 −0.690799
\(718\) 0 0
\(719\) −34.6410 −1.29189 −0.645946 0.763383i \(-0.723537\pi\)
−0.645946 + 0.763383i \(0.723537\pi\)
\(720\) 0 0
\(721\) −21.4641 −0.799365
\(722\) 0 0
\(723\) −14.8231 −0.551276
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 34.9808 1.29736 0.648682 0.761059i \(-0.275320\pi\)
0.648682 + 0.761059i \(0.275320\pi\)
\(728\) 0 0
\(729\) −2.21539 −0.0820515
\(730\) 0 0
\(731\) −54.2487 −2.00646
\(732\) 0 0
\(733\) 15.8564 0.585670 0.292835 0.956163i \(-0.405401\pi\)
0.292835 + 0.956163i \(0.405401\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 35.3205 1.30105
\(738\) 0 0
\(739\) 1.26795 0.0466423 0.0233211 0.999728i \(-0.492576\pi\)
0.0233211 + 0.999728i \(0.492576\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −25.3205 −0.928919 −0.464460 0.885594i \(-0.653751\pi\)
−0.464460 + 0.885594i \(0.653751\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −25.6077 −0.936937
\(748\) 0 0
\(749\) −69.4641 −2.53816
\(750\) 0 0
\(751\) 45.4641 1.65901 0.829504 0.558500i \(-0.188623\pi\)
0.829504 + 0.558500i \(0.188623\pi\)
\(752\) 0 0
\(753\) −17.0718 −0.622131
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 23.4641 0.852817 0.426409 0.904531i \(-0.359779\pi\)
0.426409 + 0.904531i \(0.359779\pi\)
\(758\) 0 0
\(759\) −1.46410 −0.0531435
\(760\) 0 0
\(761\) −14.0000 −0.507500 −0.253750 0.967270i \(-0.581664\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(762\) 0 0
\(763\) −54.9282 −1.98853
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.66025 −0.204380
\(768\) 0 0
\(769\) 15.0718 0.543503 0.271751 0.962367i \(-0.412397\pi\)
0.271751 + 0.962367i \(0.412397\pi\)
\(770\) 0 0
\(771\) 4.39230 0.158185
\(772\) 0 0
\(773\) −5.07180 −0.182420 −0.0912099 0.995832i \(-0.529073\pi\)
−0.0912099 + 0.995832i \(0.529073\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.46410 −0.0524569
\(780\) 0 0
\(781\) 25.3205 0.906039
\(782\) 0 0
\(783\) 37.8564 1.35288
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −18.3923 −0.655615 −0.327807 0.944745i \(-0.606310\pi\)
−0.327807 + 0.944745i \(0.606310\pi\)
\(788\) 0 0
\(789\) −8.53590 −0.303886
\(790\) 0 0
\(791\) −63.7128 −2.26537
\(792\) 0 0
\(793\) 12.3923 0.440064
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.7846 −1.65720 −0.828598 0.559844i \(-0.810861\pi\)
−0.828598 + 0.559844i \(0.810861\pi\)
\(798\) 0 0
\(799\) 33.8564 1.19775
\(800\) 0 0
\(801\) 31.8564 1.12559
\(802\) 0 0
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.105118 0.00370032
\(808\) 0 0
\(809\) 8.67949 0.305155 0.152577 0.988292i \(-0.451243\pi\)
0.152577 + 0.988292i \(0.451243\pi\)
\(810\) 0 0
\(811\) 35.9090 1.26093 0.630467 0.776216i \(-0.282863\pi\)
0.630467 + 0.776216i \(0.282863\pi\)
\(812\) 0 0
\(813\) 16.9282 0.593698
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −19.8564 −0.694688
\(818\) 0 0
\(819\) −8.53590 −0.298268
\(820\) 0 0
\(821\) −12.9282 −0.451197 −0.225599 0.974220i \(-0.572434\pi\)
−0.225599 + 0.974220i \(0.572434\pi\)
\(822\) 0 0
\(823\) −26.5885 −0.926815 −0.463408 0.886145i \(-0.653373\pi\)
−0.463408 + 0.886145i \(0.653373\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.46410 −0.120459 −0.0602293 0.998185i \(-0.519183\pi\)
−0.0602293 + 0.998185i \(0.519183\pi\)
\(828\) 0 0
\(829\) 44.3923 1.54181 0.770904 0.636951i \(-0.219805\pi\)
0.770904 + 0.636951i \(0.219805\pi\)
\(830\) 0 0
\(831\) −15.6077 −0.541425
\(832\) 0 0
\(833\) −37.3205 −1.29308
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.784610 −0.0271201
\(838\) 0 0
\(839\) 34.4449 1.18917 0.594584 0.804033i \(-0.297317\pi\)
0.594584 + 0.804033i \(0.297317\pi\)
\(840\) 0 0
\(841\) 60.5692 2.08859
\(842\) 0 0
\(843\) 3.32051 0.114364
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 12.2487 0.420871
\(848\) 0 0
\(849\) −17.6077 −0.604295
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 7.71281 0.264082 0.132041 0.991244i \(-0.457847\pi\)
0.132041 + 0.991244i \(0.457847\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 4.14359 0.141542 0.0707712 0.997493i \(-0.477454\pi\)
0.0707712 + 0.997493i \(0.477454\pi\)
\(858\) 0 0
\(859\) −12.3923 −0.422820 −0.211410 0.977397i \(-0.567806\pi\)
−0.211410 + 0.977397i \(0.567806\pi\)
\(860\) 0 0
\(861\) 1.35898 0.0463140
\(862\) 0 0
\(863\) 33.6077 1.14402 0.572010 0.820247i \(-0.306164\pi\)
0.572010 + 0.820247i \(0.306164\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −28.3397 −0.962468
\(868\) 0 0
\(869\) −17.8564 −0.605737
\(870\) 0 0
\(871\) −12.9282 −0.438055
\(872\) 0 0
\(873\) 39.0718 1.32238
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 41.7128 1.40854 0.704271 0.709931i \(-0.251274\pi\)
0.704271 + 0.709931i \(0.251274\pi\)
\(878\) 0 0
\(879\) 5.07180 0.171067
\(880\) 0 0
\(881\) 5.46410 0.184090 0.0920451 0.995755i \(-0.470660\pi\)
0.0920451 + 0.995755i \(0.470660\pi\)
\(882\) 0 0
\(883\) −22.5885 −0.760162 −0.380081 0.924953i \(-0.624104\pi\)
−0.380081 + 0.924953i \(0.624104\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −12.4449 −0.417858 −0.208929 0.977931i \(-0.566998\pi\)
−0.208929 + 0.977931i \(0.566998\pi\)
\(888\) 0 0
\(889\) −6.24871 −0.209575
\(890\) 0 0
\(891\) 12.1962 0.408586
\(892\) 0 0
\(893\) 12.3923 0.414693
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0.535898 0.0178931
\(898\) 0 0
\(899\) −1.85641 −0.0619146
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) 18.4308 0.613338
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 36.8372 1.22316 0.611579 0.791183i \(-0.290535\pi\)
0.611579 + 0.791183i \(0.290535\pi\)
\(908\) 0 0
\(909\) −12.1436 −0.402778
\(910\) 0 0
\(911\) −20.7846 −0.688625 −0.344312 0.938855i \(-0.611888\pi\)
−0.344312 + 0.938855i \(0.611888\pi\)
\(912\) 0 0
\(913\) 28.3923 0.939648
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 10.1436 0.334971
\(918\) 0 0
\(919\) 39.3205 1.29706 0.648532 0.761187i \(-0.275383\pi\)
0.648532 + 0.761187i \(0.275383\pi\)
\(920\) 0 0
\(921\) −12.1051 −0.398877
\(922\) 0 0
\(923\) −9.26795 −0.305058
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −15.2679 −0.501465
\(928\) 0 0
\(929\) 43.1769 1.41659 0.708294 0.705917i \(-0.249465\pi\)
0.708294 + 0.705917i \(0.249465\pi\)
\(930\) 0 0
\(931\) −13.6603 −0.447697
\(932\) 0 0
\(933\) −22.9282 −0.750636
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 27.0718 0.884397 0.442199 0.896917i \(-0.354199\pi\)
0.442199 + 0.896917i \(0.354199\pi\)
\(938\) 0 0
\(939\) 7.60770 0.248268
\(940\) 0 0
\(941\) 22.3923 0.729968 0.364984 0.931014i \(-0.381074\pi\)
0.364984 + 0.931014i \(0.381074\pi\)
\(942\) 0 0
\(943\) 0.392305 0.0127752
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.3923 −0.727652 −0.363826 0.931467i \(-0.618530\pi\)
−0.363826 + 0.931467i \(0.618530\pi\)
\(948\) 0 0
\(949\) −2.92820 −0.0950535
\(950\) 0 0
\(951\) −1.35898 −0.0440681
\(952\) 0 0
\(953\) 1.21539 0.0393704 0.0196852 0.999806i \(-0.493734\pi\)
0.0196852 + 0.999806i \(0.493734\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −18.9282 −0.611862
\(958\) 0 0
\(959\) 30.9282 0.998724
\(960\) 0 0
\(961\) −30.9615 −0.998759
\(962\) 0 0
\(963\) −49.4115 −1.59226
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 18.0000 0.578841 0.289420 0.957202i \(-0.406537\pi\)
0.289420 + 0.957202i \(0.406537\pi\)
\(968\) 0 0
\(969\) −14.9282 −0.479563
\(970\) 0 0
\(971\) 43.7128 1.40281 0.701405 0.712762i \(-0.252556\pi\)
0.701405 + 0.712762i \(0.252556\pi\)
\(972\) 0 0
\(973\) 46.6410 1.49524
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.92820 0.0936815 0.0468408 0.998902i \(-0.485085\pi\)
0.0468408 + 0.998902i \(0.485085\pi\)
\(978\) 0 0
\(979\) −35.3205 −1.12885
\(980\) 0 0
\(981\) −39.0718 −1.24747
\(982\) 0 0
\(983\) 15.8564 0.505741 0.252870 0.967500i \(-0.418625\pi\)
0.252870 + 0.967500i \(0.418625\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −11.5026 −0.366131
\(988\) 0 0
\(989\) 5.32051 0.169182
\(990\) 0 0
\(991\) −53.8564 −1.71081 −0.855403 0.517964i \(-0.826690\pi\)
−0.855403 + 0.517964i \(0.826690\pi\)
\(992\) 0 0
\(993\) 6.28719 0.199518
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 9.32051 0.295183 0.147592 0.989048i \(-0.452848\pi\)
0.147592 + 0.989048i \(0.452848\pi\)
\(998\) 0 0
\(999\) 0 0
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 2600.2.a.v.1.1 2
4.3 odd 2 5200.2.a.bn.1.2 2
5.2 odd 4 2600.2.d.m.1249.3 4
5.3 odd 4 2600.2.d.m.1249.2 4
5.4 even 2 520.2.a.e.1.2 2
15.14 odd 2 4680.2.a.bd.1.2 2
20.19 odd 2 1040.2.a.l.1.1 2
40.19 odd 2 4160.2.a.w.1.2 2
40.29 even 2 4160.2.a.bk.1.1 2
60.59 even 2 9360.2.a.cr.1.1 2
65.64 even 2 6760.2.a.o.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
520.2.a.e.1.2 2 5.4 even 2
1040.2.a.l.1.1 2 20.19 odd 2
2600.2.a.v.1.1 2 1.1 even 1 trivial
2600.2.d.m.1249.2 4 5.3 odd 4
2600.2.d.m.1249.3 4 5.2 odd 4
4160.2.a.w.1.2 2 40.19 odd 2
4160.2.a.bk.1.1 2 40.29 even 2
4680.2.a.bd.1.2 2 15.14 odd 2
5200.2.a.bn.1.2 2 4.3 odd 2
6760.2.a.o.1.2 2 65.64 even 2
9360.2.a.cr.1.1 2 60.59 even 2