Properties

Label 196.4.e.a.165.1
Level $196$
Weight $4$
Character 196.165
Analytic conductor $11.564$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,4,Mod(165,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("196.165");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 196.e (of order \(3\), degree \(2\), not minimal)

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: no
Analytic conductor: \(11.5643743611\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 196.165
Dual form 196.4.e.a.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.00000 + 8.66025i) q^{3} +(-4.00000 - 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +O(q^{10})\) \(q+(-5.00000 + 8.66025i) q^{3} +(-4.00000 - 6.92820i) q^{5} +(-36.5000 - 63.2199i) q^{9} +(20.0000 - 34.6410i) q^{11} +12.0000 q^{13} +80.0000 q^{15} +(-29.0000 + 50.2295i) q^{17} +(13.0000 + 22.5167i) q^{19} +(32.0000 + 55.4256i) q^{23} +(30.5000 - 52.8275i) q^{25} +460.000 q^{27} -62.0000 q^{29} +(126.000 - 218.238i) q^{31} +(200.000 + 346.410i) q^{33} +(-13.0000 - 22.5167i) q^{37} +(-60.0000 + 103.923i) q^{39} -6.00000 q^{41} +416.000 q^{43} +(-292.000 + 505.759i) q^{45} +(-198.000 - 342.946i) q^{47} +(-290.000 - 502.295i) q^{51} +(225.000 - 389.711i) q^{53} -320.000 q^{55} -260.000 q^{57} +(137.000 - 237.291i) q^{59} +(-288.000 - 498.831i) q^{61} +(-48.0000 - 83.1384i) q^{65} +(238.000 - 412.228i) q^{67} -640.000 q^{69} -448.000 q^{71} +(-79.0000 + 136.832i) q^{73} +(305.000 + 528.275i) q^{75} +(468.000 + 810.600i) q^{79} +(-1314.50 + 2276.78i) q^{81} -530.000 q^{83} +464.000 q^{85} +(310.000 - 536.936i) q^{87} +(-195.000 - 337.750i) q^{89} +(1260.00 + 2182.38i) q^{93} +(104.000 - 180.133i) q^{95} -214.000 q^{97} -2920.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 10 q^{3} - 8 q^{5} - 73 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 10 q^{3} - 8 q^{5} - 73 q^{9} + 40 q^{11} + 24 q^{13} + 160 q^{15} - 58 q^{17} + 26 q^{19} + 64 q^{23} + 61 q^{25} + 920 q^{27} - 124 q^{29} + 252 q^{31} + 400 q^{33} - 26 q^{37} - 120 q^{39} - 12 q^{41} + 832 q^{43} - 584 q^{45} - 396 q^{47} - 580 q^{51} + 450 q^{53} - 640 q^{55} - 520 q^{57} + 274 q^{59} - 576 q^{61} - 96 q^{65} + 476 q^{67} - 1280 q^{69} - 896 q^{71} - 158 q^{73} + 610 q^{75} + 936 q^{79} - 2629 q^{81} - 1060 q^{83} + 928 q^{85} + 620 q^{87} - 390 q^{89} + 2520 q^{93} + 208 q^{95} - 428 q^{97} - 5840 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −5.00000 + 8.66025i −0.962250 + 1.66667i −0.245423 + 0.969416i \(0.578927\pi\)
−0.716827 + 0.697251i \(0.754406\pi\)
\(4\) 0 0
\(5\) −4.00000 6.92820i −0.357771 0.619677i 0.629817 0.776743i \(-0.283130\pi\)
−0.987588 + 0.157066i \(0.949796\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −36.5000 63.2199i −1.35185 2.34148i
\(10\) 0 0
\(11\) 20.0000 34.6410i 0.548202 0.949514i −0.450195 0.892930i \(-0.648646\pi\)
0.998398 0.0565844i \(-0.0180210\pi\)
\(12\) 0 0
\(13\) 12.0000 0.256015 0.128008 0.991773i \(-0.459142\pi\)
0.128008 + 0.991773i \(0.459142\pi\)
\(14\) 0 0
\(15\) 80.0000 1.37706
\(16\) 0 0
\(17\) −29.0000 + 50.2295i −0.413737 + 0.716614i −0.995295 0.0968912i \(-0.969110\pi\)
0.581558 + 0.813505i \(0.302443\pi\)
\(18\) 0 0
\(19\) 13.0000 + 22.5167i 0.156969 + 0.271878i 0.933774 0.357863i \(-0.116495\pi\)
−0.776805 + 0.629741i \(0.783161\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 32.0000 + 55.4256i 0.290107 + 0.502480i 0.973835 0.227257i \(-0.0729758\pi\)
−0.683728 + 0.729737i \(0.739642\pi\)
\(24\) 0 0
\(25\) 30.5000 52.8275i 0.244000 0.422620i
\(26\) 0 0
\(27\) 460.000 3.27878
\(28\) 0 0
\(29\) −62.0000 −0.397004 −0.198502 0.980101i \(-0.563608\pi\)
−0.198502 + 0.980101i \(0.563608\pi\)
\(30\) 0 0
\(31\) 126.000 218.238i 0.730009 1.26441i −0.226870 0.973925i \(-0.572849\pi\)
0.956879 0.290487i \(-0.0938173\pi\)
\(32\) 0 0
\(33\) 200.000 + 346.410i 1.05502 + 1.82734i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −13.0000 22.5167i −0.0577618 0.100046i 0.835699 0.549188i \(-0.185063\pi\)
−0.893460 + 0.449142i \(0.851730\pi\)
\(38\) 0 0
\(39\) −60.0000 + 103.923i −0.246351 + 0.426692i
\(40\) 0 0
\(41\) −6.00000 −0.0228547 −0.0114273 0.999935i \(-0.503638\pi\)
−0.0114273 + 0.999935i \(0.503638\pi\)
\(42\) 0 0
\(43\) 416.000 1.47534 0.737668 0.675164i \(-0.235927\pi\)
0.737668 + 0.675164i \(0.235927\pi\)
\(44\) 0 0
\(45\) −292.000 + 505.759i −0.967306 + 1.67542i
\(46\) 0 0
\(47\) −198.000 342.946i −0.614495 1.06434i −0.990473 0.137708i \(-0.956026\pi\)
0.375978 0.926629i \(-0.377307\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −290.000 502.295i −0.796238 1.37912i
\(52\) 0 0
\(53\) 225.000 389.711i 0.583134 1.01002i −0.411971 0.911197i \(-0.635159\pi\)
0.995105 0.0988214i \(-0.0315073\pi\)
\(54\) 0 0
\(55\) −320.000 −0.784523
\(56\) 0 0
\(57\) −260.000 −0.604173
\(58\) 0 0
\(59\) 137.000 237.291i 0.302303 0.523604i −0.674354 0.738408i \(-0.735578\pi\)
0.976657 + 0.214804i \(0.0689112\pi\)
\(60\) 0 0
\(61\) −288.000 498.831i −0.604502 1.04703i −0.992130 0.125212i \(-0.960039\pi\)
0.387628 0.921816i \(-0.373295\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −48.0000 83.1384i −0.0915949 0.158647i
\(66\) 0 0
\(67\) 238.000 412.228i 0.433975 0.751667i −0.563236 0.826296i \(-0.690444\pi\)
0.997211 + 0.0746290i \(0.0237773\pi\)
\(68\) 0 0
\(69\) −640.000 −1.11662
\(70\) 0 0
\(71\) −448.000 −0.748843 −0.374421 0.927259i \(-0.622159\pi\)
−0.374421 + 0.927259i \(0.622159\pi\)
\(72\) 0 0
\(73\) −79.0000 + 136.832i −0.126661 + 0.219383i −0.922381 0.386281i \(-0.873759\pi\)
0.795720 + 0.605665i \(0.207093\pi\)
\(74\) 0 0
\(75\) 305.000 + 528.275i 0.469578 + 0.813333i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 468.000 + 810.600i 0.666508 + 1.15443i 0.978874 + 0.204464i \(0.0655450\pi\)
−0.312366 + 0.949962i \(0.601122\pi\)
\(80\) 0 0
\(81\) −1314.50 + 2276.78i −1.80316 + 3.12316i
\(82\) 0 0
\(83\) −530.000 −0.700904 −0.350452 0.936581i \(-0.613972\pi\)
−0.350452 + 0.936581i \(0.613972\pi\)
\(84\) 0 0
\(85\) 464.000 0.592093
\(86\) 0 0
\(87\) 310.000 536.936i 0.382017 0.661673i
\(88\) 0 0
\(89\) −195.000 337.750i −0.232247 0.402263i 0.726222 0.687460i \(-0.241274\pi\)
−0.958469 + 0.285197i \(0.907941\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1260.00 + 2182.38i 1.40490 + 2.43336i
\(94\) 0 0
\(95\) 104.000 180.133i 0.112318 0.194540i
\(96\) 0 0
\(97\) −214.000 −0.224004 −0.112002 0.993708i \(-0.535726\pi\)
−0.112002 + 0.993708i \(0.535726\pi\)
\(98\) 0 0
\(99\) −2920.00 −2.96435
\(100\) 0 0
\(101\) 716.000 1240.15i 0.705393 1.22178i −0.261157 0.965296i \(-0.584104\pi\)
0.966550 0.256480i \(-0.0825627\pi\)
\(102\) 0 0
\(103\) 382.000 + 661.643i 0.365433 + 0.632948i 0.988846 0.148945i \(-0.0475877\pi\)
−0.623413 + 0.781893i \(0.714254\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −162.000 280.592i −0.146366 0.253513i 0.783516 0.621372i \(-0.213424\pi\)
−0.929882 + 0.367859i \(0.880091\pi\)
\(108\) 0 0
\(109\) 667.000 1155.28i 0.586119 1.01519i −0.408615 0.912707i \(-0.633988\pi\)
0.994735 0.102482i \(-0.0326784\pi\)
\(110\) 0 0
\(111\) 260.000 0.222325
\(112\) 0 0
\(113\) 1798.00 1.49683 0.748414 0.663232i \(-0.230816\pi\)
0.748414 + 0.663232i \(0.230816\pi\)
\(114\) 0 0
\(115\) 256.000 443.405i 0.207584 0.359545i
\(116\) 0 0
\(117\) −438.000 758.638i −0.346095 0.599454i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −134.500 232.961i −0.101052 0.175027i
\(122\) 0 0
\(123\) 30.0000 51.9615i 0.0219919 0.0380912i
\(124\) 0 0
\(125\) −1488.00 −1.06473
\(126\) 0 0
\(127\) −384.000 −0.268303 −0.134152 0.990961i \(-0.542831\pi\)
−0.134152 + 0.990961i \(0.542831\pi\)
\(128\) 0 0
\(129\) −2080.00 + 3602.67i −1.41964 + 2.45889i
\(130\) 0 0
\(131\) −907.000 1570.97i −0.604923 1.04776i −0.992064 0.125737i \(-0.959870\pi\)
0.387140 0.922021i \(-0.373463\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1840.00 3186.97i −1.17305 2.03179i
\(136\) 0 0
\(137\) −833.000 + 1442.80i −0.519474 + 0.899756i 0.480269 + 0.877121i \(0.340539\pi\)
−0.999744 + 0.0226350i \(0.992794\pi\)
\(138\) 0 0
\(139\) −1126.00 −0.687094 −0.343547 0.939135i \(-0.611628\pi\)
−0.343547 + 0.939135i \(0.611628\pi\)
\(140\) 0 0
\(141\) 3960.00 2.36519
\(142\) 0 0
\(143\) 240.000 415.692i 0.140348 0.243090i
\(144\) 0 0
\(145\) 248.000 + 429.549i 0.142036 + 0.246014i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1347.00 2333.07i −0.740608 1.28277i −0.952219 0.305416i \(-0.901204\pi\)
0.211611 0.977354i \(-0.432129\pi\)
\(150\) 0 0
\(151\) 1324.00 2293.24i 0.713547 1.23590i −0.249970 0.968253i \(-0.580421\pi\)
0.963517 0.267646i \(-0.0862458\pi\)
\(152\) 0 0
\(153\) 4234.00 2.23725
\(154\) 0 0
\(155\) −2016.00 −1.04470
\(156\) 0 0
\(157\) −278.000 + 481.510i −0.141317 + 0.244769i −0.927993 0.372598i \(-0.878467\pi\)
0.786676 + 0.617367i \(0.211800\pi\)
\(158\) 0 0
\(159\) 2250.00 + 3897.11i 1.12224 + 1.94378i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 164.000 + 284.056i 0.0788066 + 0.136497i 0.902735 0.430196i \(-0.141556\pi\)
−0.823929 + 0.566693i \(0.808222\pi\)
\(164\) 0 0
\(165\) 1600.00 2771.28i 0.754908 1.30754i
\(166\) 0 0
\(167\) 4268.00 1.97765 0.988826 0.149077i \(-0.0476302\pi\)
0.988826 + 0.149077i \(0.0476302\pi\)
\(168\) 0 0
\(169\) −2053.00 −0.934456
\(170\) 0 0
\(171\) 949.000 1643.72i 0.424397 0.735077i
\(172\) 0 0
\(173\) −1738.00 3010.30i −0.763802 1.32294i −0.940878 0.338746i \(-0.889997\pi\)
0.177076 0.984197i \(-0.443336\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1370.00 + 2372.91i 0.581783 + 1.00768i
\(178\) 0 0
\(179\) −1134.00 + 1964.15i −0.473515 + 0.820152i −0.999540 0.0303171i \(-0.990348\pi\)
0.526026 + 0.850469i \(0.323682\pi\)
\(180\) 0 0
\(181\) 276.000 0.113342 0.0566710 0.998393i \(-0.481951\pi\)
0.0566710 + 0.998393i \(0.481951\pi\)
\(182\) 0 0
\(183\) 5760.00 2.32673
\(184\) 0 0
\(185\) −104.000 + 180.133i −0.0413310 + 0.0715874i
\(186\) 0 0
\(187\) 1160.00 + 2009.18i 0.453624 + 0.785699i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1500.00 + 2598.08i 0.568252 + 0.984242i 0.996739 + 0.0806937i \(0.0257136\pi\)
−0.428487 + 0.903548i \(0.640953\pi\)
\(192\) 0 0
\(193\) −1639.00 + 2838.83i −0.611284 + 1.05877i 0.379740 + 0.925093i \(0.376013\pi\)
−0.991024 + 0.133682i \(0.957320\pi\)
\(194\) 0 0
\(195\) 960.000 0.352549
\(196\) 0 0
\(197\) −2362.00 −0.854241 −0.427121 0.904195i \(-0.640472\pi\)
−0.427121 + 0.904195i \(0.640472\pi\)
\(198\) 0 0
\(199\) −518.000 + 897.202i −0.184523 + 0.319603i −0.943416 0.331613i \(-0.892407\pi\)
0.758893 + 0.651216i \(0.225741\pi\)
\(200\) 0 0
\(201\) 2380.00 + 4122.28i 0.835185 + 1.44658i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 24.0000 + 41.5692i 0.00817674 + 0.0141625i
\(206\) 0 0
\(207\) 2336.00 4046.07i 0.784363 1.35856i
\(208\) 0 0
\(209\) 1040.00 0.344202
\(210\) 0 0
\(211\) 3524.00 1.14977 0.574887 0.818233i \(-0.305046\pi\)
0.574887 + 0.818233i \(0.305046\pi\)
\(212\) 0 0
\(213\) 2240.00 3879.79i 0.720574 1.24807i
\(214\) 0 0
\(215\) −1664.00 2882.13i −0.527832 0.914232i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −790.000 1368.32i −0.243759 0.422203i
\(220\) 0 0
\(221\) −348.000 + 602.754i −0.105923 + 0.183464i
\(222\) 0 0
\(223\) 1336.00 0.401189 0.200595 0.979674i \(-0.435713\pi\)
0.200595 + 0.979674i \(0.435713\pi\)
\(224\) 0 0
\(225\) −4453.00 −1.31941
\(226\) 0 0
\(227\) 645.000 1117.17i 0.188591 0.326649i −0.756190 0.654352i \(-0.772941\pi\)
0.944781 + 0.327703i \(0.106275\pi\)
\(228\) 0 0
\(229\) 2762.00 + 4783.92i 0.797022 + 1.38048i 0.921547 + 0.388267i \(0.126926\pi\)
−0.124525 + 0.992216i \(0.539741\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3157.00 5468.08i −0.887648 1.53745i −0.842648 0.538464i \(-0.819005\pi\)
−0.0449994 0.998987i \(-0.514329\pi\)
\(234\) 0 0
\(235\) −1584.00 + 2743.57i −0.439697 + 0.761577i
\(236\) 0 0
\(237\) −9360.00 −2.56539
\(238\) 0 0
\(239\) −3960.00 −1.07176 −0.535881 0.844294i \(-0.680020\pi\)
−0.535881 + 0.844294i \(0.680020\pi\)
\(240\) 0 0
\(241\) −3509.00 + 6077.77i −0.937903 + 1.62450i −0.168529 + 0.985697i \(0.553902\pi\)
−0.769374 + 0.638798i \(0.779432\pi\)
\(242\) 0 0
\(243\) −6935.00 12011.8i −1.83078 3.17101i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 156.000 + 270.200i 0.0401864 + 0.0696049i
\(248\) 0 0
\(249\) 2650.00 4589.93i 0.674445 1.16817i
\(250\) 0 0
\(251\) 2394.00 0.602024 0.301012 0.953620i \(-0.402676\pi\)
0.301012 + 0.953620i \(0.402676\pi\)
\(252\) 0 0
\(253\) 2560.00 0.636149
\(254\) 0 0
\(255\) −2320.00 + 4018.36i −0.569741 + 0.986821i
\(256\) 0 0
\(257\) −1383.00 2395.43i −0.335678 0.581411i 0.647937 0.761694i \(-0.275632\pi\)
−0.983615 + 0.180283i \(0.942299\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2263.00 + 3919.63i 0.536690 + 0.929575i
\(262\) 0 0
\(263\) −3984.00 + 6900.49i −0.934084 + 1.61788i −0.157823 + 0.987467i \(0.550448\pi\)
−0.776260 + 0.630413i \(0.782886\pi\)
\(264\) 0 0
\(265\) −3600.00 −0.834514
\(266\) 0 0
\(267\) 3900.00 0.893918
\(268\) 0 0
\(269\) −1450.00 + 2511.47i −0.328654 + 0.569246i −0.982245 0.187602i \(-0.939928\pi\)
0.653591 + 0.756848i \(0.273262\pi\)
\(270\) 0 0
\(271\) 1320.00 + 2286.31i 0.295883 + 0.512484i 0.975190 0.221370i \(-0.0710528\pi\)
−0.679307 + 0.733854i \(0.737719\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1220.00 2113.10i −0.267523 0.463363i
\(276\) 0 0
\(277\) 761.000 1318.09i 0.165069 0.285908i −0.771611 0.636095i \(-0.780549\pi\)
0.936680 + 0.350187i \(0.113882\pi\)
\(278\) 0 0
\(279\) −18396.0 −3.94745
\(280\) 0 0
\(281\) −4534.00 −0.962547 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(282\) 0 0
\(283\) 2417.00 4186.37i 0.507688 0.879342i −0.492272 0.870441i \(-0.663834\pi\)
0.999960 0.00890034i \(-0.00283310\pi\)
\(284\) 0 0
\(285\) 1040.00 + 1801.33i 0.216155 + 0.374392i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 774.500 + 1341.47i 0.157643 + 0.273046i
\(290\) 0 0
\(291\) 1070.00 1853.29i 0.215548 0.373340i
\(292\) 0 0
\(293\) 4656.00 0.928350 0.464175 0.885744i \(-0.346351\pi\)
0.464175 + 0.885744i \(0.346351\pi\)
\(294\) 0 0
\(295\) −2192.00 −0.432621
\(296\) 0 0
\(297\) 9200.00 15934.9i 1.79743 3.11325i
\(298\) 0 0
\(299\) 384.000 + 665.108i 0.0742719 + 0.128643i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7160.00 + 12401.5i 1.35753 + 2.35131i
\(304\) 0 0
\(305\) −2304.00 + 3990.65i −0.432546 + 0.749192i
\(306\) 0 0
\(307\) 7238.00 1.34558 0.672792 0.739831i \(-0.265095\pi\)
0.672792 + 0.739831i \(0.265095\pi\)
\(308\) 0 0
\(309\) −7640.00 −1.40655
\(310\) 0 0
\(311\) 548.000 949.164i 0.0999171 0.173062i −0.811733 0.584029i \(-0.801476\pi\)
0.911650 + 0.410967i \(0.134809\pi\)
\(312\) 0 0
\(313\) −1909.00 3306.48i −0.344738 0.597104i 0.640568 0.767901i \(-0.278699\pi\)
−0.985306 + 0.170797i \(0.945366\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −999.000 1730.32i −0.177001 0.306575i 0.763851 0.645393i \(-0.223306\pi\)
−0.940852 + 0.338818i \(0.889973\pi\)
\(318\) 0 0
\(319\) −1240.00 + 2147.74i −0.217638 + 0.376961i
\(320\) 0 0
\(321\) 3240.00 0.563362
\(322\) 0 0
\(323\) −1508.00 −0.259775
\(324\) 0 0
\(325\) 366.000 633.931i 0.0624678 0.108197i
\(326\) 0 0
\(327\) 6670.00 + 11552.8i 1.12799 + 1.95373i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3968.00 + 6872.78i 0.658915 + 1.14127i 0.980897 + 0.194529i \(0.0623178\pi\)
−0.321981 + 0.946746i \(0.604349\pi\)
\(332\) 0 0
\(333\) −949.000 + 1643.72i −0.156171 + 0.270496i
\(334\) 0 0
\(335\) −3808.00 −0.621055
\(336\) 0 0
\(337\) 2766.00 0.447103 0.223551 0.974692i \(-0.428235\pi\)
0.223551 + 0.974692i \(0.428235\pi\)
\(338\) 0 0
\(339\) −8990.00 + 15571.1i −1.44032 + 2.49471i
\(340\) 0 0
\(341\) −5040.00 8729.54i −0.800385 1.38631i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2560.00 + 4434.05i 0.399495 + 0.691946i
\(346\) 0 0
\(347\) −4176.00 + 7233.04i −0.646050 + 1.11899i 0.338008 + 0.941143i \(0.390247\pi\)
−0.984058 + 0.177848i \(0.943086\pi\)
\(348\) 0 0
\(349\) 5924.00 0.908609 0.454304 0.890847i \(-0.349888\pi\)
0.454304 + 0.890847i \(0.349888\pi\)
\(350\) 0 0
\(351\) 5520.00 0.839418
\(352\) 0 0
\(353\) 1113.00 1927.77i 0.167816 0.290666i −0.769836 0.638242i \(-0.779662\pi\)
0.937652 + 0.347576i \(0.112995\pi\)
\(354\) 0 0
\(355\) 1792.00 + 3103.84i 0.267914 + 0.464041i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1940.00 3360.18i −0.285207 0.493993i 0.687452 0.726229i \(-0.258729\pi\)
−0.972659 + 0.232237i \(0.925396\pi\)
\(360\) 0 0
\(361\) 3091.50 5354.64i 0.450722 0.780673i
\(362\) 0 0
\(363\) 2690.00 0.388949
\(364\) 0 0
\(365\) 1264.00 0.181262
\(366\) 0 0
\(367\) −1292.00 + 2237.81i −0.183765 + 0.318291i −0.943160 0.332340i \(-0.892162\pi\)
0.759394 + 0.650630i \(0.225495\pi\)
\(368\) 0 0
\(369\) 219.000 + 379.319i 0.0308962 + 0.0535137i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5267.00 9122.71i −0.731139 1.26637i −0.956397 0.292071i \(-0.905656\pi\)
0.225257 0.974299i \(-0.427678\pi\)
\(374\) 0 0
\(375\) 7440.00 12886.5i 1.02453 1.77454i
\(376\) 0 0
\(377\) −744.000 −0.101639
\(378\) 0 0
\(379\) −4472.00 −0.606098 −0.303049 0.952975i \(-0.598005\pi\)
−0.303049 + 0.952975i \(0.598005\pi\)
\(380\) 0 0
\(381\) 1920.00 3325.54i 0.258175 0.447172i
\(382\) 0 0
\(383\) 1234.00 + 2137.35i 0.164633 + 0.285153i 0.936525 0.350601i \(-0.114023\pi\)
−0.771892 + 0.635754i \(0.780689\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15184.0 26299.5i −1.99443 3.45446i
\(388\) 0 0
\(389\) 523.000 905.863i 0.0681675 0.118070i −0.829927 0.557872i \(-0.811618\pi\)
0.898095 + 0.439802i \(0.144951\pi\)
\(390\) 0 0
\(391\) −3712.00 −0.480112
\(392\) 0 0
\(393\) 18140.0 2.32835
\(394\) 0 0
\(395\) 3744.00 6484.80i 0.476914 0.826040i
\(396\) 0 0
\(397\) 1062.00 + 1839.44i 0.134258 + 0.232541i 0.925314 0.379203i \(-0.123802\pi\)
−0.791056 + 0.611744i \(0.790468\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5799.00 10044.2i −0.722165 1.25083i −0.960130 0.279553i \(-0.909814\pi\)
0.237965 0.971274i \(-0.423520\pi\)
\(402\) 0 0
\(403\) 1512.00 2618.86i 0.186894 0.323709i
\(404\) 0 0
\(405\) 21032.0 2.58047
\(406\) 0 0
\(407\) −1040.00 −0.126661
\(408\) 0 0
\(409\) −1385.00 + 2398.89i −0.167442 + 0.290018i −0.937520 0.347932i \(-0.886884\pi\)
0.770078 + 0.637950i \(0.220217\pi\)
\(410\) 0 0
\(411\) −8330.00 14428.0i −0.999729 1.73158i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2120.00 + 3671.95i 0.250763 + 0.434335i
\(416\) 0 0
\(417\) 5630.00 9751.45i 0.661157 1.14516i
\(418\) 0 0
\(419\) −9438.00 −1.10042 −0.550211 0.835026i \(-0.685453\pi\)
−0.550211 + 0.835026i \(0.685453\pi\)
\(420\) 0 0
\(421\) 5550.00 0.642495 0.321248 0.946995i \(-0.395898\pi\)
0.321248 + 0.946995i \(0.395898\pi\)
\(422\) 0 0
\(423\) −14454.0 + 25035.1i −1.66141 + 2.87765i
\(424\) 0 0
\(425\) 1769.00 + 3064.00i 0.201904 + 0.349708i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2400.00 + 4156.92i 0.270100 + 0.467828i
\(430\) 0 0
\(431\) 1500.00 2598.08i 0.167639 0.290359i −0.769950 0.638104i \(-0.779719\pi\)
0.937589 + 0.347744i \(0.113052\pi\)
\(432\) 0 0
\(433\) −12926.0 −1.43460 −0.717302 0.696762i \(-0.754623\pi\)
−0.717302 + 0.696762i \(0.754623\pi\)
\(434\) 0 0
\(435\) −4960.00 −0.546698
\(436\) 0 0
\(437\) −832.000 + 1441.07i −0.0910754 + 0.157747i
\(438\) 0 0
\(439\) −204.000 353.338i −0.0221786 0.0384144i 0.854723 0.519084i \(-0.173727\pi\)
−0.876902 + 0.480670i \(0.840394\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7226.00 + 12515.8i 0.774983 + 1.34231i 0.934804 + 0.355164i \(0.115575\pi\)
−0.159821 + 0.987146i \(0.551092\pi\)
\(444\) 0 0
\(445\) −1560.00 + 2702.00i −0.166182 + 0.287836i
\(446\) 0 0
\(447\) 26940.0 2.85060
\(448\) 0 0
\(449\) 10258.0 1.07818 0.539092 0.842247i \(-0.318767\pi\)
0.539092 + 0.842247i \(0.318767\pi\)
\(450\) 0 0
\(451\) −120.000 + 207.846i −0.0125290 + 0.0217009i
\(452\) 0 0
\(453\) 13240.0 + 22932.4i 1.37322 + 2.37849i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2749.00 + 4761.41i 0.281385 + 0.487373i 0.971726 0.236111i \(-0.0758730\pi\)
−0.690341 + 0.723484i \(0.742540\pi\)
\(458\) 0 0
\(459\) −13340.0 + 23105.6i −1.35655 + 2.34962i
\(460\) 0 0
\(461\) 16316.0 1.64840 0.824199 0.566300i \(-0.191625\pi\)
0.824199 + 0.566300i \(0.191625\pi\)
\(462\) 0 0
\(463\) 8944.00 0.897760 0.448880 0.893592i \(-0.351823\pi\)
0.448880 + 0.893592i \(0.351823\pi\)
\(464\) 0 0
\(465\) 10080.0 17459.1i 1.00527 1.74117i
\(466\) 0 0
\(467\) −4711.00 8159.69i −0.466807 0.808534i 0.532474 0.846447i \(-0.321263\pi\)
−0.999281 + 0.0379124i \(0.987929\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2780.00 4815.10i −0.271965 0.471058i
\(472\) 0 0
\(473\) 8320.00 14410.7i 0.808782 1.40085i
\(474\) 0 0
\(475\) 1586.00 0.153201
\(476\) 0 0
\(477\) −32850.0 −3.15325
\(478\) 0 0
\(479\) 6910.00 11968.5i 0.659136 1.14166i −0.321704 0.946840i \(-0.604256\pi\)
0.980840 0.194816i \(-0.0624110\pi\)
\(480\) 0 0
\(481\) −156.000 270.200i −0.0147879 0.0256134i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 856.000 + 1482.64i 0.0801422 + 0.138810i
\(486\) 0 0
\(487\) 6632.00 11487.0i 0.617094 1.06884i −0.372920 0.927864i \(-0.621643\pi\)
0.990013 0.140974i \(-0.0450234\pi\)
\(488\) 0 0
\(489\) −3280.00 −0.303327
\(490\) 0 0
\(491\) −5940.00 −0.545964 −0.272982 0.962019i \(-0.588010\pi\)
−0.272982 + 0.962019i \(0.588010\pi\)
\(492\) 0 0
\(493\) 1798.00 3114.23i 0.164255 0.284498i
\(494\) 0 0
\(495\) 11680.0 + 20230.4i 1.06056 + 1.83694i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4126.00 + 7146.44i 0.370151 + 0.641120i 0.989588 0.143926i \(-0.0459728\pi\)
−0.619438 + 0.785046i \(0.712639\pi\)
\(500\) 0 0
\(501\) −21340.0 + 36962.0i −1.90300 + 3.29609i
\(502\) 0 0
\(503\) −4704.00 −0.416980 −0.208490 0.978024i \(-0.566855\pi\)
−0.208490 + 0.978024i \(0.566855\pi\)
\(504\) 0 0
\(505\) −11456.0 −1.00948
\(506\) 0 0
\(507\) 10265.0 17779.5i 0.899181 1.55743i
\(508\) 0 0
\(509\) −5394.00 9342.68i −0.469715 0.813570i 0.529686 0.848194i \(-0.322310\pi\)
−0.999400 + 0.0346241i \(0.988977\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 5980.00 + 10357.7i 0.514666 + 0.891427i
\(514\) 0 0
\(515\) 3056.00 5293.15i 0.261482 0.452901i
\(516\) 0 0
\(517\) −15840.0 −1.34747
\(518\) 0 0
\(519\) 34760.0 2.93987
\(520\) 0 0
\(521\) −7293.00 + 12631.8i −0.613267 + 1.06221i 0.377419 + 0.926043i \(0.376812\pi\)
−0.990686 + 0.136167i \(0.956522\pi\)
\(522\) 0 0
\(523\) 13.0000 + 22.5167i 0.00108690 + 0.00188257i 0.866568 0.499058i \(-0.166321\pi\)
−0.865481 + 0.500941i \(0.832987\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7308.00 + 12657.8i 0.604064 + 1.04627i
\(528\) 0 0
\(529\) 4035.50 6989.69i 0.331676 0.574479i
\(530\) 0 0
\(531\) −20002.0 −1.63468
\(532\) 0 0
\(533\) −72.0000 −0.00585116
\(534\) 0 0
\(535\) −1296.00 + 2244.74i −0.104731 + 0.181399i
\(536\) 0 0
\(537\) −11340.0 19641.5i −0.911280 1.57838i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5607.00 9711.61i −0.445589 0.771783i 0.552504 0.833510i \(-0.313672\pi\)
−0.998093 + 0.0617272i \(0.980339\pi\)
\(542\) 0 0
\(543\) −1380.00 + 2390.23i −0.109063 + 0.188903i
\(544\) 0 0
\(545\) −10672.0 −0.838786
\(546\) 0 0
\(547\) −5424.00 −0.423973 −0.211987 0.977273i \(-0.567993\pi\)
−0.211987 + 0.977273i \(0.567993\pi\)
\(548\) 0 0
\(549\) −21024.0 + 36414.6i −1.63439 + 2.83085i
\(550\) 0 0
\(551\) −806.000 1396.03i −0.0623172 0.107936i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1040.00 1801.33i −0.0795415 0.137770i
\(556\) 0 0
\(557\) 8809.00 15257.6i 0.670106 1.16066i −0.307767 0.951462i \(-0.599582\pi\)
0.977874 0.209197i \(-0.0670849\pi\)
\(558\) 0 0
\(559\) 4992.00 0.377709
\(560\) 0 0
\(561\) −23200.0 −1.74600
\(562\) 0 0
\(563\) −1781.00 + 3084.78i −0.133322 + 0.230920i −0.924955 0.380076i \(-0.875898\pi\)
0.791633 + 0.610997i \(0.209231\pi\)
\(564\) 0 0
\(565\) −7192.00 12456.9i −0.535522 0.927551i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1419.00 2457.78i −0.104548 0.181082i 0.809006 0.587801i \(-0.200006\pi\)
−0.913553 + 0.406719i \(0.866673\pi\)
\(570\) 0 0
\(571\) 180.000 311.769i 0.0131922 0.0228496i −0.859354 0.511381i \(-0.829134\pi\)
0.872546 + 0.488532i \(0.162467\pi\)
\(572\) 0 0
\(573\) −30000.0 −2.18720
\(574\) 0 0
\(575\) 3904.00 0.283144
\(576\) 0 0
\(577\) 11009.0 19068.1i 0.794299 1.37577i −0.128984 0.991647i \(-0.541172\pi\)
0.923283 0.384120i \(-0.125495\pi\)
\(578\) 0 0
\(579\) −16390.0 28388.3i −1.17642 2.03761i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −9000.00 15588.5i −0.639351 1.10739i
\(584\) 0 0
\(585\) −3504.00 + 6069.11i −0.247645 + 0.428934i
\(586\) 0 0
\(587\) −1454.00 −0.102237 −0.0511184 0.998693i \(-0.516279\pi\)
−0.0511184 + 0.998693i \(0.516279\pi\)
\(588\) 0 0
\(589\) 6552.00 0.458354
\(590\) 0 0
\(591\) 11810.0 20455.5i 0.821994 1.42374i
\(592\) 0 0
\(593\) 6909.00 + 11966.7i 0.478446 + 0.828693i 0.999695 0.0247118i \(-0.00786682\pi\)
−0.521248 + 0.853405i \(0.674533\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5180.00 8972.02i −0.355114 0.615076i
\(598\) 0 0
\(599\) −3348.00 + 5798.91i −0.228373 + 0.395554i −0.957326 0.289010i \(-0.906674\pi\)
0.728953 + 0.684564i \(0.240007\pi\)
\(600\) 0 0
\(601\) −10010.0 −0.679395 −0.339698 0.940535i \(-0.610325\pi\)
−0.339698 + 0.940535i \(0.610325\pi\)
\(602\) 0 0
\(603\) −34748.0 −2.34668
\(604\) 0 0
\(605\) −1076.00 + 1863.69i −0.0723068 + 0.125239i
\(606\) 0 0
\(607\) 1440.00 + 2494.15i 0.0962896 + 0.166779i 0.910146 0.414287i \(-0.135969\pi\)
−0.813856 + 0.581066i \(0.802636\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2376.00 4115.35i −0.157320 0.272487i
\(612\) 0 0
\(613\) −3261.00 + 5648.22i −0.214862 + 0.372152i −0.953230 0.302246i \(-0.902264\pi\)
0.738368 + 0.674398i \(0.235597\pi\)
\(614\) 0 0
\(615\) −480.000 −0.0314723
\(616\) 0 0
\(617\) 6614.00 0.431555 0.215778 0.976443i \(-0.430771\pi\)
0.215778 + 0.976443i \(0.430771\pi\)
\(618\) 0 0
\(619\) 2633.00 4560.49i 0.170968 0.296125i −0.767791 0.640701i \(-0.778644\pi\)
0.938759 + 0.344576i \(0.111977\pi\)
\(620\) 0 0
\(621\) 14720.0 + 25495.8i 0.951197 + 1.64752i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2139.50 + 3705.72i 0.136928 + 0.237166i
\(626\) 0 0
\(627\) −5200.00 + 9006.66i −0.331209 + 0.573671i
\(628\) 0 0
\(629\) 1508.00 0.0955928
\(630\) 0 0
\(631\) 3344.00 0.210971 0.105485 0.994421i \(-0.466360\pi\)
0.105485 + 0.994421i \(0.466360\pi\)
\(632\) 0 0
\(633\) −17620.0 + 30518.7i −1.10637 + 1.91629i
\(634\) 0 0
\(635\) 1536.00 + 2660.43i 0.0959910 + 0.166261i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 16352.0 + 28322.5i 1.01232 + 1.75340i
\(640\) 0 0
\(641\) 2441.00 4227.94i 0.150411 0.260520i −0.780967 0.624572i \(-0.785274\pi\)
0.931379 + 0.364052i \(0.118607\pi\)
\(642\) 0 0
\(643\) 15898.0 0.975048 0.487524 0.873110i \(-0.337900\pi\)
0.487524 + 0.873110i \(0.337900\pi\)
\(644\) 0 0
\(645\) 33280.0 2.03163
\(646\) 0 0
\(647\) 3066.00 5310.47i 0.186301 0.322683i −0.757713 0.652588i \(-0.773683\pi\)
0.944014 + 0.329905i \(0.107017\pi\)
\(648\) 0 0
\(649\) −5480.00 9491.64i −0.331447 0.574082i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12099.0 + 20956.1i 0.725070 + 1.25586i 0.958945 + 0.283591i \(0.0915258\pi\)
−0.233876 + 0.972266i \(0.575141\pi\)
\(654\) 0 0
\(655\) −7256.00 + 12567.8i −0.432848 + 0.749715i
\(656\) 0 0
\(657\) 11534.0 0.684907
\(658\) 0 0
\(659\) 17456.0 1.03185 0.515925 0.856634i \(-0.327448\pi\)
0.515925 + 0.856634i \(0.327448\pi\)
\(660\) 0 0
\(661\) −328.000 + 568.113i −0.0193006 + 0.0334297i −0.875514 0.483192i \(-0.839477\pi\)
0.856214 + 0.516622i \(0.172811\pi\)
\(662\) 0 0
\(663\) −3480.00 6027.54i −0.203849 0.353077i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1984.00 3436.39i −0.115174 0.199487i
\(668\) 0 0
\(669\) −6680.00 + 11570.1i −0.386044 + 0.668649i
\(670\) 0 0
\(671\) −23040.0 −1.32556
\(672\) 0 0
\(673\) −18214.0 −1.04324 −0.521618 0.853179i \(-0.674671\pi\)
−0.521618 + 0.853179i \(0.674671\pi\)
\(674\) 0 0
\(675\) 14030.0 24300.7i 0.800022 1.38568i
\(676\) 0 0
\(677\) 15126.0 + 26199.0i 0.858699 + 1.48731i 0.873170 + 0.487415i \(0.162060\pi\)
−0.0144709 + 0.999895i \(0.504606\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6450.00 + 11171.7i 0.362944 + 0.628637i
\(682\) 0 0
\(683\) 5418.00 9384.25i 0.303534 0.525737i −0.673400 0.739279i \(-0.735167\pi\)
0.976934 + 0.213542i \(0.0684999\pi\)
\(684\) 0 0
\(685\) 13328.0 0.743411
\(686\) 0 0
\(687\) −55240.0 −3.06774
\(688\) 0 0
\(689\) 2700.00 4676.54i 0.149291 0.258580i
\(690\) 0 0
\(691\) 4789.00 + 8294.79i 0.263650 + 0.456655i 0.967209 0.253982i \(-0.0817403\pi\)
−0.703559 + 0.710637i \(0.748407\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4504.00 + 7801.16i 0.245822 + 0.425777i
\(696\) 0 0
\(697\) 174.000 301.377i 0.00945584 0.0163780i
\(698\) 0 0
\(699\) 63140.0 3.41656
\(700\) 0 0
\(701\) 12442.0 0.670368 0.335184 0.942153i \(-0.391202\pi\)
0.335184 + 0.942153i \(0.391202\pi\)
\(702\) 0 0
\(703\) 338.000 585.433i 0.0181336 0.0314083i
\(704\) 0 0
\(705\) −15840.0 27435.7i −0.846197 1.46566i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 12587.0 + 21801.3i 0.666734 + 1.15482i 0.978812 + 0.204761i \(0.0656418\pi\)
−0.312078 + 0.950057i \(0.601025\pi\)
\(710\) 0 0
\(711\) 34164.0 59173.8i 1.80204 3.12122i
\(712\) 0 0
\(713\) 16128.0 0.847123
\(714\) 0 0
\(715\) −3840.00 −0.200850
\(716\) 0 0
\(717\) 19800.0 34294.6i 1.03130 1.78627i
\(718\) 0 0
\(719\) 17094.0 + 29607.7i 0.886646 + 1.53572i 0.843815 + 0.536634i \(0.180304\pi\)
0.0428311 + 0.999082i \(0.486362\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −35090.0 60777.7i −1.80499 3.12634i
\(724\) 0 0
\(725\) −1891.00 + 3275.31i −0.0968689 + 0.167782i
\(726\) 0 0
\(727\) 5204.00 0.265482 0.132741 0.991151i \(-0.457622\pi\)
0.132741 + 0.991151i \(0.457622\pi\)
\(728\) 0 0
\(729\) 67717.0 3.44038
\(730\) 0 0
\(731\) −12064.0 + 20895.5i −0.610401 + 1.05725i
\(732\) 0 0
\(733\) −16440.0 28474.9i −0.828411 1.43485i −0.899284 0.437365i \(-0.855912\pi\)
0.0708733 0.997485i \(-0.477421\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9520.00 16489.1i −0.475812 0.824131i
\(738\) 0 0
\(739\) 1956.00 3387.89i 0.0973648 0.168641i −0.813228 0.581945i \(-0.802292\pi\)
0.910593 + 0.413304i \(0.135625\pi\)
\(740\) 0 0
\(741\) −3120.00 −0.154678
\(742\) 0 0
\(743\) −16008.0 −0.790413 −0.395206 0.918592i \(-0.629327\pi\)
−0.395206 + 0.918592i \(0.629327\pi\)
\(744\) 0 0
\(745\) −10776.0 + 18664.6i −0.529936 + 0.917876i
\(746\) 0 0
\(747\) 19345.0 + 33506.5i 0.947519 + 1.64115i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4980.00 8625.61i −0.241974 0.419112i 0.719302 0.694697i \(-0.244462\pi\)
−0.961277 + 0.275585i \(0.911128\pi\)
\(752\) 0 0
\(753\) −11970.0 + 20732.6i −0.579298 + 1.00337i
\(754\) 0 0
\(755\) −21184.0 −1.02115
\(756\) 0 0
\(757\) 12378.0 0.594301 0.297151 0.954831i \(-0.403964\pi\)
0.297151 + 0.954831i \(0.403964\pi\)
\(758\) 0 0
\(759\) −12800.0 + 22170.3i −0.612135 + 1.06025i
\(760\) 0 0
\(761\) 17335.0 + 30025.1i 0.825747 + 1.43024i 0.901347 + 0.433097i \(0.142579\pi\)
−0.0756005 + 0.997138i \(0.524087\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −16936.0 29334.0i −0.800421 1.38637i
\(766\) 0 0
\(767\) 1644.00 2847.49i 0.0773943 0.134051i
\(768\) 0 0
\(769\) 10898.0 0.511043 0.255521 0.966803i \(-0.417753\pi\)
0.255521 + 0.966803i \(0.417753\pi\)
\(770\) 0 0
\(771\) 27660.0 1.29202
\(772\) 0 0
\(773\) −12904.0 + 22350.4i −0.600420 + 1.03996i 0.392337 + 0.919821i \(0.371667\pi\)
−0.992757 + 0.120136i \(0.961667\pi\)
\(774\) 0 0
\(775\) −7686.00 13312.5i −0.356244 0.617033i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −78.0000 135.100i −0.00358747 0.00621368i
\(780\) 0 0
\(781\) −8960.00 + 15519.2i −0.410517 + 0.711037i
\(782\) 0 0
\(783\) −28520.0 −1.30169
\(784\) 0 0
\(785\) 4448.00 0.202237
\(786\) 0 0
\(787\) −10527.0 + 18233.3i −0.476807 + 0.825854i −0.999647 0.0265772i \(-0.991539\pi\)
0.522840 + 0.852431i \(0.324873\pi\)
\(788\) 0 0
\(789\) −39840.0 69004.9i −1.79764 3.11361i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −3456.00 5985.97i −0.154762 0.268055i
\(794\) 0 0
\(795\) 18000.0 31176.9i 0.803012 1.39086i
\(796\) 0 0
\(797\) 24276.0 1.07892 0.539461 0.842011i \(-0.318628\pi\)
0.539461 + 0.842011i \(0.318628\pi\)
\(798\) 0 0
\(799\) 22968.0 1.01696
\(800\) 0 0
\(801\) −14235.0 + 24655.7i −0.627926 + 1.08760i
\(802\) 0 0
\(803\) 3160.00 + 5473.28i 0.138872 + 0.240533i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −14500.0 25114.7i −0.632496 1.09551i
\(808\) 0 0
\(809\) −10763.0 + 18642.1i −0.467747 + 0.810161i −0.999321 0.0368510i \(-0.988267\pi\)
0.531574 + 0.847012i \(0.321601\pi\)
\(810\) 0 0
\(811\) 12806.0 0.554475 0.277238 0.960801i \(-0.410581\pi\)
0.277238 + 0.960801i \(0.410581\pi\)
\(812\) 0 0
\(813\) −26400.0 −1.13885
\(814\) 0 0
\(815\) 1312.00 2272.45i 0.0563894 0.0976693i
\(816\) 0 0
\(817\) 5408.00 + 9366.93i 0.231581 + 0.401111i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6607.00 11443.7i −0.280860 0.486463i 0.690737 0.723106i \(-0.257286\pi\)
−0.971597 + 0.236643i \(0.923953\pi\)
\(822\) 0 0
\(823\) −16124.0 + 27927.6i −0.682925 + 1.18286i 0.291159 + 0.956675i \(0.405959\pi\)
−0.974084 + 0.226186i \(0.927374\pi\)
\(824\) 0 0
\(825\) 24400.0 1.02970
\(826\) 0 0
\(827\) −14316.0 −0.601954 −0.300977 0.953631i \(-0.597313\pi\)
−0.300977 + 0.953631i \(0.597313\pi\)
\(828\) 0 0
\(829\) 12584.0 21796.1i 0.527214 0.913161i −0.472283 0.881447i \(-0.656570\pi\)
0.999497 0.0317144i \(-0.0100967\pi\)
\(830\) 0 0
\(831\) 7610.00 + 13180.9i 0.317675 + 0.550229i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −17072.0 29569.6i −0.707546 1.22551i
\(836\) 0 0
\(837\) 57960.0 100390.i 2.39354 4.14573i
\(838\) 0 0
\(839\) −9356.00 −0.384988 −0.192494 0.981298i \(-0.561658\pi\)
−0.192494 + 0.981298i \(0.561658\pi\)
\(840\) 0 0
\(841\) −20545.0 −0.842388
\(842\) 0 0
\(843\) 22670.0 39265.6i 0.926211 1.60425i
\(844\) 0 0
\(845\) 8212.00 + 14223.6i 0.334321 + 0.579061i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 24170.0 + 41863.7i 0.977046 + 1.69229i
\(850\) 0 0
\(851\) 832.000 1441.07i 0.0335142 0.0580483i
\(852\) 0 0
\(853\) −2372.00 −0.0952119 −0.0476059 0.998866i \(-0.515159\pi\)
−0.0476059 + 0.998866i \(0.515159\pi\)
\(854\) 0 0
\(855\) −15184.0 −0.607347
\(856\) 0 0
\(857\) 5847.00 10127.3i 0.233057 0.403666i −0.725649 0.688065i \(-0.758461\pi\)
0.958706 + 0.284398i \(0.0917938\pi\)
\(858\) 0 0
\(859\) −10253.0 17758.7i −0.407250 0.705378i 0.587330 0.809347i \(-0.300179\pi\)
−0.994580 + 0.103969i \(0.966846\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14068.0 + 24366.5i 0.554902 + 0.961118i 0.997911 + 0.0646012i \(0.0205775\pi\)
−0.443009 + 0.896517i \(0.646089\pi\)
\(864\) 0 0
\(865\) −13904.0 + 24082.4i −0.546532 + 0.946621i
\(866\) 0 0
\(867\) −15490.0 −0.606768
\(868\) 0 0
\(869\) 37440.0 1.46152
\(870\) 0 0
\(871\) 2856.00 4946.74i 0.111104 0.192438i
\(872\) 0 0
\(873\) 7811.00 + 13529.0i 0.302821 + 0.524500i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 18535.0 + 32103.6i 0.713663 + 1.23610i 0.963473 + 0.267806i \(0.0862985\pi\)
−0.249810 + 0.968295i \(0.580368\pi\)
\(878\) 0 0
\(879\) −23280.0 + 40322.1i −0.893305 + 1.54725i
\(880\) 0 0
\(881\) 6198.00 0.237021 0.118511 0.992953i \(-0.462188\pi\)
0.118511 + 0.992953i \(0.462188\pi\)
\(882\) 0 0
\(883\) −31876.0 −1.21485 −0.607425 0.794377i \(-0.707798\pi\)
−0.607425 + 0.794377i \(0.707798\pi\)
\(884\) 0 0
\(885\) 10960.0 18983.3i 0.416290 0.721035i
\(886\) 0 0
\(887\) −66.0000 114.315i −0.00249838 0.00432732i 0.864774 0.502162i \(-0.167462\pi\)
−0.867272 + 0.497835i \(0.834129\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 52580.0 + 91071.2i 1.97699 + 3.42424i
\(892\) 0 0
\(893\) 5148.00 8916.60i 0.192913 0.334135i
\(894\) 0 0
\(895\) 18144.0 0.677639
\(896\) 0 0
\(897\) −7680.00 −0.285873
\(898\) 0 0
\(899\) −7812.00 + 13530.8i −0.289816 + 0.501976i
\(900\) 0 0
\(901\) 13050.0 + 22603.3i 0.482529 + 0.835765i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1104.00 1912.18i −0.0405505 0.0702355i
\(906\) 0 0
\(907\) −19122.0 + 33120.3i −0.700039 + 1.21250i 0.268413 + 0.963304i \(0.413501\pi\)
−0.968452 + 0.249200i \(0.919832\pi\)
\(908\) 0 0
\(909\) −104536. −3.81435
\(910\) 0 0
\(911\) −7008.00 −0.254869 −0.127434 0.991847i \(-0.540674\pi\)
−0.127434 + 0.991847i \(0.540674\pi\)
\(912\) 0 0
\(913\) −10600.0 + 18359.7i −0.384237 + 0.665519i
\(914\) 0 0
\(915\) −23040.0 39906.5i −0.832436 1.44182i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −18332.0 31752.0i −0.658016 1.13972i −0.981128 0.193357i \(-0.938062\pi\)
0.323112 0.946361i \(-0.395271\pi\)
\(920\) 0 0
\(921\) −36190.0 + 62682.9i −1.29479 + 2.24264i
\(922\) 0 0
\(923\) −5376.00 −0.191715
\(924\) 0 0
\(925\) −1586.00 −0.0563755
\(926\) 0 0
\(927\) 27886.0 48300.0i 0.988022 1.71130i
\(928\) 0 0
\(929\) 22755.0 + 39412.8i 0.803625 + 1.39192i 0.917216 + 0.398391i \(0.130431\pi\)
−0.113591 + 0.993528i \(0.536235\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 5480.00 + 9491.64i 0.192291 + 0.333057i
\(934\) 0 0
\(935\) 9280.00 16073.4i 0.324587 0.562200i
\(936\) 0 0
\(937\) 3838.00 0.133812 0.0669061 0.997759i \(-0.478687\pi\)
0.0669061 + 0.997759i \(0.478687\pi\)
\(938\) 0 0
\(939\) 38180.0 1.32690
\(940\) 0 0
\(941\) −8416.00 + 14576.9i −0.291556 + 0.504989i −0.974178 0.225782i \(-0.927506\pi\)
0.682622 + 0.730771i \(0.260839\pi\)
\(942\) 0 0
\(943\) −192.000 332.554i −0.00663031 0.0114840i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 20464.0 + 35444.7i 0.702208 + 1.21626i 0.967690 + 0.252144i \(0.0811355\pi\)
−0.265482 + 0.964116i \(0.585531\pi\)
\(948\) 0 0
\(949\) −948.000 + 1641.98i −0.0324272 + 0.0561655i
\(950\) 0 0
\(951\) 19980.0 0.681279
\(952\) 0 0
\(953\) −24070.0 −0.818157 −0.409079 0.912499i \(-0.634150\pi\)
−0.409079 + 0.912499i \(0.634150\pi\)
\(954\) 0 0
\(955\) 12000.0 20784.6i 0.406608 0.704266i
\(956\) 0 0
\(957\) −12400.0 21477.4i −0.418845 0.725462i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −16856.5 29196.3i −0.565825 0.980038i
\(962\) 0 0
\(963\) −11826.0 + 20483.2i −0.395730 + 0.685424i
\(964\) 0 0
\(965\) 26224.0 0.874798
\(966\) 0 0
\(967\) −17152.0 −0.570394 −0.285197 0.958469i \(-0.592059\pi\)
−0.285197 + 0.958469i \(0.592059\pi\)
\(968\) 0 0
\(969\) 7540.00 13059.7i 0.249969 0.432959i
\(970\) 0 0
\(971\) −16455.0 28500.9i −0.543837 0.941954i −0.998679 0.0513817i \(-0.983638\pi\)
0.454842 0.890572i \(-0.349696\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 3660.00 + 6339.31i 0.120219 + 0.208226i
\(976\) 0 0
\(977\) 3411.00 5908.03i 0.111697 0.193464i −0.804758 0.593603i \(-0.797705\pi\)
0.916454 + 0.400139i \(0.131038\pi\)
\(978\) 0 0
\(979\) −15600.0 −0.509273
\(980\) 0 0
\(981\) −97382.0 −3.16939
\(982\) 0 0
\(983\) −24210.0 + 41933.0i −0.785533 + 1.36058i 0.143147 + 0.989701i \(0.454278\pi\)
−0.928680 + 0.370882i \(0.879055\pi\)
\(984\) 0 0
\(985\) 9448.00 + 16364.4i 0.305623 + 0.529354i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 13312.0 + 23057.1i 0.428005 + 0.741326i
\(990\) 0 0
\(991\) 24608.0 42622.3i 0.788798 1.36624i −0.137906 0.990445i \(-0.544037\pi\)
0.926704 0.375793i \(-0.122630\pi\)
\(992\) 0 0
\(993\) −79360.0 −2.53617
\(994\) 0 0
\(995\) 8288.00 0.264068
\(996\) 0 0
\(997\) 17632.0 30539.5i 0.560091 0.970107i −0.437397 0.899269i \(-0.644099\pi\)
0.997488 0.0708379i \(-0.0225673\pi\)
\(998\) 0 0
\(999\) −5980.00 10357.7i −0.189388 0.328030i
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 196.4.e.a.165.1 2
3.2 odd 2 1764.4.k.m.361.1 2
7.2 even 3 inner 196.4.e.a.177.1 2
7.3 odd 6 28.4.a.a.1.1 1
7.4 even 3 196.4.a.d.1.1 1
7.5 odd 6 196.4.e.f.177.1 2
7.6 odd 2 196.4.e.f.165.1 2
21.2 odd 6 1764.4.k.m.1549.1 2
21.5 even 6 1764.4.k.d.1549.1 2
21.11 odd 6 1764.4.a.c.1.1 1
21.17 even 6 252.4.a.d.1.1 1
21.20 even 2 1764.4.k.d.361.1 2
28.3 even 6 112.4.a.g.1.1 1
28.11 odd 6 784.4.a.a.1.1 1
35.3 even 12 700.4.e.a.449.1 2
35.17 even 12 700.4.e.a.449.2 2
35.24 odd 6 700.4.a.n.1.1 1
56.3 even 6 448.4.a.a.1.1 1
56.45 odd 6 448.4.a.p.1.1 1
84.59 odd 6 1008.4.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.a.1.1 1 7.3 odd 6
112.4.a.g.1.1 1 28.3 even 6
196.4.a.d.1.1 1 7.4 even 3
196.4.e.a.165.1 2 1.1 even 1 trivial
196.4.e.a.177.1 2 7.2 even 3 inner
196.4.e.f.165.1 2 7.6 odd 2
196.4.e.f.177.1 2 7.5 odd 6
252.4.a.d.1.1 1 21.17 even 6
448.4.a.a.1.1 1 56.3 even 6
448.4.a.p.1.1 1 56.45 odd 6
700.4.a.n.1.1 1 35.24 odd 6
700.4.e.a.449.1 2 35.3 even 12
700.4.e.a.449.2 2 35.17 even 12
784.4.a.a.1.1 1 28.11 odd 6
1008.4.a.o.1.1 1 84.59 odd 6
1764.4.a.c.1.1 1 21.11 odd 6
1764.4.k.d.361.1 2 21.20 even 2
1764.4.k.d.1549.1 2 21.5 even 6
1764.4.k.m.361.1 2 3.2 odd 2
1764.4.k.m.1549.1 2 21.2 odd 6