Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(739,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.e (of order \(2\), degree \(1\), 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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 739.6 | ||
Root | \(3.40359i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.739 |
Dual form | 3330.2.e.d.739.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.28269 | + | 1.83159i | 0.573636 | + | 0.819110i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.06225i | − | 0.779457i | −0.920930 | − | 0.389728i | \(-0.872569\pi\) | ||
0.920930 | − | 0.389728i | \(-0.127431\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.28269 | + | 1.83159i | 0.405622 | + | 0.579198i | ||||
\(11\) | −3.77719 | −1.13886 | −0.569432 | − | 0.822038i | \(-0.692837\pi\) | ||||
−0.569432 | + | 0.822038i | \(0.692837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.88351 | −0.799742 | −0.399871 | − | 0.916571i | \(-0.630945\pi\) | ||||
−0.399871 | + | 0.916571i | \(0.630945\pi\) | |||||||
\(14\) | − | 2.06225i | − | 0.551159i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.80724 | −1.40846 | −0.704232 | − | 0.709970i | \(-0.748708\pi\) | ||||
−0.704232 | + | 0.709970i | \(0.748708\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.157282i | − | 0.0360829i | −0.999837 | − | 0.0180414i | \(-0.994257\pi\) | ||
0.999837 | − | 0.0180414i | \(-0.00574308\pi\) | |||||||
\(20\) | 1.28269 | + | 1.83159i | 0.286818 | + | 0.409555i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.77719 | −0.805299 | ||||||||
\(23\) | −5.41883 | −1.12990 | −0.564952 | − | 0.825124i | \(-0.691105\pi\) | ||||
−0.564952 | + | 0.825124i | \(0.691105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.70942 | + | 4.69871i | −0.341883 | + | 0.939742i | ||||
\(26\) | −2.88351 | −0.565503 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.06225i | − | 0.389728i | ||||||
\(29\) | 4.29061i | 0.796746i | 0.917223 | + | 0.398373i | \(0.130425\pi\) | ||||
−0.917223 | + | 0.398373i | \(0.869575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.425694i | 0.0764569i | 0.999269 | + | 0.0382285i | \(0.0121715\pi\) | ||||
−0.999269 | + | 0.0382285i | \(0.987829\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.80724 | −0.995934 | ||||||||
\(35\) | 3.77719 | − | 2.64522i | 0.638461 | − | 0.447125i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.80724 | + | 3.72698i | −0.790306 | + | 0.612713i | ||||
\(38\) | − | 0.157282i | − | 0.0255144i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.28269 | + | 1.83159i | 0.202811 | + | 0.289599i | ||||
\(41\) | −0.923733 | −0.144263 | −0.0721314 | − | 0.997395i | \(-0.522980\pi\) | ||||
−0.0721314 | + | 0.997395i | \(0.522980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8263 | −1.65099 | −0.825497 | − | 0.564406i | \(-0.809105\pi\) | ||||
−0.825497 | + | 0.564406i | \(0.809105\pi\) | |||||||
\(44\) | −3.77719 | −0.569432 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.41883 | −0.798963 | ||||||||
\(47\) | 0.676445i | 0.0986697i | 0.998782 | + | 0.0493348i | \(0.0157101\pi\) | ||||
−0.998782 | + | 0.0493348i | \(0.984290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.74713 | 0.392447 | ||||||||
\(50\) | −1.70942 | + | 4.69871i | −0.241748 | + | 0.664498i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.88351 | −0.399871 | ||||||||
\(53\) | 9.87810i | 1.35686i | 0.734664 | + | 0.678431i | \(0.237340\pi\) | ||||
−0.734664 | + | 0.678431i | \(0.762660\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.84496 | − | 6.91824i | −0.653294 | − | 0.932856i | ||||
\(56\) | − | 2.06225i | − | 0.275580i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.29061i | 0.563385i | ||||||||
\(59\) | 8.47192i | 1.10295i | 0.834192 | + | 0.551475i | \(0.185935\pi\) | ||||
−0.834192 | + | 0.551475i | \(0.814065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23904i | 0.158643i | 0.996849 | + | 0.0793215i | \(0.0252754\pi\) | ||||
−0.996849 | + | 0.0793215i | \(0.974725\pi\) | |||||||
\(62\) | 0.425694i | 0.0540632i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.69865 | − | 5.28140i | −0.458761 | − | 0.655077i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.45516i | − | 0.788623i | −0.918977 | − | 0.394312i | \(-0.870983\pi\) | ||
0.918977 | − | 0.394312i | \(-0.129017\pi\) | |||||||
\(68\) | −5.80724 | −0.704232 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.77719 | − | 2.64522i | 0.451460 | − | 0.316165i | ||||
\(71\) | 3.28329 | 0.389655 | 0.194828 | − | 0.980838i | \(-0.437585\pi\) | ||||
0.194828 | + | 0.980838i | \(0.437585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.980489i | 0.114758i | 0.998352 | + | 0.0573788i | \(0.0182743\pi\) | ||||
−0.998352 | + | 0.0573788i | \(0.981726\pi\) | |||||||
\(74\) | −4.80724 | + | 3.72698i | −0.558831 | + | 0.433253i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.157282i | − | 0.0180414i | ||||||
\(77\) | 7.78950i | 0.887696i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.04725i | 0.905387i | 0.891666 | + | 0.452693i | \(0.149537\pi\) | ||||
−0.891666 | + | 0.452693i | \(0.850463\pi\) | |||||||
\(80\) | 1.28269 | + | 1.83159i | 0.143409 | + | 0.204778i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.923733 | −0.102009 | ||||||||
\(83\) | − | 11.9496i | − | 1.31164i | −0.754916 | − | 0.655821i | \(-0.772323\pi\) | ||
0.754916 | − | 0.655821i | \(-0.227677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.44889 | − | 10.6365i | −0.807945 | − | 1.15369i | ||||
\(86\) | −10.8263 | −1.16743 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.77719 | −0.402649 | ||||||||
\(89\) | 7.65857i | 0.811807i | 0.913916 | + | 0.405903i | \(0.133043\pi\) | ||||
−0.913916 | + | 0.405903i | \(0.866957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.94652i | 0.623364i | ||||||||
\(92\) | −5.41883 | −0.564952 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.676445i | 0.0697700i | ||||||||
\(95\) | 0.288075 | − | 0.201743i | 0.0295558 | − | 0.0206984i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9571 | 1.41712 | 0.708562 | − | 0.705649i | \(-0.249344\pi\) | ||||
0.708562 | + | 0.705649i | \(0.249344\pi\) | |||||||
\(98\) | 2.74713 | 0.277502 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.70942 | + | 4.69871i | −0.170942 | + | 0.469871i | ||||
\(101\) | 8.38279 | 0.834119 | 0.417059 | − | 0.908879i | \(-0.363061\pi\) | ||||
0.417059 | + | 0.908879i | \(0.363061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4727 | 1.32751 | 0.663753 | − | 0.747951i | \(-0.268962\pi\) | ||||
0.663753 | + | 0.747951i | \(0.268962\pi\) | |||||||
\(104\) | −2.88351 | −0.282751 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.87810i | 0.959446i | ||||||||
\(107\) | − | 1.89614i | − | 0.183306i | −0.995791 | − | 0.0916532i | \(-0.970785\pi\) | ||
0.995791 | − | 0.0916532i | \(-0.0292151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.2044i | − | 1.64789i | −0.566672 | − | 0.823943i | \(-0.691769\pi\) | ||
0.566672 | − | 0.823943i | \(-0.308231\pi\) | |||||||
\(110\) | −4.84496 | − | 6.91824i | −0.461949 | − | 0.659629i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2.06225i | − | 0.194864i | ||||||
\(113\) | 1.17098 | 0.110157 | 0.0550783 | − | 0.998482i | \(-0.482459\pi\) | ||||
0.0550783 | + | 0.998482i | \(0.482459\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.95068 | − | 9.92506i | −0.648154 | − | 0.925516i | ||||
\(116\) | 4.29061i | 0.398373i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.47192i | 0.779903i | ||||||||
\(119\) | 11.9760i | 1.09784i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.26714 | 0.297012 | ||||||||
\(122\) | 1.23904i | 0.112178i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.425694i | 0.0382285i | ||||||||
\(125\) | −10.7987 | + | 2.89605i | −0.965869 | + | 0.259030i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.1128i | − | 1.42978i | −0.699236 | − | 0.714891i | \(-0.746476\pi\) | ||
0.699236 | − | 0.714891i | \(-0.253524\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.69865 | − | 5.28140i | −0.324393 | − | 0.463209i | ||||
\(131\) | − | 9.64715i | − | 0.842875i | −0.906857 | − | 0.421438i | \(-0.861526\pi\) | ||
0.906857 | − | 0.421438i | \(-0.138474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.324354 | −0.0281250 | ||||||||
\(134\) | − | 6.45516i | − | 0.557641i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.80724 | −0.497967 | ||||||||
\(137\) | − | 2.53592i | − | 0.216658i | −0.994115 | − | 0.108329i | \(-0.965450\pi\) | ||
0.994115 | − | 0.108329i | \(-0.0345501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.56000 | 0.641230 | 0.320615 | − | 0.947210i | \(-0.396110\pi\) | ||||
0.320615 | + | 0.947210i | \(0.396110\pi\) | |||||||
\(140\) | 3.77719 | − | 2.64522i | 0.319231 | − | 0.223562i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.28329 | 0.275528 | ||||||||
\(143\) | 10.8916 | 0.910798 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.85862 | + | 5.50352i | −0.652623 | + | 0.457042i | ||||
\(146\) | 0.980489i | 0.0811458i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.80724 | + | 3.72698i | −0.395153 | + | 0.306356i | ||||
\(149\) | −6.72596 | −0.551012 | −0.275506 | − | 0.961299i | \(-0.588845\pi\) | ||||
−0.275506 | + | 0.961299i | \(0.588845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8051 | −1.28620 | −0.643101 | − | 0.765781i | \(-0.722353\pi\) | ||||
−0.643101 | + | 0.765781i | \(0.722353\pi\) | |||||||
\(152\) | − | 0.157282i | − | 0.0127572i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.78950i | 0.627696i | ||||||||
\(155\) | −0.779696 | + | 0.546033i | −0.0626267 | + | 0.0438585i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.50755i | − | 0.678976i | −0.940610 | − | 0.339488i | \(-0.889746\pi\) | ||
0.940610 | − | 0.339488i | \(-0.110254\pi\) | |||||||
\(158\) | 8.04725i | 0.640205i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.28269 | + | 1.83159i | 0.101405 | + | 0.144800i | ||||
\(161\) | 11.1750i | 0.880712i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.41321 | −0.423995 | −0.211998 | − | 0.977270i | \(-0.567997\pi\) | ||||
−0.211998 | + | 0.977270i | \(0.567997\pi\) | |||||||
\(164\) | −0.923733 | −0.0721314 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 11.9496i | − | 0.927471i | ||||||
\(167\) | −2.08165 | −0.161083 | −0.0805415 | − | 0.996751i | \(-0.525665\pi\) | ||||
−0.0805415 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.68537 | −0.360413 | ||||||||
\(170\) | −7.44889 | − | 10.6365i | −0.571304 | − | 0.815780i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.8263 | −0.825497 | ||||||||
\(173\) | 12.3562i | 0.939423i | 0.882820 | + | 0.469712i | \(0.155642\pi\) | ||||
−0.882820 | + | 0.469712i | \(0.844358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.68991 | + | 3.52524i | 0.732489 | + | 0.266483i | ||||
\(176\) | −3.77719 | −0.284716 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.65857i | 0.574034i | ||||||||
\(179\) | − | 13.4571i | − | 1.00583i | −0.864336 | − | 0.502915i | \(-0.832261\pi\) | ||
0.864336 | − | 0.502915i | \(-0.167739\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.66608 | −0.272498 | −0.136249 | − | 0.990675i | \(-0.543505\pi\) | ||||
−0.136249 | + | 0.990675i | \(0.543505\pi\) | |||||||
\(182\) | 5.94652i | 0.440785i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.41883 | −0.399482 | ||||||||
\(185\) | −12.9925 | − | 4.02432i | −0.955227 | − | 0.295874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.9350 | 1.60405 | ||||||||
\(188\) | 0.676445i | 0.0493348i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.288075 | − | 0.201743i | 0.0208991 | − | 0.0146360i | ||||
\(191\) | 18.5540i | 1.34252i | 0.741221 | + | 0.671261i | \(0.234247\pi\) | ||||
−0.741221 | + | 0.671261i | \(0.765753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.89778 | 0.352550 | 0.176275 | − | 0.984341i | \(-0.443595\pi\) | ||||
0.176275 | + | 0.984341i | \(0.443595\pi\) | |||||||
\(194\) | 13.9571 | 1.00206 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.74713 | 0.196224 | ||||||||
\(197\) | − | 14.7803i | − | 1.05305i | −0.850158 | − | 0.526527i | \(-0.823494\pi\) | ||
0.850158 | − | 0.526527i | \(-0.176506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3298i | 0.874039i | 0.899452 | + | 0.437019i | \(0.143966\pi\) | ||||
−0.899452 | + | 0.437019i | \(0.856034\pi\) | |||||||
\(200\) | −1.70942 | + | 4.69871i | −0.120874 | + | 0.332249i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.38279 | 0.589811 | ||||||||
\(203\) | 8.84831 | 0.621029 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.18486 | − | 1.69190i | −0.0827544 | − | 0.118167i | ||||
\(206\) | 13.4727 | 0.938689 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.88351 | −0.199935 | ||||||||
\(209\) | 0.594082i | 0.0410935i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1805 | 0.976224 | 0.488112 | − | 0.872781i | \(-0.337686\pi\) | ||||
0.488112 | + | 0.872781i | \(0.337686\pi\) | |||||||
\(212\) | 9.87810i | 0.678431i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 1.89614i | − | 0.129617i | ||||||
\(215\) | −13.8868 | − | 19.8293i | −0.947070 | − | 1.35235i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.877887 | 0.0595949 | ||||||||
\(218\) | − | 17.2044i | − | 1.16523i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.84496 | − | 6.91824i | −0.326647 | − | 0.466428i | ||||
\(221\) | 16.7452 | 1.12641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.29071i | 0.488222i | 0.969747 | + | 0.244111i | \(0.0784962\pi\) | ||||
−0.969747 | + | 0.244111i | \(0.921504\pi\) | |||||||
\(224\) | − | 2.06225i | − | 0.137790i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.17098 | 0.0778925 | ||||||||
\(227\) | −26.3807 | −1.75095 | −0.875473 | − | 0.483267i | \(-0.839450\pi\) | ||||
−0.875473 | + | 0.483267i | \(0.839450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.5925 | −1.29471 | −0.647354 | − | 0.762190i | \(-0.724124\pi\) | ||||
−0.647354 | + | 0.762190i | \(0.724124\pi\) | |||||||
\(230\) | −6.95068 | − | 9.92506i | −0.458314 | − | 0.654439i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.29061i | 0.281692i | ||||||||
\(233\) | − | 3.69983i | − | 0.242384i | −0.992629 | − | 0.121192i | \(-0.961328\pi\) | ||
0.992629 | − | 0.121192i | \(-0.0386717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.23897 | + | 0.867669i | −0.0808213 | + | 0.0566005i | ||||
\(236\) | 8.47192i | 0.551475i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.9760i | 0.776287i | ||||||||
\(239\) | 8.68397i | 0.561719i | 0.959749 | + | 0.280860i | \(0.0906195\pi\) | ||||
−0.959749 | + | 0.280860i | \(0.909380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5610i | 1.77536i | 0.460464 | + | 0.887678i | \(0.347683\pi\) | ||||
−0.460464 | + | 0.887678i | \(0.652317\pi\) | |||||||
\(242\) | 3.26714 | 0.210020 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.23904i | 0.0793215i | ||||||||
\(245\) | 3.52371 | + | 5.03161i | 0.225122 | + | 0.321457i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.453523i | 0.0288570i | ||||||||
\(248\) | 0.425694i | 0.0270316i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.7987 | + | 2.89605i | −0.682973 | + | 0.183162i | ||||
\(251\) | − | 20.4512i | − | 1.29087i | −0.763816 | − | 0.645434i | \(-0.776676\pi\) | ||
0.763816 | − | 0.645434i | \(-0.223324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.4679 | 1.28681 | ||||||||
\(254\) | − | 16.1128i | − | 1.01101i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.8951 | −1.42815 | −0.714077 | − | 0.700067i | \(-0.753153\pi\) | ||||
−0.714077 | + | 0.700067i | \(0.753153\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.68597 | + | 9.91373i | 0.477583 | + | 0.616009i | ||||
\(260\) | −3.69865 | − | 5.28140i | −0.229380 | − | 0.327538i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 9.64715i | − | 0.596003i | ||||||
\(263\) | − | 22.1600i | − | 1.36644i | −0.730212 | − | 0.683221i | \(-0.760579\pi\) | ||
0.730212 | − | 0.683221i | \(-0.239421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0926 | + | 12.6705i | −1.11142 | + | 0.778345i | ||||
\(266\) | −0.324354 | −0.0198874 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 6.45516i | − | 0.394312i | ||||||
\(269\) | −23.9657 | −1.46121 | −0.730607 | − | 0.682798i | \(-0.760763\pi\) | ||||
−0.730607 | + | 0.682798i | \(0.760763\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.82713 | 0.596956 | 0.298478 | − | 0.954417i | \(-0.403521\pi\) | ||||
0.298478 | + | 0.954417i | \(0.403521\pi\) | |||||||
\(272\) | −5.80724 | −0.352116 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 2.53592i | − | 0.153201i | ||||||
\(275\) | 6.45678 | − | 17.7479i | 0.389359 | − | 1.07024i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.807608 | −0.0485245 | −0.0242622 | − | 0.999706i | \(-0.507724\pi\) | ||||
−0.0242622 | + | 0.999706i | \(0.507724\pi\) | |||||||
\(278\) | 7.56000 | 0.453418 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.77719 | − | 2.64522i | 0.225730 | − | 0.158082i | ||||
\(281\) | − | 1.03833i | − | 0.0619414i | −0.999520 | − | 0.0309707i | \(-0.990140\pi\) | ||
0.999520 | − | 0.0309707i | \(-0.00985986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.26151 | 0.372208 | 0.186104 | − | 0.982530i | \(-0.440414\pi\) | ||||
0.186104 | + | 0.982530i | \(0.440414\pi\) | |||||||
\(284\) | 3.28329 | 0.194828 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8916 | 0.644031 | ||||||||
\(287\) | 1.90497i | 0.112447i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7241 | 0.983769 | ||||||||
\(290\) | −7.85862 | + | 5.50352i | −0.461474 | + | 0.323178i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.980489i | 0.0573788i | ||||||||
\(293\) | 4.84496i | 0.283045i | 0.989935 | + | 0.141523i | \(0.0451998\pi\) | ||||
−0.989935 | + | 0.141523i | \(0.954800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.5170 | + | 10.8668i | −0.903437 | + | 0.632692i | ||||
\(296\) | −4.80724 | + | 3.72698i | −0.279415 | + | 0.216627i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.72596 | −0.389624 | ||||||||
\(299\) | 15.6253 | 0.903632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.3265i | 1.28688i | ||||||||
\(302\) | −15.8051 | −0.909483 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.157282i | − | 0.00902072i | ||||||
\(305\) | −2.26941 | + | 1.58931i | −0.129946 | + | 0.0910034i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.87515i | − | 0.164093i | −0.996628 | − | 0.0820467i | \(-0.973854\pi\) | ||
0.996628 | − | 0.0820467i | \(-0.0261457\pi\) | |||||||
\(308\) | 7.78950i | 0.443848i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.779696 | + | 0.546033i | −0.0442837 | + | 0.0310126i | ||||
\(311\) | − | 6.07102i | − | 0.344256i | −0.985075 | − | 0.172128i | \(-0.944936\pi\) | ||
0.985075 | − | 0.172128i | \(-0.0550643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | − | 8.50755i | − | 0.480109i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.04725i | 0.452693i | ||||||||
\(317\) | 25.5691i | 1.43610i | 0.695989 | + | 0.718052i | \(0.254966\pi\) | ||||
−0.695989 | + | 0.718052i | \(0.745034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 16.2064i | − | 0.907386i | ||||||
\(320\) | 1.28269 | + | 1.83159i | 0.0717045 | + | 0.102389i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.1750i | 0.622757i | ||||||||
\(323\) | 0.913372i | 0.0508214i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.92912 | − | 13.5488i | 0.273418 | − | 0.751551i | ||||
\(326\) | −5.41321 | −0.299810 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.923733 | −0.0510046 | ||||||||
\(329\) | 1.39500 | 0.0769087 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8578i | 0.926589i | 0.886204 | + | 0.463295i | \(0.153333\pi\) | ||||
−0.886204 | + | 0.463295i | \(0.846667\pi\) | |||||||
\(332\) | − | 11.9496i | − | 0.655821i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.08165 | −0.113903 | ||||||||
\(335\) | 11.8232 | − | 8.27996i | 0.645969 | − | 0.452383i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.7105i | − | 0.801334i | −0.916224 | − | 0.400667i | \(-0.868779\pi\) | ||
0.916224 | − | 0.400667i | \(-0.131221\pi\) | |||||||
\(338\) | −4.68537 | −0.254851 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.44889 | − | 10.6365i | −0.403973 | − | 0.576843i | ||||
\(341\) | − | 1.60793i | − | 0.0870741i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1010i | − | 1.08535i | ||||||
\(344\) | −10.8263 | −0.583715 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3562i | 0.664273i | ||||||||
\(347\) | −3.26296 | −0.175165 | −0.0875824 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875824 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2097 | −0.921213 | −0.460607 | − | 0.887604i | \(-0.652368\pi\) | ||||
−0.460607 | + | 0.887604i | \(0.652368\pi\) | |||||||
\(350\) | 9.68991 | + | 3.52524i | 0.517948 | + | 0.188432i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.77719 | −0.201325 | ||||||||
\(353\) | 4.88641 | 0.260077 | 0.130039 | − | 0.991509i | \(-0.458490\pi\) | ||||
0.130039 | + | 0.991509i | \(0.458490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.21144 | + | 6.01363i | 0.223520 | + | 0.319170i | ||||
\(356\) | 7.65857i | 0.405903i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 13.4571i | − | 0.711229i | ||||||
\(359\) | −3.39107 | −0.178974 | −0.0894870 | − | 0.995988i | \(-0.528523\pi\) | ||||
−0.0894870 | + | 0.995988i | \(0.528523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9753 | 0.998698 | ||||||||
\(362\) | −3.66608 | −0.192685 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.94652i | 0.311682i | ||||||||
\(365\) | −1.79585 | + | 1.25766i | −0.0939991 | + | 0.0658291i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.25169i | 0.482934i | 0.970409 | + | 0.241467i | \(0.0776286\pi\) | ||||
−0.970409 | + | 0.241467i | \(0.922371\pi\) | |||||||
\(368\) | −5.41883 | −0.282476 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.9925 | − | 4.02432i | −0.675448 | − | 0.209214i | ||||
\(371\) | 20.3711 | 1.05761 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4101i | 0.590792i | 0.955375 | + | 0.295396i | \(0.0954515\pi\) | ||||
−0.955375 | + | 0.295396i | \(0.904548\pi\) | |||||||
\(374\) | 21.9350 | 1.13423 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.676445i | 0.0348850i | ||||||||
\(377\) | − | 12.3720i | − | 0.637191i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.3643 | 1.86791 | 0.933954 | − | 0.357394i | \(-0.116335\pi\) | ||||
0.933954 | + | 0.357394i | \(0.116335\pi\) | |||||||
\(380\) | 0.288075 | − | 0.201743i | 0.0147779 | − | 0.0103492i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.5540i | 0.949307i | ||||||||
\(383\) | 13.6526 | 0.697615 | 0.348807 | − | 0.937194i | \(-0.386587\pi\) | ||||
0.348807 | + | 0.937194i | \(0.386587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2671 | + | 9.99151i | −0.727121 | + | 0.509214i | ||||
\(386\) | 4.89778 | 0.249290 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.9571 | 0.708562 | ||||||||
\(389\) | − | 2.36833i | − | 0.120079i | −0.998196 | − | 0.0600396i | \(-0.980877\pi\) | ||
0.998196 | − | 0.0600396i | \(-0.0191227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.4685 | 1.59143 | ||||||||
\(392\) | 2.74713 | 0.138751 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 14.7803i | − | 0.744621i | ||||||
\(395\) | −14.7392 | + | 10.3221i | −0.741611 | + | 0.519362i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.4978i | − | 1.73140i | −0.500567 | − | 0.865698i | \(-0.666875\pi\) | ||
0.500567 | − | 0.865698i | \(-0.333125\pi\) | |||||||
\(398\) | 12.3298i | 0.618039i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.70942 | + | 4.69871i | −0.0854708 | + | 0.234936i | ||||
\(401\) | 29.0777i | 1.45207i | 0.687658 | + | 0.726035i | \(0.258639\pi\) | ||||
−0.687658 | + | 0.726035i | \(0.741361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.22749i | − | 0.0611458i | ||||||
\(404\) | 8.38279 | 0.417059 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.84831 | 0.439134 | ||||||||
\(407\) | 18.1579 | − | 14.0775i | 0.900051 | − | 0.697797i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.4980i | − | 0.815773i | −0.913033 | − | 0.407887i | \(-0.866266\pi\) | ||
0.913033 | − | 0.407887i | \(-0.133734\pi\) | |||||||
\(410\) | −1.18486 | − | 1.69190i | −0.0585162 | − | 0.0835568i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.4727 | 0.663753 | ||||||||
\(413\) | 17.4712 | 0.859702 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.8868 | − | 15.3277i | 1.07438 | − | 0.752405i | ||||
\(416\) | −2.88351 | −0.141376 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.594082i | 0.0290575i | ||||||||
\(419\) | −22.9409 | −1.12074 | −0.560368 | − | 0.828244i | \(-0.689340\pi\) | ||||
−0.560368 | + | 0.828244i | \(0.689340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.72030i | 0.0838422i | 0.999121 | + | 0.0419211i | \(0.0133478\pi\) | ||||
−0.999121 | + | 0.0419211i | \(0.986652\pi\) | |||||||
\(422\) | 14.1805 | 0.690294 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.87810i | 0.479723i | ||||||||
\(425\) | 9.92699 | − | 27.2866i | 0.481530 | − | 1.32359i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.55521 | 0.123655 | ||||||||
\(428\) | − | 1.89614i | − | 0.0916532i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.8868 | − | 19.8293i | −0.669680 | − | 0.956253i | ||||
\(431\) | 2.55447i | 0.123045i | 0.998106 | + | 0.0615223i | \(0.0195955\pi\) | ||||
−0.998106 | + | 0.0615223i | \(0.980404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0446i | 1.44385i | 0.691970 | + | 0.721926i | \(0.256743\pi\) | ||||
−0.691970 | + | 0.721926i | \(0.743257\pi\) | |||||||
\(434\) | 0.877887 | 0.0421399 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 17.2044i | − | 0.823943i | ||||||
\(437\) | 0.852283i | 0.0407702i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.4265i | 1.83400i | 0.398889 | + | 0.916999i | \(0.369396\pi\) | ||||
−0.398889 | + | 0.916999i | \(0.630604\pi\) | |||||||
\(440\) | −4.84496 | − | 6.91824i | −0.230974 | − | 0.329814i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.7452 | 0.796490 | ||||||||
\(443\) | 1.00809i | 0.0478957i | 0.999713 | + | 0.0239479i | \(0.00762357\pi\) | ||||
−0.999713 | + | 0.0239479i | \(0.992376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0273 | + | 9.82357i | −0.664959 | + | 0.465682i | ||||
\(446\) | 7.29071i | 0.345225i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.06225i | − | 0.0974321i | ||||||
\(449\) | 32.1157i | 1.51563i | 0.652468 | + | 0.757817i | \(0.273734\pi\) | ||||
−0.652468 | + | 0.757817i | \(0.726266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.48911 | 0.164296 | ||||||||
\(452\) | 1.17098 | 0.0550783 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.3807 | −1.23811 | ||||||||
\(455\) | −10.8916 | + | 7.62753i | −0.510604 | + | 0.357584i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.85884 | 0.367621 | 0.183810 | − | 0.982962i | \(-0.441157\pi\) | ||||
0.183810 | + | 0.982962i | \(0.441157\pi\) | |||||||
\(458\) | −19.5925 | −0.915496 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.95068 | − | 9.92506i | −0.324077 | − | 0.462758i | ||||
\(461\) | 16.7952i | 0.782233i | 0.920341 | + | 0.391116i | \(0.127911\pi\) | ||||
−0.920341 | + | 0.391116i | \(0.872089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.46094 | −0.114370 | −0.0571848 | − | 0.998364i | \(-0.518212\pi\) | ||||
−0.0571848 | + | 0.998364i | \(0.518212\pi\) | |||||||
\(464\) | 4.29061i | 0.199187i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 3.69983i | − | 0.171391i | ||||||
\(467\) | 7.57699 | 0.350621 | 0.175311 | − | 0.984513i | \(-0.443907\pi\) | ||||
0.175311 | + | 0.984513i | \(0.443907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.3121 | −0.614698 | ||||||||
\(470\) | −1.23897 | + | 0.867669i | −0.0571493 | + | 0.0400226i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.47192i | 0.389952i | ||||||||
\(473\) | 40.8929 | 1.88026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.739021 | + | 0.268860i | 0.0339086 | + | 0.0123361i | ||||
\(476\) | 11.9760i | 0.548918i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.68397i | 0.397195i | ||||||||
\(479\) | − | 12.6993i | − | 0.580246i | −0.956989 | − | 0.290123i | \(-0.906304\pi\) | ||
0.956989 | − | 0.290123i | \(-0.0936962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8617 | − | 10.7468i | 0.632041 | − | 0.490012i | ||||
\(482\) | 27.5610i | 1.25537i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.26714 | 0.148506 | ||||||||
\(485\) | 17.9026 | + | 25.5635i | 0.812913 | + | 1.16078i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8489 | −0.491611 | −0.245806 | − | 0.969319i | \(-0.579052\pi\) | ||||
−0.245806 | + | 0.969319i | \(0.579052\pi\) | |||||||
\(488\) | 1.23904i | 0.0560888i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.52371 | + | 5.03161i | 0.159185 | + | 0.227305i | ||||
\(491\) | 17.5266 | 0.790965 | 0.395482 | − | 0.918474i | \(-0.370577\pi\) | ||||
0.395482 | + | 0.918474i | \(0.370577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 24.9166i | − | 1.12219i | ||||||
\(494\) | 0.453523i | 0.0204050i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.425694i | 0.0191142i | ||||||||
\(497\) | − | 6.77096i | − | 0.303719i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.4860i | − | 1.45427i | −0.686494 | − | 0.727135i | \(-0.740851\pi\) | ||
0.686494 | − | 0.727135i | \(-0.259149\pi\) | |||||||
\(500\) | −10.7987 | + | 2.89605i | −0.482935 | + | 0.129515i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 20.4512i | − | 0.912782i | ||||||
\(503\) | −18.1375 | −0.808712 | −0.404356 | − | 0.914602i | \(-0.632504\pi\) | ||||
−0.404356 | + | 0.914602i | \(0.632504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7525 | + | 15.3538i | 0.478481 | + | 0.683235i | ||||
\(506\) | 20.4679 | 0.909911 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 16.1128i | − | 0.714891i | ||||||
\(509\) | 15.2070 | 0.674037 | 0.337018 | − | 0.941498i | \(-0.390582\pi\) | ||||
0.337018 | + | 0.941498i | \(0.390582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.02201 | 0.0894485 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.8951 | −1.00986 | ||||||||
\(515\) | 17.2813 | + | 24.6765i | 0.761506 | + | 1.08737i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.55506i | − | 0.112371i | ||||||
\(518\) | 7.68597 | + | 9.91373i | 0.337702 | + | 0.435584i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.69865 | − | 5.28140i | −0.162196 | − | 0.231605i | ||||
\(521\) | −21.5850 | −0.945657 | −0.472829 | − | 0.881154i | \(-0.656767\pi\) | ||||
−0.472829 | + | 0.881154i | \(0.656767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.64279 | 0.290469 | 0.145234 | − | 0.989397i | \(-0.453606\pi\) | ||||
0.145234 | + | 0.989397i | \(0.453606\pi\) | |||||||
\(524\) | − | 9.64715i | − | 0.421438i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 22.1600i | − | 0.966220i | ||||||
\(527\) | − | 2.47211i | − | 0.107687i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.36374 | 0.276684 | ||||||||
\(530\) | −18.0926 | + | 12.6705i | −0.785892 | + | 0.550373i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.324354 | −0.0140625 | ||||||||
\(533\) | 2.66359 | 0.115373 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.47294 | − | 2.43215i | 0.150148 | − | 0.105151i | ||||
\(536\) | − | 6.45516i | − | 0.278820i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.9657 | −1.03323 | ||||||||
\(539\) | −10.3764 | −0.446944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.3214i | − | 0.529737i | −0.964285 | − | 0.264868i | \(-0.914671\pi\) | ||
0.964285 | − | 0.264868i | \(-0.0853286\pi\) | |||||||
\(542\) | 9.82713 | 0.422112 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.80724 | −0.248983 | ||||||||
\(545\) | 31.5114 | − | 22.0680i | 1.34980 | − | 0.945287i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.2186 | −1.63411 | −0.817054 | − | 0.576561i | \(-0.804394\pi\) | ||||
−0.817054 | + | 0.576561i | \(0.804394\pi\) | |||||||
\(548\) | − | 2.53592i | − | 0.108329i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.45678 | − | 17.7479i | 0.275318 | − | 0.756774i | ||||
\(551\) | 0.674834 | 0.0287489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.5954 | 0.705710 | ||||||||
\(554\) | −0.807608 | −0.0343120 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.56000 | 0.320615 | ||||||||
\(557\) | −32.9212 | −1.39492 | −0.697458 | − | 0.716626i | \(-0.745685\pi\) | ||||
−0.697458 | + | 0.716626i | \(0.745685\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.2177 | 1.32037 | ||||||||
\(560\) | 3.77719 | − | 2.64522i | 0.159615 | − | 0.111781i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 1.03833i | − | 0.0437992i | ||||||
\(563\) | −5.39047 | −0.227181 | −0.113591 | − | 0.993528i | \(-0.536235\pi\) | ||||
−0.113591 | + | 0.993528i | \(0.536235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.50200 | + | 2.14475i | 0.0631898 | + | 0.0902304i | ||||
\(566\) | 6.26151 | 0.263191 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.28329 | 0.137764 | ||||||||
\(569\) | − | 2.18118i | − | 0.0914399i | −0.998954 | − | 0.0457200i | \(-0.985442\pi\) | ||
0.998954 | − | 0.0457200i | \(-0.0145582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.7356 | 1.74658 | 0.873291 | − | 0.487200i | \(-0.161982\pi\) | ||||
0.873291 | + | 0.487200i | \(0.161982\pi\) | |||||||
\(572\) | 10.8916 | 0.455399 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.90497i | 0.0795118i | ||||||||
\(575\) | 9.26304 | − | 25.4615i | 0.386295 | − | 1.06182i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.9657 | −1.16423 | −0.582114 | − | 0.813107i | \(-0.697774\pi\) | ||||
−0.582114 | + | 0.813107i | \(0.697774\pi\) | |||||||
\(578\) | 16.7241 | 0.695630 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.85862 | + | 5.50352i | −0.326312 | + | 0.228521i | ||||
\(581\) | −24.6431 | −1.02237 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 37.3114i | − | 1.54528i | ||||||
\(584\) | 0.980489i | 0.0405729i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.84496i | 0.200143i | ||||||||
\(587\) | 19.4024 | 0.800825 | 0.400412 | − | 0.916335i | \(-0.368867\pi\) | ||||
0.400412 | + | 0.916335i | \(0.368867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0669539 | 0.00275879 | ||||||||
\(590\) | −15.5170 | + | 10.8668i | −0.638827 | + | 0.447381i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.80724 | + | 3.72698i | −0.197576 | + | 0.153178i | ||||
\(593\) | 12.5182i | 0.514061i | 0.966403 | + | 0.257030i | \(0.0827440\pi\) | ||||
−0.966403 | + | 0.257030i | \(0.917256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.9350 | + | 15.3615i | −0.899249 | + | 0.629759i | ||||
\(596\) | −6.72596 | −0.275506 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.6253 | 0.638964 | ||||||||
\(599\) | −11.7177 | −0.478771 | −0.239386 | − | 0.970925i | \(-0.576946\pi\) | ||||
−0.239386 | + | 0.970925i | \(0.576946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.37239 | 0.0559808 | 0.0279904 | − | 0.999608i | \(-0.491089\pi\) | ||||
0.0279904 | + | 0.999608i | \(0.491089\pi\) | |||||||
\(602\) | 22.3265i | 0.909961i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.8051 | −0.643101 | ||||||||
\(605\) | 4.19072 | + | 5.98404i | 0.170377 | + | 0.243286i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6378 | 1.00002 | 0.500008 | − | 0.866021i | \(-0.333330\pi\) | ||||
0.500008 | + | 0.866021i | \(0.333330\pi\) | |||||||
\(608\) | − | 0.157282i | − | 0.00637861i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.26941 | + | 1.58931i | −0.0918858 | + | 0.0643491i | ||||
\(611\) | − | 1.95054i | − | 0.0789102i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.6733i | 1.11771i | 0.829264 | + | 0.558857i | \(0.188760\pi\) | ||||
−0.829264 | + | 0.558857i | \(0.811240\pi\) | |||||||
\(614\) | − | 2.87515i | − | 0.116032i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.78950i | 0.313848i | ||||||||
\(617\) | 17.9433i | 0.722371i | 0.932494 | + | 0.361185i | \(0.117628\pi\) | ||||
−0.932494 | + | 0.361185i | \(0.882372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.1044 | −1.00903 | −0.504515 | − | 0.863403i | \(-0.668329\pi\) | ||||
−0.504515 | + | 0.863403i | \(0.668329\pi\) | |||||||
\(620\) | −0.779696 | + | 0.546033i | −0.0313133 | + | 0.0219292i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.07102i | − | 0.243426i | ||||||
\(623\) | 15.7939 | 0.632768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.1558 | − | 16.0641i | −0.766232 | − | 0.642564i | ||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.50755i | − | 0.339488i | ||||||
\(629\) | 27.9168 | − | 21.6435i | 1.11312 | − | 0.862983i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.8987i | 1.90682i | 0.301679 | + | 0.953409i | \(0.402453\pi\) | ||||
−0.301679 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(632\) | 8.04725i | 0.320102i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.5691i | 1.01548i | ||||||||
\(635\) | 29.5120 | − | 20.6677i | 1.17115 | − | 0.820175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.92138 | −0.313856 | ||||||||
\(638\) | − | 16.2064i | − | 0.641619i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.28269 | + | 1.83159i | 0.0507027 | + | 0.0723998i | ||||
\(641\) | 19.4541 | 0.768390 | 0.384195 | − | 0.923252i | \(-0.374479\pi\) | ||||
0.384195 | + | 0.923252i | \(0.374479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0553 | 1.02752 | 0.513760 | − | 0.857934i | \(-0.328252\pi\) | ||||
0.513760 | + | 0.857934i | \(0.328252\pi\) | |||||||
\(644\) | 11.1750i | 0.440356i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.913372i | 0.0359362i | ||||||||
\(647\) | −14.7320 | −0.579176 | −0.289588 | − | 0.957151i | \(-0.593518\pi\) | ||||
−0.289588 | + | 0.957151i | \(0.593518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 32.0000i | − | 1.25611i | ||||||
\(650\) | 4.92912 | − | 13.5488i | 0.193336 | − | 0.531427i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.41321 | −0.211998 | ||||||||
\(653\) | 30.5877 | 1.19699 | 0.598494 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598494 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6696 | − | 12.3743i | 0.690408 | − | 0.483504i | ||||
\(656\) | −0.923733 | −0.0360657 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.39500 | 0.0543827 | ||||||||
\(659\) | −29.3533 | −1.14344 | −0.571720 | − | 0.820448i | \(-0.693724\pi\) | ||||
−0.571720 | + | 0.820448i | \(0.693724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16.7963i | − | 0.653299i | −0.945145 | − | 0.326650i | \(-0.894080\pi\) | ||
0.945145 | − | 0.326650i | \(-0.105920\pi\) | |||||||
\(662\) | 16.8578i | 0.655198i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.9496i | − | 0.463735i | ||||||
\(665\) | −0.416045 | − | 0.594082i | −0.0161335 | − | 0.0230375i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 23.2501i | − | 0.900247i | ||||||
\(668\) | −2.08165 | −0.0805415 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.8232 | − | 8.27996i | 0.456769 | − | 0.319883i | ||||
\(671\) | − | 4.68009i | − | 0.180673i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.2015i | − | 0.817259i | −0.912700 | − | 0.408629i | \(-0.866007\pi\) | ||
0.912700 | − | 0.408629i | \(-0.133993\pi\) | |||||||
\(674\) | − | 14.7105i | − | 0.566628i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.68537 | −0.180207 | ||||||||
\(677\) | − | 45.9734i | − | 1.76690i | −0.468526 | − | 0.883450i | \(-0.655215\pi\) | ||
0.468526 | − | 0.883450i | \(-0.344785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 28.7829i | − | 1.10459i | ||||||
\(680\) | −7.44889 | − | 10.6365i | −0.285652 | − | 0.407890i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.60793i | − | 0.0615707i | ||||||
\(683\) | −3.06580 | −0.117309 | −0.0586547 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586547 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.64476 | − | 3.25280i | 0.177467 | − | 0.124283i | ||||
\(686\) | − | 20.1010i | − | 0.767460i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.8263 | −0.412749 | ||||||||
\(689\) | − | 28.4836i | − | 1.08514i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.43426 | 0.320854 | 0.160427 | − | 0.987048i | \(-0.448713\pi\) | ||||
0.160427 | + | 0.987048i | \(0.448713\pi\) | |||||||
\(692\) | 12.3562i | 0.469712i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.26296 | −0.123860 | ||||||||
\(695\) | 9.69713 | + | 13.8468i | 0.367833 | + | 0.525238i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.36434 | 0.203189 | ||||||||
\(698\) | −17.2097 | −0.651396 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.68991 | + | 3.52524i | 0.366244 | + | 0.133242i | ||||
\(701\) | − | 20.3110i | − | 0.767136i | −0.923513 | − | 0.383568i | \(-0.874695\pi\) | ||
0.923513 | − | 0.383568i | \(-0.125305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.586186 | + | 0.756091i | 0.0221084 | + | 0.0285165i | ||||
\(704\) | −3.77719 | −0.142358 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.88641 | 0.183902 | ||||||||
\(707\) | − | 17.2874i | − | 0.650159i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23.8789i | − | 0.896790i | −0.893836 | − | 0.448395i | \(-0.851996\pi\) | ||
0.893836 | − | 0.448395i | \(-0.148004\pi\) | |||||||
\(710\) | 4.21144 | + | 6.01363i | 0.158053 | + | 0.225688i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.65857i | 0.287017i | ||||||||
\(713\) | − | 2.30677i | − | 0.0863890i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.9705 | + | 19.9488i | 0.522466 | + | 0.746044i | ||||
\(716\) | − | 13.4571i | − | 0.502915i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.39107 | −0.126554 | ||||||||
\(719\) | −14.6971 | −0.548110 | −0.274055 | − | 0.961714i | \(-0.588365\pi\) | ||||
−0.274055 | + | 0.961714i | \(0.588365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 27.7841i | − | 1.03473i | ||||||
\(722\) | 18.9753 | 0.706186 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.66608 | −0.136249 | ||||||||
\(725\) | −20.1603 | − | 7.33444i | −0.748736 | − | 0.272394i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.61569 | 0.208274 | 0.104137 | − | 0.994563i | \(-0.466792\pi\) | ||||
0.104137 | + | 0.994563i | \(0.466792\pi\) | |||||||
\(728\) | 5.94652i | 0.220393i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.79585 | + | 1.25766i | −0.0664674 | + | 0.0465482i | ||||
\(731\) | 62.8709 | 2.32536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.7565i | 0.618917i | 0.950913 | + | 0.309459i | \(0.100148\pi\) | ||||
−0.950913 | + | 0.309459i | \(0.899852\pi\) | |||||||
\(734\) | 9.25169i | 0.341486i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.41883 | −0.199741 | ||||||||
\(737\) | 24.3823i | 0.898135i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2106 | −0.485960 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(740\) | −12.9925 | − | 4.02432i | −0.477614 | − | 0.147937i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.3711 | 0.747847 | ||||||||
\(743\) | 23.0799i | 0.846721i | 0.905961 | + | 0.423360i | \(0.139150\pi\) | ||||
−0.905961 | + | 0.423360i | \(0.860850\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.62731 | − | 12.3192i | −0.316080 | − | 0.451340i | ||||
\(746\) | 11.4101i | 0.417753i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.9350 | 0.802024 | ||||||||
\(749\) | −3.91030 | −0.142879 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0437 | 0.913856 | 0.456928 | − | 0.889504i | \(-0.348950\pi\) | ||||
0.456928 | + | 0.889504i | \(0.348950\pi\) | |||||||
\(752\) | 0.676445i | 0.0246674i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 12.3720i | − | 0.450562i | ||||||
\(755\) | −20.2731 | − | 28.9484i | −0.737812 | − | 1.05354i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.5882 | −1.22078 | −0.610392 | − | 0.792099i | \(-0.708988\pi\) | ||||
−0.610392 | + | 0.792099i | \(0.708988\pi\) | |||||||
\(758\) | 36.3643 | 1.32081 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.288075 | − | 0.201743i | 0.0104496 | − | 0.00731800i | ||||
\(761\) | 14.8529 | 0.538416 | 0.269208 | − | 0.963082i | \(-0.413238\pi\) | ||||
0.269208 | + | 0.963082i | \(0.413238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.4798 | −1.28446 | ||||||||
\(764\) | 18.5540i | 0.671261i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6526 | 0.493288 | ||||||||
\(767\) | − | 24.4289i | − | 0.882075i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.80892i | 0.317658i | 0.987306 | + | 0.158829i | \(0.0507718\pi\) | ||||
−0.987306 | + | 0.158829i | \(0.949228\pi\) | |||||||
\(770\) | −14.2671 | + | 9.99151i | −0.514152 | + | 0.360069i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.89778 | 0.176275 | ||||||||
\(773\) | 38.8401i | 1.39698i | 0.715619 | + | 0.698491i | \(0.246145\pi\) | ||||
−0.715619 | + | 0.698491i | \(0.753855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00021 | − | 0.727688i | −0.0718498 | − | 0.0261393i | ||||
\(776\) | 13.9571 | 0.501029 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.36833i | − | 0.0849089i | ||||||
\(779\) | 0.145286i | 0.00520542i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4016 | −0.443764 | ||||||||
\(782\) | 31.4685 | 1.12531 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.74713 | 0.0981118 | ||||||||
\(785\) | 15.5823 | − | 10.9125i | 0.556156 | − | 0.389485i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2645i | 1.22140i | 0.791864 | + | 0.610698i | \(0.209111\pi\) | ||||
−0.791864 | + | 0.610698i | \(0.790889\pi\) | |||||||
\(788\) | − | 14.7803i | − | 0.526527i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.7392 | + | 10.3221i | −0.524398 | + | 0.367245i | ||||
\(791\) | − | 2.41485i | − | 0.0858623i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.57279i | − | 0.126873i | ||||||
\(794\) | − | 34.4978i | − | 1.22428i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.3298i | 0.437019i | ||||||||
\(797\) | −34.0208 | −1.20508 | −0.602539 | − | 0.798089i | \(-0.705844\pi\) | ||||
−0.602539 | + | 0.798089i | \(0.705844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.92828i | − | 0.138973i | ||||||
\(800\) | −1.70942 | + | 4.69871i | −0.0604370 | + | 0.166125i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.0777i | 1.02677i | ||||||||
\(803\) | − | 3.70349i | − | 0.130693i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.4679 | + | 14.3340i | −0.721400 | + | 0.505208i | ||||
\(806\) | − | 1.22749i | − | 0.0432366i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.38279 | 0.294905 | ||||||||
\(809\) | − | 23.0866i | − | 0.811680i | −0.913944 | − | 0.405840i | \(-0.866979\pi\) | ||
0.913944 | − | 0.405840i | \(-0.133021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0477 | −0.493280 | −0.246640 | − | 0.969107i | \(-0.579327\pi\) | ||||
−0.246640 | + | 0.969107i | \(0.579327\pi\) | |||||||
\(812\) | 8.84831 | 0.310515 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.1579 | − | 14.0775i | 0.636432 | − | 0.493417i | ||||
\(815\) | −6.94347 | − | 9.91476i | −0.243219 | − | 0.347299i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.70278i | 0.0595726i | ||||||||
\(818\) | − | 16.4980i | − | 0.576839i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.18486 | − | 1.69190i | −0.0413772 | − | 0.0590836i | ||||
\(821\) | 5.87069 | 0.204888 | 0.102444 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102444 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.6536i | 1.27766i | 0.769346 | + | 0.638832i | \(0.220582\pi\) | ||||
−0.769346 | + | 0.638832i | \(0.779418\pi\) | |||||||
\(824\) | 13.4727 | 0.469345 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.4712 | 0.607901 | ||||||||
\(827\) | 31.2291 | 1.08594 | 0.542971 | − | 0.839751i | \(-0.317299\pi\) | ||||
0.542971 | + | 0.839751i | \(0.317299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.76907i | − | 0.200368i | −0.994969 | − | 0.100184i | \(-0.968057\pi\) | ||
0.994969 | − | 0.100184i | \(-0.0319431\pi\) | |||||||
\(830\) | 21.8868 | − | 15.3277i | 0.759701 | − | 0.532031i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.88351 | −0.0999677 | ||||||||
\(833\) | −15.9533 | −0.552747 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.67011 | − | 3.81272i | −0.0924030 | − | 0.131945i | ||||
\(836\) | 0.594082i | 0.0205468i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.9409 | −0.792480 | ||||||||
\(839\) | 19.1631 | 0.661582 | 0.330791 | − | 0.943704i | \(-0.392684\pi\) | ||||
0.330791 | + | 0.943704i | \(0.392684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5907 | 0.365195 | ||||||||
\(842\) | 1.72030i | 0.0592854i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.1805 | 0.488112 | ||||||||
\(845\) | −6.00987 | − | 8.58166i | −0.206746 | − | 0.295218i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.73765i | − | 0.231508i | ||||||
\(848\) | 9.87810i | 0.339215i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.92699 | − | 27.2866i | 0.340493 | − | 0.935921i | ||||
\(851\) | 26.0496 | − | 20.1959i | 0.892970 | − | 0.692307i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.1823 | 1.03342 | 0.516711 | − | 0.856160i | \(-0.327156\pi\) | ||||
0.516711 | + | 0.856160i | \(0.327156\pi\) | |||||||
\(854\) | 2.55521 | 0.0874376 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 1.89614i | − | 0.0648086i | ||||||
\(857\) | 13.4228 | 0.458513 | 0.229257 | − | 0.973366i | \(-0.426370\pi\) | ||||
0.229257 | + | 0.973366i | \(0.426370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.1243i | − | 0.857230i | −0.903487 | − | 0.428615i | \(-0.859002\pi\) | ||
0.903487 | − | 0.428615i | \(-0.140998\pi\) | |||||||
\(860\) | −13.8868 | − | 19.8293i | −0.473535 | − | 0.676173i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.55447i | 0.0870057i | ||||||||
\(863\) | 6.80983i | 0.231809i | 0.993260 | + | 0.115905i | \(0.0369767\pi\) | ||||
−0.993260 | + | 0.115905i | \(0.963023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.6314 | + | 15.8491i | −0.769491 | + | 0.538887i | ||||
\(866\) | 30.0446i | 1.02096i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.877887 | 0.0297974 | ||||||||
\(869\) | − | 30.3960i | − | 1.03111i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.6135i | 0.630695i | ||||||||
\(872\) | − | 17.2044i | − | 0.582616i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.852283i | 0.0288289i | ||||||||
\(875\) | 5.97237 | + | 22.2697i | 0.201903 | + | 0.752853i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.4096i | 0.993090i | 0.868011 | + | 0.496545i | \(0.165398\pi\) | ||||
−0.868011 | + | 0.496545i | \(0.834602\pi\) | |||||||
\(878\) | 38.4265i | 1.29683i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.84496 | − | 6.91824i | −0.163323 | − | 0.233214i | ||||
\(881\) | −50.5602 | −1.70342 | −0.851708 | − | 0.524016i | \(-0.824433\pi\) | ||||
−0.851708 | + | 0.524016i | \(0.824433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.4904 | 1.36261 | 0.681305 | − | 0.732000i | \(-0.261413\pi\) | ||||
0.681305 | + | 0.732000i | \(0.261413\pi\) | |||||||
\(884\) | 16.7452 | 0.563203 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.00809i | 0.0338674i | ||||||||
\(887\) | 8.64379i | 0.290230i | 0.989415 | + | 0.145115i | \(0.0463552\pi\) | ||||
−0.989415 | + | 0.145115i | \(0.953645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.2287 | −1.11445 | ||||||||
\(890\) | −14.0273 | + | 9.82357i | −0.470197 | + | 0.329287i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.29071i | 0.244111i | ||||||||
\(893\) | 0.106392 | 0.00356028 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.6478 | − | 17.2613i | 0.823885 | − | 0.576980i | ||||
\(896\) | − | 2.06225i | − | 0.0688949i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.1157i | 1.07171i | ||||||||
\(899\) | −1.82649 | −0.0609168 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 57.3645i | − | 1.91109i | ||||||
\(902\) | 3.48911 | 0.116175 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.17098 | 0.0389462 | ||||||||
\(905\) | −4.70244 | − | 6.71474i | −0.156314 | − | 0.223206i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.0245 | −1.09656 | −0.548281 | − | 0.836294i | \(-0.684717\pi\) | ||||
−0.548281 | + | 0.836294i | \(0.684717\pi\) | |||||||
\(908\) | −26.3807 | −0.875473 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.8916 | + | 7.62753i | −0.361052 | + | 0.252850i | ||||
\(911\) | 0.940972i | 0.0311758i | 0.999879 | + | 0.0155879i | \(0.00496198\pi\) | ||||
−0.999879 | + | 0.0155879i | \(0.995038\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.1360i | 1.49378i | ||||||||
\(914\) | 7.85884 | 0.259947 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.5925 | −0.647354 | ||||||||
\(917\) | −19.8948 | −0.656985 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5548i | 1.79960i | 0.436306 | + | 0.899798i | \(0.356287\pi\) | ||||
−0.436306 | + | 0.899798i | \(0.643713\pi\) | |||||||
\(920\) | −6.95068 | − | 9.92506i | −0.229157 | − | 0.327219i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.7952i | 0.553122i | ||||||||
\(923\) | −9.46740 | −0.311623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.29445 | − | 28.9588i | −0.305600 | − | 0.952160i | ||||
\(926\) | −2.46094 | −0.0808716 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.29061i | 0.140846i | ||||||||
\(929\) | 22.7416 | 0.746128 | 0.373064 | − | 0.927806i | \(-0.378307\pi\) | ||||
0.373064 | + | 0.927806i | \(0.378307\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.432073i | − | 0.0141606i | ||||||
\(932\) | − | 3.69983i | − | 0.121192i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.57699 | 0.247927 | ||||||||
\(935\) | 28.1358 | + | 40.1759i | 0.920140 | + | 1.31389i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.2122i | 1.41168i | 0.708370 | + | 0.705841i | \(0.249431\pi\) | ||||
−0.708370 | + | 0.705841i | \(0.750569\pi\) | |||||||
\(938\) | −13.3121 | −0.434657 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.23897 | + | 0.867669i | −0.0404107 | + | 0.0283002i | ||||
\(941\) | −32.0847 | −1.04593 | −0.522966 | − | 0.852354i | \(-0.675175\pi\) | ||||
−0.522966 | + | 0.852354i | \(0.675175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.00555 | 0.163003 | ||||||||
\(944\) | 8.47192i | 0.275737i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.8929 | 1.32954 | ||||||||
\(947\) | 8.26212 | 0.268483 | 0.134241 | − | 0.990949i | \(-0.457140\pi\) | ||||
0.134241 | + | 0.990949i | \(0.457140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.82725i | − | 0.0917764i | ||||||
\(950\) | 0.739021 | + | 0.268860i | 0.0239770 | + | 0.00872296i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.9760i | 0.388144i | ||||||||
\(953\) | 51.1883i | 1.65815i | 0.559136 | + | 0.829076i | \(0.311133\pi\) | ||||
−0.559136 | + | 0.829076i | \(0.688867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.9833 | + | 23.7991i | −1.09967 | + | 0.770120i | ||||
\(956\) | 8.68397i | 0.280860i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 12.6993i | − | 0.410296i | ||||||
\(959\) | −5.22970 | −0.168876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8188 | 0.994154 | ||||||||
\(962\) | 13.8617 | − | 10.7468i | 0.446920 | − | 0.346491i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.5610i | 0.887678i | ||||||||
\(965\) | 6.28233 | + | 8.97070i | 0.202235 | + | 0.288777i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.84215 | 0.0592395 | 0.0296197 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296197 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(968\) | 3.26714 | 0.105010 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.9026 | + | 25.5635i | 0.574817 | + | 0.820796i | ||||
\(971\) | −52.6384 | −1.68925 | −0.844624 | − | 0.535361i | \(-0.820176\pi\) | ||||
−0.844624 | + | 0.535361i | \(0.820176\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.5906i | − | 0.499811i | ||||||
\(974\) | −10.8489 | −0.347621 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.23904i | 0.0396608i | ||||||||
\(977\) | 47.7629 | 1.52807 | 0.764035 | − | 0.645174i | \(-0.223215\pi\) | ||||
0.764035 | + | 0.645174i | \(0.223215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.9278i | − | 0.924538i | ||||||
\(980\) | 3.52371 | + | 5.03161i | 0.112561 | + | 0.160729i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.5266 | 0.559297 | ||||||||
\(983\) | 34.6640i | 1.10561i | 0.833310 | + | 0.552805i | \(0.186443\pi\) | ||||
−0.833310 | + | 0.552805i | \(0.813557\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0714 | − | 18.9586i | 0.862567 | − | 0.604070i | ||||
\(986\) | − | 24.9166i | − | 0.793507i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.453523i | 0.0144285i | ||||||||
\(989\) | 58.6659 | 1.86547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.9061i | 1.45826i | 0.684378 | + | 0.729128i | \(0.260074\pi\) | ||||
−0.684378 | + | 0.729128i | \(0.739926\pi\) | |||||||
\(992\) | 0.425694i | 0.0135158i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 6.77096i | − | 0.214762i | ||||||
\(995\) | −22.5831 | + | 15.8153i | −0.715934 | + | 0.501380i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.7232 | −0.782993 | −0.391496 | − | 0.920180i | \(-0.628042\pi\) | ||||
−0.391496 | + | 0.920180i | \(0.628042\pi\) | |||||||
\(998\) | − | 32.4860i | − | 1.02832i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 3330.2.e.d.739.6 | 10 | ||
3.2 | odd | 2 | 370.2.c.a.369.1 | ✓ | 10 | ||
5.4 | even | 2 | 3330.2.e.c.739.6 | 10 | |||
15.2 | even | 4 | 1850.2.d.i.1701.1 | 20 | |||
15.8 | even | 4 | 1850.2.d.i.1701.20 | 20 | |||
15.14 | odd | 2 | 370.2.c.b.369.10 | yes | 10 | ||
37.36 | even | 2 | 3330.2.e.c.739.5 | 10 | |||
111.110 | odd | 2 | 370.2.c.b.369.1 | yes | 10 | ||
185.184 | even | 2 | inner | 3330.2.e.d.739.5 | 10 | ||
555.332 | even | 4 | 1850.2.d.i.1701.11 | 20 | |||
555.443 | even | 4 | 1850.2.d.i.1701.10 | 20 | |||
555.554 | odd | 2 | 370.2.c.a.369.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.c.a.369.1 | ✓ | 10 | 3.2 | odd | 2 | ||
370.2.c.a.369.10 | yes | 10 | 555.554 | odd | 2 | ||
370.2.c.b.369.1 | yes | 10 | 111.110 | odd | 2 | ||
370.2.c.b.369.10 | yes | 10 | 15.14 | odd | 2 | ||
1850.2.d.i.1701.1 | 20 | 15.2 | even | 4 | |||
1850.2.d.i.1701.10 | 20 | 555.443 | even | 4 | |||
1850.2.d.i.1701.11 | 20 | 555.332 | even | 4 | |||
1850.2.d.i.1701.20 | 20 | 15.8 | even | 4 | |||
3330.2.e.c.739.5 | 10 | 37.36 | even | 2 | |||
3330.2.e.c.739.6 | 10 | 5.4 | even | 2 | |||
3330.2.e.d.739.5 | 10 | 185.184 | even | 2 | inner | ||
3330.2.e.d.739.6 | 10 | 1.1 | even | 1 | trivial |