Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(101,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.l (of order \(4\), degree \(2\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 301.6 | ||
Root | \(-1.41313 + 0.0554252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.301 |
Dual form | 400.2.l.f.101.6 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41313 | − | 0.0554252i | 0.999232 | − | 0.0391915i | ||||
\(3\) | −0.488516 | − | 0.488516i | −0.282045 | − | 0.282045i | 0.551879 | − | 0.833924i | \(-0.313911\pi\) |
−0.833924 | + | 0.551879i | \(0.813911\pi\) | |||||||
\(4\) | 1.99386 | − | 0.156646i | 0.996928 | − | 0.0783229i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.717411 | − | 0.663259i | −0.292882 | − | 0.270774i | ||||
\(7\) | − | 4.71540i | − | 1.78226i | −0.453753 | − | 0.891128i | \(-0.649915\pi\) | ||
0.453753 | − | 0.891128i | \(-0.350085\pi\) | |||||||
\(8\) | 2.80889 | − | 0.331870i | 0.993093 | − | 0.117334i | ||||
\(9\) | − | 2.52270i | − | 0.840901i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.91360 | + | 3.91360i | −1.17999 | + | 1.17999i | −0.200249 | + | 0.979745i | \(0.564175\pi\) |
−0.979745 | + | 0.200249i | \(0.935825\pi\) | |||||||
\(12\) | −1.05055 | − | 0.897506i | −0.303269 | − | 0.259088i | ||||
\(13\) | −0.0878822 | − | 0.0878822i | −0.0243741 | − | 0.0243741i | 0.694815 | − | 0.719189i | \(-0.255486\pi\) |
−0.719189 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(14\) | −0.261352 | − | 6.66346i | −0.0698493 | − | 1.78089i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95092 | − | 0.624658i | 0.987731 | − | 0.156165i | ||||
\(17\) | 4.67442 | 1.13371 | 0.566857 | − | 0.823816i | \(-0.308159\pi\) | ||||
0.566857 | + | 0.823816i | \(0.308159\pi\) | |||||||
\(18\) | −0.139821 | − | 3.56490i | −0.0329562 | − | 0.840255i | ||||
\(19\) | 1.81249 | + | 1.81249i | 0.415813 | + | 0.415813i | 0.883758 | − | 0.467945i | \(-0.155005\pi\) |
−0.467945 | + | 0.883758i | \(0.655005\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30355 | + | 2.30355i | −0.502676 | + | 0.502676i | ||||
\(22\) | −5.31350 | + | 5.74732i | −1.13284 | + | 1.22533i | ||||
\(23\) | 1.63007i | 0.339893i | 0.985453 | + | 0.169946i | \(0.0543594\pi\) | ||||
−0.985453 | + | 0.169946i | \(0.945641\pi\) | |||||||
\(24\) | −1.53431 | − | 1.21006i | −0.313190 | − | 0.247003i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.129060 | − | 0.119318i | −0.0253107 | − | 0.0234002i | ||||
\(27\) | −2.69793 | + | 2.69793i | −0.519217 | + | 0.519217i | ||||
\(28\) | −0.738648 | − | 9.40184i | −0.139591 | − | 1.77678i | ||||
\(29\) | 3.26362 | + | 3.26362i | 0.606039 | + | 0.606039i | 0.941909 | − | 0.335869i | \(-0.109030\pi\) |
−0.335869 | + | 0.941909i | \(0.609030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.12875 | −0.382334 | −0.191167 | − | 0.981557i | \(-0.561227\pi\) | ||||
−0.191167 | + | 0.981557i | \(0.561227\pi\) | |||||||
\(32\) | 5.54854 | − | 1.10170i | 0.980852 | − | 0.194755i | ||||
\(33\) | 3.82371 | 0.665622 | ||||||||
\(34\) | 6.60555 | − | 0.259081i | 1.13284 | − | 0.0444320i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.395171 | − | 5.02991i | −0.0658618 | − | 0.838318i | ||||
\(37\) | 3.97797 | − | 3.97797i | 0.653974 | − | 0.653974i | −0.299973 | − | 0.953948i | \(-0.596978\pi\) |
0.953948 | + | 0.299973i | \(0.0969778\pi\) | |||||||
\(38\) | 2.66173 | + | 2.46082i | 0.431790 | + | 0.399197i | ||||
\(39\) | 0.0858637i | 0.0137492i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.25504i | 1.28922i | 0.764511 | + | 0.644611i | \(0.222980\pi\) | ||||
−0.764511 | + | 0.644611i | \(0.777020\pi\) | |||||||
\(42\) | −3.12753 | + | 3.38288i | −0.482589 | + | 0.521990i | ||||
\(43\) | 2.27336 | − | 2.27336i | 0.346685 | − | 0.346685i | −0.512188 | − | 0.858873i | \(-0.671165\pi\) |
0.858873 | + | 0.512188i | \(0.171165\pi\) | |||||||
\(44\) | −7.19010 | + | 8.41620i | −1.08395 | + | 1.26879i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0903468 | + | 2.30349i | 0.0133209 | + | 0.339631i | ||||
\(47\) | −4.06129 | −0.592400 | −0.296200 | − | 0.955126i | \(-0.595719\pi\) | ||||
−0.296200 | + | 0.955126i | \(0.595719\pi\) | |||||||
\(48\) | −2.23524 | − | 1.62493i | −0.322630 | − | 0.234539i | ||||
\(49\) | −15.2350 | −2.17643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.28353 | − | 2.28353i | −0.319758 | − | 0.319758i | ||||
\(52\) | −0.188991 | − | 0.161458i | −0.0262083 | − | 0.0223902i | ||||
\(53\) | −5.03938 | + | 5.03938i | −0.692211 | + | 0.692211i | −0.962718 | − | 0.270507i | \(-0.912809\pi\) |
0.270507 | + | 0.962718i | \(0.412809\pi\) | |||||||
\(54\) | −3.66298 | + | 3.96205i | −0.498469 | + | 0.539167i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.56490 | − | 13.2450i | −0.209119 | − | 1.76994i | ||||
\(57\) | − | 1.77086i | − | 0.234556i | ||||||
\(58\) | 4.79280 | + | 4.43103i | 0.629325 | + | 0.581822i | ||||
\(59\) | −5.16453 | + | 5.16453i | −0.672365 | + | 0.672365i | −0.958261 | − | 0.285896i | \(-0.907709\pi\) |
0.285896 | + | 0.958261i | \(0.407709\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12726 | + | 7.12726i | 0.912552 | + | 0.912552i | 0.996472 | − | 0.0839206i | \(-0.0267442\pi\) |
−0.0839206 | + | 0.996472i | \(0.526744\pi\) | |||||||
\(62\) | −3.00819 | + | 0.117986i | −0.382041 | + | 0.0149843i | ||||
\(63\) | −11.8956 | −1.49870 | ||||||||
\(64\) | 7.77972 | − | 1.86437i | 0.972466 | − | 0.233047i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.40339 | − | 0.211930i | 0.665111 | − | 0.0260868i | ||||
\(67\) | −7.49920 | − | 7.49920i | −0.916173 | − | 0.916173i | 0.0805758 | − | 0.996748i | \(-0.474324\pi\) |
−0.996748 | + | 0.0805758i | \(0.974324\pi\) | |||||||
\(68\) | 9.32012 | − | 0.732228i | 1.13023 | − | 0.0887957i | ||||
\(69\) | 0.796314 | − | 0.796314i | 0.0958649 | − | 0.0958649i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.54072i | − | 0.538884i | −0.963017 | − | 0.269442i | \(-0.913161\pi\) | ||
0.963017 | − | 0.269442i | \(-0.0868393\pi\) | |||||||
\(72\) | −0.837210 | − | 7.08600i | −0.0986662 | − | 0.835093i | ||||
\(73\) | 8.30557i | 0.972093i | 0.873933 | + | 0.486047i | \(0.161561\pi\) | ||||
−0.873933 | + | 0.486047i | \(0.838439\pi\) | |||||||
\(74\) | 5.40090 | − | 5.84186i | 0.627842 | − | 0.679102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.89776 | + | 3.32992i | 0.447104 | + | 0.381968i | ||||
\(77\) | 18.4542 | + | 18.4542i | 2.10305 | + | 2.10305i | ||||
\(78\) | 0.00475901 | + | 0.121336i | 0.000538852 | + | 0.0137386i | ||||
\(79\) | 11.5317 | 1.29742 | 0.648709 | − | 0.761037i | \(-0.275309\pi\) | ||||
0.648709 | + | 0.761037i | \(0.275309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.93215 | −0.548017 | ||||||||
\(82\) | 0.457537 | + | 11.6654i | 0.0505266 | + | 1.28823i | ||||
\(83\) | −1.16919 | − | 1.16919i | −0.128335 | − | 0.128335i | 0.640022 | − | 0.768357i | \(-0.278925\pi\) |
−0.768357 | + | 0.640022i | \(0.778925\pi\) | |||||||
\(84\) | −4.23211 | + | 4.95379i | −0.461761 | + | 0.540503i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.08655 | − | 3.33855i | 0.332831 | − | 0.360006i | ||||
\(87\) | − | 3.18866i | − | 0.341861i | ||||||
\(88\) | −9.69406 | + | 12.2917i | −1.03339 | + | 1.31030i | ||||
\(89\) | − | 3.24572i | − | 0.344046i | −0.985093 | − | 0.172023i | \(-0.944970\pi\) | ||
0.985093 | − | 0.172023i | \(-0.0550304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.414400 | + | 0.414400i | −0.0434409 | + | 0.0434409i | ||||
\(92\) | 0.255343 | + | 3.25012i | 0.0266214 | + | 0.338848i | ||||
\(93\) | 1.03993 | + | 1.03993i | 0.107835 | + | 0.107835i | ||||
\(94\) | −5.73912 | + | 0.225098i | −0.591945 | + | 0.0232171i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.24875 | − | 2.17235i | −0.331574 | − | 0.221714i | ||||
\(97\) | −13.9581 | −1.41723 | −0.708613 | − | 0.705598i | \(-0.750679\pi\) | ||||
−0.708613 | + | 0.705598i | \(0.750679\pi\) | |||||||
\(98\) | −21.5290 | + | 0.844405i | −2.17476 | + | 0.0852978i | ||||
\(99\) | 9.87285 | + | 9.87285i | 0.992258 | + | 0.992258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4088 | − | 13.4088i | 1.33422 | − | 1.33422i | 0.432672 | − | 0.901552i | \(-0.357571\pi\) |
0.901552 | − | 0.432672i | \(-0.142429\pi\) | |||||||
\(102\) | −3.35348 | − | 3.10035i | −0.332044 | − | 0.306981i | ||||
\(103\) | 13.7638i | 1.35618i | 0.734977 | + | 0.678092i | \(0.237193\pi\) | ||||
−0.734977 | + | 0.678092i | \(0.762807\pi\) | |||||||
\(104\) | −0.276017 | − | 0.217686i | −0.0270657 | − | 0.0213459i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.84197 | + | 7.40059i | −0.664551 | + | 0.718808i | ||||
\(107\) | −0.327996 | + | 0.327996i | −0.0317086 | + | 0.0317086i | −0.722783 | − | 0.691075i | \(-0.757138\pi\) |
0.691075 | + | 0.722783i | \(0.257138\pi\) | |||||||
\(108\) | −4.95666 | + | 5.80190i | −0.476955 | + | 0.558288i | ||||
\(109\) | −0.149698 | − | 0.149698i | −0.0143385 | − | 0.0143385i | 0.699901 | − | 0.714240i | \(-0.253227\pi\) |
−0.714240 | + | 0.699901i | \(0.753227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.88660 | −0.368900 | ||||||||
\(112\) | −2.94551 | − | 18.6302i | −0.278325 | − | 1.76039i | ||||
\(113\) | 5.97999 | 0.562550 | 0.281275 | − | 0.959627i | \(-0.409243\pi\) | ||||
0.281275 | + | 0.959627i | \(0.409243\pi\) | |||||||
\(114\) | −0.0981502 | − | 2.50245i | −0.00919261 | − | 0.234376i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.01843 | + | 5.99596i | 0.651644 | + | 0.556711i | ||||
\(117\) | −0.221701 | + | 0.221701i | −0.0204962 | + | 0.0204962i | ||||
\(118\) | −7.01189 | + | 7.58439i | −0.645497 | + | 0.698199i | ||||
\(119\) | − | 22.0418i | − | 2.02057i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.6325i | − | 1.78477i | ||||||
\(122\) | 10.4668 | + | 9.67669i | 0.947615 | + | 0.876086i | ||||
\(123\) | 4.03272 | − | 4.03272i | 0.363618 | − | 0.363618i | ||||
\(124\) | −4.24442 | + | 0.333459i | −0.381160 | + | 0.0299455i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −16.8100 | + | 0.659314i | −1.49755 | + | 0.0587364i | ||||
\(127\) | −2.73076 | −0.242315 | −0.121158 | − | 0.992633i | \(-0.538661\pi\) | ||||
−0.121158 | + | 0.992633i | \(0.538661\pi\) | |||||||
\(128\) | 10.8904 | − | 3.06579i | 0.962585 | − | 0.270980i | ||||
\(129\) | −2.22115 | −0.195561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.813555 | − | 0.813555i | −0.0710806 | − | 0.0710806i | 0.670673 | − | 0.741753i | \(-0.266006\pi\) |
−0.741753 | + | 0.670673i | \(0.766006\pi\) | |||||||
\(132\) | 7.62392 | − | 0.598967i | 0.663577 | − | 0.0521334i | ||||
\(133\) | 8.54661 | − | 8.54661i | 0.741085 | − | 0.741085i | ||||
\(134\) | −11.0130 | − | 10.1817i | −0.951375 | − | 0.879563i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.1299 | − | 1.55130i | 1.12588 | − | 0.133023i | ||||
\(137\) | − | 0.199812i | − | 0.0170711i | −0.999964 | − | 0.00853557i | \(-0.997283\pi\) | ||
0.999964 | − | 0.00853557i | \(-0.00271699\pi\) | |||||||
\(138\) | 1.08116 | − | 1.16943i | 0.0920342 | − | 0.0995484i | ||||
\(139\) | −11.6301 | + | 11.6301i | −0.986448 | + | 0.986448i | −0.999909 | − | 0.0134610i | \(-0.995715\pi\) |
0.0134610 | + | 0.999909i | \(0.495715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98400 | + | 1.98400i | 0.167083 | + | 0.167083i | ||||
\(142\) | −0.251670 | − | 6.41661i | −0.0211197 | − | 0.538470i | ||||
\(143\) | 0.687871 | 0.0575227 | ||||||||
\(144\) | −1.57583 | − | 9.96701i | −0.131319 | − | 0.830585i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.460338 | + | 11.7368i | 0.0380978 | + | 0.971346i | ||||
\(147\) | 7.44256 | + | 7.44256i | 0.613852 | + | 0.613852i | ||||
\(148\) | 7.30837 | − | 8.55463i | 0.600744 | − | 0.703186i | ||||
\(149\) | −1.13384 | + | 1.13384i | −0.0928880 | + | 0.0928880i | −0.752024 | − | 0.659136i | \(-0.770922\pi\) |
0.659136 | + | 0.752024i | \(0.270922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.12216i | − | 0.579593i | −0.957088 | − | 0.289797i | \(-0.906412\pi\) | ||
0.957088 | − | 0.289797i | \(-0.0935877\pi\) | |||||||
\(152\) | 5.69259 | + | 4.48957i | 0.461730 | + | 0.364152i | ||||
\(153\) | − | 11.7922i | − | 0.953341i | ||||||
\(154\) | 27.1009 | + | 25.0553i | 2.18386 | + | 2.01901i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0134502 | + | 0.171200i | 0.00107688 | + | 0.0137070i | ||||
\(157\) | −5.32145 | − | 5.32145i | −0.424698 | − | 0.424698i | 0.462120 | − | 0.886818i | \(-0.347089\pi\) |
−0.886818 | + | 0.462120i | \(0.847089\pi\) | |||||||
\(158\) | 16.2957 | − | 0.639147i | 1.29642 | − | 0.0508478i | ||||
\(159\) | 4.92363 | 0.390469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68643 | 0.605775 | ||||||||
\(162\) | −6.96976 | + | 0.273365i | −0.547596 | + | 0.0214776i | ||||
\(163\) | −12.3010 | − | 12.3010i | −0.963488 | − | 0.963488i | 0.0358685 | − | 0.999357i | \(-0.488580\pi\) |
−0.999357 | + | 0.0358685i | \(0.988580\pi\) | |||||||
\(164\) | 1.29312 | + | 16.4594i | 0.100975 | + | 1.28526i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.71702 | − | 1.58741i | −0.133266 | − | 0.123207i | ||||
\(167\) | − | 9.86820i | − | 0.763624i | −0.924240 | − | 0.381812i | \(-0.875300\pi\) | ||
0.924240 | − | 0.381812i | \(-0.124700\pi\) | |||||||
\(168\) | −5.70594 | + | 7.23490i | −0.440223 | + | 0.558184i | ||||
\(169\) | − | 12.9846i | − | 0.998812i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.57237 | − | 4.57237i | 0.349658 | − | 0.349658i | ||||
\(172\) | 4.17665 | − | 4.88887i | 0.318466 | − | 0.372773i | ||||
\(173\) | −13.4089 | − | 13.4089i | −1.01946 | − | 1.01946i | −0.999807 | − | 0.0196525i | \(-0.993744\pi\) |
−0.0196525 | − | 0.999807i | \(-0.506256\pi\) | |||||||
\(174\) | −0.176732 | − | 4.50599i | −0.0133980 | − | 0.341598i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.0177 | + | 17.9070i | −0.981243 | + | 1.34979i | ||||
\(177\) | 5.04591 | 0.379274 | ||||||||
\(178\) | −0.179895 | − | 4.58662i | −0.0134837 | − | 0.343782i | ||||
\(179\) | 0.419587 | + | 0.419587i | 0.0313614 | + | 0.0313614i | 0.722614 | − | 0.691252i | \(-0.242941\pi\) |
−0.691252 | + | 0.722614i | \(0.742941\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2605 | + | 14.2605i | −1.05998 | + | 1.05998i | −0.0618956 | + | 0.998083i | \(0.519715\pi\) |
−0.998083 | + | 0.0618956i | \(0.980285\pi\) | |||||||
\(182\) | −0.562632 | + | 0.608568i | −0.0417050 | + | 0.0451101i | ||||
\(183\) | − | 6.96356i | − | 0.514761i | ||||||
\(184\) | 0.540971 | + | 4.57868i | 0.0398809 | + | 0.337545i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.52719 | + | 1.41191i | 0.111979 | + | 0.103526i | ||||
\(187\) | −18.2938 | + | 18.2938i | −1.33777 | + | 1.33777i | ||||
\(188\) | −8.09762 | + | 0.636183i | −0.590580 | + | 0.0463984i | ||||
\(189\) | 12.7218 | + | 12.7218i | 0.925377 | + | 0.925377i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3304 | 1.25399 | 0.626993 | − | 0.779025i | \(-0.284285\pi\) | ||||
0.626993 | + | 0.779025i | \(0.284285\pi\) | |||||||
\(192\) | −4.71130 | − | 2.88974i | −0.340008 | − | 0.208549i | ||||
\(193\) | 16.8667 | 1.21409 | 0.607045 | − | 0.794667i | \(-0.292355\pi\) | ||||
0.607045 | + | 0.794667i | \(0.292355\pi\) | |||||||
\(194\) | −19.7245 | + | 0.773628i | −1.41614 | + | 0.0555432i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.3765 | + | 2.38650i | −2.16975 | + | 0.170464i | ||||
\(197\) | −3.58908 | + | 3.58908i | −0.255712 | + | 0.255712i | −0.823307 | − | 0.567596i | \(-0.807874\pi\) |
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(198\) | 14.4988 | + | 13.4044i | 1.03038 | + | 0.952608i | ||||
\(199\) | − | 6.64501i | − | 0.471052i | −0.971868 | − | 0.235526i | \(-0.924319\pi\) | ||
0.971868 | − | 0.235526i | \(-0.0756813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.32695i | 0.516803i | ||||||||
\(202\) | 18.2051 | − | 19.6915i | 1.28091 | − | 1.38549i | ||||
\(203\) | 15.3893 | − | 15.3893i | 1.08012 | − | 1.08012i | ||||
\(204\) | −4.91073 | − | 4.19532i | −0.343820 | − | 0.293731i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.762860 | + | 19.4500i | 0.0531510 | + | 1.35514i | ||||
\(207\) | 4.11218 | 0.285816 | ||||||||
\(208\) | −0.402112 | − | 0.292320i | −0.0278815 | − | 0.0202687i | ||||
\(209\) | −14.1867 | −0.981314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.90906 | + | 1.90906i | 0.131425 | + | 0.131425i | 0.769759 | − | 0.638334i | \(-0.220376\pi\) |
−0.638334 | + | 0.769759i | \(0.720376\pi\) | |||||||
\(212\) | −9.25839 | + | 10.8372i | −0.635869 | + | 0.744301i | ||||
\(213\) | −2.21821 | + | 2.21821i | −0.151989 | + | 0.151989i | ||||
\(214\) | −0.445321 | + | 0.481680i | −0.0304415 | + | 0.0329270i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.68282 | + | 8.47355i | −0.454709 | + | 0.576552i | ||||
\(217\) | 10.0379i | 0.681418i | ||||||||
\(218\) | −0.219839 | − | 0.203245i | −0.0148894 | − | 0.0137655i | ||||
\(219\) | 4.05740 | − | 4.05740i | 0.274174 | − | 0.274174i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.410798 | − | 0.410798i | −0.0276333 | − | 0.0276333i | ||||
\(222\) | −5.49226 | + | 0.215416i | −0.368617 | + | 0.0144578i | ||||
\(223\) | 24.1071 | 1.61433 | 0.807165 | − | 0.590326i | \(-0.201001\pi\) | ||||
0.807165 | + | 0.590326i | \(0.201001\pi\) | |||||||
\(224\) | −5.19497 | − | 26.1636i | −0.347103 | − | 1.74813i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.45048 | − | 0.331442i | 0.562118 | − | 0.0220472i | ||||
\(227\) | 6.67411 | + | 6.67411i | 0.442977 | + | 0.442977i | 0.893011 | − | 0.450035i | \(-0.148588\pi\) |
−0.450035 | + | 0.893011i | \(0.648588\pi\) | |||||||
\(228\) | −0.277397 | − | 3.53084i | −0.0183711 | − | 0.233835i | ||||
\(229\) | 16.0807 | − | 16.0807i | 1.06264 | − | 1.06264i | 0.0647388 | − | 0.997902i | \(-0.479379\pi\) |
0.997902 | − | 0.0647388i | \(-0.0206214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 18.0303i | − | 1.18631i | ||||||
\(232\) | 10.2503 | + | 8.08406i | 0.672962 | + | 0.530744i | ||||
\(233\) | 16.4976i | 1.08079i | 0.841411 | + | 0.540396i | \(0.181726\pi\) | ||||
−0.841411 | + | 0.540396i | \(0.818274\pi\) | |||||||
\(234\) | −0.301004 | + | 0.325579i | −0.0196772 | + | 0.0212838i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.48833 | + | 11.1063i | −0.617638 | + | 0.722961i | ||||
\(237\) | −5.63342 | − | 5.63342i | −0.365930 | − | 0.365930i | ||||
\(238\) | −1.22167 | − | 31.1478i | −0.0791891 | − | 2.01901i | ||||
\(239\) | 5.25917 | 0.340188 | 0.170094 | − | 0.985428i | \(-0.445593\pi\) | ||||
0.170094 | + | 0.985428i | \(0.445593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1126 | −0.909075 | −0.454538 | − | 0.890728i | \(-0.650196\pi\) | ||||
−0.454538 | + | 0.890728i | \(0.650196\pi\) | |||||||
\(242\) | −1.08813 | − | 27.7432i | −0.0699479 | − | 1.78340i | ||||
\(243\) | 10.5032 | + | 10.5032i | 0.673782 | + | 0.673782i | ||||
\(244\) | 15.3272 | + | 13.0943i | 0.981222 | + | 0.838275i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.47523 | − | 5.92226i | 0.349088 | − | 0.377589i | ||||
\(247\) | − | 0.318571i | − | 0.0202702i | ||||||
\(248\) | −5.97942 | + | 0.706468i | −0.379693 | + | 0.0448608i | ||||
\(249\) | 1.14234i | 0.0723927i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.98825 | + | 9.98825i | −0.630453 | + | 0.630453i | −0.948182 | − | 0.317729i | \(-0.897080\pi\) |
0.317729 | + | 0.948182i | \(0.397080\pi\) | |||||||
\(252\) | −23.7181 | + | 1.86339i | −1.49410 | + | 0.117383i | ||||
\(253\) | −6.37943 | − | 6.37943i | −0.401071 | − | 0.401071i | ||||
\(254\) | −3.85890 | + | 0.151353i | −0.242129 | + | 0.00949671i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.2196 | − | 4.93595i | 0.951225 | − | 0.308497i | ||||
\(257\) | −8.44760 | −0.526947 | −0.263474 | − | 0.964667i | \(-0.584868\pi\) | ||||
−0.263474 | + | 0.964667i | \(0.584868\pi\) | |||||||
\(258\) | −3.13877 | + | 0.123108i | −0.195411 | + | 0.00766435i | ||||
\(259\) | −18.7577 | − | 18.7577i | −1.16555 | − | 1.16555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23315 | − | 8.23315i | 0.509619 | − | 0.509619i | ||||
\(262\) | −1.19475 | − | 1.10457i | −0.0738118 | − | 0.0682403i | ||||
\(263\) | − | 18.3064i | − | 1.12882i | −0.825494 | − | 0.564410i | \(-0.809104\pi\) | ||
0.825494 | − | 0.564410i | \(-0.190896\pi\) | |||||||
\(264\) | 10.7404 | − | 1.26897i | 0.661024 | − | 0.0781000i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.6037 | − | 12.5511i | 0.711472 | − | 0.769560i | ||||
\(267\) | −1.58559 | + | 1.58559i | −0.0970364 | + | 0.0970364i | ||||
\(268\) | −16.1270 | − | 13.7776i | −0.985115 | − | 0.841601i | ||||
\(269\) | 13.5631 | + | 13.5631i | 0.826955 | + | 0.826955i | 0.987094 | − | 0.160140i | \(-0.0511945\pi\) |
−0.160140 | + | 0.987094i | \(0.551194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.24520 | −0.136386 | −0.0681930 | − | 0.997672i | \(-0.521723\pi\) | ||||
−0.0681930 | + | 0.997672i | \(0.521723\pi\) | |||||||
\(272\) | 18.4683 | − | 2.91991i | 1.11980 | − | 0.177046i | ||||
\(273\) | 0.404882 | 0.0245046 | ||||||||
\(274\) | −0.0110746 | − | 0.282360i | −0.000669044 | − | 0.0170580i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.46300 | − | 1.71247i | 0.0880620 | − | 0.103079i | ||||
\(277\) | 7.28255 | − | 7.28255i | 0.437566 | − | 0.437566i | −0.453626 | − | 0.891192i | \(-0.649870\pi\) |
0.891192 | + | 0.453626i | \(0.149870\pi\) | |||||||
\(278\) | −15.7901 | + | 17.0793i | −0.947030 | + | 1.02435i | ||||
\(279\) | 5.37020i | 0.321506i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.04084i | − | 0.360367i | −0.983633 | − | 0.180183i | \(-0.942331\pi\) | ||
0.983633 | − | 0.180183i | \(-0.0576691\pi\) | |||||||
\(282\) | 2.91361 | + | 2.69369i | 0.173503 | + | 0.160407i | ||||
\(283\) | −15.1350 | + | 15.1350i | −0.899682 | + | 0.899682i | −0.995408 | − | 0.0957259i | \(-0.969483\pi\) |
0.0957259 | + | 0.995408i | \(0.469483\pi\) | |||||||
\(284\) | −0.711284 | − | 9.05354i | −0.0422070 | − | 0.537229i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.972049 | − | 0.0381254i | 0.0574785 | − | 0.00225440i | ||||
\(287\) | 38.9259 | 2.29772 | ||||||||
\(288\) | −2.77927 | − | 13.9973i | −0.163770 | − | 0.824800i | ||||
\(289\) | 4.85021 | 0.285306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.81873 | + | 6.81873i | 0.399721 | + | 0.399721i | ||||
\(292\) | 1.30103 | + | 16.5601i | 0.0761371 | + | 0.969107i | ||||
\(293\) | −10.7777 | + | 10.7777i | −0.629637 | + | 0.629637i | −0.947977 | − | 0.318339i | \(-0.896875\pi\) |
0.318339 | + | 0.947977i | \(0.396875\pi\) | |||||||
\(294\) | 10.9298 | + | 10.1048i | 0.637438 | + | 0.589322i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.85351 | − | 12.4939i | 0.572724 | − | 0.726190i | ||||
\(297\) | − | 21.1172i | − | 1.22534i | ||||||
\(298\) | −1.53942 | + | 1.66511i | −0.0891762 | + | 0.0964571i | ||||
\(299\) | 0.143254 | − | 0.143254i | 0.00828459 | − | 0.00828459i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7198 | − | 10.7198i | −0.617881 | − | 0.617881i | ||||
\(302\) | −0.394747 | − | 10.0645i | −0.0227152 | − | 0.579148i | ||||
\(303\) | −13.1008 | −0.752621 | ||||||||
\(304\) | 8.29319 | + | 6.02882i | 0.475647 | + | 0.345776i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.653584 | − | 16.6639i | −0.0373629 | − | 0.952609i | ||||
\(307\) | 7.94378 | + | 7.94378i | 0.453376 | + | 0.453376i | 0.896473 | − | 0.443098i | \(-0.146120\pi\) |
−0.443098 | + | 0.896473i | \(0.646120\pi\) | |||||||
\(308\) | 39.6858 | + | 33.9042i | 2.26131 | + | 1.93187i | ||||
\(309\) | 6.72382 | − | 6.72382i | 0.382505 | − | 0.382505i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.1649i | 1.76720i | 0.468244 | + | 0.883599i | \(0.344887\pi\) | ||||
−0.468244 | + | 0.883599i | \(0.655113\pi\) | |||||||
\(312\) | 0.0284956 | + | 0.241182i | 0.00161325 | + | 0.0136542i | ||||
\(313\) | − | 5.35842i | − | 0.302876i | −0.988467 | − | 0.151438i | \(-0.951610\pi\) | ||
0.988467 | − | 0.151438i | \(-0.0483903\pi\) | |||||||
\(314\) | −7.81482 | − | 7.22494i | −0.441016 | − | 0.407727i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.9925 | − | 1.80639i | 1.29343 | − | 0.101617i | ||||
\(317\) | −8.88165 | − | 8.88165i | −0.498843 | − | 0.498843i | 0.412235 | − | 0.911078i | \(-0.364748\pi\) |
−0.911078 | + | 0.412235i | \(0.864748\pi\) | |||||||
\(318\) | 6.95771 | − | 0.272893i | 0.390169 | − | 0.0153031i | ||||
\(319\) | −25.5450 | −1.43025 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.320463 | 0.0178865 | ||||||||
\(322\) | 10.8619 | − | 0.426022i | 0.605310 | − | 0.0237413i | ||||
\(323\) | 8.47233 | + | 8.47233i | 0.471413 | + | 0.471413i | ||||
\(324\) | −9.83400 | + | 0.772600i | −0.546333 | + | 0.0429222i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.0646 | − | 16.7011i | −1.00051 | − | 0.924987i | ||||
\(327\) | 0.146260i | 0.00808817i | ||||||||
\(328\) | 2.73960 | + | 23.1875i | 0.151269 | + | 1.28032i | ||||
\(329\) | 19.1506i | 1.05581i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.07281 | − | 6.07281i | 0.333792 | − | 0.333792i | −0.520233 | − | 0.854025i | \(-0.674155\pi\) |
0.854025 | + | 0.520233i | \(0.174155\pi\) | |||||||
\(332\) | −2.51435 | − | 2.14805i | −0.137993 | − | 0.117890i | ||||
\(333\) | −10.0352 | − | 10.0352i | −0.549928 | − | 0.549928i | ||||
\(334\) | −0.546947 | − | 13.9450i | −0.0299276 | − | 0.763038i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.66222 | + | 10.5401i | −0.418008 | + | 0.575009i | ||||
\(337\) | −22.0227 | −1.19965 | −0.599827 | − | 0.800130i | \(-0.704764\pi\) | ||||
−0.599827 | + | 0.800130i | \(0.704764\pi\) | |||||||
\(338\) | −0.719672 | − | 18.3488i | −0.0391450 | − | 0.998044i | ||||
\(339\) | −2.92132 | − | 2.92132i | −0.158664 | − | 0.158664i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.33106 | − | 8.33106i | 0.451152 | − | 0.451152i | ||||
\(342\) | 6.20792 | − | 6.71477i | 0.335686 | − | 0.363093i | ||||
\(343\) | 38.8315i | 2.09670i | ||||||||
\(344\) | 5.63117 | − | 7.14009i | 0.303612 | − | 0.384968i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6917 | − | 18.2053i | −1.05863 | − | 0.978722i | ||||
\(347\) | 11.8920 | − | 11.8920i | 0.638395 | − | 0.638395i | −0.311765 | − | 0.950159i | \(-0.600920\pi\) |
0.950159 | + | 0.311765i | \(0.100920\pi\) | |||||||
\(348\) | −0.499490 | − | 6.35773i | −0.0267755 | − | 0.340810i | ||||
\(349\) | −8.65696 | − | 8.65696i | −0.463396 | − | 0.463396i | 0.436371 | − | 0.899767i | \(-0.356264\pi\) |
−0.899767 | + | 0.436371i | \(0.856264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.474200 | 0.0253109 | ||||||||
\(352\) | −17.4031 | + | 26.0263i | −0.927589 | + | 1.38721i | ||||
\(353\) | −26.6153 | −1.41659 | −0.708296 | − | 0.705916i | \(-0.750536\pi\) | ||||
−0.708296 | + | 0.705916i | \(0.750536\pi\) | |||||||
\(354\) | 7.13051 | − | 0.279671i | 0.378983 | − | 0.0148643i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.508429 | − | 6.47151i | −0.0269467 | − | 0.342989i | ||||
\(357\) | −10.7678 | + | 10.7678i | −0.569890 | + | 0.569890i | ||||
\(358\) | 0.616185 | + | 0.569674i | 0.0325664 | + | 0.0301082i | ||||
\(359\) | 4.85032i | 0.255990i | 0.991775 | + | 0.127995i | \(0.0408542\pi\) | ||||
−0.991775 | + | 0.127995i | \(0.959146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 12.4298i | − | 0.654199i | ||||||
\(362\) | −19.3616 | + | 20.9424i | −1.01762 | + | 1.10071i | ||||
\(363\) | −9.59078 | + | 9.59078i | −0.503385 | + | 0.503385i | ||||
\(364\) | −0.761340 | + | 0.891168i | −0.0399051 | + | 0.0467099i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.385957 | − | 9.84039i | −0.0201743 | − | 0.514365i | ||||
\(367\) | −15.6741 | −0.818182 | −0.409091 | − | 0.912494i | \(-0.634154\pi\) | ||||
−0.409091 | + | 0.912494i | \(0.634154\pi\) | |||||||
\(368\) | 1.01823 | + | 6.44027i | 0.0530792 | + | 0.335722i | ||||
\(369\) | 20.8250 | 1.08411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.7627 | + | 23.7627i | 1.23370 | + | 1.23370i | ||||
\(372\) | 2.23637 | + | 1.91057i | 0.115950 | + | 0.0990582i | ||||
\(373\) | 5.44481 | − | 5.44481i | 0.281922 | − | 0.281922i | −0.551953 | − | 0.833875i | \(-0.686117\pi\) |
0.833875 | + | 0.551953i | \(0.186117\pi\) | |||||||
\(374\) | −24.8375 | + | 26.8654i | −1.28432 | + | 1.38918i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.4077 | + | 1.34782i | −0.588308 | + | 0.0695085i | ||||
\(377\) | − | 0.573629i | − | 0.0295434i | ||||||
\(378\) | 18.6827 | + | 17.2724i | 0.960933 | + | 0.888399i | ||||
\(379\) | −17.4103 | + | 17.4103i | −0.894309 | + | 0.894309i | −0.994925 | − | 0.100616i | \(-0.967919\pi\) |
0.100616 | + | 0.994925i | \(0.467919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33402 | + | 1.33402i | 0.0683438 | + | 0.0683438i | ||||
\(382\) | 24.4901 | − | 0.960543i | 1.25302 | − | 0.0491457i | ||||
\(383\) | −9.04928 | −0.462396 | −0.231198 | − | 0.972907i | \(-0.574265\pi\) | ||||
−0.231198 | + | 0.972907i | \(0.574265\pi\) | |||||||
\(384\) | −6.81782 | − | 3.82245i | −0.347921 | − | 0.195064i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8348 | − | 0.934839i | 1.21316 | − | 0.0475821i | ||||
\(387\) | −5.73503 | − | 5.73503i | −0.291528 | − | 0.291528i | ||||
\(388\) | −27.8303 | + | 2.18647i | −1.41287 | + | 0.111001i | ||||
\(389\) | −15.3617 | + | 15.3617i | −0.778871 | + | 0.778871i | −0.979639 | − | 0.200768i | \(-0.935656\pi\) |
0.200768 | + | 0.979639i | \(0.435656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.61962i | 0.385341i | ||||||||
\(392\) | −42.7935 | + | 5.05605i | −2.16140 | + | 0.255369i | ||||
\(393\) | 0.794869i | 0.0400959i | ||||||||
\(394\) | −4.87291 | + | 5.27076i | −0.245493 | + | 0.265537i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 21.2316 | + | 18.1385i | 1.06693 | + | 0.911494i | ||||
\(397\) | −9.44519 | − | 9.44519i | −0.474041 | − | 0.474041i | 0.429179 | − | 0.903220i | \(-0.358803\pi\) |
−0.903220 | + | 0.429179i | \(0.858803\pi\) | |||||||
\(398\) | −0.368301 | − | 9.39024i | −0.0184613 | − | 0.470690i | ||||
\(399\) | −8.35031 | −0.418038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5765 | −1.07748 | −0.538739 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538739 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(402\) | 0.406098 | + | 10.3539i | 0.0202543 | + | 0.516406i | ||||
\(403\) | 0.187079 | + | 0.187079i | 0.00931907 | + | 0.00931907i | ||||
\(404\) | 24.6347 | − | 28.8356i | 1.22562 | − | 1.43462i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.8941 | − | 22.6000i | 1.03696 | − | 1.12162i | ||||
\(407\) | 31.1363i | 1.54337i | ||||||||
\(408\) | −7.17202 | − | 5.65635i | −0.355068 | − | 0.280031i | ||||
\(409\) | 4.17336i | 0.206359i | 0.994663 | + | 0.103180i | \(0.0329017\pi\) | ||||
−0.994663 | + | 0.103180i | \(0.967098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0976116 | + | 0.0976116i | −0.00481482 | + | 0.00481482i | ||||
\(412\) | 2.15604 | + | 27.4430i | 0.106220 | + | 1.35202i | ||||
\(413\) | 24.3529 | + | 24.3529i | 1.19833 | + | 1.19833i | ||||
\(414\) | 5.81103 | − | 0.227918i | 0.285597 | − | 0.0112016i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.584438 | − | 0.390798i | −0.0286544 | − | 0.0191604i | ||||
\(417\) | 11.3629 | 0.556445 | ||||||||
\(418\) | −20.0476 | + | 0.786300i | −0.980560 | + | 0.0384592i | ||||
\(419\) | 27.1191 | + | 27.1191i | 1.32485 | + | 1.32485i | 0.909794 | + | 0.415060i | \(0.136239\pi\) |
0.415060 | + | 0.909794i | \(0.363761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9594 | + | 26.9594i | −1.31392 | + | 1.31392i | −0.395421 | + | 0.918500i | \(0.629401\pi\) |
−0.918500 | + | 0.395421i | \(0.870599\pi\) | |||||||
\(422\) | 2.80355 | + | 2.59193i | 0.136475 | + | 0.126173i | ||||
\(423\) | 10.2454i | 0.498150i | ||||||||
\(424\) | −12.4826 | + | 15.8275i | −0.606210 | + | 0.768650i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.01167 | + | 3.25756i | −0.145916 | + | 0.157829i | ||||
\(427\) | 33.6079 | − | 33.6079i | 1.62640 | − | 1.62640i | ||||
\(428\) | −0.602598 | + | 0.705357i | −0.0291277 | + | 0.0340947i | ||||
\(429\) | −0.336036 | − | 0.336036i | −0.0162240 | − | 0.0162240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.4059 | −1.07925 | −0.539626 | − | 0.841905i | \(-0.681434\pi\) | ||||
−0.539626 | + | 0.841905i | \(0.681434\pi\) | |||||||
\(432\) | −8.97403 | + | 12.3446i | −0.431763 | + | 0.593930i | ||||
\(433\) | −16.8061 | −0.807649 | −0.403824 | − | 0.914837i | \(-0.632319\pi\) | ||||
−0.403824 | + | 0.914837i | \(0.632319\pi\) | |||||||
\(434\) | 0.556353 | + | 14.1848i | 0.0267058 | + | 0.680894i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.321925 | − | 0.275026i | −0.0154174 | − | 0.0131714i | ||||
\(437\) | −2.95448 | + | 2.95448i | −0.141332 | + | 0.141332i | ||||
\(438\) | 5.50874 | − | 5.95851i | 0.263218 | − | 0.284708i | ||||
\(439\) | − | 9.08322i | − | 0.433519i | −0.976225 | − | 0.216759i | \(-0.930451\pi\) | ||
0.976225 | − | 0.216759i | \(-0.0695487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.4335i | 1.83017i | ||||||||
\(442\) | −0.603279 | − | 0.557742i | −0.0286951 | − | 0.0265291i | ||||
\(443\) | 12.5397 | − | 12.5397i | 0.595781 | − | 0.595781i | −0.343406 | − | 0.939187i | \(-0.611581\pi\) |
0.939187 | + | 0.343406i | \(0.111581\pi\) | |||||||
\(444\) | −7.74933 | + | 0.608820i | −0.367767 | + | 0.0288933i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 34.0664 | − | 1.33614i | 1.61309 | − | 0.0632681i | ||||
\(447\) | 1.10780 | 0.0523972 | ||||||||
\(448\) | −8.79127 | − | 36.6845i | −0.415349 | − | 1.73318i | ||||
\(449\) | 18.0707 | 0.852811 | 0.426406 | − | 0.904532i | \(-0.359780\pi\) | ||||
0.426406 | + | 0.904532i | \(0.359780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.3069 | − | 32.3069i | −1.52127 | − | 1.52127i | ||||
\(452\) | 11.9232 | − | 0.936740i | 0.560822 | − | 0.0440605i | ||||
\(453\) | −3.47929 | + | 3.47929i | −0.163471 | + | 0.163471i | ||||
\(454\) | 9.80129 | + | 9.06146i | 0.459997 | + | 0.425275i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.587695 | − | 4.97415i | −0.0275213 | − | 0.232936i | ||||
\(457\) | − | 18.6637i | − | 0.873052i | −0.899692 | − | 0.436526i | \(-0.856209\pi\) | ||
0.899692 | − | 0.436526i | \(-0.143791\pi\) | |||||||
\(458\) | 21.8328 | − | 23.6153i | 1.02018 | − | 1.10347i | ||||
\(459\) | −12.6113 | + | 12.6113i | −0.588643 | + | 0.588643i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.831229 | − | 0.831229i | −0.0387142 | − | 0.0387142i | 0.687485 | − | 0.726199i | \(-0.258715\pi\) |
−0.726199 | + | 0.687485i | \(0.758715\pi\) | |||||||
\(462\) | −0.999335 | − | 25.4791i | −0.0464933 | − | 1.18540i | ||||
\(463\) | 7.82533 | 0.363674 | 0.181837 | − | 0.983329i | \(-0.441796\pi\) | ||||
0.181837 | + | 0.983329i | \(0.441796\pi\) | |||||||
\(464\) | 14.9330 | + | 10.8557i | 0.693246 | + | 0.503962i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.914382 | + | 23.3132i | 0.0423579 | + | 1.07996i | ||||
\(467\) | 8.75068 | + | 8.75068i | 0.404933 | + | 0.404933i | 0.879967 | − | 0.475034i | \(-0.157564\pi\) |
−0.475034 | + | 0.879967i | \(0.657564\pi\) | |||||||
\(468\) | −0.407311 | + | 0.476768i | −0.0188280 | + | 0.0220386i | ||||
\(469\) | −35.3617 | + | 35.3617i | −1.63285 | + | 1.63285i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.19922i | 0.239568i | ||||||||
\(472\) | −12.7926 | + | 16.2206i | −0.588829 | + | 0.746612i | ||||
\(473\) | 17.7941i | 0.818172i | ||||||||
\(474\) | −8.27297 | − | 7.64850i | −0.379990 | − | 0.351307i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.45275 | − | 43.9481i | −0.158257 | − | 2.01436i | ||||
\(477\) | 12.7129 | + | 12.7129i | 0.582082 | + | 0.582082i | ||||
\(478\) | 7.43188 | − | 0.291491i | 0.339926 | − | 0.0133325i | ||||
\(479\) | 2.10417 | 0.0961421 | 0.0480710 | − | 0.998844i | \(-0.484693\pi\) | ||||
0.0480710 | + | 0.998844i | \(0.484693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.699186 | −0.0318801 | ||||||||
\(482\) | −19.9430 | + | 0.782196i | −0.908377 | + | 0.0356281i | ||||
\(483\) | −3.75494 | − | 3.75494i | −0.170856 | − | 0.170856i | ||||
\(484\) | −3.07534 | − | 39.1443i | −0.139788 | − | 1.77929i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.4245 | + | 14.2602i | 0.699671 | + | 0.646858i | ||||
\(487\) | − | 4.87183i | − | 0.220764i | −0.993889 | − | 0.110382i | \(-0.964793\pi\) | ||
0.993889 | − | 0.110382i | \(-0.0352074\pi\) | |||||||
\(488\) | 22.3850 | + | 17.6544i | 1.01332 | + | 0.799175i | ||||
\(489\) | 12.0185i | 0.543494i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3582 | − | 14.3582i | 0.647975 | − | 0.647975i | −0.304528 | − | 0.952503i | \(-0.598499\pi\) |
0.952503 | + | 0.304528i | \(0.0984987\pi\) | |||||||
\(492\) | 7.40895 | − | 8.67237i | 0.334021 | − | 0.390981i | ||||
\(493\) | 15.2555 | + | 15.2555i | 0.687075 | + | 0.687075i | ||||
\(494\) | −0.0176569 | − | 0.450181i | −0.000794419 | − | 0.0202546i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.41052 | + | 1.32974i | −0.377644 | + | 0.0597071i | ||||
\(497\) | −21.4113 | −0.960429 | ||||||||
\(498\) | 0.0633143 | + | 1.61427i | 0.00283718 | + | 0.0723370i | ||||
\(499\) | −25.1060 | − | 25.1060i | −1.12390 | − | 1.12390i | −0.991150 | − | 0.132748i | \(-0.957620\pi\) |
−0.132748 | − | 0.991150i | \(-0.542380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.82077 | + | 4.82077i | −0.215376 | + | 0.215376i | ||||
\(502\) | −13.5611 | + | 14.6683i | −0.605260 | + | 0.654677i | ||||
\(503\) | − | 18.8868i | − | 0.842120i | −0.907033 | − | 0.421060i | \(-0.861658\pi\) | ||
0.907033 | − | 0.421060i | \(-0.138342\pi\) | |||||||
\(504\) | −33.4133 | + | 3.94778i | −1.48835 | + | 0.175848i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.36852 | − | 8.66136i | −0.416482 | − | 0.385044i | ||||
\(507\) | −6.34316 | + | 6.34316i | −0.281710 | + | 0.281710i | ||||
\(508\) | −5.44473 | + | 0.427761i | −0.241571 | + | 0.0189788i | ||||
\(509\) | −22.9756 | − | 22.9756i | −1.01837 | − | 1.01837i | −0.999828 | − | 0.0185459i | \(-0.994096\pi\) |
−0.0185459 | − | 0.999828i | \(-0.505904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.1641 | 1.73252 | ||||||||
\(512\) | 21.2337 | − | 7.81868i | 0.938404 | − | 0.345540i | ||||
\(513\) | −9.77993 | −0.431794 | ||||||||
\(514\) | −11.9375 | + | 0.468210i | −0.526542 | + | 0.0206519i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.42865 | + | 0.347933i | −0.194961 | + | 0.0153169i | ||||
\(517\) | 15.8942 | − | 15.8942i | 0.699028 | − | 0.699028i | ||||
\(518\) | −27.5467 | − | 25.4674i | −1.21033 | − | 1.11897i | ||||
\(519\) | 13.1009i | 0.575066i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.2089i | − | 0.885367i | −0.896678 | − | 0.442683i | \(-0.854027\pi\) | ||
0.896678 | − | 0.442683i | \(-0.145973\pi\) | |||||||
\(522\) | 11.1782 | − | 12.0908i | 0.489255 | − | 0.529201i | ||||
\(523\) | −3.93445 | + | 3.93445i | −0.172042 | + | 0.172042i | −0.787876 | − | 0.615834i | \(-0.788819\pi\) |
0.615834 | + | 0.787876i | \(0.288819\pi\) | |||||||
\(524\) | −1.74955 | − | 1.49467i | −0.0764295 | − | 0.0652951i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.01464 | − | 25.8693i | −0.0442402 | − | 1.12795i | ||||
\(527\) | −9.95066 | −0.433458 | ||||||||
\(528\) | 15.1072 | − | 2.38851i | 0.657456 | − | 0.103947i | ||||
\(529\) | 20.3429 | 0.884473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.0286 | + | 13.0286i | 0.565393 | + | 0.565393i | ||||
\(532\) | 15.7019 | − | 18.3795i | 0.680765 | − | 0.796853i | ||||
\(533\) | 0.725471 | − | 0.725471i | 0.0314237 | − | 0.0314237i | ||||
\(534\) | −2.15276 | + | 2.32852i | −0.0931589 | + | 0.100765i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −23.5532 | − | 18.5757i | −1.01734 | − | 0.802346i | ||||
\(537\) | − | 0.409950i | − | 0.0176906i | ||||||
\(538\) | 19.9181 | + | 18.4146i | 0.858729 | + | 0.793910i | ||||
\(539\) | 59.6238 | − | 59.6238i | 2.56818 | − | 2.56818i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.17895 | − | 3.17895i | −0.136674 | − | 0.136674i | 0.635460 | − | 0.772134i | \(-0.280811\pi\) |
−0.772134 | + | 0.635460i | \(0.780811\pi\) | |||||||
\(542\) | −3.17275 | + | 0.124440i | −0.136281 | + | 0.00534518i | ||||
\(543\) | 13.9330 | 0.597923 | ||||||||
\(544\) | 25.9362 | − | 5.14982i | 1.11201 | − | 0.220797i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.572150 | − | 0.0224407i | 0.0244857 | − | 0.000960372i | ||||
\(547\) | −1.32918 | − | 1.32918i | −0.0568317 | − | 0.0568317i | 0.678120 | − | 0.734951i | \(-0.262795\pi\) |
−0.734951 | + | 0.678120i | \(0.762795\pi\) | |||||||
\(548\) | −0.0312998 | − | 0.398397i | −0.00133706 | − | 0.0170187i | ||||
\(549\) | 17.9800 | − | 17.9800i | 0.767366 | − | 0.767366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.8306i | 0.503998i | ||||||||
\(552\) | 1.97249 | − | 2.50103i | 0.0839545 | − | 0.106451i | ||||
\(553\) | − | 54.3766i | − | 2.31233i | ||||||
\(554\) | 9.88754 | − | 10.6948i | 0.420081 | − | 0.454379i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3669 | + | 25.0105i | −0.906157 | + | 1.06068i | ||||
\(557\) | −24.9082 | − | 24.9082i | −1.05539 | − | 1.05539i | −0.998373 | − | 0.0570196i | \(-0.981840\pi\) |
−0.0570196 | − | 0.998373i | \(-0.518160\pi\) | |||||||
\(558\) | 0.297645 | + | 7.58878i | 0.0126003 | + | 0.321259i | ||||
\(559\) | −0.399576 | −0.0169003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.8736 | 0.754625 | ||||||||
\(562\) | −0.334815 | − | 8.53648i | −0.0141233 | − | 0.360090i | ||||
\(563\) | −3.80804 | − | 3.80804i | −0.160490 | − | 0.160490i | 0.622294 | − | 0.782784i | \(-0.286201\pi\) |
−0.782784 | + | 0.622294i | \(0.786201\pi\) | |||||||
\(564\) | 4.26660 | + | 3.64503i | 0.179656 | + | 0.153484i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.5488 | + | 22.2265i | −0.863731 | + | 0.934251i | ||||
\(567\) | 23.2571i | 0.976706i | ||||||||
\(568\) | −1.50693 | − | 12.7544i | −0.0632293 | − | 0.535162i | ||||
\(569\) | 8.43971i | 0.353811i | 0.984228 | + | 0.176905i | \(0.0566087\pi\) | ||||
−0.984228 | + | 0.176905i | \(0.943391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2821 | + | 21.2821i | −0.890629 | + | 0.890629i | −0.994582 | − | 0.103953i | \(-0.966851\pi\) |
0.103953 | + | 0.994582i | \(0.466851\pi\) | |||||||
\(572\) | 1.37152 | − | 0.107752i | 0.0573460 | − | 0.00450534i | ||||
\(573\) | −8.46619 | − | 8.46619i | −0.353680 | − | 0.353680i | ||||
\(574\) | 55.0072 | − | 2.15747i | 2.29596 | − | 0.0900512i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.70326 | − | 19.6259i | −0.195969 | − | 0.817748i | ||||
\(577\) | 36.3491 | 1.51323 | 0.756615 | − | 0.653860i | \(-0.226852\pi\) | ||||
0.756615 | + | 0.653860i | \(0.226852\pi\) | |||||||
\(578\) | 6.85396 | − | 0.268824i | 0.285087 | − | 0.0111816i | ||||
\(579\) | −8.23964 | − | 8.23964i | −0.342428 | − | 0.342428i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.51321 | + | 5.51321i | −0.228726 | + | 0.228726i | ||||
\(582\) | 10.0137 | + | 9.25780i | 0.415080 | + | 0.383748i | ||||
\(583\) | − | 39.4442i | − | 1.63361i | ||||||
\(584\) | 2.75637 | + | 23.3294i | 0.114059 | + | 0.965379i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6328 | + | 15.8275i | −0.604477 | + | 0.653830i | ||||
\(587\) | 6.55994 | − | 6.55994i | 0.270758 | − | 0.270758i | −0.558647 | − | 0.829405i | \(-0.688679\pi\) |
0.829405 | + | 0.558647i | \(0.188679\pi\) | |||||||
\(588\) | 16.0052 | + | 13.6735i | 0.660044 | + | 0.563887i | ||||
\(589\) | −3.85833 | − | 3.85833i | −0.158980 | − | 0.158980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.50665 | 0.144244 | ||||||||
\(592\) | 13.2318 | − | 18.2015i | 0.543823 | − | 0.748078i | ||||
\(593\) | 1.40974 | 0.0578911 | 0.0289455 | − | 0.999581i | \(-0.490785\pi\) | ||||
0.0289455 | + | 0.999581i | \(0.490785\pi\) | |||||||
\(594\) | −1.17043 | − | 29.8413i | −0.0480231 | − | 1.22440i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.08311 | + | 2.43833i | −0.0853274 | + | 0.0998779i | ||||
\(597\) | −3.24619 | + | 3.24619i | −0.132858 | + | 0.132858i | ||||
\(598\) | 0.194496 | − | 0.210376i | 0.00795354 | − | 0.00860291i | ||||
\(599\) | 23.3593i | 0.954435i | 0.878785 | + | 0.477218i | \(0.158355\pi\) | ||||
−0.878785 | + | 0.477218i | \(0.841645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4138i | 0.832695i | 0.909206 | + | 0.416347i | \(0.136690\pi\) | ||||
−0.909206 | + | 0.416347i | \(0.863310\pi\) | |||||||
\(602\) | −15.7426 | − | 14.5543i | −0.641622 | − | 0.593190i | ||||
\(603\) | −18.9183 | + | 18.9183i | −0.770411 | + | 0.770411i | ||||
\(604\) | −1.11566 | − | 14.2006i | −0.0453954 | − | 0.577813i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.5131 | + | 0.726115i | −0.752043 | + | 0.0294964i | ||||
\(607\) | −0.758240 | −0.0307760 | −0.0153880 | − | 0.999882i | \(-0.504898\pi\) | ||||
−0.0153880 | + | 0.999882i | \(0.504898\pi\) | |||||||
\(608\) | 12.0535 | + | 8.05983i | 0.488833 | + | 0.326869i | ||||
\(609\) | −15.0358 | −0.609283 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.356915 | + | 0.356915i | 0.0144392 | + | 0.0144392i | ||||
\(612\) | −1.84719 | − | 23.5119i | −0.0746684 | − | 0.950413i | ||||
\(613\) | −12.0341 | + | 12.0341i | −0.486052 | + | 0.486052i | −0.907058 | − | 0.421006i | \(-0.861677\pi\) |
0.421006 | + | 0.907058i | \(0.361677\pi\) | |||||||
\(614\) | 11.6659 | + | 10.7853i | 0.470796 | + | 0.435259i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 57.9602 | + | 45.7114i | 2.33528 | + | 1.84176i | ||||
\(617\) | 32.6899i | 1.31605i | 0.752998 | + | 0.658023i | \(0.228607\pi\) | ||||
−0.752998 | + | 0.658023i | \(0.771393\pi\) | |||||||
\(618\) | 9.12894 | − | 9.87428i | 0.367220 | − | 0.397202i | ||||
\(619\) | 26.3836 | − | 26.3836i | 1.06045 | − | 1.06045i | 0.0623934 | − | 0.998052i | \(-0.480127\pi\) |
0.998052 | − | 0.0623934i | \(-0.0198733\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.39781 | − | 4.39781i | −0.176478 | − | 0.176478i | ||||
\(622\) | 1.72732 | + | 44.0399i | 0.0692592 | + | 1.76584i | ||||
\(623\) | −15.3049 | −0.613178 | ||||||||
\(624\) | 0.0536355 | + | 0.339241i | 0.00214714 | + | 0.0135805i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.296991 | − | 7.57213i | −0.0118702 | − | 0.302643i | ||||
\(627\) | 6.93042 | + | 6.93042i | 0.276774 | + | 0.276774i | ||||
\(628\) | −11.4438 | − | 9.77662i | −0.456657 | − | 0.390130i | ||||
\(629\) | 18.5947 | − | 18.5947i | 0.741420 | − | 0.741420i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.08765i | 0.242345i | 0.992631 | + | 0.121173i | \(0.0386655\pi\) | ||||
−0.992631 | + | 0.121173i | \(0.961335\pi\) | |||||||
\(632\) | 32.3913 | − | 3.82703i | 1.28846 | − | 0.152231i | ||||
\(633\) | − | 1.86521i | − | 0.0741354i | ||||||
\(634\) | −13.0432 | − | 12.0586i | −0.518010 | − | 0.478909i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.81701 | − | 0.771266i | 0.389270 | − | 0.0305827i | ||||
\(637\) | 1.33889 | + | 1.33889i | 0.0530487 | + | 0.0530487i | ||||
\(638\) | −36.0983 | + | 1.41584i | −1.42915 | + | 0.0560535i | ||||
\(639\) | −11.4549 | −0.453149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1680 | 0.441111 | 0.220555 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220555 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(642\) | 0.452855 | − | 0.0177617i | 0.0178728 | − | 0.000700999i | ||||
\(643\) | 21.9585 | + | 21.9585i | 0.865957 | + | 0.865957i | 0.992022 | − | 0.126065i | \(-0.0402348\pi\) |
−0.126065 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(644\) | 15.3256 | − | 1.20405i | 0.603914 | − | 0.0474460i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4421 | + | 11.5029i | 0.489526 | + | 0.452575i | ||||
\(647\) | − | 36.9848i | − | 1.45402i | −0.686625 | − | 0.727011i | \(-0.740909\pi\) | ||
0.686625 | − | 0.727011i | \(-0.259091\pi\) | |||||||
\(648\) | −13.8539 | + | 1.63683i | −0.544231 | + | 0.0643009i | ||||
\(649\) | − | 40.4238i | − | 1.58677i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.90368 | − | 4.90368i | 0.192190 | − | 0.192190i | ||||
\(652\) | −26.4533 | − | 22.5995i | −1.03599 | − | 0.885065i | ||||
\(653\) | 18.4157 | + | 18.4157i | 0.720663 | + | 0.720663i | 0.968740 | − | 0.248077i | \(-0.0797986\pi\) |
−0.248077 | + | 0.968740i | \(0.579799\pi\) | |||||||
\(654\) | 0.00810646 | + | 0.206683i | 0.000316988 | + | 0.00808196i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.15658 | + | 32.6150i | 0.201331 | + | 1.27340i | ||||
\(657\) | 20.9525 | 0.817435 | ||||||||
\(658\) | 1.06143 | + | 27.0622i | 0.0413787 | + | 1.05500i | ||||
\(659\) | −15.5421 | − | 15.5421i | −0.605434 | − | 0.605434i | 0.336316 | − | 0.941749i | \(-0.390819\pi\) |
−0.941749 | + | 0.336316i | \(0.890819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6677 | − | 29.6677i | 1.15394 | − | 1.15394i | 0.168185 | − | 0.985755i | \(-0.446209\pi\) |
0.985755 | − | 0.168185i | \(-0.0537906\pi\) | |||||||
\(662\) | 8.24507 | − | 8.91825i | 0.320454 | − | 0.346617i | ||||
\(663\) | 0.401363i | 0.0155877i | ||||||||
\(664\) | −3.67215 | − | 2.89611i | −0.142507 | − | 0.112391i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.7373 | − | 13.6249i | −0.571058 | − | 0.527953i | ||||
\(667\) | −5.31992 | + | 5.31992i | −0.205988 | + | 0.205988i | ||||
\(668\) | −1.54581 | − | 19.6758i | −0.0598092 | − | 0.761278i | ||||
\(669\) | −11.7767 | − | 11.7767i | −0.455313 | − | 0.455313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.7864 | −2.15361 | ||||||||
\(672\) | −10.2435 | + | 15.3192i | −0.395152 | + | 0.590949i | ||||
\(673\) | 29.2198 | 1.12634 | 0.563171 | − | 0.826340i | \(-0.309581\pi\) | ||||
0.563171 | + | 0.826340i | \(0.309581\pi\) | |||||||
\(674\) | −31.1209 | + | 1.22061i | −1.19873 | + | 0.0470163i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.03397 | − | 25.8893i | −0.0782298 | − | 0.995743i | ||||
\(677\) | −17.2591 | + | 17.2591i | −0.663320 | + | 0.663320i | −0.956161 | − | 0.292841i | \(-0.905399\pi\) |
0.292841 | + | 0.956161i | \(0.405399\pi\) | |||||||
\(678\) | −4.29011 | − | 3.96628i | −0.164761 | − | 0.152324i | ||||
\(679\) | 65.8179i | 2.52586i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.52082i | − | 0.249878i | ||||||
\(682\) | 11.3111 | − | 12.2346i | 0.433124 | − | 0.468487i | ||||
\(683\) | −1.10407 | + | 1.10407i | −0.0422459 | + | 0.0422459i | −0.727914 | − | 0.685668i | \(-0.759510\pi\) |
0.685668 | + | 0.727914i | \(0.259510\pi\) | |||||||
\(684\) | 8.40041 | − | 9.83289i | 0.321198 | − | 0.375970i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.15224 | + | 54.8738i | 0.0821731 | + | 2.09509i | ||||
\(687\) | −15.7113 | −0.599425 | ||||||||
\(688\) | 7.56181 | − | 10.4020i | 0.288291 | − | 0.396571i | ||||
\(689\) | 0.885743 | 0.0337441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.4233 | − | 28.4233i | −1.08127 | − | 1.08127i | −0.996391 | − | 0.0848830i | \(-0.972948\pi\) |
−0.0848830 | − | 0.996391i | \(-0.527052\pi\) | |||||||
\(692\) | −28.8359 | − | 24.6350i | −1.09617 | − | 0.936481i | ||||
\(693\) | 46.5545 | − | 46.5545i | 1.76846 | − | 1.76846i | ||||
\(694\) | 16.1458 | − | 17.4640i | 0.612885 | − | 0.662924i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.05822 | − | 8.95660i | −0.0401118 | − | 0.339499i | ||||
\(697\) | 38.5875i | 1.46161i | ||||||||
\(698\) | −12.7132 | − | 11.7536i | −0.481201 | − | 0.444879i | ||||
\(699\) | 8.05933 | − | 8.05933i | 0.304832 | − | 0.304832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7991 | − | 23.7991i | −0.898880 | − | 0.898880i | 0.0964573 | − | 0.995337i | \(-0.469249\pi\) |
−0.995337 | + | 0.0964573i | \(0.969249\pi\) | |||||||
\(702\) | 0.670105 | − | 0.0262826i | 0.0252915 | − | 0.000991974i | ||||
\(703\) | 14.4200 | 0.543862 | ||||||||
\(704\) | −23.1503 | + | 37.7431i | −0.872510 | + | 1.42250i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.6109 | + | 1.47516i | −1.41550 | + | 0.0555184i | ||||
\(707\) | −63.2278 | − | 63.2278i | −2.37793 | − | 2.37793i | ||||
\(708\) | 10.0608 | − | 0.790421i | 0.378109 | − | 0.0297058i | ||||
\(709\) | 1.49921 | − | 1.49921i | 0.0563039 | − | 0.0563039i | −0.678394 | − | 0.734698i | \(-0.737324\pi\) |
0.734698 | + | 0.678394i | \(0.237324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 29.0911i | − | 1.09100i | ||||||
\(712\) | −1.07716 | − | 9.11688i | −0.0403682 | − | 0.341670i | ||||
\(713\) | − | 3.47000i | − | 0.129953i | ||||||
\(714\) | −14.6194 | + | 15.8130i | −0.547118 | + | 0.591787i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.902323 | + | 0.770870i | 0.0337214 | + | 0.0288088i | ||||
\(717\) | −2.56919 | − | 2.56919i | −0.0959482 | − | 0.0959482i | ||||
\(718\) | 0.268830 | + | 6.85412i | 0.0100327 | + | 0.255794i | ||||
\(719\) | 7.37612 | 0.275083 | 0.137541 | − | 0.990496i | \(-0.456080\pi\) | ||||
0.137541 | + | 0.990496i | \(0.456080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.9017 | 2.41707 | ||||||||
\(722\) | −0.688923 | − | 17.5649i | −0.0256391 | − | 0.653696i | ||||
\(723\) | 6.89425 | + | 6.89425i | 0.256400 | + | 0.256400i | ||||
\(724\) | −26.1996 | + | 30.6673i | −0.973702 | + | 1.13974i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.0214 | + | 14.0846i | −0.483270 | + | 0.522727i | ||||
\(727\) | 30.1470i | 1.11809i | 0.829137 | + | 0.559045i | \(0.188832\pi\) | ||||
−0.829137 | + | 0.559045i | \(0.811168\pi\) | |||||||
\(728\) | −1.02648 | + | 1.30153i | −0.0380438 | + | 0.0482380i | ||||
\(729\) | 4.53447i | 0.167943i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6267 | − | 10.6267i | 0.393041 | − | 0.393041i | ||||
\(732\) | −1.09081 | − | 13.8843i | −0.0403176 | − | 0.513180i | ||||
\(733\) | 1.43297 | + | 1.43297i | 0.0529279 | + | 0.0529279i | 0.733075 | − | 0.680147i | \(-0.238084\pi\) |
−0.680147 | + | 0.733075i | \(0.738084\pi\) | |||||||
\(734\) | −22.1495 | + | 0.868740i | −0.817553 | + | 0.0320658i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.79585 | + | 9.04449i | 0.0661959 | + | 0.333384i | ||||
\(737\) | 58.6977 | 2.16216 | ||||||||
\(738\) | 29.4284 | − | 1.15423i | 1.08328 | − | 0.0424879i | ||||
\(739\) | 31.0001 | + | 31.0001i | 1.14036 | + | 1.14036i | 0.988385 | + | 0.151973i | \(0.0485626\pi\) |
0.151973 | + | 0.988385i | \(0.451437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.155627 | + | 0.155627i | −0.00571710 | + | 0.00571710i | ||||
\(742\) | 34.8968 | + | 32.2626i | 1.28110 | + | 1.18440i | ||||
\(743\) | − | 38.5395i | − | 1.41388i | −0.707276 | − | 0.706938i | \(-0.750076\pi\) | ||
0.707276 | − | 0.706938i | \(-0.249924\pi\) | |||||||
\(744\) | 3.26616 | + | 2.57592i | 0.119743 | + | 0.0944378i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.39243 | − | 7.99599i | 0.270656 | − | 0.292754i | ||||
\(747\) | −2.94952 | + | 2.94952i | −0.107917 | + | 0.107917i | ||||
\(748\) | −33.6096 | + | 39.3408i | −1.22889 | + | 1.43844i | ||||
\(749\) | 1.54664 | + | 1.54664i | 0.0565128 | + | 0.0565128i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.9523 | 0.983503 | 0.491751 | − | 0.870736i | \(-0.336357\pi\) | ||||
0.491751 | + | 0.870736i | \(0.336357\pi\) | |||||||
\(752\) | −16.0458 | + | 2.53692i | −0.585132 | + | 0.0925118i | ||||
\(753\) | 9.75884 | 0.355632 | ||||||||
\(754\) | −0.0317935 | − | 0.810610i | −0.00115785 | − | 0.0295207i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.3583 | + | 23.3727i | 0.995012 | + | 0.850056i | ||||
\(757\) | −17.0688 | + | 17.0688i | −0.620377 | + | 0.620377i | −0.945628 | − | 0.325251i | \(-0.894551\pi\) |
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(758\) | −23.6380 | + | 25.5680i | −0.858573 | + | 0.928671i | ||||
\(759\) | 6.23290i | 0.226240i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.89608i | 0.249983i | 0.992158 | + | 0.124991i | \(0.0398903\pi\) | ||||
−0.992158 | + | 0.124991i | \(0.960110\pi\) | |||||||
\(762\) | 1.95907 | + | 1.81120i | 0.0709698 | + | 0.0656128i | ||||
\(763\) | −0.705886 | + | 0.705886i | −0.0255548 | + | 0.0255548i | ||||
\(764\) | 34.5544 | − | 2.71474i | 1.25013 | − | 0.0982158i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.7878 | + | 0.501558i | −0.462041 | + | 0.0181220i | ||||
\(767\) | 0.907741 | 0.0327766 | ||||||||
\(768\) | −9.84631 | − | 5.02373i | −0.355298 | − | 0.181278i | ||||
\(769\) | 11.8443 | 0.427117 | 0.213558 | − | 0.976930i | \(-0.431495\pi\) | ||||
0.213558 | + | 0.976930i | \(0.431495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.12679 | + | 4.12679i | 0.148623 | + | 0.148623i | ||||
\(772\) | 33.6297 | − | 2.64209i | 1.21036 | − | 0.0950910i | ||||
\(773\) | 3.58865 | − | 3.58865i | 0.129075 | − | 0.129075i | −0.639618 | − | 0.768693i | \(-0.720907\pi\) |
0.768693 | + | 0.639618i | \(0.220907\pi\) | |||||||
\(774\) | −8.42219 | − | 7.78646i | −0.302729 | − | 0.279878i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −39.2066 | + | 4.63226i | −1.40744 | + | 0.166288i | ||||
\(777\) | 18.3269i | 0.657474i | ||||||||
\(778\) | −20.8567 | + | 22.5595i | −0.747748 | + | 0.808798i | ||||
\(779\) | −14.9622 | + | 14.9622i | −0.536075 | + | 0.536075i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.7705 | + | 17.7705i | 0.635880 | + | 0.635880i | ||||
\(782\) | 0.422319 | + | 10.7675i | 0.0151021 | + | 0.385045i | ||||
\(783\) | −17.6100 | −0.629332 | ||||||||
\(784\) | −60.1925 | + | 9.51668i | −2.14973 | + | 0.339882i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0440558 | + | 1.12325i | 0.00157142 | + | 0.0400650i | ||||
\(787\) | 22.4800 | + | 22.4800i | 0.801326 | + | 0.801326i | 0.983303 | − | 0.181977i | \(-0.0582497\pi\) |
−0.181977 | + | 0.983303i | \(0.558250\pi\) | |||||||
\(788\) | −6.59390 | + | 7.71833i | −0.234898 | + | 0.274954i | ||||
\(789\) | −8.94296 | + | 8.94296i | −0.318378 | + | 0.318378i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 28.1981i | − | 1.00261i | ||||||
\(792\) | 31.0082 | + | 24.4552i | 1.10183 | + | 0.868979i | ||||
\(793\) | − | 1.25272i | − | 0.0444853i | ||||||
\(794\) | −13.8708 | − | 12.8238i | −0.492255 | − | 0.455098i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.04091 | − | 13.2492i | −0.0368941 | − | 0.469605i | ||||
\(797\) | 8.67589 | + | 8.67589i | 0.307316 | + | 0.307316i | 0.843867 | − | 0.536552i | \(-0.180273\pi\) |
−0.536552 | + | 0.843867i | \(0.680273\pi\) | |||||||
\(798\) | −11.8001 | + | 0.462818i | −0.417717 | + | 0.0163836i | ||||
\(799\) | −18.9842 | −0.671612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.18800 | −0.289309 | ||||||||
\(802\) | −30.4903 | + | 1.19588i | −1.07665 | + | 0.0422280i | ||||
\(803\) | −32.5046 | − | 32.5046i | −1.14706 | − | 1.14706i | ||||
\(804\) | 1.14774 | + | 14.6089i | 0.0404775 | + | 0.515216i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.274735 | + | 0.253998i | 0.00967714 | + | 0.00894668i | ||||
\(807\) | − | 13.2515i | − | 0.466476i | ||||||
\(808\) | 33.2138 | − | 42.1138i | 1.16846 | − | 1.48156i | ||||
\(809\) | 27.9066i | 0.981143i | 0.871401 | + | 0.490571i | \(0.163212\pi\) | ||||
−0.871401 | + | 0.490571i | \(0.836788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2635 | − | 15.2635i | 0.535974 | − | 0.535974i | −0.386370 | − | 0.922344i | \(-0.626271\pi\) |
0.922344 | + | 0.386370i | \(0.126271\pi\) | |||||||
\(812\) | 28.2734 | − | 33.0947i | 0.992201 | − | 1.16140i | ||||
\(813\) | 1.09681 | + | 1.09681i | 0.0384670 | + | 0.0384670i | ||||
\(814\) | 1.72574 | + | 43.9996i | 0.0604871 | + | 1.54219i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.4485 | − | 7.59562i | −0.365770 | − | 0.265900i | ||||
\(817\) | 8.24089 | 0.288312 | ||||||||
\(818\) | 0.231309 | + | 5.89749i | 0.00808754 | + | 0.206201i | ||||
\(819\) | 1.04541 | + | 1.04541i | 0.0365295 | + | 0.0365295i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2883 | − | 25.2883i | 0.882567 | − | 0.882567i | −0.111228 | − | 0.993795i | \(-0.535478\pi\) |
0.993795 | + | 0.111228i | \(0.0354782\pi\) | |||||||
\(822\) | −0.132527 | + | 0.143348i | −0.00462242 | + | 0.00499983i | ||||
\(823\) | − | 7.12228i | − | 0.248267i | −0.992266 | − | 0.124133i | \(-0.960385\pi\) | ||
0.992266 | − | 0.124133i | \(-0.0396151\pi\) | |||||||
\(824\) | 4.56778 | + | 38.6609i | 0.159126 | + | 1.34682i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.7634 | + | 33.0639i | 1.24437 | + | 1.15044i | ||||
\(827\) | −32.1618 | + | 32.1618i | −1.11837 | + | 1.11837i | −0.126394 | + | 0.991980i | \(0.540340\pi\) |
−0.991980 | + | 0.126394i | \(0.959660\pi\) | |||||||
\(828\) | 8.19909 | − | 0.644155i | 0.284938 | − | 0.0223859i | ||||
\(829\) | −34.9802 | − | 34.9802i | −1.21491 | − | 1.21491i | −0.969391 | − | 0.245522i | \(-0.921041\pi\) |
−0.245522 | − | 0.969391i | \(-0.578959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.11529 | −0.246827 | ||||||||
\(832\) | −0.847545 | − | 0.519854i | −0.0293833 | − | 0.0180227i | ||||
\(833\) | −71.2149 | −2.46745 | ||||||||
\(834\) | 16.0573 | − | 0.629793i | 0.556018 | − | 0.0218079i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.2862 | + | 2.22228i | −0.978299 | + | 0.0768593i | ||||
\(837\) | 5.74321 | − | 5.74321i | 0.198514 | − | 0.198514i | ||||
\(838\) | 39.8258 | + | 36.8196i | 1.37576 | + | 1.27191i | ||||
\(839\) | − | 11.1147i | − | 0.383721i | −0.981422 | − | 0.191861i | \(-0.938548\pi\) | ||
0.981422 | − | 0.191861i | \(-0.0614521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.69754i | − | 0.265432i | ||||||
\(842\) | −36.6028 | + | 39.5913i | −1.26142 | + | 1.36441i | ||||
\(843\) | −2.95105 | + | 2.95105i | −0.101640 | + | 0.101640i | ||||
\(844\) | 4.10543 | + | 3.50734i | 0.141315 | + | 0.120728i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.567855 | + | 14.4781i | 0.0195233 | + | 0.497767i | ||||
\(847\) | −92.5750 | −3.18092 | ||||||||
\(848\) | −16.7623 | + | 23.0581i | −0.575620 | + | 0.791818i | ||||
\(849\) | 14.7874 | 0.507501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.48436 | + | 6.48436i | 0.222281 | + | 0.222281i | ||||
\(852\) | −4.07532 | + | 4.77027i | −0.139618 | + | 0.163427i | ||||
\(853\) | −28.9107 | + | 28.9107i | −0.989884 | + | 0.989884i | −0.999949 | − | 0.0100656i | \(-0.996796\pi\) |
0.0100656 | + | 0.999949i | \(0.496796\pi\) | |||||||
\(854\) | 45.6295 | − | 49.3550i | 1.56141 | − | 1.68889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.812454 | + | 1.03016i | −0.0277691 | + | 0.0352101i | ||||
\(857\) | − | 34.1485i | − | 1.16649i | −0.812296 | − | 0.583245i | \(-0.801783\pi\) | ||
0.812296 | − | 0.583245i | \(-0.198217\pi\) | |||||||
\(858\) | −0.493486 | − | 0.456237i | −0.0168473 | − | 0.0155757i | ||||
\(859\) | 20.4589 | − | 20.4589i | 0.698047 | − | 0.698047i | −0.265942 | − | 0.963989i | \(-0.585683\pi\) |
0.963989 | + | 0.265942i | \(0.0856829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.0159 | − | 19.0159i | −0.648060 | − | 0.648060i | ||||
\(862\) | −31.6623 | + | 1.24185i | −1.07842 | + | 0.0422976i | ||||
\(863\) | 35.3591 | 1.20364 | 0.601818 | − | 0.798633i | \(-0.294443\pi\) | ||||
0.601818 | + | 0.798633i | \(0.294443\pi\) | |||||||
\(864\) | −11.9972 | + | 17.9419i | −0.408154 | + | 0.610395i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7491 | + | 0.931480i | −0.807028 | + | 0.0316530i | ||||
\(867\) | −2.36940 | − | 2.36940i | −0.0804692 | − | 0.0804692i | ||||
\(868\) | 1.57240 | + | 20.0141i | 0.0533706 | + | 0.679324i | ||||
\(869\) | −45.1304 | + | 45.1304i | −1.53094 | + | 1.53094i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.31809i | 0.0446618i | ||||||||
\(872\) | −0.470165 | − | 0.370804i | −0.0159218 | − | 0.0125570i | ||||
\(873\) | 35.2120i | 1.19175i | ||||||||
\(874\) | −4.01130 | + | 4.33880i | −0.135684 | + | 0.146762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.45430 | − | 8.72545i | 0.251857 | − | 0.294806i | ||||
\(877\) | 3.15415 | + | 3.15415i | 0.106508 | + | 0.106508i | 0.758353 | − | 0.651845i | \(-0.226005\pi\) |
−0.651845 | + | 0.758353i | \(0.726005\pi\) | |||||||
\(878\) | −0.503440 | − | 12.8358i | −0.0169903 | − | 0.433186i | ||||
\(879\) | 10.5301 | 0.355172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3066 | 0.684146 | 0.342073 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342073 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(882\) | 2.13018 | + | 54.3114i | 0.0717270 | + | 1.82876i | ||||
\(883\) | −0.523303 | − | 0.523303i | −0.0176105 | − | 0.0176105i | 0.698247 | − | 0.715857i | \(-0.253964\pi\) |
−0.715857 | + | 0.698247i | \(0.753964\pi\) | |||||||
\(884\) | −0.883423 | − | 0.754723i | −0.0297127 | − | 0.0253841i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0252 | − | 18.4153i | 0.571973 | − | 0.618673i | ||||
\(887\) | 34.8129i | 1.16890i | 0.811429 | + | 0.584452i | \(0.198690\pi\) | ||||
−0.811429 | + | 0.584452i | \(0.801310\pi\) | |||||||
\(888\) | −10.9170 | + | 1.28985i | −0.366352 | + | 0.0432845i | ||||
\(889\) | 12.8766i | 0.431868i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3024 | − | 19.3024i | 0.646656 | − | 0.646656i | ||||
\(892\) | 48.0661 | − | 3.77627i | 1.60937 | − | 0.126439i | ||||
\(893\) | −7.36103 | − | 7.36103i | −0.246328 | − | 0.246328i | ||||
\(894\) | 1.56546 | − | 0.0614001i | 0.0523569 | − | 0.00205353i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.4564 | − | 51.3527i | −0.482956 | − | 1.71557i | ||||
\(897\) | −0.139964 | −0.00467325 | ||||||||
\(898\) | 25.5363 | − | 1.00157i | 0.852156 | − | 0.0334230i | ||||
\(899\) | −6.94743 | − | 6.94743i | −0.231710 | − | 0.231710i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.5562 | + | 23.5562i | −0.784770 | + | 0.784770i | ||||
\(902\) | −47.4444 | − | 43.8631i | −1.57973 | − | 1.46048i | ||||
\(903\) | 10.4736i | 0.348540i | ||||||||
\(904\) | 16.7971 | − | 1.98458i | 0.558664 | − | 0.0660061i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.72384 | + | 5.10952i | −0.156939 | + | 0.169752i | ||||
\(907\) | 13.3188 | − | 13.3188i | 0.442244 | − | 0.442244i | −0.450521 | − | 0.892766i | \(-0.648762\pi\) |
0.892766 | + | 0.450521i | \(0.148762\pi\) | |||||||
\(908\) | 14.3527 | + | 12.2618i | 0.476311 | + | 0.406921i | ||||
\(909\) | −33.8264 | − | 33.8264i | −1.12195 | − | 1.12195i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0117 | −1.55757 | −0.778783 | − | 0.627294i | \(-0.784163\pi\) | ||||
−0.778783 | + | 0.627294i | \(0.784163\pi\) | |||||||
\(912\) | −1.10618 | − | 6.99653i | −0.0366293 | − | 0.231678i | ||||
\(913\) | 9.15148 | 0.302870 | ||||||||
\(914\) | −1.03444 | − | 26.3742i | −0.0342163 | − | 0.872382i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.5436 | − | 34.5815i | 0.976148 | − | 1.14261i | ||||
\(917\) | −3.83624 | + | 3.83624i | −0.126684 | + | 0.126684i | ||||
\(918\) | −17.1223 | + | 18.5203i | −0.565121 | + | 0.611261i | ||||
\(919\) | − | 31.3426i | − | 1.03390i | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||
0.856016 | − | 0.516949i | \(-0.172932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 7.76133i | − | 0.255745i | ||||||
\(922\) | −1.22070 | − | 1.12856i | −0.0402017 | − | 0.0371672i | ||||
\(923\) | −0.399048 | + | 0.399048i | −0.0131348 | + | 0.0131348i | ||||
\(924\) | −2.82437 | − | 35.9499i | −0.0929151 | − | 1.18266i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.0582 | − | 0.433721i | 0.363395 | − | 0.0142529i | ||||
\(927\) | 34.7219 | 1.14042 | ||||||||
\(928\) | 21.7039 | + | 14.5128i | 0.712464 | + | 0.476406i | ||||
\(929\) | 30.3384 | 0.995369 | 0.497685 | − | 0.867358i | \(-0.334184\pi\) | ||||
0.497685 | + | 0.867358i | \(0.334184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6133 | − | 27.6133i | −0.904990 | − | 0.904990i | ||||
\(932\) | 2.58427 | + | 32.8938i | 0.0846507 | + | 1.07747i | ||||
\(933\) | 15.2245 | − | 15.2245i | 0.498429 | − | 0.498429i | ||||
\(934\) | 12.8508 | + | 11.8808i | 0.420492 | + | 0.388752i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.549157 | + | 0.696309i | −0.0179498 | + | 0.0227596i | ||||
\(937\) | 14.5267i | 0.474565i | 0.971441 | + | 0.237283i | \(0.0762567\pi\) | ||||
−0.971441 | + | 0.237283i | \(0.923743\pi\) | |||||||
\(938\) | −48.0107 | + | 51.9306i | −1.56760 | + | 1.69559i | ||||
\(939\) | −2.61767 | + | 2.61767i | −0.0854245 | + | 0.0854245i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2863 | + | 37.2863i | 1.21550 | + | 1.21550i | 0.969192 | + | 0.246307i | \(0.0792172\pi\) |
0.246307 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(942\) | 0.288168 | + | 7.34716i | 0.00938902 | + | 0.239384i | ||||
\(943\) | −13.4563 | −0.438197 | ||||||||
\(944\) | −17.1786 | + | 23.6307i | −0.559116 | + | 0.769115i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.986239 | + | 25.1453i | 0.0320654 | + | 0.817543i | ||||
\(947\) | −15.8961 | − | 15.8961i | −0.516553 | − | 0.516553i | 0.399973 | − | 0.916527i | \(-0.369019\pi\) |
−0.916527 | + | 0.399973i | \(0.869019\pi\) | |||||||
\(948\) | −12.1147 | − | 10.3498i | −0.393466 | − | 0.336145i | ||||
\(949\) | 0.729912 | − | 0.729912i | 0.0236939 | − | 0.0236939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.67765i | 0.281392i | ||||||||
\(952\) | −7.31501 | − | 61.9129i | −0.237081 | − | 2.00661i | ||||
\(953\) | 33.2248i | 1.07626i | 0.842862 | + | 0.538129i | \(0.180869\pi\) | ||||
−0.842862 | + | 0.538129i | \(0.819131\pi\) | |||||||
\(954\) | 18.6695 | + | 17.2603i | 0.604447 | + | 0.558822i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.4860 | − | 0.823827i | 0.339143 | − | 0.0266445i | ||||
\(957\) | 12.4791 | + | 12.4791i | 0.403393 | + | 0.403393i | ||||
\(958\) | 2.97346 | − | 0.116624i | 0.0960682 | − | 0.00376796i | ||||
\(959\) | −0.942197 | −0.0304251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4684 | −0.853820 | ||||||||
\(962\) | −0.988038 | + | 0.0387525i | −0.0318556 | + | 0.00124943i | ||||
\(963\) | 0.827438 | + | 0.827438i | 0.0266638 | + | 0.0266638i | ||||
\(964\) | −28.1386 | + | 2.21069i | −0.906283 | + | 0.0712014i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.51433 | − | 5.09809i | −0.177421 | − | 0.164028i | ||||
\(967\) | − | 1.79116i | − | 0.0576000i | −0.999585 | − | 0.0288000i | \(-0.990831\pi\) | ||
0.999585 | − | 0.0288000i | \(-0.00916859\pi\) | |||||||
\(968\) | −6.51543 | − | 55.1455i | −0.209414 | − | 1.77244i | ||||
\(969\) | − | 8.27774i | − | 0.265919i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.31278 | − | 5.31278i | 0.170495 | − | 0.170495i | −0.616702 | − | 0.787197i | \(-0.711531\pi\) |
0.787197 | + | 0.616702i | \(0.211531\pi\) | |||||||
\(972\) | 22.5872 | + | 19.2966i | 0.724485 | + | 0.618940i | ||||
\(973\) | 54.8404 | + | 54.8404i | 1.75810 | + | 1.75810i | ||||
\(974\) | −0.270022 | − | 6.88451i | −0.00865207 | − | 0.220594i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.6114 | + | 23.7072i | 1.04386 | + | 0.758848i | ||||
\(977\) | −6.81676 | −0.218088 | −0.109044 | − | 0.994037i | \(-0.534779\pi\) | ||||
−0.109044 | + | 0.994037i | \(0.534779\pi\) | |||||||
\(978\) | 0.666126 | + | 16.9836i | 0.0213003 | + | 0.543076i | ||||
\(979\) | 12.7025 | + | 12.7025i | 0.405972 | + | 0.405972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.377643 | + | 0.377643i | −0.0120572 | + | 0.0120572i | ||||
\(982\) | 19.4941 | − | 21.0857i | 0.622082 | − | 0.672873i | ||||
\(983\) | 5.49468i | 0.175253i | 0.996153 | + | 0.0876265i | \(0.0279282\pi\) | ||||
−0.996153 | + | 0.0876265i | \(0.972072\pi\) | |||||||
\(984\) | 9.98913 | − | 12.6658i | 0.318442 | − | 0.403771i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.4036 | + | 20.7125i | 0.713475 | + | 0.659620i | ||||
\(987\) | 9.35538 | − | 9.35538i | 0.297785 | − | 0.297785i | ||||
\(988\) | −0.0499028 | − | 0.635184i | −0.00158762 | − | 0.0202079i | ||||
\(989\) | 3.70574 | + | 3.70574i | 0.117836 | + | 0.117836i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.7524 | 1.54867 | 0.774335 | − | 0.632775i | \(-0.218084\pi\) | ||||
0.774335 | + | 0.632775i | \(0.218084\pi\) | |||||||
\(992\) | −11.8114 | + | 2.34525i | −0.375013 | + | 0.0744616i | ||||
\(993\) | −5.93333 | −0.188289 | ||||||||
\(994\) | −30.2569 | + | 1.18673i | −0.959691 | + | 0.0376407i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.178942 | + | 2.27766i | 0.00567000 | + | 0.0721703i | ||||
\(997\) | 42.5246 | − | 42.5246i | 1.34677 | − | 1.34677i | 0.457618 | − | 0.889149i | \(-0.348703\pi\) |
0.889149 | − | 0.457618i | \(-0.151297\pi\) | |||||||
\(998\) | −36.8694 | − | 34.0864i | −1.16708 | − | 1.07899i | ||||
\(999\) | 21.4646i | 0.679109i |
(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 | 400.2.l.f.301.6 | yes | 12 | |
4.3 | odd | 2 | 1600.2.l.g.401.4 | 12 | |||
5.2 | odd | 4 | 400.2.q.f.349.3 | 12 | |||
5.3 | odd | 4 | 400.2.q.e.349.4 | 12 | |||
5.4 | even | 2 | 400.2.l.g.301.1 | yes | 12 | ||
16.5 | even | 4 | inner | 400.2.l.f.101.6 | ✓ | 12 | |
16.11 | odd | 4 | 1600.2.l.g.1201.4 | 12 | |||
20.3 | even | 4 | 1600.2.q.e.849.3 | 12 | |||
20.7 | even | 4 | 1600.2.q.f.849.4 | 12 | |||
20.19 | odd | 2 | 1600.2.l.f.401.3 | 12 | |||
80.27 | even | 4 | 1600.2.q.e.49.3 | 12 | |||
80.37 | odd | 4 | 400.2.q.e.149.4 | 12 | |||
80.43 | even | 4 | 1600.2.q.f.49.4 | 12 | |||
80.53 | odd | 4 | 400.2.q.f.149.3 | 12 | |||
80.59 | odd | 4 | 1600.2.l.f.1201.3 | 12 | |||
80.69 | even | 4 | 400.2.l.g.101.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.6 | ✓ | 12 | 16.5 | even | 4 | inner | |
400.2.l.f.301.6 | yes | 12 | 1.1 | even | 1 | trivial | |
400.2.l.g.101.1 | yes | 12 | 80.69 | even | 4 | ||
400.2.l.g.301.1 | yes | 12 | 5.4 | even | 2 | ||
400.2.q.e.149.4 | 12 | 80.37 | odd | 4 | |||
400.2.q.e.349.4 | 12 | 5.3 | odd | 4 | |||
400.2.q.f.149.3 | 12 | 80.53 | odd | 4 | |||
400.2.q.f.349.3 | 12 | 5.2 | odd | 4 | |||
1600.2.l.f.401.3 | 12 | 20.19 | odd | 2 | |||
1600.2.l.f.1201.3 | 12 | 80.59 | odd | 4 | |||
1600.2.l.g.401.4 | 12 | 4.3 | odd | 2 | |||
1600.2.l.g.1201.4 | 12 | 16.11 | odd | 4 | |||
1600.2.q.e.49.3 | 12 | 80.27 | even | 4 | |||
1600.2.q.e.849.3 | 12 | 20.3 | even | 4 | |||
1600.2.q.f.49.4 | 12 | 80.43 | even | 4 | |||
1600.2.q.f.849.4 | 12 | 20.7 | even | 4 |