Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (of order \(9\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 301.2 | ||
Root | \(-0.288205 + 0.499186i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.301 |
Dual form | 950.2.l.i.101.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.766044 | + | 0.642788i | 0.541675 | + | 0.454519i | ||||
\(3\) | 0.541649 | − | 0.197144i | 0.312721 | − | 0.113821i | −0.180892 | − | 0.983503i | \(-0.557898\pi\) |
0.493613 | + | 0.869682i | \(0.335676\pi\) | |||||||
\(4\) | 0.173648 | + | 0.984808i | 0.0868241 | + | 0.492404i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.541649 | + | 0.197144i | 0.221127 | + | 0.0804837i | ||||
\(7\) | −2.43209 | − | 4.21251i | −0.919245 | − | 1.59218i | −0.800564 | − | 0.599247i | \(-0.795467\pi\) |
−0.118681 | − | 0.992932i | \(-0.537866\pi\) | |||||||
\(8\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | ||||
\(9\) | −2.04362 | + | 1.71480i | −0.681205 | + | 0.571599i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.68454 | − | 4.64975i | 0.809418 | − | 1.40195i | −0.103850 | − | 0.994593i | \(-0.533116\pi\) |
0.913268 | − | 0.407360i | \(-0.133550\pi\) | |||||||
\(12\) | 0.288205 | + | 0.499186i | 0.0831977 | + | 0.144103i | ||||
\(13\) | −3.62457 | − | 1.31923i | −1.00527 | − | 0.365890i | −0.213658 | − | 0.976909i | \(-0.568538\pi\) |
−0.791616 | + | 0.611019i | \(0.790760\pi\) | |||||||
\(14\) | 0.844657 | − | 4.79029i | 0.225744 | − | 1.28026i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.234923 | + | 0.0855050i | ||||
\(17\) | −1.07407 | − | 0.901248i | −0.260499 | − | 0.218585i | 0.503178 | − | 0.864183i | \(-0.332164\pi\) |
−0.763678 | + | 0.645598i | \(0.776608\pi\) | |||||||
\(18\) | −2.66775 | −0.628795 | ||||||||
\(19\) | 4.35299 | − | 0.226908i | 0.998644 | − | 0.0520563i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14781 | − | 1.80223i | −0.468691 | − | 0.393278i | ||||
\(22\) | 5.04528 | − | 1.83633i | 1.07566 | − | 0.391507i | ||||
\(23\) | −0.927092 | − | 5.25780i | −0.193312 | − | 1.09633i | −0.914802 | − | 0.403902i | \(-0.867654\pi\) |
0.721490 | − | 0.692425i | \(-0.243457\pi\) | |||||||
\(24\) | −0.100093 | + | 0.567654i | −0.0204313 | + | 0.115872i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.92859 | − | 3.34042i | −0.378228 | − | 0.655110i | ||||
\(27\) | −1.63348 | + | 2.82926i | −0.314363 | + | 0.544492i | ||||
\(28\) | 3.72618 | − | 3.12664i | 0.704183 | − | 0.590879i | ||||
\(29\) | −2.78364 | + | 2.33575i | −0.516908 | + | 0.433738i | −0.863552 | − | 0.504259i | \(-0.831766\pi\) |
0.346644 | + | 0.937997i | \(0.387321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.10189 | − | 7.10468i | −0.736721 | − | 1.27604i | −0.953964 | − | 0.299920i | \(-0.903040\pi\) |
0.217244 | − | 0.976117i | \(-0.430293\pi\) | |||||||
\(32\) | −0.939693 | − | 0.342020i | −0.166116 | − | 0.0604612i | ||||
\(33\) | 0.537405 | − | 3.04777i | 0.0935501 | − | 0.530549i | ||||
\(34\) | −0.243471 | − | 1.38079i | −0.0417549 | − | 0.236804i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.04362 | − | 1.71480i | −0.340603 | − | 0.285800i | ||||
\(37\) | 10.4594 | 1.71951 | 0.859755 | − | 0.510706i | \(-0.170616\pi\) | ||||
0.859755 | + | 0.510706i | \(0.170616\pi\) | |||||||
\(38\) | 3.48044 | + | 2.62423i | 0.564601 | + | 0.425706i | ||||
\(39\) | −2.22332 | −0.356016 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79322 | − | 0.652678i | 0.280054 | − | 0.101931i | −0.198175 | − | 0.980167i | \(-0.563501\pi\) |
0.478228 | + | 0.878236i | \(0.341279\pi\) | |||||||
\(42\) | −0.486869 | − | 2.76117i | −0.0751256 | − | 0.426058i | ||||
\(43\) | −0.256764 | + | 1.45618i | −0.0391561 | + | 0.222065i | −0.998107 | − | 0.0615084i | \(-0.980409\pi\) |
0.958950 | + | 0.283574i | \(0.0915200\pi\) | |||||||
\(44\) | 5.04528 | + | 1.83633i | 0.760604 | + | 0.276837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.66945 | − | 4.62363i | 0.393590 | − | 0.681717i | ||||
\(47\) | 2.39030 | − | 2.00570i | 0.348661 | − | 0.292561i | −0.451591 | − | 0.892225i | \(-0.649143\pi\) |
0.800252 | + | 0.599664i | \(0.204699\pi\) | |||||||
\(48\) | −0.441556 | + | 0.370510i | −0.0637331 | + | 0.0534785i | ||||
\(49\) | −8.33016 | + | 14.4283i | −1.19002 | + | 2.06118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.759442 | − | 0.276414i | −0.106343 | − | 0.0387058i | ||||
\(52\) | 0.669793 | − | 3.79858i | 0.0928835 | − | 0.526769i | ||||
\(53\) | 0.312568 | + | 1.77266i | 0.0429346 | + | 0.243494i | 0.998721 | − | 0.0505691i | \(-0.0161035\pi\) |
−0.955786 | + | 0.294063i | \(0.904992\pi\) | |||||||
\(54\) | −3.06993 | + | 1.11736i | −0.417765 | + | 0.152054i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.86419 | 0.650004 | ||||||||
\(57\) | 2.31306 | − | 0.981070i | 0.306372 | − | 0.129946i | ||||
\(58\) | −3.63378 | −0.477139 | ||||||||
\(59\) | −5.61133 | − | 4.70846i | −0.730532 | − | 0.612990i | 0.199744 | − | 0.979848i | \(-0.435989\pi\) |
−0.930277 | + | 0.366859i | \(0.880433\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40916 | + | 7.99176i | 0.180425 | + | 1.02324i | 0.931694 | + | 0.363244i | \(0.118331\pi\) |
−0.751269 | + | 0.659996i | \(0.770558\pi\) | |||||||
\(62\) | 1.42457 | − | 8.07914i | 0.180921 | − | 1.02605i | ||||
\(63\) | 12.1939 | + | 4.43820i | 1.53628 | + | 0.559161i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.37075 | − | 1.98929i | 0.291819 | − | 0.244865i | ||||
\(67\) | −6.46916 | + | 5.42827i | −0.790334 | + | 0.663169i | −0.945828 | − | 0.324668i | \(-0.894747\pi\) |
0.155494 | + | 0.987837i | \(0.450303\pi\) | |||||||
\(68\) | 0.701047 | − | 1.21425i | 0.0850144 | − | 0.147249i | ||||
\(69\) | −1.53870 | − | 2.66511i | −0.185238 | − | 0.320842i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.04647 | − | 5.93485i | 0.124194 | − | 0.704337i | −0.857590 | − | 0.514334i | \(-0.828039\pi\) |
0.981783 | − | 0.190003i | \(-0.0608498\pi\) | |||||||
\(72\) | −0.463250 | − | 2.62722i | −0.0545945 | − | 0.309621i | ||||
\(73\) | −1.19931 | + | 0.436515i | −0.140369 | + | 0.0510902i | −0.411249 | − | 0.911523i | \(-0.634907\pi\) |
0.270880 | + | 0.962613i | \(0.412685\pi\) | |||||||
\(74\) | 8.01234 | + | 6.72316i | 0.931416 | + | 0.781551i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.979350 | + | 4.24746i | 0.112339 | + | 0.487217i | ||||
\(77\) | −26.1162 | −2.97621 | ||||||||
\(78\) | −1.70316 | − | 1.42912i | −0.192845 | − | 0.161816i | ||||
\(79\) | 15.6290 | − | 5.68848i | 1.75840 | − | 0.640004i | 0.758465 | − | 0.651714i | \(-0.225950\pi\) |
0.999931 | + | 0.0117101i | \(0.00372754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.06275 | − | 6.02717i | 0.118084 | − | 0.669685i | ||||
\(82\) | 1.79322 | + | 0.652678i | 0.198028 | + | 0.0720762i | ||||
\(83\) | 7.23049 | + | 12.5236i | 0.793649 | + | 1.37464i | 0.923693 | + | 0.383133i | \(0.125155\pi\) |
−0.130044 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(84\) | 1.40188 | − | 2.42814i | 0.152958 | − | 0.264931i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.13271 | + | 0.950453i | −0.122143 | + | 0.102490i | ||||
\(87\) | −1.04727 | + | 1.81393i | −0.112280 | + | 0.194474i | ||||
\(88\) | 2.68454 | + | 4.64975i | 0.286172 | + | 0.495665i | ||||
\(89\) | −9.02905 | − | 3.28630i | −0.957077 | − | 0.348348i | −0.184190 | − | 0.982891i | \(-0.558966\pi\) |
−0.772887 | + | 0.634543i | \(0.781188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25800 | + | 18.4770i | 0.341531 | + | 1.93692i | ||||
\(92\) | 5.01693 | − | 1.82601i | 0.523051 | − | 0.190375i | ||||
\(93\) | −3.62243 | − | 3.03958i | −0.375628 | − | 0.315189i | ||||
\(94\) | 3.12031 | 0.321836 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.576411 | −0.0588297 | ||||||||
\(97\) | 4.65687 | + | 3.90758i | 0.472834 | + | 0.396755i | 0.847827 | − | 0.530273i | \(-0.177911\pi\) |
−0.374993 | + | 0.927028i | \(0.622355\pi\) | |||||||
\(98\) | −15.6556 | + | 5.69817i | −1.58145 | + | 0.575602i | ||||
\(99\) | 2.48722 | + | 14.1057i | 0.249975 | + | 1.41768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.17995 | − | 0.429466i | −0.117409 | − | 0.0427335i | 0.282647 | − | 0.959224i | \(-0.408787\pi\) |
−0.400057 | + | 0.916490i | \(0.631010\pi\) | |||||||
\(102\) | −0.404091 | − | 0.699906i | −0.0400109 | − | 0.0693010i | ||||
\(103\) | 3.68352 | − | 6.38005i | 0.362948 | − | 0.628645i | −0.625496 | − | 0.780227i | \(-0.715103\pi\) |
0.988445 | + | 0.151582i | \(0.0484368\pi\) | |||||||
\(104\) | 2.95477 | − | 2.47935i | 0.289739 | − | 0.243120i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.900005 | + | 1.55885i | −0.0874162 | + | 0.151409i | ||||
\(107\) | −4.36539 | − | 7.56108i | −0.422018 | − | 0.730957i | 0.574119 | − | 0.818772i | \(-0.305345\pi\) |
−0.996137 | + | 0.0878153i | \(0.972011\pi\) | |||||||
\(108\) | −3.06993 | − | 1.11736i | −0.295404 | − | 0.107518i | ||||
\(109\) | 1.41173 | − | 8.00630i | 0.135219 | − | 0.766865i | −0.839488 | − | 0.543378i | \(-0.817145\pi\) |
0.974707 | − | 0.223487i | \(-0.0717439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66531 | − | 2.06200i | 0.537727 | − | 0.195717i | ||||
\(112\) | 3.72618 | + | 3.12664i | 0.352091 | + | 0.295440i | ||||
\(113\) | 4.48210 | 0.421640 | 0.210820 | − | 0.977525i | \(-0.432387\pi\) | ||||
0.210820 | + | 0.977525i | \(0.432387\pi\) | |||||||
\(114\) | 2.40253 | + | 0.735261i | 0.225017 | + | 0.0688635i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.78364 | − | 2.33575i | −0.258454 | − | 0.216869i | ||||
\(117\) | 9.66944 | − | 3.51939i | 0.893940 | − | 0.325368i | ||||
\(118\) | −1.27198 | − | 7.21378i | −0.117096 | − | 0.664082i | ||||
\(119\) | −1.18429 | + | 6.71643i | −0.108564 | + | 0.615694i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.91346 | − | 15.4386i | −0.810314 | − | 1.40351i | ||||
\(122\) | −4.05753 | + | 7.02784i | −0.367351 | + | 0.636271i | ||||
\(123\) | 0.842623 | − | 0.707045i | 0.0759768 | − | 0.0637521i | ||||
\(124\) | 6.28445 | − | 5.27328i | 0.564361 | − | 0.473555i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.48822 | + | 11.2379i | 0.578017 | + | 1.00115i | ||||
\(127\) | −0.130789 | − | 0.0476033i | −0.0116057 | − | 0.00422411i | 0.336211 | − | 0.941787i | \(-0.390855\pi\) |
−0.347816 | + | 0.937563i | \(0.613077\pi\) | |||||||
\(128\) | 0.173648 | − | 0.984808i | 0.0153485 | − | 0.0870455i | ||||
\(129\) | 0.148001 | + | 0.839357i | 0.0130308 | + | 0.0739013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.52200 | + | 7.98991i | 0.831941 | + | 0.698082i | 0.955736 | − | 0.294226i | \(-0.0950620\pi\) |
−0.123795 | + | 0.992308i | \(0.539506\pi\) | |||||||
\(132\) | 3.09479 | 0.269367 | ||||||||
\(133\) | −11.5427 | − | 17.7851i | −1.00088 | − | 1.54217i | ||||
\(134\) | −8.44489 | −0.729528 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.31754 | − | 0.479544i | 0.112978 | − | 0.0411206i | ||||
\(137\) | 2.49734 | + | 14.1631i | 0.213362 | + | 1.21004i | 0.883726 | + | 0.468004i | \(0.155027\pi\) |
−0.670364 | + | 0.742032i | \(0.733862\pi\) | |||||||
\(138\) | 0.534386 | − | 3.03065i | 0.0454899 | − | 0.257986i | ||||
\(139\) | −16.7746 | − | 6.10544i | −1.42280 | − | 0.517857i | −0.487941 | − | 0.872877i | \(-0.662252\pi\) |
−0.934859 | + | 0.355020i | \(0.884474\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.899291 | − | 1.55762i | 0.0757340 | − | 0.131175i | ||||
\(142\) | 4.61650 | − | 3.87370i | 0.387408 | − | 0.325074i | ||||
\(143\) | −15.8644 | + | 13.3118i | −1.32665 | + | 1.11319i | ||||
\(144\) | 1.33388 | − | 2.31034i | 0.111156 | − | 0.192528i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.19931 | − | 0.436515i | −0.0992559 | − | 0.0361262i | ||||
\(147\) | −1.66758 | + | 9.45729i | −0.137539 | + | 0.780024i | ||||
\(148\) | 1.81625 | + | 10.3005i | 0.149295 | + | 0.846694i | ||||
\(149\) | 2.71250 | − | 0.987271i | 0.222217 | − | 0.0808804i | −0.228512 | − | 0.973541i | \(-0.573386\pi\) |
0.450729 | + | 0.892661i | \(0.351164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.01805 | 0.164226 | 0.0821132 | − | 0.996623i | \(-0.473833\pi\) | ||||
0.0821132 | + | 0.996623i | \(0.473833\pi\) | |||||||
\(152\) | −1.97999 | + | 3.88325i | −0.160598 | + | 0.314973i | ||||
\(153\) | 3.74044 | 0.302396 | ||||||||
\(154\) | −20.0061 | − | 16.7871i | −1.61214 | − | 1.35275i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.386076 | − | 2.18954i | −0.0309108 | − | 0.175304i | ||||
\(157\) | 1.91697 | − | 10.8717i | 0.152991 | − | 0.867655i | −0.807609 | − | 0.589719i | \(-0.799239\pi\) |
0.960600 | − | 0.277936i | \(-0.0896504\pi\) | |||||||
\(158\) | 15.6290 | + | 5.68848i | 1.24337 | + | 0.452551i | ||||
\(159\) | 0.518772 | + | 0.898540i | 0.0411413 | + | 0.0712589i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8938 | + | 16.6928i | −1.56785 | + | 1.31558i | ||||
\(162\) | 4.68830 | − | 3.93395i | 0.368348 | − | 0.309081i | ||||
\(163\) | −2.96434 | + | 5.13439i | −0.232185 | + | 0.402157i | −0.958451 | − | 0.285257i | \(-0.907921\pi\) |
0.726266 | + | 0.687414i | \(0.241254\pi\) | |||||||
\(164\) | 0.954151 | + | 1.65264i | 0.0745067 | + | 0.129049i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.51112 | + | 14.2413i | −0.194901 | + | 1.10534i | ||||
\(167\) | −1.25507 | − | 7.11784i | −0.0971200 | − | 0.550795i | −0.994077 | − | 0.108677i | \(-0.965339\pi\) |
0.896957 | − | 0.442118i | \(-0.145773\pi\) | |||||||
\(168\) | 2.63468 | − | 0.958946i | 0.203270 | − | 0.0739843i | ||||
\(169\) | 1.43852 | + | 1.20707i | 0.110656 | + | 0.0928512i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.50673 | + | 7.92821i | −0.650526 | + | 0.606285i | ||||
\(172\) | −1.47864 | −0.112745 | ||||||||
\(173\) | 3.95167 | + | 3.31585i | 0.300440 | + | 0.252099i | 0.780528 | − | 0.625121i | \(-0.214951\pi\) |
−0.480087 | + | 0.877221i | \(0.659395\pi\) | |||||||
\(174\) | −1.96823 | + | 0.716378i | −0.149211 | + | 0.0543085i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.932329 | + | 5.28750i | −0.0702770 | + | 0.398560i | ||||
\(177\) | −3.96761 | − | 1.44409i | −0.298224 | − | 0.108545i | ||||
\(178\) | −4.80426 | − | 8.32122i | −0.360094 | − | 0.623701i | ||||
\(179\) | −4.09186 | + | 7.08730i | −0.305840 | + | 0.529730i | −0.977448 | − | 0.211177i | \(-0.932270\pi\) |
0.671608 | + | 0.740906i | \(0.265604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.62934 | + | 2.20628i | −0.195437 | + | 0.163991i | −0.735255 | − | 0.677791i | \(-0.762938\pi\) |
0.539818 | + | 0.841782i | \(0.318493\pi\) | |||||||
\(182\) | −9.38103 | + | 16.2484i | −0.695368 | + | 1.20441i | ||||
\(183\) | 2.33880 | + | 4.05092i | 0.172889 | + | 0.299453i | ||||
\(184\) | 5.01693 | + | 1.82601i | 0.369853 | + | 0.134616i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.821137 | − | 4.65690i | −0.0602087 | − | 0.341461i | ||||
\(187\) | −7.07395 | + | 2.57471i | −0.517298 | + | 0.188281i | ||||
\(188\) | 2.39030 | + | 2.00570i | 0.174330 | + | 0.146281i | ||||
\(189\) | 15.8911 | 1.15591 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.77584 | 0.273210 | 0.136605 | − | 0.990626i | \(-0.456381\pi\) | ||||
0.136605 | + | 0.990626i | \(0.456381\pi\) | |||||||
\(192\) | −0.441556 | − | 0.370510i | −0.0318666 | − | 0.0267392i | ||||
\(193\) | 11.4435 | − | 4.16508i | 0.823718 | − | 0.299809i | 0.104440 | − | 0.994531i | \(-0.466695\pi\) |
0.719278 | + | 0.694722i | \(0.244473\pi\) | |||||||
\(194\) | 1.05563 | + | 5.98676i | 0.0757896 | + | 0.429824i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.6556 | − | 5.69817i | −1.11826 | − | 0.407012i | ||||
\(197\) | 3.60118 | + | 6.23743i | 0.256574 | + | 0.444399i | 0.965322 | − | 0.261063i | \(-0.0840731\pi\) |
−0.708748 | + | 0.705462i | \(0.750740\pi\) | |||||||
\(198\) | −7.16167 | + | 12.4044i | −0.508958 | + | 0.881541i | ||||
\(199\) | 4.47147 | − | 3.75201i | 0.316974 | − | 0.265973i | −0.470393 | − | 0.882457i | \(-0.655888\pi\) |
0.787367 | + | 0.616484i | \(0.211443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.43386 | + | 4.21557i | −0.171671 | + | 0.297344i | ||||
\(202\) | −0.627838 | − | 1.08745i | −0.0441745 | − | 0.0765125i | ||||
\(203\) | 16.6094 | + | 6.04534i | 1.16575 | + | 0.424299i | ||||
\(204\) | 0.140339 | − | 0.795903i | 0.00982571 | − | 0.0557244i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.92276 | − | 2.51968i | 0.482332 | − | 0.175554i | ||||
\(207\) | 10.9107 | + | 9.15514i | 0.758344 | + | 0.636327i | ||||
\(208\) | 3.85718 | 0.267448 | ||||||||
\(209\) | 10.6307 | − | 20.8495i | 0.735340 | − | 1.44219i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.17443 | + | 6.85916i | 0.562751 | + | 0.472204i | 0.879231 | − | 0.476395i | \(-0.158057\pi\) |
−0.316481 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(212\) | −1.69146 | + | 0.615640i | −0.116170 | + | 0.0422823i | ||||
\(213\) | −0.603199 | − | 3.42091i | −0.0413305 | − | 0.234397i | ||||
\(214\) | 1.51608 | − | 8.59814i | 0.103637 | − | 0.587757i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.63348 | − | 2.82926i | −0.111144 | − | 0.192507i | ||||
\(217\) | −19.9523 | + | 34.5585i | −1.35445 | + | 2.34598i | ||||
\(218\) | 6.22780 | − | 5.22574i | 0.421800 | − | 0.353932i | ||||
\(219\) | −0.563551 | + | 0.472875i | −0.0380812 | + | 0.0319539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.70407 | + | 4.68358i | 0.181895 | + | 0.315052i | ||||
\(222\) | 5.66531 | + | 2.06200i | 0.380231 | + | 0.138393i | ||||
\(223\) | 0.0172725 | − | 0.0979573i | 0.00115665 | − | 0.00655971i | −0.984224 | − | 0.176927i | \(-0.943384\pi\) |
0.985381 | + | 0.170367i | \(0.0544954\pi\) | |||||||
\(224\) | 0.844657 | + | 4.79029i | 0.0564360 | + | 0.320065i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.43349 | + | 2.88104i | 0.228392 | + | 0.191644i | ||||
\(227\) | 13.8262 | 0.917680 | 0.458840 | − | 0.888519i | \(-0.348265\pi\) | ||||
0.458840 | + | 0.888519i | \(0.348265\pi\) | |||||||
\(228\) | 1.36782 | + | 2.10756i | 0.0905864 | + | 0.139576i | ||||
\(229\) | 15.5752 | 1.02924 | 0.514619 | − | 0.857419i | \(-0.327934\pi\) | ||||
0.514619 | + | 0.857419i | \(0.327934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1458 | + | 5.14865i | −0.930725 | + | 0.338756i | ||||
\(232\) | −0.630999 | − | 3.57857i | −0.0414271 | − | 0.234945i | ||||
\(233\) | 2.64658 | − | 15.0095i | 0.173384 | − | 0.983307i | −0.766610 | − | 0.642113i | \(-0.778058\pi\) |
0.939993 | − | 0.341193i | \(-0.110831\pi\) | |||||||
\(234\) | 9.66944 | + | 3.51939i | 0.632111 | + | 0.230070i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.66253 | − | 6.34369i | 0.238411 | − | 0.412939i | ||||
\(237\) | 7.34396 | − | 6.16232i | 0.477042 | − | 0.400285i | ||||
\(238\) | −5.22446 | + | 4.38384i | −0.338651 | + | 0.284162i | ||||
\(239\) | −8.41167 | + | 14.5694i | −0.544106 | + | 0.942419i | 0.454557 | + | 0.890718i | \(0.349798\pi\) |
−0.998663 | + | 0.0517011i | \(0.983536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.55776 | + | 3.11477i | 0.551254 | + | 0.200640i | 0.602604 | − | 0.798041i | \(-0.294130\pi\) |
−0.0513496 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(242\) | 3.09561 | − | 17.5561i | 0.198993 | − | 1.12855i | ||||
\(243\) | −2.31448 | − | 13.1261i | −0.148474 | − | 0.842039i | ||||
\(244\) | −7.62565 | + | 2.77551i | −0.488182 | + | 0.177684i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.09997 | 0.0701313 | ||||||||
\(247\) | −16.0770 | − | 4.92017i | −1.02296 | − | 0.313063i | ||||
\(248\) | 8.20377 | 0.520940 | ||||||||
\(249\) | 6.38533 | + | 5.35793i | 0.404654 | + | 0.339545i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91829 | + | 16.5504i | 0.184201 | + | 1.04465i | 0.926978 | + | 0.375116i | \(0.122397\pi\) |
−0.742777 | + | 0.669539i | \(0.766492\pi\) | |||||||
\(252\) | −2.25334 | + | 12.7793i | −0.141947 | + | 0.805020i | ||||
\(253\) | −26.9363 | − | 9.80400i | −1.69347 | − | 0.616372i | ||||
\(254\) | −0.0695914 | − | 0.120536i | −0.00436655 | − | 0.00756309i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | 7.58176 | − | 6.36185i | 0.472937 | − | 0.396841i | −0.374927 | − | 0.927054i | \(-0.622332\pi\) |
0.847865 | + | 0.530213i | \(0.177888\pi\) | |||||||
\(258\) | −0.426153 | + | 0.738118i | −0.0265311 | + | 0.0459532i | ||||
\(259\) | −25.4382 | − | 44.0602i | −1.58065 | − | 2.73777i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.68335 | − | 9.54674i | 0.104197 | − | 0.590929i | ||||
\(262\) | 2.15846 | + | 12.2412i | 0.133350 | + | 0.756267i | ||||
\(263\) | −21.0609 | + | 7.66554i | −1.29867 | + | 0.472677i | −0.896564 | − | 0.442915i | \(-0.853944\pi\) |
−0.402107 | + | 0.915593i | \(0.631722\pi\) | |||||||
\(264\) | 2.37075 | + | 1.98929i | 0.145909 | + | 0.122432i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.58983 | − | 21.0437i | 0.158793 | − | 1.29027i | ||||
\(267\) | −5.53845 | −0.338948 | ||||||||
\(268\) | −6.46916 | − | 5.42827i | −0.395167 | − | 0.331584i | ||||
\(269\) | −7.02217 | + | 2.55586i | −0.428149 | + | 0.155834i | −0.547101 | − | 0.837066i | \(-0.684269\pi\) |
0.118952 | + | 0.992900i | \(0.462047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.84950 | + | 10.4890i | −0.112349 | + | 0.637163i | 0.875680 | + | 0.482893i | \(0.160414\pi\) |
−0.988029 | + | 0.154271i | \(0.950697\pi\) | |||||||
\(272\) | 1.31754 | + | 0.479544i | 0.0798874 | + | 0.0290766i | ||||
\(273\) | 5.40733 | + | 9.36576i | 0.327266 | + | 0.566842i | ||||
\(274\) | −7.19080 | + | 12.4548i | −0.434412 | + | 0.752424i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.35743 | − | 1.97812i | 0.141900 | − | 0.119069i | ||||
\(277\) | −1.16317 | + | 2.01467i | −0.0698880 | + | 0.121050i | −0.898852 | − | 0.438253i | \(-0.855598\pi\) |
0.828964 | + | 0.559302i | \(0.188931\pi\) | |||||||
\(278\) | −8.92555 | − | 15.4595i | −0.535319 | − | 0.927200i | ||||
\(279\) | 20.5658 | + | 7.48532i | 1.23124 | + | 0.448135i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.96472 | − | 16.8137i | −0.176860 | − | 1.00302i | −0.935975 | − | 0.352067i | \(-0.885479\pi\) |
0.759115 | − | 0.650957i | \(-0.225632\pi\) | |||||||
\(282\) | 1.69011 | − | 0.615151i | 0.100645 | − | 0.0366317i | ||||
\(283\) | −6.48680 | − | 5.44307i | −0.385600 | − | 0.323557i | 0.429296 | − | 0.903164i | \(-0.358762\pi\) |
−0.814896 | + | 0.579607i | \(0.803206\pi\) | |||||||
\(284\) | 6.02641 | 0.357601 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.7095 | −1.22458 | ||||||||
\(287\) | −7.11069 | − | 5.96658i | −0.419731 | − | 0.352196i | ||||
\(288\) | 2.50687 | − | 0.912424i | 0.147718 | − | 0.0537651i | ||||
\(289\) | −2.61065 | − | 14.8057i | −0.153568 | − | 0.870925i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.29275 | + | 1.19846i | 0.193024 | + | 0.0702551i | ||||
\(292\) | −0.638142 | − | 1.10529i | −0.0373444 | − | 0.0646824i | ||||
\(293\) | −1.29622 | + | 2.24512i | −0.0757260 | + | 0.131161i | −0.901402 | − | 0.432984i | \(-0.857461\pi\) |
0.825676 | + | 0.564145i | \(0.190794\pi\) | |||||||
\(294\) | −7.35647 | + | 6.17281i | −0.429038 | + | 0.360006i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.22969 | + | 9.05808i | −0.303969 | + | 0.526490i | ||||
\(297\) | 8.77025 | + | 15.1905i | 0.508901 | + | 0.881443i | ||||
\(298\) | 2.71250 | + | 0.987271i | 0.157131 | + | 0.0571911i | ||||
\(299\) | −3.57596 | + | 20.2803i | −0.206803 | + | 1.17284i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.75864 | − | 2.45994i | 0.389562 | − | 0.141789i | ||||
\(302\) | 1.54591 | + | 1.29718i | 0.0889573 | + | 0.0746441i | ||||
\(303\) | −0.723785 | −0.0415804 | ||||||||
\(304\) | −4.01286 | + | 1.70203i | −0.230154 | + | 0.0976183i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.86534 | + | 2.40431i | 0.163801 | + | 0.137445i | ||||
\(307\) | −3.87311 | + | 1.40970i | −0.221050 | + | 0.0804557i | −0.450171 | − | 0.892942i | \(-0.648637\pi\) |
0.229121 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(308\) | −4.53502 | − | 25.7194i | −0.258407 | − | 1.46550i | ||||
\(309\) | 0.737387 | − | 4.18193i | 0.0419485 | − | 0.237902i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.24153 | − | 2.15040i | −0.0704008 | − | 0.121938i | 0.828676 | − | 0.559728i | \(-0.189094\pi\) |
−0.899077 | + | 0.437791i | \(0.855761\pi\) | |||||||
\(312\) | 1.11166 | − | 1.92545i | 0.0629354 | − | 0.109007i | ||||
\(313\) | −4.12243 | + | 3.45913i | −0.233014 | + | 0.195522i | −0.751817 | − | 0.659372i | \(-0.770822\pi\) |
0.518803 | + | 0.854894i | \(0.326378\pi\) | |||||||
\(314\) | 8.45667 | − | 7.09599i | 0.477238 | − | 0.400450i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.31600 | + | 14.4037i | 0.467812 | + | 0.810273i | ||||
\(317\) | 18.2914 | + | 6.65753i | 1.02735 | + | 0.373924i | 0.800071 | − | 0.599906i | \(-0.204795\pi\) |
0.227278 | + | 0.973830i | \(0.427017\pi\) | |||||||
\(318\) | −0.180168 | + | 1.02178i | −0.0101033 | + | 0.0572987i | ||||
\(319\) | 3.38788 | + | 19.2136i | 0.189685 | + | 1.07576i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.85513 | − | 3.23484i | −0.215172 | − | 0.180551i | ||||
\(322\) | −25.9695 | −1.44722 | ||||||||
\(323\) | −4.87990 | − | 3.67941i | −0.271525 | − | 0.204728i | ||||
\(324\) | 6.12015 | 0.340008 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.57114 | + | 2.02773i | −0.308557 | + | 0.112306i | ||||
\(327\) | −0.813735 | − | 4.61492i | −0.0449996 | − | 0.255206i | ||||
\(328\) | −0.331373 | + | 1.87931i | −0.0182970 | + | 0.103768i | ||||
\(329\) | −14.2625 | − | 5.19111i | −0.786315 | − | 0.286195i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.35511 | − | 16.2035i | 0.514203 | − | 0.890626i | −0.485661 | − | 0.874147i | \(-0.661421\pi\) |
0.999864 | − | 0.0164787i | \(-0.00524557\pi\) | |||||||
\(332\) | −11.0778 | + | 9.29534i | −0.607971 | + | 0.510148i | ||||
\(333\) | −21.3749 | + | 17.9357i | −1.17134 | + | 0.982870i | ||||
\(334\) | 3.61382 | − | 6.25932i | 0.197739 | − | 0.342495i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.63468 | + | 0.958946i | 0.143734 | + | 0.0523148i | ||||
\(337\) | 4.35808 | − | 24.7159i | 0.237400 | − | 1.34636i | −0.600101 | − | 0.799924i | \(-0.704873\pi\) |
0.837501 | − | 0.546436i | \(-0.184016\pi\) | |||||||
\(338\) | 0.326087 | + | 1.84933i | 0.0177368 | + | 0.100590i | ||||
\(339\) | 2.42772 | − | 0.883619i | 0.131856 | − | 0.0479916i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.0466 | −2.38526 | ||||||||
\(342\) | −11.6127 | + | 0.605335i | −0.627942 | + | 0.0327328i | ||||
\(343\) | 46.9896 | 2.53720 | ||||||||
\(344\) | −1.13271 | − | 0.950453i | −0.0610714 | − | 0.0512450i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.895772 | + | 5.08018i | 0.0481570 | + | 0.273112i | ||||
\(347\) | −3.95111 | + | 22.4078i | −0.212107 | + | 1.20292i | 0.673751 | + | 0.738958i | \(0.264682\pi\) |
−0.885857 | + | 0.463957i | \(0.846429\pi\) | |||||||
\(348\) | −1.96823 | − | 0.716378i | −0.105508 | − | 0.0384019i | ||||
\(349\) | −6.58190 | − | 11.4002i | −0.352321 | − | 0.610238i | 0.634335 | − | 0.773059i | \(-0.281274\pi\) |
−0.986656 | + | 0.162820i | \(0.947941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.65310 | − | 8.09992i | 0.515245 | − | 0.432341i | ||||
\(352\) | −4.11295 | + | 3.45117i | −0.219221 | + | 0.183948i | ||||
\(353\) | −6.15281 | + | 10.6570i | −0.327481 | + | 0.567213i | −0.982011 | − | 0.188822i | \(-0.939533\pi\) |
0.654530 | + | 0.756036i | \(0.272866\pi\) | |||||||
\(354\) | −2.11112 | − | 3.65657i | −0.112205 | − | 0.194345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.66850 | − | 9.46254i | 0.0884304 | − | 0.501513i | ||||
\(357\) | 0.682636 | + | 3.87142i | 0.0361290 | + | 0.204897i | ||||
\(358\) | −7.69017 | + | 2.79899i | −0.406438 | + | 0.147931i | ||||
\(359\) | 9.62244 | + | 8.07418i | 0.507853 | + | 0.426139i | 0.860373 | − | 0.509665i | \(-0.170231\pi\) |
−0.352520 | + | 0.935804i | \(0.614675\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8970 | − | 1.97546i | 0.994580 | − | 0.103972i | ||||
\(362\) | −3.43236 | −0.180401 | ||||||||
\(363\) | −7.87158 | − | 6.60504i | −0.413151 | − | 0.346675i | ||||
\(364\) | −17.6306 | + | 6.41700i | −0.924093 | + | 0.336342i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.812257 | + | 4.60654i | −0.0424574 | + | 0.240788i | ||||
\(367\) | 2.52261 | + | 0.918156i | 0.131679 | + | 0.0479274i | 0.407019 | − | 0.913420i | \(-0.366568\pi\) |
−0.275340 | + | 0.961347i | \(0.588790\pi\) | |||||||
\(368\) | 2.66945 | + | 4.62363i | 0.139155 | + | 0.241023i | ||||
\(369\) | −2.54544 | + | 4.40883i | −0.132510 | + | 0.229514i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.70717 | − | 5.62798i | 0.348219 | − | 0.292190i | ||||
\(372\) | 2.36437 | − | 4.09521i | 0.122587 | − | 0.212327i | ||||
\(373\) | −9.27119 | − | 16.0582i | −0.480044 | − | 0.831461i | 0.519694 | − | 0.854353i | \(-0.326046\pi\) |
−0.999738 | + | 0.0228917i | \(0.992713\pi\) | |||||||
\(374\) | −7.07395 | − | 2.57471i | −0.365785 | − | 0.133135i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.541837 | + | 3.07291i | 0.0279431 | + | 0.158473i | ||||
\(377\) | 13.1709 | − | 4.79381i | 0.678334 | − | 0.246894i | ||||
\(378\) | 12.1733 | + | 10.2146i | 0.626125 | + | 0.525381i | ||||
\(379\) | 11.5855 | 0.595108 | 0.297554 | − | 0.954705i | \(-0.403829\pi\) | ||||
0.297554 | + | 0.954705i | \(0.403829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0802265 | −0.00411013 | ||||||||
\(382\) | 2.89246 | + | 2.42706i | 0.147991 | + | 0.124179i | ||||
\(383\) | 27.3254 | − | 9.94564i | 1.39626 | − | 0.508199i | 0.469197 | − | 0.883094i | \(-0.344543\pi\) |
0.927067 | + | 0.374895i | \(0.122321\pi\) | |||||||
\(384\) | −0.100093 | − | 0.567654i | −0.00510783 | − | 0.0289680i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4435 | + | 4.16508i | 0.582457 | + | 0.211997i | ||||
\(387\) | −1.97233 | − | 3.41617i | −0.100259 | − | 0.173654i | ||||
\(388\) | −3.03956 | + | 5.26467i | −0.154310 | + | 0.267273i | ||||
\(389\) | 22.8144 | − | 19.1436i | 1.15674 | − | 0.970618i | 0.156882 | − | 0.987617i | \(-0.449856\pi\) |
0.999856 | + | 0.0169993i | \(0.00541131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.74282 | + | 6.48276i | −0.189283 | + | 0.327847i | ||||
\(392\) | −8.33016 | − | 14.4283i | −0.420737 | − | 0.728737i | ||||
\(393\) | 6.73274 | + | 2.45052i | 0.339622 | + | 0.123612i | ||||
\(394\) | −1.25068 | + | 7.09294i | −0.0630082 | + | 0.357337i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −13.4595 | + | 4.89887i | −0.676367 | + | 0.246178i | ||||
\(397\) | −4.80307 | − | 4.03025i | −0.241059 | − | 0.202273i | 0.514252 | − | 0.857639i | \(-0.328070\pi\) |
−0.755311 | + | 0.655367i | \(0.772514\pi\) | |||||||
\(398\) | 5.83709 | 0.292587 | ||||||||
\(399\) | −9.75834 | − | 7.35772i | −0.488528 | − | 0.368347i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.58485 | + | 6.36445i | 0.378769 | + | 0.317825i | 0.812219 | − | 0.583353i | \(-0.198259\pi\) |
−0.433450 | + | 0.901178i | \(0.642704\pi\) | |||||||
\(402\) | −4.57417 | + | 1.66486i | −0.228139 | + | 0.0830357i | ||||
\(403\) | 5.49483 | + | 31.1627i | 0.273717 | + | 1.55233i | ||||
\(404\) | 0.218046 | − | 1.23660i | 0.0108482 | − | 0.0615231i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.83769 | + | 15.3073i | 0.438607 | + | 0.759690i | ||||
\(407\) | 28.0786 | − | 48.6335i | 1.39180 | − | 2.41067i | ||||
\(408\) | 0.619103 | − | 0.519489i | 0.0306502 | − | 0.0257185i | ||||
\(409\) | −23.4859 | + | 19.7070i | −1.16130 | + | 0.974449i | −0.999923 | − | 0.0124433i | \(-0.996039\pi\) |
−0.161380 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.14486 | + | 7.17910i | 0.204451 | + | 0.354119i | ||||
\(412\) | 6.92276 | + | 2.51968i | 0.341060 | + | 0.124136i | ||||
\(413\) | −6.18717 | + | 35.0892i | −0.304451 | + | 1.72663i | ||||
\(414\) | 2.47325 | + | 14.0265i | 0.121554 | + | 0.689365i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.95477 | + | 2.47935i | 0.144870 | + | 0.121560i | ||||
\(417\) | −10.2896 | −0.503882 | ||||||||
\(418\) | 21.5454 | − | 9.13834i | 1.05382 | − | 0.446971i | ||||
\(419\) | 17.9296 | 0.875916 | 0.437958 | − | 0.898995i | \(-0.355702\pi\) | ||||
0.437958 | + | 0.898995i | \(0.355702\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2850 | − | 11.0228i | 1.47600 | − | 0.537220i | 0.526278 | − | 0.850313i | \(-0.323587\pi\) |
0.949723 | + | 0.313093i | \(0.101365\pi\) | |||||||
\(422\) | 1.85299 | + | 10.5088i | 0.0902022 | + | 0.511562i | ||||
\(423\) | −1.44549 | + | 8.19775i | −0.0702819 | + | 0.398588i | ||||
\(424\) | −1.69146 | − | 0.615640i | −0.0821444 | − | 0.0298981i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.73684 | − | 3.00830i | 0.0841503 | − | 0.145753i | ||||
\(427\) | 30.2382 | − | 25.3728i | 1.46333 | − | 1.22788i | ||||
\(428\) | 6.68816 | − | 5.61204i | 0.323285 | − | 0.271268i | ||||
\(429\) | −5.96858 | + | 10.3379i | −0.288166 | + | 0.499118i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.30703 | + | 0.475720i | 0.0629575 | + | 0.0229146i | 0.373307 | − | 0.927708i | \(-0.378224\pi\) |
−0.310349 | + | 0.950623i | \(0.600446\pi\) | |||||||
\(432\) | 0.567300 | − | 3.21732i | 0.0272942 | − | 0.154793i | ||||
\(433\) | −5.77441 | − | 32.7483i | −0.277500 | − | 1.57378i | −0.730906 | − | 0.682478i | \(-0.760902\pi\) |
0.453406 | − | 0.891304i | \(-0.350209\pi\) | |||||||
\(434\) | −37.4981 | + | 13.6482i | −1.79997 | + | 0.655135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.12981 | 0.389347 | ||||||||
\(437\) | −5.22866 | − | 22.6768i | −0.250121 | − | 1.08478i | ||||
\(438\) | −0.735663 | −0.0351513 | ||||||||
\(439\) | −27.6648 | − | 23.2135i | −1.32037 | − | 1.10792i | −0.986227 | − | 0.165397i | \(-0.947109\pi\) |
−0.334141 | − | 0.942523i | \(-0.608446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.71789 | − | 43.7704i | −0.367519 | − | 2.08430i | ||||
\(442\) | −0.939112 | + | 5.32597i | −0.0446690 | + | 0.253330i | ||||
\(443\) | 30.0586 | + | 10.9404i | 1.42813 | + | 0.519795i | 0.936394 | − | 0.350951i | \(-0.114142\pi\) |
0.491732 | + | 0.870746i | \(0.336364\pi\) | |||||||
\(444\) | 3.01445 | + | 5.22118i | 0.143059 | + | 0.247786i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0761973 | − | 0.0639371i | 0.00360805 | − | 0.00302751i | ||||
\(447\) | 1.27459 | − | 1.06951i | 0.0602860 | − | 0.0505860i | ||||
\(448\) | −2.43209 | + | 4.21251i | −0.114906 | + | 0.199022i | ||||
\(449\) | 1.09116 | + | 1.88995i | 0.0514951 | + | 0.0891922i | 0.890624 | − | 0.454741i | \(-0.150268\pi\) |
−0.839129 | + | 0.543933i | \(0.816935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77917 | − | 10.0902i | 0.0837777 | − | 0.475127i | ||||
\(452\) | 0.778308 | + | 4.41400i | 0.0366085 | + | 0.207617i | ||||
\(453\) | 1.09307 | − | 0.397846i | 0.0513570 | − | 0.0186924i | ||||
\(454\) | 10.5915 | + | 8.88734i | 0.497084 | + | 0.417103i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.306897 | + | 2.49370i | −0.0143718 | + | 0.116778i | ||||
\(457\) | 37.2037 | 1.74031 | 0.870157 | − | 0.492774i | \(-0.164017\pi\) | ||||
0.870157 | + | 0.492774i | \(0.164017\pi\) | |||||||
\(458\) | 11.9313 | + | 10.0115i | 0.557512 | + | 0.467808i | ||||
\(459\) | 4.30433 | − | 1.56665i | 0.200909 | − | 0.0731248i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.847556 | + | 4.80673i | −0.0394746 | + | 0.223872i | −0.998163 | − | 0.0605870i | \(-0.980703\pi\) |
0.958688 | + | 0.284459i | \(0.0918138\pi\) | |||||||
\(462\) | −14.1458 | − | 5.14865i | −0.658122 | − | 0.239537i | ||||
\(463\) | −10.1113 | − | 17.5133i | −0.469913 | − | 0.813914i | 0.529495 | − | 0.848313i | \(-0.322381\pi\) |
−0.999408 | + | 0.0343994i | \(0.989048\pi\) | |||||||
\(464\) | 1.81689 | − | 3.14694i | 0.0843470 | − | 0.146093i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.6753 | − | 9.79677i | 0.540850 | − | 0.453827i | ||||
\(467\) | 19.5063 | − | 33.7859i | 0.902644 | − | 1.56342i | 0.0785944 | − | 0.996907i | \(-0.474957\pi\) |
0.824049 | − | 0.566518i | \(-0.191710\pi\) | |||||||
\(468\) | 5.14500 | + | 8.91140i | 0.237828 | + | 0.411930i | ||||
\(469\) | 38.6003 | + | 14.0493i | 1.78239 | + | 0.648739i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10496 | − | 6.26656i | −0.0509140 | − | 0.288748i | ||||
\(472\) | 6.88331 | − | 2.50532i | 0.316830 | − | 0.115317i | ||||
\(473\) | 6.08158 | + | 5.10305i | 0.279631 | + | 0.234639i | ||||
\(474\) | 9.58686 | 0.440339 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.82004 | −0.312596 | ||||||||
\(477\) | −3.67853 | − | 3.08665i | −0.168428 | − | 0.141328i | ||||
\(478\) | −15.8088 | + | 5.75392i | −0.723076 | + | 0.263178i | ||||
\(479\) | −5.39865 | − | 30.6172i | −0.246670 | − | 1.39894i | −0.816581 | − | 0.577231i | \(-0.804133\pi\) |
0.569911 | − | 0.821707i | \(-0.306978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.9107 | − | 13.7984i | −1.72858 | − | 0.629151i | ||||
\(482\) | 4.55349 | + | 7.88688i | 0.207406 | + | 0.359237i | ||||
\(483\) | −7.48453 | + | 12.9636i | −0.340558 | + | 0.589864i | ||||
\(484\) | 13.6562 | − | 11.4589i | 0.620737 | − | 0.520860i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.66429 | − | 11.5429i | 0.302298 | − | 0.523596i | ||||
\(487\) | −13.9870 | − | 24.2263i | −0.633813 | − | 1.09780i | −0.986765 | − | 0.162155i | \(-0.948155\pi\) |
0.352952 | − | 0.935641i | \(-0.385178\pi\) | |||||||
\(488\) | −7.62565 | − | 2.77551i | −0.345197 | − | 0.125641i | ||||
\(489\) | −0.593418 | + | 3.36544i | −0.0268353 | + | 0.152191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.79400 | + | 1.01693i | −0.126091 | + | 0.0458935i | −0.404295 | − | 0.914629i | \(-0.632483\pi\) |
0.278204 | + | 0.960522i | \(0.410261\pi\) | |||||||
\(492\) | 0.842623 | + | 0.707045i | 0.0379884 | + | 0.0318760i | ||||
\(493\) | 5.09490 | 0.229463 | ||||||||
\(494\) | −9.15311 | − | 14.1032i | −0.411818 | − | 0.634533i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.28445 | + | 5.27328i | 0.282180 | + | 0.236777i | ||||
\(497\) | −27.5458 | + | 10.0258i | −1.23560 | + | 0.449720i | ||||
\(498\) | 1.44744 | + | 8.20883i | 0.0648612 | + | 0.367846i | ||||
\(499\) | 3.20155 | − | 18.1569i | 0.143321 | − | 0.812815i | −0.825379 | − | 0.564580i | \(-0.809038\pi\) |
0.968700 | − | 0.248235i | \(-0.0798506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.08304 | − | 3.60794i | −0.0930636 | − | 0.161191i | ||||
\(502\) | −8.40288 | + | 14.5542i | −0.375039 | + | 0.649586i | ||||
\(503\) | −2.50412 | + | 2.10120i | −0.111653 | + | 0.0936881i | −0.696905 | − | 0.717163i | \(-0.745440\pi\) |
0.585252 | + | 0.810852i | \(0.300996\pi\) | |||||||
\(504\) | −9.94053 | + | 8.34110i | −0.442786 | + | 0.371542i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.3325 | − | 24.8246i | −0.637157 | − | 1.10359i | ||||
\(507\) | 1.01714 | + | 0.370209i | 0.0451728 | + | 0.0164416i | ||||
\(508\) | 0.0241688 | − | 0.137068i | 0.00107232 | − | 0.00608142i | ||||
\(509\) | 6.53272 | + | 37.0489i | 0.289558 | + | 1.64216i | 0.688536 | + | 0.725202i | \(0.258254\pi\) |
−0.398978 | + | 0.916960i | \(0.630635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.75567 | + | 3.99048i | 0.210378 | + | 0.176528i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.46852 | + | 12.6864i | −0.285592 | + | 0.560118i | ||||
\(514\) | 9.89728 | 0.436550 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.800905 | + | 0.291506i | −0.0352579 | + | 0.0128328i | ||||
\(517\) | −2.90916 | − | 16.4987i | −0.127945 | − | 0.725610i | ||||
\(518\) | 8.83459 | − | 50.1034i | 0.388169 | − | 2.20142i | ||||
\(519\) | 2.79412 | + | 1.01698i | 0.122648 | + | 0.0446403i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7203 | + | 27.2284i | −0.688719 | + | 1.19290i | 0.283533 | + | 0.958962i | \(0.408493\pi\) |
−0.972252 | + | 0.233934i | \(0.924840\pi\) | |||||||
\(522\) | 7.42605 | − | 6.23119i | 0.325029 | − | 0.272732i | ||||
\(523\) | −3.43679 | + | 2.88381i | −0.150280 | + | 0.126100i | −0.714828 | − | 0.699300i | \(-0.753495\pi\) |
0.564548 | + | 0.825400i | \(0.309051\pi\) | |||||||
\(524\) | −6.21505 | + | 10.7648i | −0.271506 | + | 0.470261i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.0609 | − | 7.66554i | −0.918299 | − | 0.334233i | ||||
\(527\) | −1.99738 | + | 11.3277i | −0.0870073 | + | 0.493443i | ||||
\(528\) | 0.537405 | + | 3.04777i | 0.0233875 | + | 0.132637i | ||||
\(529\) | −5.17201 | + | 1.88246i | −0.224870 | + | 0.0818460i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.5415 | 0.848027 | ||||||||
\(532\) | 15.5106 | − | 14.4557i | 0.672469 | − | 0.626735i | ||||
\(533\) | −7.36067 | −0.318826 | ||||||||
\(534\) | −4.24270 | − | 3.56005i | −0.183599 | − | 0.154058i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.46644 | − | 8.31660i | −0.0633406 | − | 0.359222i | ||||
\(537\) | −0.819129 | + | 4.64551i | −0.0353480 | + | 0.200469i | ||||
\(538\) | −7.02217 | − | 2.55586i | −0.302747 | − | 0.110191i | ||||
\(539\) | 44.7252 | + | 77.4664i | 1.92645 | + | 3.33671i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0269 | − | 14.2873i | 0.732045 | − | 0.614259i | −0.198643 | − | 0.980072i | \(-0.563653\pi\) |
0.930688 | + | 0.365813i | \(0.119209\pi\) | |||||||
\(542\) | −8.15902 | + | 6.84623i | −0.350460 | + | 0.294071i | ||||
\(543\) | −0.989225 | + | 1.71339i | −0.0424517 | + | 0.0735285i | ||||
\(544\) | 0.701047 | + | 1.21425i | 0.0300571 | + | 0.0520605i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.87794 | + | 10.6504i | −0.0803686 | + | 0.455793i | ||||
\(547\) | 5.00894 | + | 28.4071i | 0.214167 | + | 1.21460i | 0.882347 | + | 0.470600i | \(0.155962\pi\) |
−0.668180 | + | 0.744000i | \(0.732926\pi\) | |||||||
\(548\) | −13.5143 | + | 4.91880i | −0.577302 | + | 0.210121i | ||||
\(549\) | −16.5840 | − | 13.9157i | −0.707790 | − | 0.593906i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.5871 | + | 10.7991i | −0.493629 | + | 0.460058i | ||||
\(552\) | 3.07740 | 0.130983 | ||||||||
\(553\) | −61.9739 | − | 52.0023i | −2.63540 | − | 2.21136i | ||||
\(554\) | −2.18604 | + | 0.795654i | −0.0928760 | + | 0.0338041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.09981 | − | 17.5799i | 0.131461 | − | 0.745554i | ||||
\(557\) | −26.3406 | − | 9.58721i | −1.11609 | − | 0.406223i | −0.282865 | − | 0.959160i | \(-0.591285\pi\) |
−0.833223 | + | 0.552937i | \(0.813507\pi\) | |||||||
\(558\) | 10.9428 | + | 18.9535i | 0.463246 | + | 0.802366i | ||||
\(559\) | 2.85170 | − | 4.93929i | 0.120614 | − | 0.208910i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.32401 | + | 2.78917i | −0.140340 | + | 0.117759i | ||||
\(562\) | 8.53656 | − | 14.7858i | 0.360093 | − | 0.623699i | ||||
\(563\) | −3.28614 | − | 5.69177i | −0.138494 | − | 0.239879i | 0.788432 | − | 0.615121i | \(-0.210893\pi\) |
−0.926927 | + | 0.375242i | \(0.877560\pi\) | |||||||
\(564\) | 1.69011 | + | 0.615151i | 0.0711666 | + | 0.0259025i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.47044 | − | 8.33927i | −0.0618071 | − | 0.350526i | ||||
\(567\) | −27.9742 | + | 10.1818i | −1.17481 | + | 0.427595i | ||||
\(568\) | 4.61650 | + | 3.87370i | 0.193704 | + | 0.162537i | ||||
\(569\) | 3.90032 | 0.163510 | 0.0817549 | − | 0.996652i | \(-0.473948\pi\) | ||||
0.0817549 | + | 0.996652i | \(0.473948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1559 | 0.759802 | 0.379901 | − | 0.925027i | \(-0.375958\pi\) | ||||
0.379901 | + | 0.925027i | \(0.375958\pi\) | |||||||
\(572\) | −15.8644 | − | 13.3118i | −0.663323 | − | 0.556594i | ||||
\(573\) | 2.04518 | − | 0.744385i | 0.0854386 | − | 0.0310971i | ||||
\(574\) | −1.61186 | − | 9.14132i | −0.0672778 | − | 0.381551i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.50687 | + | 0.912424i | 0.104453 | + | 0.0380177i | ||||
\(577\) | 7.00915 | + | 12.1402i | 0.291795 | + | 0.505403i | 0.974234 | − | 0.225539i | \(-0.0724142\pi\) |
−0.682439 | + | 0.730942i | \(0.739081\pi\) | |||||||
\(578\) | 7.51707 | − | 13.0199i | 0.312669 | − | 0.541558i | ||||
\(579\) | 5.37721 | − | 4.51202i | 0.223469 | − | 0.187513i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.1705 | − | 60.9170i | 1.45912 | − | 2.52726i | ||||
\(582\) | 1.75203 | + | 3.03461i | 0.0726241 | + | 0.125789i | ||||
\(583\) | 9.08155 | + | 3.30541i | 0.376119 | + | 0.136896i | ||||
\(584\) | 0.221624 | − | 1.25689i | 0.00917088 | − | 0.0520106i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.43610 | + | 0.886667i | −0.100634 | + | 0.0366279i | ||||
\(587\) | 5.83061 | + | 4.89246i | 0.240655 | + | 0.201933i | 0.755136 | − | 0.655568i | \(-0.227571\pi\) |
−0.514481 | + | 0.857502i | \(0.672015\pi\) | |||||||
\(588\) | −9.60319 | −0.396029 | ||||||||
\(589\) | −19.4676 | − | 29.9958i | −0.802148 | − | 1.23596i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.18025 | + | 2.66855i | 0.130818 | + | 0.109769i | ||||
\(592\) | −9.82860 | + | 3.57732i | −0.403953 | + | 0.147027i | ||||
\(593\) | 1.63620 | + | 9.27933i | 0.0671905 | + | 0.381056i | 0.999797 | + | 0.0201608i | \(0.00641780\pi\) |
−0.932606 | + | 0.360896i | \(0.882471\pi\) | |||||||
\(594\) | −3.04587 | + | 17.2740i | −0.124974 | + | 0.708761i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.44329 | + | 2.49986i | 0.0591196 | + | 0.102398i | ||||
\(597\) | 1.68228 | − | 2.91380i | 0.0688512 | − | 0.119254i | ||||
\(598\) | −15.7753 | + | 13.2370i | −0.645099 | + | 0.541302i | ||||
\(599\) | 10.7502 | − | 9.02053i | 0.439243 | − | 0.368569i | −0.396183 | − | 0.918172i | \(-0.629665\pi\) |
0.835426 | + | 0.549603i | \(0.185221\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78599 | + | 11.7537i | 0.276806 | + | 0.479443i | 0.970589 | − | 0.240742i | \(-0.0773906\pi\) |
−0.693783 | + | 0.720184i | \(0.744057\pi\) | |||||||
\(602\) | 6.75864 | + | 2.45994i | 0.275462 | + | 0.100260i | ||||
\(603\) | 3.91210 | − | 22.1866i | 0.159313 | − | 0.903508i | ||||
\(604\) | 0.350430 | + | 1.98739i | 0.0142588 | + | 0.0808657i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.554451 | − | 0.465240i | −0.0225231 | − | 0.0188991i | ||||
\(607\) | −2.07689 | −0.0842984 | −0.0421492 | − | 0.999111i | \(-0.513420\pi\) | ||||
−0.0421492 | + | 0.999111i | \(0.513420\pi\) | |||||||
\(608\) | −4.16808 | − | 1.27559i | −0.169038 | − | 0.0517318i | ||||
\(609\) | 10.1883 | 0.412850 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.3098 | + | 4.11642i | −0.457545 | + | 0.166533i | ||||
\(612\) | 0.649520 | + | 3.68361i | 0.0262553 | + | 0.148901i | ||||
\(613\) | 2.86849 | − | 16.2680i | 0.115857 | − | 0.657059i | −0.870465 | − | 0.492230i | \(-0.836182\pi\) |
0.986322 | − | 0.164828i | \(-0.0527071\pi\) | |||||||
\(614\) | −3.87311 | − | 1.40970i | −0.156306 | − | 0.0568908i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.0581 | − | 22.6173i | 0.526125 | − | 0.911275i | ||||
\(617\) | −17.5283 | + | 14.7080i | −0.705661 | + | 0.592120i | −0.923378 | − | 0.383892i | \(-0.874583\pi\) |
0.217717 | + | 0.976012i | \(0.430139\pi\) | |||||||
\(618\) | 3.25297 | − | 2.72956i | 0.130853 | − | 0.109799i | ||||
\(619\) | 6.66514 | − | 11.5444i | 0.267895 | − | 0.464007i | −0.700423 | − | 0.713728i | \(-0.747005\pi\) |
0.968318 | + | 0.249721i | \(0.0803388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.3901 | + | 5.96550i | 0.657711 | + | 0.239387i | ||||
\(622\) | 0.431179 | − | 2.44534i | 0.0172887 | − | 0.0980492i | ||||
\(623\) | 8.11590 | + | 46.0276i | 0.325157 | + | 1.84406i | ||||
\(624\) | 2.08924 | − | 0.760421i | 0.0836365 | − | 0.0304412i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.38145 | −0.215086 | ||||||||
\(627\) | 1.64775 | − | 13.3889i | 0.0658048 | − | 0.534700i | ||||
\(628\) | 11.0394 | 0.440520 | ||||||||
\(629\) | −11.2341 | − | 9.42649i | −0.447931 | − | 0.375859i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51546 | + | 8.59462i | 0.0603297 | + | 0.342147i | 1.00000 | 6.52024e-5i | \(2.07546e-5\pi\) | |
−0.939670 | + | 0.342081i | \(0.888868\pi\) | |||||||
\(632\) | −2.88812 | + | 16.3793i | −0.114883 | + | 0.651534i | ||||
\(633\) | 5.77991 | + | 2.10372i | 0.229731 | + | 0.0836152i | ||||
\(634\) | 9.73266 | + | 16.8575i | 0.386533 | + | 0.669495i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.794805 | + | 0.666921i | −0.0315161 | + | 0.0264451i | ||||
\(637\) | 49.2275 | − | 41.3068i | 1.95046 | − | 1.63663i | ||||
\(638\) | −9.75501 | + | 16.8962i | −0.386204 | + | 0.668926i | ||||
\(639\) | 8.03848 | + | 13.9230i | 0.317997 | + | 0.550787i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.151753 | + | 0.860632i | −0.00599387 | + | 0.0339929i | −0.987658 | − | 0.156626i | \(-0.949938\pi\) |
0.981664 | + | 0.190619i | \(0.0610494\pi\) | |||||||
\(642\) | −0.873887 | − | 4.95606i | −0.0344896 | − | 0.195600i | ||||
\(643\) | −17.8620 | + | 6.50122i | −0.704407 | + | 0.256383i | −0.669291 | − | 0.743000i | \(-0.733402\pi\) |
−0.0351158 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(644\) | −19.8938 | − | 16.6928i | −0.783924 | − | 0.657790i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.37314 | − | 5.95533i | −0.0540255 | − | 0.234309i | ||||
\(647\) | −14.4175 | −0.566810 | −0.283405 | − | 0.959000i | \(-0.591464\pi\) | ||||
−0.283405 | + | 0.959000i | \(0.591464\pi\) | |||||||
\(648\) | 4.68830 | + | 3.93395i | 0.184174 | + | 0.154540i | ||||
\(649\) | −36.9570 | + | 13.4512i | −1.45069 | + | 0.528007i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.99417 | + | 22.6520i | −0.156544 | + | 0.887804i | ||||
\(652\) | −5.57114 | − | 2.02773i | −0.218183 | − | 0.0794121i | ||||
\(653\) | 5.23384 | + | 9.06528i | 0.204816 | + | 0.354752i | 0.950074 | − | 0.312024i | \(-0.101007\pi\) |
−0.745258 | + | 0.666776i | \(0.767674\pi\) | |||||||
\(654\) | 2.34306 | − | 4.05829i | 0.0916207 | − | 0.158692i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.46184 | + | 1.22663i | −0.0570755 | + | 0.0478920i | ||||
\(657\) | 1.70240 | − | 2.94865i | 0.0664171 | − | 0.115038i | ||||
\(658\) | −7.58889 | − | 13.1444i | −0.295846 | − | 0.512420i | ||||
\(659\) | −5.20991 | − | 1.89625i | −0.202949 | − | 0.0738675i | 0.238545 | − | 0.971131i | \(-0.423329\pi\) |
−0.441495 | + | 0.897264i | \(0.645552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00125 | + | 28.3635i | 0.194526 | + | 1.10321i | 0.913092 | + | 0.407753i | \(0.133688\pi\) |
−0.718566 | + | 0.695459i | \(0.755201\pi\) | |||||||
\(662\) | 17.5818 | − | 6.39927i | 0.683338 | − | 0.248715i | ||||
\(663\) | 2.38799 | + | 2.00376i | 0.0927420 | + | 0.0778198i | ||||
\(664\) | −14.4610 | −0.561195 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.9030 | −1.08122 | ||||||||
\(667\) | 14.8616 | + | 12.4703i | 0.575443 | + | 0.482854i | ||||
\(668\) | 6.79176 | − | 2.47200i | 0.262781 | − | 0.0956445i | ||||
\(669\) | −0.00995606 | − | 0.0564636i | −0.000384924 | − | 0.00218301i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.9427 | + | 14.9019i | 1.58057 | + | 0.575282i | ||||
\(672\) | 1.40188 | + | 2.42814i | 0.0540789 | + | 0.0936674i | ||||
\(673\) | 19.9705 | − | 34.5899i | 0.769807 | − | 1.33334i | −0.167861 | − | 0.985811i | \(-0.553686\pi\) |
0.937668 | − | 0.347533i | \(-0.112981\pi\) | |||||||
\(674\) | 19.2255 | − | 16.1322i | 0.740540 | − | 0.621387i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.938930 | + | 1.62627i | −0.0361127 | + | 0.0625490i | ||||
\(677\) | 7.29022 | + | 12.6270i | 0.280186 | + | 0.485296i | 0.971430 | − | 0.237325i | \(-0.0762706\pi\) |
−0.691245 | + | 0.722621i | \(0.742937\pi\) | |||||||
\(678\) | 2.42772 | + | 0.883619i | 0.0932361 | + | 0.0339352i | ||||
\(679\) | 5.13477 | − | 29.1207i | 0.197054 | − | 1.11755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.48897 | − | 2.72576i | 0.286978 | − | 0.104451i | ||||
\(682\) | −33.7417 | − | 28.3126i | −1.29204 | − | 1.08415i | ||||
\(683\) | 26.6159 | 1.01843 | 0.509214 | − | 0.860640i | \(-0.329936\pi\) | ||||
0.509214 | + | 0.860640i | \(0.329936\pi\) | |||||||
\(684\) | −9.28494 | − | 7.00078i | −0.355018 | − | 0.267681i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.9961 | + | 30.2043i | 1.37434 | + | 1.15321i | ||||
\(687\) | 8.43628 | − | 3.07056i | 0.321864 | − | 0.117149i | ||||
\(688\) | −0.256764 | − | 1.45618i | −0.00978902 | − | 0.0555163i | ||||
\(689\) | 1.20563 | − | 6.83749i | 0.0459310 | − | 0.260488i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6248 | − | 32.2591i | −0.708521 | − | 1.22719i | −0.965406 | − | 0.260752i | \(-0.916029\pi\) |
0.256885 | − | 0.966442i | \(-0.417304\pi\) | |||||||
\(692\) | −2.57927 | + | 4.46743i | −0.0980492 | + | 0.169826i | ||||
\(693\) | 53.3714 | − | 44.7839i | 2.02741 | − | 1.70120i | ||||
\(694\) | −17.4302 | + | 14.6257i | −0.661642 | + | 0.555183i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.04727 | − | 1.81393i | −0.0396968 | − | 0.0687569i | ||||
\(697\) | −2.51426 | − | 0.915115i | −0.0952344 | − | 0.0346625i | ||||
\(698\) | 2.28587 | − | 12.9638i | 0.0865215 | − | 0.490688i | ||||
\(699\) | −1.52552 | − | 8.65165i | −0.0577004 | − | 0.327235i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.3425 | − | 25.4604i | −1.14602 | − | 0.961626i | −0.146402 | − | 0.989225i | \(-0.546769\pi\) |
−0.999619 | + | 0.0275989i | \(0.991214\pi\) | |||||||
\(702\) | 12.6012 | 0.475603 | ||||||||
\(703\) | 45.5295 | − | 2.37332i | 1.71718 | − | 0.0895114i | ||||
\(704\) | −5.36907 | −0.202354 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.5635 | + | 4.20877i | −0.435198 | + | 0.158399i | ||||
\(707\) | 1.06062 | + | 6.01505i | 0.0398886 | + | 0.226219i | ||||
\(708\) | 0.733185 | − | 4.15810i | 0.0275548 | − | 0.156271i | ||||
\(709\) | 34.4453 | + | 12.5371i | 1.29362 | + | 0.470839i | 0.894914 | − | 0.446239i | \(-0.147237\pi\) |
0.398707 | + | 0.917079i | \(0.369459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.1850 | + | 38.4256i | −0.832003 | + | 1.44107i | ||||
\(712\) | 7.36055 | − | 6.17623i | 0.275848 | − | 0.231464i | ||||
\(713\) | −33.5521 | + | 28.1536i | −1.25654 | + | 1.05436i | ||||
\(714\) | −1.96557 | + | 3.40447i | −0.0735597 | + | 0.127409i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.69017 | − | 2.79899i | −0.287395 | − | 0.104603i | ||||
\(717\) | −1.68389 | + | 9.54983i | −0.0628861 | + | 0.356645i | ||||
\(718\) | 2.18123 | + | 12.3704i | 0.0814028 | + | 0.461658i | ||||
\(719\) | −10.3333 | + | 3.76101i | −0.385367 | + | 0.140262i | −0.527436 | − | 0.849595i | \(-0.676847\pi\) |
0.142069 | + | 0.989857i | \(0.454624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.8347 | −1.33455 | ||||||||
\(722\) | 15.7458 | + | 10.6335i | 0.585997 | + | 0.395737i | ||||
\(723\) | 5.24936 | 0.195226 | ||||||||
\(724\) | −2.62934 | − | 2.20628i | −0.0977187 | − | 0.0819957i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.78434 | − | 10.1195i | −0.0662232 | − | 0.375570i | ||||
\(727\) | −7.88597 | + | 44.7236i | −0.292475 | + | 1.65871i | 0.384818 | + | 0.922992i | \(0.374264\pi\) |
−0.677293 | + | 0.735714i | \(0.736847\pi\) | |||||||
\(728\) | −17.6306 | − | 6.41700i | −0.653432 | − | 0.237830i | ||||
\(729\) | 5.33885 | + | 9.24717i | 0.197735 | + | 0.342488i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.58816 | − | 1.33262i | 0.0587402 | − | 0.0492889i | ||||
\(732\) | −3.58325 | + | 3.00670i | −0.132441 | + | 0.111131i | ||||
\(733\) | −13.5168 | + | 23.4118i | −0.499255 | + | 0.864735i | −1.00000 | 0.000859816i | \(-0.999726\pi\) | |
0.500744 | + | 0.865595i | \(0.333060\pi\) | |||||||
\(734\) | 1.34225 | + | 2.32485i | 0.0495435 | + | 0.0858119i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.927092 | + | 5.25780i | −0.0341731 | + | 0.193805i | ||||
\(737\) | 7.87342 | + | 44.6524i | 0.290021 | + | 1.64479i | ||||
\(738\) | −4.78386 | + | 1.74118i | −0.176096 | + | 0.0640938i | ||||
\(739\) | −0.964167 | − | 0.809032i | −0.0354675 | − | 0.0297607i | 0.624882 | − | 0.780720i | \(-0.285147\pi\) |
−0.660349 | + | 0.750959i | \(0.729592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.67809 | + | 0.504490i | −0.355534 | + | 0.0185329i | ||||
\(742\) | 8.75559 | 0.321428 | ||||||||
\(743\) | −40.0045 | − | 33.5678i | −1.46762 | − | 1.23148i | −0.918308 | − | 0.395867i | \(-0.870444\pi\) |
−0.549315 | − | 0.835615i | \(-0.685111\pi\) | |||||||
\(744\) | 4.44356 | − | 1.61733i | 0.162909 | − | 0.0592940i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.21985 | − | 18.2607i | 0.117887 | − | 0.668571i | ||||
\(747\) | −36.2517 | − | 13.1945i | −1.32638 | − | 0.482763i | ||||
\(748\) | −3.76397 | − | 6.51938i | −0.137624 | − | 0.238372i | ||||
\(749\) | −21.2341 | + | 36.7785i | −0.775876 | + | 1.34386i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.810409 | − | 0.680014i | 0.0295723 | − | 0.0248141i | −0.627882 | − | 0.778309i | \(-0.716078\pi\) |
0.657454 | + | 0.753495i | \(0.271633\pi\) | |||||||
\(752\) | −1.56016 | + | 2.70227i | −0.0568931 | + | 0.0985417i | ||||
\(753\) | 4.84351 | + | 8.38920i | 0.176507 | + | 0.305720i | ||||
\(754\) | 13.1709 | + | 4.79381i | 0.479655 | + | 0.174580i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.75945 | + | 15.6496i | 0.100360 | + | 0.569172i | ||||
\(757\) | 1.73900 | − | 0.632944i | 0.0632050 | − | 0.0230047i | −0.310224 | − | 0.950663i | \(-0.600404\pi\) |
0.373429 | + | 0.927659i | \(0.378182\pi\) | |||||||
\(758\) | 8.87503 | + | 7.44703i | 0.322355 | + | 0.270488i | ||||
\(759\) | −16.5228 | −0.599739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8442 | −1.15435 | −0.577176 | − | 0.816620i | \(-0.695845\pi\) | ||||
−0.577176 | + | 0.816620i | \(0.695845\pi\) | |||||||
\(762\) | −0.0614570 | − | 0.0515686i | −0.00222635 | − | 0.00186813i | ||||
\(763\) | −37.1601 | + | 13.5252i | −1.34529 | + | 0.489644i | ||||
\(764\) | 0.655668 | + | 3.71848i | 0.0237212 | + | 0.134530i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.3254 | + | 9.94564i | 0.987308 | + | 0.359351i | ||||
\(767\) | 14.1271 | + | 24.4688i | 0.510099 | + | 0.883517i | ||||
\(768\) | 0.288205 | − | 0.499186i | 0.0103997 | − | 0.0180128i | ||||
\(769\) | 0.0929228 | − | 0.0779715i | 0.00335088 | − | 0.00281172i | −0.641111 | − | 0.767448i | \(-0.721526\pi\) |
0.644462 | + | 0.764637i | \(0.277082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.85245 | − | 4.94059i | 0.102728 | − | 0.177931i | ||||
\(772\) | 6.08894 | + | 10.5463i | 0.219146 | + | 0.379571i | ||||
\(773\) | −32.7308 | − | 11.9131i | −1.17725 | − | 0.428483i | −0.322018 | − | 0.946734i | \(-0.604361\pi\) |
−0.855229 | + | 0.518251i | \(0.826583\pi\) | |||||||
\(774\) | 0.684981 | − | 3.88472i | 0.0246211 | − | 0.139633i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.71250 | + | 2.07918i | −0.205067 | + | 0.0746382i | ||||
\(777\) | −22.4648 | − | 18.8502i | −0.805919 | − | 0.676246i | ||||
\(778\) | 29.7821 | 1.06774 | ||||||||
\(779\) | 7.65776 | − | 3.24800i | 0.274368 | − | 0.116372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7863 | − | 20.7982i | −0.886923 | − | 0.744217i | ||||
\(782\) | −7.03421 | + | 2.56024i | −0.251543 | + | 0.0915541i | ||||
\(783\) | −2.06144 | − | 11.6910i | −0.0736700 | − | 0.417803i | ||||
\(784\) | 2.89303 | − | 16.4072i | 0.103323 | − | 0.585972i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.58242 | + | 6.20493i | 0.127781 | + | 0.221323i | ||||
\(787\) | 9.58626 | − | 16.6039i | 0.341713 | − | 0.591865i | −0.643038 | − | 0.765834i | \(-0.722326\pi\) |
0.984751 | + | 0.173970i | \(0.0556595\pi\) | |||||||
\(788\) | −5.51733 | + | 4.62959i | −0.196547 | + | 0.164922i | ||||
\(789\) | −9.89640 | + | 8.30406i | −0.352321 | + | 0.295632i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9009 | − | 18.8809i | −0.387591 | − | 0.671327i | ||||
\(792\) | −13.4595 | − | 4.89887i | −0.478264 | − | 0.174074i | ||||
\(793\) | 5.43540 | − | 30.8257i | 0.193017 | − | 1.09465i | ||||
\(794\) | −1.08877 | − | 6.17471i | −0.0386389 | − | 0.219132i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.47147 | + | 3.75201i | 0.158487 | + | 0.132986i | ||||
\(797\) | 22.4041 | 0.793593 | 0.396796 | − | 0.917907i | \(-0.370122\pi\) | ||||
0.396796 | + | 0.917907i | \(0.370122\pi\) | |||||||
\(798\) | −2.74587 | − | 11.9089i | −0.0972028 | − | 0.421570i | ||||
\(799\) | −4.37497 | −0.154775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0872 | − | 8.76704i | 0.851081 | − | 0.309768i | ||||
\(802\) | 1.71935 | + | 9.75090i | 0.0607122 | + | 0.344316i | ||||
\(803\) | −1.18992 | + | 6.74835i | −0.0419912 | + | 0.238144i | ||||
\(804\) | −4.57417 | − | 1.66486i | −0.161318 | − | 0.0587151i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.8217 | + | 27.4040i | −0.557297 | + | 0.965266i | ||||
\(807\) | −3.29968 | + | 2.76876i | −0.116154 | + | 0.0974649i | ||||
\(808\) | 0.961904 | − | 0.807133i | 0.0338396 | − | 0.0283948i | ||||
\(809\) | −22.7973 | + | 39.4861i | −0.801511 | + | 1.38826i | 0.117110 | + | 0.993119i | \(0.462637\pi\) |
−0.918621 | + | 0.395139i | \(0.870696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.6230 | − | 12.9657i | −1.25089 | − | 0.455288i | −0.370191 | − | 0.928956i | \(-0.620708\pi\) |
−0.880704 | + | 0.473667i | \(0.842930\pi\) | |||||||
\(812\) | −3.06930 | + | 17.4069i | −0.107711 | + | 0.610861i | ||||
\(813\) | 1.06607 | + | 6.04599i | 0.0373888 | + | 0.212042i | ||||
\(814\) | 52.7704 | − | 19.2069i | 1.84960 | − | 0.673200i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.808181 | 0.0282920 | ||||||||
\(817\) | −0.787270 | + | 6.39699i | −0.0275431 | + | 0.223802i | ||||
\(818\) | −30.6587 | −1.07196 | ||||||||
\(819\) | −38.3424 | − | 32.1731i | −1.33979 | − | 1.12422i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.63416 | + | 54.6380i | 0.336235 | + | 1.90688i | 0.414689 | + | 0.909963i | \(0.363890\pi\) |
−0.0784541 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(822\) | −1.43949 | + | 8.16377i | −0.0502081 | + | 0.284744i | ||||
\(823\) | −6.02255 | − | 2.19203i | −0.209933 | − | 0.0764094i | 0.234913 | − | 0.972016i | \(-0.424519\pi\) |
−0.444846 | + | 0.895607i | \(0.646742\pi\) | |||||||
\(824\) | 3.68352 | + | 6.38005i | 0.128322 | + | 0.222260i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.2945 | + | 22.9028i | −0.949699 | + | 0.796892i | ||||
\(827\) | −3.36481 | + | 2.82341i | −0.117006 | + | 0.0981796i | −0.699413 | − | 0.714717i | \(-0.746555\pi\) |
0.582407 | + | 0.812897i | \(0.302111\pi\) | |||||||
\(828\) | −7.12144 | + | 12.3347i | −0.247487 | + | 0.428660i | ||||
\(829\) | −25.0469 | − | 43.3826i | −0.869916 | − | 1.50674i | −0.862082 | − | 0.506769i | \(-0.830840\pi\) |
−0.00783422 | − | 0.999969i | \(-0.502494\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.232849 | + | 1.32055i | −0.00807745 | + | 0.0458095i | ||||
\(832\) | 0.669793 | + | 3.79858i | 0.0232209 | + | 0.131692i | ||||
\(833\) | 21.9506 | − | 7.98936i | 0.760543 | − | 0.276815i | ||||
\(834\) | −7.88227 | − | 6.61401i | −0.272941 | − | 0.229024i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 22.3787 | + | 6.84871i | 0.773984 | + | 0.236868i | ||||
\(837\) | 26.8013 | 0.926390 | ||||||||
\(838\) | 13.7348 | + | 11.5249i | 0.474462 | + | 0.398121i | ||||
\(839\) | −28.3895 | + | 10.3329i | −0.980115 | + | 0.356733i | −0.781885 | − | 0.623423i | \(-0.785742\pi\) |
−0.198230 | + | 0.980156i | \(0.563519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.74289 | + | 15.5557i | −0.0945823 | + | 0.536403i | ||||
\(842\) | 30.2850 | + | 11.0228i | 1.04369 | + | 0.379872i | ||||
\(843\) | −4.92056 | − | 8.52266i | −0.169473 | − | 0.293536i | ||||
\(844\) | −5.33548 | + | 9.24132i | −0.183655 | + | 0.318099i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.37672 | + | 5.35070i | −0.219236 | + | 0.183961i | ||||
\(847\) | −43.3567 | + | 75.0961i | −1.48975 | + | 2.58033i | ||||
\(848\) | −0.900005 | − | 1.55885i | −0.0309063 | − | 0.0535313i | ||||
\(849\) | −4.58664 | − | 1.66940i | −0.157413 | − | 0.0572937i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.69680 | − | 54.9933i | −0.332402 | − | 1.88515i | ||||
\(852\) | 3.26420 | − | 1.18807i | 0.111830 | − | 0.0407026i | ||||
\(853\) | 9.07579 | + | 7.61549i | 0.310749 | + | 0.260750i | 0.784802 | − | 0.619747i | \(-0.212765\pi\) |
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(854\) | 39.4731 | 1.35074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.73078 | 0.298412 | ||||||||
\(857\) | −36.4650 | − | 30.5978i | −1.24562 | − | 1.04520i | −0.997063 | − | 0.0765828i | \(-0.975599\pi\) |
−0.248558 | − | 0.968617i | \(-0.579957\pi\) | |||||||
\(858\) | −11.2173 | + | 4.08275i | −0.382951 | + | 0.139383i | ||||
\(859\) | 1.97498 | + | 11.2007i | 0.0673853 | + | 0.382161i | 0.999785 | + | 0.0207325i | \(0.00659983\pi\) |
−0.932400 | + | 0.361429i | \(0.882289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.02777 | − | 1.82996i | −0.171346 | − | 0.0623648i | ||||
\(862\) | 0.695457 | + | 1.20457i | 0.0236873 | + | 0.0410277i | ||||
\(863\) | −24.4357 | + | 42.3239i | −0.831801 | + | 1.44072i | 0.0648068 | + | 0.997898i | \(0.479357\pi\) |
−0.896608 | + | 0.442825i | \(0.853976\pi\) | |||||||
\(864\) | 2.50263 | − | 2.09996i | 0.0851412 | − | 0.0714420i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.6267 | − | 28.7984i | 0.565000 | − | 0.978608i | ||||
\(867\) | −4.33292 | − | 7.50483i | −0.147154 | − | 0.254878i | ||||
\(868\) | −37.4981 | − | 13.6482i | −1.27277 | − | 0.463250i | ||||
\(869\) | 15.5065 | − | 87.9417i | 0.526022 | − | 2.98322i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6091 | − | 11.1408i | 1.03715 | − | 0.377491i | ||||
\(872\) | 6.22780 | + | 5.22574i | 0.210900 | + | 0.176966i | ||||
\(873\) | −16.2176 | −0.548882 | ||||||||
\(874\) | 10.5710 | − | 20.7323i | 0.357568 | − | 0.701282i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.563551 | − | 0.472875i | −0.0190406 | − | 0.0159770i | ||||
\(877\) | −27.7048 | + | 10.0837i | −0.935524 | + | 0.340503i | −0.764397 | − | 0.644746i | \(-0.776963\pi\) |
−0.171127 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(878\) | −6.27110 | − | 35.5652i | −0.211639 | − | 1.20027i | ||||
\(879\) | −0.259484 | + | 1.47161i | −0.00875218 | + | 0.0496361i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8616 | + | 36.1334i | 0.702846 | + | 1.21736i | 0.967463 | + | 0.253011i | \(0.0814209\pi\) |
−0.264618 | + | 0.964353i | \(0.585246\pi\) | |||||||
\(882\) | 22.2228 | − | 38.4910i | 0.748280 | − | 1.29606i | ||||
\(883\) | −4.53603 | + | 3.80618i | −0.152650 | + | 0.128088i | −0.715914 | − | 0.698189i | \(-0.753990\pi\) |
0.563264 | + | 0.826277i | \(0.309545\pi\) | |||||||
\(884\) | −4.14287 | + | 3.47628i | −0.139340 | + | 0.116920i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.9938 | + | 27.7021i | 0.537323 | + | 0.930672i | ||||
\(887\) | −12.9931 | − | 4.72909i | −0.436265 | − | 0.158787i | 0.114545 | − | 0.993418i | \(-0.463459\pi\) |
−0.550810 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(888\) | −1.04691 | + | 5.93730i | −0.0351319 | + | 0.199243i | ||||
\(889\) | 0.117562 | + | 0.666726i | 0.00394290 | + | 0.0223613i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.1718 | − | 21.1217i | −0.843288 | − | 0.707603i | ||||
\(892\) | 0.0994685 | 0.00333045 | ||||||||
\(893\) | 9.94983 | − | 9.27316i | 0.332958 | − | 0.310315i | ||||
\(894\) | 1.66386 | 0.0556478 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.57084 | + | 1.66365i | −0.152701 | + | 0.0555787i | ||||
\(897\) | 2.06122 | + | 11.6898i | 0.0688222 | + | 0.390310i | ||||
\(898\) | −0.378957 | + | 2.14917i | −0.0126459 | + | 0.0717187i | ||||
\(899\) | 28.0129 | + | 10.1959i | 0.934282 | + | 0.340051i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26189 | − | 2.18566i | 0.0420397 | − | 0.0728149i | ||||
\(902\) | 7.84875 | − | 6.58588i | 0.261335 | − | 0.219286i | ||||
\(903\) | 3.17585 | − | 2.66485i | 0.105686 | − | 0.0886807i | ||||
\(904\) | −2.24105 | + | 3.88161i | −0.0745362 | + | 0.129100i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.09307 | + | 0.397846i | 0.0363149 | + | 0.0132175i | ||||
\(907\) | −1.45100 | + | 8.22903i | −0.0481797 | + | 0.273240i | −0.999375 | − | 0.0353489i | \(-0.988746\pi\) |
0.951195 | + | 0.308589i | \(0.0998569\pi\) | |||||||
\(908\) | 2.40090 | + | 13.6162i | 0.0796767 | + | 0.451869i | ||||
\(909\) | 3.14781 | − | 1.14571i | 0.104406 | − | 0.0380008i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.5762 | 1.31122 | 0.655609 | − | 0.755101i | \(-0.272412\pi\) | ||||
0.655609 | + | 0.755101i | \(0.272412\pi\) | |||||||
\(912\) | −1.83802 | + | 1.71302i | −0.0608628 | + | 0.0567237i | ||||
\(913\) | 77.6420 | 2.56958 | ||||||||
\(914\) | 28.4997 | + | 23.9141i | 0.942685 | + | 0.791007i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.70460 | + | 15.3386i | 0.0893626 | + | 0.506800i | ||||
\(917\) | 10.4992 | − | 59.5437i | 0.346713 | − | 1.96631i | ||||
\(918\) | 4.30433 | + | 1.56665i | 0.142064 | + | 0.0517071i | ||||
\(919\) | 19.0623 | + | 33.0169i | 0.628807 | + | 1.08913i | 0.987791 | + | 0.155782i | \(0.0497899\pi\) |
−0.358984 | + | 0.933344i | \(0.616877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.81995 | + | 1.52712i | −0.0599695 | + | 0.0503204i | ||||
\(922\) | −3.73897 | + | 3.13737i | −0.123136 | + | 0.103324i | ||||
\(923\) | −11.6225 | + | 20.1307i | −0.382559 | + | 0.662611i | ||||
\(924\) | −7.52682 | − | 13.0368i | −0.247614 | − | 0.428880i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.51163 | − | 19.9154i | 0.115399 | − | 0.654462i | ||||
\(927\) | 3.41279 | + | 19.3549i | 0.112091 | + | 0.635697i | ||||
\(928\) | 3.41464 | − | 1.24283i | 0.112091 | − | 0.0407977i | ||||
\(929\) | 29.3240 | + | 24.6058i | 0.962090 | + | 0.807289i | 0.981292 | − | 0.192527i | \(-0.0616682\pi\) |
−0.0192022 | + | 0.999816i | \(0.506113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.9872 | + | 64.6962i | −1.08111 | + | 2.12033i | ||||
\(932\) | 15.2411 | 0.499238 | ||||||||
\(933\) | −1.09641 | − | 0.919999i | −0.0358949 | − | 0.0301194i | ||||
\(934\) | 36.6598 | − | 13.3431i | 1.19955 | − | 0.436599i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.78684 | + | 10.1337i | −0.0584047 | + | 0.331230i | ||||
\(937\) | 1.77169 | + | 0.644843i | 0.0578787 | + | 0.0210661i | 0.370797 | − | 0.928714i | \(-0.379084\pi\) |
−0.312919 | + | 0.949780i | \(0.601307\pi\) | |||||||
\(938\) | 20.5388 | + | 35.5742i | 0.670615 | + | 1.16154i | ||||
\(939\) | −1.55096 | + | 2.68635i | −0.0506138 | + | 0.0876656i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.3282 | + | 9.50548i | −0.369288 | + | 0.309870i | −0.808480 | − | 0.588524i | \(-0.799709\pi\) |
0.439192 | + | 0.898393i | \(0.355265\pi\) | |||||||
\(942\) | 3.18161 | − | 5.51072i | 0.103663 | − | 0.179549i | ||||
\(943\) | −5.09413 | − | 8.82329i | −0.165888 | − | 0.287326i | ||||
\(944\) | 6.88331 | + | 2.50532i | 0.224033 | + | 0.0815412i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37858 | + | 7.81833i | 0.0448216 | + | 0.254196i | ||||
\(947\) | −5.33767 | + | 1.94275i | −0.173451 | + | 0.0631310i | −0.427286 | − | 0.904117i | \(-0.640530\pi\) |
0.253835 | + | 0.967248i | \(0.418308\pi\) | |||||||
\(948\) | 7.34396 | + | 6.16232i | 0.238521 | + | 0.200143i | ||||
\(949\) | 4.92286 | 0.159803 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2200 | 0.363834 | ||||||||
\(952\) | −5.22446 | − | 4.38384i | −0.169326 | − | 0.142081i | ||||
\(953\) | −12.0998 | + | 4.40396i | −0.391950 | + | 0.142658i | −0.530475 | − | 0.847701i | \(-0.677986\pi\) |
0.138524 | + | 0.990359i | \(0.455764\pi\) | |||||||
\(954\) | −0.833855 | − | 4.72902i | −0.0269970 | − | 0.153108i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.8088 | − | 5.75392i | −0.511292 | − | 0.186095i | ||||
\(957\) | 5.62289 | + | 9.73913i | 0.181762 | + | 0.314821i | ||||
\(958\) | 15.5448 | − | 26.9244i | 0.502229 | − | 0.869886i | ||||
\(959\) | 53.5885 | − | 44.9661i | 1.73046 | − | 1.45203i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1509 | + | 31.4384i | −0.585514 | + | 1.01414i | ||||
\(962\) | −20.1719 | − | 34.9387i | −0.650367 | − | 1.12647i | ||||
\(963\) | 21.8869 | + | 7.96618i | 0.705295 | + | 0.256706i | ||||
\(964\) | −1.58141 | + | 8.96862i | −0.0509338 | + | 0.288860i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.0663 | + | 5.11972i | −0.452577 | + | 0.164724i | ||||
\(967\) | 37.3576 | + | 31.3467i | 1.20134 | + | 1.00804i | 0.999591 | + | 0.0286047i | \(0.00910640\pi\) |
0.201747 | + | 0.979438i | \(0.435338\pi\) | |||||||
\(968\) | 17.8269 | 0.572979 | ||||||||
\(969\) | −3.36856 | − | 1.03090i | −0.108214 | − | 0.0331174i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9752 | + | 19.2784i | 0.737308 | + | 0.618675i | 0.932113 | − | 0.362167i | \(-0.117963\pi\) |
−0.194805 | + | 0.980842i | \(0.562407\pi\) | |||||||
\(972\) | 12.5248 | − | 4.55864i | 0.401732 | − | 0.146218i | ||||
\(973\) | 15.0781 | + | 85.5120i | 0.483381 | + | 2.74139i | ||||
\(974\) | 4.85765 | − | 27.5491i | 0.155649 | − | 0.882730i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.05753 | − | 7.02784i | −0.129878 | − | 0.224956i | ||||
\(977\) | −26.8514 | + | 46.5081i | −0.859054 | + | 1.48792i | 0.0137792 | + | 0.999905i | \(0.495614\pi\) |
−0.872833 | + | 0.488019i | \(0.837720\pi\) | |||||||
\(978\) | −2.61785 | + | 2.19664i | −0.0837096 | + | 0.0702407i | ||||
\(979\) | −39.5193 | + | 33.1606i | −1.26304 | + | 1.05982i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8442 | + | 18.7826i | 0.346227 | + | 0.599683i | ||||
\(982\) | −2.79400 | − | 1.01693i | −0.0891600 | − | 0.0324516i | ||||
\(983\) | 10.0589 | − | 57.0469i | 0.320829 | − | 1.81951i | −0.216665 | − | 0.976246i | \(-0.569518\pi\) |
0.537495 | − | 0.843267i | \(-0.319371\pi\) | |||||||
\(984\) | 0.191007 | + | 1.08326i | 0.00608908 | + | 0.0345329i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.90292 | + | 3.27494i | 0.124294 | + | 0.104295i | ||||
\(987\) | −8.74864 | −0.278472 | ||||||||
\(988\) | 2.05367 | − | 16.6872i | 0.0653360 | − | 0.530890i | ||||
\(989\) | 7.89434 | 0.251025 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.56906 | − | 2.39094i | 0.208673 | − | 0.0759508i | −0.235569 | − | 0.971858i | \(-0.575695\pi\) |
0.444242 | + | 0.895907i | \(0.353473\pi\) | |||||||
\(992\) | 1.42457 | + | 8.07914i | 0.0452302 | + | 0.256513i | ||||
\(993\) | 1.87275 | − | 10.6209i | 0.0594301 | − | 0.337045i | ||||
\(994\) | −27.5458 | − | 10.0258i | −0.873698 | − | 0.318000i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.16773 | + | 7.21872i | −0.132060 | + | 0.228734i | ||||
\(997\) | −29.0837 | + | 24.4042i | −0.921091 | + | 0.772887i | −0.974196 | − | 0.225702i | \(-0.927533\pi\) |
0.0531052 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(998\) | 14.1236 | − | 11.8511i | 0.447074 | − | 0.375140i | ||||
\(999\) | −17.0851 | + | 29.5923i | −0.540550 | + | 0.936260i |
(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 | 950.2.l.i.301.2 | 18 | ||
5.2 | odd | 4 | 950.2.u.g.149.2 | 36 | |||
5.3 | odd | 4 | 950.2.u.g.149.5 | 36 | |||
5.4 | even | 2 | 190.2.k.d.111.2 | yes | 18 | ||
19.6 | even | 9 | inner | 950.2.l.i.101.2 | 18 | ||
95.14 | odd | 18 | 3610.2.a.bj.1.4 | 9 | |||
95.24 | even | 18 | 3610.2.a.bi.1.6 | 9 | |||
95.44 | even | 18 | 190.2.k.d.101.2 | ✓ | 18 | ||
95.63 | odd | 36 | 950.2.u.g.899.2 | 36 | |||
95.82 | odd | 36 | 950.2.u.g.899.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.101.2 | ✓ | 18 | 95.44 | even | 18 | ||
190.2.k.d.111.2 | yes | 18 | 5.4 | even | 2 | ||
950.2.l.i.101.2 | 18 | 19.6 | even | 9 | inner | ||
950.2.l.i.301.2 | 18 | 1.1 | even | 1 | trivial | ||
950.2.u.g.149.2 | 36 | 5.2 | odd | 4 | |||
950.2.u.g.149.5 | 36 | 5.3 | odd | 4 | |||
950.2.u.g.899.2 | 36 | 95.63 | odd | 36 | |||
950.2.u.g.899.5 | 36 | 95.82 | odd | 36 | |||
3610.2.a.bi.1.6 | 9 | 95.24 | even | 18 | |||
3610.2.a.bj.1.4 | 9 | 95.14 | odd | 18 |