Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(215,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.4 | ||
Root | \(1.65604 + 0.956115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.215 |
Dual form | 567.2.i.f.269.3 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.656620i | 0.464301i | 0.972680 | + | 0.232150i | \(0.0745761\pi\) | ||||
−0.972680 | + | 0.232150i | \(0.925424\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.56885 | 0.784425 | ||||||||
\(5\) | −1.65604 | − | 2.86834i | −0.740603 | − | 1.28276i | −0.952221 | − | 0.305410i | \(-0.901207\pi\) |
0.211618 | − | 0.977352i | \(-0.432127\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78442 | + | 1.95341i | 0.674449 | + | 0.738321i | ||||
\(8\) | 2.34338i | 0.828510i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.88341 | − | 1.08739i | 0.595588 | − | 0.343863i | ||||
\(11\) | 2.02943 | + | 1.17169i | 0.611895 | + | 0.353278i | 0.773707 | − | 0.633544i | \(-0.218400\pi\) |
−0.161812 | + | 0.986822i | \(0.551734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.36834 | − | 0.790014i | −0.379510 | − | 0.219110i | 0.298095 | − | 0.954536i | \(-0.403649\pi\) |
−0.677605 | + | 0.735426i | \(0.736982\pi\) | |||||||
\(14\) | −1.28265 | + | 1.17169i | −0.342803 | + | 0.313147i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59899 | 0.399747 | ||||||||
\(17\) | −0.568650 | − | 0.984931i | −0.137918 | − | 0.238881i | 0.788790 | − | 0.614662i | \(-0.210708\pi\) |
−0.926708 | + | 0.375781i | \(0.877374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.85327 | + | 2.22469i | 0.884002 | + | 0.510379i | 0.871976 | − | 0.489549i | \(-0.162839\pi\) |
0.0120260 | + | 0.999928i | \(0.496172\pi\) | |||||||
\(20\) | −2.59808 | − | 4.50000i | −0.580948 | − | 1.00623i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.769355 | + | 1.33256i | −0.164027 | + | 0.284103i | ||||
\(23\) | 8.13484 | − | 4.69665i | 1.69623 | − | 0.979320i | 0.746957 | − | 0.664872i | \(-0.231514\pi\) |
0.949275 | − | 0.314448i | \(-0.101819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.98493 | + | 5.17005i | −0.596986 | + | 1.03401i | ||||
\(26\) | 0.518739 | − | 0.898482i | 0.101733 | − | 0.176207i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.79949 | + | 3.06461i | 0.529055 | + | 0.579158i | ||||
\(29\) | 3.16673 | − | 1.82831i | 0.588046 | − | 0.339509i | −0.176278 | − | 0.984340i | \(-0.556406\pi\) |
0.764325 | + | 0.644832i | \(0.223073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.31873i | − | 1.31448i | −0.753680 | − | 0.657241i | \(-0.771723\pi\) | ||
0.753680 | − | 0.657241i | \(-0.228277\pi\) | |||||||
\(32\) | 5.73669i | 1.01411i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.646726 | − | 0.373387i | 0.110913 | − | 0.0640354i | ||||
\(35\) | 2.64799 | − | 8.35327i | 0.447592 | − | 1.41196i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.58392 | − | 4.47548i | 0.424794 | − | 0.735764i | −0.571607 | − | 0.820527i | \(-0.693680\pi\) |
0.996401 | + | 0.0847630i | \(0.0270133\pi\) | |||||||
\(38\) | −1.46078 | + | 2.53014i | −0.236969 | + | 0.410443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.72162 | − | 3.88073i | 1.06278 | − | 0.613597i | ||||
\(41\) | −4.82277 | + | 8.35327i | −0.753189 | + | 1.30456i | 0.193080 | + | 0.981183i | \(0.438152\pi\) |
−0.946269 | + | 0.323379i | \(0.895181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08392 | + | 1.87740i | 0.165296 | + | 0.286301i | 0.936760 | − | 0.349971i | \(-0.113809\pi\) |
−0.771464 | + | 0.636273i | \(0.780475\pi\) | |||||||
\(44\) | 3.18386 | + | 1.83821i | 0.479986 | + | 0.277120i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08392 | + | 5.34150i | 0.454699 | + | 0.787562i | ||||
\(47\) | −5.58668 | −0.814901 | −0.407450 | − | 0.913227i | \(-0.633582\pi\) | ||||
−0.407450 | + | 0.913227i | \(0.633582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.631656 | + | 6.97144i | −0.0902366 | + | 0.995920i | ||||
\(50\) | −3.39476 | − | 1.95997i | −0.480092 | − | 0.277181i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.14673 | − | 1.23941i | −0.297697 | − | 0.171876i | ||||
\(53\) | −8.70349 | + | 5.02496i | −1.19552 | + | 0.690232i | −0.959552 | − | 0.281530i | \(-0.909158\pi\) |
−0.235964 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.76146i | − | 1.04655i | ||||||
\(56\) | −4.57759 | + | 4.18158i | −0.611706 | + | 0.558788i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.20051 | + | 2.07934i | 0.157634 | + | 0.273030i | ||||
\(59\) | 2.17478 | 0.283132 | 0.141566 | − | 0.989929i | \(-0.454786\pi\) | ||||
0.141566 | + | 0.989929i | \(0.454786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.00665i | − | 0.512999i | −0.966544 | − | 0.256500i | \(-0.917431\pi\) | ||
0.966544 | − | 0.256500i | \(-0.0825692\pi\) | |||||||
\(62\) | 4.80563 | 0.610315 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.568850 | −0.0711062 | ||||||||
\(65\) | 5.23317i | 0.649095i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7668 | −1.31538 | −0.657689 | − | 0.753290i | \(-0.728466\pi\) | ||||
−0.657689 | + | 0.753290i | \(0.728466\pi\) | |||||||
\(68\) | −0.892126 | − | 1.54521i | −0.108186 | − | 0.187384i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.48493 | + | 1.73872i | 0.655575 | + | 0.207817i | ||||
\(71\) | 6.39331i | 0.758746i | 0.925244 | + | 0.379373i | \(0.123860\pi\) | ||||
−0.925244 | + | 0.379373i | \(0.876140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.25176 | + | 5.34150i | −1.08284 | + | 0.625176i | −0.931660 | − | 0.363331i | \(-0.881639\pi\) |
−0.151176 | + | 0.988507i | \(0.548306\pi\) | |||||||
\(74\) | 2.93869 | + | 1.69665i | 0.341616 | + | 0.197232i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.04521 | + | 3.49020i | 0.693433 | + | 0.400354i | ||||
\(77\) | 1.33256 | + | 6.05510i | 0.151860 | + | 0.690043i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.23317 | 0.138743 | 0.0693714 | − | 0.997591i | \(-0.477901\pi\) | ||||
0.0693714 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(80\) | −2.64799 | − | 4.58645i | −0.296054 | − | 0.512780i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.48493 | − | 3.16673i | −0.605709 | − | 0.349706i | ||||
\(83\) | 0.518739 | + | 0.898482i | 0.0569390 | + | 0.0986213i | 0.893090 | − | 0.449878i | \(-0.148533\pi\) |
−0.836151 | + | 0.548499i | \(0.815199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.88341 | + | 3.26217i | −0.204285 | + | 0.353832i | ||||
\(86\) | −1.23274 | + | 0.711723i | −0.132930 | + | 0.0767471i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.74571 | + | 4.75572i | −0.292694 | + | 0.506961i | ||||
\(89\) | −3.73538 | + | 6.46986i | −0.395949 | + | 0.685804i | −0.993222 | − | 0.116234i | \(-0.962918\pi\) |
0.597273 | + | 0.802038i | \(0.296251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.898482 | − | 4.08266i | −0.0941866 | − | 0.427979i | ||||
\(92\) | 12.7623 | − | 7.36834i | 1.33057 | − | 0.768203i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 3.66833i | − | 0.378359i | ||||||
\(95\) | − | 14.7367i | − | 1.51195i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7367 | − | 6.77618i | 1.19168 | − | 0.688017i | 0.232993 | − | 0.972478i | \(-0.425148\pi\) |
0.958687 | + | 0.284462i | \(0.0918149\pi\) | |||||||
\(98\) | −4.57759 | − | 0.414758i | −0.462407 | − | 0.0418969i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.68291 | + | 8.11103i | −0.468291 | + | 0.811103i | ||||
\(101\) | 6.85219 | − | 11.8683i | 0.681819 | − | 1.18094i | −0.292607 | − | 0.956233i | \(-0.594523\pi\) |
0.974425 | − | 0.224711i | \(-0.0721440\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.23669 | + | 2.44605i | −0.417453 | + | 0.241017i | −0.693987 | − | 0.719987i | \(-0.744148\pi\) |
0.276534 | + | 0.961004i | \(0.410814\pi\) | |||||||
\(104\) | 1.85130 | − | 3.20655i | 0.181535 | − | 0.314428i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29949 | − | 5.71489i | −0.320475 | − | 0.555079i | ||||
\(107\) | −2.12487 | − | 1.22679i | −0.205419 | − | 0.118599i | 0.393762 | − | 0.919213i | \(-0.371173\pi\) |
−0.599180 | + | 0.800614i | \(0.704507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.16784 | − | 3.75481i | −0.207641 | − | 0.359645i | 0.743330 | − | 0.668925i | \(-0.233245\pi\) |
−0.950971 | + | 0.309280i | \(0.899912\pi\) | |||||||
\(110\) | 5.09633 | 0.485916 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.85327 | + | 3.12349i | 0.269609 | + | 0.295142i | ||||
\(113\) | −6.20086 | − | 3.58007i | −0.583328 | − | 0.336784i | 0.179127 | − | 0.983826i | \(-0.442673\pi\) |
−0.762455 | + | 0.647042i | \(0.776006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.9432 | − | 15.5557i | −2.51247 | − | 1.45058i | ||||
\(116\) | 4.96812 | − | 2.86834i | 0.461278 | − | 0.266319i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.42800i | 0.131458i | ||||||||
\(119\) | 0.909265 | − | 2.86834i | 0.0833522 | − | 0.262941i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.75429 | − | 4.77056i | −0.250390 | − | 0.433688i | ||||
\(122\) | 2.63085 | 0.238186 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 11.4820i | − | 1.03111i | ||||||
\(125\) | 3.21226 | 0.287313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7065 | −1.57120 | −0.785601 | − | 0.618733i | \(-0.787646\pi\) | ||||
−0.785601 | + | 0.618733i | \(0.787646\pi\) | |||||||
\(128\) | 11.0999i | 0.981098i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.43621 | −0.301375 | ||||||||
\(131\) | 6.80228 | + | 11.7819i | 0.594318 | + | 1.02939i | 0.993643 | + | 0.112579i | \(0.0359113\pi\) |
−0.399325 | + | 0.916810i | \(0.630755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.53014 | + | 11.4968i | 0.219391 | + | 0.996902i | ||||
\(134\) | − | 7.06972i | − | 0.610731i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.30807 | − | 1.33256i | 0.197915 | − | 0.114266i | ||||
\(137\) | −8.79893 | − | 5.08007i | −0.751744 | − | 0.434019i | 0.0745799 | − | 0.997215i | \(-0.476238\pi\) |
−0.826324 | + | 0.563196i | \(0.809572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.33821 | + | 1.92731i | 0.283143 | + | 0.163473i | 0.634845 | − | 0.772639i | \(-0.281064\pi\) |
−0.351703 | + | 0.936112i | \(0.614397\pi\) | |||||||
\(140\) | 4.15429 | − | 13.1050i | 0.351102 | − | 1.10758i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.19798 | −0.352286 | ||||||||
\(143\) | −1.85130 | − | 3.20655i | −0.154814 | − | 0.268145i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4884 | − | 6.05551i | −0.871018 | − | 0.502882i | ||||
\(146\) | −3.50734 | − | 6.07489i | −0.290270 | − | 0.502762i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.05378 | − | 7.02135i | 0.333219 | − | 0.577152i | ||||
\(149\) | −4.39947 | + | 2.54003i | −0.360418 | + | 0.208088i | −0.669264 | − | 0.743024i | \(-0.733391\pi\) |
0.308846 | + | 0.951112i | \(0.400057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.15277 | + | 15.8531i | −0.744842 | + | 1.29010i | 0.205427 | + | 0.978672i | \(0.434142\pi\) |
−0.950269 | + | 0.311431i | \(0.899192\pi\) | |||||||
\(152\) | −5.21329 | + | 9.02968i | −0.422854 | + | 0.732404i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.97590 | + | 0.874988i | −0.320387 | + | 0.0705085i | ||||
\(155\) | −20.9926 | + | 12.1201i | −1.68617 | + | 0.973510i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.31208i | 0.264333i | 0.991228 | + | 0.132166i | \(0.0421933\pi\) | ||||
−0.991228 | + | 0.132166i | \(0.957807\pi\) | |||||||
\(158\) | 0.809727i | 0.0644184i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.4548 | − | 9.50018i | 1.30087 | − | 0.751055i | ||||
\(161\) | 23.6905 | + | 7.50989i | 1.86708 | + | 0.591863i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.14673 | − | 1.98619i | 0.0898185 | − | 0.155570i | −0.817616 | − | 0.575764i | \(-0.804705\pi\) |
0.907434 | + | 0.420194i | \(0.138038\pi\) | |||||||
\(164\) | −7.56619 | + | 13.1050i | −0.590820 | + | 1.02333i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.589962 | + | 0.340615i | −0.0457899 | + | 0.0264368i | ||||
\(167\) | −1.33256 | + | 2.30807i | −0.103117 | + | 0.178604i | −0.912967 | − | 0.408033i | \(-0.866215\pi\) |
0.809850 | + | 0.586636i | \(0.199548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.25176 | − | 9.09631i | −0.403981 | − | 0.699716i | ||||
\(170\) | −2.14201 | − | 1.23669i | −0.164284 | − | 0.0948496i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.70051 | + | 2.94536i | 0.129662 | + | 0.224582i | ||||
\(173\) | 2.56530 | 0.195036 | 0.0975182 | − | 0.995234i | \(-0.468910\pi\) | ||||
0.0975182 | + | 0.995234i | \(0.468910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4256 | + | 3.39476i | −1.16607 | + | 0.256620i | ||||
\(176\) | 3.24503 | + | 1.87352i | 0.244603 | + | 0.141222i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.24824 | − | 2.45272i | −0.318419 | − | 0.183839i | ||||
\(179\) | 11.9828 | − | 6.91827i | 0.895636 | − | 0.517096i | 0.0198545 | − | 0.999803i | \(-0.493680\pi\) |
0.875782 | + | 0.482707i | \(0.160346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.74008i | 0.352328i | 0.984361 | + | 0.176164i | \(0.0563688\pi\) | ||||
−0.984361 | + | 0.176164i | \(0.943631\pi\) | |||||||
\(182\) | 2.68076 | − | 0.589962i | 0.198711 | − | 0.0437309i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.0060 | + | 19.0630i | 0.811376 | + | 1.40534i | ||||
\(185\) | −17.1163 | −1.25841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.66513i | − | 0.194893i | ||||||
\(188\) | −8.76466 | −0.639228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.67641 | 0.702001 | ||||||||
\(191\) | − | 8.34338i | − | 0.603706i | −0.953355 | − | 0.301853i | \(-0.902395\pi\) | ||
0.953355 | − | 0.301853i | \(-0.0976051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8442 | −1.28446 | −0.642229 | − | 0.766513i | \(-0.721990\pi\) | ||||
−0.642229 | + | 0.766513i | \(0.721990\pi\) | |||||||
\(194\) | 4.44938 | + | 7.70655i | 0.319447 | + | 0.553298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.990974 | + | 10.9371i | −0.0707838 | + | 0.781225i | ||||
\(197\) | − | 15.1102i | − | 1.07656i | −0.842767 | − | 0.538279i | \(-0.819075\pi\) | ||
0.842767 | − | 0.538279i | \(-0.180925\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | + | 4.33013i | −0.531661 | + | 0.306955i | −0.741693 | − | 0.670740i | \(-0.765977\pi\) |
0.210032 | + | 0.977695i | \(0.432643\pi\) | |||||||
\(200\) | −12.1154 | − | 6.99483i | −0.856688 | − | 0.494609i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.79300 | + | 4.49929i | 0.548313 | + | 0.316569i | ||||
\(203\) | 9.22223 | + | 2.92345i | 0.647274 | + | 0.205186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.9468 | 2.23126 | ||||||||
\(206\) | −1.60613 | − | 2.78190i | −0.111904 | − | 0.193824i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.18797 | − | 1.26322i | −0.151708 | − | 0.0875887i | ||||
\(209\) | 5.21329 | + | 9.02968i | 0.360611 | + | 0.624596i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.29047 | − | 12.6275i | 0.501897 | − | 0.869310i | −0.498101 | − | 0.867119i | \(-0.665969\pi\) |
0.999998 | − | 0.00219128i | \(-0.000697506\pi\) | |||||||
\(212\) | −13.6545 | + | 7.88341i | −0.937793 | + | 0.541435i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.805537 | − | 1.39523i | 0.0550654 | − | 0.0953760i | ||||
\(215\) | 3.59002 | − | 6.21810i | 0.244838 | − | 0.424071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2965 | − | 13.0597i | 0.970510 | − | 0.886552i | ||||
\(218\) | 2.46548 | − | 1.42345i | 0.166984 | − | 0.0964080i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 12.1766i | − | 0.820943i | ||||||
\(221\) | 1.79696i | 0.120877i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.16531 | + | 5.29159i | −0.613754 | + | 0.354351i | −0.774433 | − | 0.632655i | \(-0.781965\pi\) |
0.160679 | + | 0.987007i | \(0.448632\pi\) | |||||||
\(224\) | −11.2061 | + | 10.2367i | −0.748741 | + | 0.683967i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.35075 | − | 4.07161i | 0.156369 | − | 0.270839i | ||||
\(227\) | 3.36199 | − | 5.82314i | 0.223143 | − | 0.386495i | −0.732618 | − | 0.680640i | \(-0.761702\pi\) |
0.955761 | + | 0.294145i | \(0.0950350\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6201 | − | 6.13152i | 0.701796 | − | 0.405182i | −0.106220 | − | 0.994343i | \(-0.533875\pi\) |
0.808016 | + | 0.589161i | \(0.200541\pi\) | |||||||
\(230\) | 10.2142 | − | 17.6915i | 0.673503 | − | 1.16654i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.28442 | + | 7.42084i | 0.281286 | + | 0.487202i | ||||
\(233\) | −4.87268 | − | 2.81324i | −0.319220 | − | 0.184302i | 0.331825 | − | 0.943341i | \(-0.392336\pi\) |
−0.651045 | + | 0.759039i | \(0.725669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.25176 | + | 16.0245i | 0.603518 | + | 1.04532i | ||||
\(236\) | 3.41190 | 0.222096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.88341 | + | 0.597042i | 0.122084 | + | 0.0387005i | ||||
\(239\) | 13.8213 | + | 7.97976i | 0.894028 | + | 0.516168i | 0.875258 | − | 0.483656i | \(-0.160692\pi\) |
0.0187704 | + | 0.999824i | \(0.494025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.97338 | + | 2.29403i | 0.255948 | + | 0.147771i | 0.622485 | − | 0.782632i | \(-0.286123\pi\) |
−0.366537 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(242\) | 3.13245 | − | 1.80852i | 0.201361 | − | 0.116256i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.28583i | − | 0.402409i | ||||||
\(245\) | 21.0425 | − | 9.73317i | 1.34436 | − | 0.621830i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.51507 | − | 6.08828i | −0.223659 | − | 0.387388i | ||||
\(248\) | 17.1506 | 1.08906 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.10923i | 0.133400i | ||||||||
\(251\) | −13.8042 | −0.871314 | −0.435657 | − | 0.900113i | \(-0.643484\pi\) | ||||
−0.435657 | + | 0.900113i | \(0.643484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0121 | 1.38389 | ||||||||
\(254\) | − | 11.6265i | − | 0.729510i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.42609 | −0.526631 | ||||||||
\(257\) | −4.48215 | − | 7.76331i | −0.279589 | − | 0.484262i | 0.691694 | − | 0.722191i | \(-0.256865\pi\) |
−0.971283 | + | 0.237929i | \(0.923531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.3533 | − | 2.93869i | 0.829732 | − | 0.182601i | ||||
\(260\) | 8.21006i | 0.509166i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.73623 | + | 4.46652i | −0.477946 | + | 0.275942i | ||||
\(263\) | 24.7280 | + | 14.2767i | 1.52479 | + | 0.880340i | 0.999568 | + | 0.0293774i | \(0.00935247\pi\) |
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.8266 | + | 16.6431i | 1.77081 | + | 1.02238i | ||||
\(266\) | −7.54905 | + | 1.66134i | −0.462862 | + | 0.101863i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.8915 | −1.03181 | ||||||||
\(269\) | 11.9657 | + | 20.7251i | 0.729559 | + | 1.26363i | 0.957070 | + | 0.289858i | \(0.0936081\pi\) |
−0.227510 | + | 0.973776i | \(0.573059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6467 | + | 7.30159i | 0.768234 | + | 0.443540i | 0.832244 | − | 0.554409i | \(-0.187056\pi\) |
−0.0640103 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(272\) | −0.909265 | − | 1.57489i | −0.0551323 | − | 0.0954919i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.33568 | − | 5.77756i | 0.201516 | − | 0.349035i | ||||
\(275\) | −12.1154 | + | 6.99483i | −0.730586 | + | 0.421804i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1915 | + | 19.3842i | −0.672431 | + | 1.16468i | 0.304782 | + | 0.952422i | \(0.401416\pi\) |
−0.977213 | + | 0.212262i | \(0.931917\pi\) | |||||||
\(278\) | −1.26551 | + | 2.19193i | −0.0759005 | + | 0.131463i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.5749 | + | 6.20524i | 1.16982 | + | 0.370834i | ||||
\(281\) | −10.0517 | + | 5.80335i | −0.599634 | + | 0.346199i | −0.768897 | − | 0.639372i | \(-0.779194\pi\) |
0.169264 | + | 0.985571i | \(0.445861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.9937i | − | 0.891283i | −0.895211 | − | 0.445642i | \(-0.852976\pi\) | ||
0.895211 | − | 0.445642i | \(-0.147024\pi\) | |||||||
\(284\) | 10.0301i | 0.595179i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.10549 | − | 1.21560i | 0.124500 | − | 0.0718801i | ||||
\(287\) | −24.9233 | + | 5.48493i | −1.47117 | + | 0.323765i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.85327 | − | 13.6023i | 0.461957 | − | 0.800134i | ||||
\(290\) | 3.97617 | − | 6.88693i | 0.233489 | − | 0.404414i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.5146 | + | 8.38002i | −0.849404 | + | 0.490403i | ||||
\(293\) | 8.16762 | − | 14.1467i | 0.477157 | − | 0.826461i | −0.522500 | − | 0.852639i | \(-0.675001\pi\) |
0.999657 | + | 0.0261787i | \(0.00833389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.60152 | − | 6.23801i | −0.209688 | − | 0.363191i | ||||
\(296\) | 10.4877 | + | 6.05510i | 0.609588 | + | 0.351946i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.66784 | − | 2.88878i | −0.0966153 | − | 0.167343i | ||||
\(299\) | −14.8417 | −0.858317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.73317 | + | 5.46743i | −0.0998985 | + | 0.315137i | ||||
\(302\) | −10.4094 | − | 6.00989i | −0.598996 | − | 0.345831i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.16134 | + | 3.55725i | 0.353377 | + | 0.204022i | ||||
\(305\) | −11.4925 | + | 6.63517i | −0.658056 | + | 0.379929i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.17340i | 0.181115i | 0.995891 | + | 0.0905577i | \(0.0288650\pi\) | ||||
−0.995891 | + | 0.0905577i | \(0.971135\pi\) | |||||||
\(308\) | 2.09059 | + | 9.49955i | 0.119122 | + | 0.541287i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.95831 | − | 13.7842i | −0.452001 | − | 0.782889i | ||||
\(311\) | −25.1342 | −1.42523 | −0.712614 | − | 0.701556i | \(-0.752489\pi\) | ||||
−0.712614 | + | 0.701556i | \(0.752489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6441i | 1.05383i | 0.849919 | + | 0.526914i | \(0.176651\pi\) | ||||
−0.849919 | + | 0.526914i | \(0.823349\pi\) | |||||||
\(314\) | −2.17478 | −0.122730 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.93466 | 0.108833 | ||||||||
\(317\) | − | 7.98965i | − | 0.448744i | −0.974504 | − | 0.224372i | \(-0.927967\pi\) | ||
0.974504 | − | 0.224372i | \(-0.0720330\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.56885 | 0.479763 | ||||||||
\(320\) | 0.942037 | + | 1.63166i | 0.0526615 | + | 0.0912124i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.93115 | + | 15.5557i | −0.274802 | + | 0.866884i | ||||
\(323\) | − | 5.06028i | − | 0.281561i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.16882 | − | 4.71627i | 0.453125 | − | 0.261612i | ||||
\(326\) | 1.30417 | + | 0.752963i | 0.0722313 | + | 0.0417028i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.5749 | − | 11.3016i | −1.08084 | − | 0.624025i | ||||
\(329\) | −9.96901 | − | 10.9131i | −0.549609 | − | 0.601659i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.93466 | −0.491094 | −0.245547 | − | 0.969385i | \(-0.578967\pi\) | ||||
−0.245547 | + | 0.969385i | \(0.578967\pi\) | |||||||
\(332\) | 0.813824 | + | 1.40958i | 0.0446644 | + | 0.0773610i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.51552 | − | 0.874988i | −0.0829258 | − | 0.0478772i | ||||
\(335\) | 17.8303 | + | 30.8830i | 0.974173 | + | 1.68732i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.12263 | + | 3.67650i | −0.115627 | + | 0.200272i | −0.918030 | − | 0.396510i | \(-0.870221\pi\) |
0.802403 | + | 0.596782i | \(0.203554\pi\) | |||||||
\(338\) | 5.97282 | − | 3.44841i | 0.324879 | − | 0.187569i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.95479 | + | 5.11785i | −0.160246 | + | 0.277554i | ||||
\(341\) | 8.57528 | − | 14.8528i | 0.464377 | − | 0.804325i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7453 | + | 11.2061i | −0.796169 | + | 0.605074i | ||||
\(344\) | −4.39947 | + | 2.54003i | −0.237203 | + | 0.136949i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.68443i | 0.0905556i | ||||||||
\(347\) | 2.62648i | 0.140997i | 0.997512 | + | 0.0704985i | \(0.0224590\pi\) | ||||
−0.997512 | + | 0.0704985i | \(0.977541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.1387 | − | 16.2459i | 1.50623 | − | 0.869622i | 0.506255 | − | 0.862384i | \(-0.331029\pi\) |
0.999974 | − | 0.00723825i | \(-0.00230403\pi\) | |||||||
\(350\) | −2.22907 | − | 10.1288i | −0.119149 | − | 0.541407i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.72162 | + | 11.6422i | −0.358263 | + | 0.620531i | ||||
\(353\) | −11.6921 | + | 20.2513i | −0.622307 | + | 1.07787i | 0.366748 | + | 0.930321i | \(0.380471\pi\) |
−0.989055 | + | 0.147548i | \(0.952862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3382 | − | 10.5876i | 0.973291 | − | 0.561930i | ||||
\(356\) | −5.86024 | + | 10.1502i | −0.310592 | + | 0.537962i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.54268 | + | 7.86815i | 0.240088 | + | 0.415845i | ||||
\(359\) | 18.4900 | + | 10.6752i | 0.975865 | + | 0.563416i | 0.901019 | − | 0.433779i | \(-0.142820\pi\) |
0.0748455 | + | 0.997195i | \(0.476154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.398482 | + | 0.690192i | 0.0209728 | + | 0.0363259i | ||||
\(362\) | −3.11243 | −0.163586 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.40958 | − | 6.40508i | −0.0738823 | − | 0.335718i | ||||
\(365\) | 30.6425 | + | 17.6915i | 1.60390 | + | 0.926014i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4432 | − | 7.76146i | −0.701731 | − | 0.405145i | 0.106261 | − | 0.994338i | \(-0.466112\pi\) |
−0.807992 | + | 0.589194i | \(0.799446\pi\) | |||||||
\(368\) | 13.0075 | − | 7.50989i | 0.678064 | − | 0.391480i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.2389i | − | 0.584283i | ||||||
\(371\) | −25.3466 | − | 8.03486i | −1.31593 | − | 0.417149i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6764 | + | 20.2241i | 0.604582 | + | 1.04717i | 0.992117 | + | 0.125311i | \(0.0399930\pi\) |
−0.387536 | + | 0.921855i | \(0.626674\pi\) | |||||||
\(374\) | 1.74998 | 0.0904891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 13.0917i | − | 0.675153i | ||||||
\(377\) | −5.77756 | −0.297559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.53871 | 0.130405 | 0.0652024 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652024 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(380\) | − | 23.1196i | − | 1.18601i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.47843 | 0.280301 | ||||||||
\(383\) | −8.10207 | − | 14.0332i | −0.413996 | − | 0.717063i | 0.581326 | − | 0.813671i | \(-0.302534\pi\) |
−0.995323 | + | 0.0966078i | \(0.969201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.1613 | − | 13.8497i | 0.772693 | − | 0.705848i | ||||
\(386\) | − | 11.7169i | − | 0.596374i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.4131 | − | 10.6308i | 0.934783 | − | 0.539697i | ||||
\(389\) | −19.3410 | − | 11.1665i | −0.980626 | − | 0.566165i | −0.0781671 | − | 0.996940i | \(-0.524907\pi\) |
−0.902459 | + | 0.430775i | \(0.858240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.25176 | − | 5.34150i | −0.467881 | − | 0.270131i | ||||
\(392\) | −16.3367 | − | 1.48021i | −0.825130 | − | 0.0747619i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.92167 | 0.499847 | ||||||||
\(395\) | −2.04218 | − | 3.53717i | −0.102753 | − | 0.177974i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3116 | + | 16.3457i | 1.42092 | + | 0.820367i | 0.996377 | − | 0.0850420i | \(-0.0271025\pi\) |
0.424540 | + | 0.905409i | \(0.360436\pi\) | |||||||
\(398\) | −2.84325 | − | 4.92465i | −0.142519 | − | 0.246851i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.77287 | + | 8.26685i | −0.238643 | + | 0.413343i | ||||
\(401\) | 25.0515 | − | 14.4635i | 1.25101 | − | 0.722272i | 0.279701 | − | 0.960087i | \(-0.409765\pi\) |
0.971310 | + | 0.237815i | \(0.0764313\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.78190 | + | 10.0145i | −0.288017 | + | 0.498860i | ||||
\(404\) | 10.7501 | − | 18.6196i | 0.534835 | − | 0.926362i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.91959 | + | 6.05551i | −0.0952679 | + | 0.300530i | ||||
\(407\) | 10.4877 | − | 6.05510i | 0.519858 | − | 0.300140i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.05082i | 0.0519598i | 0.999662 | + | 0.0259799i | \(0.00827059\pi\) | ||||
−0.999662 | + | 0.0259799i | \(0.991729\pi\) | |||||||
\(410\) | 20.9769i | 1.03597i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.64673 | + | 3.83749i | −0.327461 | + | 0.189060i | ||||
\(413\) | 3.88073 | + | 4.24824i | 0.190958 | + | 0.209042i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.71810 | − | 2.97584i | 0.0843384 | − | 0.146078i | ||||
\(416\) | 4.53206 | − | 7.84976i | 0.222203 | − | 0.384866i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.92908 | + | 3.42315i | −0.290001 | + | 0.167432i | ||||
\(419\) | −1.56060 | + | 2.70304i | −0.0762402 | + | 0.132052i | −0.901625 | − | 0.432519i | \(-0.857625\pi\) |
0.825385 | + | 0.564571i | \(0.190958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.35327 | + | 7.54009i | 0.212166 | + | 0.367482i | 0.952392 | − | 0.304876i | \(-0.0986150\pi\) |
−0.740226 | + | 0.672358i | \(0.765282\pi\) | |||||||
\(422\) | 8.29145 | + | 4.78707i | 0.403621 | + | 0.233031i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.7754 | − | 20.3956i | −0.571864 | − | 0.990497i | ||||
\(425\) | 6.78952 | 0.329340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.82665 | − | 7.14957i | 0.378758 | − | 0.345992i | ||||
\(428\) | −3.33360 | − | 1.92465i | −0.161136 | − | 0.0930316i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.08293 | + | 2.35728i | 0.196897 | + | 0.113678i | ||||
\(431\) | −23.6279 | + | 13.6416i | −1.13811 | + | 0.657090i | −0.945963 | − | 0.324275i | \(-0.894880\pi\) |
−0.192151 | + | 0.981365i | \(0.561546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.8711i | 0.618547i | 0.950973 | + | 0.309274i | \(0.100086\pi\) | ||||
−0.950973 | + | 0.309274i | \(0.899914\pi\) | |||||||
\(434\) | 8.57528 | + | 9.38738i | 0.411627 | + | 0.450609i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.40101 | − | 5.89073i | −0.162879 | − | 0.282115i | ||||
\(437\) | 41.7944 | 1.99930 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.4445i | − | 0.880306i | −0.897923 | − | 0.440153i | \(-0.854924\pi\) | ||
0.897923 | − | 0.440153i | \(-0.145076\pi\) | |||||||
\(440\) | 18.1880 | 0.867081 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.17992 | −0.0561233 | ||||||||
\(443\) | − | 2.87000i | − | 0.136358i | −0.997673 | − | 0.0681790i | \(-0.978281\pi\) | ||
0.997673 | − | 0.0681790i | \(-0.0217189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.7437 | 1.17296 | ||||||||
\(446\) | −3.47457 | − | 6.01813i | −0.164526 | − | 0.284967i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.01507 | − | 1.11120i | −0.0479575 | − | 0.0524992i | ||||
\(449\) | − | 1.81675i | − | 0.0857380i | −0.999081 | − | 0.0428690i | \(-0.986350\pi\) | ||
0.999081 | − | 0.0428690i | \(-0.0136498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.5749 | + | 11.3016i | −0.921746 | + | 0.532170i | ||||
\(452\) | −9.72821 | − | 5.61659i | −0.457577 | − | 0.264182i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.82359 | + | 2.20755i | 0.179450 | + | 0.103605i | ||||
\(455\) | −10.2226 | + | 9.33821i | −0.479241 | + | 0.437782i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.15575 | 0.287954 | 0.143977 | − | 0.989581i | \(-0.454011\pi\) | ||||
0.143977 | + | 0.989581i | \(0.454011\pi\) | |||||||
\(458\) | 4.02608 | + | 6.97338i | 0.188126 | + | 0.325844i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −42.2699 | − | 24.4045i | −1.97084 | − | 1.13787i | ||||
\(461\) | −8.52537 | − | 14.7664i | −0.397066 | − | 0.687739i | 0.596296 | − | 0.802764i | \(-0.296638\pi\) |
−0.993363 | + | 0.115026i | \(0.963305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7065 | + | 25.4725i | −0.683471 | + | 1.18381i | 0.290443 | + | 0.956892i | \(0.406197\pi\) |
−0.973915 | + | 0.226915i | \(0.927136\pi\) | |||||||
\(464\) | 5.06356 | − | 2.92345i | 0.235070 | − | 0.135718i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.84723 | − | 3.19950i | 0.0855713 | − | 0.148214i | ||||
\(467\) | 13.5590 | − | 23.4849i | 0.627437 | − | 1.08675i | −0.360627 | − | 0.932710i | \(-0.617437\pi\) |
0.988064 | − | 0.154043i | \(-0.0492294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.2126 | − | 21.0321i | −0.887155 | − | 0.971171i | ||||
\(470\) | −10.5220 | + | 6.07489i | −0.485345 | + | 0.280214i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.09633i | 0.234578i | ||||||||
\(473\) | 5.08007i | 0.233582i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0035 | + | 13.2811i | −1.05547 | + | 0.609378i | ||||
\(476\) | 1.42650 | − | 4.50000i | 0.0653835 | − | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.23967 | + | 9.07538i | −0.239657 | + | 0.415098i | ||||
\(479\) | 10.7784 | − | 18.6688i | 0.492480 | − | 0.853000i | −0.507483 | − | 0.861662i | \(-0.669424\pi\) |
0.999962 | + | 0.00866176i | \(0.00275716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.07138 | + | 4.08266i | −0.322427 | + | 0.186153i | ||||
\(482\) | −1.50631 | + | 2.60900i | −0.0686104 | + | 0.118837i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.32106 | − | 7.48430i | −0.196412 | − | 0.340195i | ||||
\(485\) | −38.8728 | − | 22.4432i | −1.76512 | − | 1.01909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.29047 | + | 12.6275i | 0.330363 | + | 0.572205i | 0.982583 | − | 0.185825i | \(-0.0594956\pi\) |
−0.652220 | + | 0.758029i | \(0.726162\pi\) | |||||||
\(488\) | 9.38910 | 0.425025 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.39100 | + | 13.8170i | 0.288716 | + | 0.624187i | ||||
\(491\) | 0.245174 | + | 0.141551i | 0.0110645 | + | 0.00638811i | 0.505522 | − | 0.862814i | \(-0.331300\pi\) |
−0.494458 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.60152 | − | 2.07934i | −0.162204 | − | 0.0936486i | ||||
\(494\) | 3.99769 | − | 2.30807i | 0.179864 | − | 0.103845i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 11.7026i | − | 0.525461i | ||||||
\(497\) | −12.4888 | + | 11.4084i | −0.560198 | + | 0.511736i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.15277 | − | 10.6569i | −0.275436 | − | 0.477069i | 0.694809 | − | 0.719194i | \(-0.255489\pi\) |
−0.970245 | + | 0.242125i | \(0.922155\pi\) | |||||||
\(500\) | 5.03955 | 0.225375 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 9.06412i | − | 0.404552i | ||||||
\(503\) | 1.78425 | 0.0795559 | 0.0397779 | − | 0.999209i | \(-0.487335\pi\) | ||||
0.0397779 | + | 0.999209i | \(0.487335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.3900 | −2.01983 | ||||||||
\(506\) | 14.4536i | 0.642540i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −27.7789 | −1.23249 | ||||||||
\(509\) | −19.5362 | − | 33.8378i | −0.865928 | − | 1.49983i | −0.866122 | − | 0.499832i | \(-0.833395\pi\) |
0.000194027 | − | 1.00000i | \(-0.499938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.9432 | − | 8.54100i | −1.19190 | − | 0.377832i | ||||
\(512\) | 16.6670i | 0.736583i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.09755 | − | 2.94307i | 0.224843 | − | 0.129813i | ||||
\(515\) | 14.0322 | + | 8.10152i | 0.618334 | + | 0.356996i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3378 | − | 6.54585i | −0.498634 | − | 0.287886i | ||||
\(518\) | 1.92960 | + | 8.76803i | 0.0847820 | + | 0.385245i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.2633 | −0.537782 | ||||||||
\(521\) | 10.1814 | + | 17.6347i | 0.446056 | + | 0.772591i | 0.998125 | − | 0.0612072i | \(-0.0194950\pi\) |
−0.552070 | + | 0.833798i | \(0.686162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.24066 | + | 0.716293i | 0.0542501 | + | 0.0313213i | 0.526880 | − | 0.849940i | \(-0.323362\pi\) |
−0.472630 | + | 0.881261i | \(0.656695\pi\) | |||||||
\(524\) | 10.6718 | + | 18.4840i | 0.466198 | + | 0.807478i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.37439 | + | 16.2369i | −0.408743 | + | 0.707963i | ||||
\(527\) | −7.20844 | + | 4.16179i | −0.314005 | + | 0.181291i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.6171 | − | 56.4945i | 1.41814 | − | 2.45628i | ||||
\(530\) | −10.9282 | + | 18.9282i | −0.474690 | + | 0.822187i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.96941 | + | 18.0368i | 0.172096 | + | 0.781994i | ||||
\(533\) | 13.1984 | − | 7.62010i | 0.571686 | − | 0.330063i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.12647i | 0.351338i | ||||||||
\(536\) | − | 25.2308i | − | 1.08980i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.6085 | + | 7.85690i | −0.586706 | + | 0.338735i | ||||
\(539\) | −9.45027 | + | 13.4079i | −0.407052 | + | 0.577520i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.04521 | − | 8.73856i | 0.216910 | − | 0.375700i | −0.736951 | − | 0.675946i | \(-0.763735\pi\) |
0.953862 | + | 0.300246i | \(0.0970687\pi\) | |||||||
\(542\) | −4.79437 | + | 8.30410i | −0.205936 | + | 0.356692i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.65024 | − | 3.26217i | 0.242252 | − | 0.139864i | ||||
\(545\) | −7.18005 | + | 12.4362i | −0.307559 | + | 0.532709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.65024 | − | 6.32240i | −0.156073 | − | 0.270326i | 0.777376 | − | 0.629036i | \(-0.216550\pi\) |
−0.933449 | + | 0.358710i | \(0.883217\pi\) | |||||||
\(548\) | −13.8042 | − | 7.96986i | −0.589686 | − | 0.340456i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.59295 | − | 7.95521i | −0.195844 | − | 0.339211i | ||||
\(551\) | 16.2697 | 0.693112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.20051 | + | 2.40890i | 0.0935750 | + | 0.102437i | ||||
\(554\) | −12.7281 | − | 7.34855i | −0.540764 | − | 0.312210i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.23714 | + | 3.02367i | 0.222104 | + | 0.128232i | ||||
\(557\) | 19.7970 | − | 11.4298i | 0.838828 | − | 0.484297i | −0.0180379 | − | 0.999837i | \(-0.505742\pi\) |
0.856866 | + | 0.515540i | \(0.172409\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.42524i | − | 0.144872i | ||||||
\(560\) | 4.23410 | − | 13.3568i | 0.178923 | − | 0.564427i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.81060 | − | 6.60015i | −0.160740 | − | 0.278410i | ||||
\(563\) | −21.1096 | −0.889663 | −0.444832 | − | 0.895614i | \(-0.646736\pi\) | ||||
−0.444832 | + | 0.895614i | \(0.646736\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.7149i | 0.997694i | ||||||||
\(566\) | 9.84517 | 0.413824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.9819 | −0.628629 | ||||||||
\(569\) | 26.4536i | 1.10899i | 0.832186 | + | 0.554496i | \(0.187089\pi\) | ||||
−0.832186 | + | 0.554496i | \(0.812911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0301 | 0.503446 | 0.251723 | − | 0.967799i | \(-0.419003\pi\) | ||||
0.251723 | + | 0.967799i | \(0.419003\pi\) | |||||||
\(572\) | −2.90441 | − | 5.03059i | −0.121440 | − | 0.210340i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.60152 | − | 16.3651i | −0.150324 | − | 0.683067i | ||||
\(575\) | 56.0767i | 2.33856i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.9055 | + | 18.4207i | −1.32824 | + | 0.766862i | −0.985028 | − | 0.172395i | \(-0.944850\pi\) |
−0.343216 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(578\) | 8.93153 | + | 5.15662i | 0.371503 | + | 0.214487i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.4548 | − | 9.50018i | −0.683248 | − | 0.394473i | ||||
\(581\) | −0.829458 | + | 2.61659i | −0.0344117 | + | 0.108554i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5508 | −0.975374 | ||||||||
\(584\) | −12.5172 | − | 21.6804i | −0.517964 | − | 0.897140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.28903 | + | 5.36302i | 0.383726 | + | 0.221544i | ||||
\(587\) | −14.3856 | − | 24.9166i | −0.593758 | − | 1.02842i | −0.993721 | − | 0.111887i | \(-0.964310\pi\) |
0.399963 | − | 0.916531i | \(-0.369023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2819 | − | 28.2011i | 0.670884 | − | 1.16200i | ||||
\(590\) | 4.09601 | − | 2.36483i | 0.168630 | − | 0.0973585i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.13166 | − | 7.15624i | 0.169810 | − | 0.294120i | ||||
\(593\) | −5.29159 | + | 9.16531i | −0.217300 | + | 0.376374i | −0.953982 | − | 0.299865i | \(-0.903058\pi\) |
0.736682 | + | 0.676240i | \(0.236392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.73317 | + | 2.14201i | −0.399021 | + | 0.0878137i | ||||
\(596\) | −6.90210 | + | 3.98493i | −0.282721 | + | 0.163229i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 9.74535i | − | 0.398517i | ||||||
\(599\) | − | 18.1927i | − | 0.743333i | −0.928366 | − | 0.371666i | \(-0.878786\pi\) | ||
0.928366 | − | 0.371666i | \(-0.121214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.8719 | + | 13.2051i | −0.932963 | + | 0.538646i | −0.887747 | − | 0.460331i | \(-0.847731\pi\) |
−0.0452152 | + | 0.998977i | \(0.514397\pi\) | |||||||
\(602\) | −3.59002 | − | 1.13804i | −0.146318 | − | 0.0463829i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.3593 | + | 24.8711i | −0.584272 | + | 1.01199i | ||||
\(605\) | −9.12241 | + | 15.8005i | −0.370879 | + | 0.642381i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6312 | − | 12.4888i | 0.877983 | − | 0.506904i | 0.00799043 | − | 0.999968i | \(-0.497457\pi\) |
0.869993 | + | 0.493064i | \(0.164123\pi\) | |||||||
\(608\) | −12.7623 | + | 22.1050i | −0.517581 | + | 0.896477i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.35679 | − | 7.54618i | −0.176401 | − | 0.305536i | ||||
\(611\) | 7.64450 | + | 4.41355i | 0.309263 | + | 0.178553i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.05631 | + | 12.2219i | 0.285002 | + | 0.493637i | 0.972610 | − | 0.232445i | \(-0.0746725\pi\) |
−0.687608 | + | 0.726082i | \(0.741339\pi\) | |||||||
\(614\) | −2.08372 | −0.0840920 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1894 | + | 3.12270i | −0.571707 | + | 0.125817i | ||||
\(617\) | −12.6669 | − | 7.31324i | −0.509950 | − | 0.294420i | 0.222863 | − | 0.974850i | \(-0.428460\pi\) |
−0.732813 | + | 0.680430i | \(0.761793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9880 | + | 13.2721i | 0.923965 | + | 0.533452i | 0.884898 | − | 0.465785i | \(-0.154228\pi\) |
0.0390674 | + | 0.999237i | \(0.487561\pi\) | |||||||
\(620\) | −32.9343 | + | 19.0146i | −1.32267 | + | 0.763645i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 16.5036i | − | 0.661734i | ||||||
\(623\) | −19.3038 | + | 4.24824i | −0.773391 | + | 0.170202i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.60503 | + | 16.6364i | 0.384201 | + | 0.665456i | ||||
\(626\) | −12.2421 | −0.489293 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.19615i | 0.207349i | ||||||||
\(629\) | −5.87738 | −0.234347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.20304 | −0.326558 | −0.163279 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163279 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(632\) | 2.88979i | 0.114950i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.24617 | 0.208352 | ||||||||
\(635\) | 29.3227 | + | 50.7885i | 1.16364 | + | 2.01548i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.37186 | − | 9.04031i | 0.252462 | − | 0.358190i | ||||
\(638\) | 5.62648i | 0.222755i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.8382 | − | 18.3818i | 1.25852 | − | 0.726604i | ||||
\(641\) | 13.8996 | + | 8.02496i | 0.549003 | + | 0.316967i | 0.748720 | − | 0.662887i | \(-0.230669\pi\) |
−0.199717 | + | 0.979854i | \(0.564002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.8719 | − | 13.2051i | −0.901978 | − | 0.520757i | −0.0241366 | − | 0.999709i | \(-0.507684\pi\) |
−0.877841 | + | 0.478951i | \(0.841017\pi\) | |||||||
\(644\) | 37.1669 | + | 11.7819i | 1.46458 | + | 0.464272i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.32268 | 0.130729 | ||||||||
\(647\) | −15.8508 | − | 27.4543i | −0.623158 | − | 1.07934i | −0.988894 | − | 0.148623i | \(-0.952516\pi\) |
0.365736 | − | 0.930719i | \(-0.380817\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.41355 | + | 2.54817i | 0.173247 | + | 0.100024i | ||||
\(650\) | 3.09680 | + | 5.36382i | 0.121467 | + | 0.210386i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.79904 | − | 3.11603i | 0.0704558 | − | 0.122033i | ||||
\(653\) | −11.5096 | + | 6.64506i | −0.450405 | + | 0.260041i | −0.708001 | − | 0.706211i | \(-0.750403\pi\) |
0.257596 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5297 | − | 39.0226i | 0.880308 | − | 1.52474i | ||||
\(656\) | −7.71155 | + | 13.3568i | −0.301085 | + | 0.521495i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.16576 | − | 6.54585i | 0.279351 | − | 0.255184i | ||||
\(659\) | 31.3609 | − | 18.1062i | 1.22165 | − | 0.705319i | 0.256379 | − | 0.966576i | \(-0.417470\pi\) |
0.965269 | + | 0.261257i | \(0.0841372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.7930i | 1.97562i | 0.155674 | + | 0.987809i | \(0.450245\pi\) | ||||
−0.155674 | + | 0.987809i | \(0.549755\pi\) | |||||||
\(662\) | − | 5.86668i | − | 0.228015i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.10549 | + | 1.21560i | −0.0817087 | + | 0.0471745i | ||||
\(665\) | 28.7869 | − | 26.2965i | 1.11631 | − | 1.01973i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1739 | − | 29.7460i | 0.664975 | − | 1.15177i | ||||
\(668\) | −2.09059 | + | 3.62101i | −0.0808874 | + | 0.140101i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.2784 | + | 11.7077i | −0.783422 | + | 0.452309i | ||||
\(671\) | 4.69455 | − | 8.13120i | 0.181231 | − | 0.313902i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.66432 | − | 2.88269i | −0.0641550 | − | 0.111120i | 0.832164 | − | 0.554530i | \(-0.187102\pi\) |
−0.896319 | + | 0.443410i | \(0.853769\pi\) | |||||||
\(674\) | −2.41407 | − | 1.39376i | −0.0929864 | − | 0.0536857i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.23922 | − | 14.2707i | −0.316893 | − | 0.548875i | ||||
\(677\) | 19.9380 | 0.766280 | 0.383140 | − | 0.923690i | \(-0.374843\pi\) | ||||
0.383140 | + | 0.923690i | \(0.374843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.1799 | + | 10.8350i | 1.31171 | + | 0.415810i | ||||
\(680\) | −7.64450 | − | 4.41355i | −0.293153 | − | 0.169252i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.75267 | + | 5.63070i | 0.373449 | + | 0.215611i | ||||
\(683\) | 24.8234 | − | 14.3318i | 0.949843 | − | 0.548392i | 0.0568107 | − | 0.998385i | \(-0.481907\pi\) |
0.893032 | + | 0.449993i | \(0.148574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.6512i | 1.28574i | ||||||||
\(686\) | −7.35817 | − | 9.68204i | −0.280936 | − | 0.369662i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.73317 | + | 3.00195i | 0.0660766 | + | 0.114448i | ||||
\(689\) | 15.8792 | 0.604948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3674i | 0.774812i | 0.921909 | + | 0.387406i | \(0.126629\pi\) | ||||
−0.921909 | + | 0.387406i | \(0.873371\pi\) | |||||||
\(692\) | 4.02458 | 0.152991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.72460 | −0.0654650 | ||||||||
\(695\) | − | 12.7668i | − | 0.484273i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9699 | 0.415513 | ||||||||
\(698\) | 10.6674 | + | 18.4764i | 0.403766 | + | 0.699343i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.2005 | + | 5.32587i | −0.914693 | + | 0.201299i | ||||
\(701\) | − | 49.1172i | − | 1.85513i | −0.373659 | − | 0.927566i | \(-0.621897\pi\) | ||
0.373659 | − | 0.927566i | \(-0.378103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.9131 | − | 11.4968i | 0.751037 | − | 0.433611i | ||||
\(704\) | −1.15444 | − | 0.666515i | −0.0435095 | − | 0.0251202i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.2974 | − | 7.67727i | −0.500455 | − | 0.288938i | ||||
\(707\) | 35.4110 | − | 7.79300i | 1.33177 | − | 0.293086i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3658 | 0.877522 | 0.438761 | − | 0.898604i | \(-0.355418\pi\) | ||||
0.438761 | + | 0.898604i | \(0.355418\pi\) | |||||||
\(710\) | 6.95201 | + | 12.0412i | 0.260904 | + | 0.451900i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.1613 | − | 8.75340i | −0.568195 | − | 0.328048i | ||||
\(713\) | −34.3735 | − | 59.5367i | −1.28730 | − | 2.22967i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.13166 | + | 10.6203i | −0.229311 | + | 0.397178i | ||||
\(716\) | 18.7992 | − | 10.8537i | 0.702559 | − | 0.405623i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.00956 | + | 12.1409i | −0.261594 | + | 0.453095i | ||||
\(719\) | −6.33345 | + | 10.9699i | −0.236198 | + | 0.409107i | −0.959620 | − | 0.281299i | \(-0.909235\pi\) |
0.723422 | + | 0.690406i | \(0.242568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3382 | − | 3.91121i | −0.459499 | − | 0.145661i | ||||
\(722\) | −0.453194 | + | 0.261652i | −0.0168661 | + | 0.00973767i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.43648i | 0.276374i | ||||||||
\(725\) | 21.8295i | 0.810728i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.34172 | − | 1.35199i | 0.0868495 | − | 0.0501426i | −0.455946 | − | 0.890007i | \(-0.650699\pi\) |
0.542796 | + | 0.839865i | \(0.317366\pi\) | |||||||
\(728\) | 9.56723 | − | 2.10549i | 0.354585 | − | 0.0780345i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.6166 | + | 20.1205i | −0.429949 | + | 0.744694i | ||||
\(731\) | 1.23274 | − | 2.13517i | 0.0455946 | − | 0.0789721i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8869 | + | 10.9044i | −0.697605 | + | 0.402762i | −0.806455 | − | 0.591296i | \(-0.798616\pi\) |
0.108850 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(734\) | 5.09633 | − | 8.82710i | 0.188109 | − | 0.325814i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.9432 | + | 46.6671i | 0.993141 | + | 1.72017i | ||||
\(737\) | −21.8505 | − | 12.6154i | −0.804873 | − | 0.464694i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0633 | − | 27.8225i | −0.590899 | − | 1.02347i | −0.994112 | − | 0.108361i | \(-0.965440\pi\) |
0.403212 | − | 0.915107i | \(-0.367894\pi\) | |||||||
\(740\) | −26.8529 | −0.987131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.27585 | − | 16.6431i | 0.193683 | − | 0.610986i | ||||
\(743\) | −35.7433 | − | 20.6364i | −1.31129 | − | 0.757075i | −0.328983 | − | 0.944336i | \(-0.606706\pi\) |
−0.982310 | + | 0.187261i | \(0.940039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5714 | + | 8.41279i | 0.533854 | + | 0.308221i | ||||
\(746\) | −13.2796 | + | 7.66697i | −0.486200 | + | 0.280708i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.18118i | − | 0.152879i | ||||||
\(749\) | −1.39523 | − | 6.33987i | −0.0509806 | − | 0.231654i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.9045 | − | 39.6718i | −0.835798 | − | 1.44764i | −0.893379 | − | 0.449304i | \(-0.851672\pi\) |
0.0575810 | − | 0.998341i | \(-0.481661\pi\) | |||||||
\(752\) | −8.93303 | −0.325754 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 3.79366i | − | 0.138157i | ||||||
\(755\) | 60.6294 | 2.20653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.3427 | 1.82974 | 0.914868 | − | 0.403752i | \(-0.132294\pi\) | ||||
0.914868 | + | 0.403752i | \(0.132294\pi\) | |||||||
\(758\) | 1.66697i | 0.0605471i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 34.5337 | 1.25267 | ||||||||
\(761\) | 15.1823 | + | 26.2965i | 0.550358 | + | 0.953248i | 0.998249 | + | 0.0591594i | \(0.0188420\pi\) |
−0.447891 | + | 0.894088i | \(0.647825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.46635 | − | 10.9349i | 0.125490 | − | 0.395868i | ||||
\(764\) | − | 13.0895i | − | 0.473562i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.21448 | − | 5.31999i | 0.332933 | − | 0.192219i | ||||
\(767\) | −2.97584 | − | 1.71810i | −0.107452 | − | 0.0620372i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.8000 | + | 20.6692i | 1.29098 | + | 0.745349i | 0.978828 | − | 0.204683i | \(-0.0656163\pi\) |
0.312154 | + | 0.950032i | \(0.398950\pi\) | |||||||
\(770\) | 9.09402 | + | 9.95525i | 0.327726 | + | 0.358762i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.9949 | −1.00756 | ||||||||
\(773\) | 6.99754 | + | 12.1201i | 0.251684 | + | 0.435930i | 0.963990 | − | 0.265940i | \(-0.0856823\pi\) |
−0.712305 | + | 0.701870i | \(0.752349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.8382 | + | 21.8459i | 1.35919 | + | 0.784728i | ||||
\(776\) | 15.8792 | + | 27.5035i | 0.570029 | + | 0.987319i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.33216 | − | 12.6997i | 0.262871 | − | 0.455305i | ||||
\(779\) | −37.1669 | + | 21.4583i | −1.33164 | + | 0.768824i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.49097 | + | 12.9747i | −0.268048 | + | 0.464273i | ||||
\(782\) | 3.50734 | − | 6.07489i | 0.125422 | − | 0.217238i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.01001 | + | 11.1473i | −0.0360718 | + | 0.398116i | ||||
\(785\) | 9.50018 | − | 5.48493i | 0.339076 | − | 0.195766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4868i | 0.480753i | 0.970680 | + | 0.240377i | \(0.0772709\pi\) | ||||
−0.970680 | + | 0.240377i | \(0.922729\pi\) | |||||||
\(788\) | − | 23.7056i | − | 0.844478i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.32258 | − | 1.34094i | 0.0826335 | − | 0.0477085i | ||||
\(791\) | −4.07161 | − | 18.5012i | −0.144770 | − | 0.657827i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.16531 | + | 5.48248i | −0.112403 | + | 0.194688i | ||||
\(794\) | −10.7329 | + | 18.5900i | −0.380897 | + | 0.659733i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.7664 | + | 6.79332i | −0.417048 | + | 0.240783i | ||||
\(797\) | −4.15867 | + | 7.20304i | −0.147308 | + | 0.255145i | −0.930232 | − | 0.366973i | \(-0.880394\pi\) |
0.782924 | + | 0.622118i | \(0.213727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.17686 | + | 5.50249i | 0.112389 | + | 0.194664i | ||||
\(800\) | −29.6590 | − | 17.1236i | −1.04860 | − | 0.605411i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.49702 | + | 16.4493i | 0.335351 | + | 0.580846i | ||||
\(803\) | −25.0343 | −0.883443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.6915 | − | 80.3893i | −0.623543 | − | 2.83335i | ||||
\(806\) | −6.57575 | − | 3.79651i | −0.231621 | − | 0.133726i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 27.8120 | + | 16.0573i | 0.978424 | + | 0.564893i | ||||
\(809\) | 12.5955 | − | 7.27200i | 0.442833 | − | 0.255670i | −0.261965 | − | 0.965077i | \(-0.584371\pi\) |
0.704799 | + | 0.709407i | \(0.251037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.8287i | 1.46880i | 0.678715 | + | 0.734401i | \(0.262537\pi\) | ||||
−0.678715 | + | 0.734401i | \(0.737463\pi\) | |||||||
\(812\) | 14.4683 | + | 4.58645i | 0.507738 | + | 0.160953i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.97590 | + | 6.88647i | 0.139355 | + | 0.241371i | ||||
\(815\) | −7.59609 | −0.266079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.64553i | 0.337454i | ||||||||
\(818\) | −0.689991 | −0.0241250 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.1196 | 1.75025 | ||||||||
\(821\) | 46.4828i | 1.62226i | 0.584865 | + | 0.811131i | \(0.301148\pi\) | ||||
−0.584865 | + | 0.811131i | \(0.698852\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.73669 | 0.269684 | 0.134842 | − | 0.990867i | \(-0.456947\pi\) | ||||
0.134842 | + | 0.990867i | \(0.456947\pi\) | |||||||
\(824\) | −5.73203 | − | 9.92817i | −0.199685 | − | 0.345864i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.78948 | + | 2.54817i | −0.0970585 | + | 0.0886620i | ||||
\(827\) | 20.8898i | 0.726409i | 0.931709 | + | 0.363205i | \(0.118317\pi\) | ||||
−0.931709 | + | 0.363205i | \(0.881683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.2282 | − | 23.8031i | 1.43191 | − | 0.826716i | 0.434647 | − | 0.900601i | \(-0.356873\pi\) |
0.997267 | + | 0.0738846i | \(0.0235396\pi\) | |||||||
\(830\) | 1.95400 | + | 1.12814i | 0.0678243 | + | 0.0391584i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.778382 | + | 0.449399i | 0.0269855 | + | 0.0155801i | ||||
\(833\) | 7.22558 | − | 3.34217i | 0.250351 | − | 0.115799i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.82710 | 0.305475 | ||||||||
\(836\) | 8.17887 | + | 14.1662i | 0.282872 | + | 0.489949i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.77487 | − | 1.02472i | −0.0613118 | − | 0.0353984i | ||||
\(839\) | −11.2017 | − | 19.4020i | −0.386727 | − | 0.669831i | 0.605280 | − | 0.796013i | \(-0.293061\pi\) |
−0.992007 | + | 0.126181i | \(0.959728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.81456 | + | 13.5352i | −0.269468 | + | 0.466732i | ||||
\(842\) | −4.95098 | + | 2.85845i | −0.170622 | + | 0.0985087i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.4376 | − | 19.8106i | 0.393700 | − | 0.681909i | ||||
\(845\) | −17.3942 | + | 30.1277i | −0.598380 | + | 1.03642i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.40407 | − | 13.8930i | 0.151326 | − | 0.477368i | ||||
\(848\) | −13.9168 | + | 8.03486i | −0.477904 | + | 0.275918i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.45814i | 0.152913i | ||||||||
\(851\) | − | 48.5431i | − | 1.66404i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.9393 | + | 24.2136i | −1.43597 | + | 0.829060i | −0.997567 | − | 0.0697173i | \(-0.977790\pi\) |
−0.438406 | + | 0.898777i | \(0.644457\pi\) | |||||||
\(854\) | 4.69455 | + | 5.13914i | 0.160644 | + | 0.175858i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.87484 | − | 4.97937i | 0.0982600 | − | 0.170191i | ||||
\(857\) | −24.5327 | + | 42.4920i | −0.838023 | + | 1.45150i | 0.0535230 | + | 0.998567i | \(0.482955\pi\) |
−0.891546 | + | 0.452931i | \(0.850378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4136 | − | 6.01227i | 0.355306 | − | 0.205136i | −0.311714 | − | 0.950176i | \(-0.600903\pi\) |
0.667020 | + | 0.745040i | \(0.267570\pi\) | |||||||
\(860\) | 5.63221 | − | 9.75527i | 0.192057 | − | 0.332652i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.95732 | − | 15.5145i | −0.305088 | − | 0.528427i | ||||
\(863\) | 39.8804 | + | 23.0250i | 1.35754 | + | 0.783779i | 0.989292 | − | 0.145947i | \(-0.0466229\pi\) |
0.368252 | + | 0.929726i | \(0.379956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.24824 | − | 7.35817i | −0.144445 | − | 0.250185i | ||||
\(866\) | −8.45145 | −0.287192 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.4291 | − | 20.4887i | 0.761292 | − | 0.695433i | ||||
\(869\) | 2.50264 | + | 1.44490i | 0.0848961 | + | 0.0490148i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7327 | + | 8.50594i | 0.499199 | + | 0.288213i | ||||
\(872\) | 8.79893 | − | 5.08007i | 0.297970 | − | 0.172033i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.4430i | 0.928275i | ||||||||
\(875\) | 5.73203 | + | 6.27487i | 0.193778 | + | 0.212129i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.73669 | − | 11.6683i | −0.227482 | − | 0.394010i | 0.729579 | − | 0.683896i | \(-0.239716\pi\) |
−0.957061 | + | 0.289886i | \(0.906383\pi\) | |||||||
\(878\) | 12.1110 | 0.408727 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 12.4105i | − | 0.418357i | ||||||
\(881\) | −25.5247 | −0.859949 | −0.429974 | − | 0.902841i | \(-0.641477\pi\) | ||||
−0.429974 | + | 0.902841i | \(0.641477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.45532 | 0.217239 | 0.108619 | − | 0.994083i | \(-0.465357\pi\) | ||||
0.108619 | + | 0.994083i | \(0.465357\pi\) | |||||||
\(884\) | 2.81917i | 0.0948189i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.88450 | 0.0633111 | ||||||||
\(887\) | −16.5604 | − | 28.6834i | −0.556043 | − | 0.963096i | −0.997822 | − | 0.0659712i | \(-0.978985\pi\) |
0.441778 | − | 0.897124i | \(-0.354348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.5960 | − | 34.5882i | −1.05970 | − | 1.16005i | ||||
\(890\) | 16.2472i | 0.544608i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.3790 | + | 8.30171i | −0.481444 | + | 0.277962i | ||||
\(893\) | −21.5270 | − | 12.4286i | −0.720374 | − | 0.415908i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.6880 | − | 22.9139i | −1.32662 | − | 0.765926i | ||||
\(896\) | −21.6826 | + | 19.8069i | −0.724366 | + | 0.661701i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.19292 | 0.0398082 | ||||||||
\(899\) | −13.3809 | − | 23.1764i | −0.446278 | − | 0.772977i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.89848 | + | 5.71489i | 0.329766 | + | 0.190391i | ||||
\(902\) | −7.42084 | − | 12.8533i | −0.247087 | − | 0.427967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.38946 | − | 14.5310i | 0.279029 | − | 0.483293i | ||||
\(905\) | 13.5962 | − | 7.84976i | 0.451952 | − | 0.260935i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.10756 | + | 5.38245i | −0.103185 | + | 0.178721i | −0.912995 | − | 0.407970i | \(-0.866237\pi\) |
0.809810 | + | 0.586692i | \(0.199570\pi\) | |||||||
\(908\) | 5.27446 | − | 9.13562i | 0.175039 | − | 0.303176i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.13166 | − | 6.71234i | −0.203262 | − | 0.222512i | ||||
\(911\) | 15.6296 | − | 9.02376i | 0.517832 | − | 0.298970i | −0.218215 | − | 0.975901i | \(-0.570023\pi\) |
0.736047 | + | 0.676930i | \(0.236690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.43121i | 0.0804611i | ||||||||
\(914\) | 4.04199i | 0.133697i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.6613 | − | 9.61943i | 0.550506 | − | 0.317835i | ||||
\(917\) | −10.8768 | + | 34.3116i | −0.359182 | + | 1.13307i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.12913 | − | 7.15186i | 0.136207 | − | 0.235918i | −0.789851 | − | 0.613299i | \(-0.789842\pi\) |
0.926058 | + | 0.377381i | \(0.123175\pi\) | |||||||
\(920\) | 36.4529 | − | 63.1382i | 1.20182 | − | 2.08161i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.69590 | − | 5.59793i | 0.319318 | − | 0.184358i | ||||
\(923\) | 5.05080 | − | 8.74824i | 0.166249 | − | 0.287952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4256 | + | 26.7180i | 0.507192 | + | 0.878482i | ||||
\(926\) | −16.7258 | − | 9.65662i | −0.549642 | − | 0.317336i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.4884 | + | 18.1665i | 0.344300 | + | 0.596345i | ||||
\(929\) | 34.7709 | 1.14080 | 0.570399 | − | 0.821368i | \(-0.306789\pi\) | ||||
0.570399 | + | 0.821368i | \(0.306789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.9432 | + | 25.4576i | −0.588066 | + | 0.834341i | ||||
\(932\) | −7.64450 | − | 4.41355i | −0.250404 | − | 0.144571i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.4207 | + | 8.90314i | 0.504580 | + | 0.291320i | ||||
\(935\) | −7.64450 | + | 4.41355i | −0.250002 | + | 0.144339i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.0703i | − | 1.66839i | −0.551466 | − | 0.834197i | \(-0.685931\pi\) | ||
0.551466 | − | 0.834197i | \(-0.314069\pi\) | |||||||
\(938\) | 13.8101 | − | 12.6154i | 0.450915 | − | 0.411907i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.5146 | + | 25.1401i | 0.473415 | + | 0.819978i | ||||
\(941\) | −3.47744 | −0.113361 | −0.0566807 | − | 0.998392i | \(-0.518052\pi\) | ||||
−0.0566807 | + | 0.998392i | \(0.518052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 90.6034i | 2.95045i | ||||||||
\(944\) | 3.47744 | 0.113181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.33568 | −0.108452 | ||||||||
\(947\) | 14.3401i | 0.465989i | 0.972478 | + | 0.232995i | \(0.0748525\pi\) | ||||
−0.972478 | + | 0.232995i | \(0.925148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8794 | 0.547930 | ||||||||
\(950\) | −8.72063 | − | 15.1046i | −0.282935 | − | 0.490057i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.72162 | + | 2.13075i | 0.217849 | + | 0.0690581i | ||||
\(953\) | 7.53697i | 0.244147i | 0.992521 | + | 0.122073i | \(0.0389543\pi\) | ||||
−0.992521 | + | 0.122073i | \(0.961046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.9317 | + | 13.8170i | −0.774411 | + | 0.447106i | ||||
\(956\) | 21.6836 | + | 12.5190i | 0.701298 | + | 0.404895i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.2583 | + | 7.07735i | 0.396049 | + | 0.228659i | ||||
\(959\) | −5.77756 | − | 26.2530i | −0.186567 | − | 0.847752i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5638 | −0.727864 | ||||||||
\(962\) | −2.68076 | − | 4.64321i | −0.0864312 | − | 0.149703i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.23363 | + | 3.59899i | 0.200772 | + | 0.115916i | ||||
\(965\) | 29.5508 | + | 51.1834i | 0.951273 | + | 1.64765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.80807 | − | 10.0599i | 0.186775 | − | 0.323503i | −0.757398 | − | 0.652953i | \(-0.773530\pi\) |
0.944173 | + | 0.329450i | \(0.106863\pi\) | |||||||
\(968\) | 11.1792 | − | 6.45434i | 0.359314 | − | 0.207450i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.7367 | − | 25.5247i | 0.473167 | − | 0.819548i | ||||
\(971\) | −17.7476 | + | 30.7397i | −0.569548 | + | 0.986485i | 0.427063 | + | 0.904222i | \(0.359548\pi\) |
−0.996611 | + | 0.0822636i | \(0.973785\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.19193 | + | 9.96004i | 0.0702702 | + | 0.319304i | ||||
\(974\) | −8.29145 | + | 4.78707i | −0.265675 | + | 0.153388i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 6.40659i | − | 0.205070i | ||||||
\(977\) | 32.0094i | 1.02407i | 0.858964 | + | 0.512036i | \(0.171109\pi\) | ||||
−0.858964 | + | 0.512036i | \(0.828891\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.1613 | + | 8.75340i | −0.484559 | + | 0.279760i | ||||
\(980\) | 33.0126 | − | 15.2699i | 1.05455 | − | 0.487779i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0929453 | + | 0.160986i | −0.00296600 | + | 0.00513727i | ||||
\(983\) | 24.7324 | − | 42.8378i | 0.788841 | − | 1.36631i | −0.137837 | − | 0.990455i | \(-0.544015\pi\) |
0.926678 | − | 0.375857i | \(-0.122652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.3413 | + | 25.0231i | −1.38097 | + | 0.797302i | ||||
\(986\) | 1.36534 | − | 2.36483i | 0.0434811 | − | 0.0753115i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.51462 | − | 9.55159i | −0.175443 | − | 0.303877i | ||||
\(989\) | 17.6350 | + | 10.1816i | 0.560761 | + | 0.323756i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.97590 | − | 15.5467i | −0.285129 | − | 0.493858i | 0.687511 | − | 0.726174i | \(-0.258703\pi\) |
−0.972640 | + | 0.232316i | \(0.925370\pi\) | |||||||
\(992\) | 41.9853 | 1.33303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.49097 | − | 8.20039i | −0.237599 | − | 0.260101i | ||||
\(995\) | 24.8406 | + | 14.3417i | 0.787500 | + | 0.454663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0151 | + | 16.7519i | 0.918916 | + | 0.530537i | 0.883289 | − | 0.468828i | \(-0.155324\pi\) |
0.0356272 | + | 0.999365i | \(0.488657\pi\) | |||||||
\(998\) | 6.99754 | − | 4.04003i | 0.221503 | − | 0.127885i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.2.i.f.215.4 | 12 | ||
3.2 | odd | 2 | inner | 567.2.i.f.215.3 | 12 | ||
7.3 | odd | 6 | 567.2.s.f.458.3 | 12 | |||
9.2 | odd | 6 | 567.2.s.f.26.3 | 12 | |||
9.4 | even | 3 | 189.2.p.d.26.3 | ✓ | 12 | ||
9.5 | odd | 6 | 189.2.p.d.26.4 | yes | 12 | ||
9.7 | even | 3 | 567.2.s.f.26.4 | 12 | |||
21.17 | even | 6 | 567.2.s.f.458.4 | 12 | |||
63.5 | even | 6 | 1323.2.c.d.1322.6 | 12 | |||
63.23 | odd | 6 | 1323.2.c.d.1322.5 | 12 | |||
63.31 | odd | 6 | 189.2.p.d.80.4 | yes | 12 | ||
63.38 | even | 6 | inner | 567.2.i.f.269.3 | 12 | ||
63.40 | odd | 6 | 1323.2.c.d.1322.7 | 12 | |||
63.52 | odd | 6 | inner | 567.2.i.f.269.4 | 12 | ||
63.58 | even | 3 | 1323.2.c.d.1322.8 | 12 | |||
63.59 | even | 6 | 189.2.p.d.80.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.3 | ✓ | 12 | 9.4 | even | 3 | ||
189.2.p.d.26.4 | yes | 12 | 9.5 | odd | 6 | ||
189.2.p.d.80.3 | yes | 12 | 63.59 | even | 6 | ||
189.2.p.d.80.4 | yes | 12 | 63.31 | odd | 6 | ||
567.2.i.f.215.3 | 12 | 3.2 | odd | 2 | inner | ||
567.2.i.f.215.4 | 12 | 1.1 | even | 1 | trivial | ||
567.2.i.f.269.3 | 12 | 63.38 | even | 6 | inner | ||
567.2.i.f.269.4 | 12 | 63.52 | odd | 6 | inner | ||
567.2.s.f.26.3 | 12 | 9.2 | odd | 6 | |||
567.2.s.f.26.4 | 12 | 9.7 | even | 3 | |||
567.2.s.f.458.3 | 12 | 7.3 | odd | 6 | |||
567.2.s.f.458.4 | 12 | 21.17 | even | 6 | |||
1323.2.c.d.1322.5 | 12 | 63.23 | odd | 6 | |||
1323.2.c.d.1322.6 | 12 | 63.5 | even | 6 | |||
1323.2.c.d.1322.7 | 12 | 63.40 | odd | 6 | |||
1323.2.c.d.1322.8 | 12 | 63.58 | even | 3 |