Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(163,567)]
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([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 487.7 | ||
Root | \(1.41264 + 0.0667052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.487 |
Dual form | 567.2.e.g.163.7 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.764088 | + | 1.32344i | 0.540292 | + | 0.935813i | 0.998887 | + | 0.0471677i | \(0.0150195\pi\) |
−0.458595 | + | 0.888645i | \(0.651647\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.167661 | + | 0.290398i | −0.0838307 | + | 0.145199i | ||||
\(5\) | 1.41264 | + | 2.44676i | 0.631752 | + | 1.09423i | 0.987193 | + | 0.159527i | \(0.0509971\pi\) |
−0.355442 | + | 0.934698i | \(0.615670\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65876 | + | 2.06119i | 0.626953 | + | 0.779057i | ||||
\(8\) | 2.54392 | 0.899412 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.15876 | + | 3.73909i | −0.682661 | + | 1.18240i | ||||
\(11\) | 1.81857 | − | 3.14986i | 0.548321 | − | 0.949719i | −0.450069 | − | 0.892994i | \(-0.648601\pi\) |
0.998390 | − | 0.0567257i | \(-0.0180660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.62908 | −1.56123 | −0.780613 | − | 0.625015i | \(-0.785093\pi\) | ||||
−0.780613 | + | 0.625015i | \(0.785093\pi\) | |||||||
\(14\) | −1.46042 | + | 3.77020i | −0.390314 | + | 1.00763i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.27910 | + | 3.94752i | 0.569776 | + | 0.986880i | ||||
\(17\) | 1.60110 | − | 2.77319i | 0.388324 | − | 0.672597i | −0.603900 | − | 0.797060i | \(-0.706388\pi\) |
0.992224 | + | 0.124463i | \(0.0397209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.03544 | − | 3.52548i | −0.466962 | − | 0.808801i | 0.532326 | − | 0.846539i | \(-0.321318\pi\) |
−0.999288 | + | 0.0377382i | \(0.987985\pi\) | |||||||
\(20\) | −0.947380 | −0.211841 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.55820 | 1.18501 | ||||||||
\(23\) | 2.35159 | + | 4.07307i | 0.490340 | + | 0.849294i | 0.999938 | − | 0.0111185i | \(-0.00353920\pi\) |
−0.509598 | + | 0.860413i | \(0.670206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.49110 | + | 2.58266i | −0.298220 | + | 0.516532i | ||||
\(26\) | −4.30111 | − | 7.44975i | −0.843518 | − | 1.46102i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.876676 | + | 0.136119i | −0.165676 | + | 0.0257241i | ||||
\(29\) | −4.32626 | −0.803366 | −0.401683 | − | 0.915779i | \(-0.631575\pi\) | ||||
−0.401683 | + | 0.915779i | \(0.631575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.79099 | + | 3.10208i | −0.321670 | + | 0.557150i | −0.980833 | − | 0.194851i | \(-0.937578\pi\) |
0.659162 | + | 0.752001i | \(0.270911\pi\) | |||||||
\(32\) | −0.938949 | + | 1.62631i | −0.165984 | + | 0.287493i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89353 | 0.839233 | ||||||||
\(35\) | −2.70001 | + | 6.97032i | −0.456386 | + | 1.17820i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.15578 | + | 3.73392i | 0.354408 | + | 0.613852i | 0.987016 | − | 0.160619i | \(-0.0513492\pi\) |
−0.632609 | + | 0.774472i | \(0.718016\pi\) | |||||||
\(38\) | 3.11051 | − | 5.38756i | 0.504591 | − | 0.873977i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.59364 | + | 6.22437i | 0.568205 | + | 0.984159i | ||||
\(41\) | −3.15192 | −0.492246 | −0.246123 | − | 0.969239i | \(-0.579157\pi\) | ||||
−0.246123 | + | 0.969239i | \(0.579157\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.19325 | −1.40196 | −0.700979 | − | 0.713182i | \(-0.747253\pi\) | ||||
−0.700979 | + | 0.713182i | \(0.747253\pi\) | |||||||
\(44\) | 0.609809 | + | 1.05622i | 0.0919322 | + | 0.159231i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.59364 | + | 6.22437i | −0.529854 | + | 0.917733i | ||||
\(47\) | 2.42321 | + | 4.19713i | 0.353462 | + | 0.612215i | 0.986854 | − | 0.161617i | \(-0.0516710\pi\) |
−0.633391 | + | 0.773832i | \(0.718338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.49702 | + | 6.83805i | −0.213859 | + | 0.976864i | ||||
\(50\) | −4.55733 | −0.644504 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.943779 | − | 1.63467i | 0.130879 | − | 0.226688i | ||||
\(53\) | 7.06707 | − | 12.2405i | 0.970736 | − | 1.68136i | 0.277395 | − | 0.960756i | \(-0.410529\pi\) |
0.693342 | − | 0.720609i | \(-0.256138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2760 | 1.38561 | ||||||||
\(56\) | 4.21976 | + | 5.24351i | 0.563889 | + | 0.700693i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.30564 | − | 5.72554i | −0.434052 | − | 0.751800i | ||||
\(59\) | 0.750489 | − | 1.29988i | 0.0977053 | − | 0.169231i | −0.813029 | − | 0.582223i | \(-0.802183\pi\) |
0.910734 | + | 0.412992i | \(0.135516\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.60254 | − | 11.4359i | −0.845369 | − | 1.46422i | −0.885301 | − | 0.465019i | \(-0.846047\pi\) |
0.0399317 | − | 0.999202i | \(-0.487286\pi\) | |||||||
\(62\) | −5.47388 | −0.695184 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.24665 | 0.780831 | ||||||||
\(65\) | −7.95186 | − | 13.7730i | −0.986307 | − | 1.70833i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.34108 | − | 10.9831i | 0.774686 | − | 1.34180i | −0.160285 | − | 0.987071i | \(-0.551241\pi\) |
0.934971 | − | 0.354725i | \(-0.115425\pi\) | |||||||
\(68\) | 0.536885 | + | 0.929913i | 0.0651069 | + | 0.112768i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.2878 | + | 1.75263i | −1.34916 | + | 0.209480i | ||||
\(71\) | 2.91413 | 0.345844 | 0.172922 | − | 0.984936i | \(-0.444679\pi\) | ||||
0.172922 | + | 0.984936i | \(0.444679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.46456 | + | 2.53670i | −0.171414 | + | 0.296898i | −0.938914 | − | 0.344151i | \(-0.888167\pi\) |
0.767500 | + | 0.641048i | \(0.221500\pi\) | |||||||
\(74\) | −3.29441 | + | 5.70608i | −0.382967 | + | 0.663319i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.36506 | 0.156583 | ||||||||
\(77\) | 9.50905 | − | 1.47644i | 1.08366 | − | 0.168257i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.446763 | − | 0.773817i | −0.0502648 | − | 0.0870612i | 0.839798 | − | 0.542899i | \(-0.182673\pi\) |
−0.890063 | + | 0.455837i | \(0.849340\pi\) | |||||||
\(80\) | −6.43910 | + | 11.1528i | −0.719913 | + | 1.24693i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.40834 | − | 4.17137i | −0.265957 | − | 0.460651i | ||||
\(83\) | −8.04863 | −0.883452 | −0.441726 | − | 0.897150i | \(-0.645634\pi\) | ||||
−0.441726 | + | 0.897150i | \(0.645634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.04711 | 0.981297 | ||||||||
\(86\) | −7.02446 | − | 12.1667i | −0.757467 | − | 1.31197i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.62631 | − | 8.01300i | 0.493166 | − | 0.854189i | ||||
\(89\) | 2.82863 | + | 4.89934i | 0.299835 | + | 0.519329i | 0.976098 | − | 0.217331i | \(-0.0697352\pi\) |
−0.676263 | + | 0.736660i | \(0.736402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.33731 | − | 11.6026i | −0.978816 | − | 1.21628i | ||||
\(92\) | −1.57708 | −0.164422 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.70310 | + | 6.41396i | −0.381946 | + | 0.661549i | ||||
\(95\) | 5.75068 | − | 9.96047i | 0.590007 | − | 1.02192i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.13578 | 0.521460 | 0.260730 | − | 0.965412i | \(-0.416037\pi\) | ||||
0.260730 | + | 0.965412i | \(0.416037\pi\) | |||||||
\(98\) | −10.1936 | + | 3.24366i | −1.02971 | + | 0.327660i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 1.26223 | − | 2.18625i | 0.125597 | − | 0.217540i | −0.796369 | − | 0.604811i | \(-0.793249\pi\) |
0.921966 | + | 0.387271i | \(0.126582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.92321 | − | 8.52725i | −0.485098 | − | 0.840215i | 0.514755 | − | 0.857337i | \(-0.327883\pi\) |
−0.999853 | + | 0.0171225i | \(0.994549\pi\) | |||||||
\(104\) | −14.3199 | −1.40418 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.5995 | 2.09792 | ||||||||
\(107\) | 1.35126 | + | 2.34045i | 0.130631 | + | 0.226260i | 0.923920 | − | 0.382586i | \(-0.124966\pi\) |
−0.793289 | + | 0.608845i | \(0.791633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.52873 | − | 7.84400i | 0.433774 | − | 0.751319i | −0.563421 | − | 0.826170i | \(-0.690515\pi\) |
0.997195 | + | 0.0748515i | \(0.0238483\pi\) | |||||||
\(110\) | 7.85174 | + | 13.5996i | 0.748634 | + | 1.29667i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.35611 | + | 11.2457i | −0.411613 | + | 1.06262i | ||||
\(113\) | −0.465776 | −0.0438165 | −0.0219082 | − | 0.999760i | \(-0.506974\pi\) | ||||
−0.0219082 | + | 0.999760i | \(0.506974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.64389 | + | 11.5076i | −0.619546 | + | 1.07309i | ||||
\(116\) | 0.725346 | − | 1.25634i | 0.0673467 | − | 0.116648i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.29376 | 0.211158 | ||||||||
\(119\) | 8.37191 | − | 1.29988i | 0.767452 | − | 0.119160i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.11442 | − | 1.93024i | −0.101311 | − | 0.175476i | ||||
\(122\) | 10.0898 | − | 17.4761i | 0.913492 | − | 1.58221i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.600558 | − | 1.04020i | −0.0539317 | − | 0.0934125i | ||||
\(125\) | 5.70084 | 0.509899 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7574 | −1.39825 | −0.699123 | − | 0.715002i | \(-0.746426\pi\) | ||||
−0.699123 | + | 0.715002i | \(0.746426\pi\) | |||||||
\(128\) | 6.65089 | + | 11.5197i | 0.587861 | + | 1.01821i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.1518 | − | 21.0476i | 1.06579 | − | 1.84600i | ||||
\(131\) | 6.07396 | + | 10.5204i | 0.530685 | + | 0.919173i | 0.999359 | + | 0.0358017i | \(0.0113985\pi\) |
−0.468674 | + | 0.883371i | \(0.655268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89038 | − | 10.0434i | 0.337339 | − | 0.870870i | ||||
\(134\) | 19.3806 | 1.67423 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.07307 | − | 7.05477i | 0.349263 | − | 0.604941i | ||||
\(137\) | 1.08169 | − | 1.87353i | 0.0924146 | − | 0.160067i | −0.816112 | − | 0.577894i | \(-0.803875\pi\) |
0.908527 | + | 0.417827i | \(0.137208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.4514 | −1.81949 | −0.909743 | − | 0.415173i | \(-0.863721\pi\) | ||||
−0.909743 | + | 0.415173i | \(0.863721\pi\) | |||||||
\(140\) | −1.57148 | − | 1.95273i | −0.132814 | − | 0.165036i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.22665 | + | 3.85668i | 0.186857 | + | 0.323645i | ||||
\(143\) | −10.2369 | + | 17.7308i | −0.856053 | + | 1.48273i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.11144 | − | 10.5853i | −0.507528 | − | 0.879063i | ||||
\(146\) | −4.47622 | −0.370454 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.44576 | −0.118841 | ||||||||
\(149\) | −5.54862 | − | 9.61049i | −0.454561 | − | 0.787322i | 0.544102 | − | 0.839019i | \(-0.316870\pi\) |
−0.998663 | + | 0.0516967i | \(0.983537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.04355 | + | 1.80748i | −0.0849228 | + | 0.147091i | −0.905358 | − | 0.424649i | \(-0.860398\pi\) |
0.820436 | + | 0.571739i | \(0.193731\pi\) | |||||||
\(152\) | −5.17799 | − | 8.96855i | −0.419991 | − | 0.727445i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.21974 | + | 11.4565i | 0.742948 | + | 0.923193i | ||||
\(155\) | −10.1201 | −0.812863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8077 | − | 18.7194i | 0.862547 | − | 1.49397i | −0.00691621 | − | 0.999976i | \(-0.502202\pi\) |
0.869463 | − | 0.493998i | \(-0.164465\pi\) | |||||||
\(158\) | 0.682733 | − | 1.18253i | 0.0543153 | − | 0.0940769i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.30559 | −0.419444 | ||||||||
\(161\) | −4.49465 | + | 11.6033i | −0.354228 | + | 0.914471i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.69122 | + | 8.12543i | 0.367444 | + | 0.636432i | 0.989165 | − | 0.146807i | \(-0.0468995\pi\) |
−0.621721 | + | 0.783239i | \(0.713566\pi\) | |||||||
\(164\) | 0.528454 | − | 0.915310i | 0.0412654 | − | 0.0714737i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.14986 | − | 10.6519i | −0.477322 | − | 0.826746i | ||||
\(167\) | 17.4047 | 1.34682 | 0.673408 | − | 0.739271i | \(-0.264830\pi\) | ||||
0.673408 | + | 0.739271i | \(0.264830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.6865 | 1.43743 | ||||||||
\(170\) | 6.91279 | + | 11.9733i | 0.530187 | + | 0.918310i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.54135 | − | 2.66970i | 0.117527 | − | 0.203563i | ||||
\(173\) | 10.7738 | + | 18.6607i | 0.819116 | + | 1.41875i | 0.906334 | + | 0.422561i | \(0.138869\pi\) |
−0.0872187 | + | 0.996189i | \(0.527798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.79674 | + | 1.21058i | −0.589378 | + | 0.0915112i | ||||
\(176\) | 16.5789 | 1.24968 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.32265 | + | 7.48705i | −0.323996 | + | 0.561178i | ||||
\(179\) | −2.82863 | + | 4.89934i | −0.211422 | + | 0.366194i | −0.952160 | − | 0.305601i | \(-0.901143\pi\) |
0.740738 | + | 0.671794i | \(0.234476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.12427 | 0.0835664 | 0.0417832 | − | 0.999127i | \(-0.486696\pi\) | ||||
0.0417832 | + | 0.999127i | \(0.486696\pi\) | |||||||
\(182\) | 8.22083 | − | 21.2228i | 0.609368 | − | 1.57314i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.98225 | + | 10.3616i | 0.441018 | + | 0.763865i | ||||
\(185\) | −6.09067 | + | 10.5494i | −0.447795 | + | 0.775604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.82344 | − | 10.0865i | −0.425852 | − | 0.737597i | ||||
\(188\) | −1.62512 | −0.118524 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.5761 | 1.27510 | ||||||||
\(191\) | −1.96950 | − | 3.41127i | −0.142508 | − | 0.246831i | 0.785932 | − | 0.618312i | \(-0.212183\pi\) |
−0.928440 | + | 0.371481i | \(0.878850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.04339 | + | 15.6636i | −0.650957 | + | 1.12749i | 0.331933 | + | 0.943303i | \(0.392299\pi\) |
−0.982891 | + | 0.184189i | \(0.941034\pi\) | |||||||
\(194\) | 3.92419 | + | 6.79690i | 0.281741 | + | 0.487989i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.73476 | − | 1.58121i | −0.123912 | − | 0.112943i | ||||
\(197\) | 25.4842 | 1.81567 | 0.907836 | − | 0.419326i | \(-0.137734\pi\) | ||||
0.907836 | + | 0.419326i | \(0.137734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.31454 | + | 10.9371i | −0.447626 | + | 0.775311i | −0.998231 | − | 0.0594551i | \(-0.981064\pi\) |
0.550605 | + | 0.834766i | \(0.314397\pi\) | |||||||
\(200\) | −3.79324 | + | 6.57009i | −0.268223 | + | 0.464575i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.85782 | 0.271436 | ||||||||
\(203\) | −7.17623 | − | 8.91724i | −0.503673 | − | 0.625868i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.45252 | − | 7.71199i | −0.310977 | − | 0.538629i | ||||
\(206\) | 7.52353 | − | 13.0311i | 0.524189 | − | 0.907922i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.8292 | − | 22.2209i | −0.889548 | − | 1.54074i | ||||
\(209\) | −14.8064 | −1.02418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.31156 | 0.159134 | 0.0795670 | − | 0.996830i | \(-0.474646\pi\) | ||||
0.0795670 | + | 0.996830i | \(0.474646\pi\) | |||||||
\(212\) | 2.36975 | + | 4.10452i | 0.162755 | + | 0.281900i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.06496 | + | 3.57662i | −0.141158 | + | 0.244493i | ||||
\(215\) | −12.9868 | − | 22.4937i | −0.885689 | − | 1.53406i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.36479 | + | 1.45405i | −0.635724 | + | 0.0987071i | ||||
\(218\) | 13.8414 | 0.937458 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.72288 | + | 2.98412i | −0.116157 | + | 0.201189i | ||||
\(221\) | −9.01272 | + | 15.6105i | −0.606261 | + | 1.05008i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.29962 | 0.622749 | 0.311374 | − | 0.950287i | \(-0.399211\pi\) | ||||
0.311374 | + | 0.950287i | \(0.399211\pi\) | |||||||
\(224\) | −4.90963 | + | 0.762304i | −0.328038 | + | 0.0509336i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.355894 | − | 0.616426i | −0.0236737 | − | 0.0410040i | ||||
\(227\) | 0.964092 | − | 1.66986i | 0.0639890 | − | 0.110832i | −0.832256 | − | 0.554391i | \(-0.812951\pi\) |
0.896245 | + | 0.443559i | \(0.146284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.67059 | − | 2.89355i | −0.110396 | − | 0.191211i | 0.805534 | − | 0.592549i | \(-0.201879\pi\) |
−0.915930 | + | 0.401338i | \(0.868545\pi\) | |||||||
\(230\) | −20.3061 | −1.33894 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.0057 | −0.722556 | ||||||||
\(233\) | −10.5758 | − | 18.3178i | −0.692842 | − | 1.20004i | −0.970903 | − | 0.239474i | \(-0.923025\pi\) |
0.278061 | − | 0.960563i | \(-0.410308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.84626 | + | 11.8581i | −0.446601 | + | 0.773535i | ||||
\(236\) | 0.251656 | + | 0.435881i | 0.0163814 | + | 0.0283734i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.11720 | + | 10.0865i | 0.526160 | + | 0.653810i | ||||
\(239\) | −24.1151 | −1.55987 | −0.779937 | − | 0.625858i | \(-0.784749\pi\) | ||||
−0.779937 | + | 0.625858i | \(0.784749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.61720 | + | 7.99722i | −0.297420 | + | 0.515146i | −0.975545 | − | 0.219800i | \(-0.929459\pi\) |
0.678125 | + | 0.734947i | \(0.262793\pi\) | |||||||
\(242\) | 1.70304 | − | 2.94975i | 0.109475 | − | 0.189617i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.42796 | 0.283471 | ||||||||
\(245\) | −18.8458 | + | 5.99686i | −1.20402 | + | 0.383125i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4576 | + | 19.8452i | 0.729033 | + | 1.26272i | ||||
\(248\) | −4.55612 | + | 7.89144i | −0.289314 | + | 0.501107i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.35595 | + | 7.54472i | 0.275494 | + | 0.477170i | ||||
\(251\) | −18.5790 | −1.17270 | −0.586349 | − | 0.810058i | \(-0.699435\pi\) | ||||
−0.586349 | + | 0.810058i | \(0.699435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.1062 | 1.07545 | ||||||||
\(254\) | −12.0401 | − | 20.8540i | −0.755461 | − | 1.30850i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.91708 | + | 6.78458i | −0.244818 | + | 0.424037i | ||||
\(257\) | −5.10987 | − | 8.85056i | −0.318745 | − | 0.552083i | 0.661481 | − | 0.749962i | \(-0.269928\pi\) |
−0.980226 | + | 0.197879i | \(0.936595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.12039 | + | 10.6372i | −0.256029 | + | 0.660960i | ||||
\(260\) | 5.33288 | 0.330731 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.28209 | + | 16.0770i | −0.573449 | + | 0.993243i | ||||
\(263\) | 4.56887 | − | 7.91352i | 0.281729 | − | 0.487969i | −0.690082 | − | 0.723731i | \(-0.742425\pi\) |
0.971811 | + | 0.235763i | \(0.0757588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.9329 | 2.45306 | ||||||||
\(266\) | 16.2644 | − | 2.52533i | 0.997233 | − | 0.154838i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.12631 | + | 3.68287i | 0.129885 | + | 0.224967i | ||||
\(269\) | −11.4606 | + | 19.8504i | −0.698767 | + | 1.21030i | 0.270127 | + | 0.962825i | \(0.412934\pi\) |
−0.968894 | + | 0.247475i | \(0.920399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.65781 | + | 8.06757i | 0.282942 | + | 0.490070i | 0.972108 | − | 0.234533i | \(-0.0753562\pi\) |
−0.689166 | + | 0.724604i | \(0.742023\pi\) | |||||||
\(272\) | 14.5963 | 0.885030 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.30601 | 0.199723 | ||||||||
\(275\) | 5.42336 | + | 9.39353i | 0.327041 | + | 0.566451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0916589 | + | 0.158758i | −0.00550725 | + | 0.00953884i | −0.868766 | − | 0.495223i | \(-0.835086\pi\) |
0.863259 | + | 0.504762i | \(0.168420\pi\) | |||||||
\(278\) | −16.3908 | − | 28.3896i | −0.983053 | − | 1.70270i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.86862 | + | 17.7319i | −0.410479 | + | 1.05969i | ||||
\(281\) | −16.2019 | −0.966527 | −0.483263 | − | 0.875475i | \(-0.660549\pi\) | ||||
−0.483263 | + | 0.875475i | \(0.660549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3492 | + | 17.9253i | −0.615195 | + | 1.06555i | 0.375155 | + | 0.926962i | \(0.377590\pi\) |
−0.990350 | + | 0.138588i | \(0.955744\pi\) | |||||||
\(284\) | −0.488588 | + | 0.846258i | −0.0289923 | + | 0.0502162i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.2876 | −1.85007 | ||||||||
\(287\) | −5.22828 | − | 6.49670i | −0.308615 | − | 0.383488i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.37296 | + | 5.84213i | 0.198409 | + | 0.343655i | ||||
\(290\) | 9.33936 | − | 16.1762i | 0.548426 | − | 0.949902i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.491101 | − | 0.850612i | −0.0287395 | − | 0.0497783i | ||||
\(293\) | 16.0234 | 0.936097 | 0.468049 | − | 0.883703i | \(-0.344957\pi\) | ||||
0.468049 | + | 0.883703i | \(0.344957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.24068 | 0.246902 | ||||||||
\(296\) | 5.48413 | + | 9.49879i | 0.318758 | + | 0.552106i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.47927 | − | 14.6865i | 0.491191 | − | 0.850768i | ||||
\(299\) | −13.2373 | − | 22.9276i | −0.765532 | − | 1.32594i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.2494 | − | 18.9490i | −0.878962 | − | 1.09221i | ||||
\(302\) | −3.18945 | −0.183532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.27794 | − | 16.0699i | 0.532127 | − | 0.921670i | ||||
\(305\) | 18.6540 | − | 32.3097i | 1.06813 | − | 1.85005i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.32307 | −0.303804 | −0.151902 | − | 0.988396i | \(-0.548540\pi\) | ||||
−0.151902 | + | 0.988396i | \(0.548540\pi\) | |||||||
\(308\) | −1.16554 | + | 3.00895i | −0.0664130 | + | 0.171451i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.73262 | − | 13.3933i | −0.439183 | − | 0.760688i | ||||
\(311\) | −9.21297 | + | 15.9573i | −0.522420 | + | 0.904857i | 0.477240 | + | 0.878773i | \(0.341637\pi\) |
−0.999660 | + | 0.0260843i | \(0.991696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32344 | − | 4.02432i | −0.131329 | − | 0.227468i | 0.792860 | − | 0.609403i | \(-0.208591\pi\) |
−0.924189 | + | 0.381936i | \(0.875258\pi\) | |||||||
\(314\) | 33.0321 | 1.86411 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.299620 | 0.0168549 | ||||||||
\(317\) | 5.24006 | + | 9.07606i | 0.294311 | + | 0.509762i | 0.974824 | − | 0.222974i | \(-0.0715764\pi\) |
−0.680513 | + | 0.732736i | \(0.738243\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.86762 | + | 13.6271i | −0.440502 | + | 0.762972i | ||||
\(320\) | 8.82426 | + | 15.2841i | 0.493291 | + | 0.854405i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.7906 | + | 2.91757i | −1.04716 | + | 0.162590i | ||||
\(323\) | −13.0358 | −0.725329 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.39353 | − | 14.5380i | 0.465589 | − | 0.806424i | ||||
\(326\) | −7.16901 | + | 12.4171i | −0.397054 | + | 0.687719i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.01822 | −0.442732 | ||||||||
\(329\) | −4.63155 | + | 11.9568i | −0.255346 | + | 0.659197i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.42677 | − | 11.1315i | −0.353247 | − | 0.611842i | 0.633569 | − | 0.773686i | \(-0.281589\pi\) |
−0.986816 | + | 0.161844i | \(0.948256\pi\) | |||||||
\(332\) | 1.34944 | − | 2.33731i | 0.0740604 | − | 0.128276i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.2987 | + | 23.0341i | 0.727674 | + | 1.26037i | ||||
\(335\) | 35.8306 | 1.95764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.29218 | 0.397230 | 0.198615 | − | 0.980078i | \(-0.436356\pi\) | ||||
0.198615 | + | 0.980078i | \(0.436356\pi\) | |||||||
\(338\) | 14.2782 | + | 24.7305i | 0.776630 | + | 1.34516i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.51685 | + | 2.62726i | −0.0822628 | + | 0.142483i | ||||
\(341\) | 6.51408 | + | 11.2827i | 0.352757 | + | 0.610993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.5777 | + | 8.25707i | −0.895113 | + | 0.445840i | ||||
\(344\) | −23.3869 | −1.26094 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4642 | + | 28.5169i | −0.885123 | + | 1.53308i | ||||
\(347\) | −8.76942 | + | 15.1891i | −0.470767 | + | 0.815392i | −0.999441 | − | 0.0334327i | \(-0.989356\pi\) |
0.528674 | + | 0.848825i | \(0.322689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.0160 | 1.12496 | 0.562481 | − | 0.826810i | \(-0.309847\pi\) | ||||
0.562481 | + | 0.826810i | \(0.309847\pi\) | |||||||
\(350\) | −7.55953 | − | 9.39353i | −0.404074 | − | 0.502105i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.41510 | + | 5.91512i | 0.182025 | + | 0.315277i | ||||
\(353\) | −2.52669 | + | 4.37636i | −0.134482 | + | 0.232930i | −0.925400 | − | 0.378993i | \(-0.876270\pi\) |
0.790917 | + | 0.611923i | \(0.209604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.11662 | + | 7.13019i | 0.218487 | + | 0.378431i | ||||
\(356\) | −1.89701 | −0.100541 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.64530 | −0.456918 | ||||||||
\(359\) | 7.23806 | + | 12.5367i | 0.382010 | + | 0.661661i | 0.991349 | − | 0.131249i | \(-0.0418986\pi\) |
−0.609339 | + | 0.792910i | \(0.708565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.21398 | − | 2.10268i | 0.0638938 | − | 0.110667i | ||||
\(362\) | 0.859042 | + | 1.48791i | 0.0451503 | + | 0.0782026i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.93488 | − | 0.766226i | 0.258658 | − | 0.0401611i | ||||
\(365\) | −8.27559 | −0.433164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.46142 | + | 12.9236i | −0.389483 | + | 0.674604i | −0.992380 | − | 0.123215i | \(-0.960680\pi\) |
0.602897 | + | 0.797819i | \(0.294013\pi\) | |||||||
\(368\) | −10.7190 | + | 18.5659i | −0.558768 | + | 0.967814i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18.6152 | −0.967761 | ||||||||
\(371\) | 36.9526 | − | 5.73754i | 1.91849 | − | 0.297878i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.91054 | − | 6.77325i | −0.202480 | − | 0.350705i | 0.746847 | − | 0.664996i | \(-0.231567\pi\) |
−0.949327 | + | 0.314290i | \(0.898233\pi\) | |||||||
\(374\) | 8.89924 | − | 15.4139i | 0.460169 | − | 0.797036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.16447 | + | 10.6772i | 0.317908 | + | 0.550633i | ||||
\(377\) | 24.3528 | 1.25424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6097 | 0.596350 | 0.298175 | − | 0.954511i | \(-0.403622\pi\) | ||||
0.298175 | + | 0.954511i | \(0.403622\pi\) | |||||||
\(380\) | 1.92833 | + | 3.33997i | 0.0989214 | + | 0.171337i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.00974 | − | 5.21303i | 0.153992 | − | 0.266722i | ||||
\(383\) | −12.5382 | − | 21.7168i | −0.640672 | − | 1.10968i | −0.985283 | − | 0.170931i | \(-0.945322\pi\) |
0.344611 | − | 0.938746i | \(-0.388011\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.0454 | + | 21.1807i | 0.868713 | + | 1.07947i | ||||
\(386\) | −27.6398 | −1.40683 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.861073 | + | 1.49142i | −0.0437143 | + | 0.0757155i | ||||
\(389\) | −11.7497 | + | 20.3510i | −0.595732 | + | 1.03184i | 0.397712 | + | 0.917510i | \(0.369804\pi\) |
−0.993443 | + | 0.114327i | \(0.963529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0605 | 0.761643 | ||||||||
\(392\) | −3.80829 | + | 17.3955i | −0.192348 | + | 0.878603i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.4721 | + | 33.7267i | 0.980992 | + | 1.69913i | ||||
\(395\) | 1.26223 | − | 2.18625i | 0.0635098 | − | 0.110002i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.86170 | + | 17.0810i | 0.494945 | + | 0.857269i | 0.999983 | − | 0.00582755i | \(-0.00185498\pi\) |
−0.505038 | + | 0.863097i | \(0.668522\pi\) | |||||||
\(398\) | −19.2995 | −0.967395 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.5935 | −0.679674 | ||||||||
\(401\) | −7.18983 | − | 12.4532i | −0.359043 | − | 0.621881i | 0.628758 | − | 0.777601i | \(-0.283564\pi\) |
−0.987801 | + | 0.155720i | \(0.950230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0816 | − | 17.4618i | 0.502200 | − | 0.869836i | ||||
\(404\) | 0.423255 | + | 0.733099i | 0.0210577 | + | 0.0364730i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.31816 | − | 16.3109i | 0.313565 | − | 0.809495i | ||||
\(407\) | 15.6818 | 0.777317 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.78795 | − | 10.0250i | 0.286196 | − | 0.495705i | −0.686703 | − | 0.726938i | \(-0.740943\pi\) |
0.972898 | + | 0.231233i | \(0.0742759\pi\) | |||||||
\(410\) | 6.80424 | − | 11.7853i | 0.336037 | − | 0.582034i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.30173 | 0.162664 | ||||||||
\(413\) | 3.92419 | − | 0.609299i | 0.193097 | − | 0.0299816i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3698 | − | 19.6931i | −0.558122 | − | 0.966696i | ||||
\(416\) | 5.28542 | − | 9.15462i | 0.259139 | − | 0.448842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.3134 | − | 19.5954i | −0.553356 | − | 0.958440i | ||||
\(419\) | 34.1721 | 1.66942 | 0.834708 | − | 0.550693i | \(-0.185636\pi\) | ||||
0.834708 | + | 0.550693i | \(0.185636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2213 | −0.498156 | −0.249078 | − | 0.968483i | \(-0.580128\pi\) | ||||
−0.249078 | + | 0.968483i | \(0.580128\pi\) | |||||||
\(422\) | 1.76623 | + | 3.05920i | 0.0859789 | + | 0.148920i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.9781 | − | 31.1389i | 0.873092 | − | 1.51224i | ||||
\(425\) | 4.77480 | + | 8.27020i | 0.231612 | + | 0.401164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6196 | − | 32.5786i | 0.610705 | − | 1.57659i | ||||
\(428\) | −0.906215 | −0.0438036 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.8460 | − | 34.3744i | 0.957061 | − | 1.65768i | ||||
\(431\) | 0.0380526 | − | 0.0659090i | 0.00183293 | − | 0.00317472i | −0.865107 | − | 0.501587i | \(-0.832750\pi\) |
0.866940 | + | 0.498412i | \(0.166083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.2697 | −1.40661 | −0.703305 | − | 0.710888i | \(-0.748293\pi\) | ||||
−0.703305 | + | 0.710888i | \(0.748293\pi\) | |||||||
\(434\) | −9.07987 | − | 11.2827i | −0.435848 | − | 0.541588i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.51859 | + | 2.63027i | 0.0727271 | + | 0.125967i | ||||
\(437\) | 9.57303 | − | 16.5810i | 0.457940 | − | 0.793175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.17263 | + | 3.76310i | 0.103694 | + | 0.179603i | 0.913204 | − | 0.407503i | \(-0.133600\pi\) |
−0.809510 | + | 0.587106i | \(0.800267\pi\) | |||||||
\(440\) | 26.1412 | 1.24623 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.5461 | −1.31023 | ||||||||
\(443\) | 10.2772 | + | 17.8006i | 0.488284 | + | 0.845732i | 0.999909 | − | 0.0134764i | \(-0.00428979\pi\) |
−0.511625 | + | 0.859209i | \(0.670956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.99168 | + | 13.8420i | −0.378842 | + | 0.656173i | ||||
\(446\) | 7.10573 | + | 12.3075i | 0.336466 | + | 0.582776i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.3617 | + | 12.8755i | 0.489544 | + | 0.608312i | ||||
\(449\) | −12.4720 | −0.588588 | −0.294294 | − | 0.955715i | \(-0.595085\pi\) | ||||
−0.294294 | + | 0.955715i | \(0.595085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.73199 | + | 9.92810i | −0.269909 | + | 0.467496i | ||||
\(452\) | 0.0780926 | − | 0.135260i | 0.00367317 | − | 0.00636211i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.94661 | 0.138291 | ||||||||
\(455\) | 15.1986 | − | 39.2365i | 0.712521 | − | 1.83943i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4674 | + | 26.7903i | 0.723534 | + | 1.25320i | 0.959575 | + | 0.281454i | \(0.0908168\pi\) |
−0.236041 | + | 0.971743i | \(0.575850\pi\) | |||||||
\(458\) | 2.55296 | − | 4.42186i | 0.119292 | − | 0.206620i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.22785 | − | 3.85875i | −0.103874 | − | 0.179915i | ||||
\(461\) | 8.02281 | 0.373660 | 0.186830 | − | 0.982392i | \(-0.440179\pi\) | ||||
0.186830 | + | 0.982392i | \(0.440179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8223 | −0.781800 | −0.390900 | − | 0.920433i | \(-0.627836\pi\) | ||||
−0.390900 | + | 0.920433i | \(0.627836\pi\) | |||||||
\(464\) | −9.85998 | − | 17.0780i | −0.457738 | − | 0.792826i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.1616 | − | 27.9928i | 0.748674 | − | 1.29674i | ||||
\(467\) | −0.480399 | − | 0.832075i | −0.0222302 | − | 0.0385038i | 0.854696 | − | 0.519128i | \(-0.173743\pi\) |
−0.876926 | + | 0.480625i | \(0.840410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.1566 | − | 5.14813i | 1.53103 | − | 0.237719i | ||||
\(470\) | −20.9246 | −0.965179 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.90918 | − | 3.30680i | 0.0878773 | − | 0.152208i | ||||
\(473\) | −16.7186 | + | 28.9575i | −0.768723 | + | 1.33147i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.1402 | 0.557029 | ||||||||
\(476\) | −1.02616 | + | 2.64913i | −0.0470341 | + | 0.121423i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.4260 | − | 31.9148i | −0.842787 | − | 1.45975i | ||||
\(479\) | −12.0645 | + | 20.8964i | −0.551242 | + | 0.954779i | 0.446944 | + | 0.894562i | \(0.352512\pi\) |
−0.998185 | + | 0.0602166i | \(0.980821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1350 | − | 21.0185i | −0.553311 | − | 0.958362i | ||||
\(482\) | −14.1118 | −0.642774 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.747384 | 0.0339720 | ||||||||
\(485\) | 7.25501 | + | 12.5661i | 0.329433 | + | 0.570595i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.39944 | + | 12.8162i | −0.335301 | + | 0.580758i | −0.983543 | − | 0.180677i | \(-0.942171\pi\) |
0.648242 | + | 0.761435i | \(0.275505\pi\) | |||||||
\(488\) | −16.7963 | − | 29.0921i | −0.760335 | − | 1.31694i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.3364 | − | 20.3592i | −1.00905 | − | 0.919735i | ||||
\(491\) | 6.30383 | 0.284488 | 0.142244 | − | 0.989832i | \(-0.454568\pi\) | ||||
0.142244 | + | 0.989832i | \(0.454568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.92677 | + | 11.9975i | −0.311966 | + | 0.540341i | ||||
\(494\) | −17.5093 | + | 30.3270i | −0.787781 | + | 1.36448i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.3274 | −0.733120 | ||||||||
\(497\) | 4.83385 | + | 6.00658i | 0.216828 | + | 0.269432i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2986 | + | 24.7658i | 0.640092 | + | 1.10867i | 0.985412 | + | 0.170187i | \(0.0544370\pi\) |
−0.345320 | + | 0.938485i | \(0.612230\pi\) | |||||||
\(500\) | −0.955811 | + | 1.65551i | −0.0427452 | + | 0.0740368i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.1960 | − | 24.5882i | −0.633600 | − | 1.09743i | ||||
\(503\) | −35.4133 | −1.57900 | −0.789500 | − | 0.613750i | \(-0.789660\pi\) | ||||
−0.789500 | + | 0.613750i | \(0.789660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.13231 | 0.317384 | ||||||||
\(506\) | 13.0706 | + | 22.6390i | 0.581060 | + | 1.00642i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.64191 | − | 4.57592i | 0.117216 | − | 0.203024i | ||||
\(509\) | −16.2442 | − | 28.1357i | −0.720010 | − | 1.24709i | −0.960995 | − | 0.276565i | \(-0.910804\pi\) |
0.240985 | − | 0.970529i | \(-0.422529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.65797 | + | 1.18903i | −0.338769 | + | 0.0525997i | ||||
\(512\) | 14.6316 | 0.646630 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.80878 | − | 13.5252i | 0.344431 | − | 0.596571i | ||||
\(515\) | 13.9094 | − | 24.0919i | 0.612923 | − | 1.06161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.6272 | 0.775243 | ||||||||
\(518\) | −17.2260 | + | 2.67463i | −0.756866 | + | 0.117517i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −20.2289 | − | 35.0375i | −0.887096 | − | 1.53650i | ||||
\(521\) | 16.4909 | − | 28.5631i | 0.722479 | − | 1.25137i | −0.237524 | − | 0.971382i | \(-0.576336\pi\) |
0.960003 | − | 0.279989i | \(-0.0903308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.13133 | − | 12.3518i | −0.311831 | − | 0.540108i | 0.666928 | − | 0.745123i | \(-0.267609\pi\) |
−0.978759 | + | 0.205015i | \(0.934276\pi\) | |||||||
\(524\) | −4.07348 | −0.177951 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.9641 | 0.608863 | ||||||||
\(527\) | 5.73509 | + | 9.93347i | 0.249825 | + | 0.432709i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.440059 | − | 0.762205i | 0.0191330 | − | 0.0331393i | ||||
\(530\) | 30.5122 | + | 52.8487i | 1.32537 | + | 2.29560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.26431 | + | 2.81364i | 0.0981701 | + | 0.121987i | ||||
\(533\) | 17.7424 | 0.768508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.81768 | + | 6.61242i | −0.165053 | + | 0.285880i | ||||
\(536\) | 16.1312 | − | 27.9401i | 0.696762 | − | 1.20683i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −35.0277 | −1.51015 | ||||||||
\(539\) | 18.8165 | + | 17.1509i | 0.810484 | + | 0.738742i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.99105 | + | 13.8409i | 0.343562 | + | 0.595067i | 0.985091 | − | 0.172032i | \(-0.0550331\pi\) |
−0.641529 | + | 0.767098i | \(0.721700\pi\) | |||||||
\(542\) | −7.11796 | + | 12.3287i | −0.305743 | + | 0.529562i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00670 | + | 5.20776i | 0.128911 | + | 0.223281i | ||||
\(545\) | 25.5899 | 1.09615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0570 | −1.37066 | −0.685330 | − | 0.728233i | \(-0.740342\pi\) | ||||
−0.685330 | + | 0.728233i | \(0.740342\pi\) | |||||||
\(548\) | 0.362714 | + | 0.628238i | 0.0154944 | + | 0.0268370i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.28784 | + | 14.3550i | −0.353395 | + | 0.612098i | ||||
\(551\) | 8.80583 | + | 15.2521i | 0.375141 | + | 0.649763i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.853910 | − | 2.20444i | 0.0363120 | − | 0.0937425i | ||||
\(554\) | −0.280142 | −0.0119021 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.59657 | − | 6.22945i | 0.152529 | − | 0.264187i | ||||
\(557\) | −19.6474 | + | 34.0302i | −0.832486 | + | 1.44191i | 0.0635754 | + | 0.997977i | \(0.479750\pi\) |
−0.896061 | + | 0.443931i | \(0.853584\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.7496 | 2.18877 | ||||||||
\(560\) | −33.6691 | + | 5.22771i | −1.42278 | + | 0.220911i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.3797 | − | 21.4423i | −0.522207 | − | 0.904489i | ||||
\(563\) | 17.2532 | − | 29.8834i | 0.727134 | − | 1.25943i | −0.230955 | − | 0.972964i | \(-0.574185\pi\) |
0.958089 | − | 0.286469i | \(-0.0924816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.657973 | − | 1.13964i | −0.0276811 | − | 0.0479451i | ||||
\(566\) | −31.6308 | −1.32954 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.41332 | 0.311056 | ||||||||
\(569\) | −2.14203 | − | 3.71010i | −0.0897985 | − | 0.155536i | 0.817627 | − | 0.575748i | \(-0.195289\pi\) |
−0.907426 | + | 0.420212i | \(0.861956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5798 | + | 21.7888i | −0.526447 | + | 0.911833i | 0.473078 | + | 0.881021i | \(0.343143\pi\) |
−0.999525 | + | 0.0308128i | \(0.990190\pi\) | |||||||
\(572\) | −3.43267 | − | 5.94555i | −0.143527 | − | 0.248596i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.60312 | − | 11.8834i | 0.192131 | − | 0.496002i | ||||
\(575\) | −14.0258 | −0.584917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.1281 | − | 38.3271i | 0.921206 | − | 1.59558i | 0.123655 | − | 0.992325i | \(-0.460539\pi\) |
0.797552 | − | 0.603251i | \(-0.206128\pi\) | |||||||
\(578\) | −5.15447 | + | 8.92781i | −0.214398 | + | 0.371348i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.09861 | 0.170186 | ||||||||
\(581\) | −13.3508 | − | 16.5898i | −0.553883 | − | 0.688259i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.7040 | − | 44.5206i | −1.06455 | − | 1.84385i | ||||
\(584\) | −3.72573 | + | 6.45315i | −0.154172 | + | 0.267033i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.2433 | + | 21.2060i | 0.505766 | + | 0.876012i | ||||
\(587\) | 13.0046 | 0.536757 | 0.268378 | − | 0.963314i | \(-0.413512\pi\) | ||||
0.268378 | + | 0.963314i | \(0.413512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.5818 | 0.600831 | ||||||||
\(590\) | 3.24025 | + | 5.61228i | 0.133399 | + | 0.231054i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.82648 | + | 17.0200i | −0.403866 | + | 0.699516i | ||||
\(593\) | −14.1164 | − | 24.4503i | −0.579691 | − | 1.00405i | −0.995515 | − | 0.0946086i | \(-0.969840\pi\) |
0.415824 | − | 0.909445i | \(-0.363493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0070 | + | 18.6478i | 0.615227 | + | 0.764486i | ||||
\(596\) | 3.72116 | 0.152425 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.2289 | − | 35.0375i | 0.827221 | − | 1.43279i | ||||
\(599\) | 2.49768 | − | 4.32611i | 0.102052 | − | 0.176760i | −0.810478 | − | 0.585769i | \(-0.800792\pi\) |
0.912530 | + | 0.409010i | \(0.134126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.15787 | 0.332766 | 0.166383 | − | 0.986061i | \(-0.446791\pi\) | ||||
0.166383 | + | 0.986061i | \(0.446791\pi\) | |||||||
\(602\) | 13.4260 | − | 34.6604i | 0.547204 | − | 1.41265i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.349925 | − | 0.606089i | −0.0142383 | − | 0.0246614i | ||||
\(605\) | 3.14856 | − | 5.45347i | 0.128007 | − | 0.221715i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.36385 | − | 14.4866i | −0.339478 | − | 0.587993i | 0.644857 | − | 0.764304i | \(-0.276917\pi\) |
−0.984335 | + | 0.176310i | \(0.943584\pi\) | |||||||
\(608\) | 7.64469 | 0.310033 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 57.0133 | 2.30840 | ||||||||
\(611\) | −13.6405 | − | 23.6260i | −0.551834 | − | 0.955805i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.29381 | − | 14.3653i | 0.334984 | − | 0.580209i | −0.648498 | − | 0.761216i | \(-0.724602\pi\) |
0.983482 | + | 0.181007i | \(0.0579358\pi\) | |||||||
\(614\) | −4.06729 | − | 7.04476i | −0.164143 | − | 0.284303i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.1903 | − | 3.75596i | 0.974654 | − | 0.151332i | ||||
\(617\) | −23.7085 | −0.954470 | −0.477235 | − | 0.878776i | \(-0.658361\pi\) | ||||
−0.477235 | + | 0.878776i | \(0.658361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.91206 | − | 6.77589i | 0.157239 | − | 0.272346i | −0.776633 | − | 0.629953i | \(-0.783074\pi\) |
0.933872 | + | 0.357607i | \(0.116407\pi\) | |||||||
\(620\) | 1.69674 | − | 2.93885i | 0.0681429 | − | 0.118027i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.1581 | −1.12904 | ||||||||
\(623\) | −5.40644 | + | 13.9572i | −0.216604 | + | 0.559183i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5087 | + | 26.8619i | 0.620350 | + | 1.07448i | ||||
\(626\) | 3.55063 | − | 6.14986i | 0.141912 | − | 0.245798i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.62406 | + | 6.27706i | 0.144616 | + | 0.250482i | ||||
\(629\) | 13.8065 | 0.550500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.54669 | −0.101382 | −0.0506911 | − | 0.998714i | \(-0.516142\pi\) | ||||
−0.0506911 | + | 0.998714i | \(0.516142\pi\) | |||||||
\(632\) | −1.13653 | − | 1.96853i | −0.0452088 | − | 0.0783039i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.00774 | + | 13.8698i | −0.318028 | + | 0.550841i | ||||
\(635\) | −22.2596 | − | 38.5547i | −0.883344 | − | 1.53000i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.42682 | − | 38.4919i | 0.333883 | − | 1.52511i | ||||
\(638\) | −24.0462 | −0.951999 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.7906 | + | 32.5463i | −0.742764 | + | 1.28651i | ||||
\(641\) | −5.14269 | + | 8.90739i | −0.203124 | + | 0.351821i | −0.949533 | − | 0.313666i | \(-0.898443\pi\) |
0.746409 | + | 0.665487i | \(0.231776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.92126 | −0.194076 | −0.0970378 | − | 0.995281i | \(-0.530937\pi\) | ||||
−0.0970378 | + | 0.995281i | \(0.530937\pi\) | |||||||
\(644\) | −2.61600 | − | 3.25067i | −0.103085 | − | 0.128094i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.96047 | − | 17.2520i | −0.391890 | − | 0.678773i | ||||
\(647\) | −4.39168 | + | 7.60661i | −0.172655 | + | 0.299047i | −0.939347 | − | 0.342968i | \(-0.888568\pi\) |
0.766692 | + | 0.642015i | \(0.221901\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.72964 | − | 4.72787i | −0.107148 | − | 0.185585i | ||||
\(650\) | 25.6536 | 1.00622 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.14614 | −0.123212 | ||||||||
\(653\) | −0.887297 | − | 1.53684i | −0.0347226 | − | 0.0601414i | 0.848142 | − | 0.529769i | \(-0.177721\pi\) |
−0.882864 | + | 0.469628i | \(0.844388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1606 | + | 29.7231i | −0.670522 | + | 1.16138i | ||||
\(656\) | −7.18354 | − | 12.4423i | −0.280470 | − | 0.485788i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.3630 | + | 3.00643i | −0.754846 | + | 0.117203i | ||||
\(659\) | 2.34367 | 0.0912966 | 0.0456483 | − | 0.998958i | \(-0.485465\pi\) | ||||
0.0456483 | + | 0.998958i | \(0.485465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4547 | − | 19.8401i | 0.445537 | − | 0.771692i | −0.552553 | − | 0.833478i | \(-0.686346\pi\) |
0.998089 | + | 0.0617856i | \(0.0196795\pi\) | |||||||
\(662\) | 9.82124 | − | 17.0109i | 0.381713 | − | 0.661147i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.4751 | −0.794587 | ||||||||
\(665\) | 30.0694 | − | 4.66880i | 1.16604 | − | 0.181048i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.1736 | − | 17.6212i | −0.393922 | − | 0.682294i | ||||
\(668\) | −2.91810 | + | 5.05429i | −0.112905 | + | 0.195556i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.3778 | + | 47.4197i | 1.05770 | + | 1.83198i | ||||
\(671\) | −48.0288 | −1.85413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7349 | −1.14620 | −0.573098 | − | 0.819487i | \(-0.694259\pi\) | ||||
−0.573098 | + | 0.819487i | \(0.694259\pi\) | |||||||
\(674\) | 5.57187 | + | 9.65076i | 0.214620 | + | 0.371733i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.13301 | + | 5.42654i | −0.120500 | + | 0.208713i | ||||
\(677\) | −12.7480 | − | 22.0802i | −0.489946 | − | 0.848611i | 0.509987 | − | 0.860182i | \(-0.329650\pi\) |
−0.999933 | + | 0.0115711i | \(0.996317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.51905 | + | 10.5858i | 0.326931 | + | 0.406247i | ||||
\(680\) | 23.0151 | 0.882590 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.95466 | + | 17.2420i | −0.381184 | + | 0.660230i | ||||
\(683\) | −5.69293 | + | 9.86044i | −0.217834 | + | 0.377299i | −0.954145 | − | 0.299343i | \(-0.903232\pi\) |
0.736312 | + | 0.676643i | \(0.236566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.11212 | 0.233532 | ||||||||
\(686\) | −23.5946 | − | 15.6305i | −0.900845 | − | 0.596775i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.9524 | − | 36.2906i | −0.798801 | − | 1.38356i | ||||
\(689\) | −39.7811 | + | 68.9029i | −1.51554 | + | 2.62499i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1261 | + | 27.9313i | 0.613468 | + | 1.06256i | 0.990651 | + | 0.136419i | \(0.0435592\pi\) |
−0.377184 | + | 0.926138i | \(0.623107\pi\) | |||||||
\(692\) | −7.22539 | −0.274668 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.8024 | −1.01741 | ||||||||
\(695\) | −30.3031 | − | 52.4865i | −1.14946 | − | 1.99093i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.04653 | + | 8.74085i | −0.191151 | + | 0.331083i | ||||
\(698\) | 16.0581 | + | 27.8134i | 0.607807 | + | 1.05275i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.955663 | − | 2.46713i | 0.0361207 | − | 0.0932486i | ||||
\(701\) | 15.6291 | 0.590302 | 0.295151 | − | 0.955451i | \(-0.404630\pi\) | ||||
0.295151 | + | 0.955451i | \(0.404630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.77591 | − | 15.2003i | 0.330990 | − | 0.573291i | ||||
\(704\) | 11.3600 | − | 19.6761i | 0.428146 | − | 0.741570i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.72246 | −0.290639 | ||||||||
\(707\) | 6.60002 | − | 1.02477i | 0.248219 | − | 0.0385403i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.90824 | + | 10.2334i | 0.221888 | + | 0.384322i | 0.955381 | − | 0.295375i | \(-0.0954446\pi\) |
−0.733493 | + | 0.679697i | \(0.762111\pi\) | |||||||
\(710\) | −6.29092 | + | 10.8962i | −0.236094 | + | 0.408927i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.19582 | + | 12.4635i | 0.269675 | + | 0.467090i | ||||
\(713\) | −16.8466 | −0.630912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.8442 | −2.16325 | ||||||||
\(716\) | −0.948505 | − | 1.64286i | −0.0354473 | − | 0.0613965i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.0610 | + | 19.1583i | −0.412794 | + | 0.714980i | ||||
\(719\) | 25.3616 | + | 43.9276i | 0.945830 | + | 1.63822i | 0.754082 | + | 0.656781i | \(0.228082\pi\) |
0.191748 | + | 0.981444i | \(0.438584\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.40985 | − | 24.2923i | 0.350441 | − | 0.904694i | ||||
\(722\) | 3.71036 | 0.138085 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.188497 | + | 0.326486i | −0.00700543 | + | 0.0121338i | ||||
\(725\) | 6.45088 | − | 11.1733i | 0.239580 | − | 0.414964i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.26602 | 0.0840422 | 0.0420211 | − | 0.999117i | \(-0.486620\pi\) | ||||
0.0420211 | + | 0.999117i | \(0.486620\pi\) | |||||||
\(728\) | −23.7534 | − | 29.5161i | −0.880358 | − | 1.09394i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.32328 | − | 10.9522i | −0.234035 | − | 0.405361i | ||||
\(731\) | −14.7193 | + | 25.4946i | −0.544414 | + | 0.942952i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.8262 | + | 29.1439i | 0.621490 | + | 1.07645i | 0.989208 | + | 0.146515i | \(0.0468058\pi\) |
−0.367718 | + | 0.929937i | \(0.619861\pi\) | |||||||
\(734\) | −22.8047 | −0.841738 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.83209 | −0.325555 | ||||||||
\(737\) | −23.0634 | − | 39.9471i | −0.849553 | − | 1.47147i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.80187 | + | 16.9773i | −0.360568 | + | 0.624521i | −0.988054 | − | 0.154106i | \(-0.950750\pi\) |
0.627487 | + | 0.778627i | \(0.284084\pi\) | |||||||
\(740\) | −2.04234 | − | 3.53744i | −0.0750780 | − | 0.130039i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.8284 | + | 44.5206i | 1.31530 | + | 1.63440i | ||||
\(743\) | 48.8390 | 1.79173 | 0.895865 | − | 0.444327i | \(-0.146557\pi\) | ||||
0.895865 | + | 0.444327i | \(0.146557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.6764 | − | 27.1523i | 0.574339 | − | 0.994784i | ||||
\(746\) | 5.97599 | − | 10.3507i | 0.218796 | − | 0.378967i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.90546 | 0.142798 | ||||||||
\(749\) | −2.58269 | + | 6.66745i | −0.0943696 | + | 0.243623i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.91269 | − | 13.7052i | −0.288738 | − | 0.500109i | 0.684771 | − | 0.728759i | \(-0.259902\pi\) |
−0.973509 | + | 0.228649i | \(0.926569\pi\) | |||||||
\(752\) | −11.0455 | + | 19.1314i | −0.402788 | + | 0.697650i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.6077 | + | 32.2295i | 0.677653 | + | 1.17373i | ||||
\(755\) | −5.89663 | −0.214600 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.18728 | −0.0794982 | −0.0397491 | − | 0.999210i | \(-0.512656\pi\) | ||||
−0.0397491 | + | 0.999210i | \(0.512656\pi\) | |||||||
\(758\) | 8.87084 | + | 15.3647i | 0.322203 | + | 0.558073i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.6293 | − | 25.3386i | 0.530660 | − | 0.919129i | ||||
\(761\) | 13.8781 | + | 24.0376i | 0.503081 | + | 0.871361i | 0.999994 | + | 0.00356072i | \(0.00113341\pi\) |
−0.496913 | + | 0.867800i | \(0.665533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6801 | − | 3.67674i | 0.857276 | − | 0.133107i | ||||
\(764\) | 1.32084 | 0.0477861 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.1606 | − | 33.1871i | 0.692300 | − | 1.19910i | ||||
\(767\) | −4.22456 | + | 7.31715i | −0.152540 | + | 0.264207i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0206 | 0.361352 | 0.180676 | − | 0.983543i | \(-0.442171\pi\) | ||||
0.180676 | + | 0.983543i | \(0.442171\pi\) | |||||||
\(770\) | −15.0072 | + | 38.7425i | −0.540823 | + | 1.39618i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.03245 | − | 5.25236i | −0.109140 | − | 0.189037i | ||||
\(773\) | 21.7596 | − | 37.6887i | 0.782639 | − | 1.35557i | −0.147761 | − | 0.989023i | \(-0.547207\pi\) |
0.930400 | − | 0.366547i | \(-0.119460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.34108 | − | 9.25102i | −0.191857 | − | 0.332306i | ||||
\(776\) | 13.0650 | 0.469007 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.9111 | −1.28748 | ||||||||
\(779\) | 6.41553 | + | 11.1120i | 0.229860 | + | 0.398130i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.29957 | − | 9.17912i | 0.189633 | − | 0.328455i | ||||
\(782\) | 11.5076 | + | 19.9317i | 0.411510 | + | 0.712756i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30.4052 | + | 9.67512i | −1.08590 | + | 0.345540i | ||||
\(785\) | 61.0694 | 2.17966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.91819 | − | 5.05445i | 0.104022 | − | 0.180172i | −0.809316 | − | 0.587373i | \(-0.800162\pi\) |
0.913338 | + | 0.407202i | \(0.133495\pi\) | |||||||
\(788\) | −4.27271 | + | 7.40055i | −0.152209 | + | 0.263634i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.85782 | 0.137255 | ||||||||
\(791\) | −0.772611 | − | 0.960053i | −0.0274709 | − | 0.0341355i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.1662 | + | 64.3738i | 1.31981 | + | 2.28598i | ||||
\(794\) | −15.0704 | + | 26.1027i | −0.534829 | + | 0.926351i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.11741 | − | 3.66746i | −0.0750496 | − | 0.129990i | ||||
\(797\) | 36.5800 | 1.29573 | 0.647865 | − | 0.761755i | \(-0.275662\pi\) | ||||
0.647865 | + | 0.761755i | \(0.275662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.5192 | 0.549031 | ||||||||
\(800\) | −2.80014 | − | 4.84998i | −0.0989998 | − | 0.171473i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.9873 | − | 19.0306i | 0.387976 | − | 0.671994i | ||||
\(803\) | 5.32683 | + | 9.22634i | 0.187980 | + | 0.325590i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.7399 | + | 5.39398i | −1.22442 | + | 0.190113i | ||||
\(806\) | 30.8129 | 1.08534 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.21102 | − | 5.56164i | 0.112963 | − | 0.195658i | ||||
\(809\) | 11.0249 | − | 19.0957i | 0.387616 | − | 0.671370i | −0.604513 | − | 0.796596i | \(-0.706632\pi\) |
0.992128 | + | 0.125225i | \(0.0399654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6451 | −0.444029 | −0.222015 | − | 0.975043i | \(-0.571263\pi\) | ||||
−0.222015 | + | 0.975043i | \(0.571263\pi\) | |||||||
\(812\) | 3.79273 | − | 0.588886i | 0.133099 | − | 0.0206659i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.9823 | + | 20.7539i | 0.419978 | + | 0.727423i | ||||
\(815\) | −13.2540 | + | 22.9566i | −0.464267 | + | 0.804134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.7123 | + | 32.4107i | 0.654660 | + | 1.13391i | ||||
\(818\) | 17.6900 | 0.618517 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.98606 | 0.104278 | ||||||||
\(821\) | 15.5479 | + | 26.9298i | 0.542625 | + | 0.939855i | 0.998752 | + | 0.0499401i | \(0.0159030\pi\) |
−0.456127 | + | 0.889915i | \(0.650764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4819 | − | 42.4039i | 0.853385 | − | 1.47811i | −0.0247505 | − | 0.999694i | \(-0.507879\pi\) |
0.878135 | − | 0.478412i | \(-0.158788\pi\) | |||||||
\(824\) | −12.5242 | − | 21.6926i | −0.436303 | − | 0.755699i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.80480 | + | 4.72787i | 0.132386 | + | 0.164504i | ||||
\(827\) | −36.3827 | −1.26515 | −0.632575 | − | 0.774499i | \(-0.718002\pi\) | ||||
−0.632575 | + | 0.774499i | \(0.718002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.8702 | + | 39.6124i | −0.794316 | + | 1.37580i | 0.128957 | + | 0.991650i | \(0.458837\pi\) |
−0.923273 | + | 0.384145i | \(0.874496\pi\) | |||||||
\(830\) | 17.3751 | − | 30.0945i | 0.603098 | − | 1.04460i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35.1629 | −1.21905 | ||||||||
\(833\) | 16.5663 | + | 15.0999i | 0.573989 | + | 0.523181i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.5866 | + | 42.5852i | 0.850853 | + | 1.47372i | ||||
\(836\) | 2.48246 | − | 4.29974i | 0.0858576 | − | 0.148710i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.1105 | + | 45.2247i | 0.901972 | + | 1.56226i | ||||
\(839\) | −25.5348 | −0.881559 | −0.440779 | − | 0.897615i | \(-0.645298\pi\) | ||||
−0.440779 | + | 0.897615i | \(0.645298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.2835 | −0.354604 | ||||||||
\(842\) | −7.80998 | − | 13.5273i | −0.269150 | − | 0.466181i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.387559 | + | 0.671271i | −0.0133403 | + | 0.0231061i | ||||
\(845\) | 26.3974 | + | 45.7216i | 0.908097 | + | 1.57287i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.13003 | − | 5.49885i | 0.0731886 | − | 0.188943i | ||||
\(848\) | 64.4263 | 2.21241 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.29674 | + | 12.6383i | −0.250276 | + | 0.433491i | ||||
\(851\) | −10.1390 | + | 17.5613i | −0.347561 | + | 0.601993i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.84673 | −0.0632310 | −0.0316155 | − | 0.999500i | \(-0.510065\pi\) | ||||
−0.0316155 | + | 0.999500i | \(0.510065\pi\) | |||||||
\(854\) | 52.7583 | − | 8.19164i | 1.80535 | − | 0.280312i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.43749 | + | 5.95391i | 0.117491 | + | 0.203501i | ||||
\(857\) | 11.2424 | − | 19.4724i | 0.384033 | − | 0.665165i | −0.607601 | − | 0.794242i | \(-0.707868\pi\) |
0.991635 | + | 0.129077i | \(0.0412015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.573807 | + | 0.993864i | 0.0195781 | + | 0.0339102i | 0.875648 | − | 0.482949i | \(-0.160434\pi\) |
−0.856070 | + | 0.516859i | \(0.827101\pi\) | |||||||
\(860\) | 8.70951 | 0.296992 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.116302 | 0.00396126 | ||||||||
\(863\) | −0.897635 | − | 1.55475i | −0.0305558 | − | 0.0529243i | 0.850343 | − | 0.526229i | \(-0.176394\pi\) |
−0.880899 | + | 0.473304i | \(0.843061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.4390 | + | 52.7218i | −1.03496 | + | 1.79260i | ||||
\(866\) | −22.3646 | − | 38.7366i | −0.759980 | − | 1.31632i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.14786 | − | 2.96330i | 0.0389610 | − | 0.100581i | ||||
\(869\) | −3.24989 | −0.110245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.6944 | + | 61.8246i | −1.20946 | + | 2.09485i | ||||
\(872\) | 11.5207 | − | 19.9545i | 0.390141 | − | 0.675745i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.2585 | 0.989685 | ||||||||
\(875\) | 9.45634 | + | 11.7505i | 0.319683 | + | 0.397240i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.28998 | − | 7.43047i | −0.144862 | − | 0.250909i | 0.784459 | − | 0.620180i | \(-0.212941\pi\) |
−0.929322 | + | 0.369271i | \(0.879607\pi\) | |||||||
\(878\) | −3.32016 | + | 5.75069i | −0.112050 | + | 0.194076i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.4200 | + | 40.5646i | 0.789487 | + | 1.36743i | ||||
\(881\) | −16.5346 | −0.557066 | −0.278533 | − | 0.960427i | \(-0.589848\pi\) | ||||
−0.278533 | + | 0.960427i | \(0.589848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.4948 | −0.925273 | −0.462636 | − | 0.886548i | \(-0.653096\pi\) | ||||
−0.462636 | + | 0.886548i | \(0.653096\pi\) | |||||||
\(884\) | −3.02217 | − | 5.23455i | −0.101647 | − | 0.176057i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.7053 | + | 27.2025i | −0.527631 | + | 0.913885i | ||||
\(887\) | 21.7210 | + | 37.6218i | 0.729318 | + | 1.26322i | 0.957172 | + | 0.289521i | \(0.0934960\pi\) |
−0.227853 | + | 0.973695i | \(0.573171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.1378 | − | 32.4791i | −0.876634 | − | 1.08931i | ||||
\(890\) | −24.4254 | −0.818741 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.55919 | + | 2.70059i | −0.0522054 | + | 0.0904225i | ||||
\(893\) | 9.86461 | − | 17.0860i | 0.330107 | − | 0.571761i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9834 | −0.534265 | ||||||||
\(896\) | −12.7120 | + | 32.8172i | −0.424678 | + | 1.09634i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.52968 | − | 16.5059i | −0.318010 | − | 0.550809i | ||||
\(899\) | 7.74826 | − | 13.4204i | 0.258419 | − | 0.447595i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.6302 | − | 39.1966i | −0.753920 | − | 1.30583i | ||||
\(902\) | −17.5190 | −0.583319 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.18490 | −0.0394091 | ||||||||
\(905\) | 1.58819 | + | 2.75083i | 0.0527932 | + | 0.0914406i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.64761 | + | 9.78196i | −0.187526 | + | 0.324805i | −0.944425 | − | 0.328728i | \(-0.893380\pi\) |
0.756899 | + | 0.653532i | \(0.226714\pi\) | |||||||
\(908\) | 0.323282 | + | 0.559941i | 0.0107285 | + | 0.0185823i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 63.5402 | − | 9.86571i | 2.10634 | − | 0.327045i | ||||
\(911\) | 10.0338 | 0.332435 | 0.166217 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166217 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.6370 | + | 25.3521i | −0.484415 | + | 0.839032i | ||||
\(914\) | −23.6369 | + | 40.9403i | −0.781839 | + | 1.35418i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.12038 | 0.0370182 | ||||||||
\(917\) | −11.6093 | + | 29.9705i | −0.383373 | + | 0.989712i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.178967 | + | 0.309980i | 0.00590358 | + | 0.0102253i | 0.868962 | − | 0.494879i | \(-0.164787\pi\) |
−0.863059 | + | 0.505104i | \(0.831454\pi\) | |||||||
\(920\) | −16.9015 | + | 29.2743i | −0.557227 | + | 0.965146i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.13013 | + | 10.6177i | 0.201885 | + | 0.349675i | ||||
\(923\) | −16.4039 | −0.539941 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.8579 | −0.422766 | ||||||||
\(926\) | −12.8537 | − | 22.2633i | −0.422400 | − | 0.731619i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.06214 | − | 7.03583i | 0.133346 | − | 0.230962i | ||||
\(929\) | −16.7632 | − | 29.0347i | −0.549983 | − | 0.952599i | −0.998275 | − | 0.0587116i | \(-0.981301\pi\) |
0.448292 | − | 0.893887i | \(-0.352033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.1545 | − | 8.64073i | 0.889953 | − | 0.283188i | ||||
\(932\) | 7.09259 | 0.232326 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.734134 | − | 1.27156i | 0.0240216 | − | 0.0416066i | ||||
\(935\) | 16.4528 | − | 28.4972i | 0.538065 | − | 0.931957i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.8772 | 0.420680 | 0.210340 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210340 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(938\) | 32.1478 | + | 39.9471i | 1.04966 | + | 1.30432i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.29571 | − | 3.97628i | −0.0748777 | − | 0.129692i | ||||
\(941\) | 16.0492 | − | 27.7980i | 0.523189 | − | 0.906190i | −0.476447 | − | 0.879203i | \(-0.658075\pi\) |
0.999636 | − | 0.0269868i | \(-0.00859120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.41201 | − | 12.8380i | −0.241368 | − | 0.418062i | ||||
\(944\) | 6.84176 | 0.222680 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.0980 | −1.66134 | ||||||||
\(947\) | 8.39928 | + | 14.5480i | 0.272940 | + | 0.472746i | 0.969613 | − | 0.244642i | \(-0.0786706\pi\) |
−0.696673 | + | 0.717389i | \(0.745337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.24414 | − | 14.2793i | 0.267616 | − | 0.463524i | ||||
\(950\) | 9.27616 | + | 16.0668i | 0.300958 | + | 0.521275i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.2975 | − | 3.30680i | 0.690255 | − | 0.107174i | ||||
\(953\) | 2.69574 | 0.0873237 | 0.0436619 | − | 0.999046i | \(-0.486098\pi\) | ||||
0.0436619 | + | 0.999046i | \(0.486098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.56438 | − | 9.63780i | 0.180059 | − | 0.311872i | ||||
\(956\) | 4.04316 | − | 7.00297i | 0.130765 | − | 0.226492i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.8734 | −1.19133 | ||||||||
\(959\) | 5.65597 | − | 0.878187i | 0.182641 | − | 0.0283581i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.08474 | + | 15.7352i | 0.293056 | + | 0.507588i | ||||
\(962\) | 18.5445 | − | 32.1200i | 0.597898 | − | 1.03559i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.54825 | − | 2.68165i | −0.0498658 | − | 0.0863701i | ||||
\(965\) | −51.1002 | −1.64497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6775 | 0.439837 | 0.219919 | − | 0.975518i | \(-0.429421\pi\) | ||||
0.219919 | + | 0.975518i | \(0.429421\pi\) | |||||||
\(968\) | −2.83501 | − | 4.91038i | −0.0911206 | − | 0.157826i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.0869 | + | 19.2031i | −0.355980 | + | 0.616576i | ||||
\(971\) | 21.3133 | + | 36.9157i | 0.683977 | + | 1.18468i | 0.973757 | + | 0.227589i | \(0.0730843\pi\) |
−0.289781 | + | 0.957093i | \(0.593582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.5828 | − | 44.2155i | −1.14073 | − | 1.41748i | ||||
\(974\) | −22.6153 | −0.724641 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.0957 | − | 52.1273i | 0.963341 | − | 1.66856i | ||||
\(977\) | 2.52841 | − | 4.37934i | 0.0808911 | − | 0.140108i | −0.822742 | − | 0.568415i | \(-0.807557\pi\) |
0.903633 | + | 0.428308i | \(0.140890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.5763 | 0.657622 | ||||||||
\(980\) | 1.41824 | − | 6.47823i | 0.0453041 | − | 0.206940i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.81668 | + | 8.34274i | 0.153707 | + | 0.266227i | ||||
\(983\) | 16.6442 | − | 28.8286i | 0.530868 | − | 0.919490i | −0.468483 | − | 0.883472i | \(-0.655199\pi\) |
0.999351 | − | 0.0360177i | \(-0.0114673\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.9999 | + | 62.3537i | 1.14705 | + | 1.98675i | ||||
\(986\) | −21.1707 | −0.674211 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.68402 | −0.244461 | ||||||||
\(989\) | −21.6188 | − | 37.4448i | −0.687436 | − | 1.19067i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0440 | + | 27.7890i | −0.509653 | + | 0.882746i | 0.490284 | + | 0.871563i | \(0.336893\pi\) |
−0.999937 | + | 0.0111829i | \(0.996440\pi\) | |||||||
\(992\) | −3.36329 | − | 5.82539i | −0.106785 | − | 0.184956i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.25586 | + | 10.9869i | −0.134988 | + | 0.348482i | ||||
\(995\) | −35.6807 | −1.13115 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.6283 | − | 37.4613i | 0.684975 | − | 1.18641i | −0.288470 | − | 0.957489i | \(-0.593146\pi\) |
0.973445 | − | 0.228922i | \(-0.0735202\pi\) | |||||||
\(998\) | −21.8507 | + | 37.8466i | −0.691673 | + | 1.19801i | ||||
\(999\) | 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.e.g.487.7 | yes | 16 | |
3.2 | odd | 2 | inner | 567.2.e.g.487.2 | yes | 16 | |
7.2 | even | 3 | inner | 567.2.e.g.163.7 | yes | 16 | |
7.3 | odd | 6 | 3969.2.a.bf.1.2 | 8 | |||
7.4 | even | 3 | 3969.2.a.bg.1.2 | 8 | |||
9.2 | odd | 6 | 567.2.g.l.109.2 | 16 | |||
9.4 | even | 3 | 567.2.h.l.298.2 | 16 | |||
9.5 | odd | 6 | 567.2.h.l.298.7 | 16 | |||
9.7 | even | 3 | 567.2.g.l.109.7 | 16 | |||
21.2 | odd | 6 | inner | 567.2.e.g.163.2 | ✓ | 16 | |
21.11 | odd | 6 | 3969.2.a.bg.1.7 | 8 | |||
21.17 | even | 6 | 3969.2.a.bf.1.7 | 8 | |||
63.2 | odd | 6 | 567.2.h.l.352.7 | 16 | |||
63.16 | even | 3 | 567.2.h.l.352.2 | 16 | |||
63.23 | odd | 6 | 567.2.g.l.541.2 | 16 | |||
63.58 | even | 3 | 567.2.g.l.541.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.g.163.2 | ✓ | 16 | 21.2 | odd | 6 | inner | |
567.2.e.g.163.7 | yes | 16 | 7.2 | even | 3 | inner | |
567.2.e.g.487.2 | yes | 16 | 3.2 | odd | 2 | inner | |
567.2.e.g.487.7 | yes | 16 | 1.1 | even | 1 | trivial | |
567.2.g.l.109.2 | 16 | 9.2 | odd | 6 | |||
567.2.g.l.109.7 | 16 | 9.7 | even | 3 | |||
567.2.g.l.541.2 | 16 | 63.23 | odd | 6 | |||
567.2.g.l.541.7 | 16 | 63.58 | even | 3 | |||
567.2.h.l.298.2 | 16 | 9.4 | even | 3 | |||
567.2.h.l.298.7 | 16 | 9.5 | odd | 6 | |||
567.2.h.l.352.2 | 16 | 63.16 | even | 3 | |||
567.2.h.l.352.7 | 16 | 63.2 | odd | 6 | |||
3969.2.a.bf.1.2 | 8 | 7.3 | odd | 6 | |||
3969.2.a.bf.1.7 | 8 | 21.17 | even | 6 | |||
3969.2.a.bg.1.2 | 8 | 7.4 | even | 3 | |||
3969.2.a.bg.1.7 | 8 | 21.11 | odd | 6 |