Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + 1250 x^{4} - 100000 x^{3} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.8 | ||
Root | \(1.39977 - 1.74375i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.c.1273.8 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.14668 | + | 0.625913i | 0.960024 | + | 0.279917i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.07534 | + | 1.96052i | 0.340054 | + | 0.619971i | ||||
\(11\) | 2.07328 | 0.625117 | 0.312559 | − | 0.949898i | \(-0.398814\pi\) | ||||
0.312559 | + | 0.949898i | \(0.398814\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −0.326993 | − | 0.326993i | −0.0906916 | − | 0.0906916i | 0.660306 | − | 0.750997i | \(-0.270427\pi\) |
−0.750997 | + | 0.660306i | \(0.770427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.07534 | + | 1.96052i | 0.277653 | + | 0.506204i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.26881 | + | 1.26881i | −0.307732 | + | 0.307732i | −0.844029 | − | 0.536297i | \(-0.819823\pi\) |
0.536297 | + | 0.844029i | \(0.319823\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | 4.37232 | 1.00308 | 0.501540 | − | 0.865135i | \(-0.332767\pi\) | ||||
0.501540 | + | 0.865135i | \(0.332767\pi\) | |||||||
\(20\) | −0.625913 | + | 2.14668i | −0.139959 | + | 0.480012i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.46603 | + | 1.46603i | 0.312559 | + | 0.312559i | ||||
\(23\) | 0.635591 | − | 0.635591i | 0.132530 | − | 0.132530i | −0.637730 | − | 0.770260i | \(-0.720126\pi\) |
0.770260 | + | 0.637730i | \(0.220126\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.21646 | + | 2.68727i | 0.843293 | + | 0.537454i | ||||
\(26\) | − | 0.462438i | − | 0.0906916i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.0288926i | − | 0.00536522i | −0.999996 | − | 0.00268261i | \(-0.999146\pi\) | ||
0.999996 | − | 0.00268261i | \(-0.000853903\pi\) | |||||||
\(30\) | −0.625913 | + | 2.14668i | −0.114276 | + | 0.391928i | ||||
\(31\) | 8.03242i | 1.44267i | 0.692589 | + | 0.721333i | \(0.256470\pi\) | ||||
−0.692589 | + | 0.721333i | \(0.743530\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 1.46603 | + | 1.46603i | 0.255203 | + | 0.255203i | ||||
\(34\) | −1.79437 | −0.307732 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −8.07760 | − | 8.07760i | −1.32795 | − | 1.32795i | −0.907157 | − | 0.420793i | \(-0.861752\pi\) |
−0.420793 | − | 0.907157i | \(-0.638248\pi\) | |||||||
\(38\) | 3.09170 | + | 3.09170i | 0.501540 | + | 0.501540i | ||||
\(39\) | − | 0.462438i | − | 0.0740494i | ||||||
\(40\) | −1.96052 | + | 1.07534i | −0.309985 | + | 0.170027i | ||||
\(41\) | 10.6696i | 1.66631i | 0.553042 | + | 0.833153i | \(0.313467\pi\) | ||||
−0.553042 | + | 0.833153i | \(0.686533\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.50876 | − | 2.50876i | 0.382583 | − | 0.382583i | −0.489449 | − | 0.872032i | \(-0.662802\pi\) |
0.872032 | + | 0.489449i | \(0.162802\pi\) | |||||||
\(44\) | 2.07328i | 0.312559i | ||||||||
\(45\) | −0.625913 | + | 2.14668i | −0.0933057 | + | 0.320008i | ||||
\(46\) | 0.898861 | 0.132530 | ||||||||
\(47\) | −0.525308 | + | 0.525308i | −0.0766241 | + | 0.0766241i | −0.744380 | − | 0.667756i | \(-0.767255\pi\) |
0.667756 | + | 0.744380i | \(0.267255\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.08130 | + | 4.88168i | 0.152919 | + | 0.690374i | ||||
\(51\) | −1.79437 | −0.251262 | ||||||||
\(52\) | 0.326993 | − | 0.326993i | 0.0453458 | − | 0.0453458i | ||||
\(53\) | 7.22526 | − | 7.22526i | 0.992465 | − | 0.992465i | −0.00750666 | − | 0.999972i | \(-0.502389\pi\) |
0.999972 | + | 0.00750666i | \(0.00238947\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.45067 | + | 1.29769i | 0.600128 | + | 0.174981i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.09170 | + | 3.09170i | 0.409505 | + | 0.409505i | ||||
\(58\) | 0.0204302 | − | 0.0204302i | 0.00268261 | − | 0.00268261i | ||||
\(59\) | −13.4242 | −1.74769 | −0.873843 | − | 0.486208i | \(-0.838380\pi\) | ||||
−0.873843 | + | 0.486208i | \(0.838380\pi\) | |||||||
\(60\) | −1.96052 | + | 1.07534i | −0.253102 | + | 0.138826i | ||||
\(61\) | − | 9.84270i | − | 1.26023i | −0.776502 | − | 0.630114i | \(-0.783008\pi\) | ||
0.776502 | − | 0.630114i | \(-0.216992\pi\) | |||||||
\(62\) | −5.67978 | + | 5.67978i | −0.721333 | + | 0.721333i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.497280 | − | 0.906619i | −0.0616800 | − | 0.112452i | ||||
\(66\) | 2.07328i | 0.255203i | ||||||||
\(67\) | −3.33098 | − | 3.33098i | −0.406944 | − | 0.406944i | 0.473728 | − | 0.880671i | \(-0.342908\pi\) |
−0.880671 | + | 0.473728i | \(0.842908\pi\) | |||||||
\(68\) | −1.26881 | − | 1.26881i | −0.153866 | − | 0.153866i | ||||
\(69\) | 0.898861 | 0.108210 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.27478 | 0.269966 | 0.134983 | − | 0.990848i | \(-0.456902\pi\) | ||||
0.134983 | + | 0.990848i | \(0.456902\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 8.14046 | + | 8.14046i | 0.952768 | + | 0.952768i | 0.998934 | − | 0.0461656i | \(-0.0147002\pi\) |
−0.0461656 | + | 0.998934i | \(0.514700\pi\) | |||||||
\(74\) | − | 11.4235i | − | 1.32795i | ||||||
\(75\) | 1.08130 | + | 4.88168i | 0.124858 | + | 0.563688i | ||||
\(76\) | 4.37232i | 0.501540i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.326993 | − | 0.326993i | 0.0370247 | − | 0.0370247i | ||||
\(79\) | − | 8.01313i | − | 0.901547i | −0.892638 | − | 0.450774i | \(-0.851148\pi\) | ||
0.892638 | − | 0.450774i | \(-0.148852\pi\) | |||||||
\(80\) | −2.14668 | − | 0.625913i | −0.240006 | − | 0.0699793i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.54452 | + | 7.54452i | −0.833153 | + | 0.833153i | ||||
\(83\) | 4.26961 | + | 4.26961i | 0.468650 | + | 0.468650i | 0.901477 | − | 0.432827i | \(-0.142484\pi\) |
−0.432827 | + | 0.901477i | \(0.642484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.51790 | + | 1.92957i | −0.381570 | + | 0.209291i | ||||
\(86\) | 3.54793 | 0.382583 | ||||||||
\(87\) | 0.0204302 | − | 0.0204302i | 0.00219034 | − | 0.00219034i | ||||
\(88\) | −1.46603 | + | 1.46603i | −0.156279 | + | 0.156279i | ||||
\(89\) | −0.0197698 | −0.00209560 | −0.00104780 | − | 0.999999i | \(-0.500334\pi\) | ||||
−0.00104780 | + | 0.999999i | \(0.500334\pi\) | |||||||
\(90\) | −1.96052 | + | 1.07534i | −0.206657 | + | 0.113351i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.635591 | + | 0.635591i | 0.0662649 | + | 0.0662649i | ||||
\(93\) | −5.67978 | + | 5.67978i | −0.588966 | + | 0.588966i | ||||
\(94\) | −0.742898 | −0.0766241 | ||||||||
\(95\) | 9.38597 | + | 2.73669i | 0.962980 | + | 0.280779i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −5.65183 | + | 5.65183i | −0.573857 | + | 0.573857i | −0.933204 | − | 0.359347i | \(-0.882999\pi\) |
0.359347 | + | 0.933204i | \(0.382999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.07328i | 0.208372i | ||||||||
\(100\) | −2.68727 | + | 4.21646i | −0.268727 | + | 0.421646i | ||||
\(101\) | − | 4.18882i | − | 0.416803i | −0.978043 | − | 0.208402i | \(-0.933174\pi\) | ||
0.978043 | − | 0.208402i | \(-0.0668261\pi\) | |||||||
\(102\) | −1.26881 | − | 1.26881i | −0.125631 | − | 0.125631i | ||||
\(103\) | −2.69132 | − | 2.69132i | −0.265184 | − | 0.265184i | 0.561972 | − | 0.827156i | \(-0.310043\pi\) |
−0.827156 | + | 0.561972i | \(0.810043\pi\) | |||||||
\(104\) | 0.462438 | 0.0453458 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.2181 | 0.992465 | ||||||||
\(107\) | −12.1979 | − | 12.1979i | −1.17922 | − | 1.17922i | −0.979945 | − | 0.199271i | \(-0.936143\pi\) |
−0.199271 | − | 0.979945i | \(-0.563857\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 12.6001i | 1.20687i | 0.797412 | + | 0.603435i | \(0.206202\pi\) | ||||
−0.797412 | + | 0.603435i | \(0.793798\pi\) | |||||||
\(110\) | 2.22949 | + | 4.06470i | 0.212573 | + | 0.387554i | ||||
\(111\) | − | 11.4235i | − | 1.08427i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.87937 | − | 9.87937i | 0.929373 | − | 0.929373i | −0.0682924 | − | 0.997665i | \(-0.521755\pi\) |
0.997665 | + | 0.0682924i | \(0.0217551\pi\) | |||||||
\(114\) | 4.37232i | 0.409505i | ||||||||
\(115\) | 1.76223 | − | 0.966585i | 0.164329 | − | 0.0901345i | ||||
\(116\) | 0.0288926 | 0.00268261 | ||||||||
\(117\) | 0.326993 | − | 0.326993i | 0.0302305 | − | 0.0302305i | ||||
\(118\) | −9.49237 | − | 9.49237i | −0.873843 | − | 0.873843i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.14668 | − | 0.625913i | −0.195964 | − | 0.0571378i | ||||
\(121\) | −6.70151 | −0.609228 | ||||||||
\(122\) | 6.95984 | − | 6.95984i | 0.630114 | − | 0.630114i | ||||
\(123\) | −7.54452 | + | 7.54452i | −0.680267 | + | 0.680267i | ||||
\(124\) | −8.03242 | −0.721333 | ||||||||
\(125\) | 7.36940 | + | 8.40785i | 0.659139 | + | 0.752021i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.53710 | − | 2.53710i | −0.225132 | − | 0.225132i | 0.585524 | − | 0.810655i | \(-0.300889\pi\) |
−0.810655 | + | 0.585524i | \(0.800889\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 3.54793 | 0.312378 | ||||||||
\(130\) | 0.289446 | − | 0.992706i | 0.0253861 | − | 0.0870661i | ||||
\(131\) | − | 19.7306i | − | 1.72387i | −0.507016 | − | 0.861937i | \(-0.669251\pi\) | ||
0.507016 | − | 0.861937i | \(-0.330749\pi\) | |||||||
\(132\) | −1.46603 | + | 1.46603i | −0.127602 | + | 0.127602i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 4.71072i | − | 0.406944i | ||||||
\(135\) | −1.96052 | + | 1.07534i | −0.168735 | + | 0.0925509i | ||||
\(136\) | − | 1.79437i | − | 0.153866i | ||||||
\(137\) | 11.5948 | + | 11.5948i | 0.990612 | + | 0.990612i | 0.999956 | − | 0.00934474i | \(-0.00297456\pi\) |
−0.00934474 | + | 0.999956i | \(0.502975\pi\) | |||||||
\(138\) | 0.635591 | + | 0.635591i | 0.0541051 | + | 0.0541051i | ||||
\(139\) | −6.98433 | −0.592403 | −0.296202 | − | 0.955125i | \(-0.595720\pi\) | ||||
−0.296202 | + | 0.955125i | \(0.595720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.742898 | −0.0625633 | ||||||||
\(142\) | 1.60851 | + | 1.60851i | 0.134983 | + | 0.134983i | ||||
\(143\) | −0.677948 | − | 0.677948i | −0.0566929 | − | 0.0566929i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 0.0180843 | − | 0.0620232i | 0.00150182 | − | 0.00515075i | ||||
\(146\) | 11.5123i | 0.952768i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.07760 | − | 8.07760i | 0.663975 | − | 0.663975i | ||||
\(149\) | 8.06301i | 0.660547i | 0.943885 | + | 0.330274i | \(0.107141\pi\) | ||||
−0.943885 | + | 0.330274i | \(0.892859\pi\) | |||||||
\(150\) | −2.68727 | + | 4.21646i | −0.219415 | + | 0.344273i | ||||
\(151\) | −20.7971 | −1.69244 | −0.846222 | − | 0.532831i | \(-0.821128\pi\) | ||||
−0.846222 | + | 0.532831i | \(0.821128\pi\) | |||||||
\(152\) | −3.09170 | + | 3.09170i | −0.250770 | + | 0.250770i | ||||
\(153\) | −1.26881 | − | 1.26881i | −0.102577 | − | 0.102577i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.02760 | + | 17.2430i | −0.403826 | + | 1.38499i | ||||
\(156\) | 0.462438 | 0.0370247 | ||||||||
\(157\) | 10.0893 | − | 10.0893i | 0.805215 | − | 0.805215i | −0.178690 | − | 0.983905i | \(-0.557186\pi\) |
0.983905 | + | 0.178690i | \(0.0571861\pi\) | |||||||
\(158\) | 5.66614 | − | 5.66614i | 0.450774 | − | 0.450774i | ||||
\(159\) | 10.2181 | 0.810344 | ||||||||
\(160\) | −1.07534 | − | 1.96052i | −0.0850134 | − | 0.154993i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 8.54237 | − | 8.54237i | 0.669090 | − | 0.669090i | −0.288415 | − | 0.957505i | \(-0.593128\pi\) |
0.957505 | + | 0.288415i | \(0.0931284\pi\) | |||||||
\(164\) | −10.6696 | −0.833153 | ||||||||
\(165\) | 2.22949 | + | 4.06470i | 0.173565 | + | 0.316437i | ||||
\(166\) | 6.03813i | 0.468650i | ||||||||
\(167\) | 8.16680 | − | 8.16680i | 0.631966 | − | 0.631966i | −0.316595 | − | 0.948561i | \(-0.602540\pi\) |
0.948561 | + | 0.316595i | \(0.102540\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7862i | − | 0.983550i | ||||||
\(170\) | −3.85194 | − | 1.12312i | −0.295430 | − | 0.0861395i | ||||
\(171\) | 4.37232i | 0.334360i | ||||||||
\(172\) | 2.50876 | + | 2.50876i | 0.191291 | + | 0.191291i | ||||
\(173\) | 4.93408 | + | 4.93408i | 0.375131 | + | 0.375131i | 0.869342 | − | 0.494211i | \(-0.164543\pi\) |
−0.494211 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(174\) | 0.0288926 | 0.00219034 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.07328 | −0.156279 | ||||||||
\(177\) | −9.49237 | − | 9.49237i | −0.713490 | − | 0.713490i | ||||
\(178\) | −0.0139794 | − | 0.0139794i | −0.00104780 | − | 0.00104780i | ||||
\(179\) | 6.45209i | 0.482252i | 0.970494 | + | 0.241126i | \(0.0775167\pi\) | ||||
−0.970494 | + | 0.241126i | \(0.922483\pi\) | |||||||
\(180\) | −2.14668 | − | 0.625913i | −0.160004 | − | 0.0466528i | ||||
\(181\) | 10.5123i | 0.781370i | 0.920524 | + | 0.390685i | \(0.127762\pi\) | ||||
−0.920524 | + | 0.390685i | \(0.872238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.95984 | − | 6.95984i | 0.514486 | − | 0.514486i | ||||
\(184\) | 0.898861i | 0.0662649i | ||||||||
\(185\) | −12.2841 | − | 22.3959i | −0.903148 | − | 1.64658i | ||||
\(186\) | −8.03242 | −0.588966 | ||||||||
\(187\) | −2.63060 | + | 2.63060i | −0.192369 | + | 0.192369i | ||||
\(188\) | −0.525308 | − | 0.525308i | −0.0383120 | − | 0.0383120i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.70175 | + | 8.57202i | 0.341101 | + | 0.621880i | ||||
\(191\) | 24.8983 | 1.80158 | 0.900790 | − | 0.434254i | \(-0.142988\pi\) | ||||
0.900790 | + | 0.434254i | \(0.142988\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −8.94309 | + | 8.94309i | −0.643738 | + | 0.643738i | −0.951472 | − | 0.307734i | \(-0.900429\pi\) |
0.307734 | + | 0.951472i | \(0.400429\pi\) | |||||||
\(194\) | −7.99290 | −0.573857 | ||||||||
\(195\) | 0.289446 | − | 0.992706i | 0.0207277 | − | 0.0710892i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.46213 | − | 2.46213i | −0.175419 | − | 0.175419i | 0.613936 | − | 0.789356i | \(-0.289585\pi\) |
−0.789356 | + | 0.613936i | \(0.789585\pi\) | |||||||
\(198\) | −1.46603 | + | 1.46603i | −0.104186 | + | 0.104186i | ||||
\(199\) | −7.59741 | −0.538566 | −0.269283 | − | 0.963061i | \(-0.586787\pi\) | ||||
−0.269283 | + | 0.963061i | \(0.586787\pi\) | |||||||
\(200\) | −4.88168 | + | 1.08130i | −0.345187 | + | 0.0764597i | ||||
\(201\) | − | 4.71072i | − | 0.332268i | ||||||
\(202\) | 2.96194 | − | 2.96194i | 0.208402 | − | 0.208402i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 1.79437i | − | 0.125631i | ||||||
\(205\) | −6.67823 | + | 22.9041i | −0.466427 | + | 1.59969i | ||||
\(206\) | − | 3.80611i | − | 0.265184i | ||||||
\(207\) | 0.635591 | + | 0.635591i | 0.0441766 | + | 0.0441766i | ||||
\(208\) | 0.326993 | + | 0.326993i | 0.0226729 | + | 0.0226729i | ||||
\(209\) | 9.06504 | 0.627042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.32272 | −0.366431 | −0.183216 | − | 0.983073i | \(-0.558651\pi\) | ||||
−0.183216 | + | 0.983073i | \(0.558651\pi\) | |||||||
\(212\) | 7.22526 | + | 7.22526i | 0.496233 | + | 0.496233i | ||||
\(213\) | 1.60851 | + | 1.60851i | 0.110213 | + | 0.110213i | ||||
\(214\) | − | 17.2504i | − | 1.17922i | ||||||
\(215\) | 6.95578 | − | 3.81524i | 0.474380 | − | 0.260197i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.90962 | + | 8.90962i | −0.603435 | + | 0.603435i | ||||
\(219\) | 11.5123i | 0.777932i | ||||||||
\(220\) | −1.29769 | + | 4.45067i | −0.0874905 | + | 0.300064i | ||||
\(221\) | 0.829786 | 0.0558175 | ||||||||
\(222\) | 8.07760 | − | 8.07760i | 0.542133 | − | 0.542133i | ||||
\(223\) | −15.4987 | − | 15.4987i | −1.03787 | − | 1.03787i | −0.999254 | − | 0.0386189i | \(-0.987704\pi\) |
−0.0386189 | − | 0.999254i | \(-0.512296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.68727 | + | 4.21646i | −0.179151 | + | 0.281098i | ||||
\(226\) | 13.9715 | 0.929373 | ||||||||
\(227\) | 6.80901 | − | 6.80901i | 0.451930 | − | 0.451930i | −0.444065 | − | 0.895995i | \(-0.646464\pi\) |
0.895995 | + | 0.444065i | \(0.146464\pi\) | |||||||
\(228\) | −3.09170 | + | 3.09170i | −0.204753 | + | 0.204753i | ||||
\(229\) | 18.9728 | 1.25376 | 0.626880 | − | 0.779116i | \(-0.284332\pi\) | ||||
0.626880 | + | 0.779116i | \(0.284332\pi\) | |||||||
\(230\) | 1.92957 | + | 0.562609i | 0.127232 | + | 0.0370973i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0204302 | + | 0.0204302i | 0.00134131 | + | 0.00134131i | ||||
\(233\) | 16.3943 | − | 16.3943i | 1.07403 | − | 1.07403i | 0.0769962 | − | 0.997031i | \(-0.475467\pi\) |
0.997031 | − | 0.0769962i | \(-0.0245329\pi\) | |||||||
\(234\) | 0.462438 | 0.0302305 | ||||||||
\(235\) | −1.45647 | + | 0.798871i | −0.0950094 | + | 0.0521126i | ||||
\(236\) | − | 13.4242i | − | 0.873843i | ||||||
\(237\) | 5.66614 | − | 5.66614i | 0.368055 | − | 0.368055i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.98741i | − | 0.193239i | −0.995321 | − | 0.0966197i | \(-0.969197\pi\) | ||
0.995321 | − | 0.0966197i | \(-0.0308031\pi\) | |||||||
\(240\) | −1.07534 | − | 1.96052i | −0.0694132 | − | 0.126551i | ||||
\(241\) | 27.1053i | 1.74601i | 0.487715 | + | 0.873003i | \(0.337830\pi\) | ||||
−0.487715 | + | 0.873003i | \(0.662170\pi\) | |||||||
\(242\) | −4.73869 | − | 4.73869i | −0.304614 | − | 0.304614i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 9.84270 | 0.630114 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.6696 | −0.680267 | ||||||||
\(247\) | −1.42972 | − | 1.42972i | −0.0909708 | − | 0.0909708i | ||||
\(248\) | −5.67978 | − | 5.67978i | −0.360666 | − | 0.360666i | ||||
\(249\) | 6.03813i | 0.382651i | ||||||||
\(250\) | −0.734297 | + | 11.1562i | −0.0464410 | + | 0.705580i | ||||
\(251\) | − | 29.6570i | − | 1.87194i | −0.352086 | − | 0.935968i | \(-0.614527\pi\) | ||
0.352086 | − | 0.935968i | \(-0.385473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.31776 | − | 1.31776i | 0.0828467 | − | 0.0828467i | ||||
\(254\) | − | 3.58801i | − | 0.225132i | ||||||
\(255\) | −3.85194 | − | 1.12312i | −0.241218 | − | 0.0703326i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.26264 | + | 6.26264i | −0.390653 | + | 0.390653i | −0.874920 | − | 0.484267i | \(-0.839086\pi\) |
0.484267 | + | 0.874920i | \(0.339086\pi\) | |||||||
\(258\) | 2.50876 | + | 2.50876i | 0.156189 | + | 0.156189i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.906619 | − | 0.497280i | 0.0562261 | − | 0.0308400i | ||||
\(261\) | 0.0288926 | 0.00178841 | ||||||||
\(262\) | 13.9517 | − | 13.9517i | 0.861937 | − | 0.861937i | ||||
\(263\) | 19.4790 | − | 19.4790i | 1.20113 | − | 1.20113i | 0.227304 | − | 0.973824i | \(-0.427009\pi\) |
0.973824 | − | 0.227304i | \(-0.0729912\pi\) | |||||||
\(264\) | −2.07328 | −0.127602 | ||||||||
\(265\) | 20.0327 | − | 10.9879i | 1.23060 | − | 0.674983i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0139794 | − | 0.0139794i | −0.000855524 | − | 0.000855524i | ||||
\(268\) | 3.33098 | − | 3.33098i | 0.203472 | − | 0.203472i | ||||
\(269\) | 2.19106 | 0.133591 | 0.0667957 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667957 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(270\) | −2.14668 | − | 0.625913i | −0.130643 | − | 0.0380919i | ||||
\(271\) | − | 7.28839i | − | 0.442738i | −0.975190 | − | 0.221369i | \(-0.928947\pi\) | ||
0.975190 | − | 0.221369i | \(-0.0710526\pi\) | |||||||
\(272\) | 1.26881 | − | 1.26881i | 0.0769331 | − | 0.0769331i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.3975i | 0.990612i | ||||||||
\(275\) | 8.74191 | + | 5.57146i | 0.527157 | + | 0.335972i | ||||
\(276\) | 0.898861i | 0.0541051i | ||||||||
\(277\) | −16.6172 | − | 16.6172i | −0.998433 | − | 0.998433i | 0.00156542 | − | 0.999999i | \(-0.499502\pi\) |
−0.999999 | + | 0.00156542i | \(0.999502\pi\) | |||||||
\(278\) | −4.93867 | − | 4.93867i | −0.296202 | − | 0.296202i | ||||
\(279\) | −8.03242 | −0.480888 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.32521 | 0.0790557 | 0.0395278 | − | 0.999218i | \(-0.487415\pi\) | ||||
0.0395278 | + | 0.999218i | \(0.487415\pi\) | |||||||
\(282\) | −0.525308 | − | 0.525308i | −0.0312817 | − | 0.0312817i | ||||
\(283\) | −14.5224 | − | 14.5224i | −0.863266 | − | 0.863266i | 0.128450 | − | 0.991716i | \(-0.459000\pi\) |
−0.991716 | + | 0.128450i | \(0.959000\pi\) | |||||||
\(284\) | 2.27478i | 0.134983i | ||||||||
\(285\) | 4.70175 | + | 8.57202i | 0.278508 | + | 0.507763i | ||||
\(286\) | − | 0.958763i | − | 0.0566929i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 13.7802i | 0.810602i | ||||||||
\(290\) | 0.0566445 | − | 0.0310695i | 0.00332628 | − | 0.00182446i | ||||
\(291\) | −7.99290 | −0.468552 | ||||||||
\(292\) | −8.14046 | + | 8.14046i | −0.476384 | + | 0.476384i | ||||
\(293\) | 15.7254 | + | 15.7254i | 0.918687 | + | 0.918687i | 0.996934 | − | 0.0782467i | \(-0.0249322\pi\) |
−0.0782467 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.8175 | − | 8.40241i | −1.67782 | − | 0.489207i | ||||
\(296\) | 11.4235 | 0.663975 | ||||||||
\(297\) | −1.46603 | + | 1.46603i | −0.0850677 | + | 0.0850677i | ||||
\(298\) | −5.70141 | + | 5.70141i | −0.330274 | + | 0.330274i | ||||
\(299\) | −0.415668 | −0.0240387 | ||||||||
\(300\) | −4.88168 | + | 1.08130i | −0.281844 | + | 0.0624291i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.7058 | − | 14.7058i | −0.846222 | − | 0.846222i | ||||
\(303\) | 2.96194 | − | 2.96194i | 0.170159 | − | 0.170159i | ||||
\(304\) | −4.37232 | −0.250770 | ||||||||
\(305\) | 6.16068 | − | 21.1291i | 0.352760 | − | 1.20985i | ||||
\(306\) | − | 1.79437i | − | 0.102577i | ||||||
\(307\) | 12.0759 | − | 12.0759i | 0.689205 | − | 0.689205i | −0.272851 | − | 0.962056i | \(-0.587967\pi\) |
0.962056 | + | 0.272851i | \(0.0879666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.80611i | − | 0.216522i | ||||||
\(310\) | −15.7477 | + | 8.63761i | −0.894410 | + | 0.490583i | ||||
\(311\) | − | 20.2193i | − | 1.14653i | −0.819369 | − | 0.573267i | \(-0.805676\pi\) | ||
0.819369 | − | 0.573267i | \(-0.194324\pi\) | |||||||
\(312\) | 0.326993 | + | 0.326993i | 0.0185123 | + | 0.0185123i | ||||
\(313\) | −8.65863 | − | 8.65863i | −0.489415 | − | 0.489415i | 0.418707 | − | 0.908121i | \(-0.362484\pi\) |
−0.908121 | + | 0.418707i | \(0.862484\pi\) | |||||||
\(314\) | 14.2684 | 0.805215 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.01313 | 0.450774 | ||||||||
\(317\) | −11.3393 | − | 11.3393i | −0.636876 | − | 0.636876i | 0.312908 | − | 0.949784i | \(-0.398697\pi\) |
−0.949784 | + | 0.312908i | \(0.898697\pi\) | |||||||
\(318\) | 7.22526 | + | 7.22526i | 0.405172 | + | 0.405172i | ||||
\(319\) | − | 0.0599025i | − | 0.00335389i | ||||||
\(320\) | 0.625913 | − | 2.14668i | 0.0349896 | − | 0.120003i | ||||
\(321\) | − | 17.2504i | − | 0.962825i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.54766 | + | 5.54766i | −0.308680 | + | 0.308680i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −0.500036 | − | 2.25747i | −0.0277370 | − | 0.125222i | ||||
\(326\) | 12.0807 | 0.669090 | ||||||||
\(327\) | −8.90962 | + | 8.90962i | −0.492703 | + | 0.492703i | ||||
\(328\) | −7.54452 | − | 7.54452i | −0.416577 | − | 0.416577i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.29769 | + | 4.45067i | −0.0714357 | + | 0.245001i | ||||
\(331\) | 21.7448 | 1.19520 | 0.597602 | − | 0.801793i | \(-0.296120\pi\) | ||||
0.597602 | + | 0.801793i | \(0.296120\pi\) | |||||||
\(332\) | −4.26961 | + | 4.26961i | −0.234325 | + | 0.234325i | ||||
\(333\) | 8.07760 | − | 8.07760i | 0.442650 | − | 0.442650i | ||||
\(334\) | 11.5496 | 0.631966 | ||||||||
\(335\) | −5.06564 | − | 9.23545i | −0.276765 | − | 0.504586i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8706 | − | 17.8706i | −0.973475 | − | 0.973475i | 0.0261820 | − | 0.999657i | \(-0.491665\pi\) |
−0.999657 | + | 0.0261820i | \(0.991665\pi\) | |||||||
\(338\) | 9.04117 | − | 9.04117i | 0.491775 | − | 0.491775i | ||||
\(339\) | 13.9715 | 0.758830 | ||||||||
\(340\) | −1.92957 | − | 3.51790i | −0.104645 | − | 0.190785i | ||||
\(341\) | 16.6534i | 0.901835i | ||||||||
\(342\) | −3.09170 | + | 3.09170i | −0.167180 | + | 0.167180i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.54793i | 0.191291i | ||||||||
\(345\) | 1.92957 | + | 0.562609i | 0.103884 | + | 0.0302899i | ||||
\(346\) | 6.97784i | 0.375131i | ||||||||
\(347\) | 14.1911 | + | 14.1911i | 0.761818 | + | 0.761818i | 0.976651 | − | 0.214833i | \(-0.0689208\pi\) |
−0.214833 | + | 0.976651i | \(0.568921\pi\) | |||||||
\(348\) | 0.0204302 | + | 0.0204302i | 0.00109517 | + | 0.00109517i | ||||
\(349\) | −24.9858 | −1.33746 | −0.668730 | − | 0.743506i | \(-0.733162\pi\) | ||||
−0.668730 | + | 0.743506i | \(0.733162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.462438 | 0.0246831 | ||||||||
\(352\) | −1.46603 | − | 1.46603i | −0.0781397 | − | 0.0781397i | ||||
\(353\) | 19.1988 | + | 19.1988i | 1.02185 | + | 1.02185i | 0.999756 | + | 0.0220914i | \(0.00703248\pi\) |
0.0220914 | + | 0.999756i | \(0.492968\pi\) | |||||||
\(354\) | − | 13.4242i | − | 0.713490i | ||||||
\(355\) | 4.88322 | + | 1.42381i | 0.259174 | + | 0.0755682i | ||||
\(356\) | − | 0.0197698i | − | 0.00104780i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.56232 | + | 4.56232i | −0.241126 | + | 0.241126i | ||||
\(359\) | 16.7185i | 0.882370i | 0.897416 | + | 0.441185i | \(0.145442\pi\) | ||||
−0.897416 | + | 0.441185i | \(0.854558\pi\) | |||||||
\(360\) | −1.07534 | − | 1.96052i | −0.0566756 | − | 0.103328i | ||||
\(361\) | 0.117186 | 0.00616766 | ||||||||
\(362\) | −7.43329 | + | 7.43329i | −0.390685 | + | 0.390685i | ||||
\(363\) | −4.73869 | − | 4.73869i | −0.248716 | − | 0.248716i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3797 | + | 22.5702i | 0.647985 | + | 1.18138i | ||||
\(366\) | 9.84270 | 0.514486 | ||||||||
\(367\) | 5.94533 | − | 5.94533i | 0.310344 | − | 0.310344i | −0.534699 | − | 0.845043i | \(-0.679575\pi\) |
0.845043 | + | 0.534699i | \(0.179575\pi\) | |||||||
\(368\) | −0.635591 | + | 0.635591i | −0.0331325 | + | 0.0331325i | ||||
\(369\) | −10.6696 | −0.555435 | ||||||||
\(370\) | 7.15009 | − | 24.5225i | 0.371716 | − | 1.27486i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.67978 | − | 5.67978i | −0.294483 | − | 0.294483i | ||||
\(373\) | −0.0162120 | + | 0.0162120i | −0.000839423 | + | 0.000839423i | −0.707526 | − | 0.706687i | \(-0.750189\pi\) |
0.706687 | + | 0.707526i | \(0.250189\pi\) | |||||||
\(374\) | −3.72024 | −0.192369 | ||||||||
\(375\) | −0.734297 | + | 11.1562i | −0.0379189 | + | 0.576104i | ||||
\(376\) | − | 0.742898i | − | 0.0383120i | ||||||
\(377\) | −0.00944769 | + | 0.00944769i | −0.000486581 | + | 0.000486581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.0300i | 1.59391i | 0.604041 | + | 0.796953i | \(0.293556\pi\) | ||||
−0.604041 | + | 0.796953i | \(0.706444\pi\) | |||||||
\(380\) | −2.73669 | + | 9.38597i | −0.140389 | + | 0.481490i | ||||
\(381\) | − | 3.58801i | − | 0.183819i | ||||||
\(382\) | 17.6058 | + | 17.6058i | 0.900790 | + | 0.900790i | ||||
\(383\) | 3.47573 | + | 3.47573i | 0.177602 | + | 0.177602i | 0.790309 | − | 0.612708i | \(-0.209920\pi\) |
−0.612708 | + | 0.790309i | \(0.709920\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.6474 | −0.643738 | ||||||||
\(387\) | 2.50876 | + | 2.50876i | 0.127528 | + | 0.127528i | ||||
\(388\) | −5.65183 | − | 5.65183i | −0.286928 | − | 0.286928i | ||||
\(389\) | − | 11.0267i | − | 0.559076i | −0.960135 | − | 0.279538i | \(-0.909819\pi\) | ||
0.960135 | − | 0.279538i | \(-0.0901814\pi\) | |||||||
\(390\) | 0.906619 | − | 0.497280i | 0.0459084 | − | 0.0251808i | ||||
\(391\) | 1.61289i | 0.0815674i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.9517 | − | 13.9517i | 0.703768 | − | 0.703768i | ||||
\(394\) | − | 3.48197i | − | 0.175419i | ||||||
\(395\) | 5.01552 | − | 17.2016i | 0.252358 | − | 0.865507i | ||||
\(396\) | −2.07328 | −0.104186 | ||||||||
\(397\) | −5.75974 | + | 5.75974i | −0.289073 | + | 0.289073i | −0.836714 | − | 0.547640i | \(-0.815526\pi\) |
0.547640 | + | 0.836714i | \(0.315526\pi\) | |||||||
\(398\) | −5.37218 | − | 5.37218i | −0.269283 | − | 0.269283i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.21646 | − | 2.68727i | −0.210823 | − | 0.134364i | ||||
\(401\) | 11.7932 | 0.588926 | 0.294463 | − | 0.955663i | \(-0.404859\pi\) | ||||
0.294463 | + | 0.955663i | \(0.404859\pi\) | |||||||
\(402\) | 3.33098 | − | 3.33098i | 0.166134 | − | 0.166134i | ||||
\(403\) | 2.62655 | − | 2.62655i | 0.130838 | − | 0.130838i | ||||
\(404\) | 4.18882 | 0.208402 | ||||||||
\(405\) | −2.14668 | − | 0.625913i | −0.106669 | − | 0.0311019i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.7471 | − | 16.7471i | −0.830124 | − | 0.830124i | ||||
\(408\) | 1.26881 | − | 1.26881i | 0.0628156 | − | 0.0628156i | ||||
\(409\) | 6.26719 | 0.309892 | 0.154946 | − | 0.987923i | \(-0.450480\pi\) | ||||
0.154946 | + | 0.987923i | \(0.450480\pi\) | |||||||
\(410\) | −20.9179 | + | 11.4735i | −1.03306 | + | 0.566633i | ||||
\(411\) | 16.3975i | 0.808831i | ||||||||
\(412\) | 2.69132 | − | 2.69132i | 0.132592 | − | 0.132592i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.898861i | 0.0441766i | ||||||||
\(415\) | 6.49307 | + | 11.8379i | 0.318732 | + | 0.581099i | ||||
\(416\) | 0.462438i | 0.0226729i | ||||||||
\(417\) | −4.93867 | − | 4.93867i | −0.241848 | − | 0.241848i | ||||
\(418\) | 6.40995 | + | 6.40995i | 0.313521 | + | 0.313521i | ||||
\(419\) | −23.9790 | −1.17145 | −0.585726 | − | 0.810509i | \(-0.699190\pi\) | ||||
−0.585726 | + | 0.810509i | \(0.699190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.01218 | −0.390490 | −0.195245 | − | 0.980755i | \(-0.562550\pi\) | ||||
−0.195245 | + | 0.980755i | \(0.562550\pi\) | |||||||
\(422\) | −3.76373 | − | 3.76373i | −0.183216 | − | 0.183216i | ||||
\(423\) | −0.525308 | − | 0.525308i | −0.0255414 | − | 0.0255414i | ||||
\(424\) | 10.2181i | 0.496233i | ||||||||
\(425\) | −8.75955 | + | 1.94026i | −0.424901 | + | 0.0941165i | ||||
\(426\) | 2.27478i | 0.110213i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.1979 | − | 12.1979i | 0.589608 | − | 0.589608i | ||||
\(429\) | − | 0.958763i | − | 0.0462895i | ||||||
\(430\) | 7.61626 | + | 2.22070i | 0.367289 | + | 0.107091i | ||||
\(431\) | −17.0950 | −0.823437 | −0.411719 | − | 0.911311i | \(-0.635071\pi\) | ||||
−0.411719 | + | 0.911311i | \(0.635071\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 3.28061 | + | 3.28061i | 0.157656 | + | 0.157656i | 0.781527 | − | 0.623871i | \(-0.214441\pi\) |
−0.623871 | + | 0.781527i | \(0.714441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0566445 | − | 0.0310695i | 0.00271590 | − | 0.00148967i | ||||
\(436\) | −12.6001 | −0.603435 | ||||||||
\(437\) | 2.77901 | − | 2.77901i | 0.132938 | − | 0.132938i | ||||
\(438\) | −8.14046 | + | 8.14046i | −0.388966 | + | 0.388966i | ||||
\(439\) | 34.3470 | 1.63929 | 0.819647 | − | 0.572869i | \(-0.194170\pi\) | ||||
0.819647 | + | 0.572869i | \(0.194170\pi\) | |||||||
\(440\) | −4.06470 | + | 2.22949i | −0.193777 | + | 0.106287i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.586747 | + | 0.586747i | 0.0279087 | + | 0.0279087i | ||||
\(443\) | 19.9796 | − | 19.9796i | 0.949258 | − | 0.949258i | −0.0495155 | − | 0.998773i | \(-0.515768\pi\) |
0.998773 | + | 0.0495155i | \(0.0157677\pi\) | |||||||
\(444\) | 11.4235 | 0.542133 | ||||||||
\(445\) | −0.0424395 | − | 0.0123742i | −0.00201182 | − | 0.000586593i | ||||
\(446\) | − | 21.9185i | − | 1.03787i | ||||||
\(447\) | −5.70141 | + | 5.70141i | −0.269667 | + | 0.269667i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.0016i | − | 0.472006i | −0.971752 | − | 0.236003i | \(-0.924163\pi\) | ||
0.971752 | − | 0.236003i | \(-0.0758375\pi\) | |||||||
\(450\) | −4.88168 | + | 1.08130i | −0.230125 | + | 0.0509731i | ||||
\(451\) | 22.1210i | 1.04164i | ||||||||
\(452\) | 9.87937 | + | 9.87937i | 0.464686 | + | 0.464686i | ||||
\(453\) | −14.7058 | − | 14.7058i | −0.690937 | − | 0.690937i | ||||
\(454\) | 9.62940 | 0.451930 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.37232 | −0.204753 | ||||||||
\(457\) | −1.20959 | − | 1.20959i | −0.0565823 | − | 0.0565823i | 0.678249 | − | 0.734832i | \(-0.262739\pi\) |
−0.734832 | + | 0.678249i | \(0.762739\pi\) | |||||||
\(458\) | 13.4158 | + | 13.4158i | 0.626880 | + | 0.626880i | ||||
\(459\) | − | 1.79437i | − | 0.0837541i | ||||||
\(460\) | 0.966585 | + | 1.76223i | 0.0450672 | + | 0.0821646i | ||||
\(461\) | − | 8.80371i | − | 0.410030i | −0.978759 | − | 0.205015i | \(-0.934276\pi\) | ||
0.978759 | − | 0.205015i | \(-0.0657243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8709 | + | 19.8709i | −0.923481 | + | 0.923481i | −0.997274 | − | 0.0737924i | \(-0.976490\pi\) |
0.0737924 | + | 0.997274i | \(0.476490\pi\) | |||||||
\(464\) | 0.0288926i | 0.00134131i | ||||||||
\(465\) | −15.7477 | + | 8.63761i | −0.730283 | + | 0.400560i | ||||
\(466\) | 23.1851 | 1.07403 | ||||||||
\(467\) | −19.3690 | + | 19.3690i | −0.896291 | + | 0.896291i | −0.995106 | − | 0.0988148i | \(-0.968495\pi\) |
0.0988148 | + | 0.995106i | \(0.468495\pi\) | |||||||
\(468\) | 0.326993 | + | 0.326993i | 0.0151153 | + | 0.0151153i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.59476 | − | 0.464990i | −0.0735610 | − | 0.0214484i | ||||
\(471\) | 14.2684 | 0.657455 | ||||||||
\(472\) | 9.49237 | − | 9.49237i | 0.436922 | − | 0.436922i | ||||
\(473\) | 5.20137 | − | 5.20137i | 0.239159 | − | 0.239159i | ||||
\(474\) | 8.01313 | 0.368055 | ||||||||
\(475\) | 18.4357 | + | 11.7496i | 0.845890 | + | 0.539109i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.22526 | + | 7.22526i | 0.330822 | + | 0.330822i | ||||
\(478\) | 2.11242 | − | 2.11242i | 0.0966197 | − | 0.0966197i | ||||
\(479\) | 24.0136 | 1.09721 | 0.548605 | − | 0.836081i | \(-0.315159\pi\) | ||||
0.548605 | + | 0.836081i | \(0.315159\pi\) | |||||||
\(480\) | 0.625913 | − | 2.14668i | 0.0285689 | − | 0.0979821i | ||||
\(481\) | 5.28264i | 0.240868i | ||||||||
\(482\) | −19.1663 | + | 19.1663i | −0.873003 | + | 0.873003i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 6.70151i | − | 0.304614i | ||||||
\(485\) | −15.6702 | + | 8.59512i | −0.711549 | + | 0.390284i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −6.32464 | − | 6.32464i | −0.286597 | − | 0.286597i | 0.549136 | − | 0.835733i | \(-0.314957\pi\) |
−0.835733 | + | 0.549136i | \(0.814957\pi\) | |||||||
\(488\) | 6.95984 | + | 6.95984i | 0.315057 | + | 0.315057i | ||||
\(489\) | 12.0807 | 0.546310 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.05148 | 0.0925818 | 0.0462909 | − | 0.998928i | \(-0.485260\pi\) | ||||
0.0462909 | + | 0.998928i | \(0.485260\pi\) | |||||||
\(492\) | −7.54452 | − | 7.54452i | −0.340133 | − | 0.340133i | ||||
\(493\) | 0.0366593 | + | 0.0366593i | 0.00165105 | + | 0.00165105i | ||||
\(494\) | − | 2.02193i | − | 0.0909708i | ||||||
\(495\) | −1.29769 | + | 4.45067i | −0.0583270 | + | 0.200043i | ||||
\(496\) | − | 8.03242i | − | 0.360666i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.26961 | + | 4.26961i | −0.191326 | + | 0.191326i | ||||
\(499\) | 5.36056i | 0.239971i | 0.992776 | + | 0.119986i | \(0.0382849\pi\) | ||||
−0.992776 | + | 0.119986i | \(0.961715\pi\) | |||||||
\(500\) | −8.40785 | + | 7.36940i | −0.376011 | + | 0.329570i | ||||
\(501\) | 11.5496 | 0.515998 | ||||||||
\(502\) | 20.9707 | − | 20.9707i | 0.935968 | − | 0.935968i | ||||
\(503\) | −3.75049 | − | 3.75049i | −0.167226 | − | 0.167226i | 0.618533 | − | 0.785759i | \(-0.287727\pi\) |
−0.785759 | + | 0.618533i | \(0.787727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.62184 | − | 8.99206i | 0.116670 | − | 0.400141i | ||||
\(506\) | 1.86359 | 0.0828467 | ||||||||
\(507\) | 9.04117 | − | 9.04117i | 0.401533 | − | 0.401533i | ||||
\(508\) | 2.53710 | − | 2.53710i | 0.112566 | − | 0.112566i | ||||
\(509\) | −9.76149 | −0.432670 | −0.216335 | − | 0.976319i | \(-0.569410\pi\) | ||||
−0.216335 | + | 0.976319i | \(0.569410\pi\) | |||||||
\(510\) | −1.92957 | − | 3.51790i | −0.0854427 | − | 0.155775i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −3.09170 | + | 3.09170i | −0.136502 | + | 0.136502i | ||||
\(514\) | −8.85671 | −0.390653 | ||||||||
\(515\) | −4.09288 | − | 7.46195i | −0.180354 | − | 0.328813i | ||||
\(516\) | 3.54793i | 0.156189i | ||||||||
\(517\) | −1.08911 | + | 1.08911i | −0.0478990 | + | 0.0478990i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.97784i | 0.306293i | ||||||||
\(520\) | 0.992706 | + | 0.289446i | 0.0435331 | + | 0.0126931i | ||||
\(521\) | 23.1435i | 1.01393i | 0.861966 | + | 0.506967i | \(0.169233\pi\) | ||||
−0.861966 | + | 0.506967i | \(0.830767\pi\) | |||||||
\(522\) | 0.0204302 | + | 0.0204302i | 0.000894204 | + | 0.000894204i | ||||
\(523\) | −20.6002 | − | 20.6002i | −0.900783 | − | 0.900783i | 0.0947207 | − | 0.995504i | \(-0.469804\pi\) |
−0.995504 | + | 0.0947207i | \(0.969804\pi\) | |||||||
\(524\) | 19.7306 | 0.861937 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.5475 | 1.20113 | ||||||||
\(527\) | −10.1916 | − | 10.1916i | −0.443955 | − | 0.443955i | ||||
\(528\) | −1.46603 | − | 1.46603i | −0.0638008 | − | 0.0638008i | ||||
\(529\) | 22.1920i | 0.964872i | ||||||||
\(530\) | 21.9349 | + | 6.39562i | 0.952791 | + | 0.277808i | ||||
\(531\) | − | 13.4242i | − | 0.582562i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.48888 | − | 3.48888i | 0.151120 | − | 0.151120i | ||||
\(534\) | − | 0.0197698i | − | 0.000855524i | ||||||
\(535\) | −18.5501 | − | 33.8198i | −0.801993 | − | 1.46216i | ||||
\(536\) | 4.71072 | 0.203472 | ||||||||
\(537\) | −4.56232 | + | 4.56232i | −0.196879 | + | 0.196879i | ||||
\(538\) | 1.54931 | + | 1.54931i | 0.0667957 | + | 0.0667957i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.07534 | − | 1.96052i | −0.0462754 | − | 0.0843673i | ||||
\(541\) | −40.7258 | −1.75094 | −0.875469 | − | 0.483273i | \(-0.839448\pi\) | ||||
−0.875469 | + | 0.483273i | \(0.839448\pi\) | |||||||
\(542\) | 5.15367 | − | 5.15367i | 0.221369 | − | 0.221369i | ||||
\(543\) | −7.43329 | + | 7.43329i | −0.318993 | + | 0.318993i | ||||
\(544\) | 1.79437 | 0.0769331 | ||||||||
\(545\) | −7.88657 | + | 27.0484i | −0.337824 | + | 1.15863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.2561 | − | 24.2561i | −1.03711 | − | 1.03711i | −0.999284 | − | 0.0378306i | \(-0.987955\pi\) |
−0.0378306 | − | 0.999284i | \(-0.512045\pi\) | |||||||
\(548\) | −11.5948 | + | 11.5948i | −0.495306 | + | 0.495306i | ||||
\(549\) | 9.84270 | 0.420076 | ||||||||
\(550\) | 2.24184 | + | 10.1211i | 0.0955925 | + | 0.431564i | ||||
\(551\) | − | 0.126328i | − | 0.00538174i | ||||||
\(552\) | −0.635591 | + | 0.635591i | −0.0270525 | + | 0.0270525i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 23.5003i | − | 0.998433i | ||||||
\(555\) | 7.15009 | − | 24.5225i | 0.303505 | − | 1.04092i | ||||
\(556\) | − | 6.98433i | − | 0.296202i | ||||||
\(557\) | −24.3133 | − | 24.3133i | −1.03019 | − | 1.03019i | −0.999530 | − | 0.0306577i | \(-0.990240\pi\) |
−0.0306577 | − | 0.999530i | \(-0.509760\pi\) | |||||||
\(558\) | −5.67978 | − | 5.67978i | −0.240444 | − | 0.240444i | ||||
\(559\) | −1.64070 | −0.0693941 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.72024 | −0.157068 | ||||||||
\(562\) | 0.937068 | + | 0.937068i | 0.0395278 | + | 0.0395278i | ||||
\(563\) | −2.30717 | − | 2.30717i | −0.0972357 | − | 0.0972357i | 0.656816 | − | 0.754051i | \(-0.271903\pi\) |
−0.754051 | + | 0.656816i | \(0.771903\pi\) | |||||||
\(564\) | − | 0.742898i | − | 0.0312817i | ||||||
\(565\) | 27.3915 | − | 15.0242i | 1.15237 | − | 0.632073i | ||||
\(566\) | − | 20.5377i | − | 0.863266i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.60851 | + | 1.60851i | −0.0674916 | + | 0.0674916i | ||||
\(569\) | 11.4851i | 0.481482i | 0.970589 | + | 0.240741i | \(0.0773905\pi\) | ||||
−0.970589 | + | 0.240741i | \(0.922609\pi\) | |||||||
\(570\) | −2.73669 | + | 9.38597i | −0.114628 | + | 0.393135i | ||||
\(571\) | 2.24056 | 0.0937644 | 0.0468822 | − | 0.998900i | \(-0.485071\pi\) | ||||
0.0468822 | + | 0.998900i | \(0.485071\pi\) | |||||||
\(572\) | 0.677948 | − | 0.677948i | 0.0283464 | − | 0.0283464i | ||||
\(573\) | 17.6058 | + | 17.6058i | 0.735492 | + | 0.735492i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.38795 | − | 0.971941i | 0.182990 | − | 0.0405328i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.15283 | + | 5.15283i | −0.214515 | + | 0.214515i | −0.806182 | − | 0.591667i | \(-0.798470\pi\) |
0.591667 | + | 0.806182i | \(0.298470\pi\) | |||||||
\(578\) | −9.74409 | + | 9.74409i | −0.405301 | + | 0.405301i | ||||
\(579\) | −12.6474 | −0.525610 | ||||||||
\(580\) | 0.0620232 | + | 0.0180843i | 0.00257537 | + | 0.000750909i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.65183 | − | 5.65183i | −0.234276 | − | 0.234276i | ||||
\(583\) | 14.9800 | − | 14.9800i | 0.620407 | − | 0.620407i | ||||
\(584\) | −11.5123 | −0.476384 | ||||||||
\(585\) | 0.906619 | − | 0.497280i | 0.0374841 | − | 0.0205600i | ||||
\(586\) | 22.2391i | 0.918687i | ||||||||
\(587\) | −15.5725 | + | 15.5725i | −0.642745 | + | 0.642745i | −0.951229 | − | 0.308484i | \(-0.900178\pi\) |
0.308484 | + | 0.951229i | \(0.400178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.1203i | 1.44711i | ||||||||
\(590\) | −14.4357 | − | 26.3185i | −0.594307 | − | 1.08351i | ||||
\(591\) | − | 3.48197i | − | 0.143229i | ||||||
\(592\) | 8.07760 | + | 8.07760i | 0.331987 | + | 0.331987i | ||||
\(593\) | −11.1666 | − | 11.1666i | −0.458557 | − | 0.458557i | 0.439625 | − | 0.898182i | \(-0.355112\pi\) |
−0.898182 | + | 0.439625i | \(0.855112\pi\) | |||||||
\(594\) | −2.07328 | −0.0850677 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.06301 | −0.330274 | ||||||||
\(597\) | −5.37218 | − | 5.37218i | −0.219869 | − | 0.219869i | ||||
\(598\) | −0.293921 | − | 0.293921i | −0.0120193 | − | 0.0120193i | ||||
\(599\) | 13.7247i | 0.560776i | 0.959887 | + | 0.280388i | \(0.0904631\pi\) | ||||
−0.959887 | + | 0.280388i | \(0.909537\pi\) | |||||||
\(600\) | −4.21646 | − | 2.68727i | −0.172136 | − | 0.109707i | ||||
\(601\) | 36.5565i | 1.49117i | 0.666411 | + | 0.745585i | \(0.267830\pi\) | ||||
−0.666411 | + | 0.745585i | \(0.732170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.33098 | − | 3.33098i | 0.135648 | − | 0.135648i | ||||
\(604\) | − | 20.7971i | − | 0.846222i | ||||||
\(605\) | −14.3860 | − | 4.19457i | −0.584874 | − | 0.170533i | ||||
\(606\) | 4.18882 | 0.170159 | ||||||||
\(607\) | −22.5291 | + | 22.5291i | −0.914430 | + | 0.914430i | −0.996617 | − | 0.0821870i | \(-0.973810\pi\) |
0.0821870 | + | 0.996617i | \(0.473810\pi\) | |||||||
\(608\) | −3.09170 | − | 3.09170i | −0.125385 | − | 0.125385i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.2968 | − | 10.5843i | 0.781305 | − | 0.428545i | ||||
\(611\) | 0.343544 | 0.0138983 | ||||||||
\(612\) | 1.26881 | − | 1.26881i | 0.0512887 | − | 0.0512887i | ||||
\(613\) | 2.84302 | − | 2.84302i | 0.114828 | − | 0.114828i | −0.647358 | − | 0.762186i | \(-0.724126\pi\) |
0.762186 | + | 0.647358i | \(0.224126\pi\) | |||||||
\(614\) | 17.0778 | 0.689205 | ||||||||
\(615\) | −20.9179 | + | 11.4735i | −0.843491 | + | 0.462654i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.28987 | + | 5.28987i | 0.212962 | + | 0.212962i | 0.805525 | − | 0.592562i | \(-0.201884\pi\) |
−0.592562 | + | 0.805525i | \(0.701884\pi\) | |||||||
\(618\) | 2.69132 | − | 2.69132i | 0.108261 | − | 0.108261i | ||||
\(619\) | −16.3515 | −0.657222 | −0.328611 | − | 0.944465i | \(-0.606580\pi\) | ||||
−0.328611 | + | 0.944465i | \(0.606580\pi\) | |||||||
\(620\) | −17.2430 | − | 5.02760i | −0.692497 | − | 0.201913i | ||||
\(621\) | 0.898861i | 0.0360700i | ||||||||
\(622\) | 14.2972 | − | 14.2972i | 0.573267 | − | 0.573267i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.462438i | 0.0185123i | ||||||||
\(625\) | 10.5571 | + | 22.6616i | 0.422286 | + | 0.906463i | ||||
\(626\) | − | 12.2452i | − | 0.489415i | ||||||
\(627\) | 6.40995 | + | 6.40995i | 0.255989 | + | 0.255989i | ||||
\(628\) | 10.0893 | + | 10.0893i | 0.402607 | + | 0.402607i | ||||
\(629\) | 20.4979 | 0.817306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7268 | 1.74074 | 0.870368 | − | 0.492401i | \(-0.163881\pi\) | ||||
0.870368 | + | 0.492401i | \(0.163881\pi\) | |||||||
\(632\) | 5.66614 | + | 5.66614i | 0.225387 | + | 0.225387i | ||||
\(633\) | −3.76373 | − | 3.76373i | −0.149595 | − | 0.149595i | ||||
\(634\) | − | 16.0361i | − | 0.636876i | ||||||
\(635\) | −3.85834 | − | 7.03436i | −0.153114 | − | 0.279150i | ||||
\(636\) | 10.2181i | 0.405172i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.0423574 | − | 0.0423574i | 0.00167695 | − | 0.00167695i | ||||
\(639\) | 2.27478i | 0.0899888i | ||||||||
\(640\) | 1.96052 | − | 1.07534i | 0.0774963 | − | 0.0425067i | ||||
\(641\) | −16.0222 | −0.632838 | −0.316419 | − | 0.948619i | \(-0.602481\pi\) | ||||
−0.316419 | + | 0.948619i | \(0.602481\pi\) | |||||||
\(642\) | 12.1979 | − | 12.1979i | 0.481413 | − | 0.481413i | ||||
\(643\) | 5.28588 | + | 5.28588i | 0.208455 | + | 0.208455i | 0.803610 | − | 0.595156i | \(-0.202910\pi\) |
−0.595156 | + | 0.803610i | \(0.702910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.61626 | + | 2.22070i | 0.299890 | + | 0.0874398i | ||||
\(646\) | −7.84557 | −0.308680 | ||||||||
\(647\) | −28.4692 | + | 28.4692i | −1.11924 | + | 1.11924i | −0.127388 | + | 0.991853i | \(0.540659\pi\) |
−0.991853 | + | 0.127388i | \(0.959341\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −27.8322 | −1.09251 | ||||||||
\(650\) | 1.24270 | − | 1.94985i | 0.0487426 | − | 0.0764796i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.54237 | + | 8.54237i | 0.334545 | + | 0.334545i | ||||
\(653\) | −5.75189 | + | 5.75189i | −0.225089 | + | 0.225089i | −0.810637 | − | 0.585548i | \(-0.800879\pi\) |
0.585548 | + | 0.810637i | \(0.300879\pi\) | |||||||
\(654\) | −12.6001 | −0.492703 | ||||||||
\(655\) | 12.3497 | − | 42.3553i | 0.482542 | − | 1.65496i | ||||
\(656\) | − | 10.6696i | − | 0.416577i | ||||||
\(657\) | −8.14046 | + | 8.14046i | −0.317589 | + | 0.317589i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.0314i | 0.585540i | 0.956183 | + | 0.292770i | \(0.0945770\pi\) | ||||
−0.956183 | + | 0.292770i | \(0.905423\pi\) | |||||||
\(660\) | −4.06470 | + | 2.22949i | −0.158218 | + | 0.0867827i | ||||
\(661\) | 25.7580i | 1.00187i | 0.865485 | + | 0.500934i | \(0.167010\pi\) | ||||
−0.865485 | + | 0.500934i | \(0.832990\pi\) | |||||||
\(662\) | 15.3759 | + | 15.3759i | 0.597602 | + | 0.597602i | ||||
\(663\) | 0.586747 | + | 0.586747i | 0.0227874 | + | 0.0227874i | ||||
\(664\) | −6.03813 | −0.234325 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.4235 | 0.442650 | ||||||||
\(667\) | −0.0183639 | − | 0.0183639i | −0.000711052 | − | 0.000711052i | ||||
\(668\) | 8.16680 | + | 8.16680i | 0.315983 | + | 0.315983i | ||||
\(669\) | − | 21.9185i | − | 0.847420i | ||||||
\(670\) | 2.94850 | − | 10.1124i | 0.113910 | − | 0.390676i | ||||
\(671\) | − | 20.4067i | − | 0.787791i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.5407 | − | 15.5407i | 0.599051 | − | 0.599051i | −0.341009 | − | 0.940060i | \(-0.610769\pi\) |
0.940060 | + | 0.341009i | \(0.110769\pi\) | |||||||
\(674\) | − | 25.2729i | − | 0.973475i | ||||||
\(675\) | −4.88168 | + | 1.08130i | −0.187896 | + | 0.0416194i | ||||
\(676\) | 12.7862 | 0.491775 | ||||||||
\(677\) | 5.67922 | − | 5.67922i | 0.218270 | − | 0.218270i | −0.589499 | − | 0.807769i | \(-0.700675\pi\) |
0.807769 | + | 0.589499i | \(0.200675\pi\) | |||||||
\(678\) | 9.87937 | + | 9.87937i | 0.379415 | + | 0.379415i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.12312 | − | 3.85194i | 0.0430698 | − | 0.147715i | ||||
\(681\) | 9.62940 | 0.368999 | ||||||||
\(682\) | −11.7758 | + | 11.7758i | −0.450917 | + | 0.450917i | ||||
\(683\) | −27.3490 | + | 27.3490i | −1.04648 | + | 1.04648i | −0.0476144 | + | 0.998866i | \(0.515162\pi\) |
−0.998866 | + | 0.0476144i | \(0.984838\pi\) | |||||||
\(684\) | −4.37232 | −0.167180 | ||||||||
\(685\) | 17.6330 | + | 32.1477i | 0.673722 | + | 1.22830i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.4158 | + | 13.4158i | 0.511845 | + | 0.511845i | ||||
\(688\) | −2.50876 | + | 2.50876i | −0.0956457 | + | 0.0956457i | ||||
\(689\) | −4.72522 | −0.180016 | ||||||||
\(690\) | 0.966585 | + | 1.76223i | 0.0367972 | + | 0.0670871i | ||||
\(691\) | − | 25.5947i | − | 0.973668i | −0.873494 | − | 0.486834i | \(-0.838152\pi\) | ||
0.873494 | − | 0.486834i | \(-0.161848\pi\) | |||||||
\(692\) | −4.93408 | + | 4.93408i | −0.187566 | + | 0.187566i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.0692i | 0.761818i | ||||||||
\(695\) | −14.9931 | − | 4.37159i | −0.568721 | − | 0.165824i | ||||
\(696\) | 0.0288926i | 0.00109517i | ||||||||
\(697\) | −13.5377 | − | 13.5377i | −0.512776 | − | 0.512776i | ||||
\(698\) | −17.6676 | − | 17.6676i | −0.668730 | − | 0.668730i | ||||
\(699\) | 23.1851 | 0.876940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0066 | 1.54880 | 0.774399 | − | 0.632698i | \(-0.218052\pi\) | ||||
0.774399 | + | 0.632698i | \(0.218052\pi\) | |||||||
\(702\) | 0.326993 | + | 0.326993i | 0.0123416 | + | 0.0123416i | ||||
\(703\) | −35.3179 | − | 35.3179i | −1.33204 | − | 1.33204i | ||||
\(704\) | − | 2.07328i | − | 0.0781397i | ||||||
\(705\) | −1.59476 | − | 0.464990i | −0.0600623 | − | 0.0175125i | ||||
\(706\) | 27.1512i | 1.02185i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.49237 | − | 9.49237i | 0.356745 | − | 0.356745i | ||||
\(709\) | 15.5334i | 0.583370i | 0.956514 | + | 0.291685i | \(0.0942159\pi\) | ||||
−0.956514 | + | 0.291685i | \(0.905784\pi\) | |||||||
\(710\) | 2.44617 | + | 4.45975i | 0.0918031 | + | 0.167371i | ||||
\(711\) | 8.01313 | 0.300516 | ||||||||
\(712\) | 0.0139794 | − | 0.0139794i | 0.000523899 | − | 0.000523899i | ||||
\(713\) | 5.10533 | + | 5.10533i | 0.191196 | + | 0.191196i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.03100 | − | 1.87967i | −0.0385572 | − | 0.0702958i | ||||
\(716\) | −6.45209 | −0.241126 | ||||||||
\(717\) | 2.11242 | − | 2.11242i | 0.0788896 | − | 0.0788896i | ||||
\(718\) | −11.8218 | + | 11.8218i | −0.441185 | + | 0.441185i | ||||
\(719\) | 0.379933 | 0.0141691 | 0.00708455 | − | 0.999975i | \(-0.497745\pi\) | ||||
0.00708455 | + | 0.999975i | \(0.497745\pi\) | |||||||
\(720\) | 0.625913 | − | 2.14668i | 0.0233264 | − | 0.0800020i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.0828627 | + | 0.0828627i | 0.00308383 | + | 0.00308383i | ||||
\(723\) | −19.1663 | + | 19.1663i | −0.712804 | + | 0.712804i | ||||
\(724\) | −10.5123 | −0.390685 | ||||||||
\(725\) | 0.0776423 | − | 0.121825i | 0.00288356 | − | 0.00452446i | ||||
\(726\) | − | 6.70151i | − | 0.248716i | ||||||
\(727\) | −27.3322 | + | 27.3322i | −1.01369 | + | 1.01369i | −0.0137898 | + | 0.999905i | \(0.504390\pi\) |
−0.999905 | + | 0.0137898i | \(0.995610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −7.20573 | + | 24.7133i | −0.266696 | + | 0.914681i | ||||
\(731\) | 6.36630i | 0.235466i | ||||||||
\(732\) | 6.95984 | + | 6.95984i | 0.257243 | + | 0.257243i | ||||
\(733\) | −6.42449 | − | 6.42449i | −0.237294 | − | 0.237294i | 0.578435 | − | 0.815729i | \(-0.303664\pi\) |
−0.815729 | + | 0.578435i | \(0.803664\pi\) | |||||||
\(734\) | 8.40797 | 0.310344 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.898861 | −0.0331325 | ||||||||
\(737\) | −6.90605 | − | 6.90605i | −0.254388 | − | 0.254388i | ||||
\(738\) | −7.54452 | − | 7.54452i | −0.277718 | − | 0.277718i | ||||
\(739\) | − | 3.73900i | − | 0.137541i | −0.997632 | − | 0.0687707i | \(-0.978092\pi\) | ||
0.997632 | − | 0.0687707i | \(-0.0219077\pi\) | |||||||
\(740\) | 22.3959 | − | 12.2841i | 0.823290 | − | 0.451574i | ||||
\(741\) | − | 2.02193i | − | 0.0742774i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.84421 | − | 1.84421i | 0.0676575 | − | 0.0676575i | −0.672468 | − | 0.740126i | \(-0.734766\pi\) |
0.740126 | + | 0.672468i | \(0.234766\pi\) | |||||||
\(744\) | − | 8.03242i | − | 0.294483i | ||||||
\(745\) | −5.04675 | + | 17.3087i | −0.184898 | + | 0.634141i | ||||
\(746\) | −0.0229272 | −0.000839423 | ||||||||
\(747\) | −4.26961 | + | 4.26961i | −0.156217 | + | 0.156217i | ||||
\(748\) | −2.63060 | − | 2.63060i | −0.0961844 | − | 0.0961844i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.40785 | + | 7.36940i | −0.307011 | + | 0.269092i | ||||
\(751\) | −18.9083 | −0.689974 | −0.344987 | − | 0.938607i | \(-0.612117\pi\) | ||||
−0.344987 | + | 0.938607i | \(0.612117\pi\) | |||||||
\(752\) | 0.525308 | − | 0.525308i | 0.0191560 | − | 0.0191560i | ||||
\(753\) | 20.9707 | − | 20.9707i | 0.764214 | − | 0.764214i | ||||
\(754\) | −0.0133610 | −0.000486581 | ||||||||
\(755\) | −44.6447 | − | 13.0172i | −1.62479 | − | 0.473744i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.1051 | + | 36.1051i | 1.31226 | + | 1.31226i | 0.919744 | + | 0.392520i | \(0.128396\pi\) |
0.392520 | + | 0.919744i | \(0.371604\pi\) | |||||||
\(758\) | −21.9416 | + | 21.9416i | −0.796953 | + | 0.796953i | ||||
\(759\) | 1.86359 | 0.0676440 | ||||||||
\(760\) | −8.57202 | + | 4.70175i | −0.310940 | + | 0.170550i | ||||
\(761\) | 24.5228i | 0.888950i | 0.895791 | + | 0.444475i | \(0.146610\pi\) | ||||
−0.895791 | + | 0.444475i | \(0.853390\pi\) | |||||||
\(762\) | 2.53710 | − | 2.53710i | 0.0919096 | − | 0.0919096i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.8983i | 0.900790i | ||||||||
\(765\) | −1.92957 | − | 3.51790i | −0.0697637 | − | 0.127190i | ||||
\(766\) | 4.91543i | 0.177602i | ||||||||
\(767\) | 4.38963 | + | 4.38963i | 0.158500 | + | 0.158500i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −41.6081 | −1.50043 | −0.750213 | − | 0.661196i | \(-0.770049\pi\) | ||||
−0.750213 | + | 0.661196i | \(0.770049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.85671 | −0.318967 | ||||||||
\(772\) | −8.94309 | − | 8.94309i | −0.321869 | − | 0.321869i | ||||
\(773\) | 26.5458 | + | 26.5458i | 0.954786 | + | 0.954786i | 0.999021 | − | 0.0442349i | \(-0.0140850\pi\) |
−0.0442349 | + | 0.999021i | \(0.514085\pi\) | |||||||
\(774\) | 3.54793i | 0.127528i | ||||||||
\(775\) | −21.5853 | + | 33.8684i | −0.775366 | + | 1.21659i | ||||
\(776\) | − | 7.99290i | − | 0.286928i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.79706 | − | 7.79706i | 0.279538 | − | 0.279538i | ||||
\(779\) | 46.6508i | 1.67144i | ||||||||
\(780\) | 0.992706 | + | 0.289446i | 0.0355446 | + | 0.0103638i | ||||
\(781\) | 4.71625 | 0.168761 | ||||||||
\(782\) | −1.14049 | + | 1.14049i | −0.0407837 | + | 0.0407837i | ||||
\(783\) | 0.0204302 | + | 0.0204302i | 0.000730115 | + | 0.000730115i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.9736 | − | 15.3435i | 0.998419 | − | 0.547632i | ||||
\(786\) | 19.7306 | 0.703768 | ||||||||
\(787\) | −3.71498 | + | 3.71498i | −0.132425 | + | 0.132425i | −0.770212 | − | 0.637788i | \(-0.779850\pi\) |
0.637788 | + | 0.770212i | \(0.279850\pi\) | |||||||
\(788\) | 2.46213 | − | 2.46213i | 0.0877096 | − | 0.0877096i | ||||
\(789\) | 27.5475 | 0.980717 | ||||||||
\(790\) | 15.7099 | − | 8.61687i | 0.558933 | − | 0.306574i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.46603 | − | 1.46603i | −0.0520931 | − | 0.0520931i | ||||
\(793\) | −3.21850 | + | 3.21850i | −0.114292 | + | 0.114292i | ||||
\(794\) | −8.14551 | −0.289073 | ||||||||
\(795\) | 21.9349 | + | 6.39562i | 0.777950 | + | 0.226829i | ||||
\(796\) | − | 7.59741i | − | 0.269283i | ||||||
\(797\) | 0.406449 | − | 0.406449i | 0.0143971 | − | 0.0143971i | −0.699872 | − | 0.714269i | \(-0.746759\pi\) |
0.714269 | + | 0.699872i | \(0.246759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.33304i | − | 0.0471594i | ||||||
\(800\) | −1.08130 | − | 4.88168i | −0.0382298 | − | 0.172593i | ||||
\(801\) | − | 0.0197698i | − | 0.000698532i | ||||||
\(802\) | 8.33908 | + | 8.33908i | 0.294463 | + | 0.294463i | ||||
\(803\) | 16.8774 | + | 16.8774i | 0.595592 | + | 0.595592i | ||||
\(804\) | 4.71072 | 0.166134 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.71450 | 0.130838 | ||||||||
\(807\) | 1.54931 | + | 1.54931i | 0.0545385 | + | 0.0545385i | ||||
\(808\) | 2.96194 | + | 2.96194i | 0.104201 | + | 0.104201i | ||||
\(809\) | 35.8295i | 1.25970i | 0.776718 | + | 0.629849i | \(0.216883\pi\) | ||||
−0.776718 | + | 0.629849i | \(0.783117\pi\) | |||||||
\(810\) | −1.07534 | − | 1.96052i | −0.0377837 | − | 0.0688856i | ||||
\(811\) | 30.6135i | 1.07499i | 0.843268 | + | 0.537493i | \(0.180628\pi\) | ||||
−0.843268 | + | 0.537493i | \(0.819372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.15367 | − | 5.15367i | 0.180747 | − | 0.180747i | ||||
\(814\) | − | 23.6840i | − | 0.830124i | ||||||
\(815\) | 23.6845 | − | 12.9909i | 0.829632 | − | 0.455053i | ||||
\(816\) | 1.79437 | 0.0628156 | ||||||||
\(817\) | 10.9691 | − | 10.9691i | 0.383761 | − | 0.383761i | ||||
\(818\) | 4.43157 | + | 4.43157i | 0.154946 | + | 0.154946i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.9041 | − | 6.67823i | −0.799847 | − | 0.233214i | ||||
\(821\) | −26.8615 | −0.937471 | −0.468736 | − | 0.883338i | \(-0.655290\pi\) | ||||
−0.468736 | + | 0.883338i | \(0.655290\pi\) | |||||||
\(822\) | −11.5948 | + | 11.5948i | −0.404415 | + | 0.404415i | ||||
\(823\) | −3.80691 | + | 3.80691i | −0.132701 | + | 0.132701i | −0.770337 | − | 0.637637i | \(-0.779912\pi\) |
0.637637 | + | 0.770337i | \(0.279912\pi\) | |||||||
\(824\) | 3.80611 | 0.132592 | ||||||||
\(825\) | 2.24184 | + | 10.1211i | 0.0780510 | + | 0.352371i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.30801 | + | 5.30801i | 0.184578 | + | 0.184578i | 0.793347 | − | 0.608770i | \(-0.208337\pi\) |
−0.608770 | + | 0.793347i | \(0.708337\pi\) | |||||||
\(828\) | −0.635591 | + | 0.635591i | −0.0220883 | + | 0.0220883i | ||||
\(829\) | 42.2481 | 1.46734 | 0.733668 | − | 0.679508i | \(-0.237807\pi\) | ||||
0.733668 | + | 0.679508i | \(0.237807\pi\) | |||||||
\(830\) | −3.77935 | + | 12.9619i | −0.131183 | + | 0.449915i | ||||
\(831\) | − | 23.5003i | − | 0.815217i | ||||||
\(832\) | −0.326993 | + | 0.326993i | −0.0113364 | + | 0.0113364i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 6.98433i | − | 0.241848i | ||||||
\(835\) | 22.6432 | − | 12.4198i | 0.783600 | − | 0.429804i | ||||
\(836\) | 9.06504i | 0.313521i | ||||||||
\(837\) | −5.67978 | − | 5.67978i | −0.196322 | − | 0.196322i | ||||
\(838\) | −16.9557 | − | 16.9557i | −0.585726 | − | 0.585726i | ||||
\(839\) | −31.3254 | −1.08147 | −0.540736 | − | 0.841192i | \(-0.681854\pi\) | ||||
−0.540736 | + | 0.841192i | \(0.681854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9992 | 0.999971 | ||||||||
\(842\) | −5.66547 | − | 5.66547i | −0.195245 | − | 0.195245i | ||||
\(843\) | 0.937068 | + | 0.937068i | 0.0322743 | + | 0.0322743i | ||||
\(844\) | − | 5.32272i | − | 0.183216i | ||||||
\(845\) | 8.00302 | − | 27.4478i | 0.275312 | − | 0.944232i | ||||
\(846\) | − | 0.742898i | − | 0.0255414i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.22526 | + | 7.22526i | −0.248116 | + | 0.248116i | ||||
\(849\) | − | 20.5377i | − | 0.704854i | ||||||
\(850\) | −7.56591 | − | 4.82197i | −0.259509 | − | 0.165392i | ||||
\(851\) | −10.2681 | −0.351986 | ||||||||
\(852\) | −1.60851 | + | 1.60851i | −0.0551067 | + | 0.0551067i | ||||
\(853\) | −17.7771 | − | 17.7771i | −0.608678 | − | 0.608678i | 0.333923 | − | 0.942600i | \(-0.391628\pi\) |
−0.942600 | + | 0.333923i | \(0.891628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.73669 | + | 9.38597i | −0.0935930 | + | 0.320993i | ||||
\(856\) | 17.2504 | 0.589608 | ||||||||
\(857\) | −30.2273 | + | 30.2273i | −1.03255 | + | 1.03255i | −0.0330932 | + | 0.999452i | \(0.510536\pi\) |
−0.999452 | + | 0.0330932i | \(0.989464\pi\) | |||||||
\(858\) | 0.677948 | − | 0.677948i | 0.0231448 | − | 0.0231448i | ||||
\(859\) | −16.6575 | −0.568348 | −0.284174 | − | 0.958773i | \(-0.591719\pi\) | ||||
−0.284174 | + | 0.958773i | \(0.591719\pi\) | |||||||
\(860\) | 3.81524 | + | 6.95578i | 0.130099 | + | 0.237190i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0880 | − | 12.0880i | −0.411719 | − | 0.411719i | ||||
\(863\) | −39.3141 | + | 39.3141i | −1.33827 | + | 1.33827i | −0.440528 | + | 0.897739i | \(0.645209\pi\) |
−0.897739 | + | 0.440528i | \(0.854791\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 7.50358 | + | 13.6802i | 0.255129 | + | 0.465141i | ||||
\(866\) | 4.63948i | 0.157656i | ||||||||
\(867\) | −9.74409 | + | 9.74409i | −0.330927 | + | 0.330927i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.6134i | − | 0.563573i | ||||||
\(870\) | 0.0620232 | + | 0.0180843i | 0.00210278 | + | 0.000613114i | ||||
\(871\) | 2.17841i | 0.0738128i | ||||||||
\(872\) | −8.90962 | − | 8.90962i | −0.301718 | − | 0.301718i | ||||
\(873\) | −5.65183 | − | 5.65183i | −0.191286 | − | 0.191286i | ||||
\(874\) | 3.93011 | 0.132938 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.5123 | −0.388966 | ||||||||
\(877\) | 32.6886 | + | 32.6886i | 1.10381 | + | 1.10381i | 0.993946 | + | 0.109868i | \(0.0350428\pi\) |
0.109868 | + | 0.993946i | \(0.464957\pi\) | |||||||
\(878\) | 24.2870 | + | 24.2870i | 0.819647 | + | 0.819647i | ||||
\(879\) | 22.2391i | 0.750105i | ||||||||
\(880\) | −4.45067 | − | 1.29769i | −0.150032 | − | 0.0437452i | ||||
\(881\) | − | 1.61071i | − | 0.0542661i | −0.999632 | − | 0.0271330i | \(-0.991362\pi\) | ||
0.999632 | − | 0.0271330i | \(-0.00863778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7890 | + | 35.7890i | −1.20439 | + | 1.20439i | −0.231579 | + | 0.972816i | \(0.574389\pi\) |
−0.972816 | + | 0.231579i | \(0.925611\pi\) | |||||||
\(884\) | 0.829786i | 0.0279087i | ||||||||
\(885\) | −14.4357 | − | 26.3185i | −0.485250 | − | 0.884686i | ||||
\(886\) | 28.2554 | 0.949258 | ||||||||
\(887\) | 14.1627 | − | 14.1627i | 0.475537 | − | 0.475537i | −0.428164 | − | 0.903701i | \(-0.640839\pi\) |
0.903701 | + | 0.428164i | \(0.140839\pi\) | |||||||
\(888\) | 8.07760 | + | 8.07760i | 0.271067 | + | 0.271067i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.0212594 | − | 0.0387591i | −0.000712615 | − | 0.00129921i | ||||
\(891\) | −2.07328 | −0.0694575 | ||||||||
\(892\) | 15.4987 | − | 15.4987i | 0.518936 | − | 0.518936i | ||||
\(893\) | −2.29682 | + | 2.29682i | −0.0768600 | + | 0.0768600i | ||||
\(894\) | −8.06301 | −0.269667 | ||||||||
\(895\) | −4.03845 | + | 13.8506i | −0.134991 | + | 0.462974i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.293921 | − | 0.293921i | −0.00981375 | − | 0.00981375i | ||||
\(898\) | 7.07222 | − | 7.07222i | 0.236003 | − | 0.236003i | ||||
\(899\) | 0.232078 | 0.00774022 | ||||||||
\(900\) | −4.21646 | − | 2.68727i | −0.140549 | − | 0.0895757i | ||||
\(901\) | 18.3350i | 0.610827i | ||||||||
\(902\) | −15.6419 | + | 15.6419i | −0.520818 | + | 0.520818i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.9715i | 0.464686i | ||||||||
\(905\) | −6.57976 | + | 22.5664i | −0.218719 | + | 0.750134i | ||||
\(906\) | − | 20.7971i | − | 0.690937i | ||||||
\(907\) | −36.8528 | − | 36.8528i | −1.22368 | − | 1.22368i | −0.966315 | − | 0.257362i | \(-0.917147\pi\) |
−0.257362 | − | 0.966315i | \(-0.582853\pi\) | |||||||
\(908\) | 6.80901 | + | 6.80901i | 0.225965 | + | 0.225965i | ||||
\(909\) | 4.18882 | 0.138934 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6381 | 0.484981 | 0.242490 | − | 0.970154i | \(-0.422036\pi\) | ||||
0.242490 | + | 0.970154i | \(0.422036\pi\) | |||||||
\(912\) | −3.09170 | − | 3.09170i | −0.102376 | − | 0.102376i | ||||
\(913\) | 8.85209 | + | 8.85209i | 0.292961 | + | 0.292961i | ||||
\(914\) | − | 1.71062i | − | 0.0565823i | ||||||
\(915\) | 19.2968 | − | 10.5843i | 0.637933 | − | 0.349906i | ||||
\(916\) | 18.9728i | 0.626880i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.26881 | − | 1.26881i | 0.0418771 | − | 0.0418771i | ||||
\(919\) | − | 49.3134i | − | 1.62670i | −0.581775 | − | 0.813350i | \(-0.697642\pi\) | ||
0.581775 | − | 0.813350i | \(-0.302358\pi\) | |||||||
\(920\) | −0.562609 | + | 1.92957i | −0.0185487 | + | 0.0636159i | ||||
\(921\) | 17.0778 | 0.562734 | ||||||||
\(922\) | 6.22516 | − | 6.22516i | 0.205015 | − | 0.205015i | ||||
\(923\) | −0.743837 | − | 0.743837i | −0.0244837 | − | 0.0244837i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.3522 | − | 55.7656i | −0.406138 | − | 1.83356i | ||||
\(926\) | −28.1018 | −0.923481 | ||||||||
\(927\) | 2.69132 | − | 2.69132i | 0.0883947 | − | 0.0883947i | ||||
\(928\) | −0.0204302 | + | 0.0204302i | −0.000670653 | + | 0.000670653i | ||||
\(929\) | −50.7683 | −1.66566 | −0.832828 | − | 0.553532i | \(-0.813280\pi\) | ||||
−0.832828 | + | 0.553532i | \(0.813280\pi\) | |||||||
\(930\) | −17.2430 | − | 5.02760i | −0.565421 | − | 0.164861i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.3943 | + | 16.3943i | 0.537014 | + | 0.537014i | ||||
\(933\) | 14.2972 | − | 14.2972i | 0.468070 | − | 0.468070i | ||||
\(934\) | −27.3919 | −0.896291 | ||||||||
\(935\) | −7.29359 | + | 4.00053i | −0.238526 | + | 0.130831i | ||||
\(936\) | 0.462438i | 0.0151153i | ||||||||
\(937\) | 6.18012 | − | 6.18012i | 0.201896 | − | 0.201896i | −0.598916 | − | 0.800812i | \(-0.704402\pi\) |
0.800812 | + | 0.598916i | \(0.204402\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 12.2452i | − | 0.399605i | ||||||
\(940\) | −0.798871 | − | 1.45647i | −0.0260563 | − | 0.0475047i | ||||
\(941\) | − | 11.7207i | − | 0.382084i | −0.981582 | − | 0.191042i | \(-0.938813\pi\) | ||
0.981582 | − | 0.191042i | \(-0.0611867\pi\) | |||||||
\(942\) | 10.0893 | + | 10.0893i | 0.328728 | + | 0.328728i | ||||
\(943\) | 6.78148 | + | 6.78148i | 0.220835 | + | 0.220835i | ||||
\(944\) | 13.4242 | 0.436922 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.35584 | 0.239159 | ||||||||
\(947\) | −23.5131 | − | 23.5131i | −0.764073 | − | 0.764073i | 0.212983 | − | 0.977056i | \(-0.431682\pi\) |
−0.977056 | + | 0.212983i | \(0.931682\pi\) | |||||||
\(948\) | 5.66614 | + | 5.66614i | 0.184028 | + | 0.184028i | ||||
\(949\) | − | 5.32375i | − | 0.172816i | ||||||
\(950\) | 4.72780 | + | 21.3443i | 0.153390 | + | 0.692499i | ||||
\(951\) | − | 16.0361i | − | 0.520007i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.37438 | + | 7.37438i | −0.238879 | + | 0.238879i | −0.816386 | − | 0.577507i | \(-0.804026\pi\) |
0.577507 | + | 0.816386i | \(0.304026\pi\) | |||||||
\(954\) | 10.2181i | 0.330822i | ||||||||
\(955\) | 53.4488 | + | 15.5842i | 1.72956 | + | 0.504293i | ||||
\(956\) | 2.98741 | 0.0966197 | ||||||||
\(957\) | 0.0423574 | − | 0.0423574i | 0.00136922 | − | 0.00136922i | ||||
\(958\) | 16.9802 | + | 16.9802i | 0.548605 | + | 0.548605i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.96052 | − | 1.07534i | 0.0632755 | − | 0.0347066i | ||||
\(961\) | −33.5198 | −1.08128 | ||||||||
\(962\) | −3.73539 | + | 3.73539i | −0.120434 | + | 0.120434i | ||||
\(963\) | 12.1979 | − | 12.1979i | 0.393072 | − | 0.393072i | ||||
\(964\) | −27.1053 | −0.873003 | ||||||||
\(965\) | −24.7956 | + | 13.6003i | −0.798197 | + | 0.437811i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7706 | − | 25.7706i | −0.828725 | − | 0.828725i | 0.158615 | − | 0.987340i | \(-0.449297\pi\) |
−0.987340 | + | 0.158615i | \(0.949297\pi\) | |||||||
\(968\) | 4.73869 | − | 4.73869i | 0.152307 | − | 0.152307i | ||||
\(969\) | −7.84557 | −0.252036 | ||||||||
\(970\) | −17.1582 | − | 5.00286i | −0.550916 | − | 0.160632i | ||||
\(971\) | 54.9570i | 1.76365i | 0.471573 | + | 0.881827i | \(0.343686\pi\) | ||||
−0.471573 | + | 0.881827i | \(0.656314\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 8.94440i | − | 0.286597i | ||||||
\(975\) | 1.24270 | − | 1.94985i | 0.0397981 | − | 0.0624453i | ||||
\(976\) | 9.84270i | 0.315057i | ||||||||
\(977\) | 12.0469 | + | 12.0469i | 0.385415 | + | 0.385415i | 0.873048 | − | 0.487634i | \(-0.162140\pi\) |
−0.487634 | + | 0.873048i | \(0.662140\pi\) | |||||||
\(978\) | 8.54237 | + | 8.54237i | 0.273155 | + | 0.273155i | ||||
\(979\) | −0.0409884 | −0.00130999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6001 | −0.402290 | ||||||||
\(982\) | 1.45061 | + | 1.45061i | 0.0462909 | + | 0.0462909i | ||||
\(983\) | 17.2157 | + | 17.2157i | 0.549094 | + | 0.549094i | 0.926179 | − | 0.377084i | \(-0.123073\pi\) |
−0.377084 | + | 0.926179i | \(0.623073\pi\) | |||||||
\(984\) | − | 10.6696i | − | 0.340133i | ||||||
\(985\) | −3.74432 | − | 6.82647i | −0.119304 | − | 0.217510i | ||||
\(986\) | 0.0518441i | 0.00165105i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.42972 | − | 1.42972i | 0.0454854 | − | 0.0454854i | ||||
\(989\) | − | 3.18909i | − | 0.101407i | ||||||
\(990\) | −4.06470 | + | 2.22949i | −0.129185 | + | 0.0708578i | ||||
\(991\) | 52.6929 | 1.67384 | 0.836922 | − | 0.547322i | \(-0.184353\pi\) | ||||
0.836922 | + | 0.547322i | \(0.184353\pi\) | |||||||
\(992\) | 5.67978 | − | 5.67978i | 0.180333 | − | 0.180333i | ||||
\(993\) | 15.3759 | + | 15.3759i | 0.487940 | + | 0.487940i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.3092 | − | 4.75532i | −0.517037 | − | 0.150754i | ||||
\(996\) | −6.03813 | −0.191326 | ||||||||
\(997\) | 10.7568 | − | 10.7568i | 0.340670 | − | 0.340670i | −0.515949 | − | 0.856619i | \(-0.672561\pi\) |
0.856619 | + | 0.515949i | \(0.172561\pi\) | |||||||
\(998\) | −3.79048 | + | 3.79048i | −0.119986 | + | 0.119986i | ||||
\(999\) | 11.4235 | 0.361422 |
(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 | 1470.2.m.c.97.8 | ✓ | 16 | |
5.3 | odd | 4 | 1470.2.m.f.1273.5 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.f.97.5 | yes | 16 | ||
35.13 | even | 4 | inner | 1470.2.m.c.1273.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.c.97.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1470.2.m.c.1273.8 | yes | 16 | 35.13 | even | 4 | inner | |
1470.2.m.f.97.5 | yes | 16 | 7.6 | odd | 2 | ||
1470.2.m.f.1273.5 | yes | 16 | 5.3 | odd | 4 |