Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.508 |
Dual form | 637.2.e.f.79.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | − | 1.22474i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(3\) | 0.707107 | − | 1.22474i | 0.408248 | − | 0.707107i | −0.586445 | − | 0.809989i | \(-0.699473\pi\) |
0.994694 | + | 0.102882i | \(0.0328064\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20711 | − | 3.82282i | −0.987048 | − | 1.70962i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) |
−0.354593 | − | 0.935021i | \(-0.615380\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −3.12132 | + | 5.40629i | −0.987048 | + | 1.70962i | ||||
\(11\) | 2.12132 | − | 3.67423i | 0.639602 | − | 1.10782i | −0.345918 | − | 0.938265i | \(-0.612432\pi\) |
0.985520 | − | 0.169559i | \(-0.0542342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.24264 | −1.61184 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 0.707107 | − | 1.22474i | 0.171499 | − | 0.297044i | −0.767445 | − | 0.641114i | \(-0.778472\pi\) |
0.938944 | + | 0.344070i | \(0.111806\pi\) | |||||||
\(18\) | 0.707107 | − | 1.22474i | 0.166667 | − | 0.288675i | ||||
\(19\) | −0.621320 | − | 1.07616i | −0.142541 | − | 0.246888i | 0.785912 | − | 0.618338i | \(-0.212194\pi\) |
−0.928453 | + | 0.371451i | \(0.878861\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | 0.0857864 | + | 0.148586i | 0.0178877 | + | 0.0309824i | 0.874831 | − | 0.484429i | \(-0.160973\pi\) |
−0.856943 | + | 0.515411i | \(0.827639\pi\) | |||||||
\(24\) | −2.00000 | + | 3.46410i | −0.408248 | + | 0.707107i | ||||
\(25\) | −7.24264 | + | 12.5446i | −1.44853 | + | 2.50892i | ||||
\(26\) | 0.707107 | + | 1.22474i | 0.138675 | + | 0.240192i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.82843 | 1.08231 | 0.541156 | − | 0.840922i | \(-0.317987\pi\) | ||||
0.541156 | + | 0.840922i | \(0.317987\pi\) | |||||||
\(30\) | 4.41421 | + | 7.64564i | 0.805921 | + | 1.39590i | ||||
\(31\) | 2.62132 | − | 4.54026i | 0.470803 | − | 0.815455i | −0.528639 | − | 0.848847i | \(-0.677298\pi\) |
0.999442 | + | 0.0333918i | \(0.0106309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | − | 5.19615i | −0.522233 | − | 0.904534i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12132 | + | 5.40629i | 0.513142 | + | 0.888788i | 0.999884 | + | 0.0152420i | \(0.00485188\pi\) |
−0.486742 | + | 0.873546i | \(0.661815\pi\) | |||||||
\(38\) | −0.878680 | + | 1.52192i | −0.142541 | + | 0.246888i | ||||
\(39\) | −0.707107 | + | 1.22474i | −0.113228 | + | 0.196116i | ||||
\(40\) | 6.24264 | + | 10.8126i | 0.987048 | + | 1.70962i | ||||
\(41\) | 3.17157 | 0.495316 | 0.247658 | − | 0.968847i | \(-0.420339\pi\) | ||||
0.247658 | + | 0.968847i | \(0.420339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.20711 | − | 3.82282i | 0.329016 | − | 0.569873i | ||||
\(46\) | 0.121320 | − | 0.210133i | 0.0178877 | − | 0.0309824i | ||||
\(47\) | −2.20711 | − | 3.82282i | −0.321940 | − | 0.557616i | 0.658949 | − | 0.752188i | \(-0.271001\pi\) |
−0.980888 | + | 0.194572i | \(0.937668\pi\) | |||||||
\(48\) | 5.65685 | 0.816497 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 20.4853 | 2.89706 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.91421 | − | 5.04757i | 0.400298 | − | 0.693337i | −0.593464 | − | 0.804861i | \(-0.702240\pi\) |
0.993762 | + | 0.111524i | \(0.0355733\pi\) | |||||||
\(54\) | −4.00000 | − | 6.92820i | −0.544331 | − | 0.942809i | ||||
\(55\) | −18.7279 | −2.52527 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.75736 | −0.232768 | ||||||||
\(58\) | −4.12132 | − | 7.13834i | −0.541156 | − | 0.937309i | ||||
\(59\) | −5.82843 | + | 10.0951i | −0.758797 | + | 1.31427i | 0.184668 | + | 0.982801i | \(0.440879\pi\) |
−0.943465 | + | 0.331473i | \(0.892454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | −7.41421 | −0.941606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 2.20711 | + | 3.82282i | 0.273758 | + | 0.474163i | ||||
\(66\) | −4.24264 | + | 7.34847i | −0.522233 | + | 0.904534i | ||||
\(67\) | −1.24264 | + | 2.15232i | −0.151813 | + | 0.262947i | −0.931894 | − | 0.362731i | \(-0.881844\pi\) |
0.780081 | + | 0.625678i | \(0.215178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.242641 | 0.0292105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.07107 | 0.127112 | 0.0635562 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635562 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(72\) | −1.41421 | − | 2.44949i | −0.166667 | − | 0.288675i | ||||
\(73\) | 0.378680 | − | 0.655892i | 0.0443211 | − | 0.0767664i | −0.843014 | − | 0.537892i | \(-0.819221\pi\) |
0.887335 | + | 0.461125i | \(0.152554\pi\) | |||||||
\(74\) | 4.41421 | − | 7.64564i | 0.513142 | − | 0.888788i | ||||
\(75\) | 10.2426 | + | 17.7408i | 1.18272 | + | 2.04853i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 0.742641 | + | 1.28629i | 0.0835536 | + | 0.144719i | 0.904774 | − | 0.425892i | \(-0.140040\pi\) |
−0.821220 | + | 0.570611i | \(0.806706\pi\) | |||||||
\(80\) | 8.82843 | − | 15.2913i | 0.987048 | − | 1.70962i | ||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | −2.24264 | − | 3.88437i | −0.247658 | − | 0.428957i | ||||
\(83\) | 4.75736 | 0.522188 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.24264 | −0.677109 | ||||||||
\(86\) | 3.53553 | + | 6.12372i | 0.381246 | + | 0.660338i | ||||
\(87\) | 4.12132 | − | 7.13834i | 0.441852 | − | 0.765310i | ||||
\(88\) | −6.00000 | + | 10.3923i | −0.639602 | + | 1.10782i | ||||
\(89\) | −2.20711 | − | 3.82282i | −0.233953 | − | 0.405218i | 0.725015 | − | 0.688733i | \(-0.241833\pi\) |
−0.958968 | + | 0.283515i | \(0.908499\pi\) | |||||||
\(90\) | −6.24264 | −0.658032 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.70711 | − | 6.42090i | −0.384409 | − | 0.665816i | ||||
\(94\) | −3.12132 | + | 5.40629i | −0.321940 | + | 0.557616i | ||||
\(95\) | −2.74264 | + | 4.75039i | −0.281389 | + | 0.487380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7279 | −1.39386 | −0.696930 | − | 0.717139i | \(-0.745451\pi\) | ||||
−0.696930 | + | 0.717139i | \(0.745451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.878680 | + | 1.52192i | −0.0874319 | + | 0.151436i | −0.906425 | − | 0.422367i | \(-0.861199\pi\) |
0.818993 | + | 0.573803i | \(0.194533\pi\) | |||||||
\(102\) | −1.41421 | + | 2.44949i | −0.140028 | + | 0.242536i | ||||
\(103\) | 4.00000 | + | 6.92820i | 0.394132 | + | 0.682656i | 0.992990 | − | 0.118199i | \(-0.0377120\pi\) |
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.24264 | −0.800596 | ||||||||
\(107\) | −4.07107 | − | 7.05130i | −0.393565 | − | 0.681675i | 0.599352 | − | 0.800486i | \(-0.295425\pi\) |
−0.992917 | + | 0.118811i | \(0.962092\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.36396 | − | 7.55860i | 0.417992 | − | 0.723983i | −0.577746 | − | 0.816217i | \(-0.696067\pi\) |
0.995737 | + | 0.0922340i | \(0.0294008\pi\) | |||||||
\(110\) | 13.2426 | + | 22.9369i | 1.26264 | + | 2.18695i | ||||
\(111\) | 8.82843 | 0.837957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.3137 | −1.91095 | −0.955476 | − | 0.295067i | \(-0.904658\pi\) | ||||
−0.955476 | + | 0.295067i | \(0.904658\pi\) | |||||||
\(114\) | 1.24264 | + | 2.15232i | 0.116384 | + | 0.201583i | ||||
\(115\) | 0.378680 | − | 0.655892i | 0.0353121 | − | 0.0611623i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | 16.4853 | 1.51759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.6569 | 1.61184 | ||||||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | −4.24264 | + | 7.34847i | −0.384111 | + | 0.665299i | ||||
\(123\) | 2.24264 | − | 3.88437i | 0.202212 | − | 0.350242i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.8701 | 3.74497 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.500000 | − | 0.866025i | ||||
\(129\) | −3.53553 | + | 6.12372i | −0.311286 | + | 0.539164i | ||||
\(130\) | 3.12132 | − | 5.40629i | 0.273758 | − | 0.474163i | ||||
\(131\) | −1.41421 | − | 2.44949i | −0.123560 | − | 0.214013i | 0.797609 | − | 0.603175i | \(-0.206098\pi\) |
−0.921169 | + | 0.389162i | \(0.872765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.51472 | 0.303625 | ||||||||
\(135\) | −12.4853 | − | 21.6251i | −1.07456 | − | 1.86120i | ||||
\(136\) | −2.00000 | + | 3.46410i | −0.171499 | + | 0.297044i | ||||
\(137\) | 3.70711 | − | 6.42090i | 0.316720 | − | 0.548574i | −0.663082 | − | 0.748547i | \(-0.730752\pi\) |
0.979802 | + | 0.199972i | \(0.0640853\pi\) | |||||||
\(138\) | −0.171573 | − | 0.297173i | −0.0146053 | − | 0.0252970i | ||||
\(139\) | −2.24264 | −0.190218 | −0.0951092 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951092 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24264 | −0.525725 | ||||||||
\(142\) | −0.757359 | − | 1.31178i | −0.0635562 | − | 0.110083i | ||||
\(143\) | −2.12132 | + | 3.67423i | −0.177394 | + | 0.307255i | ||||
\(144\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(145\) | −12.8640 | − | 22.2810i | −1.06829 | − | 1.85034i | ||||
\(146\) | −1.07107 | −0.0886422 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.87868 | − | 6.71807i | −0.317754 | − | 0.550366i | 0.662265 | − | 0.749270i | \(-0.269595\pi\) |
−0.980019 | + | 0.198904i | \(0.936262\pi\) | |||||||
\(150\) | 14.4853 | − | 25.0892i | 1.18272 | − | 2.04853i | ||||
\(151\) | 9.12132 | − | 15.7986i | 0.742283 | − | 1.28567i | −0.209171 | − | 0.977879i | \(-0.567077\pi\) |
0.951454 | − | 0.307792i | \(-0.0995901\pi\) | |||||||
\(152\) | 1.75736 | + | 3.04384i | 0.142541 | + | 0.246888i | ||||
\(153\) | 1.41421 | 0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.1421 | −1.85882 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.12132 | − | 10.6024i | 0.488535 | − | 0.846167i | −0.511378 | − | 0.859356i | \(-0.670865\pi\) |
0.999913 | + | 0.0131889i | \(0.00419829\pi\) | |||||||
\(158\) | 1.05025 | − | 1.81909i | 0.0835536 | − | 0.144719i | ||||
\(159\) | −4.12132 | − | 7.13834i | −0.326842 | − | 0.566107i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.07107 | −0.555556 | ||||||||
\(163\) | 4.24264 | + | 7.34847i | 0.332309 | + | 0.575577i | 0.982964 | − | 0.183797i | \(-0.0588389\pi\) |
−0.650655 | + | 0.759374i | \(0.725506\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.2426 | + | 22.9369i | −1.03094 | + | 1.78564i | ||||
\(166\) | −3.36396 | − | 5.82655i | −0.261094 | − | 0.452228i | ||||
\(167\) | −21.3848 | −1.65480 | −0.827402 | − | 0.561610i | \(-0.810182\pi\) | ||||
−0.827402 | + | 0.561610i | \(0.810182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.41421 | + | 7.64564i | 0.338555 | + | 0.586394i | ||||
\(171\) | 0.621320 | − | 1.07616i | 0.0475136 | − | 0.0822959i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.363961 | + | 0.630399i | 0.0276714 | + | 0.0479283i | 0.879530 | − | 0.475844i | \(-0.157857\pi\) |
−0.851858 | + | 0.523773i | \(0.824524\pi\) | |||||||
\(174\) | −11.6569 | −0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.9706 | 1.27920 | ||||||||
\(177\) | 8.24264 | + | 14.2767i | 0.619555 | + | 1.07310i | ||||
\(178\) | −3.12132 | + | 5.40629i | −0.233953 | + | 0.405218i | ||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72792 | 0.500083 | 0.250041 | − | 0.968235i | \(-0.419556\pi\) | ||||
0.250041 | + | 0.968235i | \(0.419556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.48528 | −0.627250 | ||||||||
\(184\) | −0.242641 | − | 0.420266i | −0.0178877 | − | 0.0309824i | ||||
\(185\) | 13.7782 | − | 23.8645i | 1.01299 | − | 1.75455i | ||||
\(186\) | −5.24264 | + | 9.08052i | −0.384409 | + | 0.665816i | ||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.75736 | 0.562778 | ||||||||
\(191\) | −10.4142 | − | 18.0379i | −0.753546 | − | 1.30518i | −0.946094 | − | 0.323892i | \(-0.895008\pi\) |
0.192548 | − | 0.981288i | \(-0.438325\pi\) | |||||||
\(192\) | 5.65685 | − | 9.79796i | 0.408248 | − | 0.707107i | ||||
\(193\) | −1.24264 | + | 2.15232i | −0.0894472 | + | 0.154927i | −0.907278 | − | 0.420532i | \(-0.861843\pi\) |
0.817830 | + | 0.575459i | \(0.195177\pi\) | |||||||
\(194\) | 9.70711 | + | 16.8132i | 0.696930 | + | 1.20712i | ||||
\(195\) | 6.24264 | 0.447045 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6569 | 1.68548 | 0.842741 | − | 0.538320i | \(-0.180941\pi\) | ||||
0.842741 | + | 0.538320i | \(0.180941\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | 6.12132 | − | 10.6024i | 0.433929 | − | 0.751587i | −0.563279 | − | 0.826267i | \(-0.690460\pi\) |
0.997208 | + | 0.0746801i | \(0.0237936\pi\) | |||||||
\(200\) | 20.4853 | − | 35.4815i | 1.44853 | − | 2.50892i | ||||
\(201\) | 1.75736 | + | 3.04384i | 0.123955 | + | 0.214696i | ||||
\(202\) | 2.48528 | 0.174864 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00000 | − | 12.1244i | −0.488901 | − | 0.846802i | ||||
\(206\) | 5.65685 | − | 9.79796i | 0.394132 | − | 0.682656i | ||||
\(207\) | −0.0857864 | + | 0.148586i | −0.00596257 | + | 0.0103275i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.138675 | − | 0.240192i | ||||
\(209\) | −5.27208 | −0.364677 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9706 | 1.23714 | 0.618572 | − | 0.785728i | \(-0.287711\pi\) | ||||
0.618572 | + | 0.785728i | \(0.287711\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.757359 | − | 1.31178i | 0.0518934 | − | 0.0898820i | ||||
\(214\) | −5.75736 | + | 9.97204i | −0.393565 | + | 0.681675i | ||||
\(215\) | 11.0355 | + | 19.1141i | 0.752617 | + | 1.30357i | ||||
\(216\) | −16.0000 | −1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.3431 | −0.835983 | ||||||||
\(219\) | −0.535534 | − | 0.927572i | −0.0361880 | − | 0.0626795i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.707107 | + | 1.22474i | −0.0475651 | + | 0.0823853i | ||||
\(222\) | −6.24264 | − | 10.8126i | −0.418979 | − | 0.725692i | ||||
\(223\) | 9.24264 | 0.618933 | 0.309466 | − | 0.950910i | \(-0.399850\pi\) | ||||
0.309466 | + | 0.950910i | \(0.399850\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.4853 | −0.965685 | ||||||||
\(226\) | 14.3640 | + | 24.8791i | 0.955476 | + | 1.65493i | ||||
\(227\) | −10.5858 | + | 18.3351i | −0.702603 | + | 1.21694i | 0.264946 | + | 0.964263i | \(0.414646\pi\) |
−0.967550 | + | 0.252681i | \(0.918688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7279 | + | 18.5813i | 0.708921 | + | 1.22789i | 0.965258 | + | 0.261300i | \(0.0841511\pi\) |
−0.256337 | + | 0.966588i | \(0.582516\pi\) | |||||||
\(230\) | −1.07107 | −0.0706241 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.4853 | −1.08231 | ||||||||
\(233\) | 1.67157 | + | 2.89525i | 0.109508 | + | 0.189674i | 0.915571 | − | 0.402156i | \(-0.131739\pi\) |
−0.806063 | + | 0.591830i | \(0.798406\pi\) | |||||||
\(234\) | −0.707107 | + | 1.22474i | −0.0462250 | + | 0.0800641i | ||||
\(235\) | −9.74264 | + | 16.8747i | −0.635540 | + | 1.10079i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.10051 | 0.136442 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4853 | 1.32508 | 0.662541 | − | 0.749025i | \(-0.269478\pi\) | ||||
0.662541 | + | 0.749025i | \(0.269478\pi\) | |||||||
\(240\) | −12.4853 | − | 21.6251i | −0.805921 | − | 1.39590i | ||||
\(241\) | −11.1066 | + | 19.2372i | −0.715439 | + | 1.23918i | 0.247351 | + | 0.968926i | \(0.420440\pi\) |
−0.962790 | + | 0.270251i | \(0.912893\pi\) | |||||||
\(242\) | −4.94975 | + | 8.57321i | −0.318182 | + | 0.551107i | ||||
\(243\) | 4.94975 | + | 8.57321i | 0.317526 | + | 0.549972i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.34315 | −0.404424 | ||||||||
\(247\) | 0.621320 | + | 1.07616i | 0.0395337 | + | 0.0684743i | ||||
\(248\) | −7.41421 | + | 12.8418i | −0.470803 | + | 0.815455i | ||||
\(249\) | 3.36396 | − | 5.82655i | 0.213182 | − | 0.369243i | ||||
\(250\) | −29.6066 | − | 51.2801i | −1.87249 | − | 3.24324i | ||||
\(251\) | 19.4142 | 1.22541 | 0.612707 | − | 0.790310i | \(-0.290081\pi\) | ||||
0.612707 | + | 0.790310i | \(0.290081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.727922 | 0.0457641 | ||||||||
\(254\) | −1.41421 | − | 2.44949i | −0.0887357 | − | 0.153695i | ||||
\(255\) | −4.41421 | + | 7.64564i | −0.276429 | + | 0.478789i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.29289 | + | 14.3637i | 0.517296 | + | 0.895984i | 0.999798 | + | 0.0200887i | \(0.00639488\pi\) |
−0.482502 | + | 0.875895i | \(0.660272\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.91421 | + | 5.04757i | 0.180385 | + | 0.312436i | ||||
\(262\) | −2.00000 | + | 3.46410i | −0.123560 | + | 0.214013i | ||||
\(263\) | 15.9853 | − | 27.6873i | 0.985695 | − | 1.70727i | 0.346887 | − | 0.937907i | \(-0.387239\pi\) |
0.638808 | − | 0.769366i | \(-0.279428\pi\) | |||||||
\(264\) | 8.48528 | + | 14.6969i | 0.522233 | + | 0.904534i | ||||
\(265\) | −25.7279 | −1.58045 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24264 | −0.382043 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.41421 | + | 12.8418i | −0.452053 | + | 0.782978i | −0.998513 | − | 0.0545066i | \(-0.982641\pi\) |
0.546461 | + | 0.837485i | \(0.315975\pi\) | |||||||
\(270\) | −17.6569 | + | 30.5826i | −1.07456 | + | 1.86120i | ||||
\(271\) | −10.0000 | − | 17.3205i | −0.607457 | − | 1.05215i | −0.991658 | − | 0.128897i | \(-0.958856\pi\) |
0.384201 | − | 0.923249i | \(-0.374477\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4853 | −0.633439 | ||||||||
\(275\) | 30.7279 | + | 53.2223i | 1.85296 | + | 3.20943i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.74264 | + | 8.21449i | −0.284958 | + | 0.493561i | −0.972599 | − | 0.232489i | \(-0.925313\pi\) |
0.687641 | + | 0.726051i | \(0.258646\pi\) | |||||||
\(278\) | 1.58579 | + | 2.74666i | 0.0951092 | + | 0.164734i | ||||
\(279\) | 5.24264 | 0.313869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.5563 | −0.928014 | −0.464007 | − | 0.885832i | \(-0.653589\pi\) | ||||
−0.464007 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(282\) | 4.41421 | + | 7.64564i | 0.262863 | + | 0.455291i | ||||
\(283\) | −4.24264 | + | 7.34847i | −0.252199 | + | 0.436821i | −0.964131 | − | 0.265427i | \(-0.914487\pi\) |
0.711932 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.87868 | + | 6.71807i | 0.229753 | + | 0.397944i | ||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | + | 12.9904i | 0.441176 | + | 0.764140i | ||||
\(290\) | −18.1924 | + | 31.5101i | −1.06829 | + | 1.85034i | ||||
\(291\) | −9.70711 | + | 16.8132i | −0.569041 | + | 0.985607i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3848 | −1.24931 | −0.624656 | − | 0.780900i | \(-0.714761\pi\) | ||||
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 51.4558 | 2.99588 | ||||||||
\(296\) | −8.82843 | − | 15.2913i | −0.513142 | − | 0.888788i | ||||
\(297\) | 12.0000 | − | 20.7846i | 0.696311 | − | 1.20605i | ||||
\(298\) | −5.48528 | + | 9.50079i | −0.317754 | + | 0.550366i | ||||
\(299\) | −0.0857864 | − | 0.148586i | −0.00496116 | − | 0.00859298i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.7990 | −1.48457 | ||||||||
\(303\) | 1.24264 | + | 2.15232i | 0.0713878 | + | 0.123647i | ||||
\(304\) | 2.48528 | − | 4.30463i | 0.142541 | − | 0.246888i | ||||
\(305\) | −13.2426 | + | 22.9369i | −0.758271 | + | 1.31336i | ||||
\(306\) | −1.00000 | − | 1.73205i | −0.0571662 | − | 0.0990148i | ||||
\(307\) | 4.75736 | 0.271517 | 0.135758 | − | 0.990742i | \(-0.456653\pi\) | ||||
0.135758 | + | 0.990742i | \(0.456653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.3137 | 0.643614 | ||||||||
\(310\) | 16.3640 | + | 28.3432i | 0.929411 | + | 1.60979i | ||||
\(311\) | 2.29289 | − | 3.97141i | 0.130018 | − | 0.225198i | −0.793665 | − | 0.608355i | \(-0.791830\pi\) |
0.923683 | + | 0.383157i | \(0.125163\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 9.60660 | + | 16.6391i | 0.542997 | + | 0.940499i | 0.998730 | + | 0.0503822i | \(0.0160439\pi\) |
−0.455733 | + | 0.890117i | \(0.650623\pi\) | |||||||
\(314\) | −17.3137 | −0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.65685 | − | 9.79796i | −0.317721 | − | 0.550308i | 0.662291 | − | 0.749246i | \(-0.269584\pi\) |
−0.980012 | + | 0.198938i | \(0.936251\pi\) | |||||||
\(318\) | −5.82843 | + | 10.0951i | −0.326842 | + | 0.566107i | ||||
\(319\) | 12.3640 | − | 21.4150i | 0.692249 | − | 1.19901i | ||||
\(320\) | −17.6569 | − | 30.5826i | −0.987048 | − | 1.70962i | ||||
\(321\) | −11.5147 | −0.642689 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.75736 | −0.0977821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.24264 | − | 12.5446i | 0.401749 | − | 0.695850i | ||||
\(326\) | 6.00000 | − | 10.3923i | 0.332309 | − | 0.575577i | ||||
\(327\) | −6.17157 | − | 10.6895i | −0.341289 | − | 0.591129i | ||||
\(328\) | −8.97056 | −0.495316 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 37.4558 | 2.06188 | ||||||||
\(331\) | 9.00000 | + | 15.5885i | 0.494685 | + | 0.856819i | 0.999981 | − | 0.00612670i | \(-0.00195020\pi\) |
−0.505296 | + | 0.862946i | \(0.668617\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.12132 | + | 5.40629i | −0.171047 | + | 0.296263i | ||||
\(334\) | 15.1213 | + | 26.1909i | 0.827402 | + | 1.43310i | ||||
\(335\) | 10.9706 | 0.599386 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | −0.707107 | − | 1.22474i | −0.0384615 | − | 0.0666173i | ||||
\(339\) | −14.3640 | + | 24.8791i | −0.780143 | + | 1.35125i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1213 | − | 19.2627i | −0.602253 | − | 1.04313i | ||||
\(342\) | −1.75736 | −0.0950271 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.1421 | 0.762493 | ||||||||
\(345\) | −0.535534 | − | 0.927572i | −0.0288322 | − | 0.0499388i | ||||
\(346\) | 0.514719 | − | 0.891519i | 0.0276714 | − | 0.0479283i | ||||
\(347\) | −2.82843 | + | 4.89898i | −0.151838 | + | 0.262991i | −0.931903 | − | 0.362707i | \(-0.881853\pi\) |
0.780065 | + | 0.625698i | \(0.215186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.272078 | −0.0145640 | −0.00728200 | − | 0.999973i | \(-0.502318\pi\) | ||||
−0.00728200 | + | 0.999973i | \(0.502318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.24264 | + | 7.34847i | −0.225813 | + | 0.391120i | −0.956563 | − | 0.291526i | \(-0.905837\pi\) |
0.730750 | + | 0.682645i | \(0.239170\pi\) | |||||||
\(354\) | 11.6569 | − | 20.1903i | 0.619555 | − | 1.07310i | ||||
\(355\) | −2.36396 | − | 4.09450i | −0.125466 | − | 0.217314i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.7279 | −0.672692 | ||||||||
\(359\) | 4.05025 | + | 7.01524i | 0.213764 | + | 0.370250i | 0.952890 | − | 0.303317i | \(-0.0980943\pi\) |
−0.739125 | + | 0.673568i | \(0.764761\pi\) | |||||||
\(360\) | −6.24264 | + | 10.8126i | −0.329016 | + | 0.569873i | ||||
\(361\) | 8.72792 | − | 15.1172i | 0.459364 | − | 0.795642i | ||||
\(362\) | −4.75736 | − | 8.23999i | −0.250041 | − | 0.433084i | ||||
\(363\) | −9.89949 | −0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.34315 | −0.174988 | ||||||||
\(366\) | 6.00000 | + | 10.3923i | 0.313625 | + | 0.543214i | ||||
\(367\) | −0.878680 | + | 1.52192i | −0.0458667 | + | 0.0794435i | −0.888047 | − | 0.459752i | \(-0.847938\pi\) |
0.842181 | + | 0.539196i | \(0.181272\pi\) | |||||||
\(368\) | −0.343146 | + | 0.594346i | −0.0178877 | + | 0.0309824i | ||||
\(369\) | 1.58579 | + | 2.74666i | 0.0825527 | + | 0.142986i | ||||
\(370\) | −38.9706 | −2.02598 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24264 | + | 7.34847i | 0.219676 | + | 0.380489i | 0.954709 | − | 0.297542i | \(-0.0961668\pi\) |
−0.735033 | + | 0.678031i | \(0.762833\pi\) | |||||||
\(374\) | −4.24264 | + | 7.34847i | −0.219382 | + | 0.379980i | ||||
\(375\) | 29.6066 | − | 51.2801i | 1.52888 | − | 2.64809i | ||||
\(376\) | 6.24264 | + | 10.8126i | 0.321940 | + | 0.557616i | ||||
\(377\) | −5.82843 | −0.300179 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.2426 | 1.65619 | 0.828097 | − | 0.560585i | \(-0.189424\pi\) | ||||
0.828097 | + | 0.560585i | \(0.189424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.41421 | − | 2.44949i | 0.0724524 | − | 0.125491i | ||||
\(382\) | −14.7279 | + | 25.5095i | −0.753546 | + | 1.30518i | ||||
\(383\) | 1.75736 | + | 3.04384i | 0.0897969 | + | 0.155533i | 0.907425 | − | 0.420214i | \(-0.138045\pi\) |
−0.817628 | + | 0.575746i | \(0.804712\pi\) | |||||||
\(384\) | −16.0000 | −0.816497 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.51472 | 0.178894 | ||||||||
\(387\) | −2.50000 | − | 4.33013i | −0.127082 | − | 0.220113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.17157 | + | 15.8856i | −0.465017 | + | 0.805433i | −0.999202 | − | 0.0399341i | \(-0.987285\pi\) |
0.534185 | + | 0.845368i | \(0.320619\pi\) | |||||||
\(390\) | −4.41421 | − | 7.64564i | −0.223522 | − | 0.387152i | ||||
\(391\) | 0.242641 | 0.0122709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −16.7279 | − | 28.9736i | −0.842741 | − | 1.45967i | ||||
\(395\) | 3.27817 | − | 5.67796i | 0.164943 | − | 0.285689i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1066 | − | 20.9692i | −0.607613 | − | 1.05242i | −0.991633 | − | 0.129092i | \(-0.958794\pi\) |
0.384020 | − | 0.923325i | \(-0.374539\pi\) | |||||||
\(398\) | −17.3137 | −0.867858 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −57.9411 | −2.89706 | ||||||||
\(401\) | −8.82843 | − | 15.2913i | −0.440871 | − | 0.763610i | 0.556884 | − | 0.830590i | \(-0.311997\pi\) |
−0.997754 | + | 0.0669802i | \(0.978664\pi\) | |||||||
\(402\) | 2.48528 | − | 4.30463i | 0.123955 | − | 0.214696i | ||||
\(403\) | −2.62132 | + | 4.54026i | −0.130577 | + | 0.226166i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.0711 | −1.09672 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.4853 | 1.31283 | ||||||||
\(408\) | 2.82843 | + | 4.89898i | 0.140028 | + | 0.242536i | ||||
\(409\) | 2.62132 | − | 4.54026i | 0.129616 | − | 0.224501i | −0.793912 | − | 0.608033i | \(-0.791959\pi\) |
0.923528 | + | 0.383531i | \(0.125292\pi\) | |||||||
\(410\) | −9.89949 | + | 17.1464i | −0.488901 | + | 0.846802i | ||||
\(411\) | −5.24264 | − | 9.08052i | −0.258600 | − | 0.447909i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.242641 | 0.0119251 | ||||||||
\(415\) | −10.5000 | − | 18.1865i | −0.515425 | − | 0.892742i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.58579 | + | 2.74666i | −0.0776563 | + | 0.134505i | ||||
\(418\) | 3.72792 | + | 6.45695i | 0.182339 | + | 0.315820i | ||||
\(419\) | 32.8701 | 1.60581 | 0.802904 | − | 0.596109i | \(-0.203287\pi\) | ||||
0.802904 | + | 0.596109i | \(0.203287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.7279 | −0.912743 | −0.456372 | − | 0.889789i | \(-0.650851\pi\) | ||||
−0.456372 | + | 0.889789i | \(0.650851\pi\) | |||||||
\(422\) | −12.7071 | − | 22.0094i | −0.618572 | − | 1.07140i | ||||
\(423\) | 2.20711 | − | 3.82282i | 0.107313 | − | 0.185872i | ||||
\(424\) | −8.24264 | + | 14.2767i | −0.400298 | + | 0.693337i | ||||
\(425\) | 10.2426 | + | 17.7408i | 0.496841 | + | 0.860554i | ||||
\(426\) | −2.14214 | −0.103787 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00000 | + | 5.19615i | 0.144841 | + | 0.250873i | ||||
\(430\) | 15.6066 | − | 27.0314i | 0.752617 | − | 1.30357i | ||||
\(431\) | 11.8284 | − | 20.4874i | 0.569755 | − | 0.986845i | −0.426835 | − | 0.904330i | \(-0.640371\pi\) |
0.996590 | − | 0.0825154i | \(-0.0262953\pi\) | |||||||
\(432\) | 11.3137 | + | 19.5959i | 0.544331 | + | 0.942809i | ||||
\(433\) | 8.97056 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −36.3848 | −1.74452 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.106602 | − | 0.184640i | 0.00509945 | − | 0.00883251i | ||||
\(438\) | −0.757359 | + | 1.31178i | −0.0361880 | + | 0.0626795i | ||||
\(439\) | 8.75736 | + | 15.1682i | 0.417966 | + | 0.723938i | 0.995735 | − | 0.0922622i | \(-0.0294098\pi\) |
−0.577769 | + | 0.816200i | \(0.696076\pi\) | |||||||
\(440\) | 52.9706 | 2.52527 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 13.1569 | + | 22.7883i | 0.625101 | + | 1.08271i | 0.988521 | + | 0.151081i | \(0.0482756\pi\) |
−0.363420 | + | 0.931625i | \(0.618391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.74264 | + | 16.8747i | −0.461845 | + | 0.799940i | ||||
\(446\) | −6.53553 | − | 11.3199i | −0.309466 | − | 0.536012i | ||||
\(447\) | −10.9706 | −0.518890 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8284 | 1.26611 | 0.633056 | − | 0.774106i | \(-0.281800\pi\) | ||||
0.633056 | + | 0.774106i | \(0.281800\pi\) | |||||||
\(450\) | 10.2426 | + | 17.7408i | 0.482843 | + | 0.836308i | ||||
\(451\) | 6.72792 | − | 11.6531i | 0.316805 | − | 0.548723i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.8995 | − | 22.3426i | −0.606071 | − | 1.04975i | ||||
\(454\) | 29.9411 | 1.40521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.97056 | 0.232768 | ||||||||
\(457\) | −17.6066 | − | 30.4955i | −0.823602 | − | 1.42652i | −0.902983 | − | 0.429676i | \(-0.858628\pi\) |
0.0793809 | − | 0.996844i | \(-0.474706\pi\) | |||||||
\(458\) | 15.1716 | − | 26.2779i | 0.708921 | − | 1.22789i | ||||
\(459\) | 4.00000 | − | 6.92820i | 0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.17157 | 0.147715 | 0.0738574 | − | 0.997269i | \(-0.476469\pi\) | ||||
0.0738574 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.24264 | 0.197172 | 0.0985861 | − | 0.995129i | \(-0.468568\pi\) | ||||
0.0985861 | + | 0.995129i | \(0.468568\pi\) | |||||||
\(464\) | 11.6569 | + | 20.1903i | 0.541156 | + | 0.937309i | ||||
\(465\) | −16.3640 | + | 28.3432i | −0.758861 | + | 1.31438i | ||||
\(466\) | 2.36396 | − | 4.09450i | 0.109508 | − | 0.189674i | ||||
\(467\) | −7.94975 | − | 13.7694i | −0.367870 | − | 0.637170i | 0.621362 | − | 0.783524i | \(-0.286580\pi\) |
−0.989232 | + | 0.146353i | \(0.953246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 27.5563 | 1.27108 | ||||||||
\(471\) | −8.65685 | − | 14.9941i | −0.398887 | − | 0.690892i | ||||
\(472\) | 16.4853 | − | 28.5533i | 0.758797 | − | 1.31427i | ||||
\(473\) | −10.6066 | + | 18.3712i | −0.487692 | + | 0.844707i | ||||
\(474\) | −1.48528 | − | 2.57258i | −0.0682212 | − | 0.118163i | ||||
\(475\) | 18.0000 | 0.825897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.82843 | 0.266865 | ||||||||
\(478\) | −14.4853 | − | 25.0892i | −0.662541 | − | 1.14756i | ||||
\(479\) | −18.1066 | + | 31.3616i | −0.827312 | + | 1.43295i | 0.0728279 | + | 0.997345i | \(0.476798\pi\) |
−0.900140 | + | 0.435601i | \(0.856536\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.12132 | − | 5.40629i | −0.142320 | − | 0.246505i | ||||
\(482\) | 31.4142 | 1.43088 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.2990 | + | 52.4794i | 1.37581 | + | 2.38297i | ||||
\(486\) | 7.00000 | − | 12.1244i | 0.317526 | − | 0.549972i | ||||
\(487\) | −19.7279 | + | 34.1698i | −0.893957 | + | 1.54838i | −0.0588679 | + | 0.998266i | \(0.518749\pi\) |
−0.835090 | + | 0.550114i | \(0.814584\pi\) | |||||||
\(488\) | 8.48528 | + | 14.6969i | 0.384111 | + | 0.665299i | ||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6274 | −1.29194 | −0.645969 | − | 0.763364i | \(-0.723546\pi\) | ||||
−0.645969 | + | 0.763364i | \(0.723546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.12132 | − | 7.13834i | 0.185615 | − | 0.321494i | ||||
\(494\) | 0.878680 | − | 1.52192i | 0.0395337 | − | 0.0684743i | ||||
\(495\) | −9.36396 | − | 16.2189i | −0.420879 | − | 0.728983i | ||||
\(496\) | 20.9706 | 0.941606 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.51472 | −0.426365 | ||||||||
\(499\) | 19.3640 | + | 33.5394i | 0.866850 | + | 1.50143i | 0.865198 | + | 0.501430i | \(0.167192\pi\) |
0.00165145 | + | 0.999999i | \(0.499474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1213 | + | 26.1909i | −0.675571 | + | 1.17012i | ||||
\(502\) | −13.7279 | − | 23.7775i | −0.612707 | − | 1.06124i | ||||
\(503\) | 16.6274 | 0.741380 | 0.370690 | − | 0.928757i | \(-0.379121\pi\) | ||||
0.370690 | + | 0.928757i | \(0.379121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.75736 | 0.345198 | ||||||||
\(506\) | −0.514719 | − | 0.891519i | −0.0228820 | − | 0.0396328i | ||||
\(507\) | 0.707107 | − | 1.22474i | 0.0314037 | − | 0.0543928i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4497 | + | 21.5636i | 0.551825 | + | 0.955790i | 0.998143 | + | 0.0609149i | \(0.0194018\pi\) |
−0.446318 | + | 0.894875i | \(0.647265\pi\) | |||||||
\(510\) | 12.4853 | 0.552858 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −3.51472 | − | 6.08767i | −0.155179 | − | 0.268777i | ||||
\(514\) | 11.7279 | − | 20.3134i | 0.517296 | − | 0.895984i | ||||
\(515\) | 17.6569 | − | 30.5826i | 0.778054 | − | 1.34763i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.7279 | −0.823653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.02944 | 0.0451873 | ||||||||
\(520\) | −6.24264 | − | 10.8126i | −0.273758 | − | 0.474163i | ||||
\(521\) | 8.82843 | − | 15.2913i | 0.386780 | − | 0.669923i | −0.605234 | − | 0.796048i | \(-0.706920\pi\) |
0.992014 | + | 0.126124i | \(0.0402538\pi\) | |||||||
\(522\) | 4.12132 | − | 7.13834i | 0.180385 | − | 0.312436i | ||||
\(523\) | 1.48528 | + | 2.57258i | 0.0649468 | + | 0.112491i | 0.896670 | − | 0.442699i | \(-0.145979\pi\) |
−0.831724 | + | 0.555190i | \(0.812646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.2132 | −1.97139 | ||||||||
\(527\) | −3.70711 | − | 6.42090i | −0.161484 | − | 0.279699i | ||||
\(528\) | 12.0000 | − | 20.7846i | 0.522233 | − | 0.904534i | ||||
\(529\) | 11.4853 | − | 19.8931i | 0.499360 | − | 0.864917i | ||||
\(530\) | 18.1924 | + | 31.5101i | 0.790227 | + | 1.36871i | ||||
\(531\) | −11.6569 | −0.505864 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.17157 | −0.137376 | ||||||||
\(534\) | 4.41421 | + | 7.64564i | 0.191022 | + | 0.330859i | ||||
\(535\) | −17.9706 | + | 31.1259i | −0.776935 | + | 1.34569i | ||||
\(536\) | 3.51472 | − | 6.08767i | 0.151813 | − | 0.262947i | ||||
\(537\) | −6.36396 | − | 11.0227i | −0.274625 | − | 0.475665i | ||||
\(538\) | 20.9706 | 0.904105 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6066 | − | 30.4955i | −0.756967 | − | 1.31111i | −0.944391 | − | 0.328826i | \(-0.893347\pi\) |
0.187424 | − | 0.982279i | \(-0.439986\pi\) | |||||||
\(542\) | −14.1421 | + | 24.4949i | −0.607457 | + | 1.05215i | ||||
\(543\) | 4.75736 | − | 8.23999i | 0.204158 | − | 0.353612i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.5269 | −1.65031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5147 | 0.791632 | 0.395816 | − | 0.918330i | \(-0.370462\pi\) | ||||
0.395816 | + | 0.918330i | \(0.370462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 43.4558 | − | 75.2677i | 1.85296 | − | 3.20943i | ||||
\(551\) | −3.62132 | − | 6.27231i | −0.154273 | − | 0.267209i | ||||
\(552\) | −0.686292 | −0.0292105 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.4142 | 0.569915 | ||||||||
\(555\) | −19.4853 | − | 33.7495i | −0.827104 | − | 1.43259i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | + | 10.3923i | −0.254228 | + | 0.440336i | −0.964686 | − | 0.263404i | \(-0.915155\pi\) |
0.710457 | + | 0.703740i | \(0.248488\pi\) | |||||||
\(558\) | −3.70711 | − | 6.42090i | −0.156934 | − | 0.271818i | ||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.48528 | −0.358249 | ||||||||
\(562\) | 11.0000 | + | 19.0526i | 0.464007 | + | 0.803684i | ||||
\(563\) | 8.82843 | − | 15.2913i | 0.372074 | − | 0.644451i | −0.617811 | − | 0.786327i | \(-0.711980\pi\) |
0.989884 | + | 0.141876i | \(0.0453135\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.8345 | + | 77.6557i | 1.88620 | + | 3.26700i | ||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.02944 | −0.127112 | ||||||||
\(569\) | 11.5711 | + | 20.0417i | 0.485084 | + | 0.840191i | 0.999853 | − | 0.0171383i | \(-0.00545554\pi\) |
−0.514769 | + | 0.857329i | \(0.672122\pi\) | |||||||
\(570\) | 5.48528 | − | 9.50079i | 0.229753 | − | 0.397944i | ||||
\(571\) | 4.22792 | − | 7.32298i | 0.176933 | − | 0.306457i | −0.763896 | − | 0.645340i | \(-0.776716\pi\) |
0.940829 | + | 0.338883i | \(0.110049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.4558 | −1.23054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.48528 | −0.103643 | ||||||||
\(576\) | 4.00000 | + | 6.92820i | 0.166667 | + | 0.288675i | ||||
\(577\) | −13.4853 | + | 23.3572i | −0.561400 | + | 0.972373i | 0.435975 | + | 0.899959i | \(0.356404\pi\) |
−0.997375 | + | 0.0724139i | \(0.976930\pi\) | |||||||
\(578\) | 10.6066 | − | 18.3712i | 0.441176 | − | 0.764140i | ||||
\(579\) | 1.75736 | + | 3.04384i | 0.0730334 | + | 0.126497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 27.4558 | 1.13808 | ||||||||
\(583\) | −12.3640 | − | 21.4150i | −0.512063 | − | 0.886919i | ||||
\(584\) | −1.07107 | + | 1.85514i | −0.0443211 | + | 0.0767664i | ||||
\(585\) | −2.20711 | + | 3.82282i | −0.0912526 | + | 0.158054i | ||||
\(586\) | 15.1213 | + | 26.1909i | 0.624656 | + | 1.08194i | ||||
\(587\) | 24.5563 | 1.01355 | 0.506775 | − | 0.862079i | \(-0.330838\pi\) | ||||
0.506775 | + | 0.862079i | \(0.330838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51472 | −0.268434 | ||||||||
\(590\) | −36.3848 | − | 63.0203i | −1.49794 | − | 2.59450i | ||||
\(591\) | 16.7279 | − | 28.9736i | 0.688095 | − | 1.19182i | ||||
\(592\) | −12.4853 | + | 21.6251i | −0.513142 | + | 0.888788i | ||||
\(593\) | −15.2782 | − | 26.4626i | −0.627399 | − | 1.08669i | −0.988072 | − | 0.153995i | \(-0.950786\pi\) |
0.360672 | − | 0.932693i | \(-0.382547\pi\) | |||||||
\(594\) | −33.9411 | −1.39262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.65685 | − | 14.9941i | −0.354301 | − | 0.613668i | ||||
\(598\) | −0.121320 | + | 0.210133i | −0.00496116 | + | 0.00859298i | ||||
\(599\) | −5.39949 | + | 9.35220i | −0.220617 | + | 0.382121i | −0.954996 | − | 0.296620i | \(-0.904141\pi\) |
0.734378 | + | 0.678740i | \(0.237474\pi\) | |||||||
\(600\) | −28.9706 | − | 50.1785i | −1.18272 | − | 2.04853i | ||||
\(601\) | −5.02944 | −0.205155 | −0.102578 | − | 0.994725i | \(-0.532709\pi\) | ||||
−0.102578 | + | 0.994725i | \(0.532709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.48528 | −0.101208 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.4497 | + | 26.7597i | −0.628122 | + | 1.08794i | ||||
\(606\) | 1.75736 | − | 3.04384i | 0.0713878 | − | 0.123647i | ||||
\(607\) | 0.636039 | + | 1.10165i | 0.0258160 | + | 0.0447147i | 0.878645 | − | 0.477476i | \(-0.158448\pi\) |
−0.852829 | + | 0.522191i | \(0.825115\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.4558 | 1.51654 | ||||||||
\(611\) | 2.20711 | + | 3.82282i | 0.0892900 | + | 0.154655i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | −3.36396 | − | 5.82655i | −0.135758 | − | 0.235140i | ||||
\(615\) | −19.7990 | −0.798372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6569 | 0.952389 | 0.476195 | − | 0.879340i | \(-0.342016\pi\) | ||||
0.476195 | + | 0.879340i | \(0.342016\pi\) | |||||||
\(618\) | −8.00000 | − | 13.8564i | −0.321807 | − | 0.557386i | ||||
\(619\) | 16.4853 | − | 28.5533i | 0.662599 | − | 1.14766i | −0.317331 | − | 0.948315i | \(-0.602787\pi\) |
0.979930 | − | 0.199341i | \(-0.0638801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.485281 | + | 0.840532i | 0.0194737 | + | 0.0337294i | ||||
\(622\) | −6.48528 | −0.260036 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.65685 | −0.226455 | ||||||||
\(625\) | −56.1985 | − | 97.3386i | −2.24794 | − | 3.89355i | ||||
\(626\) | 13.5858 | − | 23.5313i | 0.542997 | − | 0.940499i | ||||
\(627\) | −3.72792 | + | 6.45695i | −0.148879 | + | 0.257866i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.82843 | 0.352012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | −2.10051 | − | 3.63818i | −0.0835536 | − | 0.144719i | ||||
\(633\) | 12.7071 | − | 22.0094i | 0.505062 | − | 0.874793i | ||||
\(634\) | −8.00000 | + | 13.8564i | −0.317721 | + | 0.550308i | ||||
\(635\) | −4.41421 | − | 7.64564i | −0.175173 | − | 0.303408i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −34.9706 | −1.38450 | ||||||||
\(639\) | 0.535534 | + | 0.927572i | 0.0211854 | + | 0.0366942i | ||||
\(640\) | −24.9706 | + | 43.2503i | −0.987048 | + | 1.70962i | ||||
\(641\) | −13.3284 | + | 23.0855i | −0.526441 | + | 0.911823i | 0.473084 | + | 0.881017i | \(0.343141\pi\) |
−0.999525 | + | 0.0308057i | \(0.990193\pi\) | |||||||
\(642\) | 8.14214 | + | 14.1026i | 0.321344 | + | 0.556585i | ||||
\(643\) | 4.48528 | 0.176882 | 0.0884411 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884411 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.2132 | 1.22902 | ||||||||
\(646\) | 1.24264 | + | 2.15232i | 0.0488910 | + | 0.0846818i | ||||
\(647\) | 25.2635 | − | 43.7576i | 0.993209 | − | 1.72029i | 0.395847 | − | 0.918316i | \(-0.370451\pi\) |
0.597362 | − | 0.801972i | \(-0.296216\pi\) | |||||||
\(648\) | −7.07107 | + | 12.2474i | −0.277778 | + | 0.481125i | ||||
\(649\) | 24.7279 | + | 42.8300i | 0.970656 | + | 1.68123i | ||||
\(650\) | −20.4853 | −0.803499 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.65685 | + | 4.60181i | 0.103971 | + | 0.180083i | 0.913317 | − | 0.407249i | \(-0.133512\pi\) |
−0.809346 | + | 0.587331i | \(0.800179\pi\) | |||||||
\(654\) | −8.72792 | + | 15.1172i | −0.341289 | + | 0.591129i | ||||
\(655\) | −6.24264 | + | 10.8126i | −0.243920 | + | 0.422482i | ||||
\(656\) | 6.34315 | + | 10.9867i | 0.247658 | + | 0.428957i | ||||
\(657\) | 0.757359 | 0.0295474 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.6569 | −1.03840 | −0.519202 | − | 0.854652i | \(-0.673771\pi\) | ||||
−0.519202 | + | 0.854652i | \(0.673771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.62132 | − | 16.6646i | 0.374226 | − | 0.648178i | −0.615985 | − | 0.787758i | \(-0.711242\pi\) |
0.990211 | + | 0.139580i | \(0.0445751\pi\) | |||||||
\(662\) | 12.7279 | − | 22.0454i | 0.494685 | − | 0.856819i | ||||
\(663\) | 1.00000 | + | 1.73205i | 0.0388368 | + | 0.0672673i | ||||
\(664\) | −13.4558 | −0.522188 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.82843 | 0.342095 | ||||||||
\(667\) | 0.500000 | + | 0.866025i | 0.0193601 | + | 0.0335326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.53553 | − | 11.3199i | 0.252678 | − | 0.437652i | ||||
\(670\) | −7.75736 | − | 13.4361i | −0.299693 | − | 0.519083i | ||||
\(671\) | −25.4558 | −0.982712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.9411 | 1.57816 | 0.789082 | − | 0.614288i | \(-0.210557\pi\) | ||||
0.789082 | + | 0.614288i | \(0.210557\pi\) | |||||||
\(674\) | 23.3345 | + | 40.4166i | 0.898812 | + | 1.55679i | ||||
\(675\) | −40.9706 | + | 70.9631i | −1.57696 | + | 2.73137i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6777 | − | 25.4225i | −0.564109 | − | 0.977065i | −0.997132 | − | 0.0756822i | \(-0.975887\pi\) |
0.433023 | − | 0.901383i | \(-0.357447\pi\) | |||||||
\(678\) | 40.6274 | 1.56029 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.6569 | 0.677109 | ||||||||
\(681\) | 14.9706 | + | 25.9298i | 0.573673 | + | 0.993631i | ||||
\(682\) | −15.7279 | + | 27.2416i | −0.602253 | + | 1.04313i | ||||
\(683\) | 13.4142 | − | 23.2341i | 0.513281 | − | 0.889028i | −0.486601 | − | 0.873624i | \(-0.661763\pi\) |
0.999881 | − | 0.0154036i | \(-0.00490332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.7279 | −1.25047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.3431 | 1.15766 | ||||||||
\(688\) | −10.0000 | − | 17.3205i | −0.381246 | − | 0.660338i | ||||
\(689\) | −2.91421 | + | 5.04757i | −0.111023 | + | 0.192297i | ||||
\(690\) | −0.757359 | + | 1.31178i | −0.0288322 | + | 0.0499388i | ||||
\(691\) | 15.3492 | + | 26.5857i | 0.583913 | + | 1.01137i | 0.995010 | + | 0.0997750i | \(0.0318123\pi\) |
−0.411097 | + | 0.911591i | \(0.634854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.00000 | 0.303676 | ||||||||
\(695\) | 4.94975 | + | 8.57321i | 0.187755 | + | 0.325201i | ||||
\(696\) | −11.6569 | + | 20.1903i | −0.441852 | + | 0.765310i | ||||
\(697\) | 2.24264 | − | 3.88437i | 0.0849461 | − | 0.147131i | ||||
\(698\) | 0.192388 | + | 0.333226i | 0.00728200 | + | 0.0126128i | ||||
\(699\) | 4.72792 | 0.178826 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7990 | 1.08772 | 0.543861 | − | 0.839175i | \(-0.316962\pi\) | ||||
0.543861 | + | 0.839175i | \(0.316962\pi\) | |||||||
\(702\) | 4.00000 | + | 6.92820i | 0.150970 | + | 0.261488i | ||||
\(703\) | 3.87868 | − | 6.71807i | 0.146287 | − | 0.253377i | ||||
\(704\) | 16.9706 | − | 29.3939i | 0.639602 | − | 1.10782i | ||||
\(705\) | 13.7782 | + | 23.8645i | 0.518916 | + | 0.898789i | ||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3640 | + | 21.4150i | 0.464338 | + | 0.804258i | 0.999171 | − | 0.0407002i | \(-0.0129589\pi\) |
−0.534833 | + | 0.844958i | \(0.679626\pi\) | |||||||
\(710\) | −3.34315 | + | 5.79050i | −0.125466 | + | 0.217314i | ||||
\(711\) | −0.742641 | + | 1.28629i | −0.0278512 | + | 0.0482397i | ||||
\(712\) | 6.24264 | + | 10.8126i | 0.233953 | + | 0.405218i | ||||
\(713\) | 0.899495 | 0.0336864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.7279 | 0.700385 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.4853 | − | 25.0892i | 0.540963 | − | 0.936975i | ||||
\(718\) | 5.72792 | − | 9.92105i | 0.213764 | − | 0.370250i | ||||
\(719\) | 5.12132 | + | 8.87039i | 0.190993 | + | 0.330810i | 0.945580 | − | 0.325391i | \(-0.105496\pi\) |
−0.754587 | + | 0.656201i | \(0.772163\pi\) | |||||||
\(720\) | 17.6569 | 0.658032 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.6863 | −0.918729 | ||||||||
\(723\) | 15.7071 | + | 27.2055i | 0.584154 | + | 1.01178i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.2132 | + | 73.1154i | −1.56776 | + | 2.71544i | ||||
\(726\) | 7.00000 | + | 12.1244i | 0.259794 | + | 0.449977i | ||||
\(727\) | 42.0000 | 1.55769 | 0.778847 | − | 0.627214i | \(-0.215805\pi\) | ||||
0.778847 | + | 0.627214i | \(0.215805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 2.36396 | + | 4.09450i | 0.0874941 | + | 0.151544i | ||||
\(731\) | −3.53553 | + | 6.12372i | −0.130766 | + | 0.226494i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.3492 | − | 36.9780i | −0.788552 | − | 1.36581i | −0.926854 | − | 0.375422i | \(-0.877498\pi\) |
0.138302 | − | 0.990390i | \(-0.455836\pi\) | |||||||
\(734\) | 2.48528 | 0.0917334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.27208 | + | 9.13151i | 0.194199 | + | 0.336363i | ||||
\(738\) | 2.24264 | − | 3.88437i | 0.0825527 | − | 0.142986i | ||||
\(739\) | −20.8492 | + | 36.1119i | −0.766952 | + | 1.32840i | 0.172257 | + | 0.985052i | \(0.444894\pi\) |
−0.939208 | + | 0.343347i | \(0.888439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.75736 | 0.0645582 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3431 | −0.672945 | −0.336472 | − | 0.941693i | \(-0.609234\pi\) | ||||
−0.336472 | + | 0.941693i | \(0.609234\pi\) | |||||||
\(744\) | 10.4853 | + | 18.1610i | 0.384409 | + | 0.665816i | ||||
\(745\) | −17.1213 | + | 29.6550i | −0.627277 | + | 1.08648i | ||||
\(746\) | 6.00000 | − | 10.3923i | 0.219676 | − | 0.380489i | ||||
\(747\) | 2.37868 | + | 4.11999i | 0.0870313 | + | 0.150743i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −83.7401 | −3.05776 | ||||||||
\(751\) | 0.742641 | + | 1.28629i | 0.0270993 | + | 0.0469374i | 0.879257 | − | 0.476348i | \(-0.158040\pi\) |
−0.852158 | + | 0.523285i | \(0.824706\pi\) | |||||||
\(752\) | 8.82843 | − | 15.2913i | 0.321940 | − | 0.557616i | ||||
\(753\) | 13.7279 | − | 23.7775i | 0.500273 | − | 0.866499i | ||||
\(754\) | 4.12132 | + | 7.13834i | 0.150090 | + | 0.259963i | ||||
\(755\) | −80.5269 | −2.93067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51472 | 0.164090 | 0.0820451 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820451 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(758\) | −22.7990 | − | 39.4890i | −0.828097 | − | 1.43431i | ||||
\(759\) | 0.514719 | − | 0.891519i | 0.0186831 | − | 0.0323601i | ||||
\(760\) | 7.75736 | − | 13.4361i | 0.281389 | − | 0.487380i | ||||
\(761\) | −21.6213 | − | 37.4492i | −0.783772 | − | 1.35753i | −0.929730 | − | 0.368243i | \(-0.879960\pi\) |
0.145958 | − | 0.989291i | \(-0.453374\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.12132 | − | 5.40629i | −0.112852 | − | 0.195465i | ||||
\(766\) | 2.48528 | − | 4.30463i | 0.0897969 | − | 0.155533i | ||||
\(767\) | 5.82843 | − | 10.0951i | 0.210452 | − | 0.364514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.78680 | 0.352921 | 0.176460 | − | 0.984308i | \(-0.443535\pi\) | ||||
0.176460 | + | 0.984308i | \(0.443535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4558 | 0.844742 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5858 | − | 23.5313i | 0.488647 | − | 0.846361i | −0.511268 | − | 0.859421i | \(-0.670824\pi\) |
0.999915 | + | 0.0130603i | \(0.00415735\pi\) | |||||||
\(774\) | −3.53553 | + | 6.12372i | −0.127082 | + | 0.220113i | ||||
\(775\) | 37.9706 | + | 65.7669i | 1.36394 | + | 2.36242i | ||||
\(776\) | 38.8284 | 1.39386 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.9411 | 0.930034 | ||||||||
\(779\) | −1.97056 | − | 3.41311i | −0.0706027 | − | 0.122288i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.27208 | − | 3.93535i | 0.0813013 | − | 0.140818i | ||||
\(782\) | −0.171573 | − | 0.297173i | −0.00613543 | − | 0.0106269i | ||||
\(783\) | 32.9706 | 1.17827 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.0416 | −1.92883 | ||||||||
\(786\) | 2.82843 | + | 4.89898i | 0.100887 | + | 0.174741i | ||||
\(787\) | 16.6213 | − | 28.7890i | 0.592486 | − | 1.02622i | −0.401410 | − | 0.915898i | \(-0.631480\pi\) |
0.993896 | − | 0.110318i | \(-0.0351868\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6066 | − | 39.1558i | −0.804816 | − | 1.39398i | ||||
\(790\) | −9.27208 | −0.329886 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 3.00000 | + | 5.19615i | 0.106533 | + | 0.184521i | ||||
\(794\) | −17.1213 | + | 29.6550i | −0.607613 | + | 1.05242i | ||||
\(795\) | −18.1924 | + | 31.5101i | −0.645218 | + | 1.11755i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.6569 | −1.26303 | −0.631515 | − | 0.775363i | \(-0.717567\pi\) | ||||
−0.631515 | + | 0.775363i | \(0.717567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.24264 | −0.220849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.20711 | − | 3.82282i | 0.0779843 | − | 0.135073i | ||||
\(802\) | −12.4853 | + | 21.6251i | −0.440871 | + | 0.763610i | ||||
\(803\) | −1.60660 | − | 2.78272i | −0.0566957 | − | 0.0981999i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.41421 | 0.261155 | ||||||||
\(807\) | 10.4853 | + | 18.1610i | 0.369099 | + | 0.639299i | ||||
\(808\) | 2.48528 | − | 4.30463i | 0.0874319 | − | 0.151436i | ||||
\(809\) | −0.257359 | + | 0.445759i | −0.00904827 | + | 0.0156721i | −0.870514 | − | 0.492143i | \(-0.836214\pi\) |
0.861466 | + | 0.507816i | \(0.169547\pi\) | |||||||
\(810\) | 15.6066 | + | 27.0314i | 0.548360 | + | 0.949788i | ||||
\(811\) | 45.9411 | 1.61321 | 0.806606 | − | 0.591090i | \(-0.201302\pi\) | ||||
0.806606 | + | 0.591090i | \(0.201302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.2843 | −0.991973 | ||||||||
\(814\) | −18.7279 | − | 32.4377i | −0.656413 | − | 1.13694i | ||||
\(815\) | 18.7279 | − | 32.4377i | 0.656010 | − | 1.13624i | ||||
\(816\) | 4.00000 | − | 6.92820i | 0.140028 | − | 0.242536i | ||||
\(817\) | 3.10660 | + | 5.38079i | 0.108686 | + | 0.188250i | ||||
\(818\) | −7.41421 | −0.259232 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.07107 | − | 7.05130i | −0.142081 | − | 0.246092i | 0.786199 | − | 0.617973i | \(-0.212046\pi\) |
−0.928280 | + | 0.371882i | \(0.878713\pi\) | |||||||
\(822\) | −7.41421 | + | 12.8418i | −0.258600 | + | 0.447909i | ||||
\(823\) | 3.24264 | − | 5.61642i | 0.113031 | − | 0.195776i | −0.803960 | − | 0.594684i | \(-0.797277\pi\) |
0.916991 | + | 0.398908i | \(0.130611\pi\) | |||||||
\(824\) | −11.3137 | − | 19.5959i | −0.394132 | − | 0.682656i | ||||
\(825\) | 86.9117 | 3.02588 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.45584 | 0.0506247 | 0.0253123 | − | 0.999680i | \(-0.491942\pi\) | ||||
0.0253123 | + | 0.999680i | \(0.491942\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6360 | + | 21.8863i | −0.438868 | + | 0.760141i | −0.997602 | − | 0.0692052i | \(-0.977954\pi\) |
0.558735 | + | 0.829346i | \(0.311287\pi\) | |||||||
\(830\) | −14.8492 | + | 25.7196i | −0.515425 | + | 0.892742i | ||||
\(831\) | 6.70711 | + | 11.6170i | 0.232667 | + | 0.402991i | ||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.48528 | 0.155313 | ||||||||
\(835\) | 47.1985 | + | 81.7502i | 1.63337 | + | 2.82908i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.8284 | − | 25.6836i | 0.512545 | − | 0.887755i | ||||
\(838\) | −23.2426 | − | 40.2574i | −0.802904 | − | 1.39067i | ||||
\(839\) | −38.8284 | −1.34051 | −0.670253 | − | 0.742133i | \(-0.733814\pi\) | ||||
−0.670253 | + | 0.742133i | \(0.733814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.97056 | 0.171399 | ||||||||
\(842\) | 13.2426 | + | 22.9369i | 0.456372 | + | 0.790459i | ||||
\(843\) | −11.0000 | + | 19.0526i | −0.378860 | + | 0.656205i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.20711 | − | 3.82282i | −0.0759268 | − | 0.131509i | ||||
\(846\) | −6.24264 | −0.214626 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.3137 | 0.800596 | ||||||||
\(849\) | 6.00000 | + | 10.3923i | 0.205919 | + | 0.356663i | ||||
\(850\) | 14.4853 | − | 25.0892i | 0.496841 | − | 0.860554i | ||||
\(851\) | −0.535534 | + | 0.927572i | −0.0183579 | + | 0.0317968i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2721 | 0.488667 | 0.244333 | − | 0.969691i | \(-0.421431\pi\) | ||||
0.244333 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48528 | −0.187593 | ||||||||
\(856\) | 11.5147 | + | 19.9441i | 0.393565 | + | 0.681675i | ||||
\(857\) | −9.38478 | + | 16.2549i | −0.320578 | + | 0.555257i | −0.980607 | − | 0.195983i | \(-0.937210\pi\) |
0.660030 | + | 0.751240i | \(0.270544\pi\) | |||||||
\(858\) | 4.24264 | − | 7.34847i | 0.144841 | − | 0.250873i | ||||
\(859\) | 1.48528 | + | 2.57258i | 0.0506771 | + | 0.0877754i | 0.890251 | − | 0.455470i | \(-0.150529\pi\) |
−0.839574 | + | 0.543245i | \(0.817195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.4558 | −1.13951 | ||||||||
\(863\) | 14.1421 | + | 24.4949i | 0.481404 | + | 0.833816i | 0.999772 | − | 0.0213414i | \(-0.00679371\pi\) |
−0.518368 | + | 0.855157i | \(0.673460\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60660 | − | 2.78272i | 0.0546261 | − | 0.0946152i | ||||
\(866\) | −6.34315 | − | 10.9867i | −0.215549 | − | 0.373342i | ||||
\(867\) | 21.2132 | 0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.30152 | 0.213764 | ||||||||
\(870\) | 25.7279 | + | 44.5621i | 0.872258 | + | 1.51080i | ||||
\(871\) | 1.24264 | − | 2.15232i | 0.0421053 | − | 0.0729285i | ||||
\(872\) | −12.3431 | + | 21.3790i | −0.417992 | + | 0.723983i | ||||
\(873\) | −6.86396 | − | 11.8887i | −0.232310 | − | 0.402373i | ||||
\(874\) | −0.301515 | −0.0101989 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.878680 | + | 1.52192i | 0.0296709 | + | 0.0513915i | 0.880480 | − | 0.474084i | \(-0.157221\pi\) |
−0.850809 | + | 0.525476i | \(0.823887\pi\) | |||||||
\(878\) | 12.3848 | − | 21.4511i | 0.417966 | − | 0.723938i | ||||
\(879\) | −15.1213 | + | 26.1909i | −0.510029 | + | 0.883397i | ||||
\(880\) | −37.4558 | − | 64.8754i | −1.26264 | − | 2.18695i | ||||
\(881\) | −49.1127 | −1.65465 | −0.827324 | − | 0.561724i | \(-0.810138\pi\) | ||||
−0.827324 | + | 0.561724i | \(0.810138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.3848 | − | 63.0203i | 1.22306 | − | 2.11840i | ||||
\(886\) | 18.6066 | − | 32.2276i | 0.625101 | − | 1.08271i | ||||
\(887\) | 21.5563 | + | 37.3367i | 0.723791 | + | 1.25364i | 0.959470 | + | 0.281812i | \(0.0909355\pi\) |
−0.235678 | + | 0.971831i | \(0.575731\pi\) | |||||||
\(888\) | −24.9706 | −0.837957 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27.5563 | 0.923691 | ||||||||
\(891\) | −10.6066 | − | 18.3712i | −0.355335 | − | 0.615457i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.74264 | + | 4.75039i | −0.0917790 | + | 0.158966i | ||||
\(894\) | 7.75736 | + | 13.4361i | 0.259445 | + | 0.449372i | ||||
\(895\) | −39.7279 | −1.32796 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.242641 | −0.00810154 | ||||||||
\(898\) | −18.9706 | − | 32.8580i | −0.633056 | − | 1.09648i | ||||
\(899\) | 15.2782 | − | 26.4626i | 0.509556 | − | 0.882576i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.12132 | − | 7.13834i | −0.137301 | − | 0.237812i | ||||
\(902\) | −19.0294 | −0.633611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 57.4558 | 1.91095 | ||||||||
\(905\) | −14.8492 | − | 25.7196i | −0.493606 | − | 0.854950i | ||||
\(906\) | −18.2426 | + | 31.5972i | −0.606071 | + | 1.04975i | ||||
\(907\) | 15.9853 | − | 27.6873i | 0.530783 | − | 0.919342i | −0.468572 | − | 0.883425i | \(-0.655231\pi\) |
0.999355 | − | 0.0359172i | \(-0.0114352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.75736 | −0.0582879 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0294 | −0.332290 | −0.166145 | − | 0.986101i | \(-0.553132\pi\) | ||||
−0.166145 | + | 0.986101i | \(0.553132\pi\) | |||||||
\(912\) | −3.51472 | − | 6.08767i | −0.116384 | − | 0.201583i | ||||
\(913\) | 10.0919 | − | 17.4797i | 0.333993 | − | 0.578492i | ||||
\(914\) | −24.8995 | + | 43.1272i | −0.823602 | + | 1.42652i | ||||
\(915\) | 18.7279 | + | 32.4377i | 0.619126 | + | 1.07236i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.3137 | −0.373408 | ||||||||
\(919\) | −12.0000 | − | 20.7846i | −0.395843 | − | 0.685621i | 0.597365 | − | 0.801970i | \(-0.296214\pi\) |
−0.993208 | + | 0.116348i | \(0.962881\pi\) | |||||||
\(920\) | −1.07107 | + | 1.85514i | −0.0353121 | + | 0.0611623i | ||||
\(921\) | 3.36396 | − | 5.82655i | 0.110846 | − | 0.191991i | ||||
\(922\) | −2.24264 | − | 3.88437i | −0.0738574 | − | 0.127925i | ||||
\(923\) | −1.07107 | −0.0352546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −90.4264 | −2.97320 | ||||||||
\(926\) | −3.00000 | − | 5.19615i | −0.0985861 | − | 0.170756i | ||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.55025 | − | 14.8095i | −0.280525 | − | 0.485883i | 0.690989 | − | 0.722865i | \(-0.257175\pi\) |
−0.971514 | + | 0.236982i | \(0.923842\pi\) | |||||||
\(930\) | 46.2843 | 1.51772 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.24264 | − | 5.61642i | −0.106159 | − | 0.183873i | ||||
\(934\) | −11.2426 | + | 19.4728i | −0.367870 | + | 0.637170i | ||||
\(935\) | −13.2426 | + | 22.9369i | −0.433081 | + | 0.750118i | ||||
\(936\) | 1.41421 | + | 2.44949i | 0.0462250 | + | 0.0800641i | ||||
\(937\) | 2.78680 | 0.0910407 | 0.0455203 | − | 0.998963i | \(-0.485505\pi\) | ||||
0.0455203 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.1716 | 0.886711 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9645 | + | 22.4551i | −0.422630 | + | 0.732016i | −0.996196 | − | 0.0871434i | \(-0.972226\pi\) |
0.573566 | + | 0.819159i | \(0.305560\pi\) | |||||||
\(942\) | −12.2426 | + | 21.2049i | −0.398887 | + | 0.690892i | ||||
\(943\) | 0.272078 | + | 0.471253i | 0.00886008 | + | 0.0153461i | ||||
\(944\) | −46.6274 | −1.51759 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −10.4142 | − | 18.0379i | −0.338416 | − | 0.586155i | 0.645719 | − | 0.763575i | \(-0.276558\pi\) |
−0.984135 | + | 0.177421i | \(0.943225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.378680 | + | 0.655892i | −0.0122925 | + | 0.0212912i | ||||
\(950\) | −12.7279 | − | 22.0454i | −0.412948 | − | 0.715247i | ||||
\(951\) | −16.0000 | −0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1421 | −0.555288 | −0.277644 | − | 0.960684i | \(-0.589554\pi\) | ||||
−0.277644 | + | 0.960684i | \(0.589554\pi\) | |||||||
\(954\) | −4.12132 | − | 7.13834i | −0.133433 | − | 0.231112i | ||||
\(955\) | −45.9706 | + | 79.6234i | −1.48757 | + | 2.57655i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.4853 | − | 30.2854i | −0.565219 | − | 0.978988i | ||||
\(958\) | 51.2132 | 1.65462 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −49.9411 | −1.61184 | ||||||||
\(961\) | 1.75736 | + | 3.04384i | 0.0566890 | + | 0.0981882i | ||||
\(962\) | −4.41421 | + | 7.64564i | −0.142320 | + | 0.246505i | ||||
\(963\) | 4.07107 | − | 7.05130i | 0.131188 | − | 0.227225i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.9706 | 0.353155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.6985 | −1.34093 | −0.670466 | − | 0.741940i | \(-0.733906\pi\) | ||||
−0.670466 | + | 0.741940i | \(0.733906\pi\) | |||||||
\(968\) | 9.89949 | + | 17.1464i | 0.318182 | + | 0.551107i | ||||
\(969\) | −1.24264 | + | 2.15232i | −0.0399194 | + | 0.0691424i | ||||
\(970\) | 42.8492 | − | 74.2171i | 1.37581 | − | 2.38297i | ||||
\(971\) | 3.72792 | + | 6.45695i | 0.119635 | + | 0.207213i | 0.919623 | − | 0.392802i | \(-0.128494\pi\) |
−0.799988 | + | 0.600016i | \(0.795161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 55.7990 | 1.78791 | ||||||||
\(975\) | −10.2426 | − | 17.7408i | −0.328027 | − | 0.568159i | ||||
\(976\) | 12.0000 | − | 20.7846i | 0.384111 | − | 0.665299i | ||||
\(977\) | 12.0208 | − | 20.8207i | 0.384580 | − | 0.666112i | −0.607131 | − | 0.794602i | \(-0.707680\pi\) |
0.991711 | + | 0.128490i | \(0.0410130\pi\) | |||||||
\(978\) | −8.48528 | − | 14.6969i | −0.271329 | − | 0.469956i | ||||
\(979\) | −18.7279 | −0.598547 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.72792 | 0.278661 | ||||||||
\(982\) | 20.2426 | + | 35.0613i | 0.645969 | + | 1.11885i | ||||
\(983\) | −16.5208 | + | 28.6149i | −0.526932 | + | 0.912673i | 0.472575 | + | 0.881290i | \(0.343324\pi\) |
−0.999507 | + | 0.0313830i | \(0.990009\pi\) | |||||||
\(984\) | −6.34315 | + | 10.9867i | −0.202212 | + | 0.350242i | ||||
\(985\) | −52.2132 | − | 90.4359i | −1.66365 | − | 2.88153i | ||||
\(986\) | −11.6569 | −0.371230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.428932 | − | 0.742932i | −0.0136393 | − | 0.0236239i | ||||
\(990\) | −13.2426 | + | 22.9369i | −0.420879 | + | 0.728983i | ||||
\(991\) | −17.4853 | + | 30.2854i | −0.555438 | + | 0.962047i | 0.442431 | + | 0.896803i | \(0.354116\pi\) |
−0.997869 | + | 0.0652448i | \(0.979217\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4558 | 0.807817 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.0416 | −1.71323 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2426 | − | 24.6690i | 0.451069 | − | 0.781274i | −0.547384 | − | 0.836882i | \(-0.684376\pi\) |
0.998453 | + | 0.0556074i | \(0.0177095\pi\) | |||||||
\(998\) | 27.3848 | − | 47.4318i | 0.866850 | − | 1.50143i | ||||
\(999\) | 17.6569 | + | 30.5826i | 0.558638 | + | 0.967590i |
(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 | 637.2.e.f.508.1 | 4 | ||
7.2 | even | 3 | inner | 637.2.e.f.79.1 | 4 | ||
7.3 | odd | 6 | 637.2.a.g.1.2 | 2 | |||
7.4 | even | 3 | 91.2.a.c.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 637.2.e.g.79.1 | 4 | |||
7.6 | odd | 2 | 637.2.e.g.508.1 | 4 | |||
21.11 | odd | 6 | 819.2.a.h.1.1 | 2 | |||
21.17 | even | 6 | 5733.2.a.s.1.1 | 2 | |||
28.11 | odd | 6 | 1456.2.a.q.1.2 | 2 | |||
35.4 | even | 6 | 2275.2.a.j.1.1 | 2 | |||
56.11 | odd | 6 | 5824.2.a.bk.1.1 | 2 | |||
56.53 | even | 6 | 5824.2.a.bl.1.2 | 2 | |||
91.18 | odd | 12 | 1183.2.c.d.337.1 | 4 | |||
91.25 | even | 6 | 1183.2.a.d.1.1 | 2 | |||
91.38 | odd | 6 | 8281.2.a.v.1.1 | 2 | |||
91.60 | odd | 12 | 1183.2.c.d.337.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.c.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
637.2.a.g.1.2 | 2 | 7.3 | odd | 6 | |||
637.2.e.f.79.1 | 4 | 7.2 | even | 3 | inner | ||
637.2.e.f.508.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.e.g.79.1 | 4 | 7.5 | odd | 6 | |||
637.2.e.g.508.1 | 4 | 7.6 | odd | 2 | |||
819.2.a.h.1.1 | 2 | 21.11 | odd | 6 | |||
1183.2.a.d.1.1 | 2 | 91.25 | even | 6 | |||
1183.2.c.d.337.1 | 4 | 91.18 | odd | 12 | |||
1183.2.c.d.337.3 | 4 | 91.60 | odd | 12 | |||
1456.2.a.q.1.2 | 2 | 28.11 | odd | 6 | |||
2275.2.a.j.1.1 | 2 | 35.4 | even | 6 | |||
5733.2.a.s.1.1 | 2 | 21.17 | even | 6 | |||
5824.2.a.bk.1.1 | 2 | 56.11 | odd | 6 | |||
5824.2.a.bl.1.2 | 2 | 56.53 | even | 6 | |||
8281.2.a.v.1.1 | 2 | 91.38 | odd | 6 |