Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(209,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.d (of order \(2\), degree \(1\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.2 | ||
Root | \(-1.68014 - 0.420861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.209 |
Dual form | 210.2.d.a.209.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.68014 | + | 0.420861i | −0.970030 | + | 0.242984i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.08495 | − | 1.95522i | −0.485206 | − | 0.874400i | ||||
\(6\) | 1.68014 | − | 0.420861i | 0.685915 | − | 0.171816i | ||||
\(7\) | 0.595188 | + | 2.57794i | 0.224960 | + | 0.974368i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.64575 | − | 1.41421i | 0.881917 | − | 0.471405i | ||||
\(10\) | 1.08495 | + | 1.95522i | 0.343092 | + | 0.618294i | ||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | −1.68014 | + | 0.420861i | −0.485015 | + | 0.121492i | ||||
\(13\) | 3.36028 | 0.931975 | 0.465987 | − | 0.884791i | \(-0.345699\pi\) | ||||
0.465987 | + | 0.884791i | \(0.345699\pi\) | |||||||
\(14\) | −0.595188 | − | 2.57794i | −0.159071 | − | 0.688982i | ||||
\(15\) | 2.64575 | + | 2.82843i | 0.683130 | + | 0.730297i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.75216i | 1.15257i | 0.817250 | + | 0.576284i | \(0.195498\pi\) | ||||
−0.817250 | + | 0.576284i | \(0.804502\pi\) | |||||||
\(18\) | −2.64575 | + | 1.41421i | −0.623610 | + | 0.333333i | ||||
\(19\) | 5.59388i | 1.28332i | 0.766987 | + | 0.641662i | \(0.221755\pi\) | ||||
−0.766987 | + | 0.641662i | \(0.778245\pi\) | |||||||
\(20\) | −1.08495 | − | 1.95522i | −0.242603 | − | 0.437200i | ||||
\(21\) | −2.08495 | − | 4.08080i | −0.454974 | − | 0.890505i | ||||
\(22\) | − | 2.82843i | − | 0.603023i | ||||||
\(23\) | 7.29150 | 1.52038 | 0.760192 | − | 0.649699i | \(-0.225105\pi\) | ||||
0.760192 | + | 0.649699i | \(0.225105\pi\) | |||||||
\(24\) | 1.68014 | − | 0.420861i | 0.342957 | − | 0.0859080i | ||||
\(25\) | −2.64575 | + | 4.24264i | −0.529150 | + | 0.848528i | ||||
\(26\) | −3.36028 | −0.659006 | ||||||||
\(27\) | −3.85005 | + | 3.48957i | −0.740942 | + | 0.671569i | ||||
\(28\) | 0.595188 | + | 2.57794i | 0.112480 | + | 0.487184i | ||||
\(29\) | − | 0.500983i | − | 0.0930303i | −0.998918 | − | 0.0465151i | \(-0.985188\pi\) | ||
0.998918 | − | 0.0465151i | \(-0.0148116\pi\) | |||||||
\(30\) | −2.64575 | − | 2.82843i | −0.483046 | − | 0.516398i | ||||
\(31\) | − | 3.06871i | − | 0.551157i | −0.961279 | − | 0.275578i | \(-0.911131\pi\) | ||
0.961279 | − | 0.275578i | \(-0.0888694\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.19038 | − | 4.75216i | −0.207218 | − | 0.827245i | ||||
\(34\) | − | 4.75216i | − | 0.814988i | ||||||
\(35\) | 4.39467 | − | 3.96066i | 0.742835 | − | 0.669474i | ||||
\(36\) | 2.64575 | − | 1.41421i | 0.440959 | − | 0.235702i | ||||
\(37\) | − | 3.32941i | − | 0.547352i | −0.961822 | − | 0.273676i | \(-0.911760\pi\) | ||
0.961822 | − | 0.273676i | \(-0.0882396\pi\) | |||||||
\(38\) | − | 5.59388i | − | 0.907447i | ||||||
\(39\) | −5.64575 | + | 1.41421i | −0.904044 | + | 0.226455i | ||||
\(40\) | 1.08495 | + | 1.95522i | 0.171546 | + | 0.309147i | ||||
\(41\) | 4.33981 | 0.677765 | 0.338883 | − | 0.940829i | \(-0.389951\pi\) | ||||
0.338883 | + | 0.940829i | \(0.389951\pi\) | |||||||
\(42\) | 2.08495 | + | 4.08080i | 0.321715 | + | 0.629682i | ||||
\(43\) | − | 10.3117i | − | 1.57253i | −0.617892 | − | 0.786263i | \(-0.712013\pi\) | ||
0.617892 | − | 0.786263i | \(-0.287987\pi\) | |||||||
\(44\) | 2.82843i | 0.426401i | ||||||||
\(45\) | −5.63561 | − | 3.63866i | −0.840108 | − | 0.542420i | ||||
\(46\) | −7.29150 | −1.07507 | ||||||||
\(47\) | 7.82087i | 1.14079i | 0.821370 | + | 0.570396i | \(0.193210\pi\) | ||||
−0.821370 | + | 0.570396i | \(0.806790\pi\) | |||||||
\(48\) | −1.68014 | + | 0.420861i | −0.242508 | + | 0.0607461i | ||||
\(49\) | −6.29150 | + | 3.06871i | −0.898786 | + | 0.438387i | ||||
\(50\) | 2.64575 | − | 4.24264i | 0.374166 | − | 0.600000i | ||||
\(51\) | −2.00000 | − | 7.98430i | −0.280056 | − | 1.11803i | ||||
\(52\) | 3.36028 | 0.465987 | ||||||||
\(53\) | −8.58301 | −1.17897 | −0.589483 | − | 0.807781i | \(-0.700669\pi\) | ||||
−0.589483 | + | 0.807781i | \(0.700669\pi\) | |||||||
\(54\) | 3.85005 | − | 3.48957i | 0.523925 | − | 0.474871i | ||||
\(55\) | 5.53019 | − | 3.06871i | 0.745691 | − | 0.413785i | ||||
\(56\) | −0.595188 | − | 2.57794i | −0.0795353 | − | 0.344491i | ||||
\(57\) | −2.35425 | − | 9.39851i | −0.311828 | − | 1.24486i | ||||
\(58\) | 0.500983i | 0.0657823i | ||||||||
\(59\) | −2.16991 | −0.282498 | −0.141249 | − | 0.989974i | \(-0.545112\pi\) | ||||
−0.141249 | + | 0.989974i | \(0.545112\pi\) | |||||||
\(60\) | 2.64575 | + | 2.82843i | 0.341565 | + | 0.365148i | ||||
\(61\) | − | 2.52517i | − | 0.323315i | −0.986847 | − | 0.161657i | \(-0.948316\pi\) | ||
0.986847 | − | 0.161657i | \(-0.0516839\pi\) | |||||||
\(62\) | 3.06871i | 0.389727i | ||||||||
\(63\) | 5.22047 | + | 5.97885i | 0.657717 | + | 0.753265i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.64575 | − | 6.57008i | −0.452200 | − | 0.814919i | ||||
\(66\) | 1.19038 | + | 4.75216i | 0.146525 | + | 0.584950i | ||||
\(67\) | 10.3117i | 1.25978i | 0.776684 | + | 0.629890i | \(0.216900\pi\) | ||||
−0.776684 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(68\) | 4.75216i | 0.576284i | ||||||||
\(69\) | −12.2508 | + | 3.06871i | −1.47482 | + | 0.369430i | ||||
\(70\) | −4.39467 | + | 3.96066i | −0.525264 | + | 0.473390i | ||||
\(71\) | 9.81076i | 1.16432i | 0.813073 | + | 0.582161i | \(0.197793\pi\) | ||||
−0.813073 | + | 0.582161i | \(0.802207\pi\) | |||||||
\(72\) | −2.64575 | + | 1.41421i | −0.311805 | + | 0.166667i | ||||
\(73\) | 5.53019 | 0.647260 | 0.323630 | − | 0.946184i | \(-0.395097\pi\) | ||||
0.323630 | + | 0.946184i | \(0.395097\pi\) | |||||||
\(74\) | 3.32941i | 0.387036i | ||||||||
\(75\) | 2.65967 | − | 8.24173i | 0.307113 | − | 0.951673i | ||||
\(76\) | 5.59388i | 0.641662i | ||||||||
\(77\) | −7.29150 | + | 1.68345i | −0.830944 | + | 0.191846i | ||||
\(78\) | 5.64575 | − | 1.41421i | 0.639255 | − | 0.160128i | ||||
\(79\) | 3.29150 | 0.370323 | 0.185161 | − | 0.982708i | \(-0.440719\pi\) | ||||
0.185161 | + | 0.982708i | \(0.440719\pi\) | |||||||
\(80\) | −1.08495 | − | 1.95522i | −0.121302 | − | 0.218600i | ||||
\(81\) | 5.00000 | − | 7.48331i | 0.555556 | − | 0.831479i | ||||
\(82\) | −4.33981 | −0.479252 | ||||||||
\(83\) | − | 6.97915i | − | 0.766061i | −0.923736 | − | 0.383030i | \(-0.874880\pi\) | ||
0.923736 | − | 0.383030i | \(-0.125120\pi\) | |||||||
\(84\) | −2.08495 | − | 4.08080i | −0.227487 | − | 0.445252i | ||||
\(85\) | 9.29150 | − | 5.15587i | 1.00780 | − | 0.559233i | ||||
\(86\) | 10.3117i | 1.11194i | ||||||||
\(87\) | 0.210845 | + | 0.841723i | 0.0226049 | + | 0.0902422i | ||||
\(88\) | − | 2.82843i | − | 0.301511i | ||||||
\(89\) | 15.8219 | 1.67712 | 0.838558 | − | 0.544812i | \(-0.183399\pi\) | ||||
0.838558 | + | 0.544812i | \(0.183399\pi\) | |||||||
\(90\) | 5.63561 | + | 3.63866i | 0.594046 | + | 0.383549i | ||||
\(91\) | 2.00000 | + | 8.66259i | 0.209657 | + | 0.908086i | ||||
\(92\) | 7.29150 | 0.760192 | ||||||||
\(93\) | 1.29150 | + | 5.15587i | 0.133923 | + | 0.534639i | ||||
\(94\) | − | 7.82087i | − | 0.806661i | ||||||
\(95\) | 10.9373 | − | 6.06910i | 1.12214 | − | 0.622677i | ||||
\(96\) | 1.68014 | − | 0.420861i | 0.171479 | − | 0.0429540i | ||||
\(97\) | −14.6315 | −1.48560 | −0.742802 | − | 0.669511i | \(-0.766504\pi\) | ||||
−0.742802 | + | 0.669511i | \(0.766504\pi\) | |||||||
\(98\) | 6.29150 | − | 3.06871i | 0.635538 | − | 0.309987i | ||||
\(99\) | 4.00000 | + | 7.48331i | 0.402015 | + | 0.752101i | ||||
\(100\) | −2.64575 | + | 4.24264i | −0.264575 | + | 0.424264i | ||||
\(101\) | 2.16991 | 0.215914 | 0.107957 | − | 0.994156i | \(-0.465569\pi\) | ||||
0.107957 | + | 0.994156i | \(0.465569\pi\) | |||||||
\(102\) | 2.00000 | + | 7.98430i | 0.198030 | + | 0.790563i | ||||
\(103\) | −3.14944 | −0.310323 | −0.155162 | − | 0.987889i | \(-0.549590\pi\) | ||||
−0.155162 | + | 0.987889i | \(0.549590\pi\) | |||||||
\(104\) | −3.36028 | −0.329503 | ||||||||
\(105\) | −5.71678 | + | 8.50402i | −0.557901 | + | 0.829908i | ||||
\(106\) | 8.58301 | 0.833655 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −3.85005 | + | 3.48957i | −0.370471 | + | 0.335784i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −5.53019 | + | 3.06871i | −0.527283 | + | 0.292590i | ||||
\(111\) | 1.40122 | + | 5.59388i | 0.132998 | + | 0.530948i | ||||
\(112\) | 0.595188 | + | 2.57794i | 0.0562400 | + | 0.243592i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 2.35425 | + | 9.39851i | 0.220496 | + | 0.880251i | ||||
\(115\) | −7.91094 | − | 14.2565i | −0.737699 | − | 1.32942i | ||||
\(116\) | − | 0.500983i | − | 0.0465151i | ||||||
\(117\) | 8.89047 | − | 4.75216i | 0.821925 | − | 0.439337i | ||||
\(118\) | 2.16991 | 0.199756 | ||||||||
\(119\) | −12.2508 | + | 2.82843i | −1.12303 | + | 0.259281i | ||||
\(120\) | −2.64575 | − | 2.82843i | −0.241523 | − | 0.258199i | ||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 2.52517i | 0.228618i | ||||||||
\(123\) | −7.29150 | + | 1.82646i | −0.657453 | + | 0.164686i | ||||
\(124\) | − | 3.06871i | − | 0.275578i | ||||||
\(125\) | 11.1658 | + | 0.569951i | 0.998700 | + | 0.0509780i | ||||
\(126\) | −5.22047 | − | 5.97885i | −0.465076 | − | 0.532639i | ||||
\(127\) | 3.32941i | 0.295437i | 0.989029 | + | 0.147719i | \(0.0471930\pi\) | ||||
−0.989029 | + | 0.147719i | \(0.952807\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.33981 | + | 17.3252i | 0.382099 | + | 1.52540i | ||||
\(130\) | 3.64575 | + | 6.57008i | 0.319754 | + | 0.576235i | ||||
\(131\) | −17.9918 | −1.57195 | −0.785975 | − | 0.618258i | \(-0.787839\pi\) | ||||
−0.785975 | + | 0.618258i | \(0.787839\pi\) | |||||||
\(132\) | −1.19038 | − | 4.75216i | −0.103609 | − | 0.413622i | ||||
\(133\) | −14.4207 | + | 3.32941i | −1.25043 | + | 0.288696i | ||||
\(134\) | − | 10.3117i | − | 0.890799i | ||||||
\(135\) | 11.0000 | + | 3.74166i | 0.946729 | + | 0.322031i | ||||
\(136\) | − | 4.75216i | − | 0.407494i | ||||||
\(137\) | 1.29150 | 0.110341 | 0.0551703 | − | 0.998477i | \(-0.482430\pi\) | ||||
0.0551703 | + | 0.998477i | \(0.482430\pi\) | |||||||
\(138\) | 12.2508 | − | 3.06871i | 1.04285 | − | 0.261226i | ||||
\(139\) | 0.543544i | 0.0461028i | 0.999734 | + | 0.0230514i | \(0.00733813\pi\) | ||||
−0.999734 | + | 0.0230514i | \(0.992662\pi\) | |||||||
\(140\) | 4.39467 | − | 3.96066i | 0.371418 | − | 0.334737i | ||||
\(141\) | −3.29150 | − | 13.1402i | −0.277195 | − | 1.10660i | ||||
\(142\) | − | 9.81076i | − | 0.823301i | ||||||
\(143\) | 9.50432i | 0.794791i | ||||||||
\(144\) | 2.64575 | − | 1.41421i | 0.220479 | − | 0.117851i | ||||
\(145\) | −0.979531 | + | 0.543544i | −0.0813457 | + | 0.0451388i | ||||
\(146\) | −5.53019 | −0.457682 | ||||||||
\(147\) | 9.27911 | − | 7.80372i | 0.765328 | − | 0.643640i | ||||
\(148\) | − | 3.32941i | − | 0.273676i | ||||||
\(149\) | − | 10.8127i | − | 0.885813i | −0.896568 | − | 0.442906i | \(-0.853947\pi\) | ||
0.896568 | − | 0.442906i | \(-0.146053\pi\) | |||||||
\(150\) | −2.65967 | + | 8.24173i | −0.217161 | + | 0.672935i | ||||
\(151\) | −1.41699 | −0.115313 | −0.0576567 | − | 0.998336i | \(-0.518363\pi\) | ||||
−0.0576567 | + | 0.998336i | \(0.518363\pi\) | |||||||
\(152\) | − | 5.59388i | − | 0.453724i | ||||||
\(153\) | 6.72057 | + | 12.5730i | 0.543326 | + | 1.01647i | ||||
\(154\) | 7.29150 | − | 1.68345i | 0.587566 | − | 0.135656i | ||||
\(155\) | −6.00000 | + | 3.32941i | −0.481932 | + | 0.267425i | ||||
\(156\) | −5.64575 | + | 1.41421i | −0.452022 | + | 0.113228i | ||||
\(157\) | 16.3797 | 1.30724 | 0.653622 | − | 0.756821i | \(-0.273249\pi\) | ||||
0.653622 | + | 0.756821i | \(0.273249\pi\) | |||||||
\(158\) | −3.29150 | −0.261858 | ||||||||
\(159\) | 14.4207 | − | 3.61226i | 1.14363 | − | 0.286471i | ||||
\(160\) | 1.08495 | + | 1.95522i | 0.0857731 | + | 0.154574i | ||||
\(161\) | 4.33981 | + | 18.7970i | 0.342025 | + | 1.48141i | ||||
\(162\) | −5.00000 | + | 7.48331i | −0.392837 | + | 0.587945i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 4.33981 | 0.338883 | ||||||||
\(165\) | −8.00000 | + | 7.48331i | −0.622799 | + | 0.582575i | ||||
\(166\) | 6.97915i | 0.541687i | ||||||||
\(167\) | − | 20.6921i | − | 1.60120i | −0.599198 | − | 0.800601i | \(-0.704514\pi\) | ||
0.599198 | − | 0.800601i | \(-0.295486\pi\) | |||||||
\(168\) | 2.08495 | + | 4.08080i | 0.160858 | + | 0.314841i | ||||
\(169\) | −1.70850 | −0.131423 | ||||||||
\(170\) | −9.29150 | + | 5.15587i | −0.712626 | + | 0.395437i | ||||
\(171\) | 7.91094 | + | 14.8000i | 0.604965 | + | 1.13179i | ||||
\(172\) | − | 10.3117i | − | 0.786263i | ||||||
\(173\) | 2.22699i | 0.169315i | 0.996410 | + | 0.0846574i | \(0.0269796\pi\) | ||||
−0.996410 | + | 0.0846574i | \(0.973020\pi\) | |||||||
\(174\) | −0.210845 | − | 0.841723i | −0.0159841 | − | 0.0638108i | ||||
\(175\) | −12.5120 | − | 4.29541i | −0.945816 | − | 0.324702i | ||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | 3.64575 | − | 0.913230i | 0.274031 | − | 0.0686426i | ||||
\(178\) | −15.8219 | −1.18590 | ||||||||
\(179\) | − | 24.4539i | − | 1.82777i | −0.405975 | − | 0.913884i | \(-0.633068\pi\) | ||
0.405975 | − | 0.913884i | \(-0.366932\pi\) | |||||||
\(180\) | −5.63561 | − | 3.63866i | −0.420054 | − | 0.271210i | ||||
\(181\) | − | 14.8000i | − | 1.10008i | −0.835139 | − | 0.550038i | \(-0.814613\pi\) | ||
0.835139 | − | 0.550038i | \(-0.185387\pi\) | |||||||
\(182\) | −2.00000 | − | 8.66259i | −0.148250 | − | 0.642114i | ||||
\(183\) | 1.06275 | + | 4.24264i | 0.0785604 | + | 0.313625i | ||||
\(184\) | −7.29150 | −0.537537 | ||||||||
\(185\) | −6.50972 | + | 3.61226i | −0.478604 | + | 0.265578i | ||||
\(186\) | −1.29150 | − | 5.15587i | −0.0946976 | − | 0.378047i | ||||
\(187\) | −13.4411 | −0.982913 | ||||||||
\(188\) | 7.82087i | 0.570396i | ||||||||
\(189\) | −11.2874 | − | 7.84823i | −0.821037 | − | 0.570874i | ||||
\(190\) | −10.9373 | + | 6.06910i | −0.793472 | + | 0.440299i | ||||
\(191\) | − | 0.500983i | − | 0.0362499i | −0.999836 | − | 0.0181249i | \(-0.994230\pi\) | ||
0.999836 | − | 0.0181249i | \(-0.00576966\pi\) | |||||||
\(192\) | −1.68014 | + | 0.420861i | −0.121254 | + | 0.0303731i | ||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | 14.6315 | 1.05048 | ||||||||
\(195\) | 8.89047 | + | 9.50432i | 0.636660 | + | 0.680618i | ||||
\(196\) | −6.29150 | + | 3.06871i | −0.449393 | + | 0.219194i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | −4.00000 | − | 7.48331i | −0.284268 | − | 0.531816i | ||||
\(199\) | − | 9.20614i | − | 0.652606i | −0.945265 | − | 0.326303i | \(-0.894197\pi\) | ||
0.945265 | − | 0.326303i | \(-0.105803\pi\) | |||||||
\(200\) | 2.64575 | − | 4.24264i | 0.187083 | − | 0.300000i | ||||
\(201\) | −4.33981 | − | 17.3252i | −0.306107 | − | 1.22202i | ||||
\(202\) | −2.16991 | −0.152674 | ||||||||
\(203\) | 1.29150 | − | 0.298179i | 0.0906457 | − | 0.0209281i | ||||
\(204\) | −2.00000 | − | 7.98430i | −0.140028 | − | 0.559013i | ||||
\(205\) | −4.70850 | − | 8.48528i | −0.328856 | − | 0.592638i | ||||
\(206\) | 3.14944 | 0.219432 | ||||||||
\(207\) | 19.2915 | − | 10.3117i | 1.34085 | − | 0.716716i | ||||
\(208\) | 3.36028 | 0.232994 | ||||||||
\(209\) | −15.8219 | −1.09442 | ||||||||
\(210\) | 5.71678 | − | 8.50402i | 0.394496 | − | 0.586833i | ||||
\(211\) | −21.1660 | −1.45713 | −0.728564 | − | 0.684978i | \(-0.759812\pi\) | ||||
−0.728564 | + | 0.684978i | \(0.759812\pi\) | |||||||
\(212\) | −8.58301 | −0.589483 | ||||||||
\(213\) | −4.12897 | − | 16.4835i | −0.282912 | − | 1.12943i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.1617 | + | 11.1878i | −1.37502 | + | 0.762999i | ||||
\(216\) | 3.85005 | − | 3.48957i | 0.261963 | − | 0.237435i | ||||
\(217\) | 7.91094 | − | 1.82646i | 0.537030 | − | 0.123988i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −9.29150 | + | 2.32744i | −0.627862 | + | 0.157274i | ||||
\(220\) | 5.53019 | − | 3.06871i | 0.372845 | − | 0.206893i | ||||
\(221\) | 15.9686i | 1.07416i | ||||||||
\(222\) | −1.40122 | − | 5.59388i | −0.0940438 | − | 0.375437i | ||||
\(223\) | 1.19038 | 0.0797135 | 0.0398567 | − | 0.999205i | \(-0.487310\pi\) | ||||
0.0398567 | + | 0.999205i | \(0.487310\pi\) | |||||||
\(224\) | −0.595188 | − | 2.57794i | −0.0397677 | − | 0.172246i | ||||
\(225\) | −1.00000 | + | 14.9666i | −0.0666667 | + | 0.997775i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | − | 18.1669i | − | 1.20578i | −0.797824 | − | 0.602890i | \(-0.794016\pi\) | ||
0.797824 | − | 0.602890i | \(-0.205984\pi\) | |||||||
\(228\) | −2.35425 | − | 9.39851i | −0.155914 | − | 0.622432i | ||||
\(229\) | 24.9007i | 1.64548i | 0.568415 | + | 0.822742i | \(0.307557\pi\) | ||||
−0.568415 | + | 0.822742i | \(0.692443\pi\) | |||||||
\(230\) | 7.91094 | + | 14.2565i | 0.521632 | + | 0.940044i | ||||
\(231\) | 11.5423 | − | 5.89714i | 0.759425 | − | 0.388003i | ||||
\(232\) | 0.500983i | 0.0328912i | ||||||||
\(233\) | 13.2915 | 0.870755 | 0.435378 | − | 0.900248i | \(-0.356615\pi\) | ||||
0.435378 | + | 0.900248i | \(0.356615\pi\) | |||||||
\(234\) | −8.89047 | + | 4.75216i | −0.581188 | + | 0.310658i | ||||
\(235\) | 15.2915 | − | 8.48528i | 0.997508 | − | 0.553519i | ||||
\(236\) | −2.16991 | −0.141249 | ||||||||
\(237\) | −5.53019 | + | 1.38527i | −0.359224 | + | 0.0899827i | ||||
\(238\) | 12.2508 | − | 2.82843i | 0.794099 | − | 0.183340i | ||||
\(239\) | 14.6431i | 0.947185i | 0.880744 | + | 0.473592i | \(0.157043\pi\) | ||||
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(240\) | 2.64575 | + | 2.82843i | 0.170783 | + | 0.182574i | ||||
\(241\) | − | 17.3252i | − | 1.11601i | −0.829836 | − | 0.558007i | \(-0.811566\pi\) | ||
0.829836 | − | 0.558007i | \(-0.188434\pi\) | |||||||
\(242\) | −3.00000 | −0.192847 | ||||||||
\(243\) | −5.25127 | + | 14.6773i | −0.336869 | + | 0.941551i | ||||
\(244\) | − | 2.52517i | − | 0.161657i | ||||||
\(245\) | 12.8260 | + | 8.97185i | 0.819422 | + | 0.573190i | ||||
\(246\) | 7.29150 | − | 1.82646i | 0.464889 | − | 0.116451i | ||||
\(247\) | 18.7970i | 1.19603i | ||||||||
\(248\) | 3.06871i | 0.194863i | ||||||||
\(249\) | 2.93725 | + | 11.7260i | 0.186141 | + | 0.743102i | ||||
\(250\) | −11.1658 | − | 0.569951i | −0.706187 | − | 0.0360469i | ||||
\(251\) | 6.50972 | 0.410890 | 0.205445 | − | 0.978669i | \(-0.434136\pi\) | ||||
0.205445 | + | 0.978669i | \(0.434136\pi\) | |||||||
\(252\) | 5.22047 | + | 5.97885i | 0.328859 | + | 0.376632i | ||||
\(253\) | 20.6235i | 1.29659i | ||||||||
\(254\) | − | 3.32941i | − | 0.208906i | ||||||
\(255\) | −13.4411 | + | 12.5730i | −0.841716 | + | 0.787354i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.7105i | − | 1.16713i | −0.812068 | − | 0.583563i | \(-0.801658\pi\) | ||
0.812068 | − | 0.583563i | \(-0.198342\pi\) | |||||||
\(258\) | −4.33981 | − | 17.3252i | −0.270185 | − | 1.07862i | ||||
\(259\) | 8.58301 | − | 1.98162i | 0.533322 | − | 0.123132i | ||||
\(260\) | −3.64575 | − | 6.57008i | −0.226100 | − | 0.407459i | ||||
\(261\) | −0.708497 | − | 1.32548i | −0.0438549 | − | 0.0820450i | ||||
\(262\) | 17.9918 | 1.11154 | ||||||||
\(263\) | 14.5830 | 0.899227 | 0.449613 | − | 0.893223i | \(-0.351562\pi\) | ||||
0.449613 | + | 0.893223i | \(0.351562\pi\) | |||||||
\(264\) | 1.19038 | + | 4.75216i | 0.0732626 | + | 0.292475i | ||||
\(265\) | 9.31216 | + | 16.7816i | 0.572042 | + | 1.03089i | ||||
\(266\) | 14.4207 | − | 3.32941i | 0.884188 | − | 0.204139i | ||||
\(267\) | −26.5830 | + | 6.65882i | −1.62685 | + | 0.407513i | ||||
\(268\) | 10.3117i | 0.629890i | ||||||||
\(269\) | 9.31216 | 0.567773 | 0.283886 | − | 0.958858i | \(-0.408376\pi\) | ||||
0.283886 | + | 0.958858i | \(0.408376\pi\) | |||||||
\(270\) | −11.0000 | − | 3.74166i | −0.669439 | − | 0.227710i | ||||
\(271\) | 20.3939i | 1.23884i | 0.785059 | + | 0.619421i | \(0.212632\pi\) | ||||
−0.785059 | + | 0.619421i | \(0.787368\pi\) | |||||||
\(272\) | 4.75216i | 0.288142i | ||||||||
\(273\) | −7.00603 | − | 13.7127i | −0.424024 | − | 0.829928i | ||||
\(274\) | −1.29150 | −0.0780225 | ||||||||
\(275\) | −12.0000 | − | 7.48331i | −0.723627 | − | 0.451261i | ||||
\(276\) | −12.2508 | + | 3.06871i | −0.737409 | + | 0.184715i | ||||
\(277\) | − | 6.98233i | − | 0.419528i | −0.977752 | − | 0.209764i | \(-0.932730\pi\) | ||
0.977752 | − | 0.209764i | \(-0.0672695\pi\) | |||||||
\(278\) | − | 0.543544i | − | 0.0325996i | ||||||
\(279\) | −4.33981 | − | 8.11905i | −0.259818 | − | 0.486075i | ||||
\(280\) | −4.39467 | + | 3.96066i | −0.262632 | + | 0.236695i | ||||
\(281\) | − | 9.30978i | − | 0.555375i | −0.960672 | − | 0.277687i | \(-0.910432\pi\) | ||
0.960672 | − | 0.277687i | \(-0.0895679\pi\) | |||||||
\(282\) | 3.29150 | + | 13.1402i | 0.196006 | + | 0.782486i | ||||
\(283\) | 32.2016 | 1.91419 | 0.957094 | − | 0.289779i | \(-0.0935819\pi\) | ||||
0.957094 | + | 0.289779i | \(0.0935819\pi\) | |||||||
\(284\) | 9.81076i | 0.582161i | ||||||||
\(285\) | −15.8219 | + | 14.8000i | −0.937208 | + | 0.876677i | ||||
\(286\) | − | 9.50432i | − | 0.562002i | ||||||
\(287\) | 2.58301 | + | 11.1878i | 0.152470 | + | 0.660393i | ||||
\(288\) | −2.64575 | + | 1.41421i | −0.155902 | + | 0.0833333i | ||||
\(289\) | −5.58301 | −0.328412 | ||||||||
\(290\) | 0.979531 | − | 0.543544i | 0.0575201 | − | 0.0319180i | ||||
\(291\) | 24.5830 | − | 6.15784i | 1.44108 | − | 0.360979i | ||||
\(292\) | 5.53019 | 0.323630 | ||||||||
\(293\) | 7.27733i | 0.425146i | 0.977145 | + | 0.212573i | \(0.0681843\pi\) | ||||
−0.977145 | + | 0.212573i | \(0.931816\pi\) | |||||||
\(294\) | −9.27911 | + | 7.80372i | −0.541169 | + | 0.455122i | ||||
\(295\) | 2.35425 | + | 4.24264i | 0.137070 | + | 0.247016i | ||||
\(296\) | 3.32941i | 0.193518i | ||||||||
\(297\) | −9.87000 | − | 10.8896i | −0.572716 | − | 0.631878i | ||||
\(298\) | 10.8127i | 0.626364i | ||||||||
\(299\) | 24.5015 | 1.41696 | ||||||||
\(300\) | 2.65967 | − | 8.24173i | 0.153556 | − | 0.475837i | ||||
\(301\) | 26.5830 | − | 6.13742i | 1.53222 | − | 0.353755i | ||||
\(302\) | 1.41699 | 0.0815389 | ||||||||
\(303\) | −3.64575 | + | 0.913230i | −0.209443 | + | 0.0524637i | ||||
\(304\) | 5.59388i | 0.320831i | ||||||||
\(305\) | −4.93725 | + | 2.73969i | −0.282706 | + | 0.156874i | ||||
\(306\) | −6.72057 | − | 12.5730i | −0.384189 | − | 0.718752i | ||||
\(307\) | 12.0399 | 0.687154 | 0.343577 | − | 0.939124i | \(-0.388361\pi\) | ||||
0.343577 | + | 0.939124i | \(0.388361\pi\) | |||||||
\(308\) | −7.29150 | + | 1.68345i | −0.415472 | + | 0.0959232i | ||||
\(309\) | 5.29150 | − | 1.32548i | 0.301023 | − | 0.0754038i | ||||
\(310\) | 6.00000 | − | 3.32941i | 0.340777 | − | 0.189098i | ||||
\(311\) | −24.5015 | −1.38935 | −0.694677 | − | 0.719322i | \(-0.744453\pi\) | ||||
−0.694677 | + | 0.719322i | \(0.744453\pi\) | |||||||
\(312\) | 5.64575 | − | 1.41421i | 0.319628 | − | 0.0800641i | ||||
\(313\) | −14.6315 | −0.827022 | −0.413511 | − | 0.910499i | \(-0.635698\pi\) | ||||
−0.413511 | + | 0.910499i | \(0.635698\pi\) | |||||||
\(314\) | −16.3797 | −0.924361 | ||||||||
\(315\) | 6.02599 | − | 16.6939i | 0.339526 | − | 0.940597i | ||||
\(316\) | 3.29150 | 0.185161 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | −14.4207 | + | 3.61226i | −0.808671 | + | 0.202565i | ||||
\(319\) | 1.41699 | 0.0793365 | ||||||||
\(320\) | −1.08495 | − | 1.95522i | −0.0606508 | − | 0.109300i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.33981 | − | 18.7970i | −0.241848 | − | 1.04752i | ||||
\(323\) | −26.5830 | −1.47912 | ||||||||
\(324\) | 5.00000 | − | 7.48331i | 0.277778 | − | 0.415740i | ||||
\(325\) | −8.89047 | + | 14.2565i | −0.493155 | + | 0.790807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.36028 | + | 0.841723i | −0.185824 | + | 0.0465474i | ||||
\(328\) | −4.33981 | −0.239626 | ||||||||
\(329\) | −20.1617 | + | 4.65489i | −1.11155 | + | 0.256632i | ||||
\(330\) | 8.00000 | − | 7.48331i | 0.440386 | − | 0.411943i | ||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | − | 6.97915i | − | 0.383030i | ||||||
\(333\) | −4.70850 | − | 8.80879i | −0.258024 | − | 0.482719i | ||||
\(334\) | 20.6921i | 1.13222i | ||||||||
\(335\) | 20.1617 | − | 11.1878i | 1.10155 | − | 0.611253i | ||||
\(336\) | −2.08495 | − | 4.08080i | −0.113744 | − | 0.222626i | ||||
\(337\) | 22.4499i | 1.22293i | 0.791273 | + | 0.611463i | \(0.209419\pi\) | ||||
−0.791273 | + | 0.611463i | \(0.790581\pi\) | |||||||
\(338\) | 1.70850 | 0.0929300 | ||||||||
\(339\) | 10.0808 | − | 2.52517i | 0.547517 | − | 0.137148i | ||||
\(340\) | 9.29150 | − | 5.15587i | 0.503902 | − | 0.279616i | ||||
\(341\) | 8.67963 | 0.470028 | ||||||||
\(342\) | −7.91094 | − | 14.8000i | −0.427775 | − | 0.800293i | ||||
\(343\) | −11.6556 | − | 14.3926i | −0.629342 | − | 0.777129i | ||||
\(344\) | 10.3117i | 0.555972i | ||||||||
\(345\) | 19.2915 | + | 20.6235i | 1.03862 | + | 1.11033i | ||||
\(346\) | − | 2.22699i | − | 0.119724i | ||||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 0.210845 | + | 0.841723i | 0.0113025 | + | 0.0451211i | ||||
\(349\) | − | 13.7129i | − | 0.734036i | −0.930214 | − | 0.367018i | \(-0.880379\pi\) | ||
0.930214 | − | 0.367018i | \(-0.119621\pi\) | |||||||
\(350\) | 12.5120 | + | 4.29541i | 0.668793 | + | 0.229599i | ||||
\(351\) | −12.9373 | + | 11.7260i | −0.690540 | + | 0.625885i | ||||
\(352\) | − | 2.82843i | − | 0.150756i | ||||||
\(353\) | 9.80250i | 0.521734i | 0.965375 | + | 0.260867i | \(0.0840084\pi\) | ||||
−0.965375 | + | 0.260867i | \(0.915992\pi\) | |||||||
\(354\) | −3.64575 | + | 0.913230i | −0.193769 | + | 0.0485376i | ||||
\(355\) | 19.1822 | − | 10.6442i | 1.01808 | − | 0.564936i | ||||
\(356\) | 15.8219 | 0.838558 | ||||||||
\(357\) | 19.3926 | − | 9.90803i | 1.02637 | − | 0.524388i | ||||
\(358\) | 24.4539i | 1.29243i | ||||||||
\(359\) | 4.33138i | 0.228601i | 0.993446 | + | 0.114301i | \(0.0364627\pi\) | ||||
−0.993446 | + | 0.114301i | \(0.963537\pi\) | |||||||
\(360\) | 5.63561 | + | 3.63866i | 0.297023 | + | 0.191774i | ||||
\(361\) | −12.2915 | −0.646921 | ||||||||
\(362\) | 14.8000i | 0.777872i | ||||||||
\(363\) | −5.04042 | + | 1.26258i | −0.264554 | + | 0.0662685i | ||||
\(364\) | 2.00000 | + | 8.66259i | 0.104828 | + | 0.454043i | ||||
\(365\) | −6.00000 | − | 10.8127i | −0.314054 | − | 0.565964i | ||||
\(366\) | −1.06275 | − | 4.24264i | −0.0555506 | − | 0.221766i | ||||
\(367\) | −14.6315 | −0.763759 | −0.381879 | − | 0.924212i | \(-0.624723\pi\) | ||||
−0.381879 | + | 0.924212i | \(0.624723\pi\) | |||||||
\(368\) | 7.29150 | 0.380096 | ||||||||
\(369\) | 11.4821 | − | 6.13742i | 0.597733 | − | 0.319502i | ||||
\(370\) | 6.50972 | − | 3.61226i | 0.338424 | − | 0.187792i | ||||
\(371\) | −5.10850 | − | 22.1264i | −0.265220 | − | 1.14875i | ||||
\(372\) | 1.29150 | + | 5.15587i | 0.0669613 | + | 0.267319i | ||||
\(373\) | 6.98233i | 0.361531i | 0.983526 | + | 0.180766i | \(0.0578576\pi\) | ||||
−0.983526 | + | 0.180766i | \(0.942142\pi\) | |||||||
\(374\) | 13.4411 | 0.695024 | ||||||||
\(375\) | −19.0000 | + | 3.74166i | −0.981156 | + | 0.193218i | ||||
\(376\) | − | 7.82087i | − | 0.403331i | ||||||
\(377\) | − | 1.68345i | − | 0.0867019i | ||||||
\(378\) | 11.2874 | + | 7.84823i | 0.580561 | + | 0.403669i | ||||
\(379\) | −6.58301 | −0.338146 | −0.169073 | − | 0.985604i | \(-0.554077\pi\) | ||||
−0.169073 | + | 0.985604i | \(0.554077\pi\) | |||||||
\(380\) | 10.9373 | − | 6.06910i | 0.561069 | − | 0.311338i | ||||
\(381\) | −1.40122 | − | 5.59388i | −0.0717867 | − | 0.286583i | ||||
\(382\) | 0.500983i | 0.0256325i | ||||||||
\(383\) | − | 20.6921i | − | 1.05732i | −0.848835 | − | 0.528658i | \(-0.822695\pi\) | ||
0.848835 | − | 0.528658i | \(-0.177305\pi\) | |||||||
\(384\) | 1.68014 | − | 0.420861i | 0.0857394 | − | 0.0214770i | ||||
\(385\) | 11.2024 | + | 12.4300i | 0.570929 | + | 0.633492i | ||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | −14.5830 | − | 27.2823i | −0.741296 | − | 1.38684i | ||||
\(388\) | −14.6315 | −0.742802 | ||||||||
\(389\) | 37.0931i | 1.88069i | 0.340218 | + | 0.940346i | \(0.389499\pi\) | ||||
−0.340218 | + | 0.940346i | \(0.610501\pi\) | |||||||
\(390\) | −8.89047 | − | 9.50432i | −0.450187 | − | 0.481270i | ||||
\(391\) | 34.6504i | 1.75234i | ||||||||
\(392\) | 6.29150 | − | 3.06871i | 0.317769 | − | 0.154993i | ||||
\(393\) | 30.2288 | − | 7.57205i | 1.52484 | − | 0.381959i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | −3.57113 | − | 6.43560i | −0.179683 | − | 0.323810i | ||||
\(396\) | 4.00000 | + | 7.48331i | 0.201008 | + | 0.376051i | ||||
\(397\) | 14.8424 | 0.744916 | 0.372458 | − | 0.928049i | \(-0.378515\pi\) | ||||
0.372458 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(398\) | 9.20614i | 0.461462i | ||||||||
\(399\) | 22.8275 | − | 11.6630i | 1.14281 | − | 0.583879i | ||||
\(400\) | −2.64575 | + | 4.24264i | −0.132288 | + | 0.212132i | ||||
\(401\) | − | 7.48331i | − | 0.373699i | −0.982389 | − | 0.186849i | \(-0.940172\pi\) | ||
0.982389 | − | 0.186849i | \(-0.0598277\pi\) | |||||||
\(402\) | 4.33981 | + | 17.3252i | 0.216450 | + | 0.864102i | ||||
\(403\) | − | 10.3117i | − | 0.513664i | ||||||
\(404\) | 2.16991 | 0.107957 | ||||||||
\(405\) | −20.0563 | − | 1.65704i | −0.996604 | − | 0.0823389i | ||||
\(406\) | −1.29150 | + | 0.298179i | −0.0640962 | + | 0.0147984i | ||||
\(407\) | 9.41699 | 0.466783 | ||||||||
\(408\) | 2.00000 | + | 7.98430i | 0.0990148 | + | 0.395282i | ||||
\(409\) | − | 23.4626i | − | 1.16015i | −0.814563 | − | 0.580076i | \(-0.803023\pi\) | ||
0.814563 | − | 0.580076i | \(-0.196977\pi\) | |||||||
\(410\) | 4.70850 | + | 8.48528i | 0.232536 | + | 0.419058i | ||||
\(411\) | −2.16991 | + | 0.543544i | −0.107034 | + | 0.0268110i | ||||
\(412\) | −3.14944 | −0.155162 | ||||||||
\(413\) | −1.29150 | − | 5.59388i | −0.0635507 | − | 0.275257i | ||||
\(414\) | −19.2915 | + | 10.3117i | −0.948126 | + | 0.506794i | ||||
\(415\) | −13.6458 | + | 7.57205i | −0.669844 | + | 0.371697i | ||||
\(416\) | −3.36028 | −0.164751 | ||||||||
\(417\) | −0.228757 | − | 0.913230i | −0.0112023 | − | 0.0447211i | ||||
\(418\) | 15.8219 | 0.773874 | ||||||||
\(419\) | −33.8137 | −1.65191 | −0.825953 | − | 0.563739i | \(-0.809362\pi\) | ||||
−0.825953 | + | 0.563739i | \(0.809362\pi\) | |||||||
\(420\) | −5.71678 | + | 8.50402i | −0.278950 | + | 0.414954i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 21.1660 | 1.03035 | ||||||||
\(423\) | 11.0604 | + | 20.6921i | 0.537774 | + | 1.00608i | ||||
\(424\) | 8.58301 | 0.416828 | ||||||||
\(425\) | −20.1617 | − | 12.5730i | −0.977986 | − | 0.609881i | ||||
\(426\) | 4.12897 | + | 16.4835i | 0.200049 | + | 0.798626i | ||||
\(427\) | 6.50972 | − | 1.50295i | 0.315028 | − | 0.0727328i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | − | 15.9686i | −0.193122 | − | 0.770971i | ||||
\(430\) | 20.1617 | − | 11.1878i | 0.972283 | − | 0.539522i | ||||
\(431\) | − | 8.98626i | − | 0.432853i | −0.976299 | − | 0.216427i | \(-0.930560\pi\) | ||
0.976299 | − | 0.216427i | \(-0.0694402\pi\) | |||||||
\(432\) | −3.85005 | + | 3.48957i | −0.185236 | + | 0.167892i | ||||
\(433\) | 18.5496 | 0.891439 | 0.445719 | − | 0.895173i | \(-0.352948\pi\) | ||||
0.445719 | + | 0.895173i | \(0.352948\pi\) | |||||||
\(434\) | −7.91094 | + | 1.82646i | −0.379737 | + | 0.0876729i | ||||
\(435\) | 1.41699 | − | 1.32548i | 0.0679397 | − | 0.0635518i | ||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 40.7878i | 1.95114i | ||||||||
\(438\) | 9.29150 | − | 2.32744i | 0.443965 | − | 0.111210i | ||||
\(439\) | − | 26.5313i | − | 1.26627i | −0.774041 | − | 0.633135i | \(-0.781768\pi\) | ||
0.774041 | − | 0.633135i | \(-0.218232\pi\) | |||||||
\(440\) | −5.53019 | + | 3.06871i | −0.263641 | + | 0.146295i | ||||
\(441\) | −12.3059 | + | 17.0166i | −0.585997 | + | 0.810313i | ||||
\(442\) | − | 15.9686i | − | 0.759549i | ||||||
\(443\) | −29.1660 | −1.38572 | −0.692859 | − | 0.721073i | \(-0.743649\pi\) | ||||
−0.692859 | + | 0.721073i | \(0.743649\pi\) | |||||||
\(444\) | 1.40122 | + | 5.59388i | 0.0664990 | + | 0.265474i | ||||
\(445\) | −17.1660 | − | 30.9352i | −0.813747 | − | 1.46647i | ||||
\(446\) | −1.19038 | −0.0563659 | ||||||||
\(447\) | 4.55066 | + | 18.1669i | 0.215239 | + | 0.859265i | ||||
\(448\) | 0.595188 | + | 2.57794i | 0.0281200 | + | 0.121796i | ||||
\(449\) | − | 36.5921i | − | 1.72689i | −0.504446 | − | 0.863444i | \(-0.668303\pi\) | ||
0.504446 | − | 0.863444i | \(-0.331697\pi\) | |||||||
\(450\) | 1.00000 | − | 14.9666i | 0.0471405 | − | 0.705534i | ||||
\(451\) | 12.2748i | 0.578000i | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 2.38075 | − | 0.596358i | 0.111857 | − | 0.0280194i | ||||
\(454\) | 18.1669i | 0.852615i | ||||||||
\(455\) | 14.7673 | − | 13.3089i | 0.692304 | − | 0.623933i | ||||
\(456\) | 2.35425 | + | 9.39851i | 0.110248 | + | 0.440126i | ||||
\(457\) | 8.48528i | 0.396925i | 0.980109 | + | 0.198462i | \(0.0635948\pi\) | ||||
−0.980109 | + | 0.198462i | \(0.936405\pi\) | |||||||
\(458\) | − | 24.9007i | − | 1.16353i | ||||||
\(459\) | −16.5830 | − | 18.2960i | −0.774028 | − | 0.853986i | ||||
\(460\) | −7.91094 | − | 14.2565i | −0.368850 | − | 0.664712i | ||||
\(461\) | 17.9918 | 0.837961 | 0.418981 | − | 0.907995i | \(-0.362388\pi\) | ||||
0.418981 | + | 0.907995i | \(0.362388\pi\) | |||||||
\(462\) | −11.5423 | + | 5.89714i | −0.536994 | + | 0.274360i | ||||
\(463\) | 1.50295i | 0.0698480i | 0.999390 | + | 0.0349240i | \(0.0111189\pi\) | ||||
−0.999390 | + | 0.0349240i | \(0.988881\pi\) | |||||||
\(464\) | − | 0.500983i | − | 0.0232576i | ||||||
\(465\) | 8.67963 | − | 8.11905i | 0.402508 | − | 0.376512i | ||||
\(466\) | −13.2915 | −0.615717 | ||||||||
\(467\) | − | 0.841723i | − | 0.0389503i | −0.999810 | − | 0.0194751i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194751i | \(-0.00619952\pi\) | |||||||
\(468\) | 8.89047 | − | 4.75216i | 0.410962 | − | 0.219669i | ||||
\(469\) | −26.5830 | + | 6.13742i | −1.22749 | + | 0.283400i | ||||
\(470\) | −15.2915 | + | 8.48528i | −0.705344 | + | 0.391397i | ||||
\(471\) | −27.5203 | + | 6.89360i | −1.26807 | + | 0.317640i | ||||
\(472\) | 2.16991 | 0.0998781 | ||||||||
\(473\) | 29.1660 | 1.34105 | ||||||||
\(474\) | 5.53019 | − | 1.38527i | 0.254010 | − | 0.0636274i | ||||
\(475\) | −23.7328 | − | 14.8000i | −1.08894 | − | 0.679071i | ||||
\(476\) | −12.2508 | + | 2.82843i | −0.561513 | + | 0.129641i | ||||
\(477\) | −22.7085 | + | 12.1382i | −1.03975 | + | 0.555770i | ||||
\(478\) | − | 14.6431i | − | 0.669761i | ||||||
\(479\) | 21.6991 | 0.991456 | 0.495728 | − | 0.868478i | \(-0.334901\pi\) | ||||
0.495728 | + | 0.868478i | \(0.334901\pi\) | |||||||
\(480\) | −2.64575 | − | 2.82843i | −0.120761 | − | 0.129099i | ||||
\(481\) | − | 11.1878i | − | 0.510118i | ||||||
\(482\) | 17.3252i | 0.789141i | ||||||||
\(483\) | −15.2024 | − | 29.7552i | −0.691735 | − | 1.35391i | ||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | 15.8745 | + | 28.6078i | 0.720824 | + | 1.29901i | ||||
\(486\) | 5.25127 | − | 14.6773i | 0.238202 | − | 0.665777i | ||||
\(487\) | − | 9.98823i | − | 0.452610i | −0.974056 | − | 0.226305i | \(-0.927335\pi\) | ||
0.974056 | − | 0.226305i | \(-0.0726646\pi\) | |||||||
\(488\) | 2.52517i | 0.114309i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.8260 | − | 8.97185i | −0.579419 | − | 0.405307i | ||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | −7.29150 | + | 1.82646i | −0.328726 | + | 0.0823432i | ||||
\(493\) | 2.38075 | 0.107224 | ||||||||
\(494\) | − | 18.7970i | − | 0.845718i | ||||||
\(495\) | 10.2917 | − | 15.9399i | 0.462577 | − | 0.716446i | ||||
\(496\) | − | 3.06871i | − | 0.137789i | ||||||
\(497\) | −25.2915 | + | 5.83925i | −1.13448 | + | 0.261926i | ||||
\(498\) | −2.93725 | − | 11.7260i | −0.131621 | − | 0.525453i | ||||
\(499\) | 22.5830 | 1.01095 | 0.505477 | − | 0.862840i | \(-0.331317\pi\) | ||||
0.505477 | + | 0.862840i | \(0.331317\pi\) | |||||||
\(500\) | 11.1658 | + | 0.569951i | 0.499350 | + | 0.0254890i | ||||
\(501\) | 8.70850 | + | 34.7656i | 0.389067 | + | 1.55321i | ||||
\(502\) | −6.50972 | −0.290543 | ||||||||
\(503\) | − | 15.6417i | − | 0.697431i | −0.937229 | − | 0.348715i | \(-0.886618\pi\) | ||
0.937229 | − | 0.348715i | \(-0.113382\pi\) | |||||||
\(504\) | −5.22047 | − | 5.97885i | −0.232538 | − | 0.266319i | ||||
\(505\) | −2.35425 | − | 4.24264i | −0.104763 | − | 0.188795i | ||||
\(506\) | − | 20.6235i | − | 0.916826i | ||||||
\(507\) | 2.87052 | − | 0.719041i | 0.127484 | − | 0.0319337i | ||||
\(508\) | 3.32941i | 0.147719i | ||||||||
\(509\) | 39.6909 | 1.75927 | 0.879633 | − | 0.475652i | \(-0.157788\pi\) | ||||
0.879633 | + | 0.475652i | \(0.157788\pi\) | |||||||
\(510\) | 13.4411 | − | 12.5730i | 0.595183 | − | 0.556743i | ||||
\(511\) | 3.29150 | + | 14.2565i | 0.145608 | + | 0.630669i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −19.5203 | − | 21.5367i | −0.861840 | − | 0.950869i | ||||
\(514\) | 18.7105i | 0.825283i | ||||||||
\(515\) | 3.41699 | + | 6.15784i | 0.150571 | + | 0.271347i | ||||
\(516\) | 4.33981 | + | 17.3252i | 0.191050 | + | 0.762699i | ||||
\(517\) | −22.1208 | −0.972870 | ||||||||
\(518\) | −8.58301 | + | 1.98162i | −0.377116 | + | 0.0870676i | ||||
\(519\) | −0.937254 | − | 3.74166i | −0.0411409 | − | 0.164241i | ||||
\(520\) | 3.64575 | + | 6.57008i | 0.159877 | + | 0.288117i | ||||
\(521\) | −13.0194 | −0.570392 | −0.285196 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285196 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(522\) | 0.708497 | + | 1.32548i | 0.0310101 | + | 0.0580146i | ||||
\(523\) | −16.8014 | −0.734675 | −0.367337 | − | 0.930088i | \(-0.619731\pi\) | ||||
−0.367337 | + | 0.930088i | \(0.619731\pi\) | |||||||
\(524\) | −17.9918 | −0.785975 | ||||||||
\(525\) | 22.8297 | + | 1.95109i | 0.996368 | + | 0.0851524i | ||||
\(526\) | −14.5830 | −0.635849 | ||||||||
\(527\) | 14.5830 | 0.635246 | ||||||||
\(528\) | −1.19038 | − | 4.75216i | −0.0518045 | − | 0.206811i | ||||
\(529\) | 30.1660 | 1.31157 | ||||||||
\(530\) | −9.31216 | − | 16.7816i | −0.404494 | − | 0.728948i | ||||
\(531\) | −5.74103 | + | 3.06871i | −0.249140 | + | 0.133171i | ||||
\(532\) | −14.4207 | + | 3.32941i | −0.625215 | + | 0.144348i | ||||
\(533\) | 14.5830 | 0.631660 | ||||||||
\(534\) | 26.5830 | − | 6.65882i | 1.15036 | − | 0.288155i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 10.3117i | − | 0.445399i | ||||||
\(537\) | 10.2917 | + | 41.0860i | 0.444119 | + | 1.77299i | ||||
\(538\) | −9.31216 | −0.401476 | ||||||||
\(539\) | −8.67963 | − | 17.7951i | −0.373858 | − | 0.766487i | ||||
\(540\) | 11.0000 | + | 3.74166i | 0.473365 | + | 0.161015i | ||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | − | 20.3939i | − | 0.875993i | ||||||
\(543\) | 6.22876 | + | 24.8661i | 0.267302 | + | 1.06711i | ||||
\(544\) | − | 4.75216i | − | 0.203747i | ||||||
\(545\) | −2.16991 | − | 3.91044i | −0.0929486 | − | 0.167505i | ||||
\(546\) | 7.00603 | + | 13.7127i | 0.299831 | + | 0.586848i | ||||
\(547\) | − | 16.9706i | − | 0.725609i | −0.931865 | − | 0.362804i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362804i | \(-0.118181\pi\) | |||||||
\(548\) | 1.29150 | 0.0551703 | ||||||||
\(549\) | −3.57113 | − | 6.68097i | −0.152412 | − | 0.285137i | ||||
\(550\) | 12.0000 | + | 7.48331i | 0.511682 | + | 0.319090i | ||||
\(551\) | 2.80244 | 0.119388 | ||||||||
\(552\) | 12.2508 | − | 3.06871i | 0.521427 | − | 0.130613i | ||||
\(553\) | 1.95906 | + | 8.48528i | 0.0833078 | + | 0.360831i | ||||
\(554\) | 6.98233i | 0.296651i | ||||||||
\(555\) | 9.41699 | − | 8.80879i | 0.399729 | − | 0.373912i | ||||
\(556\) | 0.543544i | 0.0230514i | ||||||||
\(557\) | −35.1660 | −1.49003 | −0.745016 | − | 0.667047i | \(-0.767558\pi\) | ||||
−0.745016 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(558\) | 4.33981 | + | 8.11905i | 0.183719 | + | 0.343707i | ||||
\(559\) | − | 34.6504i | − | 1.46555i | ||||||
\(560\) | 4.39467 | − | 3.96066i | 0.185709 | − | 0.167369i | ||||
\(561\) | 22.5830 | − | 5.65685i | 0.953455 | − | 0.238833i | ||||
\(562\) | 9.30978i | 0.392709i | ||||||||
\(563\) | − | 13.1166i | − | 0.552798i | −0.961043 | − | 0.276399i | \(-0.910859\pi\) | ||
0.961043 | − | 0.276399i | \(-0.0891411\pi\) | |||||||
\(564\) | −3.29150 | − | 13.1402i | −0.138597 | − | 0.553301i | ||||
\(565\) | 6.50972 | + | 11.7313i | 0.273866 | + | 0.493540i | ||||
\(566\) | −32.2016 | −1.35353 | ||||||||
\(567\) | 22.2674 | + | 8.43570i | 0.935145 | + | 0.354266i | ||||
\(568\) | − | 9.81076i | − | 0.411650i | ||||||
\(569\) | 33.7637i | 1.41545i | 0.706490 | + | 0.707723i | \(0.250278\pi\) | ||||
−0.706490 | + | 0.707723i | \(0.749722\pi\) | |||||||
\(570\) | 15.8219 | − | 14.8000i | 0.662706 | − | 0.619905i | ||||
\(571\) | −13.4170 | −0.561484 | −0.280742 | − | 0.959783i | \(-0.590580\pi\) | ||||
−0.280742 | + | 0.959783i | \(0.590580\pi\) | |||||||
\(572\) | 9.50432i | 0.397395i | ||||||||
\(573\) | 0.210845 | + | 0.841723i | 0.00880816 | + | 0.0351635i | ||||
\(574\) | −2.58301 | − | 11.1878i | −0.107813 | − | 0.466968i | ||||
\(575\) | −19.2915 | + | 30.9352i | −0.804511 | + | 1.29009i | ||||
\(576\) | 2.64575 | − | 1.41421i | 0.110240 | − | 0.0589256i | ||||
\(577\) | −36.3306 | −1.51246 | −0.756231 | − | 0.654305i | \(-0.772961\pi\) | ||||
−0.756231 | + | 0.654305i | \(0.772961\pi\) | |||||||
\(578\) | 5.58301 | 0.232222 | ||||||||
\(579\) | 3.57113 | + | 14.2565i | 0.148411 | + | 0.592479i | ||||
\(580\) | −0.979531 | + | 0.543544i | −0.0406728 | + | 0.0225694i | ||||
\(581\) | 17.9918 | − | 4.15390i | 0.746425 | − | 0.172333i | ||||
\(582\) | −24.5830 | + | 6.15784i | −1.01900 | + | 0.255251i | ||||
\(583\) | − | 24.2764i | − | 1.00543i | ||||||
\(584\) | −5.53019 | −0.228841 | ||||||||
\(585\) | −18.9373 | − | 12.2269i | −0.782959 | − | 0.505522i | ||||
\(586\) | − | 7.27733i | − | 0.300624i | ||||||
\(587\) | 37.7719i | 1.55901i | 0.626394 | + | 0.779507i | \(0.284530\pi\) | ||||
−0.626394 | + | 0.779507i | \(0.715470\pi\) | |||||||
\(588\) | 9.27911 | − | 7.80372i | 0.382664 | − | 0.321820i | ||||
\(589\) | 17.1660 | 0.707313 | ||||||||
\(590\) | −2.35425 | − | 4.24264i | −0.0969229 | − | 0.174667i | ||||
\(591\) | −30.2425 | + | 7.57551i | −1.24401 | + | 0.311615i | ||||
\(592\) | − | 3.32941i | − | 0.136838i | ||||||
\(593\) | − | 6.43560i | − | 0.264279i | −0.991231 | − | 0.132139i | \(-0.957815\pi\) | ||
0.991231 | − | 0.132139i | \(-0.0421846\pi\) | |||||||
\(594\) | 9.87000 | + | 10.8896i | 0.404971 | + | 0.446805i | ||||
\(595\) | 18.8217 | + | 20.8842i | 0.771614 | + | 0.856168i | ||||
\(596\) | − | 10.8127i | − | 0.442906i | ||||||
\(597\) | 3.87451 | + | 15.4676i | 0.158573 | + | 0.633047i | ||||
\(598\) | −24.5015 | −1.00194 | ||||||||
\(599\) | − | 4.15390i | − | 0.169724i | −0.996393 | − | 0.0848620i | \(-0.972955\pi\) | ||
0.996393 | − | 0.0848620i | \(-0.0270449\pi\) | |||||||
\(600\) | −2.65967 | + | 8.24173i | −0.108581 | + | 0.336467i | ||||
\(601\) | − | 6.13742i | − | 0.250351i | −0.992135 | − | 0.125175i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125175i | \(-0.0399494\pi\) | |||||||
\(602\) | −26.5830 | + | 6.13742i | −1.08344 | + | 0.250143i | ||||
\(603\) | 14.5830 | + | 27.2823i | 0.593866 | + | 1.11102i | ||||
\(604\) | −1.41699 | −0.0576567 | ||||||||
\(605\) | −3.25486 | − | 5.86565i | −0.132329 | − | 0.238473i | ||||
\(606\) | 3.64575 | − | 0.913230i | 0.148099 | − | 0.0370974i | ||||
\(607\) | −5.95188 | −0.241579 | −0.120790 | − | 0.992678i | \(-0.538543\pi\) | ||||
−0.120790 | + | 0.992678i | \(0.538543\pi\) | |||||||
\(608\) | − | 5.59388i | − | 0.226862i | ||||||
\(609\) | −2.04442 | + | 1.04453i | −0.0828439 | + | 0.0423264i | ||||
\(610\) | 4.93725 | − | 2.73969i | 0.199904 | − | 0.110927i | ||||
\(611\) | 26.2803i | 1.06319i | ||||||||
\(612\) | 6.72057 | + | 12.5730i | 0.271663 | + | 0.508235i | ||||
\(613\) | 47.5823i | 1.92183i | 0.276843 | + | 0.960915i | \(0.410712\pi\) | ||||
−0.276843 | + | 0.960915i | \(0.589288\pi\) | |||||||
\(614\) | −12.0399 | −0.485891 | ||||||||
\(615\) | 11.4821 | + | 12.2748i | 0.463002 | + | 0.494970i | ||||
\(616\) | 7.29150 | − | 1.68345i | 0.293783 | − | 0.0678280i | ||||
\(617\) | 47.1660 | 1.89883 | 0.949416 | − | 0.314021i | \(-0.101676\pi\) | ||||
0.949416 | + | 0.314021i | \(0.101676\pi\) | |||||||
\(618\) | −5.29150 | + | 1.32548i | −0.212855 | + | 0.0533185i | ||||
\(619\) | 40.2443i | 1.61755i | 0.588116 | + | 0.808777i | \(0.299870\pi\) | ||||
−0.588116 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(620\) | −6.00000 | + | 3.32941i | −0.240966 | + | 0.133712i | ||||
\(621\) | −28.0726 | + | 25.4442i | −1.12652 | + | 1.02104i | ||||
\(622\) | 24.5015 | 0.982421 | ||||||||
\(623\) | 9.41699 | + | 40.7878i | 0.377284 | + | 1.63413i | ||||
\(624\) | −5.64575 | + | 1.41421i | −0.226011 | + | 0.0566139i | ||||
\(625\) | −11.0000 | − | 22.4499i | −0.440000 | − | 0.897998i | ||||
\(626\) | 14.6315 | 0.584793 | ||||||||
\(627\) | 26.5830 | − | 6.65882i | 1.06162 | − | 0.265928i | ||||
\(628\) | 16.3797 | 0.653622 | ||||||||
\(629\) | 15.8219 | 0.630860 | ||||||||
\(630\) | −6.02599 | + | 16.6939i | −0.240081 | + | 0.665102i | ||||
\(631\) | 32.4575 | 1.29211 | 0.646057 | − | 0.763290i | \(-0.276417\pi\) | ||||
0.646057 | + | 0.763290i | \(0.276417\pi\) | |||||||
\(632\) | −3.29150 | −0.130929 | ||||||||
\(633\) | 35.5619 | − | 8.90796i | 1.41346 | − | 0.354060i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 6.50972 | − | 3.61226i | 0.258330 | − | 0.143348i | ||||
\(636\) | 14.4207 | − | 3.61226i | 0.571817 | − | 0.143235i | ||||
\(637\) | −21.1412 | + | 10.3117i | −0.837646 | + | 0.408566i | ||||
\(638\) | −1.41699 | −0.0560994 | ||||||||
\(639\) | 13.8745 | + | 25.9568i | 0.548867 | + | 1.02684i | ||||
\(640\) | 1.08495 | + | 1.95522i | 0.0428866 | + | 0.0772868i | ||||
\(641\) | − | 28.1068i | − | 1.11015i | −0.831800 | − | 0.555076i | \(-0.812689\pi\) | ||
0.831800 | − | 0.555076i | \(-0.187311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6786 | −0.894357 | −0.447178 | − | 0.894445i | \(-0.647571\pi\) | ||||
−0.447178 | + | 0.894445i | \(0.647571\pi\) | |||||||
\(644\) | 4.33981 | + | 18.7970i | 0.171013 | + | 0.740706i | ||||
\(645\) | 29.1660 | − | 27.2823i | 1.14841 | − | 1.07424i | ||||
\(646\) | 26.5830 | 1.04589 | ||||||||
\(647\) | 13.9583i | 0.548757i | 0.961622 | + | 0.274379i | \(0.0884721\pi\) | ||||
−0.961622 | + | 0.274379i | \(0.911528\pi\) | |||||||
\(648\) | −5.00000 | + | 7.48331i | −0.196419 | + | 0.293972i | ||||
\(649\) | − | 6.13742i | − | 0.240915i | ||||||
\(650\) | 8.89047 | − | 14.2565i | 0.348713 | − | 0.559185i | ||||
\(651\) | −12.5228 | + | 6.39812i | −0.490808 | + | 0.250762i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.1660 | −0.906556 | −0.453278 | − | 0.891369i | \(-0.649746\pi\) | ||||
−0.453278 | + | 0.891369i | \(0.649746\pi\) | |||||||
\(654\) | 3.36028 | − | 0.841723i | 0.131397 | − | 0.0329140i | ||||
\(655\) | 19.5203 | + | 35.1779i | 0.762720 | + | 1.37451i | ||||
\(656\) | 4.33981 | 0.169441 | ||||||||
\(657\) | 14.6315 | − | 7.82087i | 0.570830 | − | 0.305121i | ||||
\(658\) | 20.1617 | − | 4.65489i | 0.785985 | − | 0.181466i | ||||
\(659\) | 27.1048i | 1.05585i | 0.849290 | + | 0.527927i | \(0.177031\pi\) | ||||
−0.849290 | + | 0.527927i | \(0.822969\pi\) | |||||||
\(660\) | −8.00000 | + | 7.48331i | −0.311400 | + | 0.291288i | ||||
\(661\) | − | 8.66259i | − | 0.336936i | −0.985707 | − | 0.168468i | \(-0.946118\pi\) | ||
0.985707 | − | 0.168468i | \(-0.0538820\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | −6.72057 | − | 26.8295i | −0.261005 | − | 1.04197i | ||||
\(664\) | 6.97915i | 0.270843i | ||||||||
\(665\) | 22.1555 | + | 24.5833i | 0.859152 | + | 0.953299i | ||||
\(666\) | 4.70850 | + | 8.80879i | 0.182451 | + | 0.341334i | ||||
\(667\) | − | 3.65292i | − | 0.141442i | ||||||
\(668\) | − | 20.6921i | − | 0.800601i | ||||||
\(669\) | −2.00000 | + | 0.500983i | −0.0773245 | + | 0.0193691i | ||||
\(670\) | −20.1617 | + | 11.1878i | −0.778914 | + | 0.432221i | ||||
\(671\) | 7.14226 | 0.275724 | ||||||||
\(672\) | 2.08495 | + | 4.08080i | 0.0804288 | + | 0.157420i | ||||
\(673\) | − | 23.6294i | − | 0.910846i | −0.890275 | − | 0.455423i | \(-0.849488\pi\) | ||
0.890275 | − | 0.455423i | \(-0.150512\pi\) | |||||||
\(674\) | − | 22.4499i | − | 0.864740i | ||||||
\(675\) | −4.61874 | − | 25.5669i | −0.177775 | − | 0.984071i | ||||
\(676\) | −1.70850 | −0.0657114 | ||||||||
\(677\) | 6.19024i | 0.237910i | 0.992900 | + | 0.118955i | \(0.0379545\pi\) | ||||
−0.992900 | + | 0.118955i | \(0.962046\pi\) | |||||||
\(678\) | −10.0808 | + | 2.52517i | −0.387153 | + | 0.0969785i | ||||
\(679\) | −8.70850 | − | 37.7191i | −0.334201 | − | 1.44753i | ||||
\(680\) | −9.29150 | + | 5.15587i | −0.356313 | + | 0.197719i | ||||
\(681\) | 7.64575 | + | 30.5230i | 0.292986 | + | 1.16964i | ||||
\(682\) | −8.67963 | −0.332360 | ||||||||
\(683\) | 26.5830 | 1.01717 | 0.508585 | − | 0.861012i | \(-0.330169\pi\) | ||||
0.508585 | + | 0.861012i | \(0.330169\pi\) | |||||||
\(684\) | 7.91094 | + | 14.8000i | 0.302482 | + | 0.565893i | ||||
\(685\) | −1.40122 | − | 2.52517i | −0.0535379 | − | 0.0964817i | ||||
\(686\) | 11.6556 | + | 14.3926i | 0.445012 | + | 0.549513i | ||||
\(687\) | −10.4797 | − | 41.8367i | −0.399827 | − | 1.59617i | ||||
\(688\) | − | 10.3117i | − | 0.393131i | ||||||
\(689\) | −28.8413 | −1.09877 | ||||||||
\(690\) | −19.2915 | − | 20.6235i | −0.734415 | − | 0.785123i | ||||
\(691\) | − | 11.7313i | − | 0.446280i | −0.974786 | − | 0.223140i | \(-0.928369\pi\) | ||
0.974786 | − | 0.223140i | \(-0.0716307\pi\) | |||||||
\(692\) | 2.22699i | 0.0846574i | ||||||||
\(693\) | −16.9108 | + | 14.7657i | −0.642386 | + | 0.560903i | ||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 1.06275 | − | 0.589720i | 0.0403123 | − | 0.0223693i | ||||
\(696\) | −0.210845 | − | 0.841723i | −0.00799204 | − | 0.0319054i | ||||
\(697\) | 20.6235i | 0.781170i | ||||||||
\(698\) | 13.7129i | 0.519042i | ||||||||
\(699\) | −22.3316 | + | 5.59388i | −0.844659 | + | 0.211580i | ||||
\(700\) | −12.5120 | − | 4.29541i | −0.472908 | − | 0.162351i | ||||
\(701\) | − | 21.1245i | − | 0.797860i | −0.916981 | − | 0.398930i | \(-0.869382\pi\) | ||
0.916981 | − | 0.398930i | \(-0.130618\pi\) | |||||||
\(702\) | 12.9373 | − | 11.7260i | 0.488285 | − | 0.442568i | ||||
\(703\) | 18.6243 | 0.702430 | ||||||||
\(704\) | 2.82843i | 0.106600i | ||||||||
\(705\) | −22.1208 | + | 20.6921i | −0.833116 | + | 0.779309i | ||||
\(706\) | − | 9.80250i | − | 0.368922i | ||||||
\(707\) | 1.29150 | + | 5.59388i | 0.0485720 | + | 0.210380i | ||||
\(708\) | 3.64575 | − | 0.913230i | 0.137016 | − | 0.0343213i | ||||
\(709\) | −0.583005 | −0.0218952 | −0.0109476 | − | 0.999940i | \(-0.503485\pi\) | ||||
−0.0109476 | + | 0.999940i | \(0.503485\pi\) | |||||||
\(710\) | −19.1822 | + | 10.6442i | −0.719894 | + | 0.399470i | ||||
\(711\) | 8.70850 | − | 4.65489i | 0.326594 | − | 0.174572i | ||||
\(712\) | −15.8219 | −0.592950 | ||||||||
\(713\) | − | 22.3755i | − | 0.837970i | ||||||
\(714\) | −19.3926 | + | 9.90803i | −0.725751 | + | 0.370799i | ||||
\(715\) | 18.5830 | − | 10.3117i | 0.694965 | − | 0.385637i | ||||
\(716\) | − | 24.4539i | − | 0.913884i | ||||||
\(717\) | −6.16272 | − | 24.6025i | −0.230151 | − | 0.918798i | ||||
\(718\) | − | 4.33138i | − | 0.161646i | ||||||
\(719\) | 2.80244 | 0.104513 | 0.0522567 | − | 0.998634i | \(-0.483359\pi\) | ||||
0.0522567 | + | 0.998634i | \(0.483359\pi\) | |||||||
\(720\) | −5.63561 | − | 3.63866i | −0.210027 | − | 0.135605i | ||||
\(721\) | −1.87451 | − | 8.11905i | −0.0698103 | − | 0.302369i | ||||
\(722\) | 12.2915 | 0.457442 | ||||||||
\(723\) | 7.29150 | + | 29.1088i | 0.271174 | + | 1.08257i | ||||
\(724\) | − | 14.8000i | − | 0.550038i | ||||||
\(725\) | 2.12549 | + | 1.32548i | 0.0789388 | + | 0.0492270i | ||||
\(726\) | 5.04042 | − | 1.26258i | 0.187068 | − | 0.0468589i | ||||
\(727\) | 45.8536 | 1.70062 | 0.850308 | − | 0.526286i | \(-0.176416\pi\) | ||||
0.850308 | + | 0.526286i | \(0.176416\pi\) | |||||||
\(728\) | −2.00000 | − | 8.66259i | −0.0741249 | − | 0.321057i | ||||
\(729\) | 2.64575 | − | 26.8701i | 0.0979908 | − | 0.995187i | ||||
\(730\) | 6.00000 | + | 10.8127i | 0.222070 | + | 0.400197i | ||||
\(731\) | 49.0030 | 1.81244 | ||||||||
\(732\) | 1.06275 | + | 4.24264i | 0.0392802 | + | 0.156813i | ||||
\(733\) | −28.2835 | −1.04467 | −0.522337 | − | 0.852739i | \(-0.674940\pi\) | ||||
−0.522337 | + | 0.852739i | \(0.674940\pi\) | |||||||
\(734\) | 14.6315 | 0.540059 | ||||||||
\(735\) | −25.3254 | − | 9.67601i | −0.934141 | − | 0.356905i | ||||
\(736\) | −7.29150 | −0.268768 | ||||||||
\(737\) | −29.1660 | −1.07434 | ||||||||
\(738\) | −11.4821 | + | 6.13742i | −0.422661 | + | 0.225922i | ||||
\(739\) | −33.1660 | −1.22003 | −0.610016 | − | 0.792389i | \(-0.708837\pi\) | ||||
−0.610016 | + | 0.792389i | \(0.708837\pi\) | |||||||
\(740\) | −6.50972 | + | 3.61226i | −0.239302 | + | 0.132789i | ||||
\(741\) | −7.91094 | − | 31.5817i | −0.290616 | − | 1.16018i | ||||
\(742\) | 5.10850 | + | 22.1264i | 0.187539 | + | 0.812287i | ||||
\(743\) | −2.12549 | −0.0779767 | −0.0389884 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389884 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(744\) | −1.29150 | − | 5.15587i | −0.0473488 | − | 0.189023i | ||||
\(745\) | −21.1412 | + | 11.7313i | −0.774555 | + | 0.429802i | ||||
\(746\) | − | 6.98233i | − | 0.255641i | ||||||
\(747\) | −9.87000 | − | 18.4651i | −0.361125 | − | 0.675602i | ||||
\(748\) | −13.4411 | −0.491456 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.0000 | − | 3.74166i | 0.693782 | − | 0.136626i | ||||
\(751\) | −21.1660 | −0.772359 | −0.386179 | − | 0.922424i | \(-0.626205\pi\) | ||||
−0.386179 | + | 0.922424i | \(0.626205\pi\) | |||||||
\(752\) | 7.82087i | 0.285198i | ||||||||
\(753\) | −10.9373 | + | 2.73969i | −0.398576 | + | 0.0998399i | ||||
\(754\) | 1.68345i | 0.0613075i | ||||||||
\(755\) | 1.53737 | + | 2.77053i | 0.0559508 | + | 0.100830i | ||||
\(756\) | −11.2874 | − | 7.84823i | −0.410519 | − | 0.285437i | ||||
\(757\) | − | 34.2646i | − | 1.24537i | −0.782473 | − | 0.622685i | \(-0.786042\pi\) | ||
0.782473 | − | 0.622685i | \(-0.213958\pi\) | |||||||
\(758\) | 6.58301 | 0.239106 | ||||||||
\(759\) | −8.67963 | − | 34.6504i | −0.315051 | − | 1.25773i | ||||
\(760\) | −10.9373 | + | 6.06910i | −0.396736 | + | 0.220149i | ||||
\(761\) | −11.4821 | −0.416225 | −0.208112 | − | 0.978105i | \(-0.566732\pi\) | ||||
−0.208112 | + | 0.978105i | \(0.566732\pi\) | |||||||
\(762\) | 1.40122 | + | 5.59388i | 0.0507609 | + | 0.202645i | ||||
\(763\) | 1.19038 | + | 5.15587i | 0.0430945 | + | 0.186655i | ||||
\(764\) | − | 0.500983i | − | 0.0181249i | ||||||
\(765\) | 17.2915 | − | 26.7813i | 0.625176 | − | 0.968281i | ||||
\(766\) | 20.6921i | 0.747635i | ||||||||
\(767\) | −7.29150 | −0.263281 | ||||||||
\(768\) | −1.68014 | + | 0.420861i | −0.0606269 | + | 0.0151865i | ||||
\(769\) | 35.7375i | 1.28873i | 0.764720 | + | 0.644363i | \(0.222877\pi\) | ||||
−0.764720 | + | 0.644363i | \(0.777123\pi\) | |||||||
\(770\) | −11.2024 | − | 12.4300i | −0.403708 | − | 0.447947i | ||||
\(771\) | 7.87451 | + | 31.4362i | 0.283593 | + | 1.13215i | ||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | 41.9277i | 1.50803i | 0.656855 | + | 0.754017i | \(0.271887\pi\) | ||||
−0.656855 | + | 0.754017i | \(0.728113\pi\) | |||||||
\(774\) | 14.5830 | + | 27.2823i | 0.524175 | + | 0.980642i | ||||
\(775\) | 13.0194 | + | 8.11905i | 0.467672 | + | 0.291645i | ||||
\(776\) | 14.6315 | 0.525241 | ||||||||
\(777\) | −13.5867 | + | 6.94167i | −0.487419 | + | 0.249031i | ||||
\(778\) | − | 37.0931i | − | 1.32985i | ||||||
\(779\) | 24.2764i | 0.869792i | ||||||||
\(780\) | 8.89047 | + | 9.50432i | 0.318330 | + | 0.340309i | ||||
\(781\) | −27.7490 | −0.992938 | ||||||||
\(782\) | − | 34.6504i | − | 1.23909i | ||||||
\(783\) | 1.74822 | + | 1.92881i | 0.0624762 | + | 0.0689301i | ||||
\(784\) | −6.29150 | + | 3.06871i | −0.224697 | + | 0.109597i | ||||
\(785\) | −17.7712 | − | 32.0259i | −0.634283 | − | 1.14305i | ||||
\(786\) | −30.2288 | + | 7.57205i | −1.07822 | + | 0.270086i | ||||
\(787\) | −28.2835 | −1.00820 | −0.504099 | − | 0.863646i | \(-0.668175\pi\) | ||||
−0.504099 | + | 0.863646i | \(0.668175\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | −24.5015 | + | 6.13742i | −0.872277 | + | 0.218498i | ||||
\(790\) | 3.57113 | + | 6.43560i | 0.127055 | + | 0.228969i | ||||
\(791\) | −3.57113 | − | 15.4676i | −0.126975 | − | 0.549965i | ||||
\(792\) | −4.00000 | − | 7.48331i | −0.142134 | − | 0.265908i | ||||
\(793\) | − | 8.48528i | − | 0.301321i | ||||||
\(794\) | −14.8424 | −0.526735 | ||||||||
\(795\) | −22.7085 | − | 24.2764i | −0.805387 | − | 0.860995i | ||||
\(796\) | − | 9.20614i | − | 0.326303i | ||||||
\(797\) | − | 15.0982i | − | 0.534806i | −0.963585 | − | 0.267403i | \(-0.913835\pi\) | ||
0.963585 | − | 0.267403i | \(-0.0861654\pi\) | |||||||
\(798\) | −22.8275 | + | 11.6630i | −0.808086 | + | 0.412865i | ||||
\(799\) | −37.1660 | −1.31484 | ||||||||
\(800\) | 2.64575 | − | 4.24264i | 0.0935414 | − | 0.150000i | ||||
\(801\) | 41.8608 | − | 22.3755i | 1.47908 | − | 0.790600i | ||||
\(802\) | 7.48331i | 0.264245i | ||||||||
\(803\) | 15.6417i | 0.551985i | ||||||||
\(804\) | −4.33981 | − | 17.3252i | −0.153053 | − | 0.611012i | ||||
\(805\) | 32.0438 | − | 28.8792i | 1.12939 | − | 1.01786i | ||||
\(806\) | 10.3117i | 0.363216i | ||||||||
\(807\) | −15.6458 | + | 3.91913i | −0.550757 | + | 0.137960i | ||||
\(808\) | −2.16991 | −0.0763371 | ||||||||
\(809\) | − | 11.1362i | − | 0.391529i | −0.980651 | − | 0.195765i | \(-0.937281\pi\) | ||
0.980651 | − | 0.195765i | \(-0.0627188\pi\) | |||||||
\(810\) | 20.0563 | + | 1.65704i | 0.704706 | + | 0.0582224i | ||||
\(811\) | − | 24.0062i | − | 0.842970i | −0.906835 | − | 0.421485i | \(-0.861509\pi\) | ||
0.906835 | − | 0.421485i | \(-0.138491\pi\) | |||||||
\(812\) | 1.29150 | − | 0.298179i | 0.0453229 | − | 0.0104640i | ||||
\(813\) | −8.58301 | − | 34.2646i | −0.301019 | − | 1.20171i | ||||
\(814\) | −9.41699 | −0.330065 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 7.98430i | −0.0700140 | − | 0.279506i | ||||
\(817\) | 57.6827 | 2.01806 | ||||||||
\(818\) | 23.4626i | 0.820351i | ||||||||
\(819\) | 17.5423 | + | 20.0906i | 0.612976 | + | 0.702024i | ||||
\(820\) | −4.70850 | − | 8.48528i | −0.164428 | − | 0.296319i | ||||
\(821\) | − | 31.4362i | − | 1.09713i | −0.836107 | − | 0.548566i | \(-0.815174\pi\) | ||
0.836107 | − | 0.548566i | \(-0.184826\pi\) | |||||||
\(822\) | 2.16991 | − | 0.543544i | 0.0756842 | − | 0.0189583i | ||||
\(823\) | − | 11.8147i | − | 0.411834i | −0.978569 | − | 0.205917i | \(-0.933982\pi\) | ||
0.978569 | − | 0.205917i | \(-0.0660177\pi\) | |||||||
\(824\) | 3.14944 | 0.109716 | ||||||||
\(825\) | 23.3111 | + | 7.52269i | 0.811590 | + | 0.261906i | ||||
\(826\) | 1.29150 | + | 5.59388i | 0.0449371 | + | 0.194636i | ||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 19.2915 | − | 10.3117i | 0.670426 | − | 0.358358i | ||||
\(829\) | 33.2123i | 1.15351i | 0.816917 | + | 0.576755i | \(0.195681\pi\) | ||||
−0.816917 | + | 0.576755i | \(0.804319\pi\) | |||||||
\(830\) | 13.6458 | − | 7.57205i | 0.473651 | − | 0.262830i | ||||
\(831\) | 2.93859 | + | 11.7313i | 0.101939 | + | 0.406954i | ||||
\(832\) | 3.36028 | 0.116497 | ||||||||
\(833\) | −14.5830 | − | 29.8982i | −0.505271 | − | 1.03591i | ||||
\(834\) | 0.228757 | + | 0.913230i | 0.00792119 | + | 0.0316226i | ||||
\(835\) | −40.4575 | + | 22.4499i | −1.40009 | + | 0.776912i | ||||
\(836\) | −15.8219 | −0.547211 | ||||||||
\(837\) | 10.7085 | + | 11.8147i | 0.370140 | + | 0.408375i | ||||
\(838\) | 33.8137 | 1.16807 | ||||||||
\(839\) | 37.5210 | 1.29537 | 0.647684 | − | 0.761909i | \(-0.275738\pi\) | ||||
0.647684 | + | 0.761909i | \(0.275738\pi\) | |||||||
\(840\) | 5.71678 | − | 8.50402i | 0.197248 | − | 0.293417i | ||||
\(841\) | 28.7490 | 0.991345 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 3.91813 | + | 15.6417i | 0.134947 | + | 0.538730i | ||||
\(844\) | −21.1660 | −0.728564 | ||||||||
\(845\) | 1.85364 | + | 3.34048i | 0.0637672 | + | 0.114916i | ||||
\(846\) | −11.0604 | − | 20.6921i | −0.380264 | − | 0.711408i | ||||
\(847\) | 1.78556 | + | 7.73381i | 0.0613527 | + | 0.265737i | ||||
\(848\) | −8.58301 | −0.294742 | ||||||||
\(849\) | −54.1033 | + | 13.5524i | −1.85682 | + | 0.465118i | ||||
\(850\) | 20.1617 | + | 12.5730i | 0.691541 | + | 0.431251i | ||||
\(851\) | − | 24.2764i | − | 0.832184i | ||||||
\(852\) | −4.12897 | − | 16.4835i | −0.141456 | − | 0.564714i | ||||
\(853\) | 23.5220 | 0.805377 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(854\) | −6.50972 | + | 1.50295i | −0.222758 | + | 0.0514299i | ||||
\(855\) | 20.3542 | − | 31.5249i | 0.696101 | − | 1.07813i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 46.1363i | − | 1.57599i | −0.615684 | − | 0.787993i | \(-0.711120\pi\) | ||
0.615684 | − | 0.787993i | \(-0.288880\pi\) | |||||||
\(858\) | 4.00000 | + | 15.9686i | 0.136558 | + | 0.545159i | ||||
\(859\) | 22.9191i | 0.781988i | 0.920393 | + | 0.390994i | \(0.127869\pi\) | ||||
−0.920393 | + | 0.390994i | \(0.872131\pi\) | |||||||
\(860\) | −20.1617 | + | 11.1878i | −0.687508 | + | 0.381500i | ||||
\(861\) | −9.04831 | − | 17.7099i | −0.308366 | − | 0.603553i | ||||
\(862\) | 8.98626i | 0.306073i | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 3.85005 | − | 3.48957i | 0.130981 | − | 0.118718i | ||||
\(865\) | 4.35425 | − | 2.41618i | 0.148049 | − | 0.0821526i | ||||
\(866\) | −18.5496 | −0.630342 | ||||||||
\(867\) | 9.38024 | − | 2.34967i | 0.318570 | − | 0.0797990i | ||||
\(868\) | 7.91094 | − | 1.82646i | 0.268515 | − | 0.0619941i | ||||
\(869\) | 9.30978i | 0.315812i | ||||||||
\(870\) | −1.41699 | + | 1.32548i | −0.0480406 | + | 0.0449379i | ||||
\(871\) | 34.6504i | 1.17408i | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | −38.7113 | + | 20.6921i | −1.31018 | + | 0.700321i | ||||
\(874\) | − | 40.7878i | − | 1.37967i | ||||||
\(875\) | 5.17645 | + | 29.1239i | 0.174996 | + | 0.984569i | ||||
\(876\) | −9.29150 | + | 2.32744i | −0.313931 | + | 0.0786370i | ||||
\(877\) | − | 23.9529i | − | 0.808832i | −0.914575 | − | 0.404416i | \(-0.867475\pi\) | ||
0.914575 | − | 0.404416i | \(-0.132525\pi\) | |||||||
\(878\) | 26.5313i | 0.895389i | ||||||||
\(879\) | −3.06275 | − | 12.2269i | −0.103304 | − | 0.412404i | ||||
\(880\) | 5.53019 | − | 3.06871i | 0.186423 | − | 0.103446i | ||||
\(881\) | −15.8219 | −0.533053 | −0.266526 | − | 0.963828i | \(-0.585876\pi\) | ||||
−0.266526 | + | 0.963828i | \(0.585876\pi\) | |||||||
\(882\) | 12.3059 | − | 17.0166i | 0.414362 | − | 0.572978i | ||||
\(883\) | − | 30.9352i | − | 1.04105i | −0.853845 | − | 0.520527i | \(-0.825736\pi\) | ||
0.853845 | − | 0.520527i | \(-0.174264\pi\) | |||||||
\(884\) | 15.9686i | 0.537082i | ||||||||
\(885\) | −5.74103 | − | 6.13742i | −0.192983 | − | 0.206307i | ||||
\(886\) | 29.1660 | 0.979851 | ||||||||
\(887\) | − | 2.27980i | − | 0.0765483i | −0.999267 | − | 0.0382742i | \(-0.987814\pi\) | ||
0.999267 | − | 0.0382742i | \(-0.0121860\pi\) | |||||||
\(888\) | −1.40122 | − | 5.59388i | −0.0470219 | − | 0.187718i | ||||
\(889\) | −8.58301 | + | 1.98162i | −0.287865 | + | 0.0664616i | ||||
\(890\) | 17.1660 | + | 30.9352i | 0.575406 | + | 1.03695i | ||||
\(891\) | 21.1660 | + | 14.1421i | 0.709088 | + | 0.473779i | ||||
\(892\) | 1.19038 | 0.0398567 | ||||||||
\(893\) | −43.7490 | −1.46400 | ||||||||
\(894\) | −4.55066 | − | 18.1669i | −0.152197 | − | 0.607592i | ||||
\(895\) | −47.8127 | + | 26.5313i | −1.59820 | + | 0.886844i | ||||
\(896\) | −0.595188 | − | 2.57794i | −0.0198838 | − | 0.0861228i | ||||
\(897\) | −41.1660 | + | 10.3117i | −1.37449 | + | 0.344299i | ||||
\(898\) | 36.5921i | 1.22109i | ||||||||
\(899\) | −1.53737 | −0.0512743 | ||||||||
\(900\) | −1.00000 | + | 14.9666i | −0.0333333 | + | 0.498888i | ||||
\(901\) | − | 40.7878i | − | 1.35884i | ||||||
\(902\) | − | 12.2748i | − | 0.408708i | ||||||
\(903\) | −42.0802 | + | 21.4995i | −1.40034 | + | 0.715459i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | −28.9373 | + | 16.0573i | −0.961907 | + | 0.533764i | ||||
\(906\) | −2.38075 | + | 0.596358i | −0.0790952 | + | 0.0198127i | ||||
\(907\) | 33.9411i | 1.12700i | 0.826117 | + | 0.563498i | \(0.190545\pi\) | ||||
−0.826117 | + | 0.563498i | \(0.809455\pi\) | |||||||
\(908\) | − | 18.1669i | − | 0.602890i | ||||||
\(909\) | 5.74103 | − | 3.06871i | 0.190418 | − | 0.101783i | ||||
\(910\) | −14.7673 | + | 13.3089i | −0.489533 | + | 0.441187i | ||||
\(911\) | 18.2960i | 0.606175i | 0.952963 | + | 0.303087i | \(0.0980174\pi\) | ||||
−0.952963 | + | 0.303087i | \(0.901983\pi\) | |||||||
\(912\) | −2.35425 | − | 9.39851i | −0.0779570 | − | 0.311216i | ||||
\(913\) | 19.7400 | 0.653299 | ||||||||
\(914\) | − | 8.48528i | − | 0.280668i | ||||||
\(915\) | 7.14226 | − | 6.68097i | 0.236116 | − | 0.220866i | ||||
\(916\) | 24.9007i | 0.822742i | ||||||||
\(917\) | −10.7085 | − | 46.3817i | −0.353626 | − | 1.53166i | ||||
\(918\) | 16.5830 | + | 18.2960i | 0.547321 | + | 0.603859i | ||||
\(919\) | 41.8745 | 1.38131 | 0.690656 | − | 0.723183i | \(-0.257322\pi\) | ||||
0.690656 | + | 0.723183i | \(0.257322\pi\) | |||||||
\(920\) | 7.91094 | + | 14.2565i | 0.260816 | + | 0.470022i | ||||
\(921\) | −20.2288 | + | 5.06713i | −0.666560 | + | 0.166968i | ||||
\(922\) | −17.9918 | −0.592528 | ||||||||
\(923\) | 32.9669i | 1.08512i | ||||||||
\(924\) | 11.5423 | − | 5.89714i | 0.379712 | − | 0.194002i | ||||
\(925\) | 14.1255 | + | 8.80879i | 0.464443 | + | 0.289631i | ||||
\(926\) | − | 1.50295i | − | 0.0493900i | ||||||
\(927\) | −8.33263 | + | 4.45398i | −0.273680 | + | 0.146288i | ||||
\(928\) | 0.500983i | 0.0164456i | ||||||||
\(929\) | −51.8055 | −1.69968 | −0.849841 | − | 0.527039i | \(-0.823302\pi\) | ||||
−0.849841 | + | 0.527039i | \(0.823302\pi\) | |||||||
\(930\) | −8.67963 | + | 8.11905i | −0.284616 | + | 0.266234i | ||||
\(931\) | −17.1660 | − | 35.1939i | −0.562593 | − | 1.15343i | ||||
\(932\) | 13.2915 | 0.435378 | ||||||||
\(933\) | 41.1660 | − | 10.3117i | 1.34771 | − | 0.337591i | ||||
\(934\) | 0.841723i | 0.0275420i | ||||||||
\(935\) | 14.5830 | + | 26.2803i | 0.476915 | + | 0.859459i | ||||
\(936\) | −8.89047 | + | 4.75216i | −0.290594 | + | 0.155329i | ||||
\(937\) | 5.53019 | 0.180663 | 0.0903317 | − | 0.995912i | \(-0.471207\pi\) | ||||
0.0903317 | + | 0.995912i | \(0.471207\pi\) | |||||||
\(938\) | 26.5830 | − | 6.13742i | 0.867966 | − | 0.200394i | ||||
\(939\) | 24.5830 | − | 6.15784i | 0.802236 | − | 0.200953i | ||||
\(940\) | 15.2915 | − | 8.48528i | 0.498754 | − | 0.276759i | ||||
\(941\) | 0.632534 | 0.0206200 | 0.0103100 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103100 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(942\) | 27.5203 | − | 6.89360i | 0.896658 | − | 0.224605i | ||||
\(943\) | 31.6438 | 1.03046 | ||||||||
\(944\) | −2.16991 | −0.0706245 | ||||||||
\(945\) | −3.09868 | + | 30.5843i | −0.100800 | + | 0.994907i | ||||
\(946\) | −29.1660 | −0.948269 | ||||||||
\(947\) | 24.0000 | 0.779895 | 0.389948 | − | 0.920837i | \(-0.372493\pi\) | ||||
0.389948 | + | 0.920837i | \(0.372493\pi\) | |||||||
\(948\) | −5.53019 | + | 1.38527i | −0.179612 | + | 0.0449914i | ||||
\(949\) | 18.5830 | 0.603230 | ||||||||
\(950\) | 23.7328 | + | 14.8000i | 0.769995 | + | 0.480176i | ||||
\(951\) | −10.0808 | + | 2.52517i | −0.326894 | + | 0.0818842i | ||||
\(952\) | 12.2508 | − | 2.82843i | 0.397049 | − | 0.0916698i | ||||
\(953\) | 3.87451 | 0.125508 | 0.0627538 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627538 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(954\) | 22.7085 | − | 12.1382i | 0.735215 | − | 0.392989i | ||||
\(955\) | −0.979531 | + | 0.543544i | −0.0316969 | + | 0.0175887i | ||||
\(956\) | 14.6431i | 0.473592i | ||||||||
\(957\) | −2.38075 | + | 0.596358i | −0.0769588 | + | 0.0192775i | ||||
\(958\) | −21.6991 | −0.701065 | ||||||||
\(959\) | 0.768687 | + | 3.32941i | 0.0248222 | + | 0.107512i | ||||
\(960\) | 2.64575 | + | 2.82843i | 0.0853913 | + | 0.0912871i | ||||
\(961\) | 21.5830 | 0.696226 | ||||||||
\(962\) | 11.1878i | 0.360708i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 17.3252i | − | 0.558007i | ||||||
\(965\) | −16.5906 | + | 9.20614i | −0.534069 | + | 0.296356i | ||||
\(966\) | 15.2024 | + | 29.7552i | 0.489131 | + | 0.957358i | ||||
\(967\) | 26.9588i | 0.866936i | 0.901169 | + | 0.433468i | \(0.142710\pi\) | ||||
−0.901169 | + | 0.433468i | \(0.857290\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | 44.6632 | − | 11.1878i | 1.43479 | − | 0.359403i | ||||
\(970\) | −15.8745 | − | 28.6078i | −0.509700 | − | 0.918541i | ||||
\(971\) | 9.31216 | 0.298842 | 0.149421 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149421 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(972\) | −5.25127 | + | 14.6773i | −0.168435 | + | 0.470776i | ||||
\(973\) | −1.40122 | + | 0.323511i | −0.0449211 | + | 0.0103713i | ||||
\(974\) | 9.98823i | 0.320044i | ||||||||
\(975\) | 8.93725 | − | 27.6946i | 0.286221 | − | 0.886935i | ||||
\(976\) | − | 2.52517i | − | 0.0808287i | ||||||
\(977\) | −20.1255 | −0.643872 | −0.321936 | − | 0.946762i | \(-0.604334\pi\) | ||||
−0.321936 | + | 0.946762i | \(0.604334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.7510i | 1.43025i | ||||||||
\(980\) | 12.8260 | + | 8.97185i | 0.409711 | + | 0.286595i | ||||
\(981\) | 5.29150 | − | 2.82843i | 0.168945 | − | 0.0903047i | ||||
\(982\) | 14.1421i | 0.451294i | ||||||||
\(983\) | − | 29.0037i | − | 0.925074i | −0.886600 | − | 0.462537i | \(-0.846939\pi\) | ||
0.886600 | − | 0.462537i | \(-0.153061\pi\) | |||||||
\(984\) | 7.29150 | − | 1.82646i | 0.232445 | − | 0.0582254i | ||||
\(985\) | −19.5292 | − | 35.1939i | −0.622251 | − | 1.12137i | ||||
\(986\) | −2.38075 | −0.0758186 | ||||||||
\(987\) | 31.9154 | − | 16.3062i | 1.01588 | − | 0.519031i | ||||
\(988\) | 18.7970i | 0.598013i | ||||||||
\(989\) | − | 75.1881i | − | 2.39084i | ||||||
\(990\) | −10.2917 | + | 15.9399i | −0.327092 | + | 0.506604i | ||||
\(991\) | −11.2915 | −0.358686 | −0.179343 | − | 0.983787i | \(-0.557397\pi\) | ||||
−0.179343 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(992\) | 3.06871i | 0.0974317i | ||||||||
\(993\) | −13.4411 | + | 3.36689i | −0.426541 | + | 0.106845i | ||||
\(994\) | 25.2915 | − | 5.83925i | 0.802198 | − | 0.185210i | ||||
\(995\) | −18.0000 | + | 9.98823i | −0.570638 | + | 0.316648i | ||||
\(996\) | 2.93725 | + | 11.7260i | 0.0930705 | + | 0.371551i | ||||
\(997\) | 26.3244 | 0.833703 | 0.416851 | − | 0.908975i | \(-0.363134\pi\) | ||||
0.416851 | + | 0.908975i | \(0.363134\pi\) | |||||||
\(998\) | −22.5830 | −0.714853 | ||||||||
\(999\) | 11.6182 | + | 12.8184i | 0.367584 | + | 0.405556i |
(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 | 210.2.d.a.209.2 | yes | 8 | |
3.2 | odd | 2 | 210.2.d.b.209.1 | yes | 8 | ||
4.3 | odd | 2 | 1680.2.k.e.209.7 | 8 | |||
5.2 | odd | 4 | 1050.2.b.f.251.6 | 16 | |||
5.3 | odd | 4 | 1050.2.b.f.251.11 | 16 | |||
5.4 | even | 2 | 210.2.d.b.209.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 210.2.d.a.209.7 | yes | 8 | |
12.11 | even | 2 | 1680.2.k.f.209.8 | 8 | |||
15.2 | even | 4 | 1050.2.b.f.251.12 | 16 | |||
15.8 | even | 4 | 1050.2.b.f.251.5 | 16 | |||
15.14 | odd | 2 | inner | 210.2.d.a.209.8 | yes | 8 | |
20.19 | odd | 2 | 1680.2.k.f.209.2 | 8 | |||
21.20 | even | 2 | 210.2.d.b.209.8 | yes | 8 | ||
28.27 | even | 2 | 1680.2.k.e.209.2 | 8 | |||
35.13 | even | 4 | 1050.2.b.f.251.14 | 16 | |||
35.27 | even | 4 | 1050.2.b.f.251.3 | 16 | |||
35.34 | odd | 2 | 210.2.d.b.209.2 | yes | 8 | ||
60.59 | even | 2 | 1680.2.k.e.209.1 | 8 | |||
84.83 | odd | 2 | 1680.2.k.f.209.1 | 8 | |||
105.62 | odd | 4 | 1050.2.b.f.251.13 | 16 | |||
105.83 | odd | 4 | 1050.2.b.f.251.4 | 16 | |||
105.104 | even | 2 | inner | 210.2.d.a.209.1 | ✓ | 8 | |
140.139 | even | 2 | 1680.2.k.f.209.7 | 8 | |||
420.419 | odd | 2 | 1680.2.k.e.209.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.1 | ✓ | 8 | 105.104 | even | 2 | inner | |
210.2.d.a.209.2 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.d.a.209.7 | yes | 8 | 7.6 | odd | 2 | inner | |
210.2.d.a.209.8 | yes | 8 | 15.14 | odd | 2 | inner | |
210.2.d.b.209.1 | yes | 8 | 3.2 | odd | 2 | ||
210.2.d.b.209.2 | yes | 8 | 35.34 | odd | 2 | ||
210.2.d.b.209.7 | yes | 8 | 5.4 | even | 2 | ||
210.2.d.b.209.8 | yes | 8 | 21.20 | even | 2 | ||
1050.2.b.f.251.3 | 16 | 35.27 | even | 4 | |||
1050.2.b.f.251.4 | 16 | 105.83 | odd | 4 | |||
1050.2.b.f.251.5 | 16 | 15.8 | even | 4 | |||
1050.2.b.f.251.6 | 16 | 5.2 | odd | 4 | |||
1050.2.b.f.251.11 | 16 | 5.3 | odd | 4 | |||
1050.2.b.f.251.12 | 16 | 15.2 | even | 4 | |||
1050.2.b.f.251.13 | 16 | 105.62 | odd | 4 | |||
1050.2.b.f.251.14 | 16 | 35.13 | even | 4 | |||
1680.2.k.e.209.1 | 8 | 60.59 | even | 2 | |||
1680.2.k.e.209.2 | 8 | 28.27 | even | 2 | |||
1680.2.k.e.209.7 | 8 | 4.3 | odd | 2 | |||
1680.2.k.e.209.8 | 8 | 420.419 | odd | 2 | |||
1680.2.k.f.209.1 | 8 | 84.83 | odd | 2 | |||
1680.2.k.f.209.2 | 8 | 20.19 | odd | 2 | |||
1680.2.k.f.209.7 | 8 | 140.139 | even | 2 | |||
1680.2.k.f.209.8 | 8 | 12.11 | even | 2 |