Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(65,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.910294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.107 |
Dual form | 114.2.h.e.65.2 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.22474 | − | 0.707107i | 0.547723 | − | 0.316228i | −0.200480 | − | 0.979698i | \(-0.564250\pi\) |
0.748203 | + | 0.663470i | \(0.230917\pi\) | |||||||
\(6\) | −1.72474 | − | 0.158919i | −0.704124 | − | 0.0648783i | ||||
\(7\) | −0.449490 | −0.169891 | −0.0849456 | − | 0.996386i | \(-0.527072\pi\) | ||||
−0.0849456 | + | 0.996386i | \(0.527072\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | −1.22474 | − | 0.707107i | −0.387298 | − | 0.223607i | ||||
\(11\) | 3.14626i | 0.948634i | 0.880354 | + | 0.474317i | \(0.157305\pi\) | ||||
−0.880354 | + | 0.474317i | \(0.842695\pi\) | |||||||
\(12\) | 0.724745 | + | 1.57313i | 0.209216 | + | 0.454124i | ||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | 0.224745 | + | 0.389270i | 0.0600656 | + | 0.104037i | ||||
\(15\) | 0.224745 | − | 2.43916i | 0.0580289 | − | 0.629788i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.550510 | − | 0.317837i | 0.133518 | − | 0.0770869i | −0.431753 | − | 0.901992i | \(-0.642105\pi\) |
0.565271 | + | 0.824905i | \(0.308771\pi\) | |||||||
\(18\) | −1.94949 | + | 2.28024i | −0.459499 | + | 0.537457i | ||||
\(19\) | 3.17423 | + | 2.98735i | 0.728219 | + | 0.685344i | ||||
\(20\) | 1.41421i | 0.316228i | ||||||||
\(21\) | −0.449490 | + | 0.635674i | −0.0980867 | + | 0.138716i | ||||
\(22\) | 2.72474 | − | 1.57313i | 0.580918 | − | 0.335393i | ||||
\(23\) | 6.12372 | + | 3.53553i | 1.27688 | + | 0.737210i | 0.976274 | − | 0.216537i | \(-0.0694763\pi\) |
0.300610 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | 3.46410i | 0.679366i | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0.224745 | − | 0.389270i | 0.0424728 | − | 0.0735650i | ||||
\(29\) | −1.22474 | + | 2.12132i | −0.227429 | + | 0.393919i | −0.957046 | − | 0.289938i | \(-0.906365\pi\) |
0.729616 | + | 0.683857i | \(0.239699\pi\) | |||||||
\(30\) | −2.22474 | + | 1.02494i | −0.406181 | + | 0.187128i | ||||
\(31\) | 4.24264i | 0.762001i | 0.924575 | + | 0.381000i | \(0.124420\pi\) | ||||
−0.924575 | + | 0.381000i | \(0.875580\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 4.44949 | + | 3.14626i | 0.774557 | + | 0.547694i | ||||
\(34\) | −0.550510 | − | 0.317837i | −0.0944117 | − | 0.0545086i | ||||
\(35\) | −0.550510 | + | 0.317837i | −0.0930532 | + | 0.0537243i | ||||
\(36\) | 2.94949 | + | 0.548188i | 0.491582 | + | 0.0913647i | ||||
\(37\) | − | 7.70674i | − | 1.26698i | −0.773751 | − | 0.633490i | \(-0.781622\pi\) | ||
0.773751 | − | 0.633490i | \(-0.218378\pi\) | |||||||
\(38\) | 1.00000 | − | 4.24264i | 0.162221 | − | 0.688247i | ||||
\(39\) | −5.44949 | + | 2.51059i | −0.872617 | + | 0.402016i | ||||
\(40\) | 1.22474 | − | 0.707107i | 0.193649 | − | 0.111803i | ||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0.775255 | + | 0.0714323i | 0.119624 | + | 0.0110222i | ||||
\(43\) | 4.44949 | + | 7.70674i | 0.678541 | + | 1.17527i | 0.975420 | + | 0.220352i | \(0.0707207\pi\) |
−0.296880 | + | 0.954915i | \(0.595946\pi\) | |||||||
\(44\) | −2.72474 | − | 1.57313i | −0.410771 | − | 0.237159i | ||||
\(45\) | −3.22474 | − | 2.75699i | −0.480717 | − | 0.410989i | ||||
\(46\) | − | 7.07107i | − | 1.04257i | ||||||
\(47\) | −11.5732 | − | 6.68180i | −1.68813 | − | 0.974640i | −0.955952 | − | 0.293524i | \(-0.905172\pi\) |
−0.732175 | − | 0.681117i | \(-0.761495\pi\) | |||||||
\(48\) | −1.72474 | − | 0.158919i | −0.248945 | − | 0.0229379i | ||||
\(49\) | −6.79796 | −0.971137 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 0.101021 | − | 1.09638i | 0.0141457 | − | 0.153523i | ||||
\(52\) | 3.00000 | − | 1.73205i | 0.416025 | − | 0.240192i | ||||
\(53\) | 5.44949 | − | 9.43879i | 0.748545 | − | 1.29652i | −0.199975 | − | 0.979801i | \(-0.564086\pi\) |
0.948520 | − | 0.316717i | \(-0.102581\pi\) | |||||||
\(54\) | 1.27526 | + | 5.03723i | 0.173540 | + | 0.685481i | ||||
\(55\) | 2.22474 | + | 3.85337i | 0.299985 | + | 0.519588i | ||||
\(56\) | −0.449490 | −0.0600656 | ||||||||
\(57\) | 7.39898 | − | 1.50170i | 0.980019 | − | 0.198905i | ||||
\(58\) | 2.44949 | 0.321634 | ||||||||
\(59\) | −5.72474 | − | 9.91555i | −0.745298 | − | 1.29089i | −0.950055 | − | 0.312082i | \(-0.898974\pi\) |
0.204757 | − | 0.978813i | \(-0.434360\pi\) | |||||||
\(60\) | 2.00000 | + | 1.41421i | 0.258199 | + | 0.182574i | ||||
\(61\) | 0.775255 | − | 1.34278i | 0.0992612 | − | 0.171926i | −0.812118 | − | 0.583493i | \(-0.801685\pi\) |
0.911379 | + | 0.411568i | \(0.135019\pi\) | |||||||
\(62\) | 3.67423 | − | 2.12132i | 0.466628 | − | 0.269408i | ||||
\(63\) | 0.449490 | + | 1.27135i | 0.0566304 | + | 0.160175i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.89898 | −0.607644 | ||||||||
\(66\) | 0.500000 | − | 5.42650i | 0.0615457 | − | 0.667956i | ||||
\(67\) | 2.17423 | + | 1.25529i | 0.265625 | + | 0.153359i | 0.626898 | − | 0.779101i | \(-0.284324\pi\) |
−0.361273 | + | 0.932460i | \(0.617658\pi\) | |||||||
\(68\) | 0.635674i | 0.0770869i | ||||||||
\(69\) | 11.1237 | − | 5.12472i | 1.33914 | − | 0.616944i | ||||
\(70\) | 0.550510 | + | 0.317837i | 0.0657986 | + | 0.0379888i | ||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −1.00000 | − | 2.82843i | −0.117851 | − | 0.333333i | ||||
\(73\) | −4.39898 | − | 7.61926i | −0.514862 | − | 0.891766i | −0.999851 | − | 0.0172466i | \(-0.994510\pi\) |
0.484990 | − | 0.874520i | \(-0.338823\pi\) | |||||||
\(74\) | −6.67423 | + | 3.85337i | −0.775864 | + | 0.447945i | ||||
\(75\) | 2.17423 | + | 4.71940i | 0.251059 | + | 0.544949i | ||||
\(76\) | −4.17423 | + | 1.25529i | −0.478818 | + | 0.143992i | ||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | 4.89898 | + | 3.46410i | 0.554700 | + | 0.392232i | ||||
\(79\) | −7.34847 | + | 4.24264i | −0.826767 | + | 0.477334i | −0.852745 | − | 0.522328i | \(-0.825064\pi\) |
0.0259772 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(80\) | −1.22474 | − | 0.707107i | −0.136931 | − | 0.0790569i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | 17.0027i | 1.86629i | 0.359506 | + | 0.933143i | \(0.382945\pi\) | ||||
−0.359506 | + | 0.933143i | \(0.617055\pi\) | |||||||
\(84\) | −0.325765 | − | 0.707107i | −0.0355439 | − | 0.0771517i | ||||
\(85\) | 0.449490 | − | 0.778539i | 0.0487540 | − | 0.0844444i | ||||
\(86\) | 4.44949 | − | 7.70674i | 0.479801 | − | 0.831039i | ||||
\(87\) | 1.77526 | + | 3.85337i | 0.190327 | + | 0.413125i | ||||
\(88\) | 3.14626i | 0.335393i | ||||||||
\(89\) | −3.55051 | + | 6.14966i | −0.376353 | + | 0.651863i | −0.990529 | − | 0.137307i | \(-0.956155\pi\) |
0.614175 | + | 0.789170i | \(0.289489\pi\) | |||||||
\(90\) | −0.775255 | + | 4.17121i | −0.0817191 | + | 0.439684i | ||||
\(91\) | 1.34847 | + | 0.778539i | 0.141358 | + | 0.0816131i | ||||
\(92\) | −6.12372 | + | 3.53553i | −0.638442 | + | 0.368605i | ||||
\(93\) | 6.00000 | + | 4.24264i | 0.622171 | + | 0.439941i | ||||
\(94\) | 13.3636i | 1.37835i | ||||||||
\(95\) | 6.00000 | + | 1.41421i | 0.615587 | + | 0.145095i | ||||
\(96\) | 0.724745 | + | 1.57313i | 0.0739690 | + | 0.160557i | ||||
\(97\) | 2.84847 | − | 1.64456i | 0.289218 | − | 0.166980i | −0.348371 | − | 0.937357i | \(-0.613265\pi\) |
0.637589 | + | 0.770377i | \(0.279932\pi\) | |||||||
\(98\) | 3.39898 | + | 5.88721i | 0.343349 | + | 0.594698i | ||||
\(99\) | 8.89898 | − | 3.14626i | 0.894381 | − | 0.316211i | ||||
\(100\) | −1.50000 | − | 2.59808i | −0.150000 | − | 0.259808i | ||||
\(101\) | −8.57321 | − | 4.94975i | −0.853067 | − | 0.492518i | 0.00861771 | − | 0.999963i | \(-0.497257\pi\) |
−0.861684 | + | 0.507445i | \(0.830590\pi\) | |||||||
\(102\) | −1.00000 | + | 0.460702i | −0.0990148 | + | 0.0456163i | ||||
\(103\) | − | 5.02118i | − | 0.494752i | −0.968920 | − | 0.247376i | \(-0.920432\pi\) | ||
0.968920 | − | 0.247376i | \(-0.0795682\pi\) | |||||||
\(104\) | −3.00000 | − | 1.73205i | −0.294174 | − | 0.169842i | ||||
\(105\) | −0.101021 | + | 1.09638i | −0.00985859 | + | 0.106995i | ||||
\(106\) | −10.8990 | −1.05860 | ||||||||
\(107\) | 4.89898 | 0.473602 | 0.236801 | − | 0.971558i | \(-0.423901\pi\) | ||||
0.236801 | + | 0.971558i | \(0.423901\pi\) | |||||||
\(108\) | 3.72474 | − | 3.62302i | 0.358414 | − | 0.348625i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 2.22474 | − | 3.85337i | 0.212121 | − | 0.367405i | ||||
\(111\) | −10.8990 | − | 7.70674i | −1.03449 | − | 0.731492i | ||||
\(112\) | 0.224745 | + | 0.389270i | 0.0212364 | + | 0.0367825i | ||||
\(113\) | 18.7980 | 1.76836 | 0.884182 | − | 0.467143i | \(-0.154717\pi\) | ||||
0.884182 | + | 0.467143i | \(0.154717\pi\) | |||||||
\(114\) | −5.00000 | − | 5.65685i | −0.468293 | − | 0.529813i | ||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | −1.22474 | − | 2.12132i | −0.113715 | − | 0.196960i | ||||
\(117\) | −1.89898 | + | 10.2173i | −0.175561 | + | 0.944593i | ||||
\(118\) | −5.72474 | + | 9.91555i | −0.527005 | + | 0.912800i | ||||
\(119\) | −0.247449 | + | 0.142865i | −0.0226836 | + | 0.0130964i | ||||
\(120\) | 0.224745 | − | 2.43916i | 0.0205163 | − | 0.222664i | ||||
\(121\) | 1.10102 | 0.100093 | ||||||||
\(122\) | −1.55051 | −0.140377 | ||||||||
\(123\) | 5.17423 | + | 0.476756i | 0.466545 | + | 0.0429876i | ||||
\(124\) | −3.67423 | − | 2.12132i | −0.329956 | − | 0.190500i | ||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0.876276 | − | 1.02494i | 0.0780648 | − | 0.0913093i | ||||
\(127\) | −9.00000 | − | 5.19615i | −0.798621 | − | 0.461084i | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 15.3485 | + | 1.41421i | 1.35136 | + | 0.124515i | ||||
\(130\) | 2.44949 | + | 4.24264i | 0.214834 | + | 0.372104i | ||||
\(131\) | −1.92679 | + | 1.11243i | −0.168344 | + | 0.0971935i | −0.581805 | − | 0.813328i | \(-0.697653\pi\) |
0.413461 | + | 0.910522i | \(0.364320\pi\) | |||||||
\(132\) | −4.94949 | + | 2.28024i | −0.430798 | + | 0.198469i | ||||
\(133\) | −1.42679 | − | 1.34278i | −0.123718 | − | 0.116434i | ||||
\(134\) | − | 2.51059i | − | 0.216882i | ||||||
\(135\) | −7.12372 | + | 1.80348i | −0.613113 | + | 0.155219i | ||||
\(136\) | 0.550510 | − | 0.317837i | 0.0472059 | − | 0.0272543i | ||||
\(137\) | −3.39898 | − | 1.96240i | −0.290394 | − | 0.167659i | 0.347725 | − | 0.937596i | \(-0.386954\pi\) |
−0.638120 | + | 0.769937i | \(0.720288\pi\) | |||||||
\(138\) | −10.0000 | − | 7.07107i | −0.851257 | − | 0.601929i | ||||
\(139\) | 7.17423 | − | 12.4261i | 0.608511 | − | 1.05397i | −0.382975 | − | 0.923759i | \(-0.625101\pi\) |
0.991486 | − | 0.130213i | \(-0.0415661\pi\) | |||||||
\(140\) | − | 0.635674i | − | 0.0537243i | ||||||
\(141\) | −21.0227 | + | 9.68520i | −1.77043 | + | 0.815641i | ||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | 5.44949 | − | 9.43879i | 0.455709 | − | 0.789312i | ||||
\(144\) | −1.94949 | + | 2.28024i | −0.162457 | + | 0.190020i | ||||
\(145\) | 3.46410i | 0.287678i | ||||||||
\(146\) | −4.39898 | + | 7.61926i | −0.364062 | + | 0.630574i | ||||
\(147\) | −6.79796 | + | 9.61377i | −0.560686 | + | 0.792930i | ||||
\(148\) | 6.67423 | + | 3.85337i | 0.548619 | + | 0.316745i | ||||
\(149\) | −1.77526 | + | 1.02494i | −0.145435 | + | 0.0839667i | −0.570952 | − | 0.820984i | \(-0.693426\pi\) |
0.425517 | + | 0.904950i | \(0.360092\pi\) | |||||||
\(150\) | 3.00000 | − | 4.24264i | 0.244949 | − | 0.346410i | ||||
\(151\) | − | 9.61377i | − | 0.782357i | −0.920315 | − | 0.391179i | \(-0.872067\pi\) | ||
0.920315 | − | 0.391179i | \(-0.127933\pi\) | |||||||
\(152\) | 3.17423 | + | 2.98735i | 0.257464 | + | 0.242306i | ||||
\(153\) | −1.44949 | − | 1.23924i | −0.117184 | − | 0.100187i | ||||
\(154\) | −1.22474 | + | 0.707107i | −0.0986928 | + | 0.0569803i | ||||
\(155\) | 3.00000 | + | 5.19615i | 0.240966 | + | 0.417365i | ||||
\(156\) | 0.550510 | − | 5.97469i | 0.0440761 | − | 0.478358i | ||||
\(157\) | −5.34847 | − | 9.26382i | −0.426854 | − | 0.739333i | 0.569737 | − | 0.821827i | \(-0.307045\pi\) |
−0.996592 | + | 0.0824935i | \(0.973712\pi\) | |||||||
\(158\) | 7.34847 | + | 4.24264i | 0.584613 | + | 0.337526i | ||||
\(159\) | −7.89898 | − | 17.1455i | −0.626430 | − | 1.35973i | ||||
\(160\) | 1.41421i | 0.111803i | ||||||||
\(161\) | −2.75255 | − | 1.58919i | −0.216931 | − | 0.125245i | ||||
\(162\) | 8.39898 | + | 3.23375i | 0.659886 | + | 0.254067i | ||||
\(163\) | 18.3485 | 1.43716 | 0.718582 | − | 0.695443i | \(-0.244792\pi\) | ||||
0.718582 | + | 0.695443i | \(0.244792\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 7.67423 | + | 0.707107i | 0.597438 | + | 0.0550482i | ||||
\(166\) | 14.7247 | − | 8.50134i | 1.14286 | − | 0.659832i | ||||
\(167\) | 2.44949 | − | 4.24264i | 0.189547 | − | 0.328305i | −0.755552 | − | 0.655089i | \(-0.772631\pi\) |
0.945099 | + | 0.326783i | \(0.105965\pi\) | |||||||
\(168\) | −0.449490 | + | 0.635674i | −0.0346789 | + | 0.0490434i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −0.898979 | −0.0689486 | ||||||||
\(171\) | 5.27526 | − | 11.9654i | 0.403409 | − | 0.915020i | ||||
\(172\) | −8.89898 | −0.678541 | ||||||||
\(173\) | −0.550510 | − | 0.953512i | −0.0418545 | − | 0.0724942i | 0.844339 | − | 0.535809i | \(-0.179993\pi\) |
−0.886194 | + | 0.463315i | \(0.846660\pi\) | |||||||
\(174\) | 2.44949 | − | 3.46410i | 0.185695 | − | 0.262613i | ||||
\(175\) | 0.674235 | − | 1.16781i | 0.0509673 | − | 0.0882780i | ||||
\(176\) | 2.72474 | − | 1.57313i | 0.205385 | − | 0.118579i | ||||
\(177\) | −19.7474 | − | 1.81954i | −1.48431 | − | 0.136765i | ||||
\(178\) | 7.10102 | 0.532244 | ||||||||
\(179\) | 7.65153 | 0.571902 | 0.285951 | − | 0.958244i | \(-0.407690\pi\) | ||||
0.285951 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(180\) | 4.00000 | − | 1.41421i | 0.298142 | − | 0.105409i | ||||
\(181\) | 18.6742 | + | 10.7816i | 1.38804 | + | 0.801388i | 0.993095 | − | 0.117314i | \(-0.0374285\pi\) |
0.394950 | + | 0.918703i | \(0.370762\pi\) | |||||||
\(182\) | − | 1.55708i | − | 0.115418i | ||||||
\(183\) | −1.12372 | − | 2.43916i | −0.0830681 | − | 0.180308i | ||||
\(184\) | 6.12372 | + | 3.53553i | 0.451447 | + | 0.260643i | ||||
\(185\) | −5.44949 | − | 9.43879i | −0.400654 | − | 0.693954i | ||||
\(186\) | 0.674235 | − | 7.31747i | 0.0494373 | − | 0.536543i | ||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | 11.5732 | − | 6.68180i | 0.844063 | − | 0.487320i | ||||
\(189\) | 2.24745 | + | 0.635674i | 0.163478 | + | 0.0462385i | ||||
\(190\) | −1.77526 | − | 5.90326i | −0.128791 | − | 0.428267i | ||||
\(191\) | − | 8.19955i | − | 0.593299i | −0.954986 | − | 0.296649i | \(-0.904131\pi\) | ||
0.954986 | − | 0.296649i | \(-0.0958693\pi\) | |||||||
\(192\) | 1.00000 | − | 1.41421i | 0.0721688 | − | 0.102062i | ||||
\(193\) | −22.3485 | + | 12.9029i | −1.60868 | + | 0.928771i | −0.619012 | + | 0.785382i | \(0.712467\pi\) |
−0.989666 | + | 0.143389i | \(0.954200\pi\) | |||||||
\(194\) | −2.84847 | − | 1.64456i | −0.204508 | − | 0.118073i | ||||
\(195\) | −4.89898 | + | 6.92820i | −0.350823 | + | 0.496139i | ||||
\(196\) | 3.39898 | − | 5.88721i | 0.242784 | − | 0.420515i | ||||
\(197\) | 20.2918i | 1.44573i | 0.690989 | + | 0.722865i | \(0.257175\pi\) | ||||
−0.690989 | + | 0.722865i | \(0.742825\pi\) | |||||||
\(198\) | −7.17423 | − | 6.13361i | −0.509851 | − | 0.435897i | ||||
\(199\) | 1.44949 | − | 2.51059i | 0.102752 | − | 0.177971i | −0.810066 | − | 0.586339i | \(-0.800569\pi\) |
0.912817 | + | 0.408368i | \(0.133902\pi\) | |||||||
\(200\) | −1.50000 | + | 2.59808i | −0.106066 | + | 0.183712i | ||||
\(201\) | 3.94949 | − | 1.81954i | 0.278576 | − | 0.128340i | ||||
\(202\) | 9.89949i | 0.696526i | ||||||||
\(203\) | 0.550510 | − | 0.953512i | 0.0386382 | − | 0.0669234i | ||||
\(204\) | 0.898979 | + | 0.635674i | 0.0629412 | + | 0.0445061i | ||||
\(205\) | 3.67423 | + | 2.12132i | 0.256620 | + | 0.148159i | ||||
\(206\) | −4.34847 | + | 2.51059i | −0.302972 | + | 0.174921i | ||||
\(207\) | 3.87628 | − | 20.8560i | 0.269420 | − | 1.44960i | ||||
\(208\) | 3.46410i | 0.240192i | ||||||||
\(209\) | −9.39898 | + | 9.98698i | −0.650141 | + | 0.690814i | ||||
\(210\) | 1.00000 | − | 0.460702i | 0.0690066 | − | 0.0317914i | ||||
\(211\) | −1.34847 | + | 0.778539i | −0.0928325 | + | 0.0535968i | −0.545698 | − | 0.837982i | \(-0.683735\pi\) |
0.452865 | + | 0.891579i | \(0.350402\pi\) | |||||||
\(212\) | 5.44949 | + | 9.43879i | 0.374272 | + | 0.648259i | ||||
\(213\) | −10.3485 | − | 0.953512i | −0.709065 | − | 0.0653335i | ||||
\(214\) | −2.44949 | − | 4.24264i | −0.167444 | − | 0.290021i | ||||
\(215\) | 10.8990 | + | 6.29253i | 0.743304 | + | 0.429147i | ||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | − | 1.90702i | − | 0.129457i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.1742 | − | 1.39816i | −1.02538 | − | 0.0944789i | ||||
\(220\) | −4.44949 | −0.299985 | ||||||||
\(221\) | −2.20204 | −0.148125 | ||||||||
\(222\) | −1.22474 | + | 13.2922i | −0.0821995 | + | 0.892112i | ||||
\(223\) | −15.6742 | + | 9.04952i | −1.04962 | + | 0.606001i | −0.922544 | − | 0.385892i | \(-0.873894\pi\) |
−0.127080 | + | 0.991892i | \(0.540561\pi\) | |||||||
\(224\) | 0.224745 | − | 0.389270i | 0.0150164 | − | 0.0260092i | ||||
\(225\) | 8.84847 | + | 1.64456i | 0.589898 | + | 0.109638i | ||||
\(226\) | −9.39898 | − | 16.2795i | −0.625211 | − | 1.08290i | ||||
\(227\) | −0.550510 | −0.0365386 | −0.0182693 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182693 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(228\) | −2.39898 | + | 7.15855i | −0.158876 | + | 0.474087i | ||||
\(229\) | 0.898979 | 0.0594062 | 0.0297031 | − | 0.999559i | \(-0.490544\pi\) | ||||
0.0297031 | + | 0.999559i | \(0.490544\pi\) | |||||||
\(230\) | −5.00000 | − | 8.66025i | −0.329690 | − | 0.571040i | ||||
\(231\) | −2.00000 | − | 1.41421i | −0.131590 | − | 0.0930484i | ||||
\(232\) | −1.22474 | + | 2.12132i | −0.0804084 | + | 0.139272i | ||||
\(233\) | 15.3990 | − | 8.89060i | 1.00882 | − | 0.582443i | 0.0979745 | − | 0.995189i | \(-0.468764\pi\) |
0.910846 | + | 0.412746i | \(0.135430\pi\) | |||||||
\(234\) | 9.79796 | − | 3.46410i | 0.640513 | − | 0.226455i | ||||
\(235\) | −18.8990 | −1.23283 | ||||||||
\(236\) | 11.4495 | 0.745298 | ||||||||
\(237\) | −1.34847 | + | 14.6349i | −0.0875925 | + | 0.950642i | ||||
\(238\) | 0.247449 | + | 0.142865i | 0.0160397 | + | 0.00926054i | ||||
\(239\) | 21.0703i | 1.36293i | 0.731852 | + | 0.681463i | \(0.238656\pi\) | ||||
−0.731852 | + | 0.681463i | \(0.761344\pi\) | |||||||
\(240\) | −2.22474 | + | 1.02494i | −0.143607 | + | 0.0661599i | ||||
\(241\) | −5.84847 | − | 3.37662i | −0.376733 | − | 0.217507i | 0.299663 | − | 0.954045i | \(-0.403126\pi\) |
−0.676396 | + | 0.736538i | \(0.736459\pi\) | |||||||
\(242\) | −0.550510 | − | 0.953512i | −0.0353881 | − | 0.0612941i | ||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0.775255 | + | 1.34278i | 0.0496306 | + | 0.0859628i | ||||
\(245\) | −8.32577 | + | 4.80688i | −0.531914 | + | 0.307100i | ||||
\(246\) | −2.17423 | − | 4.71940i | −0.138624 | − | 0.300898i | ||||
\(247\) | −4.34847 | − | 14.4600i | −0.276686 | − | 0.920066i | ||||
\(248\) | 4.24264i | 0.269408i | ||||||||
\(249\) | 24.0454 | + | 17.0027i | 1.52382 | + | 1.07750i | ||||
\(250\) | 9.79796 | − | 5.65685i | 0.619677 | − | 0.357771i | ||||
\(251\) | 3.27526 | + | 1.89097i | 0.206732 | + | 0.119357i | 0.599792 | − | 0.800156i | \(-0.295250\pi\) |
−0.393060 | + | 0.919513i | \(0.628583\pi\) | |||||||
\(252\) | −1.32577 | − | 0.246405i | −0.0835154 | − | 0.0155221i | ||||
\(253\) | −11.1237 | + | 19.2669i | −0.699343 | + | 1.21130i | ||||
\(254\) | 10.3923i | 0.652071i | ||||||||
\(255\) | −0.651531 | − | 1.41421i | −0.0408004 | − | 0.0885615i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.50000 | − | 12.9904i | 0.467837 | − | 0.810318i | −0.531487 | − | 0.847066i | \(-0.678367\pi\) |
0.999325 | + | 0.0367485i | \(0.0117000\pi\) | |||||||
\(258\) | −6.44949 | − | 13.9993i | −0.401528 | − | 0.871557i | ||||
\(259\) | 3.46410i | 0.215249i | ||||||||
\(260\) | 2.44949 | − | 4.24264i | 0.151911 | − | 0.263117i | ||||
\(261\) | 7.22474 | + | 1.34278i | 0.447200 | + | 0.0831161i | ||||
\(262\) | 1.92679 | + | 1.11243i | 0.119037 | + | 0.0687262i | ||||
\(263\) | −7.77526 | + | 4.48905i | −0.479443 | + | 0.276806i | −0.720184 | − | 0.693783i | \(-0.755943\pi\) |
0.240741 | + | 0.970589i | \(0.422609\pi\) | |||||||
\(264\) | 4.44949 | + | 3.14626i | 0.273847 | + | 0.193639i | ||||
\(265\) | − | 15.4135i | − | 0.946843i | ||||||
\(266\) | −0.449490 | + | 1.90702i | −0.0275600 | + | 0.116927i | ||||
\(267\) | 5.14643 | + | 11.1708i | 0.314956 | + | 0.683645i | ||||
\(268\) | −2.17423 | + | 1.25529i | −0.132813 | + | 0.0766793i | ||||
\(269\) | −12.2474 | − | 21.2132i | −0.746740 | − | 1.29339i | −0.949377 | − | 0.314138i | \(-0.898285\pi\) |
0.202637 | − | 0.979254i | \(-0.435049\pi\) | |||||||
\(270\) | 5.12372 | + | 5.26758i | 0.311820 | + | 0.320575i | ||||
\(271\) | 10.0227 | + | 17.3598i | 0.608836 | + | 1.05453i | 0.991433 | + | 0.130619i | \(0.0416965\pi\) |
−0.382597 | + | 0.923915i | \(0.624970\pi\) | |||||||
\(272\) | −0.550510 | − | 0.317837i | −0.0333796 | − | 0.0192717i | ||||
\(273\) | 2.44949 | − | 1.12848i | 0.148250 | − | 0.0682990i | ||||
\(274\) | 3.92480i | 0.237106i | ||||||||
\(275\) | −8.17423 | − | 4.71940i | −0.492925 | − | 0.284590i | ||||
\(276\) | −1.12372 | + | 12.1958i | −0.0676403 | + | 0.734100i | ||||
\(277\) | 20.2474 | 1.21655 | 0.608276 | − | 0.793726i | \(-0.291862\pi\) | ||||
0.608276 | + | 0.793726i | \(0.291862\pi\) | |||||||
\(278\) | −14.3485 | −0.860564 | ||||||||
\(279\) | 12.0000 | − | 4.24264i | 0.718421 | − | 0.254000i | ||||
\(280\) | −0.550510 | + | 0.317837i | −0.0328993 | + | 0.0189944i | ||||
\(281\) | −11.2980 | + | 19.5686i | −0.673980 | + | 1.16737i | 0.302786 | + | 0.953058i | \(0.402083\pi\) |
−0.976766 | + | 0.214309i | \(0.931250\pi\) | |||||||
\(282\) | 18.8990 | + | 13.3636i | 1.12542 | + | 0.795791i | ||||
\(283\) | 4.72474 | + | 8.18350i | 0.280857 | + | 0.486458i | 0.971596 | − | 0.236646i | \(-0.0760480\pi\) |
−0.690739 | + | 0.723104i | \(0.742715\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 8.00000 | − | 7.07107i | 0.473879 | − | 0.418854i | ||||
\(286\) | −10.8990 | −0.644470 | ||||||||
\(287\) | −0.674235 | − | 1.16781i | −0.0397988 | − | 0.0689336i | ||||
\(288\) | 2.94949 | + | 0.548188i | 0.173800 | + | 0.0323023i | ||||
\(289\) | −8.29796 | + | 14.3725i | −0.488115 | + | 0.845440i | ||||
\(290\) | 3.00000 | − | 1.73205i | 0.176166 | − | 0.101710i | ||||
\(291\) | 0.522704 | − | 5.67291i | 0.0306414 | − | 0.332552i | ||||
\(292\) | 8.79796 | 0.514862 | ||||||||
\(293\) | 19.3485 | 1.13035 | 0.565175 | − | 0.824971i | \(-0.308809\pi\) | ||||
0.565175 | + | 0.824971i | \(0.308809\pi\) | |||||||
\(294\) | 11.7247 | + | 1.08032i | 0.683801 | + | 0.0630057i | ||||
\(295\) | −14.0227 | − | 8.09601i | −0.816433 | − | 0.471368i | ||||
\(296\) | − | 7.70674i | − | 0.447945i | ||||||
\(297\) | 4.44949 | − | 15.7313i | 0.258186 | − | 0.912824i | ||||
\(298\) | 1.77526 | + | 1.02494i | 0.102838 | + | 0.0593734i | ||||
\(299\) | −12.2474 | − | 21.2132i | −0.708288 | − | 1.22679i | ||||
\(300\) | −5.17423 | − | 0.476756i | −0.298735 | − | 0.0275255i | ||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | −8.32577 | + | 4.80688i | −0.479094 | + | 0.276605i | ||||
\(303\) | −15.5732 | + | 7.17461i | −0.894658 | + | 0.412170i | ||||
\(304\) | 1.00000 | − | 4.24264i | 0.0573539 | − | 0.243332i | ||||
\(305\) | − | 2.19275i | − | 0.125557i | ||||||
\(306\) | −0.348469 | + | 1.87492i | −0.0199207 | + | 0.107182i | ||||
\(307\) | 18.5227 | − | 10.6941i | 1.05715 | − | 0.610344i | 0.132505 | − | 0.991182i | \(-0.457698\pi\) |
0.924642 | + | 0.380838i | \(0.124365\pi\) | |||||||
\(308\) | 1.22474 | + | 0.707107i | 0.0697863 | + | 0.0402911i | ||||
\(309\) | −7.10102 | − | 5.02118i | −0.403963 | − | 0.285645i | ||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | − | 15.5563i | − | 0.882120i | −0.897478 | − | 0.441060i | \(-0.854603\pi\) | ||
0.897478 | − | 0.441060i | \(-0.145397\pi\) | |||||||
\(312\) | −5.44949 | + | 2.51059i | −0.308517 | + | 0.142134i | ||||
\(313\) | 9.50000 | − | 16.4545i | 0.536972 | − | 0.930062i | −0.462093 | − | 0.886831i | \(-0.652902\pi\) |
0.999065 | − | 0.0432311i | \(-0.0137652\pi\) | |||||||
\(314\) | −5.34847 | + | 9.26382i | −0.301832 | + | 0.522788i | ||||
\(315\) | 1.44949 | + | 1.23924i | 0.0816695 | + | 0.0698233i | ||||
\(316\) | − | 8.48528i | − | 0.477334i | ||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | −10.8990 | + | 15.4135i | −0.611184 | + | 0.864345i | ||||
\(319\) | −6.67423 | − | 3.85337i | −0.373685 | − | 0.215747i | ||||
\(320\) | 1.22474 | − | 0.707107i | 0.0684653 | − | 0.0395285i | ||||
\(321\) | 4.89898 | − | 6.92820i | 0.273434 | − | 0.386695i | ||||
\(322\) | 3.17837i | 0.177124i | ||||||||
\(323\) | 2.69694 | + | 0.635674i | 0.150062 | + | 0.0353699i | ||||
\(324\) | −1.39898 | − | 8.89060i | −0.0777211 | − | 0.493922i | ||||
\(325\) | 9.00000 | − | 5.19615i | 0.499230 | − | 0.288231i | ||||
\(326\) | −9.17423 | − | 15.8902i | −0.508114 | − | 0.880079i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 5.20204 | + | 3.00340i | 0.286798 | + | 0.165583i | ||||
\(330\) | −3.22474 | − | 6.99964i | −0.177516 | − | 0.385317i | ||||
\(331\) | 23.2952i | 1.28042i | 0.768200 | + | 0.640210i | \(0.221153\pi\) | ||||
−0.768200 | + | 0.640210i | \(0.778847\pi\) | |||||||
\(332\) | −14.7247 | − | 8.50134i | −0.808125 | − | 0.466571i | ||||
\(333\) | −21.7980 | + | 7.70674i | −1.19452 | + | 0.422327i | ||||
\(334\) | −4.89898 | −0.268060 | ||||||||
\(335\) | 3.55051 | 0.193985 | ||||||||
\(336\) | 0.775255 | + | 0.0714323i | 0.0422936 | + | 0.00389695i | ||||
\(337\) | −17.8485 | + | 10.3048i | −0.972268 | + | 0.561339i | −0.899927 | − | 0.436041i | \(-0.856380\pi\) |
−0.0723411 | + | 0.997380i | \(0.523047\pi\) | |||||||
\(338\) | −0.500000 | + | 0.866025i | −0.0271964 | + | 0.0471056i | ||||
\(339\) | 18.7980 | − | 26.5843i | 1.02096 | − | 1.44386i | ||||
\(340\) | 0.449490 | + | 0.778539i | 0.0243770 | + | 0.0422222i | ||||
\(341\) | −13.3485 | −0.722860 | ||||||||
\(342\) | −13.0000 | + | 1.41421i | −0.702959 | + | 0.0764719i | ||||
\(343\) | 6.20204 | 0.334879 | ||||||||
\(344\) | 4.44949 | + | 7.70674i | 0.239900 | + | 0.415520i | ||||
\(345\) | 10.0000 | − | 14.1421i | 0.538382 | − | 0.761387i | ||||
\(346\) | −0.550510 | + | 0.953512i | −0.0295956 | + | 0.0512611i | ||||
\(347\) | −3.27526 | + | 1.89097i | −0.175825 | + | 0.101513i | −0.585330 | − | 0.810795i | \(-0.699035\pi\) |
0.409505 | + | 0.912308i | \(0.365702\pi\) | |||||||
\(348\) | −4.22474 | − | 0.389270i | −0.226470 | − | 0.0208670i | ||||
\(349\) | 32.4949 | 1.73941 | 0.869706 | − | 0.493570i | \(-0.164308\pi\) | ||||
0.869706 | + | 0.493570i | \(0.164308\pi\) | |||||||
\(350\) | −1.34847 | −0.0720787 | ||||||||
\(351\) | 12.5505 | + | 12.9029i | 0.669897 | + | 0.688706i | ||||
\(352\) | −2.72474 | − | 1.57313i | −0.145229 | − | 0.0838482i | ||||
\(353\) | − | 24.9951i | − | 1.33036i | −0.746684 | − | 0.665179i | \(-0.768355\pi\) | ||
0.746684 | − | 0.665179i | \(-0.231645\pi\) | |||||||
\(354\) | 8.29796 | + | 18.0116i | 0.441032 | + | 0.957304i | ||||
\(355\) | −7.34847 | − | 4.24264i | −0.390016 | − | 0.225176i | ||||
\(356\) | −3.55051 | − | 6.14966i | −0.188177 | − | 0.325932i | ||||
\(357\) | −0.0454077 | + | 0.492810i | −0.00240323 | + | 0.0260823i | ||||
\(358\) | −3.82577 | − | 6.62642i | −0.202198 | − | 0.350217i | ||||
\(359\) | −20.8207 | + | 12.0208i | −1.09887 | + | 0.634434i | −0.935925 | − | 0.352200i | \(-0.885434\pi\) |
−0.162948 | + | 0.986635i | \(0.552100\pi\) | |||||||
\(360\) | −3.22474 | − | 2.75699i | −0.169959 | − | 0.145306i | ||||
\(361\) | 1.15153 | + | 18.9651i | 0.0606069 | + | 0.998162i | ||||
\(362\) | − | 21.5631i | − | 1.13333i | ||||||
\(363\) | 1.10102 | − | 1.55708i | 0.0577886 | − | 0.0817254i | ||||
\(364\) | −1.34847 | + | 0.778539i | −0.0706790 | + | 0.0408065i | ||||
\(365\) | −10.7753 | − | 6.22110i | −0.564003 | − | 0.325627i | ||||
\(366\) | −1.55051 | + | 2.19275i | −0.0810465 | + | 0.114617i | ||||
\(367\) | 4.32577 | − | 7.49245i | 0.225803 | − | 0.391102i | −0.730757 | − | 0.682638i | \(-0.760833\pi\) |
0.956560 | + | 0.291535i | \(0.0941661\pi\) | |||||||
\(368\) | − | 7.07107i | − | 0.368605i | ||||||
\(369\) | 5.84847 | − | 6.84072i | 0.304459 | − | 0.356113i | ||||
\(370\) | −5.44949 | + | 9.43879i | −0.283305 | + | 0.490699i | ||||
\(371\) | −2.44949 | + | 4.24264i | −0.127171 | + | 0.220267i | ||||
\(372\) | −6.67423 | + | 3.07483i | −0.346043 | + | 0.159423i | ||||
\(373\) | − | 25.4558i | − | 1.31805i | −0.752119 | − | 0.659027i | \(-0.770968\pi\) | ||
0.752119 | − | 0.659027i | \(-0.229032\pi\) | |||||||
\(374\) | 1.00000 | − | 1.73205i | 0.0517088 | − | 0.0895622i | ||||
\(375\) | 16.0000 | + | 11.3137i | 0.826236 | + | 0.584237i | ||||
\(376\) | −11.5732 | − | 6.68180i | −0.596843 | − | 0.344587i | ||||
\(377\) | 7.34847 | − | 4.24264i | 0.378465 | − | 0.218507i | ||||
\(378\) | −0.573214 | − | 2.26418i | −0.0294830 | − | 0.116457i | ||||
\(379\) | 1.55708i | 0.0799817i | 0.999200 | + | 0.0399909i | \(0.0127329\pi\) | ||||
−0.999200 | + | 0.0399909i | \(0.987267\pi\) | |||||||
\(380\) | −4.22474 | + | 4.48905i | −0.216725 | + | 0.230283i | ||||
\(381\) | −16.3485 | + | 7.53177i | −0.837557 | + | 0.385864i | ||||
\(382\) | −7.10102 | + | 4.09978i | −0.363320 | + | 0.209763i | ||||
\(383\) | −10.2247 | − | 17.7098i | −0.522460 | − | 0.904927i | −0.999659 | − | 0.0261318i | \(-0.991681\pi\) |
0.477198 | − | 0.878796i | \(-0.341652\pi\) | |||||||
\(384\) | −1.72474 | − | 0.158919i | −0.0880155 | − | 0.00810978i | ||||
\(385\) | −1.00000 | − | 1.73205i | −0.0509647 | − | 0.0882735i | ||||
\(386\) | 22.3485 | + | 12.9029i | 1.13751 | + | 0.656740i | ||||
\(387\) | 17.3485 | − | 20.2918i | 0.881872 | − | 1.03149i | ||||
\(388\) | 3.28913i | 0.166980i | ||||||||
\(389\) | 13.1010 | + | 7.56388i | 0.664248 | + | 0.383504i | 0.793894 | − | 0.608057i | \(-0.208051\pi\) |
−0.129646 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(390\) | 8.44949 | + | 0.778539i | 0.427857 | + | 0.0394229i | ||||
\(391\) | 4.49490 | 0.227317 | ||||||||
\(392\) | −6.79796 | −0.343349 | ||||||||
\(393\) | −0.353572 | + | 3.83732i | −0.0178353 | + | 0.193567i | ||||
\(394\) | 17.5732 | − | 10.1459i | 0.885326 | − | 0.511143i | ||||
\(395\) | −6.00000 | + | 10.3923i | −0.301893 | + | 0.522894i | ||||
\(396\) | −1.72474 | + | 9.27987i | −0.0866717 | + | 0.466331i | ||||
\(397\) | 2.67423 | + | 4.63191i | 0.134216 | + | 0.232469i | 0.925298 | − | 0.379242i | \(-0.123815\pi\) |
−0.791082 | + | 0.611711i | \(0.790482\pi\) | |||||||
\(398\) | −2.89898 | −0.145313 | ||||||||
\(399\) | −3.32577 | + | 0.674999i | −0.166497 | + | 0.0337922i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 3.39898 | + | 5.88721i | 0.169737 | + | 0.293993i | 0.938327 | − | 0.345748i | \(-0.112375\pi\) |
−0.768590 | + | 0.639741i | \(0.779042\pi\) | |||||||
\(402\) | −3.55051 | − | 2.51059i | −0.177083 | − | 0.125217i | ||||
\(403\) | 7.34847 | − | 12.7279i | 0.366053 | − | 0.634023i | ||||
\(404\) | 8.57321 | − | 4.94975i | 0.426533 | − | 0.246259i | ||||
\(405\) | −4.57321 | + | 11.8780i | −0.227245 | + | 0.590220i | ||||
\(406\) | −1.10102 | −0.0546427 | ||||||||
\(407\) | 24.2474 | 1.20190 | ||||||||
\(408\) | 0.101021 | − | 1.09638i | 0.00500126 | − | 0.0542787i | ||||
\(409\) | 3.15153 | + | 1.81954i | 0.155833 | + | 0.0899703i | 0.575889 | − | 0.817528i | \(-0.304656\pi\) |
−0.420056 | + | 0.907498i | \(0.637989\pi\) | |||||||
\(410\) | − | 4.24264i | − | 0.209529i | ||||||
\(411\) | −6.17423 | + | 2.84448i | −0.304553 | + | 0.140308i | ||||
\(412\) | 4.34847 | + | 2.51059i | 0.214234 | + | 0.123688i | ||||
\(413\) | 2.57321 | + | 4.45694i | 0.126620 | + | 0.219312i | ||||
\(414\) | −20.0000 | + | 7.07107i | −0.982946 | + | 0.347524i | ||||
\(415\) | 12.0227 | + | 20.8239i | 0.590171 | + | 1.02221i | ||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | −10.3990 | − | 22.5720i | −0.509240 | − | 1.10536i | ||||
\(418\) | 13.3485 | + | 3.14626i | 0.652895 | + | 0.153889i | ||||
\(419\) | 24.5344i | 1.19859i | 0.800530 | + | 0.599293i | \(0.204552\pi\) | ||||
−0.800530 | + | 0.599293i | \(0.795448\pi\) | |||||||
\(420\) | −0.898979 | − | 0.635674i | −0.0438657 | − | 0.0310177i | ||||
\(421\) | −3.97730 | + | 2.29629i | −0.193842 | + | 0.111914i | −0.593780 | − | 0.804628i | \(-0.702365\pi\) |
0.399938 | + | 0.916542i | \(0.369032\pi\) | |||||||
\(422\) | 1.34847 | + | 0.778539i | 0.0656425 | + | 0.0378987i | ||||
\(423\) | −7.32577 | + | 39.4158i | −0.356191 | + | 1.91646i | ||||
\(424\) | 5.44949 | − | 9.43879i | 0.264651 | − | 0.458388i | ||||
\(425\) | 1.90702i | 0.0925042i | ||||||||
\(426\) | 4.34847 | + | 9.43879i | 0.210684 | + | 0.457311i | ||||
\(427\) | −0.348469 | + | 0.603566i | −0.0168636 | + | 0.0292086i | ||||
\(428\) | −2.44949 | + | 4.24264i | −0.118401 | + | 0.205076i | ||||
\(429\) | −7.89898 | − | 17.1455i | −0.381366 | − | 0.827794i | ||||
\(430\) | − | 12.5851i | − | 0.606905i | ||||||
\(431\) | −1.65153 | + | 2.86054i | −0.0795514 | + | 0.137787i | −0.903056 | − | 0.429522i | \(-0.858682\pi\) |
0.823505 | + | 0.567309i | \(0.192015\pi\) | |||||||
\(432\) | 1.27526 | + | 5.03723i | 0.0613557 | + | 0.242354i | ||||
\(433\) | −17.6969 | − | 10.2173i | −0.850461 | − | 0.491014i | 0.0103456 | − | 0.999946i | \(-0.496707\pi\) |
−0.860806 | + | 0.508933i | \(0.830040\pi\) | |||||||
\(434\) | −1.65153 | + | 0.953512i | −0.0792760 | + | 0.0457700i | ||||
\(435\) | 4.89898 | + | 3.46410i | 0.234888 | + | 0.166091i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.87628 | + | 29.5163i | 0.424610 | + | 1.41196i | ||||
\(438\) | 6.37628 | + | 13.8404i | 0.304670 | + | 0.661318i | ||||
\(439\) | −9.67423 | + | 5.58542i | −0.461726 | + | 0.266578i | −0.712770 | − | 0.701398i | \(-0.752560\pi\) |
0.251044 | + | 0.967976i | \(0.419226\pi\) | |||||||
\(440\) | 2.22474 | + | 3.85337i | 0.106061 | + | 0.183702i | ||||
\(441\) | 6.79796 | + | 19.2275i | 0.323712 | + | 0.915597i | ||||
\(442\) | 1.10102 | + | 1.90702i | 0.0523702 | + | 0.0907079i | ||||
\(443\) | 16.3207 | + | 9.42274i | 0.775418 | + | 0.447688i | 0.834804 | − | 0.550547i | \(-0.185581\pi\) |
−0.0593859 | + | 0.998235i | \(0.518914\pi\) | |||||||
\(444\) | 12.1237 | − | 5.58542i | 0.575366 | − | 0.265072i | ||||
\(445\) | 10.0424i | 0.476053i | ||||||||
\(446\) | 15.6742 | + | 9.04952i | 0.742197 | + | 0.428507i | ||||
\(447\) | −0.325765 | + | 3.53553i | −0.0154082 | + | 0.167225i | ||||
\(448\) | −0.449490 | −0.0212364 | ||||||||
\(449\) | −30.7980 | −1.45345 | −0.726723 | − | 0.686931i | \(-0.758958\pi\) | ||||
−0.726723 | + | 0.686931i | \(0.758958\pi\) | |||||||
\(450\) | −3.00000 | − | 8.48528i | −0.141421 | − | 0.400000i | ||||
\(451\) | −8.17423 | + | 4.71940i | −0.384910 | + | 0.222228i | ||||
\(452\) | −9.39898 | + | 16.2795i | −0.442091 | + | 0.765724i | ||||
\(453\) | −13.5959 | − | 9.61377i | −0.638792 | − | 0.451694i | ||||
\(454\) | 0.275255 | + | 0.476756i | 0.0129184 | + | 0.0223753i | ||||
\(455\) | 2.20204 | 0.103233 | ||||||||
\(456\) | 7.39898 | − | 1.50170i | 0.346489 | − | 0.0703235i | ||||
\(457\) | −13.0000 | −0.608114 | −0.304057 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304057 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(458\) | −0.449490 | − | 0.778539i | −0.0210033 | − | 0.0363787i | ||||
\(459\) | −3.20204 | + | 0.810647i | −0.149458 | + | 0.0378378i | ||||
\(460\) | −5.00000 | + | 8.66025i | −0.233126 | + | 0.403786i | ||||
\(461\) | 33.2474 | − | 19.1954i | 1.54849 | − | 0.894020i | 0.550231 | − | 0.835013i | \(-0.314540\pi\) |
0.998258 | − | 0.0590072i | \(-0.0187935\pi\) | |||||||
\(462\) | −0.224745 | + | 2.43916i | −0.0104561 | + | 0.113480i | ||||
\(463\) | −19.7980 | −0.920089 | −0.460045 | − | 0.887896i | \(-0.652167\pi\) | ||||
−0.460045 | + | 0.887896i | \(0.652167\pi\) | |||||||
\(464\) | 2.44949 | 0.113715 | ||||||||
\(465\) | 10.3485 | + | 0.953512i | 0.479899 | + | 0.0442180i | ||||
\(466\) | −15.3990 | − | 8.89060i | −0.713344 | − | 0.411849i | ||||
\(467\) | − | 12.6172i | − | 0.583853i | −0.956441 | − | 0.291926i | \(-0.905704\pi\) | ||
0.956441 | − | 0.291926i | \(-0.0942962\pi\) | |||||||
\(468\) | −7.89898 | − | 6.75323i | −0.365130 | − | 0.312168i | ||||
\(469\) | −0.977296 | − | 0.564242i | −0.0451273 | − | 0.0260543i | ||||
\(470\) | 9.44949 | + | 16.3670i | 0.435872 | + | 0.754953i | ||||
\(471\) | −18.4495 | − | 1.69994i | −0.850108 | − | 0.0783292i | ||||
\(472\) | −5.72474 | − | 9.91555i | −0.263503 | − | 0.456400i | ||||
\(473\) | −24.2474 | + | 13.9993i | −1.11490 | + | 0.643687i | ||||
\(474\) | 13.3485 | − | 6.14966i | 0.613115 | − | 0.282463i | ||||
\(475\) | −12.5227 | + | 3.76588i | −0.574581 | + | 0.172791i | ||||
\(476\) | − | 0.285729i | − | 0.0130964i | ||||||
\(477\) | −32.1464 | − | 5.97469i | −1.47188 | − | 0.273562i | ||||
\(478\) | 18.2474 | − | 10.5352i | 0.834619 | − | 0.481867i | ||||
\(479\) | −0.853572 | − | 0.492810i | −0.0390007 | − | 0.0225171i | 0.480373 | − | 0.877064i | \(-0.340501\pi\) |
−0.519374 | + | 0.854547i | \(0.673835\pi\) | |||||||
\(480\) | 2.00000 | + | 1.41421i | 0.0912871 | + | 0.0645497i | ||||
\(481\) | −13.3485 | + | 23.1202i | −0.608638 | + | 1.05419i | ||||
\(482\) | 6.75323i | 0.307601i | ||||||||
\(483\) | −5.00000 | + | 2.30351i | −0.227508 | + | 0.104813i | ||||
\(484\) | −0.550510 | + | 0.953512i | −0.0250232 | + | 0.0433414i | ||||
\(485\) | 2.32577 | − | 4.02834i | 0.105608 | − | 0.182918i | ||||
\(486\) | 12.9722 | − | 8.64420i | 0.588431 | − | 0.392109i | ||||
\(487\) | 25.0273i | 1.13409i | 0.823686 | + | 0.567046i | \(0.191914\pi\) | ||||
−0.823686 | + | 0.567046i | \(0.808086\pi\) | |||||||
\(488\) | 0.775255 | − | 1.34278i | 0.0350942 | − | 0.0607849i | ||||
\(489\) | 18.3485 | − | 25.9487i | 0.829746 | − | 1.17344i | ||||
\(490\) | 8.32577 | + | 4.80688i | 0.376120 | + | 0.217153i | ||||
\(491\) | 13.8990 | − | 8.02458i | 0.627252 | − | 0.362144i | −0.152435 | − | 0.988314i | \(-0.548711\pi\) |
0.779687 | + | 0.626169i | \(0.215378\pi\) | |||||||
\(492\) | −3.00000 | + | 4.24264i | −0.135250 | + | 0.191273i | ||||
\(493\) | 1.55708i | 0.0701273i | ||||||||
\(494\) | −10.3485 | + | 10.9959i | −0.465600 | + | 0.494728i | ||||
\(495\) | 8.67423 | − | 10.1459i | 0.389878 | − | 0.456024i | ||||
\(496\) | 3.67423 | − | 2.12132i | 0.164978 | − | 0.0952501i | ||||
\(497\) | 1.34847 | + | 2.33562i | 0.0604871 | + | 0.104767i | ||||
\(498\) | 2.70204 | − | 29.3253i | 0.121081 | − | 1.31410i | ||||
\(499\) | −3.72474 | − | 6.45145i | −0.166742 | − | 0.288806i | 0.770530 | − | 0.637403i | \(-0.219992\pi\) |
−0.937273 | + | 0.348597i | \(0.886658\pi\) | |||||||
\(500\) | −9.79796 | − | 5.65685i | −0.438178 | − | 0.252982i | ||||
\(501\) | −3.55051 | − | 7.70674i | −0.158625 | − | 0.344312i | ||||
\(502\) | − | 3.78194i | − | 0.168796i | ||||||
\(503\) | 13.4722 | + | 7.77817i | 0.600695 | + | 0.346812i | 0.769315 | − | 0.638870i | \(-0.220598\pi\) |
−0.168620 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(504\) | 0.449490 | + | 1.27135i | 0.0200219 | + | 0.0566304i | ||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | 22.2474 | 0.989020 | ||||||||
\(507\) | −1.72474 | − | 0.158919i | −0.0765986 | − | 0.00705782i | ||||
\(508\) | 9.00000 | − | 5.19615i | 0.399310 | − | 0.230542i | ||||
\(509\) | −8.69694 | + | 15.0635i | −0.385485 | + | 0.667680i | −0.991836 | − | 0.127517i | \(-0.959299\pi\) |
0.606351 | + | 0.795197i | \(0.292633\pi\) | |||||||
\(510\) | −0.898979 | + | 1.27135i | −0.0398075 | + | 0.0562963i | ||||
\(511\) | 1.97730 | + | 3.42478i | 0.0874704 | + | 0.151503i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.6464 | − | 19.4258i | −0.514202 | − | 0.857669i | ||||
\(514\) | −15.0000 | −0.661622 | ||||||||
\(515\) | −3.55051 | − | 6.14966i | −0.156454 | − | 0.270987i | ||||
\(516\) | −8.89898 | + | 12.5851i | −0.391756 | + | 0.554026i | ||||
\(517\) | 21.0227 | − | 36.4124i | 0.924577 | − | 1.60142i | ||||
\(518\) | 3.00000 | − | 1.73205i | 0.131812 | − | 0.0761019i | ||||
\(519\) | −1.89898 | − | 0.174973i | −0.0833559 | − | 0.00768045i | ||||
\(520\) | −4.89898 | −0.214834 | ||||||||
\(521\) | 25.8990 | 1.13465 | 0.567327 | − | 0.823492i | \(-0.307977\pi\) | ||||
0.567327 | + | 0.823492i | \(0.307977\pi\) | |||||||
\(522\) | −2.44949 | − | 6.92820i | −0.107211 | − | 0.303239i | ||||
\(523\) | −5.69694 | − | 3.28913i | −0.249110 | − | 0.143824i | 0.370247 | − | 0.928933i | \(-0.379273\pi\) |
−0.619357 | + | 0.785110i | \(0.712606\pi\) | |||||||
\(524\) | − | 2.22486i | − | 0.0971935i | ||||||
\(525\) | −0.977296 | − | 2.12132i | −0.0426527 | − | 0.0925820i | ||||
\(526\) | 7.77526 | + | 4.48905i | 0.339017 | + | 0.195732i | ||||
\(527\) | 1.34847 | + | 2.33562i | 0.0587402 | + | 0.101741i | ||||
\(528\) | 0.500000 | − | 5.42650i | 0.0217597 | − | 0.236158i | ||||
\(529\) | 13.5000 | + | 23.3827i | 0.586957 | + | 1.01664i | ||||
\(530\) | −13.3485 | + | 7.70674i | −0.579820 | + | 0.334759i | ||||
\(531\) | −22.3207 | + | 26.1076i | −0.968634 | + | 1.13297i | ||||
\(532\) | 1.87628 | − | 0.564242i | 0.0813469 | − | 0.0244630i | ||||
\(533\) | − | 10.3923i | − | 0.450141i | ||||||
\(534\) | 7.10102 | − | 10.0424i | 0.307291 | − | 0.434575i | ||||
\(535\) | 6.00000 | − | 3.46410i | 0.259403 | − | 0.149766i | ||||
\(536\) | 2.17423 | + | 1.25529i | 0.0939126 | + | 0.0542205i | ||||
\(537\) | 7.65153 | − | 10.8209i | 0.330188 | − | 0.466956i | ||||
\(538\) | −12.2474 | + | 21.2132i | −0.528025 | + | 0.914566i | ||||
\(539\) | − | 21.3882i | − | 0.921254i | ||||||
\(540\) | 2.00000 | − | 7.07107i | 0.0860663 | − | 0.304290i | ||||
\(541\) | −5.34847 | + | 9.26382i | −0.229949 | + | 0.398283i | −0.957793 | − | 0.287460i | \(-0.907189\pi\) |
0.727844 | + | 0.685743i | \(0.240522\pi\) | |||||||
\(542\) | 10.0227 | − | 17.3598i | 0.430512 | − | 0.745669i | ||||
\(543\) | 33.9217 | − | 15.6278i | 1.45572 | − | 0.670652i | ||||
\(544\) | 0.635674i | 0.0272543i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.20204 | − | 1.55708i | −0.0942387 | − | 0.0666368i | ||||
\(547\) | −32.3939 | − | 18.7026i | −1.38506 | − | 0.799666i | −0.392309 | − | 0.919834i | \(-0.628323\pi\) |
−0.992754 | + | 0.120168i | \(0.961657\pi\) | |||||||
\(548\) | 3.39898 | − | 1.96240i | 0.145197 | − | 0.0838296i | ||||
\(549\) | −4.57321 | − | 0.849971i | −0.195180 | − | 0.0362759i | ||||
\(550\) | 9.43879i | 0.402471i | ||||||||
\(551\) | −10.2247 | + | 3.07483i | −0.435589 | + | 0.130992i | ||||
\(552\) | 11.1237 | − | 5.12472i | 0.473457 | − | 0.218123i | ||||
\(553\) | 3.30306 | − | 1.90702i | 0.140460 | − | 0.0810949i | ||||
\(554\) | −10.1237 | − | 17.5348i | −0.430116 | − | 0.744982i | ||||
\(555\) | −18.7980 | − | 1.73205i | −0.797929 | − | 0.0735215i | ||||
\(556\) | 7.17423 | + | 12.4261i | 0.304255 | + | 0.526986i | ||||
\(557\) | −0.247449 | − | 0.142865i | −0.0104847 | − | 0.00605337i | 0.494748 | − | 0.869036i | \(-0.335260\pi\) |
−0.505233 | + | 0.862983i | \(0.668594\pi\) | |||||||
\(558\) | −9.67423 | − | 8.27098i | −0.409543 | − | 0.350139i | ||||
\(559\) | − | 30.8270i | − | 1.30384i | ||||||
\(560\) | 0.550510 | + | 0.317837i | 0.0232633 | + | 0.0134311i | ||||
\(561\) | 3.44949 | + | 0.317837i | 0.145638 | + | 0.0134191i | ||||
\(562\) | 22.5959 | 0.953151 | ||||||||
\(563\) | −40.8434 | −1.72134 | −0.860671 | − | 0.509161i | \(-0.829956\pi\) | ||||
−0.860671 | + | 0.509161i | \(0.829956\pi\) | |||||||
\(564\) | 2.12372 | − | 23.0488i | 0.0894249 | − | 0.970529i | ||||
\(565\) | 23.0227 | − | 13.2922i | 0.968572 | − | 0.559206i | ||||
\(566\) | 4.72474 | − | 8.18350i | 0.198596 | − | 0.343978i | ||||
\(567\) | 3.14643 | − | 2.54270i | 0.132138 | − | 0.106783i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 34.2929 | 1.43763 | 0.718816 | − | 0.695201i | \(-0.244685\pi\) | ||||
0.718816 | + | 0.695201i | \(0.244685\pi\) | |||||||
\(570\) | −10.1237 | − | 3.39267i | −0.424036 | − | 0.142103i | ||||
\(571\) | 33.0454 | 1.38291 | 0.691454 | − | 0.722421i | \(-0.256971\pi\) | ||||
0.691454 | + | 0.722421i | \(0.256971\pi\) | |||||||
\(572\) | 5.44949 | + | 9.43879i | 0.227855 | + | 0.394656i | ||||
\(573\) | −11.5959 | − | 8.19955i | −0.484426 | − | 0.342541i | ||||
\(574\) | −0.674235 | + | 1.16781i | −0.0281420 | + | 0.0487434i | ||||
\(575\) | −18.3712 | + | 10.6066i | −0.766131 | + | 0.442326i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | 18.5959 | 0.774158 | 0.387079 | − | 0.922047i | \(-0.373484\pi\) | ||||
0.387079 | + | 0.922047i | \(0.373484\pi\) | |||||||
\(578\) | 16.5959 | 0.690299 | ||||||||
\(579\) | −4.10102 | + | 44.5084i | −0.170433 | + | 1.84971i | ||||
\(580\) | −3.00000 | − | 1.73205i | −0.124568 | − | 0.0719195i | ||||
\(581\) | − | 7.64253i | − | 0.317065i | ||||||
\(582\) | −5.17423 | + | 2.38378i | −0.214479 | + | 0.0988108i | ||||
\(583\) | 29.6969 | + | 17.1455i | 1.22992 | + | 0.710096i | ||||
\(584\) | −4.39898 | − | 7.61926i | −0.182031 | − | 0.315287i | ||||
\(585\) | 4.89898 | + | 13.8564i | 0.202548 | + | 0.572892i | ||||
\(586\) | −9.67423 | − | 16.7563i | −0.399639 | − | 0.692195i | ||||
\(587\) | 13.8990 | − | 8.02458i | 0.573672 | − | 0.331210i | −0.184942 | − | 0.982749i | \(-0.559210\pi\) |
0.758615 | + | 0.651540i | \(0.225877\pi\) | |||||||
\(588\) | −4.92679 | − | 10.6941i | −0.203177 | − | 0.441017i | ||||
\(589\) | −12.6742 | + | 13.4671i | −0.522233 | + | 0.554904i | ||||
\(590\) | 16.1920i | 0.666615i | ||||||||
\(591\) | 28.6969 | + | 20.2918i | 1.18043 | + | 0.834693i | ||||
\(592\) | −6.67423 | + | 3.85337i | −0.274309 | + | 0.158373i | ||||
\(593\) | −15.0959 | − | 8.71563i | −0.619915 | − | 0.357908i | 0.156921 | − | 0.987611i | \(-0.449843\pi\) |
−0.776836 | + | 0.629703i | \(0.783177\pi\) | |||||||
\(594\) | −15.8485 | + | 4.01229i | −0.650271 | + | 0.164626i | ||||
\(595\) | −0.202041 | + | 0.349945i | −0.00828287 | + | 0.0143464i | ||||
\(596\) | − | 2.04989i | − | 0.0839667i | ||||||
\(597\) | −2.10102 | − | 4.56048i | −0.0859890 | − | 0.186648i | ||||
\(598\) | −12.2474 | + | 21.2132i | −0.500835 | + | 0.867472i | ||||
\(599\) | 2.57321 | − | 4.45694i | 0.105139 | − | 0.182106i | −0.808656 | − | 0.588282i | \(-0.799805\pi\) |
0.913795 | + | 0.406176i | \(0.133138\pi\) | |||||||
\(600\) | 2.17423 | + | 4.71940i | 0.0887628 | + | 0.192669i | ||||
\(601\) | − | 14.0314i | − | 0.572352i | −0.958177 | − | 0.286176i | \(-0.907616\pi\) | ||
0.958177 | − | 0.286176i | \(-0.0923842\pi\) | |||||||
\(602\) | −2.00000 | + | 3.46410i | −0.0815139 | + | 0.141186i | ||||
\(603\) | 1.37628 | − | 7.40496i | 0.0560463 | − | 0.301553i | ||||
\(604\) | 8.32577 | + | 4.80688i | 0.338771 | + | 0.195589i | ||||
\(605\) | 1.34847 | − | 0.778539i | 0.0548231 | − | 0.0316521i | ||||
\(606\) | 14.0000 | + | 9.89949i | 0.568711 | + | 0.402139i | ||||
\(607\) | 11.5208i | 0.467614i | 0.972283 | + | 0.233807i | \(0.0751185\pi\) | ||||
−0.972283 | + | 0.233807i | \(0.924882\pi\) | |||||||
\(608\) | −4.17423 | + | 1.25529i | −0.169288 | + | 0.0509089i | ||||
\(609\) | −0.797959 | − | 1.73205i | −0.0323349 | − | 0.0701862i | ||||
\(610\) | −1.89898 | + | 1.09638i | −0.0768874 | + | 0.0443910i | ||||
\(611\) | 23.1464 | + | 40.0908i | 0.936404 | + | 1.62190i | ||||
\(612\) | 1.79796 | − | 0.635674i | 0.0726782 | − | 0.0256956i | ||||
\(613\) | −23.8990 | − | 41.3942i | −0.965271 | − | 1.67190i | −0.708886 | − | 0.705323i | \(-0.750802\pi\) |
−0.256385 | − | 0.966575i | \(-0.582531\pi\) | |||||||
\(614\) | −18.5227 | − | 10.6941i | −0.747515 | − | 0.431578i | ||||
\(615\) | 6.67423 | − | 3.07483i | 0.269131 | − | 0.123989i | ||||
\(616\) | − | 1.41421i | − | 0.0569803i | ||||||
\(617\) | −8.05051 | − | 4.64796i | −0.324101 | − | 0.187120i | 0.329118 | − | 0.944289i | \(-0.393249\pi\) |
−0.653219 | + | 0.757169i | \(0.726582\pi\) | |||||||
\(618\) | −0.797959 | + | 8.66025i | −0.0320986 | + | 0.348367i | ||||
\(619\) | −30.6969 | −1.23381 | −0.616907 | − | 0.787036i | \(-0.711615\pi\) | ||||
−0.616907 | + | 0.787036i | \(0.711615\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | −25.6186 | − | 26.3379i | −1.02804 | − | 1.05690i | ||||
\(622\) | −13.4722 | + | 7.77817i | −0.540186 | + | 0.311876i | ||||
\(623\) | 1.59592 | − | 2.76421i | 0.0639391 | − | 0.110746i | ||||
\(624\) | 4.89898 | + | 3.46410i | 0.196116 | + | 0.138675i | ||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | −19.0000 | −0.759393 | ||||||||
\(627\) | 4.72474 | + | 23.2791i | 0.188688 | + | 0.929680i | ||||
\(628\) | 10.6969 | 0.426854 | ||||||||
\(629\) | −2.44949 | − | 4.24264i | −0.0976676 | − | 0.169165i | ||||
\(630\) | 0.348469 | − | 1.87492i | 0.0138833 | − | 0.0746984i | ||||
\(631\) | 17.1237 | − | 29.6592i | 0.681685 | − | 1.18071i | −0.292782 | − | 0.956179i | \(-0.594581\pi\) |
0.974466 | − | 0.224533i | \(-0.0720857\pi\) | |||||||
\(632\) | −7.34847 | + | 4.24264i | −0.292306 | + | 0.168763i | ||||
\(633\) | −0.247449 | + | 2.68556i | −0.00983520 | + | 0.106742i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | −14.6969 | −0.583230 | ||||||||
\(636\) | 18.7980 | + | 1.73205i | 0.745388 | + | 0.0686803i | ||||
\(637\) | 20.3939 | + | 11.7744i | 0.808035 | + | 0.466519i | ||||
\(638\) | 7.70674i | 0.305113i | ||||||||
\(639\) | −11.6969 | + | 13.6814i | −0.462724 | + | 0.541229i | ||||
\(640\) | −1.22474 | − | 0.707107i | −0.0484123 | − | 0.0279508i | ||||
\(641\) | 13.1969 | + | 22.8578i | 0.521248 | + | 0.902828i | 0.999695 | + | 0.0247111i | \(0.00786658\pi\) |
−0.478447 | + | 0.878116i | \(0.658800\pi\) | |||||||
\(642\) | −8.44949 | − | 0.778539i | −0.333475 | − | 0.0307265i | ||||
\(643\) | −5.07321 | − | 8.78706i | −0.200068 | − | 0.346528i | 0.748482 | − | 0.663155i | \(-0.230783\pi\) |
−0.948550 | + | 0.316627i | \(0.897450\pi\) | |||||||
\(644\) | 2.75255 | − | 1.58919i | 0.108466 | − | 0.0626227i | ||||
\(645\) | 19.7980 | − | 9.12096i | 0.779544 | − | 0.359137i | ||||
\(646\) | −0.797959 | − | 2.65345i | −0.0313953 | − | 0.104399i | ||||
\(647\) | − | 14.7778i | − | 0.580976i | −0.956879 | − | 0.290488i | \(-0.906182\pi\) | ||
0.956879 | − | 0.290488i | \(-0.0938176\pi\) | |||||||
\(648\) | −7.00000 | + | 5.65685i | −0.274986 | + | 0.222222i | ||||
\(649\) | 31.1969 | − | 18.0116i | 1.22459 | − | 0.707016i | ||||
\(650\) | −9.00000 | − | 5.19615i | −0.353009 | − | 0.203810i | ||||
\(651\) | −2.69694 | − | 1.90702i | −0.105701 | − | 0.0747421i | ||||
\(652\) | −9.17423 | + | 15.8902i | −0.359291 | + | 0.622310i | ||||
\(653\) | − | 8.19955i | − | 0.320873i | −0.987046 | − | 0.160437i | \(-0.948710\pi\) | ||
0.987046 | − | 0.160437i | \(-0.0512902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.57321 | + | 2.72489i | −0.0614706 | + | 0.106470i | ||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | −17.1515 | + | 20.0614i | −0.669145 | + | 0.782672i | ||||
\(658\) | − | 6.00680i | − | 0.234169i | ||||||
\(659\) | 12.0000 | − | 20.7846i | 0.467454 | − | 0.809653i | −0.531855 | − | 0.846836i | \(-0.678505\pi\) |
0.999309 | + | 0.0371821i | \(0.0118382\pi\) | |||||||
\(660\) | −4.44949 | + | 6.29253i | −0.173196 | + | 0.244936i | ||||
\(661\) | 25.7196 | + | 14.8492i | 1.00038 | + | 0.577569i | 0.908360 | − | 0.418189i | \(-0.137335\pi\) |
0.0920180 | + | 0.995757i | \(0.470668\pi\) | |||||||
\(662\) | 20.1742 | − | 11.6476i | 0.784094 | − | 0.452697i | ||||
\(663\) | −2.20204 | + | 3.11416i | −0.0855202 | + | 0.120944i | ||||
\(664\) | 17.0027i | 0.659832i | ||||||||
\(665\) | −2.69694 | − | 0.635674i | −0.104583 | − | 0.0246504i | ||||
\(666\) | 17.5732 | + | 15.0242i | 0.680948 | + | 0.582177i | ||||
\(667\) | −15.0000 | + | 8.66025i | −0.580802 | + | 0.335326i | ||||
\(668\) | 2.44949 | + | 4.24264i | 0.0947736 | + | 0.164153i | ||||
\(669\) | −2.87628 | + | 31.2162i | −0.111203 | + | 1.20689i | ||||
\(670\) | −1.77526 | − | 3.07483i | −0.0685841 | − | 0.118791i | ||||
\(671\) | 4.22474 | + | 2.43916i | 0.163094 | + | 0.0941626i | ||||
\(672\) | −0.325765 | − | 0.707107i | −0.0125667 | − | 0.0272772i | ||||
\(673\) | 3.46410i | 0.133531i | 0.997769 | + | 0.0667657i | \(0.0212680\pi\) | ||||
−0.997769 | + | 0.0667657i | \(0.978732\pi\) | |||||||
\(674\) | 17.8485 | + | 10.3048i | 0.687497 | + | 0.396927i | ||||
\(675\) | 11.1742 | − | 10.8691i | 0.430096 | − | 0.418350i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 32.6969 | 1.25665 | 0.628323 | − | 0.777953i | \(-0.283742\pi\) | ||||
0.628323 | + | 0.777953i | \(0.283742\pi\) | |||||||
\(678\) | −32.4217 | − | 2.98735i | −1.24515 | − | 0.114728i | ||||
\(679\) | −1.28036 | + | 0.739215i | −0.0491356 | + | 0.0283685i | ||||
\(680\) | 0.449490 | − | 0.778539i | 0.0172371 | − | 0.0298556i | ||||
\(681\) | −0.550510 | + | 0.778539i | −0.0210956 | + | 0.0298337i | ||||
\(682\) | 6.67423 | + | 11.5601i | 0.255570 | + | 0.442660i | ||||
\(683\) | −17.3939 | −0.665558 | −0.332779 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332779 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(684\) | 7.72474 | + | 10.5512i | 0.295363 | + | 0.403436i | ||||
\(685\) | −5.55051 | −0.212074 | ||||||||
\(686\) | −3.10102 | − | 5.37113i | −0.118398 | − | 0.205071i | ||||
\(687\) | 0.898979 | − | 1.27135i | 0.0342982 | − | 0.0485050i | ||||
\(688\) | 4.44949 | − | 7.70674i | 0.169635 | − | 0.293817i | ||||
\(689\) | −32.6969 | + | 18.8776i | −1.24565 | + | 0.719179i | ||||
\(690\) | −17.2474 | − | 1.58919i | −0.656599 | − | 0.0604993i | ||||
\(691\) | −40.0000 | −1.52167 | −0.760836 | − | 0.648944i | \(-0.775211\pi\) | ||||
−0.760836 | + | 0.648944i | \(0.775211\pi\) | |||||||
\(692\) | 1.10102 | 0.0418545 | ||||||||
\(693\) | −4.00000 | + | 1.41421i | −0.151947 | + | 0.0537215i | ||||
\(694\) | 3.27526 | + | 1.89097i | 0.124327 | + | 0.0717802i | ||||
\(695\) | − | 20.2918i | − | 0.769712i | ||||||
\(696\) | 1.77526 | + | 3.85337i | 0.0672909 | + | 0.146062i | ||||
\(697\) | 1.65153 | + | 0.953512i | 0.0625562 | + | 0.0361168i | ||||
\(698\) | −16.2474 | − | 28.1414i | −0.614975 | − | 1.06517i | ||||
\(699\) | 2.82577 | − | 30.6681i | 0.106880 | − | 1.15997i | ||||
\(700\) | 0.674235 | + | 1.16781i | 0.0254837 | + | 0.0441390i | ||||
\(701\) | 8.57321 | − | 4.94975i | 0.323806 | − | 0.186949i | −0.329282 | − | 0.944232i | \(-0.606807\pi\) |
0.653088 | + | 0.757282i | \(0.273473\pi\) | |||||||
\(702\) | 4.89898 | − | 17.3205i | 0.184900 | − | 0.653720i | ||||
\(703\) | 23.0227 | − | 24.4630i | 0.868318 | − | 0.922640i | ||||
\(704\) | 3.14626i | 0.118579i | ||||||||
\(705\) | −18.8990 | + | 26.7272i | −0.711777 | + | 1.00660i | ||||
\(706\) | −21.6464 | + | 12.4976i | −0.814674 | + | 0.470352i | ||||
\(707\) | 3.85357 | + | 2.22486i | 0.144928 | + | 0.0836745i | ||||
\(708\) | 11.4495 | − | 16.1920i | 0.430298 | − | 0.608534i | ||||
\(709\) | 8.67423 | − | 15.0242i | 0.325768 | − | 0.564246i | −0.655900 | − | 0.754848i | \(-0.727711\pi\) |
0.981667 | + | 0.190602i | \(0.0610439\pi\) | |||||||
\(710\) | 8.48528i | 0.318447i | ||||||||
\(711\) | 19.3485 | + | 16.5420i | 0.725624 | + | 0.620372i | ||||
\(712\) | −3.55051 | + | 6.14966i | −0.133061 | + | 0.230468i | ||||
\(713\) | −15.0000 | + | 25.9808i | −0.561754 | + | 0.972987i | ||||
\(714\) | 0.449490 | − | 0.207081i | 0.0168217 | − | 0.00774980i | ||||
\(715\) | − | 15.4135i | − | 0.576432i | ||||||
\(716\) | −3.82577 | + | 6.62642i | −0.142976 | + | 0.247641i | ||||
\(717\) | 29.7980 | + | 21.0703i | 1.11283 | + | 0.786886i | ||||
\(718\) | 20.8207 | + | 12.0208i | 0.777020 | + | 0.448613i | ||||
\(719\) | −26.1464 | + | 15.0956i | −0.975097 | + | 0.562973i | −0.900786 | − | 0.434262i | \(-0.857009\pi\) |
−0.0743109 | + | 0.997235i | \(0.523676\pi\) | |||||||
\(720\) | −0.775255 | + | 4.17121i | −0.0288921 | + | 0.155452i | ||||
\(721\) | 2.25697i | 0.0840539i | ||||||||
\(722\) | 15.8485 | − | 10.4798i | 0.589819 | − | 0.390017i | ||||
\(723\) | −10.6237 | + | 4.89437i | −0.395101 | + | 0.182024i | ||||
\(724\) | −18.6742 | + | 10.7816i | −0.694022 | + | 0.400694i | ||||
\(725\) | −3.67423 | − | 6.36396i | −0.136458 | − | 0.236352i | ||||
\(726\) | −1.89898 | − | 0.174973i | −0.0704777 | − | 0.00649384i | ||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 1.34847 | + | 0.778539i | 0.0499776 | + | 0.0288546i | ||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 12.4422i | 0.460506i | ||||||||
\(731\) | 4.89898 | + | 2.82843i | 0.181195 | + | 0.104613i | ||||
\(732\) | 2.67423 | + | 0.246405i | 0.0988426 | + | 0.00910739i | ||||
\(733\) | −20.0454 | −0.740394 | −0.370197 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370197 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(734\) | −8.65153 | −0.319334 | ||||||||
\(735\) | −1.52781 | + | 16.5813i | −0.0563540 | + | 0.611610i | ||||
\(736\) | −6.12372 | + | 3.53553i | −0.225723 | + | 0.130322i | ||||
\(737\) | −3.94949 | + | 6.84072i | −0.145481 | + | 0.251981i | ||||
\(738\) | −8.84847 | − | 1.64456i | −0.325717 | − | 0.0605373i | ||||
\(739\) | −12.1742 | − | 21.0864i | −0.447836 | − | 0.775676i | 0.550408 | − | 0.834895i | \(-0.314472\pi\) |
−0.998245 | + | 0.0592200i | \(0.981139\pi\) | |||||||
\(740\) | 10.8990 | 0.400654 | ||||||||
\(741\) | −24.7980 | − | 8.31031i | −0.910976 | − | 0.305287i | ||||
\(742\) | 4.89898 | 0.179847 | ||||||||
\(743\) | 2.32577 | + | 4.02834i | 0.0853241 | + | 0.147786i | 0.905529 | − | 0.424284i | \(-0.139474\pi\) |
−0.820205 | + | 0.572069i | \(0.806141\pi\) | |||||||
\(744\) | 6.00000 | + | 4.24264i | 0.219971 | + | 0.155543i | ||||
\(745\) | −1.44949 | + | 2.51059i | −0.0531052 | + | 0.0919809i | ||||
\(746\) | −22.0454 | + | 12.7279i | −0.807140 | + | 0.466002i | ||||
\(747\) | 48.0908 | − | 17.0027i | 1.75955 | − | 0.622095i | ||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | −2.20204 | −0.0804608 | ||||||||
\(750\) | 1.79796 | − | 19.5133i | 0.0656522 | − | 0.712524i | ||||
\(751\) | 17.6969 | + | 10.2173i | 0.645770 | + | 0.372836i | 0.786834 | − | 0.617165i | \(-0.211719\pi\) |
−0.141063 | + | 0.990001i | \(0.545052\pi\) | |||||||
\(752\) | 13.3636i | 0.487320i | ||||||||
\(753\) | 5.94949 | − | 2.74094i | 0.216811 | − | 0.0998854i | ||||
\(754\) | −7.34847 | − | 4.24264i | −0.267615 | − | 0.154508i | ||||
\(755\) | −6.79796 | − | 11.7744i | −0.247403 | − | 0.428515i | ||||
\(756\) | −1.67423 | + | 1.62851i | −0.0608913 | + | 0.0592284i | ||||
\(757\) | 19.6969 | + | 34.1161i | 0.715897 | + | 1.23997i | 0.962612 | + | 0.270883i | \(0.0873155\pi\) |
−0.246715 | + | 0.969088i | \(0.579351\pi\) | |||||||
\(758\) | 1.34847 | − | 0.778539i | 0.0489786 | − | 0.0282778i | ||||
\(759\) | 16.1237 | + | 34.9982i | 0.585254 | + | 1.27035i | ||||
\(760\) | 6.00000 | + | 1.41421i | 0.217643 | + | 0.0512989i | ||||
\(761\) | − | 31.5734i | − | 1.14453i | −0.820067 | − | 0.572267i | \(-0.806064\pi\) | ||
0.820067 | − | 0.572267i | \(-0.193936\pi\) | |||||||
\(762\) | 14.6969 | + | 10.3923i | 0.532414 | + | 0.376473i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.10102 | + | 4.09978i | 0.256906 | + | 0.148325i | ||||
\(765\) | −2.65153 | − | 0.492810i | −0.0958663 | − | 0.0178176i | ||||
\(766\) | −10.2247 | + | 17.7098i | −0.369435 | + | 0.639880i | ||||
\(767\) | 39.6622i | 1.43212i | ||||||||
\(768\) | 0.724745 | + | 1.57313i | 0.0261520 | + | 0.0567655i | ||||
\(769\) | −1.79796 | + | 3.11416i | −0.0648361 | + | 0.112299i | −0.896621 | − | 0.442798i | \(-0.853986\pi\) |
0.831785 | + | 0.555098i | \(0.187319\pi\) | |||||||
\(770\) | −1.00000 | + | 1.73205i | −0.0360375 | + | 0.0624188i | ||||
\(771\) | −10.8712 | − | 23.5970i | −0.391516 | − | 0.849825i | ||||
\(772\) | − | 25.8058i | − | 0.928771i | ||||||
\(773\) | 1.22474 | − | 2.12132i | 0.0440510 | − | 0.0762986i | −0.843159 | − | 0.537664i | \(-0.819307\pi\) |
0.887210 | + | 0.461365i | \(0.152640\pi\) | |||||||
\(774\) | −26.2474 | − | 4.87832i | −0.943445 | − | 0.175347i | ||||
\(775\) | −11.0227 | − | 6.36396i | −0.395947 | − | 0.228600i | ||||
\(776\) | 2.84847 | − | 1.64456i | 0.102254 | − | 0.0590364i | ||||
\(777\) | 4.89898 | + | 3.46410i | 0.175750 | + | 0.124274i | ||||
\(778\) | − | 15.1278i | − | 0.542356i | ||||||
\(779\) | −3.00000 | + | 12.7279i | −0.107486 | + | 0.456025i | ||||
\(780\) | −3.55051 | − | 7.70674i | −0.127129 | − | 0.275946i | ||||
\(781\) | 16.3485 | − | 9.43879i | 0.584994 | − | 0.337747i | ||||
\(782\) | −2.24745 | − | 3.89270i | −0.0803686 | − | 0.139203i | ||||
\(783\) | 9.12372 | − | 8.87455i | 0.326055 | − | 0.317151i | ||||
\(784\) | 3.39898 | + | 5.88721i | 0.121392 | + | 0.210257i | ||||
\(785\) | −13.1010 | − | 7.56388i | −0.467595 | − | 0.269966i | ||||
\(786\) | 3.50000 | − | 1.61246i | 0.124841 | − | 0.0575144i | ||||
\(787\) | 7.53177i | 0.268479i | 0.990949 | + | 0.134239i | \(0.0428591\pi\) | ||||
−0.990949 | + | 0.134239i | \(0.957141\pi\) | |||||||
\(788\) | −17.5732 | − | 10.1459i | −0.626020 | − | 0.361433i | ||||
\(789\) | −1.42679 | + | 15.4849i | −0.0507949 | + | 0.551278i | ||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | −8.44949 | −0.300429 | ||||||||
\(792\) | 8.89898 | − | 3.14626i | 0.316211 | − | 0.111798i | ||||
\(793\) | −4.65153 | + | 2.68556i | −0.165181 | + | 0.0953671i | ||||
\(794\) | 2.67423 | − | 4.63191i | 0.0949050 | − | 0.164380i | ||||
\(795\) | −21.7980 | − | 15.4135i | −0.773094 | − | 0.546660i | ||||
\(796\) | 1.44949 | + | 2.51059i | 0.0513758 | + | 0.0889855i | ||||
\(797\) | −37.3485 | −1.32295 | −0.661475 | − | 0.749967i | \(-0.730069\pi\) | ||||
−0.661475 | + | 0.749967i | \(0.730069\pi\) | |||||||
\(798\) | 2.24745 | + | 2.54270i | 0.0795588 | + | 0.0900105i | ||||
\(799\) | −8.49490 | −0.300528 | ||||||||
\(800\) | −1.50000 | − | 2.59808i | −0.0530330 | − | 0.0918559i | ||||
\(801\) | 20.9444 | + | 3.89270i | 0.740034 | + | 0.137542i | ||||
\(802\) | 3.39898 | − | 5.88721i | 0.120022 | − | 0.207884i | ||||
\(803\) | 23.9722 | − | 13.8404i | 0.845960 | − | 0.488415i | ||||
\(804\) | −0.398979 | + | 4.33013i | −0.0140709 | + | 0.152712i | ||||
\(805\) | −4.49490 | −0.158424 | ||||||||
\(806\) | −14.6969 | −0.517678 | ||||||||
\(807\) | −42.2474 | − | 3.89270i | −1.48718 | − | 0.137029i | ||||
\(808\) | −8.57321 | − | 4.94975i | −0.301605 | − | 0.174132i | ||||
\(809\) | − | 8.02458i | − | 0.282129i | −0.990000 | − | 0.141065i | \(-0.954947\pi\) | ||
0.990000 | − | 0.141065i | \(-0.0450525\pi\) | |||||||
\(810\) | 12.5732 | − | 1.97846i | 0.441778 | − | 0.0695158i | ||||
\(811\) | 3.00000 | + | 1.73205i | 0.105344 | + | 0.0608205i | 0.551746 | − | 0.834012i | \(-0.313962\pi\) |
−0.446402 | + | 0.894832i | \(0.647295\pi\) | |||||||
\(812\) | 0.550510 | + | 0.953512i | 0.0193191 | + | 0.0334617i | ||||
\(813\) | 34.5732 | + | 3.18559i | 1.21254 | + | 0.111723i | ||||
\(814\) | −12.1237 | − | 20.9989i | −0.424936 | − | 0.736011i | ||||
\(815\) | 22.4722 | − | 12.9743i | 0.787167 | − | 0.454471i | ||||
\(816\) | −1.00000 | + | 0.460702i | −0.0350070 | + | 0.0161278i | ||||
\(817\) | −8.89898 | + | 37.7552i | −0.311336 | + | 1.32089i | ||||
\(818\) | − | 3.63907i | − | 0.127237i | ||||||
\(819\) | 0.853572 | − | 4.59259i | 0.0298262 | − | 0.160478i | ||||
\(820\) | −3.67423 | + | 2.12132i | −0.128310 | + | 0.0740797i | ||||
\(821\) | 5.44949 | + | 3.14626i | 0.190189 | + | 0.109805i | 0.592071 | − | 0.805886i | \(-0.298311\pi\) |
−0.401882 | + | 0.915691i | \(0.631644\pi\) | |||||||
\(822\) | 5.55051 | + | 3.92480i | 0.193596 | + | 0.136893i | ||||
\(823\) | 24.3485 | − | 42.1728i | 0.848734 | − | 1.47005i | −0.0336040 | − | 0.999435i | \(-0.510699\pi\) |
0.882338 | − | 0.470616i | \(-0.155968\pi\) | |||||||
\(824\) | − | 5.02118i | − | 0.174921i | ||||||
\(825\) | −14.8485 | + | 6.84072i | −0.516957 | + | 0.238163i | ||||
\(826\) | 2.57321 | − | 4.45694i | 0.0895336 | − | 0.155077i | ||||
\(827\) | 10.6237 | − | 18.4008i | 0.369423 | − | 0.639860i | −0.620052 | − | 0.784560i | \(-0.712889\pi\) |
0.989475 | + | 0.144701i | \(0.0462220\pi\) | |||||||
\(828\) | 16.1237 | + | 13.7850i | 0.560338 | + | 0.479061i | ||||
\(829\) | 19.2275i | 0.667800i | 0.942609 | + | 0.333900i | \(0.108365\pi\) | ||||
−0.942609 | + | 0.333900i | \(0.891635\pi\) | |||||||
\(830\) | 12.0227 | − | 20.8239i | 0.417314 | − | 0.722809i | ||||
\(831\) | 20.2474 | − | 28.6342i | 0.702376 | − | 0.993310i | ||||
\(832\) | −3.00000 | − | 1.73205i | −0.104006 | − | 0.0600481i | ||||
\(833\) | −3.74235 | + | 2.16064i | −0.129665 | + | 0.0748619i | ||||
\(834\) | −14.3485 | + | 20.2918i | −0.496847 | + | 0.702648i | ||||
\(835\) | − | 6.92820i | − | 0.239760i | ||||||
\(836\) | −3.94949 | − | 13.1332i | −0.136596 | − | 0.454223i | ||||
\(837\) | 6.00000 | − | 21.2132i | 0.207390 | − | 0.733236i | ||||
\(838\) | 21.2474 | − | 12.2672i | 0.733981 | − | 0.423764i | ||||
\(839\) | −6.67423 | − | 11.5601i | −0.230420 | − | 0.399099i | 0.727512 | − | 0.686095i | \(-0.240677\pi\) |
−0.957932 | + | 0.286996i | \(0.907343\pi\) | |||||||
\(840\) | −0.101021 | + | 1.09638i | −0.00348554 | + | 0.0378286i | ||||
\(841\) | 11.5000 | + | 19.9186i | 0.396552 | + | 0.686848i | ||||
\(842\) | 3.97730 | + | 2.29629i | 0.137067 | + | 0.0791355i | ||||
\(843\) | 16.3763 | + | 35.5464i | 0.564029 | + | 1.22428i | ||||
\(844\) | − | 1.55708i | − | 0.0535968i | ||||||
\(845\) | −1.22474 | − | 0.707107i | −0.0421325 | − | 0.0243252i | ||||
\(846\) | 37.7980 | − | 13.3636i | 1.29952 | − | 0.459450i | ||||
\(847\) | −0.494897 | −0.0170049 | ||||||||
\(848\) | −10.8990 | −0.374272 | ||||||||
\(849\) | 16.2980 | + | 1.50170i | 0.559345 | + | 0.0515382i | ||||
\(850\) | 1.65153 | − | 0.953512i | 0.0566470 | − | 0.0327052i | ||||
\(851\) | 27.2474 | − | 47.1940i | 0.934031 | − | 1.61779i | ||||
\(852\) | 6.00000 | − | 8.48528i | 0.205557 | − | 0.290701i | ||||
\(853\) | 5.00000 | + | 8.66025i | 0.171197 | + | 0.296521i | 0.938839 | − | 0.344358i | \(-0.111903\pi\) |
−0.767642 | + | 0.640879i | \(0.778570\pi\) | |||||||
\(854\) | 0.696938 | 0.0238487 | ||||||||
\(855\) | −2.00000 | − | 18.3848i | −0.0683986 | − | 0.628746i | ||||
\(856\) | 4.89898 | 0.167444 | ||||||||
\(857\) | −8.29796 | − | 14.3725i | −0.283453 | − | 0.490955i | 0.688780 | − | 0.724970i | \(-0.258147\pi\) |
−0.972233 | + | 0.234016i | \(0.924813\pi\) | |||||||
\(858\) | −10.8990 | + | 15.4135i | −0.372085 | + | 0.526208i | ||||
\(859\) | −9.42168 | + | 16.3188i | −0.321464 | + | 0.556791i | −0.980790 | − | 0.195065i | \(-0.937508\pi\) |
0.659327 | + | 0.751857i | \(0.270841\pi\) | |||||||
\(860\) | −10.8990 | + | 6.29253i | −0.371652 | + | 0.214573i | ||||
\(861\) | −2.32577 | − | 0.214297i | −0.0792619 | − | 0.00730322i | ||||
\(862\) | 3.30306 | 0.112503 | ||||||||
\(863\) | −16.6515 | −0.566825 | −0.283412 | − | 0.958998i | \(-0.591467\pi\) | ||||
−0.283412 | + | 0.958998i | \(0.591467\pi\) | |||||||
\(864\) | 3.72474 | − | 3.62302i | 0.126718 | − | 0.123258i | ||||
\(865\) | −1.34847 | − | 0.778539i | −0.0458493 | − | 0.0264711i | ||||
\(866\) | 20.4347i | 0.694398i | ||||||||
\(867\) | 12.0278 | + | 26.1076i | 0.408486 | + | 0.886660i | ||||
\(868\) | 1.65153 | + | 0.953512i | 0.0560566 | + | 0.0323643i | ||||
\(869\) | −13.3485 | − | 23.1202i | −0.452816 | − | 0.784300i | ||||
\(870\) | 0.550510 | − | 5.97469i | 0.0186640 | − | 0.202561i | ||||
\(871\) | −4.34847 | − | 7.53177i | −0.147342 | − | 0.255204i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.50000 | − | 6.41212i | −0.253837 | − | 0.217017i | ||||
\(874\) | 21.1237 | − | 22.4452i | 0.714521 | − | 0.759221i | ||||
\(875\) | − | 5.08540i | − | 0.171918i | ||||||
\(876\) | 8.79796 | − | 12.4422i | 0.297255 | − | 0.420383i | ||||
\(877\) | −36.3712 | + | 20.9989i | −1.22817 | + | 0.709083i | −0.966646 | − | 0.256115i | \(-0.917557\pi\) |
−0.261521 | + | 0.965198i | \(0.584224\pi\) | |||||||
\(878\) | 9.67423 | + | 5.58542i | 0.326490 | + | 0.188499i | ||||
\(879\) | 19.3485 | − | 27.3629i | 0.652608 | − | 0.922927i | ||||
\(880\) | 2.22474 | − | 3.85337i | 0.0749961 | − | 0.129897i | ||||
\(881\) | − | 10.2815i | − | 0.346394i | −0.984887 | − | 0.173197i | \(-0.944590\pi\) | ||
0.984887 | − | 0.173197i | \(-0.0554098\pi\) | |||||||
\(882\) | 13.2526 | − | 15.5010i | 0.446237 | − | 0.521945i | ||||
\(883\) | 10.4217 | − | 18.0509i | 0.350718 | − | 0.607461i | −0.635658 | − | 0.771971i | \(-0.719271\pi\) |
0.986375 | + | 0.164510i | \(0.0526044\pi\) | |||||||
\(884\) | 1.10102 | − | 1.90702i | 0.0370313 | − | 0.0641401i | ||||
\(885\) | −25.4722 | + | 11.7351i | −0.856238 | + | 0.394471i | ||||
\(886\) | − | 18.8455i | − | 0.633126i | ||||||
\(887\) | −28.0454 | + | 48.5761i | −0.941673 | + | 1.63102i | −0.179393 | + | 0.983778i | \(0.557413\pi\) |
−0.762280 | + | 0.647247i | \(0.775920\pi\) | |||||||
\(888\) | −10.8990 | − | 7.70674i | −0.365746 | − | 0.258621i | ||||
\(889\) | 4.04541 | + | 2.33562i | 0.135679 | + | 0.0783341i | ||||
\(890\) | 8.69694 | − | 5.02118i | 0.291522 | − | 0.168310i | ||||
\(891\) | −17.7980 | − | 22.0239i | −0.596254 | − | 0.737827i | ||||
\(892\) | − | 18.0990i | − | 0.606001i | ||||||
\(893\) | −16.7753 | − | 55.7828i | −0.561363 | − | 1.86670i | ||||
\(894\) | 3.22474 | − | 1.48565i | 0.107852 | − | 0.0496874i | ||||
\(895\) | 9.37117 | − | 5.41045i | 0.313244 | − | 0.180851i | ||||
\(896\) | 0.224745 | + | 0.389270i | 0.00750820 | + | 0.0130046i | ||||
\(897\) | −42.2474 | − | 3.89270i | −1.41060 | − | 0.129973i | ||||
\(898\) | 15.3990 | + | 26.6718i | 0.513871 | + | 0.890050i | ||||
\(899\) | −9.00000 | − | 5.19615i | −0.300167 | − | 0.173301i | ||||
\(900\) | −5.84847 | + | 6.84072i | −0.194949 | + | 0.228024i | ||||
\(901\) | − | 6.92820i | − | 0.230812i | ||||||
\(902\) | 8.17423 | + | 4.71940i | 0.272172 | + | 0.157139i | ||||
\(903\) | −6.89898 | − | 0.635674i | −0.229584 | − | 0.0211539i | ||||
\(904\) | 18.7980 | 0.625211 | ||||||||
\(905\) | 30.4949 | 1.01368 | ||||||||
\(906\) | −1.52781 | + | 16.5813i | −0.0507580 | + | 0.550877i | ||||
\(907\) | −32.9166 | + | 19.0044i | −1.09298 | + | 0.631031i | −0.934368 | − | 0.356311i | \(-0.884034\pi\) |
−0.158610 | + | 0.987341i | \(0.550701\pi\) | |||||||
\(908\) | 0.275255 | − | 0.476756i | 0.00913466 | − | 0.0158217i | ||||
\(909\) | −5.42679 | + | 29.1985i | −0.179995 | + | 0.968452i | ||||
\(910\) | −1.10102 | − | 1.90702i | −0.0364985 | − | 0.0632172i | ||||
\(911\) | 28.6515 | 0.949268 | 0.474634 | − | 0.880183i | \(-0.342581\pi\) | ||||
0.474634 | + | 0.880183i | \(0.342581\pi\) | |||||||
\(912\) | −5.00000 | − | 5.65685i | −0.165567 | − | 0.187317i | ||||
\(913\) | −53.4949 | −1.77042 | ||||||||
\(914\) | 6.50000 | + | 11.2583i | 0.215001 | + | 0.372392i | ||||
\(915\) | −3.10102 | − | 2.19275i | −0.102517 | − | 0.0724902i | ||||
\(916\) | −0.449490 | + | 0.778539i | −0.0148516 | + | 0.0257237i | ||||
\(917\) | 0.866070 | − | 0.500026i | 0.0286002 | − | 0.0165123i | ||||
\(918\) | 2.30306 | + | 2.36773i | 0.0760124 | + | 0.0781466i | ||||
\(919\) | −36.6969 | −1.21052 | −0.605260 | − | 0.796028i | \(-0.706931\pi\) | ||||
−0.605260 | + | 0.796028i | \(0.706931\pi\) | |||||||
\(920\) | 10.0000 | 0.329690 | ||||||||
\(921\) | 3.39898 | − | 36.8891i | 0.112000 | − | 1.21554i | ||||
\(922\) | −33.2474 | − | 19.1954i | −1.09495 | − | 0.632168i | ||||
\(923\) | 20.7846i | 0.684134i | ||||||||
\(924\) | 2.22474 | − | 1.02494i | 0.0731887 | − | 0.0337182i | ||||
\(925\) | 20.0227 | + | 11.5601i | 0.658342 | + | 0.380094i | ||||
\(926\) | 9.89898 | + | 17.1455i | 0.325301 | + | 0.563437i | ||||
\(927\) | −14.2020 | + | 5.02118i | −0.466456 | + | 0.164917i | ||||
\(928\) | −1.22474 | − | 2.12132i | −0.0402042 | − | 0.0696358i | ||||
\(929\) | 24.0959 | − | 13.9118i | 0.790561 | − | 0.456431i | −0.0495987 | − | 0.998769i | \(-0.515794\pi\) |
0.840160 | + | 0.542338i | \(0.182461\pi\) | |||||||
\(930\) | −4.34847 | − | 9.43879i | −0.142592 | − | 0.309510i | ||||
\(931\) | −21.5783 | − | 20.3079i | −0.707201 | − | 0.665563i | ||||
\(932\) | 17.7812i | 0.582443i | ||||||||
\(933\) | −22.0000 | − | 15.5563i | −0.720248 | − | 0.509292i | ||||
\(934\) | −10.9268 | + | 6.30858i | −0.357535 | + | 0.206423i | ||||
\(935\) | 2.44949 | + | 1.41421i | 0.0801069 | + | 0.0462497i | ||||
\(936\) | −1.89898 | + | 10.2173i | −0.0620701 | + | 0.333964i | ||||
\(937\) | −11.5000 | + | 19.9186i | −0.375689 | + | 0.650712i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) |
0.614741 | + | 0.788729i | \(0.289260\pi\) | |||||||
\(938\) | 1.12848i | 0.0368463i | ||||||||
\(939\) | −13.7702 | − | 29.8895i | −0.449372 | − | 0.975407i | ||||
\(940\) | 9.44949 | − | 16.3670i | 0.308208 | − | 0.533833i | ||||
\(941\) | −21.4949 | + | 37.2303i | −0.700714 | + | 1.21367i | 0.267503 | + | 0.963557i | \(0.413802\pi\) |
−0.968216 | + | 0.250114i | \(0.919532\pi\) | |||||||
\(942\) | 7.75255 | + | 16.8277i | 0.252592 | + | 0.548276i | ||||
\(943\) | 21.2132i | 0.690797i | ||||||||
\(944\) | −5.72474 | + | 9.91555i | −0.186325 | + | 0.322724i | ||||
\(945\) | 3.20204 | − | 0.810647i | 0.104162 | − | 0.0263704i | ||||
\(946\) | 24.2474 | + | 13.9993i | 0.788353 | + | 0.455156i | ||||
\(947\) | 6.55051 | − | 3.78194i | 0.212863 | − | 0.122896i | −0.389778 | − | 0.920909i | \(-0.627448\pi\) |
0.602641 | + | 0.798012i | \(0.294115\pi\) | |||||||
\(948\) | −12.0000 | − | 8.48528i | −0.389742 | − | 0.275589i | ||||
\(949\) | 30.4770i | 0.989326i | ||||||||
\(950\) | 9.52270 | + | 8.96204i | 0.308957 | + | 0.290767i | ||||
\(951\) | −4.34847 | − | 9.43879i | −0.141009 | − | 0.306074i | ||||
\(952\) | −0.247449 | + | 0.142865i | −0.00801986 | + | 0.00463027i | ||||
\(953\) | 12.3990 | + | 21.4757i | 0.401642 | + | 0.695665i | 0.993924 | − | 0.110066i | \(-0.0351062\pi\) |
−0.592282 | + | 0.805731i | \(0.701773\pi\) | |||||||
\(954\) | 10.8990 | + | 30.8270i | 0.352867 | + | 0.998060i | ||||
\(955\) | −5.79796 | − | 10.0424i | −0.187618 | − | 0.324963i | ||||
\(956\) | −18.2474 | − | 10.5352i | −0.590165 | − | 0.340732i | ||||
\(957\) | −12.1237 | + | 5.58542i | −0.391904 | + | 0.180551i | ||||
\(958\) | 0.985620i | 0.0318439i | ||||||||
\(959\) | 1.52781 | + | 0.882079i | 0.0493354 | + | 0.0284838i | ||||
\(960\) | 0.224745 | − | 2.43916i | 0.00725361 | − | 0.0787235i | ||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | 26.6969 | 0.860744 | ||||||||
\(963\) | −4.89898 | − | 13.8564i | −0.157867 | − | 0.446516i | ||||
\(964\) | 5.84847 | − | 3.37662i | 0.188367 | − | 0.108753i | ||||
\(965\) | −18.2474 | + | 31.6055i | −0.587406 | + | 1.01742i | ||||
\(966\) | 4.49490 | + | 3.17837i | 0.144621 | + | 0.102262i | ||||
\(967\) | 25.6969 | + | 44.5084i | 0.826358 | + | 1.43129i | 0.900877 | + | 0.434074i | \(0.142924\pi\) |
−0.0745193 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(968\) | 1.10102 | 0.0353881 | ||||||||
\(969\) | 3.59592 | − | 3.17837i | 0.115518 | − | 0.102104i | ||||
\(970\) | −4.65153 | −0.149352 | ||||||||
\(971\) | 4.07321 | + | 7.05501i | 0.130716 | + | 0.226406i | 0.923953 | − | 0.382507i | \(-0.124939\pi\) |
−0.793237 | + | 0.608913i | \(0.791606\pi\) | |||||||
\(972\) | −13.9722 | − | 6.91215i | −0.448158 | − | 0.221707i | ||||
\(973\) | −3.22474 | + | 5.58542i | −0.103381 | + | 0.179060i | ||||
\(974\) | 21.6742 | − | 12.5136i | 0.694487 | − | 0.400962i | ||||
\(975\) | 1.65153 | − | 17.9241i | 0.0528913 | − | 0.574030i | ||||
\(976\) | −1.55051 | −0.0496306 | ||||||||
\(977\) | −40.1010 | −1.28295 | −0.641473 | − | 0.767146i | \(-0.721676\pi\) | ||||
−0.641473 | + | 0.767146i | \(0.721676\pi\) | |||||||
\(978\) | −31.6464 | − | 2.91591i | −1.01194 | − | 0.0932406i | ||||
\(979\) | −19.3485 | − | 11.1708i | −0.618380 | − | 0.357022i | ||||
\(980\) | − | 9.61377i | − | 0.307100i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.8990 | − | 8.02458i | −0.443534 | − | 0.256075i | ||||
\(983\) | 28.8990 | + | 50.0545i | 0.921734 | + | 1.59649i | 0.796731 | + | 0.604334i | \(0.206561\pi\) |
0.125003 | + | 0.992156i | \(0.460106\pi\) | |||||||
\(984\) | 5.17423 | + | 0.476756i | 0.164949 | + | 0.0151984i | ||||
\(985\) | 14.3485 | + | 24.8523i | 0.457180 | + | 0.791859i | ||||
\(986\) | 1.34847 | − | 0.778539i | 0.0429440 | − | 0.0247937i | ||||
\(987\) | 9.44949 | − | 4.35340i | 0.300781 | − | 0.138570i | ||||
\(988\) | 14.6969 | + | 3.46410i | 0.467572 | + | 0.110208i | ||||
\(989\) | 62.9253i | 2.00091i | ||||||||
\(990\) | −13.1237 | − | 2.43916i | −0.417099 | − | 0.0775215i | ||||
\(991\) | 15.3031 | − | 8.83523i | 0.486118 | − | 0.280660i | −0.236845 | − | 0.971548i | \(-0.576113\pi\) |
0.722962 | + | 0.690887i | \(0.242780\pi\) | |||||||
\(992\) | −3.67423 | − | 2.12132i | −0.116657 | − | 0.0673520i | ||||
\(993\) | 32.9444 | + | 23.2952i | 1.04546 | + | 0.739251i | ||||
\(994\) | 1.34847 | − | 2.33562i | 0.0427708 | − | 0.0740813i | ||||
\(995\) | − | 4.09978i | − | 0.129972i | ||||||
\(996\) | −26.7474 | + | 12.3226i | −0.847525 | + | 0.390456i | ||||
\(997\) | 21.7196 | − | 37.6195i | 0.687868 | − | 1.19142i | −0.284658 | − | 0.958629i | \(-0.591880\pi\) |
0.972526 | − | 0.232793i | \(-0.0747865\pi\) | |||||||
\(998\) | −3.72474 | + | 6.45145i | −0.117905 | + | 0.204217i | ||||
\(999\) | −10.8990 | + | 38.5337i | −0.344828 | + | 1.21915i |
(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 | 114.2.h.e.107.1 | yes | 4 | |
3.2 | odd | 2 | 114.2.h.f.107.2 | yes | 4 | ||
4.3 | odd | 2 | 912.2.bn.g.449.2 | 4 | |||
12.11 | even | 2 | 912.2.bn.h.449.1 | 4 | |||
19.8 | odd | 6 | 114.2.h.f.65.2 | yes | 4 | ||
57.8 | even | 6 | inner | 114.2.h.e.65.2 | ✓ | 4 | |
76.27 | even | 6 | 912.2.bn.h.65.1 | 4 | |||
228.179 | odd | 6 | 912.2.bn.g.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.e.65.2 | ✓ | 4 | 57.8 | even | 6 | inner | |
114.2.h.e.107.1 | yes | 4 | 1.1 | even | 1 | trivial | |
114.2.h.f.65.2 | yes | 4 | 19.8 | odd | 6 | ||
114.2.h.f.107.2 | yes | 4 | 3.2 | odd | 2 | ||
912.2.bn.g.65.1 | 4 | 228.179 | odd | 6 | |||
912.2.bn.g.449.2 | 4 | 4.3 | odd | 2 | |||
912.2.bn.h.65.1 | 4 | 76.27 | even | 6 | |||
912.2.bn.h.449.1 | 4 | 12.11 | even | 2 |