Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 418.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.418 |
Dual form | 525.2.bc.b.157.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.448288 | − | 1.67303i | −0.316987 | − | 1.18301i | −0.922125 | − | 0.386892i | \(-0.873549\pi\) |
0.605138 | − | 0.796121i | \(-0.293118\pi\) | |||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 1.15539 | + | 2.38014i | 0.436698 | + | 0.899608i | ||||
\(8\) | −1.22474 | − | 1.22474i | −0.433013 | − | 0.433013i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0.965926 | − | 0.258819i | 0.278839 | − | 0.0747146i | ||||
\(13\) | −3.53553 | + | 3.53553i | −0.980581 | + | 0.980581i | −0.999815 | − | 0.0192343i | \(-0.993877\pi\) |
0.0192343 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(14\) | 3.46410 | − | 3.00000i | 0.925820 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.50000 | + | 4.33013i | −0.625000 | + | 1.08253i | ||||
\(17\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(18\) | 0.448288 | − | 1.67303i | 0.105662 | − | 0.394338i | ||||
\(19\) | −2.59808 | + | 4.50000i | −0.596040 | + | 1.03237i | 0.397360 | + | 0.917663i | \(0.369927\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 2.59808i | −0.109109 | − | 0.566947i | ||||
\(22\) | 7.34847 | − | 7.34847i | 1.56670 | − | 1.56670i | ||||
\(23\) | 3.34607 | − | 0.896575i | 0.697703 | − | 0.186949i | 0.107501 | − | 0.994205i | \(-0.465715\pi\) |
0.590201 | + | 0.807256i | \(0.299048\pi\) | |||||||
\(24\) | 0.866025 | + | 1.50000i | 0.176777 | + | 0.306186i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.50000 | + | 4.33013i | 1.47087 | + | 0.849208i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −2.19067 | − | 1.48356i | −0.413998 | − | 0.280367i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 1.73205i | 0.538816 | − | 0.311086i | −0.205783 | − | 0.978598i | \(-0.565974\pi\) |
0.744599 | + | 0.667512i | \(0.232641\pi\) | |||||||
\(32\) | 5.01910 | + | 1.34486i | 0.887260 | + | 0.237740i | ||||
\(33\) | −1.55291 | − | 5.79555i | −0.270328 | − | 1.00888i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.24144 | + | 8.36516i | 0.368490 | + | 1.37522i | 0.862627 | + | 0.505840i | \(0.168817\pi\) |
−0.494137 | + | 0.869384i | \(0.664516\pi\) | |||||||
\(38\) | 8.69333 | + | 2.32937i | 1.41024 | + | 0.377874i | ||||
\(39\) | 4.33013 | − | 2.50000i | 0.693375 | − | 0.400320i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.3923i | − | 1.62301i | −0.584349 | − | 0.811503i | \(-0.698650\pi\) | ||
0.584349 | − | 0.811503i | \(-0.301350\pi\) | |||||||
\(42\) | −4.12252 | + | 2.00120i | −0.636119 | + | 0.308792i | ||||
\(43\) | −2.44949 | − | 2.44949i | −0.373544 | − | 0.373544i | 0.495222 | − | 0.868766i | \(-0.335087\pi\) |
−0.868766 | + | 0.495222i | \(0.835087\pi\) | |||||||
\(44\) | −5.19615 | − | 3.00000i | −0.783349 | − | 0.452267i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 5.19615i | −0.442326 | − | 0.766131i | ||||
\(47\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(48\) | 3.53553 | − | 3.53553i | 0.510310 | − | 0.510310i | ||||
\(49\) | −4.33013 | + | 5.50000i | −0.618590 | + | 0.785714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.29410 | − | 4.82963i | 0.179459 | − | 0.669749i | ||||
\(53\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(54\) | −0.866025 | + | 1.50000i | −0.117851 | + | 0.204124i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 4.33013i | 0.200446 | − | 0.578638i | ||||
\(57\) | 3.67423 | − | 3.67423i | 0.486664 | − | 0.486664i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.46410 | − | 6.00000i | −0.450988 | − | 0.781133i | 0.547460 | − | 0.836832i | \(-0.315595\pi\) |
−0.998448 | + | 0.0556984i | \(0.982261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | − | 0.866025i | −0.192055 | − | 0.110883i | 0.400889 | − | 0.916127i | \(-0.368701\pi\) |
−0.592944 | + | 0.805243i | \(0.702035\pi\) | |||||||
\(62\) | −4.24264 | − | 4.24264i | −0.538816 | − | 0.538816i | ||||
\(63\) | −0.189469 | + | 2.63896i | −0.0238708 | + | 0.332478i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.00000 | + | 5.19615i | −1.10782 | + | 0.639602i | ||||
\(67\) | 8.36516 | + | 2.24144i | 1.02197 | + | 0.273835i | 0.730622 | − | 0.682783i | \(-0.239230\pi\) |
0.291346 | + | 0.956618i | \(0.405897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.46410 | −0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −0.448288 | − | 1.67303i | −0.0528312 | − | 0.197169i | ||||
\(73\) | 6.76148 | + | 1.81173i | 0.791371 | + | 0.212047i | 0.631792 | − | 0.775138i | \(-0.282320\pi\) |
0.159579 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(74\) | 12.9904 | − | 7.50000i | 1.51010 | − | 0.871857i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.19615i | − | 0.596040i | ||||||
\(77\) | −8.90138 | + | 13.1440i | −1.01441 | + | 1.49790i | ||||
\(78\) | −6.12372 | − | 6.12372i | −0.693375 | − | 0.693375i | ||||
\(79\) | −9.52628 | − | 5.50000i | −1.07179 | − | 0.618798i | −0.143120 | − | 0.989705i | \(-0.545714\pi\) |
−0.928670 | + | 0.370907i | \(0.879047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −17.3867 | + | 4.65874i | −1.92004 | + | 0.514472i | ||||
\(83\) | −8.48528 | + | 8.48528i | −0.931381 | + | 0.931381i | −0.997792 | − | 0.0664117i | \(-0.978845\pi\) |
0.0664117 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(84\) | 1.73205 | + | 2.00000i | 0.188982 | + | 0.218218i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.00000 | + | 5.19615i | −0.323498 | + | 0.560316i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.68973 | − | 10.0382i | 0.286726 | − | 1.07008i | ||||
\(89\) | −6.92820 | + | 12.0000i | −0.734388 | + | 1.27200i | 0.220603 | + | 0.975364i | \(0.429197\pi\) |
−0.954991 | + | 0.296634i | \(0.904136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5000 | − | 4.33013i | −1.31036 | − | 0.453921i | ||||
\(92\) | −2.44949 | + | 2.44949i | −0.255377 | + | 0.255377i | ||||
\(93\) | −3.34607 | + | 0.896575i | −0.346971 | + | 0.0929705i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.50000 | − | 2.59808i | −0.459279 | − | 0.265165i | ||||
\(97\) | −3.53553 | − | 3.53553i | −0.358979 | − | 0.358979i | 0.504457 | − | 0.863437i | \(-0.331693\pi\) |
−0.863437 | + | 0.504457i | \(0.831693\pi\) | |||||||
\(98\) | 11.1428 | + | 4.77886i | 1.12560 | + | 0.482738i | ||||
\(99\) | 6.00000i | 0.603023i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 1.73205i | −0.298511 | + | 0.172345i | −0.641774 | − | 0.766894i | \(-0.721801\pi\) |
0.343263 | + | 0.939239i | \(0.388468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.81173 | + | 6.76148i | 0.178515 | + | 0.666228i | 0.995926 | + | 0.0901732i | \(0.0287421\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(104\) | 8.66025 | 0.849208 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.79315 | − | 6.69213i | −0.173350 | − | 0.646953i | −0.996827 | − | 0.0796020i | \(-0.974635\pi\) |
0.823476 | − | 0.567351i | \(-0.192032\pi\) | |||||||
\(108\) | 0.965926 | + | 0.258819i | 0.0929463 | + | 0.0249049i | ||||
\(109\) | 6.06218 | − | 3.50000i | 0.580651 | − | 0.335239i | −0.180741 | − | 0.983531i | \(-0.557850\pi\) |
0.761392 | + | 0.648292i | \(0.224516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.66025i | − | 0.821995i | ||||||
\(112\) | −13.1948 | − | 0.947343i | −1.24679 | − | 0.0895155i | ||||
\(113\) | 12.2474 | + | 12.2474i | 1.15214 | + | 1.15214i | 0.986122 | + | 0.166021i | \(0.0530919\pi\) |
0.166021 | + | 0.986122i | \(0.446908\pi\) | |||||||
\(114\) | −7.79423 | − | 4.50000i | −0.729996 | − | 0.421464i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.82963 | + | 1.29410i | −0.446499 | + | 0.119639i | ||||
\(118\) | −8.48528 | + | 8.48528i | −0.781133 | + | 0.781133i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | −0.776457 | + | 2.89778i | −0.0702971 | + | 0.262352i | ||||
\(123\) | −2.68973 | + | 10.0382i | −0.242524 | + | 0.905114i | ||||
\(124\) | −1.73205 | + | 3.00000i | −0.155543 | + | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.50000 | − | 0.866025i | 0.400892 | − | 0.0771517i | ||||
\(127\) | 3.67423 | − | 3.67423i | 0.326036 | − | 0.326036i | −0.525041 | − | 0.851077i | \(-0.675950\pi\) |
0.851077 | + | 0.525041i | \(0.175950\pi\) | |||||||
\(128\) | 11.7112 | − | 3.13801i | 1.03514 | − | 0.277364i | ||||
\(129\) | 1.73205 | + | 3.00000i | 0.152499 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 1.73205i | 0.262111 | + | 0.151330i | 0.625297 | − | 0.780387i | \(-0.284978\pi\) |
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(132\) | 4.24264 | + | 4.24264i | 0.369274 | + | 0.369274i | ||||
\(133\) | −13.7124 | − | 0.984508i | −1.18902 | − | 0.0853677i | ||||
\(134\) | − | 15.0000i | − | 1.29580i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.34607 | − | 0.896575i | −0.285874 | − | 0.0765996i | 0.113033 | − | 0.993591i | \(-0.463943\pi\) |
−0.398906 | + | 0.916992i | \(0.630610\pi\) | |||||||
\(138\) | 1.55291 | + | 5.79555i | 0.132193 | + | 0.493350i | ||||
\(139\) | 22.5167 | 1.90984 | 0.954919 | − | 0.296866i | \(-0.0959415\pi\) | ||||
0.954919 | + | 0.296866i | \(0.0959415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.37945 | − | 20.0764i | −0.451434 | − | 1.68477i | ||||
\(143\) | −28.9778 | − | 7.76457i | −2.42324 | − | 0.649306i | ||||
\(144\) | −4.33013 | + | 2.50000i | −0.360844 | + | 0.208333i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 12.1244i | − | 1.00342i | ||||||
\(147\) | 5.60609 | − | 4.19187i | 0.462382 | − | 0.345740i | ||||
\(148\) | −6.12372 | − | 6.12372i | −0.503367 | − | 0.503367i | ||||
\(149\) | −5.19615 | − | 3.00000i | −0.425685 | − | 0.245770i | 0.271821 | − | 0.962348i | \(-0.412374\pi\) |
−0.697507 | + | 0.716578i | \(0.745707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | − | 14.7224i | −0.691720 | − | 1.19809i | −0.971274 | − | 0.237964i | \(-0.923520\pi\) |
0.279554 | − | 0.960130i | \(-0.409814\pi\) | |||||||
\(152\) | 8.69333 | − | 2.32937i | 0.705122 | − | 0.188937i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 25.9808 | + | 9.00000i | 2.09359 | + | 0.725241i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | + | 4.33013i | −0.200160 | + | 0.346688i | ||||
\(157\) | −5.95284 | + | 22.2163i | −0.475088 | + | 1.77305i | 0.145970 | + | 0.989289i | \(0.453370\pi\) |
−0.621058 | + | 0.783764i | \(0.713297\pi\) | |||||||
\(158\) | −4.93117 | + | 18.4034i | −0.392302 | + | 1.46409i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | + | 6.92820i | 0.472866 | + | 0.546019i | ||||
\(162\) | 1.22474 | − | 1.22474i | 0.0962250 | − | 0.0962250i | ||||
\(163\) | 1.67303 | − | 0.448288i | 0.131042 | − | 0.0351126i | −0.192702 | − | 0.981257i | \(-0.561725\pi\) |
0.323744 | + | 0.946145i | \(0.395058\pi\) | |||||||
\(164\) | 5.19615 | + | 9.00000i | 0.405751 | + | 0.702782i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.0000 | + | 10.3923i | 1.39707 | + | 0.806599i | ||||
\(167\) | −8.48528 | − | 8.48528i | −0.656611 | − | 0.656611i | 0.297966 | − | 0.954577i | \(-0.403692\pi\) |
−0.954577 | + | 0.297966i | \(0.903692\pi\) | |||||||
\(168\) | −2.56961 | + | 3.79435i | −0.198250 | + | 0.292741i | ||||
\(169\) | − | 12.0000i | − | 0.923077i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50000 | + | 2.59808i | −0.344124 | + | 0.198680i | ||||
\(172\) | 3.34607 | + | 0.896575i | 0.255135 | + | 0.0683632i | ||||
\(173\) | 1.55291 | + | 5.79555i | 0.118066 | + | 0.440628i | 0.999498 | − | 0.0316829i | \(-0.0100867\pi\) |
−0.881432 | + | 0.472311i | \(0.843420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −30.0000 | −2.26134 | ||||||||
\(177\) | 1.79315 | + | 6.69213i | 0.134781 | + | 0.503011i | ||||
\(178\) | 23.1822 | + | 6.21166i | 1.73758 | + | 0.465583i | ||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | −1.64085 | + | 22.8541i | −0.121628 | + | 1.69405i | ||||
\(183\) | 1.22474 | + | 1.22474i | 0.0905357 | + | 0.0905357i | ||||
\(184\) | −5.19615 | − | 3.00000i | −0.383065 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.00000 | + | 5.19615i | 0.219971 | + | 0.381000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.866025 | − | 2.50000i | 0.0629941 | − | 0.181848i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0.258819 | − | 0.965926i | 0.0186787 | − | 0.0697097i | ||||
\(193\) | 5.37945 | − | 20.0764i | 0.387221 | − | 1.44513i | −0.447414 | − | 0.894327i | \(-0.647655\pi\) |
0.834635 | − | 0.550803i | \(-0.185679\pi\) | |||||||
\(194\) | −4.33013 | + | 7.50000i | −0.310885 | + | 0.538469i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 9.79796 | − | 9.79796i | 0.698076 | − | 0.698076i | −0.265920 | − | 0.963995i | \(-0.585676\pi\) |
0.963995 | + | 0.265920i | \(0.0856756\pi\) | |||||||
\(198\) | 10.0382 | − | 2.68973i | 0.713384 | − | 0.191151i | ||||
\(199\) | −7.79423 | − | 13.5000i | −0.552518 | − | 0.956990i | −0.998092 | − | 0.0617444i | \(-0.980334\pi\) |
0.445574 | − | 0.895245i | \(-0.353000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.50000 | − | 4.33013i | −0.529009 | − | 0.305424i | ||||
\(202\) | 4.24264 | + | 4.24264i | 0.298511 | + | 0.298511i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.5000 | − | 6.06218i | 0.731570 | − | 0.422372i | ||||
\(207\) | 3.34607 | + | 0.896575i | 0.232568 | + | 0.0623163i | ||||
\(208\) | −6.47048 | − | 24.1481i | −0.448647 | − | 1.67437i | ||||
\(209\) | −31.1769 | −2.15655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0000 | 1.30801 | 0.654007 | − | 0.756489i | \(-0.273087\pi\) | ||||
0.654007 | + | 0.756489i | \(0.273087\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.5911 | − | 3.10583i | −0.794210 | − | 0.212808i | ||||
\(214\) | −10.3923 | + | 6.00000i | −0.710403 | + | 0.410152i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.73205i | 0.117851i | ||||||||
\(217\) | 7.58871 | + | 5.13922i | 0.515155 | + | 0.348873i | ||||
\(218\) | −8.57321 | − | 8.57321i | −0.580651 | − | 0.580651i | ||||
\(219\) | −6.06218 | − | 3.50000i | −0.409644 | − | 0.236508i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.4889 | + | 3.88229i | −0.972430 | + | 0.260562i | ||||
\(223\) | 16.2635 | − | 16.2635i | 1.08908 | − | 1.08908i | 0.0934584 | − | 0.995623i | \(-0.470208\pi\) |
0.995623 | − | 0.0934584i | \(-0.0297922\pi\) | |||||||
\(224\) | 2.59808 | + | 13.5000i | 0.173591 | + | 0.902007i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0000 | − | 25.9808i | 0.997785 | − | 1.72821i | ||||
\(227\) | 6.21166 | − | 23.1822i | 0.412282 | − | 1.53866i | −0.377936 | − | 0.925832i | \(-0.623366\pi\) |
0.790218 | − | 0.612826i | \(-0.209967\pi\) | |||||||
\(228\) | −1.34486 | + | 5.01910i | −0.0890657 | + | 0.332398i | ||||
\(229\) | 7.79423 | − | 13.5000i | 0.515057 | − | 0.892105i | −0.484790 | − | 0.874630i | \(-0.661104\pi\) |
0.999847 | − | 0.0174746i | \(-0.00556263\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 10.3923i | 0.789542 | − | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.34607 | − | 0.896575i | 0.219208 | − | 0.0587366i | −0.147543 | − | 0.989056i | \(-0.547137\pi\) |
0.366751 | + | 0.930319i | \(0.380470\pi\) | |||||||
\(234\) | 4.33013 | + | 7.50000i | 0.283069 | + | 0.490290i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | + | 3.46410i | 0.390567 | + | 0.225494i | ||||
\(237\) | 7.77817 | + | 7.77817i | 0.505247 | + | 0.505247i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50000 | − | 0.866025i | 0.0966235 | − | 0.0557856i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 41.8258 | + | 11.2072i | 2.68867 | + | 0.720426i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 1.73205 | 0.110883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.0000 | 1.14764 | ||||||||
\(247\) | −6.72432 | − | 25.0955i | −0.427858 | − | 1.59679i | ||||
\(248\) | −5.79555 | − | 1.55291i | −0.368018 | − | 0.0986102i | ||||
\(249\) | 10.3923 | − | 6.00000i | 0.658586 | − | 0.380235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.3205i | − | 1.09326i | −0.837374 | − | 0.546630i | \(-0.815910\pi\) | ||
0.837374 | − | 0.546630i | \(-0.184090\pi\) | |||||||
\(252\) | −1.15539 | − | 2.38014i | −0.0727830 | − | 0.149935i | ||||
\(253\) | 14.6969 | + | 14.6969i | 0.923989 | + | 0.923989i | ||||
\(254\) | −7.79423 | − | 4.50000i | −0.489053 | − | 0.282355i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | −17.3867 | + | 4.65874i | −1.08455 | + | 0.290604i | −0.756459 | − | 0.654041i | \(-0.773072\pi\) |
−0.328092 | + | 0.944646i | \(0.606405\pi\) | |||||||
\(258\) | 4.24264 | − | 4.24264i | 0.264135 | − | 0.264135i | ||||
\(259\) | −17.3205 | + | 15.0000i | −1.07624 | + | 0.932055i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.55291 | − | 5.79555i | 0.0959394 | − | 0.358051i | ||||
\(263\) | 3.58630 | − | 13.3843i | 0.221141 | − | 0.825309i | −0.762773 | − | 0.646666i | \(-0.776163\pi\) |
0.983914 | − | 0.178643i | \(-0.0571706\pi\) | |||||||
\(264\) | −5.19615 | + | 9.00000i | −0.319801 | + | 0.553912i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.50000 | + | 23.3827i | 0.275913 | + | 1.43368i | ||||
\(267\) | 9.79796 | − | 9.79796i | 0.599625 | − | 0.599625i | ||||
\(268\) | −8.36516 | + | 2.24144i | −0.510984 | + | 0.136918i | ||||
\(269\) | 1.73205 | + | 3.00000i | 0.105605 | + | 0.182913i | 0.913985 | − | 0.405747i | \(-0.132989\pi\) |
−0.808380 | + | 0.588661i | \(0.799655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.00000 | + | 5.19615i | 0.546711 | + | 0.315644i | 0.747794 | − | 0.663930i | \(-0.231113\pi\) |
−0.201083 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9534 | + | 7.41782i | 0.662927 | + | 0.448947i | ||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | − | 1.73205i | 0.180579 | − | 0.104257i | ||||
\(277\) | 5.01910 | + | 1.34486i | 0.301568 | + | 0.0808050i | 0.406430 | − | 0.913682i | \(-0.366773\pi\) |
−0.104862 | + | 0.994487i | \(0.533440\pi\) | |||||||
\(278\) | −10.0939 | − | 37.6711i | −0.605394 | − | 2.25936i | ||||
\(279\) | 3.46410 | 0.207390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.965926 | − | 0.258819i | −0.0574183 | − | 0.0153852i | 0.229996 | − | 0.973192i | \(-0.426129\pi\) |
−0.287414 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(284\) | −10.3923 | + | 6.00000i | −0.616670 | + | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.9615i | 3.07255i | ||||||||
\(287\) | 24.7351 | − | 12.0072i | 1.46007 | − | 0.708763i | ||||
\(288\) | 3.67423 | + | 3.67423i | 0.216506 | + | 0.216506i | ||||
\(289\) | 14.7224 | + | 8.50000i | 0.866025 | + | 0.500000i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.50000 | + | 4.33013i | 0.146553 | + | 0.253837i | ||||
\(292\) | −6.76148 | + | 1.81173i | −0.395686 | + | 0.106024i | ||||
\(293\) | 16.9706 | − | 16.9706i | 0.991431 | − | 0.991431i | −0.00853273 | − | 0.999964i | \(-0.502716\pi\) |
0.999964 | + | 0.00853273i | \(0.00271609\pi\) | |||||||
\(294\) | −9.52628 | − | 7.50000i | −0.555584 | − | 0.437409i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.50000 | − | 12.9904i | 0.435929 | − | 0.755051i | ||||
\(297\) | 1.55291 | − | 5.79555i | 0.0901092 | − | 0.336292i | ||||
\(298\) | −2.68973 | + | 10.0382i | −0.155812 | + | 0.581497i | ||||
\(299\) | −8.66025 | + | 15.0000i | −0.500835 | + | 0.867472i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | − | 8.66025i | 0.172917 | − | 0.499169i | ||||
\(302\) | −20.8207 | + | 20.8207i | −1.19809 | + | 1.19809i | ||||
\(303\) | 3.34607 | − | 0.896575i | 0.192226 | − | 0.0515069i | ||||
\(304\) | −12.9904 | − | 22.5000i | −0.745049 | − | 1.29046i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6274 | + | 22.6274i | 1.29141 | + | 1.29141i | 0.933912 | + | 0.357503i | \(0.116372\pi\) |
0.357503 | + | 0.933912i | \(0.383628\pi\) | |||||||
\(308\) | 1.13681 | − | 15.8338i | 0.0647759 | − | 0.902212i | ||||
\(309\) | − | 7.00000i | − | 0.398216i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | + | 8.66025i | −0.850572 | + | 0.491078i | −0.860844 | − | 0.508869i | \(-0.830064\pi\) |
0.0102718 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(312\) | −8.36516 | − | 2.24144i | −0.473584 | − | 0.126896i | ||||
\(313\) | 6.72930 | + | 25.1141i | 0.380362 | + | 1.41953i | 0.845349 | + | 0.534214i | \(0.179392\pi\) |
−0.464987 | + | 0.885317i | \(0.653941\pi\) | |||||||
\(314\) | 39.8372 | 2.24814 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.0000 | 0.618798 | ||||||||
\(317\) | −2.68973 | − | 10.0382i | −0.151070 | − | 0.563801i | −0.999410 | − | 0.0343491i | \(-0.989064\pi\) |
0.848340 | − | 0.529452i | \(-0.177602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.92820i | 0.386695i | ||||||||
\(322\) | 8.90138 | − | 13.1440i | 0.496055 | − | 0.732488i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.866025 | − | 0.500000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.50000 | − | 2.59808i | −0.0830773 | − | 0.143894i | ||||
\(327\) | −6.76148 | + | 1.81173i | −0.373911 | + | 0.100189i | ||||
\(328\) | −12.7279 | + | 12.7279i | −0.702782 | + | 0.702782i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.50000 | + | 11.2583i | −0.357272 | + | 0.618814i | −0.987504 | − | 0.157593i | \(-0.949627\pi\) |
0.630232 | + | 0.776407i | \(0.282960\pi\) | |||||||
\(332\) | 3.10583 | − | 11.5911i | 0.170454 | − | 0.636145i | ||||
\(333\) | −2.24144 | + | 8.36516i | −0.122830 | + | 0.458408i | ||||
\(334\) | −10.3923 | + | 18.0000i | −0.568642 | + | 0.984916i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.5000 | + | 4.33013i | 0.681931 | + | 0.236228i | ||||
\(337\) | −4.89898 | + | 4.89898i | −0.266864 | + | 0.266864i | −0.827835 | − | 0.560971i | \(-0.810428\pi\) |
0.560971 | + | 0.827835i | \(0.310428\pi\) | |||||||
\(338\) | −20.0764 | + | 5.37945i | −1.09201 | + | 0.292604i | ||||
\(339\) | −8.66025 | − | 15.0000i | −0.470360 | − | 0.814688i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0000 | + | 10.3923i | 0.974755 | + | 0.562775i | ||||
\(342\) | 6.36396 | + | 6.36396i | 0.344124 | + | 0.344124i | ||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | 6.00000i | 0.323498i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.00000 | − | 5.19615i | 0.483843 | − | 0.279347i | ||||
\(347\) | −20.0764 | − | 5.37945i | −1.07776 | − | 0.288784i | −0.324080 | − | 0.946030i | \(-0.605055\pi\) |
−0.753677 | + | 0.657245i | \(0.771722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.92820 | −0.370858 | −0.185429 | − | 0.982658i | \(-0.559368\pi\) | ||||
−0.185429 | + | 0.982658i | \(0.559368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 8.06918 | + | 30.1146i | 0.430089 | + | 1.60511i | ||||
\(353\) | −5.79555 | − | 1.55291i | −0.308466 | − | 0.0826533i | 0.101265 | − | 0.994859i | \(-0.467711\pi\) |
−0.409731 | + | 0.912206i | \(0.634378\pi\) | |||||||
\(354\) | 10.3923 | − | 6.00000i | 0.552345 | − | 0.318896i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13.8564i | − | 0.734388i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7846 | + | 12.0000i | 1.09697 | + | 0.633336i | 0.935423 | − | 0.353529i | \(-0.115019\pi\) |
0.161546 | + | 0.986865i | \(0.448352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00000 | − | 6.92820i | −0.210526 | − | 0.364642i | ||||
\(362\) | 23.1822 | − | 6.21166i | 1.21843 | − | 0.326477i | ||||
\(363\) | 17.6777 | − | 17.6777i | 0.927837 | − | 0.927837i | ||||
\(364\) | 12.9904 | − | 2.50000i | 0.680881 | − | 0.131036i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.50000 | − | 2.59808i | 0.0784063 | − | 0.135804i | ||||
\(367\) | 4.14110 | − | 15.4548i | 0.216164 | − | 0.806735i | −0.769590 | − | 0.638539i | \(-0.779539\pi\) |
0.985754 | − | 0.168196i | \(-0.0537941\pi\) | |||||||
\(368\) | −4.48288 | + | 16.7303i | −0.233686 | + | 0.872129i | ||||
\(369\) | 5.19615 | − | 9.00000i | 0.270501 | − | 0.468521i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.44949 | − | 2.44949i | 0.127000 | − | 0.127000i | ||||
\(373\) | −5.01910 | + | 1.34486i | −0.259879 | + | 0.0696344i | −0.386406 | − | 0.922329i | \(-0.626284\pi\) |
0.126527 | + | 0.991963i | \(0.459617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.57081 | − | 0.328169i | −0.235097 | − | 0.0168792i | ||||
\(379\) | 5.00000i | 0.256833i | 0.991720 | + | 0.128416i | \(0.0409894\pi\) | ||||
−0.991720 | + | 0.128416i | \(0.959011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.50000 | + | 2.59808i | −0.230542 | + | 0.133103i | ||||
\(382\) | 10.0382 | + | 2.68973i | 0.513599 | + | 0.137618i | ||||
\(383\) | −4.65874 | − | 17.3867i | −0.238051 | − | 0.888417i | −0.976750 | − | 0.214382i | \(-0.931226\pi\) |
0.738699 | − | 0.674035i | \(-0.235440\pi\) | |||||||
\(384\) | −12.1244 | −0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36.0000 | −1.83235 | ||||||||
\(387\) | −0.896575 | − | 3.34607i | −0.0455755 | − | 0.170090i | ||||
\(388\) | 4.82963 | + | 1.29410i | 0.245187 | + | 0.0656977i | ||||
\(389\) | 25.9808 | − | 15.0000i | 1.31728 | − | 0.760530i | 0.333987 | − | 0.942578i | \(-0.391606\pi\) |
0.983290 | + | 0.182047i | \(0.0582724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 12.0394 | − | 1.43280i | 0.608081 | − | 0.0723671i | ||||
\(393\) | −2.44949 | − | 2.44949i | −0.123560 | − | 0.123560i | ||||
\(394\) | −20.7846 | − | 12.0000i | −1.04711 | − | 0.604551i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | − | 5.19615i | −0.150756 | − | 0.261116i | ||||
\(397\) | −1.93185 | + | 0.517638i | −0.0969569 | + | 0.0259795i | −0.306971 | − | 0.951719i | \(-0.599316\pi\) |
0.210014 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(398\) | −19.0919 | + | 19.0919i | −0.956990 | + | 0.956990i | ||||
\(399\) | 12.9904 | + | 4.50000i | 0.650332 | + | 0.225282i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | −3.88229 | + | 14.4889i | −0.193631 | + | 0.722640i | ||||
\(403\) | −4.48288 | + | 16.7303i | −0.223308 | + | 0.833397i | ||||
\(404\) | 1.73205 | − | 3.00000i | 0.0861727 | − | 0.149256i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.7423 | + | 36.7423i | −1.82125 | + | 1.82125i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.59808 | − | 4.50000i | −0.128467 | − | 0.222511i | 0.794616 | − | 0.607112i | \(-0.207672\pi\) |
−0.923083 | + | 0.384602i | \(0.874339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | + | 1.73205i | 0.147979 | + | 0.0854358i | ||||
\(412\) | −4.94975 | − | 4.94975i | −0.243857 | − | 0.243857i | ||||
\(413\) | 10.2784 | − | 15.1774i | 0.505769 | − | 0.746832i | ||||
\(414\) | − | 6.00000i | − | 0.294884i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.5000 | + | 12.9904i | −1.10315 | + | 0.636906i | ||||
\(417\) | −21.7494 | − | 5.82774i | −1.06507 | − | 0.285386i | ||||
\(418\) | 13.9762 | + | 52.1600i | 0.683600 | + | 2.55123i | ||||
\(419\) | 3.46410 | 0.169232 | 0.0846162 | − | 0.996414i | \(-0.473034\pi\) | ||||
0.0846162 | + | 0.996414i | \(0.473034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | −0.828529 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(422\) | −8.51747 | − | 31.7876i | −0.414624 | − | 1.54740i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.7846i | 1.00702i | ||||||||
\(427\) | 0.328169 | − | 4.57081i | 0.0158812 | − | 0.221197i | ||||
\(428\) | 4.89898 | + | 4.89898i | 0.236801 | + | 0.236801i | ||||
\(429\) | 25.9808 | + | 15.0000i | 1.25436 | + | 0.724207i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | + | 25.9808i | 0.722525 | + | 1.25145i | 0.959985 | + | 0.280052i | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 4.82963 | − | 1.29410i | 0.232366 | − | 0.0622622i | ||||
\(433\) | 1.41421 | − | 1.41421i | 0.0679628 | − | 0.0679628i | −0.672308 | − | 0.740271i | \(-0.734697\pi\) |
0.740271 | + | 0.672308i | \(0.234697\pi\) | |||||||
\(434\) | 5.19615 | − | 15.0000i | 0.249423 | − | 0.720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.50000 | + | 6.06218i | −0.167620 | + | 0.290326i | ||||
\(437\) | −4.65874 | + | 17.3867i | −0.222858 | + | 0.831717i | ||||
\(438\) | −3.13801 | + | 11.7112i | −0.149940 | + | 0.559584i | ||||
\(439\) | 9.52628 | − | 16.5000i | 0.454665 | − | 0.787502i | −0.544004 | − | 0.839082i | \(-0.683092\pi\) |
0.998669 | + | 0.0515804i | \(0.0164258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.4225 | + | 6.27603i | −1.11283 | + | 0.298183i | −0.767980 | − | 0.640473i | \(-0.778738\pi\) |
−0.344854 | + | 0.938656i | \(0.612072\pi\) | |||||||
\(444\) | 4.33013 | + | 7.50000i | 0.205499 | + | 0.355934i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −34.5000 | − | 19.9186i | −1.63362 | − | 0.943172i | ||||
\(447\) | 4.24264 | + | 4.24264i | 0.200670 | + | 0.200670i | ||||
\(448\) | −2.38014 | + | 1.15539i | −0.112451 | + | 0.0545873i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.0000 | − | 31.1769i | 2.54276 | − | 1.46806i | ||||
\(452\) | −16.7303 | − | 4.48288i | −0.786928 | − | 0.210857i | ||||
\(453\) | 4.39992 | + | 16.4207i | 0.206726 | + | 0.771514i | ||||
\(454\) | −41.5692 | −1.95094 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.00000 | −0.421464 | ||||||||
\(457\) | −4.93117 | − | 18.4034i | −0.230670 | − | 0.860873i | −0.980053 | − | 0.198736i | \(-0.936316\pi\) |
0.749383 | − | 0.662137i | \(-0.230350\pi\) | |||||||
\(458\) | −26.0800 | − | 6.98811i | −1.21864 | − | 0.326533i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.46410i | 0.161339i | 0.996741 | + | 0.0806696i | \(0.0257059\pi\) | ||||
−0.996741 | + | 0.0806696i | \(0.974294\pi\) | |||||||
\(462\) | −22.7661 | − | 15.4176i | −1.05918 | − | 0.717294i | ||||
\(463\) | 6.12372 | + | 6.12372i | 0.284594 | + | 0.284594i | 0.834938 | − | 0.550344i | \(-0.185504\pi\) |
−0.550344 | + | 0.834938i | \(0.685504\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 5.79555 | − | 1.55291i | 0.268186 | − | 0.0718603i | −0.122220 | − | 0.992503i | \(-0.539001\pi\) |
0.390406 | + | 0.920643i | \(0.372335\pi\) | |||||||
\(468\) | 3.53553 | − | 3.53553i | 0.163430 | − | 0.163430i | ||||
\(469\) | 4.33013 | + | 22.5000i | 0.199947 | + | 1.03895i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5000 | − | 19.9186i | 0.529892 | − | 0.917800i | ||||
\(472\) | −3.10583 | + | 11.5911i | −0.142957 | + | 0.533524i | ||||
\(473\) | 5.37945 | − | 20.0764i | 0.247348 | − | 0.923113i | ||||
\(474\) | 9.52628 | − | 16.5000i | 0.437557 | − | 0.757870i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.8564 | + | 24.0000i | 0.633115 | + | 1.09659i | 0.986911 | + | 0.161265i | \(0.0515575\pi\) |
−0.353796 | + | 0.935323i | \(0.615109\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.5000 | − | 21.6506i | −1.70985 | − | 0.987184i | ||||
\(482\) | −2.12132 | − | 2.12132i | −0.0966235 | − | 0.0966235i | ||||
\(483\) | −4.00240 | − | 8.24504i | −0.182116 | − | 0.375163i | ||||
\(484\) | − | 25.0000i | − | 1.13636i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.50000 | + | 0.866025i | −0.0680414 | + | 0.0392837i | ||||
\(487\) | −23.4225 | − | 6.27603i | −1.06137 | − | 0.284394i | −0.314429 | − | 0.949281i | \(-0.601813\pi\) |
−0.746944 | + | 0.664887i | \(0.768480\pi\) | |||||||
\(488\) | 0.776457 | + | 2.89778i | 0.0351486 | + | 0.131176i | ||||
\(489\) | −1.73205 | −0.0783260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | −2.68973 | − | 10.0382i | −0.121262 | − | 0.452557i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −38.9711 | + | 22.5000i | −1.75339 | + | 1.01232i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3205i | 0.777714i | ||||||||
\(497\) | 13.8647 | + | 28.5617i | 0.621918 | + | 1.28117i | ||||
\(498\) | −14.6969 | − | 14.6969i | −0.658586 | − | 0.658586i | ||||
\(499\) | 19.9186 | + | 11.5000i | 0.891678 | + | 0.514811i | 0.874491 | − | 0.485042i | \(-0.161196\pi\) |
0.0171872 | + | 0.999852i | \(0.494529\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | −28.9778 | + | 7.76457i | −1.29334 | + | 0.346550i | ||||
\(503\) | 8.48528 | − | 8.48528i | 0.378340 | − | 0.378340i | −0.492163 | − | 0.870503i | \(-0.663794\pi\) |
0.870503 | + | 0.492163i | \(0.163794\pi\) | |||||||
\(504\) | 3.46410 | − | 3.00000i | 0.154303 | − | 0.133631i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.0000 | − | 31.1769i | 0.800198 | − | 1.38598i | ||||
\(507\) | −3.10583 | + | 11.5911i | −0.137935 | + | 0.514779i | ||||
\(508\) | −1.34486 | + | 5.01910i | −0.0596687 | + | 0.222686i | ||||
\(509\) | −3.46410 | + | 6.00000i | −0.153544 | + | 0.265945i | −0.932528 | − | 0.361098i | \(-0.882402\pi\) |
0.778984 | + | 0.627044i | \(0.215735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | + | 18.1865i | 0.154831 | + | 0.804525i | ||||
\(512\) | −6.12372 | + | 6.12372i | −0.270633 | + | 0.270633i | ||||
\(513\) | 5.01910 | − | 1.34486i | 0.221599 | − | 0.0593772i | ||||
\(514\) | 15.5885 | + | 27.0000i | 0.687577 | + | 1.19092i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | − | 1.73205i | −0.132068 | − | 0.0762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 32.8601 | + | 22.2535i | 1.44379 | + | 0.977761i | ||||
\(519\) | − | 6.00000i | − | 0.263371i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | − | 12.1244i | 0.920027 | − | 0.531178i | 0.0363831 | − | 0.999338i | \(-0.488416\pi\) |
0.883644 | + | 0.468160i | \(0.155083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.03528 | + | 3.86370i | 0.0452695 | + | 0.168948i | 0.984860 | − | 0.173353i | \(-0.0554603\pi\) |
−0.939590 | + | 0.342301i | \(0.888794\pi\) | |||||||
\(524\) | −3.46410 | −0.151330 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 28.9778 | + | 7.76457i | 1.26110 | + | 0.337910i | ||||
\(529\) | −9.52628 | + | 5.50000i | −0.414186 | + | 0.239130i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.92820i | − | 0.300658i | ||||||
\(532\) | 12.3676 | − | 6.00361i | 0.536202 | − | 0.260289i | ||||
\(533\) | 36.7423 | + | 36.7423i | 1.59149 | + | 1.59149i | ||||
\(534\) | −20.7846 | − | 12.0000i | −0.899438 | − | 0.519291i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.50000 | − | 12.9904i | −0.323951 | − | 0.561099i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.24264 | − | 4.24264i | 0.182913 | − | 0.182913i | ||||
\(539\) | −41.5692 | − | 6.00000i | −1.79051 | − | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.50000 | − | 6.06218i | 0.150477 | − | 0.260633i | −0.780926 | − | 0.624623i | \(-0.785252\pi\) |
0.931403 | + | 0.363990i | \(0.118586\pi\) | |||||||
\(542\) | 4.65874 | − | 17.3867i | 0.200110 | − | 0.746821i | ||||
\(543\) | 3.58630 | − | 13.3843i | 0.153903 | − | 0.574374i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.50000 | − | 21.6506i | 0.320970 | − | 0.926562i | ||||
\(547\) | 7.34847 | − | 7.34847i | 0.314198 | − | 0.314198i | −0.532336 | − | 0.846533i | \(-0.678686\pi\) |
0.846533 | + | 0.532336i | \(0.178686\pi\) | |||||||
\(548\) | 3.34607 | − | 0.896575i | 0.142937 | − | 0.0382998i | ||||
\(549\) | −0.866025 | − | 1.50000i | −0.0369611 | − | 0.0640184i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.24264 | + | 4.24264i | 0.180579 | + | 0.180579i | ||||
\(553\) | 2.08416 | − | 29.0285i | 0.0886273 | − | 1.23442i | ||||
\(554\) | − | 9.00000i | − | 0.382373i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.5000 | + | 11.2583i | −0.826984 | + | 0.477460i | ||||
\(557\) | −33.4607 | − | 8.96575i | −1.41777 | − | 0.379891i | −0.533080 | − | 0.846065i | \(-0.678966\pi\) |
−0.884693 | + | 0.466174i | \(0.845632\pi\) | |||||||
\(558\) | −1.55291 | − | 5.79555i | −0.0657401 | − | 0.245345i | ||||
\(559\) | 17.3205 | 0.732579 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.7589 | + | 40.1528i | 0.453837 | + | 1.69374i | ||||
\(563\) | 28.9778 | + | 7.76457i | 1.22127 | + | 0.327238i | 0.811174 | − | 0.584806i | \(-0.198829\pi\) |
0.410094 | + | 0.912043i | \(0.365496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.73205i | 0.0728035i | ||||||||
\(567\) | −1.48356 | + | 2.19067i | −0.0623038 | + | 0.0919995i | ||||
\(568\) | −14.6969 | − | 14.6969i | −0.616670 | − | 0.616670i | ||||
\(569\) | −25.9808 | − | 15.0000i | −1.08917 | − | 0.628833i | −0.155815 | − | 0.987786i | \(-0.549800\pi\) |
−0.933355 | + | 0.358954i | \(0.883134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.50000 | − | 9.52628i | −0.230168 | − | 0.398662i | 0.727690 | − | 0.685907i | \(-0.240594\pi\) |
−0.957857 | + | 0.287244i | \(0.907261\pi\) | |||||||
\(572\) | 28.9778 | − | 7.76457i | 1.21162 | − | 0.324653i | ||||
\(573\) | 4.24264 | − | 4.24264i | 0.177239 | − | 0.177239i | ||||
\(574\) | −31.1769 | − | 36.0000i | −1.30130 | − | 1.50261i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −8.79985 | + | 32.8415i | −0.366342 | + | 1.36721i | 0.499249 | + | 0.866458i | \(0.333609\pi\) |
−0.865592 | + | 0.500750i | \(0.833058\pi\) | |||||||
\(578\) | 7.62089 | − | 28.4416i | 0.316987 | − | 1.18301i | ||||
\(579\) | −10.3923 | + | 18.0000i | −0.431889 | + | 0.748054i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | − | 10.3923i | −1.24461 | − | 0.431145i | ||||
\(582\) | 6.12372 | − | 6.12372i | 0.253837 | − | 0.253837i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.06218 | − | 10.5000i | −0.250855 | − | 0.434493i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.0000 | − | 20.7846i | −1.48715 | − | 0.858604i | ||||
\(587\) | −21.2132 | − | 21.2132i | −0.875563 | − | 0.875563i | 0.117509 | − | 0.993072i | \(-0.462509\pi\) |
−0.993072 | + | 0.117509i | \(0.962509\pi\) | |||||||
\(588\) | −2.75908 | + | 6.43331i | −0.113782 | + | 0.265305i | ||||
\(589\) | 18.0000i | 0.741677i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | + | 6.92820i | −0.493614 | + | 0.284988i | ||||
\(592\) | −41.8258 | − | 11.2072i | −1.71903 | − | 0.460613i | ||||
\(593\) | −4.65874 | − | 17.3867i | −0.191312 | − | 0.713985i | −0.993191 | − | 0.116499i | \(-0.962833\pi\) |
0.801879 | − | 0.597486i | \(-0.203834\pi\) | |||||||
\(594\) | −10.3923 | −0.426401 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 4.03459 | + | 15.0573i | 0.165125 | + | 0.616254i | ||||
\(598\) | 28.9778 | + | 7.76457i | 1.18499 | + | 0.317517i | ||||
\(599\) | 31.1769 | − | 18.0000i | 1.27385 | − | 0.735460i | 0.298143 | − | 0.954521i | \(-0.403633\pi\) |
0.975711 | + | 0.219061i | \(0.0702994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.4449i | − | 1.20108i | −0.799594 | − | 0.600541i | \(-0.794952\pi\) | ||
0.799594 | − | 0.600541i | \(-0.205048\pi\) | |||||||
\(602\) | −15.8338 | − | 1.13681i | −0.645335 | − | 0.0463330i | ||||
\(603\) | 6.12372 | + | 6.12372i | 0.249377 | + | 0.249377i | ||||
\(604\) | 14.7224 | + | 8.50000i | 0.599047 | + | 0.345860i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | 12.5570 | − | 3.36465i | 0.509674 | − | 0.136567i | 0.00518808 | − | 0.999987i | \(-0.498349\pi\) |
0.504486 | + | 0.863420i | \(0.331682\pi\) | |||||||
\(608\) | −19.0919 | + | 19.0919i | −0.774278 | + | 0.774278i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(614\) | 27.7128 | − | 48.0000i | 1.11840 | − | 1.93712i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.0000 | − | 5.19615i | 1.08786 | − | 0.209359i | ||||
\(617\) | −9.79796 | + | 9.79796i | −0.394451 | + | 0.394451i | −0.876270 | − | 0.481820i | \(-0.839976\pi\) |
0.481820 | + | 0.876270i | \(0.339976\pi\) | |||||||
\(618\) | −11.7112 | + | 3.13801i | −0.471095 | + | 0.126229i | ||||
\(619\) | 5.19615 | + | 9.00000i | 0.208851 | + | 0.361741i | 0.951353 | − | 0.308103i | \(-0.0996943\pi\) |
−0.742502 | + | 0.669844i | \(0.766361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | − | 1.73205i | −0.120386 | − | 0.0695048i | ||||
\(622\) | 21.2132 | + | 21.2132i | 0.850572 | + | 0.850572i | ||||
\(623\) | −36.5665 | − | 2.62536i | −1.46501 | − | 0.105183i | ||||
\(624\) | 25.0000i | 1.00080i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.0000 | − | 22.5167i | 1.55875 | − | 0.899947i | ||||
\(627\) | 30.1146 | + | 8.06918i | 1.20266 | + | 0.322252i | ||||
\(628\) | −5.95284 | − | 22.2163i | −0.237544 | − | 0.886527i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0000 | 1.87104 | 0.935520 | − | 0.353273i | \(-0.114931\pi\) | ||||
0.935520 | + | 0.353273i | \(0.114931\pi\) | |||||||
\(632\) | 4.93117 | + | 18.4034i | 0.196151 | + | 0.732046i | ||||
\(633\) | −18.3526 | − | 4.91756i | −0.729450 | − | 0.195456i | ||||
\(634\) | −15.5885 | + | 9.00000i | −0.619097 | + | 0.357436i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.13613 | − | 34.7547i | −0.163879 | − | 1.37703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3923 | + | 6.00000i | 0.411113 | + | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00000 | + | 10.3923i | 0.236986 | + | 0.410471i | 0.959848 | − | 0.280521i | \(-0.0905072\pi\) |
−0.722862 | + | 0.690992i | \(0.757174\pi\) | |||||||
\(642\) | 11.5911 | − | 3.10583i | 0.457465 | − | 0.122577i | ||||
\(643\) | 3.53553 | − | 3.53553i | 0.139428 | − | 0.139428i | −0.633948 | − | 0.773376i | \(-0.718567\pi\) |
0.773376 | + | 0.633948i | \(0.218567\pi\) | |||||||
\(644\) | −8.66025 | − | 3.00000i | −0.341262 | − | 0.118217i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.65874 | − | 17.3867i | 0.183154 | − | 0.683540i | −0.811864 | − | 0.583846i | \(-0.801547\pi\) |
0.995018 | − | 0.0996938i | \(-0.0317863\pi\) | |||||||
\(648\) | 0.448288 | − | 1.67303i | 0.0176104 | − | 0.0657229i | ||||
\(649\) | 20.7846 | − | 36.0000i | 0.815867 | − | 1.41312i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | − | 6.92820i | −0.235159 | − | 0.271538i | ||||
\(652\) | −1.22474 | + | 1.22474i | −0.0479647 | + | 0.0479647i | ||||
\(653\) | −3.34607 | + | 0.896575i | −0.130942 | + | 0.0350857i | −0.323695 | − | 0.946162i | \(-0.604925\pi\) |
0.192753 | + | 0.981247i | \(0.438258\pi\) | |||||||
\(654\) | 6.06218 | + | 10.5000i | 0.237050 | + | 0.410582i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 45.0000 | + | 25.9808i | 1.75695 | + | 1.01438i | ||||
\(657\) | 4.94975 | + | 4.94975i | 0.193108 | + | 0.193108i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0000i | 1.63609i | 0.575156 | + | 0.818044i | \(0.304941\pi\) | ||||
−0.575156 | + | 0.818044i | \(0.695059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5000 | + | 19.9186i | −1.34189 | + | 0.774743i | −0.987085 | − | 0.160196i | \(-0.948788\pi\) |
−0.354809 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(662\) | 21.7494 | + | 5.82774i | 0.845315 | + | 0.226502i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.7846 | 0.806599 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.0000 | 0.581238 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 11.5911 | + | 3.10583i | 0.448474 | + | 0.120168i | ||||
\(669\) | −19.9186 | + | 11.5000i | −0.770097 | + | 0.444616i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.3923i | − | 0.401190i | ||||||
\(672\) | 0.984508 | − | 13.7124i | 0.0379782 | − | 0.528968i | ||||
\(673\) | −6.12372 | − | 6.12372i | −0.236052 | − | 0.236052i | 0.579161 | − | 0.815213i | \(-0.303380\pi\) |
−0.815213 | + | 0.579161i | \(0.803380\pi\) | |||||||
\(674\) | 10.3923 | + | 6.00000i | 0.400297 | + | 0.231111i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | 40.5689 | − | 10.8704i | 1.55919 | − | 0.417783i | 0.626782 | − | 0.779194i | \(-0.284372\pi\) |
0.932407 | + | 0.361411i | \(0.117705\pi\) | |||||||
\(678\) | −21.2132 | + | 21.2132i | −0.814688 | + | 0.814688i | ||||
\(679\) | 4.33013 | − | 12.5000i | 0.166175 | − | 0.479706i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | + | 20.7846i | −0.459841 | + | 0.796468i | ||||
\(682\) | 9.31749 | − | 34.7733i | 0.356785 | − | 1.33154i | ||||
\(683\) | −6.27603 | + | 23.4225i | −0.240146 | + | 0.896235i | 0.735616 | + | 0.677399i | \(0.236893\pi\) |
−0.975762 | + | 0.218837i | \(0.929774\pi\) | |||||||
\(684\) | 2.59808 | − | 4.50000i | 0.0993399 | − | 0.172062i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.50000 | + | 32.0429i | 0.0572703 | + | 1.22341i | ||||
\(687\) | −11.0227 | + | 11.0227i | −0.420542 | + | 0.420542i | ||||
\(688\) | 16.7303 | − | 4.48288i | 0.637838 | − | 0.170908i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.50000 | + | 4.33013i | 0.285313 | + | 0.164726i | 0.635826 | − | 0.771832i | \(-0.280659\pi\) |
−0.350513 | + | 0.936558i | \(0.613993\pi\) | |||||||
\(692\) | −4.24264 | − | 4.24264i | −0.161281 | − | 0.161281i | ||||
\(693\) | −14.2808 | + | 6.93237i | −0.542484 | + | 0.263339i | ||||
\(694\) | 36.0000i | 1.36654i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.10583 | + | 11.5911i | 0.117557 | + | 0.438730i | ||||
\(699\) | −3.46410 | −0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −2.24144 | − | 8.36516i | −0.0845977 | − | 0.315723i | ||||
\(703\) | −43.4667 | − | 11.6469i | −1.63938 | − | 0.439270i | ||||
\(704\) | −5.19615 | + | 3.00000i | −0.195837 | + | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3923i | 0.391120i | ||||||||
\(707\) | −7.58871 | − | 5.13922i | −0.285403 | − | 0.193280i | ||||
\(708\) | −4.89898 | − | 4.89898i | −0.184115 | − | 0.184115i | ||||
\(709\) | −14.7224 | − | 8.50000i | −0.552913 | − | 0.319224i | 0.197383 | − | 0.980326i | \(-0.436756\pi\) |
−0.750296 | + | 0.661102i | \(0.770089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 23.1822 | − | 6.21166i | 0.868790 | − | 0.232792i | ||||
\(713\) | 8.48528 | − | 8.48528i | 0.317776 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7589 | − | 40.1528i | 0.401519 | − | 1.49849i | ||||
\(719\) | 5.19615 | − | 9.00000i | 0.193784 | − | 0.335643i | −0.752717 | − | 0.658344i | \(-0.771257\pi\) |
0.946501 | + | 0.322700i | \(0.104591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | + | 12.1244i | −0.521387 | + | 0.451535i | ||||
\(722\) | −9.79796 | + | 9.79796i | −0.364642 | + | 0.364642i | ||||
\(723\) | −1.67303 | + | 0.448288i | −0.0622208 | + | 0.0166720i | ||||
\(724\) | −6.92820 | − | 12.0000i | −0.257485 | − | 0.445976i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −37.5000 | − | 21.6506i | −1.39176 | − | 0.803530i | ||||
\(727\) | −13.4350 | − | 13.4350i | −0.498278 | − | 0.498278i | 0.412624 | − | 0.910902i | \(-0.364612\pi\) |
−0.910902 | + | 0.412624i | \(0.864612\pi\) | |||||||
\(728\) | 10.0060 | + | 20.6126i | 0.370847 | + | 0.763954i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.67303 | − | 0.448288i | −0.0618371 | − | 0.0165692i | ||||
\(733\) | −4.91756 | − | 18.3526i | −0.181634 | − | 0.677868i | −0.995326 | − | 0.0965718i | \(-0.969212\pi\) |
0.813692 | − | 0.581297i | \(-0.197454\pi\) | |||||||
\(734\) | −27.7128 | −1.02290 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.0000 | 0.663489 | ||||||||
\(737\) | 13.4486 | + | 50.1910i | 0.495387 | + | 1.84881i | ||||
\(738\) | −17.3867 | − | 4.65874i | −0.640012 | − | 0.171491i | ||||
\(739\) | 37.2391 | − | 21.5000i | 1.36986 | − | 0.790890i | 0.378952 | − | 0.925416i | \(-0.376285\pi\) |
0.990910 | + | 0.134526i | \(0.0429512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.9808i | 0.954427i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.34847 | − | 7.34847i | −0.269589 | − | 0.269589i | 0.559345 | − | 0.828935i | \(-0.311053\pi\) |
−0.828935 | + | 0.559345i | \(0.811053\pi\) | |||||||
\(744\) | 5.19615 | + | 3.00000i | 0.190500 | + | 0.109985i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.50000 | + | 7.79423i | 0.164757 | + | 0.285367i | ||||
\(747\) | −11.5911 | + | 3.10583i | −0.424097 | + | 0.113636i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8564 | − | 12.0000i | 0.506302 | − | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.50000 | − | 16.4545i | 0.346660 | − | 0.600433i | −0.638994 | − | 0.769212i | \(-0.720649\pi\) |
0.985654 | + | 0.168779i | \(0.0539825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.48288 | + | 16.7303i | −0.163365 | + | 0.609687i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | + | 2.59808i | 0.0181848 | + | 0.0944911i | ||||
\(757\) | 6.12372 | − | 6.12372i | 0.222571 | − | 0.222571i | −0.587009 | − | 0.809580i | \(-0.699695\pi\) |
0.809580 | + | 0.587009i | \(0.199695\pi\) | |||||||
\(758\) | 8.36516 | − | 2.24144i | 0.303836 | − | 0.0814127i | ||||
\(759\) | −10.3923 | − | 18.0000i | −0.377217 | − | 0.653359i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.0000 | + | 20.7846i | 1.30500 | + | 0.753442i | 0.981257 | − | 0.192704i | \(-0.0617257\pi\) |
0.323742 | + | 0.946145i | \(0.395059\pi\) | |||||||
\(762\) | 6.36396 | + | 6.36396i | 0.230542 | + | 0.230542i | ||||
\(763\) | 15.3347 | + | 10.3849i | 0.555153 | + | 0.375960i | ||||
\(764\) | − | 6.00000i | − | 0.217072i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.0000 | + | 15.5885i | −0.975550 | + | 0.563234i | ||||
\(767\) | 33.4607 | + | 8.96575i | 1.20819 | + | 0.323735i | ||||
\(768\) | 4.91756 | + | 18.3526i | 0.177447 | + | 0.662242i | ||||
\(769\) | −6.92820 | −0.249837 | −0.124919 | − | 0.992167i | \(-0.539867\pi\) | ||||
−0.124919 | + | 0.992167i | \(0.539867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 5.37945 | + | 20.0764i | 0.193611 | + | 0.722565i | ||||
\(773\) | 34.7733 | + | 9.31749i | 1.25071 | + | 0.335127i | 0.822611 | − | 0.568605i | \(-0.192517\pi\) |
0.428099 | + | 0.903732i | \(0.359183\pi\) | |||||||
\(774\) | −5.19615 | + | 3.00000i | −0.186772 | + | 0.107833i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.66025i | 0.310885i | ||||||||
\(777\) | 20.6126 | − | 10.0060i | 0.739473 | − | 0.358964i | ||||
\(778\) | −36.7423 | − | 36.7423i | −1.31728 | − | 1.31728i | ||||
\(779\) | 46.7654 | + | 27.0000i | 1.67554 | + | 0.967375i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | + | 62.3538i | 1.28818 | + | 2.23120i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.9904 | − | 32.5000i | −0.463942 | − | 1.16071i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00000 | + | 5.19615i | −0.107006 | + | 0.185341i | ||||
\(787\) | 1.29410 | − | 4.82963i | 0.0461295 | − | 0.172158i | −0.939018 | − | 0.343868i | \(-0.888263\pi\) |
0.985147 | + | 0.171710i | \(0.0549293\pi\) | |||||||
\(788\) | −3.58630 | + | 13.3843i | −0.127757 | + | 0.476795i | ||||
\(789\) | −6.92820 | + | 12.0000i | −0.246651 | + | 0.427211i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.0000 | + | 43.3013i | −0.533339 | + | 1.53962i | ||||
\(792\) | 7.34847 | − | 7.34847i | 0.261116 | − | 0.261116i | ||||
\(793\) | 8.36516 | − | 2.24144i | 0.297056 | − | 0.0795958i | ||||
\(794\) | 1.73205 | + | 3.00000i | 0.0614682 | + | 0.106466i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.5000 | + | 7.79423i | 0.478495 | + | 0.276259i | ||||
\(797\) | 4.24264 | + | 4.24264i | 0.150282 | + | 0.150282i | 0.778244 | − | 0.627962i | \(-0.216111\pi\) |
−0.627962 | + | 0.778244i | \(0.716111\pi\) | |||||||
\(798\) | 1.70522 | − | 23.7506i | 0.0603641 | − | 0.840763i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | + | 6.92820i | −0.423999 | + | 0.244796i | ||||
\(802\) | 10.0382 | + | 2.68973i | 0.354461 | + | 0.0949775i | ||||
\(803\) | 10.8704 | + | 40.5689i | 0.383608 | + | 1.43164i | ||||
\(804\) | 8.66025 | 0.305424 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.0000 | 1.05670 | ||||||||
\(807\) | −0.896575 | − | 3.34607i | −0.0315610 | − | 0.117787i | ||||
\(808\) | 5.79555 | + | 1.55291i | 0.203887 | + | 0.0546313i | ||||
\(809\) | −25.9808 | + | 15.0000i | −0.913435 | + | 0.527372i | −0.881535 | − | 0.472119i | \(-0.843489\pi\) |
−0.0319002 | + | 0.999491i | \(0.510156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.5167i | − | 0.790667i | −0.918538 | − | 0.395333i | \(-0.870629\pi\) | ||
0.918538 | − | 0.395333i | \(-0.129371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.34847 | − | 7.34847i | −0.257722 | − | 0.257722i | ||||
\(814\) | 77.9423 | + | 45.0000i | 2.73188 | + | 1.57725i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3867 | − | 4.65874i | 0.608282 | − | 0.162989i | ||||
\(818\) | −6.36396 | + | 6.36396i | −0.222511 | + | 0.222511i | ||||
\(819\) | −8.66025 | − | 10.0000i | −0.302614 | − | 0.349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 1.55291 | − | 5.79555i | 0.0541641 | − | 0.202143i | ||||
\(823\) | 4.03459 | − | 15.0573i | 0.140637 | − | 0.524864i | −0.859274 | − | 0.511516i | \(-0.829084\pi\) |
0.999911 | − | 0.0133486i | \(-0.00424911\pi\) | |||||||
\(824\) | 6.06218 | − | 10.5000i | 0.211186 | − | 0.365785i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | − | 10.3923i | −1.04383 | − | 0.361595i | ||||
\(827\) | 29.3939 | − | 29.3939i | 1.02213 | − | 1.02213i | 0.0223756 | − | 0.999750i | \(-0.492877\pi\) |
0.999750 | − | 0.0223756i | \(-0.00712297\pi\) | |||||||
\(828\) | −3.34607 | + | 0.896575i | −0.116284 | + | 0.0311582i | ||||
\(829\) | 19.9186 | + | 34.5000i | 0.691801 | + | 1.19823i | 0.971247 | + | 0.238073i | \(0.0765158\pi\) |
−0.279446 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.50000 | − | 2.59808i | −0.156103 | − | 0.0901263i | ||||
\(832\) | −3.53553 | − | 3.53553i | −0.122573 | − | 0.122573i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 39.0000i | 1.35046i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27.0000 | − | 15.5885i | 0.933815 | − | 0.539138i | ||||
\(837\) | −3.34607 | − | 0.896575i | −0.115657 | − | 0.0309902i | ||||
\(838\) | −1.55291 | − | 5.79555i | −0.0536445 | − | 0.200204i | ||||
\(839\) | −45.0333 | −1.55472 | −0.777361 | − | 0.629054i | \(-0.783442\pi\) | ||||
−0.777361 | + | 0.629054i | \(0.783442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 7.62089 | + | 28.4416i | 0.262633 | + | 0.980161i | ||||
\(843\) | 23.1822 | + | 6.21166i | 0.798438 | + | 0.213941i | ||||
\(844\) | −16.4545 | + | 9.50000i | −0.566387 | + | 0.327003i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −65.9740 | − | 4.73672i | −2.26689 | − | 0.162756i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.866025 | + | 0.500000i | 0.0297219 | + | 0.0171600i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0000 | + | 25.9808i | 0.514193 | + | 0.890609i | ||||
\(852\) | 11.5911 | − | 3.10583i | 0.397105 | − | 0.106404i | ||||
\(853\) | −1.41421 | + | 1.41421i | −0.0484218 | + | 0.0484218i | −0.730903 | − | 0.682481i | \(-0.760901\pi\) |
0.682481 | + | 0.730903i | \(0.260901\pi\) | |||||||
\(854\) | −7.79423 | + | 1.50000i | −0.266713 | + | 0.0513289i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | 4.65874 | − | 17.3867i | 0.159140 | − | 0.593917i | −0.839576 | − | 0.543243i | \(-0.817196\pi\) |
0.998715 | − | 0.0506743i | \(-0.0161370\pi\) | |||||||
\(858\) | 13.4486 | − | 50.1910i | 0.459129 | − | 1.71349i | ||||
\(859\) | −22.5167 | + | 39.0000i | −0.768259 | + | 1.33066i | 0.170248 | + | 0.985401i | \(0.445543\pi\) |
−0.938506 | + | 0.345262i | \(0.887790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.0000 | + | 5.19615i | −0.920158 | + | 0.177084i | ||||
\(862\) | 36.7423 | − | 36.7423i | 1.25145 | − | 1.25145i | ||||
\(863\) | −26.7685 | + | 7.17260i | −0.911211 | + | 0.244158i | −0.683825 | − | 0.729646i | \(-0.739685\pi\) |
−0.227386 | + | 0.973805i | \(0.573018\pi\) | |||||||
\(864\) | −2.59808 | − | 4.50000i | −0.0883883 | − | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.00000 | − | 1.73205i | −0.101944 | − | 0.0588575i | ||||
\(867\) | −12.0208 | − | 12.0208i | −0.408248 | − | 0.408248i | ||||
\(868\) | −9.14162 | − | 0.656339i | −0.310287 | − | 0.0222776i | ||||
\(869\) | − | 66.0000i | − | 2.23890i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.5000 | + | 21.6506i | −1.27064 | + | 0.733604i | ||||
\(872\) | −11.7112 | − | 3.13801i | −0.396592 | − | 0.106267i | ||||
\(873\) | −1.29410 | − | 4.82963i | −0.0437985 | − | 0.163458i | ||||
\(874\) | 31.1769 | 1.05457 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.00000 | 0.236508 | ||||||||
\(877\) | −6.72432 | − | 25.0955i | −0.227064 | − | 0.847414i | −0.981567 | − | 0.191118i | \(-0.938789\pi\) |
0.754503 | − | 0.656297i | \(-0.227878\pi\) | |||||||
\(878\) | −31.8756 | − | 8.54103i | −1.07575 | − | 0.288246i | ||||
\(879\) | −20.7846 | + | 12.0000i | −0.701047 | + | 0.404750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 48.4974i | − | 1.63392i | −0.576695 | − | 0.816960i | \(-0.695658\pi\) | ||
0.576695 | − | 0.816960i | \(-0.304342\pi\) | |||||||
\(882\) | 7.26054 | + | 9.71003i | 0.244475 | + | 0.326954i | ||||
\(883\) | 3.67423 | + | 3.67423i | 0.123648 | + | 0.123648i | 0.766223 | − | 0.642575i | \(-0.222134\pi\) |
−0.642575 | + | 0.766223i | \(0.722134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.0000 | + | 36.3731i | 0.705509 | + | 1.22198i | ||||
\(887\) | 17.3867 | − | 4.65874i | 0.583787 | − | 0.156425i | 0.0451749 | − | 0.998979i | \(-0.485615\pi\) |
0.538612 | + | 0.842554i | \(0.318949\pi\) | |||||||
\(888\) | −10.6066 | + | 10.6066i | −0.355934 | + | 0.355934i | ||||
\(889\) | 12.9904 | + | 4.50000i | 0.435683 | + | 0.150925i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | + | 5.19615i | −0.100504 | + | 0.174078i | ||||
\(892\) | −5.95284 | + | 22.2163i | −0.199316 | + | 0.743857i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.19615 | − | 9.00000i | 0.173785 | − | 0.301005i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21.0000 | + | 24.2487i | 0.701561 | + | 0.810093i | ||||
\(897\) | 12.2474 | − | 12.2474i | 0.408930 | − | 0.408930i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −76.3675 | − | 76.3675i | −2.54276 | − | 2.54276i | ||||
\(903\) | −5.13922 | + | 7.58871i | −0.171022 | + | 0.252536i | ||||
\(904\) | − | 30.0000i | − | 0.997785i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 25.5000 | − | 14.7224i | 0.847181 | − | 0.489120i | ||||
\(907\) | 5.01910 | + | 1.34486i | 0.166656 | + | 0.0446554i | 0.341182 | − | 0.939997i | \(-0.389173\pi\) |
−0.174526 | + | 0.984653i | \(0.555839\pi\) | |||||||
\(908\) | 6.21166 | + | 23.1822i | 0.206141 | + | 0.769329i | ||||
\(909\) | −3.46410 | −0.114897 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 6.72432 | + | 25.0955i | 0.222664 | + | 0.830995i | ||||
\(913\) | −69.5467 | − | 18.6350i | −2.30166 | − | 0.616728i | ||||
\(914\) | −28.5788 | + | 16.5000i | −0.945304 | + | 0.545771i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.5885i | 0.515057i | ||||||||
\(917\) | −0.656339 | + | 9.14162i | −0.0216742 | + | 0.301883i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7128 | − | 16.0000i | −0.914161 | − | 0.527791i | −0.0323936 | − | 0.999475i | \(-0.510313\pi\) |
−0.881768 | + | 0.471684i | \(0.843646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | − | 27.7128i | −0.527218 | − | 0.913168i | ||||
\(922\) | 5.79555 | − | 1.55291i | 0.190866 | − | 0.0511425i | ||||
\(923\) | −42.4264 | + | 42.4264i | −1.39648 | + | 1.39648i | ||||
\(924\) | −5.19615 | + | 15.0000i | −0.170941 | + | 0.493464i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.50000 | − | 12.9904i | 0.246465 | − | 0.426890i | ||||
\(927\) | −1.81173 | + | 6.76148i | −0.0595051 | + | 0.222076i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1244 | − | 21.0000i | 0.397787 | − | 0.688988i | −0.595665 | − | 0.803233i | \(-0.703112\pi\) |
0.993453 | + | 0.114245i | \(0.0364449\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.5000 | − | 33.7750i | −0.442445 | − | 1.10693i | ||||
\(932\) | −2.44949 | + | 2.44949i | −0.0802357 | + | 0.0802357i | ||||
\(933\) | 16.7303 | − | 4.48288i | 0.547726 | − | 0.146763i | ||||
\(934\) | −5.19615 | − | 9.00000i | −0.170023 | − | 0.294489i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.50000 | + | 4.33013i | 0.245145 | + | 0.141535i | ||||
\(937\) | 7.07107 | + | 7.07107i | 0.231002 | + | 0.231002i | 0.813111 | − | 0.582109i | \(-0.197772\pi\) |
−0.582109 | + | 0.813111i | \(0.697772\pi\) | |||||||
\(938\) | 35.7021 | − | 17.3309i | 1.16571 | − | 0.565875i | ||||
\(939\) | − | 26.0000i | − | 0.848478i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 1.73205i | −0.0977972 | + | 0.0564632i | −0.548101 | − | 0.836412i | \(-0.684649\pi\) |
0.450304 | + | 0.892875i | \(0.351316\pi\) | |||||||
\(942\) | −38.4797 | − | 10.3106i | −1.25374 | − | 0.335938i | ||||
\(943\) | −9.31749 | − | 34.7733i | −0.303419 | − | 1.13238i | ||||
\(944\) | 34.6410 | 1.12747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.0000 | −1.17046 | ||||||||
\(947\) | 13.4486 | + | 50.1910i | 0.437022 | + | 1.63099i | 0.736181 | + | 0.676784i | \(0.236627\pi\) |
−0.299159 | + | 0.954203i | \(0.596706\pi\) | |||||||
\(948\) | −10.6252 | − | 2.84701i | −0.345090 | − | 0.0924666i | ||||
\(949\) | −30.3109 | + | 17.5000i | −0.983933 | + | 0.568074i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2474 | + | 12.2474i | 0.396734 | + | 0.396734i | 0.877079 | − | 0.480346i | \(-0.159489\pi\) |
−0.480346 | + | 0.877079i | \(0.659489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.9411 | − | 33.9411i | 1.09659 | − | 1.09659i | ||||
\(959\) | −1.73205 | − | 9.00000i | −0.0559308 | − | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | + | 16.4545i | −0.306452 | + | 0.530790i | ||||
\(962\) | −19.4114 | + | 72.4444i | −0.625850 | + | 2.33570i | ||||
\(963\) | 1.79315 | − | 6.69213i | 0.0577835 | − | 0.215651i | ||||
\(964\) | −0.866025 | + | 1.50000i | −0.0278928 | + | 0.0483117i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0000 | + | 10.3923i | −0.386094 | + | 0.334367i | ||||
\(967\) | −15.9217 | + | 15.9217i | −0.512007 | + | 0.512007i | −0.915141 | − | 0.403134i | \(-0.867921\pi\) |
0.403134 | + | 0.915141i | \(0.367921\pi\) | |||||||
\(968\) | 41.8258 | − | 11.2072i | 1.34433 | − | 0.360213i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0000 | − | 19.0526i | −1.05902 | − | 0.611426i | −0.133859 | − | 0.991000i | \(-0.542737\pi\) |
−0.925161 | + | 0.379575i | \(0.876070\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 26.0156 | + | 53.5928i | 0.834023 | + | 1.71811i | ||||
\(974\) | 42.0000i | 1.34577i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.50000 | − | 4.33013i | 0.240069 | − | 0.138604i | ||||
\(977\) | −3.34607 | − | 0.896575i | −0.107050 | − | 0.0286840i | 0.204896 | − | 0.978784i | \(-0.434314\pi\) |
−0.311946 | + | 0.950100i | \(0.600981\pi\) | |||||||
\(978\) | 0.776457 | + | 2.89778i | 0.0248284 | + | 0.0926607i | ||||
\(979\) | −83.1384 | −2.65712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00000 | 0.223493 | ||||||||
\(982\) | 8.06918 | + | 30.1146i | 0.257498 | + | 0.960995i | ||||
\(983\) | 34.7733 | + | 9.31749i | 1.10910 | + | 0.297182i | 0.766464 | − | 0.642288i | \(-0.222015\pi\) |
0.342633 | + | 0.939469i | \(0.388681\pi\) | |||||||
\(984\) | 15.5885 | − | 9.00000i | 0.496942 | − | 0.286910i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.3712 | + | 18.3712i | 0.584465 | + | 0.584465i | ||||
\(989\) | −10.3923 | − | 6.00000i | −0.330456 | − | 0.190789i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | − | 34.6410i | −0.635321 | − | 1.10041i | −0.986447 | − | 0.164080i | \(-0.947534\pi\) |
0.351126 | − | 0.936328i | \(-0.385799\pi\) | |||||||
\(992\) | 17.3867 | − | 4.65874i | 0.552027 | − | 0.147915i | ||||
\(993\) | 9.19239 | − | 9.19239i | 0.291712 | − | 0.291712i | ||||
\(994\) | 41.5692 | − | 36.0000i | 1.31850 | − | 1.14185i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | −9.05867 | + | 33.8074i | −0.286891 | + | 1.07069i | 0.660556 | + | 0.750777i | \(0.270321\pi\) |
−0.947447 | + | 0.319914i | \(0.896346\pi\) | |||||||
\(998\) | 10.3106 | − | 38.4797i | 0.326377 | − | 1.21806i | ||||
\(999\) | 4.33013 | − | 7.50000i | 0.136999 | − | 0.237289i |
(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 | 525.2.bc.b.418.1 | yes | 8 | |
5.2 | odd | 4 | inner | 525.2.bc.b.82.2 | yes | 8 | |
5.3 | odd | 4 | inner | 525.2.bc.b.82.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 525.2.bc.b.418.2 | yes | 8 | |
7.3 | odd | 6 | inner | 525.2.bc.b.493.2 | yes | 8 | |
35.3 | even | 12 | inner | 525.2.bc.b.157.2 | yes | 8 | |
35.17 | even | 12 | inner | 525.2.bc.b.157.1 | yes | 8 | |
35.24 | odd | 6 | inner | 525.2.bc.b.493.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bc.b.82.1 | ✓ | 8 | 5.3 | odd | 4 | inner | |
525.2.bc.b.82.2 | yes | 8 | 5.2 | odd | 4 | inner | |
525.2.bc.b.157.1 | yes | 8 | 35.17 | even | 12 | inner | |
525.2.bc.b.157.2 | yes | 8 | 35.3 | even | 12 | inner | |
525.2.bc.b.418.1 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bc.b.418.2 | yes | 8 | 5.4 | even | 2 | inner | |
525.2.bc.b.493.1 | yes | 8 | 35.24 | odd | 6 | inner | |
525.2.bc.b.493.2 | yes | 8 | 7.3 | odd | 6 | inner |