Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(569,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 569.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.569 |
Dual form | 980.2.q.c.949.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.59808 | + | 1.50000i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.133975 | + | 2.23205i | −0.0599153 | + | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | − | 6.00000i | −0.774597 | − | 1.54919i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.33013 | + | 2.50000i | −1.05021 | + | 0.606339i | −0.922708 | − | 0.385499i | \(-0.874029\pi\) |
−0.127502 | + | 0.991838i | \(0.540696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 6.92820i | 0.917663 | − | 1.58944i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.73205 | − | 1.00000i | −0.361158 | − | 0.208514i | 0.308431 | − | 0.951247i | \(-0.400196\pi\) |
−0.669588 | + | 0.742732i | \(0.733529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.00000i | 1.73205i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.79423 | + | 4.50000i | 1.35680 | + | 0.783349i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.66025 | + | 5.00000i | 1.42374 | + | 0.821995i | 0.996616 | − | 0.0821995i | \(-0.0261945\pi\) |
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | + | 2.59808i | 0.240192 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1962 | + | 7.39230i | 1.66902 | + | 1.10198i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.52628 | − | 5.50000i | −1.38955 | − | 0.802257i | −0.396286 | − | 0.918127i | \(-0.629701\pi\) |
−0.993264 | + | 0.115870i | \(0.963035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.50000 | − | 12.9904i | 1.05021 | − | 1.81902i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.19615 | − | 3.00000i | 0.713746 | − | 0.412082i | −0.0987002 | − | 0.995117i | \(-0.531468\pi\) |
0.812447 | + | 0.583036i | \(0.198135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | − | 3.00000i | 0.809040 | − | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.0000i | 3.17888i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | + | 8.66025i | 0.650945 | + | 1.12747i | 0.982894 | + | 0.184172i | \(0.0589603\pi\) |
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23205 | + | 0.133975i | 0.276852 | + | 0.0166175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.66025 | − | 5.00000i | 1.05802 | − | 0.610847i | 0.133135 | − | 0.991098i | \(-0.457496\pi\) |
0.924883 | + | 0.380251i | \(0.124162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66025 | − | 5.00000i | 1.01361 | − | 0.585206i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
0.912245 | + | 0.409644i | \(0.134347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.7942 | − | 5.89230i | 1.59282 | − | 0.680385i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50000 | + | 6.06218i | −0.393781 | + | 0.682048i | −0.992945 | − | 0.118578i | \(-0.962166\pi\) |
0.599164 | + | 0.800626i | \(0.295500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | − | 10.0000i | −0.542326 | − | 1.08465i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.59808 | + | 1.50000i | −0.278543 | + | 0.160817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.00000 | + | 6.92820i | −0.423999 | + | 0.734388i | −0.996326 | − | 0.0856373i | \(-0.972707\pi\) |
0.572327 | + | 0.820025i | \(0.306041\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19615 | + | 3.00000i | 0.538816 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.9282 | + | 9.85641i | 1.53160 | + | 1.01125i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000i | 0.304604i | 0.988334 | + | 0.152302i | \(0.0486686\pi\) | ||||
−0.988334 | + | 0.152302i | \(0.951331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.0000 | −1.80907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33013 | − | 2.50000i | −0.426660 | − | 0.246332i | 0.271263 | − | 0.962505i | \(-0.412559\pi\) |
−0.697923 | + | 0.716173i | \(0.745892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | + | 4.00000i | 0.669775 | + | 0.386695i | 0.795991 | − | 0.605308i | \(-0.206950\pi\) |
−0.126217 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.0000 | −2.84747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.0000i | − | 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46410 | − | 3.73205i | 0.229779 | − | 0.348016i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.19615 | − | 3.00000i | −0.480384 | − | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.5885 | + | 9.00000i | −1.40556 | + | 0.811503i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | + | 10.3923i | 0.528271 | + | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | − | 1.73205i | 0.0873704 | − | 0.151330i | −0.819028 | − | 0.573753i | \(-0.805487\pi\) |
0.906399 | + | 0.422423i | \(0.138820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.0885 | − | 1.20577i | −1.72894 | − | 0.103776i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.46410 | + | 2.00000i | −0.295958 | + | 0.170872i | −0.640626 | − | 0.767853i | \(-0.721325\pi\) |
0.344668 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.0000 | 2.77910 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.59808 | + | 1.50000i | −0.217262 | + | 0.125436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.133975 | + | 2.23205i | −0.0111260 | + | 0.185362i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | − | 7.79423i | −0.366205 | − | 0.634285i | 0.622764 | − | 0.782410i | \(-0.286010\pi\) |
−0.988969 | + | 0.148124i | \(0.952676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 30.0000i | 2.42536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | − | 2.00000i | 0.321288 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5885 | + | 9.00000i | −1.24409 | + | 0.718278i | −0.969925 | − | 0.243403i | \(-0.921736\pi\) |
−0.274169 | + | 0.961681i | \(0.588403\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | + | 15.5885i | −0.713746 | + | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.19615 | − | 3.00000i | −0.406994 | − | 0.234978i | 0.282503 | − | 0.959266i | \(-0.408835\pi\) |
−0.689497 | + | 0.724288i | \(0.742169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0885 | + | 16.7942i | −0.863235 | + | 1.30743i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.0000 | − | 41.5692i | −1.83533 | − | 3.17888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.79423 | − | 4.50000i | −0.592584 | − | 0.342129i | 0.173534 | − | 0.984828i | \(-0.444481\pi\) |
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.9808 | − | 15.0000i | −1.95283 | − | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3205 | + | 18.6603i | −0.905822 | + | 1.37193i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9904 | + | 7.50000i | 0.949951 | + | 0.548454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.50000 | + | 6.06218i | −0.253251 | + | 0.438644i | −0.964419 | − | 0.264378i | \(-0.914833\pi\) |
0.711168 | + | 0.703022i | \(0.248167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.92820 | − | 4.00000i | 0.498703 | − | 0.287926i | −0.229475 | − | 0.973315i | \(-0.573701\pi\) |
0.728178 | + | 0.685388i | \(0.240368\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | + | 3.00000i | −0.429669 | + | 0.214834i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.0000i | − | 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.00000 | − | 15.5885i | −0.637993 | − | 1.10504i | −0.985873 | − | 0.167497i | \(-0.946431\pi\) |
0.347879 | − | 0.937539i | \(-0.386902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0000 | + | 25.9808i | −1.05802 | + | 1.83254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.803848 | + | 13.3923i | −0.0561432 | + | 0.935359i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3923 | + | 6.00000i | −0.722315 | + | 0.417029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.92820 | + | 0.535898i | 0.608898 | + | 0.0365480i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0000 | + | 25.9808i | −1.01361 | + | 1.75562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | + | 4.33013i | 0.168168 | + | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.0000i | − | 1.27233i | −0.771551 | − | 0.636167i | \(-0.780519\pi\) | ||
0.771551 | − | 0.636167i | \(-0.219481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.0000 | + | 24.0000i | −1.20000 | + | 1.60000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3827 | − | 13.5000i | 1.55196 | − | 0.896026i | 0.553981 | − | 0.832529i | \(-0.313108\pi\) |
0.997982 | − | 0.0634974i | \(-0.0202255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8564 | − | 8.00000i | −0.907763 | − | 0.524097i | −0.0280525 | − | 0.999606i | \(-0.508931\pi\) |
−0.879711 | + | 0.475509i | \(0.842264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5526 | − | 20.5263i | 0.884071 | − | 1.33899i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 21.0000i | − | 1.36410i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.00000 | −0.323423 | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||||
−0.161712 | + | 0.986838i | \(0.551701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.00000 | − | 15.5885i | −0.579741 | − | 1.00414i | −0.995509 | − | 0.0946700i | \(-0.969820\pi\) |
0.415768 | − | 0.909471i | \(-0.363513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | − | 4.00000i | −0.440831 | − | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 31.1769i | 1.14070 | + | 1.97576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.9904 | + | 18.4808i | 1.75283 | + | 1.15731i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.19615 | − | 3.00000i | −0.324127 | − | 0.187135i | 0.329104 | − | 0.944294i | \(-0.393253\pi\) |
−0.653231 | + | 0.757159i | \(0.726587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 24.0000i | − | 1.46878i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.89230 | + | 13.7942i | 0.355319 | + | 0.831823i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1244 | − | 7.00000i | 0.728482 | − | 0.420589i | −0.0893846 | − | 0.995997i | \(-0.528490\pi\) |
0.817867 | + | 0.575408i | \(0.195157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000 | 0.894825 | 0.447412 | − | 0.894328i | \(-0.352346\pi\) | ||||
0.447412 | + | 0.894328i | \(0.352346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.06218 | − | 3.50000i | 0.360359 | − | 0.208053i | −0.308879 | − | 0.951101i | \(-0.599954\pi\) |
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −53.5692 | − | 3.21539i | −3.17317 | − | 0.190463i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | − | 7.79423i | −0.263795 | − | 0.456906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 15.0000i | − | 0.876309i | −0.898900 | − | 0.438155i | \(-0.855632\pi\) | ||
0.898900 | − | 0.438155i | \(-0.144368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0000 | + | 10.0000i | −1.16445 | + | 0.582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.3827 | − | 13.5000i | 1.35680 | − | 0.783349i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.1769 | + | 18.0000i | 1.79107 | + | 1.03407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.0000i | − | 1.08439i | −0.840254 | − | 0.542194i | \(-0.817594\pi\) | ||
0.840254 | − | 0.542194i | \(-0.182406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | + | 10.3923i | 0.340229 | + | 0.589294i | 0.984475 | − | 0.175525i | \(-0.0561621\pi\) |
−0.644246 | + | 0.764818i | \(0.722829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.06218 | − | 3.50000i | −0.342655 | − | 0.197832i | 0.318791 | − | 0.947825i | \(-0.396723\pi\) |
−0.661445 | + | 0.749993i | \(0.730057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2487 | + | 14.0000i | 1.36194 | + | 0.786318i | 0.989882 | − | 0.141890i | \(-0.0453179\pi\) |
0.372061 | + | 0.928208i | \(0.378651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.50000 | − | 2.59808i | −0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.0000i | 2.22566i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.598076 | + | 4.96410i | −0.0331753 | + | 0.275359i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.1865 | + | 10.5000i | 1.00572 | + | 0.580651i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51.9615 | − | 30.0000i | 2.84747 | − | 1.64399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0000 | + | 20.0000i | 0.546358 | + | 1.09272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.0000i | − | 1.19842i | −0.800593 | − | 0.599208i | \(-0.795482\pi\) | ||
0.800593 | − | 0.599208i | \(-0.204518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | + | 25.9808i | 0.814688 | + | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.803848 | + | 13.3923i | −0.0432777 | + | 0.721017i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.5885 | + | 9.00000i | −0.836832 | + | 0.483145i | −0.856186 | − | 0.516667i | \(-0.827172\pi\) |
0.0193540 | + | 0.999813i | \(0.493839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.0000 | 1.92704 | 0.963518 | − | 0.267644i | \(-0.0862451\pi\) | ||||
0.963518 | + | 0.267644i | \(0.0862451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.79423 | − | 4.50000i | 0.414845 | − | 0.239511i | −0.278024 | − | 0.960574i | \(-0.589680\pi\) |
0.692869 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0000 | − | 24.2487i | 0.738892 | − | 1.27980i | −0.214103 | − | 0.976811i | \(-0.568683\pi\) |
0.952995 | − | 0.302987i | \(-0.0979839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.00000i | 0.314918i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | + | 20.0000i | 0.523424 | + | 1.04685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4545 | − | 9.50000i | 0.858917 | − | 0.495896i | −0.00473247 | − | 0.999989i | \(-0.501506\pi\) |
0.863649 | + | 0.504093i | \(0.168173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.0000 | − | 31.1769i | 0.937043 | − | 1.62301i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7128 | − | 16.0000i | −1.43492 | − | 0.828449i | −0.437425 | − | 0.899255i | \(-0.644109\pi\) |
−0.997490 | + | 0.0708063i | \(0.977443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.3038 | + | 31.5788i | 0.583728 | + | 1.63072i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.00000i | − | 0.0515026i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | − | 5.19615i | −0.153695 | − | 0.266207i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.7846 | − | 12.0000i | −1.05654 | − | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.50000 | + | 7.79423i | 0.228159 | + | 0.395183i | 0.957263 | − | 0.289220i | \(-0.0933960\pi\) |
−0.729103 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000 | 0.505722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0622 | − | 8.62436i | −0.657229 | − | 0.433938i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7224 | + | 8.50000i | 0.738898 | + | 0.426603i | 0.821668 | − | 0.569966i | \(-0.193044\pi\) |
−0.0827707 | + | 0.996569i | \(0.526377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73205 | + | 1.00000i | −0.0862796 | + | 0.0498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | − | 9.00000i | 0.894427 | − | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 30.0000i | − | 1.48704i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | − | 3.46410i | −0.0988936 | − | 0.171289i | 0.812333 | − | 0.583193i | \(-0.198197\pi\) |
−0.911227 | + | 0.411905i | \(0.864864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.7846 | + | 1.60770i | 1.31480 | + | 0.0789187i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.9808 | + | 15.0000i | −1.27228 | + | 0.734553i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | 0.0977064 | 0.0488532 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488532 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −57.1577 | + | 33.0000i | −2.77910 | + | 1.60451i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.9904 | − | 9.82051i | 1.11520 | − | 0.476365i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.50000 | − | 7.79423i | 0.217262 | − | 0.376309i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.5000 | + | 32.0429i | 0.891114 | + | 1.54345i | 0.838542 | + | 0.544837i | \(0.183408\pi\) |
0.0525716 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.0000i | 1.82616i | 0.407777 | + | 0.913082i | \(0.366304\pi\) | ||||
−0.407777 | + | 0.913082i | \(0.633696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | − | 6.00000i | −0.143839 | − | 0.287678i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.8564 | + | 8.00000i | −0.662842 | + | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0000 | + | 22.5167i | −0.620456 | + | 1.07466i | 0.368945 | + | 0.929451i | \(0.379719\pi\) |
−0.989401 | + | 0.145210i | \(0.953614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3923 | − | 6.00000i | −0.493753 | − | 0.285069i | 0.232377 | − | 0.972626i | \(-0.425350\pi\) |
−0.726130 | + | 0.687557i | \(0.758683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.9282 | − | 9.85641i | −0.707665 | − | 0.467238i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 18.0000i | − | 0.851371i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.0000 | −0.519122 | −0.259561 | − | 0.965727i | \(-0.583578\pi\) | ||||
−0.259561 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.3827 | + | 13.5000i | 1.09861 | + | 0.634285i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0526 | − | 11.0000i | −0.891241 | − | 0.514558i | −0.0168929 | − | 0.999857i | \(-0.505377\pi\) |
−0.874348 | + | 0.485299i | \(0.838711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.5000 | − | 38.9711i | −1.05021 | − | 1.81902i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.39230 | + | 11.1962i | −0.342810 | + | 0.519209i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.9186 | + | 11.5000i | 0.921722 | + | 0.532157i | 0.884184 | − | 0.467139i | \(-0.154715\pi\) |
0.0375381 | + | 0.999295i | \(0.488048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.0000 | − | 46.7654i | 1.24409 | − | 2.15483i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3923 | + | 6.00000i | −0.477839 | + | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.0000 | + | 32.0000i | −1.10120 | + | 1.46826i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 36.0000i | − | 1.64833i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.69615 | − | 0.401924i | −0.304057 | − | 0.0182504i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.5167 | − | 13.0000i | 1.02033 | − | 0.589086i | 0.106129 | − | 0.994352i | \(-0.466154\pi\) |
0.914199 | + | 0.405266i | \(0.132821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0000 | 0.813988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0000 | 1.48927 | 0.744635 | − | 0.667472i | \(-0.232624\pi\) | ||||
0.744635 | + | 0.667472i | \(0.232624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.33013 | + | 2.50000i | −0.195019 | + | 0.112594i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.41154 | − | 40.1769i | 0.108391 | − | 1.80582i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5000 | + | 25.1147i | −0.649109 | + | 1.12429i | 0.334227 | + | 0.942493i | \(0.391525\pi\) |
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.50000 | − | 7.79423i | −0.201045 | − | 0.348220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.00000i | − | 0.0445878i | −0.999751 | − | 0.0222939i | \(-0.992903\pi\) | ||
0.999751 | − | 0.0222939i | \(-0.00709696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | − | 12.0000i | 1.06799 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.1769 | + | 18.0000i | −1.38462 | + | 0.799408i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0000 | + | 22.5167i | −0.576215 | + | 0.998033i | 0.419694 | + | 0.907666i | \(0.362138\pi\) |
−0.995908 | + | 0.0903676i | \(0.971196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 62.3538 | + | 36.0000i | 2.75299 | + | 1.58944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.16025 | − | 9.33013i | 0.271453 | − | 0.411135i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.0000i | 1.45134i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | 1.18517 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | + | 10.3923i | 0.262865 | + | 0.455295i | 0.967002 | − | 0.254769i | \(-0.0819994\pi\) |
−0.704137 | + | 0.710064i | \(0.748666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3205 | − | 10.0000i | −0.757373 | − | 0.437269i | 0.0709788 | − | 0.997478i | \(-0.477388\pi\) |
−0.828352 | + | 0.560208i | \(0.810721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.66025 | + | 5.00000i | 0.377247 | + | 0.217803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | − | 16.4545i | −0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.0000 | 2.60378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.00000i | − | 0.259889i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.85641 | + | 14.9282i | −0.426130 | + | 0.645403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.3923 | − | 6.00000i | −0.448461 | − | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.9808 | + | 15.0000i | −1.11494 | + | 0.643712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | − | 7.00000i | 0.599694 | − | 0.299847i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.01924 | − | 66.9615i | 0.170607 | − | 2.84236i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.3205 | + | 10.0000i | −0.733893 | + | 0.423714i | −0.819845 | − | 0.572586i | \(-0.805940\pi\) |
0.0859514 | + | 0.996299i | \(0.472607\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.0000 | −1.89990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.8564 | − | 8.00000i | 0.583978 | − | 0.337160i | −0.178735 | − | 0.983897i | \(-0.557200\pi\) |
0.762713 | + | 0.646737i | \(0.223867\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3205 | + | 1.33975i | 0.939031 | + | 0.0563635i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 21.0000i | − | 0.877288i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | + | 6.00000i | 0.333623 | + | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7224 | − | 8.50000i | 0.612903 | − | 0.353860i | −0.161198 | − | 0.986922i | \(-0.551536\pi\) |
0.774101 | + | 0.633062i | \(0.218202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0000 | + | 20.7846i | −0.498703 | + | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.5885 | − | 9.00000i | −0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.39230 | − | 11.1962i | 0.305634 | − | 0.462904i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | + | 25.9808i | 0.617018 | + | 1.06871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.59808 | − | 1.50000i | −0.106690 | − | 0.0615976i | 0.445705 | − | 0.895180i | \(-0.352953\pi\) |
−0.552396 | + | 0.833582i | \(0.686286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.7654 | + | 27.0000i | 1.91398 | + | 1.10504i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5000 | − | 18.1865i | −0.429018 | − | 0.743082i | 0.567768 | − | 0.823189i | \(-0.307807\pi\) |
−0.996786 | + | 0.0801071i | \(0.974474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 60.0000i | − | 2.44339i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.73205 | + | 2.46410i | 0.151729 | + | 0.100180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.33013 | − | 2.50000i | −0.175754 | − | 0.101472i | 0.409542 | − | 0.912291i | \(-0.365689\pi\) |
−0.585296 | + | 0.810819i | \(0.699022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.50000 | + | 9.52628i | −0.222506 | + | 0.385392i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3923 | + | 6.00000i | −0.419741 | + | 0.242338i | −0.694967 | − | 0.719042i | \(-0.744581\pi\) |
0.275225 | + | 0.961380i | \(0.411248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | − | 36.0000i | −0.725830 | − | 1.45166i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.00000 | + | 1.73205i | 0.0401934 | + | 0.0696170i | 0.885422 | − | 0.464787i | \(-0.153869\pi\) |
−0.845229 | + | 0.534404i | \(0.820536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.00000 | − | 15.5885i | 0.361158 | − | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 62.3538 | − | 36.0000i | 2.49017 | − | 1.43770i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.0000 | −1.99363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.79423 | − | 4.50000i | 0.309793 | − | 0.178859i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.46410 | − | 0.267949i | −0.177152 | − | 0.0106332i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.00000i | 0.197181i | 0.995128 | + | 0.0985904i | \(0.0314334\pi\) | ||||
−0.995128 | + | 0.0985904i | \(0.968567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | + | 12.0000i | −0.944999 | + | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | + | 12.0000i | −0.817127 | + | 0.471769i | −0.849425 | − | 0.527710i | \(-0.823051\pi\) |
0.0322975 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | − | 25.9808i | 0.588802 | − | 1.01983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1769 | − | 18.0000i | −1.22005 | − | 0.704394i | −0.255119 | − | 0.966910i | \(-0.582115\pi\) |
−0.964928 | + | 0.262515i | \(0.915448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.73205 | + | 2.46410i | 0.145823 | + | 0.0962804i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 60.0000i | − | 2.34082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.0000 | −1.51922 | −0.759612 | − | 0.650376i | \(-0.774611\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | + | 24.2487i | 0.544537 | + | 0.943166i | 0.998636 | + | 0.0522143i | \(0.0166279\pi\) |
−0.454099 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.9904 | − | 7.50000i | −0.504505 | − | 0.291276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.73205 | − | 1.00000i | −0.0670653 | − | 0.0387202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.5000 | + | 49.3634i | 1.10187 | + | 1.90850i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 16.0000i | − | 0.616755i | −0.951264 | − | 0.308377i | \(-0.900214\pi\) | ||
0.951264 | − | 0.308377i | \(-0.0997859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.38269 | − | 44.6769i | 0.207180 | − | 1.71962i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.52628 | + | 5.50000i | 0.366125 | + | 0.211382i | 0.671764 | − | 0.740765i | \(-0.265537\pi\) |
−0.305639 | + | 0.952147i | \(0.598870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.5000 | + | 70.1481i | −1.55196 | + | 2.68808i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.6410 | − | 20.0000i | 1.32550 | − | 0.765279i | 0.340901 | − | 0.940099i | \(-0.389268\pi\) |
0.984600 | + | 0.174820i | \(0.0559345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | − | 8.00000i | −0.152832 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 78.0000i | 2.97589i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.33975 | + | 22.3205i | −0.0508195 | + | 0.846665i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.9808 | + | 15.0000i | −0.984092 | + | 0.568166i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.0000 | 1.81553 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0000 | −0.944237 | −0.472118 | − | 0.881535i | \(-0.656511\pi\) | ||||
−0.472118 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69.2820 | − | 40.0000i | 2.61302 | − | 1.50863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.42116 | + | 73.6577i | −0.166511 | + | 2.77411i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.50000 | − | 12.9904i | 0.281668 | − | 0.487864i | −0.690127 | − | 0.723688i | \(-0.742446\pi\) |
0.971796 | + | 0.235824i | \(0.0757789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.0000 | + | 36.3731i | 0.787562 | + | 1.36410i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | − | 6.00000i | −0.112194 | − | 0.224387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.9904 | − | 7.50000i | 0.485135 | − | 0.280093i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.00000 | + | 1.73205i | −0.0372937 | + | 0.0645946i | −0.884070 | − | 0.467355i | \(-0.845207\pi\) |
0.846776 | + | 0.531949i | \(0.178540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.7654 | + | 27.0000i | 1.73922 | + | 1.00414i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.96410 | − | 0.598076i | −0.184362 | − | 0.0222120i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000i | 1.03846i | 0.854634 | + | 0.519231i | \(0.173782\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.5070 | + | 20.5000i | 1.31148 | + | 0.757185i | 0.982342 | − | 0.187096i | \(-0.0599076\pi\) |
0.329141 | + | 0.944281i | \(0.393241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9808 | − | 15.0000i | −0.957014 | − | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50000 | − | 4.33013i | −0.0919640 | − | 0.159286i | 0.816373 | − | 0.577524i | \(-0.195981\pi\) |
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | 0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.1962 | − | 7.39230i | −0.410195 | − | 0.270833i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.3538 | − | 36.0000i | −2.28141 | − | 1.31717i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | + | 11.2583i | −0.237188 | + | 0.410822i | −0.959906 | − | 0.280321i | \(-0.909559\pi\) |
0.722718 | + | 0.691143i | \(0.242893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.19615 | − | 3.00000i | 0.189358 | − | 0.109326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.0000 | − | 9.00000i | 0.655087 | − | 0.327544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0000i | 1.74459i | 0.488980 | + | 0.872295i | \(0.337369\pi\) | ||||
−0.488980 | + | 0.872295i | \(0.662631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | − | 15.5885i | −0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0000 | + | 32.9090i | −0.688749 | + | 1.19295i | 0.283493 | + | 0.958974i | \(0.408507\pi\) |
−0.972243 | + | 0.233975i | \(0.924827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −66.9615 | − | 4.01924i | −2.42100 | − | 0.145316i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.66025 | − | 5.00000i | 0.312704 | − | 0.180540i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3827 | − | 13.5000i | 0.841017 | − | 0.485561i | −0.0165929 | − | 0.999862i | \(-0.505282\pi\) |
0.857610 | + | 0.514301i | \(0.171949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.92820 | + | 9.19615i | 0.141105 | + | 0.330336i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | − | 41.5692i | 0.859889 | − | 1.48937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000i | 0.321634i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.0000 | − | 36.0000i | −0.642448 | − | 1.28490i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.59808 | − | 1.50000i | 0.0926114 | − | 0.0534692i | −0.452979 | − | 0.891521i | \(-0.649639\pi\) |
0.545590 | + | 0.838052i | \(0.316305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.0000 | − | 62.3538i | 1.28163 | − | 2.21986i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.5885 | − | 22.1769i | −1.19126 | − | 0.786534i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.0000i | 1.52314i | 0.648084 | + | 0.761569i | \(0.275571\pi\) | ||||
−0.648084 | + | 0.761569i | \(0.724429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.0000 | 1.94576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0000 | + | 41.5692i | 0.847998 | + | 1.46878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.9808 | − | 15.0000i | −0.916841 | − | 0.529339i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.19615 | + | 3.00000i | 0.182913 | + | 0.105605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.50000 | − | 9.52628i | −0.193370 | − | 0.334926i | 0.752995 | − | 0.658026i | \(-0.228608\pi\) |
−0.946365 | + | 0.323100i | \(0.895275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.00000 | −0.210688 | −0.105344 | − | 0.994436i | \(-0.533594\pi\) | ||||
−0.105344 | + | 0.994436i | \(0.533594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.39230 | − | 11.1962i | 0.258941 | − | 0.392184i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.7128 | − | 16.0000i | −0.969549 | − | 0.559769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5000 | + | 38.9711i | −0.785255 | + | 1.36010i | 0.143591 | + | 0.989637i | \(0.454135\pi\) |
−0.928846 | + | 0.370465i | \(0.879198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5885 | + | 9.00000i | −0.543379 | + | 0.313720i | −0.746447 | − | 0.665444i | \(-0.768242\pi\) |
0.203068 | + | 0.979165i | \(0.434909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.0000 | − | 27.0000i | −1.25336 | − | 0.940019i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0000 | − | 29.4449i | −0.590434 | − | 1.02266i | −0.994174 | − | 0.107788i | \(-0.965623\pi\) |
0.403739 | − | 0.914874i | \(-0.367710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0000 | + | 36.3731i | −0.728482 | + | 1.26177i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.69615 | − | 0.401924i | −0.231730 | − | 0.0139091i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.5885 | − | 9.00000i | 0.538816 | − | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.9711 | + | 22.5000i | −1.34224 | + | 0.774941i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.60770 | + | 26.7846i | −0.0553064 | + | 0.921419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5000 | + | 18.1865i | −0.360359 | + | 0.624160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0000 | − | 17.3205i | −0.342796 | − | 0.593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.0000i | − | 0.890223i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||
0.895475 | − | 0.445112i | \(-0.146836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 96.0000 | − | 48.0000i | 3.28313 | − | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0526 | + | 11.0000i | −0.650823 | + | 0.375753i | −0.788771 | − | 0.614687i | \(-0.789283\pi\) |
0.137948 | + | 0.990439i | \(0.455949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | + | 20.7846i | −0.409435 | + | 0.709162i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) |
0.585392 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.8372 | − | 23.0000i | −1.35607 | − | 0.782929i | −0.366981 | − | 0.930228i | \(-0.619609\pi\) |
−0.989092 | + | 0.147299i | \(0.952942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0885 | − | 16.7942i | 0.377019 | − | 0.571021i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.0000i | 0.815083i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 8.66025i | −0.169419 | − | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.5885 | + | 9.00000i | 0.527589 | + | 0.304604i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.6410 | + | 20.0000i | 1.16974 | + | 0.675352i | 0.953620 | − | 0.301014i | \(-0.0973250\pi\) |
0.216124 | + | 0.976366i | \(0.430658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5000 | + | 38.9711i | 0.758906 | + | 1.31446i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.0000 | 1.61716 | 0.808581 | − | 0.588386i | \(-0.200236\pi\) | ||||
0.808581 | + | 0.588386i | \(0.200236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.9615 | − | 55.9808i | 1.24245 | − | 1.88177i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3923 | − | 6.00000i | −0.348939 | − | 0.201460i | 0.315279 | − | 0.948999i | \(-0.397902\pi\) |
−0.664218 | + | 0.747539i | \(0.731235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −76.2102 | + | 44.0000i | −2.55028 | + | 1.47240i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | + | 4.00000i | −0.267411 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.00000i | − | 0.200334i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00000 | − | 1.73205i | −0.0333519 | − | 0.0577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0000 | + | 25.9808i | −0.499722 | + | 0.865545i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.33975 | + | 22.3205i | −0.0445347 | + | 0.741959i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.9090 | + | 19.0000i | −1.09272 | + | 0.630885i | −0.934300 | − | 0.356487i | \(-0.883975\pi\) |
−0.158424 | + | 0.987371i | \(0.550641\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −72.0000 | −2.38809 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.0000 | −1.72284 | −0.861418 | − | 0.507896i | \(-0.830423\pi\) | ||||
−0.861418 | + | 0.507896i | \(0.830423\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1769 | + | 18.0000i | −1.03181 | + | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.5000 | + | 47.6314i | −0.907141 | + | 1.57121i | −0.0891245 | + | 0.996020i | \(0.528407\pi\) |
−0.818017 | + | 0.575194i | \(0.804926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.5000 | + | 49.3634i | 0.939107 | + | 1.62658i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | − | 30.0000i | −1.31519 | − | 0.986394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.9808 | + | 15.0000i | −0.853320 | + | 0.492665i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.1769 | − | 18.0000i | −1.02069 | − | 0.589294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.4808 | + | 27.9904i | −0.604386 | + | 0.915383i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000i | 0.228680i | 0.993442 | + | 0.114340i | \(0.0364753\pi\) | ||||
−0.993442 | + | 0.114340i | \(0.963525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.0000 | 0.685309 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0000 | − | 34.6410i | −0.651981 | − | 1.12926i | −0.982641 | − | 0.185515i | \(-0.940605\pi\) |
0.330660 | − | 0.943750i | \(-0.392729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3923 | − | 6.00000i | −0.338420 | − | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.19615 | + | 3.00000i | 0.168852 | + | 0.0974869i | 0.582045 | − | 0.813157i | \(-0.302253\pi\) |
−0.413192 | + | 0.910644i | \(0.635586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −84.0000 | −2.72389 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.0000i | − | 1.36051i | −0.732974 | − | 0.680257i | \(-0.761868\pi\) | ||
0.732974 | − | 0.680257i | \(-0.238132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0622 | − | 8.62436i | −0.422682 | − | 0.279078i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.79423 | + | 4.50000i | 0.251952 | + | 0.145464i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.5692 | − | 24.0000i | 1.33955 | − | 0.773389i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | + | 16.0000i | 0.257529 | + | 0.515058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.0000 | − | 103.923i | −1.92748 | − | 3.33849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.00000 | − | 15.5885i | 0.288824 | − | 0.500257i | −0.684706 | − | 0.728820i | \(-0.740069\pi\) |
0.973529 | + | 0.228562i | \(0.0734025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.89230 | − | 13.7942i | −0.188705 | − | 0.441769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.9615 | − | 30.0000i | 1.66240 | − | 0.959785i | 0.690830 | − | 0.723017i | \(-0.257245\pi\) |
0.971566 | − | 0.236768i | \(-0.0760881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.0000 | −1.34096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.2583 | + | 6.50000i | −0.359085 | + | 0.207318i | −0.668679 | − | 0.743551i | \(-0.733140\pi\) |
0.309594 | + | 0.950869i | \(0.399807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3205 | + | 1.33975i | 0.711191 | + | 0.0426879i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 60.0000i | − | 1.90404i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | − | 18.0000i | 1.14128 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.8993 | + | 26.5000i | −1.45365 | + | 0.839263i | −0.998686 | − | 0.0512480i | \(-0.983680\pi\) |
−0.454961 | + | 0.890511i | \(0.650347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.0000 | + | 77.9423i | −1.42374 | + | 2.46598i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))