Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(68,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.l (of order \(12\), degree \(4\), 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: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 227.1 | ||
Root | \(-2.15988 + 0.578737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.227 |
Dual form | 245.2.l.c.68.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.258819 | + | 0.965926i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −2.15988 | + | 0.578737i | −1.24700 | + | 0.334134i | −0.821179 | − | 0.570671i | \(-0.806683\pi\) |
−0.425826 | + | 0.904805i | \(0.640016\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.578737 | + | 2.15988i | −0.258819 | + | 0.965926i | ||||
\(6\) | − | 3.16228i | − | 1.29099i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 1.73205 | − | 1.00000i | 0.577350 | − | 0.333333i | ||||
\(10\) | −2.73861 | − | 1.58114i | −0.866025 | − | 0.500000i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58114 | − | 1.58114i | −0.438529 | − | 0.438529i | 0.452988 | − | 0.891517i | \(-0.350358\pi\) |
−0.891517 | + | 0.452988i | \(0.850358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.00000i | − | 1.29099i | ||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0.578737 | + | 2.15988i | 0.140364 | + | 0.523847i | 0.999918 | + | 0.0128014i | \(0.00407493\pi\) |
−0.859554 | + | 0.511045i | \(0.829258\pi\) | |||||||
\(18\) | 0.732051 | + | 2.73205i | 0.172546 | + | 0.643951i | ||||
\(19\) | −1.58114 | − | 2.73861i | −0.362738 | − | 0.628281i | 0.625672 | − | 0.780086i | \(-0.284825\pi\) |
−0.988410 | + | 0.151805i | \(0.951491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | + | 1.00000i | 0.213201 | + | 0.213201i | ||||
\(23\) | −2.73205 | − | 0.732051i | −0.569672 | − | 0.152643i | −0.0375258 | − | 0.999296i | \(-0.511948\pi\) |
−0.532146 | + | 0.846653i | \(0.678614\pi\) | |||||||
\(24\) | 3.16228 | − | 5.47723i | 0.645497 | − | 1.11803i | ||||
\(25\) | −4.33013 | − | 2.50000i | −0.866025 | − | 0.500000i | ||||
\(26\) | 2.73861 | − | 1.58114i | 0.537086 | − | 0.310087i | ||||
\(27\) | 1.58114 | − | 1.58114i | 0.304290 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000i | 0.557086i | 0.960424 | + | 0.278543i | \(0.0898515\pi\) | ||||
−0.960424 | + | 0.278543i | \(0.910149\pi\) | |||||||
\(30\) | 6.83013 | + | 1.83013i | 1.24700 | + | 0.334134i | ||||
\(31\) | 2.73861 | + | 1.58114i | 0.491869 | + | 0.283981i | 0.725350 | − | 0.688381i | \(-0.241678\pi\) |
−0.233480 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.578737 | + | 2.15988i | −0.100745 | + | 0.375986i | ||||
\(34\) | −3.16228 | −0.542326 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.19615 | + | 8.19615i | −0.361045 | + | 1.34744i | 0.511658 | + | 0.859189i | \(0.329031\pi\) |
−0.872704 | + | 0.488250i | \(0.837635\pi\) | |||||||
\(38\) | 4.31975 | − | 1.15747i | 0.700756 | − | 0.187767i | ||||
\(39\) | 4.33013 | + | 2.50000i | 0.693375 | + | 0.400320i | ||||
\(40\) | −3.16228 | − | 5.47723i | −0.500000 | − | 0.866025i | ||||
\(41\) | 9.48683i | 1.48159i | 0.671729 | + | 0.740797i | \(0.265552\pi\) | ||||
−0.671729 | + | 0.740797i | \(0.734448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.15747 | + | 4.31975i | 0.172546 | + | 0.643951i | ||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | 6.47963 | + | 1.73621i | 0.945151 | + | 0.253252i | 0.698303 | − | 0.715802i | \(-0.253939\pi\) |
0.246847 | + | 0.969054i | \(0.420605\pi\) | |||||||
\(48\) | 6.32456 | + | 6.32456i | 0.912871 | + | 0.912871i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | − | 5.00000i | 0.707107 | − | 0.707107i | ||||
\(51\) | −2.50000 | − | 4.33013i | −0.350070 | − | 0.606339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.366025 | + | 1.36603i | 0.0502775 | + | 0.187638i | 0.986498 | − | 0.163776i | \(-0.0523675\pi\) |
−0.936220 | + | 0.351414i | \(0.885701\pi\) | |||||||
\(54\) | 1.58114 | + | 2.73861i | 0.215166 | + | 0.372678i | ||||
\(55\) | 1.58114 | + | 1.58114i | 0.213201 | + | 0.213201i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000 | + | 5.00000i | 0.662266 | + | 0.662266i | ||||
\(58\) | −4.09808 | − | 1.09808i | −0.538104 | − | 0.144184i | ||||
\(59\) | −4.74342 | + | 8.21584i | −0.617540 | + | 1.06961i | 0.372393 | + | 0.928075i | \(0.378537\pi\) |
−0.989933 | + | 0.141536i | \(0.954796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.47723 | + | 3.16228i | −0.701287 | + | 0.404888i | −0.807827 | − | 0.589420i | \(-0.799356\pi\) |
0.106540 | + | 0.994308i | \(0.466023\pi\) | |||||||
\(62\) | −3.16228 | + | 3.16228i | −0.401610 | + | 0.401610i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 4.33013 | − | 2.50000i | 0.537086 | − | 0.310087i | ||||
\(66\) | −2.73861 | − | 1.58114i | −0.337100 | − | 0.194625i | ||||
\(67\) | 1.36603 | − | 0.366025i | 0.166887 | − | 0.0447171i | −0.174408 | − | 0.984673i | \(-0.555801\pi\) |
0.341295 | + | 0.939956i | \(0.389135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.32456 | 0.761387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −1.46410 | + | 5.46410i | −0.172546 | + | 0.643951i | ||||
\(73\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(74\) | −10.3923 | − | 6.00000i | −1.20808 | − | 0.697486i | ||||
\(75\) | 10.7994 | + | 2.89368i | 1.24700 | + | 0.334134i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.00000 | + | 5.00000i | −0.566139 | + | 0.566139i | ||||
\(79\) | 11.2583 | − | 6.50000i | 1.26666 | − | 0.731307i | 0.292306 | − | 0.956325i | \(-0.405577\pi\) |
0.974355 | + | 0.225018i | \(0.0722440\pi\) | |||||||
\(80\) | 8.63950 | − | 2.31495i | 0.965926 | − | 0.258819i | ||||
\(81\) | −5.50000 | + | 9.52628i | −0.611111 | + | 1.05848i | ||||
\(82\) | −12.9593 | − | 3.47242i | −1.43111 | − | 0.383465i | ||||
\(83\) | −3.16228 | − | 3.16228i | −0.347105 | − | 0.347105i | 0.511925 | − | 0.859030i | \(-0.328933\pi\) |
−0.859030 | + | 0.511925i | \(0.828933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | −3.00000 | − | 5.19615i | −0.323498 | − | 0.560316i | ||||
\(87\) | −1.73621 | − | 6.47963i | −0.186141 | − | 0.694689i | ||||
\(88\) | 0.732051 | + | 2.73205i | 0.0780369 | + | 0.291238i | ||||
\(89\) | 3.16228 | + | 5.47723i | 0.335201 | + | 0.580585i | 0.983523 | − | 0.180781i | \(-0.0578625\pi\) |
−0.648323 | + | 0.761366i | \(0.724529\pi\) | |||||||
\(90\) | −6.32456 | −0.666667 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.83013 | − | 1.83013i | −0.708251 | − | 0.189775i | ||||
\(94\) | −4.74342 | + | 8.21584i | −0.489246 | + | 0.847399i | ||||
\(95\) | 6.83013 | − | 1.83013i | 0.700756 | − | 0.187767i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58114 | + | 1.58114i | −0.160540 | + | 0.160540i | −0.782806 | − | 0.622266i | \(-0.786212\pi\) |
0.622266 | + | 0.782806i | \(0.286212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.73861 | − | 1.58114i | −0.272502 | − | 0.157329i | 0.357522 | − | 0.933905i | \(-0.383622\pi\) |
−0.630024 | + | 0.776576i | \(0.716955\pi\) | |||||||
\(102\) | 6.83013 | − | 1.83013i | 0.676283 | − | 0.181210i | ||||
\(103\) | 4.05116 | − | 15.1191i | 0.399173 | − | 1.48973i | −0.415383 | − | 0.909647i | \(-0.636352\pi\) |
0.814556 | − | 0.580086i | \(-0.196981\pi\) | |||||||
\(104\) | 6.32456 | 0.620174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −1.09808 | + | 4.09808i | −0.106155 | + | 0.396176i | −0.998474 | − | 0.0552301i | \(-0.982411\pi\) |
0.892319 | + | 0.451406i | \(0.149077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.06218 | + | 3.50000i | 0.580651 | + | 0.335239i | 0.761392 | − | 0.648292i | \(-0.224516\pi\) |
−0.180741 | + | 0.983531i | \(0.557850\pi\) | |||||||
\(110\) | −2.73861 | + | 1.58114i | −0.261116 | + | 0.150756i | ||||
\(111\) | − | 18.9737i | − | 1.80090i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | − | 12.0000i | 1.12887 | − | 1.12887i | 0.138503 | − | 0.990362i | \(-0.455771\pi\) |
0.990362 | − | 0.138503i | \(-0.0442291\pi\) | |||||||
\(114\) | −8.66025 | + | 5.00000i | −0.811107 | + | 0.468293i | ||||
\(115\) | 3.16228 | − | 5.47723i | 0.294884 | − | 0.510754i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.31975 | − | 1.15747i | −0.399361 | − | 0.107009i | ||||
\(118\) | −9.48683 | − | 9.48683i | −0.873334 | − | 0.873334i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.0000 | + | 10.0000i | 0.912871 | + | 0.912871i | ||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −2.31495 | − | 8.63950i | −0.209586 | − | 0.782184i | ||||
\(123\) | −5.49038 | − | 20.4904i | −0.495051 | − | 1.84756i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | − | 7.90569i | 0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | + | 9.00000i | 0.798621 | + | 0.798621i | 0.982878 | − | 0.184257i | \(-0.0589879\pi\) |
−0.184257 | + | 0.982878i | \(0.558988\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.965926 | + | 0.258819i | ||||
\(129\) | 4.74342 | − | 8.21584i | 0.417635 | − | 0.723364i | ||||
\(130\) | 1.83013 | + | 6.83013i | 0.160513 | + | 0.599042i | ||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 2.50000 | + | 4.33013i | 0.215166 | + | 0.372678i | ||||
\(136\) | −5.47723 | − | 3.16228i | −0.469668 | − | 0.271163i | ||||
\(137\) | −2.73205 | + | 0.732051i | −0.233415 | + | 0.0625433i | −0.373630 | − | 0.927578i | \(-0.621887\pi\) |
0.140215 | + | 0.990121i | \(0.455220\pi\) | |||||||
\(138\) | −2.31495 | + | 8.63950i | −0.197061 | + | 0.735443i | ||||
\(139\) | −18.9737 | −1.60933 | −0.804663 | − | 0.593732i | \(-0.797654\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | −1.26323 | ||||||||
\(142\) | 2.19615 | − | 8.19615i | 0.184297 | − | 0.687806i | ||||
\(143\) | −2.15988 | + | 0.578737i | −0.180618 | + | 0.0483964i | ||||
\(144\) | −6.92820 | − | 4.00000i | −0.577350 | − | 0.333333i | ||||
\(145\) | −6.47963 | − | 1.73621i | −0.538104 | − | 0.144184i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3923 | + | 6.00000i | −0.851371 | + | 0.491539i | −0.861113 | − | 0.508413i | \(-0.830232\pi\) |
0.00974235 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(150\) | −7.90569 | + | 13.6931i | −0.645497 | + | 1.11803i | ||||
\(151\) | −4.50000 | + | 7.79423i | −0.366205 | + | 0.634285i | −0.988969 | − | 0.148124i | \(-0.952676\pi\) |
0.622764 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(152\) | 8.63950 | + | 2.31495i | 0.700756 | + | 0.187767i | ||||
\(153\) | 3.16228 | + | 3.16228i | 0.255655 | + | 0.255655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.00000 | + | 5.00000i | −0.401610 | + | 0.401610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.31495 | + | 8.63950i | 0.184753 | + | 0.689507i | 0.994683 | + | 0.102981i | \(0.0328382\pi\) |
−0.809930 | + | 0.586526i | \(0.800495\pi\) | |||||||
\(158\) | 4.75833 | + | 17.7583i | 0.378552 | + | 1.41278i | ||||
\(159\) | −1.58114 | − | 2.73861i | −0.125392 | − | 0.217186i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.0000 | − | 11.0000i | −0.864242 | − | 0.864242i | ||||
\(163\) | −8.19615 | − | 2.19615i | −0.641972 | − | 0.172016i | −0.0768756 | − | 0.997041i | \(-0.524494\pi\) |
−0.565097 | + | 0.825025i | \(0.691161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.33013 | − | 2.50000i | −0.337100 | − | 0.194625i | ||||
\(166\) | 5.47723 | − | 3.16228i | 0.425115 | − | 0.245440i | ||||
\(167\) | 11.0680 | − | 11.0680i | 0.856465 | − | 0.856465i | −0.134454 | − | 0.990920i | \(-0.542928\pi\) |
0.990920 | + | 0.134454i | \(0.0429282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.00000i | − | 0.615385i | ||||||
\(170\) | 1.83013 | − | 6.83013i | 0.140364 | − | 0.523847i | ||||
\(171\) | −5.47723 | − | 3.16228i | −0.418854 | − | 0.241825i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.05116 | + | 15.1191i | −0.308004 | + | 1.14949i | 0.622325 | + | 0.782759i | \(0.286188\pi\) |
−0.930329 | + | 0.366727i | \(0.880478\pi\) | |||||||
\(174\) | 9.48683 | 0.719195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 5.49038 | − | 20.4904i | 0.412682 | − | 1.54015i | ||||
\(178\) | −8.63950 | + | 2.31495i | −0.647558 | + | 0.173513i | ||||
\(179\) | 5.19615 | + | 3.00000i | 0.388379 | + | 0.224231i | 0.681457 | − | 0.731858i | \(-0.261346\pi\) |
−0.293079 | + | 0.956088i | \(0.594680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1359i | 1.64535i | 0.568511 | + | 0.822676i | \(0.307520\pi\) | ||||
−0.568511 | + | 0.822676i | \(0.692480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000 | − | 10.0000i | 0.739221 | − | 0.739221i | ||||
\(184\) | 6.92820 | − | 4.00000i | 0.510754 | − | 0.294884i | ||||
\(185\) | −16.4317 | − | 9.48683i | −1.20808 | − | 0.697486i | ||||
\(186\) | 5.00000 | − | 8.66025i | 0.366618 | − | 0.635001i | ||||
\(187\) | 2.15988 | + | 0.578737i | 0.157946 | + | 0.0423214i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.0000i | 0.725476i | ||||||||
\(191\) | 1.50000 | + | 2.59808i | 0.108536 | + | 0.187990i | 0.915177 | − | 0.403051i | \(-0.132050\pi\) |
−0.806641 | + | 0.591041i | \(0.798717\pi\) | |||||||
\(192\) | 4.62990 | + | 17.2790i | 0.334134 | + | 1.24700i | ||||
\(193\) | −2.92820 | − | 10.9282i | −0.210777 | − | 0.786629i | −0.987611 | − | 0.156924i | \(-0.949842\pi\) |
0.776834 | − | 0.629705i | \(-0.216824\pi\) | |||||||
\(194\) | −1.58114 | − | 2.73861i | −0.113519 | − | 0.196621i | ||||
\(195\) | −7.90569 | + | 7.90569i | −0.566139 | + | 0.566139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00000 | − | 1.00000i | −0.0712470 | − | 0.0712470i | 0.670585 | − | 0.741832i | \(-0.266043\pi\) |
−0.741832 | + | 0.670585i | \(0.766043\pi\) | |||||||
\(198\) | 2.73205 | + | 0.732051i | 0.194158 | + | 0.0520246i | ||||
\(199\) | 4.74342 | − | 8.21584i | 0.336252 | − | 0.582405i | −0.647473 | − | 0.762089i | \(-0.724174\pi\) |
0.983724 | + | 0.179683i | \(0.0575073\pi\) | |||||||
\(200\) | 13.6603 | − | 3.66025i | 0.965926 | − | 0.258819i | ||||
\(201\) | −2.73861 | + | 1.58114i | −0.193167 | + | 0.111525i | ||||
\(202\) | 3.16228 | − | 3.16228i | 0.222497 | − | 0.222497i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.4904 | − | 5.49038i | −1.43111 | − | 0.383465i | ||||
\(206\) | 19.1703 | + | 11.0680i | 1.33566 | + | 0.771142i | ||||
\(207\) | −5.46410 | + | 1.46410i | −0.379781 | + | 0.101762i | ||||
\(208\) | −2.31495 | + | 8.63950i | −0.160513 | + | 0.599042i | ||||
\(209\) | −3.16228 | −0.218739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.9593 | − | 3.47242i | 0.887954 | − | 0.237926i | ||||
\(214\) | −5.19615 | − | 3.00000i | −0.355202 | − | 0.205076i | ||||
\(215\) | −4.74342 | − | 8.21584i | −0.323498 | − | 0.560316i | ||||
\(216\) | 6.32456i | 0.430331i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.00000 | + | 7.00000i | −0.474100 | + | 0.474100i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | − | 4.33013i | 0.168168 | − | 0.291276i | ||||
\(222\) | 25.9185 | + | 6.94484i | 1.73954 | + | 0.466107i | ||||
\(223\) | 14.2302 | + | 14.2302i | 0.952928 | + | 0.952928i | 0.998941 | − | 0.0460129i | \(-0.0146515\pi\) |
−0.0460129 | + | 0.998941i | \(0.514652\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0000 | −0.666667 | ||||||||
\(226\) | 12.0000 | + | 20.7846i | 0.798228 | + | 1.38257i | ||||
\(227\) | −0.578737 | − | 2.15988i | −0.0384121 | − | 0.143356i | 0.944057 | − | 0.329783i | \(-0.106976\pi\) |
−0.982469 | + | 0.186427i | \(0.940309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.90569 | − | 13.6931i | −0.522423 | − | 0.904863i | −0.999660 | − | 0.0260883i | \(-0.991695\pi\) |
0.477237 | − | 0.878775i | \(-0.341638\pi\) | |||||||
\(230\) | 6.32456 | + | 6.32456i | 0.417029 | + | 0.417029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | − | 6.00000i | −0.393919 | − | 0.393919i | ||||
\(233\) | 24.5885 | + | 6.58846i | 1.61084 | + | 0.431624i | 0.948294 | − | 0.317394i | \(-0.102808\pi\) |
0.662550 | + | 0.749018i | \(0.269474\pi\) | |||||||
\(234\) | 3.16228 | − | 5.47723i | 0.206725 | − | 0.358057i | ||||
\(235\) | −7.50000 | + | 12.9904i | −0.489246 | + | 0.847399i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.5548 | + | 20.5548i | −1.33518 | + | 1.33518i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0000i | 1.22901i | 0.788914 | + | 0.614504i | \(0.210644\pi\) | ||||
−0.788914 | + | 0.614504i | \(0.789356\pi\) | |||||||
\(240\) | −17.3205 | + | 10.0000i | −1.11803 | + | 0.645497i | ||||
\(241\) | 21.9089 | + | 12.6491i | 1.41128 | + | 0.814801i | 0.995509 | − | 0.0946700i | \(-0.0301796\pi\) |
0.415768 | + | 0.909471i | \(0.363513\pi\) | |||||||
\(242\) | −13.6603 | + | 3.66025i | −0.878114 | + | 0.235290i | ||||
\(243\) | 4.62990 | − | 17.2790i | 0.297008 | − | 1.10845i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.0000 | 1.91273 | ||||||||
\(247\) | −1.83013 | + | 6.83013i | −0.116448 | + | 0.434591i | ||||
\(248\) | −8.63950 | + | 2.31495i | −0.548609 | + | 0.146999i | ||||
\(249\) | 8.66025 | + | 5.00000i | 0.548821 | + | 0.316862i | ||||
\(250\) | 7.90569 | + | 13.6931i | 0.500000 | + | 0.866025i | ||||
\(251\) | − | 12.6491i | − | 0.798405i | −0.916863 | − | 0.399202i | \(-0.869287\pi\) | ||
0.916863 | − | 0.399202i | \(-0.130713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | + | 2.00000i | −0.125739 | + | 0.125739i | ||||
\(254\) | −15.5885 | + | 9.00000i | −0.978107 | + | 0.564710i | ||||
\(255\) | 10.7994 | − | 2.89368i | 0.676283 | − | 0.181210i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2790 | − | 4.62990i | −1.07783 | − | 0.288805i | −0.324126 | − | 0.946014i | \(-0.605070\pi\) |
−0.753709 | + | 0.657209i | \(0.771737\pi\) | |||||||
\(258\) | 9.48683 | + | 9.48683i | 0.590624 | + | 0.590624i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.56218 | + | 9.56218i | 0.157991 | + | 0.589629i | 0.998831 | + | 0.0483454i | \(0.0153948\pi\) |
−0.840840 | + | 0.541284i | \(0.817939\pi\) | |||||||
\(264\) | −3.16228 | − | 5.47723i | −0.194625 | − | 0.337100i | ||||
\(265\) | −3.16228 | −0.194257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | − | 10.0000i | −0.611990 | − | 0.611990i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.48683 | − | 16.4317i | 0.578422 | − | 1.00186i | −0.417238 | − | 0.908797i | \(-0.637002\pi\) |
0.995661 | − | 0.0930598i | \(-0.0296648\pi\) | |||||||
\(270\) | −6.83013 | + | 1.83013i | −0.415668 | + | 0.111378i | ||||
\(271\) | 10.9545 | − | 6.32456i | 0.665436 | − | 0.384189i | −0.128909 | − | 0.991656i | \(-0.541148\pi\) |
0.794345 | + | 0.607467i | \(0.207814\pi\) | |||||||
\(272\) | 6.32456 | − | 6.32456i | 0.383482 | − | 0.383482i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.00000i | − | 0.241649i | ||||||
\(275\) | −4.33013 | + | 2.50000i | −0.261116 | + | 0.150756i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5885 | − | 6.58846i | 1.47738 | − | 0.395862i | 0.571923 | − | 0.820307i | \(-0.306197\pi\) |
0.905454 | + | 0.424445i | \(0.139531\pi\) | |||||||
\(278\) | 6.94484 | − | 25.9185i | 0.416524 | − | 1.55449i | ||||
\(279\) | 6.32456 | 0.378641 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 5.49038 | − | 20.4904i | 0.326947 | − | 1.22018i | ||||
\(283\) | 6.47963 | − | 1.73621i | 0.385174 | − | 0.103207i | −0.0610356 | − | 0.998136i | \(-0.519440\pi\) |
0.446209 | + | 0.894929i | \(0.352774\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.6931 | + | 7.90569i | −0.811107 | + | 0.468293i | ||||
\(286\) | − | 3.16228i | − | 0.186989i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3923 | − | 6.00000i | 0.611312 | − | 0.352941i | ||||
\(290\) | 4.74342 | − | 8.21584i | 0.278543 | − | 0.482451i | ||||
\(291\) | 2.50000 | − | 4.33013i | 0.146553 | − | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.90569 | − | 7.90569i | −0.461856 | − | 0.461856i | 0.437408 | − | 0.899263i | \(-0.355897\pi\) |
−0.899263 | + | 0.437408i | \(0.855897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0000 | − | 15.0000i | −0.873334 | − | 0.873334i | ||||
\(296\) | −12.0000 | − | 20.7846i | −0.697486 | − | 1.20808i | ||||
\(297\) | −0.578737 | − | 2.15988i | −0.0335817 | − | 0.125329i | ||||
\(298\) | −4.39230 | − | 16.3923i | −0.254439 | − | 0.949581i | ||||
\(299\) | 3.16228 | + | 5.47723i | 0.182879 | + | 0.316756i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.00000 | − | 9.00000i | −0.517892 | − | 0.517892i | ||||
\(303\) | 6.83013 | + | 1.83013i | 0.392381 | + | 0.105138i | ||||
\(304\) | −6.32456 | + | 10.9545i | −0.362738 | + | 0.628281i | ||||
\(305\) | −3.66025 | − | 13.6603i | −0.209586 | − | 0.782184i | ||||
\(306\) | −5.47723 | + | 3.16228i | −0.313112 | + | 0.180775i | ||||
\(307\) | −4.74342 | + | 4.74342i | −0.270721 | + | 0.270721i | −0.829390 | − | 0.558669i | \(-0.811312\pi\) |
0.558669 | + | 0.829390i | \(0.311312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.0000i | 1.99108i | ||||||||
\(310\) | −5.00000 | − | 8.66025i | −0.283981 | − | 0.491869i | ||||
\(311\) | −19.1703 | − | 11.0680i | −1.08705 | − | 0.627607i | −0.154259 | − | 0.988031i | \(-0.549299\pi\) |
−0.932789 | + | 0.360423i | \(0.882632\pi\) | |||||||
\(312\) | −13.6603 | + | 3.66025i | −0.773360 | + | 0.207221i | ||||
\(313\) | −5.20863 | + | 19.4389i | −0.294409 | + | 1.09875i | 0.647276 | + | 0.762256i | \(0.275908\pi\) |
−0.941685 | + | 0.336495i | \(0.890759\pi\) | |||||||
\(314\) | −12.6491 | −0.713831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.95448 | − | 25.9545i | 0.390603 | − | 1.45775i | −0.438540 | − | 0.898712i | \(-0.644504\pi\) |
0.829143 | − | 0.559037i | \(-0.188829\pi\) | |||||||
\(318\) | 4.31975 | − | 1.15747i | 0.242240 | − | 0.0649079i | ||||
\(319\) | 2.59808 | + | 1.50000i | 0.145464 | + | 0.0839839i | ||||
\(320\) | 17.2790 | + | 4.62990i | 0.965926 | + | 0.258819i | ||||
\(321\) | − | 9.48683i | − | 0.529503i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000 | − | 5.00000i | 0.278207 | − | 0.278207i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.89368 | + | 10.7994i | 0.160513 | + | 0.599042i | ||||
\(326\) | 6.00000 | − | 10.3923i | 0.332309 | − | 0.575577i | ||||
\(327\) | −15.1191 | − | 4.05116i | −0.836090 | − | 0.224030i | ||||
\(328\) | −18.9737 | − | 18.9737i | −1.04765 | − | 1.04765i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.00000 | − | 5.00000i | 0.275241 | − | 0.275241i | ||||
\(331\) | 3.00000 | + | 5.19615i | 0.164895 | + | 0.285606i | 0.936618 | − | 0.350352i | \(-0.113938\pi\) |
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.39230 | + | 16.3923i | 0.240697 | + | 0.898293i | ||||
\(334\) | 11.0680 | + | 19.1703i | 0.605612 | + | 1.04895i | ||||
\(335\) | 3.16228i | 0.172774i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | − | 8.00000i | −0.435788 | − | 0.435788i | 0.454804 | − | 0.890592i | \(-0.349709\pi\) |
−0.890592 | + | 0.454804i | \(0.849709\pi\) | |||||||
\(338\) | 10.9282 | + | 2.92820i | 0.594416 | + | 0.159273i | ||||
\(339\) | −18.9737 | + | 32.8634i | −1.03051 | + | 1.78489i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.73861 | − | 1.58114i | 0.148304 | − | 0.0856235i | ||||
\(342\) | 6.32456 | − | 6.32456i | 0.341993 | − | 0.341993i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 12.0000i | − | 0.646997i | ||||||
\(345\) | −3.66025 | + | 13.6603i | −0.197061 | + | 0.735443i | ||||
\(346\) | −19.1703 | − | 11.0680i | −1.03060 | − | 0.595018i | ||||
\(347\) | −32.7846 | + | 8.78461i | −1.75997 | + | 0.471583i | −0.986708 | − | 0.162504i | \(-0.948043\pi\) |
−0.773262 | + | 0.634086i | \(0.781376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.7851 | 1.86200 | 0.931001 | − | 0.365018i | \(-0.118937\pi\) | ||||
0.931001 | + | 0.365018i | \(0.118937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.4389 | + | 5.20863i | −1.03463 | + | 0.277228i | −0.735885 | − | 0.677106i | \(-0.763234\pi\) |
−0.298742 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(354\) | 25.9808 | + | 15.0000i | 1.38086 | + | 0.797241i | ||||
\(355\) | 3.47242 | − | 12.9593i | 0.184297 | − | 0.687806i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | + | 6.00000i | −0.317110 | + | 0.317110i | ||||
\(359\) | −19.0526 | + | 11.0000i | −1.00556 | + | 0.580558i | −0.909887 | − | 0.414855i | \(-0.863832\pi\) |
−0.0956683 | + | 0.995413i | \(0.530499\pi\) | |||||||
\(360\) | −10.9545 | − | 6.32456i | −0.577350 | − | 0.333333i | ||||
\(361\) | 4.50000 | − | 7.79423i | 0.236842 | − | 0.410223i | ||||
\(362\) | −30.2383 | − | 8.10232i | −1.58929 | − | 0.425848i | ||||
\(363\) | −15.8114 | − | 15.8114i | −0.829883 | − | 0.829883i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.0000 | + | 17.3205i | 0.522708 | + | 0.905357i | ||||
\(367\) | −6.36611 | − | 23.7586i | −0.332308 | − | 1.24019i | −0.906758 | − | 0.421651i | \(-0.861451\pi\) |
0.574450 | − | 0.818540i | \(-0.305216\pi\) | |||||||
\(368\) | 2.92820 | + | 10.9282i | 0.152643 | + | 0.569672i | ||||
\(369\) | 9.48683 | + | 16.4317i | 0.493865 | + | 0.855399i | ||||
\(370\) | 18.9737 | − | 18.9737i | 0.986394 | − | 0.986394i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3923 | − | 4.39230i | −0.848761 | − | 0.227425i | −0.191880 | − | 0.981418i | \(-0.561458\pi\) |
−0.656882 | + | 0.753994i | \(0.728125\pi\) | |||||||
\(374\) | −1.58114 | + | 2.73861i | −0.0817587 | + | 0.141610i | ||||
\(375\) | −12.5000 | + | 21.6506i | −0.645497 | + | 1.11803i | ||||
\(376\) | −16.4317 | + | 9.48683i | −0.847399 | + | 0.489246i | ||||
\(377\) | 4.74342 | − | 4.74342i | 0.244298 | − | 0.244298i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.6475 | − | 14.2302i | −1.26273 | − | 0.729038i | ||||
\(382\) | −4.09808 | + | 1.09808i | −0.209676 | + | 0.0561825i | ||||
\(383\) | −5.78737 | + | 21.5988i | −0.295721 | + | 1.10364i | 0.644922 | + | 0.764248i | \(0.276890\pi\) |
−0.940643 | + | 0.339397i | \(0.889777\pi\) | |||||||
\(384\) | −25.2982 | −1.29099 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −2.19615 | + | 8.19615i | −0.111637 | + | 0.416634i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.9186 | − | 11.5000i | −1.00991 | − | 0.583073i | −0.0987463 | − | 0.995113i | \(-0.531483\pi\) |
−0.911166 | + | 0.412039i | \(0.864817\pi\) | |||||||
\(390\) | −7.90569 | − | 13.6931i | −0.400320 | − | 0.693375i | ||||
\(391\) | − | 6.32456i | − | 0.319847i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.73205 | − | 1.00000i | 0.0872595 | − | 0.0503793i | ||||
\(395\) | 7.52358 | + | 28.0784i | 0.378552 | + | 1.41278i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.3981 | + | 8.68105i | 1.62602 | + | 0.435690i | 0.952761 | − | 0.303721i | \(-0.0982290\pi\) |
0.673255 | + | 0.739411i | \(0.264896\pi\) | |||||||
\(398\) | 9.48683 | + | 9.48683i | 0.475532 | + | 0.475532i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.0000i | 1.00000i | ||||||||
\(401\) | 0.500000 | + | 0.866025i | 0.0249688 | + | 0.0432472i | 0.878240 | − | 0.478220i | \(-0.158718\pi\) |
−0.853271 | + | 0.521468i | \(0.825385\pi\) | |||||||
\(402\) | −1.15747 | − | 4.31975i | −0.0577296 | − | 0.215450i | ||||
\(403\) | −1.83013 | − | 6.83013i | −0.0911651 | − | 0.340233i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.3925 | − | 17.3925i | −0.864242 | − | 0.864242i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | + | 6.00000i | 0.297409 | + | 0.297409i | ||||
\(408\) | 13.6603 | + | 3.66025i | 0.676283 | + | 0.181210i | ||||
\(409\) | −1.58114 | + | 2.73861i | −0.0781823 | + | 0.135416i | −0.902466 | − | 0.430762i | \(-0.858245\pi\) |
0.824283 | + | 0.566177i | \(0.191578\pi\) | |||||||
\(410\) | 15.0000 | − | 25.9808i | 0.740797 | − | 1.28310i | ||||
\(411\) | 5.47723 | − | 3.16228i | 0.270172 | − | 0.155984i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 8.00000i | − | 0.393179i | ||||||
\(415\) | 8.66025 | − | 5.00000i | 0.425115 | − | 0.245440i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.9808 | − | 10.9808i | 2.00684 | − | 0.537730i | ||||
\(418\) | 1.15747 | − | 4.31975i | 0.0566139 | − | 0.211286i | ||||
\(419\) | −15.8114 | −0.772437 | −0.386218 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386218 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | −6.22243 | + | 23.2224i | −0.302903 | + | 1.13045i | ||||
\(423\) | 12.9593 | − | 3.47242i | 0.630101 | − | 0.168835i | ||||
\(424\) | −3.46410 | − | 2.00000i | −0.168232 | − | 0.0971286i | ||||
\(425\) | 2.89368 | − | 10.7994i | 0.140364 | − | 0.523847i | ||||
\(426\) | 18.9737i | 0.919277i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.33013 | − | 2.50000i | 0.209061 | − | 0.120701i | ||||
\(430\) | 12.9593 | − | 3.47242i | 0.624951 | − | 0.167455i | ||||
\(431\) | 11.5000 | − | 19.9186i | 0.553936 | − | 0.959444i | −0.444050 | − | 0.896002i | \(-0.646459\pi\) |
0.997985 | − | 0.0634424i | \(-0.0202079\pi\) | |||||||
\(432\) | −8.63950 | − | 2.31495i | −0.415668 | − | 0.111378i | ||||
\(433\) | 9.48683 | + | 9.48683i | 0.455908 | + | 0.455908i | 0.897310 | − | 0.441402i | \(-0.145519\pi\) |
−0.441402 | + | 0.897310i | \(0.645519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.0000 | 0.719195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.31495 | + | 8.63950i | 0.110739 | + | 0.413283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.32456 | + | 10.9545i | 0.301855 | + | 0.522827i | 0.976556 | − | 0.215263i | \(-0.0690610\pi\) |
−0.674701 | + | 0.738091i | \(0.735728\pi\) | |||||||
\(440\) | −6.32456 | −0.301511 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.00000 | + | 5.00000i | 0.237826 | + | 0.237826i | ||||
\(443\) | −1.36603 | − | 0.366025i | −0.0649018 | − | 0.0173904i | 0.226222 | − | 0.974076i | \(-0.427363\pi\) |
−0.291124 | + | 0.956685i | \(0.594029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6603 | + | 3.66025i | −0.647558 | + | 0.173513i | ||||
\(446\) | −24.6475 | + | 14.2302i | −1.16709 | + | 0.673822i | ||||
\(447\) | 18.9737 | − | 18.9737i | 0.897424 | − | 0.897424i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.0000i | − | 0.802280i | −0.916017 | − | 0.401140i | \(-0.868614\pi\) | ||
0.916017 | − | 0.401140i | \(-0.131386\pi\) | |||||||
\(450\) | 3.66025 | − | 13.6603i | 0.172546 | − | 0.643951i | ||||
\(451\) | 8.21584 | + | 4.74342i | 0.386869 | + | 0.223359i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.20863 | − | 19.4389i | 0.244723 | − | 0.913318i | ||||
\(454\) | 3.16228 | 0.148413 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.0000 | −0.936586 | ||||||||
\(457\) | −0.366025 | + | 1.36603i | −0.0171219 | + | 0.0639000i | −0.973958 | − | 0.226727i | \(-0.927197\pi\) |
0.956836 | + | 0.290627i | \(0.0938640\pi\) | |||||||
\(458\) | 21.5988 | − | 5.78737i | 1.00924 | − | 0.270426i | ||||
\(459\) | 4.33013 | + | 2.50000i | 0.202113 | + | 0.116690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.32456i | 0.294564i | 0.989095 | + | 0.147282i | \(0.0470525\pi\) | ||||
−0.989095 | + | 0.147282i | \(0.952948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | + | 4.00000i | −0.185896 | + | 0.185896i | −0.793919 | − | 0.608023i | \(-0.791963\pi\) |
0.608023 | + | 0.793919i | \(0.291963\pi\) | |||||||
\(464\) | 10.3923 | − | 6.00000i | 0.482451 | − | 0.278543i | ||||
\(465\) | 7.90569 | − | 13.6931i | 0.366618 | − | 0.635001i | ||||
\(466\) | −18.0000 | + | 31.1769i | −0.833834 | + | 1.44424i | ||||
\(467\) | 15.1191 | + | 4.05116i | 0.699630 | + | 0.187465i | 0.591065 | − | 0.806624i | \(-0.298708\pi\) |
0.108565 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.0000 | − | 15.0000i | −0.691898 | − | 0.691898i | ||||
\(471\) | −10.0000 | − | 17.3205i | −0.460776 | − | 0.798087i | ||||
\(472\) | −6.94484 | − | 25.9185i | −0.319662 | − | 1.19300i | ||||
\(473\) | 1.09808 | + | 4.09808i | 0.0504896 | + | 0.188430i | ||||
\(474\) | −20.5548 | − | 35.6020i | −0.944113 | − | 1.63525i | ||||
\(475\) | 15.8114i | 0.725476i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 2.00000i | 0.0915737 | + | 0.0915737i | ||||
\(478\) | −25.9545 | − | 6.95448i | −1.18713 | − | 0.318091i | ||||
\(479\) | 3.16228 | − | 5.47723i | 0.144488 | − | 0.250261i | −0.784694 | − | 0.619884i | \(-0.787180\pi\) |
0.929182 | + | 0.369623i | \(0.120513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4317 | − | 9.48683i | 0.749220 | − | 0.432562i | ||||
\(482\) | −25.2982 | + | 25.2982i | −1.15230 | + | 1.15230i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.50000 | − | 4.33013i | −0.113519 | − | 0.196621i | ||||
\(486\) | 21.9089 | + | 12.6491i | 0.993808 | + | 0.573775i | ||||
\(487\) | −5.46410 | + | 1.46410i | −0.247602 | + | 0.0663448i | −0.380485 | − | 0.924787i | \(-0.624243\pi\) |
0.132883 | + | 0.991132i | \(0.457576\pi\) | |||||||
\(488\) | 4.62990 | − | 17.2790i | 0.209586 | − | 0.782184i | ||||
\(489\) | 18.9737 | 0.858019 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.0000 | −1.85030 | −0.925152 | − | 0.379597i | \(-0.876063\pi\) | ||||
−0.925152 | + | 0.379597i | \(0.876063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.47963 | + | 1.73621i | −0.291828 | + | 0.0781950i | ||||
\(494\) | −8.66025 | − | 5.00000i | −0.389643 | − | 0.224961i | ||||
\(495\) | 4.31975 | + | 1.15747i | 0.194158 | + | 0.0520246i | ||||
\(496\) | − | 12.6491i | − | 0.567962i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.0000 | + | 10.0000i | −0.448111 | + | 0.448111i | ||||
\(499\) | 16.4545 | − | 9.50000i | 0.736604 | − | 0.425278i | −0.0842294 | − | 0.996446i | \(-0.526843\pi\) |
0.820833 | + | 0.571168i | \(0.193510\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.5000 | + | 30.3109i | −0.781842 | + | 1.35419i | ||||
\(502\) | 17.2790 | + | 4.62990i | 0.771200 | + | 0.206642i | ||||
\(503\) | 7.90569 | + | 7.90569i | 0.352497 | + | 0.352497i | 0.861038 | − | 0.508541i | \(-0.169815\pi\) |
−0.508541 | + | 0.861038i | \(0.669815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00000 | − | 5.00000i | 0.222497 | − | 0.222497i | ||||
\(506\) | −2.00000 | − | 3.46410i | −0.0889108 | − | 0.153998i | ||||
\(507\) | 4.62990 | + | 17.2790i | 0.205621 | + | 0.767388i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.48683 | − | 16.4317i | −0.420496 | − | 0.728321i | 0.575492 | − | 0.817808i | \(-0.304811\pi\) |
−0.995988 | + | 0.0894865i | \(0.971477\pi\) | |||||||
\(510\) | 15.8114i | 0.700140i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | −6.83013 | − | 1.83013i | −0.301557 | − | 0.0808021i | ||||
\(514\) | 12.6491 | − | 21.9089i | 0.557928 | − | 0.966360i | ||||
\(515\) | 30.3109 | + | 17.5000i | 1.33566 | + | 0.771142i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.74342 | − | 4.74342i | 0.208615 | − | 0.208615i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 35.0000i | − | 1.53633i | ||||||
\(520\) | −3.66025 | + | 13.6603i | −0.160513 | + | 0.599042i | ||||
\(521\) | 35.6020 | + | 20.5548i | 1.55975 | + | 0.900522i | 0.997280 | + | 0.0737049i | \(0.0234823\pi\) |
0.562470 | + | 0.826817i | \(0.309851\pi\) | |||||||
\(522\) | −8.19615 | + | 2.19615i | −0.358736 | + | 0.0961230i | ||||
\(523\) | −6.94484 | + | 25.9185i | −0.303677 | + | 1.13334i | 0.630402 | + | 0.776269i | \(0.282890\pi\) |
−0.934078 | + | 0.357068i | \(0.883776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0000 | −0.610429 | ||||||||
\(527\) | −1.83013 | + | 6.83013i | −0.0797216 | + | 0.297525i | ||||
\(528\) | 8.63950 | − | 2.31495i | 0.375986 | − | 0.100745i | ||||
\(529\) | −12.9904 | − | 7.50000i | −0.564799 | − | 0.326087i | ||||
\(530\) | 1.15747 | − | 4.31975i | 0.0502775 | − | 0.187638i | ||||
\(531\) | 18.9737i | 0.823387i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0000 | − | 15.0000i | 0.649722 | − | 0.649722i | ||||
\(534\) | 17.3205 | − | 10.0000i | 0.749532 | − | 0.432742i | ||||
\(535\) | −8.21584 | − | 4.74342i | −0.355202 | − | 0.205076i | ||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | −12.9593 | − | 3.47242i | −0.559233 | − | 0.149846i | ||||
\(538\) | 18.9737 | + | 18.9737i | 0.818013 | + | 0.818013i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.50000 | − | 7.79423i | −0.193470 | − | 0.335100i | 0.752928 | − | 0.658103i | \(-0.228641\pi\) |
−0.946398 | + | 0.323003i | \(0.895308\pi\) | |||||||
\(542\) | 4.62990 | + | 17.2790i | 0.198871 | + | 0.742197i | ||||
\(543\) | −12.8109 | − | 47.8109i | −0.549768 | − | 2.05176i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0680 | + | 11.0680i | −0.474100 | + | 0.474100i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | + | 14.0000i | 0.598597 | + | 0.598597i | 0.939939 | − | 0.341342i | \(-0.110882\pi\) |
−0.341342 | + | 0.939939i | \(0.610882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.32456 | + | 10.9545i | −0.269925 | + | 0.467525i | ||||
\(550\) | −1.83013 | − | 6.83013i | −0.0780369 | − | 0.291238i | ||||
\(551\) | 8.21584 | − | 4.74342i | 0.350006 | − | 0.202076i | ||||
\(552\) | −12.6491 | + | 12.6491i | −0.538382 | + | 0.538382i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 36.0000i | 1.52949i | ||||||||
\(555\) | 40.9808 | + | 10.9808i | 1.73954 | + | 0.466107i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.19615 | − | 2.19615i | 0.347282 | − | 0.0930540i | −0.0809616 | − | 0.996717i | \(-0.525799\pi\) |
0.428244 | + | 0.903663i | \(0.359132\pi\) | |||||||
\(558\) | −2.31495 | + | 8.63950i | −0.0979996 | + | 0.365739i | ||||
\(559\) | 9.48683 | 0.401250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00000 | −0.211100 | ||||||||
\(562\) | −3.29423 | + | 12.2942i | −0.138959 | + | 0.518601i | ||||
\(563\) | −12.9593 | + | 3.47242i | −0.546167 | + | 0.146345i | −0.521344 | − | 0.853347i | \(-0.674569\pi\) |
−0.0248236 | + | 0.999692i | \(0.507902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.9737 | + | 32.8634i | 0.798228 | + | 1.38257i | ||||
\(566\) | 9.48683i | 0.398761i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | − | 12.0000i | 0.503509 | − | 0.503509i | ||||
\(569\) | −27.7128 | + | 16.0000i | −1.16178 | + | 0.670755i | −0.951730 | − | 0.306935i | \(-0.900696\pi\) |
−0.210051 | + | 0.977690i | \(0.567363\pi\) | |||||||
\(570\) | −5.78737 | − | 21.5988i | −0.242406 | − | 0.904672i | ||||
\(571\) | 13.0000 | − | 22.5167i | 0.544033 | − | 0.942293i | −0.454634 | − | 0.890678i | \(-0.650230\pi\) |
0.998667 | − | 0.0516146i | \(-0.0164367\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.74342 | − | 4.74342i | −0.198159 | − | 0.198159i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.0000 | + | 10.0000i | 0.417029 | + | 0.417029i | ||||
\(576\) | −8.00000 | − | 13.8564i | −0.333333 | − | 0.577350i | ||||
\(577\) | 7.52358 | + | 28.0784i | 0.313211 | + | 1.16892i | 0.925644 | + | 0.378396i | \(0.123524\pi\) |
−0.612433 | + | 0.790522i | \(0.709809\pi\) | |||||||
\(578\) | 4.39230 | + | 16.3923i | 0.182696 | + | 0.681830i | ||||
\(579\) | 12.6491 | + | 21.9089i | 0.525679 | + | 0.910503i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.00000 | + | 5.00000i | 0.207257 | + | 0.207257i | ||||
\(583\) | 1.36603 | + | 0.366025i | 0.0565750 | + | 0.0151592i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.00000 | − | 8.66025i | 0.206725 | − | 0.358057i | ||||
\(586\) | 13.6931 | − | 7.90569i | 0.565655 | − | 0.326581i | ||||
\(587\) | −15.8114 | + | 15.8114i | −0.652606 | + | 0.652606i | −0.953620 | − | 0.301014i | \(-0.902675\pi\) |
0.301014 | + | 0.953620i | \(0.402675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.0000i | − | 0.412043i | ||||||
\(590\) | 25.9808 | − | 15.0000i | 1.06961 | − | 0.617540i | ||||
\(591\) | 2.73861 | + | 1.58114i | 0.112651 | + | 0.0650394i | ||||
\(592\) | 32.7846 | − | 8.78461i | 1.34744 | − | 0.361045i | ||||
\(593\) | 7.52358 | − | 28.0784i | 0.308956 | − | 1.15304i | −0.620529 | − | 0.784183i | \(-0.713082\pi\) |
0.929486 | − | 0.368858i | \(-0.120251\pi\) | |||||||
\(594\) | 3.16228 | 0.129750 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.49038 | + | 20.4904i | −0.224706 | + | 0.838615i | ||||
\(598\) | −8.63950 | + | 2.31495i | −0.353296 | + | 0.0946653i | ||||
\(599\) | −11.2583 | − | 6.50000i | −0.460003 | − | 0.265583i | 0.252043 | − | 0.967716i | \(-0.418898\pi\) |
−0.712045 | + | 0.702133i | \(0.752231\pi\) | |||||||
\(600\) | −27.3861 | + | 15.8114i | −1.11803 | + | 0.645497i | ||||
\(601\) | − | 22.1359i | − | 0.902944i | −0.892285 | − | 0.451472i | \(-0.850899\pi\) | ||
0.892285 | − | 0.451472i | \(-0.149101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | − | 2.00000i | 0.0814463 | − | 0.0814463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.5988 | + | 5.78737i | −0.878114 | + | 0.235290i | ||||
\(606\) | −5.00000 | + | 8.66025i | −0.203111 | + | 0.351799i | ||||
\(607\) | −19.4389 | − | 5.20863i | −0.789000 | − | 0.211412i | −0.158251 | − | 0.987399i | \(-0.550586\pi\) |
−0.630749 | + | 0.775987i | \(0.717252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0000 | 0.809776 | ||||||||
\(611\) | −7.50000 | − | 12.9904i | −0.303418 | − | 0.525535i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.22243 | + | 23.2224i | 0.251322 | + | 0.937945i | 0.970100 | + | 0.242706i | \(0.0780350\pi\) |
−0.718778 | + | 0.695239i | \(0.755298\pi\) | |||||||
\(614\) | −4.74342 | − | 8.21584i | −0.191429 | − | 0.331564i | ||||
\(615\) | 47.4342 | 1.91273 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.00000 | + | 4.00000i | 0.161034 | + | 0.161034i | 0.783025 | − | 0.621991i | \(-0.213676\pi\) |
−0.621991 | + | 0.783025i | \(0.713676\pi\) | |||||||
\(618\) | −47.8109 | − | 12.8109i | −1.92324 | − | 0.515330i | ||||
\(619\) | 12.6491 | − | 21.9089i | 0.508411 | − | 0.880593i | −0.491542 | − | 0.870854i | \(-0.663567\pi\) |
0.999953 | − | 0.00973920i | \(-0.00310013\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.47723 | + | 3.16228i | −0.219793 | + | 0.126898i | ||||
\(622\) | 22.1359 | − | 22.1359i | 0.887570 | − | 0.887570i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 20.0000i | − | 0.800641i | ||||||
\(625\) | 12.5000 | + | 21.6506i | 0.500000 | + | 0.866025i | ||||
\(626\) | −24.6475 | − | 14.2302i | −0.985113 | − | 0.568755i | ||||
\(627\) | 6.83013 | − | 1.83013i | 0.272769 | − | 0.0730882i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9737 | −0.756530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | −9.51666 | + | 35.5167i | −0.378552 | + | 1.41278i | ||||
\(633\) | −36.7179 | + | 9.83853i | −1.45941 | + | 0.391046i | ||||
\(634\) | 32.9090 | + | 19.0000i | 1.30698 | + | 0.754586i | ||||
\(635\) | −24.6475 | + | 14.2302i | −0.978107 | + | 0.564710i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.00000 | + | 3.00000i | −0.118771 | + | 0.118771i | ||||
\(639\) | −10.3923 | + | 6.00000i | −0.411113 | + | 0.237356i | ||||
\(640\) | −12.6491 | + | 21.9089i | −0.500000 | + | 0.866025i | ||||
\(641\) | −22.0000 | + | 38.1051i | −0.868948 | + | 1.50506i | −0.00587459 | + | 0.999983i | \(0.501870\pi\) |
−0.863073 | + | 0.505079i | \(0.831463\pi\) | |||||||
\(642\) | 12.9593 | + | 3.47242i | 0.511461 | + | 0.137046i | ||||
\(643\) | 4.74342 | + | 4.74342i | 0.187062 | + | 0.187062i | 0.794425 | − | 0.607363i | \(-0.207772\pi\) |
−0.607363 | + | 0.794425i | \(0.707772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | + | 15.0000i | 0.590624 | + | 0.590624i | ||||
\(646\) | 5.00000 | + | 8.66025i | 0.196722 | + | 0.340733i | ||||
\(647\) | 4.62990 | + | 17.2790i | 0.182020 | + | 0.679308i | 0.995249 | + | 0.0973638i | \(0.0310411\pi\) |
−0.813229 | + | 0.581944i | \(0.802292\pi\) | |||||||
\(648\) | −8.05256 | − | 30.0526i | −0.316334 | − | 1.18058i | ||||
\(649\) | 4.74342 | + | 8.21584i | 0.186195 | + | 0.322500i | ||||
\(650\) | −15.8114 | −0.620174 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9545 | + | 6.95448i | 1.01568 | + | 0.272150i | 0.728000 | − | 0.685577i | \(-0.240450\pi\) |
0.287678 | + | 0.957727i | \(0.407117\pi\) | |||||||
\(654\) | 11.0680 | − | 19.1703i | 0.432792 | − | 0.749618i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.8634 | − | 18.9737i | 1.28310 | − | 0.740797i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.00000i | − | 0.0389545i | −0.999810 | − | 0.0194772i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194772i | \(-0.00620019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.9545 | − | 6.32456i | −0.426079 | − | 0.245997i | 0.271596 | − | 0.962411i | \(-0.412449\pi\) |
−0.697675 | + | 0.716415i | \(0.745782\pi\) | |||||||
\(662\) | −8.19615 | + | 2.19615i | −0.318553 | + | 0.0853559i | ||||
\(663\) | −2.89368 | + | 10.7994i | −0.112381 | + | 0.419413i | ||||
\(664\) | 12.6491 | 0.490881 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.0000 | −0.929981 | ||||||||
\(667\) | 2.19615 | − | 8.19615i | 0.0850354 | − | 0.317356i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.9711 | − | 22.5000i | −1.50671 | − | 0.869900i | ||||
\(670\) | −4.31975 | − | 1.15747i | −0.166887 | − | 0.0447171i | ||||
\(671\) | 6.32456i | 0.244157i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | + | 24.0000i | −0.925132 | + | 0.925132i | −0.997386 | − | 0.0722542i | \(-0.976981\pi\) |
0.0722542 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(674\) | 13.8564 | − | 8.00000i | 0.533729 | − | 0.308148i | ||||
\(675\) | −10.7994 | + | 2.89368i | −0.415668 | + | 0.111378i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.4389 | + | 5.20863i | 0.747097 | + | 0.200184i | 0.612230 | − | 0.790680i | \(-0.290273\pi\) |
0.134867 | + | 0.990864i | \(0.456939\pi\) | |||||||
\(678\) | −37.9473 | − | 37.9473i | −1.45736 | − | 1.45736i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.0000 | − | 10.0000i | 0.383482 | − | 0.383482i | ||||
\(681\) | 2.50000 | + | 4.33013i | 0.0958002 | + | 0.165931i | ||||
\(682\) | 1.15747 | + | 4.31975i | 0.0443220 | + | 0.165412i | ||||
\(683\) | 11.7128 | + | 43.7128i | 0.448178 | + | 1.67262i | 0.707406 | + | 0.706808i | \(0.249865\pi\) |
−0.259227 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.32456i | − | 0.241649i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.0000 | + | 25.0000i | 0.953809 | + | 0.953809i | ||||
\(688\) | 16.3923 | + | 4.39230i | 0.624951 | + | 0.167455i | ||||
\(689\) | 1.58114 | − | 2.73861i | 0.0602366 | − | 0.104333i | ||||
\(690\) | −17.3205 | − | 10.0000i | −0.659380 | − | 0.380693i | ||||
\(691\) | −27.3861 | + | 15.8114i | −1.04182 | + | 0.601494i | −0.920348 | − | 0.391102i | \(-0.872094\pi\) |
−0.121470 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 48.0000i | − | 1.82206i | ||||||
\(695\) | 10.9808 | − | 40.9808i | 0.416524 | − | 1.55449i | ||||
\(696\) | 16.4317 | + | 9.48683i | 0.622841 | + | 0.359597i | ||||
\(697\) | −20.4904 | + | 5.49038i | −0.776129 | + | 0.207963i | ||||
\(698\) | −12.7322 | + | 47.5173i | −0.481921 | + | 1.79856i | ||||
\(699\) | −56.9210 | −2.15295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 1.83013 | − | 6.83013i | 0.0690737 | − | 0.257787i | ||||
\(703\) | 25.9185 | − | 6.94484i | 0.977535 | − | 0.261930i | ||||
\(704\) | −6.92820 | − | 4.00000i | −0.261116 | − | 0.150756i | ||||
\(705\) | 8.68105 | − | 32.3981i | 0.326947 | − | 1.22018i | ||||
\(706\) | − | 28.4605i | − | 1.07113i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.79423 | − | 4.50000i | 0.292718 | − | 0.169001i | −0.346449 | − | 0.938069i | \(-0.612613\pi\) |
0.639167 | + | 0.769068i | \(0.279279\pi\) | |||||||
\(710\) | 16.4317 | + | 9.48683i | 0.616670 | + | 0.356034i | ||||
\(711\) | 13.0000 | − | 22.5167i | 0.487538 | − | 0.844441i | ||||
\(712\) | −17.2790 | − | 4.62990i | −0.647558 | − | 0.173513i | ||||
\(713\) | −6.32456 | − | 6.32456i | −0.236856 | − | 0.236856i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.00000i | − | 0.186989i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.9960 | − | 41.0376i | −0.410653 | − | 1.53258i | ||||
\(718\) | −8.05256 | − | 30.0526i | −0.300519 | − | 1.12155i | ||||
\(719\) | −15.8114 | − | 27.3861i | −0.589665 | − | 1.02133i | −0.994276 | − | 0.106841i | \(-0.965926\pi\) |
0.404611 | − | 0.914489i | \(-0.367407\pi\) | |||||||
\(720\) | 12.6491 | − | 12.6491i | 0.471405 | − | 0.471405i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.00000 | + | 9.00000i | 0.334945 | + | 0.334945i | ||||
\(723\) | −54.6410 | − | 14.6410i | −2.03212 | − | 0.544505i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.50000 | − | 12.9904i | 0.278543 | − | 0.482451i | ||||
\(726\) | 27.3861 | − | 15.8114i | 1.01639 | − | 0.586816i | ||||
\(727\) | 9.48683 | − | 9.48683i | 0.351847 | − | 0.351847i | −0.508949 | − | 0.860796i | \(-0.669966\pi\) |
0.860796 | + | 0.508949i | \(0.169966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.21584 | − | 4.74342i | −0.303874 | − | 0.175442i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.36611 | − | 23.7586i | 0.235138 | − | 0.877545i | −0.742949 | − | 0.669348i | \(-0.766574\pi\) |
0.978087 | − | 0.208197i | \(-0.0667597\pi\) | |||||||
\(734\) | 34.7851 | 1.28394 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.366025 | − | 1.36603i | 0.0134827 | − | 0.0503182i | ||||
\(738\) | −25.9185 | + | 6.94484i | −0.954074 | + | 0.255643i | ||||
\(739\) | 32.0429 | + | 18.5000i | 1.17872 | + | 0.680534i | 0.955718 | − | 0.294285i | \(-0.0950814\pi\) |
0.223001 | + | 0.974818i | \(0.428415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 15.8114i | − | 0.580846i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | + | 9.00000i | −0.330178 | + | 0.330178i | −0.852654 | − | 0.522476i | \(-0.825008\pi\) |
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(744\) | 17.3205 | − | 10.0000i | 0.635001 | − | 0.366618i | ||||
\(745\) | −6.94484 | − | 25.9185i | −0.254439 | − | 0.949581i | ||||
\(746\) | 12.0000 | − | 20.7846i | 0.439351 | − | 0.760979i | ||||
\(747\) | −8.63950 | − | 2.31495i | −0.316103 | − | 0.0846995i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −25.0000 | − | 25.0000i | −0.912871 | − | 0.912871i | ||||
\(751\) | −18.5000 | − | 32.0429i | −0.675075 | − | 1.16926i | −0.976447 | − | 0.215757i | \(-0.930778\pi\) |
0.301373 | − | 0.953506i | \(-0.402555\pi\) | |||||||
\(752\) | −6.94484 | − | 25.9185i | −0.253252 | − | 0.945151i | ||||
\(753\) | 7.32051 | + | 27.3205i | 0.266774 | + | 0.995615i | ||||
\(754\) | 4.74342 | + | 8.21584i | 0.172745 | + | 0.299203i | ||||
\(755\) | −14.2302 | − | 14.2302i | −0.517892 | − | 0.517892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | − | 16.0000i | −0.581530 | − | 0.581530i | 0.353794 | − | 0.935324i | \(-0.384892\pi\) |
−0.935324 | + | 0.353794i | \(0.884892\pi\) | |||||||
\(758\) | −10.9282 | − | 2.92820i | −0.396930 | − | 0.106357i | ||||
\(759\) | 3.16228 | − | 5.47723i | 0.114783 | − | 0.198811i | ||||
\(760\) | −10.0000 | + | 17.3205i | −0.362738 | + | 0.628281i | ||||
\(761\) | −21.9089 | + | 12.6491i | −0.794197 | + | 0.458530i | −0.841438 | − | 0.540354i | \(-0.818290\pi\) |
0.0472409 | + | 0.998884i | \(0.484957\pi\) | |||||||
\(762\) | 28.4605 | − | 28.4605i | 1.03102 | − | 1.03102i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.66025 | + | 5.00000i | −0.313112 | + | 0.180775i | ||||
\(766\) | −27.3861 | − | 15.8114i | −0.989501 | − | 0.571289i | ||||
\(767\) | 20.4904 | − | 5.49038i | 0.739865 | − | 0.198246i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1359 | −0.798243 | −0.399121 | − | 0.916898i | \(-0.630685\pi\) | ||||
−0.399121 | + | 0.916898i | \(0.630685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.0000 | 1.44056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.6771 | − | 13.3110i | 1.78676 | − | 0.478762i | 0.794973 | − | 0.606644i | \(-0.207485\pi\) |
0.991789 | + | 0.127883i | \(0.0408181\pi\) | |||||||
\(774\) | −10.3923 | − | 6.00000i | −0.373544 | − | 0.215666i | ||||
\(775\) | −7.90569 | − | 13.6931i | −0.283981 | − | 0.491869i | ||||
\(776\) | − | 6.32456i | − | 0.227038i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0000 | − | 23.0000i | 0.824590 | − | 0.824590i | ||||
\(779\) | 25.9808 | − | 15.0000i | 0.930857 | − | 0.537431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00000 | + | 5.19615i | −0.107348 | + | 0.185933i | ||||
\(782\) | 8.63950 | + | 2.31495i | 0.308948 | + | 0.0827824i | ||||
\(783\) | 4.74342 | + | 4.74342i | 0.169516 | + | 0.169516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.36611 | + | 23.7586i | 0.226927 | + | 0.846904i | 0.981623 | + | 0.190829i | \(0.0611177\pi\) |
−0.754696 | + | 0.656075i | \(0.772216\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0680 | − | 19.1703i | −0.394030 | − | 0.682480i | ||||
\(790\) | −41.1096 | −1.46261 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.00000 | + | 4.00000i | 0.142134 | + | 0.142134i | ||||
\(793\) | 13.6603 | + | 3.66025i | 0.485090 | + | 0.129979i | ||||
\(794\) | −23.7171 | + | 41.0792i | −0.841688 | + | 1.45785i | ||||
\(795\) | 6.83013 | − | 1.83013i | 0.242240 | − | 0.0649079i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58114 | − | 1.58114i | 0.0560068 | − | 0.0560068i | −0.678549 | − | 0.734555i | \(-0.737391\pi\) |
0.734555 | + | 0.678549i | \(0.237391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0000i | 0.530662i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.9545 | + | 6.32456i | 0.387056 | + | 0.223467i | ||||
\(802\) | −1.36603 | + | 0.366025i | −0.0482360 | + | 0.0129248i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | −10.9808 | + | 40.9808i | −0.386541 | + | 1.44259i | ||||
\(808\) | 8.63950 | − | 2.31495i | 0.303937 | − | 0.0814396i | ||||
\(809\) | −2.59808 | − | 1.50000i | −0.0913435 | − | 0.0527372i | 0.453632 | − | 0.891189i | \(-0.350128\pi\) |
−0.544976 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(810\) | 30.1247 | − | 17.3925i | 1.05848 | − | 0.611111i | ||||
\(811\) | 37.9473i | 1.33251i | 0.745724 | + | 0.666256i | \(0.232104\pi\) | ||||
−0.745724 | + | 0.666256i | \(0.767896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0000 | + | 20.0000i | −0.701431 | + | 0.701431i | ||||
\(814\) | −10.3923 | + | 6.00000i | −0.364250 | + | 0.210300i | ||||
\(815\) | 9.48683 | − | 16.4317i | 0.332309 | − | 0.575577i | ||||
\(816\) | −10.0000 | + | 17.3205i | −0.350070 | + | 0.606339i | ||||
\(817\) | 12.9593 | + | 3.47242i | 0.453387 | + | 0.121485i | ||||
\(818\) | −3.16228 | − | 3.16228i | −0.110566 | − | 0.110566i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5000 | + | 19.9186i | 0.401353 | + | 0.695163i | 0.993889 | − | 0.110380i | \(-0.0352068\pi\) |
−0.592537 | + | 0.805543i | \(0.701873\pi\) | |||||||
\(822\) | 2.31495 | + | 8.63950i | 0.0807431 | + | 0.301337i | ||||
\(823\) | −1.09808 | − | 4.09808i | −0.0382765 | − | 0.142850i | 0.944143 | − | 0.329535i | \(-0.106892\pi\) |
−0.982420 | + | 0.186686i | \(0.940225\pi\) | |||||||
\(824\) | 22.1359 | + | 38.3406i | 0.771142 | + | 1.33566i | ||||
\(825\) | 7.90569 | − | 7.90569i | 0.275241 | − | 0.275241i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.0000 | − | 26.0000i | −0.904109 | − | 0.904109i | 0.0916799 | − | 0.995789i | \(-0.470776\pi\) |
−0.995789 | + | 0.0916799i | \(0.970776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.2302 | + | 24.6475i | −0.494237 | + | 0.856044i | −0.999978 | − | 0.00664181i | \(-0.997886\pi\) |
0.505741 | + | 0.862685i | \(0.331219\pi\) | |||||||
\(830\) | 3.66025 | + | 13.6603i | 0.127049 | + | 0.474154i | ||||
\(831\) | −49.2950 | + | 28.4605i | −1.71003 | + | 0.987284i | ||||
\(832\) | −12.6491 | + | 12.6491i | −0.438529 | + | 0.438529i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 60.0000i | 2.07763i | ||||||||
\(835\) | 17.5000 | + | 30.3109i | 0.605612 | + | 1.04895i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.83013 | − | 1.83013i | 0.236084 | − | 0.0632584i | ||||
\(838\) | 5.78737 | − | 21.5988i | 0.199921 | − | 0.746117i | ||||
\(839\) | 50.5964 | 1.74678 | 0.873392 | − | 0.487019i | \(-0.161916\pi\) | ||||
0.873392 | + | 0.487019i | \(0.161916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −6.95448 | + | 25.9545i | −0.239667 | + | 0.894451i | ||||
\(843\) | −19.4389 | + | 5.20863i | −0.669511 | + | 0.179395i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.2790 | + | 4.62990i | 0.594416 | + | 0.159273i | ||||
\(846\) | 18.9737i | 0.652328i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | − | 4.00000i | 0.137361 | − | 0.137361i | ||||
\(849\) | −12.9904 | + | 7.50000i | −0.445829 | + | 0.257399i | ||||
\(850\) | 13.6931 | + | 7.90569i | 0.469668 | + | 0.271163i | ||||
\(851\) | 12.0000 | − | 20.7846i | 0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.0000 | − | 10.0000i | 0.341993 | − | 0.341993i | ||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −11.5747 | − | 43.1975i | −0.395386 | − | 1.47560i | −0.821122 | − | 0.570752i | \(-0.806652\pi\) |
0.425737 | − | 0.904847i | \(-0.360015\pi\) | |||||||
\(858\) | 1.83013 | + | 6.83013i | 0.0624795 | + | 0.233177i | ||||
\(859\) | −6.32456 | − | 10.9545i | −0.215791 | − | 0.373761i | 0.737726 | − | 0.675100i | \(-0.235900\pi\) |
−0.953517 | + | 0.301339i | \(0.902566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.0000 | + | 23.0000i | 0.783383 | + | 0.783383i | ||||
\(863\) | 17.7583 | + | 4.75833i | 0.604501 | + | 0.161975i | 0.548072 | − | 0.836431i | \(-0.315362\pi\) |
0.0564286 | + | 0.998407i | \(0.482029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.3109 | − | 17.5000i | −1.03060 | − | 0.595018i | ||||
\(866\) | −16.4317 | + | 9.48683i | −0.558371 | + | 0.322376i | ||||
\(867\) | −18.9737 | + | 18.9737i | −0.644379 | + | 0.644379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.0000i | − | 0.440995i | ||||||
\(870\) | −5.49038 | + | 20.4904i | −0.186141 | + | 0.694689i | ||||
\(871\) | −2.73861 | − | 1.58114i | −0.0927944 | − | 0.0535748i | ||||
\(872\) | −19.1244 | + | 5.12436i | −0.647632 | + | 0.173533i | ||||
\(873\) | −1.15747 | + | 4.31975i | −0.0391746 | + | 0.146201i | ||||
\(874\) | −12.6491 | −0.427863 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.22243 | − | 23.2224i | 0.210117 | − | 0.784166i | −0.777712 | − | 0.628621i | \(-0.783620\pi\) |
0.987829 | − | 0.155545i | \(-0.0497135\pi\) | |||||||
\(878\) | −17.2790 | + | 4.62990i | −0.583138 | + | 0.156251i | ||||
\(879\) | 21.6506 | + | 12.5000i | 0.730258 | + | 0.421615i | ||||
\(880\) | 2.31495 | − | 8.63950i | 0.0780369 | − | 0.291238i | ||||
\(881\) | − | 37.9473i | − | 1.27848i | −0.769008 | − | 0.639239i | \(-0.779249\pi\) | ||
0.769008 | − | 0.639239i | \(-0.220751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.0000 | + | 18.0000i | −0.605748 | + | 0.605748i | −0.941832 | − | 0.336084i | \(-0.890897\pi\) |
0.336084 | + | 0.941832i | \(0.390897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.0792 | + | 23.7171i | 1.38086 | + | 0.797241i | ||||
\(886\) | 1.00000 | − | 1.73205i | 0.0335957 | − | 0.0581894i | ||||
\(887\) | −4.31975 | − | 1.15747i | −0.145043 | − | 0.0388642i | 0.185567 | − | 0.982632i | \(-0.440588\pi\) |
−0.330610 | + | 0.943767i | \(0.607254\pi\) | |||||||
\(888\) | 37.9473 | + | 37.9473i | 1.27343 | + | 1.27343i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 20.0000i | − | 0.670402i | ||||||
\(891\) | 5.50000 | + | 9.52628i | 0.184257 | + | 0.319142i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.49038 | − | 20.4904i | −0.183729 | − | 0.685684i | ||||
\(894\) | 18.9737 | + | 32.8634i | 0.634574 | + | 1.09911i | ||||
\(895\) | −9.48683 | + | 9.48683i | −0.317110 | + | 0.317110i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.0000 | − | 10.0000i | −0.333890 | − | 0.333890i | ||||
\(898\) | 23.2224 | + | 6.22243i | 0.774943 | + | 0.207645i | ||||
\(899\) | −4.74342 | + | 8.21584i | −0.158202 | + | 0.274014i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.73861 | + | 1.58114i | −0.0912364 | + | 0.0526754i | ||||
\(902\) | −9.48683 | + | 9.48683i | −0.315877 | + | 0.315877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 48.0000i | 1.59646i | ||||||||
\(905\) | −47.8109 | − | 12.8109i | −1.58929 | − | 0.425848i | ||||
\(906\) | 24.6475 | + | 14.2302i | 0.818859 | + | 0.472768i | ||||
\(907\) | −30.0526 | + | 8.05256i | −0.997879 | + | 0.267381i | −0.720557 | − | 0.693396i | \(-0.756114\pi\) |
−0.277322 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.32456 | −0.209772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 7.32051 | − | 27.3205i | 0.242406 | − | 0.904672i | ||||
\(913\) | −4.31975 | + | 1.15747i | −0.142963 | + | 0.0383068i | ||||
\(914\) | −1.73205 | − | 1.00000i | −0.0572911 | − | 0.0330771i | ||||
\(915\) | 15.8114 | + | 27.3861i | 0.522708 | + | 0.905357i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.00000 | + | 5.00000i | −0.165025 | + | 0.165025i | ||||
\(919\) | −23.3827 | + | 13.5000i | −0.771324 | + | 0.445324i | −0.833347 | − | 0.552751i | \(-0.813578\pi\) |
0.0620230 | + | 0.998075i | \(0.480245\pi\) | |||||||
\(920\) | 4.62990 | + | 17.2790i | 0.152643 | + | 0.569672i | ||||
\(921\) | 7.50000 | − | 12.9904i | 0.247133 | − | 0.428048i | ||||
\(922\) | −8.63950 | − | 2.31495i | −0.284527 | − | 0.0762387i | ||||
\(923\) | 9.48683 | + | 9.48683i | 0.312263 | + | 0.312263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | − | 30.0000i | 0.986394 | − | 0.986394i | ||||
\(926\) | −4.00000 | − | 6.92820i | −0.131448 | − | 0.227675i | ||||
\(927\) | −8.10232 | − | 30.2383i | −0.266115 | − | 0.993155i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.58114 | − | 2.73861i | −0.0518755 | − | 0.0898510i | 0.838922 | − | 0.544252i | \(-0.183187\pi\) |
−0.890797 | + | 0.454401i | \(0.849853\pi\) | |||||||
\(930\) | 15.8114 | + | 15.8114i | 0.518476 | + | 0.518476i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 47.8109 | + | 12.8109i | 1.56526 | + | 0.419410i | ||||
\(934\) | −11.0680 | + | 19.1703i | −0.362155 | + | 0.627271i | ||||
\(935\) | −2.50000 | + | 4.33013i | −0.0817587 | + | 0.141610i | ||||
\(936\) | 10.9545 | − | 6.32456i | 0.358057 | − | 0.206725i | ||||
\(937\) | −14.2302 | + | 14.2302i | −0.464882 | + | 0.464882i | −0.900252 | − | 0.435370i | \(-0.856618\pi\) |
0.435370 | + | 0.900252i | \(0.356618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 45.0000i | − | 1.46852i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.8634 | − | 18.9737i | −1.07131 | − | 0.618524i | −0.142774 | − | 0.989755i | \(-0.545602\pi\) |
−0.928540 | + | 0.371231i | \(0.878936\pi\) | |||||||
\(942\) | 27.3205 | − | 7.32051i | 0.890150 | − | 0.238515i | ||||
\(943\) | 6.94484 | − | 25.9185i | 0.226155 | − | 0.844023i | ||||
\(944\) | 37.9473 | 1.23508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 2.56218 | − | 9.56218i | 0.0832596 | − | 0.310729i | −0.911719 | − | 0.410814i | \(-0.865245\pi\) |
0.994979 | + | 0.100085i | \(0.0319114\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −21.5988 | − | 5.78737i | −0.700756 | − | 0.187767i | ||||
\(951\) | 60.0833i | 1.94833i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | + | 3.00000i | −0.0971795 | + | 0.0971795i | −0.754025 | − | 0.656846i | \(-0.771890\pi\) |
0.656846 | + | 0.754025i | \(0.271890\pi\) | |||||||
\(954\) | −3.46410 | + | 2.00000i | −0.112154 | + | 0.0647524i | ||||
\(955\) | −6.47963 | + | 1.73621i | −0.209676 | + | 0.0561825i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.47963 | − | 1.73621i | −0.209457 | − | 0.0561237i | ||||
\(958\) | 6.32456 | + | 6.32456i | 0.204337 | + | 0.204337i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −40.0000 | −1.29099 | ||||||||
\(961\) | −10.5000 | − | 18.1865i | −0.338710 | − | 0.586662i | ||||
\(962\) | 6.94484 | + | 25.9185i | 0.223911 | + | 0.835646i | ||||
\(963\) | 2.19615 | + | 8.19615i | 0.0707700 | + | 0.264117i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.2982 | 0.814379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.0000 | − | 33.0000i | −1.06121 | − | 1.06121i | −0.998000 | − | 0.0632081i | \(-0.979867\pi\) |
−0.0632081 | − | 0.998000i | \(-0.520133\pi\) | |||||||
\(968\) | −27.3205 | − | 7.32051i | −0.878114 | − | 0.235290i | ||||
\(969\) | −7.90569 | + | 13.6931i | −0.253967 | + | 0.439885i | ||||
\(970\) | 6.83013 | − | 1.83013i | 0.219302 | − | 0.0587618i | ||||
\(971\) | 30.1247 | − | 17.3925i | 0.966749 | − | 0.558153i | 0.0685054 | − | 0.997651i | \(-0.478177\pi\) |
0.898244 | + | 0.439498i | \(0.144844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 8.00000i | − | 0.256337i | ||||||
\(975\) | −12.5000 | − | 21.6506i | −0.400320 | − | 0.693375i | ||||
\(976\) | 21.9089 | + | 12.6491i | 0.701287 | + | 0.404888i | ||||
\(977\) | 1.36603 | − | 0.366025i | 0.0437030 | − | 0.0117102i | −0.236901 | − | 0.971534i | \(-0.576132\pi\) |
0.280604 | + | 0.959824i | \(0.409465\pi\) | |||||||
\(978\) | −6.94484 | + | 25.9185i | −0.222072 | + | 0.828783i | ||||
\(979\) | 6.32456 | 0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 15.0070 | − | 56.0070i | 0.478894 | − | 1.78726i | ||||
\(983\) | 28.0784 | − | 7.52358i | 0.895561 | − | 0.239965i | 0.218452 | − | 0.975848i | \(-0.429899\pi\) |
0.677109 | + | 0.735883i | \(0.263233\pi\) | |||||||
\(984\) | 51.9615 | + | 30.0000i | 1.65647 | + | 0.956365i | ||||
\(985\) | 2.73861 | − | 1.58114i | 0.0872595 | − | 0.0503793i | ||||
\(986\) | − | 9.48683i | − | 0.302122i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3923 | − | 6.00000i | 0.330456 | − | 0.190789i | ||||
\(990\) | −3.16228 | + | 5.47723i | −0.100504 | + | 0.174078i | ||||
\(991\) | −2.00000 | + | 3.46410i | −0.0635321 | + | 0.110041i | −0.896042 | − | 0.443969i | \(-0.853570\pi\) |
0.832510 | + | 0.554010i | \(0.186903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.48683 | − | 9.48683i | −0.301056 | − | 0.301056i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0000 | + | 15.0000i | 0.475532 | + | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.20863 | + | 19.4389i | 0.164959 | + | 0.615636i | 0.998045 | + | 0.0624926i | \(0.0199050\pi\) |
−0.833086 | + | 0.553143i | \(0.813428\pi\) | |||||||
\(998\) | 6.95448 | + | 25.9545i | 0.220140 | + | 0.821575i | ||||
\(999\) | 9.48683 | + | 16.4317i | 0.300150 | + | 0.519875i |
(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 | 245.2.l.c.227.1 | 8 | ||
5.3 | odd | 4 | inner | 245.2.l.c.178.1 | 8 | ||
7.2 | even | 3 | inner | 245.2.l.c.117.2 | 8 | ||
7.3 | odd | 6 | 35.2.f.a.27.1 | yes | 4 | ||
7.4 | even | 3 | 35.2.f.a.27.2 | yes | 4 | ||
7.5 | odd | 6 | inner | 245.2.l.c.117.1 | 8 | ||
7.6 | odd | 2 | inner | 245.2.l.c.227.2 | 8 | ||
21.11 | odd | 6 | 315.2.p.c.307.2 | 4 | |||
21.17 | even | 6 | 315.2.p.c.307.1 | 4 | |||
28.3 | even | 6 | 560.2.bj.a.97.2 | 4 | |||
28.11 | odd | 6 | 560.2.bj.a.97.1 | 4 | |||
35.3 | even | 12 | 35.2.f.a.13.2 | yes | 4 | ||
35.4 | even | 6 | 175.2.f.c.132.1 | 4 | |||
35.13 | even | 4 | inner | 245.2.l.c.178.2 | 8 | ||
35.17 | even | 12 | 175.2.f.c.118.1 | 4 | |||
35.18 | odd | 12 | 35.2.f.a.13.1 | ✓ | 4 | ||
35.23 | odd | 12 | inner | 245.2.l.c.68.2 | 8 | ||
35.24 | odd | 6 | 175.2.f.c.132.2 | 4 | |||
35.32 | odd | 12 | 175.2.f.c.118.2 | 4 | |||
35.33 | even | 12 | inner | 245.2.l.c.68.1 | 8 | ||
105.38 | odd | 12 | 315.2.p.c.118.2 | 4 | |||
105.53 | even | 12 | 315.2.p.c.118.1 | 4 | |||
140.3 | odd | 12 | 560.2.bj.a.433.1 | 4 | |||
140.123 | even | 12 | 560.2.bj.a.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.f.a.13.1 | ✓ | 4 | 35.18 | odd | 12 | ||
35.2.f.a.13.2 | yes | 4 | 35.3 | even | 12 | ||
35.2.f.a.27.1 | yes | 4 | 7.3 | odd | 6 | ||
35.2.f.a.27.2 | yes | 4 | 7.4 | even | 3 | ||
175.2.f.c.118.1 | 4 | 35.17 | even | 12 | |||
175.2.f.c.118.2 | 4 | 35.32 | odd | 12 | |||
175.2.f.c.132.1 | 4 | 35.4 | even | 6 | |||
175.2.f.c.132.2 | 4 | 35.24 | odd | 6 | |||
245.2.l.c.68.1 | 8 | 35.33 | even | 12 | inner | ||
245.2.l.c.68.2 | 8 | 35.23 | odd | 12 | inner | ||
245.2.l.c.117.1 | 8 | 7.5 | odd | 6 | inner | ||
245.2.l.c.117.2 | 8 | 7.2 | even | 3 | inner | ||
245.2.l.c.178.1 | 8 | 5.3 | odd | 4 | inner | ||
245.2.l.c.178.2 | 8 | 35.13 | even | 4 | inner | ||
245.2.l.c.227.1 | 8 | 1.1 | even | 1 | trivial | ||
245.2.l.c.227.2 | 8 | 7.6 | odd | 2 | inner | ||
315.2.p.c.118.1 | 4 | 105.53 | even | 12 | |||
315.2.p.c.118.2 | 4 | 105.38 | odd | 12 | |||
315.2.p.c.307.1 | 4 | 21.17 | even | 6 | |||
315.2.p.c.307.2 | 4 | 21.11 | odd | 6 | |||
560.2.bj.a.97.1 | 4 | 28.11 | odd | 6 | |||
560.2.bj.a.97.2 | 4 | 28.3 | even | 6 | |||
560.2.bj.a.433.1 | 4 | 140.3 | odd | 12 | |||
560.2.bj.a.433.2 | 4 | 140.123 | even | 12 |