Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (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: | \(15.5708283941\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.h.1849.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −1.73205 | + | 1.00000i | −0.654654 | + | 0.377964i | −0.790237 | − | 0.612801i | \(-0.790043\pi\) |
0.135583 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 3.46410 | − | 1.00000i | 0.960769 | − | 0.277350i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | −0.866025 | + | 0.500000i | −0.184637 | + | 0.106600i | ||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.50000 | + | 0.866025i | 0.686406 | + | 0.169842i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.73205 | − | 1.00000i | −0.327327 | − | 0.188982i | ||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −0.866025 | + | 0.500000i | −0.150756 | + | 0.0870388i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −4.33013 | − | 2.50000i | −0.711868 | − | 0.410997i | 0.0998840 | − | 0.994999i | \(-0.468153\pi\) |
−0.811752 | + | 0.584002i | \(0.801486\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 3.50000 | + | 0.866025i | 0.560449 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | + | 8.66025i | −0.780869 | + | 1.35250i | 0.150567 | + | 0.988600i | \(0.451890\pi\) |
−0.931436 | + | 0.363905i | \(0.881443\pi\) | |||||||
\(42\) | −1.73205 | − | 1.00000i | −0.267261 | − | 0.154303i | ||||
\(43\) | 4.33013 | − | 2.50000i | 0.660338 | − | 0.381246i | −0.132068 | − | 0.991241i | \(-0.542162\pi\) |
0.792406 | + | 0.609994i | \(0.208828\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | −0.866025 | + | 0.500000i | −0.125000 | + | 0.0721688i | ||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 2.59808 | + | 2.50000i | 0.360288 | + | 0.346688i | ||||
\(53\) | 14.0000i | 1.92305i | 0.274721 | + | 0.961524i | \(0.411414\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | − | 1.73205i | −0.133631 | − | 0.231455i | ||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | −0.866025 | + | 0.500000i | −0.113715 | + | 0.0656532i | ||||
\(59\) | −2.50000 | − | 4.33013i | −0.325472 | − | 0.563735i | 0.656136 | − | 0.754643i | \(-0.272190\pi\) |
−0.981608 | + | 0.190909i | \(0.938857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | −2.59808 | − | 1.50000i | −0.329956 | − | 0.190500i | ||||
\(63\) | −1.73205 | − | 1.00000i | −0.218218 | − | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | 1.50000 | + | 2.59808i | 0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | − | 3.46410i | −0.237356 | − | 0.411113i | 0.722599 | − | 0.691268i | \(-0.242948\pi\) |
−0.959955 | + | 0.280155i | \(0.909614\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | −2.50000 | − | 4.33013i | −0.290619 | − | 0.503367i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | + | 5.19615i | −0.344124 | + | 0.596040i | ||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | 2.59808 | + | 2.50000i | 0.294174 | + | 0.283069i | ||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −8.66025 | + | 5.00000i | −0.956365 | + | 0.552158i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | −1.00000 | − | 1.73205i | −0.109109 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.00000 | 0.539164 | ||||||||
\(87\) | −0.866025 | + | 0.500000i | −0.0928477 | + | 0.0536056i | ||||
\(88\) | −0.866025 | − | 0.500000i | −0.0923186 | − | 0.0533002i | ||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | + | 5.19615i | −0.524142 | + | 0.544705i | ||||
\(92\) | 3.00000i | 0.312772i | ||||||||
\(93\) | −2.59808 | − | 1.50000i | −0.269408 | − | 0.155543i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | −2.59808 | + | 1.50000i | −0.262445 | + | 0.151523i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | −1.73205 | − | 1.00000i | −0.171499 | − | 0.0990148i | ||||
\(103\) | − | 6.00000i | − | 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | 1.00000 | + | 3.46410i | 0.0980581 | + | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.00000 | + | 12.1244i | −0.679900 | + | 1.17762i | ||||
\(107\) | −5.19615 | − | 3.00000i | −0.502331 | − | 0.290021i | 0.227345 | − | 0.973814i | \(-0.426996\pi\) |
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.50000 | − | 4.33013i | −0.237289 | − | 0.410997i | ||||
\(112\) | − | 2.00000i | − | 0.188982i | ||||||
\(113\) | 14.7224 | − | 8.50000i | 1.38497 | − | 0.799613i | 0.392227 | − | 0.919868i | \(-0.371705\pi\) |
0.992743 | + | 0.120256i | \(0.0383715\pi\) | |||||||
\(114\) | −3.00000 | + | 5.19615i | −0.280976 | + | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 2.59808 | + | 2.50000i | 0.240192 | + | 0.231125i | ||||
\(118\) | − | 5.00000i | − | 0.460287i | ||||||
\(119\) | 2.00000 | − | 3.46410i | 0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | −8.66025 | + | 5.00000i | −0.780869 | + | 0.450835i | ||||
\(124\) | −1.50000 | − | 2.59808i | −0.134704 | − | 0.233314i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | − | 1.73205i | −0.0890871 | − | 0.154303i | ||||
\(127\) | −12.1244 | − | 7.00000i | −1.07586 | − | 0.621150i | −0.146085 | − | 0.989272i | \(-0.546667\pi\) |
−0.929777 | + | 0.368122i | \(0.880001\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.00000 | 0.440225 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.0000 | 1.13582 | 0.567908 | − | 0.823092i | \(-0.307753\pi\) | ||||
0.567908 | + | 0.823092i | \(0.307753\pi\) | |||||||
\(132\) | −0.866025 | − | 0.500000i | −0.0753778 | − | 0.0435194i | ||||
\(133\) | −10.3923 | − | 6.00000i | −0.901127 | − | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | 7.79423 | − | 4.50000i | 0.665906 | − | 0.384461i | −0.128618 | − | 0.991694i | \(-0.541054\pi\) |
0.794524 | + | 0.607233i | \(0.207721\pi\) | |||||||
\(138\) | 3.00000i | 0.255377i | ||||||||
\(139\) | 5.00000 | + | 8.66025i | 0.424094 | + | 0.734553i | 0.996335 | − | 0.0855324i | \(-0.0272591\pi\) |
−0.572241 | + | 0.820086i | \(0.693926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | − | 2.59808i | 0.126323 | − | 0.218797i | ||||
\(142\) | − | 4.00000i | − | 0.335673i | ||||||
\(143\) | −0.866025 | + | 3.50000i | −0.0724207 | + | 0.292685i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | −2.59808 | + | 1.50000i | −0.214286 | + | 0.123718i | ||||
\(148\) | − | 5.00000i | − | 0.410997i | ||||||
\(149\) | 5.50000 | + | 9.52628i | 0.450578 | + | 0.780423i | 0.998422 | − | 0.0561570i | \(-0.0178847\pi\) |
−0.547844 | + | 0.836580i | \(0.684551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.0000 | 1.95309 | 0.976546 | − | 0.215308i | \(-0.0690756\pi\) | ||||
0.976546 | + | 0.215308i | \(0.0690756\pi\) | |||||||
\(152\) | −5.19615 | + | 3.00000i | −0.421464 | + | 0.243332i | ||||
\(153\) | −1.73205 | − | 1.00000i | −0.140028 | − | 0.0808452i | ||||
\(154\) | 1.00000 | − | 1.73205i | 0.0805823 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | + | 3.46410i | 0.0800641 | + | 0.277350i | ||||
\(157\) | − | 25.0000i | − | 1.99522i | −0.0691164 | − | 0.997609i | \(-0.522018\pi\) | ||
0.0691164 | − | 0.997609i | \(-0.477982\pi\) | |||||||
\(158\) | −4.33013 | − | 2.50000i | −0.344486 | − | 0.198889i | ||||
\(159\) | −7.00000 | + | 12.1244i | −0.555136 | + | 0.961524i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | 14.7224 | − | 8.50000i | 1.15315 | − | 0.665771i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
0.949653 | + | 0.313304i | \(0.101436\pi\) | |||||||
\(164\) | −10.0000 | −0.780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | −6.06218 | − | 3.50000i | −0.469105 | − | 0.270838i | 0.246760 | − | 0.969077i | \(-0.420634\pi\) |
−0.715865 | + | 0.698239i | \(0.753967\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 5.19615i | −0.229416 | + | 0.397360i | ||||
\(172\) | 4.33013 | + | 2.50000i | 0.330169 | + | 0.190623i | ||||
\(173\) | 3.46410 | − | 2.00000i | 0.263371 | − | 0.152057i | −0.362500 | − | 0.931984i | \(-0.618077\pi\) |
0.625871 | + | 0.779926i | \(0.284744\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | − | 5.00000i | − | 0.375823i | ||||||
\(178\) | 8.66025 | − | 5.00000i | 0.649113 | − | 0.374766i | ||||
\(179\) | −3.50000 | + | 6.06218i | −0.261602 | + | 0.453108i | −0.966668 | − | 0.256034i | \(-0.917584\pi\) |
0.705066 | + | 0.709142i | \(0.250918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | −6.92820 | + | 2.00000i | −0.513553 | + | 0.148250i | ||||
\(183\) | 10.0000i | 0.739221i | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.50000 | − | 2.59808i | −0.109985 | − | 0.190500i | ||||
\(187\) | − | 2.00000i | − | 0.146254i | ||||||
\(188\) | 2.59808 | − | 1.50000i | 0.189484 | − | 0.109399i | ||||
\(189\) | −1.00000 | − | 1.73205i | −0.0727393 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | − | 20.7846i | −0.868290 | − | 1.50392i | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 3.46410 | + | 2.00000i | 0.249351 | + | 0.143963i | 0.619467 | − | 0.785022i | \(-0.287349\pi\) |
−0.370116 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −10.3923 | − | 6.00000i | −0.740421 | − | 0.427482i | 0.0818013 | − | 0.996649i | \(-0.473933\pi\) |
−0.822222 | + | 0.569166i | \(0.807266\pi\) | |||||||
\(198\) | −0.866025 | − | 0.500000i | −0.0615457 | − | 0.0355335i | ||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1244 | + | 7.00000i | −0.853067 | + | 0.492518i | ||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | −1.00000 | − | 1.73205i | −0.0700140 | − | 0.121268i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.00000 | − | 5.19615i | 0.209020 | − | 0.362033i | ||||
\(207\) | 3.00000i | 0.208514i | ||||||||
\(208\) | −0.866025 | + | 3.50000i | −0.0600481 | + | 0.242681i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | − | 6.92820i | 0.275371 | − | 0.476957i | −0.694857 | − | 0.719148i | \(-0.744533\pi\) |
0.970229 | + | 0.242190i | \(0.0778659\pi\) | |||||||
\(212\) | −12.1244 | + | 7.00000i | −0.832704 | + | 0.480762i | ||||
\(213\) | − | 4.00000i | − | 0.274075i | ||||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.19615 | − | 3.00000i | 0.352738 | − | 0.203653i | ||||
\(218\) | 5.19615 | + | 3.00000i | 0.351928 | + | 0.203186i | ||||
\(219\) | 1.00000 | − | 1.73205i | 0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | + | 5.19615i | −0.336336 | + | 0.349531i | ||||
\(222\) | − | 5.00000i | − | 0.335578i | ||||||
\(223\) | −8.66025 | − | 5.00000i | −0.579934 | − | 0.334825i | 0.181173 | − | 0.983451i | \(-0.442010\pi\) |
−0.761107 | + | 0.648626i | \(0.775344\pi\) | |||||||
\(224\) | 1.00000 | − | 1.73205i | 0.0668153 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0000 | 1.13082 | ||||||||
\(227\) | −17.3205 | + | 10.0000i | −1.14960 | + | 0.663723i | −0.948790 | − | 0.315906i | \(-0.897691\pi\) |
−0.200812 | + | 0.979630i | \(0.564358\pi\) | |||||||
\(228\) | −5.19615 | + | 3.00000i | −0.344124 | + | 0.198680i | ||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | − | 1.73205i | 0.0657952 | − | 0.113961i | ||||
\(232\) | −0.866025 | − | 0.500000i | −0.0568574 | − | 0.0328266i | ||||
\(233\) | 3.00000i | 0.196537i | 0.995160 | + | 0.0982683i | \(0.0313303\pi\) | ||||
−0.995160 | + | 0.0982683i | \(0.968670\pi\) | |||||||
\(234\) | 1.00000 | + | 3.46410i | 0.0653720 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.50000 | − | 4.33013i | 0.162736 | − | 0.281867i | ||||
\(237\) | −4.33013 | − | 2.50000i | −0.281272 | − | 0.162392i | ||||
\(238\) | 3.46410 | − | 2.00000i | 0.224544 | − | 0.129641i | ||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | 10.0000i | 0.642824i | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −5.00000 | + | 8.66025i | −0.320092 | + | 0.554416i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.0000 | −0.637577 | ||||||||
\(247\) | 15.5885 | + | 15.0000i | 0.991870 | + | 0.954427i | ||||
\(248\) | − | 3.00000i | − | 0.190500i | ||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.50000 | − | 2.59808i | −0.0946792 | − | 0.163989i | 0.814795 | − | 0.579748i | \(-0.196849\pi\) |
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | −2.59808 | + | 1.50000i | −0.163340 | + | 0.0943042i | ||||
\(254\) | −7.00000 | − | 12.1244i | −0.439219 | − | 0.760750i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 18.1865 | + | 10.5000i | 1.13444 | + | 0.654972i | 0.945049 | − | 0.326929i | \(-0.106014\pi\) |
0.189396 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(258\) | 4.33013 | + | 2.50000i | 0.269582 | + | 0.155643i | ||||
\(259\) | 10.0000 | 0.621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 11.2583 | + | 6.50000i | 0.695542 | + | 0.401571i | ||||
\(263\) | −19.9186 | − | 11.5000i | −1.22823 | − | 0.709120i | −0.261573 | − | 0.965184i | \(-0.584241\pi\) |
−0.966660 | + | 0.256063i | \(0.917574\pi\) | |||||||
\(264\) | −0.500000 | − | 0.866025i | −0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.00000 | − | 10.3923i | −0.367884 | − | 0.637193i | ||||
\(267\) | 8.66025 | − | 5.00000i | 0.529999 | − | 0.305995i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5000 | − | 25.1147i | 0.880812 | − | 1.52561i | 0.0303728 | − | 0.999539i | \(-0.490331\pi\) |
0.850439 | − | 0.526073i | \(-0.176336\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | −6.92820 | + | 2.00000i | −0.419314 | + | 0.121046i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 16.4545 | − | 9.50000i | 0.988654 | − | 0.570800i | 0.0837823 | − | 0.996484i | \(-0.473300\pi\) |
0.904872 | + | 0.425684i | \(0.139967\pi\) | |||||||
\(278\) | 10.0000i | 0.599760i | ||||||||
\(279\) | −1.50000 | − | 2.59808i | −0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 2.59808 | − | 1.50000i | 0.154713 | − | 0.0893237i | ||||
\(283\) | 11.2583 | + | 6.50000i | 0.669238 | + | 0.386385i | 0.795788 | − | 0.605575i | \(-0.207057\pi\) |
−0.126550 | + | 0.991960i | \(0.540390\pi\) | |||||||
\(284\) | 2.00000 | − | 3.46410i | 0.118678 | − | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.50000 | + | 2.59808i | −0.147828 | + | 0.153627i | ||||
\(287\) | − | 20.0000i | − | 1.18056i | ||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | 1.73205 | − | 1.00000i | 0.101361 | − | 0.0585206i | ||||
\(293\) | −12.1244 | + | 7.00000i | −0.708312 | + | 0.408944i | −0.810436 | − | 0.585827i | \(-0.800770\pi\) |
0.102123 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.50000 | − | 4.33013i | 0.145310 | − | 0.251684i | ||||
\(297\) | −0.866025 | − | 0.500000i | −0.0502519 | − | 0.0290129i | ||||
\(298\) | 11.0000i | 0.637213i | ||||||||
\(299\) | 10.5000 | + | 2.59808i | 0.607231 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | + | 8.66025i | −0.288195 | + | 0.499169i | ||||
\(302\) | 20.7846 | + | 12.0000i | 1.19602 | + | 0.690522i | ||||
\(303\) | −12.1244 | + | 7.00000i | −0.696526 | + | 0.402139i | ||||
\(304\) | −6.00000 | −0.344124 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | − | 1.73205i | −0.0571662 | − | 0.0990148i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 1.73205 | − | 1.00000i | 0.0986928 | − | 0.0569803i | ||||
\(309\) | 3.00000 | − | 5.19615i | 0.170664 | − | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | −0.866025 | + | 3.50000i | −0.0490290 | + | 0.198148i | ||||
\(313\) | − | 12.0000i | − | 0.678280i | −0.940736 | − | 0.339140i | \(-0.889864\pi\) | ||
0.940736 | − | 0.339140i | \(-0.110136\pi\) | |||||||
\(314\) | 12.5000 | − | 21.6506i | 0.705416 | − | 1.22182i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | −12.1244 | + | 7.00000i | −0.679900 | + | 0.392541i | ||||
\(319\) | −0.500000 | − | 0.866025i | −0.0279946 | − | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | −5.19615 | − | 3.00000i | −0.289570 | − | 0.167183i | ||||
\(323\) | −10.3923 | − | 6.00000i | −0.578243 | − | 0.333849i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.0000 | 0.941543 | ||||||||
\(327\) | 5.19615 | + | 3.00000i | 0.287348 | + | 0.165900i | ||||
\(328\) | −8.66025 | − | 5.00000i | −0.478183 | − | 0.276079i | ||||
\(329\) | 3.00000 | + | 5.19615i | 0.165395 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 5.19615 | − | 3.00000i | 0.285176 | − | 0.164646i | ||||
\(333\) | − | 5.00000i | − | 0.273998i | ||||||
\(334\) | −3.50000 | − | 6.06218i | −0.191511 | − | 0.331708i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | − | 1.73205i | 0.0545545 | − | 0.0944911i | ||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | 12.9904 | − | 0.500000i | 0.706584 | − | 0.0271964i | ||||
\(339\) | 17.0000 | 0.923313 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.50000 | − | 2.59808i | 0.0812296 | − | 0.140694i | ||||
\(342\) | −5.19615 | + | 3.00000i | −0.280976 | + | 0.162221i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 2.50000 | + | 4.33013i | 0.134791 | + | 0.233465i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 15.5885 | − | 9.00000i | 0.836832 | − | 0.483145i | −0.0193540 | − | 0.999813i | \(-0.506161\pi\) |
0.856186 | + | 0.516667i | \(0.172828\pi\) | |||||||
\(348\) | −0.866025 | − | 0.500000i | −0.0464238 | − | 0.0268028i | ||||
\(349\) | 4.00000 | − | 6.92820i | 0.214115 | − | 0.370858i | −0.738883 | − | 0.673833i | \(-0.764647\pi\) |
0.952998 | + | 0.302975i | \(0.0979799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | + | 3.46410i | 0.0533761 | + | 0.184900i | ||||
\(352\) | − | 1.00000i | − | 0.0533002i | ||||||
\(353\) | 12.1244 | + | 7.00000i | 0.645314 | + | 0.372572i | 0.786659 | − | 0.617388i | \(-0.211809\pi\) |
−0.141344 | + | 0.989960i | \(0.545142\pi\) | |||||||
\(354\) | 2.50000 | − | 4.33013i | 0.132874 | − | 0.230144i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 3.46410 | − | 2.00000i | 0.183340 | − | 0.105851i | ||||
\(358\) | −6.06218 | + | 3.50000i | −0.320396 | + | 0.184981i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 13.8564 | + | 8.00000i | 0.728277 | + | 0.420471i | ||||
\(363\) | 10.0000i | 0.524864i | ||||||||
\(364\) | −7.00000 | − | 1.73205i | −0.366900 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.00000 | + | 8.66025i | −0.261354 | + | 0.452679i | ||||
\(367\) | 31.1769 | + | 18.0000i | 1.62742 | + | 0.939592i | 0.984859 | + | 0.173360i | \(0.0554623\pi\) |
0.642563 | + | 0.766233i | \(0.277871\pi\) | |||||||
\(368\) | −2.59808 | + | 1.50000i | −0.135434 | + | 0.0781929i | ||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0000 | − | 24.2487i | −0.726844 | − | 1.25893i | ||||
\(372\) | − | 3.00000i | − | 0.155543i | ||||||
\(373\) | 32.0429 | − | 18.5000i | 1.65912 | − | 0.957894i | 0.685999 | − | 0.727603i | \(-0.259366\pi\) |
0.973122 | − | 0.230291i | \(-0.0739678\pi\) | |||||||
\(374\) | 1.00000 | − | 1.73205i | 0.0517088 | − | 0.0895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −0.866025 | + | 3.50000i | −0.0446026 | + | 0.180259i | ||||
\(378\) | − | 2.00000i | − | 0.102869i | ||||||
\(379\) | −15.0000 | + | 25.9808i | −0.770498 | + | 1.33454i | 0.166792 | + | 0.985992i | \(0.446659\pi\) |
−0.937290 | + | 0.348550i | \(0.886674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.00000 | − | 12.1244i | −0.358621 | − | 0.621150i | ||||
\(382\) | − | 24.0000i | − | 1.22795i | ||||||
\(383\) | −23.3827 | + | 13.5000i | −1.19480 | + | 0.689818i | −0.959391 | − | 0.282079i | \(-0.908976\pi\) |
−0.235408 | + | 0.971897i | \(0.575643\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | + | 3.46410i | 0.101797 | + | 0.176318i | ||||
\(387\) | 4.33013 | + | 2.50000i | 0.220113 | + | 0.127082i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | 1.00000 | 0.0507020 | 0.0253510 | − | 0.999679i | \(-0.491930\pi\) | ||||
0.0253510 | + | 0.999679i | \(0.491930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | −2.59808 | − | 1.50000i | −0.131223 | − | 0.0757614i | ||||
\(393\) | 11.2583 | + | 6.50000i | 0.567908 | + | 0.327882i | ||||
\(394\) | −6.00000 | − | 10.3923i | −0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 11.2583 | − | 6.50000i | 0.565039 | − | 0.326226i | −0.190126 | − | 0.981760i | \(-0.560890\pi\) |
0.755166 | + | 0.655534i | \(0.227556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | − | 10.3923i | −0.300376 | − | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | + | 3.00000i | −0.517678 | + | 0.149441i | ||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.00000 | − | 1.73205i | 0.0496292 | − | 0.0859602i | ||||
\(407\) | 4.33013 | − | 2.50000i | 0.214636 | − | 0.123920i | ||||
\(408\) | − | 2.00000i | − | 0.0990148i | ||||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | 5.19615 | − | 3.00000i | 0.255996 | − | 0.147799i | ||||
\(413\) | 8.66025 | + | 5.00000i | 0.426143 | + | 0.246034i | ||||
\(414\) | −1.50000 | + | 2.59808i | −0.0737210 | + | 0.127688i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | 10.0000i | 0.489702i | ||||||||
\(418\) | −5.19615 | − | 3.00000i | −0.254152 | − | 0.146735i | ||||
\(419\) | 2.00000 | − | 3.46410i | 0.0977064 | − | 0.169232i | −0.813029 | − | 0.582224i | \(-0.802183\pi\) |
0.910735 | + | 0.412991i | \(0.135516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.0000 | 1.36464 | 0.682318 | − | 0.731055i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(422\) | 6.92820 | − | 4.00000i | 0.337260 | − | 0.194717i | ||||
\(423\) | 2.59808 | − | 1.50000i | 0.126323 | − | 0.0729325i | ||||
\(424\) | −14.0000 | −0.679900 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.00000 | − | 3.46410i | 0.0969003 | − | 0.167836i | ||||
\(427\) | −17.3205 | − | 10.0000i | −0.838198 | − | 0.483934i | ||||
\(428\) | − | 6.00000i | − | 0.290021i | ||||||
\(429\) | −2.50000 | + | 2.59808i | −0.120701 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 13.8564 | − | 8.00000i | 0.665896 | − | 0.384455i | −0.128624 | − | 0.991693i | \(-0.541056\pi\) |
0.794520 | + | 0.607238i | \(0.207723\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.00000 | + | 5.19615i | 0.143674 | + | 0.248851i | ||||
\(437\) | 18.0000i | 0.861057i | ||||||||
\(438\) | 1.73205 | − | 1.00000i | 0.0827606 | − | 0.0477818i | ||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −6.92820 | + | 2.00000i | −0.329541 | + | 0.0951303i | ||||
\(443\) | 16.0000i | 0.760183i | 0.924949 | + | 0.380091i | \(0.124107\pi\) | ||||
−0.924949 | + | 0.380091i | \(0.875893\pi\) | |||||||
\(444\) | 2.50000 | − | 4.33013i | 0.118645 | − | 0.205499i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 11.0000i | 0.520282i | ||||||||
\(448\) | 1.73205 | − | 1.00000i | 0.0818317 | − | 0.0472456i | ||||
\(449\) | −18.0000 | − | 31.1769i | −0.849473 | − | 1.47133i | −0.881680 | − | 0.471848i | \(-0.843587\pi\) |
0.0322072 | − | 0.999481i | \(-0.489746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | − | 8.66025i | −0.235441 | − | 0.407795i | ||||
\(452\) | 14.7224 | + | 8.50000i | 0.692485 | + | 0.399806i | ||||
\(453\) | 20.7846 | + | 12.0000i | 0.976546 | + | 0.563809i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | 12.1244 | + | 7.00000i | 0.567153 | + | 0.327446i | 0.756012 | − | 0.654558i | \(-0.227145\pi\) |
−0.188858 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(458\) | −19.0526 | − | 11.0000i | −0.890268 | − | 0.513996i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5000 | − | 23.3827i | −0.628758 | − | 1.08904i | −0.987801 | − | 0.155719i | \(-0.950230\pi\) |
0.359044 | − | 0.933321i | \(-0.383103\pi\) | |||||||
\(462\) | 1.73205 | − | 1.00000i | 0.0805823 | − | 0.0465242i | ||||
\(463\) | 10.0000i | 0.464739i | 0.972628 | + | 0.232370i | \(0.0746479\pi\) | ||||
−0.972628 | + | 0.232370i | \(0.925352\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50000 | + | 2.59808i | −0.0694862 | + | 0.120354i | ||||
\(467\) | 2.00000i | 0.0925490i | 0.998929 | + | 0.0462745i | \(0.0147349\pi\) | ||||
−0.998929 | + | 0.0462745i | \(0.985265\pi\) | |||||||
\(468\) | −0.866025 | + | 3.50000i | −0.0400320 | + | 0.161788i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.5000 | − | 21.6506i | 0.575970 | − | 0.997609i | ||||
\(472\) | 4.33013 | − | 2.50000i | 0.199310 | − | 0.115072i | ||||
\(473\) | 5.00000i | 0.229900i | ||||||||
\(474\) | −2.50000 | − | 4.33013i | −0.114829 | − | 0.198889i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | −12.1244 | + | 7.00000i | −0.555136 | + | 0.320508i | ||||
\(478\) | 6.92820 | + | 4.00000i | 0.316889 | + | 0.182956i | ||||
\(479\) | −2.00000 | + | 3.46410i | −0.0913823 | + | 0.158279i | −0.908093 | − | 0.418769i | \(-0.862462\pi\) |
0.816711 | + | 0.577047i | \(0.195795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | − | 4.33013i | −0.797931 | − | 0.197437i | ||||
\(482\) | 7.00000i | 0.318841i | ||||||||
\(483\) | −5.19615 | − | 3.00000i | −0.236433 | − | 0.136505i | ||||
\(484\) | −5.00000 | + | 8.66025i | −0.227273 | + | 0.393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.73205 | + | 1.00000i | −0.0784867 | + | 0.0453143i | −0.538730 | − | 0.842479i | \(-0.681096\pi\) |
0.460243 | + | 0.887793i | \(0.347762\pi\) | |||||||
\(488\) | −8.66025 | + | 5.00000i | −0.392031 | + | 0.226339i | ||||
\(489\) | 17.0000 | 0.768767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | + | 20.7846i | −0.541552 | + | 0.937996i | 0.457263 | + | 0.889332i | \(0.348830\pi\) |
−0.998815 | + | 0.0486647i | \(0.984503\pi\) | |||||||
\(492\) | −8.66025 | − | 5.00000i | −0.390434 | − | 0.225417i | ||||
\(493\) | − | 2.00000i | − | 0.0900755i | ||||||
\(494\) | 6.00000 | + | 20.7846i | 0.269953 | + | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | − | 2.59808i | 0.0673520 | − | 0.116657i | ||||
\(497\) | 6.92820 | + | 4.00000i | 0.310772 | + | 0.179425i | ||||
\(498\) | 5.19615 | − | 3.00000i | 0.232845 | − | 0.134433i | ||||
\(499\) | 40.0000 | 1.79065 | 0.895323 | − | 0.445418i | \(-0.146945\pi\) | ||||
0.895323 | + | 0.445418i | \(0.146945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.50000 | − | 6.06218i | −0.156368 | − | 0.270838i | ||||
\(502\) | − | 3.00000i | − | 0.133897i | ||||||
\(503\) | 34.6410 | − | 20.0000i | 1.54457 | − | 0.891756i | 0.546025 | − | 0.837769i | \(-0.316140\pi\) |
0.998542 | − | 0.0539870i | \(-0.0171930\pi\) | |||||||
\(504\) | 1.00000 | − | 1.73205i | 0.0445435 | − | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.00000 | −0.133366 | ||||||||
\(507\) | 12.9904 | − | 0.500000i | 0.576923 | − | 0.0222058i | ||||
\(508\) | − | 14.0000i | − | 0.621150i | ||||||
\(509\) | −4.50000 | + | 7.79423i | −0.199459 | + | 0.345473i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.19615 | + | 3.00000i | −0.229416 | + | 0.132453i | ||||
\(514\) | 10.5000 | + | 18.1865i | 0.463135 | + | 0.802174i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.50000 | + | 4.33013i | 0.110056 | + | 0.190623i | ||||
\(517\) | 2.59808 | + | 1.50000i | 0.114263 | + | 0.0659699i | ||||
\(518\) | 8.66025 | + | 5.00000i | 0.380510 | + | 0.219687i | ||||
\(519\) | 4.00000 | 0.175581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | −0.866025 | − | 0.500000i | −0.0379049 | − | 0.0218844i | ||||
\(523\) | −28.5788 | − | 16.5000i | −1.24967 | − | 0.721495i | −0.278623 | − | 0.960401i | \(-0.589878\pi\) |
−0.971043 | + | 0.238906i | \(0.923211\pi\) | |||||||
\(524\) | 6.50000 | + | 11.2583i | 0.283954 | + | 0.491822i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.5000 | − | 19.9186i | −0.501424 | − | 0.868492i | ||||
\(527\) | 5.19615 | − | 3.00000i | 0.226348 | − | 0.130682i | ||||
\(528\) | − | 1.00000i | − | 0.0435194i | ||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.50000 | − | 4.33013i | 0.108491 | − | 0.187912i | ||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | −8.66025 | + | 35.0000i | −0.375117 | + | 1.51602i | ||||
\(534\) | 10.0000 | 0.432742 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.06218 | + | 3.50000i | −0.261602 | + | 0.151036i | ||||
\(538\) | 18.0000i | 0.776035i | ||||||||
\(539\) | −1.50000 | − | 2.59808i | −0.0646096 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 25.1147 | − | 14.5000i | 1.07877 | − | 0.622828i | ||||
\(543\) | 13.8564 | + | 8.00000i | 0.594635 | + | 0.343313i | ||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.00000 | − | 1.73205i | −0.299572 | − | 0.0741249i | ||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | 7.79423 | + | 4.50000i | 0.332953 | + | 0.192230i | ||||
\(549\) | −5.00000 | + | 8.66025i | −0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −2.59808 | + | 1.50000i | −0.110581 | + | 0.0638442i | ||||
\(553\) | 8.66025 | − | 5.00000i | 0.368271 | − | 0.212622i | ||||
\(554\) | 19.0000 | 0.807233 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | + | 8.66025i | −0.212047 | + | 0.367277i | ||||
\(557\) | −29.4449 | − | 17.0000i | −1.24762 | − | 0.720313i | −0.276985 | − | 0.960874i | \(-0.589335\pi\) |
−0.970634 | + | 0.240561i | \(0.922669\pi\) | |||||||
\(558\) | − | 3.00000i | − | 0.127000i | ||||||
\(559\) | 12.5000 | − | 12.9904i | 0.528694 | − | 0.549435i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.00000 | − | 1.73205i | 0.0422200 | − | 0.0731272i | ||||
\(562\) | −25.9808 | − | 15.0000i | −1.09593 | − | 0.632737i | ||||
\(563\) | −20.7846 | + | 12.0000i | −0.875967 | + | 0.505740i | −0.869326 | − | 0.494238i | \(-0.835447\pi\) |
−0.00664037 | + | 0.999978i | \(0.502114\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.50000 | + | 11.2583i | 0.273215 | + | 0.473223i | ||||
\(567\) | − | 2.00000i | − | 0.0839921i | ||||||
\(568\) | 3.46410 | − | 2.00000i | 0.145350 | − | 0.0839181i | ||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | −3.46410 | + | 1.00000i | −0.144841 | + | 0.0418121i | ||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 10.0000 | − | 17.3205i | 0.417392 | − | 0.722944i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | −11.2583 | + | 6.50000i | −0.468285 | + | 0.270364i | ||||
\(579\) | 2.00000 | + | 3.46410i | 0.0831172 | + | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | 8.66025 | + | 5.00000i | 0.358979 | + | 0.207257i | ||||
\(583\) | −12.1244 | − | 7.00000i | −0.502140 | − | 0.289910i | ||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | −15.5885 | − | 9.00000i | −0.643404 | − | 0.371470i | 0.142520 | − | 0.989792i | \(-0.454479\pi\) |
−0.785925 | + | 0.618322i | \(0.787813\pi\) | |||||||
\(588\) | −2.59808 | − | 1.50000i | −0.107143 | − | 0.0618590i | ||||
\(589\) | −9.00000 | − | 15.5885i | −0.370839 | − | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | − | 10.3923i | −0.246807 | − | 0.427482i | ||||
\(592\) | 4.33013 | − | 2.50000i | 0.177967 | − | 0.102749i | ||||
\(593\) | − | 35.0000i | − | 1.43728i | −0.695383 | − | 0.718639i | \(-0.744765\pi\) | ||
0.695383 | − | 0.718639i | \(-0.255235\pi\) | |||||||
\(594\) | −0.500000 | − | 0.866025i | −0.0205152 | − | 0.0355335i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.50000 | + | 9.52628i | −0.225289 | + | 0.390212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.79423 | + | 7.50000i | 0.318730 | + | 0.306698i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50000 | − | 9.52628i | 0.224350 | − | 0.388585i | −0.731774 | − | 0.681547i | \(-0.761308\pi\) |
0.956124 | + | 0.292962i | \(0.0946409\pi\) | |||||||
\(602\) | −8.66025 | + | 5.00000i | −0.352966 | + | 0.203785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.0000 | + | 20.7846i | 0.488273 | + | 0.845714i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0000 | −0.568711 | ||||||||
\(607\) | 8.66025 | − | 5.00000i | 0.351509 | − | 0.202944i | −0.313841 | − | 0.949476i | \(-0.601616\pi\) |
0.665350 | + | 0.746532i | \(0.268282\pi\) | |||||||
\(608\) | −5.19615 | − | 3.00000i | −0.210732 | − | 0.121666i | ||||
\(609\) | 1.00000 | − | 1.73205i | 0.0405220 | − | 0.0701862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | − | 10.3923i | −0.121367 | − | 0.420428i | ||||
\(612\) | − | 2.00000i | − | 0.0808452i | ||||||
\(613\) | 32.0429 | + | 18.5000i | 1.29420 | + | 0.747208i | 0.979396 | − | 0.201948i | \(-0.0647272\pi\) |
0.314806 | + | 0.949156i | \(0.398061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −2.59808 | + | 1.50000i | −0.104595 | + | 0.0603877i | −0.551385 | − | 0.834251i | \(-0.685900\pi\) |
0.446790 | + | 0.894639i | \(0.352567\pi\) | |||||||
\(618\) | 5.19615 | − | 3.00000i | 0.209020 | − | 0.120678i | ||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.0000i | 0.801283i | ||||||||
\(624\) | −2.50000 | + | 2.59808i | −0.100080 | + | 0.104006i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.00000 | − | 10.3923i | 0.239808 | − | 0.415360i | ||||
\(627\) | −5.19615 | − | 3.00000i | −0.207514 | − | 0.119808i | ||||
\(628\) | 21.6506 | − | 12.5000i | 0.863954 | − | 0.498804i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | − | 41.5692i | −0.955425 | − | 1.65484i | −0.733393 | − | 0.679805i | \(-0.762064\pi\) |
−0.222032 | − | 0.975039i | \(-0.571269\pi\) | |||||||
\(632\) | − | 5.00000i | − | 0.198889i | ||||||
\(633\) | 6.92820 | − | 4.00000i | 0.275371 | − | 0.158986i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.0000 | −0.555136 | ||||||||
\(637\) | −2.59808 | + | 10.5000i | −0.102940 | + | 0.416025i | ||||
\(638\) | − | 1.00000i | − | 0.0395904i | ||||||
\(639\) | 2.00000 | − | 3.46410i | 0.0791188 | − | 0.137038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | − | 6.00000i | − | 0.236801i | ||||||
\(643\) | −34.6410 | + | 20.0000i | −1.36611 | + | 0.788723i | −0.990429 | − | 0.138027i | \(-0.955924\pi\) |
−0.375680 | + | 0.926750i | \(0.622591\pi\) | |||||||
\(644\) | −3.00000 | − | 5.19615i | −0.118217 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 5.00000 | 0.196267 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | 0.235159 | ||||||||
\(652\) | 14.7224 | + | 8.50000i | 0.576575 | + | 0.332886i | ||||
\(653\) | 15.5885 | + | 9.00000i | 0.610023 | + | 0.352197i | 0.772975 | − | 0.634437i | \(-0.218768\pi\) |
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.00000 | − | 8.66025i | −0.195217 | − | 0.338126i | ||||
\(657\) | 1.73205 | − | 1.00000i | 0.0675737 | − | 0.0390137i | ||||
\(658\) | 6.00000i | 0.233904i | ||||||||
\(659\) | −6.50000 | − | 11.2583i | −0.253204 | − | 0.438562i | 0.711202 | − | 0.702988i | \(-0.248151\pi\) |
−0.964406 | + | 0.264425i | \(0.914818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | − | 10.3923i | 0.233373 | − | 0.404214i | −0.725426 | − | 0.688301i | \(-0.758357\pi\) |
0.958799 | + | 0.284087i | \(0.0916904\pi\) | |||||||
\(662\) | − | 4.00000i | − | 0.155464i | ||||||
\(663\) | −6.92820 | + | 2.00000i | −0.269069 | + | 0.0776736i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.50000 | − | 4.33013i | 0.0968730 | − | 0.167789i | ||||
\(667\) | −2.59808 | + | 1.50000i | −0.100598 | + | 0.0580802i | ||||
\(668\) | − | 7.00000i | − | 0.270838i | ||||||
\(669\) | −5.00000 | − | 8.66025i | −0.193311 | − | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | 1.73205 | − | 1.00000i | 0.0668153 | − | 0.0385758i | ||||
\(673\) | 13.8564 | + | 8.00000i | 0.534125 | + | 0.308377i | 0.742695 | − | 0.669630i | \(-0.233547\pi\) |
−0.208569 | + | 0.978008i | \(0.566881\pi\) | |||||||
\(674\) | −11.0000 | + | 19.0526i | −0.423704 | + | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5000 | + | 6.06218i | 0.442308 | + | 0.233161i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 14.7224 | + | 8.50000i | 0.565412 | + | 0.326441i | ||||
\(679\) | −10.0000 | + | 17.3205i | −0.383765 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 2.59808 | − | 1.50000i | 0.0994855 | − | 0.0574380i | ||||
\(683\) | −38.1051 | + | 22.0000i | −1.45805 | + | 0.841807i | −0.998916 | − | 0.0465592i | \(-0.985174\pi\) |
−0.459136 | + | 0.888366i | \(0.651841\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | −19.0526 | − | 11.0000i | −0.726900 | − | 0.419676i | ||||
\(688\) | 5.00000i | 0.190623i | ||||||||
\(689\) | 14.0000 | + | 48.4974i | 0.533358 | + | 1.84760i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00000 | − | 12.1244i | 0.266293 | − | 0.461232i | −0.701609 | − | 0.712562i | \(-0.747535\pi\) |
0.967901 | + | 0.251330i | \(0.0808679\pi\) | |||||||
\(692\) | 3.46410 | + | 2.00000i | 0.131685 | + | 0.0760286i | ||||
\(693\) | 1.73205 | − | 1.00000i | 0.0657952 | − | 0.0379869i | ||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.500000 | − | 0.866025i | −0.0189525 | − | 0.0328266i | ||||
\(697\) | − | 20.0000i | − | 0.757554i | ||||||
\(698\) | 6.92820 | − | 4.00000i | 0.262236 | − | 0.151402i | ||||
\(699\) | −1.50000 | + | 2.59808i | −0.0567352 | + | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | −0.866025 | + | 3.50000i | −0.0326860 | + | 0.132099i | ||||
\(703\) | − | 30.0000i | − | 1.13147i | ||||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.00000 | + | 12.1244i | 0.263448 | + | 0.456306i | ||||
\(707\) | − | 28.0000i | − | 1.05305i | ||||||
\(708\) | 4.33013 | − | 2.50000i | 0.162736 | − | 0.0939558i | ||||
\(709\) | −8.00000 | − | 13.8564i | −0.300446 | − | 0.520388i | 0.675791 | − | 0.737093i | \(-0.263802\pi\) |
−0.976237 | + | 0.216705i | \(0.930469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | 8.66025 | + | 5.00000i | 0.324557 | + | 0.187383i | ||||
\(713\) | −7.79423 | − | 4.50000i | −0.291896 | − | 0.168526i | ||||
\(714\) | 4.00000 | 0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.00000 | −0.261602 | ||||||||
\(717\) | 6.92820 | + | 4.00000i | 0.258738 | + | 0.149383i | ||||
\(718\) | −10.3923 | − | 6.00000i | −0.387837 | − | 0.223918i | ||||
\(719\) | −24.0000 | − | 41.5692i | −0.895049 | − | 1.55027i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
−0.0613050 | − | 0.998119i | \(-0.519526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | + | 10.3923i | 0.223452 | + | 0.387030i | ||||
\(722\) | −14.7224 | + | 8.50000i | −0.547912 | + | 0.316337i | ||||
\(723\) | 7.00000i | 0.260333i | ||||||||
\(724\) | 8.00000 | + | 13.8564i | 0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | + | 8.66025i | −0.185567 | + | 0.321412i | ||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | −5.19615 | − | 5.00000i | −0.192582 | − | 0.185312i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.00000 | + | 8.66025i | −0.184932 | + | 0.320311i | ||||
\(732\) | −8.66025 | + | 5.00000i | −0.320092 | + | 0.184805i | ||||
\(733\) | 14.0000i | 0.517102i | 0.965998 | + | 0.258551i | \(0.0832450\pi\) | ||||
−0.965998 | + | 0.258551i | \(0.916755\pi\) | |||||||
\(734\) | 18.0000 | + | 31.1769i | 0.664392 | + | 1.15076i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −8.66025 | − | 5.00000i | −0.318788 | − | 0.184053i | ||||
\(739\) | 12.0000 | − | 20.7846i | 0.441427 | − | 0.764574i | −0.556369 | − | 0.830936i | \(-0.687806\pi\) |
0.997796 | + | 0.0663614i | \(0.0211390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | + | 20.7846i | 0.220416 | + | 0.763542i | ||||
\(742\) | − | 28.0000i | − | 1.02791i | ||||||
\(743\) | 12.9904 | + | 7.50000i | 0.476571 | + | 0.275148i | 0.718986 | − | 0.695024i | \(-0.244606\pi\) |
−0.242415 | + | 0.970173i | \(0.577940\pi\) | |||||||
\(744\) | 1.50000 | − | 2.59808i | 0.0549927 | − | 0.0952501i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 37.0000 | 1.35467 | ||||||||
\(747\) | 5.19615 | − | 3.00000i | 0.190117 | − | 0.109764i | ||||
\(748\) | 1.73205 | − | 1.00000i | 0.0633300 | − | 0.0365636i | ||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5000 | + | 35.5070i | −0.748056 | + | 1.29567i | 0.200698 | + | 0.979653i | \(0.435679\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 2.59808 | + | 1.50000i | 0.0947421 | + | 0.0546994i | ||||
\(753\) | − | 3.00000i | − | 0.109326i | ||||||
\(754\) | −2.50000 | + | 2.59808i | −0.0910446 | + | 0.0946164i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.00000 | − | 1.73205i | 0.0363696 | − | 0.0629941i | ||||
\(757\) | −46.7654 | − | 27.0000i | −1.69972 | − | 0.981332i | −0.946020 | − | 0.324109i | \(-0.894935\pi\) |
−0.753697 | − | 0.657222i | \(-0.771731\pi\) | |||||||
\(758\) | −25.9808 | + | 15.0000i | −0.943664 | + | 0.544825i | ||||
\(759\) | −3.00000 | −0.108893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | + | 17.3205i | 0.362500 | + | 0.627868i | 0.988372 | − | 0.152058i | \(-0.0485900\pi\) |
−0.625872 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(762\) | − | 14.0000i | − | 0.507166i | ||||||
\(763\) | −10.3923 | + | 6.00000i | −0.376227 | + | 0.217215i | ||||
\(764\) | 12.0000 | − | 20.7846i | 0.434145 | − | 0.751961i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.0000 | −0.975550 | ||||||||
\(767\) | −12.9904 | − | 12.5000i | −0.469055 | − | 0.451349i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −14.5000 | + | 25.1147i | −0.522883 | + | 0.905661i | 0.476762 | + | 0.879032i | \(0.341810\pi\) |
−0.999645 | + | 0.0266282i | \(0.991523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5000 | + | 18.1865i | 0.378148 | + | 0.654972i | ||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | −13.8564 | + | 8.00000i | −0.498380 | + | 0.287740i | −0.728044 | − | 0.685530i | \(-0.759571\pi\) |
0.229664 | + | 0.973270i | \(0.426237\pi\) | |||||||
\(774\) | 2.50000 | + | 4.33013i | 0.0898606 | + | 0.155643i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 8.66025 | + | 5.00000i | 0.310685 | + | 0.179374i | ||||
\(778\) | 0.866025 | + | 0.500000i | 0.0310485 | + | 0.0179259i | ||||
\(779\) | −60.0000 | −2.14972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | −5.19615 | − | 3.00000i | −0.185814 | − | 0.107280i | ||||
\(783\) | −0.866025 | − | 0.500000i | −0.0309492 | − | 0.0178685i | ||||
\(784\) | −1.50000 | − | 2.59808i | −0.0535714 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.50000 | + | 11.2583i | 0.231847 | + | 0.401571i | ||||
\(787\) | −21.6506 | + | 12.5000i | −0.771762 | + | 0.445577i | −0.833503 | − | 0.552515i | \(-0.813668\pi\) |
0.0617409 | + | 0.998092i | \(0.480335\pi\) | |||||||
\(788\) | − | 12.0000i | − | 0.427482i | ||||||
\(789\) | −11.5000 | − | 19.9186i | −0.409411 | − | 0.709120i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.0000 | + | 29.4449i | −0.604450 | + | 1.04694i | ||||
\(792\) | − | 1.00000i | − | 0.0355335i | ||||||
\(793\) | 25.9808 | + | 25.0000i | 0.922604 | + | 0.887776i | ||||
\(794\) | 13.0000 | 0.461353 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.0333 | − | 26.0000i | 1.59516 | − | 0.920967i | 0.602761 | − | 0.797922i | \(-0.294067\pi\) |
0.992401 | − | 0.123045i | \(-0.0392661\pi\) | |||||||
\(798\) | − | 12.0000i | − | 0.424795i | ||||||
\(799\) | 3.00000 | + | 5.19615i | 0.106132 | + | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 10.3923 | − | 6.00000i | 0.366965 | − | 0.211867i | ||||
\(803\) | 1.73205 | + | 1.00000i | 0.0611227 | + | 0.0352892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.5000 | − | 2.59808i | −0.369847 | − | 0.0915133i | ||||
\(807\) | 18.0000i | 0.633630i | ||||||||
\(808\) | −12.1244 | − | 7.00000i | −0.426533 | − | 0.246259i | ||||
\(809\) | 1.00000 | − | 1.73205i | 0.0351581 | − | 0.0608957i | −0.847911 | − | 0.530139i | \(-0.822140\pi\) |
0.883069 | + | 0.469243i | \(0.155473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 1.73205 | − | 1.00000i | 0.0607831 | − | 0.0350931i | ||||
\(813\) | 25.1147 | − | 14.5000i | 0.880812 | − | 0.508537i | ||||
\(814\) | 5.00000 | 0.175250 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | − | 1.73205i | 0.0350070 | − | 0.0606339i | ||||
\(817\) | 25.9808 | + | 15.0000i | 0.908952 | + | 0.524784i | ||||
\(818\) | − | 26.0000i | − | 0.909069i | ||||||
\(819\) | −7.00000 | − | 1.73205i | −0.244600 | − | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.5000 | + | 19.9186i | −0.401353 | + | 0.695163i | −0.993889 | − | 0.110380i | \(-0.964793\pi\) |
0.592537 | + | 0.805543i | \(0.298127\pi\) | |||||||
\(822\) | 7.79423 | + | 4.50000i | 0.271855 | + | 0.156956i | ||||
\(823\) | −19.0526 | + | 11.0000i | −0.664130 | + | 0.383436i | −0.793849 | − | 0.608115i | \(-0.791926\pi\) |
0.129719 | + | 0.991551i | \(0.458593\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | + | 8.66025i | 0.173972 | + | 0.301329i | ||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | −2.59808 | + | 1.50000i | −0.0902894 | + | 0.0521286i | ||||
\(829\) | 13.0000 | − | 22.5167i | 0.451509 | − | 0.782036i | −0.546971 | − | 0.837151i | \(-0.684219\pi\) |
0.998480 | + | 0.0551154i | \(0.0175527\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.0000 | 0.659103 | ||||||||
\(832\) | −3.46410 | + | 1.00000i | −0.120096 | + | 0.0346688i | ||||
\(833\) | − | 6.00000i | − | 0.207888i | ||||||
\(834\) | −5.00000 | + | 8.66025i | −0.173136 | + | 0.299880i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | − | 3.00000i | − | 0.103695i | ||||||
\(838\) | 3.46410 | − | 2.00000i | 0.119665 | − | 0.0690889i | ||||
\(839\) | 19.0000 | + | 32.9090i | 0.655953 | + | 1.13614i | 0.981654 | + | 0.190671i | \(0.0610663\pi\) |
−0.325701 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 24.2487 | + | 14.0000i | 0.835666 | + | 0.482472i | ||||
\(843\) | −25.9808 | − | 15.0000i | −0.894825 | − | 0.516627i | ||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −17.3205 | − | 10.0000i | −0.595140 | − | 0.343604i | ||||
\(848\) | −12.1244 | − | 7.00000i | −0.416352 | − | 0.240381i | ||||
\(849\) | 6.50000 | + | 11.2583i | 0.223079 | + | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.50000 | − | 12.9904i | −0.257097 | − | 0.445305i | ||||
\(852\) | 3.46410 | − | 2.00000i | 0.118678 | − | 0.0685189i | ||||
\(853\) | 7.00000i | 0.239675i | 0.992793 | + | 0.119838i | \(0.0382374\pi\) | ||||
−0.992793 | + | 0.119838i | \(0.961763\pi\) | |||||||
\(854\) | −10.0000 | − | 17.3205i | −0.342193 | − | 0.592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | 35.0000i | 1.19558i | 0.801654 | + | 0.597789i | \(0.203954\pi\) | ||||
−0.801654 | + | 0.597789i | \(0.796046\pi\) | |||||||
\(858\) | −3.46410 | + | 1.00000i | −0.118262 | + | 0.0341394i | ||||
\(859\) | −18.0000 | −0.614152 | −0.307076 | − | 0.951685i | \(-0.599351\pi\) | ||||
−0.307076 | + | 0.951685i | \(0.599351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.0000 | − | 17.3205i | 0.340799 | − | 0.590281i | ||||
\(862\) | −10.3923 | + | 6.00000i | −0.353963 | + | 0.204361i | ||||
\(863\) | − | 51.0000i | − | 1.73606i | −0.496512 | − | 0.868030i | \(-0.665386\pi\) | ||
0.496512 | − | 0.868030i | \(-0.334614\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | −11.2583 | + | 6.50000i | −0.382353 | + | 0.220752i | ||||
\(868\) | 5.19615 | + | 3.00000i | 0.176369 | + | 0.101827i | ||||
\(869\) | 2.50000 | − | 4.33013i | 0.0848067 | − | 0.146889i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000i | 0.203186i | ||||||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | −9.00000 | + | 15.5885i | −0.304430 | + | 0.527287i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −11.2583 | + | 6.50000i | −0.380167 | + | 0.219489i | −0.677891 | − | 0.735163i | \(-0.737106\pi\) |
0.297724 | + | 0.954652i | \(0.403772\pi\) | |||||||
\(878\) | 24.2487 | − | 14.0000i | 0.818354 | − | 0.472477i | ||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0000 | + | 46.7654i | −0.909653 | + | 1.57557i | −0.0951067 | + | 0.995467i | \(0.530319\pi\) |
−0.814546 | + | 0.580098i | \(0.803014\pi\) | |||||||
\(882\) | −2.59808 | − | 1.50000i | −0.0874818 | − | 0.0505076i | ||||
\(883\) | − | 1.00000i | − | 0.0336527i | −0.999858 | − | 0.0168263i | \(-0.994644\pi\) | ||
0.999858 | − | 0.0168263i | \(-0.00535624\pi\) | |||||||
\(884\) | −7.00000 | − | 1.73205i | −0.235435 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00000 | + | 13.8564i | −0.268765 | + | 0.465515i | ||||
\(887\) | 0.866025 | + | 0.500000i | 0.0290783 | + | 0.0167884i | 0.514469 | − | 0.857509i | \(-0.327989\pi\) |
−0.485390 | + | 0.874298i | \(0.661323\pi\) | |||||||
\(888\) | 4.33013 | − | 2.50000i | 0.145310 | − | 0.0838945i | ||||
\(889\) | 28.0000 | 0.939090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | − | 10.0000i | − | 0.334825i | ||||||
\(893\) | 15.5885 | − | 9.00000i | 0.521648 | − | 0.301174i | ||||
\(894\) | −5.50000 | + | 9.52628i | −0.183948 | + | 0.318606i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 7.79423 | + | 7.50000i | 0.260242 | + | 0.250418i | ||||
\(898\) | − | 36.0000i | − | 1.20134i | ||||||
\(899\) | 1.50000 | − | 2.59808i | 0.0500278 | − | 0.0866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.0000 | − | 24.2487i | −0.466408 | − | 0.807842i | ||||
\(902\) | − | 10.0000i | − | 0.332964i | ||||||
\(903\) | −8.66025 | + | 5.00000i | −0.288195 | + | 0.166390i | ||||
\(904\) | 8.50000 | + | 14.7224i | 0.282706 | + | 0.489661i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.0000 | + | 20.7846i | 0.398673 | + | 0.690522i | ||||
\(907\) | −45.8993 | − | 26.5000i | −1.52406 | − | 0.879918i | −0.999594 | − | 0.0284883i | \(-0.990931\pi\) |
−0.524469 | − | 0.851430i | \(-0.675736\pi\) | |||||||
\(908\) | −17.3205 | − | 10.0000i | −0.574801 | − | 0.331862i | ||||
\(909\) | −14.0000 | −0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0000 | 1.12647 | 0.563235 | − | 0.826297i | \(-0.309557\pi\) | ||||
0.563235 | + | 0.826297i | \(0.309557\pi\) | |||||||
\(912\) | −5.19615 | − | 3.00000i | −0.172062 | − | 0.0993399i | ||||
\(913\) | 5.19615 | + | 3.00000i | 0.171968 | + | 0.0992855i | ||||
\(914\) | 7.00000 | + | 12.1244i | 0.231539 | + | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.0000 | − | 19.0526i | −0.363450 | − | 0.629514i | ||||
\(917\) | −22.5167 | + | 13.0000i | −0.743566 | + | 0.429298i | ||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | −28.0000 | − | 48.4974i | −0.923635 | − | 1.59978i | −0.793742 | − | 0.608254i | \(-0.791870\pi\) |
−0.129893 | − | 0.991528i | \(-0.541463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 27.0000i | − | 0.889198i | ||||||
\(923\) | −10.3923 | − | 10.0000i | −0.342067 | − | 0.329154i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.00000 | + | 8.66025i | −0.164310 | + | 0.284594i | ||||
\(927\) | 5.19615 | − | 3.00000i | 0.170664 | − | 0.0985329i | ||||
\(928\) | − | 1.00000i | − | 0.0328266i | ||||||
\(929\) | 12.0000 | + | 20.7846i | 0.393707 | + | 0.681921i | 0.992935 | − | 0.118657i | \(-0.0378590\pi\) |
−0.599228 | + | 0.800578i | \(0.704526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | −2.59808 | + | 1.50000i | −0.0851028 | + | 0.0491341i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.00000 | + | 1.73205i | −0.0327210 | + | 0.0566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.50000 | + | 2.59808i | −0.0817151 | + | 0.0849208i | ||||
\(937\) | 18.0000i | 0.588034i | 0.955800 | + | 0.294017i | \(0.0949923\pi\) | ||||
−0.955800 | + | 0.294017i | \(0.905008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.00000 | − | 10.3923i | 0.195803 | − | 0.339140i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0000 | 0.847576 | 0.423788 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423788 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(942\) | 21.6506 | − | 12.5000i | 0.705416 | − | 0.407272i | ||||
\(943\) | −25.9808 | + | 15.0000i | −0.846050 | + | 0.488467i | ||||
\(944\) | 5.00000 | 0.162736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.50000 | + | 4.33013i | −0.0812820 | + | 0.140785i | ||||
\(947\) | 45.0333 | + | 26.0000i | 1.46339 | + | 0.844886i | 0.999166 | − | 0.0408333i | \(-0.0130013\pi\) |
0.464220 | + | 0.885720i | \(0.346335\pi\) | |||||||
\(948\) | − | 5.00000i | − | 0.162392i | ||||||
\(949\) | −2.00000 | − | 6.92820i | −0.0649227 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | − | 10.3923i | 0.194563 | − | 0.336994i | ||||
\(952\) | 3.46410 | + | 2.00000i | 0.112272 | + | 0.0648204i | ||||
\(953\) | 12.9904 | − | 7.50000i | 0.420800 | − | 0.242949i | −0.274620 | − | 0.961553i | \(-0.588552\pi\) |
0.695419 | + | 0.718604i | \(0.255219\pi\) | |||||||
\(954\) | −14.0000 | −0.453267 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.00000 | + | 6.92820i | 0.129369 | + | 0.224074i | ||||
\(957\) | − | 1.00000i | − | 0.0323254i | ||||||
\(958\) | −3.46410 | + | 2.00000i | −0.111920 | + | 0.0646171i | ||||
\(959\) | −9.00000 | + | 15.5885i | −0.290625 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | −12.9904 | − | 12.5000i | −0.418827 | − | 0.403016i | ||||
\(963\) | − | 6.00000i | − | 0.193347i | ||||||
\(964\) | −3.50000 | + | 6.06218i | −0.112727 | + | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.00000 | − | 5.19615i | −0.0965234 | − | 0.167183i | ||||
\(967\) | − | 16.0000i | − | 0.514525i | −0.966342 | − | 0.257263i | \(-0.917179\pi\) | ||
0.966342 | − | 0.257263i | \(-0.0828206\pi\) | |||||||
\(968\) | −8.66025 | + | 5.00000i | −0.278351 | + | 0.160706i | ||||
\(969\) | −6.00000 | − | 10.3923i | −0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | + | 34.6410i | 0.641831 | + | 1.11168i | 0.985024 | + | 0.172418i | \(0.0551581\pi\) |
−0.343193 | + | 0.939265i | \(0.611509\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | −17.3205 | − | 10.0000i | −0.555270 | − | 0.320585i | ||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | −33.7750 | − | 19.5000i | −1.08056 | − | 0.623860i | −0.149511 | − | 0.988760i | \(-0.547770\pi\) |
−0.931047 | + | 0.364900i | \(0.881103\pi\) | |||||||
\(978\) | 14.7224 | + | 8.50000i | 0.470771 | + | 0.271800i | ||||
\(979\) | 5.00000 | + | 8.66025i | 0.159801 | + | 0.276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | + | 5.19615i | 0.0957826 | + | 0.165900i | ||||
\(982\) | −20.7846 | + | 12.0000i | −0.663264 | + | 0.382935i | ||||
\(983\) | − | 25.0000i | − | 0.797376i | −0.917087 | − | 0.398688i | \(-0.869466\pi\) | ||
0.917087 | − | 0.398688i | \(-0.130534\pi\) | |||||||
\(984\) | −5.00000 | − | 8.66025i | −0.159394 | − | 0.276079i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.00000 | − | 1.73205i | 0.0318465 | − | 0.0551597i | ||||
\(987\) | 6.00000i | 0.190982i | ||||||||
\(988\) | −5.19615 | + | 21.0000i | −0.165312 | + | 0.668099i | ||||
\(989\) | 15.0000 | 0.476972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5000 | + | 33.7750i | −0.619438 | + | 1.07290i | 0.370151 | + | 0.928972i | \(0.379306\pi\) |
−0.989588 | + | 0.143926i | \(0.954027\pi\) | |||||||
\(992\) | 2.59808 | − | 1.50000i | 0.0824890 | − | 0.0476250i | ||||
\(993\) | − | 4.00000i | − | 0.126936i | ||||||
\(994\) | 4.00000 | + | 6.92820i | 0.126872 | + | 0.219749i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 1.73205 | − | 1.00000i | 0.0548546 | − | 0.0316703i | −0.472322 | − | 0.881426i | \(-0.656584\pi\) |
0.527176 | + | 0.849756i | \(0.323251\pi\) | |||||||
\(998\) | 34.6410 | + | 20.0000i | 1.09654 | + | 0.633089i | ||||
\(999\) | 2.50000 | − | 4.33013i | 0.0790965 | − | 0.136999i |
(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 | 1950.2.z.h.1699.2 | 4 | ||
5.2 | odd | 4 | 390.2.i.a.61.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1950.2.i.s.451.1 | 2 | |||
5.4 | even | 2 | inner | 1950.2.z.h.1699.1 | 4 | ||
13.3 | even | 3 | inner | 1950.2.z.h.1849.1 | 4 | ||
15.2 | even | 4 | 1170.2.i.k.451.1 | 2 | |||
65.3 | odd | 12 | 1950.2.i.s.601.1 | 2 | |||
65.7 | even | 12 | 5070.2.b.g.1351.2 | 2 | |||
65.17 | odd | 12 | 5070.2.a.f.1.1 | 1 | |||
65.22 | odd | 12 | 5070.2.a.o.1.1 | 1 | |||
65.29 | even | 6 | inner | 1950.2.z.h.1849.2 | 4 | ||
65.32 | even | 12 | 5070.2.b.g.1351.1 | 2 | |||
65.42 | odd | 12 | 390.2.i.a.211.1 | yes | 2 | ||
195.107 | even | 12 | 1170.2.i.k.991.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.a.61.1 | ✓ | 2 | 5.2 | odd | 4 | ||
390.2.i.a.211.1 | yes | 2 | 65.42 | odd | 12 | ||
1170.2.i.k.451.1 | 2 | 15.2 | even | 4 | |||
1170.2.i.k.991.1 | 2 | 195.107 | even | 12 | |||
1950.2.i.s.451.1 | 2 | 5.3 | odd | 4 | |||
1950.2.i.s.601.1 | 2 | 65.3 | odd | 12 | |||
1950.2.z.h.1699.1 | 4 | 5.4 | even | 2 | inner | ||
1950.2.z.h.1699.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.z.h.1849.1 | 4 | 13.3 | even | 3 | inner | ||
1950.2.z.h.1849.2 | 4 | 65.29 | even | 6 | inner | ||
5070.2.a.f.1.1 | 1 | 65.17 | odd | 12 | |||
5070.2.a.o.1.1 | 1 | 65.22 | odd | 12 | |||
5070.2.b.g.1351.1 | 2 | 65.32 | even | 12 | |||
5070.2.b.g.1351.2 | 2 | 65.7 | even | 12 |