Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(49,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.j (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: | \(3.59326809096\) |
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 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.349 |
Dual form | 450.2.j.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | − | 1.50000i | −0.500000 | − | 0.866025i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | 0.654654 | − | 0.755929i | \(-0.272814\pi\) |
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0.866025 | − | 1.50000i | 0.250000 | − | 0.433013i | ||||
\(13\) | −1.73205 | + | 1.00000i | −0.480384 | + | 0.277350i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) |
0.240192 | + | 0.970725i | \(0.422790\pi\) | |||||||
\(14\) | −0.500000 | − | 0.866025i | −0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 2.59808 | − | 1.50000i | 0.612372 | − | 0.353553i | ||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.73205i | − | 0.377964i | ||||||
\(22\) | 5.19615 | − | 3.00000i | 1.10782 | − | 0.639602i | ||||
\(23\) | −7.79423 | + | 4.50000i | −1.62521 | + | 0.938315i | −0.639713 | + | 0.768613i | \(0.720947\pi\) |
−0.985496 | + | 0.169701i | \(0.945720\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 10.3923 | 1.80907 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | −3.46410 | − | 2.00000i | −0.561951 | − | 0.324443i | ||||
\(39\) | 3.00000 | + | 1.73205i | 0.480384 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | −0.866025 | + | 1.50000i | −0.133631 | + | 0.231455i | ||||
\(43\) | 6.92820 | + | 4.00000i | 1.05654 | + | 0.609994i | 0.924473 | − | 0.381246i | \(-0.124505\pi\) |
0.132068 | + | 0.991241i | \(0.457838\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.00000 | 1.32698 | ||||||||
\(47\) | 2.59808 | + | 1.50000i | 0.378968 | + | 0.218797i | 0.677369 | − | 0.735643i | \(-0.263120\pi\) |
−0.298401 | + | 0.954441i | \(0.596453\pi\) | |||||||
\(48\) | 1.73205 | 0.250000 | ||||||||
\(49\) | −3.00000 | − | 5.19615i | −0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.73205 | − | 1.00000i | −0.240192 | − | 0.138675i | ||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | −3.46410 | − | 6.00000i | −0.458831 | − | 0.794719i | ||||
\(58\) | −2.59808 | + | 1.50000i | −0.341144 | + | 0.196960i | ||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | −2.59808 | + | 1.50000i | −0.327327 | + | 0.188982i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.00000 | − | 5.19615i | −1.10782 | − | 0.639602i | ||||
\(67\) | −11.2583 | + | 6.50000i | −1.37542 | + | 0.794101i | −0.991605 | − | 0.129307i | \(-0.958725\pi\) |
−0.383819 | + | 0.923408i | \(0.625391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5000 | + | 7.79423i | 1.62521 | + | 0.938315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | −5.19615 | + | 3.00000i | −0.592157 | + | 0.341882i | ||||
\(78\) | −1.73205 | − | 3.00000i | −0.196116 | − | 0.339683i | ||||
\(79\) | −5.00000 | + | 8.66025i | −0.562544 | + | 0.974355i | 0.434730 | + | 0.900561i | \(0.356844\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | − | 3.00000i | − | 0.331295i | ||||||
\(83\) | −7.79423 | − | 4.50000i | −0.855528 | − | 0.493939i | 0.00698436 | − | 0.999976i | \(-0.497777\pi\) |
−0.862512 | + | 0.506036i | \(0.831110\pi\) | |||||||
\(84\) | 1.50000 | − | 0.866025i | 0.163663 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 6.92820i | −0.431331 | − | 0.747087i | ||||
\(87\) | −5.19615 | −0.557086 | ||||||||
\(88\) | 5.19615 | + | 3.00000i | 0.553912 | + | 0.319801i | ||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | −7.79423 | − | 4.50000i | −0.812605 | − | 0.469157i | ||||
\(93\) | 3.46410 | − | 6.00000i | 0.359211 | − | 0.622171i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.50000 | − | 0.866025i | −0.153093 | − | 0.0883883i | ||||
\(97\) | −1.73205 | − | 1.00000i | −0.175863 | − | 0.101535i | 0.409484 | − | 0.912317i | \(-0.365709\pi\) |
−0.585348 | + | 0.810782i | \(0.699042\pi\) | |||||||
\(98\) | 6.00000i | 0.606092i | ||||||||
\(99\) | −9.00000 | − | 15.5885i | −0.904534 | − | 1.56670i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | + | 4.00000i | −0.682656 | + | 0.394132i | −0.800855 | − | 0.598858i | \(-0.795621\pi\) |
0.118199 | + | 0.992990i | \(0.462288\pi\) | |||||||
\(104\) | 1.00000 | + | 1.73205i | 0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | + | 5.19615i | −0.291386 | + | 0.504695i | ||||
\(107\) | − | 3.00000i | − | 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 2.59808 | + | 4.50000i | 0.250000 | + | 0.433013i | ||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | − | 6.92820i | 1.13899 | − | 0.657596i | ||||
\(112\) | −0.866025 | + | 0.500000i | −0.0818317 | + | 0.0472456i | ||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 6.92820i | 0.648886i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | − | 6.00000i | − | 0.552345i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −11.2583 | + | 6.50000i | −1.01928 | + | 0.588482i | ||||
\(123\) | 2.59808 | − | 4.50000i | 0.234261 | − | 0.405751i | ||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | − | 7.00000i | − | 0.621150i | −0.950549 | − | 0.310575i | \(-0.899478\pi\) | ||
0.950549 | − | 0.310575i | \(-0.100522\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | − | 13.8564i | − | 1.21999i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 5.19615 | + | 9.00000i | 0.452267 | + | 0.783349i | ||||
\(133\) | 3.46410 | + | 2.00000i | 0.300376 | + | 0.173422i | ||||
\(134\) | 13.0000 | 1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | −7.79423 | − | 13.5000i | −0.663489 | − | 1.14920i | ||||
\(139\) | −8.00000 | − | 13.8564i | −0.678551 | − | 1.17529i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.296866 | − | 0.954919i | \(-0.404058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.19615i | − | 0.437595i | ||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | − | 3.46410i | 0.165521 | − | 0.286691i | ||||
\(147\) | −5.19615 | + | 9.00000i | −0.428571 | + | 0.742307i | ||||
\(148\) | −6.92820 | + | 4.00000i | −0.569495 | + | 0.328798i | ||||
\(149\) | −1.50000 | − | 2.59808i | −0.122885 | − | 0.212843i | 0.798019 | − | 0.602632i | \(-0.205881\pi\) |
−0.920904 | + | 0.389789i | \(0.872548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.00000 | + | 12.1244i | −0.569652 | + | 0.986666i | 0.426948 | + | 0.904276i | \(0.359589\pi\) |
−0.996600 | + | 0.0823900i | \(0.973745\pi\) | |||||||
\(152\) | − | 4.00000i | − | 0.324443i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.46410i | 0.277350i | ||||||||
\(157\) | 12.1244 | − | 7.00000i | 0.967629 | − | 0.558661i | 0.0691164 | − | 0.997609i | \(-0.477982\pi\) |
0.898513 | + | 0.438948i | \(0.144649\pi\) | |||||||
\(158\) | 8.66025 | − | 5.00000i | 0.688973 | − | 0.397779i | ||||
\(159\) | −9.00000 | + | 5.19615i | −0.713746 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | −0.709299 | ||||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | + | 7.79423i | 0.349268 | + | 0.604949i | ||||
\(167\) | −2.59808 | + | 1.50000i | −0.201045 | + | 0.116073i | −0.597143 | − | 0.802135i | \(-0.703697\pi\) |
0.396098 | + | 0.918208i | \(0.370364\pi\) | |||||||
\(168\) | −1.73205 | −0.133631 | ||||||||
\(169\) | −4.50000 | + | 7.79423i | −0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | + | 10.3923i | −0.458831 | + | 0.794719i | ||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | 20.7846 | + | 12.0000i | 1.58022 | + | 0.912343i | 0.994826 | + | 0.101598i | \(0.0323955\pi\) |
0.585399 | + | 0.810745i | \(0.300938\pi\) | |||||||
\(174\) | 4.50000 | + | 2.59808i | 0.341144 | + | 0.196960i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | − | 5.19615i | −0.226134 | − | 0.391675i | ||||
\(177\) | 5.19615 | − | 9.00000i | 0.390567 | − | 0.676481i | ||||
\(178\) | 7.79423 | + | 4.50000i | 0.584202 | + | 0.337289i | ||||
\(179\) | 18.0000 | 1.34538 | 0.672692 | − | 0.739923i | \(-0.265138\pi\) | ||||
0.672692 | + | 0.739923i | \(0.265138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 1.73205 | + | 1.00000i | 0.128388 | + | 0.0741249i | ||||
\(183\) | −22.5167 | −1.66448 | ||||||||
\(184\) | 4.50000 | + | 7.79423i | 0.331744 | + | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | + | 3.46410i | −0.439941 | + | 0.254000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 0.866025 | + | 1.50000i | 0.0625000 | + | 0.108253i | ||||
\(193\) | −1.73205 | + | 1.00000i | −0.124676 | + | 0.0719816i | −0.561041 | − | 0.827788i | \(-0.689599\pi\) |
0.436365 | + | 0.899770i | \(0.356266\pi\) | |||||||
\(194\) | 1.00000 | + | 1.73205i | 0.0717958 | + | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | − | 12.0000i | − | 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 18.0000i | 1.27920i | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5000 | + | 11.2583i | 1.37542 | + | 0.794101i | ||||
\(202\) | 5.19615 | − | 3.00000i | 0.365600 | − | 0.211079i | ||||
\(203\) | 2.59808 | − | 1.50000i | 0.182349 | − | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | − | 27.0000i | − | 1.87663i | ||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | −12.0000 | + | 20.7846i | −0.830057 | + | 1.43770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | − | 1.73205i | −0.0688428 | − | 0.119239i | 0.829549 | − | 0.558433i | \(-0.188597\pi\) |
−0.898392 | + | 0.439194i | \(0.855264\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | 5.19615 | + | 9.00000i | 0.356034 | + | 0.616670i | ||||
\(214\) | −1.50000 | + | 2.59808i | −0.102538 | + | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | −6.06218 | − | 3.50000i | −0.410582 | − | 0.237050i | ||||
\(219\) | 6.00000 | − | 3.46410i | 0.405442 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.8564 | −0.929981 | ||||||||
\(223\) | −0.866025 | − | 0.500000i | −0.0579934 | − | 0.0334825i | 0.470723 | − | 0.882281i | \(-0.343993\pi\) |
−0.528716 | + | 0.848799i | \(0.677326\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3923 | + | 6.00000i | 0.689761 | + | 0.398234i | 0.803523 | − | 0.595274i | \(-0.202957\pi\) |
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(228\) | 3.46410 | − | 6.00000i | 0.229416 | − | 0.397360i | ||||
\(229\) | −6.50000 | − | 11.2583i | −0.429532 | − | 0.743971i | 0.567300 | − | 0.823511i | \(-0.307988\pi\) |
−0.996832 | + | 0.0795401i | \(0.974655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.00000 | + | 5.19615i | 0.592157 | + | 0.341882i | ||||
\(232\) | −2.59808 | − | 1.50000i | −0.170572 | − | 0.0984798i | ||||
\(233\) | 12.0000i | 0.786146i | 0.919507 | + | 0.393073i | \(0.128588\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00000 | + | 5.19615i | −0.195283 | + | 0.338241i | ||||
\(237\) | 17.3205 | 1.12509 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5000 | + | 25.1147i | −0.934027 | + | 1.61778i | −0.157667 | + | 0.987492i | \(0.550397\pi\) |
−0.776360 | + | 0.630290i | \(0.782936\pi\) | |||||||
\(242\) | 25.0000i | 1.60706i | ||||||||
\(243\) | −7.79423 | + | 13.5000i | −0.500000 | + | 0.866025i | ||||
\(244\) | 13.0000 | 0.832240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.50000 | + | 2.59808i | −0.286910 | + | 0.165647i | ||||
\(247\) | −6.92820 | + | 4.00000i | −0.440831 | + | 0.254514i | ||||
\(248\) | 3.46410 | − | 2.00000i | 0.219971 | − | 0.127000i | ||||
\(249\) | 15.5885i | 0.987878i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −2.59808 | − | 1.50000i | −0.163663 | − | 0.0944911i | ||||
\(253\) | − | 54.0000i | − | 3.39495i | ||||||
\(254\) | −3.50000 | + | 6.06218i | −0.219610 | + | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.5885 | − | 9.00000i | 0.972381 | − | 0.561405i | 0.0724199 | − | 0.997374i | \(-0.476928\pi\) |
0.899961 | + | 0.435970i | \(0.143595\pi\) | |||||||
\(258\) | −6.92820 | + | 12.0000i | −0.431331 | + | 0.747087i | ||||
\(259\) | −4.00000 | + | 6.92820i | −0.248548 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | − | 18.0000i | − | 1.11204i | ||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.00000 | − | 3.46410i | −0.122628 | − | 0.212398i | ||||
\(267\) | 7.79423 | + | 13.5000i | 0.476999 | + | 0.826187i | ||||
\(268\) | −11.2583 | − | 6.50000i | −0.687712 | − | 0.397051i | ||||
\(269\) | −21.0000 | −1.28039 | −0.640196 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73205 | + | 3.00000i | 0.104828 | + | 0.181568i | ||||
\(274\) | −6.00000 | − | 10.3923i | −0.362473 | − | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.5885i | 0.938315i | ||||||||
\(277\) | −6.92820 | − | 4.00000i | −0.416275 | − | 0.240337i | 0.277207 | − | 0.960810i | \(-0.410591\pi\) |
−0.693482 | + | 0.720473i | \(0.743925\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.50000 | − | 12.9904i | 0.447412 | − | 0.774941i | −0.550804 | − | 0.834634i | \(-0.685679\pi\) |
0.998217 | + | 0.0596933i | \(0.0190123\pi\) | |||||||
\(282\) | −2.59808 | + | 4.50000i | −0.154713 | + | 0.267971i | ||||
\(283\) | 11.2583 | − | 6.50000i | 0.669238 | − | 0.386385i | −0.126550 | − | 0.991960i | \(-0.540390\pi\) |
0.795788 | + | 0.605575i | \(0.207057\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | + | 10.3923i | −0.354787 | + | 0.614510i | ||||
\(287\) | 3.00000i | 0.177084i | ||||||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.46410i | 0.203069i | ||||||||
\(292\) | −3.46410 | + | 2.00000i | −0.202721 | + | 0.117041i | ||||
\(293\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(294\) | 9.00000 | − | 5.19615i | 0.524891 | − | 0.303046i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.00000 | 0.464991 | ||||||||
\(297\) | −15.5885 | + | 27.0000i | −0.904534 | + | 1.56670i | ||||
\(298\) | 3.00000i | 0.173785i | ||||||||
\(299\) | 9.00000 | − | 15.5885i | 0.520483 | − | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 12.1244 | − | 7.00000i | 0.697678 | − | 0.402805i | ||||
\(303\) | 10.3923 | 0.597022 | ||||||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | −5.19615 | − | 3.00000i | −0.296078 | − | 0.170941i | ||||
\(309\) | 12.0000 | + | 6.92820i | 0.682656 | + | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | 1.73205 | − | 3.00000i | 0.0980581 | − | 0.169842i | ||||
\(313\) | 1.73205 | + | 1.00000i | 0.0979013 | + | 0.0565233i | 0.548151 | − | 0.836379i | \(-0.315332\pi\) |
−0.450250 | + | 0.892903i | \(0.648665\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 5.19615 | + | 3.00000i | 0.291845 | + | 0.168497i | 0.638774 | − | 0.769395i | \(-0.279442\pi\) |
−0.346929 | + | 0.937892i | \(0.612775\pi\) | |||||||
\(318\) | 10.3923 | 0.582772 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 7.79423 | + | 4.50000i | 0.434355 | + | 0.250775i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | −6.06218 | − | 10.5000i | −0.335239 | − | 0.580651i | ||||
\(328\) | 2.59808 | − | 1.50000i | 0.143455 | − | 0.0828236i | ||||
\(329\) | 1.50000 | + | 2.59808i | 0.0826977 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | − | 9.00000i | − | 0.493939i | ||||||
\(333\) | −20.7846 | − | 12.0000i | −1.13899 | − | 0.657596i | ||||
\(334\) | 3.00000 | 0.164153 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.50000 | + | 0.866025i | 0.0818317 | + | 0.0472456i | ||||
\(337\) | 6.92820 | − | 4.00000i | 0.377403 | − | 0.217894i | −0.299285 | − | 0.954164i | \(-0.596748\pi\) |
0.676688 | + | 0.736270i | \(0.263415\pi\) | |||||||
\(338\) | 7.79423 | − | 4.50000i | 0.423950 | − | 0.244768i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 10.3923 | − | 6.00000i | 0.561951 | − | 0.324443i | ||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 4.00000 | − | 6.92820i | 0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | − | 20.7846i | −0.645124 | − | 1.11739i | ||||
\(347\) | 10.3923 | − | 6.00000i | 0.557888 | − | 0.322097i | −0.194409 | − | 0.980921i | \(-0.562279\pi\) |
0.752297 | + | 0.658824i | \(0.228946\pi\) | |||||||
\(348\) | −2.59808 | − | 4.50000i | −0.139272 | − | 0.241225i | ||||
\(349\) | 11.5000 | − | 19.9186i | 0.615581 | − | 1.06622i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.990282 | − | 0.139072i | \(-0.0444119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | + | 5.19615i | −0.480384 | + | 0.277350i | ||||
\(352\) | 6.00000i | 0.319801i | ||||||||
\(353\) | 20.7846 | + | 12.0000i | 1.10625 | + | 0.638696i | 0.937856 | − | 0.347024i | \(-0.112808\pi\) |
0.168397 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(354\) | −9.00000 | + | 5.19615i | −0.478345 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.50000 | − | 7.79423i | −0.238500 | − | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.5885 | − | 9.00000i | −0.823876 | − | 0.475665i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | −4.33013 | − | 2.50000i | −0.227586 | − | 0.131397i | ||||
\(363\) | −21.6506 | + | 37.5000i | −1.13636 | + | 1.96824i | ||||
\(364\) | −1.00000 | − | 1.73205i | −0.0524142 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19.5000 | + | 11.2583i | 1.01928 | + | 0.588482i | ||||
\(367\) | −6.92820 | − | 4.00000i | −0.361649 | − | 0.208798i | 0.308155 | − | 0.951336i | \(-0.400289\pi\) |
−0.669804 | + | 0.742538i | \(0.733622\pi\) | |||||||
\(368\) | − | 9.00000i | − | 0.469157i | ||||||
\(369\) | −9.00000 | −0.468521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | − | 5.19615i | 0.155752 | − | 0.269771i | ||||
\(372\) | 6.92820 | 0.359211 | ||||||||
\(373\) | −22.5167 | + | 13.0000i | −1.16587 | + | 0.673114i | −0.952703 | − | 0.303902i | \(-0.901711\pi\) |
−0.213165 | + | 0.977016i | \(0.568377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | −2.59808 | − | 4.50000i | −0.133631 | − | 0.231455i | ||||
\(379\) | 22.0000 | 1.13006 | 0.565032 | − | 0.825069i | \(-0.308864\pi\) | ||||
0.565032 | + | 0.825069i | \(0.308864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5000 | + | 6.06218i | −0.537931 | + | 0.310575i | ||||
\(382\) | −10.3923 | + | 6.00000i | −0.531717 | + | 0.306987i | ||||
\(383\) | 10.3923 | − | 6.00000i | 0.531022 | − | 0.306586i | −0.210411 | − | 0.977613i | \(-0.567480\pi\) |
0.741433 | + | 0.671027i | \(0.234147\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | −20.7846 | + | 12.0000i | −1.05654 | + | 0.609994i | ||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | 10.5000 | − | 18.1865i | 0.532371 | − | 0.922094i | −0.466915 | − | 0.884302i | \(-0.654634\pi\) |
0.999286 | − | 0.0377914i | \(-0.0120322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.19615 | + | 3.00000i | −0.262445 | + | 0.151523i | ||||
\(393\) | 15.5885 | − | 27.0000i | 0.786334 | − | 1.36197i | ||||
\(394\) | −6.00000 | + | 10.3923i | −0.302276 | + | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.00000 | − | 15.5885i | 0.452267 | − | 0.783349i | ||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | 6.92820 | + | 4.00000i | 0.347279 | + | 0.200502i | ||||
\(399\) | − | 6.92820i | − | 0.346844i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | −11.2583 | − | 19.5000i | −0.561514 | − | 0.972572i | ||||
\(403\) | −6.92820 | − | 4.00000i | −0.345118 | − | 0.199254i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | −0.148888 | ||||||||
\(407\) | −41.5692 | − | 24.0000i | −2.06051 | − | 1.18964i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 20.7846i | − | 1.02523i | ||||||
\(412\) | −6.92820 | − | 4.00000i | −0.341328 | − | 0.197066i | ||||
\(413\) | 6.00000i | 0.295241i | ||||||||
\(414\) | −13.5000 | + | 23.3827i | −0.663489 | + | 1.14920i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | −13.8564 | + | 24.0000i | −0.678551 | + | 1.17529i | ||||
\(418\) | 20.7846 | − | 12.0000i | 1.01661 | − | 0.586939i | ||||
\(419\) | −15.0000 | − | 25.9808i | −0.732798 | − | 1.26924i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.222885 | − | 0.974845i | \(-0.428453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 2.00000i | 0.0973585i | ||||||||
\(423\) | −7.79423 | + | 4.50000i | −0.378968 | + | 0.218797i | ||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 10.3923i | − | 0.503509i | ||||||
\(427\) | 11.2583 | − | 6.50000i | 0.544829 | − | 0.314557i | ||||
\(428\) | 2.59808 | − | 1.50000i | 0.125583 | − | 0.0725052i | ||||
\(429\) | −18.0000 | + | 10.3923i | −0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | −2.59808 | + | 4.50000i | −0.125000 | + | 0.216506i | ||||
\(433\) | 16.0000i | 0.768911i | 0.923144 | + | 0.384455i | \(0.125611\pi\) | ||||
−0.923144 | + | 0.384455i | \(0.874389\pi\) | |||||||
\(434\) | 2.00000 | − | 3.46410i | 0.0960031 | − | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50000 | + | 6.06218i | 0.167620 | + | 0.290326i | ||||
\(437\) | −31.1769 | + | 18.0000i | −1.49139 | + | 0.861057i | ||||
\(438\) | −6.92820 | −0.331042 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0000 | 0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.79423 | + | 4.50000i | 0.370315 | + | 0.213801i | 0.673596 | − | 0.739100i | \(-0.264749\pi\) |
−0.303281 | + | 0.952901i | \(0.598082\pi\) | |||||||
\(444\) | 12.0000 | + | 6.92820i | 0.569495 | + | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.500000 | + | 0.866025i | 0.0236757 | + | 0.0410075i | ||||
\(447\) | −2.59808 | + | 4.50000i | −0.122885 | + | 0.212843i | ||||
\(448\) | −0.866025 | − | 0.500000i | −0.0409159 | − | 0.0236228i | ||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.2487 | 1.13930 | ||||||||
\(454\) | −6.00000 | − | 10.3923i | −0.281594 | − | 0.487735i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.00000 | + | 3.46410i | −0.280976 | + | 0.162221i | ||||
\(457\) | −6.92820 | − | 4.00000i | −0.324088 | − | 0.187112i | 0.329125 | − | 0.944286i | \(-0.393246\pi\) |
−0.653213 | + | 0.757174i | \(0.726579\pi\) | |||||||
\(458\) | 13.0000i | 0.607450i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5000 | − | 23.3827i | 0.628758 | − | 1.08904i | −0.359044 | − | 0.933321i | \(-0.616897\pi\) |
0.987801 | − | 0.155719i | \(-0.0497696\pi\) | |||||||
\(462\) | −5.19615 | − | 9.00000i | −0.241747 | − | 0.418718i | ||||
\(463\) | 3.46410 | − | 2.00000i | 0.160990 | − | 0.0929479i | −0.417340 | − | 0.908750i | \(-0.637038\pi\) |
0.578331 | + | 0.815802i | \(0.303704\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | − | 10.3923i | 0.277945 | − | 0.481414i | ||||
\(467\) | 36.0000i | 1.66588i | 0.553362 | + | 0.832941i | \(0.313345\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(468\) | 5.19615 | − | 3.00000i | 0.240192 | − | 0.138675i | ||||
\(469\) | −13.0000 | −0.600284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0000 | − | 12.1244i | −0.967629 | − | 0.558661i | ||||
\(472\) | 5.19615 | − | 3.00000i | 0.239172 | − | 0.138086i | ||||
\(473\) | −41.5692 | + | 24.0000i | −1.91135 | + | 1.10352i | ||||
\(474\) | −15.0000 | − | 8.66025i | −0.688973 | − | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.5885 | + | 9.00000i | 0.713746 | + | 0.412082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | + | 25.9808i | −0.685367 | + | 1.18709i | 0.287954 | + | 0.957644i | \(0.407025\pi\) |
−0.973321 | + | 0.229447i | \(0.926308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 25.1147 | − | 14.5000i | 1.14394 | − | 0.660457i | ||||
\(483\) | 7.79423 | + | 13.5000i | 0.354650 | + | 0.614271i | ||||
\(484\) | 12.5000 | − | 21.6506i | 0.568182 | − | 0.984120i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.5000 | − | 7.79423i | 0.612372 | − | 0.353553i | ||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | −11.2583 | − | 6.50000i | −0.509641 | − | 0.294241i | ||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | − | 10.3923i | −0.270776 | − | 0.468998i | 0.698285 | − | 0.715820i | \(-0.253947\pi\) |
−0.969061 | + | 0.246822i | \(0.920614\pi\) | |||||||
\(492\) | 5.19615 | 0.234261 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −5.19615 | − | 3.00000i | −0.233079 | − | 0.134568i | ||||
\(498\) | 7.79423 | − | 13.5000i | 0.349268 | − | 0.604949i | ||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.50000 | + | 2.59808i | 0.201045 | + | 0.116073i | ||||
\(502\) | −10.3923 | − | 6.00000i | −0.463831 | − | 0.267793i | ||||
\(503\) | − | 27.0000i | − | 1.20387i | −0.798545 | − | 0.601935i | \(-0.794397\pi\) | ||
0.798545 | − | 0.601935i | \(-0.205603\pi\) | |||||||
\(504\) | 1.50000 | + | 2.59808i | 0.0668153 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −27.0000 | + | 46.7654i | −1.20030 | + | 2.07897i | ||||
\(507\) | 15.5885 | 0.692308 | ||||||||
\(508\) | 6.06218 | − | 3.50000i | 0.268966 | − | 0.155287i | ||||
\(509\) | 7.50000 | + | 12.9904i | 0.332432 | + | 0.575789i | 0.982988 | − | 0.183669i | \(-0.0587976\pi\) |
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 20.7846 | 0.917663 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.0000 | − | 6.92820i | 0.528271 | − | 0.304997i | ||||
\(517\) | −15.5885 | + | 9.00000i | −0.685580 | + | 0.395820i | ||||
\(518\) | 6.92820 | − | 4.00000i | 0.304408 | − | 0.175750i | ||||
\(519\) | − | 41.5692i | − | 1.82469i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | − | 9.00000i | − | 0.393919i | ||||||
\(523\) | 19.0000i | 0.830812i | 0.909636 | + | 0.415406i | \(0.136360\pi\) | ||||
−0.909636 | + | 0.415406i | \(0.863640\pi\) | |||||||
\(524\) | −9.00000 | + | 15.5885i | −0.393167 | + | 0.680985i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5.19615 | + | 9.00000i | −0.226134 | + | 0.391675i | ||||
\(529\) | 29.0000 | − | 50.2295i | 1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 4.00000i | 0.173422i | ||||||||
\(533\) | −5.19615 | − | 3.00000i | −0.225070 | − | 0.129944i | ||||
\(534\) | − | 15.5885i | − | 0.674579i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.50000 | + | 11.2583i | 0.280757 | + | 0.486286i | ||||
\(537\) | −15.5885 | − | 27.0000i | −0.672692 | − | 1.16514i | ||||
\(538\) | 18.1865 | + | 10.5000i | 0.784077 | + | 0.452687i | ||||
\(539\) | 36.0000 | 1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 3.46410 | + | 2.00000i | 0.148796 | + | 0.0859074i | ||||
\(543\) | −4.33013 | − | 7.50000i | −0.185824 | − | 0.321856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 3.46410i | − | 0.148250i | ||||||
\(547\) | 37.2391 | + | 21.5000i | 1.59223 | + | 0.919274i | 0.992924 | + | 0.118753i | \(0.0378896\pi\) |
0.599305 | + | 0.800521i | \(0.295444\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | 19.5000 | + | 33.7750i | 0.832240 | + | 1.44148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | − | 10.3923i | 0.255609 | − | 0.442727i | ||||
\(552\) | 7.79423 | − | 13.5000i | 0.331744 | − | 0.574598i | ||||
\(553\) | −8.66025 | + | 5.00000i | −0.368271 | + | 0.212622i | ||||
\(554\) | 4.00000 | + | 6.92820i | 0.169944 | + | 0.294351i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.00000 | − | 13.8564i | 0.339276 | − | 0.587643i | ||||
\(557\) | − | 6.00000i | − | 0.254228i | −0.991888 | − | 0.127114i | \(-0.959429\pi\) | ||
0.991888 | − | 0.127114i | \(-0.0405714\pi\) | |||||||
\(558\) | 10.3923 | + | 6.00000i | 0.439941 | + | 0.254000i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.9904 | + | 7.50000i | −0.547966 | + | 0.316368i | ||||
\(563\) | 2.59808 | − | 1.50000i | 0.109496 | − | 0.0632175i | −0.444252 | − | 0.895902i | \(-0.646530\pi\) |
0.553748 | + | 0.832684i | \(0.313197\pi\) | |||||||
\(564\) | 4.50000 | − | 2.59808i | 0.189484 | − | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.0000 | −0.546431 | ||||||||
\(567\) | − | 9.00000i | − | 0.377964i | ||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | + | 34.6410i | 0.836974 | + | 1.44968i | 0.892413 | + | 0.451219i | \(0.149011\pi\) |
−0.0554391 | + | 0.998462i | \(0.517656\pi\) | |||||||
\(572\) | 10.3923 | − | 6.00000i | 0.434524 | − | 0.250873i | ||||
\(573\) | −20.7846 | −0.868290 | ||||||||
\(574\) | 1.50000 | − | 2.59808i | 0.0626088 | − | 0.108442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | − | 10.0000i | − | 0.416305i | −0.978096 | − | 0.208153i | \(-0.933255\pi\) | ||
0.978096 | − | 0.208153i | \(-0.0667451\pi\) | |||||||
\(578\) | −14.7224 | − | 8.50000i | −0.612372 | − | 0.353553i | ||||
\(579\) | 3.00000 | + | 1.73205i | 0.124676 | + | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50000 | − | 7.79423i | −0.186691 | − | 0.323359i | ||||
\(582\) | 1.73205 | − | 3.00000i | 0.0717958 | − | 0.124354i | ||||
\(583\) | 31.1769 | + | 18.0000i | 1.29122 | + | 0.745484i | ||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.9904 | + | 7.50000i | 0.536170 | + | 0.309558i | 0.743525 | − | 0.668708i | \(-0.233152\pi\) |
−0.207355 | + | 0.978266i | \(0.566486\pi\) | |||||||
\(588\) | −10.3923 | −0.428571 | ||||||||
\(589\) | 8.00000 | + | 13.8564i | 0.329634 | + | 0.570943i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | + | 10.3923i | −0.740421 | + | 0.427482i | ||||
\(592\) | −6.92820 | − | 4.00000i | −0.284747 | − | 0.164399i | ||||
\(593\) | − | 24.0000i | − | 0.985562i | −0.870153 | − | 0.492781i | \(-0.835980\pi\) | ||
0.870153 | − | 0.492781i | \(-0.164020\pi\) | |||||||
\(594\) | 27.0000 | − | 15.5885i | 1.10782 | − | 0.639602i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.50000 | − | 2.59808i | 0.0614424 | − | 0.106421i | ||||
\(597\) | 6.92820 | + | 12.0000i | 0.283552 | + | 0.491127i | ||||
\(598\) | −15.5885 | + | 9.00000i | −0.637459 | + | 0.368037i | ||||
\(599\) | −3.00000 | − | 5.19615i | −0.122577 | − | 0.212309i | 0.798206 | − | 0.602384i | \(-0.205782\pi\) |
−0.920783 | + | 0.390075i | \(0.872449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | + | 22.5167i | −0.530281 | + | 0.918474i | 0.469095 | + | 0.883148i | \(0.344580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | − | 8.00000i | − | 0.326056i | ||||||
\(603\) | − | 39.0000i | − | 1.58820i | ||||||
\(604\) | −14.0000 | −0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.00000 | − | 5.19615i | −0.365600 | − | 0.211079i | ||||
\(607\) | 25.1147 | − | 14.5000i | 1.01938 | − | 0.588537i | 0.105453 | − | 0.994424i | \(-0.466371\pi\) |
0.913923 | + | 0.405887i | \(0.133038\pi\) | |||||||
\(608\) | 3.46410 | − | 2.00000i | 0.140488 | − | 0.0811107i | ||||
\(609\) | −4.50000 | − | 2.59808i | −0.182349 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.0000i | 1.61558i | 0.589467 | + | 0.807792i | \(0.299338\pi\) | ||||
−0.589467 | + | 0.807792i | \(0.700662\pi\) | |||||||
\(614\) | −3.50000 | + | 6.06218i | −0.141249 | + | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | + | 5.19615i | 0.120873 | + | 0.209359i | ||||
\(617\) | 10.3923 | − | 6.00000i | 0.418378 | − | 0.241551i | −0.276005 | − | 0.961156i | \(-0.589011\pi\) |
0.694383 | + | 0.719605i | \(0.255677\pi\) | |||||||
\(618\) | −6.92820 | − | 12.0000i | −0.278693 | − | 0.482711i | ||||
\(619\) | −20.0000 | + | 34.6410i | −0.803868 | + | 1.39234i | 0.113185 | + | 0.993574i | \(0.463895\pi\) |
−0.917053 | + | 0.398766i | \(0.869439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.5000 | + | 23.3827i | −1.62521 | + | 0.938315i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | −7.79423 | − | 4.50000i | −0.312269 | − | 0.180289i | ||||
\(624\) | −3.00000 | + | 1.73205i | −0.120096 | + | 0.0693375i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.00000 | − | 1.73205i | −0.0399680 | − | 0.0692267i | ||||
\(627\) | 41.5692 | 1.66011 | ||||||||
\(628\) | 12.1244 | + | 7.00000i | 0.483814 | + | 0.279330i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 8.66025 | + | 5.00000i | 0.344486 | + | 0.198889i | ||||
\(633\) | −1.73205 | + | 3.00000i | −0.0688428 | + | 0.119239i | ||||
\(634\) | −3.00000 | − | 5.19615i | −0.119145 | − | 0.206366i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.00000 | − | 5.19615i | −0.356873 | − | 0.206041i | ||||
\(637\) | 10.3923 | + | 6.00000i | 0.411758 | + | 0.237729i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 9.00000 | − | 15.5885i | 0.356034 | − | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | + | 28.5788i | −0.651711 | + | 1.12880i | 0.330997 | + | 0.943632i | \(0.392615\pi\) |
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(642\) | 5.19615 | 0.205076 | ||||||||
\(643\) | 26.8468 | − | 15.5000i | 1.05873 | − | 0.611260i | 0.133652 | − | 0.991028i | \(-0.457330\pi\) |
0.925082 | + | 0.379768i | \(0.123996\pi\) | |||||||
\(644\) | −4.50000 | − | 7.79423i | −0.177325 | − | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.00000i | − | 0.117942i | −0.998260 | − | 0.0589711i | \(-0.981218\pi\) | ||
0.998260 | − | 0.0589711i | \(-0.0187820\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | − | 3.46410i | 0.235159 | − | 0.135769i | ||||
\(652\) | −3.46410 | + | 2.00000i | −0.135665 | + | 0.0783260i | ||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 12.1244i | 0.474100i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | −10.3923 | − | 6.00000i | −0.405442 | − | 0.234082i | ||||
\(658\) | − | 3.00000i | − | 0.116952i | ||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0000 | + | 39.8372i | 0.894596 | + | 1.54949i | 0.834303 | + | 0.551306i | \(0.185870\pi\) |
0.0602929 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(662\) | −8.66025 | + | 5.00000i | −0.336590 | + | 0.194331i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0000 | + | 20.7846i | 0.464991 | + | 0.805387i | ||||
\(667\) | 27.0000i | 1.04544i | ||||||||
\(668\) | −2.59808 | − | 1.50000i | −0.100523 | − | 0.0580367i | ||||
\(669\) | 1.73205i | 0.0669650i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.0000 | + | 67.5500i | 1.50558 | + | 2.60774i | ||||
\(672\) | −0.866025 | − | 1.50000i | −0.0334077 | − | 0.0578638i | ||||
\(673\) | −39.8372 | − | 23.0000i | −1.53561 | − | 0.886585i | −0.999088 | − | 0.0426985i | \(-0.986405\pi\) |
−0.536522 | − | 0.843886i | \(-0.680262\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −15.5885 | − | 9.00000i | −0.599113 | − | 0.345898i | 0.169580 | − | 0.985517i | \(-0.445759\pi\) |
−0.768693 | + | 0.639618i | \(0.779092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 20.7846i | − | 0.796468i | ||||||
\(682\) | 20.7846 | + | 12.0000i | 0.795884 | + | 0.459504i | ||||
\(683\) | − | 12.0000i | − | 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | −12.0000 | −0.458831 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | −11.2583 | + | 19.5000i | −0.429532 | + | 0.743971i | ||||
\(688\) | −6.92820 | + | 4.00000i | −0.264135 | + | 0.152499i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | − | 8.66025i | 0.190209 | − | 0.329452i | −0.755110 | − | 0.655598i | \(-0.772417\pi\) |
0.945319 | + | 0.326146i | \(0.105750\pi\) | |||||||
\(692\) | 24.0000i | 0.912343i | ||||||||
\(693\) | − | 18.0000i | − | 0.683763i | ||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.19615i | 0.196960i | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −19.9186 | + | 11.5000i | −0.753930 | + | 0.435281i | ||||
\(699\) | 18.0000 | − | 10.3923i | 0.680823 | − | 0.393073i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.0000 | −1.69963 | −0.849813 | − | 0.527084i | \(-0.823285\pi\) | ||||
−0.849813 | + | 0.527084i | \(0.823285\pi\) | |||||||
\(702\) | 10.3923 | 0.392232 | ||||||||
\(703\) | 32.0000i | 1.20690i | ||||||||
\(704\) | 3.00000 | − | 5.19615i | 0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | − | 20.7846i | −0.451626 | − | 0.782239i | ||||
\(707\) | −5.19615 | + | 3.00000i | −0.195421 | + | 0.112827i | ||||
\(708\) | 10.3923 | 0.390567 | ||||||||
\(709\) | 5.50000 | − | 9.52628i | 0.206557 | − | 0.357767i | −0.744071 | − | 0.668101i | \(-0.767108\pi\) |
0.950628 | + | 0.310334i | \(0.100441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0000 | − | 25.9808i | −0.562544 | − | 0.974355i | ||||
\(712\) | 9.00000i | 0.337289i | ||||||||
\(713\) | −31.1769 | − | 18.0000i | −1.16758 | − | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3923 | − | 6.00000i | −0.387837 | − | 0.223918i | ||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 2.59808 | + | 1.50000i | 0.0966904 | + | 0.0558242i | ||||
\(723\) | 50.2295 | 1.86805 | ||||||||
\(724\) | 2.50000 | + | 4.33013i | 0.0929118 | + | 0.160928i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 37.5000 | − | 21.6506i | 1.39176 | − | 0.803530i | ||||
\(727\) | −45.8993 | − | 26.5000i | −1.70231 | − | 0.982831i | −0.943411 | − | 0.331625i | \(-0.892403\pi\) |
−0.758901 | − | 0.651206i | \(-0.774263\pi\) | |||||||
\(728\) | 2.00000i | 0.0741249i | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −11.2583 | − | 19.5000i | −0.416120 | − | 0.720741i | ||||
\(733\) | −12.1244 | + | 7.00000i | −0.447823 | + | 0.258551i | −0.706910 | − | 0.707303i | \(-0.749912\pi\) |
0.259087 | + | 0.965854i | \(0.416578\pi\) | |||||||
\(734\) | 4.00000 | + | 6.92820i | 0.147643 | + | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.50000 | + | 7.79423i | −0.165872 | + | 0.287299i | ||||
\(737\) | − | 78.0000i | − | 2.87317i | ||||||
\(738\) | 7.79423 | + | 4.50000i | 0.286910 | + | 0.165647i | ||||
\(739\) | −2.00000 | −0.0735712 | −0.0367856 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367856 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | + | 6.92820i | 0.440831 | + | 0.254514i | ||||
\(742\) | −5.19615 | + | 3.00000i | −0.190757 | + | 0.110133i | ||||
\(743\) | 12.9904 | − | 7.50000i | 0.476571 | − | 0.275148i | −0.242415 | − | 0.970173i | \(-0.577940\pi\) |
0.718986 | + | 0.695024i | \(0.244606\pi\) | |||||||
\(744\) | −6.00000 | − | 3.46410i | −0.219971 | − | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | 23.3827 | − | 13.5000i | 0.855528 | − | 0.493939i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.50000 | − | 2.59808i | 0.0548088 | − | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | − | 1.73205i | −0.0364905 | − | 0.0632034i | 0.847203 | − | 0.531269i | \(-0.178285\pi\) |
−0.883694 | + | 0.468065i | \(0.844951\pi\) | |||||||
\(752\) | −2.59808 | + | 1.50000i | −0.0947421 | + | 0.0546994i | ||||
\(753\) | −10.3923 | − | 18.0000i | −0.378717 | − | 0.655956i | ||||
\(754\) | 3.00000 | − | 5.19615i | 0.109254 | − | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.19615i | 0.188982i | ||||||||
\(757\) | − | 46.0000i | − | 1.67190i | −0.548807 | − | 0.835949i | \(-0.684918\pi\) | ||
0.548807 | − | 0.835949i | \(-0.315082\pi\) | |||||||
\(758\) | −19.0526 | − | 11.0000i | −0.692020 | − | 0.399538i | ||||
\(759\) | −81.0000 | + | 46.7654i | −2.94011 | + | 1.69748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5000 | + | 28.5788i | 0.598125 | + | 1.03598i | 0.993098 | + | 0.117289i | \(0.0374205\pi\) |
−0.394973 | + | 0.918693i | \(0.629246\pi\) | |||||||
\(762\) | 12.1244 | 0.439219 | ||||||||
\(763\) | 6.06218 | + | 3.50000i | 0.219466 | + | 0.126709i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | −10.3923 | − | 6.00000i | −0.375244 | − | 0.216647i | ||||
\(768\) | −0.866025 | + | 1.50000i | −0.0312500 | + | 0.0541266i | ||||
\(769\) | 14.5000 | + | 25.1147i | 0.522883 | + | 0.905661i | 0.999645 | + | 0.0266282i | \(0.00847701\pi\) |
−0.476762 | + | 0.879032i | \(0.658190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.0000 | − | 15.5885i | −0.972381 | − | 0.561405i | ||||
\(772\) | −1.73205 | − | 1.00000i | −0.0623379 | − | 0.0359908i | ||||
\(773\) | 48.0000i | 1.72644i | 0.504828 | + | 0.863220i | \(0.331556\pi\) | ||||
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(774\) | 24.0000 | 0.862662 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.00000 | + | 1.73205i | −0.0358979 | + | 0.0621770i | ||||
\(777\) | 13.8564 | 0.497096 | ||||||||
\(778\) | −18.1865 | + | 10.5000i | −0.652019 | + | 0.376443i | ||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.79423 | − | 13.5000i | 0.278543 | − | 0.482451i | ||||
\(784\) | 6.00000 | 0.214286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −27.0000 | + | 15.5885i | −0.963058 | + | 0.556022i | ||||
\(787\) | 17.3205 | − | 10.0000i | 0.617409 | − | 0.356462i | −0.158450 | − | 0.987367i | \(-0.550650\pi\) |
0.775860 | + | 0.630905i | \(0.217316\pi\) | |||||||
\(788\) | 10.3923 | − | 6.00000i | 0.370211 | − | 0.213741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −15.5885 | + | 9.00000i | −0.553912 | + | 0.319801i | ||||
\(793\) | 26.0000i | 0.923287i | ||||||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | − | 6.92820i | −0.141776 | − | 0.245564i | ||||
\(797\) | −36.3731 | + | 21.0000i | −1.28840 | + | 0.743858i | −0.978369 | − | 0.206868i | \(-0.933673\pi\) |
−0.310031 | + | 0.950726i | \(0.600340\pi\) | |||||||
\(798\) | −3.46410 | + | 6.00000i | −0.122628 | + | 0.212398i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5000 | − | 23.3827i | 0.476999 | − | 0.826187i | ||||
\(802\) | 6.00000i | 0.211867i | ||||||||
\(803\) | −20.7846 | − | 12.0000i | −0.733473 | − | 0.423471i | ||||
\(804\) | 22.5167i | 0.794101i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | + | 6.92820i | 0.140894 | + | 0.244036i | ||||
\(807\) | 18.1865 | + | 31.5000i | 0.640196 | + | 1.10885i | ||||
\(808\) | 5.19615 | + | 3.00000i | 0.182800 | + | 0.105540i | ||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 2.59808 | + | 1.50000i | 0.0911746 | + | 0.0526397i | ||||
\(813\) | 3.46410 | + | 6.00000i | 0.121491 | + | 0.210429i | ||||
\(814\) | 24.0000 | + | 41.5692i | 0.841200 | + | 1.45700i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.7128 | + | 16.0000i | 0.969549 | + | 0.559769i | ||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 3.00000 | − | 5.19615i | 0.104828 | − | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 23.3827i | −0.471153 | + | 0.816061i | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | −10.3923 | + | 18.0000i | −0.362473 | + | 0.627822i | ||||
\(823\) | 21.6506 | − | 12.5000i | 0.754694 | − | 0.435723i | −0.0726937 | − | 0.997354i | \(-0.523160\pi\) |
0.827387 | + | 0.561632i | \(0.189826\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | − | 5.19615i | 0.104383 | − | 0.180797i | ||||
\(827\) | 3.00000i | 0.104320i | 0.998639 | + | 0.0521601i | \(0.0166106\pi\) | ||||
−0.998639 | + | 0.0521601i | \(0.983389\pi\) | |||||||
\(828\) | 23.3827 | − | 13.5000i | 0.812605 | − | 0.469157i | ||||
\(829\) | 7.00000 | 0.243120 | 0.121560 | − | 0.992584i | \(-0.461210\pi\) | ||||
0.121560 | + | 0.992584i | \(0.461210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8564i | 0.480673i | ||||||||
\(832\) | 1.73205 | − | 1.00000i | 0.0600481 | − | 0.0346688i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 24.0000 | − | 13.8564i | 0.831052 | − | 0.479808i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.0000 | −0.830057 | ||||||||
\(837\) | 10.3923 | + | 18.0000i | 0.359211 | + | 0.622171i | ||||
\(838\) | 30.0000i | 1.03633i | ||||||||
\(839\) | 18.0000 | − | 31.1769i | 0.621429 | − | 1.07635i | −0.367791 | − | 0.929909i | \(-0.619886\pi\) |
0.989220 | − | 0.146438i | \(-0.0467809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | −19.0526 | + | 11.0000i | −0.656595 | + | 0.379085i | ||||
\(843\) | −25.9808 | −0.894825 | ||||||||
\(844\) | 1.00000 | − | 1.73205i | 0.0344214 | − | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | − | 25.0000i | − | 0.859010i | ||||||
\(848\) | 5.19615 | + | 3.00000i | 0.178437 | + | 0.103020i | ||||
\(849\) | −19.5000 | − | 11.2583i | −0.669238 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | − | 62.3538i | −1.23406 | − | 2.13746i | ||||
\(852\) | −5.19615 | + | 9.00000i | −0.178017 | + | 0.308335i | ||||
\(853\) | −8.66025 | − | 5.00000i | −0.296521 | − | 0.171197i | 0.344358 | − | 0.938839i | \(-0.388097\pi\) |
−0.640879 | + | 0.767642i | \(0.721430\pi\) | |||||||
\(854\) | −13.0000 | −0.444851 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 36.3731 | + | 21.0000i | 1.24248 | + | 0.717346i | 0.969599 | − | 0.244701i | \(-0.0786899\pi\) |
0.272882 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(858\) | 20.7846 | 0.709575 | ||||||||
\(859\) | −17.0000 | − | 29.4449i | −0.580033 | − | 1.00465i | −0.995475 | − | 0.0950262i | \(-0.969707\pi\) |
0.415442 | − | 0.909620i | \(-0.363627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.50000 | − | 2.59808i | 0.153360 | − | 0.0885422i | ||||
\(862\) | −5.19615 | − | 3.00000i | −0.176982 | − | 0.102180i | ||||
\(863\) | − | 3.00000i | − | 0.102121i | −0.998696 | − | 0.0510606i | \(-0.983740\pi\) | ||
0.998696 | − | 0.0510606i | \(-0.0162602\pi\) | |||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.00000 | − | 13.8564i | 0.271851 | − | 0.470860i | ||||
\(867\) | −14.7224 | − | 25.5000i | −0.500000 | − | 0.866025i | ||||
\(868\) | −3.46410 | + | 2.00000i | −0.117579 | + | 0.0678844i | ||||
\(869\) | −30.0000 | − | 51.9615i | −1.01768 | − | 1.76267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0000 | − | 22.5167i | 0.440488 | − | 0.762948i | ||||
\(872\) | − | 7.00000i | − | 0.237050i | ||||||
\(873\) | 5.19615 | − | 3.00000i | 0.175863 | − | 0.101535i | ||||
\(874\) | 36.0000 | 1.21772 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | + | 3.46410i | 0.202721 | + | 0.117041i | ||||
\(877\) | −19.0526 | + | 11.0000i | −0.643359 | + | 0.371444i | −0.785907 | − | 0.618344i | \(-0.787804\pi\) |
0.142548 | + | 0.989788i | \(0.454470\pi\) | |||||||
\(878\) | 24.2487 | − | 14.0000i | 0.818354 | − | 0.472477i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0000 | 0.707508 | 0.353754 | − | 0.935339i | \(-0.384905\pi\) | ||||
0.353754 | + | 0.935339i | \(0.384905\pi\) | |||||||
\(882\) | −15.5885 | − | 9.00000i | −0.524891 | − | 0.303046i | ||||
\(883\) | 31.0000i | 1.04323i | 0.853180 | + | 0.521617i | \(0.174671\pi\) | ||||
−0.853180 | + | 0.521617i | \(0.825329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | − | 7.79423i | −0.151180 | − | 0.261852i | ||||
\(887\) | 31.1769 | − | 18.0000i | 1.04682 | − | 0.604381i | 0.125061 | − | 0.992149i | \(-0.460087\pi\) |
0.921757 | + | 0.387768i | \(0.126754\pi\) | |||||||
\(888\) | −6.92820 | − | 12.0000i | −0.232495 | − | 0.402694i | ||||
\(889\) | 3.50000 | − | 6.06218i | 0.117386 | − | 0.203319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.0000 | 1.80907 | ||||||||
\(892\) | − | 1.00000i | − | 0.0334825i | ||||||
\(893\) | 10.3923 | + | 6.00000i | 0.347765 | + | 0.200782i | ||||
\(894\) | 4.50000 | − | 2.59808i | 0.150503 | − | 0.0868927i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −31.1769 | −1.04097 | ||||||||
\(898\) | 5.19615 | + | 3.00000i | 0.173398 | + | 0.100111i | ||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 15.5885 | + | 9.00000i | 0.519039 | + | 0.299667i | ||||
\(903\) | 6.92820 | − | 12.0000i | 0.230556 | − | 0.399335i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.0000 | − | 12.1244i | −0.697678 | − | 0.402805i | ||||
\(907\) | 32.0429 | + | 18.5000i | 1.06397 | + | 0.614282i | 0.926527 | − | 0.376228i | \(-0.122779\pi\) |
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | −9.00000 | − | 15.5885i | −0.298511 | − | 0.517036i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000 | − | 25.9808i | 0.496972 | − | 0.860781i | −0.503022 | − | 0.864274i | \(-0.667778\pi\) |
0.999994 | + | 0.00349271i | \(0.00111177\pi\) | |||||||
\(912\) | 6.92820 | 0.229416 | ||||||||
\(913\) | 46.7654 | − | 27.0000i | 1.54771 | − | 0.893570i | ||||
\(914\) | 4.00000 | + | 6.92820i | 0.132308 | + | 0.229165i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.50000 | − | 11.2583i | 0.214766 | − | 0.371986i | ||||
\(917\) | 18.0000i | 0.594412i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.0000 | −1.25350 | −0.626752 | − | 0.779219i | \(-0.715616\pi\) | ||||
−0.626752 | + | 0.779219i | \(0.715616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5000 | + | 6.06218i | −0.345987 | + | 0.199756i | ||||
\(922\) | −23.3827 | + | 13.5000i | −0.770068 | + | 0.444599i | ||||
\(923\) | 10.3923 | − | 6.00000i | 0.342067 | − | 0.197492i | ||||
\(924\) | 10.3923i | 0.341882i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.00000 | −0.131448 | ||||||||
\(927\) | − | 24.0000i | − | 0.788263i | ||||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0000 | − | 20.7846i | −0.393284 | − | 0.681188i | ||||
\(932\) | −10.3923 | + | 6.00000i | −0.340411 | + | 0.196537i | ||||
\(933\) | −10.3923 | + | 18.0000i | −0.340229 | + | 0.589294i | ||||
\(934\) | 18.0000 | − | 31.1769i | 0.588978 | − | 1.02014i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 56.0000i | 1.82944i | 0.404088 | + | 0.914720i | \(0.367589\pi\) | ||||
−0.404088 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(938\) | 11.2583 | + | 6.50000i | 0.367598 | + | 0.212233i | ||||
\(939\) | − | 3.46410i | − | 0.113047i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5000 | − | 18.1865i | −0.342290 | − | 0.592864i | 0.642567 | − | 0.766229i | \(-0.277869\pi\) |
−0.984858 | + | 0.173365i | \(0.944536\pi\) | |||||||
\(942\) | 12.1244 | + | 21.0000i | 0.395033 | + | 0.684217i | ||||
\(943\) | −23.3827 | − | 13.5000i | −0.761445 | − | 0.439620i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.0000 | 1.56061 | ||||||||
\(947\) | −33.7750 | − | 19.5000i | −1.09754 | − | 0.633665i | −0.161966 | − | 0.986796i | \(-0.551783\pi\) |
−0.935574 | + | 0.353131i | \(0.885117\pi\) | |||||||
\(948\) | 8.66025 | + | 15.0000i | 0.281272 | + | 0.487177i | ||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.3923i | − | 0.336994i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | −9.00000 | − | 15.5885i | −0.291386 | − | 0.504695i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.5885 | − | 27.0000i | 0.503903 | − | 0.872786i | ||||
\(958\) | 25.9808 | − | 15.0000i | 0.839400 | − | 0.484628i | ||||
\(959\) | 6.00000 | + | 10.3923i | 0.193750 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 16.0000i | 0.515861i | ||||||||
\(963\) | 7.79423 | + | 4.50000i | 0.251166 | + | 0.145010i | ||||
\(964\) | −29.0000 | −0.934027 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | − | 15.5885i | − | 0.501550i | ||||||
\(967\) | −32.0429 | + | 18.5000i | −1.03043 | + | 0.594920i | −0.917108 | − | 0.398638i | \(-0.869483\pi\) |
−0.113323 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(968\) | −21.6506 | + | 12.5000i | −0.695878 | + | 0.401765i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | −15.5885 | −0.500000 | ||||||||
\(973\) | − | 16.0000i | − | 0.512936i | ||||||
\(974\) | 4.00000 | − | 6.92820i | 0.128168 | − | 0.221994i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.50000 | + | 11.2583i | 0.208060 | + | 0.360370i | ||||
\(977\) | −36.3731 | + | 21.0000i | −1.16368 | + | 0.671850i | −0.952183 | − | 0.305530i | \(-0.901167\pi\) |
−0.211495 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(978\) | −6.92820 | −0.221540 | ||||||||
\(979\) | 27.0000 | − | 46.7654i | 0.862924 | − | 1.49463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5000 | + | 18.1865i | −0.335239 | + | 0.580651i | ||||
\(982\) | 12.0000i | 0.382935i | ||||||||
\(983\) | 7.79423 | + | 4.50000i | 0.248597 | + | 0.143528i | 0.619122 | − | 0.785295i | \(-0.287489\pi\) |
−0.370525 | + | 0.928823i | \(0.620822\pi\) | |||||||
\(984\) | −4.50000 | − | 2.59808i | −0.143455 | − | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.59808 | − | 4.50000i | 0.0826977 | − | 0.143237i | ||||
\(988\) | −6.92820 | − | 4.00000i | −0.220416 | − | 0.127257i | ||||
\(989\) | −72.0000 | −2.28947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | −0.317660 | −0.158830 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158830 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(992\) | 3.46410 | + | 2.00000i | 0.109985 | + | 0.0635001i | ||||
\(993\) | −17.3205 | −0.549650 | ||||||||
\(994\) | 3.00000 | + | 5.19615i | 0.0951542 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.5000 | + | 7.79423i | −0.427764 | + | 0.246970i | ||||
\(997\) | 8.66025 | + | 5.00000i | 0.274273 | + | 0.158352i | 0.630828 | − | 0.775923i | \(-0.282715\pi\) |
−0.356555 | + | 0.934274i | \(0.616049\pi\) | |||||||
\(998\) | − | 32.0000i | − | 1.01294i | ||||||
\(999\) | 41.5692i | 1.31519i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))