Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(169,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bh (of order \(6\), degree \(2\), 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: | \(2.51528766367\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.169 |
Dual form | 315.2.bh.b.274.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.133975 | + | 2.23205i | 0.0599153 | + | 0.998203i | ||||
\(6\) | 3.00000 | − | 1.73205i | 1.22474 | − | 0.707107i | ||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 2.00000 | − | 4.00000i | 0.632456 | − | 1.26491i | ||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | −3.46410 | −1.00000 | ||||||||
\(13\) | 1.73205 | − | 1.00000i | 0.480384 | − | 0.277350i | −0.240192 | − | 0.970725i | \(-0.577210\pi\) |
0.720577 | + | 0.693375i | \(0.243877\pi\) | |||||||
\(14\) | −1.00000 | − | 1.73205i | −0.267261 | − | 0.462910i | ||||
\(15\) | −3.46410 | − | 1.73205i | −0.894427 | − | 0.447214i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 6.00000i | 1.41421i | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | −3.73205 | + | 2.46410i | −0.834512 | + | 0.550990i | ||||
\(21\) | −1.50000 | + | 0.866025i | −0.327327 | + | 0.188982i | ||||
\(22\) | 5.19615 | − | 3.00000i | 1.10782 | − | 0.639602i | ||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | −2.50000 | + | 4.33013i | −0.464238 | + | 0.804084i | −0.999167 | − | 0.0408130i | \(-0.987005\pi\) |
0.534928 | + | 0.844897i | \(0.320339\pi\) | |||||||
\(30\) | 4.26795 | + | 6.46410i | 0.779217 | + | 1.18018i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −6.92820 | + | 4.00000i | −1.22474 | + | 0.707107i | ||||
\(33\) | −2.59808 | − | 4.50000i | −0.452267 | − | 0.783349i | ||||
\(34\) | −2.00000 | + | 3.46410i | −0.342997 | + | 0.594089i | ||||
\(35\) | −1.00000 | + | 2.00000i | −0.169031 | + | 0.338062i | ||||
\(36\) | 3.00000 | − | 5.19615i | 0.500000 | − | 0.866025i | ||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 10.3923 | + | 6.00000i | 1.68585 | + | 0.973329i | ||||
\(39\) | 3.46410i | 0.554700i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | − | 6.92820i | −0.624695 | − | 1.08200i | −0.988600 | − | 0.150567i | \(-0.951890\pi\) |
0.363905 | − | 0.931436i | \(-0.381443\pi\) | |||||||
\(42\) | 3.46410 | 0.534522 | ||||||||
\(43\) | 1.73205 | + | 1.00000i | 0.264135 | + | 0.152499i | 0.626219 | − | 0.779647i | \(-0.284601\pi\) |
−0.362084 | + | 0.932145i | \(0.617935\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 5.59808 | − | 3.69615i | 0.834512 | − | 0.550990i | ||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | −2.59808 | − | 1.50000i | −0.378968 | − | 0.218797i | 0.298401 | − | 0.954441i | \(-0.403547\pi\) |
−0.677369 | + | 0.735643i | \(0.736880\pi\) | |||||||
\(48\) | 3.46410 | + | 6.00000i | 0.500000 | + | 0.866025i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 9.19615 | + | 3.92820i | 1.30053 | + | 0.555532i | ||||
\(51\) | 3.00000 | + | 1.73205i | 0.420084 | + | 0.242536i | ||||
\(52\) | 3.46410 | + | 2.00000i | 0.480384 | + | 0.277350i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −9.00000 | − | 5.19615i | −1.22474 | − | 0.707107i | ||||
\(55\) | −6.00000 | − | 3.00000i | −0.809040 | − | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.19615 | − | 9.00000i | 0.688247 | − | 1.19208i | ||||
\(58\) | 8.66025 | − | 5.00000i | 1.13715 | − | 0.656532i | ||||
\(59\) | −7.00000 | − | 12.1244i | −0.911322 | − | 1.57846i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
−0.0991242 | − | 0.995075i | \(-0.531604\pi\) | |||||||
\(60\) | −0.464102 | − | 7.73205i | −0.0599153 | − | 0.998203i | ||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | − | 8.00000i | − | 1.01600i | ||||||
\(63\) | − | 3.00000i | − | 0.377964i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 2.46410 | + | 3.73205i | 0.305634 | + | 0.462904i | ||||
\(66\) | 10.3923i | 1.27920i | ||||||||
\(67\) | −8.66025 | + | 5.00000i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(68\) | 3.46410 | − | 2.00000i | 0.420084 | − | 0.242536i | ||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | 3.73205 | − | 2.46410i | 0.446065 | − | 0.294516i | ||||
\(71\) | 7.00000 | 0.830747 | 0.415374 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415374 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.00000i | − | 1.05337i | −0.850060 | − | 0.526685i | \(-0.823435\pi\) | ||
0.850060 | − | 0.526685i | \(-0.176565\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 3.40192 | − | 7.96410i | 0.392820 | − | 0.919615i | ||||
\(76\) | −6.00000 | − | 10.3923i | −0.688247 | − | 1.19208i | ||||
\(77\) | −2.59808 | + | 1.50000i | −0.296078 | + | 0.170941i | ||||
\(78\) | 3.46410 | − | 6.00000i | 0.392232 | − | 0.679366i | ||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 8.00000 | + | 4.00000i | 0.894427 | + | 0.447214i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 16.0000i | 1.76690i | ||||||||
\(83\) | 14.7224 | + | 8.50000i | 1.61600 | + | 0.932996i | 0.987942 | + | 0.154828i | \(0.0494822\pi\) |
0.628055 | + | 0.778169i | \(0.283851\pi\) | |||||||
\(84\) | −3.00000 | − | 1.73205i | −0.327327 | − | 0.188982i | ||||
\(85\) | 4.46410 | − | 0.267949i | 0.484200 | − | 0.0290632i | ||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | −4.33013 | − | 7.50000i | −0.464238 | − | 0.804084i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | −13.3923 | + | 0.803848i | −1.41167 | + | 0.0847330i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −10.3923 | − | 6.00000i | −1.08347 | − | 0.625543i | ||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 3.00000 | + | 5.19615i | 0.309426 | + | 0.535942i | ||||
\(95\) | −0.803848 | − | 13.3923i | −0.0824730 | − | 1.37402i | ||||
\(96\) | − | 13.8564i | − | 1.41421i | ||||||
\(97\) | −6.06218 | − | 3.50000i | −0.615521 | − | 0.355371i | 0.159602 | − | 0.987181i | \(-0.448979\pi\) |
−0.775123 | + | 0.631810i | \(0.782312\pi\) | |||||||
\(98\) | − | 2.00000i | − | 0.202031i | ||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | −6.00000 | − | 8.00000i | −0.600000 | − | 0.800000i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | −3.46410 | − | 6.00000i | −0.342997 | − | 0.594089i | ||||
\(103\) | −4.33013 | + | 2.50000i | −0.426660 | + | 0.246332i | −0.697923 | − | 0.716173i | \(-0.745892\pi\) |
0.271263 | + | 0.962505i | \(0.412559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.13397 | − | 3.23205i | −0.208255 | − | 0.315416i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0000i | 1.54678i | 0.633932 | + | 0.773389i | \(0.281440\pi\) | ||||
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(108\) | 5.19615 | + | 9.00000i | 0.500000 | + | 0.866025i | ||||
\(109\) | 19.0000 | 1.81987 | 0.909935 | − | 0.414751i | \(-0.136131\pi\) | ||||
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 7.39230 | + | 11.1962i | 0.704829 | + | 1.06751i | ||||
\(111\) | −3.00000 | − | 1.73205i | −0.284747 | − | 0.164399i | ||||
\(112\) | 3.46410 | − | 2.00000i | 0.327327 | − | 0.188982i | ||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | −18.0000 | + | 10.3923i | −1.68585 | + | 0.973329i | ||||
\(115\) | −7.39230 | − | 11.1962i | −0.689336 | − | 1.04405i | ||||
\(116\) | −10.0000 | −0.928477 | ||||||||
\(117\) | −5.19615 | − | 3.00000i | −0.480384 | − | 0.277350i | ||||
\(118\) | 28.0000i | 2.57761i | ||||||||
\(119\) | 1.00000 | − | 1.73205i | 0.0916698 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 17.3205 | − | 10.0000i | 1.56813 | − | 0.905357i | ||||
\(123\) | 13.8564 | 1.24939 | ||||||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | −3.00000 | + | 5.19615i | −0.267261 | + | 0.462910i | ||||
\(127\) | 20.0000i | 1.77471i | 0.461084 | + | 0.887357i | \(0.347461\pi\) | ||||
−0.461084 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.00000 | + | 1.73205i | −0.264135 | + | 0.152499i | ||||
\(130\) | −0.535898 | − | 8.92820i | −0.0470014 | − | 0.783055i | ||||
\(131\) | 7.00000 | + | 12.1244i | 0.611593 | + | 1.05931i | 0.990972 | + | 0.134069i | \(0.0428042\pi\) |
−0.379379 | + | 0.925241i | \(0.623862\pi\) | |||||||
\(132\) | 5.19615 | − | 9.00000i | 0.452267 | − | 0.783349i | ||||
\(133\) | −5.19615 | − | 3.00000i | −0.450564 | − | 0.260133i | ||||
\(134\) | 20.0000 | 1.72774 | ||||||||
\(135\) | 0.696152 | + | 11.5981i | 0.0599153 | + | 0.998203i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | −10.3923 | + | 18.0000i | −0.884652 | + | 1.53226i | ||||
\(139\) | 10.0000 | + | 17.3205i | 0.848189 | + | 1.46911i | 0.882823 | + | 0.469706i | \(0.155640\pi\) |
−0.0346338 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(140\) | −4.46410 | + | 0.267949i | −0.377285 | + | 0.0226458i | ||||
\(141\) | 4.50000 | − | 2.59808i | 0.378968 | − | 0.218797i | ||||
\(142\) | −12.1244 | − | 7.00000i | −1.01745 | − | 0.587427i | ||||
\(143\) | 6.00000i | 0.501745i | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | −10.0000 | − | 5.00000i | −0.830455 | − | 0.415227i | ||||
\(146\) | −9.00000 | + | 15.5885i | −0.744845 | + | 1.29011i | ||||
\(147\) | −1.73205 | −0.142857 | ||||||||
\(148\) | −3.46410 | + | 2.00000i | −0.284747 | + | 0.164399i | ||||
\(149\) | −2.50000 | − | 4.33013i | −0.204808 | − | 0.354738i | 0.745264 | − | 0.666770i | \(-0.232324\pi\) |
−0.950072 | + | 0.312032i | \(0.898990\pi\) | |||||||
\(150\) | −13.8564 | + | 10.3923i | −1.13137 | + | 0.848528i | ||||
\(151\) | −10.0000 | + | 17.3205i | −0.813788 | + | 1.40952i | 0.0964061 | + | 0.995342i | \(0.469265\pi\) |
−0.910195 | + | 0.414181i | \(0.864068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.19615 | + | 3.00000i | −0.420084 | + | 0.242536i | ||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | −7.46410 | + | 4.92820i | −0.599531 | + | 0.395843i | ||||
\(156\) | −6.00000 | + | 3.46410i | −0.480384 | + | 0.277350i | ||||
\(157\) | 7.79423 | − | 4.50000i | 0.622047 | − | 0.359139i | −0.155618 | − | 0.987817i | \(-0.549737\pi\) |
0.777666 | + | 0.628678i | \(0.216404\pi\) | |||||||
\(158\) | −1.73205 | + | 1.00000i | −0.137795 | + | 0.0795557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.85641 | − | 14.9282i | −0.779217 | − | 1.18018i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 15.5885 | − | 9.00000i | 1.22474 | − | 0.707107i | ||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 8.00000 | − | 13.8564i | 0.624695 | − | 1.08200i | ||||
\(165\) | 9.69615 | − | 6.40192i | 0.754844 | − | 0.498389i | ||||
\(166\) | −17.0000 | − | 29.4449i | −1.31946 | − | 2.28536i | ||||
\(167\) | −10.3923 | + | 6.00000i | −0.804181 | + | 0.464294i | −0.844931 | − | 0.534875i | \(-0.820359\pi\) |
0.0407502 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50000 | + | 7.79423i | −0.346154 | + | 0.599556i | ||||
\(170\) | −8.00000 | − | 4.00000i | −0.613572 | − | 0.306786i | ||||
\(171\) | 9.00000 | + | 15.5885i | 0.688247 | + | 1.19208i | ||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 12.9904 | + | 7.50000i | 0.987640 | + | 0.570214i | 0.904568 | − | 0.426329i | \(-0.140193\pi\) |
0.0830722 | + | 0.996544i | \(0.473527\pi\) | |||||||
\(174\) | 17.3205i | 1.31306i | ||||||||
\(175\) | −4.59808 | − | 1.96410i | −0.347582 | − | 0.148472i | ||||
\(176\) | 6.00000 | + | 10.3923i | 0.452267 | + | 0.783349i | ||||
\(177\) | 24.2487 | 1.82264 | ||||||||
\(178\) | −20.7846 | − | 12.0000i | −1.55787 | − | 0.899438i | ||||
\(179\) | 11.0000 | 0.822179 | 0.411089 | − | 0.911595i | \(-0.365148\pi\) | ||||
0.411089 | + | 0.911595i | \(0.365148\pi\) | |||||||
\(180\) | 12.0000 | + | 6.00000i | 0.894427 | + | 0.447214i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −3.46410 | − | 2.00000i | −0.256776 | − | 0.148250i | ||||
\(183\) | −8.66025 | − | 15.0000i | −0.640184 | − | 1.10883i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.46410 | + | 0.267949i | −0.328207 | + | 0.0197000i | ||||
\(186\) | 12.0000 | + | 6.92820i | 0.879883 | + | 0.508001i | ||||
\(187\) | 5.19615 | + | 3.00000i | 0.379980 | + | 0.219382i | ||||
\(188\) | − | 6.00000i | − | 0.437595i | ||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | −12.0000 | + | 24.0000i | −0.870572 | + | 1.74114i | ||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | −6.92820 | + | 12.0000i | −0.500000 | + | 0.866025i | ||||
\(193\) | 12.1244 | − | 7.00000i | 0.872730 | − | 0.503871i | 0.00447566 | − | 0.999990i | \(-0.498575\pi\) |
0.868255 | + | 0.496119i | \(0.165242\pi\) | |||||||
\(194\) | 7.00000 | + | 12.1244i | 0.502571 | + | 0.870478i | ||||
\(195\) | −7.73205 | + | 0.464102i | −0.553704 | + | 0.0332350i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | −15.5885 | − | 9.00000i | −1.10782 | − | 0.639602i | ||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 17.3205i | − | 1.22169i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.33013 | + | 2.50000i | −0.303915 | + | 0.175466i | ||||
\(204\) | 6.92820i | 0.485071i | ||||||||
\(205\) | 14.9282 | − | 9.85641i | 1.04263 | − | 0.688401i | ||||
\(206\) | 10.0000 | 0.696733 | ||||||||
\(207\) | 15.5885 | + | 9.00000i | 1.08347 | + | 0.625543i | ||||
\(208\) | − | 8.00000i | − | 0.554700i | ||||||
\(209\) | 9.00000 | − | 15.5885i | 0.622543 | − | 1.07828i | ||||
\(210\) | 0.464102 | + | 7.73205i | 0.0320261 | + | 0.533562i | ||||
\(211\) | −8.50000 | − | 14.7224i | −0.585164 | − | 1.01353i | −0.994855 | − | 0.101310i | \(-0.967697\pi\) |
0.409691 | − | 0.912224i | \(-0.365637\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.06218 | + | 10.5000i | −0.415374 | + | 0.719448i | ||||
\(214\) | 16.0000 | − | 27.7128i | 1.09374 | − | 1.89441i | ||||
\(215\) | −2.00000 | + | 4.00000i | −0.136399 | + | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | −32.9090 | − | 19.0000i | −2.22888 | − | 1.28684i | ||||
\(219\) | 13.5000 | + | 7.79423i | 0.912245 | + | 0.526685i | ||||
\(220\) | −0.803848 | − | 13.3923i | −0.0541954 | − | 0.902909i | ||||
\(221\) | −2.00000 | − | 3.46410i | −0.134535 | − | 0.233021i | ||||
\(222\) | 3.46410 | + | 6.00000i | 0.232495 | + | 0.402694i | ||||
\(223\) | 20.7846 | + | 12.0000i | 1.39184 | + | 0.803579i | 0.993519 | − | 0.113666i | \(-0.0362595\pi\) |
0.398321 | + | 0.917246i | \(0.369593\pi\) | |||||||
\(224\) | −8.00000 | −0.534522 | ||||||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3205 | − | 10.0000i | −1.14960 | − | 0.663723i | −0.200812 | − | 0.979630i | \(-0.564358\pi\) |
−0.948790 | + | 0.315906i | \(0.897691\pi\) | |||||||
\(228\) | 20.7846 | 1.37649 | ||||||||
\(229\) | −5.00000 | − | 8.66025i | −0.330409 | − | 0.572286i | 0.652183 | − | 0.758062i | \(-0.273853\pi\) |
−0.982592 | + | 0.185776i | \(0.940520\pi\) | |||||||
\(230\) | 1.60770 | + | 26.7846i | 0.106008 | + | 1.76612i | ||||
\(231\) | − | 5.19615i | − | 0.341882i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.0000i | − | 1.04819i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||
0.851658 | − | 0.524097i | \(-0.175597\pi\) | |||||||
\(234\) | 6.00000 | + | 10.3923i | 0.392232 | + | 0.679366i | ||||
\(235\) | 3.00000 | − | 6.00000i | 0.195698 | − | 0.391397i | ||||
\(236\) | 14.0000 | − | 24.2487i | 0.911322 | − | 1.57846i | ||||
\(237\) | 0.866025 | + | 1.50000i | 0.0562544 | + | 0.0974355i | ||||
\(238\) | −3.46410 | + | 2.00000i | −0.224544 | + | 0.129641i | ||||
\(239\) | −4.50000 | − | 7.79423i | −0.291081 | − | 0.504167i | 0.682985 | − | 0.730433i | \(-0.260682\pi\) |
−0.974066 | + | 0.226266i | \(0.927348\pi\) | |||||||
\(240\) | −12.9282 | + | 8.53590i | −0.834512 | + | 0.550990i | ||||
\(241\) | −2.00000 | + | 3.46410i | −0.128831 | + | 0.223142i | −0.923224 | − | 0.384262i | \(-0.874456\pi\) |
0.794393 | + | 0.607404i | \(0.207789\pi\) | |||||||
\(242\) | − | 4.00000i | − | 0.257130i | ||||||
\(243\) | −7.79423 | − | 13.5000i | −0.500000 | − | 0.866025i | ||||
\(244\) | −20.0000 | −1.28037 | ||||||||
\(245\) | −1.86603 | + | 1.23205i | −0.119216 | + | 0.0787128i | ||||
\(246\) | −24.0000 | − | 13.8564i | −1.53018 | − | 0.883452i | ||||
\(247\) | −10.3923 | + | 6.00000i | −0.661247 | + | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.5000 | + | 14.7224i | −1.61600 | + | 0.932996i | ||||
\(250\) | −7.53590 | + | 21.0526i | −0.476612 | + | 1.33148i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 5.19615 | − | 3.00000i | 0.327327 | − | 0.188982i | ||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | 20.0000 | − | 34.6410i | 1.25491 | − | 2.17357i | ||||
\(255\) | −3.46410 | + | 6.92820i | −0.216930 | + | 0.433861i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 6.06218 | − | 3.50000i | 0.378148 | − | 0.218324i | −0.298864 | − | 0.954296i | \(-0.596608\pi\) |
0.677012 | + | 0.735972i | \(0.263274\pi\) | |||||||
\(258\) | 6.92820 | 0.431331 | ||||||||
\(259\) | −1.00000 | + | 1.73205i | −0.0621370 | + | 0.107624i | ||||
\(260\) | −4.00000 | + | 8.00000i | −0.248069 | + | 0.496139i | ||||
\(261\) | 15.0000 | 0.928477 | ||||||||
\(262\) | − | 28.0000i | − | 1.72985i | ||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.00000 | + | 10.3923i | 0.367884 | + | 0.637193i | ||||
\(267\) | −10.3923 | + | 18.0000i | −0.635999 | + | 1.10158i | ||||
\(268\) | −17.3205 | − | 10.0000i | −1.05802 | − | 0.610847i | ||||
\(269\) | −16.0000 | −0.975537 | −0.487769 | − | 0.872973i | \(-0.662189\pi\) | ||||
−0.487769 | + | 0.872973i | \(0.662189\pi\) | |||||||
\(270\) | 10.3923 | − | 20.7846i | 0.632456 | − | 1.26491i | ||||
\(271\) | −14.0000 | −0.850439 | −0.425220 | − | 0.905090i | \(-0.639803\pi\) | ||||
−0.425220 | + | 0.905090i | \(0.639803\pi\) | |||||||
\(272\) | −6.92820 | − | 4.00000i | −0.420084 | − | 0.242536i | ||||
\(273\) | −1.73205 | + | 3.00000i | −0.104828 | + | 0.181568i | ||||
\(274\) | 18.0000 | + | 31.1769i | 1.08742 | + | 1.88347i | ||||
\(275\) | 5.89230 | − | 13.7942i | 0.355319 | − | 0.831823i | ||||
\(276\) | 18.0000 | − | 10.3923i | 1.08347 | − | 0.625543i | ||||
\(277\) | 24.2487 | + | 14.0000i | 1.45696 | + | 0.841178i | 0.998861 | − | 0.0477206i | \(-0.0151957\pi\) |
0.458103 | + | 0.888899i | \(0.348529\pi\) | |||||||
\(278\) | − | 40.0000i | − | 2.39904i | ||||||
\(279\) | 6.00000 | − | 10.3923i | 0.359211 | − | 0.622171i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50000 | + | 6.06218i | −0.208792 | + | 0.361639i | −0.951334 | − | 0.308160i | \(-0.900287\pi\) |
0.742542 | + | 0.669800i | \(0.233620\pi\) | |||||||
\(282\) | −10.3923 | −0.618853 | ||||||||
\(283\) | 6.06218 | − | 3.50000i | 0.360359 | − | 0.208053i | −0.308879 | − | 0.951101i | \(-0.599954\pi\) |
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(284\) | 7.00000 | + | 12.1244i | 0.415374 | + | 0.719448i | ||||
\(285\) | 20.7846 | + | 10.3923i | 1.23117 | + | 0.615587i | ||||
\(286\) | 6.00000 | − | 10.3923i | 0.354787 | − | 0.614510i | ||||
\(287\) | − | 8.00000i | − | 0.472225i | ||||||
\(288\) | 20.7846 | + | 12.0000i | 1.22474 | + | 0.707107i | ||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 12.3205 | + | 18.6603i | 0.723485 | + | 1.09577i | ||||
\(291\) | 10.5000 | − | 6.06218i | 0.615521 | − | 0.355371i | ||||
\(292\) | 15.5885 | − | 9.00000i | 0.912245 | − | 0.526685i | ||||
\(293\) | −23.3827 | + | 13.5000i | −1.36603 | + | 0.788678i | −0.990419 | − | 0.138098i | \(-0.955901\pi\) |
−0.375613 | + | 0.926777i | \(0.622568\pi\) | |||||||
\(294\) | 3.00000 | + | 1.73205i | 0.174964 | + | 0.101015i | ||||
\(295\) | 26.1244 | − | 17.2487i | 1.52102 | − | 1.00426i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.79423 | + | 13.5000i | −0.452267 | + | 0.783349i | ||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | 17.1962 | − | 2.07180i | 0.992820 | − | 0.119615i | ||||
\(301\) | 1.00000 | + | 1.73205i | 0.0576390 | + | 0.0998337i | ||||
\(302\) | 34.6410 | − | 20.0000i | 1.99337 | − | 1.15087i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.0000 | + | 20.7846i | −0.688247 | + | 1.19208i | ||||
\(305\) | −20.0000 | − | 10.0000i | −1.14520 | − | 0.572598i | ||||
\(306\) | 12.0000 | 0.685994 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | −5.19615 | − | 3.00000i | −0.296078 | − | 0.170941i | ||||
\(309\) | − | 8.66025i | − | 0.492665i | ||||||
\(310\) | 17.8564 | − | 1.07180i | 1.01418 | − | 0.0608740i | ||||
\(311\) | 3.00000 | + | 5.19615i | 0.170114 | + | 0.294647i | 0.938460 | − | 0.345389i | \(-0.112253\pi\) |
−0.768345 | + | 0.640036i | \(0.778920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.79423 | + | 4.50000i | 0.440556 | + | 0.254355i | 0.703833 | − | 0.710365i | \(-0.251470\pi\) |
−0.263278 | + | 0.964720i | \(0.584803\pi\) | |||||||
\(314\) | −18.0000 | −1.01580 | ||||||||
\(315\) | 6.69615 | − | 0.401924i | 0.377285 | − | 0.0226458i | ||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 25.9808 | + | 15.0000i | 1.45922 | + | 0.842484i | 0.998973 | − | 0.0453045i | \(-0.0144258\pi\) |
0.460252 | + | 0.887788i | \(0.347759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50000 | − | 12.9904i | −0.419919 | − | 0.727322i | ||||
\(320\) | 1.07180 | + | 17.8564i | 0.0599153 | + | 0.998203i | ||||
\(321\) | −24.0000 | − | 13.8564i | −1.33955 | − | 0.773389i | ||||
\(322\) | 10.3923 | + | 6.00000i | 0.579141 | + | 0.334367i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | −18.0000 | −1.00000 | ||||||||
\(325\) | −8.00000 | + | 6.00000i | −0.443760 | + | 0.332820i | ||||
\(326\) | −4.00000 | + | 6.92820i | −0.221540 | + | 0.383718i | ||||
\(327\) | −16.4545 | + | 28.5000i | −0.909935 | + | 1.57605i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | − | 2.59808i | −0.0826977 | − | 0.143237i | ||||
\(330\) | −23.1962 | + | 1.39230i | −1.27691 | + | 0.0766439i | ||||
\(331\) | −13.5000 | + | 23.3827i | −0.742027 | + | 1.28523i | 0.209544 | + | 0.977799i | \(0.432802\pi\) |
−0.951571 | + | 0.307429i | \(0.900531\pi\) | |||||||
\(332\) | 34.0000i | 1.86599i | ||||||||
\(333\) | 5.19615 | − | 3.00000i | 0.284747 | − | 0.164399i | ||||
\(334\) | 24.0000 | 1.31322 | ||||||||
\(335\) | −12.3205 | − | 18.6603i | −0.673141 | − | 1.01952i | ||||
\(336\) | 6.92820i | 0.377964i | ||||||||
\(337\) | −15.5885 | + | 9.00000i | −0.849157 | + | 0.490261i | −0.860366 | − | 0.509676i | \(-0.829765\pi\) |
0.0112091 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(338\) | 15.5885 | − | 9.00000i | 0.847900 | − | 0.489535i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.92820 | + | 7.46410i | 0.267269 | + | 0.404798i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | − | 36.0000i | − | 1.94666i | ||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.1962 | − | 1.39230i | 1.24884 | − | 0.0749592i | ||||
\(346\) | −15.0000 | − | 25.9808i | −0.806405 | − | 1.39673i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 8.66025 | − | 15.0000i | 0.464238 | − | 0.804084i | ||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | 6.00000 | + | 8.00000i | 0.320713 | + | 0.427618i | ||||
\(351\) | 9.00000 | − | 5.19615i | 0.480384 | − | 0.277350i | ||||
\(352\) | − | 24.0000i | − | 1.27920i | ||||||
\(353\) | 9.52628 | + | 5.50000i | 0.507033 | + | 0.292735i | 0.731613 | − | 0.681720i | \(-0.238768\pi\) |
−0.224580 | + | 0.974456i | \(0.572101\pi\) | |||||||
\(354\) | −42.0000 | − | 24.2487i | −2.23227 | − | 1.28880i | ||||
\(355\) | 0.937822 | + | 15.6244i | 0.0497744 | + | 0.829255i | ||||
\(356\) | 12.0000 | + | 20.7846i | 0.635999 | + | 1.10158i | ||||
\(357\) | 1.73205 | + | 3.00000i | 0.0916698 | + | 0.158777i | ||||
\(358\) | −19.0526 | − | 11.0000i | −1.00696 | − | 0.581368i | ||||
\(359\) | −4.00000 | −0.211112 | −0.105556 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105556 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.46410 | −0.181818 | ||||||||
\(364\) | 2.00000 | + | 3.46410i | 0.104828 | + | 0.181568i | ||||
\(365\) | 20.0885 | − | 1.20577i | 1.05148 | − | 0.0631130i | ||||
\(366\) | 34.6410i | 1.81071i | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | −12.0000 | + | 20.7846i | −0.624695 | + | 1.08200i | ||||
\(370\) | 8.00000 | + | 4.00000i | 0.415900 | + | 0.207950i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.92820 | − | 12.0000i | −0.359211 | − | 0.622171i | ||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | −6.00000 | − | 10.3923i | −0.310253 | − | 0.537373i | ||||
\(375\) | 18.2321 | + | 6.52628i | 0.941499 | + | 0.337016i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0000i | 0.515026i | ||||||||
\(378\) | −5.19615 | − | 9.00000i | −0.267261 | − | 0.462910i | ||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 22.3923 | − | 14.7846i | 1.14870 | − | 0.758434i | ||||
\(381\) | −30.0000 | − | 17.3205i | −1.53695 | − | 0.887357i | ||||
\(382\) | −5.19615 | + | 3.00000i | −0.265858 | + | 0.153493i | ||||
\(383\) | 4.33013 | − | 2.50000i | 0.221259 | − | 0.127744i | −0.385274 | − | 0.922802i | \(-0.625893\pi\) |
0.606533 | + | 0.795058i | \(0.292560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.69615 | − | 5.59808i | −0.188373 | − | 0.285304i | ||||
\(386\) | −28.0000 | −1.42516 | ||||||||
\(387\) | − | 6.00000i | − | 0.304997i | ||||||
\(388\) | − | 14.0000i | − | 0.710742i | ||||||
\(389\) | −9.50000 | + | 16.4545i | −0.481669 | + | 0.834275i | −0.999779 | − | 0.0210389i | \(-0.993303\pi\) |
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(390\) | 13.8564 | + | 6.92820i | 0.701646 | + | 0.350823i | ||||
\(391\) | 6.00000 | + | 10.3923i | 0.303433 | + | 0.525561i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.2487 | −1.22319 | ||||||||
\(394\) | 8.00000 | − | 13.8564i | 0.403034 | − | 0.698076i | ||||
\(395\) | 2.00000 | + | 1.00000i | 0.100631 | + | 0.0503155i | ||||
\(396\) | 9.00000 | + | 15.5885i | 0.452267 | + | 0.783349i | ||||
\(397\) | − | 17.0000i | − | 0.853206i | −0.904439 | − | 0.426603i | \(-0.859710\pi\) | ||
0.904439 | − | 0.426603i | \(-0.140290\pi\) | |||||||
\(398\) | 13.8564 | + | 8.00000i | 0.694559 | + | 0.401004i | ||||
\(399\) | 9.00000 | − | 5.19615i | 0.450564 | − | 0.260133i | ||||
\(400\) | −7.85641 | + | 18.3923i | −0.392820 | + | 0.919615i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | −17.3205 | + | 30.0000i | −0.863868 | + | 1.49626i | ||||
\(403\) | 6.92820 | + | 4.00000i | 0.345118 | + | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | − | 9.00000i | −0.894427 | − | 0.447214i | ||||
\(406\) | 10.0000 | 0.496292 | ||||||||
\(407\) | −5.19615 | − | 3.00000i | −0.257564 | − | 0.148704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.00000 | + | 6.92820i | 0.197787 | + | 0.342578i | 0.947811 | − | 0.318834i | \(-0.103291\pi\) |
−0.750023 | + | 0.661411i | \(0.769958\pi\) | |||||||
\(410\) | −35.7128 | + | 2.14359i | −1.76373 | + | 0.105865i | ||||
\(411\) | 27.0000 | − | 15.5885i | 1.33181 | − | 0.768922i | ||||
\(412\) | −8.66025 | − | 5.00000i | −0.426660 | − | 0.246332i | ||||
\(413\) | − | 14.0000i | − | 0.688895i | ||||||
\(414\) | −18.0000 | − | 31.1769i | −0.884652 | − | 1.53226i | ||||
\(415\) | −17.0000 | + | 34.0000i | −0.834497 | + | 1.66899i | ||||
\(416\) | −8.00000 | + | 13.8564i | −0.392232 | + | 0.679366i | ||||
\(417\) | −34.6410 | −1.69638 | ||||||||
\(418\) | −31.1769 | + | 18.0000i | −1.52491 | + | 0.880409i | ||||
\(419\) | −15.0000 | − | 25.9808i | −0.732798 | − | 1.26924i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.222885 | − | 0.974845i | \(-0.428453\pi\) | |||||||
\(420\) | 3.46410 | − | 6.92820i | 0.169031 | − | 0.338062i | ||||
\(421\) | 7.50000 | − | 12.9904i | 0.365528 | − | 0.633112i | −0.623333 | − | 0.781956i | \(-0.714222\pi\) |
0.988861 | + | 0.148844i | \(0.0475552\pi\) | |||||||
\(422\) | 34.0000i | 1.65509i | ||||||||
\(423\) | 9.00000i | 0.437595i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.19615 | + | 9.92820i | 0.0580219 | + | 0.481589i | ||||
\(426\) | 21.0000 | − | 12.1244i | 1.01745 | − | 0.587427i | ||||
\(427\) | −8.66025 | + | 5.00000i | −0.419099 | + | 0.241967i | ||||
\(428\) | −27.7128 | + | 16.0000i | −1.33955 | + | 0.773389i | ||||
\(429\) | −9.00000 | − | 5.19615i | −0.434524 | − | 0.250873i | ||||
\(430\) | 7.46410 | − | 4.92820i | 0.359951 | − | 0.237659i | ||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 10.3923 | − | 18.0000i | 0.500000 | − | 0.866025i | ||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 4.00000 | − | 6.92820i | 0.192006 | − | 0.332564i | ||||
\(435\) | 16.1603 | − | 10.6699i | 0.774825 | − | 0.511581i | ||||
\(436\) | 19.0000 | + | 32.9090i | 0.909935 | + | 1.57605i | ||||
\(437\) | 31.1769 | − | 18.0000i | 1.49139 | − | 0.861057i | ||||
\(438\) | −15.5885 | − | 27.0000i | −0.744845 | − | 1.29011i | ||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | −3.46410 | − | 2.00000i | −0.164584 | − | 0.0950229i | 0.415445 | − | 0.909618i | \(-0.363626\pi\) |
−0.580030 | + | 0.814595i | \(0.696959\pi\) | |||||||
\(444\) | − | 6.92820i | − | 0.328798i | ||||||
\(445\) | 1.60770 | + | 26.7846i | 0.0762121 | + | 1.26971i | ||||
\(446\) | −24.0000 | − | 41.5692i | −1.13643 | − | 1.96836i | ||||
\(447\) | 8.66025 | 0.409616 | ||||||||
\(448\) | 6.92820 | + | 4.00000i | 0.327327 | + | 0.188982i | ||||
\(449\) | −31.0000 | −1.46298 | −0.731490 | − | 0.681852i | \(-0.761175\pi\) | ||||
−0.731490 | + | 0.681852i | \(0.761175\pi\) | |||||||
\(450\) | −3.58846 | − | 29.7846i | −0.169161 | − | 1.40406i | ||||
\(451\) | 24.0000 | 1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.3205 | − | 30.0000i | −0.813788 | − | 1.40952i | ||||
\(454\) | 20.0000 | + | 34.6410i | 0.938647 | + | 1.62578i | ||||
\(455\) | 0.267949 | + | 4.46410i | 0.0125617 | + | 0.209280i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.2487 | − | 14.0000i | −1.13431 | − | 0.654892i | −0.189292 | − | 0.981921i | \(-0.560619\pi\) |
−0.945015 | + | 0.327028i | \(0.893953\pi\) | |||||||
\(458\) | 20.0000i | 0.934539i | ||||||||
\(459\) | − | 10.3923i | − | 0.485071i | ||||||
\(460\) | 12.0000 | − | 24.0000i | 0.559503 | − | 1.11901i | ||||
\(461\) | 6.00000 | − | 10.3923i | 0.279448 | − | 0.484018i | −0.691800 | − | 0.722089i | \(-0.743182\pi\) |
0.971248 | + | 0.238071i | \(0.0765153\pi\) | |||||||
\(462\) | −5.19615 | + | 9.00000i | −0.241747 | + | 0.418718i | ||||
\(463\) | 5.19615 | − | 3.00000i | 0.241486 | − | 0.139422i | −0.374374 | − | 0.927278i | \(-0.622142\pi\) |
0.615859 | + | 0.787856i | \(0.288809\pi\) | |||||||
\(464\) | 10.0000 | + | 17.3205i | 0.464238 | + | 0.804084i | ||||
\(465\) | −0.928203 | − | 15.4641i | −0.0430444 | − | 0.717131i | ||||
\(466\) | −16.0000 | + | 27.7128i | −0.741186 | + | 1.28377i | ||||
\(467\) | − | 3.00000i | − | 0.138823i | −0.997588 | − | 0.0694117i | \(-0.977888\pi\) | ||
0.997588 | − | 0.0694117i | \(-0.0221122\pi\) | |||||||
\(468\) | − | 12.0000i | − | 0.554700i | ||||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | −11.1962 | + | 7.39230i | −0.516440 | + | 0.340982i | ||||
\(471\) | 15.5885i | 0.718278i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.19615 | + | 3.00000i | −0.238919 | + | 0.137940i | ||||
\(474\) | − | 3.46410i | − | 0.159111i | ||||||
\(475\) | 29.7846 | − | 3.58846i | 1.36661 | − | 0.164650i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000i | 0.823301i | ||||||||
\(479\) | 18.0000 | − | 31.1769i | 0.822441 | − | 1.42451i | −0.0814184 | − | 0.996680i | \(-0.525945\pi\) |
0.903859 | − | 0.427830i | \(-0.140722\pi\) | |||||||
\(480\) | 30.9282 | − | 1.85641i | 1.41167 | − | 0.0847330i | ||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | 6.92820 | − | 4.00000i | 0.315571 | − | 0.182195i | ||||
\(483\) | 5.19615 | − | 9.00000i | 0.236433 | − | 0.409514i | ||||
\(484\) | −2.00000 | + | 3.46410i | −0.0909091 | + | 0.157459i | ||||
\(485\) | 7.00000 | − | 14.0000i | 0.317854 | − | 0.635707i | ||||
\(486\) | 31.1769i | 1.41421i | ||||||||
\(487\) | − | 12.0000i | − | 0.543772i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | + | 3.46410i | 0.271329 | + | 0.156652i | ||||
\(490\) | 4.46410 | − | 0.267949i | 0.201668 | − | 0.0121047i | ||||
\(491\) | −14.0000 | − | 24.2487i | −0.631811 | − | 1.09433i | −0.987181 | − | 0.159603i | \(-0.948978\pi\) |
0.355370 | − | 0.934726i | \(-0.384355\pi\) | |||||||
\(492\) | 13.8564 | + | 24.0000i | 0.624695 | + | 1.08200i | ||||
\(493\) | 8.66025 | + | 5.00000i | 0.390038 | + | 0.225189i | ||||
\(494\) | 24.0000 | 1.07981 | ||||||||
\(495\) | 1.20577 | + | 20.0885i | 0.0541954 | + | 0.902909i | ||||
\(496\) | 16.0000 | 0.718421 | ||||||||
\(497\) | 6.06218 | + | 3.50000i | 0.271926 | + | 0.156996i | ||||
\(498\) | 58.8897 | 2.63891 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 17.0526 | − | 14.4641i | 0.762614 | − | 0.646854i | ||||
\(501\) | − | 20.7846i | − | 0.928588i | ||||||
\(502\) | −31.1769 | − | 18.0000i | −1.39149 | − | 0.803379i | ||||
\(503\) | − | 27.0000i | − | 1.20387i | −0.798545 | − | 0.601935i | \(-0.794397\pi\) | ||
0.798545 | − | 0.601935i | \(-0.205603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.0000 | + | 31.1769i | −0.800198 | + | 1.38598i | ||||
\(507\) | −7.79423 | − | 13.5000i | −0.346154 | − | 0.599556i | ||||
\(508\) | −34.6410 | + | 20.0000i | −1.53695 | + | 0.887357i | ||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 12.9282 | − | 8.53590i | 0.572470 | − | 0.377976i | ||||
\(511\) | 4.50000 | − | 7.79423i | 0.199068 | − | 0.344796i | ||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | −31.1769 | −1.37649 | ||||||||
\(514\) | −14.0000 | −0.617514 | ||||||||
\(515\) | −6.16025 | − | 9.33013i | −0.271453 | − | 0.411135i | ||||
\(516\) | −6.00000 | − | 3.46410i | −0.264135 | − | 0.152499i | ||||
\(517\) | 7.79423 | − | 4.50000i | 0.342790 | − | 0.197910i | ||||
\(518\) | 3.46410 | − | 2.00000i | 0.152204 | − | 0.0878750i | ||||
\(519\) | −22.5000 | + | 12.9904i | −0.987640 | + | 0.570214i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | −25.9808 | − | 15.0000i | −1.13715 | − | 0.656532i | ||||
\(523\) | − | 23.0000i | − | 1.00572i | −0.864368 | − | 0.502860i | \(-0.832281\pi\) | ||
0.864368 | − | 0.502860i | \(-0.167719\pi\) | |||||||
\(524\) | −14.0000 | + | 24.2487i | −0.611593 | + | 1.05931i | ||||
\(525\) | 6.92820 | − | 5.19615i | 0.302372 | − | 0.226779i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.92820 | − | 4.00000i | 0.301797 | − | 0.174243i | ||||
\(528\) | −20.7846 | −0.904534 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.0000 | + | 36.3731i | −0.911322 | + | 1.57846i | ||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | −13.8564 | − | 8.00000i | −0.600188 | − | 0.346518i | ||||
\(534\) | 36.0000 | − | 20.7846i | 1.55787 | − | 0.899438i | ||||
\(535\) | −35.7128 | + | 2.14359i | −1.54400 | + | 0.0926756i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.52628 | + | 16.5000i | −0.411089 | + | 0.712028i | ||||
\(538\) | 27.7128 | + | 16.0000i | 1.19478 | + | 0.689809i | ||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | −19.3923 | + | 12.8038i | −0.834512 | + | 0.550990i | ||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 24.2487 | + | 14.0000i | 1.04157 | + | 0.601351i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | + | 13.8564i | 0.342997 | + | 0.594089i | ||||
\(545\) | 2.54552 | + | 42.4090i | 0.109038 | + | 1.81660i | ||||
\(546\) | 6.00000 | − | 3.46410i | 0.256776 | − | 0.148250i | ||||
\(547\) | 19.0526 | + | 11.0000i | 0.814629 | + | 0.470326i | 0.848561 | − | 0.529098i | \(-0.177470\pi\) |
−0.0339321 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(548\) | − | 36.0000i | − | 1.53784i | ||||||
\(549\) | 30.0000 | 1.28037 | ||||||||
\(550\) | −24.0000 | + | 18.0000i | −1.02336 | + | 0.767523i | ||||
\(551\) | 15.0000 | − | 25.9808i | 0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.866025 | − | 0.500000i | 0.0368271 | − | 0.0212622i | ||||
\(554\) | −28.0000 | − | 48.4974i | −1.18961 | − | 2.06046i | ||||
\(555\) | 3.46410 | − | 6.92820i | 0.147043 | − | 0.294086i | ||||
\(556\) | −20.0000 | + | 34.6410i | −0.848189 | + | 1.46911i | ||||
\(557\) | 2.00000i | 0.0847427i | 0.999102 | + | 0.0423714i | \(0.0134913\pi\) | ||||
−0.999102 | + | 0.0423714i | \(0.986509\pi\) | |||||||
\(558\) | −20.7846 | + | 12.0000i | −0.879883 | + | 0.508001i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 4.92820 | + | 7.46410i | 0.208255 | + | 0.315416i | ||||
\(561\) | −9.00000 | + | 5.19615i | −0.379980 | + | 0.219382i | ||||
\(562\) | 12.1244 | − | 7.00000i | 0.511435 | − | 0.295277i | ||||
\(563\) | −7.79423 | + | 4.50000i | −0.328488 | + | 0.189652i | −0.655169 | − | 0.755482i | \(-0.727403\pi\) |
0.326682 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(564\) | 9.00000 | + | 5.19615i | 0.378968 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | −7.79423 | + | 4.50000i | −0.327327 | + | 0.188982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5000 | + | 33.7750i | −0.817483 | + | 1.41592i | 0.0900490 | + | 0.995937i | \(0.471298\pi\) |
−0.907532 | + | 0.419984i | \(0.862036\pi\) | |||||||
\(570\) | −25.6077 | − | 38.7846i | −1.07259 | − | 1.62451i | ||||
\(571\) | 22.5000 | + | 38.9711i | 0.941596 | + | 1.63089i | 0.762428 | + | 0.647073i | \(0.224007\pi\) |
0.179168 | + | 0.983819i | \(0.442660\pi\) | |||||||
\(572\) | −10.3923 | + | 6.00000i | −0.434524 | + | 0.250873i | ||||
\(573\) | 2.59808 | + | 4.50000i | 0.108536 | + | 0.187990i | ||||
\(574\) | −8.00000 | + | 13.8564i | −0.333914 | + | 0.578355i | ||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | − | 7.00000i | − | 0.291414i | −0.989328 | − | 0.145707i | \(-0.953454\pi\) | ||
0.989328 | − | 0.145707i | \(-0.0465456\pi\) | |||||||
\(578\) | −22.5167 | − | 13.0000i | −0.936570 | − | 0.540729i | ||||
\(579\) | 24.2487i | 1.00774i | ||||||||
\(580\) | −1.33975 | − | 22.3205i | −0.0556299 | − | 0.926809i | ||||
\(581\) | 8.50000 | + | 14.7224i | 0.352639 | + | 0.610789i | ||||
\(582\) | −24.2487 | −1.00514 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | − | 12.0000i | 0.248069 | − | 0.496139i | ||||
\(586\) | 54.0000 | 2.23072 | ||||||||
\(587\) | 20.7846 | + | 12.0000i | 0.857873 | + | 0.495293i | 0.863299 | − | 0.504692i | \(-0.168394\pi\) |
−0.00542667 | + | 0.999985i | \(0.501727\pi\) | |||||||
\(588\) | −1.73205 | − | 3.00000i | −0.0714286 | − | 0.123718i | ||||
\(589\) | −12.0000 | − | 20.7846i | −0.494451 | − | 0.856415i | ||||
\(590\) | −62.4974 | + | 3.75129i | −2.57298 | + | 0.154438i | ||||
\(591\) | −12.0000 | − | 6.92820i | −0.493614 | − | 0.284988i | ||||
\(592\) | 6.92820 | + | 4.00000i | 0.284747 | + | 0.164399i | ||||
\(593\) | 43.0000i | 1.76580i | 0.469563 | + | 0.882899i | \(0.344412\pi\) | ||||
−0.469563 | + | 0.882899i | \(0.655588\pi\) | |||||||
\(594\) | 27.0000 | − | 15.5885i | 1.10782 | − | 0.639602i | ||||
\(595\) | 4.00000 | + | 2.00000i | 0.163984 | + | 0.0819920i | ||||
\(596\) | 5.00000 | − | 8.66025i | 0.204808 | − | 0.354738i | ||||
\(597\) | 6.92820 | − | 12.0000i | 0.283552 | − | 0.491127i | ||||
\(598\) | 20.7846 | − | 12.0000i | 0.849946 | − | 0.490716i | ||||
\(599\) | 20.0000 | + | 34.6410i | 0.817178 | + | 1.41539i | 0.907754 | + | 0.419504i | \(0.137796\pi\) |
−0.0905757 | + | 0.995890i | \(0.528871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.00000 | − | 6.92820i | 0.163163 | − | 0.282607i | −0.772838 | − | 0.634603i | \(-0.781164\pi\) |
0.936002 | + | 0.351996i | \(0.114497\pi\) | |||||||
\(602\) | − | 4.00000i | − | 0.163028i | ||||||
\(603\) | 25.9808 | + | 15.0000i | 1.05802 | + | 0.610847i | ||||
\(604\) | −40.0000 | −1.62758 | ||||||||
\(605\) | −3.73205 | + | 2.46410i | −0.151729 | + | 0.100180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7750 | − | 19.5000i | 1.37088 | − | 0.791481i | 0.379845 | − | 0.925050i | \(-0.375977\pi\) |
0.991039 | + | 0.133570i | \(0.0426439\pi\) | |||||||
\(608\) | 41.5692 | − | 24.0000i | 1.68585 | − | 0.973329i | ||||
\(609\) | − | 8.66025i | − | 0.350931i | ||||||
\(610\) | 24.6410 | + | 37.3205i | 0.997686 | + | 1.51106i | ||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | −10.3923 | − | 6.00000i | −0.420084 | − | 0.242536i | ||||
\(613\) | 8.00000i | 0.323117i | 0.986863 | + | 0.161558i | \(0.0516520\pi\) | ||||
−0.986863 | + | 0.161558i | \(0.948348\pi\) | |||||||
\(614\) | 4.00000 | − | 6.92820i | 0.161427 | − | 0.279600i | ||||
\(615\) | 1.85641 | + | 30.9282i | 0.0748575 | + | 1.24715i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.92820 | + | 4.00000i | −0.278919 | + | 0.161034i | −0.632934 | − | 0.774206i | \(-0.718150\pi\) |
0.354015 | + | 0.935240i | \(0.384816\pi\) | |||||||
\(618\) | −8.66025 | + | 15.0000i | −0.348367 | + | 0.603388i | ||||
\(619\) | −10.0000 | + | 17.3205i | −0.401934 | + | 0.696170i | −0.993959 | − | 0.109749i | \(-0.964995\pi\) |
0.592025 | + | 0.805919i | \(0.298329\pi\) | |||||||
\(620\) | −16.0000 | − | 8.00000i | −0.642575 | − | 0.321288i | ||||
\(621\) | −27.0000 | + | 15.5885i | −1.08347 | + | 0.625543i | ||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | 10.3923 | + | 6.00000i | 0.416359 | + | 0.240385i | ||||
\(624\) | 12.0000 | + | 6.92820i | 0.480384 | + | 0.277350i | ||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | −9.00000 | − | 15.5885i | −0.359712 | − | 0.623040i | ||||
\(627\) | 15.5885 | + | 27.0000i | 0.622543 | + | 1.07828i | ||||
\(628\) | 15.5885 | + | 9.00000i | 0.622047 | + | 0.359139i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | −12.0000 | − | 6.00000i | −0.478091 | − | 0.239046i | ||||
\(631\) | −5.00000 | −0.199047 | −0.0995234 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995234 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.4449 | 1.17033 | ||||||||
\(634\) | −30.0000 | − | 51.9615i | −1.19145 | − | 2.06366i | ||||
\(635\) | −44.6410 | + | 2.67949i | −1.77152 | + | 0.106332i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.73205 | + | 1.00000i | 0.0686264 | + | 0.0396214i | ||||
\(638\) | 30.0000i | 1.18771i | ||||||||
\(639\) | −10.5000 | − | 18.1865i | −0.415374 | − | 0.719448i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0000 | + | 29.4449i | −0.671460 | + | 1.16300i | 0.306031 | + | 0.952022i | \(0.400999\pi\) |
−0.977490 | + | 0.210981i | \(0.932334\pi\) | |||||||
\(642\) | 27.7128 | + | 48.0000i | 1.09374 | + | 1.89441i | ||||
\(643\) | 4.33013 | − | 2.50000i | 0.170764 | − | 0.0985904i | −0.412182 | − | 0.911101i | \(-0.635233\pi\) |
0.582946 | + | 0.812511i | \(0.301900\pi\) | |||||||
\(644\) | −6.00000 | − | 10.3923i | −0.236433 | − | 0.409514i | ||||
\(645\) | −4.26795 | − | 6.46410i | −0.168050 | − | 0.254524i | ||||
\(646\) | 12.0000 | − | 20.7846i | 0.472134 | − | 0.817760i | ||||
\(647\) | − | 32.0000i | − | 1.25805i | −0.777385 | − | 0.629025i | \(-0.783454\pi\) | ||
0.777385 | − | 0.629025i | \(-0.216546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.0000 | 1.64864 | ||||||||
\(650\) | 19.8564 | − | 2.39230i | 0.778832 | − | 0.0938339i | ||||
\(651\) | −6.00000 | − | 3.46410i | −0.235159 | − | 0.135769i | ||||
\(652\) | 6.92820 | − | 4.00000i | 0.271329 | − | 0.156652i | ||||
\(653\) | 8.66025 | − | 5.00000i | 0.338902 | − | 0.195665i | −0.320884 | − | 0.947118i | \(-0.603980\pi\) |
0.659786 | + | 0.751453i | \(0.270647\pi\) | |||||||
\(654\) | 57.0000 | − | 32.9090i | 2.22888 | − | 1.28684i | ||||
\(655\) | −26.1244 | + | 17.2487i | −1.02076 | + | 0.673963i | ||||
\(656\) | −32.0000 | −1.24939 | ||||||||
\(657\) | −23.3827 | + | 13.5000i | −0.912245 | + | 0.526685i | ||||
\(658\) | 6.00000i | 0.233904i | ||||||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 20.7846 | + | 10.3923i | 0.809040 | + | 0.404520i | ||||
\(661\) | −12.0000 | − | 20.7846i | −0.466746 | − | 0.808428i | 0.532533 | − | 0.846410i | \(-0.321240\pi\) |
−0.999278 | + | 0.0379819i | \(0.987907\pi\) | |||||||
\(662\) | 46.7654 | − | 27.0000i | 1.81759 | − | 1.04938i | ||||
\(663\) | 6.92820 | 0.269069 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | − | 12.0000i | 0.232670 | − | 0.465340i | ||||
\(666\) | −12.0000 | −0.464991 | ||||||||
\(667\) | − | 30.0000i | − | 1.16160i | ||||||
\(668\) | −20.7846 | − | 12.0000i | −0.804181 | − | 0.464294i | ||||
\(669\) | −36.0000 | + | 20.7846i | −1.39184 | + | 0.803579i | ||||
\(670\) | 2.67949 | + | 44.6410i | 0.103518 | + | 1.72463i | ||||
\(671\) | −15.0000 | − | 25.9808i | −0.579069 | − | 1.00298i | ||||
\(672\) | 6.92820 | − | 12.0000i | 0.267261 | − | 0.462910i | ||||
\(673\) | −10.3923 | − | 6.00000i | −0.400594 | − | 0.231283i | 0.286146 | − | 0.958186i | \(-0.407626\pi\) |
−0.686740 | + | 0.726903i | \(0.740959\pi\) | |||||||
\(674\) | 36.0000 | 1.38667 | ||||||||
\(675\) | −25.7942 | + | 3.10770i | −0.992820 | + | 0.119615i | ||||
\(676\) | −18.0000 | −0.692308 | ||||||||
\(677\) | 19.0526 | + | 11.0000i | 0.732249 | + | 0.422764i | 0.819244 | − | 0.573444i | \(-0.194393\pi\) |
−0.0869952 | + | 0.996209i | \(0.527726\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.50000 | − | 6.06218i | −0.134318 | − | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.0000 | − | 17.3205i | 1.14960 | − | 0.663723i | ||||
\(682\) | 20.7846 | + | 12.0000i | 0.795884 | + | 0.459504i | ||||
\(683\) | − | 4.00000i | − | 0.153056i | −0.997067 | − | 0.0765279i | \(-0.975617\pi\) | ||
0.997067 | − | 0.0765279i | \(-0.0243834\pi\) | |||||||
\(684\) | −18.0000 | + | 31.1769i | −0.688247 | + | 1.19208i | ||||
\(685\) | 18.0000 | − | 36.0000i | 0.687745 | − | 1.37549i | ||||
\(686\) | 1.00000 | − | 1.73205i | 0.0381802 | − | 0.0661300i | ||||
\(687\) | 17.3205 | 0.660819 | ||||||||
\(688\) | 6.92820 | − | 4.00000i | 0.264135 | − | 0.152499i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −41.5692 | − | 20.7846i | −1.58251 | − | 0.791257i | ||||
\(691\) | 25.0000 | − | 43.3013i | 0.951045 | − | 1.64726i | 0.207875 | − | 0.978155i | \(-0.433345\pi\) |
0.743170 | − | 0.669102i | \(-0.233321\pi\) | |||||||
\(692\) | 30.0000i | 1.14043i | ||||||||
\(693\) | 7.79423 | + | 4.50000i | 0.296078 | + | 0.170941i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.3205 | + | 24.6410i | −1.41565 | + | 0.934687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8564 | + | 8.00000i | −0.524849 | + | 0.303022i | ||||
\(698\) | −17.3205 | + | 10.0000i | −0.655591 | + | 0.378506i | ||||
\(699\) | 24.0000 | + | 13.8564i | 0.907763 | + | 0.524097i | ||||
\(700\) | −1.19615 | − | 9.92820i | −0.0452103 | − | 0.375251i | ||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | −20.7846 | −0.784465 | ||||||||
\(703\) | − | 12.0000i | − | 0.452589i | ||||||
\(704\) | −12.0000 | + | 20.7846i | −0.452267 | + | 0.783349i | ||||
\(705\) | 6.40192 | + | 9.69615i | 0.241110 | + | 0.365178i | ||||
\(706\) | −11.0000 | − | 19.0526i | −0.413990 | − | 0.717053i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 24.2487 | + | 42.0000i | 0.911322 | + | 1.57846i | ||||
\(709\) | 17.5000 | − | 30.3109i | 0.657226 | − | 1.13835i | −0.324104 | − | 0.946021i | \(-0.605063\pi\) |
0.981331 | − | 0.192328i | \(-0.0616038\pi\) | |||||||
\(710\) | 14.0000 | − | 28.0000i | 0.525411 | − | 1.05082i | ||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7846 | − | 12.0000i | −0.778390 | − | 0.449404i | ||||
\(714\) | − | 6.92820i | − | 0.259281i | ||||||
\(715\) | −13.3923 | + | 0.803848i | −0.500844 | + | 0.0300622i | ||||
\(716\) | 11.0000 | + | 19.0526i | 0.411089 | + | 0.712028i | ||||
\(717\) | 15.5885 | 0.582162 | ||||||||
\(718\) | 6.92820 | + | 4.00000i | 0.258558 | + | 0.149279i | ||||
\(719\) | 18.0000 | 0.671287 | 0.335643 | − | 0.941989i | \(-0.391046\pi\) | ||||
0.335643 | + | 0.941989i | \(0.391046\pi\) | |||||||
\(720\) | −1.60770 | − | 26.7846i | −0.0599153 | − | 0.998203i | ||||
\(721\) | −5.00000 | −0.186210 | ||||||||
\(722\) | −29.4449 | − | 17.0000i | −1.09582 | − | 0.632674i | ||||
\(723\) | −3.46410 | − | 6.00000i | −0.128831 | − | 0.223142i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.82051 | − | 22.9904i | 0.364725 | − | 0.853841i | ||||
\(726\) | 6.00000 | + | 3.46410i | 0.222681 | + | 0.128565i | ||||
\(727\) | −40.7032 | − | 23.5000i | −1.50960 | − | 0.871567i | −0.999937 | − | 0.0111912i | \(-0.996438\pi\) |
−0.509661 | − | 0.860376i | \(-0.670229\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −36.0000 | − | 18.0000i | −1.33242 | − | 0.666210i | ||||
\(731\) | 2.00000 | − | 3.46410i | 0.0739727 | − | 0.128124i | ||||
\(732\) | 17.3205 | − | 30.0000i | 0.640184 | − | 1.10883i | ||||
\(733\) | 9.52628 | − | 5.50000i | 0.351861 | − | 0.203147i | −0.313644 | − | 0.949541i | \(-0.601550\pi\) |
0.665505 | + | 0.746394i | \(0.268216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.232051 | − | 3.86603i | −0.00855932 | − | 0.142600i | ||||
\(736\) | 24.0000 | − | 41.5692i | 0.884652 | − | 1.53226i | ||||
\(737\) | − | 30.0000i | − | 1.10506i | ||||||
\(738\) | 41.5692 | − | 24.0000i | 1.53018 | − | 0.883452i | ||||
\(739\) | −1.00000 | −0.0367856 | −0.0183928 | − | 0.999831i | \(-0.505855\pi\) | ||||
−0.0183928 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(740\) | −4.92820 | − | 7.46410i | −0.181164 | − | 0.274386i | ||||
\(741\) | − | 20.7846i | − | 0.763542i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.66025 | + | 5.00000i | −0.317714 | + | 0.183432i | −0.650373 | − | 0.759615i | \(-0.725387\pi\) |
0.332659 | + | 0.943047i | \(0.392054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.33013 | − | 6.16025i | 0.341829 | − | 0.225694i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 51.0000i | − | 1.86599i | ||||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | −8.00000 | + | 13.8564i | −0.292314 | + | 0.506302i | ||||
\(750\) | −25.0526 | − | 29.5359i | −0.914790 | − | 1.07850i | ||||
\(751\) | −7.50000 | − | 12.9904i | −0.273679 | − | 0.474026i | 0.696122 | − | 0.717923i | \(-0.254907\pi\) |
−0.969801 | + | 0.243898i | \(0.921574\pi\) | |||||||
\(752\) | −10.3923 | + | 6.00000i | −0.378968 | + | 0.218797i | ||||
\(753\) | −15.5885 | + | 27.0000i | −0.568075 | + | 0.983935i | ||||
\(754\) | 10.0000 | − | 17.3205i | 0.364179 | − | 0.630776i | ||||
\(755\) | −40.0000 | − | 20.0000i | −1.45575 | − | 0.727875i | ||||
\(756\) | 10.3923i | 0.377964i | ||||||||
\(757\) | − | 10.0000i | − | 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | 39.8372 | + | 23.0000i | 1.44695 | + | 0.835398i | ||||
\(759\) | 27.0000 | + | 15.5885i | 0.980038 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.00000 | − | 12.1244i | −0.253750 | − | 0.439508i | 0.710805 | − | 0.703389i | \(-0.248331\pi\) |
−0.964555 | + | 0.263881i | \(0.914997\pi\) | |||||||
\(762\) | 34.6410 | + | 60.0000i | 1.25491 | + | 2.17357i | ||||
\(763\) | 16.4545 | + | 9.50000i | 0.595692 | + | 0.343923i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | −7.39230 | − | 11.1962i | −0.267269 | − | 0.404798i | ||||
\(766\) | −10.0000 | −0.361315 | ||||||||
\(767\) | −24.2487 | − | 14.0000i | −0.875570 | − | 0.505511i | ||||
\(768\) | 27.7128 | 1.00000 | ||||||||
\(769\) | 9.00000 | + | 15.5885i | 0.324548 | + | 0.562134i | 0.981421 | − | 0.191867i | \(-0.0614544\pi\) |
−0.656873 | + | 0.754002i | \(0.728121\pi\) | |||||||
\(770\) | 0.803848 | + | 13.3923i | 0.0289687 | + | 0.482625i | ||||
\(771\) | 12.1244i | 0.436648i | ||||||||
\(772\) | 24.2487 | + | 14.0000i | 0.872730 | + | 0.503871i | ||||
\(773\) | 27.0000i | 0.971123i | 0.874203 | + | 0.485561i | \(0.161385\pi\) | ||||
−0.874203 | + | 0.485561i | \(0.838615\pi\) | |||||||
\(774\) | −6.00000 | + | 10.3923i | −0.215666 | + | 0.373544i | ||||
\(775\) | −12.0000 | − | 16.0000i | −0.431053 | − | 0.574737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.73205 | − | 3.00000i | −0.0621370 | − | 0.107624i | ||||
\(778\) | 32.9090 | − | 19.0000i | 1.17984 | − | 0.681183i | ||||
\(779\) | 24.0000 | + | 41.5692i | 0.859889 | + | 1.48937i | ||||
\(780\) | −8.53590 | − | 12.9282i | −0.305634 | − | 0.462904i | ||||
\(781\) | −10.5000 | + | 18.1865i | −0.375720 | + | 0.650765i | ||||
\(782\) | − | 24.0000i | − | 0.858238i | ||||||
\(783\) | −12.9904 | + | 22.5000i | −0.464238 | + | 0.804084i | ||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | 11.0885 | + | 16.7942i | 0.395764 | + | 0.599412i | ||||
\(786\) | 42.0000 | + | 24.2487i | 1.49809 | + | 0.864923i | ||||
\(787\) | −34.6410 | + | 20.0000i | −1.23482 | + | 0.712923i | −0.968031 | − | 0.250832i | \(-0.919296\pi\) |
−0.266788 | + | 0.963755i | \(0.585962\pi\) | |||||||
\(788\) | −13.8564 | + | 8.00000i | −0.493614 | + | 0.284988i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.46410 | − | 3.73205i | −0.0876688 | − | 0.132780i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000i | 0.710221i | ||||||||
\(794\) | −17.0000 | + | 29.4449i | −0.603307 | + | 1.04496i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.00000 | − | 13.8564i | −0.283552 | − | 0.491127i | ||||
\(797\) | −19.0526 | + | 11.0000i | −0.674876 | + | 0.389640i | −0.797922 | − | 0.602761i | \(-0.794067\pi\) |
0.123045 | + | 0.992401i | \(0.460734\pi\) | |||||||
\(798\) | −20.7846 | −0.735767 | ||||||||
\(799\) | −3.00000 | + | 5.19615i | −0.106132 | + | 0.183827i | ||||
\(800\) | 32.0000 | − | 24.0000i | 1.13137 | − | 0.848528i | ||||
\(801\) | −18.0000 | − | 31.1769i | −0.635999 | − | 1.10158i | ||||
\(802\) | − | 30.0000i | − | 1.05934i | ||||||
\(803\) | 23.3827 | + | 13.5000i | 0.825157 | + | 0.476405i | ||||
\(804\) | 30.0000 | − | 17.3205i | 1.05802 | − | 0.610847i | ||||
\(805\) | −0.803848 | − | 13.3923i | −0.0283319 | − | 0.472017i | ||||
\(806\) | −8.00000 | − | 13.8564i | −0.281788 | − | 0.488071i | ||||
\(807\) | 13.8564 | − | 24.0000i | 0.487769 | − | 0.844840i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 22.1769 | + | 33.5885i | 0.779217 | + | 1.18018i | ||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | −8.66025 | − | 5.00000i | −0.303915 | − | 0.175466i | ||||
\(813\) | 12.1244 | − | 21.0000i | 0.425220 | − | 0.736502i | ||||
\(814\) | 6.00000 | + | 10.3923i | 0.210300 | + | 0.364250i | ||||
\(815\) | 8.92820 | − | 0.535898i | 0.312741 | − | 0.0187717i | ||||
\(816\) | 12.0000 | − | 6.92820i | 0.420084 | − | 0.242536i | ||||
\(817\) | −10.3923 | − | 6.00000i | −0.363581 | − | 0.209913i | ||||
\(818\) | − | 16.0000i | − | 0.559427i | ||||||
\(819\) | −3.00000 | − | 5.19615i | −0.104828 | − | 0.181568i | ||||
\(820\) | 32.0000 | + | 16.0000i | 1.11749 | + | 0.558744i | ||||
\(821\) | 25.0000 | − | 43.3013i | 0.872506 | − | 1.51122i | 0.0131101 | − | 0.999914i | \(-0.495827\pi\) |
0.859396 | − | 0.511311i | \(-0.170840\pi\) | |||||||
\(822\) | −62.3538 | −2.17484 | ||||||||
\(823\) | 3.46410 | − | 2.00000i | 0.120751 | − | 0.0697156i | −0.438408 | − | 0.898776i | \(-0.644457\pi\) |
0.559159 | + | 0.829060i | \(0.311124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.5885 | + | 20.7846i | 0.542720 | + | 0.723627i | ||||
\(826\) | −14.0000 | + | 24.2487i | −0.487122 | + | 0.843721i | ||||
\(827\) | 30.0000i | 1.04320i | 0.853189 | + | 0.521601i | \(0.174665\pi\) | ||||
−0.853189 | + | 0.521601i | \(0.825335\pi\) | |||||||
\(828\) | 36.0000i | 1.25109i | ||||||||
\(829\) | 24.0000 | 0.833554 | 0.416777 | − | 0.909009i | \(-0.363160\pi\) | ||||
0.416777 | + | 0.909009i | \(0.363160\pi\) | |||||||
\(830\) | 63.4449 | − | 41.8897i | 2.20220 | − | 1.45401i | ||||
\(831\) | −42.0000 | + | 24.2487i | −1.45696 | + | 0.841178i | ||||
\(832\) | 13.8564 | − | 8.00000i | 0.480384 | − | 0.277350i | ||||
\(833\) | 1.73205 | − | 1.00000i | 0.0600120 | − | 0.0346479i | ||||
\(834\) | 60.0000 | + | 34.6410i | 2.07763 | + | 1.19952i | ||||
\(835\) | −14.7846 | − | 22.3923i | −0.511643 | − | 0.774918i | ||||
\(836\) | 36.0000 | 1.24509 | ||||||||
\(837\) | 10.3923 | + | 18.0000i | 0.359211 | + | 0.622171i | ||||
\(838\) | 60.0000i | 2.07267i | ||||||||
\(839\) | 24.0000 | − | 41.5692i | 0.828572 | − | 1.43513i | −0.0705865 | − | 0.997506i | \(-0.522487\pi\) |
0.899158 | − | 0.437623i | \(-0.144180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | + | 3.46410i | 0.0689655 | + | 0.119452i | ||||
\(842\) | −25.9808 | + | 15.0000i | −0.895356 | + | 0.516934i | ||||
\(843\) | −6.06218 | − | 10.5000i | −0.208792 | − | 0.361639i | ||||
\(844\) | 17.0000 | − | 29.4449i | 0.585164 | − | 1.01353i | ||||
\(845\) | −18.0000 | − | 9.00000i | −0.619219 | − | 0.309609i | ||||
\(846\) | 9.00000 | − | 15.5885i | 0.309426 | − | 0.535942i | ||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.1244i | 0.416107i | ||||||||
\(850\) | 7.85641 | − | 18.3923i | 0.269473 | − | 0.630851i | ||||
\(851\) | −6.00000 | − | 10.3923i | −0.205677 | − | 0.356244i | ||||
\(852\) | −24.2487 | −0.830747 | ||||||||
\(853\) | −36.3731 | − | 21.0000i | −1.24539 | − | 0.719026i | −0.275204 | − | 0.961386i | \(-0.588745\pi\) |
−0.970186 | + | 0.242360i | \(0.922079\pi\) | |||||||
\(854\) | 20.0000 | 0.684386 | ||||||||
\(855\) | −33.5885 | + | 22.1769i | −1.14870 | + | 0.758434i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.1865 | − | 10.5000i | −0.621240 | − | 0.358673i | 0.156112 | − | 0.987739i | \(-0.450104\pi\) |
−0.777352 | + | 0.629066i | \(0.783437\pi\) | |||||||
\(858\) | 10.3923 | + | 18.0000i | 0.354787 | + | 0.614510i | ||||
\(859\) | −19.0000 | − | 32.9090i | −0.648272 | − | 1.12284i | −0.983535 | − | 0.180715i | \(-0.942159\pi\) |
0.335264 | − | 0.942124i | \(-0.391175\pi\) | |||||||
\(860\) | −8.92820 | + | 0.535898i | −0.304449 | + | 0.0182740i | ||||
\(861\) | 12.0000 | + | 6.92820i | 0.408959 | + | 0.236113i | ||||
\(862\) | −27.7128 | − | 16.0000i | −0.943902 | − | 0.544962i | ||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | −36.0000 | + | 20.7846i | −1.22474 | + | 0.707107i | ||||
\(865\) | −15.0000 | + | 30.0000i | −0.510015 | + | 1.02003i | ||||
\(866\) | −2.00000 | + | 3.46410i | −0.0679628 | + | 0.117715i | ||||
\(867\) | −11.2583 | + | 19.5000i | −0.382353 | + | 0.662255i | ||||
\(868\) | −6.92820 | + | 4.00000i | −0.235159 | + | 0.135769i | ||||
\(869\) | 1.50000 | + | 2.59808i | 0.0508840 | + | 0.0881337i | ||||
\(870\) | −38.6603 | + | 2.32051i | −1.31071 | + | 0.0786726i | ||||
\(871\) | −10.0000 | + | 17.3205i | −0.338837 | + | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.0000i | 0.710742i | ||||||||
\(874\) | −72.0000 | −2.43544 | ||||||||
\(875\) | 3.76795 | − | 10.5263i | 0.127380 | − | 0.355853i | ||||
\(876\) | 31.1769i | 1.05337i | ||||||||
\(877\) | −29.4449 | + | 17.0000i | −0.994282 | + | 0.574049i | −0.906552 | − | 0.422095i | \(-0.861295\pi\) |
−0.0877308 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 46.7654i | − | 1.57736i | ||||||
\(880\) | −22.3923 | + | 14.7846i | −0.754844 | + | 0.498389i | ||||
\(881\) | 50.0000 | 1.68454 | 0.842271 | − | 0.539054i | \(-0.181218\pi\) | ||||
0.842271 | + | 0.539054i | \(0.181218\pi\) | |||||||
\(882\) | −5.19615 | + | 3.00000i | −0.174964 | + | 0.101015i | ||||
\(883\) | − | 42.0000i | − | 1.41341i | −0.707507 | − | 0.706706i | \(-0.750180\pi\) | ||
0.707507 | − | 0.706706i | \(-0.249820\pi\) | |||||||
\(884\) | 4.00000 | − | 6.92820i | 0.134535 | − | 0.233021i | ||||
\(885\) | 3.24871 | + | 54.1244i | 0.109204 | + | 1.81937i | ||||
\(886\) | 4.00000 | + | 6.92820i | 0.134383 | + | 0.232758i | ||||
\(887\) | −13.8564 | + | 8.00000i | −0.465253 | + | 0.268614i | −0.714250 | − | 0.699890i | \(-0.753232\pi\) |
0.248998 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | + | 17.3205i | −0.335389 | + | 0.580911i | ||||
\(890\) | 24.0000 | − | 48.0000i | 0.804482 | − | 1.60896i | ||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 48.0000i | 1.60716i | ||||||||
\(893\) | 15.5885 | + | 9.00000i | 0.521648 | + | 0.301174i | ||||
\(894\) | −15.0000 | − | 8.66025i | −0.501675 | − | 0.289642i | ||||
\(895\) | 1.47372 | + | 24.5526i | 0.0492610 | + | 0.820702i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.3923 | − | 18.0000i | −0.346989 | − | 0.601003i | ||||
\(898\) | 53.6936 | + | 31.0000i | 1.79178 | + | 1.03448i | ||||
\(899\) | −20.0000 | −0.667037 | ||||||||
\(900\) | −11.7846 | + | 27.5885i | −0.392820 | + | 0.919615i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −41.5692 | − | 24.0000i | −1.38410 | − | 0.799113i | ||||
\(903\) | −3.46410 | −0.115278 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 69.2820i | 2.30174i | ||||||||
\(907\) | 12.1244 | + | 7.00000i | 0.402583 | + | 0.232431i | 0.687598 | − | 0.726092i | \(-0.258665\pi\) |
−0.285015 | + | 0.958523i | \(0.591999\pi\) | |||||||
\(908\) | − | 40.0000i | − | 1.32745i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.00000 | − | 8.00000i | 0.132599 | − | 0.265197i | ||||
\(911\) | 13.5000 | − | 23.3827i | 0.447275 | − | 0.774703i | −0.550933 | − | 0.834550i | \(-0.685728\pi\) |
0.998208 | + | 0.0598468i | \(0.0190612\pi\) | |||||||
\(912\) | −20.7846 | − | 36.0000i | −0.688247 | − | 1.19208i | ||||
\(913\) | −44.1673 | + | 25.5000i | −1.46172 | + | 0.843927i | ||||
\(914\) | 28.0000 | + | 48.4974i | 0.926158 | + | 1.60415i | ||||
\(915\) | 32.3205 | − | 21.3397i | 1.06848 | − | 0.705470i | ||||
\(916\) | 10.0000 | − | 17.3205i | 0.330409 | − | 0.572286i | ||||
\(917\) | 14.0000i | 0.462321i | ||||||||
\(918\) | −10.3923 | + | 18.0000i | −0.342997 | + | 0.594089i | ||||
\(919\) | −55.0000 | −1.81428 | −0.907141 | − | 0.420826i | \(-0.861740\pi\) | ||||
−0.907141 | + | 0.420826i | \(0.861740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | − | 3.46410i | −0.197707 | − | 0.114146i | ||||
\(922\) | −20.7846 | + | 12.0000i | −0.684505 | + | 0.395199i | ||||
\(923\) | 12.1244 | − | 7.00000i | 0.399078 | − | 0.230408i | ||||
\(924\) | 9.00000 | − | 5.19615i | 0.296078 | − | 0.170941i | ||||
\(925\) | −1.19615 | − | 9.92820i | −0.0393292 | − | 0.326437i | ||||
\(926\) | −12.0000 | −0.394344 | ||||||||
\(927\) | 12.9904 | + | 7.50000i | 0.426660 | + | 0.246332i | ||||
\(928\) | − | 40.0000i | − | 1.31306i | ||||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | −13.8564 | + | 27.7128i | −0.454369 | + | 0.908739i | ||||
\(931\) | −3.00000 | − | 5.19615i | −0.0983210 | − | 0.170297i | ||||
\(932\) | 27.7128 | − | 16.0000i | 0.907763 | − | 0.524097i | ||||
\(933\) | −10.3923 | −0.340229 | ||||||||
\(934\) | −3.00000 | + | 5.19615i | −0.0981630 | + | 0.170023i | ||||
\(935\) | −6.00000 | + | 12.0000i | −0.196221 | + | 0.392442i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 17.3205 | + | 10.0000i | 0.565535 | + | 0.326512i | ||||
\(939\) | −13.5000 | + | 7.79423i | −0.440556 | + | 0.254355i | ||||
\(940\) | 13.3923 | − | 0.803848i | 0.436809 | − | 0.0262186i | ||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 15.5885 | − | 27.0000i | 0.507899 | − | 0.879708i | ||||
\(943\) | 41.5692 | + | 24.0000i | 1.35368 | + | 0.781548i | ||||
\(944\) | −56.0000 | −1.82264 | ||||||||
\(945\) | −5.19615 | + | 10.3923i | −0.169031 | + | 0.338062i | ||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −31.1769 | − | 18.0000i | −1.01311 | − | 0.584921i | −0.101012 | − | 0.994885i | \(-0.532208\pi\) |
−0.912102 | + | 0.409964i | \(0.865541\pi\) | |||||||
\(948\) | −1.73205 | + | 3.00000i | −0.0562544 | + | 0.0974355i | ||||
\(949\) | −9.00000 | − | 15.5885i | −0.292152 | − | 0.506023i | ||||
\(950\) | −55.1769 | − | 23.5692i | −1.79018 | − | 0.764686i | ||||
\(951\) | −45.0000 | + | 25.9808i | −1.45922 | + | 0.842484i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | + | 3.00000i | 0.194155 | + | 0.0970777i | ||||
\(956\) | 9.00000 | − | 15.5885i | 0.291081 | − | 0.504167i | ||||
\(957\) | 25.9808 | 0.839839 | ||||||||
\(958\) | −62.3538 | + | 36.0000i | −2.01456 | + | 1.16311i | ||||
\(959\) | −9.00000 | − | 15.5885i | −0.290625 | − | 0.503378i | ||||
\(960\) | −27.7128 | − | 13.8564i | −0.894427 | − | 0.447214i | ||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | − | 8.00000i | − | 0.257930i | ||||||
\(963\) | 41.5692 | − | 24.0000i | 1.33955 | − | 0.773389i | ||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 17.2487 | + | 26.1244i | 0.555256 | + | 0.840973i | ||||
\(966\) | −18.0000 | + | 10.3923i | −0.579141 | + | 0.334367i | ||||
\(967\) | −1.73205 | + | 1.00000i | −0.0556990 | + | 0.0321578i | −0.527591 | − | 0.849499i | \(-0.676905\pi\) |
0.471892 | + | 0.881656i | \(0.343571\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.0000 | − | 10.3923i | −0.578243 | − | 0.333849i | ||||
\(970\) | −26.1244 | + | 17.2487i | −0.838803 | + | 0.553823i | ||||
\(971\) | 10.0000 | 0.320915 | 0.160458 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160458 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(972\) | 15.5885 | − | 27.0000i | 0.500000 | − | 0.866025i | ||||
\(973\) | 20.0000i | 0.641171i | ||||||||
\(974\) | −12.0000 | + | 20.7846i | −0.384505 | + | 0.665982i | ||||
\(975\) | −2.07180 | − | 17.1962i | −0.0663506 | − | 0.550718i | ||||
\(976\) | 20.0000 | + | 34.6410i | 0.640184 | + | 1.10883i | ||||
\(977\) | 36.3731 | − | 21.0000i | 1.16368 | − | 0.671850i | 0.211495 | − | 0.977379i | \(-0.432167\pi\) |
0.952183 | + | 0.305530i | \(0.0988335\pi\) | |||||||
\(978\) | −6.92820 | − | 12.0000i | −0.221540 | − | 0.383718i | ||||
\(979\) | −18.0000 | + | 31.1769i | −0.575282 | + | 0.996419i | ||||
\(980\) | −4.00000 | − | 2.00000i | −0.127775 | − | 0.0638877i | ||||
\(981\) | −28.5000 | − | 49.3634i | −0.909935 | − | 1.57605i | ||||
\(982\) | 56.0000i | 1.78703i | ||||||||
\(983\) | −2.59808 | − | 1.50000i | −0.0828658 | − | 0.0478426i | 0.457995 | − | 0.888955i | \(-0.348568\pi\) |
−0.540860 | + | 0.841112i | \(0.681901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8564 | + | 1.07180i | −0.568952 | + | 0.0341503i | ||||
\(986\) | −10.0000 | − | 17.3205i | −0.318465 | − | 0.551597i | ||||
\(987\) | 5.19615 | 0.165395 | ||||||||
\(988\) | −20.7846 | − | 12.0000i | −0.661247 | − | 0.381771i | ||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 18.0000 | − | 36.0000i | 0.572078 | − | 1.14416i | ||||
\(991\) | −35.0000 | −1.11181 | −0.555906 | − | 0.831245i | \(-0.687628\pi\) | ||||
−0.555906 | + | 0.831245i | \(0.687628\pi\) | |||||||
\(992\) | −27.7128 | − | 16.0000i | −0.879883 | − | 0.508001i | ||||
\(993\) | −23.3827 | − | 40.5000i | −0.742027 | − | 1.28523i | ||||
\(994\) | −7.00000 | − | 12.1244i | −0.222027 | − | 0.384561i | ||||
\(995\) | −1.07180 | − | 17.8564i | −0.0339782 | − | 0.566086i | ||||
\(996\) | −51.0000 | − | 29.4449i | −1.61600 | − | 0.932996i | ||||
\(997\) | 21.6506 | + | 12.5000i | 0.685682 | + | 0.395879i | 0.801993 | − | 0.597334i | \(-0.203773\pi\) |
−0.116310 | + | 0.993213i | \(0.537107\pi\) | |||||||
\(998\) | − | 8.00000i | − | 0.253236i | ||||||
\(999\) | 10.3923i | 0.328798i |
(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 | 315.2.bh.b.169.1 | ✓ | 4 | |
3.2 | odd | 2 | 945.2.bh.b.694.2 | 4 | |||
5.4 | even | 2 | inner | 315.2.bh.b.169.2 | yes | 4 | |
9.4 | even | 3 | inner | 315.2.bh.b.274.2 | yes | 4 | |
9.5 | odd | 6 | 945.2.bh.b.64.1 | 4 | |||
15.14 | odd | 2 | 945.2.bh.b.694.1 | 4 | |||
45.4 | even | 6 | inner | 315.2.bh.b.274.1 | yes | 4 | |
45.14 | odd | 6 | 945.2.bh.b.64.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bh.b.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
315.2.bh.b.169.2 | yes | 4 | 5.4 | even | 2 | inner | |
315.2.bh.b.274.1 | yes | 4 | 45.4 | even | 6 | inner | |
315.2.bh.b.274.2 | yes | 4 | 9.4 | even | 3 | inner | |
945.2.bh.b.64.1 | 4 | 9.5 | odd | 6 | |||
945.2.bh.b.64.2 | 4 | 45.14 | odd | 6 | |||
945.2.bh.b.694.1 | 4 | 15.14 | odd | 2 | |||
945.2.bh.b.694.2 | 4 | 3.2 | odd | 2 |