Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(161,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.p (of order \(4\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.281 |
Dual form | 390.2.p.d.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −0.292893 | − | 1.70711i | −0.119573 | − | 0.696923i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | −1.41421 | − | 1.41421i | −0.426401 | − | 0.426401i | 0.460999 | − | 0.887401i | \(-0.347491\pi\) |
−0.887401 | + | 0.460999i | \(0.847491\pi\) | |||||||
\(12\) | −1.41421 | − | 1.00000i | −0.408248 | − | 0.288675i | ||||
\(13\) | −3.00000 | + | 2.00000i | −0.832050 | + | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.292893 | − | 1.70711i | −0.0756247 | − | 0.440773i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | −2.70711 | − | 1.29289i | −0.638071 | − | 0.304738i | ||||
\(19\) | 6.00000 | + | 6.00000i | 1.37649 | + | 1.37649i | 0.850469 | + | 0.526026i | \(0.176318\pi\) |
0.526026 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(20\) | −0.707107 | − | 0.707107i | −0.158114 | − | 0.158114i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 1.41421 | 0.294884 | 0.147442 | − | 0.989071i | \(-0.452896\pi\) | ||||
0.147442 | + | 0.989071i | \(0.452896\pi\) | |||||||
\(24\) | −1.70711 | + | 0.292893i | −0.348462 | + | 0.0597866i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | −0.707107 | + | 3.53553i | −0.138675 | + | 0.693375i | ||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.41421i | − | 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | −1.41421 | − | 1.00000i | −0.258199 | − | 0.182574i | ||||
\(31\) | −3.00000 | − | 3.00000i | −0.538816 | − | 0.538816i | 0.384365 | − | 0.923181i | \(-0.374420\pi\) |
−0.923181 | + | 0.384365i | \(0.874420\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.41421 | + | 0.585786i | −0.594338 | + | 0.101972i | ||||
\(34\) | 3.00000 | − | 3.00000i | 0.514496 | − | 0.514496i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82843 | + | 1.00000i | −0.471405 | + | 0.166667i | ||||
\(37\) | 5.00000 | − | 5.00000i | 0.821995 | − | 0.821995i | −0.164399 | − | 0.986394i | \(-0.552568\pi\) |
0.986394 | + | 0.164399i | \(0.0525685\pi\) | |||||||
\(38\) | 8.48528 | 1.37649 | ||||||||
\(39\) | −0.171573 | + | 6.24264i | −0.0274736 | + | 0.999623i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −7.07107 | + | 7.07107i | −1.10432 | + | 1.10432i | −0.110432 | + | 0.993884i | \(0.535223\pi\) |
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | −1.41421 | + | 1.41421i | −0.213201 | + | 0.213201i | ||||
\(45\) | −2.70711 | − | 1.29289i | −0.403552 | − | 0.192733i | ||||
\(46\) | 1.00000 | − | 1.00000i | 0.147442 | − | 0.147442i | ||||
\(47\) | 4.24264 | + | 4.24264i | 0.618853 | + | 0.618853i | 0.945237 | − | 0.326384i | \(-0.105830\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(48\) | −1.00000 | + | 1.41421i | −0.144338 | + | 0.204124i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.100000 | − | 0.100000i | ||||
\(51\) | 4.24264 | − | 6.00000i | 0.594089 | − | 0.840168i | ||||
\(52\) | 2.00000 | + | 3.00000i | 0.277350 | + | 0.416025i | ||||
\(53\) | − | 11.3137i | − | 1.55406i | −0.629465 | − | 0.777029i | \(-0.716726\pi\) | ||
0.629465 | − | 0.777029i | \(-0.283274\pi\) | |||||||
\(54\) | −4.53553 | + | 2.53553i | −0.617208 | + | 0.345042i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.4853 | − | 2.48528i | 1.91862 | − | 0.329184i | ||||
\(58\) | −1.00000 | − | 1.00000i | −0.131306 | − | 0.131306i | ||||
\(59\) | 2.82843 | + | 2.82843i | 0.368230 | + | 0.368230i | 0.866831 | − | 0.498601i | \(-0.166153\pi\) |
−0.498601 | + | 0.866831i | \(0.666153\pi\) | |||||||
\(60\) | −1.70711 | + | 0.292893i | −0.220387 | + | 0.0378124i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −4.24264 | −0.538816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.707107 | + | 3.53553i | −0.0877058 | + | 0.438529i | ||||
\(66\) | −2.00000 | + | 2.82843i | −0.246183 | + | 0.348155i | ||||
\(67\) | 5.00000 | + | 5.00000i | 0.610847 | + | 0.610847i | 0.943167 | − | 0.332320i | \(-0.107831\pi\) |
−0.332320 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(68\) | − | 4.24264i | − | 0.514496i | ||||||
\(69\) | 1.41421 | − | 2.00000i | 0.170251 | − | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | + | 5.65685i | −0.671345 | + | 0.671345i | −0.958026 | − | 0.286681i | \(-0.907448\pi\) |
0.286681 | + | 0.958026i | \(0.407448\pi\) | |||||||
\(72\) | −1.29289 | + | 2.70711i | −0.152369 | + | 0.319036i | ||||
\(73\) | 6.00000 | − | 6.00000i | 0.702247 | − | 0.702247i | −0.262646 | − | 0.964892i | \(-0.584595\pi\) |
0.964892 | + | 0.262646i | \(0.0845950\pi\) | |||||||
\(74\) | − | 7.07107i | − | 0.821995i | ||||||
\(75\) | −1.41421 | − | 1.00000i | −0.163299 | − | 0.115470i | ||||
\(76\) | 6.00000 | − | 6.00000i | 0.688247 | − | 0.688247i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.29289 | + | 4.53553i | 0.486074 | + | 0.513548i | ||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −0.707107 | + | 0.707107i | −0.0790569 | + | 0.0790569i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 10.0000i | 1.10432i | ||||||||
\(83\) | −5.65685 | + | 5.65685i | −0.620920 | + | 0.620920i | −0.945767 | − | 0.324846i | \(-0.894687\pi\) |
0.324846 | + | 0.945767i | \(0.394687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | − | 3.00000i | 0.325396 | − | 0.325396i | ||||
\(86\) | 2.82843 | + | 2.82843i | 0.304997 | + | 0.304997i | ||||
\(87\) | −2.00000 | − | 1.41421i | −0.214423 | − | 0.151620i | ||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | −4.24264 | − | 4.24264i | −0.449719 | − | 0.449719i | 0.445542 | − | 0.895261i | \(-0.353011\pi\) |
−0.895261 | + | 0.445542i | \(0.853011\pi\) | |||||||
\(90\) | −2.82843 | + | 1.00000i | −0.298142 | + | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.41421i | − | 0.147442i | ||||||
\(93\) | −7.24264 | + | 1.24264i | −0.751027 | + | 0.128856i | ||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 8.48528 | 0.870572 | ||||||||
\(96\) | 0.292893 | + | 1.70711i | 0.0298933 | + | 0.174231i | ||||
\(97\) | 10.0000 | + | 10.0000i | 1.01535 | + | 1.01535i | 0.999880 | + | 0.0154658i | \(0.00492310\pi\) |
0.0154658 | + | 0.999880i | \(0.495077\pi\) | |||||||
\(98\) | 4.94975 | + | 4.94975i | 0.500000 | + | 0.500000i | ||||
\(99\) | −2.58579 | + | 5.41421i | −0.259881 | + | 0.544149i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −15.5563 | −1.54791 | −0.773957 | − | 0.633238i | \(-0.781726\pi\) | ||||
−0.773957 | + | 0.633238i | \(0.781726\pi\) | |||||||
\(102\) | −1.24264 | − | 7.24264i | −0.123040 | − | 0.717128i | ||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | 3.53553 | + | 0.707107i | 0.346688 | + | 0.0693375i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | − | 8.00000i | −0.777029 | − | 0.777029i | ||||
\(107\) | 11.3137i | 1.09374i | 0.837218 | + | 0.546869i | \(0.184180\pi\) | ||||
−0.837218 | + | 0.546869i | \(0.815820\pi\) | |||||||
\(108\) | −1.41421 | + | 5.00000i | −0.136083 | + | 0.481125i | ||||
\(109\) | 2.00000 | + | 2.00000i | 0.191565 | + | 0.191565i | 0.796372 | − | 0.604807i | \(-0.206750\pi\) |
−0.604807 | + | 0.796372i | \(0.706750\pi\) | |||||||
\(110\) | −1.41421 | + | 1.41421i | −0.134840 | + | 0.134840i | ||||
\(111\) | −2.07107 | − | 12.0711i | −0.196577 | − | 1.14574i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.07107i | − | 0.665190i | −0.943070 | − | 0.332595i | \(-0.892076\pi\) | ||
0.943070 | − | 0.332595i | \(-0.107924\pi\) | |||||||
\(114\) | 8.48528 | − | 12.0000i | 0.794719 | − | 1.12390i | ||||
\(115\) | 1.00000 | − | 1.00000i | 0.0932505 | − | 0.0932505i | ||||
\(116\) | −1.41421 | −0.131306 | ||||||||
\(117\) | 8.65685 | + | 6.48528i | 0.800326 | + | 0.599564i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 1.41421i | −0.0912871 | + | 0.129099i | ||||
\(121\) | − | 7.00000i | − | 0.636364i | ||||||
\(122\) | 1.41421 | − | 1.41421i | 0.128037 | − | 0.128037i | ||||
\(123\) | 2.92893 | + | 17.0711i | 0.264093 | + | 1.53925i | ||||
\(124\) | −3.00000 | + | 3.00000i | −0.269408 | + | 0.269408i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.00000i | − | 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 5.65685 | + | 4.00000i | 0.498058 | + | 0.352180i | ||||
\(130\) | 2.00000 | + | 3.00000i | 0.175412 | + | 0.263117i | ||||
\(131\) | 7.07107i | 0.617802i | 0.951094 | + | 0.308901i | \(0.0999612\pi\) | ||||
−0.951094 | + | 0.308901i | \(0.900039\pi\) | |||||||
\(132\) | 0.585786 | + | 3.41421i | 0.0509862 | + | 0.297169i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.07107 | 0.610847 | ||||||||
\(135\) | −4.53553 | + | 2.53553i | −0.390357 | + | 0.218224i | ||||
\(136\) | −3.00000 | − | 3.00000i | −0.257248 | − | 0.257248i | ||||
\(137\) | −14.1421 | − | 14.1421i | −1.20824 | − | 1.20824i | −0.971595 | − | 0.236649i | \(-0.923951\pi\) |
−0.236649 | − | 0.971595i | \(-0.576049\pi\) | |||||||
\(138\) | −0.414214 | − | 2.41421i | −0.0352602 | − | 0.205512i | ||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2426 | − | 1.75736i | 0.862586 | − | 0.147996i | ||||
\(142\) | 8.00000i | 0.671345i | ||||||||
\(143\) | 7.07107 | + | 1.41421i | 0.591312 | + | 0.118262i | ||||
\(144\) | 1.00000 | + | 2.82843i | 0.0833333 | + | 0.235702i | ||||
\(145\) | −1.00000 | − | 1.00000i | −0.0830455 | − | 0.0830455i | ||||
\(146\) | − | 8.48528i | − | 0.702247i | ||||||
\(147\) | 9.89949 | + | 7.00000i | 0.816497 | + | 0.577350i | ||||
\(148\) | −5.00000 | − | 5.00000i | −0.410997 | − | 0.410997i | ||||
\(149\) | −7.07107 | + | 7.07107i | −0.579284 | + | 0.579284i | −0.934706 | − | 0.355422i | \(-0.884337\pi\) |
0.355422 | + | 0.934706i | \(0.384337\pi\) | |||||||
\(150\) | −1.70711 | + | 0.292893i | −0.139385 | + | 0.0239146i | ||||
\(151\) | −13.0000 | + | 13.0000i | −1.05792 | + | 1.05792i | −0.0597092 | + | 0.998216i | \(0.519017\pi\) |
−0.998216 | + | 0.0597092i | \(0.980983\pi\) | |||||||
\(152\) | − | 8.48528i | − | 0.688247i | ||||||
\(153\) | −4.24264 | − | 12.0000i | −0.342997 | − | 0.970143i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.24264 | −0.340777 | ||||||||
\(156\) | 6.24264 | + | 0.171573i | 0.499811 | + | 0.0137368i | ||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 5.65685 | − | 5.65685i | 0.450035 | − | 0.450035i | ||||
\(159\) | −16.0000 | − | 11.3137i | −1.26888 | − | 0.897235i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.949747 | + | 8.94975i | −0.0746192 | + | 0.703159i | ||||
\(163\) | −11.0000 | + | 11.0000i | −0.861586 | + | 0.861586i | −0.991522 | − | 0.129936i | \(-0.958523\pi\) |
0.129936 | + | 0.991522i | \(0.458523\pi\) | |||||||
\(164\) | 7.07107 | + | 7.07107i | 0.552158 | + | 0.552158i | ||||
\(165\) | −2.00000 | + | 2.82843i | −0.155700 | + | 0.220193i | ||||
\(166\) | 8.00000i | 0.620920i | ||||||||
\(167\) | 11.3137 | + | 11.3137i | 0.875481 | + | 0.875481i | 0.993063 | − | 0.117582i | \(-0.0375143\pi\) |
−0.117582 | + | 0.993063i | \(0.537514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | − | 4.24264i | − | 0.325396i | ||||||
\(171\) | 10.9706 | − | 22.9706i | 0.838940 | − | 1.75660i | ||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | 2.82843 | 0.215041 | 0.107521 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107521 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(174\) | −2.41421 | + | 0.414214i | −0.183021 | + | 0.0314014i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.41421 | + | 1.41421i | 0.106600 | + | 0.106600i | ||||
\(177\) | 6.82843 | − | 1.17157i | 0.513256 | − | 0.0880608i | ||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | −18.3848 | −1.37414 | −0.687071 | − | 0.726590i | \(-0.741104\pi\) | ||||
−0.687071 | + | 0.726590i | \(0.741104\pi\) | |||||||
\(180\) | −1.29289 | + | 2.70711i | −0.0963666 | + | 0.201776i | ||||
\(181\) | − | 18.0000i | − | 1.33793i | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||
0.743294 | − | 0.668965i | \(-0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | − | 2.82843i | 0.147844 | − | 0.209083i | ||||
\(184\) | −1.00000 | − | 1.00000i | −0.0737210 | − | 0.0737210i | ||||
\(185\) | − | 7.07107i | − | 0.519875i | ||||||
\(186\) | −4.24264 | + | 6.00000i | −0.311086 | + | 0.439941i | ||||
\(187\) | −6.00000 | − | 6.00000i | −0.438763 | − | 0.438763i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 6.00000i | 0.435286 | − | 0.435286i | ||||
\(191\) | − | 19.7990i | − | 1.43260i | −0.697790 | − | 0.716302i | \(-0.745833\pi\) | ||
0.697790 | − | 0.716302i | \(-0.254167\pi\) | |||||||
\(192\) | 1.41421 | + | 1.00000i | 0.102062 | + | 0.0721688i | ||||
\(193\) | −6.00000 | + | 6.00000i | −0.431889 | + | 0.431889i | −0.889271 | − | 0.457381i | \(-0.848787\pi\) |
0.457381 | + | 0.889271i | \(0.348787\pi\) | |||||||
\(194\) | 14.1421 | 1.01535 | ||||||||
\(195\) | 4.29289 | + | 4.53553i | 0.307420 | + | 0.324796i | ||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | 9.89949 | − | 9.89949i | 0.705310 | − | 0.705310i | −0.260235 | − | 0.965545i | \(-0.583800\pi\) |
0.965545 | + | 0.260235i | \(0.0838002\pi\) | |||||||
\(198\) | 2.00000 | + | 5.65685i | 0.142134 | + | 0.402015i | ||||
\(199\) | − | 2.00000i | − | 0.141776i | −0.997484 | − | 0.0708881i | \(-0.977417\pi\) | ||
0.997484 | − | 0.0708881i | \(-0.0225833\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.0500000 | + | 0.0500000i | ||||
\(201\) | 12.0711 | − | 2.07107i | 0.851427 | − | 0.146082i | ||||
\(202\) | −11.0000 | + | 11.0000i | −0.773957 | + | 0.773957i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | − | 4.24264i | −0.420084 | − | 0.297044i | ||||
\(205\) | 10.0000i | 0.698430i | ||||||||
\(206\) | −5.65685 | − | 5.65685i | −0.394132 | − | 0.394132i | ||||
\(207\) | −1.41421 | − | 4.00000i | −0.0982946 | − | 0.278019i | ||||
\(208\) | 3.00000 | − | 2.00000i | 0.208013 | − | 0.138675i | ||||
\(209\) | − | 16.9706i | − | 1.17388i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.0000 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(212\) | −11.3137 | −0.777029 | ||||||||
\(213\) | 2.34315 | + | 13.6569i | 0.160550 | + | 0.935752i | ||||
\(214\) | 8.00000 | + | 8.00000i | 0.546869 | + | 0.546869i | ||||
\(215\) | 2.82843 | + | 2.82843i | 0.192897 | + | 0.192897i | ||||
\(216\) | 2.53553 | + | 4.53553i | 0.172521 | + | 0.308604i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.82843 | 0.191565 | ||||||||
\(219\) | −2.48528 | − | 14.4853i | −0.167940 | − | 0.978825i | ||||
\(220\) | 2.00000i | 0.134840i | ||||||||
\(221\) | −12.7279 | + | 8.48528i | −0.856173 | + | 0.570782i | ||||
\(222\) | −10.0000 | − | 7.07107i | −0.671156 | − | 0.474579i | ||||
\(223\) | −10.0000 | − | 10.0000i | −0.669650 | − | 0.669650i | 0.287985 | − | 0.957635i | \(-0.407015\pi\) |
−0.957635 | + | 0.287985i | \(0.907015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | + | 1.00000i | −0.188562 | + | 0.0666667i | ||||
\(226\) | −5.00000 | − | 5.00000i | −0.332595 | − | 0.332595i | ||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | −2.48528 | − | 14.4853i | −0.164592 | − | 0.959311i | ||||
\(229\) | 6.00000 | − | 6.00000i | 0.396491 | − | 0.396491i | −0.480502 | − | 0.876993i | \(-0.659546\pi\) |
0.876993 | + | 0.480502i | \(0.159546\pi\) | |||||||
\(230\) | − | 1.41421i | − | 0.0932505i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | + | 1.00000i | −0.0656532 | + | 0.0656532i | ||||
\(233\) | 18.3848 | 1.20443 | 0.602213 | − | 0.798335i | \(-0.294286\pi\) | ||||
0.602213 | + | 0.798335i | \(0.294286\pi\) | |||||||
\(234\) | 10.7071 | − | 1.53553i | 0.699945 | − | 0.100381i | ||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 2.82843 | − | 2.82843i | 0.184115 | − | 0.184115i | ||||
\(237\) | 8.00000 | − | 11.3137i | 0.519656 | − | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0.292893 | + | 1.70711i | 0.0189062 | + | 0.110193i | ||||
\(241\) | −1.00000 | + | 1.00000i | −0.0644157 | + | 0.0644157i | −0.738581 | − | 0.674165i | \(-0.764504\pi\) |
0.674165 | + | 0.738581i | \(0.264504\pi\) | |||||||
\(242\) | −4.94975 | − | 4.94975i | −0.318182 | − | 0.318182i | ||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | 4.94975 | + | 4.94975i | 0.316228 | + | 0.316228i | ||||
\(246\) | 14.1421 | + | 10.0000i | 0.901670 | + | 0.637577i | ||||
\(247\) | −30.0000 | − | 6.00000i | −1.90885 | − | 0.381771i | ||||
\(248\) | 4.24264i | 0.269408i | ||||||||
\(249\) | 2.34315 | + | 13.6569i | 0.148491 | + | 0.865468i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −4.24264 | −0.267793 | −0.133897 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133897 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | − | 2.00000i | −0.125739 | − | 0.125739i | ||||
\(254\) | −2.82843 | − | 2.82843i | −0.177471 | − | 0.177471i | ||||
\(255\) | −1.24264 | − | 7.24264i | −0.0778172 | − | 0.453552i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.41421 | 0.0882162 | 0.0441081 | − | 0.999027i | \(-0.485955\pi\) | ||||
0.0441081 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(258\) | 6.82843 | − | 1.17157i | 0.425119 | − | 0.0729389i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.53553 | + | 0.707107i | 0.219265 | + | 0.0438529i | ||||
\(261\) | −4.00000 | + | 1.41421i | −0.247594 | + | 0.0875376i | ||||
\(262\) | 5.00000 | + | 5.00000i | 0.308901 | + | 0.308901i | ||||
\(263\) | 4.24264i | 0.261612i | 0.991408 | + | 0.130806i | \(0.0417566\pi\) | ||||
−0.991408 | + | 0.130806i | \(0.958243\pi\) | |||||||
\(264\) | 2.82843 | + | 2.00000i | 0.174078 | + | 0.123091i | ||||
\(265\) | −8.00000 | − | 8.00000i | −0.491436 | − | 0.491436i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.2426 | + | 1.75736i | −0.626839 | + | 0.107549i | ||||
\(268\) | 5.00000 | − | 5.00000i | 0.305424 | − | 0.305424i | ||||
\(269\) | − | 1.41421i | − | 0.0862261i | −0.999070 | − | 0.0431131i | \(-0.986272\pi\) | ||
0.999070 | − | 0.0431131i | \(-0.0137276\pi\) | |||||||
\(270\) | −1.41421 | + | 5.00000i | −0.0860663 | + | 0.304290i | ||||
\(271\) | −3.00000 | + | 3.00000i | −0.182237 | + | 0.182237i | −0.792330 | − | 0.610093i | \(-0.791132\pi\) |
0.610093 | + | 0.792330i | \(0.291132\pi\) | |||||||
\(272\) | −4.24264 | −0.257248 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.0000 | −1.20824 | ||||||||
\(275\) | −1.41421 | + | 1.41421i | −0.0852803 | + | 0.0852803i | ||||
\(276\) | −2.00000 | − | 1.41421i | −0.120386 | − | 0.0851257i | ||||
\(277\) | − | 28.0000i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | −11.3137 | + | 11.3137i | −0.678551 | + | 0.678551i | ||||
\(279\) | −5.48528 | + | 11.4853i | −0.328395 | + | 0.687606i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7279 | + | 12.7279i | 0.759284 | + | 0.759284i | 0.976192 | − | 0.216908i | \(-0.0695971\pi\) |
−0.216908 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(282\) | 6.00000 | − | 8.48528i | 0.357295 | − | 0.505291i | ||||
\(283\) | 6.00000i | 0.356663i | 0.983970 | + | 0.178331i | \(0.0570699\pi\) | ||||
−0.983970 | + | 0.178331i | \(0.942930\pi\) | |||||||
\(284\) | 5.65685 | + | 5.65685i | 0.335673 | + | 0.335673i | ||||
\(285\) | 8.48528 | − | 12.0000i | 0.502625 | − | 0.710819i | ||||
\(286\) | 6.00000 | − | 4.00000i | 0.354787 | − | 0.236525i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.70711 | + | 1.29289i | 0.159518 | + | 0.0761845i | ||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.41421 | −0.0830455 | ||||||||
\(291\) | 24.1421 | − | 4.14214i | 1.41524 | − | 0.242816i | ||||
\(292\) | −6.00000 | − | 6.00000i | −0.351123 | − | 0.351123i | ||||
\(293\) | −9.89949 | − | 9.89949i | −0.578335 | − | 0.578335i | 0.356110 | − | 0.934444i | \(-0.384103\pi\) |
−0.934444 | + | 0.356110i | \(0.884103\pi\) | |||||||
\(294\) | 11.9497 | − | 2.05025i | 0.696923 | − | 0.119573i | ||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −7.07107 | −0.410997 | ||||||||
\(297\) | 5.07107 | + | 9.07107i | 0.294253 | + | 0.526357i | ||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | −4.24264 | + | 2.82843i | −0.245358 | + | 0.163572i | ||||
\(300\) | −1.00000 | + | 1.41421i | −0.0577350 | + | 0.0816497i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.3848i | 1.05792i | ||||||||
\(303\) | −15.5563 | + | 22.0000i | −0.893689 | + | 1.26387i | ||||
\(304\) | −6.00000 | − | 6.00000i | −0.344124 | − | 0.344124i | ||||
\(305\) | 1.41421 | − | 1.41421i | 0.0809776 | − | 0.0809776i | ||||
\(306\) | −11.4853 | − | 5.48528i | −0.656570 | − | 0.313573i | ||||
\(307\) | 23.0000 | − | 23.0000i | 1.31268 | − | 1.31268i | 0.393246 | − | 0.919433i | \(-0.371352\pi\) |
0.919433 | − | 0.393246i | \(-0.128648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3137 | − | 8.00000i | −0.643614 | − | 0.455104i | ||||
\(310\) | −3.00000 | + | 3.00000i | −0.170389 | + | 0.170389i | ||||
\(311\) | 2.82843 | 0.160385 | 0.0801927 | − | 0.996779i | \(-0.474446\pi\) | ||||
0.0801927 | + | 0.996779i | \(0.474446\pi\) | |||||||
\(312\) | 4.53553 | − | 4.29289i | 0.256774 | − | 0.243037i | ||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | −4.24264 | + | 4.24264i | −0.239426 | + | 0.239426i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.00000i | − | 0.450035i | ||||||
\(317\) | −18.3848 | + | 18.3848i | −1.03259 | + | 1.03259i | −0.0331412 | + | 0.999451i | \(0.510551\pi\) |
−0.999451 | + | 0.0331412i | \(0.989449\pi\) | |||||||
\(318\) | −19.3137 | + | 3.31371i | −1.08306 | + | 0.185824i | ||||
\(319\) | −2.00000 | + | 2.00000i | −0.111979 | + | 0.111979i | ||||
\(320\) | 0.707107 | + | 0.707107i | 0.0395285 | + | 0.0395285i | ||||
\(321\) | 16.0000 | + | 11.3137i | 0.893033 | + | 0.631470i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4558 | + | 25.4558i | 1.41640 | + | 1.41640i | ||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | 2.00000 | + | 3.00000i | 0.110940 | + | 0.166410i | ||||
\(326\) | 15.5563i | 0.861586i | ||||||||
\(327\) | 4.82843 | − | 0.828427i | 0.267013 | − | 0.0458121i | ||||
\(328\) | 10.0000 | 0.552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.585786 | + | 3.41421i | 0.0322465 | + | 0.187946i | ||||
\(331\) | 24.0000 | + | 24.0000i | 1.31916 | + | 1.31916i | 0.914442 | + | 0.404718i | \(0.132630\pi\) |
0.404718 | + | 0.914442i | \(0.367370\pi\) | |||||||
\(332\) | 5.65685 | + | 5.65685i | 0.310460 | + | 0.310460i | ||||
\(333\) | −19.1421 | − | 9.14214i | −1.04898 | − | 0.500986i | ||||
\(334\) | 16.0000 | 0.875481 | ||||||||
\(335\) | 7.07107 | 0.386334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | −4.94975 | − | 12.0208i | −0.269231 | − | 0.653846i | ||||
\(339\) | −10.0000 | − | 7.07107i | −0.543125 | − | 0.384048i | ||||
\(340\) | −3.00000 | − | 3.00000i | −0.162698 | − | 0.162698i | ||||
\(341\) | 8.48528i | 0.459504i | ||||||||
\(342\) | −8.48528 | − | 24.0000i | −0.458831 | − | 1.29777i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.82843 | − | 2.82843i | 0.152499 | − | 0.152499i | ||||
\(345\) | −0.414214 | − | 2.41421i | −0.0223005 | − | 0.129977i | ||||
\(346\) | 2.00000 | − | 2.00000i | 0.107521 | − | 0.107521i | ||||
\(347\) | − | 11.3137i | − | 0.607352i | −0.952775 | − | 0.303676i | \(-0.901786\pi\) | ||
0.952775 | − | 0.303676i | \(-0.0982140\pi\) | |||||||
\(348\) | −1.41421 | + | 2.00000i | −0.0758098 | + | 0.107211i | ||||
\(349\) | −12.0000 | + | 12.0000i | −0.642345 | + | 0.642345i | −0.951131 | − | 0.308786i | \(-0.900077\pi\) |
0.308786 | + | 0.951131i | \(0.400077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8284 | − | 5.75736i | 0.951611 | − | 0.307305i | ||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | 25.4558 | − | 25.4558i | 1.35488 | − | 1.35488i | 0.474766 | − | 0.880112i | \(-0.342533\pi\) |
0.880112 | − | 0.474766i | \(-0.157467\pi\) | |||||||
\(354\) | 4.00000 | − | 5.65685i | 0.212598 | − | 0.300658i | ||||
\(355\) | 8.00000i | 0.424596i | ||||||||
\(356\) | −4.24264 | + | 4.24264i | −0.224860 | + | 0.224860i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.0000 | + | 13.0000i | −0.687071 | + | 0.687071i | ||||
\(359\) | 16.9706 | + | 16.9706i | 0.895672 | + | 0.895672i | 0.995050 | − | 0.0993777i | \(-0.0316852\pi\) |
−0.0993777 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(360\) | 1.00000 | + | 2.82843i | 0.0527046 | + | 0.149071i | ||||
\(361\) | 53.0000i | 2.78947i | ||||||||
\(362\) | −12.7279 | − | 12.7279i | −0.668965 | − | 0.668965i | ||||
\(363\) | −9.89949 | − | 7.00000i | −0.519589 | − | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.48528i | − | 0.444140i | ||||||
\(366\) | −0.585786 | − | 3.41421i | −0.0306195 | − | 0.178464i | ||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | −1.41421 | −0.0737210 | ||||||||
\(369\) | 27.0711 | + | 12.9289i | 1.40926 | + | 0.673053i | ||||
\(370\) | −5.00000 | − | 5.00000i | −0.259938 | − | 0.259938i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.24264 | + | 7.24264i | 0.0644279 | + | 0.375513i | ||||
\(373\) | −32.0000 | −1.65690 | −0.828449 | − | 0.560065i | \(-0.810776\pi\) | ||||
−0.828449 | + | 0.560065i | \(0.810776\pi\) | |||||||
\(374\) | −8.48528 | −0.438763 | ||||||||
\(375\) | −1.70711 | + | 0.292893i | −0.0881546 | + | 0.0151249i | ||||
\(376\) | − | 6.00000i | − | 0.309426i | ||||||
\(377\) | 2.82843 | + | 4.24264i | 0.145671 | + | 0.218507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | + | 16.0000i | 0.821865 | + | 0.821865i | 0.986375 | − | 0.164511i | \(-0.0526045\pi\) |
−0.164511 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(380\) | − | 8.48528i | − | 0.435286i | ||||||
\(381\) | −5.65685 | − | 4.00000i | −0.289809 | − | 0.204926i | ||||
\(382\) | −14.0000 | − | 14.0000i | −0.716302 | − | 0.716302i | ||||
\(383\) | −16.9706 | + | 16.9706i | −0.867155 | + | 0.867155i | −0.992157 | − | 0.125001i | \(-0.960106\pi\) |
0.125001 | + | 0.992157i | \(0.460106\pi\) | |||||||
\(384\) | 1.70711 | − | 0.292893i | 0.0871154 | − | 0.0149466i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 11.3137 | − | 4.00000i | 0.575108 | − | 0.203331i | ||||
\(388\) | 10.0000 | − | 10.0000i | 0.507673 | − | 0.507673i | ||||
\(389\) | −26.8701 | −1.36237 | −0.681183 | − | 0.732113i | \(-0.738534\pi\) | ||||
−0.681183 | + | 0.732113i | \(0.738534\pi\) | |||||||
\(390\) | 6.24264 | + | 0.171573i | 0.316108 | + | 0.00868793i | ||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | 4.94975 | − | 4.94975i | 0.250000 | − | 0.250000i | ||||
\(393\) | 10.0000 | + | 7.07107i | 0.504433 | + | 0.356688i | ||||
\(394\) | − | 14.0000i | − | 0.705310i | ||||||
\(395\) | 5.65685 | − | 5.65685i | 0.284627 | − | 0.284627i | ||||
\(396\) | 5.41421 | + | 2.58579i | 0.272074 | + | 0.129941i | ||||
\(397\) | 3.00000 | − | 3.00000i | 0.150566 | − | 0.150566i | −0.627805 | − | 0.778371i | \(-0.716046\pi\) |
0.778371 | + | 0.627805i | \(0.216046\pi\) | |||||||
\(398\) | −1.41421 | − | 1.41421i | −0.0708881 | − | 0.0708881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | 4.24264 | + | 4.24264i | 0.211867 | + | 0.211867i | 0.805060 | − | 0.593193i | \(-0.202133\pi\) |
−0.593193 | + | 0.805060i | \(0.702133\pi\) | |||||||
\(402\) | 7.07107 | − | 10.0000i | 0.352673 | − | 0.498755i | ||||
\(403\) | 15.0000 | + | 3.00000i | 0.747203 | + | 0.149441i | ||||
\(404\) | 15.5563i | 0.773957i | ||||||||
\(405\) | −0.949747 | + | 8.94975i | −0.0471933 | + | 0.444717i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.1421 | −0.701000 | ||||||||
\(408\) | −7.24264 | + | 1.24264i | −0.358564 | + | 0.0615199i | ||||
\(409\) | −3.00000 | − | 3.00000i | −0.148340 | − | 0.148340i | 0.629036 | − | 0.777376i | \(-0.283450\pi\) |
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(410\) | 7.07107 | + | 7.07107i | 0.349215 | + | 0.349215i | ||||
\(411\) | −34.1421 | + | 5.85786i | −1.68411 | + | 0.288947i | ||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.82843 | − | 1.82843i | −0.188157 | − | 0.0898623i | ||||
\(415\) | 8.00000i | 0.392705i | ||||||||
\(416\) | 0.707107 | − | 3.53553i | 0.0346688 | − | 0.173344i | ||||
\(417\) | −16.0000 | + | 22.6274i | −0.783523 | + | 1.10807i | ||||
\(418\) | −12.0000 | − | 12.0000i | −0.586939 | − | 0.586939i | ||||
\(419\) | 15.5563i | 0.759977i | 0.924991 | + | 0.379989i | \(0.124072\pi\) | ||||
−0.924991 | + | 0.379989i | \(0.875928\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000 | + | 12.0000i | 0.584844 | + | 0.584844i | 0.936231 | − | 0.351386i | \(-0.114290\pi\) |
−0.351386 | + | 0.936231i | \(0.614290\pi\) | |||||||
\(422\) | −16.9706 | + | 16.9706i | −0.826114 | + | 0.826114i | ||||
\(423\) | 7.75736 | − | 16.2426i | 0.377176 | − | 0.789744i | ||||
\(424\) | −8.00000 | + | 8.00000i | −0.388514 | + | 0.388514i | ||||
\(425\) | − | 4.24264i | − | 0.205798i | ||||||
\(426\) | 11.3137 | + | 8.00000i | 0.548151 | + | 0.387601i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.3137 | 0.546869 | ||||||||
\(429\) | 9.07107 | − | 8.58579i | 0.437955 | − | 0.414526i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | 25.4558 | − | 25.4558i | 1.22616 | − | 1.22616i | 0.260762 | − | 0.965403i | \(-0.416026\pi\) |
0.965403 | − | 0.260762i | \(-0.0839737\pi\) | |||||||
\(432\) | 5.00000 | + | 1.41421i | 0.240563 | + | 0.0680414i | ||||
\(433\) | 14.0000i | 0.672797i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.41421 | + | 0.414214i | −0.115753 | + | 0.0198600i | ||||
\(436\) | 2.00000 | − | 2.00000i | 0.0957826 | − | 0.0957826i | ||||
\(437\) | 8.48528 | + | 8.48528i | 0.405906 | + | 0.405906i | ||||
\(438\) | −12.0000 | − | 8.48528i | −0.573382 | − | 0.405442i | ||||
\(439\) | − | 6.00000i | − | 0.286364i | −0.989696 | − | 0.143182i | \(-0.954267\pi\) | ||
0.989696 | − | 0.143182i | \(-0.0457335\pi\) | |||||||
\(440\) | 1.41421 | + | 1.41421i | 0.0674200 | + | 0.0674200i | ||||
\(441\) | 19.7990 | − | 7.00000i | 0.942809 | − | 0.333333i | ||||
\(442\) | −3.00000 | + | 15.0000i | −0.142695 | + | 0.713477i | ||||
\(443\) | − | 8.48528i | − | 0.403148i | −0.979473 | − | 0.201574i | \(-0.935394\pi\) | ||
0.979473 | − | 0.201574i | \(-0.0646056\pi\) | |||||||
\(444\) | −12.0711 | + | 2.07107i | −0.572868 | + | 0.0982885i | ||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −14.1421 | −0.669650 | ||||||||
\(447\) | 2.92893 | + | 17.0711i | 0.138534 | + | 0.807434i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.7279 | − | 12.7279i | −0.600668 | − | 0.600668i | 0.339822 | − | 0.940490i | \(-0.389633\pi\) |
−0.940490 | + | 0.339822i | \(0.889633\pi\) | |||||||
\(450\) | −1.29289 | + | 2.70711i | −0.0609476 | + | 0.127614i | ||||
\(451\) | 20.0000 | 0.941763 | ||||||||
\(452\) | −7.07107 | −0.332595 | ||||||||
\(453\) | 5.38478 | + | 31.3848i | 0.252999 | + | 1.47459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0000 | − | 8.48528i | −0.561951 | − | 0.397360i | ||||
\(457\) | 6.00000 | + | 6.00000i | 0.280668 | + | 0.280668i | 0.833375 | − | 0.552707i | \(-0.186405\pi\) |
−0.552707 | + | 0.833375i | \(0.686405\pi\) | |||||||
\(458\) | − | 8.48528i | − | 0.396491i | ||||||
\(459\) | −21.2132 | − | 6.00000i | −0.990148 | − | 0.280056i | ||||
\(460\) | −1.00000 | − | 1.00000i | −0.0466252 | − | 0.0466252i | ||||
\(461\) | −2.82843 | + | 2.82843i | −0.131733 | + | 0.131733i | −0.769899 | − | 0.638166i | \(-0.779693\pi\) |
0.638166 | + | 0.769899i | \(0.279693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000 | − | 22.0000i | 1.02243 | − | 1.02243i | 0.0226840 | − | 0.999743i | \(-0.492779\pi\) |
0.999743 | − | 0.0226840i | \(-0.00722117\pi\) | |||||||
\(464\) | 1.41421i | 0.0656532i | ||||||||
\(465\) | −4.24264 | + | 6.00000i | −0.196748 | + | 0.278243i | ||||
\(466\) | 13.0000 | − | 13.0000i | 0.602213 | − | 0.602213i | ||||
\(467\) | 2.82843 | 0.130884 | 0.0654420 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654420 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(468\) | 6.48528 | − | 8.65685i | 0.299782 | − | 0.400163i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.24264 | − | 4.24264i | 0.195698 | − | 0.195698i | ||||
\(471\) | −6.00000 | + | 8.48528i | −0.276465 | + | 0.390981i | ||||
\(472\) | − | 4.00000i | − | 0.184115i | ||||||
\(473\) | 5.65685 | − | 5.65685i | 0.260102 | − | 0.260102i | ||||
\(474\) | −2.34315 | − | 13.6569i | −0.107624 | − | 0.627280i | ||||
\(475\) | 6.00000 | − | 6.00000i | 0.275299 | − | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.0000 | + | 11.3137i | −1.46518 | + | 0.518019i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1421 | + | 14.1421i | 0.646171 | + | 0.646171i | 0.952065 | − | 0.305895i | \(-0.0989555\pi\) |
−0.305895 | + | 0.952065i | \(0.598956\pi\) | |||||||
\(480\) | 1.41421 | + | 1.00000i | 0.0645497 | + | 0.0456435i | ||||
\(481\) | −5.00000 | + | 25.0000i | −0.227980 | + | 1.13990i | ||||
\(482\) | 1.41421i | 0.0644157i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 14.1421 | 0.642161 | ||||||||
\(486\) | 11.7071 | + | 10.2929i | 0.531045 | + | 0.466895i | ||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | −1.41421 | − | 1.41421i | −0.0640184 | − | 0.0640184i | ||||
\(489\) | 4.55635 | + | 26.5563i | 0.206045 | + | 1.20092i | ||||
\(490\) | 7.00000 | 0.316228 | ||||||||
\(491\) | 15.5563 | 0.702048 | 0.351024 | − | 0.936366i | \(-0.385834\pi\) | ||||
0.351024 | + | 0.936366i | \(0.385834\pi\) | |||||||
\(492\) | 17.0711 | − | 2.92893i | 0.769623 | − | 0.132046i | ||||
\(493\) | − | 6.00000i | − | 0.270226i | ||||||
\(494\) | −25.4558 | + | 16.9706i | −1.14531 | + | 0.763542i | ||||
\(495\) | 2.00000 | + | 5.65685i | 0.0898933 | + | 0.254257i | ||||
\(496\) | 3.00000 | + | 3.00000i | 0.134704 | + | 0.134704i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.3137 | + | 8.00000i | 0.506979 | + | 0.358489i | ||||
\(499\) | −18.0000 | − | 18.0000i | −0.805791 | − | 0.805791i | 0.178203 | − | 0.983994i | \(-0.442972\pi\) |
−0.983994 | + | 0.178203i | \(0.942972\pi\) | |||||||
\(500\) | −0.707107 | + | 0.707107i | −0.0316228 | + | 0.0316228i | ||||
\(501\) | 27.3137 | − | 4.68629i | 1.22029 | − | 0.209368i | ||||
\(502\) | −3.00000 | + | 3.00000i | −0.133897 | + | 0.133897i | ||||
\(503\) | − | 9.89949i | − | 0.441397i | −0.975342 | − | 0.220698i | \(-0.929166\pi\) | ||
0.975342 | − | 0.220698i | \(-0.0708336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0000 | + | 11.0000i | −0.489494 | + | 0.489494i | ||||
\(506\) | −2.82843 | −0.125739 | ||||||||
\(507\) | −11.9706 | − | 19.0711i | −0.531631 | − | 0.846976i | ||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | −14.1421 | + | 14.1421i | −0.626839 | + | 0.626839i | −0.947271 | − | 0.320432i | \(-0.896172\pi\) |
0.320432 | + | 0.947271i | \(0.396172\pi\) | |||||||
\(510\) | −6.00000 | − | 4.24264i | −0.265684 | − | 0.187867i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −21.5147 | − | 38.4853i | −0.949898 | − | 1.69917i | ||||
\(514\) | 1.00000 | − | 1.00000i | 0.0441081 | − | 0.0441081i | ||||
\(515\) | −5.65685 | − | 5.65685i | −0.249271 | − | 0.249271i | ||||
\(516\) | 4.00000 | − | 5.65685i | 0.176090 | − | 0.249029i | ||||
\(517\) | − | 12.0000i | − | 0.527759i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82843 | − | 4.00000i | 0.124154 | − | 0.175581i | ||||
\(520\) | 3.00000 | − | 2.00000i | 0.131559 | − | 0.0877058i | ||||
\(521\) | − | 5.65685i | − | 0.247831i | −0.992293 | − | 0.123916i | \(-0.960455\pi\) | ||
0.992293 | − | 0.123916i | \(-0.0395452\pi\) | |||||||
\(522\) | −1.82843 | + | 3.82843i | −0.0800281 | + | 0.167566i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 7.07107 | 0.308901 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.00000 | + | 3.00000i | 0.130806 | + | 0.130806i | ||||
\(527\) | −12.7279 | − | 12.7279i | −0.554437 | − | 0.554437i | ||||
\(528\) | 3.41421 | − | 0.585786i | 0.148585 | − | 0.0254931i | ||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | −11.3137 | −0.491436 | ||||||||
\(531\) | 5.17157 | − | 10.8284i | 0.224427 | − | 0.469914i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.07107 | − | 35.3553i | 0.306282 | − | 1.53141i | ||||
\(534\) | −6.00000 | + | 8.48528i | −0.259645 | + | 0.367194i | ||||
\(535\) | 8.00000 | + | 8.00000i | 0.345870 | + | 0.345870i | ||||
\(536\) | − | 7.07107i | − | 0.305424i | ||||||
\(537\) | −18.3848 | + | 26.0000i | −0.793362 | + | 1.12198i | ||||
\(538\) | −1.00000 | − | 1.00000i | −0.0431131 | − | 0.0431131i | ||||
\(539\) | 9.89949 | − | 9.89949i | 0.426401 | − | 0.426401i | ||||
\(540\) | 2.53553 | + | 4.53553i | 0.109112 | + | 0.195178i | ||||
\(541\) | −8.00000 | + | 8.00000i | −0.343947 | + | 0.343947i | −0.857849 | − | 0.513902i | \(-0.828199\pi\) |
0.513902 | + | 0.857849i | \(0.328199\pi\) | |||||||
\(542\) | 4.24264i | 0.182237i | ||||||||
\(543\) | −25.4558 | − | 18.0000i | −1.09241 | − | 0.772454i | ||||
\(544\) | −3.00000 | + | 3.00000i | −0.128624 | + | 0.128624i | ||||
\(545\) | 2.82843 | 0.121157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | −14.1421 | + | 14.1421i | −0.604122 | + | 0.604122i | ||||
\(549\) | −2.00000 | − | 5.65685i | −0.0853579 | − | 0.241429i | ||||
\(550\) | 2.00000i | 0.0852803i | ||||||||
\(551\) | 8.48528 | − | 8.48528i | 0.361485 | − | 0.361485i | ||||
\(552\) | −2.41421 | + | 0.414214i | −0.102756 | + | 0.0176301i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19.7990 | − | 19.7990i | −0.841178 | − | 0.841178i | ||||
\(555\) | −10.0000 | − | 7.07107i | −0.424476 | − | 0.300150i | ||||
\(556\) | 16.0000i | 0.678551i | ||||||||
\(557\) | −18.3848 | − | 18.3848i | −0.778988 | − | 0.778988i | 0.200671 | − | 0.979659i | \(-0.435688\pi\) |
−0.979659 | + | 0.200671i | \(0.935688\pi\) | |||||||
\(558\) | 4.24264 | + | 12.0000i | 0.179605 | + | 0.508001i | ||||
\(559\) | −8.00000 | − | 12.0000i | −0.338364 | − | 0.507546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4853 | + | 2.48528i | −0.611569 | + | 0.104929i | ||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | 19.7990 | 0.834428 | 0.417214 | − | 0.908808i | \(-0.363007\pi\) | ||||
0.417214 | + | 0.908808i | \(0.363007\pi\) | |||||||
\(564\) | −1.75736 | − | 10.2426i | −0.0739982 | − | 0.431293i | ||||
\(565\) | −5.00000 | − | 5.00000i | −0.210352 | − | 0.210352i | ||||
\(566\) | 4.24264 | + | 4.24264i | 0.178331 | + | 0.178331i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 45.2548 | 1.89718 | 0.948591 | − | 0.316506i | \(-0.102510\pi\) | ||||
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(570\) | −2.48528 | − | 14.4853i | −0.104097 | − | 0.606722i | ||||
\(571\) | − | 12.0000i | − | 0.502184i | −0.967963 | − | 0.251092i | \(-0.919210\pi\) | ||
0.967963 | − | 0.251092i | \(-0.0807897\pi\) | |||||||
\(572\) | 1.41421 | − | 7.07107i | 0.0591312 | − | 0.295656i | ||||
\(573\) | −28.0000 | − | 19.7990i | −1.16972 | − | 0.827115i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.41421i | − | 0.0589768i | ||||||
\(576\) | 2.82843 | − | 1.00000i | 0.117851 | − | 0.0416667i | ||||
\(577\) | 26.0000 | + | 26.0000i | 1.08239 | + | 1.08239i | 0.996286 | + | 0.0861084i | \(0.0274431\pi\) |
0.0861084 | + | 0.996286i | \(0.472557\pi\) | |||||||
\(578\) | 0.707107 | − | 0.707107i | 0.0294118 | − | 0.0294118i | ||||
\(579\) | 2.48528 | + | 14.4853i | 0.103285 | + | 0.601988i | ||||
\(580\) | −1.00000 | + | 1.00000i | −0.0415227 | + | 0.0415227i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.1421 | − | 20.0000i | 0.586210 | − | 0.829027i | ||||
\(583\) | −16.0000 | + | 16.0000i | −0.662652 | + | 0.662652i | ||||
\(584\) | −8.48528 | −0.351123 | ||||||||
\(585\) | 10.7071 | − | 1.53553i | 0.442684 | − | 0.0634865i | ||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | −19.7990 | + | 19.7990i | −0.817192 | + | 0.817192i | −0.985700 | − | 0.168508i | \(-0.946105\pi\) |
0.168508 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(588\) | 7.00000 | − | 9.89949i | 0.288675 | − | 0.408248i | ||||
\(589\) | − | 36.0000i | − | 1.48335i | ||||||
\(590\) | 2.82843 | − | 2.82843i | 0.116445 | − | 0.116445i | ||||
\(591\) | −4.10051 | − | 23.8995i | −0.168672 | − | 0.983094i | ||||
\(592\) | −5.00000 | + | 5.00000i | −0.205499 | + | 0.205499i | ||||
\(593\) | −25.4558 | − | 25.4558i | −1.04535 | − | 1.04535i | −0.998922 | − | 0.0464244i | \(-0.985217\pi\) |
−0.0464244 | − | 0.998922i | \(-0.514783\pi\) | |||||||
\(594\) | 10.0000 | + | 2.82843i | 0.410305 | + | 0.116052i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.07107 | + | 7.07107i | 0.289642 | + | 0.289642i | ||||
\(597\) | −2.82843 | − | 2.00000i | −0.115760 | − | 0.0818546i | ||||
\(598\) | −1.00000 | + | 5.00000i | −0.0408930 | + | 0.204465i | ||||
\(599\) | − | 45.2548i | − | 1.84906i | −0.381106 | − | 0.924531i | \(-0.624457\pi\) | ||
0.381106 | − | 0.924531i | \(-0.375543\pi\) | |||||||
\(600\) | 0.292893 | + | 1.70711i | 0.0119573 | + | 0.0696923i | ||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.14214 | − | 19.1421i | 0.372297 | − | 0.779528i | ||||
\(604\) | 13.0000 | + | 13.0000i | 0.528962 | + | 0.528962i | ||||
\(605\) | −4.94975 | − | 4.94975i | −0.201236 | − | 0.201236i | ||||
\(606\) | 4.55635 | + | 26.5563i | 0.185089 | + | 1.07878i | ||||
\(607\) | 36.0000 | 1.46119 | 0.730597 | − | 0.682808i | \(-0.239242\pi\) | ||||
0.730597 | + | 0.682808i | \(0.239242\pi\) | |||||||
\(608\) | −8.48528 | −0.344124 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 2.00000i | − | 0.0809776i | ||||||
\(611\) | −21.2132 | − | 4.24264i | −0.858194 | − | 0.171639i | ||||
\(612\) | −12.0000 | + | 4.24264i | −0.485071 | + | 0.171499i | ||||
\(613\) | −9.00000 | − | 9.00000i | −0.363507 | − | 0.363507i | 0.501596 | − | 0.865102i | \(-0.332747\pi\) |
−0.865102 | + | 0.501596i | \(0.832747\pi\) | |||||||
\(614\) | − | 32.5269i | − | 1.31268i | ||||||
\(615\) | 14.1421 | + | 10.0000i | 0.570266 | + | 0.403239i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.07107 | − | 7.07107i | 0.284670 | − | 0.284670i | −0.550298 | − | 0.834968i | \(-0.685486\pi\) |
0.834968 | + | 0.550298i | \(0.185486\pi\) | |||||||
\(618\) | −13.6569 | + | 2.34315i | −0.549359 | + | 0.0942551i | ||||
\(619\) | 32.0000 | − | 32.0000i | 1.28619 | − | 1.28619i | 0.349105 | − | 0.937084i | \(-0.386486\pi\) |
0.937084 | − | 0.349105i | \(-0.113514\pi\) | |||||||
\(620\) | 4.24264i | 0.170389i | ||||||||
\(621\) | −7.07107 | − | 2.00000i | −0.283752 | − | 0.0802572i | ||||
\(622\) | 2.00000 | − | 2.00000i | 0.0801927 | − | 0.0801927i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.171573 | − | 6.24264i | 0.00686841 | − | 0.249906i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 18.3848 | − | 18.3848i | 0.734803 | − | 0.734803i | ||||
\(627\) | −24.0000 | − | 16.9706i | −0.958468 | − | 0.677739i | ||||
\(628\) | 6.00000i | 0.239426i | ||||||||
\(629\) | 21.2132 | − | 21.2132i | 0.845826 | − | 0.845826i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00000 | − | 9.00000i | 0.358284 | − | 0.358284i | −0.504896 | − | 0.863180i | \(-0.668469\pi\) |
0.863180 | + | 0.504896i | \(0.168469\pi\) | |||||||
\(632\) | −5.65685 | − | 5.65685i | −0.225018 | − | 0.225018i | ||||
\(633\) | −24.0000 | + | 33.9411i | −0.953914 | + | 1.34904i | ||||
\(634\) | 26.0000i | 1.03259i | ||||||||
\(635\) | −2.82843 | − | 2.82843i | −0.112243 | − | 0.112243i | ||||
\(636\) | −11.3137 | + | 16.0000i | −0.448618 | + | 0.634441i | ||||
\(637\) | −14.0000 | − | 21.0000i | −0.554700 | − | 0.832050i | ||||
\(638\) | 2.82843i | 0.111979i | ||||||||
\(639\) | 21.6569 | + | 10.3431i | 0.856732 | + | 0.409169i | ||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.5980 | −1.56403 | −0.782013 | − | 0.623262i | \(-0.785807\pi\) | ||||
−0.782013 | + | 0.623262i | \(0.785807\pi\) | |||||||
\(642\) | 19.3137 | − | 3.31371i | 0.762251 | − | 0.130782i | ||||
\(643\) | −21.0000 | − | 21.0000i | −0.828159 | − | 0.828159i | 0.159103 | − | 0.987262i | \(-0.449140\pi\) |
−0.987262 | + | 0.159103i | \(0.949140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.82843 | − | 1.17157i | 0.268869 | − | 0.0461306i | ||||
\(646\) | 36.0000 | 1.41640 | ||||||||
\(647\) | 7.07107 | 0.277992 | 0.138996 | − | 0.990293i | \(-0.455612\pi\) | ||||
0.138996 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(648\) | 8.94975 | + | 0.949747i | 0.351579 | + | 0.0373096i | ||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | 3.53553 | + | 0.707107i | 0.138675 | + | 0.0277350i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.0000 | + | 11.0000i | 0.430793 | + | 0.430793i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 2.82843 | − | 4.00000i | 0.110600 | − | 0.156412i | ||||
\(655\) | 5.00000 | + | 5.00000i | 0.195366 | + | 0.195366i | ||||
\(656\) | 7.07107 | − | 7.07107i | 0.276079 | − | 0.276079i | ||||
\(657\) | −22.9706 | − | 10.9706i | −0.896167 | − | 0.428002i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.89949i | − | 0.385630i | −0.981235 | − | 0.192815i | \(-0.938238\pi\) | ||
0.981235 | − | 0.192815i | \(-0.0617617\pi\) | |||||||
\(660\) | 2.82843 | + | 2.00000i | 0.110096 | + | 0.0778499i | ||||
\(661\) | −22.0000 | + | 22.0000i | −0.855701 | + | 0.855701i | −0.990828 | − | 0.135127i | \(-0.956856\pi\) |
0.135127 | + | 0.990828i | \(0.456856\pi\) | |||||||
\(662\) | 33.9411 | 1.31916 | ||||||||
\(663\) | −0.727922 | + | 26.4853i | −0.0282702 | + | 1.02860i | ||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.0000 | + | 7.07107i | −0.774984 | + | 0.273998i | ||||
\(667\) | − | 2.00000i | − | 0.0774403i | ||||||
\(668\) | 11.3137 | − | 11.3137i | 0.437741 | − | 0.437741i | ||||
\(669\) | −24.1421 | + | 4.14214i | −0.933389 | + | 0.160144i | ||||
\(670\) | 5.00000 | − | 5.00000i | 0.193167 | − | 0.193167i | ||||
\(671\) | −2.82843 | − | 2.82843i | −0.109190 | − | 0.109190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.00000i | 0.231283i | 0.993291 | + | 0.115642i | \(0.0368924\pi\) | ||||
−0.993291 | + | 0.115642i | \(0.963108\pi\) | |||||||
\(674\) | −9.89949 | − | 9.89949i | −0.381314 | − | 0.381314i | ||||
\(675\) | −1.41421 | + | 5.00000i | −0.0544331 | + | 0.192450i | ||||
\(676\) | −12.0000 | − | 5.00000i | −0.461538 | − | 0.192308i | ||||
\(677\) | 36.7696i | 1.41317i | 0.707629 | + | 0.706584i | \(0.249765\pi\) | ||||
−0.707629 | + | 0.706584i | \(0.750235\pi\) | |||||||
\(678\) | −12.0711 | + | 2.07107i | −0.463587 | + | 0.0795389i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.24264 | −0.162698 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | + | 6.00000i | 0.229752 | + | 0.229752i | ||||
\(683\) | 16.9706 | + | 16.9706i | 0.649361 | + | 0.649361i | 0.952838 | − | 0.303478i | \(-0.0981479\pi\) |
−0.303478 | + | 0.952838i | \(0.598148\pi\) | |||||||
\(684\) | −22.9706 | − | 10.9706i | −0.878301 | − | 0.419470i | ||||
\(685\) | −20.0000 | −0.764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.48528 | − | 14.4853i | −0.0948194 | − | 0.552648i | ||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 22.6274 | + | 33.9411i | 0.862036 | + | 1.29305i | ||||
\(690\) | −2.00000 | − | 1.41421i | −0.0761387 | − | 0.0538382i | ||||
\(691\) | −16.0000 | − | 16.0000i | −0.608669 | − | 0.608669i | 0.333929 | − | 0.942598i | \(-0.391625\pi\) |
−0.942598 | + | 0.333929i | \(0.891625\pi\) | |||||||
\(692\) | − | 2.82843i | − | 0.107521i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | − | 8.00000i | −0.303676 | − | 0.303676i | ||||
\(695\) | −11.3137 | + | 11.3137i | −0.429153 | + | 0.429153i | ||||
\(696\) | 0.414214 | + | 2.41421i | 0.0157007 | + | 0.0915105i | ||||
\(697\) | −30.0000 | + | 30.0000i | −1.13633 | + | 1.13633i | ||||
\(698\) | 16.9706i | 0.642345i | ||||||||
\(699\) | 18.3848 | − | 26.0000i | 0.695376 | − | 0.983410i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41421 | 0.0534141 | 0.0267071 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267071 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(702\) | 8.53553 | − | 16.6777i | 0.322153 | − | 0.629458i | ||||
\(703\) | 60.0000 | 2.26294 | ||||||||
\(704\) | 1.41421 | − | 1.41421i | 0.0533002 | − | 0.0533002i | ||||
\(705\) | 6.00000 | − | 8.48528i | 0.225973 | − | 0.319574i | ||||
\(706\) | − | 36.0000i | − | 1.35488i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.17157 | − | 6.82843i | −0.0440304 | − | 0.256628i | ||||
\(709\) | −18.0000 | + | 18.0000i | −0.676004 | + | 0.676004i | −0.959094 | − | 0.283089i | \(-0.908641\pi\) |
0.283089 | + | 0.959094i | \(0.408641\pi\) | |||||||
\(710\) | 5.65685 | + | 5.65685i | 0.212298 | + | 0.212298i | ||||
\(711\) | −8.00000 | − | 22.6274i | −0.300023 | − | 0.848594i | ||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | −4.24264 | − | 4.24264i | −0.158888 | − | 0.158888i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | − | 4.00000i | 0.224387 | − | 0.149592i | ||||
\(716\) | 18.3848i | 0.687071i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.0000 | 0.895672 | ||||||||
\(719\) | 45.2548 | 1.68772 | 0.843860 | − | 0.536563i | \(-0.180278\pi\) | ||||
0.843860 | + | 0.536563i | \(0.180278\pi\) | |||||||
\(720\) | 2.70711 | + | 1.29289i | 0.100888 | + | 0.0481833i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.4767 | + | 37.4767i | 1.39474 | + | 1.39474i | ||||
\(723\) | 0.414214 | + | 2.41421i | 0.0154048 | + | 0.0897856i | ||||
\(724\) | −18.0000 | −0.668965 | ||||||||
\(725\) | −1.41421 | −0.0525226 | ||||||||
\(726\) | −11.9497 | + | 2.05025i | −0.443497 | + | 0.0760920i | ||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | −6.00000 | − | 6.00000i | −0.222070 | − | 0.222070i | ||||
\(731\) | 16.9706i | 0.627679i | ||||||||
\(732\) | −2.82843 | − | 2.00000i | −0.104542 | − | 0.0739221i | ||||
\(733\) | −9.00000 | − | 9.00000i | −0.332423 | − | 0.332423i | 0.521083 | − | 0.853506i | \(-0.325528\pi\) |
−0.853506 | + | 0.521083i | \(0.825528\pi\) | |||||||
\(734\) | −5.65685 | + | 5.65685i | −0.208798 | + | 0.208798i | ||||
\(735\) | 11.9497 | − | 2.05025i | 0.440773 | − | 0.0756247i | ||||
\(736\) | −1.00000 | + | 1.00000i | −0.0368605 | + | 0.0368605i | ||||
\(737\) | − | 14.1421i | − | 0.520932i | ||||||
\(738\) | 28.2843 | − | 10.0000i | 1.04116 | − | 0.368105i | ||||
\(739\) | −12.0000 | + | 12.0000i | −0.441427 | + | 0.441427i | −0.892491 | − | 0.451064i | \(-0.851045\pi\) |
0.451064 | + | 0.892491i | \(0.351045\pi\) | |||||||
\(740\) | −7.07107 | −0.259938 | ||||||||
\(741\) | −38.4853 | + | 36.4264i | −1.41379 | + | 1.33816i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3848 | + | 18.3848i | −0.674472 | + | 0.674472i | −0.958744 | − | 0.284272i | \(-0.908248\pi\) |
0.284272 | + | 0.958744i | \(0.408248\pi\) | |||||||
\(744\) | 6.00000 | + | 4.24264i | 0.219971 | + | 0.155543i | ||||
\(745\) | 10.0000i | 0.366372i | ||||||||
\(746\) | −22.6274 | + | 22.6274i | −0.828449 | + | 0.828449i | ||||
\(747\) | 21.6569 | + | 10.3431i | 0.792383 | + | 0.378436i | ||||
\(748\) | −6.00000 | + | 6.00000i | −0.219382 | + | 0.219382i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | + | 1.41421i | −0.0365148 | + | 0.0516398i | ||||
\(751\) | − | 10.0000i | − | 0.364905i | −0.983215 | − | 0.182453i | \(-0.941596\pi\) | ||
0.983215 | − | 0.182453i | \(-0.0584036\pi\) | |||||||
\(752\) | −4.24264 | − | 4.24264i | −0.154713 | − | 0.154713i | ||||
\(753\) | −4.24264 | + | 6.00000i | −0.154610 | + | 0.218652i | ||||
\(754\) | 5.00000 | + | 1.00000i | 0.182089 | + | 0.0364179i | ||||
\(755\) | 18.3848i | 0.669091i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 22.6274 | 0.821865 | ||||||||
\(759\) | −4.82843 | + | 0.828427i | −0.175261 | + | 0.0300700i | ||||
\(760\) | −6.00000 | − | 6.00000i | −0.217643 | − | 0.217643i | ||||
\(761\) | 9.89949 | + | 9.89949i | 0.358856 | + | 0.358856i | 0.863391 | − | 0.504535i | \(-0.168336\pi\) |
−0.504535 | + | 0.863391i | \(0.668336\pi\) | |||||||
\(762\) | −6.82843 | + | 1.17157i | −0.247368 | + | 0.0424416i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.7990 | −0.716302 | ||||||||
\(765\) | −11.4853 | − | 5.48528i | −0.415251 | − | 0.198321i | ||||
\(766\) | 24.0000i | 0.867155i | ||||||||
\(767\) | −14.1421 | − | 2.82843i | −0.510643 | − | 0.102129i | ||||
\(768\) | 1.00000 | − | 1.41421i | 0.0360844 | − | 0.0510310i | ||||
\(769\) | −21.0000 | − | 21.0000i | −0.757279 | − | 0.757279i | 0.218547 | − | 0.975826i | \(-0.429868\pi\) |
−0.975826 | + | 0.218547i | \(0.929868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41421 | − | 2.00000i | 0.0509317 | − | 0.0720282i | ||||
\(772\) | 6.00000 | + | 6.00000i | 0.215945 | + | 0.215945i | ||||
\(773\) | −4.24264 | + | 4.24264i | −0.152597 | + | 0.152597i | −0.779277 | − | 0.626680i | \(-0.784413\pi\) |
0.626680 | + | 0.779277i | \(0.284413\pi\) | |||||||
\(774\) | 5.17157 | − | 10.8284i | 0.185888 | − | 0.389220i |