Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.m (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: | \(6.14848095564\) |
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 | 197.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.197 |
Dual form | 770.2.m.c.43.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 2.00000 | − | 2.00000i | 1.15470 | − | 1.15470i | 0.169102 | − | 0.985599i | \(-0.445913\pi\) |
0.985599 | − | 0.169102i | \(-0.0540867\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 2.82843i | 1.15470i | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 5.00000i | − | 1.66667i | ||||||
\(10\) | 2.12132 | + | 0.707107i | 0.670820 | + | 0.223607i | ||||
\(11\) | 3.00000 | − | 1.41421i | 0.904534 | − | 0.426401i | ||||
\(12\) | −2.00000 | − | 2.00000i | −0.577350 | − | 0.577350i | ||||
\(13\) | 1.41421 | + | 1.41421i | 0.392232 | + | 0.392232i | 0.875482 | − | 0.483250i | \(-0.160544\pi\) |
−0.483250 | + | 0.875482i | \(0.660544\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | −6.00000 | − | 2.00000i | −1.54919 | − | 0.516398i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.41421 | − | 1.41421i | 0.342997 | − | 0.342997i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) |
0.857493 | + | 0.514496i | \(0.172021\pi\) | |||||||
\(18\) | 3.53553 | + | 3.53553i | 0.833333 | + | 0.833333i | ||||
\(19\) | −4.24264 | −0.973329 | −0.486664 | − | 0.873589i | \(-0.661786\pi\) | ||||
−0.486664 | + | 0.873589i | \(0.661786\pi\) | |||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | − | 2.82843i | − | 0.617213i | ||||||
\(22\) | −1.12132 | + | 3.12132i | −0.239066 | + | 0.665468i | ||||
\(23\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(24\) | 2.82843 | 0.577350 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −4.00000 | − | 4.00000i | −0.769800 | − | 0.769800i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 1.41421 | 0.262613 | 0.131306 | − | 0.991342i | \(-0.458083\pi\) | ||||
0.131306 | + | 0.991342i | \(0.458083\pi\) | |||||||
\(30\) | 5.65685 | − | 2.82843i | 1.03280 | − | 0.516398i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.17157 | − | 8.82843i | 0.552100 | − | 1.53683i | ||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | −2.12132 | − | 0.707107i | −0.358569 | − | 0.119523i | ||||
\(36\) | −5.00000 | −0.833333 | ||||||||
\(37\) | −4.00000 | − | 4.00000i | −0.657596 | − | 0.657596i | 0.297215 | − | 0.954811i | \(-0.403942\pi\) |
−0.954811 | + | 0.297215i | \(0.903942\pi\) | |||||||
\(38\) | 3.00000 | − | 3.00000i | 0.486664 | − | 0.486664i | ||||
\(39\) | 5.65685 | 0.905822 | ||||||||
\(40\) | 0.707107 | − | 2.12132i | 0.111803 | − | 0.335410i | ||||
\(41\) | 4.24264i | 0.662589i | 0.943527 | + | 0.331295i | \(0.107485\pi\) | ||||
−0.943527 | + | 0.331295i | \(0.892515\pi\) | |||||||
\(42\) | 2.00000 | + | 2.00000i | 0.308607 | + | 0.308607i | ||||
\(43\) | −5.65685 | − | 5.65685i | −0.862662 | − | 0.862662i | 0.128984 | − | 0.991647i | \(-0.458828\pi\) |
−0.991647 | + | 0.128984i | \(0.958828\pi\) | |||||||
\(44\) | −1.41421 | − | 3.00000i | −0.213201 | − | 0.452267i | ||||
\(45\) | −10.0000 | + | 5.00000i | −1.49071 | + | 0.745356i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00000 | + | 5.00000i | 0.729325 | + | 0.729325i | 0.970485 | − | 0.241160i | \(-0.0775280\pi\) |
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(48\) | −2.00000 | + | 2.00000i | −0.288675 | + | 0.288675i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −0.707107 | − | 4.94975i | −0.100000 | − | 0.700000i | ||||
\(51\) | − | 5.65685i | − | 0.792118i | ||||||
\(52\) | 1.41421 | − | 1.41421i | 0.196116 | − | 0.196116i | ||||
\(53\) | −6.00000 | + | 6.00000i | −0.824163 | + | 0.824163i | −0.986702 | − | 0.162539i | \(-0.948032\pi\) |
0.162539 | + | 0.986702i | \(0.448032\pi\) | |||||||
\(54\) | 5.65685 | 0.769800 | ||||||||
\(55\) | −5.82843 | − | 4.58579i | −0.785905 | − | 0.618347i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −8.48528 | + | 8.48528i | −1.12390 | + | 1.12390i | ||||
\(58\) | −1.00000 | + | 1.00000i | −0.131306 | + | 0.131306i | ||||
\(59\) | − | 8.00000i | − | 1.04151i | −0.853706 | − | 0.520756i | \(-0.825650\pi\) | ||
0.853706 | − | 0.520756i | \(-0.174350\pi\) | |||||||
\(60\) | −2.00000 | + | 6.00000i | −0.258199 | + | 0.774597i | ||||
\(61\) | 5.65685i | 0.724286i | 0.932123 | + | 0.362143i | \(0.117955\pi\) | ||||
−0.932123 | + | 0.362143i | \(0.882045\pi\) | |||||||
\(62\) | −1.41421 | + | 1.41421i | −0.179605 | + | 0.179605i | ||||
\(63\) | −3.53553 | − | 3.53553i | −0.445435 | − | 0.445435i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.41421 | − | 4.24264i | 0.175412 | − | 0.526235i | ||||
\(66\) | 4.00000 | + | 8.48528i | 0.492366 | + | 1.04447i | ||||
\(67\) | 3.00000 | + | 3.00000i | 0.366508 | + | 0.366508i | 0.866202 | − | 0.499694i | \(-0.166554\pi\) |
−0.499694 | + | 0.866202i | \(0.666554\pi\) | |||||||
\(68\) | −1.41421 | − | 1.41421i | −0.171499 | − | 0.171499i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | − | 1.00000i | 0.239046 | − | 0.119523i | ||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 3.53553 | − | 3.53553i | 0.416667 | − | 0.416667i | ||||
\(73\) | −11.3137 | − | 11.3137i | −1.32417 | − | 1.32417i | −0.910366 | − | 0.413803i | \(-0.864200\pi\) |
−0.413803 | − | 0.910366i | \(-0.635800\pi\) | |||||||
\(74\) | 5.65685 | 0.657596 | ||||||||
\(75\) | 2.00000 | + | 14.0000i | 0.230940 | + | 1.61658i | ||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | 1.12132 | − | 3.12132i | 0.127786 | − | 0.355707i | ||||
\(78\) | −4.00000 | + | 4.00000i | −0.452911 | + | 0.452911i | ||||
\(79\) | −7.07107 | −0.795557 | −0.397779 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397779 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.00000 | − | 3.00000i | −0.331295 | − | 0.331295i | ||||
\(83\) | 7.07107 | + | 7.07107i | 0.776151 | + | 0.776151i | 0.979174 | − | 0.203023i | \(-0.0650767\pi\) |
−0.203023 | + | 0.979174i | \(0.565077\pi\) | |||||||
\(84\) | −2.82843 | −0.308607 | ||||||||
\(85\) | −4.24264 | − | 1.41421i | −0.460179 | − | 0.153393i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 2.82843 | − | 2.82843i | 0.303239 | − | 0.303239i | ||||
\(88\) | 3.12132 | + | 1.12132i | 0.332734 | + | 0.119533i | ||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 3.53553 | − | 10.6066i | 0.372678 | − | 1.11803i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | − | 4.00000i | 0.414781 | − | 0.414781i | ||||
\(94\) | −7.07107 | −0.729325 | ||||||||
\(95\) | 4.24264 | + | 8.48528i | 0.435286 | + | 0.870572i | ||||
\(96\) | − | 2.82843i | − | 0.288675i | ||||||
\(97\) | 2.00000 | + | 2.00000i | 0.203069 | + | 0.203069i | 0.801314 | − | 0.598244i | \(-0.204135\pi\) |
−0.598244 | + | 0.801314i | \(0.704135\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | −7.07107 | − | 15.0000i | −0.710669 | − | 1.50756i | ||||
\(100\) | 4.00000 | + | 3.00000i | 0.400000 | + | 0.300000i | ||||
\(101\) | 19.7990i | 1.97007i | 0.172345 | + | 0.985037i | \(0.444865\pi\) | ||||
−0.172345 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(102\) | 4.00000 | + | 4.00000i | 0.396059 | + | 0.396059i | ||||
\(103\) | 3.00000 | − | 3.00000i | 0.295599 | − | 0.295599i | −0.543688 | − | 0.839287i | \(-0.682973\pi\) |
0.839287 | + | 0.543688i | \(0.182973\pi\) | |||||||
\(104\) | 2.00000i | 0.196116i | ||||||||
\(105\) | −5.65685 | + | 2.82843i | −0.552052 | + | 0.276026i | ||||
\(106\) | − | 8.48528i | − | 0.824163i | ||||||
\(107\) | 14.1421 | − | 14.1421i | 1.36717 | − | 1.36717i | 0.502726 | − | 0.864446i | \(-0.332330\pi\) |
0.864446 | − | 0.502726i | \(-0.167670\pi\) | |||||||
\(108\) | −4.00000 | + | 4.00000i | −0.384900 | + | 0.384900i | ||||
\(109\) | 18.3848 | 1.76094 | 0.880471 | − | 0.474100i | \(-0.157226\pi\) | ||||
0.880471 | + | 0.474100i | \(0.157226\pi\) | |||||||
\(110\) | 7.36396 | − | 0.878680i | 0.702126 | − | 0.0837788i | ||||
\(111\) | −16.0000 | −1.51865 | ||||||||
\(112\) | −0.707107 | + | 0.707107i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | 13.0000 | − | 13.0000i | 1.22294 | − | 1.22294i | 0.256354 | − | 0.966583i | \(-0.417479\pi\) |
0.966583 | − | 0.256354i | \(-0.0825214\pi\) | |||||||
\(114\) | − | 12.0000i | − | 1.12390i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.41421i | − | 0.131306i | ||||||
\(117\) | 7.07107 | − | 7.07107i | 0.653720 | − | 0.653720i | ||||
\(118\) | 5.65685 | + | 5.65685i | 0.520756 | + | 0.520756i | ||||
\(119\) | − | 2.00000i | − | 0.183340i | ||||||
\(120\) | −2.82843 | − | 5.65685i | −0.258199 | − | 0.516398i | ||||
\(121\) | 7.00000 | − | 8.48528i | 0.636364 | − | 0.771389i | ||||
\(122\) | −4.00000 | − | 4.00000i | −0.362143 | − | 0.362143i | ||||
\(123\) | 8.48528 | + | 8.48528i | 0.765092 | + | 0.765092i | ||||
\(124\) | − | 2.00000i | − | 0.179605i | ||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 5.00000 | 0.445435 | ||||||||
\(127\) | 9.89949 | − | 9.89949i | 0.878438 | − | 0.878438i | −0.114935 | − | 0.993373i | \(-0.536666\pi\) |
0.993373 | + | 0.114935i | \(0.0366659\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −22.6274 | −1.99223 | ||||||||
\(130\) | 2.00000 | + | 4.00000i | 0.175412 | + | 0.350823i | ||||
\(131\) | 15.5563i | 1.35916i | 0.733599 | + | 0.679582i | \(0.237839\pi\) | ||||
−0.733599 | + | 0.679582i | \(0.762161\pi\) | |||||||
\(132\) | −8.82843 | − | 3.17157i | −0.768416 | − | 0.276050i | ||||
\(133\) | −3.00000 | + | 3.00000i | −0.260133 | + | 0.260133i | ||||
\(134\) | −4.24264 | −0.366508 | ||||||||
\(135\) | −4.00000 | + | 12.0000i | −0.344265 | + | 1.03280i | ||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | −5.00000 | − | 5.00000i | −0.427179 | − | 0.427179i | 0.460487 | − | 0.887666i | \(-0.347675\pi\) |
−0.887666 | + | 0.460487i | \(0.847675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41421 | 0.119952 | 0.0599760 | − | 0.998200i | \(-0.480898\pi\) | ||||
0.0599760 | + | 0.998200i | \(0.480898\pi\) | |||||||
\(140\) | −0.707107 | + | 2.12132i | −0.0597614 | + | 0.179284i | ||||
\(141\) | 20.0000 | 1.68430 | ||||||||
\(142\) | −5.65685 | + | 5.65685i | −0.474713 | + | 0.474713i | ||||
\(143\) | 6.24264 | + | 2.24264i | 0.522036 | + | 0.187539i | ||||
\(144\) | 5.00000i | 0.416667i | ||||||||
\(145\) | −1.41421 | − | 2.82843i | −0.117444 | − | 0.234888i | ||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | −2.00000 | − | 2.00000i | −0.164957 | − | 0.164957i | ||||
\(148\) | −4.00000 | + | 4.00000i | −0.328798 | + | 0.328798i | ||||
\(149\) | 1.41421 | 0.115857 | 0.0579284 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579284 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(150\) | −11.3137 | − | 8.48528i | −0.923760 | − | 0.692820i | ||||
\(151\) | 9.89949i | 0.805609i | 0.915286 | + | 0.402805i | \(0.131965\pi\) | ||||
−0.915286 | + | 0.402805i | \(0.868035\pi\) | |||||||
\(152\) | −3.00000 | − | 3.00000i | −0.243332 | − | 0.243332i | ||||
\(153\) | −7.07107 | − | 7.07107i | −0.571662 | − | 0.571662i | ||||
\(154\) | 1.41421 | + | 3.00000i | 0.113961 | + | 0.241747i | ||||
\(155\) | −2.00000 | − | 4.00000i | −0.160644 | − | 0.321288i | ||||
\(156\) | − | 5.65685i | − | 0.452911i | ||||||
\(157\) | 13.0000 | + | 13.0000i | 1.03751 | + | 1.03751i | 0.999268 | + | 0.0382445i | \(0.0121766\pi\) |
0.0382445 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(158\) | 5.00000 | − | 5.00000i | 0.397779 | − | 0.397779i | ||||
\(159\) | 24.0000i | 1.90332i | ||||||||
\(160\) | −2.12132 | − | 0.707107i | −0.167705 | − | 0.0559017i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −15.0000 | + | 15.0000i | −1.17489 | + | 1.17489i | −0.193862 | + | 0.981029i | \(0.562101\pi\) |
−0.981029 | + | 0.193862i | \(0.937899\pi\) | |||||||
\(164\) | 4.24264 | 0.331295 | ||||||||
\(165\) | −20.8284 | + | 2.48528i | −1.62149 | + | 0.193479i | ||||
\(166\) | −10.0000 | −0.776151 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 2.00000 | − | 2.00000i | 0.154303 | − | 0.154303i | ||||
\(169\) | − | 9.00000i | − | 0.692308i | ||||||
\(170\) | 4.00000 | − | 2.00000i | 0.306786 | − | 0.153393i | ||||
\(171\) | 21.2132i | 1.62221i | ||||||||
\(172\) | −5.65685 | + | 5.65685i | −0.431331 | + | 0.431331i | ||||
\(173\) | −7.07107 | − | 7.07107i | −0.537603 | − | 0.537603i | 0.385221 | − | 0.922824i | \(-0.374125\pi\) |
−0.922824 | + | 0.385221i | \(0.874125\pi\) | |||||||
\(174\) | 4.00000i | 0.303239i | ||||||||
\(175\) | 0.707107 | + | 4.94975i | 0.0534522 | + | 0.374166i | ||||
\(176\) | −3.00000 | + | 1.41421i | −0.226134 | + | 0.106600i | ||||
\(177\) | −16.0000 | − | 16.0000i | −1.20263 | − | 1.20263i | ||||
\(178\) | −4.24264 | − | 4.24264i | −0.317999 | − | 0.317999i | ||||
\(179\) | 18.0000i | 1.34538i | 0.739923 | + | 0.672692i | \(0.234862\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | 5.00000 | + | 10.0000i | 0.372678 | + | 0.745356i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −1.41421 | + | 1.41421i | −0.104828 | + | 0.104828i | ||||
\(183\) | 11.3137 | + | 11.3137i | 0.836333 | + | 0.836333i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | + | 12.0000i | −0.294086 | + | 0.882258i | ||||
\(186\) | 5.65685i | 0.414781i | ||||||||
\(187\) | 2.24264 | − | 6.24264i | 0.163998 | − | 0.456507i | ||||
\(188\) | 5.00000 | − | 5.00000i | 0.364662 | − | 0.364662i | ||||
\(189\) | −5.65685 | −0.411476 | ||||||||
\(190\) | −9.00000 | − | 3.00000i | −0.652929 | − | 0.217643i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 2.00000 | + | 2.00000i | 0.144338 | + | 0.144338i | ||||
\(193\) | −12.7279 | − | 12.7279i | −0.916176 | − | 0.916176i | 0.0805728 | − | 0.996749i | \(-0.474325\pi\) |
−0.996749 | + | 0.0805728i | \(0.974325\pi\) | |||||||
\(194\) | −2.82843 | −0.203069 | ||||||||
\(195\) | −5.65685 | − | 11.3137i | −0.405096 | − | 0.810191i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 15.6066 | + | 5.60660i | 1.10911 | + | 0.398444i | ||||
\(199\) | 16.0000i | 1.13421i | 0.823646 | + | 0.567105i | \(0.191937\pi\) | ||||
−0.823646 | + | 0.567105i | \(0.808063\pi\) | |||||||
\(200\) | −4.94975 | + | 0.707107i | −0.350000 | + | 0.0500000i | ||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | −14.0000 | − | 14.0000i | −0.985037 | − | 0.985037i | ||||
\(203\) | 1.00000 | − | 1.00000i | 0.0701862 | − | 0.0701862i | ||||
\(204\) | −5.65685 | −0.396059 | ||||||||
\(205\) | 8.48528 | − | 4.24264i | 0.592638 | − | 0.296319i | ||||
\(206\) | 4.24264i | 0.295599i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.41421 | − | 1.41421i | −0.0980581 | − | 0.0980581i | ||||
\(209\) | −12.7279 | + | 6.00000i | −0.880409 | + | 0.415029i | ||||
\(210\) | 2.00000 | − | 6.00000i | 0.138013 | − | 0.414039i | ||||
\(211\) | 11.3137i | 0.778868i | 0.921054 | + | 0.389434i | \(0.127329\pi\) | ||||
−0.921054 | + | 0.389434i | \(0.872671\pi\) | |||||||
\(212\) | 6.00000 | + | 6.00000i | 0.412082 | + | 0.412082i | ||||
\(213\) | 16.0000 | − | 16.0000i | 1.09630 | − | 1.09630i | ||||
\(214\) | 20.0000i | 1.36717i | ||||||||
\(215\) | −5.65685 | + | 16.9706i | −0.385794 | + | 1.15738i | ||||
\(216\) | − | 5.65685i | − | 0.384900i | ||||||
\(217\) | 1.41421 | − | 1.41421i | 0.0960031 | − | 0.0960031i | ||||
\(218\) | −13.0000 | + | 13.0000i | −0.880471 | + | 0.880471i | ||||
\(219\) | −45.2548 | −3.05804 | ||||||||
\(220\) | −4.58579 | + | 5.82843i | −0.309174 | + | 0.392952i | ||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 11.3137 | − | 11.3137i | 0.759326 | − | 0.759326i | ||||
\(223\) | 1.00000 | − | 1.00000i | 0.0669650 | − | 0.0669650i | −0.672831 | − | 0.739796i | \(-0.734922\pi\) |
0.739796 | + | 0.672831i | \(0.234922\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 20.0000 | + | 15.0000i | 1.33333 | + | 1.00000i | ||||
\(226\) | 18.3848i | 1.22294i | ||||||||
\(227\) | 8.48528 | − | 8.48528i | 0.563188 | − | 0.563188i | −0.367024 | − | 0.930212i | \(-0.619623\pi\) |
0.930212 | + | 0.367024i | \(0.119623\pi\) | |||||||
\(228\) | 8.48528 | + | 8.48528i | 0.561951 | + | 0.561951i | ||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | − | 8.48528i | −0.263181 | − | 0.558291i | ||||
\(232\) | 1.00000 | + | 1.00000i | 0.0656532 | + | 0.0656532i | ||||
\(233\) | 9.89949 | + | 9.89949i | 0.648537 | + | 0.648537i | 0.952639 | − | 0.304102i | \(-0.0983564\pi\) |
−0.304102 | + | 0.952639i | \(0.598356\pi\) | |||||||
\(234\) | 10.0000i | 0.653720i | ||||||||
\(235\) | 5.00000 | − | 15.0000i | 0.326164 | − | 0.978492i | ||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | −14.1421 | + | 14.1421i | −0.918630 | + | 0.918630i | ||||
\(238\) | 1.41421 | + | 1.41421i | 0.0916698 | + | 0.0916698i | ||||
\(239\) | −1.41421 | −0.0914779 | −0.0457389 | − | 0.998953i | \(-0.514564\pi\) | ||||
−0.0457389 | + | 0.998953i | \(0.514564\pi\) | |||||||
\(240\) | 6.00000 | + | 2.00000i | 0.387298 | + | 0.129099i | ||||
\(241\) | − | 24.0416i | − | 1.54866i | −0.632783 | − | 0.774329i | \(-0.718088\pi\) | ||
0.632783 | − | 0.774329i | \(-0.281912\pi\) | |||||||
\(242\) | 1.05025 | + | 10.9497i | 0.0675128 | + | 0.703876i | ||||
\(243\) | 10.0000 | − | 10.0000i | 0.641500 | − | 0.641500i | ||||
\(244\) | 5.65685 | 0.362143 | ||||||||
\(245\) | −2.00000 | + | 1.00000i | −0.127775 | + | 0.0638877i | ||||
\(246\) | −12.0000 | −0.765092 | ||||||||
\(247\) | −6.00000 | − | 6.00000i | −0.381771 | − | 0.381771i | ||||
\(248\) | 1.41421 | + | 1.41421i | 0.0898027 | + | 0.0898027i | ||||
\(249\) | 28.2843 | 1.79244 | ||||||||
\(250\) | −9.19239 | + | 6.36396i | −0.581378 | + | 0.402492i | ||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | −3.53553 | + | 3.53553i | −0.222718 | + | 0.222718i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.0000i | 0.878438i | ||||||||
\(255\) | −11.3137 | + | 5.65685i | −0.708492 | + | 0.354246i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 16.0000 | − | 16.0000i | 0.996116 | − | 0.996116i | ||||
\(259\) | −5.65685 | −0.351500 | ||||||||
\(260\) | −4.24264 | − | 1.41421i | −0.263117 | − | 0.0877058i | ||||
\(261\) | − | 7.07107i | − | 0.437688i | ||||||
\(262\) | −11.0000 | − | 11.0000i | −0.679582 | − | 0.679582i | ||||
\(263\) | 7.07107 | + | 7.07107i | 0.436021 | + | 0.436021i | 0.890670 | − | 0.454650i | \(-0.150236\pi\) |
−0.454650 | + | 0.890670i | \(0.650236\pi\) | |||||||
\(264\) | 8.48528 | − | 4.00000i | 0.522233 | − | 0.246183i | ||||
\(265\) | 18.0000 | + | 6.00000i | 1.10573 | + | 0.368577i | ||||
\(266\) | − | 4.24264i | − | 0.260133i | ||||||
\(267\) | 12.0000 | + | 12.0000i | 0.734388 | + | 0.734388i | ||||
\(268\) | 3.00000 | − | 3.00000i | 0.183254 | − | 0.183254i | ||||
\(269\) | 24.0000i | 1.46331i | 0.681677 | + | 0.731653i | \(0.261251\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | −5.65685 | − | 11.3137i | −0.344265 | − | 0.688530i | ||||
\(271\) | 8.48528i | 0.515444i | 0.966219 | + | 0.257722i | \(0.0829719\pi\) | ||||
−0.966219 | + | 0.257722i | \(0.917028\pi\) | |||||||
\(272\) | −1.41421 | + | 1.41421i | −0.0857493 | + | 0.0857493i | ||||
\(273\) | 4.00000 | − | 4.00000i | 0.242091 | − | 0.242091i | ||||
\(274\) | 7.07107 | 0.427179 | ||||||||
\(275\) | −3.34315 | + | 16.2426i | −0.201599 | + | 0.979468i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7990 | − | 19.7990i | 1.18961 | − | 1.18961i | 0.212430 | − | 0.977176i | \(-0.431862\pi\) |
0.977176 | − | 0.212430i | \(-0.0681376\pi\) | |||||||
\(278\) | −1.00000 | + | 1.00000i | −0.0599760 | + | 0.0599760i | ||||
\(279\) | − | 10.0000i | − | 0.598684i | ||||||
\(280\) | −1.00000 | − | 2.00000i | −0.0597614 | − | 0.119523i | ||||
\(281\) | − | 28.2843i | − | 1.68730i | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||
0.536895 | − | 0.843649i | \(-0.319597\pi\) | |||||||
\(282\) | −14.1421 | + | 14.1421i | −0.842152 | + | 0.842152i | ||||
\(283\) | −19.7990 | − | 19.7990i | −1.17693 | − | 1.17693i | −0.980523 | − | 0.196405i | \(-0.937073\pi\) |
−0.196405 | − | 0.980523i | \(-0.562927\pi\) | |||||||
\(284\) | − | 8.00000i | − | 0.474713i | ||||||
\(285\) | 25.4558 | + | 8.48528i | 1.50787 | + | 0.502625i | ||||
\(286\) | −6.00000 | + | 2.82843i | −0.354787 | + | 0.167248i | ||||
\(287\) | 3.00000 | + | 3.00000i | 0.177084 | + | 0.177084i | ||||
\(288\) | −3.53553 | − | 3.53553i | −0.208333 | − | 0.208333i | ||||
\(289\) | 13.0000i | 0.764706i | ||||||||
\(290\) | 3.00000 | + | 1.00000i | 0.176166 | + | 0.0587220i | ||||
\(291\) | 8.00000 | 0.468968 | ||||||||
\(292\) | −11.3137 | + | 11.3137i | −0.662085 | + | 0.662085i | ||||
\(293\) | −1.41421 | − | 1.41421i | −0.0826192 | − | 0.0826192i | 0.664589 | − | 0.747209i | \(-0.268606\pi\) |
−0.747209 | + | 0.664589i | \(0.768606\pi\) | |||||||
\(294\) | 2.82843 | 0.164957 | ||||||||
\(295\) | −16.0000 | + | 8.00000i | −0.931556 | + | 0.465778i | ||||
\(296\) | − | 5.65685i | − | 0.328798i | ||||||
\(297\) | −17.6569 | − | 6.34315i | −1.02455 | − | 0.368067i | ||||
\(298\) | −1.00000 | + | 1.00000i | −0.0579284 | + | 0.0579284i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14.0000 | − | 2.00000i | 0.808290 | − | 0.115470i | ||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | −7.00000 | − | 7.00000i | −0.402805 | − | 0.402805i | ||||
\(303\) | 39.5980 | + | 39.5980i | 2.27484 | + | 2.27484i | ||||
\(304\) | 4.24264 | 0.243332 | ||||||||
\(305\) | 11.3137 | − | 5.65685i | 0.647821 | − | 0.323911i | ||||
\(306\) | 10.0000 | 0.571662 | ||||||||
\(307\) | −19.7990 | + | 19.7990i | −1.12999 | + | 1.12999i | −0.139810 | + | 0.990178i | \(0.544649\pi\) |
−0.990178 | + | 0.139810i | \(0.955351\pi\) | |||||||
\(308\) | −3.12132 | − | 1.12132i | −0.177854 | − | 0.0638932i | ||||
\(309\) | − | 12.0000i | − | 0.682656i | ||||||
\(310\) | 4.24264 | + | 1.41421i | 0.240966 | + | 0.0803219i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 4.00000 | + | 4.00000i | 0.226455 | + | 0.226455i | ||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | −18.3848 | −1.03751 | ||||||||
\(315\) | −3.53553 | + | 10.6066i | −0.199205 | + | 0.597614i | ||||
\(316\) | 7.07107i | 0.397779i | ||||||||
\(317\) | −22.0000 | − | 22.0000i | −1.23564 | − | 1.23564i | −0.961764 | − | 0.273879i | \(-0.911693\pi\) |
−0.273879 | − | 0.961764i | \(-0.588307\pi\) | |||||||
\(318\) | −16.9706 | − | 16.9706i | −0.951662 | − | 0.951662i | ||||
\(319\) | 4.24264 | − | 2.00000i | 0.237542 | − | 0.111979i | ||||
\(320\) | 2.00000 | − | 1.00000i | 0.111803 | − | 0.0559017i | ||||
\(321\) | − | 56.5685i | − | 3.15735i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | + | 6.00000i | −0.333849 | + | 0.333849i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −9.89949 | + | 1.41421i | −0.549125 | + | 0.0784465i | ||||
\(326\) | − | 21.2132i | − | 1.17489i | ||||||
\(327\) | 36.7696 | − | 36.7696i | 2.03336 | − | 2.03336i | ||||
\(328\) | −3.00000 | + | 3.00000i | −0.165647 | + | 0.165647i | ||||
\(329\) | 7.07107 | 0.389841 | ||||||||
\(330\) | 12.9706 | − | 16.4853i | 0.714006 | − | 0.907485i | ||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 7.07107 | − | 7.07107i | 0.388075 | − | 0.388075i | ||||
\(333\) | −20.0000 | + | 20.0000i | −1.09599 | + | 1.09599i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | − | 9.00000i | 0.163908 | − | 0.491723i | ||||
\(336\) | 2.82843i | 0.154303i | ||||||||
\(337\) | 1.41421 | − | 1.41421i | 0.0770371 | − | 0.0770371i | −0.667538 | − | 0.744575i | \(-0.732652\pi\) |
0.744575 | + | 0.667538i | \(0.232652\pi\) | |||||||
\(338\) | 6.36396 | + | 6.36396i | 0.346154 | + | 0.346154i | ||||
\(339\) | − | 52.0000i | − | 2.82425i | ||||||
\(340\) | −1.41421 | + | 4.24264i | −0.0766965 | + | 0.230089i | ||||
\(341\) | 6.00000 | − | 2.82843i | 0.324918 | − | 0.153168i | ||||
\(342\) | −15.0000 | − | 15.0000i | −0.811107 | − | 0.811107i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.0000 | 0.537603 | ||||||||
\(347\) | 8.48528 | − | 8.48528i | 0.455514 | − | 0.455514i | −0.441666 | − | 0.897180i | \(-0.645612\pi\) |
0.897180 | + | 0.441666i | \(0.145612\pi\) | |||||||
\(348\) | −2.82843 | − | 2.82843i | −0.151620 | − | 0.151620i | ||||
\(349\) | −8.48528 | −0.454207 | −0.227103 | − | 0.973871i | \(-0.572926\pi\) | ||||
−0.227103 | + | 0.973871i | \(0.572926\pi\) | |||||||
\(350\) | −4.00000 | − | 3.00000i | −0.213809 | − | 0.160357i | ||||
\(351\) | − | 11.3137i | − | 0.603881i | ||||||
\(352\) | 1.12132 | − | 3.12132i | 0.0597666 | − | 0.166367i | ||||
\(353\) | 12.0000 | − | 12.0000i | 0.638696 | − | 0.638696i | −0.311538 | − | 0.950234i | \(-0.600844\pi\) |
0.950234 | + | 0.311538i | \(0.100844\pi\) | |||||||
\(354\) | 22.6274 | 1.20263 | ||||||||
\(355\) | −8.00000 | − | 16.0000i | −0.424596 | − | 0.849192i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −4.00000 | − | 4.00000i | −0.211702 | − | 0.211702i | ||||
\(358\) | −12.7279 | − | 12.7279i | −0.672692 | − | 0.672692i | ||||
\(359\) | −1.41421 | −0.0746393 | −0.0373197 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373197 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(360\) | −10.6066 | − | 3.53553i | −0.559017 | − | 0.186339i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 7.07107 | − | 7.07107i | 0.371647 | − | 0.371647i | ||||
\(363\) | −2.97056 | − | 30.9706i | −0.155914 | − | 1.62553i | ||||
\(364\) | − | 2.00000i | − | 0.104828i | ||||||
\(365\) | −11.3137 | + | 33.9411i | −0.592187 | + | 1.77656i | ||||
\(366\) | −16.0000 | −0.836333 | ||||||||
\(367\) | −9.00000 | − | 9.00000i | −0.469796 | − | 0.469796i | 0.432052 | − | 0.901849i | \(-0.357790\pi\) |
−0.901849 | + | 0.432052i | \(0.857790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.2132 | 1.10432 | ||||||||
\(370\) | −5.65685 | − | 11.3137i | −0.294086 | − | 0.588172i | ||||
\(371\) | 8.48528i | 0.440534i | ||||||||
\(372\) | −4.00000 | − | 4.00000i | −0.207390 | − | 0.207390i | ||||
\(373\) | 22.6274 | + | 22.6274i | 1.17160 | + | 1.17160i | 0.981827 | + | 0.189776i | \(0.0607761\pi\) |
0.189776 | + | 0.981827i | \(0.439224\pi\) | |||||||
\(374\) | 2.82843 | + | 6.00000i | 0.146254 | + | 0.310253i | ||||
\(375\) | 26.0000 | − | 18.0000i | 1.34263 | − | 0.929516i | ||||
\(376\) | 7.07107i | 0.364662i | ||||||||
\(377\) | 2.00000 | + | 2.00000i | 0.103005 | + | 0.103005i | ||||
\(378\) | 4.00000 | − | 4.00000i | 0.205738 | − | 0.205738i | ||||
\(379\) | 14.0000i | 0.719132i | 0.933120 | + | 0.359566i | \(0.117075\pi\) | ||||
−0.933120 | + | 0.359566i | \(0.882925\pi\) | |||||||
\(380\) | 8.48528 | − | 4.24264i | 0.435286 | − | 0.217643i | ||||
\(381\) | − | 39.5980i | − | 2.02867i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.0000 | + | 23.0000i | −1.17525 | + | 1.17525i | −0.194304 | + | 0.980941i | \(0.562245\pi\) |
−0.980941 | + | 0.194304i | \(0.937755\pi\) | |||||||
\(384\) | −2.82843 | −0.144338 | ||||||||
\(385\) | −7.36396 | + | 0.878680i | −0.375302 | + | 0.0447817i | ||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | −28.2843 | + | 28.2843i | −1.43777 | + | 1.43777i | ||||
\(388\) | 2.00000 | − | 2.00000i | 0.101535 | − | 0.101535i | ||||
\(389\) | − | 2.00000i | − | 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | 12.0000 | + | 4.00000i | 0.607644 | + | 0.202548i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 31.1127 | + | 31.1127i | 1.56943 | + | 1.56943i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.07107 | + | 14.1421i | 0.355784 | + | 0.711568i | ||||
\(396\) | −15.0000 | + | 7.07107i | −0.753778 | + | 0.355335i | ||||
\(397\) | −23.0000 | − | 23.0000i | −1.15434 | − | 1.15434i | −0.985674 | − | 0.168663i | \(-0.946055\pi\) |
−0.168663 | − | 0.985674i | \(-0.553945\pi\) | |||||||
\(398\) | −11.3137 | − | 11.3137i | −0.567105 | − | 0.567105i | ||||
\(399\) | 12.0000i | 0.600751i | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 34.0000 | 1.69788 | 0.848939 | − | 0.528490i | \(-0.177242\pi\) | ||||
0.848939 | + | 0.528490i | \(0.177242\pi\) | |||||||
\(402\) | −8.48528 | + | 8.48528i | −0.423207 | + | 0.423207i | ||||
\(403\) | 2.82843 | + | 2.82843i | 0.140894 | + | 0.140894i | ||||
\(404\) | 19.7990 | 0.985037 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | 1.41421i | 0.0701862i | ||||||||
\(407\) | −17.6569 | − | 6.34315i | −0.875218 | − | 0.314418i | ||||
\(408\) | 4.00000 | − | 4.00000i | 0.198030 | − | 0.198030i | ||||
\(409\) | 29.6985 | 1.46850 | 0.734248 | − | 0.678882i | \(-0.237535\pi\) | ||||
0.734248 | + | 0.678882i | \(0.237535\pi\) | |||||||
\(410\) | −3.00000 | + | 9.00000i | −0.148159 | + | 0.444478i | ||||
\(411\) | −20.0000 | −0.986527 | ||||||||
\(412\) | −3.00000 | − | 3.00000i | −0.147799 | − | 0.147799i | ||||
\(413\) | −5.65685 | − | 5.65685i | −0.278356 | − | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.07107 | − | 21.2132i | 0.347105 | − | 1.04132i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 2.82843 | − | 2.82843i | 0.138509 | − | 0.138509i | ||||
\(418\) | 4.75736 | − | 13.2426i | 0.232690 | − | 0.647719i | ||||
\(419\) | − | 40.0000i | − | 1.95413i | −0.212946 | − | 0.977064i | \(-0.568306\pi\) | ||
0.212946 | − | 0.977064i | \(-0.431694\pi\) | |||||||
\(420\) | 2.82843 | + | 5.65685i | 0.138013 | + | 0.276026i | ||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −8.00000 | − | 8.00000i | −0.389434 | − | 0.389434i | ||||
\(423\) | 25.0000 | − | 25.0000i | 1.21554 | − | 1.21554i | ||||
\(424\) | −8.48528 | −0.412082 | ||||||||
\(425\) | 1.41421 | + | 9.89949i | 0.0685994 | + | 0.480196i | ||||
\(426\) | 22.6274i | 1.09630i | ||||||||
\(427\) | 4.00000 | + | 4.00000i | 0.193574 | + | 0.193574i | ||||
\(428\) | −14.1421 | − | 14.1421i | −0.683586 | − | 0.683586i | ||||
\(429\) | 16.9706 | − | 8.00000i | 0.819346 | − | 0.386244i | ||||
\(430\) | −8.00000 | − | 16.0000i | −0.385794 | − | 0.771589i | ||||
\(431\) | 1.41421i | 0.0681203i | 0.999420 | + | 0.0340601i | \(0.0108438\pi\) | ||||
−0.999420 | + | 0.0340601i | \(0.989156\pi\) | |||||||
\(432\) | 4.00000 | + | 4.00000i | 0.192450 | + | 0.192450i | ||||
\(433\) | −24.0000 | + | 24.0000i | −1.15337 | + | 1.15337i | −0.167493 | + | 0.985873i | \(0.553567\pi\) |
−0.985873 | + | 0.167493i | \(0.946433\pi\) | |||||||
\(434\) | 2.00000i | 0.0960031i | ||||||||
\(435\) | −8.48528 | − | 2.82843i | −0.406838 | − | 0.135613i | ||||
\(436\) | − | 18.3848i | − | 0.880471i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 32.0000 | − | 32.0000i | 1.52902 | − | 1.52902i | ||||
\(439\) | −25.4558 | −1.21494 | −0.607471 | − | 0.794342i | \(-0.707816\pi\) | ||||
−0.607471 | + | 0.794342i | \(0.707816\pi\) | |||||||
\(440\) | −0.878680 | − | 7.36396i | −0.0418894 | − | 0.351063i | ||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | −2.82843 | + | 2.82843i | −0.134535 | + | 0.134535i | ||||
\(443\) | −15.0000 | + | 15.0000i | −0.712672 | + | 0.712672i | −0.967093 | − | 0.254422i | \(-0.918115\pi\) |
0.254422 | + | 0.967093i | \(0.418115\pi\) | |||||||
\(444\) | 16.0000i | 0.759326i | ||||||||
\(445\) | 12.0000 | − | 6.00000i | 0.568855 | − | 0.284427i | ||||
\(446\) | 1.41421i | 0.0669650i | ||||||||
\(447\) | 2.82843 | − | 2.82843i | 0.133780 | − | 0.133780i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 40.0000i | − | 1.88772i | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||
0.330350 | − | 0.943858i | \(-0.392833\pi\) | |||||||
\(450\) | −24.7487 | + | 3.53553i | −1.16667 | + | 0.166667i | ||||
\(451\) | 6.00000 | + | 12.7279i | 0.282529 | + | 0.599334i | ||||
\(452\) | −13.0000 | − | 13.0000i | −0.611469 | − | 0.611469i | ||||
\(453\) | 19.7990 | + | 19.7990i | 0.930238 | + | 0.930238i | ||||
\(454\) | 12.0000i | 0.563188i | ||||||||
\(455\) | −2.00000 | − | 4.00000i | −0.0937614 | − | 0.187523i | ||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | 9.89949 | − | 9.89949i | 0.463079 | − | 0.463079i | −0.436584 | − | 0.899663i | \(-0.643812\pi\) |
0.899663 | + | 0.436584i | \(0.143812\pi\) | |||||||
\(458\) | −14.1421 | − | 14.1421i | −0.660819 | − | 0.660819i | ||||
\(459\) | −11.3137 | −0.528079 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 8.82843 | + | 3.17157i | 0.410736 | + | 0.147555i | ||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | −1.41421 | −0.0656532 | ||||||||
\(465\) | −12.0000 | − | 4.00000i | −0.556487 | − | 0.185496i | ||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | −8.00000 | − | 8.00000i | −0.370196 | − | 0.370196i | 0.497353 | − | 0.867548i | \(-0.334306\pi\) |
−0.867548 | + | 0.497353i | \(0.834306\pi\) | |||||||
\(468\) | −7.07107 | − | 7.07107i | −0.326860 | − | 0.326860i | ||||
\(469\) | 4.24264 | 0.195907 | ||||||||
\(470\) | 7.07107 | + | 14.1421i | 0.326164 | + | 0.652328i | ||||
\(471\) | 52.0000 | 2.39603 | ||||||||
\(472\) | 5.65685 | − | 5.65685i | 0.260378 | − | 0.260378i | ||||
\(473\) | −24.9706 | − | 8.97056i | −1.14815 | − | 0.412467i | ||||
\(474\) | − | 20.0000i | − | 0.918630i | ||||||
\(475\) | 12.7279 | − | 16.9706i | 0.583997 | − | 0.778663i | ||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 30.0000 | + | 30.0000i | 1.37361 | + | 1.37361i | ||||
\(478\) | 1.00000 | − | 1.00000i | 0.0457389 | − | 0.0457389i | ||||
\(479\) | 36.7696 | 1.68004 | 0.840022 | − | 0.542553i | \(-0.182542\pi\) | ||||
0.840022 | + | 0.542553i | \(0.182542\pi\) | |||||||
\(480\) | −5.65685 | + | 2.82843i | −0.258199 | + | 0.129099i | ||||
\(481\) | − | 11.3137i | − | 0.515861i | ||||||
\(482\) | 17.0000 | + | 17.0000i | 0.774329 | + | 0.774329i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.48528 | − | 7.00000i | −0.385695 | − | 0.318182i | ||||
\(485\) | 2.00000 | − | 6.00000i | 0.0908153 | − | 0.272446i | ||||
\(486\) | 14.1421i | 0.641500i | ||||||||
\(487\) | 10.0000 | + | 10.0000i | 0.453143 | + | 0.453143i | 0.896396 | − | 0.443253i | \(-0.146176\pi\) |
−0.443253 | + | 0.896396i | \(0.646176\pi\) | |||||||
\(488\) | −4.00000 | + | 4.00000i | −0.181071 | + | 0.181071i | ||||
\(489\) | 60.0000i | 2.71329i | ||||||||
\(490\) | 0.707107 | − | 2.12132i | 0.0319438 | − | 0.0958315i | ||||
\(491\) | 36.7696i | 1.65939i | 0.558219 | + | 0.829693i | \(0.311485\pi\) | ||||
−0.558219 | + | 0.829693i | \(0.688515\pi\) | |||||||
\(492\) | 8.48528 | − | 8.48528i | 0.382546 | − | 0.382546i | ||||
\(493\) | 2.00000 | − | 2.00000i | 0.0900755 | − | 0.0900755i | ||||
\(494\) | 8.48528 | 0.381771 | ||||||||
\(495\) | −22.9289 | + | 29.1421i | −1.03058 | + | 1.30984i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 5.65685 | − | 5.65685i | 0.253745 | − | 0.253745i | ||||
\(498\) | −20.0000 | + | 20.0000i | −0.896221 | + | 0.896221i | ||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 2.00000 | − | 11.0000i | 0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.82843 | + | 2.82843i | −0.126239 | + | 0.126239i | ||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | − | 5.00000i | − | 0.222718i | ||||||
\(505\) | 39.5980 | − | 19.7990i | 1.76209 | − | 0.881043i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.0000 | − | 18.0000i | −0.799408 | − | 0.799408i | ||||
\(508\) | −9.89949 | − | 9.89949i | −0.439219 | − | 0.439219i | ||||
\(509\) | − | 18.0000i | − | 0.797836i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) | ||
0.916987 | − | 0.398918i | \(-0.130614\pi\) | |||||||
\(510\) | 4.00000 | − | 12.0000i | 0.177123 | − | 0.531369i | ||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 16.9706 | + | 16.9706i | 0.749269 | + | 0.749269i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.00000 | − | 3.00000i | −0.396587 | − | 0.132196i | ||||
\(516\) | 22.6274i | 0.996116i | ||||||||
\(517\) | 22.0711 | + | 7.92893i | 0.970684 | + | 0.348714i | ||||
\(518\) | 4.00000 | − | 4.00000i | 0.175750 | − | 0.175750i | ||||
\(519\) | −28.2843 | −1.24154 | ||||||||
\(520\) | 4.00000 | − | 2.00000i | 0.175412 | − | 0.0877058i | ||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | 5.00000 | + | 5.00000i | 0.218844 | + | 0.218844i | ||||
\(523\) | 14.1421 | + | 14.1421i | 0.618392 | + | 0.618392i | 0.945119 | − | 0.326727i | \(-0.105946\pi\) |
−0.326727 | + | 0.945119i | \(0.605946\pi\) | |||||||
\(524\) | 15.5563 | 0.679582 | ||||||||
\(525\) | 11.3137 | + | 8.48528i | 0.493771 | + | 0.370328i | ||||
\(526\) | −10.0000 | −0.436021 | ||||||||
\(527\) | 2.82843 | − | 2.82843i | 0.123208 | − | 0.123208i | ||||
\(528\) | −3.17157 | + | 8.82843i | −0.138025 | + | 0.384208i | ||||
\(529\) | 23.0000i | 1.00000i | ||||||||
\(530\) | −16.9706 | + | 8.48528i | −0.737154 | + | 0.368577i | ||||
\(531\) | −40.0000 | −1.73585 | ||||||||
\(532\) | 3.00000 | + | 3.00000i | 0.130066 | + | 0.130066i | ||||
\(533\) | −6.00000 | + | 6.00000i | −0.259889 | + | 0.259889i | ||||
\(534\) | −16.9706 | −0.734388 | ||||||||
\(535\) | −42.4264 | − | 14.1421i | −1.83425 | − | 0.611418i | ||||
\(536\) | 4.24264i | 0.183254i | ||||||||
\(537\) | 36.0000 | + | 36.0000i | 1.55351 | + | 1.55351i | ||||
\(538\) | −16.9706 | − | 16.9706i | −0.731653 | − | 0.731653i | ||||
\(539\) | −1.41421 | − | 3.00000i | −0.0609145 | − | 0.129219i | ||||
\(540\) | 12.0000 | + | 4.00000i | 0.516398 | + | 0.172133i | ||||
\(541\) | − | 24.0416i | − | 1.03363i | −0.856097 | − | 0.516815i | \(-0.827117\pi\) | ||
0.856097 | − | 0.516815i | \(-0.172883\pi\) | |||||||
\(542\) | −6.00000 | − | 6.00000i | −0.257722 | − | 0.257722i | ||||
\(543\) | −20.0000 | + | 20.0000i | −0.858282 | + | 0.858282i | ||||
\(544\) | − | 2.00000i | − | 0.0857493i | ||||||
\(545\) | −18.3848 | − | 36.7696i | −0.787517 | − | 1.57503i | ||||
\(546\) | 5.65685i | 0.242091i | ||||||||
\(547\) | −8.48528 | + | 8.48528i | −0.362804 | + | 0.362804i | −0.864844 | − | 0.502040i | \(-0.832583\pi\) |
0.502040 | + | 0.864844i | \(0.332583\pi\) | |||||||
\(548\) | −5.00000 | + | 5.00000i | −0.213589 | + | 0.213589i | ||||
\(549\) | 28.2843 | 1.20714 | ||||||||
\(550\) | −9.12132 | − | 13.8492i | −0.388934 | − | 0.590534i | ||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | + | 5.00000i | −0.212622 | + | 0.212622i | ||||
\(554\) | 28.0000i | 1.18961i | ||||||||
\(555\) | 16.0000 | + | 32.0000i | 0.679162 | + | 1.35832i | ||||
\(556\) | − | 1.41421i | − | 0.0599760i | ||||||
\(557\) | −12.7279 | + | 12.7279i | −0.539299 | + | 0.539299i | −0.923323 | − | 0.384024i | \(-0.874538\pi\) |
0.384024 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(558\) | 7.07107 | + | 7.07107i | 0.299342 | + | 0.299342i | ||||
\(559\) | − | 16.0000i | − | 0.676728i | ||||||
\(560\) | 2.12132 | + | 0.707107i | 0.0896421 | + | 0.0298807i | ||||
\(561\) | −8.00000 | − | 16.9706i | −0.337760 | − | 0.716498i | ||||
\(562\) | 20.0000 | + | 20.0000i | 0.843649 | + | 0.843649i | ||||
\(563\) | 21.2132 | + | 21.2132i | 0.894030 | + | 0.894030i | 0.994900 | − | 0.100870i | \(-0.0321625\pi\) |
−0.100870 | + | 0.994900i | \(0.532163\pi\) | |||||||
\(564\) | − | 20.0000i | − | 0.842152i | ||||||
\(565\) | −39.0000 | − | 13.0000i | −1.64074 | − | 0.546914i | ||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | −0.707107 | + | 0.707107i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | 5.65685 | + | 5.65685i | 0.237356 | + | 0.237356i | ||||
\(569\) | −33.9411 | −1.42289 | −0.711443 | − | 0.702744i | \(-0.751958\pi\) | ||||
−0.711443 | + | 0.702744i | \(0.751958\pi\) | |||||||
\(570\) | −24.0000 | + | 12.0000i | −1.00525 | + | 0.502625i | ||||
\(571\) | 16.9706i | 0.710196i | 0.934829 | + | 0.355098i | \(0.115552\pi\) | ||||
−0.934829 | + | 0.355098i | \(0.884448\pi\) | |||||||
\(572\) | 2.24264 | − | 6.24264i | 0.0937695 | − | 0.261018i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.24264 | −0.177084 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.00000 | 0.208333 | ||||||||
\(577\) | −6.00000 | − | 6.00000i | −0.249783 | − | 0.249783i | 0.571098 | − | 0.820882i | \(-0.306517\pi\) |
−0.820882 | + | 0.571098i | \(0.806517\pi\) | |||||||
\(578\) | −9.19239 | − | 9.19239i | −0.382353 | − | 0.382353i | ||||
\(579\) | −50.9117 | −2.11582 | ||||||||
\(580\) | −2.82843 | + | 1.41421i | −0.117444 | + | 0.0587220i | ||||
\(581\) | 10.0000 | 0.414870 | ||||||||
\(582\) | −5.65685 | + | 5.65685i | −0.234484 | + | 0.234484i | ||||
\(583\) | −9.51472 | + | 26.4853i | −0.394059 | + | 1.09691i | ||||
\(584\) | − | 16.0000i | − | 0.662085i | ||||||
\(585\) | −21.2132 | − | 7.07107i | −0.877058 | − | 0.292353i | ||||
\(586\) | 2.00000 | 0.0826192 | ||||||||
\(587\) | 4.00000 | + | 4.00000i | 0.165098 | + | 0.165098i | 0.784821 | − | 0.619723i | \(-0.212755\pi\) |
−0.619723 | + | 0.784821i | \(0.712755\pi\) | |||||||
\(588\) | −2.00000 | + | 2.00000i | −0.0824786 | + | 0.0824786i | ||||
\(589\) | −8.48528 | −0.349630 | ||||||||
\(590\) | 5.65685 | − | 16.9706i | 0.232889 | − | 0.698667i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | + | 4.00000i | 0.164399 | + | 0.164399i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 16.9706 | − | 8.00000i | 0.696311 | − | 0.328244i | ||||
\(595\) | −4.00000 | + | 2.00000i | −0.163984 | + | 0.0819920i | ||||
\(596\) | − | 1.41421i | − | 0.0579284i | ||||||
\(597\) | 32.0000 | + | 32.0000i | 1.30967 | + | 1.30967i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −8.48528 | + | 11.3137i | −0.346410 | + | 0.461880i | ||||
\(601\) | 21.2132i | 0.865305i | 0.901561 | + | 0.432652i | \(0.142422\pi\) | ||||
−0.901561 | + | 0.432652i | \(0.857578\pi\) | |||||||
\(602\) | 5.65685 | − | 5.65685i | 0.230556 | − | 0.230556i | ||||
\(603\) | 15.0000 | − | 15.0000i | 0.610847 | − | 0.610847i | ||||
\(604\) | 9.89949 | 0.402805 | ||||||||
\(605\) | −23.9706 | − | 5.51472i | −0.974542 | − | 0.224205i | ||||
\(606\) | −56.0000 | −2.27484 | ||||||||
\(607\) | −19.7990 | + | 19.7990i | −0.803616 | + | 0.803616i | −0.983659 | − | 0.180043i | \(-0.942376\pi\) |
0.180043 | + | 0.983659i | \(0.442376\pi\) | |||||||
\(608\) | −3.00000 | + | 3.00000i | −0.121666 | + | 0.121666i | ||||
\(609\) | − | 4.00000i | − | 0.162088i | ||||||
\(610\) | −4.00000 | + | 12.0000i | −0.161955 | + | 0.485866i | ||||
\(611\) | 14.1421i | 0.572130i | ||||||||
\(612\) | −7.07107 | + | 7.07107i | −0.285831 | + | 0.285831i | ||||
\(613\) | −9.89949 | − | 9.89949i | −0.399837 | − | 0.399837i | 0.478339 | − | 0.878175i | \(-0.341239\pi\) |
−0.878175 | + | 0.478339i | \(0.841239\pi\) | |||||||
\(614\) | − | 28.0000i | − | 1.12999i | ||||||
\(615\) | 8.48528 | − | 25.4558i | 0.342160 | − | 1.02648i | ||||
\(616\) | 3.00000 | − | 1.41421i | 0.120873 | − | 0.0569803i | ||||
\(617\) | −17.0000 | − | 17.0000i | −0.684394 | − | 0.684394i | 0.276593 | − | 0.960987i | \(-0.410795\pi\) |
−0.960987 | + | 0.276593i | \(0.910795\pi\) | |||||||
\(618\) | 8.48528 | + | 8.48528i | 0.341328 | + | 0.341328i | ||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | −4.00000 | + | 2.00000i | −0.160644 | + | 0.0803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.24264 | + | 4.24264i | 0.169978 | + | 0.169978i | ||||
\(624\) | −5.65685 | −0.226455 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.4558 | + | 37.4558i | −0.537375 | + | 1.49584i | ||||
\(628\) | 13.0000 | − | 13.0000i | 0.518756 | − | 0.518756i | ||||
\(629\) | −11.3137 | −0.451107 | ||||||||
\(630\) | −5.00000 | − | 10.0000i | −0.199205 | − | 0.398410i | ||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | −5.00000 | − | 5.00000i | −0.198889 | − | 0.198889i | ||||
\(633\) | 22.6274 | + | 22.6274i | 0.899359 | + | 0.899359i | ||||
\(634\) | 31.1127 | 1.23564 | ||||||||
\(635\) | −29.6985 | − | 9.89949i | −1.17855 | − | 0.392849i | ||||
\(636\) | 24.0000 | 0.951662 | ||||||||
\(637\) | 1.41421 | − | 1.41421i | 0.0560332 | − | 0.0560332i | ||||
\(638\) | −1.58579 | + | 4.41421i | −0.0627819 | + | 0.174760i | ||||
\(639\) | − | 40.0000i | − | 1.58238i | ||||||
\(640\) | −0.707107 | + | 2.12132i | −0.0279508 | + | 0.0838525i | ||||
\(641\) | 24.0000 | 0.947943 | 0.473972 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473972 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(642\) | 40.0000 | + | 40.0000i | 1.57867 | + | 1.57867i | ||||
\(643\) | 6.00000 | − | 6.00000i | 0.236617 | − | 0.236617i | −0.578831 | − | 0.815448i | \(-0.696491\pi\) |
0.815448 | + | 0.578831i | \(0.196491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.6274 | + | 45.2548i | 0.890954 | + | 1.78191i | ||||
\(646\) | − | 8.48528i | − | 0.333849i | ||||||
\(647\) | 5.00000 | + | 5.00000i | 0.196570 | + | 0.196570i | 0.798528 | − | 0.601958i | \(-0.205612\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | −11.3137 | − | 24.0000i | −0.444102 | − | 0.942082i | ||||
\(650\) | 6.00000 | − | 8.00000i | 0.235339 | − | 0.313786i | ||||
\(651\) | − | 5.65685i | − | 0.221710i | ||||||
\(652\) | 15.0000 | + | 15.0000i | 0.587445 | + | 0.587445i | ||||
\(653\) | −10.0000 | + | 10.0000i | −0.391330 | + | 0.391330i | −0.875161 | − | 0.483831i | \(-0.839245\pi\) |
0.483831 | + | 0.875161i | \(0.339245\pi\) | |||||||
\(654\) | 52.0000i | 2.03336i | ||||||||
\(655\) | 31.1127 | − | 15.5563i | 1.21567 | − | 0.607837i | ||||
\(656\) | − | 4.24264i | − | 0.165647i | ||||||
\(657\) | −56.5685 | + | 56.5685i | −2.20695 | + | 2.20695i | ||||
\(658\) | −5.00000 | + | 5.00000i | −0.194920 | + | 0.194920i | ||||
\(659\) | −36.7696 | −1.43234 | −0.716169 | − | 0.697927i | \(-0.754106\pi\) | ||||
−0.716169 | + | 0.697927i | \(0.754106\pi\) | |||||||
\(660\) | 2.48528 | + | 20.8284i | 0.0967394 | + | 0.810745i | ||||
\(661\) | 16.0000 | 0.622328 | 0.311164 | − | 0.950356i | \(-0.399281\pi\) | ||||
0.311164 | + | 0.950356i | \(0.399281\pi\) | |||||||
\(662\) | 19.7990 | − | 19.7990i | 0.769510 | − | 0.769510i | ||||
\(663\) | 8.00000 | − | 8.00000i | 0.310694 | − | 0.310694i | ||||
\(664\) | 10.0000i | 0.388075i | ||||||||
\(665\) | 9.00000 | + | 3.00000i | 0.349005 | + | 0.116335i | ||||
\(666\) | − | 28.2843i | − | 1.09599i | ||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 4.00000i | − | 0.154649i | ||||||
\(670\) | 4.24264 | + | 8.48528i | 0.163908 | + | 0.327815i | ||||
\(671\) | 8.00000 | + | 16.9706i | 0.308837 | + | 0.655141i | ||||
\(672\) | −2.00000 | − | 2.00000i | −0.0771517 | − | 0.0771517i | ||||
\(673\) | −21.2132 | − | 21.2132i | −0.817709 | − | 0.817709i | 0.168067 | − | 0.985776i | \(-0.446248\pi\) |
−0.985776 | + | 0.168067i | \(0.946248\pi\) | |||||||
\(674\) | 2.00000i | 0.0770371i | ||||||||
\(675\) | 28.0000 | − | 4.00000i | 1.07772 | − | 0.153960i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −12.7279 | + | 12.7279i | −0.489174 | + | 0.489174i | −0.908045 | − | 0.418872i | \(-0.862426\pi\) |
0.418872 | + | 0.908045i | \(0.362426\pi\) | |||||||
\(678\) | 36.7696 | + | 36.7696i | 1.41213 | + | 1.41213i | ||||
\(679\) | 2.82843 | 0.108545 | ||||||||
\(680\) | −2.00000 | − | 4.00000i | −0.0766965 | − | 0.153393i | ||||
\(681\) | − | 33.9411i | − | 1.30063i | ||||||
\(682\) | −2.24264 | + | 6.24264i | −0.0858752 | + | 0.239043i | ||||
\(683\) | 5.00000 | − | 5.00000i | 0.191320 | − | 0.191320i | −0.604946 | − | 0.796266i | \(-0.706805\pi\) |
0.796266 | + | 0.604946i | \(0.206805\pi\) | |||||||
\(684\) | 21.2132 | 0.811107 | ||||||||
\(685\) | −5.00000 | + | 15.0000i | −0.191040 | + | 0.573121i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 40.0000 | + | 40.0000i | 1.52610 | + | 1.52610i | ||||
\(688\) | 5.65685 | + | 5.65685i | 0.215666 | + | 0.215666i | ||||
\(689\) | −16.9706 | −0.646527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | −7.07107 | + | 7.07107i | −0.268802 | + | 0.268802i | ||||
\(693\) | −15.6066 | − | 5.60660i | −0.592846 | − | 0.212977i | ||||
\(694\) | 12.0000i | 0.455514i | ||||||||
\(695\) | −1.41421 | − | 2.82843i | −0.0536442 | − | 0.107288i | ||||
\(696\) | 4.00000 | 0.151620 | ||||||||
\(697\) | 6.00000 | + | 6.00000i | 0.227266 | + | 0.227266i | ||||
\(698\) | 6.00000 | − | 6.00000i | 0.227103 | − | 0.227103i | ||||
\(699\) | 39.5980 | 1.49773 | ||||||||
\(700\) | 4.94975 | − | 0.707107i | 0.187083 | − | 0.0267261i | ||||
\(701\) | 7.07107i | 0.267071i | 0.991044 | + | 0.133535i | \(0.0426329\pi\) | ||||
−0.991044 | + | 0.133535i | \(0.957367\pi\) | |||||||
\(702\) | 8.00000 | + | 8.00000i | 0.301941 | + | 0.301941i | ||||
\(703\) | 16.9706 | + | 16.9706i | 0.640057 | + | 0.640057i | ||||
\(704\) | 1.41421 | + | 3.00000i | 0.0533002 | + | 0.113067i | ||||
\(705\) | −20.0000 | − | 40.0000i | −0.753244 | − | 1.50649i | ||||
\(706\) | 16.9706i | 0.638696i | ||||||||
\(707\) | 14.0000 | + | 14.0000i | 0.526524 | + | 0.526524i | ||||
\(708\) | −16.0000 | + | 16.0000i | −0.601317 | + | 0.601317i | ||||
\(709\) | 10.0000i | 0.375558i | 0.982211 | + | 0.187779i | \(0.0601289\pi\) | ||||
−0.982211 | + | 0.187779i | \(0.939871\pi\) | |||||||
\(710\) | 16.9706 | + | 5.65685i | 0.636894 | + | 0.212298i | ||||
\(711\) | 35.3553i | 1.32593i | ||||||||
\(712\) | −4.24264 | + | 4.24264i | −0.159000 | + | 0.159000i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 5.65685 | 0.211702 | ||||||||
\(715\) | −1.75736 | − | 14.7279i | −0.0657215 | − | 0.550793i | ||||
\(716\) | 18.0000 | 0.672692 | ||||||||
\(717\) | −2.82843 | + | 2.82843i | −0.105630 | + | 0.105630i | ||||
\(718\) | 1.00000 | − | 1.00000i | 0.0373197 | − | 0.0373197i | ||||
\(719\) | 10.0000i | 0.372937i | 0.982461 | + | 0.186469i | \(0.0597042\pi\) | ||||
−0.982461 | + | 0.186469i | \(0.940296\pi\) | |||||||
\(720\) | 10.0000 | − | 5.00000i | 0.372678 | − | 0.186339i | ||||
\(721\) | − | 4.24264i | − | 0.158004i | ||||||
\(722\) | 0.707107 | − | 0.707107i | 0.0263158 | − | 0.0263158i | ||||
\(723\) | −48.0833 | − | 48.0833i | −1.78824 | − | 1.78824i | ||||
\(724\) | 10.0000i | 0.371647i | ||||||||
\(725\) | −4.24264 | + | 5.65685i | −0.157568 | + | 0.210090i | ||||
\(726\) | 24.0000 | + | 19.7990i | 0.890724 | + | 0.734809i | ||||
\(727\) | −5.00000 | − | 5.00000i | −0.185440 | − | 0.185440i | 0.608282 | − | 0.793721i | \(-0.291859\pi\) |
−0.793721 | + | 0.608282i | \(0.791859\pi\) | |||||||
\(728\) | 1.41421 | + | 1.41421i | 0.0524142 | + | 0.0524142i | ||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | −16.0000 | − | 32.0000i | −0.592187 | − | 1.18437i | ||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 11.3137 | − | 11.3137i | 0.418167 | − | 0.418167i | ||||
\(733\) | −32.5269 | − | 32.5269i | −1.20141 | − | 1.20141i | −0.973738 | − | 0.227671i | \(-0.926889\pi\) |
−0.227671 | − | 0.973738i | \(-0.573111\pi\) | |||||||
\(734\) | 12.7279 | 0.469796 | ||||||||
\(735\) | −2.00000 | + | 6.00000i | −0.0737711 | + | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2426 | + | 4.75736i | 0.487799 | + | 0.175240i | ||||
\(738\) | −15.0000 | + | 15.0000i | −0.552158 | + | 0.552158i | ||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 12.0000 | + | 4.00000i | 0.441129 | + | 0.147043i | ||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | −6.00000 | − | 6.00000i | −0.220267 | − | 0.220267i | ||||
\(743\) | 1.41421 | + | 1.41421i | 0.0518825 | + | 0.0518825i | 0.732572 | − | 0.680690i | \(-0.238320\pi\) |
−0.680690 | + | 0.732572i | \(0.738320\pi\) | |||||||
\(744\) | 5.65685 | 0.207390 | ||||||||
\(745\) | −1.41421 | − | 2.82843i | −0.0518128 | − | 0.103626i | ||||
\(746\) | −32.0000 | −1.17160 | ||||||||
\(747\) | 35.3553 | − | 35.3553i | 1.29358 | − | 1.29358i | ||||
\(748\) | −6.24264 | − | 2.24264i | −0.228254 | − | 0.0819991i | ||||
\(749\) | − | 20.0000i | − | 0.730784i | ||||||
\(750\) | −5.65685 | + | 31.1127i | −0.206559 | + | 1.13608i | ||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | −5.00000 | − | 5.00000i | −0.182331 | − | 0.182331i | ||||
\(753\) | 8.00000 | − | 8.00000i | 0.291536 | − | 0.291536i | ||||
\(754\) | −2.82843 | −0.103005 | ||||||||
\(755\) | 19.7990 | − | 9.89949i | 0.720559 | − | 0.360280i | ||||
\(756\) | 5.65685i | 0.205738i | ||||||||
\(757\) | 12.0000 | + | 12.0000i | 0.436147 | + | 0.436147i | 0.890713 | − | 0.454566i | \(-0.150206\pi\) |
−0.454566 | + | 0.890713i | \(0.650206\pi\) | |||||||
\(758\) | −9.89949 | − | 9.89949i | −0.359566 | − | 0.359566i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | + | 9.00000i | −0.108821 | + | 0.326464i | ||||
\(761\) | − | 24.0416i | − | 0.871508i | −0.900066 | − | 0.435754i | \(-0.856482\pi\) | ||
0.900066 | − | 0.435754i | \(-0.143518\pi\) | |||||||
\(762\) | 28.0000 | + | 28.0000i | 1.01433 | + | 1.01433i | ||||
\(763\) | 13.0000 | − | 13.0000i | 0.470632 | − | 0.470632i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.07107 | + | 21.2132i | −0.255655 | + | 0.766965i | ||||
\(766\) | − | 32.5269i | − | 1.17525i | ||||||
\(767\) | 11.3137 | − | 11.3137i | 0.408514 | − | 0.408514i | ||||
\(768\) | 2.00000 | − | 2.00000i | 0.0721688 | − | 0.0721688i | ||||
\(769\) | 4.24264 | 0.152994 | 0.0764968 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764968 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(770\) | 4.58579 | − | 5.82843i | 0.165260 | − | 0.210042i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.7279 | + | 12.7279i | −0.458088 | + | 0.458088i | ||||
\(773\) | −25.0000 | + | 25.0000i | −0.899188 | + | 0.899188i | −0.995364 | − | 0.0961768i | \(-0.969339\pi\) |
0.0961768 | + | 0.995364i | \(0.469339\pi\) | |||||||
\(774\) | − | 40.0000i | − | 1.43777i | ||||||
\(775\) | −6.00000 | + | 8.00000i | −0.215526 | + | 0.287368i | ||||
\(776\) | 2.82843i | 0.101535i | ||||||||
\(777\) | −11.3137 | + | 11.3137i | −0.405877 | + | 0.405877i | ||||
\(778\) | 1.41421 | + | 1.41421i | 0.0507020 | + | 0.0507020i | ||||
\(779\) | − | 18.0000i | − | 0.644917i | ||||||
\(780\) | −11.3137 | + | 5.65685i | −0.405096 | + | 0.202548i | ||||
\(781\) | 24.0000 | − | 11.3137i | 0.858788 | − | 0.404836i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.65685 | − | 5.65685i | −0.202159 | − | 0.202159i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 13.0000 | − | 39.0000i | 0.463990 | − | 1.39197i | ||||
\(786\) | −44.0000 | −1.56943 | ||||||||
\(787\) | 15.5563 | − | 15.5563i | 0.554524 | − | 0.554524i | −0.373219 | − | 0.927743i | \(-0.621746\pi\) |
0.927743 | + | 0.373219i | \(0.121746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.2843 | 1.00695 | ||||||||
\(790\) | −15.0000 | − | 5.00000i | −0.533676 | − | 0.177892i | ||||
\(791\) | − | 18.3848i | − | 0.653687i | ||||||
\(792\) | 5.60660 | − | 15.6066i | 0.199222 | − | 0.554556i | ||||
\(793\) | −8.00000 | + | 8.00000i | −0.284088 | + | 0.284088i | ||||
\(794\) | 32.5269 | 1.15434 | ||||||||
\(795\) | 48.0000 | − | 24.0000i | 1.70238 | − | 0.851192i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | −25.0000 | − | 25.0000i | −0.885545 | − | 0.885545i | 0.108546 | − | 0.994091i | \(-0.465381\pi\) |
−0.994091 | + | 0.108546i | \(0.965381\pi\) | |||||||
\(798\) | −8.48528 | − | 8.48528i | −0.300376 | − | 0.300376i | ||||
\(799\) | 14.1421 | 0.500313 | ||||||||
\(800\) | 0.707107 | + | 4.94975i | 0.0250000 | + | 0.175000i | ||||
\(801\) | 30.0000 | 1.06000 | ||||||||
\(802\) | −24.0416 | + | 24.0416i | −0.848939 | + | 0.848939i | ||||
\(803\) | −49.9411 | − | 17.9411i | −1.76238 | − | 0.633129i | ||||
\(804\) | − | 12.0000i | − | 0.423207i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 48.0000 | + | 48.0000i | 1.68968 | + | 1.68968i | ||||
\(808\) | −14.0000 | + | 14.0000i | −0.492518 | + | 0.492518i | ||||
\(809\) | 16.9706 | 0.596653 | 0.298327 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298327 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(810\) | −2.12132 | − | 0.707107i | −0.0745356 | − | 0.0248452i | ||||
\(811\) | 41.0122i | 1.44013i | 0.693905 | + | 0.720066i | \(0.255889\pi\) | ||||
−0.693905 | + | 0.720066i | \(0.744111\pi\) | |||||||
\(812\) | −1.00000 | − | 1.00000i | −0.0350931 | − | 0.0350931i | ||||
\(813\) | 16.9706 | + | 16.9706i | 0.595184 | + | 0.595184i | ||||
\(814\) | 16.9706 | − | 8.00000i | 0.594818 | − | 0.280400i | ||||
\(815\) | 45.0000 | + | 15.0000i | 1.57628 | + | 0.525427i | ||||
\(816\) | 5.65685i | 0.198030i | ||||||||
\(817\) | 24.0000 | + | 24.0000i | 0.839654 | + | 0.839654i | ||||
\(818\) | −21.0000 | + | 21.0000i | −0.734248 | + | 0.734248i | ||||
\(819\) | − | 10.0000i | − | 0.349428i | ||||||
\(820\) | −4.24264 | − | 8.48528i | −0.148159 | − | 0.296319i | ||||
\(821\) | − | 29.6985i | − | 1.03648i | −0.855234 | − | 0.518242i | \(-0.826587\pi\) | ||
0.855234 | − | 0.518242i | \(-0.173413\pi\) | |||||||
\(822\) | 14.1421 | − | 14.1421i | 0.493264 | − | 0.493264i | ||||
\(823\) | 18.0000 | − | 18.0000i | 0.627441 | − | 0.627441i | −0.319983 | − | 0.947423i | \(-0.603677\pi\) |
0.947423 | + | 0.319983i | \(0.103677\pi\) | |||||||
\(824\) | 4.24264 | 0.147799 | ||||||||
\(825\) | 25.7990 | + | 39.1716i | 0.898206 | + | 1.36378i | ||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | 5.65685 | − | 5.65685i | 0.196708 | − | 0.196708i | −0.601879 | − | 0.798587i | \(-0.705581\pi\) |
0.798587 | + | 0.601879i | \(0.205581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.00000i | − | 0.0694629i | −0.999397 | − | 0.0347314i | \(-0.988942\pi\) | ||
0.999397 | − | 0.0347314i | \(-0.0110576\pi\) | |||||||
\(830\) | 10.0000 | + | 20.0000i | 0.347105 | + | 0.694210i | ||||
\(831\) | − | 79.1960i | − | 2.74728i | ||||||
\(832\) | −1.41421 | + | 1.41421i | −0.0490290 | + | 0.0490290i | ||||
\(833\) | −1.41421 | − | 1.41421i | −0.0489996 | − | 0.0489996i | ||||
\(834\) | 4.00000i | 0.138509i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | + | 12.7279i | 0.207514 | + | 0.440204i | ||||
\(837\) | −8.00000 | − | 8.00000i | −0.276520 | − | 0.276520i | ||||
\(838\) | 28.2843 | + | 28.2843i | 0.977064 | + | 0.977064i | ||||
\(839\) | − | 42.0000i | − | 1.45000i | −0.688748 | − | 0.725001i | \(-0.741839\pi\) | ||
0.688748 | − | 0.725001i | \(-0.258161\pi\) | |||||||
\(840\) | −6.00000 | − | 2.00000i | −0.207020 | − | 0.0690066i | ||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | −7.07107 | + | 7.07107i | −0.243685 | + | 0.243685i | ||||
\(843\) | −56.5685 | − | 56.5685i | −1.94832 | − | 1.94832i | ||||
\(844\) | 11.3137 | 0.389434 | ||||||||
\(845\) | −18.0000 | + | 9.00000i | −0.619219 | + | 0.309609i | ||||
\(846\) | 35.3553i | 1.21554i | ||||||||
\(847\) | −1.05025 | − | 10.9497i | −0.0360871 | − | 0.376238i | ||||
\(848\) | 6.00000 | − | 6.00000i | 0.206041 | − | 0.206041i | ||||
\(849\) | −79.1960 | −2.71800 | ||||||||
\(850\) | −8.00000 | − | 6.00000i | −0.274398 | − | 0.205798i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −16.0000 | − | 16.0000i | −0.548151 | − | 0.548151i | ||||
\(853\) | −4.24264 | − | 4.24264i | −0.145265 | − | 0.145265i | 0.630734 | − | 0.775999i | \(-0.282754\pi\) |
−0.775999 | + | 0.630734i | \(0.782754\pi\) | |||||||
\(854\) | −5.65685 | −0.193574 | ||||||||
\(855\) | 42.4264 | − | 21.2132i | 1.45095 | − | 0.725476i | ||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | −14.1421 | + | 14.1421i | −0.483086 | + | 0.483086i | −0.906116 | − | 0.423030i | \(-0.860967\pi\) |
0.423030 | + | 0.906116i | \(0.360967\pi\) | |||||||
\(858\) | −6.34315 | + | 17.6569i | −0.216551 | + | 0.602795i | ||||
\(859\) | 16.0000i | 0.545913i | 0.962026 | + | 0.272956i | \(0.0880015\pi\) | ||||
−0.962026 | + | 0.272956i | \(0.911998\pi\) | |||||||
\(860\) | 16.9706 | + | 5.65685i | 0.578691 | + | 0.192897i | ||||
\(861\) | 12.0000 | 0.408959 | ||||||||
\(862\) | −1.00000 | − | 1.00000i | −0.0340601 | − | 0.0340601i | ||||
\(863\) | −14.0000 | + | 14.0000i | −0.476566 | + | 0.476566i | −0.904031 | − | 0.427466i | \(-0.859406\pi\) |
0.427466 | + | 0.904031i | \(0.359406\pi\) | |||||||
\(864\) | −5.65685 | −0.192450 | ||||||||
\(865\) | −7.07107 | + | 21.2132i | −0.240424 | + | 0.721271i | ||||
\(866\) | − | 33.9411i | − | 1.15337i | ||||||
\(867\) | 26.0000 | + | 26.0000i | 0.883006 | + | 0.883006i | ||||
\(868\) | −1.41421 | − | 1.41421i | −0.0480015 | − | 0.0480015i | ||||
\(869\) | −21.2132 | + | 10.0000i | −0.719609 | + | 0.339227i | ||||
\(870\) | 8.00000 | − | 4.00000i | 0.271225 | − | 0.135613i | ||||
\(871\) | 8.48528i | 0.287513i | ||||||||
\(872\) | 13.0000 | + | 13.0000i | 0.440236 | + | 0.440236i | ||||
\(873\) | 10.0000 | − | 10.0000i | 0.338449 | − | 0.338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.19239 | − | 6.36396i | 0.310759 | − | 0.215141i | ||||
\(876\) | 45.2548i | 1.52902i | ||||||||
\(877\) | −19.7990 | + | 19.7990i | −0.668564 | + | 0.668564i | −0.957384 | − | 0.288819i | \(-0.906737\pi\) |
0.288819 | + | 0.957384i | \(0.406737\pi\) | |||||||
\(878\) | 18.0000 | − | 18.0000i | 0.607471 | − | 0.607471i | ||||
\(879\) | −5.65685 | −0.190801 | ||||||||
\(880\) | 5.82843 | + | 4.58579i | 0.196476 | + | 0.154587i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 3.53553 | − | 3.53553i | 0.119048 | − | 0.119048i | ||||
\(883\) | 9.00000 | − | 9.00000i | 0.302874 | − | 0.302874i | −0.539263 | − | 0.842137i | \(-0.681297\pi\) |
0.842137 | + | 0.539263i | \(0.181297\pi\) | |||||||
\(884\) | − | 4.00000i | − | 0.134535i | ||||||
\(885\) | −16.0000 | + | 48.0000i | −0.537834 | + | 1.61350i | ||||
\(886\) | − | 21.2132i | − | 0.712672i | ||||||
\(887\) | −5.65685 | + | 5.65685i | −0.189939 | + | 0.189939i | −0.795670 | − | 0.605731i | \(-0.792881\pi\) |
0.605731 | + | 0.795670i | \(0.292881\pi\) | |||||||
\(888\) | −11.3137 | − | 11.3137i | −0.379663 | − | 0.379663i | ||||
\(889\) | − | 14.0000i | − | 0.469545i | ||||||
\(890\) | −4.24264 | + | 12.7279i | −0.142214 | + | 0.426641i | ||||
\(891\) | −3.00000 | + | 1.41421i | −0.100504 | + | 0.0473779i | ||||
\(892\) | −1.00000 | − | 1.00000i | −0.0334825 | − | 0.0334825i | ||||
\(893\) | −21.2132 | − | 21.2132i | −0.709873 | − | 0.709873i | ||||
\(894\) | 4.00000i | 0.133780i | ||||||||
\(895\) | 36.0000 | − | 18.0000i | 1.20335 | − | 0.601674i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.2843 | + | 28.2843i | 0.943858 | + | 0.943858i | ||||
\(899\) | 2.82843 | 0.0943333 | ||||||||
\(900\) | 15.0000 | − | 20.0000i | 0.500000 | − | 0.666667i | ||||
\(901\) | 16.9706i | 0.565371i | ||||||||
\(902\) | −13.2426 | − | 4.75736i | −0.440932 | − | 0.158403i | ||||
\(903\) | −16.0000 | + | 16.0000i | −0.532447 | + | 0.532447i | ||||
\(904\) | 18.3848 | 0.611469 | ||||||||
\(905\) | 10.0000 | + | 20.0000i | 0.332411 | + | 0.664822i | ||||
\(906\) | −28.0000 | −0.930238 | ||||||||
\(907\) | −1.00000 | − | 1.00000i | −0.0332045 | − | 0.0332045i | 0.690310 | − | 0.723514i | \(-0.257474\pi\) |
−0.723514 | + | 0.690310i | \(0.757474\pi\) | |||||||
\(908\) | −8.48528 | − | 8.48528i | −0.281594 | − | 0.281594i | ||||
\(909\) | 98.9949 | 3.28346 | ||||||||
\(910\) | 4.24264 | + | 1.41421i | 0.140642 | + | 0.0468807i | ||||
\(911\) | −20.0000 | −0.662630 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(912\) | 8.48528 | − | 8.48528i | 0.280976 | − | 0.280976i | ||||
\(913\) | 31.2132 | + | 11.2132i | 1.03301 | + | 0.371103i | ||||
\(914\) | 14.0000i | 0.463079i | ||||||||
\(915\) | 11.3137 | − | 33.9411i | 0.374020 | − | 1.12206i | ||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 11.0000 | + | 11.0000i | 0.363252 | + | 0.363252i | ||||
\(918\) | 8.00000 | − | 8.00000i | 0.264039 | − | 0.264039i | ||||
\(919\) | −24.0416 | −0.793060 | −0.396530 | − | 0.918022i | \(-0.629786\pi\) | ||||
−0.396530 | + | 0.918022i | \(0.629786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 79.1960i | 2.60960i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3137 | + | 11.3137i | 0.372395 | + | 0.372395i | ||||
\(924\) | −8.48528 | + | 4.00000i | −0.279145 | + | 0.131590i | ||||
\(925\) | 28.0000 | − | 4.00000i | 0.920634 | − | 0.131519i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0000 | − | 15.0000i | −0.492665 | − | 0.492665i | ||||
\(928\) | 1.00000 | − | 1.00000i | 0.0328266 | − | 0.0328266i | ||||
\(929\) | − | 38.0000i | − | 1.24674i | −0.781927 | − | 0.623370i | \(-0.785763\pi\) | ||
0.781927 | − | 0.623370i | \(-0.214237\pi\) | |||||||
\(930\) | 11.3137 | − | 5.65685i | 0.370991 | − | 0.185496i | ||||
\(931\) | 4.24264i | 0.139047i | ||||||||
\(932\) | 9.89949 | − | 9.89949i | 0.324269 | − | 0.324269i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.3137 | 0.370196 | ||||||||
\(935\) | −14.7279 | + | 1.75736i | −0.481655 | + | 0.0574718i | ||||
\(936\) | 10.0000 | 0.326860 | ||||||||
\(937\) | −29.6985 | + | 29.6985i | −0.970207 | + | 0.970207i | −0.999569 | − | 0.0293616i | \(-0.990653\pi\) |
0.0293616 | + | 0.999569i | \(0.490653\pi\) | |||||||
\(938\) | −3.00000 | + | 3.00000i | −0.0979535 | + | 0.0979535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.0000 | − | 5.00000i | −0.489246 | − | 0.163082i | ||||
\(941\) | 59.3970i | 1.93629i | 0.250398 | + | 0.968143i | \(0.419438\pi\) | ||||
−0.250398 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(942\) | −36.7696 | + | 36.7696i | −1.19802 | + | 1.19802i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 8.00000i | 0.260378i | ||||||||
\(945\) | 5.65685 | + | 11.3137i | 0.184017 | + | 0.368035i | ||||
\(946\) | 24.0000 | − | 11.3137i | 0.780307 | − | 0.367840i | ||||
\(947\) | −19.0000 | − | 19.0000i | −0.617417 | − | 0.617417i | 0.327451 | − | 0.944868i | \(-0.393810\pi\) |
−0.944868 | + | 0.327451i | \(0.893810\pi\) | |||||||
\(948\) | 14.1421 | + | 14.1421i | 0.459315 | + | 0.459315i | ||||
\(949\) | − | 32.0000i | − | 1.03876i | ||||||
\(950\) | 3.00000 | + | 21.0000i | 0.0973329 | + | 0.681330i | ||||
\(951\) | −88.0000 | −2.85360 | ||||||||
\(952\) | 1.41421 | − | 1.41421i | 0.0458349 | − | 0.0458349i | ||||
\(953\) | 1.41421 | + | 1.41421i | 0.0458109 | + | 0.0458109i | 0.729641 | − | 0.683830i | \(-0.239687\pi\) |
−0.683830 | + | 0.729641i | \(0.739687\pi\) | |||||||
\(954\) | −42.4264 | −1.37361 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.41421i | 0.0457389i | ||||||||
\(957\) | 4.48528 | − | 12.4853i | 0.144989 | − | 0.403592i | ||||
\(958\) | −26.0000 | + | 26.0000i | −0.840022 | + | 0.840022i | ||||
\(959\) | −7.07107 | −0.228337 | ||||||||
\(960\) | 2.00000 | − | 6.00000i | 0.0645497 | − | 0.193649i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 8.00000 | + | 8.00000i | 0.257930 | + | 0.257930i | ||||
\(963\) | −70.7107 | − | 70.7107i | −2.27862 | − | 2.27862i | ||||
\(964\) | −24.0416 | −0.774329 | ||||||||
\(965\) | −12.7279 | + | 38.1838i | −0.409726 | + | 1.22918i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2132 | − | 21.2132i | 0.682171 | − | 0.682171i | −0.278318 | − | 0.960489i | \(-0.589777\pi\) |
0.960489 | + | 0.278318i | \(0.0897770\pi\) | |||||||
\(968\) | 10.9497 | − | 1.05025i | 0.351938 | − | 0.0337564i | ||||
\(969\) | 24.0000i | 0.770991i | ||||||||
\(970\) | 2.82843 | + | 5.65685i | 0.0908153 | + | 0.181631i | ||||
\(971\) | 28.0000 | 0.898563 | 0.449281 | − | 0.893390i | \(-0.351680\pi\) | ||||
0.449281 | + | 0.893390i | \(0.351680\pi\) | |||||||
\(972\) | −10.0000 | − | 10.0000i | −0.320750 | − | 0.320750i | ||||
\(973\) | 1.00000 | − | 1.00000i | 0.0320585 | − | 0.0320585i | ||||
\(974\) | −14.1421 | −0.453143 | ||||||||
\(975\) | −16.9706 | + | 22.6274i | −0.543493 | + | 0.724657i | ||||
\(976\) | − | 5.65685i | − | 0.181071i | ||||||
\(977\) | −35.0000 | − | 35.0000i | −1.11975 | − | 1.11975i | −0.991778 | − | 0.127971i | \(-0.959153\pi\) |
−0.127971 | − | 0.991778i | \(-0.540847\pi\) | |||||||
\(978\) | −42.4264 | − | 42.4264i | −1.35665 | − | 1.35665i | ||||
\(979\) | 8.48528 | + | 18.0000i | 0.271191 | + | 0.575282i | ||||
\(980\) | 1.00000 | + | 2.00000i | 0.0319438 | + | 0.0638877i | ||||
\(981\) | − | 91.9239i | − | 2.93490i | ||||||
\(982\) | −26.0000 | − | 26.0000i | −0.829693 | − | 0.829693i | ||||
\(983\) | −39.0000 | + | 39.0000i | −1.24391 | + | 1.24391i | −0.285540 | + | 0.958367i | \(0.592173\pi\) |
−0.958367 | + | 0.285540i | \(0.907827\pi\) | |||||||
\(984\) | 12.0000i | 0.382546i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.82843i | 0.0900755i | ||||||||
\(987\) | 14.1421 | − | 14.1421i | 0.450149 | − | 0.450149i | ||||
\(988\) | −6.00000 | + | 6.00000i | −0.190885 | + | 0.190885i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −4.39340 | − | 36.8198i | −0.139631 | − | 1.17021i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 1.41421 | − | 1.41421i | 0.0449013 | − | 0.0449013i | ||||
\(993\) | −56.0000 | + | 56.0000i | −1.77711 | + | 1.77711i | ||||
\(994\) | 8.00000i | 0.253745i | ||||||||
\(995\) | 32.0000 | − | 16.0000i | 1.01447 | − | 0.507234i | ||||
\(996\) | − | 28.2843i | − | 0.896221i | ||||||
\(997\) | 7.07107 | − | 7.07107i | 0.223943 | − | 0.223943i | −0.586214 | − | 0.810157i | \(-0.699382\pi\) |
0.810157 | + | 0.586214i | \(0.199382\pi\) | |||||||
\(998\) | −14.1421 | − | 14.1421i | −0.447661 | − | 0.447661i | ||||
\(999\) | 32.0000i | 1.01244i |
(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 | 770.2.m.c.197.1 | yes | 4 | |
5.3 | odd | 4 | inner | 770.2.m.c.43.2 | yes | 4 | |
11.10 | odd | 2 | inner | 770.2.m.c.197.2 | yes | 4 | |
55.43 | even | 4 | inner | 770.2.m.c.43.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.c.43.1 | ✓ | 4 | 55.43 | even | 4 | inner | |
770.2.m.c.43.2 | yes | 4 | 5.3 | odd | 4 | inner | |
770.2.m.c.197.1 | yes | 4 | 1.1 | even | 1 | trivial | |
770.2.m.c.197.2 | yes | 4 | 11.10 | odd | 2 | inner |