Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(23,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.e (of order \(3\), 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: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.67 |
Dual form | 154.2.e.b.23.1 |
$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −0.500000 | − | 2.59808i | −0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | −2.50000 | + | 4.33013i | −0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 2.50000 | + | 0.866025i | 0.385758 | + | 0.133631i | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 2.50000 | + | 4.33013i | 0.340207 | + | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | + | 0.866025i | 0.334077 | + | 0.115728i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −1.50000 | − | 2.59808i | −0.196960 | − | 0.341144i | ||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 1.00000 | + | 5.19615i | 0.125988 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 1.00000 | + | 1.73205i | 0.117851 | + | 0.204124i | ||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 2.50000 | + | 4.33013i | 0.288675 | + | 0.500000i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 2.00000 | − | 1.73205i | 0.227921 | − | 0.197386i | ||||
\(78\) | 5.00000 | 0.566139 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −0.500000 | − | 2.59808i | −0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5000 | + | 4.33013i | 1.31036 | + | 0.453921i | ||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −13.0000 | −1.31995 | −0.659975 | − | 0.751288i | \(-0.729433\pi\) | ||||
−0.659975 | + | 0.751288i | \(0.729433\pi\) | |||||||
\(98\) | 1.00000 | − | 6.92820i | 0.101015 | − | 0.699854i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 2.50000 | − | 4.33013i | 0.240563 | − | 0.416667i | ||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −0.500000 | − | 2.59808i | −0.0472456 | − | 0.245495i | ||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.50000 | + | 2.59808i | −0.139272 | + | 0.241225i | ||||
\(117\) | 5.00000 | + | 8.66025i | 0.462250 | + | 0.800641i | ||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | −12.0000 | + | 10.3923i | −1.10004 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 3.50000 | − | 6.06218i | 0.316875 | − | 0.548844i | ||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | − | 3.46410i | 0.356348 | − | 0.308607i | ||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −1.00000 | − | 5.19615i | −0.0867110 | − | 0.450564i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | −7.50000 | + | 12.9904i | −0.640768 | + | 1.10984i | 0.344493 | + | 0.938789i | \(0.388051\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(138\) | −3.00000 | − | 5.19615i | −0.255377 | − | 0.442326i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | 2.50000 | − | 4.33013i | 0.209061 | − | 0.362103i | ||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 2.50000 | − | 4.33013i | 0.204124 | − | 0.353553i | ||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | −1.00000 | − | 1.73205i | −0.0811107 | − | 0.140488i | ||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | −2.50000 | − | 0.866025i | −0.201456 | − | 0.0697863i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | − | 4.33013i | −0.200160 | − | 0.346688i | ||||
\(157\) | 2.00000 | − | 3.46410i | 0.159617 | − | 0.276465i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | 0.500000 | − | 0.866025i | 0.0397779 | − | 0.0688973i | ||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | − | 15.5885i | −0.236433 | − | 1.22854i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.50000 | − | 14.7224i | −0.665771 | − | 1.15315i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | 9.00000 | 0.696441 | 0.348220 | − | 0.937413i | \(-0.386786\pi\) | ||||
0.348220 | + | 0.937413i | \(0.386786\pi\) | |||||||
\(168\) | −2.00000 | + | 1.73205i | −0.154303 | + | 0.133631i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 10.0000 | − | 8.66025i | 0.755929 | − | 0.654654i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −4.50000 | + | 7.79423i | −0.336346 | + | 0.582568i | −0.983742 | − | 0.179585i | \(-0.942524\pi\) |
0.647397 | + | 0.762153i | \(0.275858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −2.50000 | − | 12.9904i | −0.185312 | − | 0.962911i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.00000 | + | 6.92820i | −0.293294 | + | 0.508001i | ||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | −12.5000 | − | 4.33013i | −0.909241 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | 6.50000 | + | 11.2583i | 0.466673 | + | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | −9.00000 | −0.641223 | −0.320612 | − | 0.947211i | \(-0.603888\pi\) | ||||
−0.320612 | + | 0.947211i | \(0.603888\pi\) | |||||||
\(198\) | −1.00000 | − | 1.73205i | −0.0710669 | − | 0.123091i | ||||
\(199\) | −7.00000 | + | 12.1244i | −0.496217 | + | 0.859473i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | 6.50000 | + | 11.2583i | 0.458475 | + | 0.794101i | ||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | 7.50000 | + | 2.59808i | 0.526397 | + | 0.182349i | ||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.00000 | − | 3.46410i | 0.139347 | − | 0.241355i | ||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | −2.50000 | − | 4.33013i | −0.173344 | − | 0.300240i | ||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −16.0000 | + | 13.8564i | −1.08615 | + | 0.940634i | ||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | 5.00000 | + | 8.66025i | 0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | ||||
\(222\) | −1.00000 | − | 1.73205i | −0.0671156 | − | 0.116248i | ||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 10.0000 | 0.666667 | ||||||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | 3.00000 | − | 5.19615i | 0.199117 | − | 0.344881i | −0.749125 | − | 0.662428i | \(-0.769526\pi\) |
0.948242 | + | 0.317547i | \(0.102859\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.500000 | + | 2.59808i | 0.0328976 | + | 0.170941i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 15.0000 | + | 25.9808i | 0.982683 | + | 1.70206i | 0.651813 | + | 0.758380i | \(0.274009\pi\) |
0.330870 | + | 0.943676i | \(0.392658\pi\) | |||||||
\(234\) | 5.00000 | − | 8.66025i | 0.326860 | − | 0.566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50000 | + | 2.59808i | 0.0976417 | + | 0.169120i | ||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 15.0000 | + | 5.19615i | 0.972306 | + | 0.336817i | ||||
\(239\) | 21.0000 | 1.35838 | 0.679189 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679189 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | −4.00000 | + | 6.92820i | −0.254000 | + | 0.439941i | ||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −5.00000 | − | 1.73205i | −0.314970 | − | 0.109109i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 6.50000 | + | 11.2583i | 0.407846 | + | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −13.5000 | − | 23.3827i | −0.842107 | − | 1.45857i | −0.888110 | − | 0.459631i | \(-0.847982\pi\) |
0.0460033 | − | 0.998941i | \(-0.485352\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | −1.00000 | − | 5.19615i | −0.0621370 | − | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | 1.50000 | − | 2.59808i | 0.0924940 | − | 0.160204i | −0.816066 | − | 0.577959i | \(-0.803849\pi\) |
0.908560 | + | 0.417755i | \(0.137183\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | + | 3.46410i | −0.245256 | + | 0.212398i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 6.50000 | + | 11.2583i | 0.397051 | + | 0.687712i | ||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | −10.0000 | + | 8.66025i | −0.605228 | + | 0.524142i | ||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | −3.00000 | + | 5.19615i | −0.180579 | + | 0.312772i | ||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 2.00000 | + | 3.46410i | 0.119952 | + | 0.207763i | ||||
\(279\) | −16.0000 | −0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | 11.0000 | − | 19.0526i | 0.653882 | − | 1.13256i | −0.328291 | − | 0.944577i | \(-0.606473\pi\) |
0.982173 | − | 0.187980i | \(-0.0601941\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.00000 | −0.295656 | ||||||||
\(287\) | −15.0000 | − | 5.19615i | −0.885422 | − | 0.306719i | ||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.50000 | − | 11.2583i | 0.381037 | − | 0.659975i | ||||
\(292\) | 5.00000 | + | 8.66025i | 0.292603 | + | 0.506803i | ||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 5.50000 | + | 4.33013i | 0.320767 | + | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −2.50000 | + | 4.33013i | −0.145065 | + | 0.251259i | ||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | −15.0000 | − | 25.9808i | −0.867472 | − | 1.50251i | ||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | −1.00000 | −0.0575435 | ||||||||
\(303\) | −1.50000 | − | 2.59808i | −0.0861727 | − | 0.149256i | ||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | + | 10.3923i | 0.342997 | + | 0.594089i | ||||
\(307\) | 32.0000 | 1.82634 | 0.913168 | − | 0.407583i | \(-0.133628\pi\) | ||||
0.913168 | + | 0.407583i | \(0.133628\pi\) | |||||||
\(308\) | 0.500000 | + | 2.59808i | 0.0284901 | + | 0.148039i | ||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | −2.50000 | + | 4.33013i | −0.141535 | + | 0.245145i | ||||
\(313\) | 3.50000 | + | 6.06218i | 0.197832 | + | 0.342655i | 0.947825 | − | 0.318791i | \(-0.103277\pi\) |
−0.749993 | + | 0.661445i | \(0.769943\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | 12.0000 | + | 20.7846i | 0.673987 | + | 1.16738i | 0.976764 | + | 0.214318i | \(0.0687530\pi\) |
−0.302777 | + | 0.953062i | \(0.597914\pi\) | |||||||
\(318\) | 6.00000 | − | 10.3923i | 0.336463 | − | 0.582772i | ||||
\(319\) | 1.50000 | − | 2.59808i | 0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | + | 10.3923i | −0.668734 | + | 0.579141i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 12.5000 | − | 21.6506i | 0.693375 | − | 1.20096i | ||||
\(326\) | −8.50000 | + | 14.7224i | −0.470771 | + | 0.815400i | ||||
\(327\) | −7.00000 | − | 12.1244i | −0.387101 | − | 0.670478i | ||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | −3.00000 | − | 15.5885i | −0.165395 | − | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | + | 11.2583i | 0.357272 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503735\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | −4.50000 | − | 7.79423i | −0.246229 | − | 0.426481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | + | 0.866025i | 0.136386 | + | 0.0472456i | ||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | −4.50000 | + | 7.79423i | −0.244406 | + | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.50000 | − | 12.9904i | 0.403202 | − | 0.698367i | ||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | −12.5000 | − | 4.33013i | −0.668153 | − | 0.231455i | ||||
\(351\) | −25.0000 | −1.33440 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −15.0000 | + | 25.9808i | −0.798369 | + | 1.38282i | 0.122308 | + | 0.992492i | \(0.460970\pi\) |
−0.920677 | + | 0.390324i | \(0.872363\pi\) | |||||||
\(354\) | 1.50000 | − | 2.59808i | 0.0797241 | − | 0.138086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −3.00000 | − | 15.5885i | −0.158777 | − | 0.825029i | ||||
\(358\) | 9.00000 | 0.475665 | ||||||||
\(359\) | 4.50000 | + | 7.79423i | 0.237501 | + | 0.411364i | 0.959997 | − | 0.280012i | \(-0.0903384\pi\) |
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −10.0000 | + | 8.66025i | −0.524142 | + | 0.453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.50000 | + | 6.06218i | 0.182948 | + | 0.316875i | ||||
\(367\) | −19.0000 | + | 32.9090i | −0.991792 | + | 1.71783i | −0.385164 | + | 0.922848i | \(0.625855\pi\) |
−0.606628 | + | 0.794986i | \(0.707478\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | −6.00000 | − | 10.3923i | −0.312348 | − | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000 | − | 20.7846i | 1.24602 | − | 1.07908i | ||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | 15.0000 | 0.772539 | ||||||||
\(378\) | 2.50000 | + | 12.9904i | 0.128586 | + | 0.668153i | ||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | − | 11.2583i | 0.333005 | − | 0.576782i | ||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | −6.00000 | − | 10.3923i | −0.306586 | − | 0.531022i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.977613 | + | 0.210411i | \(0.932520\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | 6.50000 | − | 11.2583i | 0.329988 | − | 0.571555i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 5.50000 | + | 4.33013i | 0.277792 | + | 0.218704i | ||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | 14.0000 | 0.701757 | ||||||||
\(399\) | 5.00000 | + | 1.73205i | 0.250313 | + | 0.0867110i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 4.50000 | + | 7.79423i | 0.224719 | + | 0.389225i | 0.956235 | − | 0.292599i | \(-0.0945202\pi\) |
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(402\) | 6.50000 | − | 11.2583i | 0.324191 | − | 0.561514i | ||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.50000 | − | 7.79423i | −0.0744438 | − | 0.386821i | ||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | −3.00000 | − | 5.19615i | −0.148522 | − | 0.257248i | ||||
\(409\) | 2.00000 | − | 3.46410i | 0.0988936 | − | 0.171289i | −0.812333 | − | 0.583193i | \(-0.801803\pi\) |
0.911227 | + | 0.411905i | \(0.135136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.50000 | − | 12.9904i | −0.369948 | − | 0.640768i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 6.00000 | − | 5.19615i | 0.295241 | − | 0.255686i | ||||
\(414\) | −12.0000 | −0.589768 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | 1.00000 | + | 1.73205i | 0.0489116 | + | 0.0847174i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | −13.0000 | − | 22.5167i | −0.632830 | − | 1.09609i | ||||
\(423\) | 6.00000 | − | 10.3923i | 0.291730 | − | 0.505291i | ||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | 15.0000 | + | 25.9808i | 0.727607 | + | 1.26025i | ||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 3.50000 | + | 18.1865i | 0.169377 | + | 0.880108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.50000 | + | 4.33013i | 0.120701 | + | 0.209061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.50000 | + | 12.9904i | −0.361262 | + | 0.625725i | −0.988169 | − | 0.153370i | \(-0.950987\pi\) |
0.626907 | + | 0.779094i | \(0.284321\pi\) | |||||||
\(432\) | 2.50000 | + | 4.33013i | 0.120281 | + | 0.208333i | ||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 20.0000 | + | 6.92820i | 0.960031 | + | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | −6.00000 | + | 10.3923i | −0.287019 | + | 0.497131i | ||||
\(438\) | 5.00000 | − | 8.66025i | 0.238909 | − | 0.413803i | ||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | + | 13.8564i | −0.0952381 | + | 0.659829i | ||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | −1.00000 | + | 1.73205i | −0.0474579 | + | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.00000 | + | 8.66025i | 0.236757 | + | 0.410075i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 2.50000 | + | 0.866025i | 0.118114 | + | 0.0409159i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −5.00000 | − | 8.66025i | −0.235702 | − | 0.408248i | ||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −4.50000 | + | 7.79423i | −0.211662 | + | 0.366610i | ||||
\(453\) | 0.500000 | + | 0.866025i | 0.0234920 | + | 0.0406894i | ||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | −10.0000 | + | 17.3205i | −0.467269 | + | 0.809334i | ||||
\(459\) | 15.0000 | − | 25.9808i | 0.700140 | − | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.0000 | 1.81641 | 0.908206 | − | 0.418524i | \(-0.137453\pi\) | ||||
0.908206 | + | 0.418524i | \(0.137453\pi\) | |||||||
\(462\) | 2.00000 | − | 1.73205i | 0.0930484 | − | 0.0805823i | ||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0000 | − | 25.9808i | 0.694862 | − | 1.20354i | ||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | −10.0000 | −0.462250 | ||||||||
\(469\) | 26.0000 | − | 22.5167i | 1.20057 | − | 1.03972i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00000 | + | 3.46410i | 0.0921551 | + | 0.159617i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | 0.500000 | + | 0.866025i | 0.0229658 | + | 0.0397779i | ||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | −3.00000 | − | 15.5885i | −0.137505 | − | 0.714496i | ||||
\(477\) | 24.0000 | 1.09888 | ||||||||
\(478\) | −10.5000 | − | 18.1865i | −0.480259 | − | 0.831833i | ||||
\(479\) | 1.50000 | − | 2.59808i | 0.0685367 | − | 0.118709i | −0.829721 | − | 0.558179i | \(-0.811500\pi\) |
0.898257 | + | 0.439470i | \(0.144834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | − | 8.66025i | −0.227980 | − | 0.394874i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 15.0000 | + | 5.19615i | 0.682524 | + | 0.236433i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.00000 | + | 13.8564i | −0.362887 | + | 0.628539i | ||||
\(487\) | 2.00000 | − | 3.46410i | 0.0906287 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(488\) | 3.50000 | + | 6.06218i | 0.158438 | + | 0.274422i | ||||
\(489\) | 17.0000 | 0.768767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 3.00000 | + | 5.19615i | 0.135250 | + | 0.234261i | ||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | −5.00000 | + | 8.66025i | −0.224961 | + | 0.389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −30.0000 | − | 10.3923i | −1.34568 | − | 0.466159i | ||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −4.00000 | − | 6.92820i | −0.179065 | − | 0.310149i | 0.762496 | − | 0.646993i | \(-0.223974\pi\) |
−0.941560 | + | 0.336844i | \(0.890640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | −6.00000 | − | 10.3923i | −0.267793 | − | 0.463831i | ||||
\(503\) | 21.0000 | 0.936344 | 0.468172 | − | 0.883637i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883637i | \(0.344913\pi\) | |||||||
\(504\) | 1.00000 | + | 5.19615i | 0.0445435 | + | 0.231455i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | − | 17.3205i | 0.884748 | − | 0.766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.00000 | + | 8.66025i | 0.220755 | + | 0.382360i | ||||
\(514\) | −13.5000 | + | 23.3827i | −0.595459 | + | 1.03137i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | −4.00000 | + | 3.46410i | −0.175750 | + | 0.152204i | ||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | 6.00000 | 0.262111 | ||||||||
\(525\) | 2.50000 | + | 12.9904i | 0.109109 | + | 0.566947i | ||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | −24.0000 | − | 41.5692i | −1.04546 | − | 1.81078i | ||||
\(528\) | 0.500000 | − | 0.866025i | 0.0217597 | − | 0.0376889i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 5.00000 | + | 1.73205i | 0.216777 | + | 0.0750939i | ||||
\(533\) | −30.0000 | −1.29944 | ||||||||
\(534\) | −3.00000 | − | 5.19615i | −0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.50000 | − | 11.2583i | 0.280757 | − | 0.486286i | ||||
\(537\) | −4.50000 | − | 7.79423i | −0.194189 | − | 0.336346i | ||||
\(538\) | −24.0000 | −1.03471 | ||||||||
\(539\) | 6.50000 | − | 2.59808i | 0.279975 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50000 | − | 4.33013i | −0.107483 | − | 0.186167i | 0.807267 | − | 0.590187i | \(-0.200946\pi\) |
−0.914750 | + | 0.404020i | \(0.867613\pi\) | |||||||
\(542\) | 12.5000 | − | 21.6506i | 0.536921 | − | 0.929974i | ||||
\(543\) | 5.00000 | − | 8.66025i | 0.214571 | − | 0.371647i | ||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.5000 | + | 4.33013i | 0.534951 | + | 0.185312i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −7.50000 | − | 12.9904i | −0.320384 | − | 0.554922i | ||||
\(549\) | −7.00000 | + | 12.1244i | −0.298753 | + | 0.517455i | ||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | 6.00000 | 0.255377 | ||||||||
\(553\) | 0.500000 | + | 2.59808i | 0.0212622 | + | 0.110481i | ||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | 3.00000 | − | 5.19615i | 0.127114 | − | 0.220168i | −0.795443 | − | 0.606028i | \(-0.792762\pi\) |
0.922557 | + | 0.385860i | \(0.126095\pi\) | |||||||
\(558\) | 8.00000 | + | 13.8564i | 0.338667 | + | 0.586588i | ||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | −2.00000 | + | 1.73205i | −0.0839921 | + | 0.0727393i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 2.50000 | + | 4.33013i | 0.104530 | + | 0.181052i | ||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 3.00000 | + | 15.5885i | 0.125218 | + | 0.650650i | ||||
\(575\) | −30.0000 | −1.25109 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0000 | + | 5.19615i | 0.622305 | + | 0.215573i | ||||
\(582\) | −13.0000 | −0.538867 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 5.00000 | − | 8.66025i | 0.206901 | − | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | 9.00000 | 0.371470 | 0.185735 | − | 0.982600i | \(-0.440533\pi\) | ||||
0.185735 | + | 0.982600i | \(0.440533\pi\) | |||||||
\(588\) | 1.00000 | − | 6.92820i | 0.0412393 | − | 0.285714i | ||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.50000 | − | 7.79423i | 0.185105 | − | 0.320612i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | −12.0000 | − | 20.7846i | −0.492781 | − | 0.853522i | 0.507184 | − | 0.861838i | \(-0.330686\pi\) |
−0.999965 | + | 0.00831589i | \(0.997353\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −7.00000 | − | 12.1244i | −0.286491 | − | 0.496217i | ||||
\(598\) | −15.0000 | + | 25.9808i | −0.613396 | + | 1.06243i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 2.50000 | + | 4.33013i | 0.102062 | + | 0.176777i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 2.00000 | + | 10.3923i | 0.0815139 | + | 0.423559i | ||||
\(603\) | 26.0000 | 1.05880 | ||||||||
\(604\) | 0.500000 | + | 0.866025i | 0.0203447 | + | 0.0352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.50000 | + | 2.59808i | −0.0609333 | + | 0.105540i | ||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −6.00000 | + | 5.19615i | −0.243132 | + | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | − | 25.9808i | −0.606835 | − | 1.05107i | ||||
\(612\) | 6.00000 | − | 10.3923i | 0.242536 | − | 0.420084i | ||||
\(613\) | −13.0000 | + | 22.5167i | −0.525065 | + | 0.909439i | 0.474509 | + | 0.880251i | \(0.342626\pi\) |
−0.999574 | + | 0.0291886i | \(0.990708\pi\) | |||||||
\(614\) | −16.0000 | − | 27.7128i | −0.645707 | − | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 1.73205i | 0.0805823 | − | 0.0697863i | ||||
\(617\) | 21.0000 | 0.845428 | 0.422714 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422714 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(618\) | 2.00000 | + | 3.46410i | 0.0804518 | + | 0.139347i | ||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | + | 25.9808i | 0.601929 | + | 1.04257i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | −3.00000 | − | 15.5885i | −0.120192 | − | 0.624538i | ||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 3.50000 | − | 6.06218i | 0.139888 | − | 0.242293i | ||||
\(627\) | 1.00000 | − | 1.73205i | 0.0399362 | − | 0.0691714i | ||||
\(628\) | 2.00000 | + | 3.46410i | 0.0798087 | + | 0.138233i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0.500000 | + | 0.866025i | 0.0198889 | + | 0.0344486i | ||||
\(633\) | −13.0000 | + | 22.5167i | −0.516704 | + | 0.894957i | ||||
\(634\) | 12.0000 | − | 20.7846i | 0.476581 | − | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | 27.5000 | + | 21.6506i | 1.08959 | + | 0.857829i | ||||
\(638\) | −3.00000 | −0.118771 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0000 | −0.749287 | −0.374643 | − | 0.927169i | \(-0.622235\pi\) | ||||
−0.374643 | + | 0.927169i | \(0.622235\pi\) | |||||||
\(644\) | 15.0000 | + | 5.19615i | 0.591083 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | −18.0000 | + | 31.1769i | −0.707653 | + | 1.22569i | 0.258073 | + | 0.966126i | \(0.416913\pi\) |
−0.965726 | + | 0.259565i | \(0.916421\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −1.50000 | − | 2.59808i | −0.0588802 | − | 0.101983i | ||||
\(650\) | −25.0000 | −0.980581 | ||||||||
\(651\) | −4.00000 | − | 20.7846i | −0.156772 | − | 0.814613i | ||||
\(652\) | 17.0000 | 0.665771 | ||||||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | −7.00000 | + | 12.1244i | −0.273722 | + | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | + | 5.19615i | 0.117130 | + | 0.202876i | ||||
\(657\) | 20.0000 | 0.780274 | ||||||||
\(658\) | −12.0000 | + | 10.3923i | −0.467809 | + | 0.405134i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | − | 29.4449i | 0.661223 | − | 1.14527i | −0.319071 | − | 0.947731i | \(-0.603371\pi\) |
0.980294 | − | 0.197542i | \(-0.0632958\pi\) | |||||||
\(662\) | 6.50000 | − | 11.2583i | 0.252630 | − | 0.437567i | ||||
\(663\) | −15.0000 | − | 25.9808i | −0.582552 | − | 1.00901i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | −4.50000 | + | 7.79423i | −0.174110 | + | 0.301568i | ||||
\(669\) | 5.00000 | − | 8.66025i | 0.193311 | − | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.00000 | 0.270232 | ||||||||
\(672\) | −0.500000 | − | 2.59808i | −0.0192879 | − | 0.100223i | ||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | 11.0000 | + | 19.0526i | 0.423704 | + | 0.733877i | ||||
\(675\) | −12.5000 | + | 21.6506i | −0.481125 | + | 0.833333i | ||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | −21.0000 | − | 36.3731i | −0.807096 | − | 1.39793i | −0.914867 | − | 0.403755i | \(-0.867705\pi\) |
0.107772 | − | 0.994176i | \(-0.465628\pi\) | |||||||
\(678\) | 9.00000 | 0.345643 | ||||||||
\(679\) | −32.5000 | − | 11.2583i | −1.24724 | − | 0.432055i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | + | 5.19615i | 0.114960 | + | 0.199117i | ||||
\(682\) | 4.00000 | − | 6.92820i | 0.153168 | − | 0.265295i | ||||
\(683\) | 22.5000 | − | 38.9711i | 0.860939 | − | 1.49119i | −0.0100856 | − | 0.999949i | \(-0.503210\pi\) |
0.871024 | − | 0.491240i | \(-0.163456\pi\) | |||||||
\(684\) | 2.00000 | + | 3.46410i | 0.0764719 | + | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 20.0000 | 0.763048 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 30.0000 | − | 51.9615i | 1.14291 | − | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5000 | − | 30.3109i | −0.665731 | − | 1.15308i | −0.979086 | − | 0.203445i | \(-0.934786\pi\) |
0.313355 | − | 0.949636i | \(-0.398547\pi\) | |||||||
\(692\) | −15.0000 | −0.570214 | ||||||||
\(693\) | 5.00000 | + | 1.73205i | 0.189934 | + | 0.0657952i | ||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | 17.0000 | + | 29.4449i | 0.643459 | + | 1.11450i | ||||
\(699\) | −30.0000 | −1.13470 | ||||||||
\(700\) | 2.50000 | + | 12.9904i | 0.0944911 | + | 0.490990i | ||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | 12.5000 | + | 21.6506i | 0.471782 | + | 0.817151i | ||||
\(703\) | −2.00000 | + | 3.46410i | −0.0754314 | + | 0.130651i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.0000 | 1.12906 | ||||||||
\(707\) | −6.00000 | + | 5.19615i | −0.225653 | + | 0.195421i | ||||
\(708\) | −3.00000 | −0.112747 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | + | 1.73205i | −0.0375029 | + | 0.0649570i | ||||
\(712\) | −3.00000 | − | 5.19615i | −0.112430 | − | 0.194734i | ||||
\(713\) | 48.0000 | 1.79761 | ||||||||
\(714\) | −12.0000 | + | 10.3923i | −0.449089 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.50000 | − | 7.79423i | −0.168173 | − | 0.291284i | ||||
\(717\) | −10.5000 | + | 18.1865i | −0.392130 | + | 0.679189i | ||||
\(718\) | 4.50000 | − | 7.79423i | 0.167939 | − | 0.290878i | ||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | + | 10.3923i | 0.0744839 | + | 0.387030i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 5.00000 | + | 8.66025i | 0.185952 | + | 0.322078i | ||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | 7.50000 | − | 12.9904i | 0.278543 | − | 0.482451i | ||||
\(726\) | −0.500000 | − | 0.866025i | −0.0185567 | − | 0.0321412i | ||||
\(727\) | 50.0000 | 1.85440 | 0.927199 | − | 0.374570i | \(-0.122210\pi\) | ||||
0.927199 | + | 0.374570i | \(0.122210\pi\) | |||||||
\(728\) | 12.5000 | + | 4.33013i | 0.463281 | + | 0.160485i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | 3.50000 | − | 6.06218i | 0.129364 | − | 0.224065i | ||||
\(733\) | 21.5000 | + | 37.2391i | 0.794121 | + | 1.37546i | 0.923396 | + | 0.383849i | \(0.125402\pi\) |
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 38.0000 | 1.40261 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | −6.50000 | − | 11.2583i | −0.239431 | − | 0.414706i | ||||
\(738\) | −6.00000 | + | 10.3923i | −0.220863 | + | 0.382546i | ||||
\(739\) | −1.00000 | + | 1.73205i | −0.0367856 | + | 0.0637145i | −0.883832 | − | 0.467804i | \(-0.845045\pi\) |
0.847046 | + | 0.531519i | \(0.178379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0000 | 0.367359 | ||||||||
\(742\) | −30.0000 | − | 10.3923i | −1.10133 | − | 0.381514i | ||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | −4.00000 | − | 6.92820i | −0.146647 | − | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.50000 | + | 9.52628i | −0.201369 | + | 0.348782i | ||||
\(747\) | 6.00000 | + | 10.3923i | 0.219529 | + | 0.380235i | ||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | −3.00000 | + | 5.19615i | −0.109399 | + | 0.189484i | ||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | −7.50000 | − | 12.9904i | −0.273134 | − | 0.473082i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.0000 | − | 8.66025i | 0.363696 | − | 0.314970i | ||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 12.5000 | + | 21.6506i | 0.454020 | + | 0.786386i | ||||
\(759\) | 3.00000 | − | 5.19615i | 0.108893 | − | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | − | 25.9808i | −0.543750 | − | 0.941802i | −0.998684 | − | 0.0512772i | \(-0.983671\pi\) |
0.454935 | − | 0.890525i | \(-0.349663\pi\) | |||||||
\(762\) | −13.0000 | −0.470940 | ||||||||
\(763\) | −28.0000 | + | 24.2487i | −1.01367 | + | 0.877862i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | + | 10.3923i | −0.216789 | + | 0.375489i | ||||
\(767\) | 7.50000 | − | 12.9904i | 0.270809 | − | 0.469055i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.0000 | 0.972381 | ||||||||
\(772\) | 11.0000 | + | 19.0526i | 0.395899 | + | 0.685717i | ||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | −4.00000 | + | 6.92820i | −0.143777 | + | 0.249029i | ||||
\(775\) | 20.0000 | + | 34.6410i | 0.718421 | + | 1.24434i | ||||
\(776\) | −13.0000 | −0.466673 | ||||||||
\(777\) | 5.00000 | + | 1.73205i | 0.179374 | + | 0.0621370i | ||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 10.3923i | −0.214697 | + | 0.371866i | ||||
\(782\) | −18.0000 | − | 31.1769i | −0.643679 | − | 1.11488i | ||||
\(783\) | −15.0000 | −0.536056 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00000 | − | 5.19615i | −0.107006 | − | 0.185341i | ||||
\(787\) | −7.00000 | + | 12.1244i | −0.249523 | + | 0.432187i | −0.963394 | − | 0.268091i | \(-0.913607\pi\) |
0.713871 | + | 0.700278i | \(0.246941\pi\) | |||||||
\(788\) | 4.50000 | − | 7.79423i | 0.160306 | − | 0.277658i | ||||
\(789\) | 1.50000 | + | 2.59808i | 0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.5000 | + | 7.79423i | 0.800008 | + | 0.277131i | ||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 17.5000 | + | 30.3109i | 0.621443 | + | 1.07637i | ||||
\(794\) | −1.00000 | + | 1.73205i | −0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | −1.00000 | − | 5.19615i | −0.0353996 | − | 0.183942i | ||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 2.50000 | + | 4.33013i | 0.0883883 | + | 0.153093i | ||||
\(801\) | 6.00000 | − | 10.3923i | 0.212000 | − | 0.367194i | ||||
\(802\) | 4.50000 | − | 7.79423i | 0.158901 | − | 0.275224i | ||||
\(803\) | −5.00000 | − | 8.66025i | −0.176446 | − | 0.305614i | ||||
\(804\) | −13.0000 | −0.458475 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.0000 | 1.40894 | ||||||||
\(807\) | 12.0000 | + | 20.7846i | 0.422420 | + | 0.731653i | ||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | −18.0000 | + | 31.1769i | −0.632846 | + | 1.09612i | 0.354121 | + | 0.935200i | \(0.384780\pi\) |
−0.986967 | + | 0.160922i | \(0.948553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −6.00000 | + | 5.19615i | −0.210559 | + | 0.182349i | ||||
\(813\) | −25.0000 | −0.876788 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 4.00000 | + | 6.92820i | 0.139942 | + | 0.242387i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 5.00000 | + | 25.9808i | 0.174714 | + | 0.907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | − | 23.3827i | −0.471153 | − | 0.816061i | 0.528302 | − | 0.849056i | \(-0.322829\pi\) |
−0.999456 | + | 0.0329950i | \(0.989495\pi\) | |||||||
\(822\) | −7.50000 | + | 12.9904i | −0.261593 | + | 0.453092i | ||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | 5.00000 | 0.174078 | ||||||||
\(826\) | −7.50000 | − | 2.59808i | −0.260958 | − | 0.0903986i | ||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 6.00000 | + | 10.3923i | 0.208514 | + | 0.361158i | ||||
\(829\) | 8.00000 | − | 13.8564i | 0.277851 | − | 0.481253i | −0.692999 | − | 0.720938i | \(-0.743711\pi\) |
0.970851 | + | 0.239686i | \(0.0770444\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.500000 | + | 0.866025i | 0.0173448 | + | 0.0300421i | ||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | −39.0000 | + | 15.5885i | −1.35127 | + | 0.540108i | ||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.00000 | − | 1.73205i | 0.0345857 | − | 0.0599042i | ||||
\(837\) | 20.0000 | − | 34.6410i | 0.691301 | − | 1.19737i | ||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 8.00000 | + | 13.8564i | 0.275698 | + | 0.477523i | ||||
\(843\) | 3.00000 | − | 5.19615i | 0.103325 | − | 0.178965i | ||||
\(844\) | −13.0000 | + | 22.5167i | −0.447478 | + | 0.775055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | −0.500000 | − | 2.59808i | −0.0171802 | − | 0.0892710i | ||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | 11.0000 | + | 19.0526i | 0.377519 | + | 0.653882i | ||||
\(850\) | 15.0000 | − | 25.9808i | 0.514496 | − | 0.891133i | ||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | 6.00000 | + | 10.3923i | 0.205557 | + | 0.356034i | ||||
\(853\) | −58.0000 | −1.98588 | −0.992941 | − | 0.118609i | \(-0.962157\pi\) | ||||
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 14.0000 | − | 12.1244i | 0.479070 | − | 0.414887i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0000 | + | 41.5692i | −0.819824 | + | 1.41998i | 0.0859870 | + | 0.996296i | \(0.472596\pi\) |
−0.905811 | + | 0.423681i | \(0.860738\pi\) | |||||||
\(858\) | 2.50000 | − | 4.33013i | 0.0853486 | − | 0.147828i | ||||
\(859\) | −17.5000 | − | 30.3109i | −0.597092 | − | 1.03419i | −0.993248 | − | 0.116011i | \(-0.962989\pi\) |
0.396156 | − | 0.918183i | \(-0.370344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 10.3923i | 0.408959 | − | 0.354169i | ||||
\(862\) | 15.0000 | 0.510902 | ||||||||
\(863\) | −3.00000 | − | 5.19615i | −0.102121 | − | 0.176879i | 0.810437 | − | 0.585826i | \(-0.199230\pi\) |
−0.912558 | + | 0.408946i | \(0.865896\pi\) | |||||||
\(864\) | 2.50000 | − | 4.33013i | 0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.00000 | − | 12.1244i | −0.237870 | − | 0.412002i | ||||
\(867\) | 19.0000 | 0.645274 | ||||||||
\(868\) | −4.00000 | − | 20.7846i | −0.135769 | − | 0.705476i | ||||
\(869\) | 1.00000 | 0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.5000 | − | 56.2917i | 1.10122 | − | 1.90737i | ||||
\(872\) | −7.00000 | + | 12.1244i | −0.237050 | + | 0.410582i | ||||
\(873\) | −13.0000 | − | 22.5167i | −0.439983 | − | 0.762073i | ||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 18.5000 | + | 32.0429i | 0.624701 | + | 1.08201i | 0.988599 | + | 0.150574i | \(0.0481123\pi\) |
−0.363898 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(878\) | 9.50000 | − | 16.4545i | 0.320609 | − | 0.555312i | ||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | 13.0000 | − | 5.19615i | 0.437733 | − | 0.174964i | ||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −15.0000 | − | 25.9808i | −0.504505 | − | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | −28.5000 | − | 49.3634i | −0.956936 | − | 1.65746i | −0.729873 | − | 0.683582i | \(-0.760421\pi\) |
−0.227063 | − | 0.973880i | \(-0.572912\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −32.5000 | − | 11.2583i | −1.09002 | − | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 5.00000 | − | 8.66025i | 0.167412 | − | 0.289967i | ||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 3.00000 | + | 5.19615i | 0.100335 | + | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | 30.0000 | 1.00167 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | −12.0000 | + | 20.7846i | −0.400222 | + | 0.693206i | ||||
\(900\) | −5.00000 | + | 8.66025i | −0.166667 | + | 0.288675i | ||||
\(901\) | 36.0000 | + | 62.3538i | 1.19933 | + | 2.07731i | ||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 8.00000 | − | 6.92820i | 0.266223 | − | 0.230556i | ||||
\(904\) | 9.00000 | 0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.500000 | − | 0.866025i | 0.0166114 | − | 0.0287718i | ||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | 3.00000 | + | 5.19615i | 0.0995585 | + | 0.172440i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | 11.0000 | − | 19.0526i | 0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | −3.00000 | − | 15.5885i | −0.0990687 | − | 0.514776i | ||||
\(918\) | −30.0000 | −0.990148 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | + | 27.7128i | −0.527218 | + | 0.913168i | ||||
\(922\) | −19.5000 | − | 33.7750i | −0.642198 | − | 1.11232i | ||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | −2.50000 | − | 0.866025i | −0.0822440 | − | 0.0284901i | ||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | −13.0000 | − | 22.5167i | −0.427207 | − | 0.739943i | ||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | −1.50000 | + | 2.59808i | −0.0492399 | + | 0.0852860i | ||||
\(929\) | −7.50000 | − | 12.9904i | −0.246067 | − | 0.426201i | 0.716364 | − | 0.697727i | \(-0.245805\pi\) |
−0.962431 | + | 0.271526i | \(0.912472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | − | 13.8564i | 0.0655474 | − | 0.454125i | ||||
\(932\) | −30.0000 | −0.982683 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.00000 | + | 8.66025i | 0.163430 | + | 0.283069i | ||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | −32.5000 | − | 11.2583i | −1.06116 | − | 0.367598i | ||||
\(939\) | −7.00000 | −0.228436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5000 | − | 23.3827i | 0.440087 | − | 0.762254i | −0.557608 | − | 0.830104i | \(-0.688281\pi\) |
0.997695 | + | 0.0678506i | \(0.0216141\pi\) | |||||||
\(942\) | 2.00000 | − | 3.46410i | 0.0651635 | − | 0.112867i | ||||
\(943\) | 18.0000 | + | 31.1769i | 0.586161 | + | 1.01526i | ||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 12.0000 | + | 20.7846i | 0.389948 | + | 0.675409i | 0.992442 | − | 0.122714i | \(-0.0391598\pi\) |
−0.602494 | + | 0.798123i | \(0.705826\pi\) | |||||||
\(948\) | 0.500000 | − | 0.866025i | 0.0162392 | − | 0.0281272i | ||||
\(949\) | 25.0000 | − | 43.3013i | 0.811534 | − | 1.40562i | ||||
\(950\) | 5.00000 | + | 8.66025i | 0.162221 | + | 0.280976i | ||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | −12.0000 | + | 10.3923i | −0.388922 | + | 0.336817i | ||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | −12.0000 | − | 20.7846i | −0.388514 | − | 0.672927i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.5000 | + | 18.1865i | −0.339594 | + | 0.588195i | ||||
\(957\) | 1.50000 | + | 2.59808i | 0.0484881 | + | 0.0839839i | ||||
\(958\) | −3.00000 | −0.0969256 | ||||||||
\(959\) | −30.0000 | + | 25.9808i | −0.968751 | + | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −5.00000 | + | 8.66025i | −0.161206 | + | 0.279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.00000 | − | 15.5885i | −0.0965234 | − | 0.501550i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | −6.00000 | + | 10.3923i | −0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5000 | + | 28.5788i | 0.529510 | + | 0.917139i | 0.999408 | + | 0.0344175i | \(0.0109576\pi\) |
−0.469897 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(972\) | 16.0000 | 0.513200 | ||||||||
\(973\) | −10.0000 | − | 3.46410i | −0.320585 | − | 0.111054i | ||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | 12.5000 | + | 21.6506i | 0.400320 | + | 0.693375i | ||||
\(976\) | 3.50000 | − | 6.06218i | 0.112032 | − | 0.194046i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | −8.50000 | − | 14.7224i | −0.271800 | − | 0.470771i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0000 | −0.893971 | ||||||||
\(982\) | 15.0000 | + | 25.9808i | 0.478669 | + | 0.829079i | ||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | 15.0000 | + | 5.19615i | 0.477455 | + | 0.165395i | ||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | −4.00000 | − | 6.92820i | −0.127000 | − | 0.219971i | ||||
\(993\) | −13.0000 | −0.412543 | ||||||||
\(994\) | 6.00000 | + | 31.1769i | 0.190308 | + | 0.988872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | − | 5.19615i | −0.0950586 | − | 0.164646i | ||||
\(997\) | 23.0000 | − | 39.8372i | 0.728417 | − | 1.26166i | −0.229135 | − | 0.973395i | \(-0.573590\pi\) |
0.957552 | − | 0.288261i | \(-0.0930771\pi\) | |||||||
\(998\) | −4.00000 | + | 6.92820i | −0.126618 | + | 0.219308i | ||||
\(999\) | 5.00000 | + | 8.66025i | 0.158193 | + | 0.273998i |
(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 | 154.2.e.b.67.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.n.991.1 | 2 | |||
4.3 | odd | 2 | 1232.2.q.c.529.1 | 2 | |||
7.2 | even | 3 | inner | 154.2.e.b.23.1 | ✓ | 2 | |
7.3 | odd | 6 | 1078.2.a.i.1.1 | 1 | |||
7.4 | even | 3 | 1078.2.a.k.1.1 | 1 | |||
7.5 | odd | 6 | 1078.2.e.d.177.1 | 2 | |||
7.6 | odd | 2 | 1078.2.e.d.67.1 | 2 | |||
21.2 | odd | 6 | 1386.2.k.n.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.o.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.l.1.1 | 1 | |||
28.3 | even | 6 | 8624.2.a.t.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.l.1.1 | 1 | |||
28.23 | odd | 6 | 1232.2.q.c.177.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.b.23.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
154.2.e.b.67.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1078.2.a.i.1.1 | 1 | 7.3 | odd | 6 | |||
1078.2.a.k.1.1 | 1 | 7.4 | even | 3 | |||
1078.2.e.d.67.1 | 2 | 7.6 | odd | 2 | |||
1078.2.e.d.177.1 | 2 | 7.5 | odd | 6 | |||
1232.2.q.c.177.1 | 2 | 28.23 | odd | 6 | |||
1232.2.q.c.529.1 | 2 | 4.3 | odd | 2 | |||
1386.2.k.n.793.1 | 2 | 21.2 | odd | 6 | |||
1386.2.k.n.991.1 | 2 | 3.2 | odd | 2 | |||
8624.2.a.l.1.1 | 1 | 28.11 | odd | 6 | |||
8624.2.a.t.1.1 | 1 | 28.3 | even | 6 | |||
9702.2.a.l.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.o.1.1 | 1 | 21.11 | odd | 6 |