Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(193,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7318940317\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.961 |
Dual form | 1344.2.q.c.193.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 7.79423i | 0.808224 | + | 1.39988i | 0.914093 | + | 0.405505i | \(0.132904\pi\) |
−0.105869 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 5.19615i | −0.169031 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | − | 2.59808i | 0.246598 | − | 0.427121i | −0.715981 | − | 0.698119i | \(-0.754020\pi\) |
0.962580 | + | 0.270998i | \(0.0873538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | + | 10.3923i | 0.824163 | + | 1.42749i | 0.902557 | + | 0.430570i | \(0.141688\pi\) |
−0.0783936 | + | 0.996922i | \(0.524979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | − | 8.66025i | 0.640184 | − | 1.10883i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.985391 | − | 0.170305i | \(-0.0544754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.50000 | + | 4.33013i | 0.305424 | + | 0.529009i | 0.977356 | − | 0.211604i | \(-0.0678686\pi\) |
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 2.59808i | 0.175562 | + | 0.304082i | 0.940356 | − | 0.340193i | \(-0.110493\pi\) |
−0.764794 | + | 0.644275i | \(0.777159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 3.46410i | 0.455842 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | + | 3.46410i | 0.214423 | + | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.00000 | + | 13.8564i | −0.847998 | + | 1.46878i | 0.0349934 | + | 0.999388i | \(0.488859\pi\) |
−0.882992 | + | 0.469389i | \(0.844474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50000 | − | 7.79423i | 0.466628 | − | 0.808224i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.50000 | + | 6.06218i | −0.344865 | + | 0.597324i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.00000 | − | 1.73205i | 0.487950 | − | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | − | 6.92820i | 0.386695 | − | 0.669775i | −0.605308 | − | 0.795991i | \(-0.706950\pi\) |
0.992003 | + | 0.126217i | \(0.0402834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50000 | + | 7.79423i | 0.431022 | + | 0.746552i | 0.996962 | − | 0.0778949i | \(-0.0248199\pi\) |
−0.565940 | + | 0.824447i | \(0.691487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0000 | 1.33103 | 0.665517 | − | 0.746382i | \(-0.268211\pi\) | ||||
0.665517 | + | 0.746382i | \(0.268211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.50000 | − | 4.33013i | −0.220113 | − | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | + | 2.59808i | −0.0433555 | + | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | + | 1.73205i | −0.0860663 | + | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | −0.254457 | −0.127228 | − | 0.991873i | \(-0.540608\pi\) | ||||
−0.127228 | + | 0.991873i | \(0.540608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 6.92820i | 0.332182 | − | 0.575356i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.0000 | −1.44579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | + | 3.46410i | 0.155700 | + | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.0000 | 1.08335 | 0.541676 | − | 0.840587i | \(-0.317790\pi\) | ||||
0.541676 | + | 0.840587i | \(0.317790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.00000 | − | 6.92820i | 0.304114 | − | 0.526742i | −0.672949 | − | 0.739689i | \(-0.734973\pi\) |
0.977064 | + | 0.212947i | \(0.0683062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | − | 10.3923i | 0.450988 | − | 0.781133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00000 | − | 1.73205i | −0.0747435 | − | 0.129460i | 0.826231 | − | 0.563331i | \(-0.190480\pi\) |
−0.900975 | + | 0.433872i | \(0.857147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | − | 9.52628i | −0.395899 | − | 0.685717i | 0.597317 | − | 0.802005i | \(-0.296234\pi\) |
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0000 | −1.13995 | −0.569976 | − | 0.821661i | \(-0.693048\pi\) | ||||
−0.569976 | + | 0.821661i | \(0.693048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.50000 | − | 4.33013i | 0.176336 | − | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0000 | + | 3.46410i | −0.701862 | + | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | − | 17.3205i | 0.698430 | − | 1.20972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | − | 5.19615i | −0.205557 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | + | 15.5885i | 1.22192 | + | 1.05821i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50000 | − | 2.59808i | 0.101361 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.50000 | + | 16.4545i | −0.627778 | + | 1.08734i | 0.360219 | + | 0.932868i | \(0.382702\pi\) |
−0.987997 | + | 0.154475i | \(0.950631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | − | 5.19615i | 0.0657952 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | − | 10.3923i | −0.391397 | − | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | + | 13.8564i | 0.127775 | + | 0.885253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.500000 | − | 0.866025i | 0.0318142 | − | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0000 | + | 22.5167i | −0.810918 | + | 1.40455i | 0.101305 | + | 0.994855i | \(0.467698\pi\) |
−0.912222 | + | 0.409695i | \(0.865635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50000 | − | 7.79423i | 0.0932055 | − | 0.484310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | − | 3.46410i | 0.123797 | − | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.00000 | + | 3.46410i | 0.123325 | + | 0.213606i | 0.921077 | − | 0.389380i | \(-0.127311\pi\) |
−0.797752 | + | 0.602986i | \(0.793977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0000 | −1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0000 | 0.979184 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | + | 1.73205i | 0.121046 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.00000 | −0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.50000 | + | 9.52628i | 0.326941 | + | 0.566279i | 0.981903 | − | 0.189383i | \(-0.0606488\pi\) |
−0.654962 | + | 0.755662i | \(0.727315\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | + | 1.73205i | −0.0592349 | + | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.0000 | + | 8.66025i | −1.47570 | + | 0.511199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.00000 | −0.467365 | −0.233682 | − | 0.972313i | \(-0.575078\pi\) | ||||
−0.233682 | + | 0.972313i | \(0.575078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5000 | − | 4.33013i | 0.720488 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00000 | − | 1.73205i | 0.0574485 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.0000 | + | 17.3205i | 0.572598 | + | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0000 | −0.970241 | −0.485121 | − | 0.874447i | \(-0.661224\pi\) | ||||
−0.485121 | + | 0.874447i | \(0.661224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.00000 | 0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | − | 3.46410i | −0.225374 | − | 0.195180i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0000 | − | 20.7846i | 0.673987 | − | 1.16738i | −0.302777 | − | 0.953062i | \(-0.597914\pi\) |
0.976764 | − | 0.214318i | \(-0.0687530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | − | 0.866025i | −0.0277350 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.50000 | − | 7.79423i | 0.248851 | − | 0.431022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | + | 15.5885i | −0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5000 | − | 21.6506i | 0.687062 | − | 1.19003i | −0.285722 | − | 0.958313i | \(-0.592233\pi\) |
0.972784 | − | 0.231714i | \(-0.0744333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50000 | + | 2.59808i | 0.0821995 | + | 0.142374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0000 | −0.546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.00000 | − | 8.66025i | −0.271563 | − | 0.470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.00000 | + | 15.5885i | −0.487377 | + | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.0000 | − | 27.7128i | −0.858925 | − | 1.48770i | −0.872955 | − | 0.487800i | \(-0.837799\pi\) |
0.0140303 | − | 0.999902i | \(-0.495534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0000 | − | 29.4449i | −0.904819 | − | 1.56719i | −0.821160 | − | 0.570697i | \(-0.806673\pi\) |
−0.0836583 | − | 0.996495i | \(-0.526660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0000 | − | 17.3205i | 0.527780 | − | 0.914141i | −0.471696 | − | 0.881761i | \(-0.656358\pi\) |
0.999476 | − | 0.0323801i | \(-0.0103087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.50000 | − | 7.79423i | −0.234898 | − | 0.406855i | 0.724345 | − | 0.689438i | \(-0.242142\pi\) |
−0.959243 | + | 0.282582i | \(0.908809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.00000 | − | 8.66025i | 0.260290 | − | 0.450835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000 | + | 20.7846i | 1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5000 | − | 19.9186i | 0.595447 | − | 1.03135i | −0.398036 | − | 0.917370i | \(-0.630308\pi\) |
0.993484 | − | 0.113975i | \(-0.0363585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.00000 | + | 10.3923i | 0.309839 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.00000 | 0.154100 | 0.0770498 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770498 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.50000 | − | 12.9904i | −0.384237 | − | 0.665517i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | + | 10.3923i | −0.306586 | + | 0.531022i | −0.977613 | − | 0.210411i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | + | 3.46410i | −0.509647 | + | 0.176547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.50000 | + | 4.33013i | −0.127082 | + | 0.220113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.0000 | −0.706207 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | − | 1.73205i | −0.0503155 | − | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.50000 | + | 7.79423i | −0.225849 | + | 0.391181i | −0.956574 | − | 0.291491i | \(-0.905849\pi\) |
0.730725 | + | 0.682672i | \(0.239182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.50000 | − | 0.866025i | 0.125157 | − | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | − | 31.1769i | 0.898877 | − | 1.55690i | 0.0699455 | − | 0.997551i | \(-0.477717\pi\) |
0.828932 | − | 0.559350i | \(-0.188949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | − | 7.79423i | −0.224161 | − | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | − | 4.33013i | −0.123617 | − | 0.214111i | 0.797574 | − | 0.603220i | \(-0.206116\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | + | 20.7846i | 1.18096 | + | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.50000 | + | 2.59808i | 0.0734553 | + | 0.127228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.00000 | 0.341159 | 0.170580 | − | 0.985344i | \(-0.445436\pi\) | ||||
0.170580 | + | 0.985344i | \(0.445436\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00000 | − | 25.9808i | 0.241967 | − | 1.25730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | + | 1.73205i | −0.0482805 | + | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | − | 15.5885i | −0.433515 | − | 0.750870i | 0.563658 | − | 0.826008i | \(-0.309393\pi\) |
−0.997173 | + | 0.0751385i | \(0.976060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0000 | 1.48976 | 0.744882 | − | 0.667196i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667196i | \(0.232506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | + | 10.3923i | −0.285069 | + | 0.493753i | −0.972626 | − | 0.232377i | \(-0.925350\pi\) |
0.687557 | + | 0.726130i | \(0.258683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | − | 27.7128i | −0.758473 | − | 1.31371i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | + | 13.8564i | −0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | − | 5.19615i | 0.0468807 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50000 | − | 9.52628i | 0.257279 | − | 0.445621i | −0.708233 | − | 0.705979i | \(-0.750507\pi\) |
0.965512 | + | 0.260358i | \(0.0838407\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0000 | −0.931493 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.00000 | + | 15.5885i | 0.417365 | + | 0.722897i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00000 | + | 5.19615i | −0.138823 | + | 0.240449i | −0.927052 | − | 0.374934i | \(-0.877665\pi\) |
0.788228 | + | 0.615383i | \(0.210999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 8.66025i | 0.461757 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0000 | − | 24.2487i | −0.639676 | − | 1.10795i | −0.985504 | − | 0.169654i | \(-0.945735\pi\) |
0.345827 | − | 0.938298i | \(-0.387598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50000 | + | 2.59808i | −0.0683941 | + | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | − | 10.3923i | 0.272446 | − | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5000 | + | 26.8468i | 0.702372 | + | 1.21654i | 0.967632 | + | 0.252367i | \(0.0812090\pi\) |
−0.265260 | + | 0.964177i | \(0.585458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.0000 | −1.26362 | −0.631811 | − | 0.775122i | \(-0.717688\pi\) | ||||
−0.631811 | + | 0.775122i | \(0.717688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | − | 3.46410i | 0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.0000 | − | 5.19615i | 0.672842 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5000 | + | 32.0429i | −0.828174 | + | 1.43444i | 0.0712957 | + | 0.997455i | \(0.477287\pi\) |
−0.899469 | + | 0.436984i | \(0.856047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00000 | − | 12.1244i | −0.312737 | − | 0.541676i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.0000 | 1.87269 | 0.936344 | − | 0.351085i | \(-0.114187\pi\) | ||||
0.936344 | + | 0.351085i | \(0.114187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | + | 10.3923i | 0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 5.19615i | 0.265424 | + | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.00000 | − | 12.1244i | −0.308457 | − | 0.534263i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.00000 | −0.351161 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | − | 10.3923i | −0.262865 | − | 0.455295i | 0.704137 | − | 0.710064i | \(-0.251334\pi\) |
−0.967002 | + | 0.254769i | \(0.918001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5000 | + | 26.8468i | −0.677768 | + | 1.17393i | 0.297884 | + | 0.954602i | \(0.403719\pi\) |
−0.975652 | + | 0.219326i | \(0.929614\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.500000 | − | 2.59808i | 0.0218218 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0000 | 0.433148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | + | 13.8564i | 0.345870 | + | 0.599065i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.00000 | + | 1.73205i | −0.0431532 | + | 0.0747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.0000 | + | 5.19615i | 0.559950 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.50000 | + | 16.4545i | −0.408437 | + | 0.707433i | −0.994715 | − | 0.102677i | \(-0.967259\pi\) |
0.586278 | + | 0.810110i | \(0.300593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.50000 | + | 11.2583i | 0.278942 | + | 0.483141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0000 | −0.771035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | − | 3.46410i | 0.0852029 | − | 0.147576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00000 | − | 5.19615i | 0.127343 | − | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00000 | − | 1.73205i | −0.0423714 | − | 0.0733893i | 0.844062 | − | 0.536246i | \(-0.180158\pi\) |
−0.886433 | + | 0.462856i | \(0.846825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0000 | + | 22.5167i | 0.547885 | + | 0.948964i | 0.998419 | + | 0.0562051i | \(0.0179001\pi\) |
−0.450535 | + | 0.892759i | \(0.648767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0000 | + | 17.3205i | −0.420703 | + | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | − | 1.73205i | −0.0839921 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0000 | − | 22.5167i | 0.544988 | − | 0.943948i | −0.453619 | − | 0.891196i | \(-0.649867\pi\) |
0.998608 | − | 0.0527519i | \(-0.0167993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | + | 16.4545i | 0.397563 | + | 0.688599i | 0.993425 | − | 0.114488i | \(-0.0365228\pi\) |
−0.595862 | + | 0.803087i | \(0.703189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.0000 | −0.417756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | + | 14.7224i | 0.353860 | + | 0.612903i | 0.986922 | − | 0.161198i | \(-0.0515357\pi\) |
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.50000 | + | 9.52628i | −0.228572 | + | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0000 | − | 5.19615i | 0.622305 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 20.7846i | −0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | + | 1.73205i | 0.0413449 | + | 0.0716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.0000 | 0.660391 | 0.330195 | − | 0.943913i | \(-0.392885\pi\) | ||||
0.330195 | + | 0.943913i | \(0.392885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.00000 | + | 13.8564i | 0.329076 | + | 0.569976i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00000 | − | 5.19615i | 0.123195 | − | 0.213380i | −0.797831 | − | 0.602881i | \(-0.794019\pi\) |
0.921026 | + | 0.389501i | \(0.127353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.00000 | −0.203616 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5000 | − | 19.9186i | 0.466771 | − | 0.808470i | −0.532509 | − | 0.846424i | \(-0.678751\pi\) |
0.999279 | + | 0.0379540i | \(0.0120840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | + | 6.92820i | 0.324176 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | + | 29.4449i | 0.686624 | + | 1.18927i | 0.972924 | + | 0.231127i | \(0.0742412\pi\) |
−0.286300 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.0000 | −0.806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | + | 41.5692i | −0.320513 | + | 1.66544i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.00000 | + | 1.73205i | 0.0399362 | + | 0.0691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.00000 | − | 3.46410i | −0.0794929 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.0000 | + | 25.9808i | −0.595257 | + | 1.03102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0000 | −0.749287 | −0.374643 | − | 0.927169i | \(-0.622235\pi\) | ||||
−0.374643 | + | 0.927169i | \(0.622235\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.00000 | + | 1.73205i | 0.0393141 | + | 0.0680939i | 0.885013 | − | 0.465566i | \(-0.154149\pi\) |
−0.845699 | + | 0.533660i | \(0.820816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | + | 20.7846i | −0.471041 | + | 0.815867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.50000 | − | 23.3827i | 0.176369 | − | 0.916440i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.0000 | + | 24.2487i | 0.547025 | + | 0.947476i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | −0.117041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5000 | − | 35.5070i | −0.797358 | − | 1.38106i | −0.921331 | − | 0.388778i | \(-0.872897\pi\) |
0.123974 | − | 0.992286i | \(-0.460436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | − | 3.46410i | −0.155113 | − | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.0000 | 0.772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0000 | −1.58043 | −0.790217 | − | 0.612827i | \(-0.790032\pi\) | ||||
−0.790217 | + | 0.612827i | \(0.790032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | − | 10.3923i | 0.230599 | − | 0.399409i | −0.727386 | − | 0.686229i | \(-0.759265\pi\) |
0.957984 | + | 0.286820i | \(0.0925982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0000 | + | 5.19615i | −0.575647 | + | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | + | 15.5885i | −0.344881 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0000 | −0.916993 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.0000 | 0.724895 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5000 | − | 32.0429i | 0.703773 | − | 1.21897i | −0.263359 | − | 0.964698i | \(-0.584830\pi\) |
0.967132 | − | 0.254273i | \(-0.0818362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.00000 | + | 1.73205i | −0.189934 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.00000 | − | 5.19615i | 0.113796 | − | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.50000 | + | 2.59808i | 0.0565736 | + | 0.0979883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | + | 10.3923i | −0.225973 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.00000 | + | 3.46410i | 0.150435 | + | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0000 | − | 25.9808i | 0.563337 | − | 0.975728i | −0.433865 | − | 0.900978i | \(-0.642851\pi\) |
0.997202 | − | 0.0747503i | \(-0.0238160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.500000 | − | 0.866025i | −0.0187515 | − | 0.0324785i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.00000 | + | 15.5885i | −0.335643 | + | 0.581351i | −0.983608 | − | 0.180319i | \(-0.942287\pi\) |
0.647965 | + | 0.761670i | \(0.275620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | + | 18.1865i | −0.130347 | + | 0.677302i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.00000 | + | 12.1244i | −0.260333 | + | 0.450910i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | − | 3.46410i | −0.0742781 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0000 | 0.482143 | 0.241072 | − | 0.970507i | \(-0.422501\pi\) | ||||
0.241072 | + | 0.970507i | \(0.422501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.50000 | + | 12.9904i | −0.277019 | + | 0.479811i | −0.970642 | − | 0.240527i | \(-0.922680\pi\) |
0.693624 | + | 0.720338i | \(0.256013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.0000 | − | 8.66025i | 0.405741 | − | 0.319438i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.50000 | + | 12.9904i | 0.275892 | + | 0.477859i | 0.970360 | − | 0.241665i | \(-0.0776935\pi\) |
−0.694468 | + | 0.719524i | \(0.744360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00000 | −0.0367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.0000 | −1.54083 | −0.770415 | − | 0.637542i | \(-0.779951\pi\) | ||||
−0.770415 | + | 0.637542i | \(0.779951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | − | 20.7846i | −0.439646 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | + | 5.19615i | −0.109764 | + | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | − | 20.7846i | 0.146157 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | + | 6.92820i | 0.145768 | + | 0.252478i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0000 | − | 41.5692i | 0.869999 | − | 1.50688i | 0.00800331 | − | 0.999968i | \(-0.497452\pi\) |
0.861996 | − | 0.506915i | \(-0.169214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000 | + | 15.5885i | 0.651644 | + | 0.564340i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | − | 10.3923i | −0.216647 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.0000 | −1.76699 | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||||
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.0000 | 0.936367 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.0000 | − | 29.4449i | −0.611448 | − | 1.05906i | −0.990997 | − | 0.133887i | \(-0.957254\pi\) |
0.379549 | − | 0.925172i | \(-0.376079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.50000 | + | 7.79423i | −0.161645 | + | 0.279977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.50000 | + | 2.59808i | −0.269061 | + | 0.0932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.00000 | − | 8.66025i | 0.179144 | − | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | + | 10.3923i | 0.214697 | + | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.00000 | −0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.0000 | 0.999363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | − | 34.6410i | −0.712923 | − | 1.23482i | −0.963755 | − | 0.266788i | \(-0.914038\pi\) |
0.250832 | − | 0.968031i | \(-0.419296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.00000 | − | 3.46410i | 0.0712019 | − | 0.123325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.0000 | − | 8.66025i | 0.888898 | − | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | + | 8.66025i | −0.177555 | + | 0.307535i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.0000 | + | 20.7846i | 0.425596 | + | 0.737154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000 | 0.283375 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00000 | − | 13.8564i | −0.282666 | − | 0.489592i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | + | 5.19615i | −0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.00000 | − | 5.19615i | 0.105605 | − | 0.182913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | + | 4.33013i | −0.0874639 | + | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.500000 | − | 2.59808i | 0.0174714 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00000 | − | 1.73205i | 0.0349002 | − | 0.0604490i | −0.848048 | − | 0.529920i | \(-0.822222\pi\) |
0.882948 | + | 0.469471i | \(0.155555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.0000 | −1.04320 | −0.521601 | − | 0.853189i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853189i | \(0.674665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5000 | + | 35.5070i | 0.711994 | + | 1.23321i | 0.964107 | + | 0.265513i | \(0.0855412\pi\) |
−0.252113 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.50000 | − | 11.2583i | 0.225483 | − | 0.390547i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | + | 24.2487i | −0.484490 | + | 0.839161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | + | 7.79423i | 0.155543 | + | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.00000 | + | 3.46410i | 0.0688837 | + | 0.119310i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | − | 20.7846i | 0.412813 | − | 0.715012i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.50000 | − | 18.1865i | 0.120261 | − | 0.624897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.50000 | − | 9.52628i | 0.188760 | − | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.0000 | −1.19838 | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||||
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0000 | + | 27.7128i | 0.546550 | + | 0.946652i | 0.998508 | + | 0.0546125i | \(0.0173923\pi\) |
−0.451958 | + | 0.892039i | \(0.649274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | + | 17.3205i | 0.681598 | + | 0.590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | + | 46.7654i | −0.919091 | + | 1.59191i | −0.118291 | + | 0.992979i | \(0.537742\pi\) |
−0.800799 | + | 0.598933i | \(0.795592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 13.8564i | 0.272008 | + | 0.471132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.00000 | −0.0678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.50000 | − | 4.33013i | −0.0847093 | − | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | − | 5.19615i | 0.101535 | − | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.0000 | + | 10.3923i | −1.01419 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0000 | + | 32.9090i | −0.641584 | + | 1.11126i | 0.343495 | + | 0.939155i | \(0.388389\pi\) |
−0.985079 | + | 0.172102i | \(0.944944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.00000 | + | 6.92820i | 0.134917 | + | 0.233682i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.0000 | 0.808581 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | + | 20.7846i | 0.403376 | + | 0.698667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0000 | + | 29.4449i | −0.570804 | + | 0.988662i | 0.425679 | + | 0.904874i | \(0.360035\pi\) |
−0.996484 | + | 0.0837878i | \(0.973298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.5000 | − | 12.9904i | 1.25771 | − | 0.435683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.0000 | − | 8.66025i | −0.332779 | − | 0.288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.0000 | − | 22.5167i | 0.432135 | − | 0.748479i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | + | 32.0429i | 0.614282 | + | 1.06397i | 0.990510 | + | 0.137441i | \(0.0438878\pi\) |
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | + | 10.3923i | 0.198571 | + | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.0000 | − | 17.3205i | 0.330590 | − | 0.572598i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.00000 | − | 36.3731i | 0.231160 | − | 1.20114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5000 | − | 19.9186i | 0.379350 | − | 0.657053i | −0.611618 | − | 0.791153i | \(-0.709481\pi\) |
0.990968 | + | 0.134100i | \(0.0428143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.50000 | + | 14.7224i | 0.280085 | + | 0.485121i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.50000 | − | 6.06218i | −0.114955 | − | 0.199108i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | + | 6.92820i | 0.0327737 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.00000 | + | 5.19615i | −0.0982156 | + | 0.170114i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0000 | 0.490029 | 0.245014 | − | 0.969519i | \(-0.421207\pi\) | ||||
0.245014 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.00000 | −0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.00000 | − | 3.46410i | −0.0651981 | − | 0.112926i | 0.831584 | − | 0.555399i | \(-0.187435\pi\) |
−0.896782 | + | 0.442473i | \(0.854101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | + | 5.19615i | −0.0325300 | + | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.00000 | − | 8.66025i | 0.162478 | − | 0.281420i | −0.773279 | − | 0.634066i | \(-0.781385\pi\) |
0.935757 | + | 0.352646i | \(0.114718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.50000 | − | 2.59808i | −0.0486921 | − | 0.0843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0000 | 1.42530 | 0.712650 | − | 0.701520i | \(-0.247495\pi\) | ||||
0.712650 | + | 0.701520i | \(0.247495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0000 | + | 17.3205i | 0.323592 | + | 0.560478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.00000 | + | 6.92820i | −0.129302 | + | 0.223957i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.0000 | + | 20.7846i | 0.775000 | + | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | + | 43.3013i | −0.806452 | + | 1.39682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | + | 6.92820i | 0.128898 | + | 0.223258i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.0000 | 0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0000 | −0.610999 | −0.305499 | − | 0.952192i | \(-0.598823\pi\) | ||||
−0.305499 | + | 0.952192i | \(0.598823\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.50000 | + | 2.59808i | −0.240439 | + | 0.0832905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.500000 | + | 0.866025i | −0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | + | 15.5885i | 0.287936 | + | 0.498719i | 0.973317 | − | 0.229465i | \(-0.0736978\pi\) |
−0.685381 | + | 0.728184i | \(0.740364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.0000 | −1.02272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | −0.287348 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | − | 27.7128i | 0.509802 | − | 0.883004i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.0000 | − | 5.19615i | 0.477455 | − | 0.165395i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.50000 | + | 14.7224i | 0.270011 | + | 0.467673i | 0.968864 | − | 0.247592i | \(-0.0796392\pi\) |
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.0000 | −0.793351 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.50000 | + | 16.4545i | 0.300868 | + | 0.521119i | 0.976333 | − | 0.216274i | \(-0.0693903\pi\) |
−0.675465 | + | 0.737392i | \(0.736057\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.50000 | − | 2.59808i | 0.0474579 | − | 0.0821995i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))