Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1261,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1261");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.l (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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 19x^{2} + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1261.1 | ||
Root | \(2.17945 + 3.77492i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1261 |
Dual form | 1710.2.l.k.1531.1 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.35890 | −1.64751 | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 2.17945 | + | 3.77492i | 0.582482 | + | 1.00889i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.67945 | + | 2.90889i | 0.407326 | + | 0.705510i | 0.994589 | − | 0.103886i | \(-0.0331278\pi\) |
−0.587263 | + | 0.809396i | \(0.699795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.17945 | − | 3.77492i | −0.500000 | − | 0.866025i | ||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.17945 | − | 3.77492i | 0.411877 | − | 0.713392i | ||||
\(29\) | 4.67945 | − | 8.10504i | 0.868952 | − | 1.50507i | 0.00588307 | − | 0.999983i | \(-0.498127\pi\) |
0.863069 | − | 0.505086i | \(-0.168539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.7178 | −1.92497 | −0.962487 | − | 0.271329i | \(-0.912537\pi\) | ||||
−0.962487 | + | 0.271329i | \(0.912537\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.67945 | − | 2.90889i | 0.288023 | − | 0.498871i | ||||
\(35\) | 2.17945 | + | 3.77492i | 0.368394 | + | 0.638077i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | −2.17945 | + | 3.77492i | −0.353553 | + | 0.612372i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −3.17945 | − | 5.50697i | −0.496547 | − | 0.860044i | 0.503445 | − | 0.864027i | \(-0.332065\pi\) |
−0.999992 | + | 0.00398308i | \(0.998732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | + | 8.66025i | 0.762493 | + | 1.32068i | 0.941562 | + | 0.336840i | \(0.109358\pi\) |
−0.179069 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | −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 | ||||||||
\(49\) | 12.0000 | 1.71429 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | + | 3.46410i | 0.277350 | + | 0.480384i | ||||
\(53\) | −6.53835 | + | 11.3248i | −0.898111 | + | 1.55557i | −0.0682050 | + | 0.997671i | \(0.521727\pi\) |
−0.829906 | + | 0.557903i | \(0.811606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | −4.35890 | −0.582482 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.35890 | −1.22888 | ||||||||
\(59\) | 6.35890 | + | 11.0139i | 0.827858 | + | 1.43389i | 0.899715 | + | 0.436477i | \(0.143774\pi\) |
−0.0718571 | + | 0.997415i | \(0.522893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67945 | + | 4.64094i | −0.343068 | + | 0.594212i | −0.985001 | − | 0.172549i | \(-0.944800\pi\) |
0.641933 | + | 0.766761i | \(0.278133\pi\) | |||||||
\(62\) | 5.35890 | + | 9.28189i | 0.680581 | + | 1.17880i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.67945 | + | 9.83710i | −0.693855 | + | 1.20179i | 0.276710 | + | 0.960953i | \(0.410756\pi\) |
−0.970565 | + | 0.240839i | \(0.922577\pi\) | |||||||
\(68\) | −3.35890 | −0.407326 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.17945 | − | 3.77492i | 0.260494 | − | 0.451189i | ||||
\(71\) | −5.03835 | − | 8.72668i | −0.597942 | − | 1.03567i | −0.993124 | − | 0.117063i | \(-0.962652\pi\) |
0.395183 | − | 0.918603i | \(-0.370681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.32055 | − | 4.01931i | −0.271600 | − | 0.470425i | 0.697672 | − | 0.716418i | \(-0.254219\pi\) |
−0.969272 | + | 0.245993i | \(0.920886\pi\) | |||||||
\(74\) | 3.50000 | + | 6.06218i | 0.406867 | + | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.35890 | 0.500000 | ||||||||
\(77\) | −13.0767 | −1.49023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.35890 | + | 4.08573i | 0.265397 | + | 0.459681i | 0.967668 | − | 0.252229i | \(-0.0811637\pi\) |
−0.702271 | + | 0.711910i | \(0.747830\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.17945 | + | 5.50697i | −0.351111 | + | 0.608143i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.67945 | − | 2.90889i | 0.182162 | − | 0.315514i | ||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 0.179449 | − | 0.310816i | 0.0190216 | − | 0.0329464i | −0.856358 | − | 0.516383i | \(-0.827278\pi\) |
0.875380 | + | 0.483436i | \(0.160612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.71780 | + | 15.0997i | −0.913874 | + | 1.58288i | ||||
\(92\) | −1.50000 | − | 2.59808i | −0.156386 | − | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −2.17945 | + | 3.77492i | −0.223607 | + | 0.387298i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.03835 | + | 12.1908i | 0.714636 | + | 1.23779i | 0.963100 | + | 0.269145i | \(0.0867410\pi\) |
−0.248464 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(98\) | −6.00000 | − | 10.3923i | −0.606092 | − | 1.04978i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −6.35890 | + | 11.0139i | −0.632734 | + | 1.09593i | 0.354256 | + | 0.935148i | \(0.384734\pi\) |
−0.986990 | + | 0.160779i | \(0.948599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3589 | −1.02069 | −0.510346 | − | 0.859969i | \(-0.670483\pi\) | ||||
−0.510346 | + | 0.859969i | \(0.670483\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.0767 | 1.27012 | ||||||||
\(107\) | −9.35890 | −0.904759 | −0.452379 | − | 0.891826i | \(-0.649425\pi\) | ||||
−0.452379 | + | 0.891826i | \(0.649425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.32055 | − | 9.21546i | −0.509616 | − | 0.882681i | −0.999938 | − | 0.0111398i | \(-0.996454\pi\) |
0.490322 | − | 0.871542i | \(-0.336879\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.17945 | + | 3.77492i | 0.205939 | + | 0.356696i | ||||
\(113\) | −3.35890 | −0.315979 | −0.157989 | − | 0.987441i | \(-0.550501\pi\) | ||||
−0.157989 | + | 0.987441i | \(0.550501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | 4.67945 | + | 8.10504i | 0.434476 | + | 0.752534i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.35890 | − | 11.0139i | 0.585384 | − | 1.01391i | ||||
\(119\) | −7.32055 | − | 12.6796i | −0.671074 | − | 1.16233i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 5.35890 | 0.485172 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.35890 | − | 9.28189i | 0.481243 | − | 0.833538i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.17945 | − | 8.97107i | 0.459602 | − | 0.796054i | −0.539338 | − | 0.842089i | \(-0.681325\pi\) |
0.998940 | + | 0.0460357i | \(0.0146588\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.50000 | + | 16.4545i | 0.823754 | + | 1.42678i | ||||
\(134\) | 11.3589 | 0.981259 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.67945 | + | 2.90889i | 0.144012 | + | 0.249435i | ||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.641101 | + | 1.11042i | −0.0543775 | + | 0.0941846i | −0.891933 | − | 0.452168i | \(-0.850651\pi\) |
0.837555 | + | 0.546353i | \(0.183984\pi\) | |||||||
\(140\) | −4.35890 | −0.368394 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.03835 | + | 8.72668i | −0.422809 | + | 0.732326i | ||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.35890 | −0.777214 | ||||||||
\(146\) | −2.32055 | + | 4.01931i | −0.192050 | + | 0.332641i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50000 | − | 6.06218i | 0.287698 | − | 0.498308i | ||||
\(149\) | −5.03835 | − | 8.72668i | −0.412758 | − | 0.714917i | 0.582433 | − | 0.812879i | \(-0.302101\pi\) |
−0.995190 | + | 0.0979619i | \(0.968768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.07670 | −0.168999 | −0.0844996 | − | 0.996424i | \(-0.526929\pi\) | ||||
−0.0844996 | + | 0.996424i | \(0.526929\pi\) | |||||||
\(152\) | −2.17945 | − | 3.77492i | −0.176777 | − | 0.306186i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.53835 | + | 11.3248i | 0.526875 | + | 0.912574i | ||||
\(155\) | 5.35890 | + | 9.28189i | 0.430437 | + | 0.745539i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.50000 | − | 4.33013i | −0.199522 | − | 0.345582i | 0.748852 | − | 0.662738i | \(-0.230606\pi\) |
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(158\) | 2.35890 | − | 4.08573i | 0.187664 | − | 0.325043i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.53835 | − | 11.3248i | 0.515294 | − | 0.892515i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.71780 | −0.369526 | −0.184763 | − | 0.982783i | \(-0.559152\pi\) | ||||
−0.184763 | + | 0.982783i | \(0.559152\pi\) | |||||||
\(164\) | 6.35890 | 0.496547 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | −11.2178 | + | 19.4298i | −0.868059 | + | 1.50352i | −0.00408215 | + | 0.999992i | \(0.501299\pi\) |
−0.863977 | + | 0.503531i | \(0.832034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | −3.35890 | −0.257616 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | 9.17945 | + | 15.8993i | 0.697901 | + | 1.20880i | 0.969193 | + | 0.246302i | \(0.0792156\pi\) |
−0.271292 | + | 0.962497i | \(0.587451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.17945 | − | 3.77492i | 0.164751 | − | 0.285357i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.358899 | −0.0269006 | ||||||||
\(179\) | −15.7178 | −1.17480 | −0.587402 | − | 0.809296i | \(-0.699849\pi\) | ||||
−0.587402 | + | 0.809296i | \(0.699849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.03835 | + | 15.6549i | −0.671815 | + | 1.16362i | 0.305574 | + | 0.952168i | \(0.401152\pi\) |
−0.977389 | + | 0.211450i | \(0.932182\pi\) | |||||||
\(182\) | 17.4356 | 1.29241 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 3.50000 | + | 6.06218i | 0.257325 | + | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.03835 | + | 8.72668i | 0.368441 | + | 0.638158i | ||||
\(188\) | −3.00000 | − | 5.19615i | −0.218797 | − | 0.378968i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.35890 | 0.316228 | ||||||||
\(191\) | 19.4356 | 1.40631 | 0.703155 | − | 0.711036i | \(-0.251774\pi\) | ||||
0.703155 | + | 0.711036i | \(0.251774\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0383 | − | 20.8510i | −0.866539 | − | 1.50089i | −0.865511 | − | 0.500891i | \(-0.833006\pi\) |
−0.00102867 | − | 0.999999i | \(-0.500327\pi\) | |||||||
\(194\) | 7.03835 | − | 12.1908i | 0.505324 | − | 0.875247i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | + | 10.3923i | −0.428571 | + | 0.742307i | ||||
\(197\) | 5.64110 | 0.401912 | 0.200956 | − | 0.979600i | \(-0.435595\pi\) | ||||
0.200956 | + | 0.979600i | \(0.435595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.32055 | + | 14.4116i | −0.589828 | + | 1.02161i | 0.404426 | + | 0.914571i | \(0.367471\pi\) |
−0.994255 | + | 0.107042i | \(0.965862\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.7178 | 0.894821 | ||||||||
\(203\) | −20.3972 | + | 35.3291i | −1.43161 | + | 2.47961i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.17945 | + | 5.50697i | −0.222062 | + | 0.384623i | ||||
\(206\) | 5.17945 | + | 8.97107i | 0.360869 | + | 0.625044i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | −6.53835 | − | 11.3248i | −0.452267 | − | 0.783349i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53835 | − | 13.0568i | −0.518961 | − | 0.898867i | −0.999757 | − | 0.0220348i | \(-0.992986\pi\) |
0.480796 | − | 0.876833i | \(-0.340348\pi\) | |||||||
\(212\) | −6.53835 | − | 11.3248i | −0.449056 | − | 0.777787i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.67945 | + | 8.10504i | 0.319881 | + | 0.554049i | ||||
\(215\) | 5.00000 | − | 8.66025i | 0.340997 | − | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 46.7178 | 3.17141 | ||||||||
\(218\) | −5.32055 | + | 9.21546i | −0.360353 | + | 0.624150i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | 13.4356 | 0.903776 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1794 | − | 17.6313i | −0.681666 | − | 1.18068i | −0.974472 | − | 0.224509i | \(-0.927922\pi\) |
0.292806 | − | 0.956172i | \(-0.405411\pi\) | |||||||
\(224\) | 2.17945 | − | 3.77492i | 0.145621 | − | 0.252222i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.67945 | + | 2.90889i | 0.111715 | + | 0.193497i | ||||
\(227\) | 3.35890 | 0.222938 | 0.111469 | − | 0.993768i | \(-0.464444\pi\) | ||||
0.111469 | + | 0.993768i | \(0.464444\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.71780 | 0.576088 | 0.288044 | − | 0.957617i | \(-0.406995\pi\) | ||||
0.288044 | + | 0.957617i | \(0.406995\pi\) | |||||||
\(230\) | −1.50000 | − | 2.59808i | −0.0989071 | − | 0.171312i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.67945 | − | 8.10504i | 0.307221 | − | 0.532122i | ||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | −12.7178 | −0.827858 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.32055 | + | 12.6796i | −0.474521 | + | 0.821894i | ||||
\(239\) | 13.4356 | 0.869076 | 0.434538 | − | 0.900653i | \(-0.356912\pi\) | ||||
0.434538 | + | 0.900653i | \(0.356912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | − | 3.46410i | 0.128831 | − | 0.223142i | −0.794393 | − | 0.607404i | \(-0.792211\pi\) |
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.67945 | − | 4.64094i | −0.171534 | − | 0.297106i | ||||
\(245\) | −6.00000 | − | 10.3923i | −0.383326 | − | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.4356 | −1.10940 | ||||||||
\(248\) | −10.7178 | −0.680581 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.50000 | + | 7.79423i | −0.282913 | + | 0.490019i | ||||
\(254\) | −10.3589 | −0.649975 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.71780 | + | 6.43941i | −0.231910 | + | 0.401680i | −0.958370 | − | 0.285529i | \(-0.907831\pi\) |
0.726460 | + | 0.687208i | \(0.241164\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.5123 | 1.89594 | ||||||||
\(260\) | 2.00000 | − | 3.46410i | 0.124035 | − | 0.214834i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.50000 | + | 2.59808i | −0.0926703 | + | 0.160510i | ||||
\(263\) | −4.14110 | − | 7.17260i | −0.255351 | − | 0.442281i | 0.709640 | − | 0.704565i | \(-0.248858\pi\) |
−0.964991 | + | 0.262284i | \(0.915524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0767 | 0.803295 | ||||||||
\(266\) | 9.50000 | − | 16.4545i | 0.582482 | − | 1.00889i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.67945 | − | 9.83710i | −0.346928 | − | 0.600896i | ||||
\(269\) | 1.67945 | + | 2.90889i | 0.102398 | + | 0.177358i | 0.912672 | − | 0.408693i | \(-0.134015\pi\) |
−0.810274 | + | 0.586051i | \(0.800682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.35890 | + | 4.08573i | 0.143293 | + | 0.248191i | 0.928735 | − | 0.370745i | \(-0.120898\pi\) |
−0.785442 | + | 0.618935i | \(0.787564\pi\) | |||||||
\(272\) | 1.67945 | − | 2.90889i | 0.101832 | − | 0.176377i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.240337 | −0.120168 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120168 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(278\) | 1.28220 | 0.0769014 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.17945 | + | 3.77492i | 0.130247 | + | 0.225594i | ||||
\(281\) | 0.538348 | − | 0.932447i | 0.0321152 | − | 0.0556251i | −0.849521 | − | 0.527555i | \(-0.823109\pi\) |
0.881636 | + | 0.471930i | \(0.156442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.35890 | − | 7.54983i | −0.259110 | − | 0.448791i | 0.706894 | − | 0.707319i | \(-0.250096\pi\) |
−0.966004 | + | 0.258528i | \(0.916762\pi\) | |||||||
\(284\) | 10.0767 | 0.597942 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 13.8589 | + | 24.0043i | 0.818065 | + | 1.41693i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.85890 | − | 4.95176i | 0.168171 | − | 0.291280i | ||||
\(290\) | 4.67945 | + | 8.10504i | 0.274787 | + | 0.475945i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.64110 | 0.271600 | ||||||||
\(293\) | −5.64110 | −0.329557 | −0.164778 | − | 0.986331i | \(-0.552691\pi\) | ||||
−0.164778 | + | 0.986331i | \(0.552691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.35890 | − | 11.0139i | 0.370229 | − | 0.641256i | ||||
\(296\) | −7.00000 | −0.406867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.03835 | + | 8.72668i | −0.291864 | + | 0.505523i | ||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.7945 | − | 37.7492i | −1.25621 | − | 2.17583i | ||||
\(302\) | 1.03835 | + | 1.79847i | 0.0597502 | + | 0.103490i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.17945 | + | 3.77492i | −0.125000 | + | 0.216506i | ||||
\(305\) | 5.35890 | 0.306850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.679449 | + | 1.17684i | 0.0387782 | + | 0.0671659i | 0.884763 | − | 0.466041i | \(-0.154320\pi\) |
−0.845985 | + | 0.533207i | \(0.820987\pi\) | |||||||
\(308\) | 6.53835 | − | 11.3248i | 0.372557 | − | 0.645288i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.35890 | − | 9.28189i | 0.304365 | − | 0.527176i | ||||
\(311\) | −1.43560 | −0.0814052 | −0.0407026 | − | 0.999171i | \(-0.512960\pi\) | ||||
−0.0407026 | + | 0.999171i | \(0.512960\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.71780 | − | 15.0997i | 0.492759 | − | 0.853484i | −0.507206 | − | 0.861825i | \(-0.669322\pi\) |
0.999965 | + | 0.00834102i | \(0.00265506\pi\) | |||||||
\(314\) | −2.50000 | + | 4.33013i | −0.141083 | + | 0.244363i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.71780 | −0.265397 | ||||||||
\(317\) | 9.53835 | − | 16.5209i | 0.535727 | − | 0.927906i | −0.463401 | − | 0.886149i | \(-0.653371\pi\) |
0.999128 | − | 0.0417576i | \(-0.0132957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0383 | − | 24.3151i | 0.785997 | − | 1.36139i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.0767 | −0.728736 | ||||||||
\(323\) | 7.32055 | − | 12.6796i | 0.407326 | − | 0.705510i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | 2.35890 | + | 4.08573i | 0.130647 | + | 0.226288i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.17945 | − | 5.50697i | −0.175556 | − | 0.304071i | ||||
\(329\) | 13.0767 | − | 22.6495i | 0.720942 | − | 1.24871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3589 | 0.789236 | 0.394618 | − | 0.918845i | \(-0.370877\pi\) | ||||
0.394618 | + | 0.918845i | \(0.370877\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.4356 | 1.22762 | ||||||||
\(335\) | 11.3589 | 0.620603 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0767 | − | 19.1854i | −0.603386 | − | 1.04510i | −0.992304 | − | 0.123823i | \(-0.960484\pi\) |
0.388918 | − | 0.921272i | \(-0.372849\pi\) | |||||||
\(338\) | −1.50000 | + | 2.59808i | −0.0815892 | + | 0.141317i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.67945 | + | 2.90889i | 0.0910809 | + | 0.157757i | ||||
\(341\) | −32.1534 | −1.74120 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.7945 | −1.17679 | ||||||||
\(344\) | 5.00000 | + | 8.66025i | 0.269582 | + | 0.466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.17945 | − | 15.8993i | 0.493490 | − | 0.854750i | ||||
\(347\) | −3.71780 | − | 6.43941i | −0.199582 | − | 0.345686i | 0.748811 | − | 0.662784i | \(-0.230625\pi\) |
−0.948393 | + | 0.317098i | \(0.897292\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0766968 | 0.00410549 | 0.00205274 | − | 0.999998i | \(-0.499347\pi\) | ||||
0.00205274 | + | 0.999998i | \(0.499347\pi\) | |||||||
\(350\) | −4.35890 | −0.232993 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | 10.0767 | 0.536328 | 0.268164 | − | 0.963373i | \(-0.413583\pi\) | ||||
0.268164 | + | 0.963373i | \(0.413583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.03835 | + | 8.72668i | −0.267408 | + | 0.463164i | ||||
\(356\) | 0.179449 | + | 0.310816i | 0.00951080 | + | 0.0164732i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.85890 | + | 13.6120i | 0.415356 | + | 0.719417i | ||||
\(359\) | 7.67945 | + | 13.3012i | 0.405306 | + | 0.702010i | 0.994357 | − | 0.106085i | \(-0.0338317\pi\) |
−0.589051 | + | 0.808096i | \(0.700498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 18.0767 | 0.950090 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.71780 | − | 15.0997i | −0.456937 | − | 0.791438i | ||||
\(365\) | −2.32055 | + | 4.01931i | −0.121463 | + | 0.210380i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.35890 | + | 12.7460i | −0.384131 | + | 0.665335i | −0.991648 | − | 0.128972i | \(-0.958832\pi\) |
0.607517 | + | 0.794307i | \(0.292166\pi\) | |||||||
\(368\) | 3.00000 | 0.156386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.50000 | − | 6.06218i | 0.181956 | − | 0.315158i | ||||
\(371\) | 28.5000 | − | 49.3634i | 1.47965 | − | 2.56282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | 0.569558 | 0.284779 | − | 0.958593i | \(-0.408080\pi\) | ||||
0.284779 | + | 0.958593i | \(0.408080\pi\) | |||||||
\(374\) | 5.03835 | − | 8.72668i | 0.260527 | − | 0.451246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | + | 5.19615i | −0.154713 | + | 0.267971i | ||||
\(377\) | −18.7178 | − | 32.4202i | −0.964016 | − | 1.66972i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7178 | 0.756002 | 0.378001 | − | 0.925805i | \(-0.376611\pi\) | ||||
0.378001 | + | 0.925805i | \(0.376611\pi\) | |||||||
\(380\) | −2.17945 | − | 3.77492i | −0.111803 | − | 0.193649i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.71780 | − | 16.8317i | −0.497206 | − | 0.861186i | ||||
\(383\) | 3.00000 | + | 5.19615i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.53835 | + | 11.3248i | 0.333225 | + | 0.577163i | ||||
\(386\) | −12.0383 | + | 20.8510i | −0.612736 | + | 1.06129i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.0767 | −0.714636 | ||||||||
\(389\) | 2.03835 | − | 3.53052i | 0.103348 | − | 0.179005i | −0.809714 | − | 0.586825i | \(-0.800378\pi\) |
0.913062 | + | 0.407820i | \(0.133711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0767 | −0.509600 | ||||||||
\(392\) | 12.0000 | 0.606092 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.82055 | − | 4.88534i | −0.142097 | − | 0.246120i | ||||
\(395\) | 2.35890 | − | 4.08573i | 0.118689 | − | 0.205576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.21780 | − | 5.57339i | −0.161497 | − | 0.279720i | 0.773909 | − | 0.633297i | \(-0.218299\pi\) |
−0.935406 | + | 0.353576i | \(0.884965\pi\) | |||||||
\(398\) | 16.6411 | 0.834143 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.4356 | + | 37.1275i | −1.06778 | + | 1.84945i | ||||
\(404\) | −6.35890 | − | 11.0139i | −0.316367 | − | 0.547964i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.7945 | 2.02460 | ||||||||
\(407\) | −21.0000 | −1.04093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | 6.35890 | 0.314044 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.17945 | − | 8.97107i | 0.255173 | − | 0.441973i | ||||
\(413\) | −27.7178 | − | 48.0086i | −1.36390 | − | 2.36235i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 5.19615i | −0.147264 | − | 0.255069i | ||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.53835 | + | 11.3248i | −0.319801 | + | 0.553912i | ||||
\(419\) | −15.7178 | −0.767865 | −0.383932 | − | 0.923361i | \(-0.625430\pi\) | ||||
−0.383932 | + | 0.923361i | \(0.625430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0383 | − | 31.2433i | −0.879135 | − | 1.52271i | −0.852291 | − | 0.523067i | \(-0.824788\pi\) |
−0.0268440 | − | 0.999640i | \(-0.508546\pi\) | |||||||
\(422\) | −7.53835 | + | 13.0568i | −0.366961 | + | 0.635595i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.53835 | + | 11.3248i | −0.317530 | + | 0.549979i | ||||
\(425\) | −3.35890 | −0.162931 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.6794 | − | 20.2294i | 0.565208 | − | 0.978969i | ||||
\(428\) | 4.67945 | − | 8.10504i | 0.226190 | − | 0.391772i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.0000 | −0.482243 | ||||||||
\(431\) | 5.39725 | − | 9.34831i | 0.259976 | − | 0.450292i | −0.706259 | − | 0.707954i | \(-0.749619\pi\) |
0.966235 | + | 0.257661i | \(0.0829519\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3972 | + | 31.8650i | −0.884115 | + | 1.53133i | −0.0373910 | + | 0.999301i | \(0.511905\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(434\) | −23.3589 | − | 40.4588i | −1.12126 | − | 1.94208i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.6411 | 0.509616 | ||||||||
\(437\) | 13.0767 | 0.625543 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6794 | − | 20.2294i | −0.557430 | − | 0.965497i | −0.997710 | − | 0.0676362i | \(-0.978454\pi\) |
0.440280 | − | 0.897860i | \(-0.354879\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.71780 | − | 11.6356i | −0.319533 | − | 0.553447i | ||||
\(443\) | −1.32055 | + | 2.28726i | −0.0627412 | + | 0.108671i | −0.895690 | − | 0.444679i | \(-0.853318\pi\) |
0.832949 | + | 0.553350i | \(0.186651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.358899 | −0.0170134 | ||||||||
\(446\) | −10.1794 | + | 17.6313i | −0.482011 | + | 0.834867i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.35890 | −0.205939 | ||||||||
\(449\) | −0.358899 | −0.0169375 | −0.00846874 | − | 0.999964i | \(-0.502696\pi\) | ||||
−0.00846874 | + | 0.999964i | \(0.502696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.53835 | − | 16.5209i | −0.449143 | − | 0.777939i | ||||
\(452\) | 1.67945 | − | 2.90889i | 0.0789947 | − | 0.136823i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.67945 | − | 2.90889i | −0.0788205 | − | 0.136521i | ||||
\(455\) | 17.4356 | 0.817393 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.6411 | −1.43333 | −0.716665 | − | 0.697417i | \(-0.754332\pi\) | ||||
−0.716665 | + | 0.697417i | \(0.754332\pi\) | |||||||
\(458\) | −4.35890 | − | 7.54983i | −0.203678 | − | 0.352781i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.50000 | + | 2.59808i | −0.0699379 | + | 0.121136i | ||||
\(461\) | 9.00000 | + | 15.5885i | 0.419172 | + | 0.726027i | 0.995856 | − | 0.0909401i | \(-0.0289872\pi\) |
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7945 | −0.826980 | −0.413490 | − | 0.910509i | \(-0.635690\pi\) | ||||
−0.413490 | + | 0.910509i | \(0.635690\pi\) | |||||||
\(464\) | −9.35890 | −0.434476 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | −28.7945 | −1.33245 | −0.666225 | − | 0.745751i | \(-0.732091\pi\) | ||||
−0.666225 | + | 0.745751i | \(0.732091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7561 | − | 42.8789i | 1.14313 | − | 1.97996i | ||||
\(470\) | −3.00000 | − | 5.19615i | −0.138380 | − | 0.239681i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.35890 | + | 11.0139i | 0.292692 | + | 0.506957i | ||||
\(473\) | 15.0000 | + | 25.9808i | 0.689701 | + | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.35890 | 0.200000 | ||||||||
\(476\) | 14.6411 | 0.671074 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.71780 | − | 11.6356i | −0.307265 | − | 0.532198i | ||||
\(479\) | −11.0383 | + | 19.1190i | −0.504355 | + | 0.873569i | 0.495632 | + | 0.868532i | \(0.334936\pi\) |
−0.999987 | + | 0.00503606i | \(0.998397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0000 | + | 24.2487i | −0.638345 | + | 1.10565i | ||||
\(482\) | −4.00000 | −0.182195 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 7.03835 | − | 12.1908i | 0.319595 | − | 0.553555i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.64110 | −0.436880 | −0.218440 | − | 0.975850i | \(-0.570097\pi\) | ||||
−0.218440 | + | 0.975850i | \(0.570097\pi\) | |||||||
\(488\) | −2.67945 | + | 4.64094i | −0.121293 | + | 0.210086i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.00000 | + | 10.3923i | −0.271052 | + | 0.469476i | ||||
\(491\) | 7.50000 | + | 12.9904i | 0.338470 | + | 0.586248i | 0.984145 | − | 0.177365i | \(-0.0567572\pi\) |
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.4356 | 1.41579 | ||||||||
\(494\) | 8.71780 | + | 15.0997i | 0.392232 | + | 0.679366i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.35890 | + | 9.28189i | 0.240622 | + | 0.416769i | ||||
\(497\) | 21.9617 | + | 38.0387i | 0.985115 | + | 1.70627i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.82055 | + | 13.5456i | 0.350096 | + | 0.606384i | 0.986266 | − | 0.165165i | \(-0.0528157\pi\) |
−0.636170 | + | 0.771549i | \(0.719482\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | 14.9356 | − | 25.8692i | 0.665945 | − | 1.15345i | −0.313083 | − | 0.949726i | \(-0.601362\pi\) |
0.979028 | − | 0.203725i | \(-0.0653049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.7178 | 0.565935 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.17945 | + | 8.97107i | 0.229801 | + | 0.398027i | ||||
\(509\) | 12.3589 | − | 21.4062i | 0.547799 | − | 0.948815i | −0.450626 | − | 0.892713i | \(-0.648799\pi\) |
0.998425 | − | 0.0561023i | \(-0.0178673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1150 | + | 17.5198i | 0.447463 | + | 0.775029i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.43560 | 0.327970 | ||||||||
\(515\) | 5.17945 | + | 8.97107i | 0.228234 | + | 0.395313i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | + | 15.5885i | −0.395820 | + | 0.685580i | ||||
\(518\) | −15.2561 | − | 26.4244i | −0.670317 | − | 1.16102i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.00000 | −0.175412 | ||||||||
\(521\) | −23.2822 | −1.02001 | −0.510006 | − | 0.860171i | \(-0.670357\pi\) | ||||
−0.510006 | + | 0.860171i | \(0.670357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.3972 | − | 33.5970i | 0.848182 | − | 1.46910i | −0.0346461 | − | 0.999400i | \(-0.511030\pi\) |
0.882829 | − | 0.469695i | \(-0.155636\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.14110 | + | 7.17260i | −0.180561 | + | 0.312740i | ||||
\(527\) | −18.0000 | − | 31.1769i | −0.784092 | − | 1.35809i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | −6.53835 | − | 11.3248i | −0.284008 | − | 0.491916i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.0000 | −0.823754 | ||||||||
\(533\) | −25.4356 | −1.10174 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.67945 | + | 8.10504i | 0.202310 | + | 0.350412i | ||||
\(536\) | −5.67945 | + | 9.83710i | −0.245315 | + | 0.424898i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.67945 | − | 2.90889i | 0.0724062 | − | 0.125411i | ||||
\(539\) | 36.0000 | 1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.64110 | − | 8.03862i | 0.199537 | − | 0.345607i | −0.748842 | − | 0.662749i | \(-0.769390\pi\) |
0.948378 | + | 0.317142i | \(0.102723\pi\) | |||||||
\(542\) | 2.35890 | − | 4.08573i | 0.101323 | − | 0.175497i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.35890 | −0.144012 | ||||||||
\(545\) | −5.32055 | + | 9.21546i | −0.227907 | + | 0.394747i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07670 | − | 5.32900i | 0.131550 | − | 0.227851i | −0.792724 | − | 0.609580i | \(-0.791338\pi\) |
0.924274 | + | 0.381729i | \(0.124671\pi\) | |||||||
\(548\) | 6.00000 | + | 10.3923i | 0.256307 | + | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.00000 | 0.127920 | ||||||||
\(551\) | −40.7945 | −1.73790 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2822 | − | 17.8093i | −0.437244 | − | 0.757328i | ||||
\(554\) | 2.00000 | + | 3.46410i | 0.0849719 | + | 0.147176i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.641101 | − | 1.11042i | −0.0271887 | − | 0.0470923i | ||||
\(557\) | −5.46165 | + | 9.45986i | −0.231418 | + | 0.400827i | −0.958226 | − | 0.286014i | \(-0.907670\pi\) |
0.726808 | + | 0.686841i | \(0.241003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 2.17945 | − | 3.77492i | 0.0920985 | − | 0.159519i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.07670 | −0.0454177 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.67945 | + | 2.90889i | 0.0706550 | + | 0.122378i | ||||
\(566\) | −4.35890 | + | 7.54983i | −0.183218 | + | 0.317343i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.03835 | − | 8.72668i | −0.211404 | − | 0.366163i | ||||
\(569\) | 37.7945 | 1.58443 | 0.792214 | − | 0.610244i | \(-0.208928\pi\) | ||||
0.792214 | + | 0.610244i | \(0.208928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.1534 | 1.42928 | 0.714638 | − | 0.699495i | \(-0.246592\pi\) | ||||
0.714638 | + | 0.699495i | \(0.246592\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.8589 | − | 24.0043i | 0.578459 | − | 1.00192i | ||||
\(575\) | −1.50000 | − | 2.59808i | −0.0625543 | − | 0.108347i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7945 | 0.782425 | 0.391213 | − | 0.920300i | \(-0.372056\pi\) | ||||
0.391213 | + | 0.920300i | \(0.372056\pi\) | |||||||
\(578\) | −5.71780 | −0.237829 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.67945 | − | 8.10504i | 0.194304 | − | 0.336544i | ||||
\(581\) | −26.1534 | −1.08503 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.6150 | + | 33.9743i | −0.812372 | + | 1.40707i | ||||
\(584\) | −2.32055 | − | 4.01931i | −0.0960251 | − | 0.166320i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.82055 | + | 4.88534i | 0.116516 | + | 0.201811i | ||||
\(587\) | −21.3589 | − | 36.9947i | −0.881576 | − | 1.52693i | −0.849588 | − | 0.527446i | \(-0.823150\pi\) |
−0.0319878 | − | 0.999488i | \(-0.510184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.3589 | + | 40.4588i | 0.962487 | + | 1.66708i | ||||
\(590\) | −12.7178 | −0.523583 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.50000 | + | 6.06218i | 0.143849 | + | 0.249154i | ||||
\(593\) | 3.96165 | − | 6.86178i | 0.162686 | − | 0.281780i | −0.773145 | − | 0.634229i | \(-0.781318\pi\) |
0.935831 | + | 0.352449i | \(0.114651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.32055 | + | 12.6796i | −0.300113 | + | 0.519812i | ||||
\(596\) | 10.0767 | 0.412758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.00000 | − | 10.3923i | 0.245358 | − | 0.424973i | ||||
\(599\) | 13.3206 | − | 23.0719i | 0.544263 | − | 0.942691i | −0.454390 | − | 0.890803i | \(-0.650143\pi\) |
0.998653 | − | 0.0518882i | \(-0.0165239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.71780 | 0.233234 | 0.116617 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116617 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(602\) | −21.7945 | + | 37.7492i | −0.888277 | + | 1.53854i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.03835 | − | 1.79847i | 0.0422498 | − | 0.0731788i | ||||
\(605\) | 1.00000 | + | 1.73205i | 0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7945 | −1.45285 | −0.726427 | − | 0.687244i | \(-0.758820\pi\) | ||||
−0.726427 | + | 0.687244i | \(0.758820\pi\) | |||||||
\(608\) | 4.35890 | 0.176777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.67945 | − | 4.64094i | −0.108488 | − | 0.187906i | ||||
\(611\) | 12.0000 | + | 20.7846i | 0.485468 | + | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.21780 | − | 5.57339i | −0.129966 | − | 0.225107i | 0.793697 | − | 0.608313i | \(-0.208153\pi\) |
−0.923663 | + | 0.383206i | \(0.874820\pi\) | |||||||
\(614\) | 0.679449 | − | 1.17684i | 0.0274203 | − | 0.0474934i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.0767 | −0.526875 | ||||||||
\(617\) | −0.717798 | + | 1.24326i | −0.0288975 | + | 0.0500519i | −0.880112 | − | 0.474765i | \(-0.842533\pi\) |
0.851215 | + | 0.524817i | \(0.175866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.64110 | −0.146348 | −0.0731741 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731741 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(620\) | −10.7178 | −0.430437 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.717798 | + | 1.24326i | 0.0287811 | + | 0.0498503i | ||||
\(623\) | −0.782202 | + | 1.35481i | −0.0313383 | + | 0.0542795i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −17.4356 | −0.696867 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.00000 | 0.199522 | ||||||||
\(629\) | −11.7561 | − | 20.3622i | −0.468748 | − | 0.811896i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.6794 | + | 35.8179i | −0.823236 | + | 1.42589i | 0.0800242 | + | 0.996793i | \(0.474500\pi\) |
−0.903260 | + | 0.429093i | \(0.858833\pi\) | |||||||
\(632\) | 2.35890 | + | 4.08573i | 0.0938320 | + | 0.162522i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.0767 | −0.757632 | ||||||||
\(635\) | −10.3589 | −0.411080 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | − | 41.5692i | 0.950915 | − | 1.64703i | ||||
\(638\) | −28.0767 | −1.11157 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −5.64110 | − | 9.77067i | −0.222810 | − | 0.385918i | 0.732850 | − | 0.680390i | \(-0.238190\pi\) |
−0.955660 | + | 0.294472i | \(0.904856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.7561 | + | 34.2186i | 0.779106 | + | 1.34945i | 0.932457 | + | 0.361280i | \(0.117660\pi\) |
−0.153351 | + | 0.988172i | \(0.549007\pi\) | |||||||
\(644\) | 6.53835 | + | 11.3248i | 0.257647 | + | 0.446258i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.6411 | −0.576046 | ||||||||
\(647\) | 17.1534 | 0.674369 | 0.337185 | − | 0.941438i | \(-0.390525\pi\) | ||||
0.337185 | + | 0.941438i | \(0.390525\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0767 | + | 33.0418i | 0.748826 | + | 1.29700i | ||||
\(650\) | 2.00000 | − | 3.46410i | 0.0784465 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.35890 | − | 4.08573i | 0.0923816 | − | 0.160010i | ||||
\(653\) | 25.0767 | 0.981327 | 0.490663 | − | 0.871349i | \(-0.336754\pi\) | ||||
0.490663 | + | 0.871349i | \(0.336754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.50000 | + | 2.59808i | −0.0586098 | + | 0.101515i | ||||
\(656\) | −3.17945 | + | 5.50697i | −0.124137 | + | 0.215011i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.1534 | −1.01957 | ||||||||
\(659\) | −19.8589 | + | 34.3966i | −0.773593 | + | 1.33990i | 0.161989 | + | 0.986793i | \(0.448209\pi\) |
−0.935582 | + | 0.353110i | \(0.885124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.71780 | − | 15.0997i | 0.339083 | − | 0.587309i | −0.645177 | − | 0.764033i | \(-0.723217\pi\) |
0.984261 | + | 0.176724i | \(0.0565499\pi\) | |||||||
\(662\) | −7.17945 | − | 12.4352i | −0.279037 | − | 0.483307i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 9.50000 | − | 16.4545i | 0.368394 | − | 0.638077i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0383 | + | 24.3151i | 0.543567 | + | 0.941486i | ||||
\(668\) | −11.2178 | − | 19.4298i | −0.434030 | − | 0.751761i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.67945 | − | 9.83710i | −0.219416 | − | 0.380040i | ||||
\(671\) | −8.03835 | + | 13.9228i | −0.310317 | + | 0.537485i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.2822 | −0.820369 | −0.410184 | − | 0.912003i | \(-0.634536\pi\) | ||||
−0.410184 | + | 0.912003i | \(0.634536\pi\) | |||||||
\(674\) | −11.0767 | + | 19.1854i | −0.426658 | + | 0.738994i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −7.07670 | −0.271980 | −0.135990 | − | 0.990710i | \(-0.543421\pi\) | ||||
−0.135990 | + | 0.990710i | \(0.543421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.6794 | − | 53.1384i | −1.17737 | − | 2.03926i | ||||
\(680\) | 1.67945 | − | 2.90889i | 0.0644039 | − | 0.111551i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.0767 | + | 27.8457i | 0.615609 | + | 1.06627i | ||||
\(683\) | 22.7945 | 0.872207 | 0.436104 | − | 0.899896i | \(-0.356358\pi\) | ||||
0.436104 | + | 0.899896i | \(0.356358\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 10.8972 | + | 18.8746i | 0.416059 | + | 0.720635i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | 26.1534 | + | 45.2990i | 0.996365 | + | 1.72575i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.6411 | 1.20368 | 0.601842 | − | 0.798615i | \(-0.294434\pi\) | ||||
0.601842 | + | 0.798615i | \(0.294434\pi\) | |||||||
\(692\) | −18.3589 | −0.697901 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.71780 | + | 6.43941i | −0.141126 | + | 0.244437i | ||||
\(695\) | 1.28220 | 0.0486367 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6794 | − | 18.4973i | 0.404513 | − | 0.700637i | ||||
\(698\) | −0.0383484 | − | 0.0664214i | −0.00145151 | − | 0.00251409i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.17945 | + | 3.77492i | 0.0823754 | + | 0.142678i | ||||
\(701\) | 9.00000 | + | 15.5885i | 0.339925 | + | 0.588768i | 0.984418 | − | 0.175842i | \(-0.0562649\pi\) |
−0.644493 | + | 0.764610i | \(0.722932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2561 | + | 26.4244i | 0.575396 | + | 0.996616i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.03835 | − | 8.72668i | −0.189621 | − | 0.328433i | ||||
\(707\) | 27.7178 | − | 48.0086i | 1.04244 | − | 1.80555i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3972 | − | 23.2047i | 0.503144 | − | 0.871471i | −0.496849 | − | 0.867837i | \(-0.665510\pi\) |
0.999993 | − | 0.00363441i | \(-0.00115687\pi\) | |||||||
\(710\) | 10.0767 | 0.378172 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.179449 | − | 0.310816i | 0.00672515 | − | 0.0116483i | ||||
\(713\) | 16.0767 | − | 27.8457i | 0.602077 | − | 1.04283i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 7.85890 | − | 13.6120i | 0.293701 | − | 0.508705i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.67945 | − | 13.3012i | 0.286595 | − | 0.496396i | ||||
\(719\) | −8.64110 | − | 14.9668i | −0.322259 | − | 0.558168i | 0.658695 | − | 0.752410i | \(-0.271109\pi\) |
−0.980954 | + | 0.194242i | \(0.937775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.1534 | 1.68160 | ||||||||
\(722\) | 19.0000 | 0.707107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.03835 | − | 15.6549i | −0.335908 | − | 0.581809i | ||||
\(725\) | 4.67945 | + | 8.10504i | 0.173790 | + | 0.301014i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0767 | + | 26.1136i | 0.559164 | + | 0.968500i | 0.997567 | + | 0.0697214i | \(0.0222110\pi\) |
−0.438403 | + | 0.898779i | \(0.644456\pi\) | |||||||
\(728\) | −8.71780 | + | 15.0997i | −0.323103 | + | 0.559631i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.64110 | 0.171775 | ||||||||
\(731\) | −16.7945 | + | 29.0889i | −0.621167 | + | 1.07589i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.56440 | 0.353269 | 0.176635 | − | 0.984276i | \(-0.443479\pi\) | ||||
0.176635 | + | 0.984276i | \(0.443479\pi\) | |||||||
\(734\) | 14.7178 | 0.543244 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.50000 | − | 2.59808i | −0.0552907 | − | 0.0957664i | ||||
\(737\) | −17.0383 | + | 29.5113i | −0.627616 | + | 1.08706i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.17945 | + | 14.1672i | 0.300886 | + | 0.521150i | 0.976337 | − | 0.216255i | \(-0.0693843\pi\) |
−0.675451 | + | 0.737405i | \(0.736051\pi\) | |||||||
\(740\) | −7.00000 | −0.257325 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −57.0000 | −2.09254 | ||||||||
\(743\) | 4.50000 | + | 7.79423i | 0.165089 | + | 0.285943i | 0.936687 | − | 0.350168i | \(-0.113876\pi\) |
−0.771598 | + | 0.636111i | \(0.780542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.03835 | + | 8.72668i | −0.184591 | + | 0.319721i | ||||
\(746\) | −5.50000 | − | 9.52628i | −0.201369 | − | 0.348782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.0767 | −0.368441 | ||||||||
\(749\) | 40.7945 | 1.49060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4356 | + | 19.8070i | −0.417291 | + | 0.722769i | −0.995666 | − | 0.0930021i | \(-0.970354\pi\) |
0.578375 | + | 0.815771i | \(0.303687\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.7178 | + | 32.4202i | −0.681662 | + | 1.18067i | ||||
\(755\) | 1.03835 | + | 1.79847i | 0.0377894 | + | 0.0654531i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.9356 | − | 43.1897i | −0.906300 | − | 1.56976i | −0.819163 | − | 0.573561i | \(-0.805562\pi\) |
−0.0871365 | − | 0.996196i | \(-0.527772\pi\) | |||||||
\(758\) | −7.35890 | − | 12.7460i | −0.267287 | − | 0.462955i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.17945 | + | 3.77492i | −0.0790569 | + | 0.136931i | ||||
\(761\) | 7.07670 | 0.256530 | 0.128265 | − | 0.991740i | \(-0.459059\pi\) | ||||
0.128265 | + | 0.991740i | \(0.459059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.1917 | + | 40.1693i | 0.839597 | + | 1.45423i | ||||
\(764\) | −9.71780 | + | 16.8317i | −0.351578 | + | 0.608950i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.00000 | − | 5.19615i | 0.108394 | − | 0.187745i | ||||
\(767\) | 50.8712 | 1.83685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.35890 | + | 2.35368i | −0.0490031 | + | 0.0848759i | −0.889487 | − | 0.456961i | \(-0.848938\pi\) |
0.840483 | + | 0.541837i | \(0.182271\pi\) | |||||||
\(770\) | 6.53835 | − | 11.3248i | 0.235626 | − | 0.408116i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.0767 | 0.866539 | ||||||||
\(773\) | −0.897247 | + | 1.55408i | −0.0322717 | + | 0.0558963i | −0.881710 | − | 0.471791i | \(-0.843608\pi\) |
0.849438 | + | 0.527688i | \(0.176941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.35890 | − | 9.28189i | 0.192497 | − | 0.333415i | ||||
\(776\) | 7.03835 | + | 12.1908i | 0.252662 | + | 0.437623i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.07670 | −0.146157 | ||||||||
\(779\) | −13.8589 | + | 24.0043i | −0.496547 | + | 0.860044i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.1150 | − | 26.1800i | −0.540859 | − | 0.936795i | ||||
\(782\) | 5.03835 | + | 8.72668i | 0.180171 | + | 0.312065i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | − | 10.3923i | −0.214286 | − | 0.371154i | ||||
\(785\) | −2.50000 | + | 4.33013i | −0.0892288 | + | 0.154549i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0767 | −0.715657 | −0.357828 | − | 0.933787i | \(-0.616483\pi\) | ||||
−0.357828 | + | 0.933787i | \(0.616483\pi\) | |||||||
\(788\) | −2.82055 | + | 4.88534i | −0.100478 | + | 0.174033i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.71780 | −0.167852 | ||||||||
\(791\) | 14.6411 | 0.520578 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.7178 | + | 18.5638i | 0.380600 | + | 0.659219i | ||||
\(794\) | −3.21780 | + | 5.57339i | −0.114195 | + | 0.197792i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.32055 | − | 14.4116i | −0.294914 | − | 0.510806i | ||||
\(797\) | −1.07670 | −0.0381386 | −0.0190693 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190693 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1534 | −0.712976 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | −6.96165 | − | 12.0579i | −0.245671 | − | 0.425515i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.0767 | −0.460893 | ||||||||
\(806\) | 42.8712 | 1.51007 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.35890 | + | 11.0139i | −0.223705 | + | 0.387469i | ||||
\(809\) | 1.43560 | 0.0504729 | 0.0252364 | − | 0.999682i | \(-0.491966\pi\) | ||||
0.0252364 | + | 0.999682i | \(0.491966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.5383 | − | 25.1812i | 0.510510 | − | 0.884230i | −0.489415 | − | 0.872051i | \(-0.662790\pi\) |
0.999926 | − | 0.0121793i | \(-0.00387687\pi\) | |||||||
\(812\) | −20.3972 | − | 35.3291i | −0.715803 | − | 1.23981i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.5000 | + | 18.1865i | 0.368025 | + | 0.637438i | ||||
\(815\) | 2.35890 | + | 4.08573i | 0.0826286 | + | 0.143117i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7945 | − | 37.7492i | 0.762493 | − | 1.32068i | ||||
\(818\) | 11.0000 | 0.384606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.17945 | − | 5.50697i | −0.111031 | − | 0.192312i | ||||
\(821\) | −9.71780 | + | 16.8317i | −0.339153 | + | 0.587431i | −0.984274 | − | 0.176650i | \(-0.943474\pi\) |
0.645120 | + | 0.764081i | \(0.276807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1794 | + | 33.2198i | −0.668554 | + | 1.15797i | 0.309755 | + | 0.950816i | \(0.399753\pi\) |
−0.978309 | + | 0.207152i | \(0.933580\pi\) | |||||||
\(824\) | −10.3589 | −0.360869 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.7178 | + | 48.0086i | −0.964426 | + | 1.67043i | ||||
\(827\) | −19.6794 | + | 34.0858i | −0.684322 | + | 1.18528i | 0.289328 | + | 0.957230i | \(0.406568\pi\) |
−0.973650 | + | 0.228050i | \(0.926765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.153394 | −0.00532758 | −0.00266379 | − | 0.999996i | \(-0.500848\pi\) | ||||
−0.00266379 | + | 0.999996i | \(0.500848\pi\) | |||||||
\(830\) | −3.00000 | + | 5.19615i | −0.104132 | + | 0.180361i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | − | 3.46410i | 0.0693375 | − | 0.120096i | ||||
\(833\) | 20.1534 | + | 34.9067i | 0.698274 | + | 1.20945i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.4356 | 0.776416 | ||||||||
\(836\) | 13.0767 | 0.452267 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.85890 | + | 13.6120i | 0.271481 | + | 0.470219i | ||||
\(839\) | −0.358899 | − | 0.621631i | −0.0123906 | − | 0.0214611i | 0.859764 | − | 0.510692i | \(-0.170611\pi\) |
−0.872154 | + | 0.489231i | \(0.837277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.2945 | − | 50.7396i | −1.01015 | − | 1.74964i | ||||
\(842\) | −18.0383 | + | 31.2433i | −0.621643 | + | 1.07672i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.0767 | 0.518961 | ||||||||
\(845\) | −1.50000 | + | 2.59808i | −0.0516016 | + | 0.0893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.71780 | 0.299547 | ||||||||
\(848\) | 13.0767 | 0.449056 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.67945 | + | 2.90889i | 0.0576046 | + | 0.0997742i | ||||
\(851\) | 10.5000 | − | 18.1865i | 0.359935 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.71780 | − | 13.3676i | −0.264252 | − | 0.457699i | 0.703115 | − | 0.711076i | \(-0.251792\pi\) |
−0.967367 | + | 0.253378i | \(0.918459\pi\) | |||||||
\(854\) | −23.3589 | −0.799325 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.35890 | −0.319881 | ||||||||
\(857\) | −12.7178 | − | 22.0279i | −0.434432 | − | 0.752458i | 0.562817 | − | 0.826581i | \(-0.309717\pi\) |
−0.997249 | + | 0.0741235i | \(0.976384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.46165 | − | 2.53165i | 0.0498709 | − | 0.0863789i | −0.840012 | − | 0.542567i | \(-0.817452\pi\) |
0.889883 | + | 0.456188i | \(0.150786\pi\) | |||||||
\(860\) | 5.00000 | + | 8.66025i | 0.170499 | + | 0.295312i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.7945 | −0.367662 | ||||||||
\(863\) | 21.0000 | 0.714848 | 0.357424 | − | 0.933942i | \(-0.383655\pi\) | ||||
0.357424 | + | 0.933942i | \(0.383655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.17945 | − | 15.8993i | 0.312111 | − | 0.540591i | ||||
\(866\) | 36.7945 | 1.25033 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.3589 | + | 40.4588i | −0.792853 | + | 1.37326i | ||||
\(869\) | 7.07670 | + | 12.2572i | 0.240060 | + | 0.415797i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.7178 | + | 39.3484i | 0.769763 | + | 1.33327i | ||||
\(872\) | −5.32055 | − | 9.21546i | −0.180177 | − | 0.312075i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.53835 | − | 11.3248i | −0.221163 | − | 0.383065i | ||||
\(875\) | −4.35890 | −0.147358 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | + | 11.2583i | 0.219489 | + | 0.380167i | 0.954652 | − | 0.297724i | \(-0.0962275\pi\) |
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(878\) | −11.6794 | + | 20.2294i | −0.394162 | + | 0.682709i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | 19.0767 | 0.642710 | 0.321355 | − | 0.946959i | \(-0.395862\pi\) | ||||
0.321355 | + | 0.946959i | \(0.395862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.96165 | − | 15.5220i | 0.301584 | − | 0.522358i | −0.674911 | − | 0.737899i | \(-0.735818\pi\) |
0.976495 | + | 0.215541i | \(0.0691514\pi\) | |||||||
\(884\) | −6.71780 | + | 11.6356i | −0.225944 | + | 0.391346i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.64110 | 0.0887295 | ||||||||
\(887\) | 1.07670 | − | 1.86489i | 0.0361519 | − | 0.0626170i | −0.847383 | − | 0.530982i | \(-0.821823\pi\) |
0.883535 | + | 0.468365i | \(0.155157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5767 | + | 39.1040i | −0.757198 | + | 1.31151i | ||||
\(890\) | 0.179449 | + | 0.310816i | 0.00601516 | + | 0.0104186i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.3589 | 0.681666 | ||||||||
\(893\) | 26.1534 | 0.875190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.85890 | + | 13.6120i | 0.262694 | + | 0.454999i | ||||
\(896\) | 2.17945 | + | 3.77492i | 0.0728103 | + | 0.126111i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.179449 | + | 0.310816i | 0.00598831 | + | 0.0103721i | ||||
\(899\) | −50.1534 | + | 86.8682i | −1.67271 | + | 2.89722i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.9233 | −1.46330 | ||||||||
\(902\) | −9.53835 | + | 16.5209i | −0.317592 | + | 0.550086i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.35890 | −0.111715 | ||||||||
\(905\) | 18.0767 | 0.600890 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.7178 | + | 20.2958i | 0.389083 | + | 0.673912i | 0.992326 | − | 0.123645i | \(-0.0394586\pi\) |
−0.603243 | + | 0.797557i | \(0.706125\pi\) | |||||||
\(908\) | −1.67945 | + | 2.90889i | −0.0557345 | + | 0.0965350i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.71780 | − | 15.0997i | −0.288992 | − | 0.500549i | ||||
\(911\) | −35.2822 | −1.16895 | −0.584476 | − | 0.811411i | \(-0.698700\pi\) | ||||
−0.584476 | + | 0.811411i | \(0.698700\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | 0.595713 | ||||||||
\(914\) | 15.3206 | + | 26.5360i | 0.506759 | + | 0.877732i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.35890 | + | 7.54983i | −0.144022 | + | 0.249454i | ||||
\(917\) | 6.53835 | + | 11.3248i | 0.215915 | + | 0.373976i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3589 | −1.23236 | −0.616178 | − | 0.787607i | \(-0.711320\pi\) | ||||
−0.616178 | + | 0.787607i | \(0.711320\pi\) | |||||||
\(920\) | 3.00000 | 0.0989071 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.00000 | − | 15.5885i | 0.296399 | − | 0.513378i | ||||
\(923\) | −40.3068 | −1.32671 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50000 | − | 6.06218i | 0.115079 | − | 0.199323i | ||||
\(926\) | 8.89725 | + | 15.4105i | 0.292382 | + | 0.506420i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.67945 | + | 8.10504i | 0.153610 | + | 0.266061i | ||||
\(929\) | −13.2561 | − | 22.9603i | −0.434920 | − | 0.753304i | 0.562369 | − | 0.826886i | \(-0.309890\pi\) |
−0.997289 | + | 0.0735827i | \(0.976557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.1534 | − | 45.2990i | −0.857143 | − | 1.48461i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.3972 | + | 24.9368i | 0.471092 | + | 0.815956i | ||||
\(935\) | 5.03835 | − | 8.72668i | 0.164772 | − | 0.285393i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.3972 | + | 31.8650i | −0.601012 | + | 1.04098i | 0.391656 | + | 0.920112i | \(0.371902\pi\) |
−0.992668 | + | 0.120872i | \(0.961431\pi\) | |||||||
\(938\) | −49.5123 | −1.61663 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | −12.1150 | + | 20.9839i | −0.394939 | + | 0.684055i | −0.993093 | − | 0.117326i | \(-0.962568\pi\) |
0.598154 | + | 0.801381i | \(0.295901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0767 | 0.621223 | ||||||||
\(944\) | 6.35890 | − | 11.0139i | 0.206965 | − | 0.358473i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.0000 | − | 25.9808i | 0.487692 | − | 0.844707i | ||||
\(947\) | −8.03835 | − | 13.9228i | −0.261211 | − | 0.452431i | 0.705353 | − | 0.708856i | \(-0.250789\pi\) |
−0.966564 | + | 0.256425i | \(0.917455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.5644 | −0.602626 | ||||||||
\(950\) | −2.17945 | − | 3.77492i | −0.0707107 | − | 0.122474i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.32055 | − | 12.6796i | −0.237260 | − | 0.410947i | ||||
\(953\) | 6.71780 | + | 11.6356i | 0.217611 | + | 0.376913i | 0.954077 | − | 0.299561i | \(-0.0968403\pi\) |
−0.736466 | + | 0.676474i | \(0.763507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.71780 | − | 16.8317i | −0.314461 | − | 0.544662i | ||||
\(956\) | −6.71780 | + | 11.6356i | −0.217269 | + | 0.376321i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.0767 | 0.713266 | ||||||||
\(959\) | −26.1534 | + | 45.2990i | −0.844537 | + | 1.46278i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 83.8712 | 2.70552 | ||||||||
\(962\) | 28.0000 | 0.902756 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | + | 3.46410i | 0.0644157 | + | 0.111571i | ||||
\(965\) | −12.0383 | + | 20.8510i | −0.387528 | + | 0.671218i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.07670 | − | 3.59694i | −0.0667821 | − | 0.115670i | 0.830701 | − | 0.556719i | \(-0.187940\pi\) |
−0.897483 | + | 0.441049i | \(0.854607\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0767 | −0.451975 | ||||||||
\(971\) | −10.4356 | − | 18.0750i | −0.334894 | − | 0.580054i | 0.648570 | − | 0.761155i | \(-0.275367\pi\) |
−0.983465 | + | 0.181101i | \(0.942034\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.79449 | − | 4.84021i | 0.0895874 | − | 0.155170i | ||||
\(974\) | 4.82055 | + | 8.34944i | 0.154460 | + | 0.267533i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.35890 | 0.171534 | ||||||||
\(977\) | −9.35890 | −0.299418 | −0.149709 | − | 0.988730i | \(-0.547834\pi\) | ||||
−0.149709 | + | 0.988730i | \(0.547834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.538348 | − | 0.932447i | 0.0172057 | − | 0.0298011i | ||||
\(980\) | 12.0000 | 0.383326 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.50000 | − | 12.9904i | 0.239335 | − | 0.414540i | ||||
\(983\) | 27.2945 | + | 47.2755i | 0.870559 | + | 1.50785i | 0.861419 | + | 0.507895i | \(0.169576\pi\) |
0.00913990 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.82055 | − | 4.88534i | −0.0898702 | − | 0.155660i | ||||
\(986\) | −15.7178 | − | 27.2240i | −0.500557 | − | 0.866990i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.71780 | − | 15.0997i | 0.277350 | − | 0.480384i | ||||
\(989\) | −30.0000 | −0.953945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6794 | − | 46.2102i | −0.847501 | − | 1.46791i | −0.883432 | − | 0.468560i | \(-0.844773\pi\) |
0.0359311 | − | 0.999354i | \(-0.488560\pi\) | |||||||
\(992\) | 5.35890 | − | 9.28189i | 0.170145 | − | 0.294700i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.9617 | − | 38.0387i | 0.696581 | − | 1.20651i | ||||
\(995\) | 16.6411 | 0.527558 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.8589 | + | 25.7364i | −0.470586 | + | 0.815079i | −0.999434 | − | 0.0336376i | \(-0.989291\pi\) |
0.528848 | + | 0.848717i | \(0.322624\pi\) | |||||||
\(998\) | 7.82055 | − | 13.5456i | 0.247555 | − | 0.428778i | ||||
\(999\) | 0 | 0 |
(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 | 1710.2.l.k.1261.1 | 4 | ||
3.2 | odd | 2 | 570.2.i.h.121.1 | ✓ | 4 | ||
19.11 | even | 3 | inner | 1710.2.l.k.1531.1 | 4 | ||
57.11 | odd | 6 | 570.2.i.h.391.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.h.121.1 | ✓ | 4 | 3.2 | odd | 2 | ||
570.2.i.h.391.1 | yes | 4 | 57.11 | odd | 6 | ||
1710.2.l.k.1261.1 | 4 | 1.1 | even | 1 | trivial | ||
1710.2.l.k.1531.1 | 4 | 19.11 | even | 3 | inner |