Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.1 | ||
Root | \(0.809017 - 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.d.508.1 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30902 | + | 2.26728i | −0.925615 | + | 1.60321i | −0.135045 | + | 0.990839i | \(0.543118\pi\) |
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 1.11803 | + | 1.93649i | 0.645497 | + | 1.11803i | 0.984186 | + | 0.177136i | \(0.0566831\pi\) |
−0.338689 | + | 0.940898i | \(0.609984\pi\) | |||||||
\(4\) | −2.42705 | − | 4.20378i | −1.21353 | − | 2.10189i | ||||
\(5\) | 1.11803 | − | 1.93649i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(6\) | −5.85410 | −2.38993 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 7.47214 | 2.64180 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 2.92705 | + | 5.06980i | 0.925615 | + | 1.60321i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 5.42705 | − | 9.39993i | 1.56665 | − | 2.71353i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.54508 | + | 2.26728i | −1.74925 | + | 0.605957i | ||||
\(15\) | 5.00000 | 1.29099 | ||||||||
\(16\) | −4.92705 | + | 8.53390i | −1.23176 | + | 2.13348i | ||||
\(17\) | −0.736068 | − | 1.27491i | −0.178523 | − | 0.309210i | 0.762852 | − | 0.646573i | \(-0.223798\pi\) |
−0.941375 | + | 0.337363i | \(0.890465\pi\) | |||||||
\(18\) | −2.61803 | − | 4.53457i | −0.617077 | − | 1.06881i | ||||
\(19\) | 1.50000 | − | 2.59808i | 0.344124 | − | 0.596040i | −0.641071 | − | 0.767482i | \(-0.721509\pi\) |
0.985194 | + | 0.171442i | \(0.0548427\pi\) | |||||||
\(20\) | −10.8541 | −2.42705 | ||||||||
\(21\) | −1.11803 | + | 5.80948i | −0.243975 | + | 1.26773i | ||||
\(22\) | 7.85410 | 1.67450 | ||||||||
\(23\) | 4.11803 | − | 7.13264i | 0.858669 | − | 1.48726i | −0.0145291 | − | 0.999894i | \(-0.504625\pi\) |
0.873199 | − | 0.487365i | \(-0.162042\pi\) | |||||||
\(24\) | 8.35410 | + | 14.4697i | 1.70527 | + | 2.95362i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 2.42705 | − | 12.6113i | 0.458670 | − | 2.38332i | ||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | −6.54508 | + | 11.3364i | −1.19496 | + | 2.06974i | ||||
\(31\) | 2.50000 | + | 4.33013i | 0.449013 | + | 0.777714i | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) |
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | −5.42705 | − | 9.39993i | −0.959376 | − | 1.66169i | ||||
\(33\) | 3.35410 | − | 5.80948i | 0.583874 | − | 1.01130i | ||||
\(34\) | 3.85410 | 0.660973 | ||||||||
\(35\) | 5.59017 | − | 1.93649i | 0.944911 | − | 0.327327i | ||||
\(36\) | 9.70820 | 1.61803 | ||||||||
\(37\) | 2.35410 | − | 4.07742i | 0.387012 | − | 0.670324i | −0.605034 | − | 0.796200i | \(-0.706841\pi\) |
0.992046 | + | 0.125875i | \(0.0401739\pi\) | |||||||
\(38\) | 3.92705 | + | 6.80185i | 0.637052 | + | 1.10341i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.35410 | − | 14.4697i | 1.32090 | − | 2.28787i | ||||
\(41\) | 4.47214 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(42\) | −11.7082 | − | 10.1396i | −1.80662 | − | 1.56457i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −7.28115 | + | 12.6113i | −1.09768 | + | 1.90123i | ||||
\(45\) | 2.23607 | + | 3.87298i | 0.333333 | + | 0.577350i | ||||
\(46\) | 10.7812 | + | 18.6735i | 1.58959 | + | 2.75326i | ||||
\(47\) | −3.73607 | + | 6.47106i | −0.544962 | + | 0.943901i | 0.453648 | + | 0.891181i | \(0.350122\pi\) |
−0.998609 | + | 0.0527200i | \(0.983211\pi\) | |||||||
\(48\) | −22.0344 | −3.18040 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.64590 | − | 2.85078i | 0.230472 | − | 0.399189i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.73607 | + | 6.47106i | 0.513188 | + | 0.888868i | 0.999883 | + | 0.0152962i | \(0.00486912\pi\) |
−0.486695 | + | 0.873572i | \(0.661798\pi\) | |||||||
\(54\) | −2.92705 | + | 5.06980i | −0.398321 | + | 0.689913i | ||||
\(55\) | −6.70820 | −0.904534 | ||||||||
\(56\) | 14.9443 | + | 12.9421i | 1.99701 | + | 1.72946i | ||||
\(57\) | 6.70820 | 0.888523 | ||||||||
\(58\) | −5.85410 | + | 10.1396i | −0.768681 | + | 1.33139i | ||||
\(59\) | −0.736068 | − | 1.27491i | −0.0958279 | − | 0.165979i | 0.814126 | − | 0.580688i | \(-0.197217\pi\) |
−0.909954 | + | 0.414710i | \(0.863883\pi\) | |||||||
\(60\) | −12.1353 | − | 21.0189i | −1.56665 | − | 2.71353i | ||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | −13.0902 | −1.66245 | ||||||||
\(63\) | −5.00000 | + | 1.73205i | −0.629941 | + | 0.218218i | ||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.78115 | + | 15.2094i | 1.08089 | + | 1.87215i | ||||
\(67\) | −1.50000 | − | 2.59808i | −0.183254 | − | 0.317406i | 0.759733 | − | 0.650236i | \(-0.225330\pi\) |
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(68\) | −3.57295 | + | 6.18853i | −0.433284 | + | 0.750469i | ||||
\(69\) | 18.4164 | 2.21707 | ||||||||
\(70\) | −2.92705 | + | 15.2094i | −0.349850 | + | 1.81787i | ||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | −7.47214 | + | 12.9421i | −0.880600 | + | 1.52524i | ||||
\(73\) | −1.35410 | − | 2.34537i | −0.158486 | − | 0.274505i | 0.775837 | − | 0.630933i | \(-0.217328\pi\) |
−0.934323 | + | 0.356428i | \(0.883994\pi\) | |||||||
\(74\) | 6.16312 | + | 10.6748i | 0.716448 | + | 1.24092i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.5623 | −1.67041 | ||||||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.35410 | − | 2.34537i | 0.152348 | − | 0.263875i | −0.779742 | − | 0.626101i | \(-0.784650\pi\) |
0.932090 | + | 0.362226i | \(0.117983\pi\) | |||||||
\(80\) | 11.0172 | + | 19.0824i | 1.23176 | + | 2.13348i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −5.85410 | + | 10.1396i | −0.646477 | + | 1.11973i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 27.1353 | − | 9.39993i | 2.96070 | − | 1.02562i | ||||
\(85\) | −3.29180 | −0.357045 | ||||||||
\(86\) | 10.4721 | − | 18.1383i | 1.12924 | − | 1.95590i | ||||
\(87\) | 5.00000 | + | 8.66025i | 0.536056 | + | 0.928477i | ||||
\(88\) | −11.2082 | − | 19.4132i | −1.19480 | − | 2.06945i | ||||
\(89\) | 1.11803 | − | 1.93649i | 0.118511 | − | 0.205268i | −0.800667 | − | 0.599110i | \(-0.795521\pi\) |
0.919178 | + | 0.393842i | \(0.128854\pi\) | |||||||
\(90\) | −11.7082 | −1.23415 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −39.9787 | −4.16807 | ||||||||
\(93\) | −5.59017 | + | 9.68246i | −0.579674 | + | 1.00402i | ||||
\(94\) | −9.78115 | − | 16.9415i | −1.00885 | − | 1.74738i | ||||
\(95\) | −3.35410 | − | 5.80948i | −0.344124 | − | 0.596040i | ||||
\(96\) | 12.1353 | − | 21.0189i | 1.23855 | − | 2.14523i | ||||
\(97\) | −9.41641 | −0.956091 | −0.478046 | − | 0.878335i | \(-0.658655\pi\) | ||||
−0.478046 | + | 0.878335i | \(0.658655\pi\) | |||||||
\(98\) | −17.0172 | − | 6.80185i | −1.71900 | − | 0.687091i | ||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 4.30902 | + | 7.46344i | 0.426656 | + | 0.738990i | ||||
\(103\) | 1.35410 | − | 2.34537i | 0.133424 | − | 0.231097i | −0.791571 | − | 0.611078i | \(-0.790736\pi\) |
0.924994 | + | 0.379981i | \(0.124070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0000 | + | 8.66025i | 0.975900 | + | 0.845154i | ||||
\(106\) | −19.5623 | −1.90006 | ||||||||
\(107\) | 4.88197 | − | 8.45581i | 0.471957 | − | 0.817454i | −0.527528 | − | 0.849538i | \(-0.676881\pi\) |
0.999485 | + | 0.0320835i | \(0.0102142\pi\) | |||||||
\(108\) | −5.42705 | − | 9.39993i | −0.522218 | − | 0.904508i | ||||
\(109\) | −1.35410 | − | 2.34537i | −0.129699 | − | 0.224646i | 0.793861 | − | 0.608100i | \(-0.208068\pi\) |
−0.923560 | + | 0.383454i | \(0.874735\pi\) | |||||||
\(110\) | 8.78115 | − | 15.2094i | 0.837250 | − | 1.45016i | ||||
\(111\) | 10.5279 | 0.999261 | ||||||||
\(112\) | −24.6353 | + | 8.53390i | −2.32781 | + | 0.806378i | ||||
\(113\) | 2.94427 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(114\) | −8.78115 | + | 15.2094i | −0.822430 | + | 1.42449i | ||||
\(115\) | −9.20820 | − | 15.9491i | −0.858669 | − | 1.48726i | ||||
\(116\) | −10.8541 | − | 18.7999i | −1.00778 | − | 1.74552i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.85410 | 0.354799 | ||||||||
\(119\) | 0.736068 | − | 3.82472i | 0.0674752 | − | 0.350612i | ||||
\(120\) | 37.3607 | 3.41055 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −3.92705 | − | 6.80185i | −0.355538 | − | 0.615811i | ||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 12.1353 | − | 21.0189i | 1.08978 | − | 1.88755i | ||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 2.61803 | − | 13.6037i | 0.233233 | − | 1.21191i | ||||
\(127\) | −11.4164 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(128\) | −0.545085 | + | 0.944115i | −0.0481792 | + | 0.0834488i | ||||
\(129\) | −8.94427 | − | 15.4919i | −0.787499 | − | 1.36399i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.11803 | − | 7.13264i | 0.359794 | − | 0.623182i | −0.628132 | − | 0.778107i | \(-0.716180\pi\) |
0.987926 | + | 0.154925i | \(0.0495135\pi\) | |||||||
\(132\) | −32.5623 | −2.83418 | ||||||||
\(133\) | 7.50000 | − | 2.59808i | 0.650332 | − | 0.225282i | ||||
\(134\) | 7.85410 | 0.678491 | ||||||||
\(135\) | 2.50000 | − | 4.33013i | 0.215166 | − | 0.372678i | ||||
\(136\) | −5.50000 | − | 9.52628i | −0.471621 | − | 0.816872i | ||||
\(137\) | −4.11803 | − | 7.13264i | −0.351827 | − | 0.609383i | 0.634742 | − | 0.772724i | \(-0.281106\pi\) |
−0.986570 | + | 0.163341i | \(0.947773\pi\) | |||||||
\(138\) | −24.1074 | + | 41.7552i | −2.05216 | + | 3.55444i | ||||
\(139\) | −23.4164 | −1.98615 | −0.993077 | − | 0.117466i | \(-0.962523\pi\) | ||||
−0.993077 | + | 0.117466i | \(0.962523\pi\) | |||||||
\(140\) | −21.7082 | − | 18.7999i | −1.83468 | − | 1.58888i | ||||
\(141\) | −16.7082 | −1.40708 | ||||||||
\(142\) | −11.7082 | + | 20.2792i | −0.982531 | + | 1.70179i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.85410 | − | 17.0678i | −0.821175 | − | 1.42232i | ||||
\(145\) | 5.00000 | − | 8.66025i | 0.415227 | − | 0.719195i | ||||
\(146\) | 7.09017 | 0.586787 | ||||||||
\(147\) | −12.2984 | + | 9.68246i | −1.01435 | + | 0.798596i | ||||
\(148\) | −22.8541 | −1.87860 | ||||||||
\(149\) | 0.354102 | − | 0.613323i | 0.0290092 | − | 0.0502453i | −0.851156 | − | 0.524912i | \(-0.824098\pi\) |
0.880166 | + | 0.474667i | \(0.157431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2082 | + | 17.6811i | 0.830732 | + | 1.43887i | 0.897459 | + | 0.441098i | \(0.145411\pi\) |
−0.0667268 | + | 0.997771i | \(0.521256\pi\) | |||||||
\(152\) | 11.2082 | − | 19.4132i | 0.909105 | − | 1.57462i | ||||
\(153\) | 2.94427 | 0.238030 | ||||||||
\(154\) | 15.7082 | + | 13.6037i | 1.26580 | + | 1.09622i | ||||
\(155\) | 11.1803 | 0.898027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | 3.54508 | + | 6.14027i | 0.282032 | + | 0.488493i | ||||
\(159\) | −8.35410 | + | 14.4697i | −0.662523 | + | 1.14752i | ||||
\(160\) | −24.2705 | −1.91875 | ||||||||
\(161\) | 20.5902 | − | 7.13264i | 1.62273 | − | 0.562131i | ||||
\(162\) | −28.7984 | −2.26261 | ||||||||
\(163\) | −8.20820 | + | 14.2170i | −0.642916 | + | 1.11356i | 0.341862 | + | 0.939750i | \(0.388942\pi\) |
−0.984779 | + | 0.173813i | \(0.944391\pi\) | |||||||
\(164\) | −10.8541 | − | 18.7999i | −0.847563 | − | 1.46802i | ||||
\(165\) | −7.50000 | − | 12.9904i | −0.583874 | − | 1.01130i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.4721 | −1.73895 | −0.869473 | − | 0.493980i | \(-0.835541\pi\) | ||||
−0.869473 | + | 0.493980i | \(0.835541\pi\) | |||||||
\(168\) | −8.35410 | + | 43.4092i | −0.644533 | + | 3.34909i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.30902 | − | 7.46344i | 0.330487 | − | 0.572419i | ||||
\(171\) | 3.00000 | + | 5.19615i | 0.229416 | + | 0.397360i | ||||
\(172\) | 19.4164 | + | 33.6302i | 1.48049 | + | 2.56428i | ||||
\(173\) | 8.20820 | − | 14.2170i | 0.624058 | − | 1.08090i | −0.364664 | − | 0.931139i | \(-0.618816\pi\) |
0.988722 | − | 0.149761i | \(-0.0478505\pi\) | |||||||
\(174\) | −26.1803 | −1.98473 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 29.5623 | 2.22834 | ||||||||
\(177\) | 1.64590 | − | 2.85078i | 0.123713 | − | 0.214278i | ||||
\(178\) | 2.92705 | + | 5.06980i | 0.219392 | + | 0.379998i | ||||
\(179\) | 10.0623 | + | 17.4284i | 0.752092 | + | 1.30266i | 0.946807 | + | 0.321802i | \(0.104288\pi\) |
−0.194715 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(180\) | 10.8541 | − | 18.7999i | 0.809017 | − | 1.40126i | ||||
\(181\) | −25.4164 | −1.88919 | −0.944593 | − | 0.328243i | \(-0.893544\pi\) | ||||
−0.944593 | + | 0.328243i | \(0.893544\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.70820 | −0.495885 | ||||||||
\(184\) | 30.7705 | − | 53.2961i | 2.26843 | − | 3.92904i | ||||
\(185\) | −5.26393 | − | 9.11740i | −0.387012 | − | 0.670324i | ||||
\(186\) | −14.6353 | − | 25.3490i | −1.07311 | − | 1.85868i | ||||
\(187\) | −2.20820 | + | 3.82472i | −0.161480 | + | 0.279691i | ||||
\(188\) | 36.2705 | 2.64530 | ||||||||
\(189\) | 4.47214 | + | 3.87298i | 0.325300 | + | 0.281718i | ||||
\(190\) | 17.5623 | 1.27410 | ||||||||
\(191\) | −5.59017 | + | 9.68246i | −0.404491 | + | 0.700598i | −0.994262 | − | 0.106972i | \(-0.965884\pi\) |
0.589772 | + | 0.807570i | \(0.299218\pi\) | |||||||
\(192\) | 9.73607 | + | 16.8634i | 0.702640 | + | 1.21701i | ||||
\(193\) | 0.354102 | + | 0.613323i | 0.0254888 | + | 0.0441479i | 0.878488 | − | 0.477764i | \(-0.158552\pi\) |
−0.853000 | + | 0.521912i | \(0.825219\pi\) | |||||||
\(194\) | 12.3262 | − | 21.3497i | 0.884972 | − | 1.53282i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26.6976 | − | 21.0189i | 1.90697 | − | 1.50135i | ||||
\(197\) | 9.05573 | 0.645194 | 0.322597 | − | 0.946536i | \(-0.395444\pi\) | ||||
0.322597 | + | 0.946536i | \(0.395444\pi\) | |||||||
\(198\) | −7.85410 | + | 13.6037i | −0.558167 | + | 0.966773i | ||||
\(199\) | 10.3541 | + | 17.9338i | 0.733983 | + | 1.27130i | 0.955168 | + | 0.296064i | \(0.0956741\pi\) |
−0.221185 | + | 0.975232i | \(0.570993\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.35410 | − | 5.80948i | 0.236580 | − | 0.409769i | ||||
\(202\) | −23.5623 | −1.65784 | ||||||||
\(203\) | 8.94427 | + | 7.74597i | 0.627765 | + | 0.543660i | ||||
\(204\) | −15.9787 | −1.11873 | ||||||||
\(205\) | 5.00000 | − | 8.66025i | 0.349215 | − | 0.604858i | ||||
\(206\) | 3.54508 | + | 6.14027i | 0.246998 | + | 0.427813i | ||||
\(207\) | 8.23607 | + | 14.2653i | 0.572446 | + | 0.991506i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | −32.7254 | + | 11.3364i | −2.25827 | + | 0.782287i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 18.1353 | − | 31.4112i | 1.24553 | − | 2.15733i | ||||
\(213\) | 10.0000 | + | 17.3205i | 0.685189 | + | 1.18678i | ||||
\(214\) | 12.7812 | + | 22.1376i | 0.873702 | + | 1.51330i | ||||
\(215\) | −8.94427 | + | 15.4919i | −0.609994 | + | 1.05654i | ||||
\(216\) | 16.7082 | 1.13685 | ||||||||
\(217\) | −2.50000 | + | 12.9904i | −0.169711 | + | 0.881845i | ||||
\(218\) | 7.09017 | 0.480207 | ||||||||
\(219\) | 3.02786 | − | 5.24441i | 0.204604 | − | 0.354385i | ||||
\(220\) | 16.2812 | + | 28.1998i | 1.09768 | + | 1.90123i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.7812 | + | 23.8697i | −0.924930 | + | 1.60203i | ||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 5.42705 | − | 28.1998i | 0.362610 | − | 1.88418i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.85410 | + | 6.67550i | −0.256371 | + | 0.444048i | ||||
\(227\) | 2.97214 | + | 5.14789i | 0.197268 | + | 0.341677i | 0.947642 | − | 0.319336i | \(-0.103460\pi\) |
−0.750374 | + | 0.661014i | \(0.770127\pi\) | |||||||
\(228\) | −16.2812 | − | 28.1998i | −1.07825 | − | 1.86758i | ||||
\(229\) | 12.0623 | − | 20.8925i | 0.797100 | − | 1.38062i | −0.124398 | − | 0.992232i | \(-0.539700\pi\) |
0.921497 | − | 0.388385i | \(-0.126967\pi\) | |||||||
\(230\) | 48.2148 | 3.17919 | ||||||||
\(231\) | 16.7705 | − | 5.80948i | 1.10342 | − | 0.382235i | ||||
\(232\) | 33.4164 | 2.19389 | ||||||||
\(233\) | −5.97214 | + | 10.3440i | −0.391248 | + | 0.677661i | −0.992614 | − | 0.121312i | \(-0.961290\pi\) |
0.601367 | + | 0.798973i | \(0.294623\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.35410 | + | 14.4697i | 0.544962 | + | 0.943901i | ||||
\(236\) | −3.57295 | + | 6.18853i | −0.232579 | + | 0.402839i | ||||
\(237\) | 6.05573 | 0.393362 | ||||||||
\(238\) | 7.70820 | + | 6.67550i | 0.499649 | + | 0.432708i | ||||
\(239\) | −19.4164 | −1.25594 | −0.627972 | − | 0.778236i | \(-0.716115\pi\) | ||||
−0.627972 | + | 0.778236i | \(0.716115\pi\) | |||||||
\(240\) | −24.6353 | + | 42.6695i | −1.59020 | + | 2.75431i | ||||
\(241\) | 2.35410 | + | 4.07742i | 0.151641 | + | 0.262650i | 0.931831 | − | 0.362893i | \(-0.118211\pi\) |
−0.780190 | + | 0.625543i | \(0.784878\pi\) | |||||||
\(242\) | 2.61803 | + | 4.53457i | 0.168294 | + | 0.291493i | ||||
\(243\) | −8.94427 | + | 15.4919i | −0.573775 | + | 0.993808i | ||||
\(244\) | 14.5623 | 0.932256 | ||||||||
\(245\) | 14.5344 | + | 5.80948i | 0.928571 | + | 0.371154i | ||||
\(246\) | −26.1803 | −1.66920 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 18.6803 | + | 32.3553i | 1.18620 | + | 2.05456i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.6353 | + | 25.3490i | −0.925615 | + | 1.60321i | ||||
\(251\) | 1.52786 | 0.0964379 | 0.0482190 | − | 0.998837i | \(-0.484645\pi\) | ||||
0.0482190 | + | 0.998837i | \(0.484645\pi\) | |||||||
\(252\) | 19.4164 | + | 16.8151i | 1.22312 | + | 1.05925i | ||||
\(253\) | −24.7082 | −1.55339 | ||||||||
\(254\) | 14.9443 | − | 25.8842i | 0.937687 | − | 1.62412i | ||||
\(255\) | −3.68034 | − | 6.37454i | −0.230472 | − | 0.399189i | ||||
\(256\) | 7.28115 | + | 12.6113i | 0.455072 | + | 0.788208i | ||||
\(257\) | 0.0278640 | − | 0.0482619i | 0.00173811 | − | 0.00301050i | −0.865155 | − | 0.501504i | \(-0.832780\pi\) |
0.866893 | + | 0.498494i | \(0.166113\pi\) | |||||||
\(258\) | 46.8328 | 2.91568 | ||||||||
\(259\) | 11.7705 | − | 4.07742i | 0.731384 | − | 0.253359i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.47214 | + | 7.74597i | −0.276818 | + | 0.479463i | ||||
\(262\) | 10.7812 | + | 18.6735i | 0.666062 | + | 1.15365i | ||||
\(263\) | −13.0623 | − | 22.6246i | −0.805456 | − | 1.39509i | −0.915983 | − | 0.401218i | \(-0.868587\pi\) |
0.110526 | − | 0.993873i | \(-0.464746\pi\) | |||||||
\(264\) | 25.0623 | − | 43.4092i | 1.54248 | − | 2.67165i | ||||
\(265\) | 16.7082 | 1.02638 | ||||||||
\(266\) | −3.92705 | + | 20.4056i | −0.240783 | + | 1.25114i | ||||
\(267\) | 5.00000 | 0.305995 | ||||||||
\(268\) | −7.28115 | + | 12.6113i | −0.444767 | + | 0.770359i | ||||
\(269\) | −6.73607 | − | 11.6672i | −0.410705 | − | 0.711362i | 0.584262 | − | 0.811565i | \(-0.301384\pi\) |
−0.994967 | + | 0.100203i | \(0.968051\pi\) | |||||||
\(270\) | 6.54508 | + | 11.3364i | 0.398321 | + | 0.689913i | ||||
\(271\) | −10.2082 | + | 17.6811i | −0.620104 | + | 1.07405i | 0.369362 | + | 0.929286i | \(0.379576\pi\) |
−0.989466 | + | 0.144766i | \(0.953757\pi\) | |||||||
\(272\) | 14.5066 | 0.879590 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.5623 | 1.30263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −44.6976 | − | 77.4184i | −2.69048 | − | 4.66004i | ||||
\(277\) | 0.208204 | + | 0.360620i | 0.0125098 | + | 0.0216675i | 0.872213 | − | 0.489127i | \(-0.162685\pi\) |
−0.859703 | + | 0.510795i | \(0.829351\pi\) | |||||||
\(278\) | 30.6525 | − | 53.0916i | 1.83841 | − | 3.18423i | ||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 41.7705 | − | 14.4697i | 2.49627 | − | 0.864732i | ||||
\(281\) | −26.9443 | −1.60736 | −0.803680 | − | 0.595061i | \(-0.797128\pi\) | ||||
−0.803680 | + | 0.595061i | \(0.797128\pi\) | |||||||
\(282\) | 21.8713 | − | 37.8822i | 1.30242 | − | 2.25585i | ||||
\(283\) | −13.0623 | − | 22.6246i | −0.776473 | − | 1.34489i | −0.933963 | − | 0.357371i | \(-0.883673\pi\) |
0.157489 | − | 0.987521i | \(-0.449660\pi\) | |||||||
\(284\) | −21.7082 | − | 37.5997i | −1.28814 | − | 2.23113i | ||||
\(285\) | 7.50000 | − | 12.9904i | 0.444262 | − | 0.769484i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94427 | + | 7.74597i | 0.527964 | + | 0.457230i | ||||
\(288\) | 21.7082 | 1.27917 | ||||||||
\(289\) | 7.41641 | − | 12.8456i | 0.436259 | − | 0.755623i | ||||
\(290\) | 13.0902 | + | 22.6728i | 0.768681 | + | 1.33139i | ||||
\(291\) | −10.5279 | − | 18.2348i | −0.617154 | − | 1.06894i | ||||
\(292\) | −6.57295 | + | 11.3847i | −0.384653 | + | 0.666238i | ||||
\(293\) | 14.9443 | 0.873054 | 0.436527 | − | 0.899691i | \(-0.356208\pi\) | ||||
0.436527 | + | 0.899691i | \(0.356208\pi\) | |||||||
\(294\) | −5.85410 | − | 40.5584i | −0.341418 | − | 2.36541i | ||||
\(295\) | −3.29180 | −0.191656 | ||||||||
\(296\) | 17.5902 | − | 30.4671i | 1.02241 | − | 1.77086i | ||||
\(297\) | −3.35410 | − | 5.80948i | −0.194625 | − | 0.337100i | ||||
\(298\) | 0.927051 | + | 1.60570i | 0.0537026 | + | 0.0930157i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | − | 13.8564i | −0.922225 | − | 0.798670i | ||||
\(302\) | −53.4508 | −3.07575 | ||||||||
\(303\) | −10.0623 | + | 17.4284i | −0.578064 | + | 1.00124i | ||||
\(304\) | 14.7812 | + | 25.6017i | 0.847757 | + | 1.46836i | ||||
\(305\) | 3.35410 | + | 5.80948i | 0.192055 | + | 0.332650i | ||||
\(306\) | −3.85410 | + | 6.67550i | −0.220324 | + | 0.381613i | ||||
\(307\) | −19.4164 | −1.10815 | −0.554076 | − | 0.832466i | \(-0.686928\pi\) | ||||
−0.554076 | + | 0.832466i | \(0.686928\pi\) | |||||||
\(308\) | −36.4058 | + | 12.6113i | −2.07441 | + | 0.718597i | ||||
\(309\) | 6.05573 | 0.344498 | ||||||||
\(310\) | −14.6353 | + | 25.3490i | −0.831227 | + | 1.43973i | ||||
\(311\) | 13.8820 | + | 24.0443i | 0.787174 | + | 1.36343i | 0.927692 | + | 0.373347i | \(0.121790\pi\) |
−0.140518 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.79180 | − | 4.83553i | 0.157802 | − | 0.273320i | −0.776274 | − | 0.630396i | \(-0.782893\pi\) |
0.934076 | + | 0.357075i | \(0.116226\pi\) | |||||||
\(314\) | 18.3262 | 1.03421 | ||||||||
\(315\) | −2.23607 | + | 11.6190i | −0.125988 | + | 0.654654i | ||||
\(316\) | −13.1459 | −0.739515 | ||||||||
\(317\) | −4.11803 | + | 7.13264i | −0.231292 | + | 0.400609i | −0.958189 | − | 0.286138i | \(-0.907629\pi\) |
0.726897 | + | 0.686747i | \(0.240962\pi\) | |||||||
\(318\) | −21.8713 | − | 37.8822i | −1.22648 | − | 2.12433i | ||||
\(319\) | −6.70820 | − | 11.6190i | −0.375587 | − | 0.650536i | ||||
\(320\) | 9.73607 | − | 16.8634i | 0.544263 | − | 0.942691i | ||||
\(321\) | 21.8328 | 1.21859 | ||||||||
\(322\) | −10.7812 | + | 56.0205i | −0.600810 | + | 3.12190i | ||||
\(323\) | −4.41641 | −0.245736 | ||||||||
\(324\) | 26.6976 | − | 46.2415i | 1.48320 | − | 2.56897i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.4894 | − | 37.2207i | −1.19019 | − | 2.06146i | ||||
\(327\) | 3.02786 | − | 5.24441i | 0.167441 | − | 0.290017i | ||||
\(328\) | 33.4164 | 1.84511 | ||||||||
\(329\) | −18.6803 | + | 6.47106i | −1.02988 | + | 0.356761i | ||||
\(330\) | 39.2705 | 2.16177 | ||||||||
\(331\) | −0.791796 | + | 1.37143i | −0.0435210 | + | 0.0753807i | −0.886965 | − | 0.461836i | \(-0.847191\pi\) |
0.843444 | + | 0.537217i | \(0.180524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.70820 | + | 8.15485i | 0.258008 | + | 0.446883i | ||||
\(334\) | 29.4164 | − | 50.9507i | 1.60959 | − | 2.78790i | ||||
\(335\) | −6.70820 | −0.366508 | ||||||||
\(336\) | −44.0689 | − | 38.1648i | −2.40415 | − | 2.08206i | ||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.29180 | + | 5.70156i | 0.178786 | + | 0.309666i | ||||
\(340\) | 7.98936 | + | 13.8380i | 0.433284 | + | 0.750469i | ||||
\(341\) | 7.50000 | − | 12.9904i | 0.406148 | − | 0.703469i | ||||
\(342\) | −15.7082 | −0.849402 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −59.7771 | −3.22296 | ||||||||
\(345\) | 20.5902 | − | 35.6632i | 1.10854 | − | 1.92004i | ||||
\(346\) | 21.4894 | + | 37.2207i | 1.15527 | + | 2.00099i | ||||
\(347\) | −11.5344 | − | 19.9782i | −0.619201 | − | 1.07249i | −0.989632 | − | 0.143628i | \(-0.954123\pi\) |
0.370430 | − | 0.928860i | \(-0.379210\pi\) | |||||||
\(348\) | 24.2705 | − | 42.0378i | 1.30104 | − | 2.25346i | ||||
\(349\) | 29.4164 | 1.57462 | 0.787312 | − | 0.616555i | \(-0.211472\pi\) | ||||
0.787312 | + | 0.616555i | \(0.211472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.2812 | + | 28.1998i | −0.867788 | + | 1.50305i | ||||
\(353\) | 8.64590 | + | 14.9751i | 0.460175 | + | 0.797046i | 0.998969 | − | 0.0453912i | \(-0.0144534\pi\) |
−0.538795 | + | 0.842437i | \(0.681120\pi\) | |||||||
\(354\) | 4.30902 | + | 7.46344i | 0.229022 | + | 0.396677i | ||||
\(355\) | 10.0000 | − | 17.3205i | 0.530745 | − | 0.919277i | ||||
\(356\) | −10.8541 | −0.575266 | ||||||||
\(357\) | 8.22949 | − | 2.85078i | 0.435551 | − | 0.150879i | ||||
\(358\) | −52.6869 | −2.78459 | ||||||||
\(359\) | 5.97214 | − | 10.3440i | 0.315197 | − | 0.545938i | −0.664282 | − | 0.747482i | \(-0.731263\pi\) |
0.979479 | + | 0.201544i | \(0.0645960\pi\) | |||||||
\(360\) | 16.7082 | + | 28.9395i | 0.880600 | + | 1.52524i | ||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | 33.2705 | − | 57.6262i | 1.74866 | − | 3.02877i | ||||
\(363\) | 4.47214 | 0.234726 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.05573 | −0.316971 | ||||||||
\(366\) | 8.78115 | − | 15.2094i | 0.458998 | − | 0.795008i | ||||
\(367\) | 6.35410 | + | 11.0056i | 0.331681 | + | 0.574489i | 0.982842 | − | 0.184451i | \(-0.0590508\pi\) |
−0.651160 | + | 0.758940i | \(0.725717\pi\) | |||||||
\(368\) | 40.5795 | + | 70.2858i | 2.11535 | + | 3.66390i | ||||
\(369\) | −4.47214 | + | 7.74597i | −0.232810 | + | 0.403239i | ||||
\(370\) | 27.5623 | 1.43290 | ||||||||
\(371\) | −3.73607 | + | 19.4132i | −0.193967 | + | 1.00788i | ||||
\(372\) | 54.2705 | 2.81379 | ||||||||
\(373\) | 0.791796 | − | 1.37143i | 0.0409976 | − | 0.0710100i | −0.844798 | − | 0.535085i | \(-0.820280\pi\) |
0.885796 | + | 0.464075i | \(0.153613\pi\) | |||||||
\(374\) | −5.78115 | − | 10.0133i | −0.298936 | − | 0.517773i | ||||
\(375\) | 12.5000 | + | 21.6506i | 0.645497 | + | 1.11803i | ||||
\(376\) | −27.9164 | + | 48.3526i | −1.43968 | + | 2.49360i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −14.6353 | + | 5.06980i | −0.752756 | + | 0.260762i | ||||
\(379\) | 15.4164 | 0.791888 | 0.395944 | − | 0.918275i | \(-0.370417\pi\) | ||||
0.395944 | + | 0.918275i | \(0.370417\pi\) | |||||||
\(380\) | −16.2812 | + | 28.1998i | −0.835206 | + | 1.44662i | ||||
\(381\) | −12.7639 | − | 22.1078i | −0.653916 | − | 1.13262i | ||||
\(382\) | −14.6353 | − | 25.3490i | −0.748805 | − | 1.29697i | ||||
\(383\) | 7.50000 | − | 12.9904i | 0.383232 | − | 0.663777i | −0.608290 | − | 0.793715i | \(-0.708144\pi\) |
0.991522 | + | 0.129937i | \(0.0414776\pi\) | |||||||
\(384\) | −2.43769 | −0.124398 | ||||||||
\(385\) | −13.4164 | − | 11.6190i | −0.683763 | − | 0.592157i | ||||
\(386\) | −1.85410 | −0.0943713 | ||||||||
\(387\) | 8.00000 | − | 13.8564i | 0.406663 | − | 0.704361i | ||||
\(388\) | 22.8541 | + | 39.5845i | 1.16024 | + | 2.00960i | ||||
\(389\) | −0.736068 | − | 1.27491i | −0.0373201 | − | 0.0646404i | 0.846762 | − | 0.531972i | \(-0.178549\pi\) |
−0.884082 | + | 0.467332i | \(0.845215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1246 | −0.613168 | ||||||||
\(392\) | 7.47214 | + | 51.7685i | 0.377400 | + | 2.61470i | ||||
\(393\) | 18.4164 | 0.928985 | ||||||||
\(394\) | −11.8541 | + | 20.5319i | −0.597201 | + | 1.03438i | ||||
\(395\) | −3.02786 | − | 5.24441i | −0.152348 | − | 0.263875i | ||||
\(396\) | −14.5623 | − | 25.2227i | −0.731783 | − | 1.26749i | ||||
\(397\) | −13.0623 | + | 22.6246i | −0.655578 | + | 1.13549i | 0.326170 | + | 0.945311i | \(0.394242\pi\) |
−0.981748 | + | 0.190184i | \(0.939092\pi\) | |||||||
\(398\) | −54.2148 | −2.71754 | ||||||||
\(399\) | 13.4164 | + | 11.6190i | 0.671660 | + | 0.581675i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.11803 | − | 12.3288i | 0.355458 | − | 0.615671i | −0.631739 | − | 0.775182i | \(-0.717658\pi\) |
0.987196 | + | 0.159511i | \(0.0509917\pi\) | |||||||
\(402\) | 8.78115 | + | 15.2094i | 0.437964 | + | 0.758576i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 21.8435 | − | 37.8340i | 1.08675 | − | 1.88231i | ||||
\(405\) | 24.5967 | 1.22222 | ||||||||
\(406\) | −29.2705 | + | 10.1396i | −1.45267 | + | 0.503220i | ||||
\(407\) | −14.1246 | −0.700131 | ||||||||
\(408\) | 12.2984 | − | 21.3014i | 0.608860 | − | 1.05458i | ||||
\(409\) | 4.35410 | + | 7.54153i | 0.215296 | + | 0.372904i | 0.953364 | − | 0.301822i | \(-0.0975949\pi\) |
−0.738068 | + | 0.674727i | \(0.764262\pi\) | |||||||
\(410\) | 13.0902 | + | 22.6728i | 0.646477 | + | 1.11973i | ||||
\(411\) | 9.20820 | − | 15.9491i | 0.454207 | − | 0.786710i | ||||
\(412\) | −13.1459 | −0.647652 | ||||||||
\(413\) | 0.736068 | − | 3.82472i | 0.0362195 | − | 0.188202i | ||||
\(414\) | −43.1246 | −2.11946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.1803 | − | 45.3457i | −1.28206 | − | 2.22059i | ||||
\(418\) | 11.7812 | − | 20.4056i | 0.576235 | − | 0.998068i | ||||
\(419\) | 32.9443 | 1.60943 | 0.804717 | − | 0.593659i | \(-0.202317\pi\) | ||||
0.804717 | + | 0.593659i | \(0.202317\pi\) | |||||||
\(420\) | 12.1353 | − | 63.0566i | 0.592140 | − | 3.07685i | ||||
\(421\) | −13.4164 | −0.653876 | −0.326938 | − | 0.945046i | \(-0.606017\pi\) | ||||
−0.326938 | + | 0.945046i | \(0.606017\pi\) | |||||||
\(422\) | −5.23607 | + | 9.06914i | −0.254888 | + | 0.441479i | ||||
\(423\) | −7.47214 | − | 12.9421i | −0.363308 | − | 0.629267i | ||||
\(424\) | 27.9164 | + | 48.3526i | 1.35574 | + | 2.34821i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −52.3607 | −2.53688 | ||||||||
\(427\) | −7.50000 | + | 2.59808i | −0.362950 | + | 0.125730i | ||||
\(428\) | −47.3951 | −2.29093 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.4164 | − | 40.5584i | −1.12924 | − | 1.95590i | ||||
\(431\) | −15.6803 | − | 27.1591i | −0.755295 | − | 1.30821i | −0.945227 | − | 0.326413i | \(-0.894160\pi\) |
0.189932 | − | 0.981797i | \(-0.439173\pi\) | |||||||
\(432\) | −11.0172 | + | 19.0824i | −0.530066 | + | 0.918102i | ||||
\(433\) | 29.4164 | 1.41366 | 0.706831 | − | 0.707382i | \(-0.250124\pi\) | ||||
0.706831 | + | 0.707382i | \(0.250124\pi\) | |||||||
\(434\) | −26.1803 | − | 22.6728i | −1.25670 | − | 1.08833i | ||||
\(435\) | 22.3607 | 1.07211 | ||||||||
\(436\) | −6.57295 | + | 11.3847i | −0.314787 | + | 0.545227i | ||||
\(437\) | −12.3541 | − | 21.3979i | −0.590977 | − | 1.02360i | ||||
\(438\) | 7.92705 | + | 13.7301i | 0.378769 | + | 0.656047i | ||||
\(439\) | −12.0623 | + | 20.8925i | −0.575702 | + | 0.997146i | 0.420262 | + | 0.907403i | \(0.361938\pi\) |
−0.995965 | + | 0.0897433i | \(0.971395\pi\) | |||||||
\(440\) | −50.1246 | −2.38960 | ||||||||
\(441\) | −13.0000 | − | 5.19615i | −0.619048 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.11803 | + | 1.93649i | −0.0531194 | + | 0.0920055i | −0.891362 | − | 0.453291i | \(-0.850250\pi\) |
0.838243 | + | 0.545297i | \(0.183583\pi\) | |||||||
\(444\) | −25.5517 | − | 44.2568i | −1.21263 | − | 2.10033i | ||||
\(445\) | −2.50000 | − | 4.33013i | −0.118511 | − | 0.205268i | ||||
\(446\) | −5.23607 | + | 9.06914i | −0.247935 | + | 0.429436i | ||||
\(447\) | 1.58359 | 0.0749013 | ||||||||
\(448\) | 17.4164 | + | 15.0831i | 0.822848 | + | 0.712607i | ||||
\(449\) | 34.3607 | 1.62158 | 0.810790 | − | 0.585337i | \(-0.199038\pi\) | ||||
0.810790 | + | 0.585337i | \(0.199038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.70820 | − | 11.6190i | −0.315877 | − | 0.547115i | ||||
\(452\) | −7.14590 | − | 12.3771i | −0.336115 | − | 0.582168i | ||||
\(453\) | −22.8262 | + | 39.5362i | −1.07247 | + | 1.85757i | ||||
\(454\) | −15.5623 | −0.730375 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 50.1246 | 2.34730 | ||||||||
\(457\) | −3.06231 | + | 5.30407i | −0.143249 | + | 0.248114i | −0.928718 | − | 0.370786i | \(-0.879088\pi\) |
0.785470 | + | 0.618900i | \(0.212422\pi\) | |||||||
\(458\) | 31.5795 | + | 54.6973i | 1.47561 | + | 2.55584i | ||||
\(459\) | −1.64590 | − | 2.85078i | −0.0768239 | − | 0.133063i | ||||
\(460\) | −44.6976 | + | 77.4184i | −2.08403 | + | 3.60965i | ||||
\(461\) | −34.3607 | −1.60034 | −0.800168 | − | 0.599776i | \(-0.795256\pi\) | ||||
−0.800168 | + | 0.599776i | \(0.795256\pi\) | |||||||
\(462\) | −8.78115 | + | 45.6282i | −0.408536 | + | 2.12282i | ||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | −22.0344 | + | 38.1648i | −1.02292 | + | 1.77176i | ||||
\(465\) | 12.5000 | + | 21.6506i | 0.579674 | + | 1.00402i | ||||
\(466\) | −15.6353 | − | 27.0811i | −0.724289 | − | 1.25451i | ||||
\(467\) | −4.82624 | + | 8.35929i | −0.223332 | + | 0.386822i | −0.955818 | − | 0.293960i | \(-0.905027\pi\) |
0.732486 | + | 0.680782i | \(0.238360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.50000 | − | 7.79423i | 0.0692636 | − | 0.359904i | ||||
\(470\) | −43.7426 | −2.01770 | ||||||||
\(471\) | 7.82624 | − | 13.5554i | 0.360614 | − | 0.624602i | ||||
\(472\) | −5.50000 | − | 9.52628i | −0.253158 | − | 0.438483i | ||||
\(473\) | 12.0000 | + | 20.7846i | 0.551761 | + | 0.955677i | ||||
\(474\) | −7.92705 | + | 13.7301i | −0.364102 | + | 0.630642i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −17.8647 | + | 6.18853i | −0.818829 | + | 0.283651i | ||||
\(477\) | −14.9443 | −0.684251 | ||||||||
\(478\) | 25.4164 | − | 44.0225i | 1.16252 | − | 2.01354i | ||||
\(479\) | 11.9164 | + | 20.6398i | 0.544475 | + | 0.943058i | 0.998640 | + | 0.0521401i | \(0.0166043\pi\) |
−0.454165 | + | 0.890917i | \(0.650062\pi\) | |||||||
\(480\) | −27.1353 | − | 46.9996i | −1.23855 | − | 2.14523i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.3262 | −0.561445 | ||||||||
\(483\) | 36.8328 | + | 31.8982i | 1.67595 | + | 1.45142i | ||||
\(484\) | −9.70820 | −0.441282 | ||||||||
\(485\) | −10.5279 | + | 18.2348i | −0.478046 | + | 0.827999i | ||||
\(486\) | −23.4164 | − | 40.5584i | −1.06219 | − | 1.83977i | ||||
\(487\) | −10.9164 | − | 18.9078i | −0.494670 | − | 0.856793i | 0.505311 | − | 0.862937i | \(-0.331378\pi\) |
−0.999981 | + | 0.00614405i | \(0.998044\pi\) | |||||||
\(488\) | −11.2082 | + | 19.4132i | −0.507372 | + | 0.878793i | ||||
\(489\) | −36.7082 | −1.66000 | ||||||||
\(490\) | −32.1976 | + | 25.3490i | −1.45454 | + | 1.14515i | ||||
\(491\) | −25.5279 | −1.15206 | −0.576028 | − | 0.817430i | \(-0.695398\pi\) | ||||
−0.576028 | + | 0.817430i | \(0.695398\pi\) | |||||||
\(492\) | 24.2705 | − | 42.0378i | 1.09420 | − | 1.89521i | ||||
\(493\) | −3.29180 | − | 5.70156i | −0.148255 | − | 0.256785i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.70820 | − | 11.6190i | 0.301511 | − | 0.522233i | ||||
\(496\) | −49.2705 | −2.21231 | ||||||||
\(497\) | 17.8885 | + | 15.4919i | 0.802411 | + | 0.694908i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2082 | − | 22.8773i | 0.591280 | − | 1.02413i | −0.402780 | − | 0.915297i | \(-0.631956\pi\) |
0.994060 | − | 0.108831i | \(-0.0347107\pi\) | |||||||
\(500\) | −27.1353 | − | 46.9996i | −1.21353 | − | 2.10189i | ||||
\(501\) | −25.1246 | − | 43.5171i | −1.12248 | − | 1.94420i | ||||
\(502\) | −2.00000 | + | 3.46410i | −0.0892644 | + | 0.154610i | ||||
\(503\) | 20.9443 | 0.933859 | 0.466929 | − | 0.884295i | \(-0.345360\pi\) | ||||
0.466929 | + | 0.884295i | \(0.345360\pi\) | |||||||
\(504\) | −37.3607 | + | 12.9421i | −1.66418 | + | 0.576488i | ||||
\(505\) | 20.1246 | 0.895533 | ||||||||
\(506\) | 32.3435 | − | 56.0205i | 1.43784 | − | 2.49042i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.7082 | + | 47.9920i | 1.22935 | + | 2.12930i | ||||
\(509\) | −10.1180 | + | 17.5249i | −0.448474 | + | 0.776780i | −0.998287 | − | 0.0585081i | \(-0.981366\pi\) |
0.549813 | + | 0.835288i | \(0.314699\pi\) | |||||||
\(510\) | 19.2705 | 0.853313 | ||||||||
\(511\) | 1.35410 | − | 7.03612i | 0.0599019 | − | 0.311260i | ||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | 3.35410 | − | 5.80948i | 0.148087 | − | 0.256495i | ||||
\(514\) | 0.0729490 | + | 0.126351i | 0.00321764 | + | 0.00557312i | ||||
\(515\) | −3.02786 | − | 5.24441i | −0.133424 | − | 0.231097i | ||||
\(516\) | −43.4164 | + | 75.1994i | −1.91130 | + | 3.31047i | ||||
\(517\) | 22.4164 | 0.985872 | ||||||||
\(518\) | −6.16312 | + | 32.0245i | −0.270792 | + | 1.40708i | ||||
\(519\) | 36.7082 | 1.61131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.97214 | + | 15.5402i | 0.393076 | + | 0.680828i | 0.992854 | − | 0.119339i | \(-0.0380775\pi\) |
−0.599777 | + | 0.800167i | \(0.704744\pi\) | |||||||
\(522\) | −11.7082 | − | 20.2792i | −0.512454 | − | 0.887597i | ||||
\(523\) | −16.3541 | + | 28.3261i | −0.715115 | + | 1.23862i | 0.247800 | + | 0.968811i | \(0.420292\pi\) |
−0.962915 | + | 0.269804i | \(0.913041\pi\) | |||||||
\(524\) | −39.9787 | −1.74648 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 68.3951 | 2.98217 | ||||||||
\(527\) | 3.68034 | − | 6.37454i | 0.160318 | − | 0.277679i | ||||
\(528\) | 33.0517 | + | 57.2472i | 1.43839 | + | 2.49136i | ||||
\(529\) | −22.4164 | − | 38.8264i | −0.974626 | − | 1.68810i | ||||
\(530\) | −21.8713 | + | 37.8822i | −0.950030 | + | 1.64550i | ||||
\(531\) | 2.94427 | 0.127771 | ||||||||
\(532\) | −29.1246 | − | 25.2227i | −1.26271 | − | 1.09354i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.54508 | + | 11.3364i | −0.283234 | + | 0.490575i | ||||
\(535\) | −10.9164 | − | 18.9078i | −0.471957 | − | 0.817454i | ||||
\(536\) | −11.2082 | − | 19.4132i | −0.484121 | − | 0.838522i | ||||
\(537\) | −22.5000 | + | 38.9711i | −0.970947 | + | 1.68173i | ||||
\(538\) | 35.2705 | 1.52062 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | −24.2705 | −1.04444 | ||||||||
\(541\) | 0.645898 | − | 1.11873i | 0.0277693 | − | 0.0480979i | −0.851807 | − | 0.523856i | \(-0.824493\pi\) |
0.879576 | + | 0.475758i | \(0.157826\pi\) | |||||||
\(542\) | −26.7254 | − | 46.2898i | −1.14796 | − | 1.98832i | ||||
\(543\) | −28.4164 | − | 49.2187i | −1.21946 | − | 2.11217i | ||||
\(544\) | −7.98936 | + | 13.8380i | −0.342541 | + | 0.593298i | ||||
\(545\) | −6.05573 | −0.259399 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.58359 | −0.195980 | −0.0979901 | − | 0.995187i | \(-0.531241\pi\) | ||||
−0.0979901 | + | 0.995187i | \(0.531241\pi\) | |||||||
\(548\) | −19.9894 | + | 34.6226i | −0.853903 | + | 1.47900i | ||||
\(549\) | −3.00000 | − | 5.19615i | −0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.70820 | − | 11.6190i | 0.285779 | − | 0.494984i | ||||
\(552\) | 137.610 | 5.85707 | ||||||||
\(553\) | 6.77051 | − | 2.34537i | 0.287911 | − | 0.0997354i | ||||
\(554\) | −1.09017 | −0.0463169 | ||||||||
\(555\) | 11.7705 | − | 20.3871i | 0.499630 | − | 0.865385i | ||||
\(556\) | 56.8328 | + | 98.4373i | 2.41025 | + | 4.17467i | ||||
\(557\) | −9.35410 | − | 16.2018i | −0.396346 | − | 0.686491i | 0.596926 | − | 0.802296i | \(-0.296389\pi\) |
−0.993272 | + | 0.115805i | \(0.963055\pi\) | |||||||
\(558\) | 13.0902 | − | 22.6728i | 0.554151 | − | 0.959818i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −11.0172 | + | 57.2472i | −0.465563 | + | 2.41913i | ||||
\(561\) | −9.87539 | −0.416939 | ||||||||
\(562\) | 35.2705 | − | 61.0903i | 1.48780 | − | 2.57694i | ||||
\(563\) | −6.29837 | − | 10.9091i | −0.265445 | − | 0.459764i | 0.702235 | − | 0.711945i | \(-0.252185\pi\) |
−0.967680 | + | 0.252181i | \(0.918852\pi\) | |||||||
\(564\) | 40.5517 | + | 70.2375i | 1.70753 | + | 2.95753i | ||||
\(565\) | 3.29180 | − | 5.70156i | 0.138487 | − | 0.239866i | ||||
\(566\) | 68.3951 | 2.87486 | ||||||||
\(567\) | −5.50000 | + | 28.5788i | −0.230978 | + | 1.20020i | ||||
\(568\) | 66.8328 | 2.80424 | ||||||||
\(569\) | −12.7361 | + | 22.0595i | −0.533924 | + | 0.924783i | 0.465291 | + | 0.885158i | \(0.345950\pi\) |
−0.999215 | + | 0.0396252i | \(0.987384\pi\) | |||||||
\(570\) | 19.6353 | + | 34.0093i | 0.822430 | + | 1.42449i | ||||
\(571\) | 18.0623 | + | 31.2848i | 0.755884 | + | 1.30923i | 0.944934 | + | 0.327262i | \(0.106126\pi\) |
−0.189050 | + | 0.981968i | \(0.560541\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0000 | −1.04439 | ||||||||
\(574\) | −29.2705 | + | 10.1396i | −1.22173 | + | 0.423219i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.70820 | + | 15.0831i | −0.362842 | + | 0.628460i | ||||
\(577\) | −9.64590 | − | 16.7072i | −0.401564 | − | 0.695529i | 0.592351 | − | 0.805680i | \(-0.298200\pi\) |
−0.993915 | + | 0.110151i | \(0.964867\pi\) | |||||||
\(578\) | 19.4164 | + | 33.6302i | 0.807616 | + | 1.39883i | ||||
\(579\) | −0.791796 | + | 1.37143i | −0.0329059 | + | 0.0569947i | ||||
\(580\) | −48.5410 | −2.01556 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 55.1246 | 2.28499 | ||||||||
\(583\) | 11.2082 | − | 19.4132i | 0.464196 | − | 0.804012i | ||||
\(584\) | −10.1180 | − | 17.5249i | −0.418687 | − | 0.725188i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.5623 | + | 33.8829i | −0.808111 | + | 1.39969i | ||||
\(587\) | 6.11146 | 0.252247 | 0.126123 | − | 0.992015i | \(-0.459746\pi\) | ||||
0.126123 | + | 0.992015i | \(0.459746\pi\) | |||||||
\(588\) | 70.5517 | + | 28.1998i | 2.90950 | + | 1.16294i | ||||
\(589\) | 15.0000 | 0.618064 | ||||||||
\(590\) | 4.30902 | − | 7.46344i | 0.177399 | − | 0.307265i | ||||
\(591\) | 10.1246 | + | 17.5363i | 0.416471 | + | 0.721349i | ||||
\(592\) | 23.1976 | + | 40.1794i | 0.953414 | + | 1.65136i | ||||
\(593\) | 13.8820 | − | 24.0443i | 0.570064 | − | 0.987380i | −0.426495 | − | 0.904490i | \(-0.640252\pi\) |
0.996559 | − | 0.0828898i | \(-0.0264149\pi\) | |||||||
\(594\) | 17.5623 | 0.720590 | ||||||||
\(595\) | −6.58359 | − | 5.70156i | −0.269901 | − | 0.233741i | ||||
\(596\) | −3.43769 | −0.140813 | ||||||||
\(597\) | −23.1525 | + | 40.1013i | −0.947568 | + | 1.64124i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.53444 | + | 14.7821i | 0.348708 | + | 0.603980i | 0.986020 | − | 0.166626i | \(-0.0532872\pi\) |
−0.637312 | + | 0.770606i | \(0.719954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 52.3607 | − | 18.1383i | 2.13406 | − | 0.739261i | ||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | 49.5517 | − | 85.8260i | 2.01623 | − | 3.49221i | ||||
\(605\) | −2.23607 | − | 3.87298i | −0.0909091 | − | 0.157459i | ||||
\(606\) | −26.3435 | − | 45.6282i | −1.07013 | − | 1.85352i | ||||
\(607\) | −12.0623 | + | 20.8925i | −0.489594 | + | 0.848001i | −0.999928 | − | 0.0119745i | \(-0.996188\pi\) |
0.510334 | + | 0.859976i | \(0.329522\pi\) | |||||||
\(608\) | −32.5623 | −1.32058 | ||||||||
\(609\) | −5.00000 | + | 25.9808i | −0.202610 | + | 1.05279i | ||||
\(610\) | −17.5623 | −0.711077 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.14590 | − | 12.3771i | −0.288856 | − | 0.500313i | ||||
\(613\) | −9.06231 | − | 15.6964i | −0.366023 | − | 0.633971i | 0.622917 | − | 0.782288i | \(-0.285948\pi\) |
−0.988940 | + | 0.148318i | \(0.952614\pi\) | |||||||
\(614\) | 25.4164 | − | 44.0225i | 1.02572 | − | 1.77660i | ||||
\(615\) | 22.3607 | 0.901670 | ||||||||
\(616\) | 11.2082 | − | 58.2395i | 0.451591 | − | 2.34654i | ||||
\(617\) | 4.47214 | 0.180041 | 0.0900207 | − | 0.995940i | \(-0.471307\pi\) | ||||
0.0900207 | + | 0.995940i | \(0.471307\pi\) | |||||||
\(618\) | −7.92705 | + | 13.7301i | −0.318873 | + | 0.552304i | ||||
\(619\) | 8.50000 | + | 14.7224i | 0.341644 | + | 0.591744i | 0.984738 | − | 0.174042i | \(-0.0556830\pi\) |
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | −27.1353 | − | 46.9996i | −1.08978 | − | 1.88755i | ||||
\(621\) | 9.20820 | − | 15.9491i | 0.369512 | − | 0.640014i | ||||
\(622\) | −72.6869 | −2.91448 | ||||||||
\(623\) | 5.59017 | − | 1.93649i | 0.223965 | − | 0.0775839i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | 7.30902 | + | 12.6596i | 0.292127 | + | 0.505979i | ||||
\(627\) | −10.0623 | − | 17.4284i | −0.401850 | − | 0.696024i | ||||
\(628\) | −16.9894 | + | 29.4264i | −0.677949 | + | 1.17424i | ||||
\(629\) | −6.93112 | −0.276362 | ||||||||
\(630\) | −23.4164 | − | 20.2792i | −0.932932 | − | 0.807943i | ||||
\(631\) | −22.8328 | −0.908960 | −0.454480 | − | 0.890757i | \(-0.650175\pi\) | ||||
−0.454480 | + | 0.890757i | \(0.650175\pi\) | |||||||
\(632\) | 10.1180 | − | 17.5249i | 0.402474 | − | 0.697105i | ||||
\(633\) | 4.47214 | + | 7.74597i | 0.177751 | + | 0.307875i | ||||
\(634\) | −10.7812 | − | 18.6735i | −0.428174 | − | 0.741620i | ||||
\(635\) | −12.7639 | + | 22.1078i | −0.506521 | + | 0.877320i | ||||
\(636\) | 81.1033 | 3.21596 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 35.1246 | 1.39060 | ||||||||
\(639\) | −8.94427 | + | 15.4919i | −0.353830 | + | 0.612851i | ||||
\(640\) | 1.21885 | + | 2.11111i | 0.0481792 | + | 0.0834488i | ||||
\(641\) | −5.97214 | − | 10.3440i | −0.235885 | − | 0.408565i | 0.723644 | − | 0.690173i | \(-0.242466\pi\) |
−0.959530 | + | 0.281608i | \(0.909132\pi\) | |||||||
\(642\) | −28.5795 | + | 49.5012i | −1.12794 | + | 1.95366i | ||||
\(643\) | −34.8328 | −1.37367 | −0.686836 | − | 0.726812i | \(-0.741001\pi\) | ||||
−0.686836 | + | 0.726812i | \(0.741001\pi\) | |||||||
\(644\) | −79.9574 | − | 69.2452i | −3.15076 | − | 2.72864i | ||||
\(645\) | −40.0000 | −1.57500 | ||||||||
\(646\) | 5.78115 | − | 10.0133i | 0.227456 | − | 0.393966i | ||||
\(647\) | −10.1180 | − | 17.5249i | −0.397781 | − | 0.688977i | 0.595671 | − | 0.803229i | \(-0.296886\pi\) |
−0.993452 | + | 0.114252i | \(0.963553\pi\) | |||||||
\(648\) | 41.0967 | + | 71.1817i | 1.61443 | + | 2.79628i | ||||
\(649\) | −2.20820 | + | 3.82472i | −0.0866796 | + | 0.150133i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.9508 | + | 9.68246i | −1.09548 | + | 0.379485i | ||||
\(652\) | 79.6869 | 3.12078 | ||||||||
\(653\) | −2.26393 | + | 3.92125i | −0.0885945 | + | 0.153450i | −0.906917 | − | 0.421309i | \(-0.861571\pi\) |
0.818323 | + | 0.574759i | \(0.194904\pi\) | |||||||
\(654\) | 7.92705 | + | 13.7301i | 0.309972 | + | 0.536888i | ||||
\(655\) | −9.20820 | − | 15.9491i | −0.359794 | − | 0.623182i | ||||
\(656\) | −22.0344 | + | 38.1648i | −0.860300 | + | 1.49008i | ||||
\(657\) | 5.41641 | 0.211314 | ||||||||
\(658\) | 9.78115 | − | 50.8244i | 0.381309 | − | 1.98134i | ||||
\(659\) | −8.94427 | −0.348419 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(660\) | −36.4058 | + | 63.0566i | −1.41709 | + | 2.45448i | ||||
\(661\) | −3.35410 | − | 5.80948i | −0.130459 | − | 0.225962i | 0.793394 | − | 0.608708i | \(-0.208312\pi\) |
−0.923854 | + | 0.382746i | \(0.874979\pi\) | |||||||
\(662\) | −2.07295 | − | 3.59045i | −0.0805675 | − | 0.139547i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.35410 | − | 17.4284i | 0.130066 | − | 0.675845i | ||||
\(666\) | −24.6525 | −0.955264 | ||||||||
\(667\) | 18.4164 | − | 31.8982i | 0.713086 | − | 1.23510i | ||||
\(668\) | 54.5410 | + | 94.4678i | 2.11026 | + | 3.65507i | ||||
\(669\) | 4.47214 | + | 7.74597i | 0.172903 | + | 0.299476i | ||||
\(670\) | 8.78115 | − | 15.2094i | 0.339246 | − | 0.587591i | ||||
\(671\) | 9.00000 | 0.347441 | ||||||||
\(672\) | 60.6763 | − | 21.0189i | 2.34064 | − | 0.810821i | ||||
\(673\) | −9.41641 | −0.362976 | −0.181488 | − | 0.983393i | \(-0.558091\pi\) | ||||
−0.181488 | + | 0.983393i | \(0.558091\pi\) | |||||||
\(674\) | −23.5623 | + | 40.8111i | −0.907586 | + | 1.57199i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.44427 | − | 2.50155i | 0.0555079 | − | 0.0961425i | −0.836936 | − | 0.547300i | \(-0.815656\pi\) |
0.892444 | + | 0.451158i | \(0.148989\pi\) | |||||||
\(678\) | −17.2361 | −0.661947 | ||||||||
\(679\) | −18.8328 | − | 16.3097i | −0.722737 | − | 0.625909i | ||||
\(680\) | −24.5967 | −0.943242 | ||||||||
\(681\) | −6.64590 | + | 11.5110i | −0.254671 | + | 0.441104i | ||||
\(682\) | 19.6353 | + | 34.0093i | 0.751873 | + | 1.30228i | ||||
\(683\) | −6.73607 | − | 11.6672i | −0.257748 | − | 0.446433i | 0.707890 | − | 0.706323i | \(-0.249647\pi\) |
−0.965638 | + | 0.259889i | \(0.916314\pi\) | |||||||
\(684\) | 14.5623 | − | 25.2227i | 0.556804 | − | 0.964412i | ||||
\(685\) | −18.4164 | −0.703655 | ||||||||
\(686\) | −22.2533 | − | 43.0784i | −0.849635 | − | 1.64474i | ||||
\(687\) | 53.9443 | 2.05810 | ||||||||
\(688\) | 39.4164 | − | 68.2712i | 1.50274 | − | 2.60282i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 53.9058 | + | 93.3675i | 2.05216 | + | 3.55444i | ||||
\(691\) | −25.9164 | + | 44.8885i | −0.985907 | + | 1.70764i | −0.348070 | + | 0.937468i | \(0.613163\pi\) |
−0.637836 | + | 0.770172i | \(0.720170\pi\) | |||||||
\(692\) | −79.6869 | −3.02924 | ||||||||
\(693\) | 12.0000 | + | 10.3923i | 0.455842 | + | 0.394771i | ||||
\(694\) | 60.3951 | 2.29257 | ||||||||
\(695\) | −26.1803 | + | 45.3457i | −0.993077 | + | 1.72006i | ||||
\(696\) | 37.3607 | + | 64.7106i | 1.41615 | + | 2.45285i | ||||
\(697\) | −3.29180 | − | 5.70156i | −0.124686 | − | 0.215962i | ||||
\(698\) | −38.5066 | + | 66.6953i | −1.45750 | + | 2.52446i | ||||
\(699\) | −26.7082 | −1.01020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.3607 | −0.844551 | −0.422276 | − | 0.906467i | \(-0.638769\pi\) | ||||
−0.422276 | + | 0.906467i | \(0.638769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.06231 | − | 12.2323i | −0.266360 | − | 0.461349i | ||||
\(704\) | −13.0623 | − | 22.6246i | −0.492304 | − | 0.852696i | ||||
\(705\) | −18.6803 | + | 32.3553i | −0.703542 | + | 1.21857i | ||||
\(706\) | −45.2705 | −1.70378 | ||||||||
\(707\) | −4.50000 | + | 23.3827i | −0.169240 | + | 0.879396i | ||||
\(708\) | −15.9787 | −0.600517 | ||||||||
\(709\) | −25.0623 | + | 43.4092i | −0.941235 | + | 1.63027i | −0.178114 | + | 0.984010i | \(0.557000\pi\) |
−0.763120 | + | 0.646256i | \(0.776334\pi\) | |||||||
\(710\) | 26.1803 | + | 45.3457i | 0.982531 | + | 1.70179i | ||||
\(711\) | 2.70820 | + | 4.69075i | 0.101566 | + | 0.175917i | ||||
\(712\) | 8.35410 | − | 14.4697i | 0.313083 | − | 0.542276i | ||||
\(713\) | 41.1803 | 1.54222 | ||||||||
\(714\) | −4.30902 | + | 22.3903i | −0.161261 | + | 0.837936i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 48.8435 | − | 84.5994i | 1.82537 | − | 3.16163i | ||||
\(717\) | −21.7082 | − | 37.5997i | −0.810708 | − | 1.40419i | ||||
\(718\) | 15.6353 | + | 27.0811i | 0.583503 | + | 1.01066i | ||||
\(719\) | −12.3541 | + | 21.3979i | −0.460730 | + | 0.798008i | −0.998998 | − | 0.0447660i | \(-0.985746\pi\) |
0.538267 | + | 0.842774i | \(0.319079\pi\) | |||||||
\(720\) | −44.0689 | −1.64235 | ||||||||
\(721\) | 6.77051 | − | 2.34537i | 0.252147 | − | 0.0873463i | ||||
\(722\) | −26.1803 | −0.974331 | ||||||||
\(723\) | −5.26393 | + | 9.11740i | −0.195768 | + | 0.339080i | ||||
\(724\) | 61.6869 | + | 106.845i | 2.29258 | + | 3.97086i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.85410 | + | 10.1396i | −0.217266 | + | 0.376316i | ||||
\(727\) | −38.8328 | −1.44023 | −0.720115 | − | 0.693855i | \(-0.755911\pi\) | ||||
−0.720115 | + | 0.693855i | \(0.755911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 7.92705 | − | 13.7301i | 0.293393 | − | 0.508172i | ||||
\(731\) | 5.88854 | + | 10.1993i | 0.217796 | + | 0.377233i | ||||
\(732\) | 16.2812 | + | 28.1998i | 0.601769 | + | 1.04229i | ||||
\(733\) | 14.3541 | − | 24.8620i | 0.530181 | − | 0.918300i | −0.469199 | − | 0.883092i | \(-0.655457\pi\) |
0.999380 | − | 0.0352078i | \(-0.0112093\pi\) | |||||||
\(734\) | −33.2705 | −1.22804 | ||||||||
\(735\) | 5.00000 | + | 34.6410i | 0.184428 | + | 1.27775i | ||||
\(736\) | −89.3951 | −3.29515 | ||||||||
\(737\) | −4.50000 | + | 7.79423i | −0.165760 | + | 0.287104i | ||||
\(738\) | −11.7082 | − | 20.2792i | −0.430985 | − | 0.746488i | ||||
\(739\) | −8.91641 | − | 15.4437i | −0.327995 | − | 0.568105i | 0.654119 | − | 0.756392i | \(-0.273040\pi\) |
−0.982114 | + | 0.188287i | \(0.939706\pi\) | |||||||
\(740\) | −25.5517 | + | 44.2568i | −0.939298 | + | 1.62691i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −39.1246 | − | 33.8829i | −1.43631 | − | 1.24388i | ||||
\(743\) | −32.9443 | −1.20861 | −0.604304 | − | 0.796754i | \(-0.706549\pi\) | ||||
−0.604304 | + | 0.796754i | \(0.706549\pi\) | |||||||
\(744\) | −41.7705 | + | 72.3486i | −1.53138 | + | 2.65243i | ||||
\(745\) | −0.791796 | − | 1.37143i | −0.0290092 | − | 0.0502453i | ||||
\(746\) | 2.07295 | + | 3.59045i | 0.0758961 | + | 0.131456i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.4377 | 0.783840 | ||||||||
\(749\) | 24.4098 | − | 8.45581i | 0.891916 | − | 0.308969i | ||||
\(750\) | −65.4508 | −2.38993 | ||||||||
\(751\) | 5.06231 | − | 8.76817i | 0.184726 | − | 0.319955i | −0.758758 | − | 0.651373i | \(-0.774194\pi\) |
0.943484 | + | 0.331417i | \(0.107527\pi\) | |||||||
\(752\) | −36.8156 | − | 63.7665i | −1.34253 | − | 2.32532i | ||||
\(753\) | 1.70820 | + | 2.95870i | 0.0622504 | + | 0.107821i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.6525 | 1.66146 | ||||||||
\(756\) | 5.42705 | − | 28.1998i | 0.197380 | − | 1.02562i | ||||
\(757\) | −52.8328 | −1.92024 | −0.960121 | − | 0.279586i | \(-0.909803\pi\) | ||||
−0.960121 | + | 0.279586i | \(0.909803\pi\) | |||||||
\(758\) | −20.1803 | + | 34.9534i | −0.732983 | + | 1.26956i | ||||
\(759\) | −27.6246 | − | 47.8472i | −1.00271 | − | 1.73674i | ||||
\(760\) | −25.0623 | − | 43.4092i | −0.909105 | − | 1.57462i | ||||
\(761\) | −16.7705 | + | 29.0474i | −0.607931 | + | 1.05297i | 0.383650 | + | 0.923478i | \(0.374667\pi\) |
−0.991581 | + | 0.129488i | \(0.958667\pi\) | |||||||
\(762\) | 66.8328 | 2.42110 | ||||||||
\(763\) | 1.35410 | − | 7.03612i | 0.0490218 | − | 0.254725i | ||||
\(764\) | 54.2705 | 1.96344 | ||||||||
\(765\) | 3.29180 | − | 5.70156i | 0.119015 | − | 0.206140i | ||||
\(766\) | 19.6353 | + | 34.0093i | 0.709451 | + | 1.22880i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.2812 | + | 28.1998i | −0.587496 | + | 1.01757i | ||||
\(769\) | −46.0000 | −1.65880 | −0.829401 | − | 0.558653i | \(-0.811318\pi\) | ||||
−0.829401 | + | 0.558653i | \(0.811318\pi\) | |||||||
\(770\) | 43.9058 | − | 15.2094i | 1.58225 | − | 0.548109i | ||||
\(771\) | 0.124612 | 0.00448778 | ||||||||
\(772\) | 1.71885 | − | 2.97713i | 0.0618627 | − | 0.107149i | ||||
\(773\) | −23.5344 | − | 40.7628i | −0.846475 | − | 1.46614i | −0.884334 | − | 0.466855i | \(-0.845387\pi\) |
0.0378590 | − | 0.999283i | \(-0.487946\pi\) | |||||||
\(774\) | 20.9443 | + | 36.2765i | 0.752826 | + | 1.30393i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −70.3607 | −2.52580 | ||||||||
\(777\) | 21.0557 | + | 18.2348i | 0.755370 | + | 0.654170i | ||||
\(778\) | 3.85410 | 0.138176 | ||||||||
\(779\) | 6.70820 | − | 11.6190i | 0.240346 | − | 0.416292i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4164 | − | 23.2379i | −0.480077 | − | 0.831517i | ||||
\(782\) | 15.8713 | − | 27.4899i | 0.567557 | − | 0.983038i | ||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | −64.0517 | − | 25.6017i | −2.28756 | − | 0.914347i | ||||
\(785\) | −15.6525 | −0.558661 | ||||||||
\(786\) | −24.1074 | + | 41.7552i | −0.859882 | + | 1.48936i | ||||
\(787\) | 10.2082 | + | 17.6811i | 0.363883 | + | 0.630264i | 0.988596 | − | 0.150590i | \(-0.0481174\pi\) |
−0.624713 | + | 0.780854i | \(0.714784\pi\) | |||||||
\(788\) | −21.9787 | − | 38.0682i | −0.782959 | − | 1.35613i | ||||
\(789\) | 29.2082 | − | 50.5901i | 1.03984 | − | 1.80106i | ||||
\(790\) | 15.8541 | 0.564064 | ||||||||
\(791\) | 5.88854 | + | 5.09963i | 0.209373 | + | 0.181322i | ||||
\(792\) | 44.8328 | 1.59306 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −34.1976 | − | 59.2319i | −1.21363 | − | 2.10206i | ||||
\(795\) | 18.6803 | + | 32.3553i | 0.662523 | + | 1.14752i | ||||
\(796\) | 50.2599 | − | 87.0526i | 1.78141 | − | 3.08550i | ||||
\(797\) | 9.05573 | 0.320770 | 0.160385 | − | 0.987055i | \(-0.448726\pi\) | ||||
0.160385 | + | 0.987055i | \(0.448726\pi\) | |||||||
\(798\) | −43.9058 | + | 15.2094i | −1.55425 | + | 0.538407i | ||||
\(799\) | 11.0000 | 0.389152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.23607 | + | 3.87298i | 0.0790076 | + | 0.136845i | ||||
\(802\) | 18.6353 | + | 32.2772i | 0.658034 | + | 1.13975i | ||||
\(803\) | −4.06231 | + | 7.03612i | −0.143356 | + | 0.248299i | ||||
\(804\) | −32.5623 | −1.14838 | ||||||||
\(805\) | 9.20820 | − | 47.8472i | 0.324547 | − | 1.68639i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0623 | − | 26.0887i | 0.530218 | − | 0.918365i | ||||
\(808\) | 33.6246 | + | 58.2395i | 1.18291 | + | 2.04886i | ||||
\(809\) | −11.2082 | − | 19.4132i | −0.394059 | − | 0.682531i | 0.598921 | − | 0.800808i | \(-0.295596\pi\) |
−0.992981 | + | 0.118277i | \(0.962263\pi\) | |||||||
\(810\) | −32.1976 | + | 55.7678i | −1.13131 | + | 1.95948i | ||||
\(811\) | 14.8328 | 0.520851 | 0.260425 | − | 0.965494i | \(-0.416137\pi\) | ||||
0.260425 | + | 0.965494i | \(0.416137\pi\) | |||||||
\(812\) | 10.8541 | − | 56.3996i | 0.380904 | − | 1.97924i | ||||
\(813\) | −45.6525 | −1.60110 | ||||||||
\(814\) | 18.4894 | − | 32.0245i | 0.648052 | − | 1.12246i | ||||
\(815\) | 18.3541 | + | 31.7902i | 0.642916 | + | 1.11356i | ||||
\(816\) | 16.2188 | + | 28.0919i | 0.567773 | + | 0.983412i | ||||
\(817\) | −12.0000 | + | 20.7846i | −0.419827 | + | 0.727161i | ||||
\(818\) | −22.7984 | −0.797126 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.5410 | −1.69513 | ||||||||
\(821\) | 19.1180 | − | 33.1134i | 0.667224 | − | 1.15567i | −0.311453 | − | 0.950261i | \(-0.600816\pi\) |
0.978677 | − | 0.205404i | \(-0.0658509\pi\) | |||||||
\(822\) | 24.1074 | + | 41.7552i | 0.840842 | + | 1.45638i | ||||
\(823\) | −17.0623 | − | 29.5528i | −0.594755 | − | 1.03015i | −0.993581 | − | 0.113119i | \(-0.963916\pi\) |
0.398827 | − | 0.917026i | \(-0.369417\pi\) | |||||||
\(824\) | 10.1180 | − | 17.5249i | 0.352478 | − | 0.610511i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.70820 | + | 6.67550i | 0.268203 | + | 0.232270i | ||||
\(827\) | −26.8328 | −0.933068 | −0.466534 | − | 0.884503i | \(-0.654498\pi\) | ||||
−0.466534 | + | 0.884503i | \(0.654498\pi\) | |||||||
\(828\) | 39.9787 | − | 69.2452i | 1.38936 | − | 2.40644i | ||||
\(829\) | 12.5000 | + | 21.6506i | 0.434143 | + | 0.751958i | 0.997225 | − | 0.0744432i | \(-0.0237179\pi\) |
−0.563082 | + | 0.826401i | \(0.690385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.465558 | + | 0.806370i | −0.0161500 | + | 0.0279727i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.09675 | − | 6.37454i | 0.280536 | − | 0.220865i | ||||
\(834\) | 137.082 | 4.74676 | ||||||||
\(835\) | −25.1246 | + | 43.5171i | −0.869473 | + | 1.50597i | ||||
\(836\) | 21.8435 | + | 37.8340i | 0.755472 | + | 1.30852i | ||||
\(837\) | 5.59017 | + | 9.68246i | 0.193225 | + | 0.334675i | ||||
\(838\) | −43.1246 | + | 74.6940i | −1.48971 | + | 2.58026i | ||||
\(839\) | 5.88854 | 0.203295 | 0.101648 | − | 0.994820i | \(-0.467589\pi\) | ||||
0.101648 | + | 0.994820i | \(0.467589\pi\) | |||||||
\(840\) | 74.7214 | + | 64.7106i | 2.57813 | + | 2.23273i | ||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 17.5623 | − | 30.4188i | 0.605237 | − | 1.04830i | ||||
\(843\) | −30.1246 | − | 52.1774i | −1.03755 | − | 1.79708i | ||||
\(844\) | −9.70820 | − | 16.8151i | −0.334170 | − | 0.578800i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 39.1246 | 1.34513 | ||||||||
\(847\) | 5.00000 | − | 1.73205i | 0.171802 | − | 0.0595140i | ||||
\(848\) | −73.6312 | −2.52851 | ||||||||
\(849\) | 29.2082 | − | 50.5901i | 1.00242 | − | 1.73625i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.3885 | − | 33.5819i | −0.664631 | − | 1.15117i | ||||
\(852\) | 48.5410 | − | 84.0755i | 1.66299 | − | 2.88038i | ||||
\(853\) | 52.2492 | 1.78898 | 0.894490 | − | 0.447089i | \(-0.147539\pi\) | ||||
0.894490 | + | 0.447089i | \(0.147539\pi\) | |||||||
\(854\) | 3.92705 | − | 20.4056i | 0.134381 | − | 0.698264i | ||||
\(855\) | 13.4164 | 0.458831 | ||||||||
\(856\) | 36.4787 | − | 63.1830i | 1.24682 | − | 2.15955i | ||||
\(857\) | 0.680340 | + | 1.17838i | 0.0232400 | + | 0.0402528i | 0.877411 | − | 0.479739i | \(-0.159268\pi\) |
−0.854172 | + | 0.519991i | \(0.825935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3541 | + | 17.9338i | −0.353277 | + | 0.611894i | −0.986822 | − | 0.161812i | \(-0.948266\pi\) |
0.633544 | + | 0.773707i | \(0.281599\pi\) | |||||||
\(860\) | 86.8328 | 2.96097 | ||||||||
\(861\) | −5.00000 | + | 25.9808i | −0.170400 | + | 0.885422i | ||||
\(862\) | 82.1033 | 2.79645 | ||||||||
\(863\) | 11.9721 | − | 20.7363i | 0.407536 | − | 0.705873i | −0.587077 | − | 0.809531i | \(-0.699721\pi\) |
0.994613 | + | 0.103658i | \(0.0330547\pi\) | |||||||
\(864\) | −12.1353 | − | 21.0189i | −0.412850 | − | 0.715077i | ||||
\(865\) | −18.3541 | − | 31.7902i | −0.624058 | − | 1.08090i | ||||
\(866\) | −38.5066 | + | 66.6953i | −1.30851 | + | 2.26640i | ||||
\(867\) | 33.1672 | 1.12642 | ||||||||
\(868\) | 60.6763 | − | 21.0189i | 2.05949 | − | 0.713427i | ||||
\(869\) | −8.12461 | −0.275609 | ||||||||
\(870\) | −29.2705 | + | 50.6980i | −0.992363 | + | 1.71882i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10.1180 | − | 17.5249i | −0.342640 | − | 0.593470i | ||||
\(873\) | 9.41641 | − | 16.3097i | 0.318697 | − | 0.552000i | ||||
\(874\) | 64.6869 | 2.18807 | ||||||||
\(875\) | 22.3607 | + | 19.3649i | 0.755929 | + | 0.654654i | ||||
\(876\) | −29.3951 | −0.993169 | ||||||||
\(877\) | 16.0623 | − | 27.8207i | 0.542386 | − | 0.939439i | −0.456381 | − | 0.889785i | \(-0.650855\pi\) |
0.998766 | − | 0.0496548i | \(-0.0158121\pi\) | |||||||
\(878\) | −31.5795 | − | 54.6973i | −1.06576 | − | 1.84595i | ||||
\(879\) | 16.7082 | + | 28.9395i | 0.563554 | + | 0.976104i | ||||
\(880\) | 33.0517 | − | 57.2472i | 1.11417 | − | 1.92980i | ||||
\(881\) | 43.3050 | 1.45898 | 0.729490 | − | 0.683991i | \(-0.239757\pi\) | ||||
0.729490 | + | 0.683991i | \(0.239757\pi\) | |||||||
\(882\) | 28.7984 | − | 22.6728i | 0.969692 | − | 0.763434i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.68034 | − | 6.37454i | −0.123713 | − | 0.214278i | ||||
\(886\) | −2.92705 | − | 5.06980i | −0.0983362 | − | 0.170323i | ||||
\(887\) | 10.1180 | − | 17.5249i | 0.339730 | − | 0.588430i | −0.644652 | − | 0.764477i | \(-0.722998\pi\) |
0.984382 | + | 0.176046i | \(0.0563309\pi\) | |||||||
\(888\) | 78.6656 | 2.63985 | ||||||||
\(889\) | −22.8328 | − | 19.7738i | −0.765788 | − | 0.663192i | ||||
\(890\) | 13.0902 | 0.438783 | ||||||||
\(891\) | 16.5000 | − | 28.5788i | 0.552771 | − | 0.957427i | ||||
\(892\) | −9.70820 | − | 16.8151i | −0.325055 | − | 0.563011i | ||||
\(893\) | 11.2082 | + | 19.4132i | 0.375068 | + | 0.649637i | ||||
\(894\) | −2.07295 | + | 3.59045i | −0.0693298 | + | 0.120083i | ||||
\(895\) | 45.0000 | 1.50418 | ||||||||
\(896\) | −2.72542 | + | 0.944115i | −0.0910501 | + | 0.0315407i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.9787 | + | 77.9054i | −1.50096 | + | 2.59974i | ||||
\(899\) | 11.1803 | + | 19.3649i | 0.372885 | + | 0.645856i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.50000 | − | 9.52628i | 0.183232 | − | 0.317366i | ||||
\(902\) | 35.1246 | 1.16952 | ||||||||
\(903\) | 8.94427 | − | 46.4758i | 0.297647 | − | 1.54662i | ||||
\(904\) | 22.0000 | 0.731709 | ||||||||
\(905\) | −28.4164 | + | 49.2187i | −0.944593 | + | 1.63608i | ||||
\(906\) | −59.7599 | − | 103.507i | −1.98539 | − | 3.43879i | ||||
\(907\) | −9.35410 | − | 16.2018i | −0.310598 | − | 0.537971i | 0.667894 | − | 0.744256i | \(-0.267196\pi\) |
−0.978492 | + | 0.206285i | \(0.933863\pi\) | |||||||
\(908\) | 14.4271 | − | 24.9884i | 0.478779 | − | 0.829269i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.2492 | −1.13473 | −0.567364 | − | 0.823467i | \(-0.692037\pi\) | ||||
−0.567364 | + | 0.823467i | \(0.692037\pi\) | |||||||
\(912\) | −33.0517 | + | 57.2472i | −1.09445 | + | 1.89564i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −8.01722 | − | 13.8862i | −0.265186 | − | 0.459316i | ||||
\(915\) | −7.50000 | + | 12.9904i | −0.247942 | + | 0.429449i | ||||
\(916\) | −117.103 | −3.86920 | ||||||||
\(917\) | 20.5902 | − | 7.13264i | 0.679947 | − | 0.235541i | ||||
\(918\) | 8.61803 | 0.284438 | ||||||||
\(919\) | −10.0623 | + | 17.4284i | −0.331925 | + | 0.574911i | −0.982889 | − | 0.184198i | \(-0.941031\pi\) |
0.650964 | + | 0.759108i | \(0.274365\pi\) | |||||||
\(920\) | −68.8050 | − | 119.174i | −2.26843 | − | 3.92904i | ||||
\(921\) | −21.7082 | − | 37.5997i | −0.715310 | − | 1.23895i | ||||
\(922\) | 44.9787 | − | 77.9054i | 1.48130 | − | 2.56568i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −65.1246 | − | 56.3996i | −2.14244 | − | 1.85541i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.4164 | + | 54.4148i | −1.03241 | + | 1.78818i | ||||
\(927\) | 2.70820 | + | 4.69075i | 0.0889491 | + | 0.154064i | ||||
\(928\) | −24.2705 | − | 42.0378i | −0.796719 | − | 1.37996i | ||||
\(929\) | −12.4098 | + | 21.4945i | −0.407153 | + | 0.705210i | −0.994569 | − | 0.104075i | \(-0.966812\pi\) |
0.587416 | + | 0.809285i | \(0.300145\pi\) | |||||||
\(930\) | −65.4508 | −2.14622 | ||||||||
\(931\) | 19.5000 | + | 7.79423i | 0.639087 | + | 0.255446i | ||||
\(932\) | 57.9787 | 1.89916 | ||||||||
\(933\) | −31.0410 | + | 53.7646i | −1.01624 | + | 1.76017i | ||||
\(934\) | −12.6353 | − | 21.8849i | −0.413438 | − | 0.716096i | ||||
\(935\) | 4.93769 | + | 8.55234i | 0.161480 | + | 0.279691i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.4164 | 0.830318 | 0.415159 | − | 0.909749i | \(-0.363726\pi\) | ||||
0.415159 | + | 0.909749i | \(0.363726\pi\) | |||||||
\(938\) | 15.7082 | + | 13.6037i | 0.512891 | + | 0.444177i | ||||
\(939\) | 12.4853 | 0.407442 | ||||||||
\(940\) | 40.5517 | − | 70.2375i | 1.32265 | − | 2.29090i | ||||
\(941\) | 25.1180 | + | 43.5057i | 0.818825 | + | 1.41825i | 0.906549 | + | 0.422101i | \(0.138707\pi\) |
−0.0877244 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(942\) | 20.4894 | + | 35.4886i | 0.667579 | + | 1.15628i | ||||
\(943\) | 18.4164 | − | 31.8982i | 0.599721 | − | 1.03875i | ||||
\(944\) | 14.5066 | 0.472149 | ||||||||
\(945\) | 12.5000 | − | 4.33013i | 0.406625 | − | 0.140859i | ||||
\(946\) | −62.8328 | −2.04287 | ||||||||
\(947\) | −11.2639 | + | 19.5097i | −0.366029 | + | 0.633980i | −0.988941 | − | 0.148312i | \(-0.952616\pi\) |
0.622912 | + | 0.782292i | \(0.285949\pi\) | |||||||
\(948\) | −14.6976 | − | 25.4569i | −0.477355 | − | 0.826802i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.4164 | −0.597193 | ||||||||
\(952\) | 5.50000 | − | 28.5788i | 0.178256 | − | 0.926245i | ||||
\(953\) | −41.7771 | −1.35329 | −0.676646 | − | 0.736308i | \(-0.736567\pi\) | ||||
−0.676646 | + | 0.736308i | \(0.736567\pi\) | |||||||
\(954\) | 19.5623 | − | 33.8829i | 0.633353 | − | 1.09700i | ||||
\(955\) | 12.5000 | + | 21.6506i | 0.404491 | + | 0.700598i | ||||
\(956\) | 47.1246 | + | 81.6222i | 1.52412 | + | 2.63985i | ||||
\(957\) | 15.0000 | − | 25.9808i | 0.484881 | − | 0.839839i | ||||
\(958\) | −62.3951 | −2.01589 | ||||||||
\(959\) | 4.11803 | − | 21.3979i | 0.132978 | − | 0.690975i | ||||
\(960\) | 43.5410 | 1.40528 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.76393 | + | 16.9116i | 0.314638 | + | 0.544970i | ||||
\(964\) | 11.4271 | − | 19.7922i | 0.368041 | − | 0.637465i | ||||
\(965\) | 1.58359 | 0.0509776 | ||||||||
\(966\) | −120.537 | + | 41.7552i | −3.87821 | + | 1.34345i | ||||
\(967\) | −16.5836 | −0.533292 | −0.266646 | − | 0.963794i | \(-0.585916\pi\) | ||||
−0.266646 | + | 0.963794i | \(0.585916\pi\) | |||||||
\(968\) | 7.47214 | − | 12.9421i | 0.240164 | − | 0.415975i | ||||
\(969\) | −4.93769 | − | 8.55234i | −0.158622 | − | 0.274741i | ||||
\(970\) | −27.5623 | − | 47.7393i | −0.884972 | − | 1.53282i | ||||
\(971\) | 5.64590 | − | 9.77898i | 0.181185 | − | 0.313822i | −0.761099 | − | 0.648636i | \(-0.775340\pi\) |
0.942285 | + | 0.334813i | \(0.108673\pi\) | |||||||
\(972\) | 86.8328 | 2.78516 | ||||||||
\(973\) | −46.8328 | − | 40.5584i | −1.50139 | − | 1.30024i | ||||
\(974\) | 57.1591 | 1.83149 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.7812 | − | 25.6017i | −0.473133 | − | 0.819491i | ||||
\(977\) | −1.17376 | − | 2.03302i | −0.0375520 | − | 0.0650419i | 0.846639 | − | 0.532168i | \(-0.178623\pi\) |
−0.884191 | + | 0.467126i | \(0.845289\pi\) | |||||||
\(978\) | 48.0517 | − | 83.2279i | 1.53652 | − | 2.66134i | ||||
\(979\) | −6.70820 | −0.214395 | ||||||||
\(980\) | −10.8541 | − | 75.1994i | −0.346722 | − | 2.40216i | ||||
\(981\) | 5.41641 | 0.172933 | ||||||||
\(982\) | 33.4164 | − | 57.8789i | 1.06636 | − | 1.84699i | ||||
\(983\) | 3.73607 | + | 6.47106i | 0.119162 | + | 0.206395i | 0.919436 | − | 0.393240i | \(-0.128646\pi\) |
−0.800274 | + | 0.599635i | \(0.795313\pi\) | |||||||
\(984\) | 37.3607 | + | 64.7106i | 1.19101 | + | 2.06290i | ||||
\(985\) | 10.1246 | − | 17.5363i | 0.322597 | − | 0.558754i | ||||
\(986\) | 17.2361 | 0.548908 | ||||||||
\(987\) | −33.4164 | − | 28.9395i | −1.06366 | − | 0.921153i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.9443 | + | 57.0612i | −1.04757 | + | 1.81444i | ||||
\(990\) | 17.5623 | + | 30.4188i | 0.558167 | + | 0.966773i | ||||
\(991\) | −15.3541 | − | 26.5941i | −0.487739 | − | 0.844789i | 0.512161 | − | 0.858889i | \(-0.328845\pi\) |
−0.999901 | + | 0.0141002i | \(0.995512\pi\) | |||||||
\(992\) | 27.1353 | − | 46.9996i | 0.861545 | − | 1.49224i | ||||
\(993\) | −3.54102 | −0.112371 | ||||||||
\(994\) | −58.5410 | + | 20.2792i | −1.85681 | + | 0.643217i | ||||
\(995\) | 46.3050 | 1.46797 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.2082 | − | 22.8773i | −0.418308 | − | 0.724531i | 0.577461 | − | 0.816418i | \(-0.304043\pi\) |
−0.995769 | + | 0.0918873i | \(0.970710\pi\) | |||||||
\(998\) | 34.5795 | + | 59.8935i | 1.09460 | + | 1.89590i | ||||
\(999\) | 5.26393 | − | 9.11740i | 0.166543 | − | 0.288462i |
(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 | 1183.2.e.d.170.1 | 4 | ||
7.2 | even | 3 | 8281.2.a.z.1.2 | 2 | |||
7.4 | even | 3 | inner | 1183.2.e.d.508.1 | 4 | ||
7.5 | odd | 6 | 8281.2.a.ba.1.2 | 2 | |||
13.12 | even | 2 | 91.2.e.b.79.2 | yes | 4 | ||
39.38 | odd | 2 | 819.2.j.c.352.1 | 4 | |||
52.51 | odd | 2 | 1456.2.r.j.625.1 | 4 | |||
91.12 | odd | 6 | 637.2.a.e.1.1 | 2 | |||
91.25 | even | 6 | 91.2.e.b.53.2 | ✓ | 4 | ||
91.38 | odd | 6 | 637.2.e.h.508.2 | 4 | |||
91.51 | even | 6 | 637.2.a.f.1.1 | 2 | |||
91.90 | odd | 2 | 637.2.e.h.79.2 | 4 | |||
273.116 | odd | 6 | 819.2.j.c.235.1 | 4 | |||
273.194 | even | 6 | 5733.2.a.w.1.2 | 2 | |||
273.233 | odd | 6 | 5733.2.a.v.1.2 | 2 | |||
364.207 | odd | 6 | 1456.2.r.j.417.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.b.53.2 | ✓ | 4 | 91.25 | even | 6 | ||
91.2.e.b.79.2 | yes | 4 | 13.12 | even | 2 | ||
637.2.a.e.1.1 | 2 | 91.12 | odd | 6 | |||
637.2.a.f.1.1 | 2 | 91.51 | even | 6 | |||
637.2.e.h.79.2 | 4 | 91.90 | odd | 2 | |||
637.2.e.h.508.2 | 4 | 91.38 | odd | 6 | |||
819.2.j.c.235.1 | 4 | 273.116 | odd | 6 | |||
819.2.j.c.352.1 | 4 | 39.38 | odd | 2 | |||
1183.2.e.d.170.1 | 4 | 1.1 | even | 1 | trivial | ||
1183.2.e.d.508.1 | 4 | 7.4 | even | 3 | inner | ||
1456.2.r.j.417.1 | 4 | 364.207 | odd | 6 | |||
1456.2.r.j.625.1 | 4 | 52.51 | odd | 2 | |||
5733.2.a.v.1.2 | 2 | 273.233 | odd | 6 | |||
5733.2.a.w.1.2 | 2 | 273.194 | even | 6 | |||
8281.2.a.z.1.2 | 2 | 7.2 | even | 3 | |||
8281.2.a.ba.1.2 | 2 | 7.5 | odd | 6 |