Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(0.222521 - 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.22 |
Dual form | 169.2.c.b.146.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12349 | + | 1.94594i | −0.794427 | + | 1.37599i | 0.128775 | + | 0.991674i | \(0.458896\pi\) |
−0.923202 | + | 0.384315i | \(0.874438\pi\) | |||||||
\(3\) | 0.277479 | − | 0.480608i | 0.160203 | − | 0.277479i | −0.774739 | − | 0.632282i | \(-0.782119\pi\) |
0.934941 | + | 0.354803i | \(0.115452\pi\) | |||||||
\(4\) | −1.52446 | − | 2.64044i | −0.762229 | − | 1.32022i | ||||
\(5\) | 1.44504 | 0.646242 | 0.323121 | − | 0.946358i | \(-0.395268\pi\) | ||||
0.323121 | + | 0.946358i | \(0.395268\pi\) | |||||||
\(6\) | 0.623490 | + | 1.07992i | 0.254539 | + | 0.440874i | ||||
\(7\) | 1.02446 | + | 1.77441i | 0.387209 | + | 0.670666i | 0.992073 | − | 0.125663i | \(-0.0401059\pi\) |
−0.604864 | + | 0.796329i | \(0.706773\pi\) | |||||||
\(8\) | 2.35690 | 0.833289 | ||||||||
\(9\) | 1.34601 | + | 2.33136i | 0.448670 | + | 0.777120i | ||||
\(10\) | −1.62349 | + | 2.81197i | −0.513393 | + | 0.889222i | ||||
\(11\) | −1.27748 | + | 2.21266i | −0.385174 | + | 0.667142i | −0.991793 | − | 0.127851i | \(-0.959192\pi\) |
0.606619 | + | 0.794993i | \(0.292525\pi\) | |||||||
\(12\) | −1.69202 | −0.488445 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.60388 | −1.23044 | ||||||||
\(15\) | 0.400969 | − | 0.694498i | 0.103530 | − | 0.179319i | ||||
\(16\) | 0.400969 | − | 0.694498i | 0.100242 | − | 0.173625i | ||||
\(17\) | 2.64795 | + | 4.58638i | 0.642222 | + | 1.11236i | 0.984936 | + | 0.172921i | \(0.0553205\pi\) |
−0.342714 | + | 0.939440i | \(0.611346\pi\) | |||||||
\(18\) | −6.04892 | −1.42574 | ||||||||
\(19\) | −2.92543 | − | 5.06699i | −0.671139 | − | 1.16245i | −0.977581 | − | 0.210558i | \(-0.932472\pi\) |
0.306442 | − | 0.951889i | \(-0.400861\pi\) | |||||||
\(20\) | −2.20291 | − | 3.81555i | −0.492585 | − | 0.853182i | ||||
\(21\) | 1.13706 | 0.248128 | ||||||||
\(22\) | −2.87047 | − | 4.97180i | −0.611986 | − | 1.05999i | ||||
\(23\) | 0.945042 | − | 1.63686i | 0.197055 | − | 0.341309i | −0.750517 | − | 0.660851i | \(-0.770196\pi\) |
0.947572 | + | 0.319542i | \(0.103529\pi\) | |||||||
\(24\) | 0.653989 | − | 1.13274i | 0.133495 | − | 0.231220i | ||||
\(25\) | −2.91185 | −0.582371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.15883 | 0.607918 | ||||||||
\(28\) | 3.12349 | − | 5.41004i | 0.590284 | − | 1.02240i | ||||
\(29\) | −1.13437 | + | 1.96480i | −0.210648 | + | 0.364853i | −0.951918 | − | 0.306354i | \(-0.900891\pi\) |
0.741269 | + | 0.671208i | \(0.234224\pi\) | |||||||
\(30\) | 0.900969 | + | 1.56052i | 0.164494 | + | 0.284911i | ||||
\(31\) | 4.26875 | 0.766690 | 0.383345 | − | 0.923605i | \(-0.374772\pi\) | ||||
0.383345 | + | 0.923605i | \(0.374772\pi\) | |||||||
\(32\) | 3.25786 | + | 5.64279i | 0.575915 | + | 0.997513i | ||||
\(33\) | 0.708947 | + | 1.22793i | 0.123412 | + | 0.213756i | ||||
\(34\) | −11.8998 | −2.04079 | ||||||||
\(35\) | 1.48039 | + | 2.56410i | 0.250231 | + | 0.433413i | ||||
\(36\) | 4.10388 | − | 7.10812i | 0.683979 | − | 1.18469i | ||||
\(37\) | 2.67845 | − | 4.63921i | 0.440334 | − | 0.762681i | −0.557380 | − | 0.830258i | \(-0.688193\pi\) |
0.997714 | + | 0.0675764i | \(0.0215267\pi\) | |||||||
\(38\) | 13.1468 | 2.13268 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.40581 | 0.538506 | ||||||||
\(41\) | 0.637063 | − | 1.10343i | 0.0994926 | − | 0.172326i | −0.811982 | − | 0.583682i | \(-0.801611\pi\) |
0.911475 | + | 0.411356i | \(0.134945\pi\) | |||||||
\(42\) | −1.27748 | + | 2.21266i | −0.197119 | + | 0.341421i | ||||
\(43\) | −3.06853 | − | 5.31485i | −0.467947 | − | 0.810507i | 0.531382 | − | 0.847132i | \(-0.321673\pi\) |
−0.999329 | + | 0.0366246i | \(0.988339\pi\) | |||||||
\(44\) | 7.78986 | 1.17437 | ||||||||
\(45\) | 1.94504 | + | 3.36891i | 0.289950 | + | 0.502208i | ||||
\(46\) | 2.12349 | + | 3.67799i | 0.313091 | + | 0.542290i | ||||
\(47\) | 2.95108 | 0.430460 | 0.215230 | − | 0.976563i | \(-0.430950\pi\) | ||||
0.215230 | + | 0.976563i | \(0.430950\pi\) | |||||||
\(48\) | −0.222521 | − | 0.385418i | −0.0321181 | − | 0.0556302i | ||||
\(49\) | 1.40097 | − | 2.42655i | 0.200138 | − | 0.346650i | ||||
\(50\) | 3.27144 | − | 5.66630i | 0.462651 | − | 0.801335i | ||||
\(51\) | 2.93900 | 0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.52111 | 0.758382 | 0.379191 | − | 0.925318i | \(-0.376202\pi\) | ||||
0.379191 | + | 0.925318i | \(0.376202\pi\) | |||||||
\(54\) | −3.54892 | + | 6.14691i | −0.482946 | + | 0.836488i | ||||
\(55\) | −1.84601 | + | 3.19738i | −0.248916 | + | 0.431135i | ||||
\(56\) | 2.41454 | + | 4.18211i | 0.322657 | + | 0.558858i | ||||
\(57\) | −3.24698 | −0.430073 | ||||||||
\(58\) | −2.54892 | − | 4.41485i | −0.334689 | − | 0.579699i | ||||
\(59\) | −6.10388 | − | 10.5722i | −0.794657 | − | 1.37639i | −0.923057 | − | 0.384664i | \(-0.874317\pi\) |
0.128400 | − | 0.991722i | \(-0.459016\pi\) | |||||||
\(60\) | −2.44504 | −0.315654 | ||||||||
\(61\) | −4.28232 | − | 7.41720i | −0.548295 | − | 0.949675i | −0.998392 | − | 0.0566953i | \(-0.981944\pi\) |
0.450096 | − | 0.892980i | \(-0.351390\pi\) | |||||||
\(62\) | −4.79590 | + | 8.30674i | −0.609080 | + | 1.05496i | ||||
\(63\) | −2.75786 | + | 4.77676i | −0.347458 | + | 0.601815i | ||||
\(64\) | −13.0368 | −1.62960 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.18598 | −0.392167 | ||||||||
\(67\) | 0.288364 | − | 0.499461i | 0.0352293 | − | 0.0610189i | −0.847873 | − | 0.530199i | \(-0.822117\pi\) |
0.883102 | + | 0.469180i | \(0.155451\pi\) | |||||||
\(68\) | 8.07338 | − | 13.9835i | 0.979041 | − | 1.69575i | ||||
\(69\) | −0.524459 | − | 0.908389i | −0.0631374 | − | 0.109357i | ||||
\(70\) | −6.65279 | −0.795161 | ||||||||
\(71\) | −2.29709 | − | 3.97868i | −0.272615 | − | 0.472183i | 0.696916 | − | 0.717153i | \(-0.254555\pi\) |
−0.969531 | + | 0.244970i | \(0.921222\pi\) | |||||||
\(72\) | 3.17241 | + | 5.49477i | 0.373872 | + | 0.647565i | ||||
\(73\) | 10.5526 | 1.23508 | 0.617542 | − | 0.786538i | \(-0.288128\pi\) | ||||
0.617542 | + | 0.786538i | \(0.288128\pi\) | |||||||
\(74\) | 6.01842 | + | 10.4242i | 0.699627 | + | 1.21179i | ||||
\(75\) | −0.807979 | + | 1.39946i | −0.0932973 | + | 0.161596i | ||||
\(76\) | −8.91939 | + | 15.4488i | −1.02312 | + | 1.77210i | ||||
\(77\) | −5.23490 | −0.596572 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7778 | −1.77514 | −0.887569 | − | 0.460674i | \(-0.847608\pi\) | ||||
−0.887569 | + | 0.460674i | \(0.847608\pi\) | |||||||
\(80\) | 0.579417 | − | 1.00358i | 0.0647808 | − | 0.112204i | ||||
\(81\) | −3.16152 | + | 5.47592i | −0.351280 | + | 0.608435i | ||||
\(82\) | 1.43147 | + | 2.47938i | 0.158079 | + | 0.273801i | ||||
\(83\) | −7.72348 | −0.847762 | −0.423881 | − | 0.905718i | \(-0.639333\pi\) | ||||
−0.423881 | + | 0.905718i | \(0.639333\pi\) | |||||||
\(84\) | −1.73341 | − | 3.00235i | −0.189130 | − | 0.327583i | ||||
\(85\) | 3.82640 | + | 6.62751i | 0.415031 | + | 0.718855i | ||||
\(86\) | 13.7899 | 1.48700 | ||||||||
\(87\) | 0.629531 | + | 1.09038i | 0.0674928 | + | 0.116901i | ||||
\(88\) | −3.01089 | + | 5.21501i | −0.320961 | + | 0.555922i | ||||
\(89\) | 3.30678 | − | 5.72751i | 0.350518 | − | 0.607115i | −0.635822 | − | 0.771836i | \(-0.719339\pi\) |
0.986340 | + | 0.164720i | \(0.0526721\pi\) | |||||||
\(90\) | −8.74094 | −0.921376 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.76271 | −0.600804 | ||||||||
\(93\) | 1.18449 | − | 2.05159i | 0.122826 | − | 0.212740i | ||||
\(94\) | −3.31551 | + | 5.74263i | −0.341969 | + | 0.592307i | ||||
\(95\) | −4.22737 | − | 7.32201i | −0.433719 | − | 0.751223i | ||||
\(96\) | 3.61596 | 0.369052 | ||||||||
\(97\) | 5.96346 | + | 10.3290i | 0.605498 | + | 1.04875i | 0.991973 | + | 0.126453i | \(0.0403592\pi\) |
−0.386475 | + | 0.922300i | \(0.626307\pi\) | |||||||
\(98\) | 3.14795 | + | 5.45241i | 0.317991 | + | 0.550776i | ||||
\(99\) | −6.87800 | −0.691265 | ||||||||
\(100\) | 4.43900 | + | 7.68858i | 0.443900 | + | 0.768858i | ||||
\(101\) | −6.53199 | + | 11.3137i | −0.649957 | + | 1.12576i | 0.333175 | + | 0.942865i | \(0.391880\pi\) |
−0.983133 | + | 0.182894i | \(0.941453\pi\) | |||||||
\(102\) | −3.30194 | + | 5.71912i | −0.326941 | + | 0.566278i | ||||
\(103\) | 9.16852 | 0.903401 | 0.451701 | − | 0.892170i | \(-0.350818\pi\) | ||||
0.451701 | + | 0.892170i | \(0.350818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64310 | 0.160351 | ||||||||
\(106\) | −6.20291 | + | 10.7437i | −0.602480 | + | 1.04353i | ||||
\(107\) | 3.44989 | − | 5.97538i | 0.333513 | − | 0.577662i | −0.649685 | − | 0.760204i | \(-0.725099\pi\) |
0.983198 | + | 0.182542i | \(0.0584325\pi\) | |||||||
\(108\) | −4.81551 | − | 8.34071i | −0.463373 | − | 0.802585i | ||||
\(109\) | −0.121998 | −0.0116853 | −0.00584264 | − | 0.999983i | \(-0.501860\pi\) | ||||
−0.00584264 | + | 0.999983i | \(0.501860\pi\) | |||||||
\(110\) | −4.14795 | − | 7.18446i | −0.395491 | − | 0.685011i | ||||
\(111\) | −1.48643 | − | 2.57457i | −0.141085 | − | 0.244367i | ||||
\(112\) | 1.64310 | 0.155259 | ||||||||
\(113\) | −3.65399 | − | 6.32890i | −0.343738 | − | 0.595372i | 0.641385 | − | 0.767219i | \(-0.278360\pi\) |
−0.985124 | + | 0.171847i | \(0.945027\pi\) | |||||||
\(114\) | 3.64795 | − | 6.31843i | 0.341662 | − | 0.591775i | ||||
\(115\) | 1.36563 | − | 2.36533i | 0.127345 | − | 0.220568i | ||||
\(116\) | 6.91723 | 0.642249 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.4306 | 2.52519 | ||||||||
\(119\) | −5.42543 | + | 9.39712i | −0.497348 | + | 0.861432i | ||||
\(120\) | 0.945042 | − | 1.63686i | 0.0862701 | − | 0.149424i | ||||
\(121\) | 2.23609 | + | 3.87303i | 0.203281 | + | 0.352094i | ||||
\(122\) | 19.2446 | 1.74232 | ||||||||
\(123\) | −0.353543 | − | 0.612355i | −0.0318779 | − | 0.0552142i | ||||
\(124\) | −6.50753 | − | 11.2714i | −0.584394 | − | 1.01220i | ||||
\(125\) | −11.4330 | −1.02260 | ||||||||
\(126\) | −6.19687 | − | 10.7333i | −0.552061 | − | 0.956197i | ||||
\(127\) | 9.48523 | − | 16.4289i | 0.841678 | − | 1.45783i | −0.0467971 | − | 0.998904i | \(-0.514901\pi\) |
0.888475 | − | 0.458925i | \(-0.151765\pi\) | |||||||
\(128\) | 8.13102 | − | 14.0833i | 0.718688 | − | 1.24480i | ||||
\(129\) | −3.40581 | −0.299865 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.25667 | 0.284536 | 0.142268 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142268 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(132\) | 2.16152 | − | 3.74387i | 0.188136 | − | 0.325862i | ||||
\(133\) | 5.99396 | − | 10.3818i | 0.519742 | − | 0.900220i | ||||
\(134\) | 0.647948 | + | 1.12228i | 0.0559742 | + | 0.0969502i | ||||
\(135\) | 4.56465 | 0.392862 | ||||||||
\(136\) | 6.24094 | + | 10.8096i | 0.535156 | + | 0.926918i | ||||
\(137\) | 0.396125 | + | 0.686108i | 0.0338432 | + | 0.0586181i | 0.882451 | − | 0.470405i | \(-0.155892\pi\) |
−0.848608 | + | 0.529023i | \(0.822559\pi\) | |||||||
\(138\) | 2.35690 | 0.200632 | ||||||||
\(139\) | 5.66972 | + | 9.82024i | 0.480899 | + | 0.832942i | 0.999760 | − | 0.0219169i | \(-0.00697694\pi\) |
−0.518861 | + | 0.854859i | \(0.673644\pi\) | |||||||
\(140\) | 4.51357 | − | 7.81774i | 0.381467 | − | 0.660720i | ||||
\(141\) | 0.818864 | − | 1.41831i | 0.0689608 | − | 0.119444i | ||||
\(142\) | 10.3230 | 0.866291 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.15883 | 0.179903 | ||||||||
\(145\) | −1.63922 | + | 2.83921i | −0.136130 | + | 0.235784i | ||||
\(146\) | −11.8557 | + | 20.5347i | −0.981185 | + | 1.69946i | ||||
\(147\) | −0.777479 | − | 1.34663i | −0.0641254 | − | 0.111068i | ||||
\(148\) | −16.3327 | −1.34254 | ||||||||
\(149\) | 4.20291 | + | 7.27965i | 0.344316 | + | 0.596372i | 0.985229 | − | 0.171241i | \(-0.0547777\pi\) |
−0.640914 | + | 0.767613i | \(0.721444\pi\) | |||||||
\(150\) | −1.81551 | − | 3.14456i | −0.148236 | − | 0.256752i | ||||
\(151\) | −14.1293 | −1.14983 | −0.574913 | − | 0.818215i | \(-0.694964\pi\) | ||||
−0.574913 | + | 0.818215i | \(0.694964\pi\) | |||||||
\(152\) | −6.89493 | − | 11.9424i | −0.559253 | − | 0.968654i | ||||
\(153\) | −7.12833 | + | 12.3466i | −0.576292 | + | 0.998166i | ||||
\(154\) | 5.88135 | − | 10.1868i | 0.473933 | − | 0.820876i | ||||
\(155\) | 6.16852 | 0.495468 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.43296 | −0.752832 | −0.376416 | − | 0.926451i | \(-0.622844\pi\) | ||||
−0.376416 | + | 0.926451i | \(0.622844\pi\) | |||||||
\(158\) | 17.7262 | − | 30.7026i | 1.41022 | − | 2.44257i | ||||
\(159\) | 1.53199 | − | 2.65349i | 0.121495 | − | 0.210435i | ||||
\(160\) | 4.70775 | + | 8.15406i | 0.372180 | + | 0.644635i | ||||
\(161\) | 3.87263 | 0.305206 | ||||||||
\(162\) | −7.10388 | − | 12.3043i | −0.558133 | − | 0.966715i | ||||
\(163\) | 4.35205 | + | 7.53797i | 0.340879 | + | 0.590420i | 0.984596 | − | 0.174844i | \(-0.0559420\pi\) |
−0.643717 | + | 0.765263i | \(0.722609\pi\) | |||||||
\(164\) | −3.88471 | −0.303345 | ||||||||
\(165\) | 1.02446 | + | 1.77441i | 0.0797540 | + | 0.138138i | ||||
\(166\) | 8.67725 | − | 15.0294i | 0.673485 | − | 1.16651i | ||||
\(167\) | −11.9269 | + | 20.6580i | −0.922933 | + | 1.59857i | −0.128080 | + | 0.991764i | \(0.540881\pi\) |
−0.794853 | + | 0.606803i | \(0.792452\pi\) | |||||||
\(168\) | 2.67994 | 0.206762 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −17.1957 | −1.31885 | ||||||||
\(171\) | 7.87531 | − | 13.6404i | 0.602240 | − | 1.04311i | ||||
\(172\) | −9.35570 | + | 16.2045i | −0.713365 | + | 1.23559i | ||||
\(173\) | 9.42758 | + | 16.3291i | 0.716766 | + | 1.24147i | 0.962274 | + | 0.272081i | \(0.0877117\pi\) |
−0.245509 | + | 0.969394i | \(0.578955\pi\) | |||||||
\(174\) | −2.82908 | −0.214472 | ||||||||
\(175\) | −2.98307 | − | 5.16684i | −0.225499 | − | 0.390576i | ||||
\(176\) | 1.02446 | + | 1.77441i | 0.0772215 | + | 0.133752i | ||||
\(177\) | −6.77479 | −0.509224 | ||||||||
\(178\) | 7.43027 | + | 12.8696i | 0.556922 | + | 0.964618i | ||||
\(179\) | −3.01089 | + | 5.21501i | −0.225044 | + | 0.389788i | −0.956333 | − | 0.292280i | \(-0.905586\pi\) |
0.731289 | + | 0.682068i | \(0.238919\pi\) | |||||||
\(180\) | 5.93027 | − | 10.2715i | 0.442016 | − | 0.765595i | ||||
\(181\) | −4.77777 | −0.355129 | −0.177565 | − | 0.984109i | \(-0.556822\pi\) | ||||
−0.177565 | + | 0.984109i | \(0.556822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.75302 | −0.351353 | ||||||||
\(184\) | 2.22737 | − | 3.85791i | 0.164204 | − | 0.284409i | ||||
\(185\) | 3.87047 | − | 6.70385i | 0.284563 | − | 0.492877i | ||||
\(186\) | 2.66152 | + | 4.60989i | 0.195152 | + | 0.338014i | ||||
\(187\) | −13.5308 | −0.989470 | ||||||||
\(188\) | −4.49880 | − | 7.79216i | −0.328109 | − | 0.568301i | ||||
\(189\) | 3.23609 | + | 5.60508i | 0.235391 | + | 0.407710i | ||||
\(190\) | 18.9976 | 1.37823 | ||||||||
\(191\) | −9.21528 | − | 15.9613i | −0.666795 | − | 1.15492i | −0.978795 | − | 0.204840i | \(-0.934333\pi\) |
0.312001 | − | 0.950082i | \(-0.399001\pi\) | |||||||
\(192\) | −3.61745 | + | 6.26561i | −0.261067 | + | 0.452181i | ||||
\(193\) | 3.02715 | − | 5.24317i | 0.217899 | − | 0.377412i | −0.736267 | − | 0.676692i | \(-0.763413\pi\) |
0.954165 | + | 0.299280i | \(0.0967464\pi\) | |||||||
\(194\) | −26.7995 | −1.92410 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54288 | −0.610205 | ||||||||
\(197\) | −5.70775 | + | 9.88611i | −0.406660 | + | 0.704357i | −0.994513 | − | 0.104611i | \(-0.966640\pi\) |
0.587853 | + | 0.808968i | \(0.299973\pi\) | |||||||
\(198\) | 7.72737 | − | 13.3842i | 0.549160 | − | 0.951173i | ||||
\(199\) | 6.95257 | + | 12.0422i | 0.492855 | + | 0.853650i | 0.999966 | − | 0.00823084i | \(-0.00261999\pi\) |
−0.507111 | + | 0.861881i | \(0.669287\pi\) | |||||||
\(200\) | −6.86294 | −0.485283 | ||||||||
\(201\) | −0.160030 | − | 0.277180i | −0.0112876 | − | 0.0195508i | ||||
\(202\) | −14.6773 | − | 25.4217i | −1.03269 | − | 1.78867i | ||||
\(203\) | −4.64848 | −0.326259 | ||||||||
\(204\) | −4.48039 | − | 7.76026i | −0.313690 | − | 0.543327i | ||||
\(205\) | 0.920583 | − | 1.59450i | 0.0642963 | − | 0.111364i | ||||
\(206\) | −10.3007 | + | 17.8414i | −0.717687 | + | 1.24307i | ||||
\(207\) | 5.08815 | 0.353651 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9487 | 1.03402 | ||||||||
\(210\) | −1.84601 | + | 3.19738i | −0.127387 | + | 0.220640i | ||||
\(211\) | 6.62229 | − | 11.4701i | 0.455897 | − | 0.789638i | −0.542842 | − | 0.839835i | \(-0.682652\pi\) |
0.998739 | + | 0.0501974i | \(0.0159850\pi\) | |||||||
\(212\) | −8.41670 | − | 14.5781i | −0.578061 | − | 1.00123i | ||||
\(213\) | −2.54958 | −0.174694 | ||||||||
\(214\) | 7.75182 | + | 13.4266i | 0.529904 | + | 0.917820i | ||||
\(215\) | −4.43416 | − | 7.68018i | −0.302407 | − | 0.523784i | ||||
\(216\) | 7.44504 | 0.506571 | ||||||||
\(217\) | 4.37316 | + | 7.57453i | 0.296869 | + | 0.514193i | ||||
\(218\) | 0.137063 | − | 0.237401i | 0.00928310 | − | 0.0160788i | ||||
\(219\) | 2.92812 | − | 5.07165i | 0.197864 | − | 0.342710i | ||||
\(220\) | 11.2567 | 0.758924 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.67994 | 0.448328 | ||||||||
\(223\) | −3.66756 | + | 6.35241i | −0.245598 | + | 0.425389i | −0.962300 | − | 0.271992i | \(-0.912318\pi\) |
0.716701 | + | 0.697380i | \(0.245651\pi\) | |||||||
\(224\) | −6.67510 | + | 11.5616i | −0.445999 | + | 0.772492i | ||||
\(225\) | −3.91939 | − | 6.78858i | −0.261292 | − | 0.452572i | ||||
\(226\) | 16.4209 | 1.09230 | ||||||||
\(227\) | −4.33728 | − | 7.51239i | −0.287875 | − | 0.498615i | 0.685427 | − | 0.728141i | \(-0.259616\pi\) |
−0.973302 | + | 0.229526i | \(0.926282\pi\) | |||||||
\(228\) | 4.94989 | + | 8.57345i | 0.327814 | + | 0.567791i | ||||
\(229\) | 13.6866 | 0.904439 | 0.452219 | − | 0.891907i | \(-0.350632\pi\) | ||||
0.452219 | + | 0.891907i | \(0.350632\pi\) | |||||||
\(230\) | 3.06853 | + | 5.31485i | 0.202333 | + | 0.350451i | ||||
\(231\) | −1.45257 | + | 2.51593i | −0.0955724 | + | 0.165536i | ||||
\(232\) | −2.67360 | + | 4.63082i | −0.175531 | + | 0.304028i | ||||
\(233\) | −5.08815 | −0.333336 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.26444 | 0.278181 | ||||||||
\(236\) | −18.6102 | + | 32.2338i | −1.21142 | + | 2.09824i | ||||
\(237\) | −4.37800 | + | 7.58292i | −0.284382 | + | 0.492564i | ||||
\(238\) | −12.1908 | − | 21.1151i | −0.790214 | − | 1.36869i | ||||
\(239\) | 10.9239 | 0.706611 | 0.353305 | − | 0.935508i | \(-0.385058\pi\) | ||||
0.353305 | + | 0.935508i | \(0.385058\pi\) | |||||||
\(240\) | −0.321552 | − | 0.556945i | −0.0207561 | − | 0.0359506i | ||||
\(241\) | 5.95742 | + | 10.3186i | 0.383751 | + | 0.664676i | 0.991595 | − | 0.129380i | \(-0.0412987\pi\) |
−0.607844 | + | 0.794056i | \(0.707965\pi\) | |||||||
\(242\) | −10.0489 | −0.645969 | ||||||||
\(243\) | 6.49276 | + | 11.2458i | 0.416511 | + | 0.721418i | ||||
\(244\) | −13.0565 | + | 22.6144i | −0.835854 | + | 1.44774i | ||||
\(245\) | 2.02446 | − | 3.50647i | 0.129338 | − | 0.224020i | ||||
\(246\) | 1.58881 | 0.101299 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.0610 | 0.638874 | ||||||||
\(249\) | −2.14310 | + | 3.71197i | −0.135814 | + | 0.235236i | ||||
\(250\) | 12.8448 | − | 22.2479i | 0.812377 | − | 1.40708i | ||||
\(251\) | −11.1739 | − | 19.3538i | −0.705290 | − | 1.22160i | −0.966587 | − | 0.256340i | \(-0.917483\pi\) |
0.261296 | − | 0.965259i | \(-0.415850\pi\) | |||||||
\(252\) | 16.8170 | 1.05937 | ||||||||
\(253\) | 2.41454 | + | 4.18211i | 0.151801 | + | 0.262927i | ||||
\(254\) | 21.3131 | + | 36.9154i | 1.33730 | + | 2.31628i | ||||
\(255\) | 4.24698 | 0.265956 | ||||||||
\(256\) | 5.23341 | + | 9.06453i | 0.327088 | + | 0.566533i | ||||
\(257\) | 9.33004 | − | 16.1601i | 0.581992 | − | 1.00804i | −0.413251 | − | 0.910617i | \(-0.635607\pi\) |
0.995243 | − | 0.0974228i | \(-0.0310599\pi\) | |||||||
\(258\) | 3.82640 | − | 6.62751i | 0.238221 | − | 0.412611i | ||||
\(259\) | 10.9758 | 0.682005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10752 | −0.378046 | ||||||||
\(262\) | −3.65883 | + | 6.33729i | −0.226043 | + | 0.391519i | ||||
\(263\) | −7.19955 | + | 12.4700i | −0.443944 | + | 0.768933i | −0.997978 | − | 0.0635610i | \(-0.979754\pi\) |
0.554034 | + | 0.832494i | \(0.313088\pi\) | |||||||
\(264\) | 1.67092 | + | 2.89411i | 0.102838 | + | 0.178120i | ||||
\(265\) | 7.97823 | 0.490099 | ||||||||
\(266\) | 13.4683 | + | 23.3278i | 0.825795 | + | 1.43032i | ||||
\(267\) | −1.83513 | − | 3.17853i | −0.112308 | − | 0.194523i | ||||
\(268\) | −1.75840 | −0.107411 | ||||||||
\(269\) | −0.326396 | − | 0.565335i | −0.0199007 | − | 0.0344691i | 0.855904 | − | 0.517136i | \(-0.173002\pi\) |
−0.875804 | + | 0.482666i | \(0.839668\pi\) | |||||||
\(270\) | −5.12833 | + | 8.88254i | −0.312100 | + | 0.540574i | ||||
\(271\) | −0.997844 | + | 1.72832i | −0.0606147 | + | 0.104988i | −0.894740 | − | 0.446587i | \(-0.852639\pi\) |
0.834126 | + | 0.551574i | \(0.185973\pi\) | |||||||
\(272\) | 4.24698 | 0.257511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.78017 | −0.107544 | ||||||||
\(275\) | 3.71983 | − | 6.44294i | 0.224314 | − | 0.388524i | ||||
\(276\) | −1.59903 | + | 2.76960i | −0.0962504 | + | 0.166711i | ||||
\(277\) | −5.89224 | − | 10.2057i | −0.354030 | − | 0.613199i | 0.632921 | − | 0.774216i | \(-0.281856\pi\) |
−0.986952 | + | 0.161018i | \(0.948522\pi\) | |||||||
\(278\) | −25.4795 | −1.52816 | ||||||||
\(279\) | 5.74578 | + | 9.95199i | 0.343991 | + | 0.595810i | ||||
\(280\) | 3.48911 | + | 6.04332i | 0.208514 | + | 0.361158i | ||||
\(281\) | 6.47219 | 0.386098 | 0.193049 | − | 0.981189i | \(-0.438162\pi\) | ||||
0.193049 | + | 0.981189i | \(0.438162\pi\) | |||||||
\(282\) | 1.83997 | + | 3.18692i | 0.109569 | + | 0.189778i | ||||
\(283\) | −3.29052 | + | 5.69935i | −0.195601 | + | 0.338791i | −0.947097 | − | 0.320946i | \(-0.895999\pi\) |
0.751496 | + | 0.659737i | \(0.229332\pi\) | |||||||
\(284\) | −7.00365 | + | 12.1307i | −0.415590 | + | 0.719823i | ||||
\(285\) | −4.69202 | −0.277931 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.61058 | 0.154098 | ||||||||
\(288\) | −8.77024 | + | 15.1905i | −0.516791 | + | 0.895109i | ||||
\(289\) | −5.52326 | + | 9.56657i | −0.324898 | + | 0.562739i | ||||
\(290\) | −3.68329 | − | 6.37965i | −0.216290 | − | 0.374626i | ||||
\(291\) | 6.61894 | 0.388009 | ||||||||
\(292\) | −16.0869 | − | 27.8634i | −0.941418 | − | 1.63058i | ||||
\(293\) | −12.1691 | − | 21.0774i | −0.710924 | − | 1.23136i | −0.964511 | − | 0.264044i | \(-0.914944\pi\) |
0.253587 | − | 0.967313i | \(-0.418390\pi\) | |||||||
\(294\) | 3.49396 | 0.203772 | ||||||||
\(295\) | −8.82036 | − | 15.2773i | −0.513541 | − | 0.889479i | ||||
\(296\) | 6.31282 | − | 10.9341i | 0.366925 | − | 0.635533i | ||||
\(297\) | −4.03534 | + | 6.98942i | −0.234154 | + | 0.405567i | ||||
\(298\) | −18.8877 | −1.09413 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.92692 | 0.284456 | ||||||||
\(301\) | 6.28717 | − | 10.8897i | 0.362386 | − | 0.627672i | ||||
\(302\) | 15.8741 | − | 27.4948i | 0.913453 | − | 1.58215i | ||||
\(303\) | 3.62498 | + | 6.27865i | 0.208250 | + | 0.360699i | ||||
\(304\) | −4.69202 | −0.269106 | ||||||||
\(305\) | −6.18814 | − | 10.7182i | −0.354332 | − | 0.613720i | ||||
\(306\) | −16.0172 | − | 27.7426i | −0.915644 | − | 1.58594i | ||||
\(307\) | 14.0737 | 0.803227 | 0.401613 | − | 0.915809i | \(-0.368450\pi\) | ||||
0.401613 | + | 0.915809i | \(0.368450\pi\) | |||||||
\(308\) | 7.98039 | + | 13.8224i | 0.454725 | + | 0.787606i | ||||
\(309\) | 2.54407 | − | 4.40646i | 0.144727 | − | 0.250675i | ||||
\(310\) | −6.93027 | + | 12.0036i | −0.393613 | + | 0.681758i | ||||
\(311\) | −29.7700 | −1.68810 | −0.844051 | − | 0.536263i | \(-0.819836\pi\) | ||||
−0.844051 | + | 0.536263i | \(0.819836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.47889 | −0.422732 | −0.211366 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211366 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(314\) | 10.5978 | − | 18.3560i | 0.598070 | − | 1.03589i | ||||
\(315\) | −3.98523 | + | 6.90262i | −0.224542 | + | 0.388919i | ||||
\(316\) | 24.0526 | + | 41.6603i | 1.35306 | + | 2.34357i | ||||
\(317\) | −30.0301 | −1.68666 | −0.843330 | − | 0.537396i | \(-0.819408\pi\) | ||||
−0.843330 | + | 0.537396i | \(0.819408\pi\) | |||||||
\(318\) | 3.44235 | + | 5.96233i | 0.193038 | + | 0.334351i | ||||
\(319\) | −2.89828 | − | 5.01997i | −0.162273 | − | 0.281064i | ||||
\(320\) | −18.8388 | −1.05312 | ||||||||
\(321\) | −1.91454 | − | 3.31608i | −0.106859 | − | 0.185086i | ||||
\(322\) | −4.35086 | + | 7.53590i | −0.242464 | + | 0.419959i | ||||
\(323\) | 15.4928 | − | 26.8343i | 0.862040 | − | 1.49310i | ||||
\(324\) | 19.2784 | 1.07102 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.5579 | −1.08321 | ||||||||
\(327\) | −0.0338518 | + | 0.0586331i | −0.00187201 | + | 0.00324242i | ||||
\(328\) | 1.50149 | − | 2.60066i | 0.0829060 | − | 0.143597i | ||||
\(329\) | 3.02326 | + | 5.23644i | 0.166678 | + | 0.288694i | ||||
\(330\) | −4.60388 | −0.253435 | ||||||||
\(331\) | −7.85839 | − | 13.6111i | −0.431936 | − | 0.748135i | 0.565104 | − | 0.825020i | \(-0.308836\pi\) |
−0.997040 | + | 0.0768845i | \(0.975503\pi\) | |||||||
\(332\) | 11.7741 | + | 20.3934i | 0.646189 | + | 1.11923i | ||||
\(333\) | 14.4209 | 0.790259 | ||||||||
\(334\) | −26.7995 | − | 46.4182i | −1.46641 | − | 2.53989i | ||||
\(335\) | 0.416698 | − | 0.721743i | 0.0227667 | − | 0.0394330i | ||||
\(336\) | 0.455927 | − | 0.789689i | 0.0248729 | − | 0.0430811i | ||||
\(337\) | 1.95407 | 0.106445 | 0.0532224 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532224 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.05562 | −0.220271 | ||||||||
\(340\) | 11.6664 | − | 20.2067i | 0.632698 | − | 1.09586i | ||||
\(341\) | −5.45324 | + | 9.44529i | −0.295309 | + | 0.511491i | ||||
\(342\) | 17.6957 | + | 30.6498i | 0.956872 | + | 1.65735i | ||||
\(343\) | 20.0834 | 1.08440 | ||||||||
\(344\) | −7.23221 | − | 12.5266i | −0.389935 | − | 0.675387i | ||||
\(345\) | −0.757865 | − | 1.31266i | −0.0408021 | − | 0.0706713i | ||||
\(346\) | −42.3672 | −2.27767 | ||||||||
\(347\) | 8.56249 | + | 14.8307i | 0.459659 | + | 0.796152i | 0.998943 | − | 0.0459718i | \(-0.0146384\pi\) |
−0.539284 | + | 0.842124i | \(0.681305\pi\) | |||||||
\(348\) | 1.91939 | − | 3.32448i | 0.102890 | − | 0.178211i | ||||
\(349\) | −5.23341 | + | 9.06453i | −0.280138 | + | 0.485213i | −0.971418 | − | 0.237373i | \(-0.923713\pi\) |
0.691281 | + | 0.722586i | \(0.257047\pi\) | |||||||
\(350\) | 13.4058 | 0.716571 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.6474 | −0.887310 | ||||||||
\(353\) | 7.76540 | − | 13.4501i | 0.413310 | − | 0.715875i | −0.581939 | − | 0.813232i | \(-0.697706\pi\) |
0.995249 | + | 0.0973578i | \(0.0310391\pi\) | |||||||
\(354\) | 7.61141 | − | 13.1833i | 0.404542 | − | 0.700687i | ||||
\(355\) | −3.31940 | − | 5.74936i | −0.176175 | − | 0.305144i | ||||
\(356\) | −20.1642 | −1.06870 | ||||||||
\(357\) | 3.01089 | + | 5.21501i | 0.159353 | + | 0.276007i | ||||
\(358\) | −6.76540 | − | 11.7180i | −0.357562 | − | 0.619316i | ||||
\(359\) | 21.4263 | 1.13083 | 0.565417 | − | 0.824805i | \(-0.308715\pi\) | ||||
0.565417 | + | 0.824805i | \(0.308715\pi\) | |||||||
\(360\) | 4.58426 | + | 7.94017i | 0.241612 | + | 0.418484i | ||||
\(361\) | −7.61625 | + | 13.1917i | −0.400855 | + | 0.694302i | ||||
\(362\) | 5.36778 | − | 9.29727i | 0.282124 | − | 0.488654i | ||||
\(363\) | 2.48188 | 0.130265 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2489 | 0.798164 | ||||||||
\(366\) | 5.33997 | − | 9.24910i | 0.279125 | − | 0.483458i | ||||
\(367\) | −17.1516 | + | 29.7074i | −0.895306 | + | 1.55072i | −0.0618807 | + | 0.998084i | \(0.519710\pi\) |
−0.833425 | + | 0.552632i | \(0.813624\pi\) | |||||||
\(368\) | −0.757865 | − | 1.31266i | −0.0395064 | − | 0.0684271i | ||||
\(369\) | 3.42998 | 0.178557 | ||||||||
\(370\) | 8.69687 | + | 15.0634i | 0.452129 | + | 0.783110i | ||||
\(371\) | 5.65615 | + | 9.79673i | 0.293652 | + | 0.508621i | ||||
\(372\) | −7.22282 | −0.374486 | ||||||||
\(373\) | 6.29805 | + | 10.9085i | 0.326101 | + | 0.564823i | 0.981735 | − | 0.190256i | \(-0.0609318\pi\) |
−0.655634 | + | 0.755079i | \(0.727598\pi\) | |||||||
\(374\) | 15.2017 | − | 26.3301i | 0.786062 | − | 1.36150i | ||||
\(375\) | −3.17241 | + | 5.49477i | −0.163822 | + | 0.283749i | ||||
\(376\) | 6.95539 | 0.358697 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −14.5429 | −0.748005 | ||||||||
\(379\) | 8.26928 | − | 14.3228i | 0.424765 | − | 0.735714i | −0.571634 | − | 0.820509i | \(-0.693690\pi\) |
0.996398 | + | 0.0847951i | \(0.0270236\pi\) | |||||||
\(380\) | −12.8889 | + | 22.3242i | −0.661186 | + | 1.14521i | ||||
\(381\) | −5.26391 | − | 9.11735i | −0.269678 | − | 0.467096i | ||||
\(382\) | 41.4131 | 2.11888 | ||||||||
\(383\) | 3.76809 | + | 6.52652i | 0.192540 | + | 0.333489i | 0.946091 | − | 0.323900i | \(-0.104994\pi\) |
−0.753551 | + | 0.657389i | \(0.771661\pi\) | |||||||
\(384\) | −4.51238 | − | 7.81567i | −0.230271 | − | 0.398842i | ||||
\(385\) | −7.56465 | −0.385530 | ||||||||
\(386\) | 6.80194 | + | 11.7813i | 0.346210 | + | 0.599652i | ||||
\(387\) | 8.26055 | − | 14.3077i | 0.419908 | − | 0.727301i | ||||
\(388\) | 18.1821 | − | 31.4923i | 0.923056 | − | 1.59878i | ||||
\(389\) | 35.5555 | 1.80274 | 0.901369 | − | 0.433052i | \(-0.142563\pi\) | ||||
0.901369 | + | 0.433052i | \(0.142563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0097 | 0.506212 | ||||||||
\(392\) | 3.30194 | − | 5.71912i | 0.166773 | − | 0.288859i | ||||
\(393\) | 0.903657 | − | 1.56518i | 0.0455835 | − | 0.0789529i | ||||
\(394\) | −12.8252 | − | 22.2139i | −0.646124 | − | 1.11912i | ||||
\(395\) | −22.7995 | −1.14717 | ||||||||
\(396\) | 10.4852 | + | 18.1610i | 0.526903 | + | 0.912622i | ||||
\(397\) | 0.675760 | + | 1.17045i | 0.0339154 | + | 0.0587432i | 0.882485 | − | 0.470341i | \(-0.155869\pi\) |
−0.848569 | + | 0.529084i | \(0.822536\pi\) | |||||||
\(398\) | −31.2446 | −1.56615 | ||||||||
\(399\) | −3.32640 | − | 5.76149i | −0.166528 | − | 0.288435i | ||||
\(400\) | −1.16756 | + | 2.02228i | −0.0583781 | + | 0.101114i | ||||
\(401\) | 0.289561 | − | 0.501534i | 0.0144600 | − | 0.0250454i | −0.858705 | − | 0.512470i | \(-0.828730\pi\) |
0.873165 | + | 0.487425i | \(0.162064\pi\) | |||||||
\(402\) | 0.719169 | 0.0358689 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 39.8310 | 1.98167 | ||||||||
\(405\) | −4.56853 | + | 7.91293i | −0.227012 | + | 0.393197i | ||||
\(406\) | 5.22252 | − | 9.04567i | 0.259189 | − | 0.448929i | ||||
\(407\) | 6.84332 | + | 11.8530i | 0.339211 | + | 0.587531i | ||||
\(408\) | 6.92692 | 0.342934 | ||||||||
\(409\) | −7.57875 | − | 13.1268i | −0.374745 | − | 0.649078i | 0.615544 | − | 0.788103i | \(-0.288936\pi\) |
−0.990289 | + | 0.139025i | \(0.955603\pi\) | |||||||
\(410\) | 2.06853 | + | 3.58280i | 0.102157 | + | 0.176942i | ||||
\(411\) | 0.439665 | 0.0216871 | ||||||||
\(412\) | −13.9770 | − | 24.2089i | −0.688599 | − | 1.19269i | ||||
\(413\) | 12.5063 | − | 21.6616i | 0.615397 | − | 1.06590i | ||||
\(414\) | −5.71648 | + | 9.90123i | −0.280950 | + | 0.486619i | ||||
\(415\) | −11.1608 | −0.547860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.29291 | 0.308165 | ||||||||
\(418\) | −16.7947 | + | 29.0893i | −0.821456 | + | 1.42280i | ||||
\(419\) | 17.8617 | − | 30.9374i | 0.872603 | − | 1.51139i | 0.0133088 | − | 0.999911i | \(-0.495764\pi\) |
0.859294 | − | 0.511481i | \(-0.170903\pi\) | |||||||
\(420\) | −2.50484 | − | 4.33852i | −0.122224 | − | 0.211698i | ||||
\(421\) | 35.0465 | 1.70806 | 0.854032 | − | 0.520221i | \(-0.174151\pi\) | ||||
0.854032 | + | 0.520221i | \(0.174151\pi\) | |||||||
\(422\) | 14.8802 | + | 25.7732i | 0.724355 | + | 1.25462i | ||||
\(423\) | 3.97219 | + | 6.88003i | 0.193134 | + | 0.334519i | ||||
\(424\) | 13.0127 | 0.631951 | ||||||||
\(425\) | −7.71044 | − | 13.3549i | −0.374011 | − | 0.647806i | ||||
\(426\) | 2.86443 | − | 4.96134i | 0.138782 | − | 0.240378i | ||||
\(427\) | 8.77413 | − | 15.1972i | 0.424610 | − | 0.735446i | ||||
\(428\) | −21.0368 | −1.01685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.9269 | 0.960961 | ||||||||
\(431\) | −17.1407 | + | 29.6886i | −0.825639 | + | 1.43005i | 0.0757909 | + | 0.997124i | \(0.475852\pi\) |
−0.901430 | + | 0.432925i | \(0.857481\pi\) | |||||||
\(432\) | 1.26659 | − | 2.19381i | 0.0609390 | − | 0.105549i | ||||
\(433\) | −6.86927 | − | 11.8979i | −0.330116 | − | 0.571778i | 0.652418 | − | 0.757859i | \(-0.273755\pi\) |
−0.982534 | + | 0.186081i | \(0.940421\pi\) | |||||||
\(434\) | −19.6528 | −0.943364 | ||||||||
\(435\) | 0.909698 | + | 1.57564i | 0.0436167 | + | 0.0755463i | ||||
\(436\) | 0.185981 | + | 0.322128i | 0.00890686 | + | 0.0154271i | ||||
\(437\) | −11.0586 | −0.529005 | ||||||||
\(438\) | 6.57942 | + | 11.3959i | 0.314377 | + | 0.544516i | ||||
\(439\) | −5.12014 | + | 8.86834i | −0.244371 | + | 0.423263i | −0.961955 | − | 0.273210i | \(-0.911915\pi\) |
0.717584 | + | 0.696472i | \(0.245248\pi\) | |||||||
\(440\) | −4.35086 | + | 7.53590i | −0.207419 | + | 0.359260i | ||||
\(441\) | 7.54288 | 0.359185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1763 | 0.578513 | 0.289257 | − | 0.957252i | \(-0.406592\pi\) | ||||
0.289257 | + | 0.957252i | \(0.406592\pi\) | |||||||
\(444\) | −4.53199 | + | 7.84964i | −0.215079 | + | 0.372527i | ||||
\(445\) | 4.77844 | − | 8.27650i | 0.226520 | − | 0.392344i | ||||
\(446\) | −8.24094 | − | 14.2737i | −0.390220 | − | 0.675880i | ||||
\(447\) | 4.66487 | 0.220641 | ||||||||
\(448\) | −13.3557 | − | 23.1327i | −0.630997 | − | 1.09292i | ||||
\(449\) | −6.45257 | − | 11.1762i | −0.304516 | − | 0.527437i | 0.672638 | − | 0.739972i | \(-0.265161\pi\) |
−0.977153 | + | 0.212535i | \(0.931828\pi\) | |||||||
\(450\) | 17.6136 | 0.830311 | ||||||||
\(451\) | 1.62767 | + | 2.81921i | 0.0766440 | + | 0.132751i | ||||
\(452\) | −11.1407 | + | 19.2963i | −0.524015 | + | 0.907621i | ||||
\(453\) | −3.92058 | + | 6.79065i | −0.184205 | + | 0.319053i | ||||
\(454\) | 19.4916 | 0.914785 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.65279 | −0.358375 | ||||||||
\(457\) | 2.32855 | − | 4.03317i | 0.108925 | − | 0.188664i | −0.806410 | − | 0.591357i | \(-0.798592\pi\) |
0.915335 | + | 0.402693i | \(0.131926\pi\) | |||||||
\(458\) | −15.3768 | + | 26.6334i | −0.718511 | + | 1.24450i | ||||
\(459\) | 8.36443 | + | 14.4876i | 0.390418 | + | 0.676224i | ||||
\(460\) | −8.32736 | −0.388265 | ||||||||
\(461\) | −15.7702 | − | 27.3149i | −0.734493 | − | 1.27218i | −0.954945 | − | 0.296782i | \(-0.904087\pi\) |
0.220452 | − | 0.975398i | \(-0.429247\pi\) | |||||||
\(462\) | −3.26391 | − | 5.65325i | −0.151851 | − | 0.263013i | ||||
\(463\) | −17.6504 | −0.820284 | −0.410142 | − | 0.912022i | \(-0.634521\pi\) | ||||
−0.410142 | + | 0.912022i | \(0.634521\pi\) | |||||||
\(464\) | 0.909698 | + | 1.57564i | 0.0422317 | + | 0.0731474i | ||||
\(465\) | 1.71164 | − | 2.96464i | 0.0793752 | − | 0.137482i | ||||
\(466\) | 5.71648 | − | 9.90123i | 0.264811 | − | 0.458666i | ||||
\(467\) | −32.1726 | −1.48877 | −0.744385 | − | 0.667751i | \(-0.767257\pi\) | ||||
−0.744385 | + | 0.667751i | \(0.767257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.18167 | 0.0545644 | ||||||||
\(470\) | −4.79105 | + | 8.29835i | −0.220995 | + | 0.382774i | ||||
\(471\) | −2.61745 | + | 4.53355i | −0.120606 | + | 0.208895i | ||||
\(472\) | −14.3862 | − | 24.9176i | −0.662178 | − | 1.14693i | ||||
\(473\) | 15.6799 | 0.720964 | ||||||||
\(474\) | −9.83728 | − | 17.0387i | −0.451841 | − | 0.782612i | ||||
\(475\) | 8.51842 | + | 14.7543i | 0.390852 | + | 0.676975i | ||||
\(476\) | 33.0834 | 1.51637 | ||||||||
\(477\) | 7.43147 | + | 12.8717i | 0.340264 | + | 0.589354i | ||||
\(478\) | −12.2729 | + | 21.2573i | −0.561351 | + | 0.972288i | ||||
\(479\) | −17.4499 | + | 30.2241i | −0.797306 | + | 1.38097i | 0.124059 | + | 0.992275i | \(0.460409\pi\) |
−0.921365 | + | 0.388699i | \(0.872925\pi\) | |||||||
\(480\) | 5.22521 | 0.238497 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26.7724 | −1.21945 | ||||||||
\(483\) | 1.07457 | − | 1.86121i | 0.0488947 | − | 0.0846882i | ||||
\(484\) | 6.81767 | − | 11.8085i | 0.309894 | − | 0.536752i | ||||
\(485\) | 8.61745 | + | 14.9259i | 0.391298 | + | 0.677748i | ||||
\(486\) | −29.1782 | −1.32355 | ||||||||
\(487\) | 20.9175 | + | 36.2302i | 0.947864 | + | 1.64175i | 0.749914 | + | 0.661536i | \(0.230095\pi\) |
0.197950 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(488\) | −10.0930 | − | 17.4816i | −0.456888 | − | 0.791354i | ||||
\(489\) | 4.83041 | 0.218439 | ||||||||
\(490\) | 4.54892 | + | 7.87896i | 0.205499 | + | 0.355935i | ||||
\(491\) | −10.9227 | + | 18.9187i | −0.492936 | + | 0.853791i | −0.999967 | − | 0.00813732i | \(-0.997410\pi\) |
0.507031 | + | 0.861928i | \(0.330743\pi\) | |||||||
\(492\) | −1.07792 | + | 1.86702i | −0.0485966 | + | 0.0841718i | ||||
\(493\) | −12.0151 | −0.541131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.93900 | −0.446725 | ||||||||
\(496\) | 1.71164 | − | 2.96464i | 0.0768547 | − | 0.133116i | ||||
\(497\) | 4.70655 | − | 8.15199i | 0.211118 | − | 0.365667i | ||||
\(498\) | −4.81551 | − | 8.34071i | −0.215788 | − | 0.373756i | ||||
\(499\) | −23.5472 | −1.05412 | −0.527058 | − | 0.849829i | \(-0.676705\pi\) | ||||
−0.527058 | + | 0.849829i | \(0.676705\pi\) | |||||||
\(500\) | 17.4291 | + | 30.1880i | 0.779452 | + | 1.35005i | ||||
\(501\) | 6.61894 | + | 11.4643i | 0.295712 | + | 0.512189i | ||||
\(502\) | 50.2150 | 2.24121 | ||||||||
\(503\) | 3.54341 | + | 6.13736i | 0.157993 | + | 0.273652i | 0.934145 | − | 0.356894i | \(-0.116164\pi\) |
−0.776152 | + | 0.630546i | \(0.782831\pi\) | |||||||
\(504\) | −6.50000 | + | 11.2583i | −0.289533 | + | 0.501486i | ||||
\(505\) | −9.43900 | + | 16.3488i | −0.420030 | + | 0.727513i | ||||
\(506\) | −10.8509 | −0.482379 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57.8394 | −2.56621 | ||||||||
\(509\) | 3.80947 | − | 6.59820i | 0.168852 | − | 0.292460i | −0.769165 | − | 0.639051i | \(-0.779327\pi\) |
0.938016 | + | 0.346591i | \(0.112661\pi\) | |||||||
\(510\) | −4.77144 | + | 8.26437i | −0.211283 | + | 0.365953i | ||||
\(511\) | 10.8107 | + | 18.7246i | 0.478236 | + | 0.828329i | ||||
\(512\) | 9.00538 | 0.397985 | ||||||||
\(513\) | −9.24094 | − | 16.0058i | −0.407997 | − | 0.706672i | ||||
\(514\) | 20.9644 | + | 36.3114i | 0.924701 | + | 1.60163i | ||||
\(515\) | 13.2489 | 0.583816 | ||||||||
\(516\) | 5.19202 | + | 8.99284i | 0.228566 | + | 0.395888i | ||||
\(517\) | −3.76995 | + | 6.52974i | −0.165802 | + | 0.287178i | ||||
\(518\) | −12.3312 | + | 21.3583i | −0.541804 | + | 0.938431i | ||||
\(519\) | 10.4638 | 0.459311 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.5133 | −1.73111 | −0.865555 | − | 0.500813i | \(-0.833034\pi\) | ||||
−0.865555 | + | 0.500813i | \(0.833034\pi\) | |||||||
\(522\) | 6.86174 | − | 11.8849i | 0.300330 | − | 0.520187i | ||||
\(523\) | 7.90970 | − | 13.7000i | 0.345867 | − | 0.599059i | −0.639644 | − | 0.768671i | \(-0.720918\pi\) |
0.985511 | + | 0.169612i | \(0.0542515\pi\) | |||||||
\(524\) | −4.96466 | − | 8.59904i | −0.216882 | − | 0.375651i | ||||
\(525\) | −3.31096 | −0.144502 | ||||||||
\(526\) | −16.1773 | − | 28.0198i | −0.705362 | − | 1.22172i | ||||
\(527\) | 11.3034 | + | 19.5781i | 0.492385 | + | 0.852836i | ||||
\(528\) | 1.13706 | 0.0494843 | ||||||||
\(529\) | 9.71379 | + | 16.8248i | 0.422339 | + | 0.731512i | ||||
\(530\) | −8.96346 | + | 15.5252i | −0.389348 | + | 0.674370i | ||||
\(531\) | 16.4318 | − | 28.4606i | 0.713078 | − | 1.23509i | ||||
\(532\) | −36.5502 | −1.58465 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 8.24698 | 0.356882 | ||||||||
\(535\) | 4.98523 | − | 8.63467i | 0.215530 | − | 0.373309i | ||||
\(536\) | 0.679644 | − | 1.17718i | 0.0293562 | − | 0.0508464i | ||||
\(537\) | 1.67092 | + | 2.89411i | 0.0721053 | + | 0.124890i | ||||
\(538\) | 1.46681 | 0.0632388 | ||||||||
\(539\) | 3.57942 | + | 6.19973i | 0.154176 | + | 0.267041i | ||||
\(540\) | −6.95862 | − | 12.0527i | −0.299451 | − | 0.518665i | ||||
\(541\) | −34.4819 | −1.48249 | −0.741246 | − | 0.671234i | \(-0.765765\pi\) | ||||
−0.741246 | + | 0.671234i | \(0.765765\pi\) | |||||||
\(542\) | −2.24214 | − | 3.88349i | −0.0963080 | − | 0.166810i | ||||
\(543\) | −1.32573 | + | 2.29624i | −0.0568926 | + | 0.0985409i | ||||
\(544\) | −17.2533 | + | 29.8836i | −0.739730 | + | 1.28125i | ||||
\(545\) | −0.176292 | −0.00755152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.8582 | 1.57594 | 0.787970 | − | 0.615713i | \(-0.211132\pi\) | ||||
0.787970 | + | 0.615713i | \(0.211132\pi\) | |||||||
\(548\) | 1.20775 | − | 2.09189i | 0.0515926 | − | 0.0893609i | ||||
\(549\) | 11.5281 | − | 19.9673i | 0.492008 | − | 0.852182i | ||||
\(550\) | 8.35839 | + | 14.4772i | 0.356403 | + | 0.617308i | ||||
\(551\) | 13.2741 | 0.565497 | ||||||||
\(552\) | −1.23609 | − | 2.14098i | −0.0526117 | − | 0.0911261i | ||||
\(553\) | −16.1637 | − | 27.9963i | −0.687350 | − | 1.19052i | ||||
\(554\) | 26.4795 | 1.12501 | ||||||||
\(555\) | −2.14795 | − | 3.72036i | −0.0911753 | − | 0.157920i | ||||
\(556\) | 17.2865 | − | 29.9411i | 0.733111 | − | 1.26979i | ||||
\(557\) | 0.638260 | − | 1.10550i | 0.0270439 | − | 0.0468415i | −0.852187 | − | 0.523238i | \(-0.824724\pi\) |
0.879231 | + | 0.476396i | \(0.158057\pi\) | |||||||
\(558\) | −25.8213 | −1.09310 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.37435 | 0.100335 | ||||||||
\(561\) | −3.75451 | + | 6.50301i | −0.158516 | + | 0.274557i | ||||
\(562\) | −7.27144 | + | 12.5945i | −0.306727 | + | 0.531267i | ||||
\(563\) | 4.56369 | + | 7.90454i | 0.192336 | + | 0.333137i | 0.946024 | − | 0.324096i | \(-0.105060\pi\) |
−0.753688 | + | 0.657233i | \(0.771727\pi\) | |||||||
\(564\) | −4.99330 | −0.210256 | ||||||||
\(565\) | −5.28017 | − | 9.14552i | −0.222138 | − | 0.384755i | ||||
\(566\) | −7.39373 | − | 12.8063i | −0.310782 | − | 0.538290i | ||||
\(567\) | −12.9554 | −0.544075 | ||||||||
\(568\) | −5.41401 | − | 9.37734i | −0.227167 | − | 0.393464i | ||||
\(569\) | 2.86078 | − | 4.95502i | 0.119930 | − | 0.207725i | −0.799810 | − | 0.600254i | \(-0.795066\pi\) |
0.919740 | + | 0.392529i | \(0.128400\pi\) | |||||||
\(570\) | 5.27144 | − | 9.13040i | 0.220796 | − | 0.382430i | ||||
\(571\) | 7.60148 | 0.318112 | 0.159056 | − | 0.987270i | \(-0.449155\pi\) | ||||
0.159056 | + | 0.987270i | \(0.449155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.2282 | −0.427289 | ||||||||
\(574\) | −2.93296 | + | 5.08004i | −0.122419 | + | 0.212037i | ||||
\(575\) | −2.75182 | + | 4.76630i | −0.114759 | + | 0.198768i | ||||
\(576\) | −17.5477 | − | 30.3935i | −0.731155 | − | 1.26640i | ||||
\(577\) | −45.1564 | −1.87989 | −0.939944 | − | 0.341330i | \(-0.889123\pi\) | ||||
−0.939944 | + | 0.341330i | \(0.889123\pi\) | |||||||
\(578\) | −12.4107 | − | 21.4959i | −0.516215 | − | 0.894111i | ||||
\(579\) | −1.67994 | − | 2.90974i | −0.0698159 | − | 0.120925i | ||||
\(580\) | 9.99569 | 0.415048 | ||||||||
\(581\) | −7.91239 | − | 13.7047i | −0.328261 | − | 0.568565i | ||||
\(582\) | −7.43631 | + | 12.8801i | −0.308245 | + | 0.533896i | ||||
\(583\) | −7.05310 | + | 12.2163i | −0.292109 | + | 0.505948i | ||||
\(584\) | 24.8713 | 1.02918 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 54.6872 | 2.25911 | ||||||||
\(587\) | −16.2020 | + | 28.0627i | −0.668728 | + | 1.15827i | 0.309532 | + | 0.950889i | \(0.399828\pi\) |
−0.978260 | + | 0.207382i | \(0.933506\pi\) | |||||||
\(588\) | −2.37047 | + | 4.10577i | −0.0977565 | + | 0.169319i | ||||
\(589\) | −12.4879 | − | 21.6297i | −0.514556 | − | 0.891237i | ||||
\(590\) | 39.6383 | 1.63188 | ||||||||
\(591\) | 3.16756 | + | 5.48638i | 0.130296 | + | 0.225680i | ||||
\(592\) | −2.14795 | − | 3.72036i | −0.0882801 | − | 0.152906i | ||||
\(593\) | −36.6848 | −1.50647 | −0.753233 | − | 0.657754i | \(-0.771507\pi\) | ||||
−0.753233 | + | 0.657754i | \(0.771507\pi\) | |||||||
\(594\) | −9.06734 | − | 15.7051i | −0.372037 | − | 0.644387i | ||||
\(595\) | −7.83997 | + | 13.5792i | −0.321407 | + | 0.556694i | ||||
\(596\) | 12.8143 | − | 22.1950i | 0.524895 | − | 0.909144i | ||||
\(597\) | 7.71678 | 0.315827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.99223 | −0.408271 | −0.204136 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204136 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(600\) | −1.90432 | + | 3.29838i | −0.0777436 | + | 0.134656i | ||||
\(601\) | 0.905813 | − | 1.56891i | 0.0369489 | − | 0.0639974i | −0.846960 | − | 0.531657i | \(-0.821569\pi\) |
0.883908 | + | 0.467660i | \(0.154903\pi\) | |||||||
\(602\) | 14.1271 | + | 24.4689i | 0.575779 | + | 0.997279i | ||||
\(603\) | 1.55257 | 0.0632253 | ||||||||
\(604\) | 21.5395 | + | 37.3076i | 0.876431 | + | 1.51802i | ||||
\(605\) | 3.23125 | + | 5.59669i | 0.131369 | + | 0.227538i | ||||
\(606\) | −16.2905 | −0.661757 | ||||||||
\(607\) | −5.60806 | − | 9.71344i | −0.227624 | − | 0.394256i | 0.729479 | − | 0.684003i | \(-0.239762\pi\) |
−0.957103 | + | 0.289746i | \(0.906429\pi\) | |||||||
\(608\) | 19.0613 | − | 33.0151i | 0.773038 | − | 1.33894i | ||||
\(609\) | −1.28986 | + | 2.23410i | −0.0522676 | + | 0.0905302i | ||||
\(610\) | 27.8092 | 1.12596 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 43.4674 | 1.75707 | ||||||||
\(613\) | −10.4472 | + | 18.0951i | −0.421958 | + | 0.730853i | −0.996131 | − | 0.0878810i | \(-0.971990\pi\) |
0.574173 | + | 0.818734i | \(0.305324\pi\) | |||||||
\(614\) | −15.8116 | + | 27.3865i | −0.638105 | + | 1.10523i | ||||
\(615\) | −0.510885 | − | 0.884879i | −0.0206009 | − | 0.0356818i | ||||
\(616\) | −12.3381 | −0.497117 | ||||||||
\(617\) | 6.04958 | + | 10.4782i | 0.243547 | + | 0.421836i | 0.961722 | − | 0.274027i | \(-0.0883557\pi\) |
−0.718175 | + | 0.695862i | \(0.755022\pi\) | |||||||
\(618\) | 5.71648 | + | 9.90123i | 0.229951 | + | 0.398286i | ||||
\(619\) | 10.5526 | 0.424143 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(620\) | −9.40366 | − | 16.2876i | −0.377660 | − | 0.654126i | ||||
\(621\) | 2.98523 | − | 5.17057i | 0.119793 | − | 0.207488i | ||||
\(622\) | 33.4463 | − | 57.9307i | 1.34107 | − | 2.32281i | ||||
\(623\) | 13.5506 | 0.542895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96184 | −0.0784735 | ||||||||
\(626\) | 8.40246 | − | 14.5535i | 0.335830 | − | 0.581674i | ||||
\(627\) | 4.14795 | − | 7.18446i | 0.165653 | − | 0.286920i | ||||
\(628\) | 14.3802 | + | 24.9072i | 0.573831 | + | 0.993904i | ||||
\(629\) | 28.3696 | 1.13117 | ||||||||
\(630\) | −8.95473 | − | 15.5100i | −0.356765 | − | 0.617935i | ||||
\(631\) | −6.92572 | − | 11.9957i | −0.275709 | − | 0.477541i | 0.694605 | − | 0.719391i | \(-0.255579\pi\) |
−0.970314 | + | 0.241850i | \(0.922246\pi\) | |||||||
\(632\) | −37.1866 | −1.47920 | ||||||||
\(633\) | −3.67510 | − | 6.36545i | −0.146072 | − | 0.253004i | ||||
\(634\) | 33.7385 | − | 58.4369i | 1.33993 | − | 2.32082i | ||||
\(635\) | 13.7066 | − | 23.7404i | 0.543928 | − | 0.942111i | ||||
\(636\) | −9.34183 | −0.370428 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.0248 | 0.515655 | ||||||||
\(639\) | 6.18382 | − | 10.7107i | 0.244628 | − | 0.423709i | ||||
\(640\) | 11.7497 | − | 20.3510i | 0.464446 | − | 0.804445i | ||||
\(641\) | −17.4804 | − | 30.2769i | −0.690434 | − | 1.19587i | −0.971696 | − | 0.236235i | \(-0.924086\pi\) |
0.281262 | − | 0.959631i | \(-0.409247\pi\) | |||||||
\(642\) | 8.60388 | 0.339568 | ||||||||
\(643\) | 16.6990 | + | 28.9236i | 0.658545 | + | 1.14063i | 0.980992 | + | 0.194046i | \(0.0621612\pi\) |
−0.322447 | + | 0.946587i | \(0.604505\pi\) | |||||||
\(644\) | −5.90366 | − | 10.2254i | −0.232637 | − | 0.402939i | ||||
\(645\) | −4.92154 | −0.193786 | ||||||||
\(646\) | 34.8119 | + | 60.2960i | 1.36966 | + | 2.37232i | ||||
\(647\) | −1.16421 | + | 2.01647i | −0.0457698 | + | 0.0792757i | −0.888003 | − | 0.459838i | \(-0.847907\pi\) |
0.842233 | + | 0.539114i | \(0.181241\pi\) | |||||||
\(648\) | −7.45138 | + | 12.9062i | −0.292718 | + | 0.507002i | ||||
\(649\) | 31.1903 | 1.22433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85384 | 0.190237 | ||||||||
\(652\) | 13.2690 | − | 22.9827i | 0.519656 | − | 0.900070i | ||||
\(653\) | −7.28568 | + | 12.6192i | −0.285111 | + | 0.493826i | −0.972636 | − | 0.232334i | \(-0.925364\pi\) |
0.687525 | + | 0.726160i | \(0.258697\pi\) | |||||||
\(654\) | −0.0760644 | − | 0.131747i | −0.00297435 | − | 0.00515173i | ||||
\(655\) | 4.70602 | 0.183879 | ||||||||
\(656\) | −0.510885 | − | 0.884879i | −0.0199467 | − | 0.0345487i | ||||
\(657\) | 14.2039 | + | 24.6018i | 0.554146 | + | 0.959808i | ||||
\(658\) | −13.5864 | −0.529654 | ||||||||
\(659\) | −5.56973 | − | 9.64705i | −0.216966 | − | 0.375796i | 0.736913 | − | 0.675988i | \(-0.236283\pi\) |
−0.953879 | + | 0.300192i | \(0.902949\pi\) | |||||||
\(660\) | 3.12349 | − | 5.41004i | 0.121582 | − | 0.210586i | ||||
\(661\) | −6.92490 | + | 11.9943i | −0.269347 | + | 0.466523i | −0.968693 | − | 0.248260i | \(-0.920141\pi\) |
0.699346 | + | 0.714783i | \(0.253475\pi\) | |||||||
\(662\) | 35.3153 | 1.37257 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.2034 | −0.706430 | ||||||||
\(665\) | 8.66152 | − | 15.0022i | 0.335879 | − | 0.581760i | ||||
\(666\) | −16.2017 | + | 28.0622i | −0.627804 | + | 1.08739i | ||||
\(667\) | 2.14406 | + | 3.71363i | 0.0830185 | + | 0.143792i | ||||
\(668\) | 72.7284 | 2.81395 | ||||||||
\(669\) | 2.03534 | + | 3.52532i | 0.0786909 | + | 0.136297i | ||||
\(670\) | 0.936313 | + | 1.62174i | 0.0361729 | + | 0.0626533i | ||||
\(671\) | 21.8823 | 0.844757 | ||||||||
\(672\) | 3.70440 | + | 6.41621i | 0.142900 | + | 0.247511i | ||||
\(673\) | 3.26487 | − | 5.65491i | 0.125851 | − | 0.217981i | −0.796214 | − | 0.605015i | \(-0.793167\pi\) |
0.922065 | + | 0.387034i | \(0.126500\pi\) | |||||||
\(674\) | −2.19537 | + | 3.80250i | −0.0845626 | + | 0.146467i | ||||
\(675\) | −9.19806 | −0.354034 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.3104 | −0.434693 | −0.217346 | − | 0.976095i | \(-0.569740\pi\) | ||||
−0.217346 | + | 0.976095i | \(0.569740\pi\) | |||||||
\(678\) | 4.55645 | − | 7.89200i | 0.174989 | − | 0.303091i | ||||
\(679\) | −12.2186 | + | 21.1633i | −0.468908 | + | 0.812173i | ||||
\(680\) | 9.01842 | + | 15.6204i | 0.345841 | + | 0.599013i | ||||
\(681\) | −4.81402 | −0.184474 | ||||||||
\(682\) | −12.2533 | − | 21.2234i | −0.469204 | − | 0.812685i | ||||
\(683\) | 7.08964 | + | 12.2796i | 0.271277 | + | 0.469866i | 0.969189 | − | 0.246317i | \(-0.0792206\pi\) |
−0.697912 | + | 0.716184i | \(0.745887\pi\) | |||||||
\(684\) | −48.0224 | −1.83618 | ||||||||
\(685\) | 0.572417 | + | 0.991455i | 0.0218709 | + | 0.0378815i | ||||
\(686\) | −22.5635 | + | 39.0810i | −0.861477 | + | 1.49212i | ||||
\(687\) | 3.79776 | − | 6.57791i | 0.144893 | − | 0.250963i | ||||
\(688\) | −4.92154 | −0.187632 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.40581 | 0.129657 | ||||||||
\(691\) | 15.3976 | − | 26.6695i | 0.585753 | − | 1.01455i | −0.409028 | − | 0.912522i | \(-0.634132\pi\) |
0.994781 | − | 0.102032i | \(-0.0325344\pi\) | |||||||
\(692\) | 28.7439 | − | 49.7859i | 1.09268 | − | 1.89258i | ||||
\(693\) | −7.04623 | − | 12.2044i | −0.267664 | − | 0.463608i | ||||
\(694\) | −38.4795 | −1.46066 | ||||||||
\(695\) | 8.19298 | + | 14.1907i | 0.310777 | + | 0.538282i | ||||
\(696\) | 1.48374 | + | 2.56991i | 0.0562409 | + | 0.0974122i | ||||
\(697\) | 6.74764 | 0.255585 | ||||||||
\(698\) | −11.7594 | − | 20.3678i | −0.445098 | − | 0.770933i | ||||
\(699\) | −1.41185 | + | 2.44540i | −0.0534012 | + | 0.0924936i | ||||
\(700\) | −9.09515 | + | 15.7533i | −0.343764 | + | 0.595417i | ||||
\(701\) | 6.73184 | 0.254258 | 0.127129 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127129 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.3424 | −1.18210 | ||||||||
\(704\) | 16.6543 | − | 28.8461i | 0.627682 | − | 1.08718i | ||||
\(705\) | 1.18329 | − | 2.04952i | 0.0445654 | − | 0.0771895i | ||||
\(706\) | 17.4487 | + | 30.2220i | 0.656690 | + | 1.13742i | ||||
\(707\) | −26.7670 | −1.00668 | ||||||||
\(708\) | 10.3279 | + | 17.8884i | 0.388146 | + | 0.672288i | ||||
\(709\) | −23.8126 | − | 41.2446i | −0.894300 | − | 1.54897i | −0.834668 | − | 0.550753i | \(-0.814340\pi\) |
−0.0596324 | − | 0.998220i | \(-0.518993\pi\) | |||||||
\(710\) | 14.9172 | 0.559834 | ||||||||
\(711\) | −21.2371 | − | 36.7837i | −0.796452 | − | 1.37949i | ||||
\(712\) | 7.79374 | − | 13.4992i | 0.292083 | − | 0.505902i | ||||
\(713\) | 4.03415 | − | 6.98735i | 0.151080 | − | 0.261678i | ||||
\(714\) | −13.5308 | −0.506377 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.3599 | 0.686141 | ||||||||
\(717\) | 3.03116 | − | 5.25013i | 0.113201 | − | 0.196070i | ||||
\(718\) | −24.0722 | + | 41.6942i | −0.898366 | + | 1.55602i | ||||
\(719\) | 2.99665 | + | 5.19035i | 0.111756 | + | 0.193567i | 0.916478 | − | 0.400084i | \(-0.131019\pi\) |
−0.804722 | + | 0.593651i | \(0.797686\pi\) | |||||||
\(720\) | 3.11960 | 0.116261 | ||||||||
\(721\) | 9.39277 | + | 16.2688i | 0.349805 | + | 0.605880i | ||||
\(722\) | −17.1136 | − | 29.6416i | −0.636901 | − | 1.10314i | ||||
\(723\) | 6.61224 | 0.245912 | ||||||||
\(724\) | 7.28352 | + | 12.6154i | 0.270690 | + | 0.468849i | ||||
\(725\) | 3.30313 | − | 5.72120i | 0.122675 | − | 0.212480i | ||||
\(726\) | −2.78836 | + | 4.82959i | −0.103486 | + | 0.179243i | ||||
\(727\) | −24.1226 | −0.894657 | −0.447329 | − | 0.894370i | \(-0.647625\pi\) | ||||
−0.447329 | + | 0.894370i | \(0.647625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7627 | −0.435656 | ||||||||
\(730\) | −17.1320 | + | 29.6735i | −0.634083 | + | 1.09826i | ||||
\(731\) | 16.2506 | − | 28.1469i | 0.601051 | − | 1.04105i | ||||
\(732\) | 7.24578 | + | 12.5501i | 0.267812 | + | 0.463864i | ||||
\(733\) | −36.0646 | −1.33208 | −0.666038 | − | 0.745918i | \(-0.732011\pi\) | ||||
−0.666038 | + | 0.745918i | \(0.732011\pi\) | |||||||
\(734\) | −38.5393 | − | 66.7520i | −1.42251 | − | 2.46386i | ||||
\(735\) | −1.12349 | − | 1.94594i | −0.0414405 | − | 0.0717771i | ||||
\(736\) | 12.3153 | 0.453947 | ||||||||
\(737\) | 0.736758 | + | 1.27610i | 0.0271388 | + | 0.0470059i | ||||
\(738\) | −3.85354 | + | 6.67453i | −0.141851 | + | 0.245693i | ||||
\(739\) | 13.7627 | − | 23.8377i | 0.506269 | − | 0.876884i | −0.493704 | − | 0.869630i | \(-0.664357\pi\) |
0.999974 | − | 0.00725452i | \(-0.00230920\pi\) | |||||||
\(740\) | −23.6015 | −0.867608 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.4185 | −0.933142 | ||||||||
\(743\) | −5.23460 | + | 9.06660i | −0.192039 | + | 0.332621i | −0.945926 | − | 0.324383i | \(-0.894843\pi\) |
0.753887 | + | 0.657004i | \(0.228177\pi\) | |||||||
\(744\) | 2.79172 | − | 4.83539i | 0.102349 | − | 0.177274i | ||||
\(745\) | 6.07338 | + | 10.5194i | 0.222511 | + | 0.385401i | ||||
\(746\) | −28.3032 | −1.03625 | ||||||||
\(747\) | −10.3959 | − | 18.0062i | −0.380366 | − | 0.658813i | ||||
\(748\) | 20.6271 | + | 35.7273i | 0.754203 | + | 1.30632i | ||||
\(749\) | 14.1371 | 0.516557 | ||||||||
\(750\) | −7.12833 | − | 12.3466i | −0.260290 | − | 0.450835i | ||||
\(751\) | −2.03385 | + | 3.52273i | −0.0742163 | + | 0.128546i | −0.900745 | − | 0.434348i | \(-0.856979\pi\) |
0.826529 | + | 0.562894i | \(0.190312\pi\) | |||||||
\(752\) | 1.18329 | − | 2.04952i | 0.0431502 | − | 0.0747384i | ||||
\(753\) | −12.4021 | −0.451957 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.4174 | −0.743066 | ||||||||
\(756\) | 9.86658 | − | 17.0894i | 0.358844 | − | 0.621536i | ||||
\(757\) | −10.2168 | + | 17.6960i | −0.371335 | + | 0.643171i | −0.989771 | − | 0.142664i | \(-0.954433\pi\) |
0.618436 | + | 0.785835i | \(0.287767\pi\) | |||||||
\(758\) | 18.5809 | + | 32.1831i | 0.674889 | + | 1.16894i | ||||
\(759\) | 2.67994 | 0.0972757 | ||||||||
\(760\) | −9.96346 | − | 17.2572i | −0.361413 | − | 0.625985i | ||||
\(761\) | −13.5118 | − | 23.4032i | −0.489804 | − | 0.848365i | 0.510127 | − | 0.860099i | \(-0.329598\pi\) |
−0.999931 | + | 0.0117336i | \(0.996265\pi\) | |||||||
\(762\) | 23.6558 | 0.856958 | ||||||||
\(763\) | −0.124982 | − | 0.216475i | −0.00452464 | − | 0.00783691i | ||||
\(764\) | −28.0966 | + | 48.6648i | −1.01650 | + | 1.76063i | ||||
\(765\) | −10.3007 | + | 17.8414i | −0.372424 | + | 0.645057i | ||||
\(766\) | −16.9336 | −0.611837 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.80864 | 0.209601 | ||||||||
\(769\) | −18.9703 | + | 32.8576i | −0.684088 | + | 1.18487i | 0.289635 | + | 0.957137i | \(0.406466\pi\) |
−0.973723 | + | 0.227737i | \(0.926867\pi\) | |||||||
\(770\) | 8.49880 | − | 14.7204i | 0.306276 | − | 0.530485i | ||||
\(771\) | −5.17778 | − | 8.96818i | −0.186473 | − | 0.322981i | ||||
\(772\) | −18.4590 | −0.664355 | ||||||||
\(773\) | −8.16876 | − | 14.1487i | −0.293810 | − | 0.508894i | 0.680897 | − | 0.732379i | \(-0.261590\pi\) |
−0.974707 | + | 0.223485i | \(0.928257\pi\) | |||||||
\(774\) | 18.5613 | + | 32.1491i | 0.667172 | + | 1.15558i | ||||
\(775\) | −12.4300 | −0.446498 | ||||||||
\(776\) | 14.0553 | + | 24.3444i | 0.504554 | + | 0.873914i | ||||
\(777\) | 3.04556 | − | 5.27507i | 0.109259 | − | 0.189242i | ||||
\(778\) | −39.9463 | + | 69.1890i | −1.43214 | + | 2.48055i | ||||
\(779\) | −7.45473 | −0.267093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7380 | 0.420017 | ||||||||
\(782\) | −11.2458 | + | 19.4783i | −0.402148 | + | 0.696541i | ||||
\(783\) | −3.58330 | + | 6.20646i | −0.128057 | + | 0.221801i | ||||
\(784\) | −1.12349 | − | 1.94594i | −0.0401246 | − | 0.0694979i | ||||
\(785\) | −13.6310 | −0.486512 | ||||||||
\(786\) | 2.03050 | + | 3.51693i | 0.0724255 | + | 0.125445i | ||||
\(787\) | −9.34535 | − | 16.1866i | −0.333126 | − | 0.576991i | 0.649997 | − | 0.759936i | \(-0.274770\pi\) |
−0.983123 | + | 0.182946i | \(0.941437\pi\) | |||||||
\(788\) | 34.8049 | 1.23987 | ||||||||
\(789\) | 3.99545 | + | 6.92032i | 0.142242 | + | 0.246370i | ||||
\(790\) | 25.6151 | − | 44.3666i | 0.911343 | − | 1.57849i | ||||
\(791\) | 7.48672 | − | 12.9674i | 0.266197 | − | 0.461067i | ||||
\(792\) | −16.2107 | −0.576023 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.03684 | −0.107773 | ||||||||
\(795\) | 2.21379 | − | 3.83440i | 0.0785151 | − | 0.135992i | ||||
\(796\) | 21.1978 | − | 36.7157i | 0.751337 | − | 1.30135i | ||||
\(797\) | −14.6259 | − | 25.3329i | −0.518077 | − | 0.897336i | −0.999779 | − | 0.0210013i | \(-0.993315\pi\) |
0.481702 | − | 0.876335i | \(-0.340019\pi\) | |||||||
\(798\) | 14.9487 | 0.529178 | ||||||||
\(799\) | 7.81431 | + | 13.5348i | 0.276451 | + | 0.478826i | ||||
\(800\) | −9.48643 | − | 16.4310i | −0.335396 | − | 0.580923i | ||||
\(801\) | 17.8039 | 0.629068 | ||||||||
\(802\) | 0.650637 | + | 1.12694i | 0.0229748 | + | 0.0397935i | ||||
\(803\) | −13.4807 | + | 23.3492i | −0.475723 | + | 0.823976i | ||||
\(804\) | −0.487918 | + | 0.845099i | −0.0172076 | + | 0.0298044i | ||||
\(805\) | 5.59611 | 0.197237 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.362273 | −0.0127526 | ||||||||
\(808\) | −15.3952 | + | 26.6653i | −0.541602 | + | 0.938082i | ||||
\(809\) | 3.32544 | − | 5.75983i | 0.116916 | − | 0.202505i | −0.801628 | − | 0.597823i | \(-0.796032\pi\) |
0.918544 | + | 0.395319i | \(0.129366\pi\) | |||||||
\(810\) | −10.2654 | − | 17.7802i | −0.360689 | − | 0.624732i | ||||
\(811\) | −3.89200 | −0.136667 | −0.0683333 | − | 0.997663i | \(-0.521768\pi\) | ||||
−0.0683333 | + | 0.997663i | \(0.521768\pi\) | |||||||
\(812\) | 7.08642 | + | 12.2740i | 0.248684 | + | 0.430734i | ||||
\(813\) | 0.553762 | + | 0.959143i | 0.0194213 | + | 0.0336386i | ||||
\(814\) | −30.7536 | −1.07791 | ||||||||
\(815\) | 6.28890 | + | 10.8927i | 0.220290 | + | 0.381554i | ||||
\(816\) | 1.17845 | − | 2.04113i | 0.0412539 | − | 0.0714539i | ||||
\(817\) | −17.9535 | + | 31.0964i | −0.628115 | + | 1.08793i | ||||
\(818\) | 34.0586 | 1.19083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.61356 | −0.196034 | ||||||||
\(821\) | 22.9991 | − | 39.8356i | 0.802674 | − | 1.39027i | −0.115176 | − | 0.993345i | \(-0.536743\pi\) |
0.917850 | − | 0.396927i | \(-0.129923\pi\) | |||||||
\(822\) | −0.493959 | + | 0.855562i | −0.0172288 | + | 0.0298412i | ||||
\(823\) | −3.97650 | − | 6.88750i | −0.138612 | − | 0.240083i | 0.788359 | − | 0.615215i | \(-0.210931\pi\) |
−0.926971 | + | 0.375132i | \(0.877597\pi\) | |||||||
\(824\) | 21.6093 | 0.752794 | ||||||||
\(825\) | −2.06435 | − | 3.57556i | −0.0718715 | − | 0.124485i | ||||
\(826\) | 28.1015 | + | 48.6732i | 0.977776 | + | 1.69356i | ||||
\(827\) | −27.9648 | −0.972432 | −0.486216 | − | 0.873839i | \(-0.661623\pi\) | ||||
−0.486216 | + | 0.873839i | \(0.661623\pi\) | |||||||
\(828\) | −7.75667 | − | 13.4349i | −0.269563 | − | 0.466897i | ||||
\(829\) | −13.8155 | + | 23.9292i | −0.479833 | + | 0.831094i | −0.999732 | − | 0.0231329i | \(-0.992636\pi\) |
0.519900 | + | 0.854227i | \(0.325969\pi\) | |||||||
\(830\) | 12.5390 | − | 21.7182i | 0.435235 | − | 0.753849i | ||||
\(831\) | −6.53989 | −0.226866 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8388 | 0.514133 | ||||||||
\(834\) | −7.07002 | + | 12.2456i | −0.244815 | + | 0.424032i | ||||
\(835\) | −17.2349 | + | 29.8517i | −0.596438 | + | 1.03306i | ||||
\(836\) | −22.7887 | − | 39.4711i | −0.788162 | − | 1.36514i | ||||
\(837\) | 13.4843 | 0.466085 | ||||||||
\(838\) | 40.1350 | + | 69.5158i | 1.38644 | + | 2.40138i | ||||
\(839\) | 14.3424 | + | 24.8418i | 0.495155 | + | 0.857634i | 0.999984 | − | 0.00558509i | \(-0.00177780\pi\) |
−0.504829 | + | 0.863219i | \(0.668444\pi\) | |||||||
\(840\) | 3.87263 | 0.133618 | ||||||||
\(841\) | 11.9264 | + | 20.6571i | 0.411255 | + | 0.712314i | ||||
\(842\) | −39.3744 | + | 68.1985i | −1.35693 | + | 2.35027i | ||||
\(843\) | 1.79590 | − | 3.11058i | 0.0618540 | − | 0.107134i | ||||
\(844\) | −40.3817 | −1.38999 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.8509 | −0.613725 | ||||||||
\(847\) | −4.58157 | + | 7.93552i | −0.157425 | + | 0.272668i | ||||
\(848\) | 2.21379 | − | 3.83440i | 0.0760219 | − | 0.131674i | ||||
\(849\) | 1.82610 | + | 3.16290i | 0.0626716 | + | 0.108550i | ||||
\(850\) | 34.6504 | 1.18850 | ||||||||
\(851\) | −5.06249 | − | 8.76849i | −0.173540 | − | 0.300580i | ||||
\(852\) | 3.88673 | + | 6.73202i | 0.133157 | + | 0.230635i | ||||
\(853\) | 43.2078 | 1.47941 | 0.739703 | − | 0.672934i | \(-0.234966\pi\) | ||||
0.739703 | + | 0.672934i | \(0.234966\pi\) | |||||||
\(854\) | 19.7153 | + | 34.1479i | 0.674643 | + | 1.16852i | ||||
\(855\) | 11.3802 | − | 19.7110i | 0.389193 | − | 0.674102i | ||||
\(856\) | 8.13102 | − | 14.0833i | 0.277913 | − | 0.481359i | ||||
\(857\) | 35.1685 | 1.20133 | 0.600667 | − | 0.799499i | \(-0.294902\pi\) | ||||
0.600667 | + | 0.799499i | \(0.294902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3793 | 0.934168 | 0.467084 | − | 0.884213i | \(-0.345305\pi\) | ||||
0.467084 | + | 0.884213i | \(0.345305\pi\) | |||||||
\(860\) | −13.5194 | + | 23.4162i | −0.461007 | + | 0.798487i | ||||
\(861\) | 0.724381 | − | 1.25467i | 0.0246869 | − | 0.0427589i | ||||
\(862\) | −38.5148 | − | 66.7096i | −1.31182 | − | 2.27214i | ||||
\(863\) | 41.3913 | 1.40898 | 0.704489 | − | 0.709715i | \(-0.251176\pi\) | ||||
0.704489 | + | 0.709715i | \(0.251176\pi\) | |||||||
\(864\) | 10.2911 | + | 17.8246i | 0.350109 | + | 0.606406i | ||||
\(865\) | 13.6233 | + | 23.5962i | 0.463204 | + | 0.802294i | ||||
\(866\) | 30.8702 | 1.04901 | ||||||||
\(867\) | 3.06518 | + | 5.30905i | 0.104099 | + | 0.180305i | ||||
\(868\) | 13.3334 | − | 23.0941i | 0.452565 | − | 0.783866i | ||||
\(869\) | 20.1558 | − | 34.9108i | 0.683738 | − | 1.18427i | ||||
\(870\) | −4.08815 | −0.138601 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.287536 | −0.00973721 | ||||||||
\(873\) | −16.0538 | + | 27.8059i | −0.543338 | + | 0.941088i | ||||
\(874\) | 12.4242 | − | 21.5194i | 0.420256 | − | 0.727905i | ||||
\(875\) | −11.7126 | − | 20.2868i | −0.395958 | − | 0.685819i | ||||
\(876\) | −17.8552 | −0.603270 | ||||||||
\(877\) | −12.3736 | − | 21.4317i | −0.417826 | − | 0.723696i | 0.577894 | − | 0.816112i | \(-0.303875\pi\) |
−0.995721 | + | 0.0924153i | \(0.970541\pi\) | |||||||
\(878\) | −11.5048 | − | 19.9270i | −0.388270 | − | 0.672503i | ||||
\(879\) | −13.5066 | −0.455567 | ||||||||
\(880\) | 1.48039 | + | 2.56410i | 0.0499038 | + | 0.0864359i | ||||
\(881\) | 14.2937 | − | 24.7575i | 0.481568 | − | 0.834101i | −0.518208 | − | 0.855255i | \(-0.673401\pi\) |
0.999776 | + | 0.0211538i | \(0.00673397\pi\) | |||||||
\(882\) | −8.47434 | + | 14.6780i | −0.285346 | + | 0.494234i | ||||
\(883\) | 9.61702 | 0.323639 | 0.161819 | − | 0.986820i | \(-0.448264\pi\) | ||||
0.161819 | + | 0.986820i | \(0.448264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.78986 | −0.329082 | ||||||||
\(886\) | −13.6799 | + | 23.6944i | −0.459587 | + | 0.796027i | ||||
\(887\) | −7.98307 | + | 13.8271i | −0.268045 | + | 0.464268i | −0.968357 | − | 0.249569i | \(-0.919711\pi\) |
0.700312 | + | 0.713837i | \(0.253044\pi\) | |||||||
\(888\) | −3.50335 | − | 6.06798i | −0.117565 | − | 0.203628i | ||||
\(889\) | 38.8689 | 1.30362 | ||||||||
\(890\) | 10.7371 | + | 18.5971i | 0.359907 | + | 0.623377i | ||||
\(891\) | −8.07756 | − | 13.9907i | −0.270608 | − | 0.468707i | ||||
\(892\) | 22.3642 | 0.748809 | ||||||||
\(893\) | −8.63318 | − | 14.9531i | −0.288898 | − | 0.500387i | ||||
\(894\) | −5.24094 | + | 9.07757i | −0.175283 | + | 0.303599i | ||||
\(895\) | −4.35086 | + | 7.53590i | −0.145433 | + | 0.251897i | ||||
\(896\) | 33.3196 | 1.11313 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.9976 | 0.967663 | ||||||||
\(899\) | −4.84236 | + | 8.38722i | −0.161502 | + | 0.279729i | ||||
\(900\) | −11.9499 | + | 20.6978i | −0.398330 | + | 0.689927i | ||||
\(901\) | 14.6196 | + | 25.3219i | 0.487050 | + | 0.843595i | ||||
\(902\) | −7.31468 | −0.243552 | ||||||||
\(903\) | −3.48911 | − | 6.04332i | −0.116110 | − | 0.201109i | ||||
\(904\) | −8.61207 | − | 14.9165i | −0.286433 | − | 0.496117i | ||||
\(905\) | −6.90408 | −0.229500 | ||||||||
\(906\) | −8.80947 | − | 15.2585i | −0.292675 | − | 0.506928i | ||||
\(907\) | 14.4182 | − | 24.9730i | 0.478748 | − | 0.829216i | −0.520955 | − | 0.853584i | \(-0.674424\pi\) |
0.999703 | + | 0.0243681i | \(0.00775737\pi\) | |||||||
\(908\) | −13.2240 | + | 22.9047i | −0.438854 | + | 0.760118i | ||||
\(909\) | −35.1685 | −1.16647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5633 | 1.27766 | 0.638830 | − | 0.769348i | \(-0.279419\pi\) | ||||
0.638830 | + | 0.769348i | \(0.279419\pi\) | |||||||
\(912\) | −1.30194 | + | 2.25502i | −0.0431115 | + | 0.0746713i | ||||
\(913\) | 9.86658 | − | 17.0894i | 0.326536 | − | 0.565577i | ||||
\(914\) | 5.23221 | + | 9.06245i | 0.173066 | + | 0.299759i | ||||
\(915\) | −6.86831 | −0.227059 | ||||||||
\(916\) | −20.8647 | − | 36.1388i | −0.689390 | − | 1.19406i | ||||
\(917\) | 3.33632 | + | 5.77868i | 0.110175 | + | 0.190829i | ||||
\(918\) | −37.5894 | −1.24064 | ||||||||
\(919\) | −4.43751 | − | 7.68599i | −0.146380 | − | 0.253537i | 0.783507 | − | 0.621383i | \(-0.213429\pi\) |
−0.929887 | + | 0.367845i | \(0.880096\pi\) | |||||||
\(920\) | 3.21864 | − | 5.57484i | 0.106115 | − | 0.183797i | ||||
\(921\) | 3.90515 | − | 6.76392i | 0.128679 | − | 0.222879i | ||||
\(922\) | 70.8708 | 2.33401 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 8.85756 | 0.291392 | ||||||||
\(925\) | −7.79925 | + | 13.5087i | −0.256438 | + | 0.444163i | ||||
\(926\) | 19.8300 | − | 34.3466i | 0.651656 | − | 1.12870i | ||||
\(927\) | 12.3409 | + | 21.3751i | 0.405329 | + | 0.702051i | ||||
\(928\) | −14.7826 | −0.485261 | ||||||||
\(929\) | 12.1148 | + | 20.9834i | 0.397472 | + | 0.688442i | 0.993413 | − | 0.114586i | \(-0.0365541\pi\) |
−0.595941 | + | 0.803028i | \(0.703221\pi\) | |||||||
\(930\) | 3.84601 | + | 6.66149i | 0.126116 | + | 0.218439i | ||||
\(931\) | −16.3937 | −0.537283 | ||||||||
\(932\) | 7.75667 | + | 13.4349i | 0.254078 | + | 0.440076i | ||||
\(933\) | −8.26055 | + | 14.3077i | −0.270438 | + | 0.468413i | ||||
\(934\) | 36.1456 | − | 62.6059i | 1.18272 | − | 2.04853i | ||||
\(935\) | −19.5526 | −0.639437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2644 | 0.564005 | 0.282002 | − | 0.959414i | \(-0.409001\pi\) | ||||
0.282002 | + | 0.959414i | \(0.409001\pi\) | |||||||
\(938\) | −1.32759 | + | 2.29946i | −0.0433474 | + | 0.0750800i | ||||
\(939\) | −2.07524 | + | 3.59441i | −0.0677228 | + | 0.117299i | ||||
\(940\) | −6.50096 | − | 11.2600i | −0.212038 | − | 0.367260i | ||||
\(941\) | −4.34050 | −0.141496 | −0.0707482 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707482 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(942\) | −5.88135 | − | 10.1868i | −0.191625 | − | 0.331904i | ||||
\(943\) | −1.20410 | − | 2.08557i | −0.0392110 | − | 0.0679154i | ||||
\(944\) | −9.78986 | −0.318633 | ||||||||
\(945\) | 4.67629 | + | 8.09958i | 0.152120 | + | 0.263479i | ||||
\(946\) | −17.6163 | + | 30.5122i | −0.572754 | + | 0.992039i | ||||
\(947\) | −22.5073 | + | 38.9838i | −0.731389 | + | 1.26680i | 0.224901 | + | 0.974382i | \(0.427794\pi\) |
−0.956290 | + | 0.292421i | \(0.905539\pi\) | |||||||
\(948\) | 26.6963 | 0.867057 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −38.2814 | −1.24201 | ||||||||
\(951\) | −8.33273 | + | 14.4327i | −0.270207 | + | 0.468013i | ||||
\(952\) | −12.7872 | + | 22.1480i | −0.414434 | + | 0.717822i | ||||
\(953\) | 23.4429 | + | 40.6044i | 0.759391 | + | 1.31530i | 0.943161 | + | 0.332335i | \(0.107837\pi\) |
−0.183770 | + | 0.982969i | \(0.558830\pi\) | |||||||
\(954\) | −33.3967 | −1.08126 | ||||||||
\(955\) | −13.3165 | − | 23.0648i | −0.430911 | − | 0.746360i | ||||
\(956\) | −16.6531 | − | 28.8440i | −0.538599 | − | 0.932881i | ||||
\(957\) | −3.21685 | −0.103986 | ||||||||
\(958\) | −39.2095 | − | 67.9129i | −1.26680 | − | 2.19417i | ||||
\(959\) | −0.811626 | + | 1.40578i | −0.0262088 | + | 0.0453949i | ||||
\(960\) | −5.22737 | + | 9.05406i | −0.168712 | + | 0.292219i | ||||
\(961\) | −12.7778 | −0.412186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.5743 | 0.598550 | ||||||||
\(964\) | 18.1637 | − | 31.4604i | 0.585013 | − | 1.01327i | ||||
\(965\) | 4.37435 | − | 7.57660i | 0.140815 | − | 0.243900i | ||||
\(966\) | 2.41454 | + | 4.18211i | 0.0776866 | + | 0.134557i | ||||
\(967\) | −6.29457 | −0.202420 | −0.101210 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101210 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(968\) | 5.27024 | + | 9.12833i | 0.169392 | + | 0.293396i | ||||
\(969\) | −8.59783 | − | 14.8919i | −0.276202 | − | 0.478396i | ||||
\(970\) | −38.7265 | −1.24343 | ||||||||
\(971\) | 20.9034 | + | 36.2058i | 0.670823 | + | 1.16190i | 0.977671 | + | 0.210141i | \(0.0673922\pi\) |
−0.306848 | + | 0.951758i | \(0.599274\pi\) | |||||||
\(972\) | 19.7959 | − | 34.2875i | 0.634954 | − | 1.09977i | ||||
\(973\) | −11.6168 | + | 20.1209i | −0.372417 | + | 0.645045i | ||||
\(974\) | −94.0025 | −3.01203 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.86831 | −0.219849 | ||||||||
\(977\) | 11.8765 | − | 20.5707i | 0.379963 | − | 0.658116i | −0.611093 | − | 0.791559i | \(-0.709270\pi\) |
0.991056 | + | 0.133443i | \(0.0426033\pi\) | |||||||
\(978\) | −5.42692 | + | 9.39970i | −0.173534 | + | 0.300569i | ||||
\(979\) | 8.44869 | + | 14.6336i | 0.270021 | + | 0.467691i | ||||
\(980\) | −12.3448 | −0.394341 | ||||||||
\(981\) | −0.164210 | − | 0.284421i | −0.00524284 | − | 0.00908086i | ||||
\(982\) | −24.5432 | − | 42.5100i | −0.783204 | − | 1.35655i | ||||
\(983\) | 55.7251 | 1.77736 | 0.888678 | − | 0.458532i | \(-0.151625\pi\) | ||||
0.888678 | + | 0.458532i | \(0.151625\pi\) | |||||||
\(984\) | −0.833265 | − | 1.44326i | −0.0265635 | − | 0.0460094i | ||||
\(985\) | −8.24794 | + | 14.2858i | −0.262801 | + | 0.455185i | ||||
\(986\) | 13.4988 | − | 23.3806i | 0.429889 | − | 0.744590i | ||||
\(987\) | 3.35557 | 0.106809 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5996 | −0.368845 | ||||||||
\(990\) | 11.1664 | − | 19.3407i | 0.354890 | − | 0.614688i | ||||
\(991\) | 17.7756 | − | 30.7883i | 0.564661 | − | 0.978022i | −0.432420 | − | 0.901672i | \(-0.642340\pi\) |
0.997081 | − | 0.0763495i | \(-0.0243265\pi\) | |||||||
\(992\) | 13.9070 | + | 24.0876i | 0.441548 | + | 0.764784i | ||||
\(993\) | −8.72215 | −0.276789 | ||||||||
\(994\) | 10.5755 | + | 18.3174i | 0.335436 | + | 0.580991i | ||||
\(995\) | 10.0468 | + | 17.4015i | 0.318504 | + | 0.551665i | ||||
\(996\) | 13.0683 | 0.414085 | ||||||||
\(997\) | −3.30529 | − | 5.72493i | −0.104680 | − | 0.181310i | 0.808928 | − | 0.587908i | \(-0.200048\pi\) |
−0.913607 | + | 0.406598i | \(0.866715\pi\) | |||||||
\(998\) | 26.4550 | − | 45.8214i | 0.837419 | − | 1.45045i | ||||
\(999\) | 8.46077 | − | 14.6545i | 0.267687 | − | 0.463647i |
(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 | 169.2.c.b.22.1 | 6 | ||
13.2 | odd | 12 | 169.2.e.b.23.1 | 12 | |||
13.3 | even | 3 | inner | 169.2.c.b.146.1 | 6 | ||
13.4 | even | 6 | 169.2.a.b.1.1 | ✓ | 3 | ||
13.5 | odd | 4 | 169.2.e.b.147.6 | 12 | |||
13.6 | odd | 12 | 169.2.b.b.168.1 | 6 | |||
13.7 | odd | 12 | 169.2.b.b.168.6 | 6 | |||
13.8 | odd | 4 | 169.2.e.b.147.1 | 12 | |||
13.9 | even | 3 | 169.2.a.c.1.3 | yes | 3 | ||
13.10 | even | 6 | 169.2.c.c.146.3 | 6 | |||
13.11 | odd | 12 | 169.2.e.b.23.6 | 12 | |||
13.12 | even | 2 | 169.2.c.c.22.3 | 6 | |||
39.17 | odd | 6 | 1521.2.a.r.1.3 | 3 | |||
39.20 | even | 12 | 1521.2.b.l.1351.1 | 6 | |||
39.32 | even | 12 | 1521.2.b.l.1351.6 | 6 | |||
39.35 | odd | 6 | 1521.2.a.o.1.1 | 3 | |||
52.7 | even | 12 | 2704.2.f.o.337.4 | 6 | |||
52.19 | even | 12 | 2704.2.f.o.337.3 | 6 | |||
52.35 | odd | 6 | 2704.2.a.ba.1.2 | 3 | |||
52.43 | odd | 6 | 2704.2.a.z.1.2 | 3 | |||
65.4 | even | 6 | 4225.2.a.bg.1.3 | 3 | |||
65.9 | even | 6 | 4225.2.a.bb.1.1 | 3 | |||
91.48 | odd | 6 | 8281.2.a.bj.1.3 | 3 | |||
91.69 | odd | 6 | 8281.2.a.bf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.1 | ✓ | 3 | 13.4 | even | 6 | ||
169.2.a.c.1.3 | yes | 3 | 13.9 | even | 3 | ||
169.2.b.b.168.1 | 6 | 13.6 | odd | 12 | |||
169.2.b.b.168.6 | 6 | 13.7 | odd | 12 | |||
169.2.c.b.22.1 | 6 | 1.1 | even | 1 | trivial | ||
169.2.c.b.146.1 | 6 | 13.3 | even | 3 | inner | ||
169.2.c.c.22.3 | 6 | 13.12 | even | 2 | |||
169.2.c.c.146.3 | 6 | 13.10 | even | 6 | |||
169.2.e.b.23.1 | 12 | 13.2 | odd | 12 | |||
169.2.e.b.23.6 | 12 | 13.11 | odd | 12 | |||
169.2.e.b.147.1 | 12 | 13.8 | odd | 4 | |||
169.2.e.b.147.6 | 12 | 13.5 | odd | 4 | |||
1521.2.a.o.1.1 | 3 | 39.35 | odd | 6 | |||
1521.2.a.r.1.3 | 3 | 39.17 | odd | 6 | |||
1521.2.b.l.1351.1 | 6 | 39.20 | even | 12 | |||
1521.2.b.l.1351.6 | 6 | 39.32 | even | 12 | |||
2704.2.a.z.1.2 | 3 | 52.43 | odd | 6 | |||
2704.2.a.ba.1.2 | 3 | 52.35 | odd | 6 | |||
2704.2.f.o.337.3 | 6 | 52.19 | even | 12 | |||
2704.2.f.o.337.4 | 6 | 52.7 | even | 12 | |||
4225.2.a.bb.1.1 | 3 | 65.9 | even | 6 | |||
4225.2.a.bg.1.3 | 3 | 65.4 | even | 6 | |||
8281.2.a.bf.1.1 | 3 | 91.69 | odd | 6 | |||
8281.2.a.bj.1.3 | 3 | 91.48 | odd | 6 |