Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.7 | ||
Root | \(0.117630 - 0.893490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.d.97.7 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.19306 | − | 1.89119i | 0.533554 | − | 0.845766i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −0.493652 | − | 2.18090i | −0.156106 | − | 0.689660i | ||||
\(11\) | −1.97875 | −0.596616 | −0.298308 | − | 0.954470i | \(-0.596422\pi\) | ||||
−0.298308 | + | 0.954470i | \(0.596422\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 2.19222 | − | 2.19222i | 0.608011 | − | 0.608011i | −0.334415 | − | 0.942426i | \(-0.608539\pi\) |
0.942426 | + | 0.334415i | \(0.108539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.493652 | + | 2.18090i | 0.127460 | + | 0.563105i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.25469 | + | 3.25469i | 0.789378 | + | 0.789378i | 0.981392 | − | 0.192014i | \(-0.0615020\pi\) |
−0.192014 | + | 0.981392i | \(0.561502\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 4.21878 | 0.967856 | 0.483928 | − | 0.875108i | \(-0.339210\pi\) | ||||
0.483928 | + | 0.875108i | \(0.339210\pi\) | |||||||
\(20\) | −1.89119 | − | 1.19306i | −0.422883 | − | 0.266777i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.39919 | + | 1.39919i | −0.298308 | + | 0.298308i | ||||
\(23\) | −4.15953 | − | 4.15953i | −0.867322 | − | 0.867322i | 0.124854 | − | 0.992175i | \(-0.460154\pi\) |
−0.992175 | + | 0.124854i | \(0.960154\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.15321 | − | 4.51262i | −0.430641 | − | 0.902523i | ||||
\(26\) | − | 3.10026i | − | 0.608011i | ||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.94996i | − | 1.66197i | −0.556298 | − | 0.830983i | \(-0.687779\pi\) | ||
0.556298 | − | 0.830983i | \(-0.312221\pi\) | |||||||
\(30\) | 1.89119 | + | 1.19306i | 0.345283 | + | 0.217822i | ||||
\(31\) | − | 1.73386i | − | 0.311411i | −0.987804 | − | 0.155705i | \(-0.950235\pi\) | ||
0.987804 | − | 0.155705i | \(-0.0497650\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.39919 | − | 1.39919i | 0.243568 | − | 0.243568i | ||||
\(34\) | 4.60282 | 0.789378 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −1.96004 | + | 1.96004i | −0.322229 | + | 0.322229i | −0.849622 | − | 0.527393i | \(-0.823170\pi\) |
0.527393 | + | 0.849622i | \(0.323170\pi\) | |||||||
\(38\) | 2.98313 | − | 2.98313i | 0.483928 | − | 0.483928i | ||||
\(39\) | 3.10026i | 0.496439i | ||||||||
\(40\) | −2.18090 | + | 0.493652i | −0.344830 | + | 0.0780532i | ||||
\(41\) | 6.55691i | 1.02402i | 0.858980 | + | 0.512008i | \(0.171098\pi\) | ||||
−0.858980 | + | 0.512008i | \(0.828902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.33724 | − | 6.33724i | −0.966421 | − | 0.966421i | 0.0330335 | − | 0.999454i | \(-0.489483\pi\) |
−0.999454 | + | 0.0330335i | \(0.989483\pi\) | |||||||
\(44\) | 1.97875i | 0.298308i | ||||||||
\(45\) | −1.89119 | − | 1.19306i | −0.281922 | − | 0.177851i | ||||
\(46\) | −5.88246 | −0.867322 | ||||||||
\(47\) | −4.29932 | − | 4.29932i | −0.627120 | − | 0.627120i | 0.320222 | − | 0.947343i | \(-0.396242\pi\) |
−0.947343 | + | 0.320222i | \(0.896242\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.71345 | − | 1.66835i | −0.666582 | − | 0.235941i | ||||
\(51\) | −4.60282 | −0.644524 | ||||||||
\(52\) | −2.19222 | − | 2.19222i | −0.304006 | − | 0.304006i | ||||
\(53\) | 8.08484 | + | 8.08484i | 1.11054 | + | 1.11054i | 0.993077 | + | 0.117461i | \(0.0374756\pi\) |
0.117461 | + | 0.993077i | \(0.462524\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.36077 | + | 3.74220i | −0.318327 | + | 0.504598i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.98313 | + | 2.98313i | −0.395125 | + | 0.395125i | ||||
\(58\) | −6.32858 | − | 6.32858i | −0.830983 | − | 0.830983i | ||||
\(59\) | −4.20702 | −0.547708 | −0.273854 | − | 0.961771i | \(-0.588298\pi\) | ||||
−0.273854 | + | 0.961771i | \(0.588298\pi\) | |||||||
\(60\) | 2.18090 | − | 0.493652i | 0.281552 | − | 0.0637302i | ||||
\(61\) | − | 11.1200i | − | 1.42377i | −0.702298 | − | 0.711883i | \(-0.747843\pi\) | ||
0.702298 | − | 0.711883i | \(-0.252157\pi\) | |||||||
\(62\) | −1.22602 | − | 1.22602i | −0.155705 | − | 0.155705i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −1.53045 | − | 6.76135i | −0.189829 | − | 0.838642i | ||||
\(66\) | − | 1.97875i | − | 0.243568i | ||||||
\(67\) | 3.89769 | − | 3.89769i | 0.476179 | − | 0.476179i | −0.427729 | − | 0.903907i | \(-0.640686\pi\) |
0.903907 | + | 0.427729i | \(0.140686\pi\) | |||||||
\(68\) | 3.25469 | − | 3.25469i | 0.394689 | − | 0.394689i | ||||
\(69\) | 5.88246 | 0.708165 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.86002 | −0.458100 | −0.229050 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229050 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 10.7621 | − | 10.7621i | 1.25961 | − | 1.25961i | 0.308328 | − | 0.951280i | \(-0.400231\pi\) |
0.951280 | − | 0.308328i | \(-0.0997693\pi\) | |||||||
\(74\) | 2.77192i | 0.322229i | ||||||||
\(75\) | 4.71345 | + | 1.66835i | 0.544262 | + | 0.192645i | ||||
\(76\) | − | 4.21878i | − | 0.483928i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.19222 | + | 2.19222i | 0.248220 | + | 0.248220i | ||||
\(79\) | 2.55514i | 0.287476i | 0.989616 | + | 0.143738i | \(0.0459123\pi\) | ||||
−0.989616 | + | 0.143738i | \(0.954088\pi\) | |||||||
\(80\) | −1.19306 | + | 1.89119i | −0.133388 | + | 0.211442i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.63643 | + | 4.63643i | 0.512008 | + | 0.512008i | ||||
\(83\) | −9.52969 | + | 9.52969i | −1.04602 | + | 1.04602i | −0.0471311 | + | 0.998889i | \(0.515008\pi\) |
−0.998889 | + | 0.0471311i | \(0.984992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0383 | − | 2.27219i | 1.08880 | − | 0.246454i | ||||
\(86\) | −8.96222 | −0.966421 | ||||||||
\(87\) | 6.32858 | + | 6.32858i | 0.678495 | + | 0.678495i | ||||
\(88\) | 1.39919 | + | 1.39919i | 0.149154 | + | 0.149154i | ||||
\(89\) | 6.19187 | 0.656337 | 0.328168 | − | 0.944619i | \(-0.393569\pi\) | ||||
0.328168 | + | 0.944619i | \(0.393569\pi\) | |||||||
\(90\) | −2.18090 | + | 0.493652i | −0.229887 | + | 0.0520355i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.15953 | + | 4.15953i | −0.433661 | + | 0.433661i | ||||
\(93\) | 1.22602 | + | 1.22602i | 0.127133 | + | 0.127133i | ||||
\(94\) | −6.08016 | −0.627120 | ||||||||
\(95\) | 5.03327 | − | 7.97853i | 0.516403 | − | 0.818580i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 1.48031 | + | 1.48031i | 0.150303 | + | 0.150303i | 0.778253 | − | 0.627951i | \(-0.216106\pi\) |
−0.627951 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.97875i | 0.198872i | ||||||||
\(100\) | −4.51262 | + | 2.15321i | −0.451262 | + | 0.215321i | ||||
\(101\) | − | 10.0472i | − | 0.999733i | −0.866102 | − | 0.499866i | \(-0.833382\pi\) | ||
0.866102 | − | 0.499866i | \(-0.166618\pi\) | |||||||
\(102\) | −3.25469 | + | 3.25469i | −0.322262 | + | 0.322262i | ||||
\(103\) | 3.52695 | − | 3.52695i | 0.347521 | − | 0.347521i | −0.511665 | − | 0.859185i | \(-0.670971\pi\) |
0.859185 | + | 0.511665i | \(0.170971\pi\) | |||||||
\(104\) | −3.10026 | −0.304006 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.4337 | 1.11054 | ||||||||
\(107\) | 4.27775 | − | 4.27775i | 0.413545 | − | 0.413545i | −0.469426 | − | 0.882972i | \(-0.655539\pi\) |
0.882972 | + | 0.469426i | \(0.155539\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 9.74899i | − | 0.933784i | −0.884314 | − | 0.466892i | \(-0.845374\pi\) | ||
0.884314 | − | 0.466892i | \(-0.154626\pi\) | |||||||
\(110\) | 0.976815 | + | 4.31545i | 0.0931356 | + | 0.411462i | ||||
\(111\) | − | 2.77192i | − | 0.263099i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.02504 | + | 6.02504i | 0.566788 | + | 0.566788i | 0.931227 | − | 0.364439i | \(-0.118739\pi\) |
−0.364439 | + | 0.931227i | \(0.618739\pi\) | |||||||
\(114\) | 4.21878i | 0.395125i | ||||||||
\(115\) | −12.8290 | + | 2.90389i | −1.19631 | + | 0.270789i | ||||
\(116\) | −8.94996 | −0.830983 | ||||||||
\(117\) | −2.19222 | − | 2.19222i | −0.202670 | − | 0.202670i | ||||
\(118\) | −2.97481 | + | 2.97481i | −0.273854 | + | 0.273854i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.19306 | − | 1.89119i | 0.108911 | − | 0.172641i | ||||
\(121\) | −7.08454 | −0.644049 | ||||||||
\(122\) | −7.86301 | − | 7.86301i | −0.711883 | − | 0.711883i | ||||
\(123\) | −4.63643 | − | 4.63643i | −0.418053 | − | 0.418053i | ||||
\(124\) | −1.73386 | −0.155705 | ||||||||
\(125\) | −11.1031 | − | 1.31171i | −0.993094 | − | 0.117323i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.92770 | + | 8.92770i | −0.792205 | + | 0.792205i | −0.981852 | − | 0.189647i | \(-0.939266\pi\) |
0.189647 | + | 0.981852i | \(0.439266\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.96222 | 0.789079 | ||||||||
\(130\) | −5.86319 | − | 3.69881i | −0.514236 | − | 0.324407i | ||||
\(131\) | 5.12160i | 0.447476i | 0.974649 | + | 0.223738i | \(0.0718260\pi\) | ||||
−0.974649 | + | 0.223738i | \(0.928174\pi\) | |||||||
\(132\) | −1.39919 | − | 1.39919i | −0.121784 | − | 0.121784i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 5.51217i | − | 0.476179i | ||||||
\(135\) | 2.18090 | − | 0.493652i | 0.187702 | − | 0.0424868i | ||||
\(136\) | − | 4.60282i | − | 0.394689i | ||||||
\(137\) | −8.18996 | + | 8.18996i | −0.699715 | + | 0.699715i | −0.964349 | − | 0.264634i | \(-0.914749\pi\) |
0.264634 | + | 0.964349i | \(0.414749\pi\) | |||||||
\(138\) | 4.15953 | − | 4.15953i | 0.354083 | − | 0.354083i | ||||
\(139\) | −2.87054 | −0.243476 | −0.121738 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121738 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.08016 | 0.512042 | ||||||||
\(142\) | −2.72944 | + | 2.72944i | −0.229050 | + | 0.229050i | ||||
\(143\) | −4.33785 | + | 4.33785i | −0.362750 | + | 0.362750i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −16.9261 | − | 10.6779i | −1.40563 | − | 0.886748i | ||||
\(146\) | − | 15.2199i | − | 1.25961i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.96004 | + | 1.96004i | 0.161114 | + | 0.161114i | ||||
\(149\) | − | 15.5796i | − | 1.27633i | −0.769898 | − | 0.638167i | \(-0.779693\pi\) | ||
0.769898 | − | 0.638167i | \(-0.220307\pi\) | |||||||
\(150\) | 4.51262 | − | 2.15321i | 0.368454 | − | 0.175809i | ||||
\(151\) | 21.1906 | 1.72446 | 0.862232 | − | 0.506513i | \(-0.169066\pi\) | ||||
0.862232 | + | 0.506513i | \(0.169066\pi\) | |||||||
\(152\) | −2.98313 | − | 2.98313i | −0.241964 | − | 0.241964i | ||||
\(153\) | 3.25469 | − | 3.25469i | 0.263126 | − | 0.263126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.27906 | − | 2.06860i | −0.263381 | − | 0.166154i | ||||
\(156\) | 3.10026 | 0.248220 | ||||||||
\(157\) | 10.7362 | + | 10.7362i | 0.856846 | + | 0.856846i | 0.990965 | − | 0.134119i | \(-0.0428206\pi\) |
−0.134119 | + | 0.990965i | \(0.542821\pi\) | |||||||
\(158\) | 1.80676 | + | 1.80676i | 0.143738 | + | 0.143738i | ||||
\(159\) | −11.4337 | −0.906751 | ||||||||
\(160\) | 0.493652 | + | 2.18090i | 0.0390266 | + | 0.172415i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 15.7848 | + | 15.7848i | 1.23636 | + | 1.23636i | 0.961479 | + | 0.274879i | \(0.0886378\pi\) |
0.274879 | + | 0.961479i | \(0.411362\pi\) | |||||||
\(164\) | 6.55691 | 0.512008 | ||||||||
\(165\) | −0.976815 | − | 4.31545i | −0.0760449 | − | 0.335958i | ||||
\(166\) | 13.4770i | 1.04602i | ||||||||
\(167\) | 6.91224 | + | 6.91224i | 0.534885 | + | 0.534885i | 0.922022 | − | 0.387137i | \(-0.126536\pi\) |
−0.387137 | + | 0.922022i | \(0.626536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.38837i | 0.260644i | ||||||||
\(170\) | 5.49145 | − | 8.70482i | 0.421175 | − | 0.667629i | ||||
\(171\) | − | 4.21878i | − | 0.322619i | ||||||
\(172\) | −6.33724 | + | 6.33724i | −0.483210 | + | 0.483210i | ||||
\(173\) | −3.20151 | + | 3.20151i | −0.243406 | + | 0.243406i | −0.818258 | − | 0.574852i | \(-0.805060\pi\) |
0.574852 | + | 0.818258i | \(0.305060\pi\) | |||||||
\(174\) | 8.94996 | 0.678495 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.97875 | 0.149154 | ||||||||
\(177\) | 2.97481 | − | 2.97481i | 0.223601 | − | 0.223601i | ||||
\(178\) | 4.37831 | − | 4.37831i | 0.328168 | − | 0.328168i | ||||
\(179\) | − | 2.06788i | − | 0.154561i | −0.997009 | − | 0.0772803i | \(-0.975376\pi\) | ||
0.997009 | − | 0.0772803i | \(-0.0246236\pi\) | |||||||
\(180\) | −1.19306 | + | 1.89119i | −0.0889256 | + | 0.140961i | ||||
\(181\) | 6.13199i | 0.455787i | 0.973686 | + | 0.227894i | \(0.0731839\pi\) | ||||
−0.973686 | + | 0.227894i | \(0.926816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.86301 | + | 7.86301i | 0.581250 | + | 0.581250i | ||||
\(184\) | 5.88246i | 0.433661i | ||||||||
\(185\) | 1.36836 | + | 6.04526i | 0.100604 | + | 0.444456i | ||||
\(186\) | 1.73386 | 0.127133 | ||||||||
\(187\) | −6.44022 | − | 6.44022i | −0.470956 | − | 0.470956i | ||||
\(188\) | −4.29932 | + | 4.29932i | −0.313560 | + | 0.313560i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.08261 | − | 9.20073i | −0.151088 | − | 0.667491i | ||||
\(191\) | −16.1661 | −1.16974 | −0.584869 | − | 0.811128i | \(-0.698854\pi\) | ||||
−0.584869 | + | 0.811128i | \(0.698854\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 15.4085 | + | 15.4085i | 1.10913 | + | 1.10913i | 0.993265 | + | 0.115864i | \(0.0369636\pi\) |
0.115864 | + | 0.993265i | \(0.463036\pi\) | |||||||
\(194\) | 2.09348 | 0.150303 | ||||||||
\(195\) | 5.86319 | + | 3.69881i | 0.419872 | + | 0.264877i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.628120 | + | 0.628120i | −0.0447517 | + | 0.0447517i | −0.729129 | − | 0.684377i | \(-0.760074\pi\) |
0.684377 | + | 0.729129i | \(0.260074\pi\) | |||||||
\(198\) | 1.39919 | + | 1.39919i | 0.0994361 | + | 0.0994361i | ||||
\(199\) | −9.62495 | −0.682295 | −0.341147 | − | 0.940010i | \(-0.610816\pi\) | ||||
−0.341147 | + | 0.940010i | \(0.610816\pi\) | |||||||
\(200\) | −1.66835 | + | 4.71345i | −0.117970 | + | 0.333291i | ||||
\(201\) | 5.51217i | 0.388798i | ||||||||
\(202\) | −7.10444 | − | 7.10444i | −0.499866 | − | 0.499866i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.60282i | 0.322262i | ||||||||
\(205\) | 12.4004 | + | 7.82280i | 0.866079 | + | 0.546368i | ||||
\(206\) | − | 4.98786i | − | 0.347521i | ||||||
\(207\) | −4.15953 | + | 4.15953i | −0.289107 | + | 0.289107i | ||||
\(208\) | −2.19222 | + | 2.19222i | −0.152003 | + | 0.152003i | ||||
\(209\) | −8.34793 | −0.577439 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2669 | 0.775648 | 0.387824 | − | 0.921733i | \(-0.373227\pi\) | ||||
0.387824 | + | 0.921733i | \(0.373227\pi\) | |||||||
\(212\) | 8.08484 | − | 8.08484i | 0.555269 | − | 0.555269i | ||||
\(213\) | 2.72944 | − | 2.72944i | 0.187018 | − | 0.187018i | ||||
\(214\) | − | 6.04965i | − | 0.413545i | ||||||
\(215\) | −19.5457 | + | 4.42421i | −1.33300 | + | 0.301729i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.89357 | − | 6.89357i | −0.466892 | − | 0.466892i | ||||
\(219\) | 15.2199i | 1.02847i | ||||||||
\(220\) | 3.74220 | + | 2.36077i | 0.252299 | + | 0.159163i | ||||
\(221\) | 14.2700 | 0.959901 | ||||||||
\(222\) | −1.96004 | − | 1.96004i | −0.131549 | − | 0.131549i | ||||
\(223\) | 13.1718 | − | 13.1718i | 0.882048 | − | 0.882048i | −0.111694 | − | 0.993743i | \(-0.535628\pi\) |
0.993743 | + | 0.111694i | \(0.0356277\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.51262 | + | 2.15321i | −0.300841 | + | 0.143547i | ||||
\(226\) | 8.52069 | 0.566788 | ||||||||
\(227\) | 19.0312 | + | 19.0312i | 1.26314 | + | 1.26314i | 0.949561 | + | 0.313583i | \(0.101529\pi\) |
0.313583 | + | 0.949561i | \(0.398471\pi\) | |||||||
\(228\) | 2.98313 | + | 2.98313i | 0.197563 | + | 0.197563i | ||||
\(229\) | 26.8905 | 1.77697 | 0.888486 | − | 0.458904i | \(-0.151758\pi\) | ||||
0.888486 | + | 0.458904i | \(0.151758\pi\) | |||||||
\(230\) | −7.01814 | + | 11.1249i | −0.462762 | + | 0.733551i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.32858 | + | 6.32858i | −0.415491 | + | 0.415491i | ||||
\(233\) | −0.651418 | − | 0.651418i | −0.0426758 | − | 0.0426758i | 0.685447 | − | 0.728123i | \(-0.259607\pi\) |
−0.728123 | + | 0.685447i | \(0.759607\pi\) | |||||||
\(234\) | −3.10026 | −0.202670 | ||||||||
\(235\) | −13.2602 | + | 3.00148i | −0.865000 | + | 0.195795i | ||||
\(236\) | 4.20702i | 0.273854i | ||||||||
\(237\) | −1.80676 | − | 1.80676i | −0.117362 | − | 0.117362i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.3432i | − | 1.63931i | −0.572856 | − | 0.819656i | \(-0.694164\pi\) | ||
0.572856 | − | 0.819656i | \(-0.305836\pi\) | |||||||
\(240\) | −0.493652 | − | 2.18090i | −0.0318651 | − | 0.140776i | ||||
\(241\) | 21.1200i | 1.36046i | 0.732999 | + | 0.680230i | \(0.238120\pi\) | ||||
−0.732999 | + | 0.680230i | \(0.761880\pi\) | |||||||
\(242\) | −5.00952 | + | 5.00952i | −0.322024 | + | 0.322024i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −11.1200 | −0.711883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.55691 | −0.418053 | ||||||||
\(247\) | 9.24849 | − | 9.24849i | 0.588467 | − | 0.588467i | ||||
\(248\) | −1.22602 | + | 1.22602i | −0.0778527 | + | 0.0778527i | ||||
\(249\) | − | 13.4770i | − | 0.854072i | ||||||
\(250\) | −8.77861 | + | 6.92358i | −0.555208 | + | 0.437886i | ||||
\(251\) | 2.70623i | 0.170816i | 0.996346 | + | 0.0854078i | \(0.0272193\pi\) | ||||
−0.996346 | + | 0.0854078i | \(0.972781\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.23068 | + | 8.23068i | 0.517458 | + | 0.517458i | ||||
\(254\) | 12.6257i | 0.792205i | ||||||||
\(255\) | −5.49145 | + | 8.70482i | −0.343888 | + | 0.545117i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9862 | + | 16.9862i | 1.05957 | + | 1.05957i | 0.998110 | + | 0.0614577i | \(0.0195749\pi\) |
0.0614577 | + | 0.998110i | \(0.480425\pi\) | |||||||
\(258\) | 6.33724 | − | 6.33724i | 0.394540 | − | 0.394540i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.76135 | + | 1.53045i | −0.419321 | + | 0.0949145i | ||||
\(261\) | −8.94996 | −0.553989 | ||||||||
\(262\) | 3.62152 | + | 3.62152i | 0.223738 | + | 0.223738i | ||||
\(263\) | 0.601271 | + | 0.601271i | 0.0370759 | + | 0.0370759i | 0.725402 | − | 0.688326i | \(-0.241654\pi\) |
−0.688326 | + | 0.725402i | \(0.741654\pi\) | |||||||
\(264\) | −1.97875 | −0.121784 | ||||||||
\(265\) | 24.9357 | − | 5.64426i | 1.53179 | − | 0.346724i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.37831 | + | 4.37831i | −0.267948 | + | 0.267948i | ||||
\(268\) | −3.89769 | − | 3.89769i | −0.238089 | − | 0.238089i | ||||
\(269\) | −11.6434 | −0.709912 | −0.354956 | − | 0.934883i | \(-0.615504\pi\) | ||||
−0.354956 | + | 0.934883i | \(0.615504\pi\) | |||||||
\(270\) | 1.19306 | − | 1.89119i | 0.0726074 | − | 0.115094i | ||||
\(271\) | 23.3447i | 1.41809i | 0.705162 | + | 0.709046i | \(0.250874\pi\) | ||||
−0.705162 | + | 0.709046i | \(0.749126\pi\) | |||||||
\(272\) | −3.25469 | − | 3.25469i | −0.197344 | − | 0.197344i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5824i | 0.699715i | ||||||||
\(275\) | 4.26066 | + | 8.92935i | 0.256928 | + | 0.538460i | ||||
\(276\) | − | 5.88246i | − | 0.354083i | ||||||
\(277\) | 6.68198 | − | 6.68198i | 0.401481 | − | 0.401481i | −0.477274 | − | 0.878755i | \(-0.658375\pi\) |
0.878755 | + | 0.477274i | \(0.158375\pi\) | |||||||
\(278\) | −2.02978 | + | 2.02978i | −0.121738 | + | 0.121738i | ||||
\(279\) | −1.73386 | −0.103804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.7320 | −0.699871 | −0.349935 | − | 0.936774i | \(-0.613796\pi\) | ||||
−0.349935 | + | 0.936774i | \(0.613796\pi\) | |||||||
\(282\) | 4.29932 | − | 4.29932i | 0.256021 | − | 0.256021i | ||||
\(283\) | −2.57938 | + | 2.57938i | −0.153328 | + | 0.153328i | −0.779603 | − | 0.626275i | \(-0.784579\pi\) |
0.626275 | + | 0.779603i | \(0.284579\pi\) | |||||||
\(284\) | 3.86002i | 0.229050i | ||||||||
\(285\) | 2.08261 | + | 9.20073i | 0.123363 | + | 0.545004i | ||||
\(286\) | 6.13465i | 0.362750i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 4.18598i | 0.246234i | ||||||||
\(290\) | −19.5189 | + | 4.41816i | −1.14619 | + | 0.259443i | ||||
\(291\) | −2.09348 | −0.122722 | ||||||||
\(292\) | −10.7621 | − | 10.7621i | −0.629804 | − | 0.629804i | ||||
\(293\) | −8.62354 | + | 8.62354i | −0.503793 | + | 0.503793i | −0.912614 | − | 0.408822i | \(-0.865940\pi\) |
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.01924 | + | 7.95628i | −0.292231 | + | 0.463233i | ||||
\(296\) | 2.77192 | 0.161114 | ||||||||
\(297\) | −1.39919 | − | 1.39919i | −0.0811892 | − | 0.0811892i | ||||
\(298\) | −11.0165 | − | 11.0165i | −0.638167 | − | 0.638167i | ||||
\(299\) | −18.2372 | −1.05468 | ||||||||
\(300\) | 1.66835 | − | 4.71345i | 0.0963225 | − | 0.272131i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.9840 | − | 14.9840i | 0.862232 | − | 0.862232i | ||||
\(303\) | 7.10444 | + | 7.10444i | 0.408139 | + | 0.408139i | ||||
\(304\) | −4.21878 | −0.241964 | ||||||||
\(305\) | −21.0300 | − | 13.2668i | −1.20417 | − | 0.759656i | ||||
\(306\) | − | 4.60282i | − | 0.263126i | ||||||
\(307\) | 15.9933 | + | 15.9933i | 0.912785 | + | 0.912785i | 0.996490 | − | 0.0837060i | \(-0.0266757\pi\) |
−0.0837060 | + | 0.996490i | \(0.526676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.98786i | 0.283750i | ||||||||
\(310\) | −3.78137 | + | 0.855923i | −0.214767 | + | 0.0486132i | ||||
\(311\) | 7.74252i | 0.439038i | 0.975608 | + | 0.219519i | \(0.0704488\pi\) | ||||
−0.975608 | + | 0.219519i | \(0.929551\pi\) | |||||||
\(312\) | 2.19222 | − | 2.19222i | 0.124110 | − | 0.124110i | ||||
\(313\) | 14.1742 | − | 14.1742i | 0.801171 | − | 0.801171i | −0.182108 | − | 0.983279i | \(-0.558292\pi\) |
0.983279 | + | 0.182108i | \(0.0582920\pi\) | |||||||
\(314\) | 15.1833 | 0.856846 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.55514 | 0.143738 | ||||||||
\(317\) | −2.10741 | + | 2.10741i | −0.118364 | + | 0.118364i | −0.763808 | − | 0.645444i | \(-0.776672\pi\) |
0.645444 | + | 0.763808i | \(0.276672\pi\) | |||||||
\(318\) | −8.08484 | + | 8.08484i | −0.453375 | + | 0.453375i | ||||
\(319\) | 17.7098i | 0.991556i | ||||||||
\(320\) | 1.89119 | + | 1.19306i | 0.105721 | + | 0.0666942i | ||||
\(321\) | 6.04965i | 0.337658i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.7308 | + | 13.7308i | 0.764004 | + | 0.764004i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −14.6129 | − | 5.17234i | −0.810579 | − | 0.286910i | ||||
\(326\) | 22.3230 | 1.23636 | ||||||||
\(327\) | 6.89357 | + | 6.89357i | 0.381216 | + | 0.381216i | ||||
\(328\) | 4.63643 | − | 4.63643i | 0.256004 | − | 0.256004i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.74220 | − | 2.36077i | −0.206001 | − | 0.129956i | ||||
\(331\) | 27.8372 | 1.53007 | 0.765035 | − | 0.643989i | \(-0.222722\pi\) | ||||
0.765035 | + | 0.643989i | \(0.222722\pi\) | |||||||
\(332\) | 9.52969 | + | 9.52969i | 0.523010 | + | 0.523010i | ||||
\(333\) | 1.96004 | + | 1.96004i | 0.107410 | + | 0.107410i | ||||
\(334\) | 9.77538 | 0.534885 | ||||||||
\(335\) | −2.72109 | − | 12.0215i | −0.148669 | − | 0.656803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1567 | + | 17.1567i | −0.934583 | + | 0.934583i | −0.997988 | − | 0.0634051i | \(-0.979804\pi\) |
0.0634051 | + | 0.997988i | \(0.479804\pi\) | |||||||
\(338\) | 2.39594 | + | 2.39594i | 0.130322 | + | 0.130322i | ||||
\(339\) | −8.52069 | −0.462780 | ||||||||
\(340\) | −2.27219 | − | 10.0383i | −0.123227 | − | 0.544402i | ||||
\(341\) | 3.43088i | 0.185793i | ||||||||
\(342\) | −2.98313 | − | 2.98313i | −0.161309 | − | 0.161309i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.96222i | 0.483210i | ||||||||
\(345\) | 7.01814 | − | 11.1249i | 0.377844 | − | 0.598942i | ||||
\(346\) | 4.52762i | 0.243406i | ||||||||
\(347\) | −17.7080 | + | 17.7080i | −0.950613 | + | 0.950613i | −0.998837 | − | 0.0482236i | \(-0.984644\pi\) |
0.0482236 | + | 0.998837i | \(0.484644\pi\) | |||||||
\(348\) | 6.32858 | − | 6.32858i | 0.339247 | − | 0.339247i | ||||
\(349\) | −18.0130 | −0.964212 | −0.482106 | − | 0.876113i | \(-0.660128\pi\) | ||||
−0.482106 | + | 0.876113i | \(0.660128\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.10026 | 0.165480 | ||||||||
\(352\) | 1.39919 | − | 1.39919i | 0.0745770 | − | 0.0745770i | ||||
\(353\) | −5.37260 | + | 5.37260i | −0.285955 | + | 0.285955i | −0.835478 | − | 0.549524i | \(-0.814809\pi\) |
0.549524 | + | 0.835478i | \(0.314809\pi\) | |||||||
\(354\) | − | 4.20702i | − | 0.223601i | ||||||
\(355\) | −4.60524 | + | 7.30003i | −0.244421 | + | 0.387445i | ||||
\(356\) | − | 6.19187i | − | 0.328168i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.46221 | − | 1.46221i | −0.0772803 | − | 0.0772803i | ||||
\(359\) | 3.28672i | 0.173466i | 0.996232 | + | 0.0867332i | \(0.0276428\pi\) | ||||
−0.996232 | + | 0.0867332i | \(0.972357\pi\) | |||||||
\(360\) | 0.493652 | + | 2.18090i | 0.0260177 | + | 0.114943i | ||||
\(361\) | −1.20185 | −0.0632555 | ||||||||
\(362\) | 4.33597 | + | 4.33597i | 0.227894 | + | 0.227894i | ||||
\(363\) | 5.00952 | − | 5.00952i | 0.262932 | − | 0.262932i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.51333 | − | 33.1930i | −0.393266 | − | 1.73740i | ||||
\(366\) | 11.1200 | 0.581250 | ||||||||
\(367\) | −2.29639 | − | 2.29639i | −0.119871 | − | 0.119871i | 0.644627 | − | 0.764497i | \(-0.277013\pi\) |
−0.764497 | + | 0.644627i | \(0.777013\pi\) | |||||||
\(368\) | 4.15953 | + | 4.15953i | 0.216830 | + | 0.216830i | ||||
\(369\) | 6.55691 | 0.341339 | ||||||||
\(370\) | 5.24222 | + | 3.30707i | 0.272530 | + | 0.171926i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.22602 | − | 1.22602i | 0.0635664 | − | 0.0635664i | ||||
\(373\) | −11.1484 | − | 11.1484i | −0.577243 | − | 0.577243i | 0.356900 | − | 0.934143i | \(-0.383834\pi\) |
−0.934143 | + | 0.356900i | \(0.883834\pi\) | |||||||
\(374\) | −9.10785 | −0.470956 | ||||||||
\(375\) | 8.77861 | − | 6.92358i | 0.453326 | − | 0.357532i | ||||
\(376\) | 6.08016i | 0.313560i | ||||||||
\(377\) | −19.6203 | − | 19.6203i | −1.01049 | − | 1.01049i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.7428i | − | 1.11685i | −0.829555 | − | 0.558426i | \(-0.811406\pi\) | ||
0.829555 | − | 0.558426i | \(-0.188594\pi\) | |||||||
\(380\) | −7.97853 | − | 5.03327i | −0.409290 | − | 0.258201i | ||||
\(381\) | − | 12.6257i | − | 0.646833i | ||||||
\(382\) | −11.4312 | + | 11.4312i | −0.584869 | + | 0.584869i | ||||
\(383\) | −12.6486 | + | 12.6486i | −0.646316 | + | 0.646316i | −0.952101 | − | 0.305785i | \(-0.901081\pi\) |
0.305785 | + | 0.952101i | \(0.401081\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.7909 | 1.10913 | ||||||||
\(387\) | −6.33724 | + | 6.33724i | −0.322140 | + | 0.322140i | ||||
\(388\) | 1.48031 | − | 1.48031i | 0.0751514 | − | 0.0751514i | ||||
\(389\) | 5.03599i | 0.255335i | 0.991817 | + | 0.127667i | \(0.0407490\pi\) | ||||
−0.991817 | + | 0.127667i | \(0.959251\pi\) | |||||||
\(390\) | 6.76135 | − | 1.53045i | 0.342374 | − | 0.0774973i | ||||
\(391\) | − | 27.0759i | − | 1.36929i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.62152 | − | 3.62152i | −0.182681 | − | 0.182681i | ||||
\(394\) | 0.888296i | 0.0447517i | ||||||||
\(395\) | 4.83226 | + | 3.04844i | 0.243138 | + | 0.153384i | ||||
\(396\) | 1.97875 | 0.0994361 | ||||||||
\(397\) | 10.4332 | + | 10.4332i | 0.523625 | + | 0.523625i | 0.918664 | − | 0.395039i | \(-0.129269\pi\) |
−0.395039 | + | 0.918664i | \(0.629269\pi\) | |||||||
\(398\) | −6.80587 | + | 6.80587i | −0.341147 | + | 0.341147i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.15321 | + | 4.51262i | 0.107660 | + | 0.225631i | ||||
\(401\) | −8.69371 | −0.434143 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(402\) | 3.89769 | + | 3.89769i | 0.194399 | + | 0.194399i | ||||
\(403\) | −3.80100 | − | 3.80100i | −0.189341 | − | 0.189341i | ||||
\(404\) | −10.0472 | −0.499866 | ||||||||
\(405\) | −1.19306 | + | 1.89119i | −0.0592837 | + | 0.0939740i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.87844 | − | 3.87844i | 0.192247 | − | 0.192247i | ||||
\(408\) | 3.25469 | + | 3.25469i | 0.161131 | + | 0.161131i | ||||
\(409\) | 18.9819 | 0.938595 | 0.469297 | − | 0.883040i | \(-0.344507\pi\) | ||||
0.469297 | + | 0.883040i | \(0.344507\pi\) | |||||||
\(410\) | 14.2999 | − | 3.23683i | 0.706223 | − | 0.159856i | ||||
\(411\) | − | 11.5824i | − | 0.571315i | ||||||
\(412\) | −3.52695 | − | 3.52695i | −0.173760 | − | 0.173760i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.88246i | 0.289107i | ||||||||
\(415\) | 6.65295 | + | 29.3920i | 0.326581 | + | 1.44280i | ||||
\(416\) | 3.10026i | 0.152003i | ||||||||
\(417\) | 2.02978 | − | 2.02978i | 0.0993985 | − | 0.0993985i | ||||
\(418\) | −5.90288 | + | 5.90288i | −0.288719 | + | 0.288719i | ||||
\(419\) | 11.9171 | 0.582188 | 0.291094 | − | 0.956695i | \(-0.405981\pi\) | ||||
0.291094 | + | 0.956695i | \(0.405981\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.95263 | 0.338850 | 0.169425 | − | 0.985543i | \(-0.445809\pi\) | ||||
0.169425 | + | 0.985543i | \(0.445809\pi\) | |||||||
\(422\) | 7.96693 | − | 7.96693i | 0.387824 | − | 0.387824i | ||||
\(423\) | −4.29932 | + | 4.29932i | −0.209040 | + | 0.209040i | ||||
\(424\) | − | 11.4337i | − | 0.555269i | ||||||
\(425\) | 7.67914 | − | 21.6952i | 0.372493 | − | 1.05237i | ||||
\(426\) | − | 3.86002i | − | 0.187018i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.27775 | − | 4.27775i | −0.206773 | − | 0.206773i | ||||
\(429\) | − | 6.13465i | − | 0.296184i | ||||||
\(430\) | −10.6925 | + | 16.9493i | −0.515637 | + | 0.817366i | ||||
\(431\) | 6.24783 | 0.300947 | 0.150474 | − | 0.988614i | \(-0.451920\pi\) | ||||
0.150474 | + | 0.988614i | \(0.451920\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 15.1544 | − | 15.1544i | 0.728274 | − | 0.728274i | −0.242002 | − | 0.970276i | \(-0.577804\pi\) |
0.970276 | + | 0.242002i | \(0.0778040\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.5189 | − | 4.41816i | 0.935861 | − | 0.211835i | ||||
\(436\) | −9.74899 | −0.466892 | ||||||||
\(437\) | −17.5482 | − | 17.5482i | −0.839442 | − | 0.839442i | ||||
\(438\) | 10.7621 | + | 10.7621i | 0.514233 | + | 0.514233i | ||||
\(439\) | −32.7459 | −1.56288 | −0.781438 | − | 0.623983i | \(-0.785513\pi\) | ||||
−0.781438 | + | 0.623983i | \(0.785513\pi\) | |||||||
\(440\) | 4.31545 | − | 0.976815i | 0.205731 | − | 0.0465678i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0904 | − | 10.0904i | 0.479951 | − | 0.479951i | ||||
\(443\) | 21.7443 | + | 21.7443i | 1.03310 | + | 1.03310i | 0.999433 | + | 0.0336677i | \(0.0107188\pi\) |
0.0336677 | + | 0.999433i | \(0.489281\pi\) | |||||||
\(444\) | −2.77192 | −0.131549 | ||||||||
\(445\) | 7.38728 | − | 11.7100i | 0.350191 | − | 0.555107i | ||||
\(446\) | − | 18.6277i | − | 0.882048i | ||||||
\(447\) | 11.0165 | + | 11.0165i | 0.521061 | + | 0.521061i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.8713i | − | 0.796207i | −0.917341 | − | 0.398103i | \(-0.869669\pi\) | ||
0.917341 | − | 0.398103i | \(-0.130331\pi\) | |||||||
\(450\) | −1.66835 | + | 4.71345i | −0.0786470 | + | 0.222194i | ||||
\(451\) | − | 12.9745i | − | 0.610945i | ||||||
\(452\) | 6.02504 | − | 6.02504i | 0.283394 | − | 0.283394i | ||||
\(453\) | −14.9840 | + | 14.9840i | −0.704010 | + | 0.704010i | ||||
\(454\) | 26.9142 | 1.26314 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.21878 | 0.197563 | ||||||||
\(457\) | 14.0344 | − | 14.0344i | 0.656503 | − | 0.656503i | −0.298048 | − | 0.954551i | \(-0.596336\pi\) |
0.954551 | + | 0.298048i | \(0.0963356\pi\) | |||||||
\(458\) | 19.0144 | − | 19.0144i | 0.888486 | − | 0.888486i | ||||
\(459\) | 4.60282i | 0.214841i | ||||||||
\(460\) | 2.90389 | + | 12.8290i | 0.135394 | + | 0.598157i | ||||
\(461\) | 15.7775i | 0.734830i | 0.930057 | + | 0.367415i | \(0.119757\pi\) | ||||
−0.930057 | + | 0.367415i | \(0.880243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.48617 | + | 4.48617i | 0.208490 | + | 0.208490i | 0.803625 | − | 0.595135i | \(-0.202902\pi\) |
−0.595135 | + | 0.803625i | \(0.702902\pi\) | |||||||
\(464\) | 8.94996i | 0.415491i | ||||||||
\(465\) | 3.78137 | − | 0.855923i | 0.175357 | − | 0.0396925i | ||||
\(466\) | −0.921244 | −0.0426758 | ||||||||
\(467\) | 12.3390 | + | 12.3390i | 0.570982 | + | 0.570982i | 0.932403 | − | 0.361421i | \(-0.117708\pi\) |
−0.361421 | + | 0.932403i | \(0.617708\pi\) | |||||||
\(468\) | −2.19222 | + | 2.19222i | −0.101335 | + | 0.101335i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.25401 | + | 11.4987i | −0.334602 | + | 0.530397i | ||||
\(471\) | −15.1833 | −0.699612 | ||||||||
\(472\) | 2.97481 | + | 2.97481i | 0.136927 | + | 0.136927i | ||||
\(473\) | 12.5398 | + | 12.5398i | 0.576582 | + | 0.576582i | ||||
\(474\) | −2.55514 | −0.117362 | ||||||||
\(475\) | −9.08391 | − | 19.0378i | −0.416799 | − | 0.873512i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.08484 | − | 8.08484i | 0.370180 | − | 0.370180i | ||||
\(478\) | −17.9203 | − | 17.9203i | −0.819656 | − | 0.819656i | ||||
\(479\) | −31.7496 | −1.45068 | −0.725339 | − | 0.688392i | \(-0.758317\pi\) | ||||
−0.725339 | + | 0.688392i | \(0.758317\pi\) | |||||||
\(480\) | −1.89119 | − | 1.19306i | −0.0863207 | − | 0.0544556i | ||||
\(481\) | 8.59367i | 0.391837i | ||||||||
\(482\) | 14.9341 | + | 14.9341i | 0.680230 | + | 0.680230i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.08454i | 0.322024i | ||||||||
\(485\) | 4.56565 | − | 1.03345i | 0.207316 | − | 0.0469264i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −21.1482 | + | 21.1482i | −0.958316 | + | 0.958316i | −0.999165 | − | 0.0408497i | \(-0.986994\pi\) |
0.0408497 | + | 0.999165i | \(0.486994\pi\) | |||||||
\(488\) | −7.86301 | + | 7.86301i | −0.355942 | + | 0.355942i | ||||
\(489\) | −22.3230 | −1.00948 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.57179 | 0.0709340 | 0.0354670 | − | 0.999371i | \(-0.488708\pi\) | ||||
0.0354670 | + | 0.999371i | \(0.488708\pi\) | |||||||
\(492\) | −4.63643 | + | 4.63643i | −0.209027 | + | 0.209027i | ||||
\(493\) | 29.1293 | − | 29.1293i | 1.31192 | − | 1.31192i | ||||
\(494\) | − | 13.0793i | − | 0.588467i | ||||||
\(495\) | 3.74220 | + | 2.36077i | 0.168199 | + | 0.106109i | ||||
\(496\) | 1.73386i | 0.0778527i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.52969 | − | 9.52969i | −0.427036 | − | 0.427036i | ||||
\(499\) | − | 14.2595i | − | 0.638345i | −0.947697 | − | 0.319172i | \(-0.896595\pi\) | ||
0.947697 | − | 0.319172i | \(-0.103405\pi\) | |||||||
\(500\) | −1.31171 | + | 11.1031i | −0.0586613 | + | 0.496547i | ||||
\(501\) | −9.77538 | −0.436732 | ||||||||
\(502\) | 1.91359 | + | 1.91359i | 0.0854078 | + | 0.0854078i | ||||
\(503\) | 28.7896 | − | 28.7896i | 1.28367 | − | 1.28367i | 0.345100 | − | 0.938566i | \(-0.387845\pi\) |
0.938566 | − | 0.345100i | \(-0.112155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.0012 | − | 11.9869i | −0.845540 | − | 0.533411i | ||||
\(506\) | 11.6399 | 0.517458 | ||||||||
\(507\) | −2.39594 | − | 2.39594i | −0.106407 | − | 0.106407i | ||||
\(508\) | 8.92770 | + | 8.92770i | 0.396102 | + | 0.396102i | ||||
\(509\) | −14.6188 | −0.647969 | −0.323984 | − | 0.946062i | \(-0.605023\pi\) | ||||
−0.323984 | + | 0.946062i | \(0.605023\pi\) | |||||||
\(510\) | 2.27219 | + | 10.0383i | 0.100614 | + | 0.444502i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 2.98313 | + | 2.98313i | 0.131708 | + | 0.131708i | ||||
\(514\) | 24.0221 | 1.05957 | ||||||||
\(515\) | −2.46227 | − | 10.8780i | −0.108500 | − | 0.479342i | ||||
\(516\) | − | 8.96222i | − | 0.394540i | ||||||
\(517\) | 8.50729 | + | 8.50729i | 0.374150 | + | 0.374150i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.52762i | − | 0.198740i | ||||||
\(520\) | −3.69881 | + | 5.86319i | −0.162203 | + | 0.257118i | ||||
\(521\) | − | 15.3751i | − | 0.673597i | −0.941577 | − | 0.336798i | \(-0.890656\pi\) | ||
0.941577 | − | 0.336798i | \(-0.109344\pi\) | |||||||
\(522\) | −6.32858 | + | 6.32858i | −0.276994 | + | 0.276994i | ||||
\(523\) | 16.5574 | − | 16.5574i | 0.724002 | − | 0.724002i | −0.245416 | − | 0.969418i | \(-0.578924\pi\) |
0.969418 | + | 0.245416i | \(0.0789244\pi\) | |||||||
\(524\) | 5.12160 | 0.223738 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.850325 | 0.0370759 | ||||||||
\(527\) | 5.64318 | − | 5.64318i | 0.245821 | − | 0.245821i | ||||
\(528\) | −1.39919 | + | 1.39919i | −0.0608919 | + | 0.0608919i | ||||
\(529\) | 11.6033i | 0.504493i | ||||||||
\(530\) | 13.6411 | − | 21.6233i | 0.592532 | − | 0.939256i | ||||
\(531\) | 4.20702i | 0.182569i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.3742 | + | 14.3742i | 0.622614 | + | 0.622614i | ||||
\(534\) | 6.19187i | 0.267948i | ||||||||
\(535\) | −2.98642 | − | 13.1937i | −0.129114 | − | 0.570411i | ||||
\(536\) | −5.51217 | −0.238089 | ||||||||
\(537\) | 1.46221 | + | 1.46221i | 0.0630991 | + | 0.0630991i | ||||
\(538\) | −8.23314 | + | 8.23314i | −0.354956 | + | 0.354956i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.493652 | − | 2.18090i | −0.0212434 | − | 0.0938508i | ||||
\(541\) | 7.96874 | 0.342603 | 0.171301 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(542\) | 16.5072 | + | 16.5072i | 0.709046 | + | 0.709046i | ||||
\(543\) | −4.33597 | − | 4.33597i | −0.186074 | − | 0.186074i | ||||
\(544\) | −4.60282 | −0.197344 | ||||||||
\(545\) | −18.4372 | − | 11.6311i | −0.789763 | − | 0.498224i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.88082 | + | 5.88082i | −0.251446 | + | 0.251446i | −0.821563 | − | 0.570117i | \(-0.806898\pi\) |
0.570117 | + | 0.821563i | \(0.306898\pi\) | |||||||
\(548\) | 8.18996 | + | 8.18996i | 0.349858 | + | 0.349858i | ||||
\(549\) | −11.1200 | −0.474589 | ||||||||
\(550\) | 9.32675 | + | 3.30126i | 0.397694 | + | 0.140766i | ||||
\(551\) | − | 37.7580i | − | 1.60854i | ||||||
\(552\) | −4.15953 | − | 4.15953i | −0.177041 | − | 0.177041i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 9.44974i | − | 0.401481i | ||||||
\(555\) | −5.24222 | − | 3.30707i | −0.222520 | − | 0.140377i | ||||
\(556\) | 2.87054i | 0.121738i | ||||||||
\(557\) | 18.5354 | − | 18.5354i | 0.785370 | − | 0.785370i | −0.195361 | − | 0.980731i | \(-0.562588\pi\) |
0.980731 | + | 0.195361i | \(0.0625878\pi\) | |||||||
\(558\) | −1.22602 | + | 1.22602i | −0.0519018 | + | 0.0519018i | ||||
\(559\) | −27.7852 | −1.17519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.10785 | 0.384534 | ||||||||
\(562\) | −8.29575 | + | 8.29575i | −0.349935 | + | 0.349935i | ||||
\(563\) | −0.618308 | + | 0.618308i | −0.0260586 | + | 0.0260586i | −0.720016 | − | 0.693957i | \(-0.755866\pi\) |
0.693957 | + | 0.720016i | \(0.255866\pi\) | |||||||
\(564\) | − | 6.08016i | − | 0.256021i | ||||||
\(565\) | 18.5827 | − | 4.20625i | 0.781782 | − | 0.176958i | ||||
\(566\) | 3.64779i | 0.153328i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.72944 | + | 2.72944i | 0.114525 | + | 0.114525i | ||||
\(569\) | − | 33.0102i | − | 1.38386i | −0.721965 | − | 0.691929i | \(-0.756761\pi\) | ||
0.721965 | − | 0.691929i | \(-0.243239\pi\) | |||||||
\(570\) | 7.97853 | + | 5.03327i | 0.334184 | + | 0.210821i | ||||
\(571\) | 4.79189 | 0.200534 | 0.100267 | − | 0.994961i | \(-0.468030\pi\) | ||||
0.100267 | + | 0.994961i | \(0.468030\pi\) | |||||||
\(572\) | 4.33785 | + | 4.33785i | 0.181375 | + | 0.181375i | ||||
\(573\) | 11.4312 | − | 11.4312i | 0.477544 | − | 0.477544i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.81403 | + | 27.7267i | −0.409273 | + | 1.15628i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.0871 | + | 23.0871i | 0.961128 | + | 0.961128i | 0.999272 | − | 0.0381442i | \(-0.0121446\pi\) |
−0.0381442 | + | 0.999272i | \(0.512145\pi\) | |||||||
\(578\) | 2.95994 | + | 2.95994i | 0.123117 | + | 0.123117i | ||||
\(579\) | −21.7909 | −0.905600 | ||||||||
\(580\) | −10.6779 | + | 16.9261i | −0.443374 | + | 0.702817i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.48031 | + | 1.48031i | −0.0613609 | + | 0.0613609i | ||||
\(583\) | −15.9979 | − | 15.9979i | −0.662566 | − | 0.662566i | ||||
\(584\) | −15.2199 | −0.629804 | ||||||||
\(585\) | −6.76135 | + | 1.53045i | −0.279547 | + | 0.0632763i | ||||
\(586\) | 12.1955i | 0.503793i | ||||||||
\(587\) | 6.03856 | + | 6.03856i | 0.249238 | + | 0.249238i | 0.820658 | − | 0.571420i | \(-0.193607\pi\) |
−0.571420 | + | 0.820658i | \(0.693607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.31479i | − | 0.301401i | ||||||
\(590\) | 2.07680 | + | 9.17508i | 0.0855007 | + | 0.377732i | ||||
\(591\) | − | 0.888296i | − | 0.0365396i | ||||||
\(592\) | 1.96004 | − | 1.96004i | 0.0805572 | − | 0.0805572i | ||||
\(593\) | 2.87821 | − | 2.87821i | 0.118194 | − | 0.118194i | −0.645536 | − | 0.763730i | \(-0.723366\pi\) |
0.763730 | + | 0.645536i | \(0.223366\pi\) | |||||||
\(594\) | −1.97875 | −0.0811892 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.5796 | −0.638167 | ||||||||
\(597\) | 6.80587 | − | 6.80587i | 0.278546 | − | 0.278546i | ||||
\(598\) | −12.8956 | + | 12.8956i | −0.527341 | + | 0.527341i | ||||
\(599\) | − | 34.1269i | − | 1.39439i | −0.716884 | − | 0.697193i | \(-0.754432\pi\) | ||
0.716884 | − | 0.697193i | \(-0.245568\pi\) | |||||||
\(600\) | −2.15321 | − | 4.51262i | −0.0879043 | − | 0.184227i | ||||
\(601\) | 9.99405i | 0.407666i | 0.979006 | + | 0.203833i | \(0.0653399\pi\) | ||||
−0.979006 | + | 0.203833i | \(0.934660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.89769 | − | 3.89769i | −0.158726 | − | 0.158726i | ||||
\(604\) | − | 21.1906i | − | 0.862232i | ||||||
\(605\) | −8.45229 | + | 13.3982i | −0.343635 | + | 0.544715i | ||||
\(606\) | 10.0472 | 0.408139 | ||||||||
\(607\) | −12.9256 | − | 12.9256i | −0.524633 | − | 0.524633i | 0.394334 | − | 0.918967i | \(-0.370975\pi\) |
−0.918967 | + | 0.394334i | \(0.870975\pi\) | |||||||
\(608\) | −2.98313 | + | 2.98313i | −0.120982 | + | 0.120982i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.2515 | + | 5.48939i | −0.981915 | + | 0.222259i | ||||
\(611\) | −18.8501 | −0.762593 | ||||||||
\(612\) | −3.25469 | − | 3.25469i | −0.131563 | − | 0.131563i | ||||
\(613\) | −21.0944 | − | 21.0944i | −0.851995 | − | 0.851995i | 0.138383 | − | 0.990379i | \(-0.455809\pi\) |
−0.990379 | + | 0.138383i | \(0.955809\pi\) | |||||||
\(614\) | 22.6179 | 0.912785 | ||||||||
\(615\) | −14.2999 | + | 3.23683i | −0.576629 | + | 0.130521i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.0246 | + | 35.0246i | −1.41004 | + | 1.41004i | −0.650721 | + | 0.759317i | \(0.725533\pi\) |
−0.759317 | + | 0.650721i | \(0.774467\pi\) | |||||||
\(618\) | 3.52695 | + | 3.52695i | 0.141875 | + | 0.141875i | ||||
\(619\) | 11.5154 | 0.462843 | 0.231422 | − | 0.972854i | \(-0.425662\pi\) | ||||
0.231422 | + | 0.972854i | \(0.425662\pi\) | |||||||
\(620\) | −2.06860 | + | 3.27906i | −0.0830771 | + | 0.131690i | ||||
\(621\) | − | 5.88246i | − | 0.236055i | ||||||
\(622\) | 5.47479 | + | 5.47479i | 0.219519 | + | 0.219519i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 3.10026i | − | 0.124110i | ||||||
\(625\) | −15.7274 | + | 19.4332i | −0.629096 | + | 0.777327i | ||||
\(626\) | − | 20.0453i | − | 0.801171i | ||||||
\(627\) | 5.90288 | − | 5.90288i | 0.235738 | − | 0.235738i | ||||
\(628\) | 10.7362 | − | 10.7362i | 0.428423 | − | 0.428423i | ||||
\(629\) | −12.7586 | −0.508720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4477 | 0.734390 | 0.367195 | − | 0.930144i | \(-0.380318\pi\) | ||||
0.367195 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(632\) | 1.80676 | − | 1.80676i | 0.0718690 | − | 0.0718690i | ||||
\(633\) | −7.96693 | + | 7.96693i | −0.316657 | + | 0.316657i | ||||
\(634\) | 2.98032i | 0.118364i | ||||||||
\(635\) | 6.23268 | + | 27.5353i | 0.247336 | + | 1.09270i | ||||
\(636\) | 11.4337i | 0.453375i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.5227 | + | 12.5227i | 0.495778 | + | 0.495778i | ||||
\(639\) | 3.86002i | 0.152700i | ||||||||
\(640\) | 2.18090 | − | 0.493652i | 0.0862075 | − | 0.0195133i | ||||
\(641\) | −19.4846 | −0.769594 | −0.384797 | − | 0.923001i | \(-0.625729\pi\) | ||||
−0.384797 | + | 0.923001i | \(0.625729\pi\) | |||||||
\(642\) | 4.27775 | + | 4.27775i | 0.168829 | + | 0.168829i | ||||
\(643\) | −28.2707 | + | 28.2707i | −1.11489 | + | 1.11489i | −0.122408 | + | 0.992480i | \(0.539062\pi\) |
−0.992480 | + | 0.122408i | \(0.960938\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6925 | − | 16.9493i | 0.421016 | − | 0.667377i | ||||
\(646\) | 19.4183 | 0.764004 | ||||||||
\(647\) | −17.6276 | − | 17.6276i | −0.693012 | − | 0.693012i | 0.269882 | − | 0.962893i | \(-0.413015\pi\) |
−0.962893 | + | 0.269882i | \(0.913015\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 8.32466 | 0.326771 | ||||||||
\(650\) | −13.9903 | + | 6.67550i | −0.548744 | + | 0.261835i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.7848 | − | 15.7848i | 0.618179 | − | 0.618179i | ||||
\(653\) | −35.1733 | − | 35.1733i | −1.37644 | − | 1.37644i | −0.850559 | − | 0.525880i | \(-0.823736\pi\) |
−0.525880 | − | 0.850559i | \(-0.676264\pi\) | |||||||
\(654\) | 9.74899 | 0.381216 | ||||||||
\(655\) | 9.68592 | + | 6.11038i | 0.378460 | + | 0.238752i | ||||
\(656\) | − | 6.55691i | − | 0.256004i | ||||||
\(657\) | −10.7621 | − | 10.7621i | −0.419869 | − | 0.419869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.5644i | 1.54121i | 0.637312 | + | 0.770606i | \(0.280046\pi\) | ||||
−0.637312 | + | 0.770606i | \(0.719954\pi\) | |||||||
\(660\) | −4.31545 | + | 0.976815i | −0.167979 | + | 0.0380225i | ||||
\(661\) | − | 2.02066i | − | 0.0785948i | −0.999228 | − | 0.0392974i | \(-0.987488\pi\) | ||
0.999228 | − | 0.0392974i | \(-0.0125120\pi\) | |||||||
\(662\) | 19.6839 | − | 19.6839i | 0.765035 | − | 0.765035i | ||||
\(663\) | −10.0904 | + | 10.0904i | −0.391878 | + | 0.391878i | ||||
\(664\) | 13.4770 | 0.523010 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.77192 | 0.107410 | ||||||||
\(667\) | −37.2276 | + | 37.2276i | −1.44146 | + | 1.44146i | ||||
\(668\) | 6.91224 | − | 6.91224i | 0.267442 | − | 0.267442i | ||||
\(669\) | 18.6277i | 0.720190i | ||||||||
\(670\) | −10.4246 | − | 6.57636i | −0.402736 | − | 0.254067i | ||||
\(671\) | 22.0037i | 0.849442i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7775 | − | 19.7775i | −0.762366 | − | 0.762366i | 0.214383 | − | 0.976750i | \(-0.431226\pi\) |
−0.976750 | + | 0.214383i | \(0.931226\pi\) | |||||||
\(674\) | 24.2632i | 0.934583i | ||||||||
\(675\) | 1.66835 | − | 4.71345i | 0.0642150 | − | 0.181421i | ||||
\(676\) | 3.38837 | 0.130322 | ||||||||
\(677\) | 12.1336 | + | 12.1336i | 0.466332 | + | 0.466332i | 0.900724 | − | 0.434392i | \(-0.143037\pi\) |
−0.434392 | + | 0.900724i | \(0.643037\pi\) | |||||||
\(678\) | −6.02504 | + | 6.02504i | −0.231390 | + | 0.231390i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.70482 | − | 5.49145i | −0.333815 | − | 0.210588i | ||||
\(681\) | −26.9142 | −1.03135 | ||||||||
\(682\) | 2.42600 | + | 2.42600i | 0.0928963 | + | 0.0928963i | ||||
\(683\) | 0.356641 | + | 0.356641i | 0.0136465 | + | 0.0136465i | 0.713897 | − | 0.700251i | \(-0.246928\pi\) |
−0.700251 | + | 0.713897i | \(0.746928\pi\) | |||||||
\(684\) | −4.21878 | −0.161309 | ||||||||
\(685\) | 5.71765 | + | 25.2599i | 0.218460 | + | 0.965131i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.0144 | + | 19.0144i | −0.725445 | + | 0.725445i | ||||
\(688\) | 6.33724 | + | 6.33724i | 0.241605 | + | 0.241605i | ||||
\(689\) | 35.4475 | 1.35044 | ||||||||
\(690\) | −2.90389 | − | 12.8290i | −0.110549 | − | 0.488393i | ||||
\(691\) | − | 15.6342i | − | 0.594753i | −0.954760 | − | 0.297376i | \(-0.903888\pi\) | ||
0.954760 | − | 0.297376i | \(-0.0961116\pi\) | |||||||
\(692\) | 3.20151 | + | 3.20151i | 0.121703 | + | 0.121703i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.0428i | 0.950613i | ||||||||
\(695\) | −3.42473 | + | 5.42873i | −0.129907 | + | 0.205924i | ||||
\(696\) | − | 8.94996i | − | 0.339247i | ||||||
\(697\) | −21.3407 | + | 21.3407i | −0.808336 | + | 0.808336i | ||||
\(698\) | −12.7371 | + | 12.7371i | −0.482106 | + | 0.482106i | ||||
\(699\) | 0.921244 | 0.0348447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.02724 | 0.303185 | 0.151592 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151592 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(702\) | 2.19222 | − | 2.19222i | 0.0827399 | − | 0.0827399i | ||||
\(703\) | −8.26899 | + | 8.26899i | −0.311871 | + | 0.311871i | ||||
\(704\) | − | 1.97875i | − | 0.0745770i | ||||||
\(705\) | 7.25401 | − | 11.4987i | 0.273202 | − | 0.433068i | ||||
\(706\) | 7.59800i | 0.285955i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.97481 | − | 2.97481i | −0.111800 | − | 0.111800i | ||||
\(709\) | − | 13.6783i | − | 0.513698i | −0.966452 | − | 0.256849i | \(-0.917316\pi\) | ||
0.966452 | − | 0.256849i | \(-0.0826843\pi\) | |||||||
\(710\) | 1.90550 | + | 8.41829i | 0.0715123 | + | 0.315933i | ||||
\(711\) | 2.55514 | 0.0958253 | ||||||||
\(712\) | −4.37831 | − | 4.37831i | −0.164084 | − | 0.164084i | ||||
\(713\) | −7.21204 | + | 7.21204i | −0.270093 | + | 0.270093i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.02838 | + | 13.3790i | 0.113255 | + | 0.500348i | ||||
\(716\) | −2.06788 | −0.0772803 | ||||||||
\(717\) | 17.9203 | + | 17.9203i | 0.669246 | + | 0.669246i | ||||
\(718\) | 2.32406 | + | 2.32406i | 0.0867332 | + | 0.0867332i | ||||
\(719\) | 21.0471 | 0.784924 | 0.392462 | − | 0.919768i | \(-0.371623\pi\) | ||||
0.392462 | + | 0.919768i | \(0.371623\pi\) | |||||||
\(720\) | 1.89119 | + | 1.19306i | 0.0704805 | + | 0.0444628i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.849839 | + | 0.849839i | −0.0316277 | + | 0.0316277i | ||||
\(723\) | −14.9341 | − | 14.9341i | −0.555405 | − | 0.555405i | ||||
\(724\) | 6.13199 | 0.227894 | ||||||||
\(725\) | −40.3877 | + | 19.2711i | −1.49996 | + | 0.715711i | ||||
\(726\) | − | 7.08454i | − | 0.262932i | ||||||
\(727\) | −11.2251 | − | 11.2251i | −0.416317 | − | 0.416317i | 0.467615 | − | 0.883932i | \(-0.345113\pi\) |
−0.883932 | + | 0.467615i | \(0.845113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −28.7837 | − | 18.1583i | −1.06533 | − | 0.672068i | ||||
\(731\) | − | 41.2515i | − | 1.52574i | ||||||
\(732\) | 7.86301 | − | 7.86301i | 0.290625 | − | 0.290625i | ||||
\(733\) | 20.3304 | − | 20.3304i | 0.750922 | − | 0.750922i | −0.223730 | − | 0.974651i | \(-0.571823\pi\) |
0.974651 | + | 0.223730i | \(0.0718233\pi\) | |||||||
\(734\) | −3.24759 | −0.119871 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.88246 | 0.216830 | ||||||||
\(737\) | −7.71257 | + | 7.71257i | −0.284096 | + | 0.284096i | ||||
\(738\) | 4.63643 | − | 4.63643i | 0.170669 | − | 0.170669i | ||||
\(739\) | 41.9841i | 1.54441i | 0.635373 | + | 0.772205i | \(0.280846\pi\) | ||||
−0.635373 | + | 0.772205i | \(0.719154\pi\) | |||||||
\(740\) | 6.04526 | − | 1.36836i | 0.222228 | − | 0.0503019i | ||||
\(741\) | 13.0793i | 0.480482i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.63799 | + | 8.63799i | 0.316897 | + | 0.316897i | 0.847574 | − | 0.530677i | \(-0.178062\pi\) |
−0.530677 | + | 0.847574i | \(0.678062\pi\) | |||||||
\(744\) | − | 1.73386i | − | 0.0635664i | ||||||
\(745\) | −29.4641 | − | 18.5875i | −1.07948 | − | 0.680993i | ||||
\(746\) | −15.7662 | −0.577243 | ||||||||
\(747\) | 9.52969 | + | 9.52969i | 0.348673 | + | 0.348673i | ||||
\(748\) | −6.44022 | + | 6.44022i | −0.235478 | + | 0.235478i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.31171 | − | 11.1031i | 0.0478968 | − | 0.405429i | ||||
\(751\) | 31.7446 | 1.15838 | 0.579188 | − | 0.815194i | \(-0.303370\pi\) | ||||
0.579188 | + | 0.815194i | \(0.303370\pi\) | |||||||
\(752\) | 4.29932 | + | 4.29932i | 0.156780 | + | 0.156780i | ||||
\(753\) | −1.91359 | − | 1.91359i | −0.0697351 | − | 0.0697351i | ||||
\(754\) | −27.7472 | −1.01049 | ||||||||
\(755\) | 25.2817 | − | 40.0754i | 0.920094 | − | 1.45849i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.81959 | + | 9.81959i | −0.356899 | + | 0.356899i | −0.862669 | − | 0.505770i | \(-0.831209\pi\) |
0.505770 | + | 0.862669i | \(0.331209\pi\) | |||||||
\(758\) | −15.3745 | − | 15.3745i | −0.558426 | − | 0.558426i | ||||
\(759\) | −11.6399 | −0.422503 | ||||||||
\(760\) | −9.20073 | + | 2.08261i | −0.333746 | + | 0.0755442i | ||||
\(761\) | − | 31.9432i | − | 1.15794i | −0.815349 | − | 0.578970i | \(-0.803455\pi\) | ||
0.815349 | − | 0.578970i | \(-0.196545\pi\) | |||||||
\(762\) | −8.92770 | − | 8.92770i | −0.323416 | − | 0.323416i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.1661i | 0.584869i | ||||||||
\(765\) | −2.27219 | − | 10.0383i | −0.0821513 | − | 0.362935i | ||||
\(766\) | 17.8879i | 0.646316i | ||||||||
\(767\) | −9.22271 | + | 9.22271i | −0.333013 | + | 0.333013i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −26.3715 | −0.950981 | −0.475490 | − | 0.879721i | \(-0.657729\pi\) | ||||
−0.475490 | + | 0.879721i | \(0.657729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0221 | −0.865133 | ||||||||
\(772\) | 15.4085 | − | 15.4085i | 0.554564 | − | 0.554564i | ||||
\(773\) | 32.5441 | − | 32.5441i | 1.17053 | − | 1.17053i | 0.188448 | − | 0.982083i | \(-0.439654\pi\) |
0.982083 | − | 0.188448i | \(-0.0603457\pi\) | |||||||
\(774\) | 8.96222i | 0.322140i | ||||||||
\(775\) | −7.82425 | + | 3.73336i | −0.281055 | + | 0.134106i | ||||
\(776\) | − | 2.09348i | − | 0.0751514i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.56098 | + | 3.56098i | 0.127667 | + | 0.127667i | ||||
\(779\) | 27.6622i | 0.991100i | ||||||||
\(780\) | 3.69881 | − | 5.86319i | 0.132438 | − | 0.209936i | ||||
\(781\) | 7.63802 | 0.273310 | ||||||||
\(782\) | −19.1456 | − | 19.1456i | −0.684644 | − | 0.684644i | ||||
\(783\) | 6.32858 | − | 6.32858i | 0.226165 | − | 0.226165i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.1133 | − | 7.49528i | 1.18186 | − | 0.267518i | ||||
\(786\) | −5.12160 | −0.182681 | ||||||||
\(787\) | −8.01108 | − | 8.01108i | −0.285564 | − | 0.285564i | 0.549759 | − | 0.835323i | \(-0.314720\pi\) |
−0.835323 | + | 0.549759i | \(0.814720\pi\) | |||||||
\(788\) | 0.628120 | + | 0.628120i | 0.0223759 | + | 0.0223759i | ||||
\(789\) | −0.850325 | −0.0302724 | ||||||||
\(790\) | 5.57250 | − | 1.26135i | 0.198261 | − | 0.0448768i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.39919 | − | 1.39919i | 0.0497180 | − | 0.0497180i | ||||
\(793\) | −24.3774 | − | 24.3774i | −0.865666 | − | 0.865666i | ||||
\(794\) | 14.7547 | 0.523625 | ||||||||
\(795\) | −13.6411 | + | 21.6233i | −0.483800 | + | 0.766899i | ||||
\(796\) | 9.62495i | 0.341147i | ||||||||
\(797\) | 24.7239 | + | 24.7239i | 0.875767 | + | 0.875767i | 0.993093 | − | 0.117327i | \(-0.0374325\pi\) |
−0.117327 | + | 0.993093i | \(0.537432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 27.9859i | − | 0.990070i | ||||||
\(800\) | 4.71345 | + | 1.66835i | 0.166646 | + | 0.0589852i | ||||
\(801\) | − | 6.19187i | − | 0.218779i | ||||||
\(802\) | −6.14738 | + | 6.14738i | −0.217072 | + | 0.217072i | ||||
\(803\) | −21.2955 | + | 21.2955i | −0.751503 | + | 0.751503i | ||||
\(804\) | 5.51217 | 0.194399 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.37542 | −0.189341 | ||||||||
\(807\) | 8.23314 | − | 8.23314i | 0.289820 | − | 0.289820i | ||||
\(808\) | −7.10444 | + | 7.10444i | −0.249933 | + | 0.249933i | ||||
\(809\) | 5.79908i | 0.203885i | 0.994790 | + | 0.101942i | \(0.0325057\pi\) | ||||
−0.994790 | + | 0.101942i | \(0.967494\pi\) | |||||||
\(810\) | 0.493652 | + | 2.18090i | 0.0173452 | + | 0.0766289i | ||||
\(811\) | − | 28.8064i | − | 1.01153i | −0.862671 | − | 0.505765i | \(-0.831210\pi\) | ||
0.862671 | − | 0.505765i | \(-0.168790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5072 | − | 16.5072i | −0.578934 | − | 0.578934i | ||||
\(814\) | − | 5.48494i | − | 0.192247i | ||||||
\(815\) | 48.6842 | − | 11.0198i | 1.70533 | − | 0.386007i | ||||
\(816\) | 4.60282 | 0.161131 | ||||||||
\(817\) | −26.7355 | − | 26.7355i | −0.935356 | − | 0.935356i | ||||
\(818\) | 13.4222 | − | 13.4222i | 0.469297 | − | 0.469297i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.82280 | − | 12.4004i | 0.273184 | − | 0.433039i | ||||
\(821\) | 4.51799 | 0.157679 | 0.0788395 | − | 0.996887i | \(-0.474879\pi\) | ||||
0.0788395 | + | 0.996887i | \(0.474879\pi\) | |||||||
\(822\) | −8.18996 | − | 8.18996i | −0.285658 | − | 0.285658i | ||||
\(823\) | −15.8260 | − | 15.8260i | −0.551659 | − | 0.551659i | 0.375261 | − | 0.926919i | \(-0.377553\pi\) |
−0.926919 | + | 0.375261i | \(0.877553\pi\) | |||||||
\(824\) | −4.98786 | −0.173760 | ||||||||
\(825\) | −9.32675 | − | 3.30126i | −0.324716 | − | 0.114935i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5410 | − | 22.5410i | 0.783826 | − | 0.783826i | −0.196648 | − | 0.980474i | \(-0.563006\pi\) |
0.980474 | + | 0.196648i | \(0.0630057\pi\) | |||||||
\(828\) | 4.15953 | + | 4.15953i | 0.144554 | + | 0.144554i | ||||
\(829\) | −7.22693 | −0.251002 | −0.125501 | − | 0.992094i | \(-0.540054\pi\) | ||||
−0.125501 | + | 0.992094i | \(0.540054\pi\) | |||||||
\(830\) | 25.4876 | + | 16.0789i | 0.884688 | + | 0.558108i | ||||
\(831\) | 9.44974i | 0.327808i | ||||||||
\(832\) | 2.19222 | + | 2.19222i | 0.0760014 | + | 0.0760014i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 2.87054i | − | 0.0993985i | ||||||
\(835\) | 21.3191 | − | 4.82563i | 0.737777 | − | 0.166998i | ||||
\(836\) | 8.34793i | 0.288719i | ||||||||
\(837\) | 1.22602 | − | 1.22602i | 0.0423776 | − | 0.0423776i | ||||
\(838\) | 8.42665 | − | 8.42665i | 0.291094 | − | 0.291094i | ||||
\(839\) | 5.52622 | 0.190786 | 0.0953932 | − | 0.995440i | \(-0.469589\pi\) | ||||
0.0953932 | + | 0.995440i | \(0.469589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −51.1018 | −1.76213 | ||||||||
\(842\) | 4.91625 | − | 4.91625i | 0.169425 | − | 0.169425i | ||||
\(843\) | 8.29575 | − | 8.29575i | 0.285721 | − | 0.285721i | ||||
\(844\) | − | 11.2669i | − | 0.387824i | ||||||
\(845\) | 6.40806 | + | 4.04254i | 0.220444 | + | 0.139068i | ||||
\(846\) | 6.08016i | 0.209040i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.08484 | − | 8.08484i | −0.277635 | − | 0.277635i | ||||
\(849\) | − | 3.64779i | − | 0.125192i | ||||||
\(850\) | −9.91083 | − | 20.7708i | −0.339939 | − | 0.712432i | ||||
\(851\) | 16.3057 | 0.558952 | ||||||||
\(852\) | −2.72944 | − | 2.72944i | −0.0935092 | − | 0.0935092i | ||||
\(853\) | −10.4649 | + | 10.4649i | −0.358313 | + | 0.358313i | −0.863191 | − | 0.504878i | \(-0.831538\pi\) |
0.504878 | + | 0.863191i | \(0.331538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.97853 | − | 5.03327i | −0.272860 | − | 0.172134i | ||||
\(856\) | −6.04965 | −0.206773 | ||||||||
\(857\) | 1.52003 | + | 1.52003i | 0.0519233 | + | 0.0519233i | 0.732592 | − | 0.680668i | \(-0.238311\pi\) |
−0.680668 | + | 0.732592i | \(0.738311\pi\) | |||||||
\(858\) | −4.33785 | − | 4.33785i | −0.148092 | − | 0.148092i | ||||
\(859\) | 7.18910 | 0.245289 | 0.122644 | − | 0.992451i | \(-0.460863\pi\) | ||||
0.122644 | + | 0.992451i | \(0.460863\pi\) | |||||||
\(860\) | 4.42421 | + | 19.5457i | 0.150864 | + | 0.666502i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.41788 | − | 4.41788i | 0.150474 | − | 0.150474i | ||||
\(863\) | 28.6663 | + | 28.6663i | 0.975812 | + | 0.975812i | 0.999714 | − | 0.0239027i | \(-0.00760919\pi\) |
−0.0239027 | + | 0.999714i | \(0.507609\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 2.23507 | + | 9.87426i | 0.0759945 | + | 0.335735i | ||||
\(866\) | − | 21.4316i | − | 0.728274i | ||||||
\(867\) | −2.95994 | − | 2.95994i | −0.100525 | − | 0.100525i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.05600i | − | 0.171513i | ||||||
\(870\) | 10.6779 | − | 16.9261i | 0.362013 | − | 0.573848i | ||||
\(871\) | − | 17.0892i | − | 0.579044i | ||||||
\(872\) | −6.89357 | + | 6.89357i | −0.233446 | + | 0.233446i | ||||
\(873\) | 1.48031 | − | 1.48031i | 0.0501009 | − | 0.0501009i | ||||
\(874\) | −24.8168 | −0.839442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.2199 | 0.514233 | ||||||||
\(877\) | −36.1279 | + | 36.1279i | −1.21995 | + | 1.21995i | −0.252303 | + | 0.967648i | \(0.581188\pi\) |
−0.967648 | + | 0.252303i | \(0.918812\pi\) | |||||||
\(878\) | −23.1548 | + | 23.1548i | −0.781438 | + | 0.781438i | ||||
\(879\) | − | 12.1955i | − | 0.411345i | ||||||
\(880\) | 2.36077 | − | 3.74220i | 0.0795817 | − | 0.126150i | ||||
\(881\) | − | 27.9972i | − | 0.943251i | −0.881799 | − | 0.471625i | \(-0.843667\pi\) | ||
0.881799 | − | 0.471625i | \(-0.156333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.66131 | + | 4.66131i | 0.156865 | + | 0.156865i | 0.781176 | − | 0.624311i | \(-0.214620\pi\) |
−0.624311 | + | 0.781176i | \(0.714620\pi\) | |||||||
\(884\) | − | 14.2700i | − | 0.479951i | ||||||
\(885\) | −2.07680 | − | 9.17508i | −0.0698110 | − | 0.308417i | ||||
\(886\) | 30.7510 | 1.03310 | ||||||||
\(887\) | 9.84950 | + | 9.84950i | 0.330714 | + | 0.330714i | 0.852857 | − | 0.522144i | \(-0.174868\pi\) |
−0.522144 | + | 0.852857i | \(0.674868\pi\) | |||||||
\(888\) | −1.96004 | + | 1.96004i | −0.0657747 | + | 0.0657747i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.05663 | − | 13.5038i | −0.102458 | − | 0.452649i | ||||
\(891\) | 1.97875 | 0.0662907 | ||||||||
\(892\) | −13.1718 | − | 13.1718i | −0.441024 | − | 0.441024i | ||||
\(893\) | −18.1379 | − | 18.1379i | −0.606962 | − | 0.606962i | ||||
\(894\) | 15.5796 | 0.521061 | ||||||||
\(895\) | −3.91075 | − | 2.46711i | −0.130722 | − | 0.0824663i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.8956 | − | 12.8956i | 0.430573 | − | 0.430573i | ||||
\(898\) | −11.9298 | − | 11.9298i | −0.398103 | − | 0.398103i | ||||
\(899\) | −15.5180 | −0.517554 | ||||||||
\(900\) | 2.15321 | + | 4.51262i | 0.0717735 | + | 0.150421i | ||||
\(901\) | 52.6273i | 1.75327i | ||||||||
\(902\) | −9.17435 | − | 9.17435i | −0.305473 | − | 0.305473i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.52069i | − | 0.283394i | ||||||
\(905\) | 11.5968 | + | 7.31585i | 0.385490 | + | 0.243187i | ||||
\(906\) | 21.1906i | 0.704010i | ||||||||
\(907\) | 19.0839 | − | 19.0839i | 0.633670 | − | 0.633670i | −0.315316 | − | 0.948987i | \(-0.602111\pi\) |
0.948987 | + | 0.315316i | \(0.102111\pi\) | |||||||
\(908\) | 19.0312 | − | 19.0312i | 0.631572 | − | 0.631572i | ||||
\(909\) | −10.0472 | −0.333244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5364 | −0.514744 | −0.257372 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257372 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(912\) | 2.98313 | − | 2.98313i | 0.0987814 | − | 0.0987814i | ||||
\(913\) | 18.8569 | − | 18.8569i | 0.624073 | − | 0.624073i | ||||
\(914\) | − | 19.8477i | − | 0.656503i | ||||||
\(915\) | 24.2515 | − | 5.48939i | 0.801730 | − | 0.181474i | ||||
\(916\) | − | 26.8905i | − | 0.888486i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.25469 | + | 3.25469i | 0.107421 | + | 0.107421i | ||||
\(919\) | − | 37.8644i | − | 1.24903i | −0.781013 | − | 0.624515i | \(-0.785297\pi\) | ||
0.781013 | − | 0.624515i | \(-0.214703\pi\) | |||||||
\(920\) | 11.1249 | + | 7.01814i | 0.366776 | + | 0.231381i | ||||
\(921\) | −22.6179 | −0.745285 | ||||||||
\(922\) | 11.1564 | + | 11.1564i | 0.367415 | + | 0.367415i | ||||
\(923\) | −8.46199 | + | 8.46199i | −0.278530 | + | 0.278530i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.0653 | + | 4.62454i | 0.429584 | + | 0.152054i | ||||
\(926\) | 6.34440 | 0.208490 | ||||||||
\(927\) | −3.52695 | − | 3.52695i | −0.115840 | − | 0.115840i | ||||
\(928\) | 6.32858 | + | 6.32858i | 0.207746 | + | 0.207746i | ||||
\(929\) | −17.5137 | −0.574606 | −0.287303 | − | 0.957840i | \(-0.592759\pi\) | ||||
−0.287303 | + | 0.957840i | \(0.592759\pi\) | |||||||
\(930\) | 2.06860 | − | 3.27906i | 0.0678322 | − | 0.107525i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.651418 | + | 0.651418i | −0.0213379 | + | 0.0213379i | ||||
\(933\) | −5.47479 | − | 5.47479i | −0.179236 | − | 0.179236i | ||||
\(934\) | 17.4500 | 0.570982 | ||||||||
\(935\) | −19.8633 | + | 4.49610i | −0.649598 | + | 0.147038i | ||||
\(936\) | 3.10026i | 0.101335i | ||||||||
\(937\) | 2.68964 | + | 2.68964i | 0.0878666 | + | 0.0878666i | 0.749674 | − | 0.661807i | \(-0.230210\pi\) |
−0.661807 | + | 0.749674i | \(0.730210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.0453i | 0.654153i | ||||||||
\(940\) | 3.00148 | + | 13.2602i | 0.0978975 | + | 0.432500i | ||||
\(941\) | 32.4048i | 1.05637i | 0.849131 | + | 0.528183i | \(0.177126\pi\) | ||||
−0.849131 | + | 0.528183i | \(0.822874\pi\) | |||||||
\(942\) | −10.7362 | + | 10.7362i | −0.349806 | + | 0.349806i | ||||
\(943\) | 27.2736 | − | 27.2736i | 0.888152 | − | 0.888152i | ||||
\(944\) | 4.20702 | 0.136927 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.7340 | 0.576582 | ||||||||
\(947\) | −27.1338 | + | 27.1338i | −0.881729 | + | 0.881729i | −0.993710 | − | 0.111982i | \(-0.964280\pi\) |
0.111982 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(948\) | −1.80676 | + | 1.80676i | −0.0586808 | + | 0.0586808i | ||||
\(949\) | − | 47.1857i | − | 1.53171i | ||||||
\(950\) | −19.8850 | − | 7.03843i | −0.645155 | − | 0.228357i | ||||
\(951\) | − | 2.98032i | − | 0.0966436i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2232 | + | 12.2232i | 0.395949 | + | 0.395949i | 0.876801 | − | 0.480853i | \(-0.159673\pi\) |
−0.480853 | + | 0.876801i | \(0.659673\pi\) | |||||||
\(954\) | − | 11.4337i | − | 0.370180i | ||||||
\(955\) | −19.2872 | + | 30.5732i | −0.624118 | + | 0.989326i | ||||
\(956\) | −25.3432 | −0.819656 | ||||||||
\(957\) | −12.5227 | − | 12.5227i | −0.404801 | − | 0.404801i | ||||
\(958\) | −22.4504 | + | 22.4504i | −0.725339 | + | 0.725339i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.18090 | + | 0.493652i | −0.0703881 | + | 0.0159325i | ||||
\(961\) | 27.9937 | 0.903023 | ||||||||
\(962\) | 6.07664 | + | 6.07664i | 0.195919 | + | 0.195919i | ||||
\(963\) | −4.27775 | − | 4.27775i | −0.137848 | − | 0.137848i | ||||
\(964\) | 21.1200 | 0.680230 | ||||||||
\(965\) | 47.5237 | − | 10.7571i | 1.52984 | − | 0.346284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7551 | − | 24.7551i | 0.796071 | − | 0.796071i | −0.186402 | − | 0.982474i | \(-0.559683\pi\) |
0.982474 | + | 0.186402i | \(0.0596827\pi\) | |||||||
\(968\) | 5.00952 | + | 5.00952i | 0.161012 | + | 0.161012i | ||||
\(969\) | −19.4183 | −0.623806 | ||||||||
\(970\) | 2.49765 | − | 3.95916i | 0.0801946 | − | 0.127121i | ||||
\(971\) | − | 10.2123i | − | 0.327729i | −0.986483 | − | 0.163864i | \(-0.947604\pi\) | ||
0.986483 | − | 0.163864i | \(-0.0523959\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.9080i | 0.958316i | ||||||||
\(975\) | 13.9903 | − | 6.67550i | 0.448048 | − | 0.213787i | ||||
\(976\) | 11.1200i | 0.355942i | ||||||||
\(977\) | −11.3259 | + | 11.3259i | −0.362348 | + | 0.362348i | −0.864677 | − | 0.502328i | \(-0.832477\pi\) |
0.502328 | + | 0.864677i | \(0.332477\pi\) | |||||||
\(978\) | −15.7848 | + | 15.7848i | −0.504741 | + | 0.504741i | ||||
\(979\) | −12.2522 | −0.391581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.74899 | −0.311261 | ||||||||
\(982\) | 1.11143 | − | 1.11143i | 0.0354670 | − | 0.0354670i | ||||
\(983\) | −5.39290 | + | 5.39290i | −0.172007 | + | 0.172007i | −0.787860 | − | 0.615854i | \(-0.788811\pi\) |
0.615854 | + | 0.787860i | \(0.288811\pi\) | |||||||
\(984\) | 6.55691i | 0.209027i | ||||||||
\(985\) | 0.438509 | + | 1.93728i | 0.0139721 | + | 0.0617269i | ||||
\(986\) | − | 41.1951i | − | 1.31192i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.24849 | − | 9.24849i | −0.294234 | − | 0.294234i | ||||
\(989\) | 52.7199i | 1.67640i | ||||||||
\(990\) | 4.31545 | − | 0.976815i | 0.137154 | − | 0.0310452i | ||||
\(991\) | 50.8757 | 1.61612 | 0.808060 | − | 0.589100i | \(-0.200517\pi\) | ||||
0.808060 | + | 0.589100i | \(0.200517\pi\) | |||||||
\(992\) | 1.22602 | + | 1.22602i | 0.0389263 | + | 0.0389263i | ||||
\(993\) | −19.6839 | + | 19.6839i | −0.624648 | + | 0.624648i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.4832 | + | 18.2026i | −0.364041 | + | 0.577062i | ||||
\(996\) | −13.4770 | −0.427036 | ||||||||
\(997\) | −28.7960 | − | 28.7960i | −0.911980 | − | 0.911980i | 0.0844482 | − | 0.996428i | \(-0.473087\pi\) |
−0.996428 | + | 0.0844482i | \(0.973087\pi\) | |||||||
\(998\) | −10.0830 | − | 10.0830i | −0.319172 | − | 0.319172i | ||||
\(999\) | −2.77192 | −0.0876995 |
(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 | 1470.2.m.d.1273.7 | 16 | ||
5.2 | odd | 4 | 1470.2.m.e.97.6 | 16 | |||
7.4 | even | 3 | 210.2.u.a.103.3 | ✓ | 16 | ||
7.5 | odd | 6 | 210.2.u.b.73.2 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.e.1273.6 | 16 | |||
21.5 | even | 6 | 630.2.bv.b.73.3 | 16 | |||
21.11 | odd | 6 | 630.2.bv.a.523.2 | 16 | |||
35.4 | even | 6 | 1050.2.bc.h.943.2 | 16 | |||
35.12 | even | 12 | 210.2.u.a.157.3 | yes | 16 | ||
35.18 | odd | 12 | 1050.2.bc.g.607.4 | 16 | |||
35.19 | odd | 6 | 1050.2.bc.g.493.4 | 16 | |||
35.27 | even | 4 | inner | 1470.2.m.d.97.7 | 16 | ||
35.32 | odd | 12 | 210.2.u.b.187.2 | yes | 16 | ||
35.33 | even | 12 | 1050.2.bc.h.157.2 | 16 | |||
105.32 | even | 12 | 630.2.bv.b.397.3 | 16 | |||
105.47 | odd | 12 | 630.2.bv.a.577.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.3 | ✓ | 16 | 7.4 | even | 3 | ||
210.2.u.a.157.3 | yes | 16 | 35.12 | even | 12 | ||
210.2.u.b.73.2 | yes | 16 | 7.5 | odd | 6 | ||
210.2.u.b.187.2 | yes | 16 | 35.32 | odd | 12 | ||
630.2.bv.a.523.2 | 16 | 21.11 | odd | 6 | |||
630.2.bv.a.577.2 | 16 | 105.47 | odd | 12 | |||
630.2.bv.b.73.3 | 16 | 21.5 | even | 6 | |||
630.2.bv.b.397.3 | 16 | 105.32 | even | 12 | |||
1050.2.bc.g.493.4 | 16 | 35.19 | odd | 6 | |||
1050.2.bc.g.607.4 | 16 | 35.18 | odd | 12 | |||
1050.2.bc.h.157.2 | 16 | 35.33 | even | 12 | |||
1050.2.bc.h.943.2 | 16 | 35.4 | even | 6 | |||
1470.2.m.d.97.7 | 16 | 35.27 | even | 4 | inner | ||
1470.2.m.d.1273.7 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.e.97.6 | 16 | 5.2 | odd | 4 | |||
1470.2.m.e.1273.6 | 16 | 7.6 | odd | 2 |