Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.293 |
Dual form | 450.2.p.e.407.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.707107 | − | 0.707107i | ||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 1.50000i | −0.353553 | − | 0.612372i | ||||
\(7\) | 4.57081 | + | 1.22474i | 1.72760 | + | 0.462910i | 0.979629 | − | 0.200817i | \(-0.0643596\pi\) |
0.747975 | + | 0.663727i | \(0.231026\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 1.73205i | 0.904534 | − | 0.522233i | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | −1.67303 | + | 0.448288i | −0.482963 | + | 0.129410i | ||||
\(13\) | −4.57081 | + | 1.22474i | −1.26771 | + | 0.339683i | −0.829155 | − | 0.559019i | \(-0.811178\pi\) |
−0.438560 | + | 0.898702i | \(0.644511\pi\) | |||||||
\(14\) | 2.36603 | − | 4.09808i | 0.632347 | − | 1.09526i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | −2.89778 | − | 0.776457i | −0.683013 | − | 0.183013i | ||||
\(19\) | 3.19615i | 0.733248i | 0.930369 | + | 0.366624i | \(0.119486\pi\) | ||||
−0.930369 | + | 0.366624i | \(0.880514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.09808 | − | 4.09808i | 1.54893 | − | 0.894274i | ||||
\(22\) | −0.896575 | − | 3.34607i | −0.191151 | − | 0.713384i | ||||
\(23\) | 0.568406 | + | 2.12132i | 0.118521 | + | 0.442326i | 0.999526 | − | 0.0307805i | \(-0.00979929\pi\) |
−0.881005 | + | 0.473106i | \(0.843133\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.73205i | 0.928032i | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | −3.34607 | − | 3.34607i | −0.632347 | − | 0.632347i | ||||
\(29\) | −5.36603 | − | 9.29423i | −0.996446 | − | 1.72589i | −0.571173 | − | 0.820830i | \(-0.693511\pi\) |
−0.425273 | − | 0.905065i | \(-0.639822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0980762 | + | 0.169873i | −0.0176150 | + | 0.0305101i | −0.874699 | − | 0.484667i | \(-0.838941\pi\) |
0.857084 | + | 0.515177i | \(0.172274\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 1.55291 | − | 5.79555i | 0.270328 | − | 1.00888i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −5.79555 | + | 5.79555i | −0.952783 | + | 0.952783i | −0.998934 | − | 0.0461511i | \(-0.985304\pi\) |
0.0461511 | + | 0.998934i | \(0.485304\pi\) | |||||||
\(38\) | 3.08725 | + | 0.827225i | 0.500817 | + | 0.134194i | ||||
\(39\) | −4.09808 | + | 7.09808i | −0.656217 | + | 1.13660i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 0.866025i | −0.234261 | − | 0.135250i | 0.378275 | − | 0.925693i | \(-0.376517\pi\) |
−0.612536 | + | 0.790443i | \(0.709851\pi\) | |||||||
\(42\) | −2.12132 | − | 7.91688i | −0.327327 | − | 1.22160i | ||||
\(43\) | 0.120118 | − | 0.448288i | 0.0183179 | − | 0.0683632i | −0.956162 | − | 0.292839i | \(-0.905400\pi\) |
0.974480 | + | 0.224475i | \(0.0720668\pi\) | |||||||
\(44\) | −3.46410 | −0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19615 | 0.323805 | ||||||||
\(47\) | −1.55291 | + | 5.79555i | −0.226516 | + | 0.845369i | 0.755276 | + | 0.655407i | \(0.227503\pi\) |
−0.981792 | + | 0.189961i | \(0.939164\pi\) | |||||||
\(48\) | 1.67303 | + | 0.448288i | 0.241481 | + | 0.0647048i | ||||
\(49\) | 13.3301 | + | 7.69615i | 1.90430 | + | 1.09945i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.57081 | + | 1.22474i | 0.633857 | + | 0.169842i | ||||
\(53\) | −5.79555 | + | 5.79555i | −0.796081 | + | 0.796081i | −0.982475 | − | 0.186394i | \(-0.940320\pi\) |
0.186394 | + | 0.982475i | \(0.440320\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.09808 | + | 2.36603i | −0.547628 | + | 0.316173i | ||||
\(57\) | 3.91447 | + | 3.91447i | 0.518484 | + | 0.518484i | ||||
\(58\) | −10.3664 | + | 2.77766i | −1.36117 | + | 0.364725i | ||||
\(59\) | 2.76795 | − | 4.79423i | 0.360356 | − | 0.624155i | −0.627663 | − | 0.778485i | \(-0.715988\pi\) |
0.988019 | + | 0.154330i | \(0.0493218\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | 0.138701 | + | 0.138701i | 0.0176150 | + | 0.0176150i | ||||
\(63\) | 3.67423 | − | 13.7124i | 0.462910 | − | 1.72760i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.19615 | − | 3.00000i | −0.639602 | − | 0.369274i | ||||
\(67\) | 1.43280 | + | 5.34727i | 0.175044 | + | 0.653273i | 0.996544 | + | 0.0830646i | \(0.0264708\pi\) |
−0.821500 | + | 0.570208i | \(0.806863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.29423 | + | 1.90192i | 0.396579 | + | 0.228965i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.26795i | − | 0.862547i | −0.902221 | − | 0.431273i | \(-0.858064\pi\) | ||
0.902221 | − | 0.431273i | \(-0.141936\pi\) | |||||||
\(72\) | 2.12132 | + | 2.12132i | 0.250000 | + | 0.250000i | ||||
\(73\) | 3.67423 | + | 3.67423i | 0.430037 | + | 0.430037i | 0.888641 | − | 0.458604i | \(-0.151650\pi\) |
−0.458604 | + | 0.888641i | \(0.651650\pi\) | |||||||
\(74\) | 4.09808 | + | 7.09808i | 0.476392 | + | 0.825135i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59808 | − | 2.76795i | 0.183312 | − | 0.317506i | ||||
\(77\) | 15.8338 | − | 4.24264i | 1.80442 | − | 0.483494i | ||||
\(78\) | 5.79555 | + | 5.79555i | 0.656217 | + | 0.656217i | ||||
\(79\) | −8.66025 | + | 5.00000i | −0.974355 | + | 0.562544i | −0.900561 | − | 0.434730i | \(-0.856844\pi\) |
−0.0737937 | + | 0.997274i | \(0.523511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −1.22474 | + | 1.22474i | −0.135250 | + | 0.135250i | ||||
\(83\) | 16.6102 | + | 4.45069i | 1.82321 | + | 0.488527i | 0.997176 | − | 0.0750978i | \(-0.0239269\pi\) |
0.826031 | + | 0.563625i | \(0.190594\pi\) | |||||||
\(84\) | −8.19615 | −0.894274 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.401924 | − | 0.232051i | −0.0433406 | − | 0.0250227i | ||||
\(87\) | −17.9551 | − | 4.81105i | −1.92499 | − | 0.515798i | ||||
\(88\) | −0.896575 | + | 3.34607i | −0.0955753 | + | 0.356692i | ||||
\(89\) | 8.66025 | 0.917985 | 0.458993 | − | 0.888440i | \(-0.348210\pi\) | ||||
0.458993 | + | 0.888440i | \(0.348210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3923 | −2.34735 | ||||||||
\(92\) | 0.568406 | − | 2.12132i | 0.0592604 | − | 0.221163i | ||||
\(93\) | 0.0879327 | + | 0.328169i | 0.00911820 | + | 0.0340296i | ||||
\(94\) | 5.19615 | + | 3.00000i | 0.535942 | + | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | − | 1.50000i | 0.0883883 | − | 0.153093i | ||||
\(97\) | 2.56961 | + | 0.688524i | 0.260904 | + | 0.0699091i | 0.386900 | − | 0.922122i | \(-0.373546\pi\) |
−0.125996 | + | 0.992031i | \(0.540213\pi\) | |||||||
\(98\) | 10.8840 | − | 10.8840i | 1.09945 | − | 1.09945i | ||||
\(99\) | −5.19615 | − | 9.00000i | −0.522233 | − | 0.904534i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.29423 | − | 3.63397i | 0.626299 | − | 0.361594i | −0.153018 | − | 0.988223i | \(-0.548899\pi\) |
0.779317 | + | 0.626629i | \(0.215566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0382 | − | 2.68973i | 0.989093 | − | 0.265027i | 0.272223 | − | 0.962234i | \(-0.412241\pi\) |
0.716869 | + | 0.697207i | \(0.245574\pi\) | |||||||
\(104\) | 2.36603 | − | 4.09808i | 0.232008 | − | 0.401849i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.09808 | + | 7.09808i | 0.398040 | + | 0.689426i | ||||
\(107\) | −7.91688 | − | 7.91688i | −0.765353 | − | 0.765353i | 0.211931 | − | 0.977285i | \(-0.432025\pi\) |
−0.977285 | + | 0.211931i | \(0.932025\pi\) | |||||||
\(108\) | 1.34486 | + | 5.01910i | 0.129410 | + | 0.482963i | ||||
\(109\) | − | 1.80385i | − | 0.172777i | −0.996262 | − | 0.0863886i | \(-0.972467\pi\) | ||
0.996262 | − | 0.0863886i | \(-0.0275327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.1962i | 1.34744i | ||||||||
\(112\) | 1.22474 | + | 4.57081i | 0.115728 | + | 0.431901i | ||||
\(113\) | 3.46618 | + | 12.9360i | 0.326071 | + | 1.21691i | 0.913231 | + | 0.407443i | \(0.133579\pi\) |
−0.587160 | + | 0.809471i | \(0.699754\pi\) | |||||||
\(114\) | 4.79423 | − | 2.76795i | 0.449021 | − | 0.259242i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.7321i | 0.996446i | ||||||||
\(117\) | 3.67423 | + | 13.7124i | 0.339683 | + | 1.26771i | ||||
\(118\) | −3.91447 | − | 3.91447i | −0.360356 | − | 0.360356i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 3.86370 | − | 1.03528i | 0.349803 | − | 0.0937295i | ||||
\(123\) | −2.89778 | + | 0.776457i | −0.261284 | + | 0.0700108i | ||||
\(124\) | 0.169873 | − | 0.0980762i | 0.0152550 | − | 0.00880750i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.2942 | − | 7.09808i | −1.09526 | − | 0.632347i | ||||
\(127\) | −5.79555 | + | 5.79555i | −0.514272 | + | 0.514272i | −0.915833 | − | 0.401560i | \(-0.868468\pi\) |
0.401560 | + | 0.915833i | \(0.368468\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | −0.401924 | − | 0.696152i | −0.0353874 | − | 0.0612928i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 3.46410i | −0.524222 | − | 0.302660i | 0.214438 | − | 0.976738i | \(-0.431208\pi\) |
−0.738661 | + | 0.674078i | \(0.764541\pi\) | |||||||
\(132\) | −4.24264 | + | 4.24264i | −0.369274 | + | 0.369274i | ||||
\(133\) | −3.91447 | + | 14.6090i | −0.339428 | + | 1.26676i | ||||
\(134\) | 5.53590 | 0.478229 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46618 | − | 12.9360i | 0.296136 | − | 1.10519i | −0.644175 | − | 0.764878i | \(-0.722799\pi\) |
0.940311 | − | 0.340317i | \(-0.110534\pi\) | |||||||
\(138\) | 2.68973 | − | 2.68973i | 0.228965 | − | 0.228965i | ||||
\(139\) | 6.92820 | + | 4.00000i | 0.587643 | + | 0.339276i | 0.764165 | − | 0.645021i | \(-0.223151\pi\) |
−0.176522 | + | 0.984297i | \(0.556485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.19615 | + | 9.00000i | 0.437595 | + | 0.757937i | ||||
\(142\) | −7.02030 | − | 1.88108i | −0.589130 | − | 0.157857i | ||||
\(143\) | −11.5911 | + | 11.5911i | −0.969297 | + | 0.969297i | ||||
\(144\) | 2.59808 | − | 1.50000i | 0.216506 | − | 0.125000i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.50000 | − | 2.59808i | 0.372423 | − | 0.215018i | ||||
\(147\) | 25.7518 | − | 6.90018i | 2.12397 | − | 0.569117i | ||||
\(148\) | 7.91688 | − | 2.12132i | 0.650763 | − | 0.174371i | ||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | −2.26002 | − | 2.26002i | −0.183312 | − | 0.183312i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 16.3923i | − | 1.32093i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.09808 | − | 4.09808i | 0.568301 | − | 0.328109i | ||||
\(157\) | −5.13922 | − | 19.1798i | −0.410154 | − | 1.53072i | −0.794348 | − | 0.607463i | \(-0.792187\pi\) |
0.384194 | − | 0.923253i | \(-0.374480\pi\) | |||||||
\(158\) | 2.58819 | + | 9.65926i | 0.205905 | + | 0.768449i | ||||
\(159\) | 14.1962i | 1.12583i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | −2.32937 | + | 8.69333i | −0.183013 | + | 0.683013i | ||||
\(163\) | −10.1261 | − | 10.1261i | −0.793140 | − | 0.793140i | 0.188864 | − | 0.982003i | \(-0.439520\pi\) |
−0.982003 | + | 0.188864i | \(0.939520\pi\) | |||||||
\(164\) | 0.866025 | + | 1.50000i | 0.0676252 | + | 0.117130i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.59808 | − | 14.8923i | 0.667340 | − | 1.15587i | ||||
\(167\) | −15.8338 | + | 4.24264i | −1.22525 | + | 0.328305i | −0.812729 | − | 0.582642i | \(-0.802019\pi\) |
−0.412523 | + | 0.910947i | \(0.635352\pi\) | |||||||
\(168\) | −2.12132 | + | 7.91688i | −0.163663 | + | 0.610800i | ||||
\(169\) | 8.13397 | − | 4.69615i | 0.625690 | − | 0.361242i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.58846 | 0.733248 | ||||||||
\(172\) | −0.328169 | + | 0.328169i | −0.0250227 | + | 0.0250227i | ||||
\(173\) | −15.8338 | − | 4.24264i | −1.20382 | − | 0.322562i | −0.399484 | − | 0.916740i | \(-0.630811\pi\) |
−0.804334 | + | 0.594178i | \(0.797477\pi\) | |||||||
\(174\) | −9.29423 | + | 16.0981i | −0.704594 | + | 1.22039i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | + | 1.73205i | 0.226134 | + | 0.130558i | ||||
\(177\) | −2.48168 | − | 9.26174i | −0.186534 | − | 0.696155i | ||||
\(178\) | 2.24144 | − | 8.36516i | 0.168003 | − | 0.626995i | ||||
\(179\) | −22.8564 | −1.70837 | −0.854184 | − | 0.519971i | \(-0.825943\pi\) | ||||
−0.854184 | + | 0.519971i | \(0.825943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3923 | −0.921113 | −0.460556 | − | 0.887630i | \(-0.652350\pi\) | ||||
−0.460556 | + | 0.887630i | \(0.652350\pi\) | |||||||
\(182\) | −5.79555 | + | 21.6293i | −0.429595 | + | 1.60327i | ||||
\(183\) | 6.69213 | + | 1.79315i | 0.494697 | + | 0.132554i | ||||
\(184\) | −1.90192 | − | 1.09808i | −0.140212 | − | 0.0809513i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.339746 | 0.0249114 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | −12.2942 | − | 21.2942i | −0.894274 | − | 1.54893i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 1.73205i | 0.217072 | − | 0.125327i | −0.387522 | − | 0.921861i | \(-0.626669\pi\) |
0.604594 | + | 0.796534i | \(0.293335\pi\) | |||||||
\(192\) | −1.22474 | − | 1.22474i | −0.0883883 | − | 0.0883883i | ||||
\(193\) | 10.6945 | − | 2.86559i | 0.769809 | − | 0.206270i | 0.147522 | − | 0.989059i | \(-0.452870\pi\) |
0.622287 | + | 0.782789i | \(0.286204\pi\) | |||||||
\(194\) | 1.33013 | − | 2.30385i | 0.0954976 | − | 0.165407i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.69615 | − | 13.3301i | −0.549725 | − | 0.952152i | ||||
\(197\) | 10.0382 | + | 10.0382i | 0.715192 | + | 0.715192i | 0.967617 | − | 0.252425i | \(-0.0812280\pi\) |
−0.252425 | + | 0.967617i | \(0.581228\pi\) | |||||||
\(198\) | −10.0382 | + | 2.68973i | −0.713384 | + | 0.191151i | ||||
\(199\) | − | 20.3923i | − | 1.44557i | −0.691072 | − | 0.722786i | \(-0.742861\pi\) | ||
0.691072 | − | 0.722786i | \(-0.257139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.30385 | + | 4.79423i | 0.585708 | + | 0.338159i | ||||
\(202\) | −1.88108 | − | 7.02030i | −0.132353 | − | 0.493947i | ||||
\(203\) | −13.1440 | − | 49.0542i | −0.922530 | − | 3.44293i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 10.3923i | − | 0.724066i | ||||||
\(207\) | 6.36396 | − | 1.70522i | 0.442326 | − | 0.118521i | ||||
\(208\) | −3.34607 | − | 3.34607i | −0.232008 | − | 0.232008i | ||||
\(209\) | 5.53590 | + | 9.58846i | 0.382926 | + | 0.663247i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.598076 | + | 1.03590i | −0.0411733 | + | 0.0713142i | −0.885878 | − | 0.463919i | \(-0.846443\pi\) |
0.844704 | + | 0.535233i | \(0.179776\pi\) | |||||||
\(212\) | 7.91688 | − | 2.12132i | 0.543733 | − | 0.145693i | ||||
\(213\) | −8.90138 | − | 8.90138i | −0.609913 | − | 0.609913i | ||||
\(214\) | −9.69615 | + | 5.59808i | −0.662815 | + | 0.382677i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.19615 | 0.353553 | ||||||||
\(217\) | −0.656339 | + | 0.656339i | −0.0445552 | + | 0.0445552i | ||||
\(218\) | −1.74238 | − | 0.466870i | −0.118009 | − | 0.0316204i | ||||
\(219\) | 9.00000 | 0.608164 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 13.7124 | + | 3.67423i | 0.920318 | + | 0.246598i | ||||
\(223\) | 0.656339 | − | 2.44949i | 0.0439517 | − | 0.164030i | −0.940462 | − | 0.339899i | \(-0.889607\pi\) |
0.984414 | + | 0.175869i | \(0.0562736\pi\) | |||||||
\(224\) | 4.73205 | 0.316173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3923 | 0.890843 | ||||||||
\(227\) | 3.31388 | − | 12.3676i | 0.219950 | − | 0.820864i | −0.764415 | − | 0.644724i | \(-0.776972\pi\) |
0.984365 | − | 0.176140i | \(-0.0563611\pi\) | |||||||
\(228\) | −1.43280 | − | 5.34727i | −0.0948892 | − | 0.354131i | ||||
\(229\) | 5.02628 | + | 2.90192i | 0.332146 | + | 0.191765i | 0.656793 | − | 0.754071i | \(-0.271912\pi\) |
−0.324648 | + | 0.945835i | \(0.605246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.1962 | − | 24.5885i | 0.934038 | − | 1.61780i | ||||
\(232\) | 10.3664 | + | 2.77766i | 0.680585 | + | 0.182362i | ||||
\(233\) | −3.25813 | + | 3.25813i | −0.213447 | + | 0.213447i | −0.805730 | − | 0.592283i | \(-0.798227\pi\) |
0.592283 | + | 0.805730i | \(0.298227\pi\) | |||||||
\(234\) | 14.1962 | 0.928032 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.79423 | + | 2.76795i | −0.312078 | + | 0.180178i | ||||
\(237\) | −4.48288 | + | 16.7303i | −0.291194 | + | 1.08675i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.90192 | − | 3.29423i | 0.123025 | − | 0.213086i | −0.797934 | − | 0.602745i | \(-0.794074\pi\) |
0.920959 | + | 0.389659i | \(0.127407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.69615 | − | 8.13397i | −0.302506 | − | 0.523955i | 0.674197 | − | 0.738551i | \(-0.264490\pi\) |
−0.976703 | + | 0.214596i | \(0.931156\pi\) | |||||||
\(242\) | −0.707107 | − | 0.707107i | −0.0454545 | − | 0.0454545i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.707107 | + | 0.707107i | ||||
\(244\) | − | 4.00000i | − | 0.256074i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.00000i | 0.191273i | ||||||||
\(247\) | −3.91447 | − | 14.6090i | −0.249072 | − | 0.929549i | ||||
\(248\) | −0.0507680 | − | 0.189469i | −0.00322377 | − | 0.0120313i | ||||
\(249\) | 25.7942 | − | 14.8923i | 1.63464 | − | 0.943761i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.00000i | − | 0.568075i | −0.958813 | − | 0.284037i | \(-0.908326\pi\) | ||
0.958813 | − | 0.284037i | \(-0.0916740\pi\) | |||||||
\(252\) | −10.0382 | + | 10.0382i | −0.632347 | + | 0.632347i | ||||
\(253\) | 5.37945 | + | 5.37945i | 0.338203 | + | 0.338203i | ||||
\(254\) | 4.09808 | + | 7.09808i | 0.257136 | + | 0.445373i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −24.5271 | + | 6.57201i | −1.52996 | + | 0.409951i | −0.923005 | − | 0.384787i | \(-0.874275\pi\) |
−0.606952 | + | 0.794738i | \(0.707608\pi\) | |||||||
\(258\) | −0.776457 | + | 0.208051i | −0.0483401 | + | 0.0129527i | ||||
\(259\) | −33.5885 | + | 19.3923i | −2.08709 | + | 1.20498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.8827 | + | 16.0981i | −1.72589 | + | 0.996446i | ||||
\(262\) | −4.89898 | + | 4.89898i | −0.302660 | + | 0.302660i | ||||
\(263\) | −12.1595 | − | 3.25813i | −0.749788 | − | 0.200905i | −0.136364 | − | 0.990659i | \(-0.543542\pi\) |
−0.613424 | + | 0.789754i | \(0.710208\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.0981 | + | 7.56218i | 0.803095 | + | 0.463667i | ||||
\(267\) | 10.6066 | − | 10.6066i | 0.649113 | − | 0.649113i | ||||
\(268\) | 1.43280 | − | 5.34727i | 0.0875219 | − | 0.326636i | ||||
\(269\) | 10.0526 | 0.612915 | 0.306458 | − | 0.951884i | \(-0.400856\pi\) | ||||
0.306458 | + | 0.951884i | \(0.400856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.5885 | 1.61513 | 0.807567 | − | 0.589776i | \(-0.200784\pi\) | ||||
0.807567 | + | 0.589776i | \(0.200784\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.4249 | + | 27.4249i | −1.65983 | + | 1.65983i | ||||
\(274\) | −11.5981 | − | 6.69615i | −0.700665 | − | 0.404529i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.90192 | − | 3.29423i | −0.114482 | − | 0.198289i | ||||
\(277\) | 18.8516 | + | 5.05128i | 1.13269 | + | 0.303502i | 0.776007 | − | 0.630725i | \(-0.217242\pi\) |
0.356679 | + | 0.934227i | \(0.383909\pi\) | |||||||
\(278\) | 5.65685 | − | 5.65685i | 0.339276 | − | 0.339276i | ||||
\(279\) | 0.509619 | + | 0.294229i | 0.0305101 | + | 0.0176150i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | − | 5.19615i | 0.536895 | − | 0.309976i | −0.206925 | − | 0.978357i | \(-0.566345\pi\) |
0.743820 | + | 0.668380i | \(0.233012\pi\) | |||||||
\(282\) | 10.0382 | − | 2.68973i | 0.597766 | − | 0.160171i | ||||
\(283\) | −3.79435 | + | 1.01669i | −0.225551 | + | 0.0604362i | −0.369824 | − | 0.929102i | \(-0.620582\pi\) |
0.144274 | + | 0.989538i | \(0.453915\pi\) | |||||||
\(284\) | −3.63397 | + | 6.29423i | −0.215637 | + | 0.373494i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.19615 | + | 14.1962i | 0.484649 | + | 0.839436i | ||||
\(287\) | −5.79555 | − | 5.79555i | −0.342101 | − | 0.342101i | ||||
\(288\) | −0.776457 | − | 2.89778i | −0.0457532 | − | 0.170753i | ||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.99038 | − | 2.30385i | 0.233920 | − | 0.135054i | ||||
\(292\) | −1.34486 | − | 5.01910i | −0.0787022 | − | 0.293720i | ||||
\(293\) | 0.984508 | + | 3.67423i | 0.0575156 | + | 0.214651i | 0.988703 | − | 0.149891i | \(-0.0478922\pi\) |
−0.931187 | + | 0.364542i | \(0.881226\pi\) | |||||||
\(294\) | − | 26.6603i | − | 1.55486i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 8.19615i | − | 0.476392i | ||||||
\(297\) | −17.3867 | − | 4.65874i | −1.00888 | − | 0.270328i | ||||
\(298\) | 12.7279 | + | 12.7279i | 0.737309 | + | 0.737309i | ||||
\(299\) | −5.19615 | − | 9.00000i | −0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.09808 | − | 1.90192i | 0.0632921 | − | 0.109625i | ||||
\(302\) | 7.72741 | − | 2.07055i | 0.444662 | − | 0.119147i | ||||
\(303\) | 3.25813 | − | 12.1595i | 0.187175 | − | 0.698546i | ||||
\(304\) | −2.76795 | + | 1.59808i | −0.158753 | + | 0.0916560i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.44949 | + | 2.44949i | −0.139800 | + | 0.139800i | −0.773543 | − | 0.633743i | \(-0.781517\pi\) |
0.633743 | + | 0.773543i | \(0.281517\pi\) | |||||||
\(308\) | −15.8338 | − | 4.24264i | −0.902212 | − | 0.241747i | ||||
\(309\) | 9.00000 | − | 15.5885i | 0.511992 | − | 0.886796i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.58846 | − | 5.53590i | −0.543712 | − | 0.313912i | 0.202870 | − | 0.979206i | \(-0.434973\pi\) |
−0.746582 | + | 0.665294i | \(0.768306\pi\) | |||||||
\(312\) | −2.12132 | − | 7.91688i | −0.120096 | − | 0.448205i | ||||
\(313\) | 5.34727 | − | 19.9563i | 0.302245 | − | 1.12800i | −0.633045 | − | 0.774115i | \(-0.718195\pi\) |
0.935291 | − | 0.353880i | \(-0.115138\pi\) | |||||||
\(314\) | −19.8564 | −1.12056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −1.70522 | + | 6.36396i | −0.0957746 | + | 0.357436i | −0.997136 | − | 0.0756325i | \(-0.975902\pi\) |
0.901361 | + | 0.433068i | \(0.142569\pi\) | |||||||
\(318\) | 13.7124 | + | 3.67423i | 0.768955 | + | 0.206041i | ||||
\(319\) | −32.1962 | − | 18.5885i | −1.80264 | − | 1.04075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.3923 | −1.08237 | ||||||||
\(322\) | 10.0382 | + | 2.68973i | 0.559407 | + | 0.149893i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.79423 | + | 4.50000i | 0.433013 | + | 0.250000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4019 | + | 7.16025i | −0.686879 | + | 0.396570i | ||||
\(327\) | −2.20925 | − | 2.20925i | −0.122172 | − | 0.122172i | ||||
\(328\) | 1.67303 | − | 0.448288i | 0.0923778 | − | 0.0247525i | ||||
\(329\) | −14.1962 | + | 24.5885i | −0.782659 | + | 1.35561i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.79423 | + | 11.7679i | 0.373445 | + | 0.646825i | 0.990093 | − | 0.140414i | \(-0.0448433\pi\) |
−0.616648 | + | 0.787239i | \(0.711510\pi\) | |||||||
\(332\) | −12.1595 | − | 12.1595i | −0.667340 | − | 0.667340i | ||||
\(333\) | 17.3867 | + | 17.3867i | 0.952783 | + | 0.952783i | ||||
\(334\) | 16.3923i | 0.896947i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.09808 | + | 4.09808i | 0.387232 | + | 0.223568i | ||||
\(337\) | −5.31508 | − | 19.8362i | −0.289531 | − | 1.08054i | −0.945464 | − | 0.325725i | \(-0.894391\pi\) |
0.655933 | − | 0.754819i | \(-0.272275\pi\) | |||||||
\(338\) | −2.43091 | − | 9.07227i | −0.132224 | − | 0.493466i | ||||
\(339\) | 20.0885 | + | 11.5981i | 1.09106 | + | 0.629921i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.679492i | 0.0367966i | ||||||||
\(342\) | 2.48168 | − | 9.26174i | 0.134194 | − | 0.500817i | ||||
\(343\) | 28.0812 | + | 28.0812i | 1.51624 | + | 1.51624i | ||||
\(344\) | 0.232051 | + | 0.401924i | 0.0125113 | + | 0.0216703i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.19615 | + | 14.1962i | −0.440628 | + | 0.763190i | ||||
\(347\) | −8.48528 | + | 2.27362i | −0.455514 | + | 0.122055i | −0.479278 | − | 0.877663i | \(-0.659102\pi\) |
0.0237644 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(348\) | 13.1440 | + | 13.1440i | 0.704594 | + | 0.704594i | ||||
\(349\) | −1.73205 | + | 1.00000i | −0.0927146 | + | 0.0535288i | −0.545640 | − | 0.838019i | \(-0.683714\pi\) |
0.452926 | + | 0.891548i | \(0.350380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.2942 | + | 12.2942i | 1.13660 | + | 0.656217i | ||||
\(352\) | 2.44949 | − | 2.44949i | 0.130558 | − | 0.130558i | ||||
\(353\) | 14.4889 | + | 3.88229i | 0.771166 | + | 0.206633i | 0.622886 | − | 0.782312i | \(-0.285960\pi\) |
0.148279 | + | 0.988946i | \(0.452627\pi\) | |||||||
\(354\) | −9.58846 | −0.509621 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | − | 4.33013i | −0.397499 | − | 0.229496i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.91567 | + | 22.0776i | −0.312653 | + | 1.16684i | ||||
\(359\) | 35.3205 | 1.86415 | 0.932073 | − | 0.362272i | \(-0.117999\pi\) | ||||
0.932073 | + | 0.362272i | \(0.117999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.78461 | 0.462348 | ||||||||
\(362\) | −3.20736 | + | 11.9700i | −0.168575 | + | 0.629132i | ||||
\(363\) | −0.448288 | − | 1.67303i | −0.0235290 | − | 0.0878114i | ||||
\(364\) | 19.3923 | + | 11.1962i | 1.01643 | + | 0.586838i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.46410 | − | 6.00000i | 0.181071 | − | 0.313625i | ||||
\(367\) | 4.00240 | + | 1.07244i | 0.208924 | + | 0.0559810i | 0.361763 | − | 0.932270i | \(-0.382175\pi\) |
−0.152839 | + | 0.988251i | \(0.548842\pi\) | |||||||
\(368\) | −1.55291 | + | 1.55291i | −0.0809513 | + | 0.0809513i | ||||
\(369\) | −2.59808 | + | 4.50000i | −0.135250 | + | 0.234261i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.5885 | + | 19.3923i | −1.74383 | + | 1.00680i | ||||
\(372\) | 0.0879327 | − | 0.328169i | 0.00455910 | − | 0.0170148i | ||||
\(373\) | 22.5259 | − | 6.03579i | 1.16635 | − | 0.312521i | 0.376848 | − | 0.926275i | \(-0.377008\pi\) |
0.789498 | + | 0.613754i | \(0.210341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | 35.9101 | + | 35.9101i | 1.84947 | + | 1.84947i | ||||
\(378\) | −23.7506 | + | 6.36396i | −1.22160 | + | 0.327327i | ||||
\(379\) | − | 0.392305i | − | 0.0201513i | −0.999949 | − | 0.0100757i | \(-0.996793\pi\) | ||
0.999949 | − | 0.0100757i | \(-0.00320724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1962i | 0.727291i | ||||||||
\(382\) | −0.896575 | − | 3.34607i | −0.0458728 | − | 0.171200i | ||||
\(383\) | 1.40061 | + | 5.22715i | 0.0715678 | + | 0.267095i | 0.992433 | − | 0.122786i | \(-0.0391829\pi\) |
−0.920865 | + | 0.389881i | \(0.872516\pi\) | |||||||
\(384\) | −1.50000 | + | 0.866025i | −0.0765466 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.0718i | − | 0.563540i | ||||||
\(387\) | −1.34486 | − | 0.360355i | −0.0683632 | − | 0.0183179i | ||||
\(388\) | −1.88108 | − | 1.88108i | −0.0954976 | − | 0.0954976i | ||||
\(389\) | −5.19615 | − | 9.00000i | −0.263455 | − | 0.456318i | 0.703702 | − | 0.710495i | \(-0.251529\pi\) |
−0.967158 | + | 0.254177i | \(0.918196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −14.8678 | + | 3.98382i | −0.750939 | + | 0.201213i | ||||
\(393\) | −11.5911 | + | 3.10583i | −0.584694 | + | 0.156668i | ||||
\(394\) | 12.2942 | − | 7.09808i | 0.619374 | − | 0.357596i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.3923i | 0.522233i | ||||||||
\(397\) | 10.9348 | − | 10.9348i | 0.548800 | − | 0.548800i | −0.377293 | − | 0.926094i | \(-0.623145\pi\) |
0.926094 | + | 0.377293i | \(0.123145\pi\) | |||||||
\(398\) | −19.6975 | − | 5.27792i | −0.987344 | − | 0.264558i | ||||
\(399\) | 13.0981 | + | 22.6865i | 0.655724 | + | 1.13575i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | + | 5.19615i | 0.449439 | + | 0.259483i | 0.707593 | − | 0.706620i | \(-0.249781\pi\) |
−0.258154 | + | 0.966104i | \(0.583114\pi\) | |||||||
\(402\) | 6.78006 | − | 6.78006i | 0.338159 | − | 0.338159i | ||||
\(403\) | 0.240237 | − | 0.896575i | 0.0119670 | − | 0.0446616i | ||||
\(404\) | −7.26795 | −0.361594 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.7846 | −2.52040 | ||||||||
\(407\) | −7.34847 | + | 27.4249i | −0.364250 | + | 1.35940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5263 | + | 10.6962i | 0.916066 | + | 0.528891i | 0.882378 | − | 0.470542i | \(-0.155941\pi\) |
0.0336878 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5981 | − | 20.0885i | −0.572091 | − | 0.990891i | ||||
\(412\) | −10.0382 | − | 2.68973i | −0.494546 | − | 0.132513i | ||||
\(413\) | 18.5235 | − | 18.5235i | 0.911481 | − | 0.911481i | ||||
\(414\) | − | 6.58846i | − | 0.323805i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.09808 | + | 2.36603i | −0.200925 | + | 0.116004i | ||||
\(417\) | 13.3843 | − | 3.58630i | 0.655430 | − | 0.175622i | ||||
\(418\) | 10.6945 | − | 2.86559i | 0.523087 | − | 0.140161i | ||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2942 | − | 19.5622i | −0.550447 | − | 0.953402i | −0.998242 | − | 0.0592661i | \(-0.981124\pi\) |
0.447795 | − | 0.894136i | \(-0.352209\pi\) | |||||||
\(422\) | 0.845807 | + | 0.845807i | 0.0411733 | + | 0.0411733i | ||||
\(423\) | 17.3867 | + | 4.65874i | 0.845369 | + | 0.226516i | ||||
\(424\) | − | 8.19615i | − | 0.398040i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.9019 | + | 6.29423i | −0.528200 | + | 0.304956i | ||||
\(427\) | 4.89898 | + | 18.2832i | 0.237078 | + | 0.884788i | ||||
\(428\) | 2.89778 | + | 10.8147i | 0.140069 | + | 0.522746i | ||||
\(429\) | 28.3923i | 1.37079i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.1244i | 1.01752i | 0.860907 | + | 0.508762i | \(0.169897\pi\) | ||||
−0.860907 | + | 0.508762i | \(0.830103\pi\) | |||||||
\(432\) | 1.34486 | − | 5.01910i | 0.0647048 | − | 0.241481i | ||||
\(433\) | −12.0716 | − | 12.0716i | −0.580123 | − | 0.580123i | 0.354814 | − | 0.934937i | \(-0.384544\pi\) |
−0.934937 | + | 0.354814i | \(0.884544\pi\) | |||||||
\(434\) | 0.464102 | + | 0.803848i | 0.0222776 | + | 0.0385859i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.901924 | + | 1.56218i | −0.0431943 | + | 0.0748147i | ||||
\(437\) | −6.78006 | + | 1.81671i | −0.324334 | + | 0.0869051i | ||||
\(438\) | 2.32937 | − | 8.69333i | 0.111302 | − | 0.415383i | ||||
\(439\) | 1.22243 | − | 0.705771i | 0.0583435 | − | 0.0336846i | −0.470545 | − | 0.882376i | \(-0.655942\pi\) |
0.528888 | + | 0.848692i | \(0.322609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.0885 | − | 39.9904i | 1.09945 | − | 1.90430i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0382 | + | 2.68973i | 0.476929 | + | 0.127793i | 0.489272 | − | 0.872131i | \(-0.337262\pi\) |
−0.0123433 | + | 0.999924i | \(0.503929\pi\) | |||||||
\(444\) | 7.09808 | − | 12.2942i | 0.336860 | − | 0.583458i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.19615 | − | 1.26795i | −0.103991 | − | 0.0600391i | ||||
\(447\) | 8.06918 | + | 30.1146i | 0.381659 | + | 1.42437i | ||||
\(448\) | 1.22474 | − | 4.57081i | 0.0578638 | − | 0.215950i | ||||
\(449\) | −30.1244 | −1.42166 | −0.710828 | − | 0.703366i | \(-0.751680\pi\) | ||||
−0.710828 | + | 0.703366i | \(0.751680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 3.46618 | − | 12.9360i | 0.163036 | − | 0.608457i | ||||
\(453\) | 13.3843 | + | 3.58630i | 0.628847 | + | 0.168499i | ||||
\(454\) | −11.0885 | − | 6.40192i | −0.520407 | − | 0.300457i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.53590 | −0.259242 | ||||||||
\(457\) | −26.6484 | − | 7.14042i | −1.24656 | − | 0.334015i | −0.425553 | − | 0.904933i | \(-0.639920\pi\) |
−0.821007 | + | 0.570919i | \(0.806587\pi\) | |||||||
\(458\) | 4.10394 | − | 4.10394i | 0.191765 | − | 0.191765i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.70577 | + | 5.02628i | −0.405468 | + | 0.234097i | −0.688841 | − | 0.724913i | \(-0.741880\pi\) |
0.283373 | + | 0.959010i | \(0.408547\pi\) | |||||||
\(462\) | −20.0764 | − | 20.0764i | −0.934038 | − | 0.934038i | ||||
\(463\) | 2.12132 | − | 0.568406i | 0.0985861 | − | 0.0264161i | −0.209189 | − | 0.977875i | \(-0.567082\pi\) |
0.307775 | + | 0.951459i | \(0.400416\pi\) | |||||||
\(464\) | 5.36603 | − | 9.29423i | 0.249111 | − | 0.431474i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.30385 | + | 3.99038i | 0.106724 | + | 0.184851i | ||||
\(467\) | −6.78006 | − | 6.78006i | −0.313744 | − | 0.313744i | 0.532614 | − | 0.846358i | \(-0.321210\pi\) |
−0.846358 | + | 0.532614i | \(0.821210\pi\) | |||||||
\(468\) | 3.67423 | − | 13.7124i | 0.169842 | − | 0.633857i | ||||
\(469\) | 26.1962i | 1.20963i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.7846 | − | 17.1962i | −1.37240 | − | 0.792357i | ||||
\(472\) | 1.43280 | + | 5.34727i | 0.0659498 | + | 0.246128i | ||||
\(473\) | −0.416102 | − | 1.55291i | −0.0191324 | − | 0.0714031i | ||||
\(474\) | 15.0000 | + | 8.66025i | 0.688973 | + | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.3867 | + | 17.3867i | 0.796081 | + | 0.796081i | ||||
\(478\) | −2.68973 | − | 2.68973i | −0.123025 | − | 0.123025i | ||||
\(479\) | 1.56218 | + | 2.70577i | 0.0713777 | + | 0.123630i | 0.899505 | − | 0.436910i | \(-0.143927\pi\) |
−0.828128 | + | 0.560540i | \(0.810594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.3923 | − | 33.5885i | 0.884213 | − | 1.53150i | ||||
\(482\) | −9.07227 | + | 2.43091i | −0.413231 | + | 0.110725i | ||||
\(483\) | 12.7279 | + | 12.7279i | 0.579141 | + | 0.579141i | ||||
\(484\) | −0.866025 | + | 0.500000i | −0.0393648 | + | 0.0227273i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.79423 | + | 13.5000i | 0.353553 | + | 0.612372i | ||||
\(487\) | −11.3509 | + | 11.3509i | −0.514357 | + | 0.514357i | −0.915858 | − | 0.401501i | \(-0.868489\pi\) |
0.401501 | + | 0.915858i | \(0.368489\pi\) | |||||||
\(488\) | −3.86370 | − | 1.03528i | −0.174902 | − | 0.0468648i | ||||
\(489\) | −24.8038 | −1.12167 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.2058 | − | 9.35641i | −0.731356 | − | 0.422249i | 0.0875619 | − | 0.996159i | \(-0.472092\pi\) |
−0.818918 | + | 0.573910i | \(0.805426\pi\) | |||||||
\(492\) | 2.89778 | + | 0.776457i | 0.130642 | + | 0.0350054i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −15.1244 | −0.680477 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.196152 | −0.00880750 | ||||||||
\(497\) | 8.90138 | − | 33.2204i | 0.399282 | − | 1.49014i | ||||
\(498\) | −7.70882 | − | 28.7697i | −0.345441 | − | 1.28920i | ||||
\(499\) | −10.0359 | − | 5.79423i | −0.449269 | − | 0.259385i | 0.258253 | − | 0.966077i | \(-0.416853\pi\) |
−0.707521 | + | 0.706692i | \(0.750187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.1962 | + | 24.5885i | −0.634237 | + | 1.09853i | ||||
\(502\) | −8.69333 | − | 2.32937i | −0.388002 | − | 0.103965i | ||||
\(503\) | −3.82654 | + | 3.82654i | −0.170617 | + | 0.170617i | −0.787250 | − | 0.616633i | \(-0.788496\pi\) |
0.616633 | + | 0.787250i | \(0.288496\pi\) | |||||||
\(504\) | 7.09808 | + | 12.2942i | 0.316173 | + | 0.547628i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.58846 | − | 3.80385i | 0.292893 | − | 0.169102i | ||||
\(507\) | 4.21046 | − | 15.7136i | 0.186993 | − | 0.697867i | ||||
\(508\) | 7.91688 | − | 2.12132i | 0.351255 | − | 0.0941184i | ||||
\(509\) | −10.3923 | + | 18.0000i | −0.460631 | + | 0.797836i | −0.998992 | − | 0.0448779i | \(-0.985710\pi\) |
0.538362 | + | 0.842714i | \(0.319043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2942 | + | 21.2942i | 0.543865 | + | 0.942001i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 11.7434 | − | 11.7434i | 0.518484 | − | 0.518484i | ||||
\(514\) | 25.3923i | 1.12001i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.803848i | 0.0353874i | ||||||||
\(517\) | 5.37945 | + | 20.0764i | 0.236588 | + | 0.882959i | ||||
\(518\) | 10.0382 | + | 37.4631i | 0.441053 | + | 1.64603i | ||||
\(519\) | −24.5885 | + | 14.1962i | −1.07931 | + | 0.623142i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.78461i | − | 0.121996i | −0.998138 | − | 0.0609980i | \(-0.980572\pi\) | ||
0.998138 | − | 0.0609980i | \(-0.0194283\pi\) | |||||||
\(522\) | 8.33298 | + | 31.0991i | 0.364725 | + | 1.36117i | ||||
\(523\) | −23.9909 | − | 23.9909i | −1.04905 | − | 1.04905i | −0.998733 | − | 0.0503137i | \(-0.983978\pi\) |
−0.0503137 | − | 0.998733i | \(-0.516022\pi\) | |||||||
\(524\) | 3.46410 | + | 6.00000i | 0.151330 | + | 0.262111i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.29423 | + | 10.9019i | −0.274441 | + | 0.475346i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.79555 | − | 1.55291i | 0.252219 | − | 0.0675819i | ||||
\(529\) | 15.7417 | − | 9.08846i | 0.684420 | − | 0.395150i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.3827 | − | 8.30385i | −0.624155 | − | 0.360356i | ||||
\(532\) | 10.6945 | − | 10.6945i | 0.463667 | − | 0.463667i | ||||
\(533\) | 7.91688 | + | 2.12132i | 0.342918 | + | 0.0918846i | ||||
\(534\) | −7.50000 | − | 12.9904i | −0.324557 | − | 0.562149i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.79423 | − | 2.76795i | −0.207079 | − | 0.119557i | ||||
\(537\) | −27.9933 | + | 27.9933i | −1.20800 | + | 1.20800i | ||||
\(538\) | 2.60179 | − | 9.71003i | 0.112171 | − | 0.418629i | ||||
\(539\) | 53.3205 | 2.29668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.39230 | −0.360813 | −0.180407 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180407 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(542\) | 6.88160 | − | 25.6825i | 0.295590 | − | 1.10316i | ||||
\(543\) | −15.1774 | + | 15.1774i | −0.651325 | + | 0.651325i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.3923 | + | 33.5885i | 0.829914 | + | 1.43745i | ||||
\(547\) | 38.8079 | + | 10.3986i | 1.65931 | + | 0.444610i | 0.962197 | − | 0.272354i | \(-0.0878023\pi\) |
0.697110 | + | 0.716964i | \(0.254469\pi\) | |||||||
\(548\) | −9.46979 | + | 9.46979i | −0.404529 | + | 0.404529i | ||||
\(549\) | 10.3923 | − | 6.00000i | 0.443533 | − | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.7058 | − | 17.1506i | 1.26551 | − | 0.730642i | ||||
\(552\) | −3.67423 | + | 0.984508i | −0.156386 | + | 0.0419035i | ||||
\(553\) | −45.7081 | + | 12.2474i | −1.94371 | + | 0.520814i | ||||
\(554\) | 9.75833 | − | 16.9019i | 0.414592 | − | 0.718094i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | − | 6.92820i | −0.169638 | − | 0.293821i | ||||
\(557\) | −3.10583 | − | 3.10583i | −0.131598 | − | 0.131598i | 0.638240 | − | 0.769838i | \(-0.279663\pi\) |
−0.769838 | + | 0.638240i | \(0.779663\pi\) | |||||||
\(558\) | 0.416102 | − | 0.416102i | 0.0176150 | − | 0.0176150i | ||||
\(559\) | 2.19615i | 0.0928874i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.68973 | − | 10.0382i | −0.113459 | − | 0.423436i | ||||
\(563\) | −0.624153 | − | 2.32937i | −0.0263049 | − | 0.0981713i | 0.951525 | − | 0.307570i | \(-0.0995159\pi\) |
−0.977830 | + | 0.209399i | \(0.932849\pi\) | |||||||
\(564\) | − | 10.3923i | − | 0.437595i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.92820i | 0.165115i | ||||||||
\(567\) | −41.1373 | − | 11.0227i | −1.72760 | − | 0.462910i | ||||
\(568\) | 5.13922 | + | 5.13922i | 0.215637 | + | 0.215637i | ||||
\(569\) | 12.4641 | + | 21.5885i | 0.522522 | + | 0.905035i | 0.999657 | + | 0.0262048i | \(0.00834220\pi\) |
−0.477134 | + | 0.878830i | \(0.658324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.59808 | + | 16.6244i | −0.401667 | + | 0.695708i | −0.993927 | − | 0.110039i | \(-0.964902\pi\) |
0.592260 | + | 0.805747i | \(0.298236\pi\) | |||||||
\(572\) | 15.8338 | − | 4.24264i | 0.662042 | − | 0.177394i | ||||
\(573\) | 1.55291 | − | 5.79555i | 0.0648739 | − | 0.242113i | ||||
\(574\) | −7.09808 | + | 4.09808i | −0.296268 | + | 0.171050i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 15.9217 | − | 15.9217i | 0.662828 | − | 0.662828i | −0.293217 | − | 0.956046i | \(-0.594726\pi\) |
0.956046 | + | 0.293217i | \(0.0947260\pi\) | |||||||
\(578\) | −16.4207 | − | 4.39992i | −0.683013 | − | 0.183013i | ||||
\(579\) | 9.58846 | − | 16.6077i | 0.398483 | − | 0.690192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 70.4711 | + | 40.6865i | 2.92364 | + | 1.68796i | ||||
\(582\) | −1.19256 | − | 4.45069i | −0.0494332 | − | 0.184487i | ||||
\(583\) | −7.34847 | + | 27.4249i | −0.304342 | + | 1.13582i | ||||
\(584\) | −5.19615 | −0.215018 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.80385 | 0.157135 | ||||||||
\(587\) | 1.13681 | − | 4.24264i | 0.0469213 | − | 0.175113i | −0.938489 | − | 0.345310i | \(-0.887774\pi\) |
0.985410 | + | 0.170197i | \(0.0544405\pi\) | |||||||
\(588\) | −25.7518 | − | 6.90018i | −1.06199 | − | 0.284559i | ||||
\(589\) | −0.542940 | − | 0.313467i | −0.0223715 | − | 0.0129162i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5885 | 1.01143 | ||||||||
\(592\) | −7.91688 | − | 2.12132i | −0.325382 | − | 0.0871857i | ||||
\(593\) | 14.8492 | − | 14.8492i | 0.609785 | − | 0.609785i | −0.333105 | − | 0.942890i | \(-0.608096\pi\) |
0.942890 | + | 0.333105i | \(0.108096\pi\) | |||||||
\(594\) | −9.00000 | + | 15.5885i | −0.369274 | + | 0.639602i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.5885 | − | 9.00000i | 0.638528 | − | 0.368654i | ||||
\(597\) | −24.9754 | − | 24.9754i | −1.02217 | − | 1.02217i | ||||
\(598\) | −10.0382 | + | 2.68973i | −0.410492 | + | 0.109991i | ||||
\(599\) | 3.63397 | − | 6.29423i | 0.148480 | − | 0.257175i | −0.782186 | − | 0.623045i | \(-0.785895\pi\) |
0.930666 | + | 0.365870i | \(0.119229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.3923 | + | 24.9282i | 0.587074 | + | 1.01684i | 0.994613 | + | 0.103655i | \(0.0330537\pi\) |
−0.407539 | + | 0.913188i | \(0.633613\pi\) | |||||||
\(602\) | −1.55291 | − | 1.55291i | −0.0632921 | − | 0.0632921i | ||||
\(603\) | 16.0418 | − | 4.29839i | 0.653273 | − | 0.175044i | ||||
\(604\) | − | 8.00000i | − | 0.325515i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.9019 | − | 6.29423i | −0.442860 | − | 0.255686i | ||||
\(607\) | 12.5756 | + | 46.9328i | 0.510429 | + | 1.90495i | 0.415864 | + | 0.909427i | \(0.363479\pi\) |
0.0945643 | + | 0.995519i | \(0.469854\pi\) | |||||||
\(608\) | 0.827225 | + | 3.08725i | 0.0335484 | + | 0.125204i | ||||
\(609\) | −76.1769 | − | 43.9808i | −3.08684 | − | 1.78219i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.3923i | − | 1.14863i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0382 | − | 10.0382i | −0.405439 | − | 0.405439i | 0.474706 | − | 0.880145i | \(-0.342555\pi\) |
−0.880145 | + | 0.474706i | \(0.842555\pi\) | |||||||
\(614\) | 1.73205 | + | 3.00000i | 0.0698999 | + | 0.121070i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.19615 | + | 14.1962i | −0.330232 | + | 0.571979i | ||||
\(617\) | 11.3831 | − | 3.05008i | 0.458265 | − | 0.122792i | −0.0222993 | − | 0.999751i | \(-0.507099\pi\) |
0.480564 | + | 0.876960i | \(0.340432\pi\) | |||||||
\(618\) | −12.7279 | − | 12.7279i | −0.511992 | − | 0.511992i | ||||
\(619\) | 41.2128 | − | 23.7942i | 1.65648 | − | 0.956371i | 0.682164 | − | 0.731200i | \(-0.261039\pi\) |
0.974319 | − | 0.225171i | \(-0.0722941\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.70577 | − | 9.88269i | 0.228965 | − | 0.396579i | ||||
\(622\) | −7.82894 | + | 7.82894i | −0.313912 | + | 0.313912i | ||||
\(623\) | 39.5844 | + | 10.6066i | 1.58591 | + | 0.424945i | ||||
\(624\) | −8.19615 | −0.328109 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.8923 | − | 10.3301i | −0.715120 | − | 0.412875i | ||||
\(627\) | 18.5235 | + | 4.96335i | 0.739756 | + | 0.198217i | ||||
\(628\) | −5.13922 | + | 19.1798i | −0.205077 | + | 0.765358i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.784610 | −0.0312348 | −0.0156174 | − | 0.999878i | \(-0.504971\pi\) | ||||
−0.0156174 | + | 0.999878i | \(0.504971\pi\) | |||||||
\(632\) | 2.58819 | − | 9.65926i | 0.102953 | − | 0.384225i | ||||
\(633\) | 0.536220 | + | 2.00120i | 0.0213128 | + | 0.0795406i | ||||
\(634\) | 5.70577 | + | 3.29423i | 0.226605 | + | 0.130831i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.09808 | − | 12.2942i | 0.281457 | − | 0.487498i | ||||
\(637\) | −70.3553 | − | 18.8516i | −2.78758 | − | 0.746929i | ||||
\(638\) | −26.2880 | + | 26.2880i | −1.04075 | + | 1.04075i | ||||
\(639\) | −21.8038 | −0.862547 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.0885 | + | 18.5263i | −1.26742 | + | 0.731744i | −0.974499 | − | 0.224393i | \(-0.927960\pi\) |
−0.292919 | + | 0.956137i | \(0.594627\pi\) | |||||||
\(642\) | −5.01910 | + | 18.7315i | −0.198088 | + | 0.739274i | ||||
\(643\) | −36.1182 | + | 9.67784i | −1.42436 | + | 0.381657i | −0.887029 | − | 0.461713i | \(-0.847235\pi\) |
−0.537333 | + | 0.843370i | \(0.680568\pi\) | |||||||
\(644\) | 5.19615 | − | 9.00000i | 0.204757 | − | 0.354650i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0382 | − | 10.0382i | −0.394642 | − | 0.394642i | 0.481696 | − | 0.876338i | \(-0.340021\pi\) |
−0.876338 | + | 0.481696i | \(0.840021\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | − | 19.1769i | − | 0.752760i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.60770i | 0.0630105i | ||||||||
\(652\) | 3.70642 | + | 13.8325i | 0.145155 | + | 0.541724i | ||||
\(653\) | −2.12132 | − | 7.91688i | −0.0830137 | − | 0.309811i | 0.911917 | − | 0.410375i | \(-0.134602\pi\) |
−0.994931 | + | 0.100564i | \(0.967935\pi\) | |||||||
\(654\) | −2.70577 | + | 1.56218i | −0.105804 | + | 0.0610860i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.73205i | − | 0.0676252i | ||||||
\(657\) | 11.0227 | − | 11.0227i | 0.430037 | − | 0.430037i | ||||
\(658\) | 20.0764 | + | 20.0764i | 0.782659 | + | 0.782659i | ||||
\(659\) | −20.0885 | − | 34.7942i | −0.782535 | − | 1.35539i | −0.930461 | − | 0.366392i | \(-0.880593\pi\) |
0.147925 | − | 0.988999i | \(-0.452740\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5885 | − | 33.9282i | 0.761903 | − | 1.31965i | −0.179966 | − | 0.983673i | \(-0.557599\pi\) |
0.941869 | − | 0.335981i | \(-0.109068\pi\) | |||||||
\(662\) | 13.1254 | − | 3.51695i | 0.510135 | − | 0.136690i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.8923 | + | 8.59808i | −0.577934 | + | 0.333670i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.2942 | − | 12.2942i | 0.825135 | − | 0.476392i | ||||
\(667\) | 16.6660 | − | 16.6660i | 0.645308 | − | 0.645308i | ||||
\(668\) | 15.8338 | + | 4.24264i | 0.612626 | + | 0.164153i | ||||
\(669\) | −2.19615 | − | 3.80385i | −0.0849082 | − | 0.147065i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | + | 6.92820i | 0.463255 | + | 0.267460i | ||||
\(672\) | 5.79555 | − | 5.79555i | 0.223568 | − | 0.223568i | ||||
\(673\) | 5.79555 | − | 21.6293i | 0.223402 | − | 0.833748i | −0.759636 | − | 0.650348i | \(-0.774623\pi\) |
0.983038 | − | 0.183400i | \(-0.0587104\pi\) | |||||||
\(674\) | −20.5359 | −0.791013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.39230 | −0.361242 | ||||||||
\(677\) | 6.36396 | − | 23.7506i | 0.244587 | − | 0.912811i | −0.729004 | − | 0.684510i | \(-0.760016\pi\) |
0.973591 | − | 0.228301i | \(-0.0733170\pi\) | |||||||
\(678\) | 16.4022 | − | 16.4022i | 0.629921 | − | 0.629921i | ||||
\(679\) | 10.9019 | + | 6.29423i | 0.418377 | + | 0.241550i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0885 | − | 19.2058i | −0.424911 | − | 0.735967i | ||||
\(682\) | 0.656339 | + | 0.175865i | 0.0251325 | + | 0.00673424i | ||||
\(683\) | −5.94786 | + | 5.94786i | −0.227588 | + | 0.227588i | −0.811685 | − | 0.584096i | \(-0.801449\pi\) |
0.584096 | + | 0.811685i | \(0.301449\pi\) | |||||||
\(684\) | −8.30385 | − | 4.79423i | −0.317506 | − | 0.183312i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 34.3923 | − | 19.8564i | 1.31310 | − | 0.758121i | ||||
\(687\) | 9.71003 | − | 2.60179i | 0.370461 | − | 0.0992646i | ||||
\(688\) | 0.448288 | − | 0.120118i | 0.0170908 | − | 0.00457947i | ||||
\(689\) | 19.3923 | − | 33.5885i | 0.738788 | − | 1.27962i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7942 | − | 37.7487i | −0.829092 | − | 1.43603i | −0.898752 | − | 0.438458i | \(-0.855525\pi\) |
0.0696602 | − | 0.997571i | \(-0.477808\pi\) | |||||||
\(692\) | 11.5911 | + | 11.5911i | 0.440628 | + | 0.440628i | ||||
\(693\) | −12.7279 | − | 47.5013i | −0.483494 | − | 1.80442i | ||||
\(694\) | 8.78461i | 0.333459i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.0981 | − | 9.29423i | 0.610196 | − | 0.352297i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.517638 | + | 1.93185i | 0.0195929 | + | 0.0731217i | ||||
\(699\) | 7.98076i | 0.301860i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.5359i | − | 0.549013i | −0.961585 | − | 0.274507i | \(-0.911485\pi\) | ||
0.961585 | − | 0.274507i | \(-0.0885145\pi\) | |||||||
\(702\) | 17.3867 | − | 17.3867i | 0.656217 | − | 0.656217i | ||||
\(703\) | −18.5235 | − | 18.5235i | −0.698626 | − | 0.698626i | ||||
\(704\) | −1.73205 | − | 3.00000i | −0.0652791 | − | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.50000 | − | 12.9904i | 0.282266 | − | 0.488899i | ||||
\(707\) | 33.2204 | − | 8.90138i | 1.24938 | − | 0.334771i | ||||
\(708\) | −2.48168 | + | 9.26174i | −0.0932671 | + | 0.348077i | ||||
\(709\) | 31.3468 | − | 18.0981i | 1.17725 | − | 0.679688i | 0.221876 | − | 0.975075i | \(-0.428782\pi\) |
0.955378 | + | 0.295387i | \(0.0954487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | −6.12372 | + | 6.12372i | −0.229496 | + | 0.229496i | ||||
\(713\) | −0.416102 | − | 0.111494i | −0.0155831 | − | 0.00417549i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7942 | + | 11.4282i | 0.739745 | + | 0.427092i | ||||
\(717\) | −1.70522 | − | 6.36396i | −0.0636825 | − | 0.237666i | ||||
\(718\) | 9.14162 | − | 34.1170i | 0.341162 | − | 1.27323i | ||||
\(719\) | 14.8756 | 0.554768 | 0.277384 | − | 0.960759i | \(-0.410533\pi\) | ||||
0.277384 | + | 0.960759i | \(0.410533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.1769 | 1.83144 | ||||||||
\(722\) | 2.27362 | − | 8.48528i | 0.0846155 | − | 0.315789i | ||||
\(723\) | −15.7136 | − | 4.21046i | −0.584396 | − | 0.156589i | ||||
\(724\) | 10.7321 | + | 6.19615i | 0.398854 | + | 0.230278i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.73205 | −0.0642824 | ||||||||
\(727\) | −6.69213 | − | 1.79315i | −0.248197 | − | 0.0665043i | 0.132575 | − | 0.991173i | \(-0.457675\pi\) |
−0.380773 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(728\) | 15.8338 | − | 15.8338i | 0.586838 | − | 0.586838i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.89898 | − | 4.89898i | −0.181071 | − | 0.181071i | ||||
\(733\) | −13.1440 | + | 3.52193i | −0.485486 | + | 0.130085i | −0.493256 | − | 0.869884i | \(-0.664193\pi\) |
0.00777015 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(734\) | 2.07180 | − | 3.58846i | 0.0764714 | − | 0.132452i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.09808 | + | 1.90192i | 0.0404756 | + | 0.0701058i | ||||
\(737\) | 13.5601 | + | 13.5601i | 0.499494 | + | 0.499494i | ||||
\(738\) | 3.67423 | + | 3.67423i | 0.135250 | + | 0.135250i | ||||
\(739\) | 19.5885i | 0.720573i | 0.932842 | + | 0.360287i | \(0.117321\pi\) | ||||
−0.932842 | + | 0.360287i | \(0.882679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.6865 | − | 13.0981i | −0.833411 | − | 0.481170i | ||||
\(742\) | 10.0382 | + | 37.4631i | 0.368514 | + | 1.37531i | ||||
\(743\) | 8.63759 | + | 32.2359i | 0.316882 | + | 1.18262i | 0.922224 | + | 0.386655i | \(0.126370\pi\) |
−0.605342 | + | 0.795965i | \(0.706964\pi\) | |||||||
\(744\) | −0.294229 | − | 0.169873i | −0.0107869 | − | 0.00622785i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 23.3205i | − | 0.853824i | ||||||
\(747\) | 13.3521 | − | 49.8306i | 0.488527 | − | 1.82321i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.4904 | − | 45.8827i | −0.967937 | − | 1.67652i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.29423 | + | 9.16987i | −0.193189 | + | 0.334613i | −0.946305 | − | 0.323274i | \(-0.895216\pi\) |
0.753116 | + | 0.657887i | \(0.228550\pi\) | |||||||
\(752\) | −5.79555 | + | 1.55291i | −0.211342 | + | 0.0566290i | ||||
\(753\) | −11.0227 | − | 11.0227i | −0.401690 | − | 0.401690i | ||||
\(754\) | 43.9808 | − | 25.3923i | 1.60168 | − | 0.924733i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 24.5885i | 0.894274i | ||||||||
\(757\) | −27.6651 | + | 27.6651i | −1.00551 | + | 1.00551i | −0.00552030 | + | 0.999985i | \(0.501757\pi\) |
−0.999985 | + | 0.00552030i | \(0.998243\pi\) | |||||||
\(758\) | −0.378937 | − | 0.101536i | −0.0137636 | − | 0.00368795i | ||||
\(759\) | 13.1769 | 0.478292 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.0885 | − | 23.7224i | −1.48946 | − | 0.859937i | −0.489528 | − | 0.871988i | \(-0.662831\pi\) |
−0.999927 | + | 0.0120501i | \(0.996164\pi\) | |||||||
\(762\) | 13.7124 | + | 3.67423i | 0.496749 | + | 0.133103i | ||||
\(763\) | 2.20925 | − | 8.24504i | 0.0799803 | − | 0.298491i | ||||
\(764\) | −3.46410 | −0.125327 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.41154 | 0.195527 | ||||||||
\(767\) | −6.78006 | + | 25.3035i | −0.244814 | + | 0.913658i | ||||
\(768\) | 0.448288 | + | 1.67303i | 0.0161762 | + | 0.0603704i | ||||
\(769\) | −10.9186 | − | 6.30385i | −0.393734 | − | 0.227323i | 0.290043 | − | 0.957014i | \(-0.406331\pi\) |
−0.683777 | + | 0.729691i | \(0.739664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.9904 | + | 38.0885i | −0.791964 | + | 1.37172i | ||||
\(772\) | −10.6945 | − | 2.86559i | −0.384905 | − | 0.103135i | ||||
\(773\) | −35.9101 | + | 35.9101i | −1.29160 | + | 1.29160i | −0.357800 | + | 0.933798i | \(0.616473\pi\) |
−0.933798 | + | 0.357800i | \(0.883527\pi\) | |||||||
\(774\) | −0.696152 | + | 1.20577i | −0.0250227 | + | 0.0433406i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.30385 | + | 1.33013i | −0.0827033 | + | 0.0477488i | ||||
\(777\) | −17.3867 | + | 64.8879i | −0.623743 | + | 2.32784i | ||||
\(778\) | −10.0382 | + | 2.68973i | −0.359887 | + | 0.0964314i | ||||
\(779\) | 2.76795 | − | 4.79423i | 0.0991721 | − | 0.171771i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5885 | − | 21.8038i | −0.450450 | − | 0.780203i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.4331 | + | 53.8652i | −0.515798 | + | 1.92499i | ||||
\(784\) | 15.3923i | 0.549725i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.0000i | 0.428026i | ||||||||
\(787\) | −4.48288 | − | 16.7303i | −0.159797 | − | 0.596372i | −0.998647 | − | 0.0520081i | \(-0.983438\pi\) |
0.838849 | − | 0.544364i | \(-0.183229\pi\) | |||||||
\(788\) | −3.67423 | − | 13.7124i | −0.130889 | − | 0.488485i | ||||
\(789\) | −18.8827 | + | 10.9019i | −0.672241 | + | 0.388119i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.3731i | 2.25329i | ||||||||
\(792\) | 10.0382 | + | 2.68973i | 0.356692 | + | 0.0955753i | ||||
\(793\) | −13.3843 | − | 13.3843i | −0.475289 | − | 0.475289i | ||||
\(794\) | −7.73205 | − | 13.3923i | −0.274400 | − | 0.475275i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.1962 | + | 17.6603i | −0.361393 | + | 0.625951i | ||||
\(797\) | 39.5844 | − | 10.6066i | 1.40215 | − | 0.375705i | 0.523034 | − | 0.852312i | \(-0.324800\pi\) |
0.879117 | + | 0.476607i | \(0.158133\pi\) | |||||||
\(798\) | 25.3035 | − | 6.78006i | 0.895736 | − | 0.240012i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 25.9808i | − | 0.917985i | ||||||
\(802\) | 7.34847 | − | 7.34847i | 0.259483 | − | 0.259483i | ||||
\(803\) | 17.3867 | + | 4.65874i | 0.613562 | + | 0.164403i | ||||
\(804\) | −4.79423 | − | 8.30385i | −0.169079 | − | 0.292854i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.803848 | − | 0.464102i | −0.0283143 | − | 0.0163473i | ||||
\(807\) | 12.3118 | − | 12.3118i | 0.433397 | − | 0.433397i | ||||
\(808\) | −1.88108 | + | 7.02030i | −0.0661763 | + | 0.246973i | ||||
\(809\) | 1.73205 | 0.0608957 | 0.0304478 | − | 0.999536i | \(-0.490307\pi\) | ||||
0.0304478 | + | 0.999536i | \(0.490307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.3731 | 1.20700 | 0.603501 | − | 0.797362i | \(-0.293772\pi\) | ||||
0.603501 | + | 0.797362i | \(0.293772\pi\) | |||||||
\(812\) | −13.1440 | + | 49.0542i | −0.461265 | + | 1.72146i | ||||
\(813\) | 32.5641 | − | 32.5641i | 1.14207 | − | 1.14207i | ||||
\(814\) | 24.5885 | + | 14.1962i | 0.861825 | + | 0.497575i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.43280 | + | 0.383917i | 0.0501272 | + | 0.0134315i | ||||
\(818\) | 15.1266 | − | 15.1266i | 0.528891 | − | 0.528891i | ||||
\(819\) | 67.1769i | 2.34735i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5885 | − | 7.26795i | 0.439340 | − | 0.253653i | −0.263978 | − | 0.964529i | \(-0.585034\pi\) |
0.703318 | + | 0.710876i | \(0.251701\pi\) | |||||||
\(822\) | −22.4058 | + | 6.00361i | −0.781491 | + | 0.209400i | ||||
\(823\) | −39.2562 | + | 10.5187i | −1.36839 | + | 0.366658i | −0.866889 | − | 0.498502i | \(-0.833884\pi\) |
−0.501497 | + | 0.865160i | \(0.667217\pi\) | |||||||
\(824\) | −5.19615 | + | 9.00000i | −0.181017 | + | 0.313530i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.0981 | − | 22.6865i | −0.455740 | − | 0.789365i | ||||
\(827\) | −0.568406 | − | 0.568406i | −0.0197654 | − | 0.0197654i | 0.697155 | − | 0.716920i | \(-0.254449\pi\) |
−0.716920 | + | 0.697155i | \(0.754449\pi\) | |||||||
\(828\) | −6.36396 | − | 1.70522i | −0.221163 | − | 0.0592604i | ||||
\(829\) | 28.5885i | 0.992918i | 0.868060 | + | 0.496459i | \(0.165367\pi\) | ||||
−0.868060 | + | 0.496459i | \(0.834633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2750 | − | 16.9019i | 1.01554 | − | 0.586321i | ||||
\(832\) | 1.22474 | + | 4.57081i | 0.0424604 | + | 0.158464i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 13.8564i | − | 0.479808i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 11.0718i | − | 0.382926i | ||||||
\(837\) | 0.984508 | − | 0.263798i | 0.0340296 | − | 0.00911820i | ||||
\(838\) | −6.36396 | − | 6.36396i | −0.219839 | − | 0.219839i | ||||
\(839\) | 6.75833 | + | 11.7058i | 0.233323 | + | 0.404128i | 0.958784 | − | 0.284136i | \(-0.0917066\pi\) |
−0.725461 | + | 0.688264i | \(0.758373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0885 | + | 74.6314i | −1.48581 | + | 2.57350i | ||||
\(842\) | −21.8188 | + | 5.84632i | −0.751925 | + | 0.201478i | ||||
\(843\) | 4.65874 | − | 17.3867i | 0.160456 | − | 0.598829i | ||||
\(844\) | 1.03590 | − | 0.598076i | 0.0356571 | − | 0.0205866i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.00000 | − | 15.5885i | 0.309426 | − | 0.535942i | ||||
\(847\) | 3.34607 | − | 3.34607i | 0.114972 | − | 0.114972i | ||||
\(848\) | −7.91688 | − | 2.12132i | −0.271867 | − | 0.0728464i | ||||
\(849\) | −3.40192 | + | 5.89230i | −0.116754 | + | 0.202223i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5885 | − | 9.00000i | −0.534365 | − | 0.308516i | ||||
\(852\) | 3.25813 | + | 12.1595i | 0.111622 | + | 0.416578i | ||||
\(853\) | −4.83461 | + | 18.0430i | −0.165534 | + | 0.617781i | 0.832438 | + | 0.554119i | \(0.186945\pi\) |
−0.997972 | + | 0.0636620i | \(0.979722\pi\) | |||||||
\(854\) | 18.9282 | 0.647710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1962 | 0.382677 | ||||||||
\(857\) | 10.8147 | − | 40.3608i | 0.369422 | − | 1.37870i | −0.491905 | − | 0.870649i | \(-0.663699\pi\) |
0.861327 | − | 0.508051i | \(-0.169634\pi\) | |||||||
\(858\) | 27.4249 | + | 7.34847i | 0.936269 | + | 0.250873i | ||||
\(859\) | −36.0167 | − | 20.7942i | −1.22887 | − | 0.709490i | −0.262079 | − | 0.965047i | \(-0.584408\pi\) |
−0.966794 | + | 0.255557i | \(0.917741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.1962 | −0.483804 | ||||||||
\(862\) | 20.4046 | + | 5.46739i | 0.694982 | + | 0.186220i | ||||
\(863\) | 33.2204 | − | 33.2204i | 1.13084 | − | 1.13084i | 0.140798 | − | 0.990038i | \(-0.455033\pi\) |
0.990038 | − | 0.140798i | \(-0.0449667\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.7846 | + | 8.53590i | −0.502401 | + | 0.290062i | ||||
\(867\) | −20.8207 | − | 20.8207i | −0.707107 | − | 0.707107i | ||||
\(868\) | 0.896575 | − | 0.240237i | 0.0304318 | − | 0.00815416i | ||||
\(869\) | −17.3205 | + | 30.0000i | −0.587558 | + | 1.01768i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0981 | − | 22.6865i | −0.443811 | − | 0.768704i | ||||
\(872\) | 1.27551 | + | 1.27551i | 0.0431943 | + | 0.0431943i | ||||
\(873\) | 2.06557 | − | 7.70882i | 0.0699091 | − | 0.260904i | ||||
\(874\) | 7.01924i | 0.237429i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.79423 | − | 4.50000i | −0.263343 | − | 0.152041i | ||||
\(877\) | −9.55772 | − | 35.6699i | −0.322741 | − | 1.20449i | −0.916563 | − | 0.399890i | \(-0.869048\pi\) |
0.593822 | − | 0.804597i | \(-0.297618\pi\) | |||||||
\(878\) | −0.365334 | − | 1.36345i | −0.0123294 | − | 0.0460141i | ||||
\(879\) | 5.70577 | + | 3.29423i | 0.192451 | + | 0.111112i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.6795i | 0.629328i | 0.949203 | + | 0.314664i | \(0.101892\pi\) | ||||
−0.949203 | + | 0.314664i | \(0.898108\pi\) | |||||||
\(882\) | −32.6520 | − | 32.6520i | −1.09945 | − | 1.09945i | ||||
\(883\) | 18.2832 | + | 18.2832i | 0.615280 | + | 0.615280i | 0.944317 | − | 0.329037i | \(-0.106724\pi\) |
−0.329037 | + | 0.944317i | \(0.606724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.19615 | − | 9.00000i | 0.174568 | − | 0.302361i | ||||
\(887\) | −10.0382 | + | 2.68973i | −0.337050 | + | 0.0903122i | −0.423374 | − | 0.905955i | \(-0.639154\pi\) |
0.0863246 | + | 0.996267i | \(0.472488\pi\) | |||||||
\(888\) | −10.0382 | − | 10.0382i | −0.336860 | − | 0.336860i | ||||
\(889\) | −33.5885 | + | 19.3923i | −1.12652 | + | 0.650397i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.0000 | + | 15.5885i | −0.904534 | + | 0.522233i | ||||
\(892\) | −1.79315 | + | 1.79315i | −0.0600391 | + | 0.0600391i | ||||
\(893\) | −18.5235 | − | 4.96335i | −0.619865 | − | 0.166092i | ||||
\(894\) | 31.1769 | 1.04271 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.09808 | − | 2.36603i | −0.136907 | − | 0.0790434i | ||||
\(897\) | −17.3867 | − | 4.65874i | −0.580524 | − | 0.155551i | ||||
\(898\) | −7.79676 | + | 29.0979i | −0.260181 | + | 0.971009i | ||||
\(899\) | 2.10512 | 0.0702096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1.55291 | + | 5.79555i | −0.0517064 | + | 0.192971i | ||||
\(903\) | −0.984508 | − | 3.67423i | −0.0327624 | − | 0.122271i | ||||
\(904\) | −11.5981 | − | 6.69615i | −0.385746 | − | 0.222711i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.92820 | − | 12.0000i | 0.230174 | − | 0.398673i | ||||
\(907\) | 31.8756 | + | 8.54103i | 1.05841 | + | 0.283600i | 0.745723 | − | 0.666256i | \(-0.232104\pi\) |
0.312687 | + | 0.949856i | \(0.398771\pi\) | |||||||
\(908\) | −9.05369 | + | 9.05369i | −0.300457 | + | 0.300457i | ||||
\(909\) | −10.9019 | − | 18.8827i | −0.361594 | − | 0.626299i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8827 | − | 19.5622i | 1.12258 | − | 0.648124i | 0.180524 | − | 0.983571i | \(-0.442221\pi\) |
0.942059 | + | 0.335447i | \(0.108887\pi\) | |||||||
\(912\) | −1.43280 | + | 5.34727i | −0.0474446 | + | 0.177066i | ||||
\(913\) | 57.5394 | − | 15.4176i | 1.90428 | − | 0.510250i | ||||
\(914\) | −13.7942 | + | 23.8923i | −0.456273 | + | 0.790287i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.90192 | − | 5.02628i | −0.0958823 | − | 0.166073i | ||||
\(917\) | −23.1822 | − | 23.1822i | −0.765544 | − | 0.765544i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.5885i | 1.93265i | 0.257316 | + | 0.966327i | \(0.417162\pi\) | ||||
−0.257316 | + | 0.966327i | \(0.582838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000i | 0.197707i | ||||||||
\(922\) | 2.60179 | + | 9.71003i | 0.0856855 | + | 0.319783i | ||||
\(923\) | 8.90138 | + | 33.2204i | 0.292993 | + | 1.09346i | ||||
\(924\) | −24.5885 | + | 14.1962i | −0.808901 | + | 0.467019i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 2.19615i | − | 0.0721700i | ||||||
\(927\) | −8.06918 | − | 30.1146i | −0.265027 | − | 0.989093i | ||||
\(928\) | −7.58871 | − | 7.58871i | −0.249111 | − | 0.249111i | ||||
\(929\) | 15.9282 | + | 27.5885i | 0.522587 | + | 0.905148i | 0.999655 | + | 0.0262811i | \(0.00836650\pi\) |
−0.477067 | + | 0.878867i | \(0.658300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.5981 | + | 42.6051i | −0.806169 | + | 1.39633i | ||||
\(932\) | 4.45069 | − | 1.19256i | 0.145787 | − | 0.0390636i | ||||
\(933\) | −18.5235 | + | 4.96335i | −0.606431 | + | 0.162493i | ||||
\(934\) | −8.30385 | + | 4.79423i | −0.271710 | + | 0.156872i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.2942 | − | 7.09808i | −0.401849 | − | 0.232008i | ||||
\(937\) | 17.7148 | − | 17.7148i | 0.578718 | − | 0.578718i | −0.355832 | − | 0.934550i | \(-0.615802\pi\) |
0.934550 | + | 0.355832i | \(0.115802\pi\) | |||||||
\(938\) | 25.3035 | + | 6.78006i | 0.826190 | + | 0.221377i | ||||
\(939\) | −17.8923 | − | 30.9904i | −0.583893 | − | 1.01133i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.88269 | + | 5.70577i | 0.322166 | + | 0.186003i | 0.652358 | − | 0.757911i | \(-0.273780\pi\) |
−0.330191 | + | 0.943914i | \(0.607113\pi\) | |||||||
\(942\) | −24.3190 | + | 24.3190i | −0.792357 | + | 0.792357i | ||||
\(943\) | 0.984508 | − | 3.67423i | 0.0320600 | − | 0.119650i | ||||
\(944\) | 5.53590 | 0.180178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.60770 | −0.0522707 | ||||||||
\(947\) | −10.9670 | + | 40.9292i | −0.356378 | + | 1.33002i | 0.522363 | + | 0.852723i | \(0.325051\pi\) |
−0.878741 | + | 0.477298i | \(0.841616\pi\) | |||||||
\(948\) | 12.2474 | − | 12.2474i | 0.397779 | − | 0.397779i | ||||
\(949\) | −21.2942 | − | 12.2942i | −0.691240 | − | 0.399088i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.70577 | + | 9.88269i | 0.185022 | + | 0.320468i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.8647 | − | 13.8647i | 0.449123 | − | 0.449123i | −0.445940 | − | 0.895063i | \(-0.647131\pi\) |
0.895063 | + | 0.445940i | \(0.147131\pi\) | |||||||
\(954\) | 21.2942 | − | 12.2942i | 0.689426 | − | 0.398040i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.29423 | + | 1.90192i | −0.106543 | + | 0.0615126i | ||||
\(957\) | −62.1982 | + | 16.6660i | −2.01058 | + | 0.538734i | ||||
\(958\) | 3.01790 | − | 0.808643i | 0.0975038 | − | 0.0261261i | ||||
\(959\) | 31.6865 | − | 54.8827i | 1.02321 | − | 1.77225i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4808 | + | 26.8135i | 0.499379 | + | 0.864951i | ||||
\(962\) | −27.4249 | − | 27.4249i | −0.884213 | − | 0.884213i | ||||
\(963\) | −23.7506 | + | 23.7506i | −0.765353 | + | 0.765353i | ||||
\(964\) | 9.39230i | 0.302506i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.5885 | − | 9.00000i | 0.501550 | − | 0.289570i | ||||
\(967\) | 10.7589 | + | 40.1528i | 0.345983 | + | 1.29123i | 0.891460 | + | 0.453100i | \(0.149682\pi\) |
−0.545476 | + | 0.838126i | \(0.683651\pi\) | |||||||
\(968\) | 0.258819 | + | 0.965926i | 0.00831876 | + | 0.0310460i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.0333i | 1.73401i | 0.498298 | + | 0.867006i | \(0.333959\pi\) | ||||
−0.498298 | + | 0.867006i | \(0.666041\pi\) | |||||||
\(972\) | 15.0573 | − | 4.03459i | 0.482963 | − | 0.129410i | ||||
\(973\) | 26.7685 | + | 26.7685i | 0.858159 | + | 0.858159i | ||||
\(974\) | 8.02628 | + | 13.9019i | 0.257179 | + | 0.445446i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | + | 3.46410i | −0.0640184 | + | 0.110883i | ||||
\(977\) | −44.6035 | + | 11.9515i | −1.42699 | + | 0.382361i | −0.887959 | − | 0.459923i | \(-0.847877\pi\) |
−0.539033 | + | 0.842285i | \(0.681210\pi\) | |||||||
\(978\) | −6.41971 | + | 23.9587i | −0.205280 | + | 0.766114i | ||||
\(979\) | 25.9808 | − | 15.0000i | 0.830349 | − | 0.479402i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.41154 | −0.172777 | ||||||||
\(982\) | −13.2320 | + | 13.2320i | −0.422249 | + | 0.422249i | ||||
\(983\) | −41.7057 | − | 11.1750i | −1.33021 | − | 0.356427i | −0.477414 | − | 0.878679i | \(-0.658426\pi\) |
−0.852792 | + | 0.522251i | \(0.825092\pi\) | |||||||
\(984\) | 1.50000 | − | 2.59808i | 0.0478183 | − | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.7279 | + | 47.5013i | 0.405134 | + | 1.51198i | ||||
\(988\) | −3.91447 | + | 14.6090i | −0.124536 | + | 0.464774i | ||||
\(989\) | 1.01924 | 0.0324099 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1769 | −0.926835 | −0.463418 | − | 0.886140i | \(-0.653377\pi\) | ||||
−0.463418 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(992\) | −0.0507680 | + | 0.189469i | −0.00161189 | + | 0.00601564i | ||||
\(993\) | 22.7339 | + | 6.09154i | 0.721440 | + | 0.193309i | ||||
\(994\) | −29.7846 | − | 17.1962i | −0.944710 | − | 0.545429i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −29.7846 | −0.943761 | ||||||||
\(997\) | 21.0609 | + | 5.64325i | 0.667005 | + | 0.178724i | 0.576405 | − | 0.817164i | \(-0.304455\pi\) |
0.0905999 | + | 0.995887i | \(0.471122\pi\) | |||||||
\(998\) | −8.19428 | + | 8.19428i | −0.259385 | + | 0.259385i | ||||
\(999\) | 42.5885 | 1.34744 |
(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 | 450.2.p.e.293.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.a.1043.1 | 8 | |||
5.2 | odd | 4 | 450.2.p.c.257.2 | yes | 8 | ||
5.3 | odd | 4 | 450.2.p.c.257.1 | ✓ | 8 | ||
5.4 | even | 2 | inner | 450.2.p.e.293.1 | yes | 8 | |
9.2 | odd | 6 | 450.2.p.c.443.2 | yes | 8 | ||
9.7 | even | 3 | 1350.2.q.d.143.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.d.557.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.d.557.2 | 8 | |||
15.14 | odd | 2 | 1350.2.q.a.1043.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.e.407.2 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.a.1007.1 | 8 | |||
45.29 | odd | 6 | 450.2.p.c.443.1 | yes | 8 | ||
45.34 | even | 6 | 1350.2.q.d.143.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.e.407.1 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.a.1007.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.c.257.1 | ✓ | 8 | 5.3 | odd | 4 | ||
450.2.p.c.257.2 | yes | 8 | 5.2 | odd | 4 | ||
450.2.p.c.443.1 | yes | 8 | 45.29 | odd | 6 | ||
450.2.p.c.443.2 | yes | 8 | 9.2 | odd | 6 | ||
450.2.p.e.293.1 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.e.293.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.e.407.1 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.e.407.2 | yes | 8 | 45.2 | even | 12 | inner | |
1350.2.q.a.1007.1 | 8 | 45.7 | odd | 12 | |||
1350.2.q.a.1007.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.a.1043.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.a.1043.2 | 8 | 15.14 | odd | 2 | |||
1350.2.q.d.143.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.d.143.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.d.557.1 | 8 | 15.2 | even | 4 | |||
1350.2.q.d.557.2 | 8 | 15.8 | even | 4 |