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 | 257.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.257 |
Dual form | 450.2.p.c.443.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | ||||
\(3\) | −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 | ||||
\(7\) | −1.22474 | + | 4.57081i | −0.462910 | + | 1.72760i | 0.200817 | + | 0.979629i | \(0.435640\pi\) |
−0.663727 | + | 0.747975i | \(0.731026\pi\) | |||||||
\(8\) | 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 | \(0.158432\pi\) | |||||||
\(12\) | −0.448288 | − | 1.67303i | −0.129410 | − | 0.482963i | ||||
\(13\) | 1.22474 | + | 4.57081i | 0.339683 | + | 1.26771i | 0.898702 | + | 0.438560i | \(0.144511\pi\) |
−0.559019 | + | 0.829155i | \(0.688822\pi\) | |||||||
\(14\) | −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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | −0.776457 | + | 2.89778i | −0.183013 | + | 0.683013i | ||||
\(19\) | − | 3.19615i | − | 0.733248i | −0.930369 | − | 0.366624i | \(-0.880514\pi\) | ||
0.930369 | − | 0.366624i | \(-0.119486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.09808 | − | 4.09808i | 1.54893 | − | 0.894274i | ||||
\(22\) | 3.34607 | − | 0.896575i | 0.713384 | − | 0.191151i | ||||
\(23\) | 2.12132 | − | 0.568406i | 0.442326 | − | 0.118521i | −0.0307805 | − | 0.999526i | \(-0.509799\pi\) |
0.473106 | + | 0.881005i | \(0.343133\pi\) | |||||||
\(24\) | − | 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 | \(0.306489\pi\) |
0.425273 | + | 0.905065i | \(0.360178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0980762 | + | 0.169873i | −0.0176150 | + | 0.0305101i | −0.874699 | − | 0.484667i | \(-0.838941\pi\) |
0.857084 | + | 0.515177i | \(0.172274\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | −5.79555 | − | 1.55291i | −1.00888 | − | 0.270328i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −5.79555 | − | 5.79555i | −0.952783 | − | 0.952783i | 0.0461511 | − | 0.998934i | \(-0.485304\pi\) |
−0.998934 | + | 0.0461511i | \(0.985304\pi\) | |||||||
\(38\) | 0.827225 | − | 3.08725i | 0.134194 | − | 0.500817i | ||||
\(39\) | 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 | \(0.709851\pi\) | |||||||
\(42\) | 7.91688 | − | 2.12132i | 1.22160 | − | 0.327327i | ||||
\(43\) | −0.448288 | − | 0.120118i | −0.0683632 | − | 0.0183179i | 0.224475 | − | 0.974480i | \(-0.427933\pi\) |
−0.292839 | + | 0.956162i | \(0.594600\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19615 | 0.323805 | ||||||||
\(47\) | −5.79555 | − | 1.55291i | −0.845369 | − | 0.226516i | −0.189961 | − | 0.981792i | \(-0.560836\pi\) |
−0.655407 | + | 0.755276i | \(0.727503\pi\) | |||||||
\(48\) | 0.448288 | − | 1.67303i | 0.0647048 | − | 0.241481i | ||||
\(49\) | −13.3301 | − | 7.69615i | −1.90430 | − | 1.09945i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.22474 | + | 4.57081i | −0.169842 | + | 0.633857i | ||||
\(53\) | 5.79555 | + | 5.79555i | 0.796081 | + | 0.796081i | 0.982475 | − | 0.186394i | \(-0.0596802\pi\) |
−0.186394 | + | 0.982475i | \(0.559680\pi\) | |||||||
\(54\) | 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 | ||||
\(58\) | 2.77766 | + | 10.3664i | 0.364725 | + | 1.36117i | ||||
\(59\) | −2.76795 | + | 4.79423i | −0.360356 | + | 0.624155i | −0.988019 | − | 0.154330i | \(-0.950678\pi\) |
0.627663 | + | 0.778485i | \(0.284012\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | −13.7124 | − | 3.67423i | −1.72760 | − | 0.462910i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.19615 | − | 3.00000i | −0.639602 | − | 0.369274i | ||||
\(67\) | −5.34727 | + | 1.43280i | −0.653273 | + | 0.175044i | −0.570208 | − | 0.821500i | \(-0.693137\pi\) |
−0.0830646 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(68\) | 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 | −0.458604 | − | 0.888641i | \(-0.651650\pi\) |
0.888641 | + | 0.458604i | \(0.151650\pi\) | |||||||
\(74\) | −4.09808 | − | 7.09808i | −0.476392 | − | 0.825135i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59808 | − | 2.76795i | 0.183312 | − | 0.317506i | ||||
\(77\) | 4.24264 | + | 15.8338i | 0.483494 | + | 1.80442i | ||||
\(78\) | 5.79555 | − | 5.79555i | 0.656217 | − | 0.656217i | ||||
\(79\) | 8.66025 | − | 5.00000i | 0.974355 | − | 0.562544i | 0.0737937 | − | 0.997274i | \(-0.476489\pi\) |
0.900561 | + | 0.434730i | \(0.143156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −1.22474 | − | 1.22474i | −0.135250 | − | 0.135250i | ||||
\(83\) | 4.45069 | − | 16.6102i | 0.488527 | − | 1.82321i | −0.0750978 | − | 0.997176i | \(-0.523927\pi\) |
0.563625 | − | 0.826031i | \(-0.309406\pi\) | |||||||
\(84\) | 8.19615 | 0.894274 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.401924 | − | 0.232051i | −0.0433406 | − | 0.0250227i | ||||
\(87\) | 4.81105 | − | 17.9551i | 0.515798 | − | 1.92499i | ||||
\(88\) | 3.34607 | + | 0.896575i | 0.356692 | + | 0.0955753i | ||||
\(89\) | −8.66025 | −0.917985 | −0.458993 | − | 0.888440i | \(-0.651790\pi\) | ||||
−0.458993 | + | 0.888440i | \(0.651790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3923 | −2.34735 | ||||||||
\(92\) | 2.12132 | + | 0.568406i | 0.221163 | + | 0.0592604i | ||||
\(93\) | 0.328169 | − | 0.0879327i | 0.0340296 | − | 0.00911820i | ||||
\(94\) | −5.19615 | − | 3.00000i | −0.535942 | − | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | − | 1.50000i | 0.0883883 | − | 0.153093i | ||||
\(97\) | −0.688524 | + | 2.56961i | −0.0699091 | + | 0.260904i | −0.992031 | − | 0.125996i | \(-0.959787\pi\) |
0.922122 | + | 0.386900i | \(0.126454\pi\) | |||||||
\(98\) | −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 | ||||||||
\(103\) | −2.68973 | − | 10.0382i | −0.265027 | − | 0.989093i | −0.962234 | − | 0.272223i | \(-0.912241\pi\) |
0.697207 | − | 0.716869i | \(-0.254426\pi\) | |||||||
\(104\) | −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 | \(-0.567975\pi\) |
0.977285 | + | 0.211931i | \(0.0679753\pi\) | |||||||
\(108\) | 5.01910 | − | 1.34486i | 0.482963 | − | 0.129410i | ||||
\(109\) | 1.80385i | 0.172777i | 0.996262 | + | 0.0863886i | \(0.0275327\pi\) | ||||
−0.996262 | + | 0.0863886i | \(0.972467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.1962i | 1.34744i | ||||||||
\(112\) | −4.57081 | + | 1.22474i | −0.431901 | + | 0.115728i | ||||
\(113\) | 12.9360 | − | 3.46618i | 1.21691 | − | 0.326071i | 0.407443 | − | 0.913231i | \(-0.366421\pi\) |
0.809471 | + | 0.587160i | \(0.199754\pi\) | |||||||
\(114\) | −4.79423 | + | 2.76795i | −0.449021 | + | 0.259242i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.7321i | 0.996446i | ||||||||
\(117\) | −13.7124 | + | 3.67423i | −1.26771 | + | 0.339683i | ||||
\(118\) | −3.91447 | + | 3.91447i | −0.360356 | + | 0.360356i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.03528 | + | 3.86370i | 0.0937295 | + | 0.349803i | ||||
\(123\) | 0.776457 | + | 2.89778i | 0.0700108 | + | 0.261284i | ||||
\(124\) | −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 | 0.401560 | − | 0.915833i | \(-0.368468\pi\) |
−0.915833 | + | 0.401560i | \(0.868468\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | 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 | ||||
\(133\) | 14.6090 | + | 3.91447i | 1.26676 | + | 0.339428i | ||||
\(134\) | −5.53590 | −0.478229 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9360 | + | 3.46618i | 1.10519 | + | 0.296136i | 0.764878 | − | 0.644175i | \(-0.222799\pi\) |
0.340317 | + | 0.940311i | \(0.389466\pi\) | |||||||
\(138\) | −2.68973 | − | 2.68973i | −0.228965 | − | 0.228965i | ||||
\(139\) | −6.92820 | − | 4.00000i | −0.587643 | − | 0.339276i | 0.176522 | − | 0.984297i | \(-0.443515\pi\) |
−0.764165 | + | 0.645021i | \(0.776849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.19615 | + | 9.00000i | 0.437595 | + | 0.757937i | ||||
\(142\) | 1.88108 | − | 7.02030i | 0.157857 | − | 0.589130i | ||||
\(143\) | 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 | ||||
\(147\) | 6.90018 | + | 25.7518i | 0.569117 | + | 2.12397i | ||||
\(148\) | −2.12132 | − | 7.91688i | −0.174371 | − | 0.650763i | ||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 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 | ||||
\(157\) | 19.1798 | − | 5.13922i | 1.53072 | − | 0.410154i | 0.607463 | − | 0.794348i | \(-0.292187\pi\) |
0.923253 | + | 0.384194i | \(0.125520\pi\) | |||||||
\(158\) | 9.65926 | − | 2.58819i | 0.768449 | − | 0.205905i | ||||
\(159\) | − | 14.1962i | − | 1.12583i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | −8.69333 | − | 2.32937i | −0.683013 | − | 0.183013i | ||||
\(163\) | −10.1261 | + | 10.1261i | −0.793140 | + | 0.793140i | −0.982003 | − | 0.188864i | \(-0.939520\pi\) |
0.188864 | + | 0.982003i | \(0.439520\pi\) | |||||||
\(164\) | −0.866025 | − | 1.50000i | −0.0676252 | − | 0.117130i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.59808 | − | 14.8923i | 0.667340 | − | 1.15587i | ||||
\(167\) | −4.24264 | − | 15.8338i | −0.328305 | − | 1.22525i | −0.910947 | − | 0.412523i | \(-0.864648\pi\) |
0.582642 | − | 0.812729i | \(-0.302019\pi\) | |||||||
\(168\) | 7.91688 | + | 2.12132i | 0.610800 | + | 0.163663i | ||||
\(169\) | −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 | ||||
\(173\) | −4.24264 | + | 15.8338i | −0.322562 | + | 1.20382i | 0.594178 | + | 0.804334i | \(0.297477\pi\) |
−0.916740 | + | 0.399484i | \(0.869189\pi\) | |||||||
\(174\) | 9.29423 | − | 16.0981i | 0.704594 | − | 1.22039i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | + | 1.73205i | 0.226134 | + | 0.130558i | ||||
\(177\) | 9.26174 | − | 2.48168i | 0.696155 | − | 0.186534i | ||||
\(178\) | −8.36516 | − | 2.24144i | −0.626995 | − | 0.168003i | ||||
\(179\) | 22.8564 | 1.70837 | 0.854184 | − | 0.519971i | \(-0.174057\pi\) | ||||
0.854184 | + | 0.519971i | \(0.174057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3923 | −0.921113 | −0.460556 | − | 0.887630i | \(-0.652350\pi\) | ||||
−0.460556 | + | 0.887630i | \(0.652350\pi\) | |||||||
\(182\) | −21.6293 | − | 5.79555i | −1.60327 | − | 0.429595i | ||||
\(183\) | 1.79315 | − | 6.69213i | 0.132554 | − | 0.494697i | ||||
\(184\) | 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 | ||||
\(193\) | −2.86559 | − | 10.6945i | −0.206270 | − | 0.769809i | −0.989059 | − | 0.147522i | \(-0.952870\pi\) |
0.782789 | − | 0.622287i | \(-0.213796\pi\) | |||||||
\(194\) | −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 | \(-0.918772\pi\) |
0.252425 | + | 0.967617i | \(0.418772\pi\) | |||||||
\(198\) | 2.68973 | + | 10.0382i | 0.191151 | + | 0.713384i | ||||
\(199\) | 20.3923i | 1.44557i | 0.691072 | + | 0.722786i | \(0.257139\pi\) | ||||
−0.691072 | + | 0.722786i | \(0.742861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.30385 | + | 4.79423i | 0.585708 | + | 0.338159i | ||||
\(202\) | 7.02030 | − | 1.88108i | 0.493947 | − | 0.132353i | ||||
\(203\) | −49.0542 | + | 13.1440i | −3.44293 | + | 0.922530i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 10.3923i | − | 0.724066i | ||||||
\(207\) | 1.70522 | + | 6.36396i | 0.118521 | + | 0.442326i | ||||
\(208\) | −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 | \(0.179776\pi\) | |||||||
\(212\) | 2.12132 | + | 7.91688i | 0.145693 | + | 0.543733i | ||||
\(213\) | −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 | ||||
\(218\) | −0.466870 | + | 1.74238i | −0.0316204 | + | 0.118009i | ||||
\(219\) | −9.00000 | −0.608164 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.67423 | + | 13.7124i | −0.246598 | + | 0.920318i | ||||
\(223\) | −2.44949 | − | 0.656339i | −0.164030 | − | 0.0439517i | 0.175869 | − | 0.984414i | \(-0.443726\pi\) |
−0.339899 | + | 0.940462i | \(0.610393\pi\) | |||||||
\(224\) | −4.73205 | −0.316173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3923 | 0.890843 | ||||||||
\(227\) | 12.3676 | + | 3.31388i | 0.820864 | + | 0.219950i | 0.644724 | − | 0.764415i | \(-0.276972\pi\) |
0.176140 | + | 0.984365i | \(0.443639\pi\) | |||||||
\(228\) | −5.34727 | + | 1.43280i | −0.354131 | + | 0.0948892i | ||||
\(229\) | −5.02628 | − | 2.90192i | −0.332146 | − | 0.191765i | 0.324648 | − | 0.945835i | \(-0.394754\pi\) |
−0.656793 | + | 0.754071i | \(0.728088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.1962 | − | 24.5885i | 0.934038 | − | 1.61780i | ||||
\(232\) | −2.77766 | + | 10.3664i | −0.182362 | + | 0.680585i | ||||
\(233\) | 3.25813 | + | 3.25813i | 0.213447 | + | 0.213447i | 0.805730 | − | 0.592283i | \(-0.201773\pi\) |
−0.592283 | + | 0.805730i | \(0.701773\pi\) | |||||||
\(234\) | −14.1962 | −0.928032 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.79423 | + | 2.76795i | −0.312078 | + | 0.180178i | ||||
\(237\) | −16.7303 | − | 4.48288i | −1.08675 | − | 0.291194i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.90192 | + | 3.29423i | −0.123025 | + | 0.213086i | −0.920959 | − | 0.389659i | \(-0.872593\pi\) |
0.797934 | + | 0.602745i | \(0.205926\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | 14.6090 | − | 3.91447i | 0.929549 | − | 0.249072i | ||||
\(248\) | −0.189469 | + | 0.0507680i | −0.0120313 | + | 0.00322377i | ||||
\(249\) | −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 | ||||
\(257\) | −6.57201 | − | 24.5271i | −0.409951 | − | 1.52996i | −0.794738 | − | 0.606952i | \(-0.792392\pi\) |
0.384787 | − | 0.923005i | \(-0.374275\pi\) | |||||||
\(258\) | 0.208051 | + | 0.776457i | 0.0129527 | + | 0.0483401i | ||||
\(259\) | 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 | ||||
\(263\) | −3.25813 | + | 12.1595i | −0.200905 | + | 0.749788i | 0.789754 | + | 0.613424i | \(0.210208\pi\) |
−0.990659 | + | 0.136364i | \(0.956458\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | −5.34727 | − | 1.43280i | −0.326636 | − | 0.0875219i | ||||
\(269\) | −10.0526 | −0.612915 | −0.306458 | − | 0.951884i | \(-0.599144\pi\) | ||||
−0.306458 | + | 0.951884i | \(0.599144\pi\) | |||||||
\(270\) | 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 | ||||
\(277\) | −5.05128 | + | 18.8516i | −0.303502 | + | 1.13269i | 0.630725 | + | 0.776007i | \(0.282758\pi\) |
−0.934227 | + | 0.356679i | \(0.883909\pi\) | |||||||
\(278\) | −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 | \(0.233012\pi\) | |||||||
\(282\) | 2.68973 | + | 10.0382i | 0.160171 | + | 0.597766i | ||||
\(283\) | 1.01669 | + | 3.79435i | 0.0604362 | + | 0.225551i | 0.989538 | − | 0.144274i | \(-0.0460845\pi\) |
−0.929102 | + | 0.369824i | \(0.879418\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | −2.89778 | + | 0.776457i | −0.170753 | + | 0.0457532i | ||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.99038 | − | 2.30385i | 0.233920 | − | 0.135054i | ||||
\(292\) | 5.01910 | − | 1.34486i | 0.293720 | − | 0.0787022i | ||||
\(293\) | 3.67423 | − | 0.984508i | 0.214651 | − | 0.0575156i | −0.149891 | − | 0.988703i | \(-0.547892\pi\) |
0.364542 | + | 0.931187i | \(0.381226\pi\) | |||||||
\(294\) | 26.6603i | 1.55486i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 8.19615i | − | 0.476392i | ||||||
\(297\) | 4.65874 | − | 17.3867i | 0.270328 | − | 1.00888i | ||||
\(298\) | 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 | ||||
\(302\) | 2.07055 | + | 7.72741i | 0.119147 | + | 0.444662i | ||||
\(303\) | −12.1595 | − | 3.25813i | −0.698546 | − | 0.187175i | ||||
\(304\) | 2.76795 | − | 1.59808i | 0.158753 | − | 0.0916560i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.44949 | − | 2.44949i | −0.139800 | − | 0.139800i | 0.633743 | − | 0.773543i | \(-0.281517\pi\) |
−0.773543 | + | 0.633743i | \(0.781517\pi\) | |||||||
\(308\) | −4.24264 | + | 15.8338i | −0.241747 | + | 0.902212i | ||||
\(309\) | −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 | \(0.768306\pi\) | |||||||
\(312\) | 7.91688 | − | 2.12132i | 0.448205 | − | 0.120096i | ||||
\(313\) | −19.9563 | − | 5.34727i | −1.12800 | − | 0.302245i | −0.353880 | − | 0.935291i | \(-0.615138\pi\) |
−0.774115 | + | 0.633045i | \(0.781805\pi\) | |||||||
\(314\) | 19.8564 | 1.12056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −6.36396 | − | 1.70522i | −0.357436 | − | 0.0957746i | 0.0756325 | − | 0.997136i | \(-0.475902\pi\) |
−0.433068 | + | 0.901361i | \(0.642569\pi\) | |||||||
\(318\) | 3.67423 | − | 13.7124i | 0.206041 | − | 0.768955i | ||||
\(319\) | 32.1962 | + | 18.5885i | 1.80264 | + | 1.04075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.3923 | −1.08237 | ||||||||
\(322\) | −2.68973 | + | 10.0382i | −0.149893 | + | 0.559407i | ||||
\(323\) | 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 | ||||
\(328\) | −0.448288 | − | 1.67303i | −0.0247525 | − | 0.0923778i | ||||
\(329\) | 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 | ||||
\(337\) | 19.8362 | − | 5.31508i | 1.08054 | − | 0.289531i | 0.325725 | − | 0.945464i | \(-0.394391\pi\) |
0.754819 | + | 0.655933i | \(0.227725\pi\) | |||||||
\(338\) | −9.07227 | + | 2.43091i | −0.493466 | + | 0.132224i | ||||
\(339\) | −20.0885 | − | 11.5981i | −1.09106 | − | 0.629921i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.679492i | 0.0367966i | ||||||||
\(342\) | 9.26174 | + | 2.48168i | 0.500817 | + | 0.134194i | ||||
\(343\) | 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 | ||||
\(347\) | −2.27362 | − | 8.48528i | −0.122055 | − | 0.455514i | 0.877663 | − | 0.479278i | \(-0.159102\pi\) |
−0.999718 | + | 0.0237644i | \(0.992435\pi\) | |||||||
\(348\) | 13.1440 | − | 13.1440i | 0.704594 | − | 0.704594i | ||||
\(349\) | 1.73205 | − | 1.00000i | 0.0927146 | − | 0.0535288i | −0.452926 | − | 0.891548i | \(-0.649620\pi\) |
0.545640 | + | 0.838019i | \(0.316286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.2942 | + | 12.2942i | 1.13660 | + | 0.656217i | ||||
\(352\) | 2.44949 | + | 2.44949i | 0.130558 | + | 0.130558i | ||||
\(353\) | 3.88229 | − | 14.4889i | 0.206633 | − | 0.771166i | −0.782312 | − | 0.622886i | \(-0.785960\pi\) |
0.988946 | − | 0.148279i | \(-0.0473735\pi\) | |||||||
\(354\) | 9.58846 | 0.509621 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | − | 4.33013i | −0.397499 | − | 0.229496i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.0776 | + | 5.91567i | 1.16684 | + | 0.312653i | ||||
\(359\) | −35.3205 | −1.86415 | −0.932073 | − | 0.362272i | \(-0.882001\pi\) | ||||
−0.932073 | + | 0.362272i | \(0.882001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.78461 | 0.462348 | ||||||||
\(362\) | −11.9700 | − | 3.20736i | −0.629132 | − | 0.168575i | ||||
\(363\) | −1.67303 | + | 0.448288i | −0.0878114 | + | 0.0235290i | ||||
\(364\) | −19.3923 | − | 11.1962i | −1.01643 | − | 0.586838i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.46410 | − | 6.00000i | 0.181071 | − | 0.313625i | ||||
\(367\) | −1.07244 | + | 4.00240i | −0.0559810 | + | 0.208924i | −0.988251 | − | 0.152839i | \(-0.951158\pi\) |
0.932270 | + | 0.361763i | \(0.117825\pi\) | |||||||
\(368\) | 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 | ||||
\(372\) | 0.328169 | + | 0.0879327i | 0.0170148 | + | 0.00455910i | ||||
\(373\) | −6.03579 | − | 22.5259i | −0.312521 | − | 1.16635i | −0.926275 | − | 0.376848i | \(-0.877008\pi\) |
0.613754 | − | 0.789498i | \(-0.289659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −35.9101 | + | 35.9101i | −1.84947 | + | 1.84947i | ||||
\(378\) | 6.36396 | + | 23.7506i | 0.327327 | + | 1.22160i | ||||
\(379\) | 0.392305i | 0.0201513i | 0.999949 | + | 0.0100757i | \(0.00320724\pi\) | ||||
−0.999949 | + | 0.0100757i | \(0.996793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1962i | 0.727291i | ||||||||
\(382\) | 3.34607 | − | 0.896575i | 0.171200 | − | 0.0458728i | ||||
\(383\) | 5.22715 | − | 1.40061i | 0.267095 | − | 0.0715678i | −0.122786 | − | 0.992433i | \(-0.539183\pi\) |
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(384\) | 1.50000 | − | 0.866025i | 0.0765466 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.0718i | − | 0.563540i | ||||||
\(387\) | 0.360355 | − | 1.34486i | 0.0183179 | − | 0.0683632i | ||||
\(388\) | −1.88108 | + | 1.88108i | −0.0954976 | + | 0.0954976i | ||||
\(389\) | 5.19615 | + | 9.00000i | 0.263455 | + | 0.456318i | 0.967158 | − | 0.254177i | \(-0.0818045\pi\) |
−0.703702 | + | 0.710495i | \(0.748471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.98382 | − | 14.8678i | −0.201213 | − | 0.750939i | ||||
\(393\) | 3.10583 | + | 11.5911i | 0.156668 | + | 0.584694i | ||||
\(394\) | −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 | 0.926094 | − | 0.377293i | \(-0.123145\pi\) |
−0.377293 | + | 0.926094i | \(0.623145\pi\) | |||||||
\(398\) | −5.27792 | + | 19.6975i | −0.264558 | + | 0.987344i | ||||
\(399\) | −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 | ||||
\(403\) | −0.896575 | − | 0.240237i | −0.0446616 | − | 0.0119670i | ||||
\(404\) | 7.26795 | 0.361594 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.7846 | −2.52040 | ||||||||
\(407\) | −27.4249 | − | 7.34847i | −1.35940 | − | 0.364250i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5263 | − | 10.6962i | −0.916066 | − | 0.528891i | −0.0336878 | − | 0.999432i | \(-0.510725\pi\) |
−0.882378 | + | 0.470542i | \(0.844059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5981 | − | 20.0885i | −0.572091 | − | 0.990891i | ||||
\(412\) | 2.68973 | − | 10.0382i | 0.132513 | − | 0.494546i | ||||
\(413\) | −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 | ||||
\(417\) | 3.58630 | + | 13.3843i | 0.175622 | + | 0.655430i | ||||
\(418\) | −2.86559 | − | 10.6945i | −0.140161 | − | 0.523087i | ||||
\(419\) | −4.50000 | + | 7.79423i | −0.219839 | + | 0.380773i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 4.65874 | − | 17.3867i | 0.226516 | − | 0.845369i | ||||
\(424\) | 8.19615i | 0.398040i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.9019 | + | 6.29423i | −0.528200 | + | 0.304956i | ||||
\(427\) | −18.2832 | + | 4.89898i | −0.884788 | + | 0.237078i | ||||
\(428\) | 10.8147 | − | 2.89778i | 0.522746 | − | 0.140069i | ||||
\(429\) | − | 28.3923i | − | 1.37079i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.1244i | 1.01752i | 0.860907 | + | 0.508762i | \(0.169897\pi\) | ||||
−0.860907 | + | 0.508762i | \(0.830103\pi\) | |||||||
\(432\) | 5.01910 | + | 1.34486i | 0.241481 | + | 0.0647048i | ||||
\(433\) | −12.0716 | + | 12.0716i | −0.580123 | + | 0.580123i | −0.934937 | − | 0.354814i | \(-0.884544\pi\) |
0.354814 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(434\) | −0.464102 | − | 0.803848i | −0.0222776 | − | 0.0385859i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.901924 | + | 1.56218i | −0.0431943 | + | 0.0748147i | ||||
\(437\) | −1.81671 | − | 6.78006i | −0.0869051 | − | 0.324334i | ||||
\(438\) | −8.69333 | − | 2.32937i | −0.415383 | − | 0.111302i | ||||
\(439\) | −1.22243 | + | 0.705771i | −0.0583435 | + | 0.0336846i | −0.528888 | − | 0.848692i | \(-0.677391\pi\) |
0.470545 | + | 0.882376i | \(0.344058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.0885 | − | 39.9904i | 1.09945 | − | 1.90430i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.68973 | − | 10.0382i | 0.127793 | − | 0.476929i | −0.872131 | − | 0.489272i | \(-0.837262\pi\) |
0.999924 | + | 0.0123433i | \(0.00392908\pi\) | |||||||
\(444\) | −7.09808 | + | 12.2942i | −0.336860 | + | 0.583458i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.19615 | − | 1.26795i | −0.103991 | − | 0.0600391i | ||||
\(447\) | −30.1146 | + | 8.06918i | −1.42437 | + | 0.381659i | ||||
\(448\) | −4.57081 | − | 1.22474i | −0.215950 | − | 0.0578638i | ||||
\(449\) | 30.1244 | 1.42166 | 0.710828 | − | 0.703366i | \(-0.248320\pi\) | ||||
0.710828 | + | 0.703366i | \(0.248320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 12.9360 | + | 3.46618i | 0.608457 | + | 0.163036i | ||||
\(453\) | 3.58630 | − | 13.3843i | 0.168499 | − | 0.628847i | ||||
\(454\) | 11.0885 | + | 6.40192i | 0.520407 | + | 0.300457i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.53590 | −0.259242 | ||||||||
\(457\) | 7.14042 | − | 26.6484i | 0.334015 | − | 1.24656i | −0.570919 | − | 0.821007i | \(-0.693413\pi\) |
0.904933 | − | 0.425553i | \(-0.139920\pi\) | |||||||
\(458\) | −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 | ||||
\(463\) | −0.568406 | − | 2.12132i | −0.0264161 | − | 0.0985861i | 0.951459 | − | 0.307775i | \(-0.0995844\pi\) |
−0.977875 | + | 0.209189i | \(0.932918\pi\) | |||||||
\(464\) | −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 | \(-0.678790\pi\) |
0.846358 | + | 0.532614i | \(0.178790\pi\) | |||||||
\(468\) | −13.7124 | − | 3.67423i | −0.633857 | − | 0.169842i | ||||
\(469\) | − | 26.1962i | − | 1.20963i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.7846 | − | 17.1962i | −1.37240 | − | 0.792357i | ||||
\(472\) | −5.34727 | + | 1.43280i | −0.246128 | + | 0.0659498i | ||||
\(473\) | −1.55291 | + | 0.416102i | −0.0714031 | + | 0.0191324i | ||||
\(474\) | −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 | 0.828128 | − | 0.560540i | \(-0.189406\pi\) |
−0.899505 | + | 0.436910i | \(0.856073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.3923 | − | 33.5885i | 0.884213 | − | 1.53150i | ||||
\(482\) | −2.43091 | − | 9.07227i | −0.110725 | − | 0.413231i | ||||
\(483\) | 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 | 0.401501 | − | 0.915858i | \(-0.368489\pi\) |
−0.915858 | + | 0.401501i | \(0.868489\pi\) | |||||||
\(488\) | −1.03528 | + | 3.86370i | −0.0468648 | + | 0.174902i | ||||
\(489\) | 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 | \(0.805426\pi\) | |||||||
\(492\) | −0.776457 | + | 2.89778i | −0.0350054 | + | 0.130642i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 15.1244 | 0.680477 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.196152 | −0.00880750 | ||||||||
\(497\) | 33.2204 | + | 8.90138i | 1.49014 | + | 0.399282i | ||||
\(498\) | −28.7697 | + | 7.70882i | −1.28920 | + | 0.345441i | ||||
\(499\) | 10.0359 | + | 5.79423i | 0.449269 | + | 0.259385i | 0.707521 | − | 0.706692i | \(-0.249813\pi\) |
−0.258253 | + | 0.966077i | \(0.583147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.1962 | + | 24.5885i | −0.634237 | + | 1.09853i | ||||
\(502\) | 2.32937 | − | 8.69333i | 0.103965 | − | 0.388002i | ||||
\(503\) | 3.82654 | + | 3.82654i | 0.170617 | + | 0.170617i | 0.787250 | − | 0.616633i | \(-0.211504\pi\) |
−0.616633 | + | 0.787250i | \(0.711504\pi\) | |||||||
\(504\) | −7.09808 | − | 12.2942i | −0.316173 | − | 0.547628i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.58846 | − | 3.80385i | 0.292893 | − | 0.169102i | ||||
\(507\) | 15.7136 | + | 4.21046i | 0.697867 | + | 0.186993i | ||||
\(508\) | −2.12132 | − | 7.91688i | −0.0941184 | − | 0.351255i | ||||
\(509\) | 10.3923 | − | 18.0000i | 0.460631 | − | 0.797836i | −0.538362 | − | 0.842714i | \(-0.680957\pi\) |
0.998992 | + | 0.0448779i | \(0.0142899\pi\) | |||||||
\(510\) | 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 | ||||||||
\(517\) | −20.0764 | + | 5.37945i | −0.882959 | + | 0.236588i | ||||
\(518\) | 37.4631 | − | 10.0382i | 1.64603 | − | 0.441053i | ||||
\(519\) | 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 | \(-0.0194283\pi\) | |||||||
\(522\) | −31.0991 | + | 8.33298i | −1.36117 | + | 0.364725i | ||||
\(523\) | −23.9909 | + | 23.9909i | −1.04905 | + | 1.04905i | −0.0503137 | + | 0.998733i | \(0.516022\pi\) |
−0.998733 | + | 0.0503137i | \(0.983978\pi\) | |||||||
\(524\) | −3.46410 | − | 6.00000i | −0.151330 | − | 0.262111i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.29423 | + | 10.9019i | −0.274441 | + | 0.475346i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.55291 | − | 5.79555i | −0.0675819 | − | 0.252219i | ||||
\(529\) | −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 | ||||
\(533\) | 2.12132 | − | 7.91688i | 0.0918846 | − | 0.342918i | ||||
\(534\) | 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 | ||||
\(538\) | −9.71003 | − | 2.60179i | −0.418629 | − | 0.112171i | ||||
\(539\) | −53.3205 | −2.29668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.39230 | −0.360813 | −0.180407 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180407 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(542\) | 25.6825 | + | 6.88160i | 1.10316 | + | 0.295590i | ||||
\(543\) | 15.1774 | + | 15.1774i | 0.651325 | + | 0.651325i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.3923 | + | 33.5885i | 0.829914 | + | 1.43745i | ||||
\(547\) | −10.3986 | + | 38.8079i | −0.444610 | + | 1.65931i | 0.272354 | + | 0.962197i | \(0.412198\pi\) |
−0.716964 | + | 0.697110i | \(0.754469\pi\) | |||||||
\(548\) | 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 | ||||
\(552\) | −0.984508 | − | 3.67423i | −0.0419035 | − | 0.156386i | ||||
\(553\) | 12.2474 | + | 45.7081i | 0.520814 | + | 1.94371i | ||||
\(554\) | −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 | \(-0.720337\pi\) |
0.769838 | + | 0.638240i | \(0.220337\pi\) | |||||||
\(558\) | −0.416102 | − | 0.416102i | −0.0176150 | − | 0.0176150i | ||||
\(559\) | − | 2.19615i | − | 0.0928874i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0382 | − | 2.68973i | 0.423436 | − | 0.113459i | ||||
\(563\) | −2.32937 | + | 0.624153i | −0.0981713 | + | 0.0263049i | −0.307570 | − | 0.951525i | \(-0.599516\pi\) |
0.209399 | + | 0.977830i | \(0.432849\pi\) | |||||||
\(564\) | 10.3923i | 0.437595i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.92820i | 0.165115i | ||||||||
\(567\) | 11.0227 | − | 41.1373i | 0.462910 | − | 1.72760i | ||||
\(568\) | 5.13922 | − | 5.13922i | 0.215637 | − | 0.215637i | ||||
\(569\) | −12.4641 | − | 21.5885i | −0.522522 | − | 0.905035i | −0.999657 | − | 0.0262048i | \(-0.991658\pi\) |
0.477134 | − | 0.878830i | \(-0.341676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.59808 | + | 16.6244i | −0.401667 | + | 0.695708i | −0.993927 | − | 0.110039i | \(-0.964902\pi\) |
0.592260 | + | 0.805747i | \(0.298236\pi\) | |||||||
\(572\) | 4.24264 | + | 15.8338i | 0.177394 | + | 0.662042i | ||||
\(573\) | −5.79555 | − | 1.55291i | −0.242113 | − | 0.0648739i | ||||
\(574\) | 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 | 0.956046 | − | 0.293217i | \(-0.0947260\pi\) |
−0.293217 | + | 0.956046i | \(0.594726\pi\) | |||||||
\(578\) | −4.39992 | + | 16.4207i | −0.183013 | + | 0.683013i | ||||
\(579\) | −9.58846 | + | 16.6077i | −0.398483 | + | 0.690192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 70.4711 | + | 40.6865i | 2.92364 | + | 1.68796i | ||||
\(582\) | 4.45069 | − | 1.19256i | 0.184487 | − | 0.0494332i | ||||
\(583\) | 27.4249 | + | 7.34847i | 1.13582 | + | 0.304342i | ||||
\(584\) | 5.19615 | 0.215018 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.80385 | 0.157135 | ||||||||
\(587\) | 4.24264 | + | 1.13681i | 0.175113 | + | 0.0469213i | 0.345310 | − | 0.938489i | \(-0.387774\pi\) |
−0.170197 | + | 0.985410i | \(0.554441\pi\) | |||||||
\(588\) | −6.90018 | + | 25.7518i | −0.284559 | + | 1.06199i | ||||
\(589\) | 0.542940 | + | 0.313467i | 0.0223715 | + | 0.0129162i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5885 | 1.01143 | ||||||||
\(592\) | 2.12132 | − | 7.91688i | 0.0871857 | − | 0.325382i | ||||
\(593\) | −14.8492 | − | 14.8492i | −0.609785 | − | 0.609785i | 0.333105 | − | 0.942890i | \(-0.391904\pi\) |
−0.942890 | + | 0.333105i | \(0.891904\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | 2.68973 | + | 10.0382i | 0.109991 | + | 0.410492i | ||||
\(599\) | −3.63397 | + | 6.29423i | −0.148480 | + | 0.257175i | −0.930666 | − | 0.365870i | \(-0.880771\pi\) |
0.782186 | + | 0.623045i | \(0.214105\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | −4.29839 | − | 16.0418i | −0.175044 | − | 0.653273i | ||||
\(604\) | 8.00000i | 0.325515i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.9019 | − | 6.29423i | −0.442860 | − | 0.255686i | ||||
\(607\) | −46.9328 | + | 12.5756i | −1.90495 | + | 0.510429i | −0.909427 | + | 0.415864i | \(0.863479\pi\) |
−0.995519 | + | 0.0945643i | \(0.969854\pi\) | |||||||
\(608\) | 3.08725 | − | 0.827225i | 0.125204 | − | 0.0335484i | ||||
\(609\) | 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 | −0.880145 | − | 0.474706i | \(-0.842555\pi\) |
0.474706 | + | 0.880145i | \(0.342555\pi\) | |||||||
\(614\) | −1.73205 | − | 3.00000i | −0.0698999 | − | 0.121070i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.19615 | + | 14.1962i | −0.330232 | + | 0.571979i | ||||
\(617\) | 3.05008 | + | 11.3831i | 0.122792 | + | 0.458265i | 0.999751 | − | 0.0222993i | \(-0.00709866\pi\) |
−0.876960 | + | 0.480564i | \(0.840432\pi\) | |||||||
\(618\) | −12.7279 | + | 12.7279i | −0.511992 | + | 0.511992i | ||||
\(619\) | −41.2128 | + | 23.7942i | −1.65648 | + | 0.956371i | −0.682164 | + | 0.731200i | \(0.738961\pi\) |
−0.974319 | + | 0.225171i | \(0.927706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.70577 | − | 9.88269i | 0.228965 | − | 0.396579i | ||||
\(622\) | −7.82894 | − | 7.82894i | −0.313912 | − | 0.313912i | ||||
\(623\) | 10.6066 | − | 39.5844i | 0.424945 | − | 1.58591i | ||||
\(624\) | 8.19615 | 0.328109 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.8923 | − | 10.3301i | −0.715120 | − | 0.412875i | ||||
\(627\) | −4.96335 | + | 18.5235i | −0.198217 | + | 0.739756i | ||||
\(628\) | 19.1798 | + | 5.13922i | 0.765358 | + | 0.205077i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.784610 | −0.0312348 | −0.0156174 | − | 0.999878i | \(-0.504971\pi\) | ||||
−0.0156174 | + | 0.999878i | \(0.504971\pi\) | |||||||
\(632\) | 9.65926 | + | 2.58819i | 0.384225 | + | 0.102953i | ||||
\(633\) | 2.00120 | − | 0.536220i | 0.0795406 | − | 0.0213128i | ||||
\(634\) | −5.70577 | − | 3.29423i | −0.226605 | − | 0.130831i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.09808 | − | 12.2942i | 0.281457 | − | 0.487498i | ||||
\(637\) | 18.8516 | − | 70.3553i | 0.746929 | − | 2.78758i | ||||
\(638\) | 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 | \(0.594627\pi\) | |||||||
\(642\) | −18.7315 | − | 5.01910i | −0.739274 | − | 0.198088i | ||||
\(643\) | 9.67784 | + | 36.1182i | 0.381657 | + | 1.42436i | 0.843370 | + | 0.537333i | \(0.180568\pi\) |
−0.461713 | + | 0.887029i | \(0.652765\pi\) | |||||||
\(644\) | −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 | \(-0.659979\pi\) |
0.876338 | + | 0.481696i | \(0.159979\pi\) | |||||||
\(648\) | −6.36396 | − | 6.36396i | −0.250000 | − | 0.250000i | ||||
\(649\) | 19.1769i | 0.752760i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.60770i | 0.0630105i | ||||||||
\(652\) | −13.8325 | + | 3.70642i | −0.541724 | + | 0.145155i | ||||
\(653\) | −7.91688 | + | 2.12132i | −0.309811 | + | 0.0830137i | −0.410375 | − | 0.911917i | \(-0.634602\pi\) |
0.100564 | + | 0.994931i | \(0.467935\pi\) | |||||||
\(654\) | 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 | \(0.119407\pi\) |
−0.147925 | + | 0.988999i | \(0.547260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5885 | − | 33.9282i | 0.761903 | − | 1.31965i | −0.179966 | − | 0.983673i | \(-0.557599\pi\) |
0.941869 | − | 0.335981i | \(-0.109068\pi\) | |||||||
\(662\) | 3.51695 | + | 13.1254i | 0.136690 | + | 0.510135i | ||||
\(663\) | 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 | ||||
\(668\) | 4.24264 | − | 15.8338i | 0.164153 | − | 0.612626i | ||||
\(669\) | 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 | ||||
\(673\) | −21.6293 | − | 5.79555i | −0.833748 | − | 0.223402i | −0.183400 | − | 0.983038i | \(-0.558710\pi\) |
−0.650348 | + | 0.759636i | \(0.725377\pi\) | |||||||
\(674\) | 20.5359 | 0.791013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.39230 | −0.361242 | ||||||||
\(677\) | 23.7506 | + | 6.36396i | 0.912811 | + | 0.244587i | 0.684510 | − | 0.729004i | \(-0.260016\pi\) |
0.228301 | + | 0.973591i | \(0.426683\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | −0.175865 | + | 0.656339i | −0.00673424 | + | 0.0251325i | ||||
\(683\) | 5.94786 | + | 5.94786i | 0.227588 | + | 0.227588i | 0.811685 | − | 0.584096i | \(-0.198551\pi\) |
−0.584096 | + | 0.811685i | \(0.698551\pi\) | |||||||
\(684\) | 8.30385 | + | 4.79423i | 0.317506 | + | 0.183312i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 34.3923 | − | 19.8564i | 1.31310 | − | 0.758121i | ||||
\(687\) | 2.60179 | + | 9.71003i | 0.0992646 | + | 0.370461i | ||||
\(688\) | −0.120118 | − | 0.448288i | −0.00457947 | − | 0.0170908i | ||||
\(689\) | −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 | ||||
\(693\) | −47.5013 | + | 12.7279i | −1.80442 | + | 0.483494i | ||||
\(694\) | − | 8.78461i | − | 0.333459i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.0981 | − | 9.29423i | 0.610196 | − | 0.352297i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.93185 | − | 0.517638i | 0.0731217 | − | 0.0195929i | ||||
\(699\) | − | 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 | ||||
\(707\) | 8.90138 | + | 33.2204i | 0.334771 | + | 1.24938i | ||||
\(708\) | 9.26174 | + | 2.48168i | 0.348077 | + | 0.0932671i | ||||
\(709\) | −31.3468 | + | 18.0981i | −1.17725 | + | 0.679688i | −0.955378 | − | 0.295387i | \(-0.904551\pi\) |
−0.221876 | + | 0.975075i | \(0.571218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | −6.12372 | − | 6.12372i | −0.229496 | − | 0.229496i | ||||
\(713\) | −0.111494 | + | 0.416102i | −0.00417549 | + | 0.0155831i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7942 | + | 11.4282i | 0.739745 | + | 0.427092i | ||||
\(717\) | 6.36396 | − | 1.70522i | 0.237666 | − | 0.0636825i | ||||
\(718\) | −34.1170 | − | 9.14162i | −1.27323 | − | 0.341162i | ||||
\(719\) | −14.8756 | −0.554768 | −0.277384 | − | 0.960759i | \(-0.589467\pi\) | ||||
−0.277384 | + | 0.960759i | \(0.589467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.1769 | 1.83144 | ||||||||
\(722\) | 8.48528 | + | 2.27362i | 0.315789 | + | 0.0846155i | ||||
\(723\) | −4.21046 | + | 15.7136i | −0.156589 | + | 0.584396i | ||||
\(724\) | −10.7321 | − | 6.19615i | −0.398854 | − | 0.230278i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.73205 | −0.0642824 | ||||||||
\(727\) | 1.79315 | − | 6.69213i | 0.0665043 | − | 0.248197i | −0.924669 | − | 0.380773i | \(-0.875658\pi\) |
0.991173 | + | 0.132575i | \(0.0423247\pi\) | |||||||
\(728\) | −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 | ||||
\(733\) | 3.52193 | + | 13.1440i | 0.130085 | + | 0.485486i | 0.999970 | − | 0.00777015i | \(-0.00247334\pi\) |
−0.869884 | + | 0.493256i | \(0.835807\pi\) | |||||||
\(734\) | −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 | \(-0.882679\pi\) | ||
0.932842 | − | 0.360287i | \(-0.117321\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.6865 | − | 13.0981i | −0.833411 | − | 0.481170i | ||||
\(742\) | −37.4631 | + | 10.0382i | −1.37531 | + | 0.368514i | ||||
\(743\) | 32.2359 | − | 8.63759i | 1.18262 | − | 0.316882i | 0.386655 | − | 0.922224i | \(-0.373630\pi\) |
0.795965 | + | 0.605342i | \(0.206964\pi\) | |||||||
\(744\) | 0.294229 | + | 0.169873i | 0.0107869 | + | 0.00622785i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 23.3205i | − | 0.853824i | ||||||
\(747\) | 49.8306 | + | 13.3521i | 1.82321 | + | 0.488527i | ||||
\(748\) | 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 | \(0.228550\pi\) | |||||||
\(752\) | −1.55291 | − | 5.79555i | −0.0566290 | − | 0.211342i | ||||
\(753\) | −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 | −0.999985 | − | 0.00552030i | \(-0.998243\pi\) |
−0.00552030 | − | 0.999985i | \(-0.501757\pi\) | |||||||
\(758\) | −0.101536 | + | 0.378937i | −0.00368795 | + | 0.0137636i | ||||
\(759\) | −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 | \(0.996164\pi\) | |||||||
\(762\) | −3.67423 | + | 13.7124i | −0.133103 | + | 0.496749i | ||||
\(763\) | −8.24504 | − | 2.20925i | −0.298491 | − | 0.0799803i | ||||
\(764\) | 3.46410 | 0.125327 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.41154 | 0.195527 | ||||||||
\(767\) | −25.3035 | − | 6.78006i | −0.913658 | − | 0.244814i | ||||
\(768\) | 1.67303 | − | 0.448288i | 0.0603704 | − | 0.0161762i | ||||
\(769\) | 10.9186 | + | 6.30385i | 0.393734 | + | 0.227323i | 0.683777 | − | 0.729691i | \(-0.260336\pi\) |
−0.290043 | + | 0.957014i | \(0.593669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.9904 | + | 38.0885i | −0.791964 | + | 1.37172i | ||||
\(772\) | 2.86559 | − | 10.6945i | 0.103135 | − | 0.384905i | ||||
\(773\) | 35.9101 | + | 35.9101i | 1.29160 | + | 1.29160i | 0.933798 | + | 0.357800i | \(0.116473\pi\) |
0.357800 | + | 0.933798i | \(0.383527\pi\) | |||||||
\(774\) | 0.696152 | − | 1.20577i | 0.0250227 | − | 0.0433406i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.30385 | + | 1.33013i | −0.0827033 | + | 0.0477488i | ||||
\(777\) | −64.8879 | − | 17.3867i | −2.32784 | − | 0.623743i | ||||
\(778\) | 2.68973 | + | 10.0382i | 0.0964314 | + | 0.359887i | ||||
\(779\) | −2.76795 | + | 4.79423i | −0.0991721 | + | 0.171771i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5885 | − | 21.8038i | −0.450450 | − | 0.780203i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 53.8652 | + | 14.4331i | 1.92499 | + | 0.515798i | ||||
\(784\) | − | 15.3923i | − | 0.549725i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.0000i | 0.428026i | ||||||||
\(787\) | 16.7303 | − | 4.48288i | 0.596372 | − | 0.159797i | 0.0520081 | − | 0.998647i | \(-0.483438\pi\) |
0.544364 | + | 0.838849i | \(0.316771\pi\) | |||||||
\(788\) | −13.7124 | + | 3.67423i | −0.488485 | + | 0.130889i | ||||
\(789\) | 18.8827 | − | 10.9019i | 0.672241 | − | 0.388119i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.3731i | 2.25329i | ||||||||
\(792\) | −2.68973 | + | 10.0382i | −0.0955753 | + | 0.356692i | ||||
\(793\) | −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 | ||||
\(797\) | 10.6066 | + | 39.5844i | 0.375705 | + | 1.40215i | 0.852312 | + | 0.523034i | \(0.175200\pi\) |
−0.476607 | + | 0.879117i | \(0.658133\pi\) | |||||||
\(798\) | −6.78006 | − | 25.3035i | −0.240012 | − | 0.895736i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 25.9808i | − | 0.917985i | ||||||
\(802\) | 7.34847 | + | 7.34847i | 0.259483 | + | 0.259483i | ||||
\(803\) | 4.65874 | − | 17.3867i | 0.164403 | − | 0.613562i | ||||
\(804\) | 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 | ||||
\(808\) | 7.02030 | + | 1.88108i | 0.246973 | + | 0.0661763i | ||||
\(809\) | −1.73205 | −0.0608957 | −0.0304478 | − | 0.999536i | \(-0.509693\pi\) | ||||
−0.0304478 | + | 0.999536i | \(0.509693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.3731 | 1.20700 | 0.603501 | − | 0.797362i | \(-0.293772\pi\) | ||||
0.603501 | + | 0.797362i | \(0.293772\pi\) | |||||||
\(812\) | −49.0542 | − | 13.1440i | −1.72146 | − | 0.461265i | ||||
\(813\) | −32.5641 | − | 32.5641i | −1.14207 | − | 1.14207i | ||||
\(814\) | −24.5885 | − | 14.1962i | −0.861825 | − | 0.497575i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.383917 | + | 1.43280i | −0.0134315 | + | 0.0501272i | ||||
\(818\) | −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 | \(0.251701\pi\) | |||||||
\(822\) | −6.00361 | − | 22.4058i | −0.209400 | − | 0.781491i | ||||
\(823\) | 10.5187 | + | 39.2562i | 0.366658 | + | 1.36839i | 0.865160 | + | 0.501497i | \(0.167217\pi\) |
−0.498502 | + | 0.866889i | \(0.666116\pi\) | |||||||
\(824\) | 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 | \(-0.745551\pi\) |
0.716920 | + | 0.697155i | \(0.245551\pi\) | |||||||
\(828\) | −1.70522 | + | 6.36396i | −0.0592604 | + | 0.221163i | ||||
\(829\) | − | 28.5885i | − | 0.992918i | −0.868060 | − | 0.496459i | \(-0.834633\pi\) | ||
0.868060 | − | 0.496459i | \(-0.165367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2750 | − | 16.9019i | 1.01554 | − | 0.586321i | ||||
\(832\) | −4.57081 | + | 1.22474i | −0.158464 | + | 0.0424604i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.8564i | 0.479808i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 11.0718i | − | 0.382926i | ||||||
\(837\) | 0.263798 | + | 0.984508i | 0.00911820 | + | 0.0340296i | ||||
\(838\) | −6.36396 | + | 6.36396i | −0.219839 | + | 0.219839i | ||||
\(839\) | −6.75833 | − | 11.7058i | −0.233323 | − | 0.404128i | 0.725461 | − | 0.688264i | \(-0.241627\pi\) |
−0.958784 | + | 0.284136i | \(0.908293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0885 | + | 74.6314i | −1.48581 | + | 2.57350i | ||||
\(842\) | −5.84632 | − | 21.8188i | −0.201478 | − | 0.751925i | ||||
\(843\) | −17.3867 | − | 4.65874i | −0.598829 | − | 0.160456i | ||||
\(844\) | −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 | ||||
\(848\) | −2.12132 | + | 7.91688i | −0.0728464 | + | 0.271867i | ||||
\(849\) | 3.40192 | − | 5.89230i | 0.116754 | − | 0.202223i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5885 | − | 9.00000i | −0.534365 | − | 0.308516i | ||||
\(852\) | −12.1595 | + | 3.25813i | −0.416578 | + | 0.111622i | ||||
\(853\) | 18.0430 | + | 4.83461i | 0.617781 | + | 0.165534i | 0.554119 | − | 0.832438i | \(-0.313055\pi\) |
0.0636620 | + | 0.997972i | \(0.479722\pi\) | |||||||
\(854\) | −18.9282 | −0.647710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1962 | 0.382677 | ||||||||
\(857\) | 40.3608 | + | 10.8147i | 1.37870 | + | 0.369422i | 0.870649 | − | 0.491905i | \(-0.163699\pi\) |
0.508051 | + | 0.861327i | \(0.330366\pi\) | |||||||
\(858\) | 7.34847 | − | 27.4249i | 0.250873 | − | 0.936269i | ||||
\(859\) | 36.0167 | + | 20.7942i | 1.22887 | + | 0.709490i | 0.966794 | − | 0.255557i | \(-0.0822587\pi\) |
0.262079 | + | 0.965047i | \(0.415592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.1962 | −0.483804 | ||||||||
\(862\) | −5.46739 | + | 20.4046i | −0.186220 | + | 0.694982i | ||||
\(863\) | −33.2204 | − | 33.2204i | −1.13084 | − | 1.13084i | −0.990038 | − | 0.140798i | \(-0.955033\pi\) |
−0.140798 | − | 0.990038i | \(-0.544967\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | −0.240237 | − | 0.896575i | −0.00815416 | − | 0.0304318i | ||||
\(869\) | 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 | ||||
\(873\) | −7.70882 | − | 2.06557i | −0.260904 | − | 0.0699091i | ||||
\(874\) | − | 7.01924i | − | 0.237429i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.79423 | − | 4.50000i | −0.263343 | − | 0.152041i | ||||
\(877\) | 35.6699 | − | 9.55772i | 1.20449 | − | 0.322741i | 0.399890 | − | 0.916563i | \(-0.369048\pi\) |
0.804597 | + | 0.593822i | \(0.202382\pi\) | |||||||
\(878\) | −1.36345 | + | 0.365334i | −0.0460141 | + | 0.0123294i | ||||
\(879\) | −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 | −0.329037 | − | 0.944317i | \(-0.606724\pi\) |
0.944317 | + | 0.329037i | \(0.106724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.19615 | − | 9.00000i | 0.174568 | − | 0.302361i | ||||
\(887\) | −2.68973 | − | 10.0382i | −0.0903122 | − | 0.337050i | 0.905955 | − | 0.423374i | \(-0.139154\pi\) |
−0.996267 | + | 0.0863246i | \(0.972488\pi\) | |||||||
\(888\) | −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 | ||||
\(893\) | −4.96335 | + | 18.5235i | −0.166092 | + | 0.619865i | ||||
\(894\) | −31.1769 | −1.04271 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.09808 | − | 2.36603i | −0.136907 | − | 0.0790434i | ||||
\(897\) | 4.65874 | − | 17.3867i | 0.155551 | − | 0.580524i | ||||
\(898\) | 29.0979 | + | 7.79676i | 0.971009 | + | 0.260181i | ||||
\(899\) | −2.10512 | −0.0702096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −5.79555 | − | 1.55291i | −0.192971 | − | 0.0517064i | ||||
\(903\) | −3.67423 | + | 0.984508i | −0.122271 | + | 0.0327624i | ||||
\(904\) | 11.5981 | + | 6.69615i | 0.385746 | + | 0.222711i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.92820 | − | 12.0000i | 0.230174 | − | 0.398673i | ||||
\(907\) | −8.54103 | + | 31.8756i | −0.283600 | + | 1.05841i | 0.666256 | + | 0.745723i | \(0.267896\pi\) |
−0.949856 | + | 0.312687i | \(0.898771\pi\) | |||||||
\(908\) | 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 | \(0.108887\pi\) | |||||||
\(912\) | −5.34727 | − | 1.43280i | −0.177066 | − | 0.0474446i | ||||
\(913\) | −15.4176 | − | 57.5394i | −0.510250 | − | 1.90428i | ||||
\(914\) | 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 | \(-0.582838\pi\) | ||
0.257316 | − | 0.966327i | \(-0.417162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000i | 0.197707i | ||||||||
\(922\) | −9.71003 | + | 2.60179i | −0.319783 | + | 0.0856855i | ||||
\(923\) | 33.2204 | − | 8.90138i | 1.09346 | − | 0.292993i | ||||
\(924\) | 24.5885 | − | 14.1962i | 0.808901 | − | 0.467019i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 2.19615i | − | 0.0721700i | ||||||
\(927\) | 30.1146 | − | 8.06918i | 0.989093 | − | 0.265027i | ||||
\(928\) | −7.58871 | + | 7.58871i | −0.249111 | + | 0.249111i | ||||
\(929\) | −15.9282 | − | 27.5885i | −0.522587 | − | 0.905148i | −0.999655 | − | 0.0262811i | \(-0.991634\pi\) |
0.477067 | − | 0.878867i | \(-0.341700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.5981 | + | 42.6051i | −0.806169 | + | 1.39633i | ||||
\(932\) | 1.19256 | + | 4.45069i | 0.0390636 | + | 0.145787i | ||||
\(933\) | 4.96335 | + | 18.5235i | 0.162493 | + | 0.606431i | ||||
\(934\) | 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 | 0.934550 | − | 0.355832i | \(-0.115802\pi\) |
−0.355832 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(938\) | 6.78006 | − | 25.3035i | 0.221377 | − | 0.826190i | ||||
\(939\) | 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 | ||||
\(943\) | −3.67423 | − | 0.984508i | −0.119650 | − | 0.0320600i | ||||
\(944\) | −5.53590 | −0.180178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.60770 | −0.0522707 | ||||||||
\(947\) | −40.9292 | − | 10.9670i | −1.33002 | − | 0.356378i | −0.477298 | − | 0.878741i | \(-0.658384\pi\) |
−0.852723 | + | 0.522363i | \(0.825051\pi\) | |||||||
\(948\) | −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 | \(-0.352869\pi\) |
−0.895063 | + | 0.445940i | \(0.852869\pi\) | |||||||
\(954\) | −21.2942 | + | 12.2942i | −0.689426 | + | 0.398040i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.29423 | + | 1.90192i | −0.106543 | + | 0.0615126i | ||||
\(957\) | −16.6660 | − | 62.1982i | −0.538734 | − | 2.01058i | ||||
\(958\) | −0.808643 | − | 3.01790i | −0.0261261 | − | 0.0975038i | ||||
\(959\) | −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 | ||||
\(967\) | −40.1528 | + | 10.7589i | −1.29123 | + | 0.345983i | −0.838126 | − | 0.545476i | \(-0.816349\pi\) |
−0.453100 | + | 0.891460i | \(0.649682\pi\) | |||||||
\(968\) | 0.965926 | − | 0.258819i | 0.0310460 | − | 0.00831876i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.0333i | 1.73401i | 0.498298 | + | 0.867006i | \(0.333959\pi\) | ||||
−0.498298 | + | 0.867006i | \(0.666041\pi\) | |||||||
\(972\) | 4.03459 | + | 15.0573i | 0.129410 | + | 0.482963i | ||||
\(973\) | 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 | ||||
\(977\) | −11.9515 | − | 44.6035i | −0.382361 | − | 1.42699i | −0.842285 | − | 0.539033i | \(-0.818790\pi\) |
0.459923 | − | 0.887959i | \(-0.347877\pi\) | |||||||
\(978\) | 23.9587 | + | 6.41971i | 0.766114 | + | 0.205280i | ||||
\(979\) | −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 | ||||
\(983\) | −11.1750 | + | 41.7057i | −0.356427 | + | 1.33021i | 0.522251 | + | 0.852792i | \(0.325092\pi\) |
−0.878679 | + | 0.477414i | \(0.841574\pi\) | |||||||
\(984\) | −1.50000 | + | 2.59808i | −0.0478183 | + | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.5013 | + | 12.7279i | −1.51198 | + | 0.405134i | ||||
\(988\) | 14.6090 | + | 3.91447i | 0.464774 | + | 0.124536i | ||||
\(989\) | −1.01924 | −0.0324099 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1769 | −0.926835 | −0.463418 | − | 0.886140i | \(-0.653377\pi\) | ||||
−0.463418 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(992\) | −0.189469 | − | 0.0507680i | −0.00601564 | − | 0.00161189i | ||||
\(993\) | 6.09154 | − | 22.7339i | 0.193309 | − | 0.721440i | ||||
\(994\) | 29.7846 | + | 17.1962i | 0.944710 | + | 0.545429i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −29.7846 | −0.943761 | ||||||||
\(997\) | −5.64325 | + | 21.0609i | −0.178724 | + | 0.667005i | 0.817164 | + | 0.576405i | \(0.195545\pi\) |
−0.995887 | + | 0.0905999i | \(0.971122\pi\) | |||||||
\(998\) | 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.c.257.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.d.557.1 | 8 | |||
5.2 | odd | 4 | 450.2.p.e.293.1 | yes | 8 | ||
5.3 | odd | 4 | 450.2.p.e.293.2 | yes | 8 | ||
5.4 | even | 2 | inner | 450.2.p.c.257.1 | ✓ | 8 | |
9.2 | odd | 6 | 450.2.p.e.407.2 | yes | 8 | ||
9.7 | even | 3 | 1350.2.q.a.1007.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.a.1043.2 | 8 | |||
15.8 | even | 4 | 1350.2.q.a.1043.1 | 8 | |||
15.14 | odd | 2 | 1350.2.q.d.557.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.c.443.1 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.d.143.2 | 8 | |||
45.29 | odd | 6 | 450.2.p.e.407.1 | yes | 8 | ||
45.34 | even | 6 | 1350.2.q.a.1007.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.c.443.2 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.d.143.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.c.257.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
450.2.p.c.257.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.c.443.1 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.c.443.2 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.e.293.1 | yes | 8 | 5.2 | odd | 4 | ||
450.2.p.e.293.2 | yes | 8 | 5.3 | odd | 4 | ||
450.2.p.e.407.1 | yes | 8 | 45.29 | odd | 6 | ||
450.2.p.e.407.2 | yes | 8 | 9.2 | odd | 6 | ||
1350.2.q.a.1007.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.a.1007.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.a.1043.1 | 8 | 15.8 | even | 4 | |||
1350.2.q.a.1043.2 | 8 | 15.2 | even | 4 | |||
1350.2.q.d.143.1 | 8 | 45.43 | odd | 12 | |||
1350.2.q.d.143.2 | 8 | 45.7 | odd | 12 | |||
1350.2.q.d.557.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.d.557.2 | 8 | 15.14 | odd | 2 |