Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(269,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.269 |
Dual form | 370.2.n.b.359.2 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.133975 | + | 2.23205i | 0.0599153 | + | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | − | 2.00000i | 1.30931 | − | 0.755929i | 0.327327 | − | 0.944911i | \(-0.393852\pi\) |
0.981981 | + | 0.188982i | \(0.0605189\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.866025 | − | 0.500000i | 0.240192 | − | 0.138675i | −0.375073 | − | 0.926995i | \(-0.622382\pi\) |
0.615265 | + | 0.788320i | \(0.289049\pi\) | |||||||
\(14\) | 4.00000 | 1.06904 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 5.19615 | + | 3.00000i | 1.26025 | + | 0.727607i | 0.973123 | − | 0.230285i | \(-0.0739659\pi\) |
0.287129 | + | 0.957892i | \(0.407299\pi\) | |||||||
\(18\) | −2.59808 | + | 1.50000i | −0.612372 | + | 0.353553i | ||||
\(19\) | −1.50000 | − | 2.59808i | −0.344124 | − | 0.596040i | 0.641071 | − | 0.767482i | \(-0.278491\pi\) |
−0.985194 | + | 0.171442i | \(0.945157\pi\) | |||||||
\(20\) | −1.86603 | + | 1.23205i | −0.417256 | + | 0.275495i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.59808 | − | 1.50000i | −0.553912 | − | 0.319801i | ||||
\(23\) | − | 1.00000i | − | 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.46410 | + | 2.00000i | 0.654654 | + | 0.377964i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | + | 5.19615i | 0.514496 | + | 0.891133i | ||||
\(35\) | 4.92820 | + | 7.46410i | 0.833018 | + | 1.26166i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −2.59808 | − | 5.50000i | −0.427121 | − | 0.904194i | ||||
\(38\) | − | 3.00000i | − | 0.486664i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23205 | + | 0.133975i | −0.352918 | + | 0.0211832i | ||||
\(41\) | 5.00000 | + | 8.66025i | 0.780869 | + | 1.35250i | 0.931436 | + | 0.363905i | \(0.118557\pi\) |
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | −6.00000 | − | 3.00000i | −0.894427 | − | 0.447214i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | − | 11.0000i | − | 1.60451i | −0.596978 | − | 0.802257i | \(-0.703632\pi\) | ||
0.596978 | − | 0.802257i | \(-0.296368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | −4.59808 | − | 1.96410i | −0.650266 | − | 0.277766i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.866025 | + | 0.500000i | 0.120096 | + | 0.0693375i | ||||
\(53\) | −8.66025 | − | 5.00000i | −1.18958 | − | 0.686803i | −0.231367 | − | 0.972867i | \(-0.574320\pi\) |
−0.958211 | + | 0.286064i | \(0.907653\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.401924 | − | 6.69615i | −0.0541954 | − | 0.902909i | ||||
\(56\) | 2.00000 | + | 3.46410i | 0.267261 | + | 0.462910i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.19615 | + | 3.00000i | 0.682288 | + | 0.393919i | ||||
\(59\) | 7.50000 | − | 12.9904i | 0.976417 | − | 1.69120i | 0.301239 | − | 0.953549i | \(-0.402600\pi\) |
0.675178 | − | 0.737655i | \(-0.264067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 10.3923i | −0.768221 | − | 1.33060i | −0.938527 | − | 0.345207i | \(-0.887809\pi\) |
0.170305 | − | 0.985391i | \(-0.445525\pi\) | |||||||
\(62\) | −3.46410 | − | 2.00000i | −0.439941 | − | 0.254000i | ||||
\(63\) | 12.0000i | 1.51186i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.23205 | + | 1.86603i | 0.152817 | + | 0.231452i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73205 | − | 1.00000i | 0.211604 | − | 0.122169i | −0.390453 | − | 0.920623i | \(-0.627682\pi\) |
0.602056 | + | 0.798454i | \(0.294348\pi\) | |||||||
\(68\) | 6.00000i | 0.727607i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.535898 | + | 8.92820i | 0.0640521 | + | 1.06712i | ||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 0.500000 | − | 6.06218i | 0.0581238 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.50000 | − | 2.59808i | 0.172062 | − | 0.298020i | ||||
\(77\) | −10.3923 | + | 6.00000i | −1.18431 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 10.0000i | 1.10432i | ||||||||
\(83\) | −5.19615 | − | 3.00000i | −0.570352 | − | 0.329293i | 0.186938 | − | 0.982372i | \(-0.440144\pi\) |
−0.757290 | + | 0.653079i | \(0.773477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 12.0000i | −0.650791 | + | 1.30158i | ||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.00000i | − | 0.319801i | ||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | −3.69615 | − | 5.59808i | −0.389609 | − | 0.590089i | ||||
\(91\) | 2.00000 | − | 3.46410i | 0.209657 | − | 0.363137i | ||||
\(92\) | 0.866025 | − | 0.500000i | 0.0902894 | − | 0.0521286i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.50000 | − | 9.52628i | 0.567282 | − | 0.982561i | ||||
\(95\) | 5.59808 | − | 3.69615i | 0.574351 | − | 0.379217i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 7.79423 | − | 4.50000i | 0.787336 | − | 0.454569i | ||||
\(99\) | 4.50000 | − | 7.79423i | 0.452267 | − | 0.783349i | ||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −4.00000 | −0.398015 | −0.199007 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199007 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00000i | 0.886796i | 0.896325 | + | 0.443398i | \(0.146227\pi\) | ||||
−0.896325 | + | 0.443398i | \(0.853773\pi\) | |||||||
\(104\) | 0.500000 | + | 0.866025i | 0.0490290 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.00000 | − | 8.66025i | −0.485643 | − | 0.841158i | ||||
\(107\) | 6.92820 | − | 4.00000i | 0.669775 | − | 0.386695i | −0.126217 | − | 0.992003i | \(-0.540283\pi\) |
0.795991 | + | 0.605308i | \(0.206950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | 3.00000 | − | 6.00000i | 0.286039 | − | 0.572078i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | −8.66025 | − | 5.00000i | −0.814688 | − | 0.470360i | 0.0338931 | − | 0.999425i | \(-0.489209\pi\) |
−0.848581 | + | 0.529065i | \(0.822543\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.23205 | − | 0.133975i | 0.208140 | − | 0.0124932i | ||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | 3.00000i | 0.277350i | ||||||||
\(118\) | 12.9904 | − | 7.50000i | 1.19586 | − | 0.690431i | ||||
\(119\) | 24.0000 | 2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 12.0000i | − | 1.08643i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | −6.00000 | + | 10.3923i | −0.534522 | + | 0.925820i | ||||
\(127\) | 14.7224 | + | 8.50000i | 1.30640 | + | 0.754253i | 0.981494 | − | 0.191492i | \(-0.0613325\pi\) |
0.324910 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.133975 | + | 2.23205i | 0.0117503 | + | 0.195764i | ||||
\(131\) | −10.0000 | + | 17.3205i | −0.873704 | + | 1.51330i | −0.0155672 | + | 0.999879i | \(0.504955\pi\) |
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3923 | − | 6.00000i | −0.901127 | − | 0.520266i | ||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | −4.00000 | + | 8.00000i | −0.338062 | + | 0.676123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | −2.59808 | + | 1.50000i | −0.217262 | + | 0.125436i | ||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 0.803848 | + | 13.3923i | 0.0667559 | + | 1.11217i | ||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.46410 | − | 5.00000i | 0.284747 | − | 0.410997i | ||||
\(149\) | 16.0000 | 1.31077 | 0.655386 | − | 0.755295i | \(-0.272506\pi\) | ||||
0.655386 | + | 0.755295i | \(0.272506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 2.59808 | − | 1.50000i | 0.210732 | − | 0.121666i | ||||
\(153\) | −15.5885 | + | 9.00000i | −1.26025 | + | 0.727607i | ||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | −0.535898 | − | 8.92820i | −0.0430444 | − | 0.717131i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.33013 | + | 2.50000i | 0.345582 | + | 0.199522i | 0.662738 | − | 0.748852i | \(-0.269394\pi\) |
−0.317156 | + | 0.948373i | \(0.602728\pi\) | |||||||
\(158\) | 4.00000i | 0.318223i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.23205 | − | 1.86603i | −0.0974022 | − | 0.147522i | ||||
\(161\) | −2.00000 | − | 3.46410i | −0.157622 | − | 0.273009i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 5.19615 | + | 3.00000i | 0.406994 | + | 0.234978i | 0.689497 | − | 0.724288i | \(-0.257831\pi\) |
−0.282503 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(164\) | −5.00000 | + | 8.66025i | −0.390434 | + | 0.676252i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | −6.92820 | + | 4.00000i | −0.536120 | + | 0.309529i | −0.743505 | − | 0.668730i | \(-0.766838\pi\) |
0.207385 | + | 0.978259i | \(0.433505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | + | 10.3923i | −0.461538 | + | 0.799408i | ||||
\(170\) | −11.1962 | + | 7.39230i | −0.858706 | + | 0.566964i | ||||
\(171\) | 9.00000 | 0.688247 | ||||||||
\(172\) | 1.73205 | − | 1.00000i | 0.132068 | − | 0.0762493i | ||||
\(173\) | 4.33013 | + | 2.50000i | 0.329213 | + | 0.190071i | 0.655492 | − | 0.755202i | \(-0.272461\pi\) |
−0.326278 | + | 0.945274i | \(0.605795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0000 | + | 12.0000i | −1.20949 | + | 0.907115i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9904 | + | 7.50000i | −0.973670 | + | 0.562149i | ||||
\(179\) | −1.00000 | −0.0747435 | −0.0373718 | − | 0.999301i | \(-0.511899\pi\) | ||||
−0.0373718 | + | 0.999301i | \(0.511899\pi\) | |||||||
\(180\) | −0.401924 | − | 6.69615i | −0.0299576 | − | 0.499102i | ||||
\(181\) | 8.00000 | + | 13.8564i | 0.594635 | + | 1.02994i | 0.993598 | + | 0.112972i | \(0.0360369\pi\) |
−0.398963 | + | 0.916967i | \(0.630630\pi\) | |||||||
\(182\) | 3.46410 | − | 2.00000i | 0.256776 | − | 0.148250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 11.9282 | − | 6.53590i | 0.876979 | − | 0.480529i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5885 | − | 9.00000i | −1.13994 | − | 0.658145i | ||||
\(188\) | 9.52628 | − | 5.50000i | 0.694775 | − | 0.401129i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.69615 | − | 0.401924i | 0.485790 | − | 0.0291586i | ||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.0000i | − | 1.15171i | −0.817554 | − | 0.575853i | \(-0.804670\pi\) | ||
0.817554 | − | 0.575853i | \(-0.195330\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 19.0526 | + | 11.0000i | 1.35744 | + | 0.783718i | 0.989278 | − | 0.146045i | \(-0.0466543\pi\) |
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(198\) | 7.79423 | − | 4.50000i | 0.553912 | − | 0.319801i | ||||
\(199\) | −22.0000 | −1.55954 | −0.779769 | − | 0.626067i | \(-0.784664\pi\) | ||||
−0.779769 | + | 0.626067i | \(0.784664\pi\) | |||||||
\(200\) | −0.598076 | − | 4.96410i | −0.0422904 | − | 0.351015i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.46410 | − | 2.00000i | −0.243733 | − | 0.140720i | ||||
\(203\) | 20.7846 | − | 12.0000i | 1.45879 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.6603 | + | 12.3205i | −1.30329 | + | 0.860502i | ||||
\(206\) | −4.50000 | + | 7.79423i | −0.313530 | + | 0.543050i | ||||
\(207\) | 2.59808 | + | 1.50000i | 0.180579 | + | 0.104257i | ||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | 4.50000 | + | 7.79423i | 0.311272 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | − | 10.0000i | − | 0.686803i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | 4.46410 | − | 0.267949i | 0.304449 | − | 0.0182740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8564 | + | 8.00000i | −0.940634 | + | 0.543075i | ||||
\(218\) | 8.66025 | − | 5.00000i | 0.586546 | − | 0.338643i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.59808 | − | 3.69615i | 0.377422 | − | 0.249195i | ||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.00000i | − | 0.334825i | −0.985887 | − | 0.167412i | \(-0.946459\pi\) | ||
0.985887 | − | 0.167412i | \(-0.0535411\pi\) | |||||||
\(224\) | −2.00000 | + | 3.46410i | −0.133631 | + | 0.231455i | ||||
\(225\) | 5.89230 | − | 13.7942i | 0.392820 | − | 0.919615i | ||||
\(226\) | −5.00000 | − | 8.66025i | −0.332595 | − | 0.576072i | ||||
\(227\) | −24.2487 | + | 14.0000i | −1.60944 | + | 0.929213i | −0.619949 | + | 0.784642i | \(0.712847\pi\) |
−0.989494 | + | 0.144571i | \(0.953820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 2.00000 | + | 1.00000i | 0.131876 | + | 0.0659380i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | −1.50000 | + | 2.59808i | −0.0980581 | + | 0.169842i | ||||
\(235\) | 24.5526 | − | 1.47372i | 1.60163 | − | 0.0961349i | ||||
\(236\) | 15.0000 | 0.976417 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.7846 | + | 12.0000i | 1.34727 | + | 0.777844i | ||||
\(239\) | −10.0000 | + | 17.3205i | −0.646846 | + | 1.12037i | 0.337026 | + | 0.941495i | \(0.390579\pi\) |
−0.983872 | + | 0.178875i | \(0.942754\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | − | 10.3923i | 0.384111 | − | 0.665299i | ||||
\(245\) | 18.0000 | + | 9.00000i | 1.14998 | + | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.59808 | − | 1.50000i | −0.165312 | − | 0.0954427i | ||||
\(248\) | − | 4.00000i | − | 0.254000i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.76795 | − | 10.5263i | 0.238306 | − | 0.665740i | ||||
\(251\) | −1.00000 | −0.0631194 | −0.0315597 | − | 0.999502i | \(-0.510047\pi\) | ||||
−0.0315597 | + | 0.999502i | \(0.510047\pi\) | |||||||
\(252\) | −10.3923 | + | 6.00000i | −0.654654 | + | 0.377964i | ||||
\(253\) | 3.00000i | 0.188608i | ||||||||
\(254\) | 8.50000 | + | 14.7224i | 0.533337 | + | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0000 | − | 13.8564i | −1.24274 | − | 0.860995i | ||||
\(260\) | −1.00000 | + | 2.00000i | −0.0620174 | + | 0.124035i | ||||
\(261\) | −9.00000 | + | 15.5885i | −0.557086 | + | 0.964901i | ||||
\(262\) | −17.3205 | + | 10.0000i | −1.07006 | + | 0.617802i | ||||
\(263\) | −16.4545 | + | 9.50000i | −1.01463 | + | 0.585795i | −0.912543 | − | 0.408981i | \(-0.865884\pi\) |
−0.102084 | + | 0.994776i | \(0.532551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | − | 20.0000i | 0.614295 | − | 1.22859i | ||||
\(266\) | −6.00000 | − | 10.3923i | −0.367884 | − | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.73205 | + | 1.00000i | 0.105802 | + | 0.0610847i | ||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | −5.19615 | + | 3.00000i | −0.315063 | + | 0.181902i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | + | 5.19615i | −0.181237 | + | 0.313911i | ||||
\(275\) | 14.8923 | − | 1.79423i | 0.898040 | − | 0.108196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.19615 | + | 3.00000i | −0.312207 | + | 0.180253i | −0.647913 | − | 0.761714i | \(-0.724358\pi\) |
0.335707 | + | 0.941966i | \(0.391025\pi\) | |||||||
\(278\) | −4.33013 | + | 2.50000i | −0.259704 | + | 0.149940i | ||||
\(279\) | 6.00000 | − | 10.3923i | 0.359211 | − | 0.622171i | ||||
\(280\) | −7.46410 | + | 4.92820i | −0.446065 | + | 0.294516i | ||||
\(281\) | 1.50000 | − | 2.59808i | 0.0894825 | − | 0.154988i | −0.817810 | − | 0.575488i | \(-0.804812\pi\) |
0.907293 | + | 0.420500i | \(0.138145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46410 | + | 2.00000i | −0.205919 | + | 0.118888i | −0.599414 | − | 0.800439i | \(-0.704600\pi\) |
0.393494 | + | 0.919327i | \(0.371266\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.00000 | −0.177394 | ||||||||
\(287\) | 34.6410 | + | 20.0000i | 2.04479 | + | 1.18056i | ||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | −6.00000 | + | 12.0000i | −0.352332 | + | 0.704664i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.73205 | − | 1.00000i | 0.101361 | − | 0.0585206i | ||||
\(293\) | −2.59808 | + | 1.50000i | −0.151781 | + | 0.0876309i | −0.573967 | − | 0.818878i | \(-0.694596\pi\) |
0.422186 | + | 0.906509i | \(0.361263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.0000 | + | 15.0000i | 1.74667 | + | 0.873334i | ||||
\(296\) | 5.50000 | − | 2.59808i | 0.319681 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.8564 | + | 8.00000i | 0.802680 | + | 0.463428i | ||||
\(299\) | −0.500000 | − | 0.866025i | −0.0289157 | − | 0.0500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 6.92820i | −0.230556 | − | 0.399335i | ||||
\(302\) | 2.00000i | 0.115087i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | 22.3923 | − | 14.7846i | 1.28218 | − | 0.846564i | ||||
\(306\) | −18.0000 | −1.02899 | ||||||||
\(307\) | − | 32.0000i | − | 1.82634i | −0.407583 | − | 0.913168i | \(-0.633628\pi\) | ||
0.407583 | − | 0.913168i | \(-0.366372\pi\) | |||||||
\(308\) | −10.3923 | − | 6.00000i | −0.592157 | − | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | − | 8.00000i | 0.227185 | − | 0.454369i | ||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.7128 | − | 16.0000i | −1.56642 | − | 0.904373i | −0.996581 | − | 0.0826174i | \(-0.973672\pi\) |
−0.569839 | − | 0.821756i | \(-0.692995\pi\) | |||||||
\(314\) | 2.50000 | + | 4.33013i | 0.141083 | + | 0.244363i | ||||
\(315\) | −26.7846 | + | 1.60770i | −1.50914 | + | 0.0905834i | ||||
\(316\) | −2.00000 | + | 3.46410i | −0.112509 | + | 0.194871i | ||||
\(317\) | −7.79423 | − | 4.50000i | −0.437767 | − | 0.252745i | 0.264883 | − | 0.964281i | \(-0.414667\pi\) |
−0.702650 | + | 0.711535i | \(0.748000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | −0.133975 | − | 2.23205i | −0.00748941 | − | 0.124775i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 4.00000i | − | 0.222911i | ||||||
\(323\) | − | 18.0000i | − | 1.00155i | ||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | −4.00000 | + | 3.00000i | −0.221880 | + | 0.166410i | ||||
\(326\) | 3.00000 | + | 5.19615i | 0.166155 | + | 0.287788i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.66025 | + | 5.00000i | −0.478183 | + | 0.276079i | ||||
\(329\) | −22.0000 | − | 38.1051i | −1.21290 | − | 2.10080i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | − | 11.2583i | 0.357272 | − | 0.618814i | −0.630232 | − | 0.776407i | \(-0.717040\pi\) |
0.987504 | + | 0.157593i | \(0.0503735\pi\) | |||||||
\(332\) | − | 6.00000i | − | 0.329293i | ||||||
\(333\) | 18.1865 | + | 1.50000i | 0.996616 | + | 0.0821995i | ||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 2.46410 | + | 3.73205i | 0.134628 | + | 0.203904i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.92820 | − | 4.00000i | 0.377403 | − | 0.217894i | −0.299285 | − | 0.954164i | \(-0.596748\pi\) |
0.676688 | + | 0.736270i | \(0.263415\pi\) | |||||||
\(338\) | −10.3923 | + | 6.00000i | −0.565267 | + | 0.326357i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.3923 | + | 0.803848i | −0.726300 | + | 0.0435948i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 7.79423 | + | 4.50000i | 0.421464 | + | 0.243332i | ||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.50000 | + | 4.33013i | 0.134401 | + | 0.232789i | ||||
\(347\) | − | 30.0000i | − | 1.61048i | −0.592946 | − | 0.805242i | \(-0.702035\pi\) | ||
0.592946 | − | 0.805242i | \(-0.297965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.00000 | − | 5.19615i | 0.160586 | − | 0.278144i | −0.774493 | − | 0.632583i | \(-0.781995\pi\) |
0.935079 | + | 0.354439i | \(0.115328\pi\) | |||||||
\(350\) | −19.8564 | + | 2.39230i | −1.06137 | + | 0.127874i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59808 | − | 1.50000i | 0.138478 | − | 0.0799503i | ||||
\(353\) | 15.5885 | + | 9.00000i | 0.829690 | + | 0.479022i | 0.853746 | − | 0.520689i | \(-0.174325\pi\) |
−0.0240566 | + | 0.999711i | \(0.507658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1962 | + | 7.39230i | −0.594230 | + | 0.392343i | ||||
\(356\) | −15.0000 | −0.794998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.866025 | − | 0.500000i | −0.0457709 | − | 0.0264258i | ||||
\(359\) | 26.0000 | 1.37223 | 0.686114 | − | 0.727494i | \(-0.259315\pi\) | ||||
0.686114 | + | 0.727494i | \(0.259315\pi\) | |||||||
\(360\) | 3.00000 | − | 6.00000i | 0.158114 | − | 0.316228i | ||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | 16.0000i | 0.840941i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 4.46410 | − | 0.267949i | 0.233662 | − | 0.0140251i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2583 | − | 6.50000i | 0.587680 | − | 0.339297i | −0.176500 | − | 0.984301i | \(-0.556477\pi\) |
0.764180 | + | 0.645003i | \(0.223144\pi\) | |||||||
\(368\) | 0.866025 | + | 0.500000i | 0.0451447 | + | 0.0260643i | ||||
\(369\) | −30.0000 | −1.56174 | ||||||||
\(370\) | 13.5981 | + | 0.303848i | 0.706930 | + | 0.0157963i | ||||
\(371\) | −40.0000 | −2.07670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.9186 | + | 11.5000i | −1.03135 | + | 0.595447i | −0.917370 | − | 0.398036i | \(-0.869692\pi\) |
−0.113975 | + | 0.993484i | \(0.536359\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0000 | 0.567282 | ||||||||
\(377\) | 5.19615 | − | 3.00000i | 0.267615 | − | 0.154508i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | + | 20.7846i | −0.616399 | + | 1.06763i | 0.373739 | + | 0.927534i | \(0.378076\pi\) |
−0.990137 | + | 0.140100i | \(0.955258\pi\) | |||||||
\(380\) | 6.00000 | + | 3.00000i | 0.307794 | + | 0.153897i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.46410 | + | 2.00000i | 0.177239 | + | 0.102329i | ||||
\(383\) | −14.7224 | + | 8.50000i | −0.752281 | + | 0.434330i | −0.826518 | − | 0.562911i | \(-0.809681\pi\) |
0.0742364 | + | 0.997241i | \(0.476348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.7846 | − | 22.3923i | −0.753493 | − | 1.14122i | ||||
\(386\) | 8.00000 | − | 13.8564i | 0.407189 | − | 0.705273i | ||||
\(387\) | 5.19615 | + | 3.00000i | 0.264135 | + | 0.152499i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | −2.00000 | − | 3.46410i | −0.101404 | − | 0.175637i | 0.810859 | − | 0.585241i | \(-0.199000\pi\) |
−0.912263 | + | 0.409604i | \(0.865667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | − | 5.19615i | 0.151717 | − | 0.262781i | ||||
\(392\) | 7.79423 | + | 4.50000i | 0.393668 | + | 0.227284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.0000 | + | 19.0526i | 0.554172 | + | 0.959854i | ||||
\(395\) | −7.46410 | + | 4.92820i | −0.375560 | + | 0.247965i | ||||
\(396\) | 9.00000 | 0.452267 | ||||||||
\(397\) | 5.00000i | 0.250943i | 0.992097 | + | 0.125471i | \(0.0400443\pi\) | ||||
−0.992097 | + | 0.125471i | \(0.959956\pi\) | |||||||
\(398\) | −19.0526 | − | 11.0000i | −0.955018 | − | 0.551380i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.96410 | − | 4.59808i | 0.0982051 | − | 0.229904i | ||||
\(401\) | 25.0000 | 1.24844 | 0.624220 | − | 0.781248i | \(-0.285417\pi\) | ||||
0.624220 | + | 0.781248i | \(0.285417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46410 | + | 2.00000i | −0.172559 | + | 0.0996271i | ||||
\(404\) | −2.00000 | − | 3.46410i | −0.0995037 | − | 0.172345i | ||||
\(405\) | 16.7942 | − | 11.0885i | 0.834512 | − | 0.550990i | ||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | 7.79423 | + | 16.5000i | 0.386346 | + | 0.817875i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | \(0.349725\pi\) |
−0.998674 | + | 0.0514740i | \(0.983608\pi\) | |||||||
\(410\) | −22.3205 | + | 1.33975i | −1.10233 | + | 0.0661653i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.79423 | + | 4.50000i | −0.383994 | + | 0.221699i | ||||
\(413\) | − | 60.0000i | − | 2.95241i | ||||||
\(414\) | 1.50000 | + | 2.59808i | 0.0737210 | + | 0.127688i | ||||
\(415\) | 6.00000 | − | 12.0000i | 0.294528 | − | 0.589057i | ||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.00000i | 0.440204i | ||||||||
\(419\) | −12.5000 | + | 21.6506i | −0.610665 | + | 1.05770i | 0.380464 | + | 0.924796i | \(0.375764\pi\) |
−0.991129 | + | 0.132907i | \(0.957569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −0.866025 | − | 0.500000i | −0.0421575 | − | 0.0243396i | ||||
\(423\) | 28.5788 | + | 16.5000i | 1.38955 | + | 0.802257i | ||||
\(424\) | 5.00000 | − | 8.66025i | 0.242821 | − | 0.420579i | ||||
\(425\) | −27.5885 | − | 11.7846i | −1.33824 | − | 0.571638i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.5692 | − | 24.0000i | −2.01168 | − | 1.16144i | ||||
\(428\) | 6.92820 | + | 4.00000i | 0.334887 | + | 0.193347i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | + | 2.00000i | 0.192897 | + | 0.0964486i | ||||
\(431\) | 8.00000 | + | 13.8564i | 0.385346 | + | 0.667440i | 0.991817 | − | 0.127666i | \(-0.0407486\pi\) |
−0.606471 | + | 0.795106i | \(0.707415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0000i | 1.63394i | 0.576683 | + | 0.816968i | \(0.304347\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | −16.0000 | −0.768025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | −2.59808 | + | 1.50000i | −0.124283 | + | 0.0717547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.00000 | − | 1.73205i | −0.0477274 | − | 0.0826663i | 0.841175 | − | 0.540763i | \(-0.181865\pi\) |
−0.888902 | + | 0.458097i | \(0.848531\pi\) | |||||||
\(440\) | 6.69615 | − | 0.401924i | 0.319227 | − | 0.0191610i | ||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | 5.19615 | + | 3.00000i | 0.247156 | + | 0.142695i | ||||
\(443\) | − | 34.0000i | − | 1.61539i | −0.589601 | − | 0.807694i | \(-0.700715\pi\) | ||
0.589601 | − | 0.807694i | \(-0.299285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.0000 | − | 15.0000i | −1.42214 | − | 0.711068i | ||||
\(446\) | 2.50000 | − | 4.33013i | 0.118378 | − | 0.205037i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.46410 | + | 2.00000i | −0.163663 | + | 0.0944911i | ||||
\(449\) | −15.0000 | − | 25.9808i | −0.707894 | − | 1.22611i | −0.965637 | − | 0.259895i | \(-0.916312\pi\) |
0.257743 | − | 0.966213i | \(-0.417021\pi\) | |||||||
\(450\) | 12.0000 | − | 9.00000i | 0.565685 | − | 0.424264i | ||||
\(451\) | −15.0000 | − | 25.9808i | −0.706322 | − | 1.22339i | ||||
\(452\) | − | 10.0000i | − | 0.470360i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.0000 | −1.31411 | ||||||||
\(455\) | 8.00000 | + | 4.00000i | 0.375046 | + | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.5167 | − | 13.0000i | 1.05328 | − | 0.608114i | 0.129718 | − | 0.991551i | \(-0.458593\pi\) |
0.923567 | + | 0.383437i | \(0.125260\pi\) | |||||||
\(458\) | 2.00000i | 0.0934539i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.23205 | + | 1.86603i | 0.0574447 | + | 0.0870039i | ||||
\(461\) | −18.0000 | + | 31.1769i | −0.838344 | + | 1.45205i | 0.0529352 | + | 0.998598i | \(0.483142\pi\) |
−0.891279 | + | 0.453456i | \(0.850191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.92820 | + | 4.00000i | −0.321981 | + | 0.185896i | −0.652275 | − | 0.757982i | \(-0.726185\pi\) |
0.330294 | + | 0.943878i | \(0.392852\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | − | 6.00000i | − | 0.277647i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) | ||
0.990317 | − | 0.138823i | \(-0.0443321\pi\) | |||||||
\(468\) | −2.59808 | + | 1.50000i | −0.120096 | + | 0.0693375i | ||||
\(469\) | 4.00000 | − | 6.92820i | 0.184703 | − | 0.319915i | ||||
\(470\) | 22.0000 | + | 11.0000i | 1.01478 | + | 0.507392i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.9904 | + | 7.50000i | 0.597931 | + | 0.345215i | ||||
\(473\) | 6.00000i | 0.275880i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.00000 | + | 12.0000i | 0.412948 | + | 0.550598i | ||||
\(476\) | 12.0000 | + | 20.7846i | 0.550019 | + | 0.952661i | ||||
\(477\) | 25.9808 | − | 15.0000i | 1.18958 | − | 0.686803i | ||||
\(478\) | −17.3205 | + | 10.0000i | −0.792222 | + | 0.457389i | ||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | − | 3.46410i | −0.227980 | − | 0.157949i | ||||
\(482\) | − | 7.00000i | − | 0.318841i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | −4.46410 | + | 0.267949i | −0.202704 | + | 0.0121669i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0000i | − | 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 10.3923 | − | 6.00000i | 0.470438 | − | 0.271607i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.0885 | + | 16.7942i | 0.500925 | + | 0.758686i | ||||
\(491\) | 15.0000 | 0.676941 | 0.338470 | − | 0.940977i | \(-0.390091\pi\) | ||||
0.338470 | + | 0.940977i | \(0.390091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.1769 | + | 18.0000i | 1.40414 | + | 0.810679i | ||||
\(494\) | −1.50000 | − | 2.59808i | −0.0674882 | − | 0.116893i | ||||
\(495\) | 18.0000 | + | 9.00000i | 0.809040 | + | 0.404520i | ||||
\(496\) | 2.00000 | − | 3.46410i | 0.0898027 | − | 0.155543i | ||||
\(497\) | 20.7846 | + | 12.0000i | 0.932317 | + | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000 | + | 31.1769i | 0.805791 | + | 1.39567i | 0.915756 | + | 0.401735i | \(0.131593\pi\) |
−0.109965 | + | 0.993935i | \(0.535074\pi\) | |||||||
\(500\) | 8.52628 | − | 7.23205i | 0.381307 | − | 0.323427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.866025 | − | 0.500000i | −0.0386526 | − | 0.0223161i | ||||
\(503\) | 13.8564 | + | 8.00000i | 0.617827 | + | 0.356702i | 0.776022 | − | 0.630705i | \(-0.217234\pi\) |
−0.158196 | + | 0.987408i | \(0.550568\pi\) | |||||||
\(504\) | −12.0000 | −0.534522 | ||||||||
\(505\) | −0.535898 | − | 8.92820i | −0.0238472 | − | 0.397300i | ||||
\(506\) | −1.50000 | + | 2.59808i | −0.0666831 | + | 0.115499i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.0000i | 0.754253i | ||||||||
\(509\) | −18.0000 | + | 31.1769i | −0.797836 | + | 1.38189i | 0.123187 | + | 0.992384i | \(0.460689\pi\) |
−0.921023 | + | 0.389509i | \(0.872645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | − | 6.92820i | −0.176950 | − | 0.306486i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0885 | + | 1.20577i | −0.885203 | + | 0.0531326i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.0000i | 1.45134i | ||||||||
\(518\) | −10.3923 | − | 22.0000i | −0.456612 | − | 0.966625i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.86603 | + | 1.23205i | −0.0818306 | + | 0.0540290i | ||||
\(521\) | −2.50000 | − | 4.33013i | −0.109527 | − | 0.189706i | 0.806052 | − | 0.591845i | \(-0.201600\pi\) |
−0.915579 | + | 0.402139i | \(0.868267\pi\) | |||||||
\(522\) | −15.5885 | + | 9.00000i | −0.682288 | + | 0.393919i | ||||
\(523\) | −13.8564 | + | 8.00000i | −0.605898 | + | 0.349816i | −0.771358 | − | 0.636401i | \(-0.780422\pi\) |
0.165460 | + | 0.986216i | \(0.447089\pi\) | |||||||
\(524\) | −20.0000 | −0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0000 | −0.828439 | ||||||||
\(527\) | −20.7846 | − | 12.0000i | −0.905392 | − | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 18.6603 | − | 12.3205i | 0.810550 | − | 0.535169i | ||||
\(531\) | 22.5000 | + | 38.9711i | 0.976417 | + | 1.69120i | ||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | 8.66025 | + | 5.00000i | 0.375117 | + | 0.216574i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.85641 | + | 14.9282i | 0.426130 | + | 0.645403i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.1244 | − | 7.00000i | −0.522718 | − | 0.301791i | ||||
\(539\) | −13.5000 | + | 23.3827i | −0.581486 | + | 1.00716i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 17.3205 | − | 10.0000i | 0.743980 | − | 0.429537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 20.0000 | + | 10.0000i | 0.856706 | + | 0.428353i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.0000i | − | 0.427569i | −0.976881 | − | 0.213785i | \(-0.931421\pi\) | ||
0.976881 | − | 0.213785i | \(-0.0685791\pi\) | |||||||
\(548\) | −5.19615 | + | 3.00000i | −0.221969 | + | 0.128154i | ||||
\(549\) | 36.0000 | 1.53644 | ||||||||
\(550\) | 13.7942 | + | 5.89230i | 0.588188 | + | 0.251249i | ||||
\(551\) | −9.00000 | − | 15.5885i | −0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8564 | + | 8.00000i | 0.589234 | + | 0.340195i | ||||
\(554\) | −6.00000 | −0.254916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | −0.212047 | ||||||||
\(557\) | 28.5788 | + | 16.5000i | 1.21092 | + | 0.699127i | 0.962961 | − | 0.269642i | \(-0.0869053\pi\) |
0.247964 | + | 0.968769i | \(0.420239\pi\) | |||||||
\(558\) | 10.3923 | − | 6.00000i | 0.439941 | − | 0.254000i | ||||
\(559\) | −1.00000 | − | 1.73205i | −0.0422955 | − | 0.0732579i | ||||
\(560\) | −8.92820 | + | 0.535898i | −0.377285 | + | 0.0226458i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.59808 | − | 1.50000i | 0.109593 | − | 0.0632737i | ||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | − | 20.0000i | 0.420703 | − | 0.841406i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −31.1769 | − | 18.0000i | −1.30931 | − | 0.755929i | ||||
\(568\) | −5.19615 | + | 3.00000i | −0.218026 | + | 0.125877i | ||||
\(569\) | −5.00000 | −0.209611 | −0.104805 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104805 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.50000 | + | 11.2583i | −0.272017 | + | 0.471146i | −0.969378 | − | 0.245573i | \(-0.921024\pi\) |
0.697362 | + | 0.716720i | \(0.254357\pi\) | |||||||
\(572\) | −2.59808 | − | 1.50000i | −0.108631 | − | 0.0627182i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0000 | + | 34.6410i | 0.834784 | + | 1.44589i | ||||
\(575\) | 0.598076 | + | 4.96410i | 0.0249415 | + | 0.207017i | ||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | 17.3205 | + | 10.0000i | 0.721062 | + | 0.416305i | 0.815144 | − | 0.579259i | \(-0.196658\pi\) |
−0.0940813 | + | 0.995565i | \(0.529991\pi\) | |||||||
\(578\) | 19.0000i | 0.790296i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.1962 | + | 7.39230i | −0.464895 | + | 0.306949i | ||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9808 | + | 15.0000i | 1.07601 | + | 0.621237i | ||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | −6.69615 | + | 0.401924i | −0.276852 | + | 0.0166175i | ||||
\(586\) | −3.00000 | −0.123929 | ||||||||
\(587\) | −31.1769 | + | 18.0000i | −1.28681 | + | 0.742940i | −0.978084 | − | 0.208212i | \(-0.933236\pi\) |
−0.308725 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | + | 10.3923i | 0.247226 | + | 0.428207i | ||||
\(590\) | 18.4808 | + | 27.9904i | 0.760841 | + | 1.15235i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.06218 | + | 0.500000i | 0.249154 | + | 0.0205499i | ||||
\(593\) | − | 42.0000i | − | 1.72473i | −0.506284 | − | 0.862367i | \(-0.668981\pi\) | ||
0.506284 | − | 0.862367i | \(-0.331019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.21539 | + | 53.5692i | 0.131818 | + | 2.19612i | ||||
\(596\) | 8.00000 | + | 13.8564i | 0.327693 | + | 0.567581i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 1.00000i | − | 0.0408930i | ||||||
\(599\) | −7.00000 | − | 12.1244i | −0.286012 | − | 0.495388i | 0.686842 | − | 0.726807i | \(-0.258996\pi\) |
−0.972854 | + | 0.231419i | \(0.925663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5000 | − | 30.3109i | 0.713840 | − | 1.23641i | −0.249565 | − | 0.968358i | \(-0.580288\pi\) |
0.963405 | − | 0.268049i | \(-0.0863789\pi\) | |||||||
\(602\) | − | 8.00000i | − | 0.326056i | ||||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | −1.00000 | + | 1.73205i | −0.0406894 | + | 0.0704761i | ||||
\(605\) | −0.267949 | − | 4.46410i | −0.0108937 | − | 0.181492i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 2.59808 | + | 1.50000i | 0.105366 | + | 0.0608330i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.7846 | − | 1.60770i | 1.08448 | − | 0.0650937i | ||||
\(611\) | −5.50000 | − | 9.52628i | −0.222506 | − | 0.385392i | ||||
\(612\) | −15.5885 | − | 9.00000i | −0.630126 | − | 0.363803i | ||||
\(613\) | 7.79423 | + | 4.50000i | 0.314806 | + | 0.181753i | 0.649075 | − | 0.760724i | \(-0.275156\pi\) |
−0.334269 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(614\) | 16.0000 | − | 27.7128i | 0.645707 | − | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | − | 10.3923i | −0.241747 | − | 0.418718i | ||||
\(617\) | −15.5885 | − | 9.00000i | −0.627568 | − | 0.362326i | 0.152242 | − | 0.988343i | \(-0.451351\pi\) |
−0.779809 | + | 0.626017i | \(0.784684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 7.46410 | − | 4.92820i | 0.299766 | − | 0.197921i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.7846 | − | 12.0000i | 0.833387 | − | 0.481156i | ||||
\(623\) | 60.0000i | 2.40385i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | −16.0000 | − | 27.7128i | −0.639489 | − | 1.10763i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.00000i | 0.199522i | ||||||||
\(629\) | 3.00000 | − | 36.3731i | 0.119618 | − | 1.45029i | ||||
\(630\) | −24.0000 | − | 12.0000i | −0.956183 | − | 0.478091i | ||||
\(631\) | 1.00000 | − | 1.73205i | 0.0398094 | − | 0.0689519i | −0.845434 | − | 0.534080i | \(-0.820658\pi\) |
0.885244 | + | 0.465128i | \(0.153992\pi\) | |||||||
\(632\) | −3.46410 | + | 2.00000i | −0.137795 | + | 0.0795557i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.50000 | − | 7.79423i | −0.178718 | − | 0.309548i | ||||
\(635\) | −17.0000 | + | 34.0000i | −0.674624 | + | 1.34925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.00000i | − | 0.356593i | ||||||
\(638\) | −15.5885 | − | 9.00000i | −0.617153 | − | 0.356313i | ||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | −17.5000 | + | 30.3109i | −0.691208 | + | 1.19721i | 0.280234 | + | 0.959932i | \(0.409588\pi\) |
−0.971442 | + | 0.237276i | \(0.923745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.0000i | − | 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | 2.00000 | − | 3.46410i | 0.0788110 | − | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | − | 15.5885i | 0.354100 | − | 0.613320i | ||||
\(647\) | −42.4352 | + | 24.5000i | −1.66830 | + | 0.963194i | −0.699748 | + | 0.714390i | \(0.746704\pi\) |
−0.968554 | + | 0.248805i | \(0.919962\pi\) | |||||||
\(648\) | 7.79423 | − | 4.50000i | 0.306186 | − | 0.176777i | ||||
\(649\) | −22.5000 | + | 38.9711i | −0.883202 | + | 1.52975i | ||||
\(650\) | −4.96410 | + | 0.598076i | −0.194708 | + | 0.0234585i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000i | 0.234978i | ||||||||
\(653\) | 21.6506 | − | 12.5000i | 0.847255 | − | 0.489163i | −0.0124688 | − | 0.999922i | \(-0.503969\pi\) |
0.859724 | + | 0.510759i | \(0.170636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.0000 | − | 20.0000i | −1.56293 | − | 0.781465i | ||||
\(656\) | −10.0000 | −0.390434 | ||||||||
\(657\) | 5.19615 | + | 3.00000i | 0.202721 | + | 0.117041i | ||||
\(658\) | − | 44.0000i | − | 1.71530i | ||||||
\(659\) | 13.5000 | + | 23.3827i | 0.525885 | + | 0.910860i | 0.999545 | + | 0.0301523i | \(0.00959924\pi\) |
−0.473660 | + | 0.880708i | \(0.657067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | 11.2583 | − | 6.50000i | 0.437567 | − | 0.252630i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.00000 | − | 5.19615i | 0.116423 | − | 0.201650i | ||||
\(665\) | 12.0000 | − | 24.0000i | 0.465340 | − | 0.930680i | ||||
\(666\) | 15.0000 | + | 10.3923i | 0.581238 | + | 0.402694i | ||||
\(667\) | − | 6.00000i | − | 0.232321i | ||||||
\(668\) | −6.92820 | − | 4.00000i | −0.268060 | − | 0.154765i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.267949 | + | 4.46410i | 0.0103518 | + | 0.172463i | ||||
\(671\) | 18.0000 | + | 31.1769i | 0.694882 | + | 1.20357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7846 | − | 12.0000i | 0.801188 | − | 0.462566i | −0.0426985 | − | 0.999088i | \(-0.513595\pi\) |
0.843886 | + | 0.536522i | \(0.180262\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 27.0000i | 1.03769i | 0.854867 | + | 0.518847i | \(0.173639\pi\) | ||||
−0.854867 | + | 0.518847i | \(0.826361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | + | 6.92820i | 0.153506 | + | 0.265880i | ||||
\(680\) | −12.0000 | − | 6.00000i | −0.460179 | − | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.3923 | + | 6.00000i | 0.397942 | + | 0.229752i | ||||
\(683\) | −22.5167 | − | 13.0000i | −0.861576 | − | 0.497431i | 0.00296369 | − | 0.999996i | \(-0.499057\pi\) |
−0.864540 | + | 0.502564i | \(0.832390\pi\) | |||||||
\(684\) | 4.50000 | + | 7.79423i | 0.172062 | + | 0.298020i | ||||
\(685\) | −13.3923 | + | 0.803848i | −0.511694 | + | 0.0307134i | ||||
\(686\) | 4.00000 | − | 6.92820i | 0.152721 | − | 0.264520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.73205 | + | 1.00000i | 0.0660338 | + | 0.0381246i | ||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | − | 27.7128i | 0.608669 | − | 1.05425i | −0.382791 | − | 0.923835i | \(-0.625037\pi\) |
0.991460 | − | 0.130410i | \(-0.0416295\pi\) | |||||||
\(692\) | 5.00000i | 0.190071i | ||||||||
\(693\) | − | 36.0000i | − | 1.36753i | ||||||
\(694\) | 15.0000 | − | 25.9808i | 0.569392 | − | 0.986216i | ||||
\(695\) | −10.0000 | − | 5.00000i | −0.379322 | − | 0.189661i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 60.0000i | 2.27266i | ||||||||
\(698\) | 5.19615 | − | 3.00000i | 0.196677 | − | 0.113552i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.3923 | − | 7.85641i | −0.695164 | − | 0.296944i | ||||
\(701\) | 8.00000 | − | 13.8564i | 0.302156 | − | 0.523349i | −0.674468 | − | 0.738304i | \(-0.735627\pi\) |
0.976624 | + | 0.214955i | \(0.0689604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.3923 | + | 15.0000i | −0.391953 | + | 0.565736i | ||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | + | 15.5885i | 0.338719 | + | 0.586679i | ||||
\(707\) | −13.8564 | + | 8.00000i | −0.521124 | + | 0.300871i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0000 | 0.600893 | 0.300446 | − | 0.953799i | \(-0.402864\pi\) | ||||
0.300446 | + | 0.953799i | \(0.402864\pi\) | |||||||
\(710\) | −13.3923 | + | 0.803848i | −0.502604 | + | 0.0301679i | ||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | −12.9904 | − | 7.50000i | −0.486835 | − | 0.281074i | ||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.69615 | − | 5.59808i | −0.138228 | − | 0.209356i | ||||
\(716\) | −0.500000 | − | 0.866025i | −0.0186859 | − | 0.0323649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.5167 | + | 13.0000i | 0.840314 | + | 0.485156i | ||||
\(719\) | 19.0000 | − | 32.9090i | 0.708580 | − | 1.22730i | −0.256803 | − | 0.966464i | \(-0.582669\pi\) |
0.965384 | − | 0.260834i | \(-0.0839974\pi\) | |||||||
\(720\) | 5.59808 | − | 3.69615i | 0.208628 | − | 0.137747i | ||||
\(721\) | 18.0000 | + | 31.1769i | 0.670355 | + | 1.16109i | ||||
\(722\) | 8.66025 | − | 5.00000i | 0.322301 | − | 0.186081i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | −29.7846 | + | 3.58846i | −1.10617 | + | 0.133272i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.2391 | − | 21.5000i | 1.38112 | − | 0.797391i | 0.388829 | − | 0.921310i | \(-0.372880\pi\) |
0.992292 | + | 0.123919i | \(0.0395463\pi\) | |||||||
\(728\) | 3.46410 | + | 2.00000i | 0.128388 | + | 0.0741249i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 4.00000 | + | 2.00000i | 0.148047 | + | 0.0740233i | ||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0429 | + | 18.5000i | −1.18353 | + | 0.683313i | −0.956829 | − | 0.290651i | \(-0.906128\pi\) |
−0.226704 | + | 0.973964i | \(0.572795\pi\) | |||||||
\(734\) | 13.0000 | 0.479839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | + | 0.866025i | 0.0184302 | + | 0.0319221i | ||||
\(737\) | −5.19615 | + | 3.00000i | −0.191403 | + | 0.110506i | ||||
\(738\) | −25.9808 | − | 15.0000i | −0.956365 | − | 0.552158i | ||||
\(739\) | −15.0000 | −0.551784 | −0.275892 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275892 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(740\) | 11.6244 | + | 7.06218i | 0.427320 | + | 0.259611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.6410 | − | 20.0000i | −1.27171 | − | 0.734223i | ||||
\(743\) | −35.5070 | + | 20.5000i | −1.30263 | + | 0.752072i | −0.980854 | − | 0.194745i | \(-0.937612\pi\) |
−0.321773 | + | 0.946817i | \(0.604279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.14359 | + | 35.7128i | 0.0785352 | + | 1.30842i | ||||
\(746\) | −23.0000 | −0.842090 | ||||||||
\(747\) | 15.5885 | − | 9.00000i | 0.570352 | − | 0.329293i | ||||
\(748\) | − | 18.0000i | − | 0.658145i | ||||||
\(749\) | 16.0000 | − | 27.7128i | 0.584627 | − | 1.01260i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | 0.364905 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(752\) | 9.52628 | + | 5.50000i | 0.347388 | + | 0.200564i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | 0.218507 | ||||||||
\(755\) | −3.73205 | + | 2.46410i | −0.135823 | + | 0.0896778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1147 | − | 14.5000i | −0.912811 | − | 0.527011i | −0.0314762 | − | 0.999505i | \(-0.510021\pi\) |
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | −20.7846 | + | 12.0000i | −0.754931 | + | 0.435860i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.69615 | + | 5.59808i | 0.134074 | + | 0.203064i | ||||
\(761\) | −0.500000 | + | 0.866025i | −0.0181250 | + | 0.0313934i | −0.874946 | − | 0.484221i | \(-0.839103\pi\) |
0.856821 | + | 0.515615i | \(0.172436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 40.0000i | − | 1.44810i | ||||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | −22.1769 | − | 33.5885i | −0.801808 | − | 1.21439i | ||||
\(766\) | −17.0000 | −0.614235 | ||||||||
\(767\) | − | 15.0000i | − | 0.541619i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | −1.60770 | − | 26.7846i | −0.0579373 | − | 0.965250i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.8564 | − | 8.00000i | 0.498703 | − | 0.287926i | ||||
\(773\) | −7.79423 | + | 4.50000i | −0.280339 | + | 0.161854i | −0.633577 | − | 0.773680i | \(-0.718414\pi\) |
0.353238 | + | 0.935534i | \(0.385081\pi\) | |||||||
\(774\) | 3.00000 | + | 5.19615i | 0.107833 | + | 0.186772i | ||||
\(775\) | 19.8564 | − | 2.39230i | 0.713263 | − | 0.0859341i | ||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.00000i | − | 0.143407i | ||||||
\(779\) | 15.0000 | − | 25.9808i | 0.537431 | − | 0.930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | 5.19615 | − | 3.00000i | 0.185814 | − | 0.107280i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.50000 | + | 7.79423i | 0.160714 | + | 0.278365i | ||||
\(785\) | −5.00000 | + | 10.0000i | −0.178458 | + | 0.356915i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.0000i | − | 1.35455i | −0.735728 | − | 0.677277i | \(-0.763160\pi\) | ||
0.735728 | − | 0.677277i | \(-0.236840\pi\) | |||||||
\(788\) | 22.0000i | 0.783718i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.92820 | + | 0.535898i | −0.317651 | + | 0.0190664i | ||||
\(791\) | −40.0000 | −1.42224 | ||||||||
\(792\) | 7.79423 | + | 4.50000i | 0.276956 | + | 0.159901i | ||||
\(793\) | −10.3923 | − | 6.00000i | −0.369042 | − | 0.213066i | ||||
\(794\) | −2.50000 | + | 4.33013i | −0.0887217 | + | 0.153670i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0000 | − | 19.0526i | −0.389885 | − | 0.675300i | ||||
\(797\) | 12.9904 | + | 7.50000i | 0.460143 | + | 0.265664i | 0.712104 | − | 0.702074i | \(-0.247742\pi\) |
−0.251961 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.0000 | − | 57.1577i | 1.16746 | − | 2.02209i | ||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | −22.5000 | − | 38.9711i | −0.794998 | − | 1.37698i | ||||
\(802\) | 21.6506 | + | 12.5000i | 0.764511 | + | 0.441390i | ||||
\(803\) | 6.00000i | 0.211735i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.46410 | − | 4.92820i | 0.263075 | − | 0.173696i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.00000i | − | 0.140720i | ||||||
\(809\) | −22.5000 | − | 38.9711i | −0.791058 | − | 1.37015i | −0.925312 | − | 0.379206i | \(-0.876197\pi\) |
0.134255 | − | 0.990947i | \(-0.457136\pi\) | |||||||
\(810\) | 20.0885 | − | 1.20577i | 0.705836 | − | 0.0423665i | ||||
\(811\) | 16.5000 | + | 28.5788i | 0.579393 | + | 1.00354i | 0.995549 | + | 0.0942453i | \(0.0300438\pi\) |
−0.416156 | + | 0.909293i | \(0.636623\pi\) | |||||||
\(812\) | 20.7846 | + | 12.0000i | 0.729397 | + | 0.421117i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.50000 | + | 18.1865i | −0.0525750 | + | 0.637438i | ||||
\(815\) | −6.00000 | + | 12.0000i | −0.210171 | + | 0.420342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.19615 | + | 3.00000i | −0.181790 | + | 0.104957i | ||||
\(818\) | −19.0526 | + | 11.0000i | −0.666157 | + | 0.384606i | ||||
\(819\) | 6.00000 | + | 10.3923i | 0.209657 | + | 0.363137i | ||||
\(820\) | −20.0000 | − | 10.0000i | −0.698430 | − | 0.349215i | ||||
\(821\) | 19.0000 | + | 32.9090i | 0.663105 | + | 1.14853i | 0.979795 | + | 0.200002i | \(0.0640949\pi\) |
−0.316691 | + | 0.948529i | \(0.602572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8564 | + | 8.00000i | 0.483004 | + | 0.278862i | 0.721668 | − | 0.692240i | \(-0.243376\pi\) |
−0.238664 | + | 0.971102i | \(0.576709\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | − | 51.9615i | 1.04383 | − | 1.80797i | ||||
\(827\) | −10.3923 | + | 6.00000i | −0.361376 | + | 0.208640i | −0.669684 | − | 0.742646i | \(-0.733571\pi\) |
0.308308 | + | 0.951286i | \(0.400237\pi\) | |||||||
\(828\) | 3.00000i | 0.104257i | ||||||||
\(829\) | 2.00000 | − | 3.46410i | 0.0694629 | − | 0.120313i | −0.829202 | − | 0.558949i | \(-0.811205\pi\) |
0.898665 | + | 0.438636i | \(0.144538\pi\) | |||||||
\(830\) | 11.1962 | − | 7.39230i | 0.388624 | − | 0.256591i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.866025 | + | 0.500000i | −0.0300240 | + | 0.0173344i | ||||
\(833\) | 46.7654 | − | 27.0000i | 1.62032 | − | 0.935495i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.85641 | − | 14.9282i | −0.341095 | − | 0.516612i | ||||
\(836\) | −4.50000 | + | 7.79423i | −0.155636 | + | 0.269569i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.6506 | + | 12.5000i | −0.747909 | + | 0.431805i | ||||
\(839\) | −6.00000 | + | 10.3923i | −0.207143 | + | 0.358782i | −0.950813 | − | 0.309764i | \(-0.899750\pi\) |
0.743670 | + | 0.668546i | \(0.233083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −5.19615 | − | 3.00000i | −0.179071 | − | 0.103387i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.500000 | − | 0.866025i | −0.0172107 | − | 0.0298098i | ||||
\(845\) | −24.0000 | − | 12.0000i | −0.825625 | − | 0.412813i | ||||
\(846\) | 16.5000 | + | 28.5788i | 0.567282 | + | 0.982561i | ||||
\(847\) | −6.92820 | + | 4.00000i | −0.238056 | + | 0.137442i | ||||
\(848\) | 8.66025 | − | 5.00000i | 0.297394 | − | 0.171701i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.0000 | − | 24.0000i | −0.617395 | − | 0.823193i | ||||
\(851\) | −5.50000 | + | 2.59808i | −0.188538 | + | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1865 | + | 10.5000i | 0.622695 | + | 0.359513i | 0.777918 | − | 0.628366i | \(-0.216276\pi\) |
−0.155222 | + | 0.987880i | \(0.549609\pi\) | |||||||
\(854\) | −24.0000 | − | 41.5692i | −0.821263 | − | 1.42247i | ||||
\(855\) | 1.20577 | + | 20.0885i | 0.0412365 | + | 0.687011i | ||||
\(856\) | 4.00000 | + | 6.92820i | 0.136717 | + | 0.236801i | ||||
\(857\) | 22.0000i | 0.751506i | 0.926720 | + | 0.375753i | \(0.122616\pi\) | ||||
−0.926720 | + | 0.375753i | \(0.877384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0000 | −0.648272 | −0.324136 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(860\) | 2.46410 | + | 3.73205i | 0.0840252 | + | 0.127262i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0000i | 0.544962i | ||||||||
\(863\) | 38.9711 | + | 22.5000i | 1.32659 | + | 0.765909i | 0.984771 | − | 0.173856i | \(-0.0556227\pi\) |
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00000 | + | 10.0000i | −0.170005 | + | 0.340010i | ||||
\(866\) | −17.0000 | + | 29.4449i | −0.577684 | + | 1.00058i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.8564 | − | 8.00000i | −0.470317 | − | 0.271538i | ||||
\(869\) | −6.00000 | − | 10.3923i | −0.203536 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00000 | − | 1.73205i | 0.0338837 | − | 0.0586883i | ||||
\(872\) | 8.66025 | + | 5.00000i | 0.293273 | + | 0.169321i | ||||
\(873\) | −5.19615 | − | 3.00000i | −0.175863 | − | 0.101535i | ||||
\(874\) | −3.00000 | −0.101477 | ||||||||
\(875\) | −28.9282 | − | 34.1051i | −0.977952 | − | 1.15296i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000i | 0.371444i | 0.982602 | + | 0.185722i | \(0.0594623\pi\) | ||||
−0.982602 | + | 0.185722i | \(0.940538\pi\) | |||||||
\(878\) | − | 2.00000i | − | 0.0674967i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | + | 3.00000i | 0.202260 | + | 0.101130i | ||||
\(881\) | −4.50000 | − | 7.79423i | −0.151609 | − | 0.262594i | 0.780210 | − | 0.625517i | \(-0.215112\pi\) |
−0.931819 | + | 0.362923i | \(0.881779\pi\) | |||||||
\(882\) | 27.0000i | 0.909137i | ||||||||
\(883\) | −1.73205 | + | 1.00000i | −0.0582882 | + | 0.0336527i | −0.528861 | − | 0.848709i | \(-0.677381\pi\) |
0.470573 | + | 0.882361i | \(0.344047\pi\) | |||||||
\(884\) | 3.00000 | + | 5.19615i | 0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0000 | − | 29.4449i | 0.571126 | − | 0.989220i | ||||
\(887\) | − | 8.00000i | − | 0.268614i | −0.990940 | − | 0.134307i | \(-0.957119\pi\) | ||
0.990940 | − | 0.134307i | \(-0.0428808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.0000 | 2.28065 | ||||||||
\(890\) | −18.4808 | − | 27.9904i | −0.619477 | − | 0.938240i | ||||
\(891\) | 13.5000 | + | 23.3827i | 0.452267 | + | 0.783349i | ||||
\(892\) | 4.33013 | − | 2.50000i | 0.144983 | − | 0.0837062i | ||||
\(893\) | −28.5788 | + | 16.5000i | −0.956354 | + | 0.552151i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.133975 | − | 2.23205i | −0.00447828 | − | 0.0746092i | ||||
\(896\) | −4.00000 | −0.133631 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 30.0000i | − | 1.00111i | ||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 14.8923 | − | 1.79423i | 0.496410 | − | 0.0598076i | ||||
\(901\) | −30.0000 | − | 51.9615i | −0.999445 | − | 1.73109i | ||||
\(902\) | − | 30.0000i | − | 0.998891i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.00000 | − | 8.66025i | 0.166298 | − | 0.288036i | ||||
\(905\) | −29.8564 | + | 19.7128i | −0.992461 | + | 0.655276i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.4974 | + | 28.0000i | −1.61033 | + | 0.929725i | −0.621038 | + | 0.783781i | \(0.713289\pi\) |
−0.989293 | + | 0.145944i | \(0.953378\pi\) | |||||||
\(908\) | −24.2487 | − | 14.0000i | −0.804722 | − | 0.464606i | ||||
\(909\) | 6.00000 | − | 10.3923i | 0.199007 | − | 0.344691i | ||||
\(910\) | 4.92820 | + | 7.46410i | 0.163368 | + | 0.247433i | ||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5885 | + | 9.00000i | 0.515903 | + | 0.297857i | ||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.00000 | + | 1.73205i | −0.0330409 | + | 0.0572286i | ||||
\(917\) | 80.0000i | 2.64183i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0.133975 | + | 2.23205i | 0.00441701 | + | 0.0735885i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −31.1769 | + | 18.0000i | −1.02676 | + | 0.592798i | ||||
\(923\) | 5.19615 | + | 3.00000i | 0.171033 | + | 0.0987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.1865 | + | 25.7487i | 0.532210 | + | 0.846612i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | −23.3827 | − | 13.5000i | −0.767988 | − | 0.443398i | ||||
\(928\) | −5.19615 | + | 3.00000i | −0.170572 | + | 0.0984798i | ||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.0000 | −0.884889 | ||||||||
\(932\) | −15.5885 | + | 9.00000i | −0.510617 | + | 0.294805i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.00000 | − | 5.19615i | 0.0981630 | − | 0.170023i | ||||
\(935\) | 18.0000 | − | 36.0000i | 0.588663 | − | 1.17733i | ||||
\(936\) | −3.00000 | −0.0980581 | ||||||||
\(937\) | 12.1244 | + | 7.00000i | 0.396085 | + | 0.228680i | 0.684794 | − | 0.728737i | \(-0.259892\pi\) |
−0.288708 | + | 0.957417i | \(0.593226\pi\) | |||||||
\(938\) | 6.92820 | − | 4.00000i | 0.226214 | − | 0.130605i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.5526 | + | 20.5263i | 0.442036 | + | 0.669493i | ||||
\(941\) | 20.0000 | − | 34.6410i | 0.651981 | − | 1.12926i | −0.330660 | − | 0.943750i | \(-0.607271\pi\) |
0.982641 | − | 0.185515i | \(-0.0593953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.66025 | − | 5.00000i | 0.282017 | − | 0.162822i | ||||
\(944\) | 7.50000 | + | 12.9904i | 0.244104 | + | 0.422801i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.00000 | + | 5.19615i | −0.0975384 | + | 0.168941i | ||||
\(947\) | −39.8372 | − | 23.0000i | −1.29453 | − | 0.747400i | −0.315080 | − | 0.949065i | \(-0.602031\pi\) |
−0.979454 | + | 0.201666i | \(0.935365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | − | 1.73205i | −0.0324614 | − | 0.0562247i | ||||
\(950\) | 1.79423 | + | 14.8923i | 0.0582125 | + | 0.483170i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.0000i | 0.777844i | ||||||||
\(953\) | 31.1769 | + | 18.0000i | 1.00992 | + | 0.583077i | 0.911168 | − | 0.412035i | \(-0.135182\pi\) |
0.0987513 | + | 0.995112i | \(0.468515\pi\) | |||||||
\(954\) | 30.0000 | 0.971286 | ||||||||
\(955\) | 0.535898 | + | 8.92820i | 0.0173413 | + | 0.288910i | ||||
\(956\) | −20.0000 | −0.646846 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.19615 | − | 3.00000i | 0.167880 | − | 0.0969256i | ||||
\(959\) | 12.0000 | + | 20.7846i | 0.387500 | + | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −2.59808 | − | 5.50000i | −0.0837653 | − | 0.177327i | ||||
\(963\) | 24.0000i | 0.773389i | ||||||||
\(964\) | 3.50000 | − | 6.06218i | 0.112727 | − | 0.195250i | ||||
\(965\) | 35.7128 | − | 2.14359i | 1.14964 | − | 0.0690047i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.5070 | − | 20.5000i | 1.14183 | − | 0.659236i | 0.194946 | − | 0.980814i | \(-0.437547\pi\) |
0.946883 | + | 0.321578i | \(0.104213\pi\) | |||||||
\(968\) | − | 2.00000i | − | 0.0642824i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.00000 | − | 2.00000i | −0.128432 | − | 0.0642161i | ||||
\(971\) | −26.5000 | + | 45.8993i | −0.850425 | + | 1.47298i | 0.0303994 | + | 0.999538i | \(0.490322\pi\) |
−0.880825 | + | 0.473442i | \(0.843011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000i | 0.641171i | ||||||||
\(974\) | 12.0000 | − | 20.7846i | 0.384505 | − | 0.665982i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0000 | 0.384111 | ||||||||
\(977\) | −51.9615 | − | 30.0000i | −1.66240 | − | 0.959785i | −0.971566 | − | 0.236768i | \(-0.923912\pi\) |
−0.690830 | − | 0.723017i | \(-0.742755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5000 | − | 38.9711i | 0.719103 | − | 1.24552i | ||||
\(980\) | 1.20577 | + | 20.0885i | 0.0385170 | + | 0.641702i | ||||
\(981\) | 15.0000 | + | 25.9808i | 0.478913 | + | 0.829502i | ||||
\(982\) | 12.9904 | + | 7.50000i | 0.414540 | + | 0.239335i | ||||
\(983\) | −14.7224 | − | 8.50000i | −0.469573 | − | 0.271108i | 0.246488 | − | 0.969146i | \(-0.420723\pi\) |
−0.716061 | + | 0.698038i | \(0.754057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.0000 | + | 44.0000i | −0.700978 | + | 1.40196i | ||||
\(986\) | 18.0000 | + | 31.1769i | 0.573237 | + | 0.992875i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 3.00000i | − | 0.0954427i | ||||||
\(989\) | −2.00000 | −0.0635963 | ||||||||
\(990\) | 11.0885 | + | 16.7942i | 0.352414 | + | 0.533756i | ||||
\(991\) | −18.0000 | −0.571789 | −0.285894 | − | 0.958261i | \(-0.592291\pi\) | ||||
−0.285894 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(992\) | 3.46410 | − | 2.00000i | 0.109985 | − | 0.0635001i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0000 | + | 20.7846i | 0.380617 | + | 0.659248i | ||||
\(995\) | −2.94744 | − | 49.1051i | −0.0934402 | − | 1.55674i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.7224 | + | 8.50000i | 0.466264 | + | 0.269198i | 0.714675 | − | 0.699457i | \(-0.246575\pi\) |
−0.248410 | + | 0.968655i | \(0.579908\pi\) | |||||||
\(998\) | 36.0000i | 1.13956i | ||||||||
\(999\) | 0 | 0 |
(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 | 370.2.n.b.269.2 | yes | 4 | |
5.4 | even | 2 | inner | 370.2.n.b.269.1 | ✓ | 4 | |
37.26 | even | 3 | inner | 370.2.n.b.359.1 | yes | 4 | |
185.174 | even | 6 | inner | 370.2.n.b.359.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.n.b.269.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
370.2.n.b.269.2 | yes | 4 | 1.1 | even | 1 | trivial | |
370.2.n.b.359.1 | yes | 4 | 37.26 | even | 3 | inner | |
370.2.n.b.359.2 | yes | 4 | 185.174 | even | 6 | inner |