Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(19,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 91.6 | ||
Root | \(1.78012 - 0.911682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.91 |
Dual form | 144.3.m.c.19.6 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.78012 | + | 0.911682i | 0.890061 | + | 0.455841i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.33767 | + | 3.24581i | 0.584418 | + | 0.811453i | ||||
\(5\) | −1.00772 | − | 1.00772i | −0.201544 | − | 0.201544i | 0.599117 | − | 0.800661i | \(-0.295518\pi\) |
−0.800661 | + | 0.599117i | \(0.795518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0236 | 1.43194 | 0.715969 | − | 0.698133i | \(-0.245985\pi\) | ||||
0.715969 | + | 0.698133i | \(0.245985\pi\) | |||||||
\(8\) | 1.20220 | + | 7.90915i | 0.150274 | + | 0.988644i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.875146 | − | 2.71259i | −0.0875146 | − | 0.271259i | ||||
\(11\) | −2.26517 | + | 2.26517i | −0.205925 | + | 0.205925i | −0.802533 | − | 0.596608i | \(-0.796515\pi\) |
0.596608 | + | 0.802533i | \(0.296515\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.88229 | + | 6.88229i | −0.529407 | + | 0.529407i | −0.920395 | − | 0.390989i | \(-0.872133\pi\) |
0.390989 | + | 0.920395i | \(0.372133\pi\) | |||||||
\(14\) | 17.8432 | + | 9.13830i | 1.27451 | + | 0.652736i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.07058 | + | 15.1753i | −0.316911 | + | 0.948455i | ||||
\(17\) | 22.3801 | 1.31648 | 0.658240 | − | 0.752809i | \(-0.271301\pi\) | ||||
0.658240 | + | 0.752809i | \(0.271301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.8918 | − | 16.8918i | −0.889041 | − | 0.889041i | 0.105390 | − | 0.994431i | \(-0.466391\pi\) |
−0.994431 | + | 0.105390i | \(0.966391\pi\) | |||||||
\(20\) | 0.915151 | − | 5.62660i | 0.0457575 | − | 0.281330i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.09740 | + | 1.96717i | −0.277155 | + | 0.0894167i | ||||
\(23\) | −33.2007 | −1.44351 | −0.721755 | − | 0.692149i | \(-0.756664\pi\) | ||||
−0.721755 | + | 0.692149i | \(0.756664\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 22.9690i | − | 0.918760i | ||||||
\(26\) | −18.5258 | + | 5.97686i | −0.712530 | + | 0.229879i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23.4318 | + | 32.5346i | 0.836850 | + | 1.16195i | ||||
\(29\) | 24.6412 | − | 24.6412i | 0.849696 | − | 0.849696i | −0.140399 | − | 0.990095i | \(-0.544839\pi\) |
0.990095 | + | 0.140399i | \(0.0448385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 41.3761i | − | 1.33471i | −0.744738 | − | 0.667357i | \(-0.767426\pi\) | ||
0.744738 | − | 0.667357i | \(-0.232574\pi\) | |||||||
\(32\) | −22.8613 | + | 22.3911i | −0.714415 | + | 0.699722i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 39.8394 | + | 20.4036i | 1.17175 | + | 0.600105i | ||||
\(35\) | −10.1010 | − | 10.1010i | −0.288599 | − | 0.288599i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.60031 | − | 6.60031i | −0.178387 | − | 0.178387i | 0.612266 | − | 0.790652i | \(-0.290258\pi\) |
−0.790652 | + | 0.612266i | \(0.790258\pi\) | |||||||
\(38\) | −14.6695 | − | 45.4693i | −0.386039 | − | 1.19656i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.75875 | − | 9.18170i | 0.168969 | − | 0.229543i | ||||
\(41\) | 47.1477i | 1.14994i | 0.818173 | + | 0.574972i | \(0.194987\pi\) | ||||
−0.818173 | + | 0.574972i | \(0.805013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.8218 | + | 48.8218i | −1.13539 | + | 1.13539i | −0.146124 | + | 0.989266i | \(0.546680\pi\) |
−0.989266 | + | 0.146124i | \(0.953320\pi\) | |||||||
\(44\) | −12.6475 | − | 2.05709i | −0.287444 | − | 0.0467521i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −59.1013 | − | 30.2685i | −1.28481 | − | 0.658011i | ||||
\(47\) | − | 45.6048i | − | 0.970315i | −0.874427 | − | 0.485157i | \(-0.838762\pi\) | ||
0.874427 | − | 0.485157i | \(-0.161238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 51.4717 | 1.05044 | ||||||||
\(50\) | 20.9404 | − | 40.8876i | 0.418808 | − | 0.817752i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −38.4271 | − | 6.25007i | −0.738983 | − | 0.120194i | ||||
\(53\) | −25.1401 | − | 25.1401i | −0.474341 | − | 0.474341i | 0.428975 | − | 0.903316i | \(-0.358875\pi\) |
−0.903316 | + | 0.428975i | \(0.858875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.56532 | 0.0830059 | ||||||||
\(56\) | 12.0503 | + | 79.2779i | 0.215184 | + | 1.41568i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 66.3292 | − | 21.3994i | 1.14361 | − | 0.368955i | ||||
\(59\) | −6.23974 | + | 6.23974i | −0.105758 | + | 0.105758i | −0.758006 | − | 0.652248i | \(-0.773826\pi\) |
0.652248 | + | 0.758006i | \(0.273826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.9513 | − | 35.9513i | 0.589366 | − | 0.589366i | −0.348093 | − | 0.937460i | \(-0.613171\pi\) |
0.937460 | + | 0.348093i | \(0.113171\pi\) | |||||||
\(62\) | 37.7219 | − | 73.6546i | 0.608417 | − | 1.18798i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −61.1095 | + | 19.0167i | −0.954835 | + | 0.297136i | ||||
\(65\) | 13.8709 | 0.213398 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2045 | + | 10.2045i | 0.152307 | + | 0.152307i | 0.779147 | − | 0.626841i | \(-0.215652\pi\) |
−0.626841 | + | 0.779147i | \(0.715652\pi\) | |||||||
\(68\) | 52.3174 | + | 72.6417i | 0.769374 | + | 1.06826i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.77208 | − | 27.1898i | −0.125315 | − | 0.388426i | ||||
\(71\) | −11.9529 | −0.168350 | −0.0841752 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841752 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 111.332i | 1.52510i | 0.646929 | + | 0.762550i | \(0.276053\pi\) | ||||
−0.646929 | + | 0.762550i | \(0.723947\pi\) | |||||||
\(74\) | −5.73197 | − | 17.7667i | −0.0774591 | − | 0.240091i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.3401 | − | 94.3149i | 0.201843 | − | 1.24099i | ||||
\(77\) | −22.7051 | + | 22.7051i | −0.294871 | + | 0.294871i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.46031i | 0.0564596i | 0.999601 | + | 0.0282298i | \(0.00898702\pi\) | ||||
−0.999601 | + | 0.0282298i | \(0.991013\pi\) | |||||||
\(80\) | 20.4022 | − | 10.1827i | 0.255027 | − | 0.127284i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −42.9837 | + | 83.9287i | −0.524192 | + | 1.02352i | ||||
\(83\) | −10.1751 | − | 10.1751i | −0.122592 | − | 0.122592i | 0.643149 | − | 0.765741i | \(-0.277627\pi\) |
−0.765741 | + | 0.643149i | \(0.777627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.5530 | − | 22.5530i | −0.265329 | − | 0.265329i | ||||
\(86\) | −131.419 | + | 42.3988i | −1.52812 | + | 0.493010i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20.6388 | − | 15.1924i | −0.234532 | − | 0.172641i | ||||
\(89\) | 21.9364i | 0.246476i | 0.992377 | + | 0.123238i | \(0.0393279\pi\) | ||||
−0.992377 | + | 0.123238i | \(0.960672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −68.9850 | + | 68.9850i | −0.758077 | + | 0.758077i | ||||
\(92\) | −77.6124 | − | 107.763i | −0.843613 | − | 1.17134i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 41.5771 | − | 81.1821i | 0.442309 | − | 0.863640i | ||||
\(95\) | 34.0444i | 0.358362i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 107.309 | 1.10628 | 0.553140 | − | 0.833088i | \(-0.313429\pi\) | ||||
0.553140 | + | 0.833088i | \(0.313429\pi\) | |||||||
\(98\) | 91.6260 | + | 46.9259i | 0.934959 | + | 0.478835i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 74.5530 | − | 53.6940i | 0.745530 | − | 0.536940i | ||||
\(101\) | 100.780 | + | 100.780i | 0.997824 | + | 0.997824i | 0.999998 | − | 0.00217389i | \(-0.000691973\pi\) |
−0.00217389 | + | 0.999998i | \(0.500692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.0562 | 0.563653 | 0.281826 | − | 0.959465i | \(-0.409060\pi\) | ||||
0.281826 | + | 0.959465i | \(0.409060\pi\) | |||||||
\(104\) | −62.7069 | − | 46.1592i | −0.602951 | − | 0.443839i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.8327 | − | 67.6722i | −0.205968 | − | 0.638417i | ||||
\(107\) | −112.747 | + | 112.747i | −1.05371 | + | 1.05371i | −0.0552381 | + | 0.998473i | \(0.517592\pi\) |
−0.998473 | + | 0.0552381i | \(0.982408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.1384 | + | 81.1384i | −0.744389 | + | 0.744389i | −0.973419 | − | 0.229030i | \(-0.926445\pi\) |
0.229030 | + | 0.973419i | \(0.426445\pi\) | |||||||
\(110\) | 8.12684 | + | 4.16212i | 0.0738803 | + | 0.0378375i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −50.8252 | + | 152.110i | −0.453797 | + | 1.35813i | ||||
\(113\) | 171.844 | 1.52074 | 0.760371 | − | 0.649489i | \(-0.225017\pi\) | ||||
0.760371 | + | 0.649489i | \(0.225017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.4571 | + | 33.4571i | 0.290931 | + | 0.290931i | ||||
\(116\) | 137.584 | + | 22.3776i | 1.18607 | + | 0.192910i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.7962 | + | 5.41884i | −0.142340 | + | 0.0459224i | ||||
\(119\) | 224.329 | 1.88512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 110.738i | 0.915190i | ||||||||
\(122\) | 96.7740 | − | 31.2216i | 0.793230 | − | 0.255915i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 134.299 | − | 96.7238i | 1.08306 | − | 0.780031i | ||||
\(125\) | −48.3394 | + | 48.3394i | −0.386715 | + | 0.386715i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 36.8333i | − | 0.290026i | −0.989430 | − | 0.145013i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145013i | \(-0.0463224\pi\) | |||||||
\(128\) | −126.119 | − | 21.8603i | −0.985309 | − | 0.170784i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.6918 | + | 12.6458i | 0.189937 | + | 0.0972754i | ||||
\(131\) | 12.3686 | + | 12.3686i | 0.0944170 | + | 0.0944170i | 0.752738 | − | 0.658321i | \(-0.228733\pi\) |
−0.658321 | + | 0.752738i | \(0.728733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −169.316 | − | 169.316i | −1.27305 | − | 1.27305i | ||||
\(134\) | 8.86204 | + | 27.4686i | 0.0661347 | + | 0.204990i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 26.9053 | + | 177.008i | 0.197833 | + | 1.30153i | ||||
\(137\) | − | 145.679i | − | 1.06335i | −0.846949 | − | 0.531674i | \(-0.821563\pi\) | ||
0.846949 | − | 0.531674i | \(-0.178437\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.5709 | − | 82.5709i | 0.594035 | − | 0.594035i | −0.344684 | − | 0.938719i | \(-0.612014\pi\) |
0.938719 | + | 0.344684i | \(0.112014\pi\) | |||||||
\(140\) | 9.17307 | − | 56.3985i | 0.0655219 | − | 0.402847i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.2776 | − | 10.8972i | −0.149842 | − | 0.0767410i | ||||
\(143\) | − | 31.1791i | − | 0.218036i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −49.6629 | −0.342503 | ||||||||
\(146\) | −101.500 | + | 198.185i | −0.695203 | + | 1.35743i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.99399 | − | 36.8527i | 0.0405000 | − | 0.249005i | ||||
\(149\) | −196.248 | − | 196.248i | −1.31710 | − | 1.31710i | −0.916059 | − | 0.401043i | \(-0.868648\pi\) |
−0.401043 | − | 0.916059i | \(-0.631352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 64.5007 | 0.427157 | 0.213578 | − | 0.976926i | \(-0.431488\pi\) | ||||
0.213578 | + | 0.976926i | \(0.431488\pi\) | |||||||
\(152\) | 113.292 | − | 153.907i | 0.745345 | − | 1.01254i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −61.1177 | + | 19.7180i | −0.396868 | + | 0.128039i | ||||
\(155\) | −41.6956 | + | 41.6956i | −0.269004 | + | 0.269004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 54.4202 | − | 54.4202i | 0.346625 | − | 0.346625i | −0.512226 | − | 0.858851i | \(-0.671179\pi\) |
0.858851 | + | 0.512226i | \(0.171179\pi\) | |||||||
\(158\) | −4.06638 | + | 7.93990i | −0.0257366 | + | 0.0502525i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 45.6018 | + | 0.473799i | 0.285011 | + | 0.00296124i | ||||
\(161\) | −332.789 | −2.06701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.803 | + | 104.803i | 0.642961 | + | 0.642961i | 0.951282 | − | 0.308321i | \(-0.0997671\pi\) |
−0.308321 | + | 0.951282i | \(0.599767\pi\) | |||||||
\(164\) | −153.033 | + | 110.216i | −0.933126 | + | 0.672048i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.83647 | − | 27.3894i | −0.0532317 | − | 0.164996i | ||||
\(167\) | −53.3110 | −0.319228 | −0.159614 | − | 0.987180i | \(-0.551025\pi\) | ||||
−0.159614 | + | 0.987180i | \(0.551025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 74.2683i | 0.439457i | ||||||||
\(170\) | −19.5859 | − | 60.7081i | −0.115211 | − | 0.357107i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −272.596 | − | 44.3370i | −1.58486 | − | 0.257773i | ||||
\(173\) | 41.5780 | − | 41.5780i | 0.240335 | − | 0.240335i | −0.576654 | − | 0.816989i | \(-0.695642\pi\) |
0.816989 | + | 0.576654i | \(0.195642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 230.231i | − | 1.31561i | ||||||
\(176\) | −22.8889 | − | 45.8604i | −0.130051 | − | 0.260570i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.9990 | + | 39.0495i | −0.112354 | + | 0.219379i | ||||
\(179\) | −53.0709 | − | 53.0709i | −0.296486 | − | 0.296486i | 0.543150 | − | 0.839636i | \(-0.317231\pi\) |
−0.839636 | + | 0.543150i | \(0.817231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −66.6042 | − | 66.6042i | −0.367979 | − | 0.367979i | 0.498761 | − | 0.866740i | \(-0.333789\pi\) |
−0.866740 | + | 0.498761i | \(0.833789\pi\) | |||||||
\(182\) | −185.694 | + | 59.9094i | −1.02030 | + | 0.329172i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −39.9138 | − | 262.590i | −0.216923 | − | 1.42712i | ||||
\(185\) | 13.3025i | 0.0719056i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −50.6949 | + | 50.6949i | −0.271096 | + | 0.271096i | ||||
\(188\) | 148.025 | − | 106.609i | 0.787365 | − | 0.567070i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −31.0377 | + | 60.6032i | −0.163356 | + | 0.318964i | ||||
\(191\) | − | 113.753i | − | 0.595567i | −0.954633 | − | 0.297784i | \(-0.903753\pi\) | ||
0.954633 | − | 0.297784i | \(-0.0962474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.5596 | −0.137615 | −0.0688073 | − | 0.997630i | \(-0.521919\pi\) | ||||
−0.0688073 | + | 0.997630i | \(0.521919\pi\) | |||||||
\(194\) | 191.023 | + | 97.8318i | 0.984657 | + | 0.504288i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 120.324 | + | 167.068i | 0.613898 | + | 0.852386i | ||||
\(197\) | −51.8935 | − | 51.8935i | −0.263419 | − | 0.263419i | 0.563023 | − | 0.826442i | \(-0.309638\pi\) |
−0.826442 | + | 0.563023i | \(0.809638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −136.741 | −0.687140 | −0.343570 | − | 0.939127i | \(-0.611636\pi\) | ||||
−0.343570 | + | 0.939127i | \(0.611636\pi\) | |||||||
\(200\) | 181.665 | − | 27.6132i | 0.908327 | − | 0.138066i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 87.5216 | + | 271.281i | 0.433275 | + | 1.34297i | ||||
\(203\) | 246.992 | − | 246.992i | 1.21671 | − | 1.21671i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 47.5118 | − | 47.5118i | 0.231765 | − | 0.231765i | ||||
\(206\) | 103.347 | + | 52.9288i | 0.501686 | + | 0.256936i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −69.5435 | − | 139.338i | −0.334344 | − | 0.669893i | ||||
\(209\) | 76.5255 | 0.366151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −141.171 | − | 141.171i | −0.669057 | − | 0.669057i | 0.288441 | − | 0.957498i | \(-0.406863\pi\) |
−0.957498 | + | 0.288441i | \(0.906863\pi\) | |||||||
\(212\) | 22.8307 | − | 140.369i | 0.107692 | − | 0.662119i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −303.493 | + | 97.9142i | −1.41819 | + | 0.457543i | ||||
\(215\) | 98.3975 | 0.457663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 414.736i | − | 1.91123i | ||||||
\(218\) | −218.409 | + | 70.4639i | −1.00188 | + | 0.323229i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.6722 | + | 14.8182i | 0.0485101 | + | 0.0673554i | ||||
\(221\) | −154.027 | + | 154.027i | −0.696953 | + | 0.696953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 122.607i | 0.549806i | 0.961472 | + | 0.274903i | \(0.0886457\pi\) | ||||
−0.961472 | + | 0.274903i | \(0.911354\pi\) | |||||||
\(224\) | −229.151 | + | 224.439i | −1.02300 | + | 1.00196i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 305.903 | + | 156.667i | 1.35355 | + | 0.693216i | ||||
\(227\) | 295.844 | + | 295.844i | 1.30328 | + | 1.30328i | 0.926168 | + | 0.377112i | \(0.123083\pi\) |
0.377112 | + | 0.926168i | \(0.376917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73.3817 | + | 73.3817i | 0.320444 | + | 0.320444i | 0.848937 | − | 0.528493i | \(-0.177243\pi\) |
−0.528493 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(230\) | 29.0555 | + | 90.0599i | 0.126328 | + | 0.391565i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 224.514 | + | 165.267i | 0.967735 | + | 0.712359i | ||||
\(233\) | 156.229i | 0.670509i | 0.942128 | + | 0.335255i | \(0.108822\pi\) | ||||
−0.942128 | + | 0.335255i | \(0.891178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −45.9569 | + | 45.9569i | −0.195561 | + | 0.195561i | ||||
\(236\) | −34.8395 | − | 5.66655i | −0.147625 | − | 0.0240108i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 399.333 | + | 204.516i | 1.67787 | + | 0.859313i | ||||
\(239\) | − | 13.1716i | − | 0.0551113i | −0.999620 | − | 0.0275557i | \(-0.991228\pi\) | ||
0.999620 | − | 0.0275557i | \(-0.00877235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −189.519 | −0.786386 | −0.393193 | − | 0.919456i | \(-0.628630\pi\) | ||||
−0.393193 | + | 0.919456i | \(0.628630\pi\) | |||||||
\(242\) | −100.958 | + | 197.127i | −0.417181 | + | 0.814575i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 200.734 | + | 32.6488i | 0.822679 | + | 0.133807i | ||||
\(245\) | −51.8692 | − | 51.8692i | −0.211711 | − | 0.211711i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 232.508 | 0.941328 | ||||||||
\(248\) | 327.250 | − | 49.7422i | 1.31956 | − | 0.200573i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −130.120 | + | 41.9799i | −0.520481 | + | 0.167920i | ||||
\(251\) | 27.4434 | − | 27.4434i | 0.109336 | − | 0.109336i | −0.650322 | − | 0.759658i | \(-0.725366\pi\) |
0.759658 | + | 0.650322i | \(0.225366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 75.2053 | − | 75.2053i | 0.297254 | − | 0.297254i | ||||
\(254\) | 33.5802 | − | 65.5678i | 0.132206 | − | 0.258141i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −204.578 | − | 153.895i | −0.799135 | − | 0.601152i | ||||
\(257\) | −135.375 | −0.526752 | −0.263376 | − | 0.964693i | \(-0.584836\pi\) | ||||
−0.263376 | + | 0.964693i | \(0.584836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −66.1586 | − | 66.1586i | −0.255438 | − | 0.255438i | ||||
\(260\) | 32.4255 | + | 45.0222i | 0.124714 | + | 0.173162i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7414 | + | 33.2939i | 0.0409978 | + | 0.127076i | ||||
\(263\) | −31.6123 | −0.120199 | −0.0600994 | − | 0.998192i | \(-0.519142\pi\) | ||||
−0.0600994 | + | 0.998192i | \(0.519142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 50.6684i | 0.191201i | ||||||||
\(266\) | −147.041 | − | 455.765i | −0.552784 | − | 1.71340i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.26715 | + | 56.9769i | −0.0345789 | + | 0.212600i | ||||
\(269\) | 194.213 | − | 194.213i | 0.721981 | − | 0.721981i | −0.247028 | − | 0.969008i | \(-0.579454\pi\) |
0.969008 | + | 0.247028i | \(0.0794538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 291.647i | 1.07619i | 0.842884 | + | 0.538095i | \(0.180856\pi\) | ||||
−0.842884 | + | 0.538095i | \(0.819144\pi\) | |||||||
\(272\) | −113.480 | + | 339.625i | −0.417207 | + | 1.24862i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 132.813 | − | 259.326i | 0.484717 | − | 0.946444i | ||||
\(275\) | 52.0287 | + | 52.0287i | 0.189195 | + | 0.189195i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 305.166 | + | 305.166i | 1.10168 | + | 1.10168i | 0.994208 | + | 0.107475i | \(0.0342765\pi\) |
0.107475 | + | 0.994208i | \(0.465723\pi\) | |||||||
\(278\) | 222.265 | − | 71.7079i | 0.799513 | − | 0.257942i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 67.7467 | − | 92.0333i | 0.241952 | − | 0.328691i | ||||
\(281\) | 211.861i | 0.753955i | 0.926222 | + | 0.376978i | \(0.123037\pi\) | ||||
−0.926222 | + | 0.376978i | \(0.876963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 105.325 | − | 105.325i | 0.372175 | − | 0.372175i | −0.496094 | − | 0.868269i | \(-0.665233\pi\) |
0.868269 | + | 0.496094i | \(0.165233\pi\) | |||||||
\(284\) | −27.9419 | − | 38.7968i | −0.0983870 | − | 0.136608i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.4254 | − | 55.5027i | 0.0993897 | − | 0.194065i | ||||
\(287\) | 472.588i | 1.64665i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 211.871 | 0.733117 | ||||||||
\(290\) | −88.4060 | − | 45.2768i | −0.304848 | − | 0.156127i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −361.364 | + | 260.258i | −1.23755 | + | 0.891296i | ||||
\(293\) | 171.289 | + | 171.289i | 0.584603 | + | 0.584603i | 0.936165 | − | 0.351562i | \(-0.114349\pi\) |
−0.351562 | + | 0.936165i | \(0.614349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.5758 | 0.0426300 | ||||||||
\(296\) | 44.2680 | − | 60.1377i | 0.149554 | − | 0.203168i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −170.430 | − | 528.262i | −0.571912 | − | 1.77269i | ||||
\(299\) | 228.497 | − | 228.497i | 0.764204 | − | 0.764204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −489.368 | + | 489.368i | −1.62581 | + | 1.62581i | ||||
\(302\) | 114.819 | + | 58.8041i | 0.380196 | + | 0.194716i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 341.988 | − | 170.686i | 1.12496 | − | 0.561468i | ||||
\(305\) | −72.4579 | −0.237567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.1124 | − | 27.1124i | −0.0883140 | − | 0.0883140i | 0.661570 | − | 0.749884i | \(-0.269891\pi\) |
−0.749884 | + | 0.661570i | \(0.769891\pi\) | |||||||
\(308\) | −126.773 | − | 20.6194i | −0.411602 | − | 0.0669460i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −112.236 | + | 36.2102i | −0.362053 | + | 0.116807i | ||||
\(311\) | −371.124 | −1.19333 | −0.596663 | − | 0.802492i | \(-0.703507\pi\) | ||||
−0.596663 | + | 0.802492i | \(0.703507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 374.501i | − | 1.19649i | −0.801313 | − | 0.598245i | \(-0.795865\pi\) | ||
0.801313 | − | 0.598245i | \(-0.204135\pi\) | |||||||
\(314\) | 146.488 | − | 47.2607i | 0.466524 | − | 0.150512i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.4773 | + | 10.4267i | −0.0458143 | + | 0.0329960i | ||||
\(317\) | 48.5840 | − | 48.5840i | 0.153262 | − | 0.153262i | −0.626311 | − | 0.779573i | \(-0.715436\pi\) |
0.779573 | + | 0.626311i | \(0.215436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 111.633i | 0.349947i | ||||||||
\(320\) | 80.7448 | + | 42.4178i | 0.252328 | + | 0.132555i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −592.406 | − | 303.398i | −1.83977 | − | 0.942230i | ||||
\(323\) | −378.040 | − | 378.040i | −1.17040 | − | 1.17040i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 158.079 | + | 158.079i | 0.486398 | + | 0.486398i | ||||
\(326\) | 91.0149 | + | 282.108i | 0.279187 | + | 0.865363i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −372.899 | + | 56.6808i | −1.13689 | + | 0.172807i | ||||
\(329\) | − | 457.122i | − | 1.38943i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.88883 | + | 1.88883i | −0.00570644 | + | 0.00570644i | −0.709954 | − | 0.704248i | \(-0.751284\pi\) |
0.704248 | + | 0.709954i | \(0.251284\pi\) | |||||||
\(332\) | 9.24040 | − | 56.8125i | 0.0278325 | − | 0.171122i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −94.9001 | − | 48.6027i | −0.284132 | − | 0.145517i | ||||
\(335\) | − | 20.5667i | − | 0.0613931i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −386.980 | −1.14831 | −0.574154 | − | 0.818747i | \(-0.694669\pi\) | ||||
−0.574154 | + | 0.818747i | \(0.694669\pi\) | |||||||
\(338\) | −67.7090 | + | 132.207i | −0.200323 | + | 0.391144i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.4812 | − | 125.924i | 0.0602388 | − | 0.370365i | ||||
\(341\) | 93.7240 | + | 93.7240i | 0.274851 | + | 0.274851i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.7757 | 0.0722325 | ||||||||
\(344\) | −444.832 | − | 327.446i | −1.29312 | − | 0.951877i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 111.920 | − | 36.1080i | 0.323468 | − | 0.104358i | ||||
\(347\) | −441.887 | + | 441.887i | −1.27345 | + | 1.27345i | −0.329183 | + | 0.944266i | \(0.606773\pi\) |
−0.944266 | + | 0.329183i | \(0.893227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 119.382 | − | 119.382i | 0.342068 | − | 0.342068i | −0.515076 | − | 0.857144i | \(-0.672236\pi\) |
0.857144 | + | 0.515076i | \(0.172236\pi\) | |||||||
\(350\) | 209.898 | − | 409.840i | 0.599707 | − | 1.17097i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.06501 | − | 102.504i | 0.00302560 | − | 0.291206i | ||||
\(353\) | 515.642 | 1.46074 | 0.730371 | − | 0.683050i | \(-0.239347\pi\) | ||||
0.730371 | + | 0.683050i | \(0.239347\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0452 | + | 12.0452i | 0.0339301 | + | 0.0339301i | ||||
\(356\) | −71.2014 | + | 51.2801i | −0.200004 | + | 0.144045i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −46.0890 | − | 142.857i | −0.128740 | − | 0.399041i | ||||
\(359\) | −428.264 | −1.19294 | −0.596468 | − | 0.802637i | \(-0.703430\pi\) | ||||
−0.596468 | + | 0.802637i | \(0.703430\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 209.664i | 0.580786i | ||||||||
\(362\) | −57.8418 | − | 179.286i | −0.159784 | − | 0.495264i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −385.177 | − | 62.6480i | −1.05818 | − | 0.172110i | ||||
\(365\) | 112.192 | − | 112.192i | 0.307375 | − | 0.307375i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 219.482i | 0.598043i | 0.954246 | + | 0.299021i | \(0.0966602\pi\) | ||||
−0.954246 | + | 0.299021i | \(0.903340\pi\) | |||||||
\(368\) | 168.347 | − | 503.830i | 0.457464 | − | 1.36910i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.1277 | + | 23.6802i | −0.0327775 | + | 0.0640004i | ||||
\(371\) | −251.993 | − | 251.993i | −0.679226 | − | 0.679226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 425.005 | + | 425.005i | 1.13942 | + | 1.13942i | 0.988554 | + | 0.150870i | \(0.0482075\pi\) |
0.150870 | + | 0.988554i | \(0.451793\pi\) | |||||||
\(374\) | −136.461 | + | 44.0255i | −0.364868 | + | 0.117715i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 360.695 | − | 54.8259i | 0.959296 | − | 0.145814i | ||||
\(377\) | 339.175i | 0.899669i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 365.916 | − | 365.916i | 0.965476 | − | 0.965476i | −0.0339473 | − | 0.999424i | \(-0.510808\pi\) |
0.999424 | + | 0.0339473i | \(0.0108078\pi\) | |||||||
\(380\) | −110.502 | + | 79.5846i | −0.290794 | + | 0.209433i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 103.707 | − | 202.495i | 0.271484 | − | 0.530091i | ||||
\(383\) | − | 213.276i | − | 0.556857i | −0.960457 | − | 0.278428i | \(-0.910187\pi\) | ||
0.960457 | − | 0.278428i | \(-0.0898135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.7608 | 0.118859 | ||||||||
\(386\) | −47.2793 | − | 24.2139i | −0.122485 | − | 0.0627303i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 250.854 | + | 348.305i | 0.646530 | + | 0.897694i | ||||
\(389\) | 210.798 | + | 210.798i | 0.541898 | + | 0.541898i | 0.924085 | − | 0.382187i | \(-0.124829\pi\) |
−0.382187 | + | 0.924085i | \(0.624829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −743.037 | −1.90035 | ||||||||
\(392\) | 61.8791 | + | 407.098i | 0.157855 | + | 1.03852i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −45.0665 | − | 139.687i | −0.114382 | − | 0.354536i | ||||
\(395\) | 4.49475 | − | 4.49475i | 0.0113791 | − | 0.0113791i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 392.907 | − | 392.907i | 0.989690 | − | 0.989690i | −0.0102579 | − | 0.999947i | \(-0.503265\pi\) |
0.999947 | + | 0.0102579i | \(0.00326524\pi\) | |||||||
\(398\) | −243.415 | − | 124.664i | −0.611597 | − | 0.313226i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 348.561 | + | 116.466i | 0.871403 | + | 0.291165i | ||||
\(401\) | −29.3290 | −0.0731396 | −0.0365698 | − | 0.999331i | \(-0.511643\pi\) | ||||
−0.0365698 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 284.762 | + | 284.762i | 0.706606 | + | 0.706606i | ||||
\(404\) | −91.5224 | + | 562.705i | −0.226541 | + | 1.39283i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 664.855 | − | 214.498i | 1.63757 | − | 0.528321i | ||||
\(407\) | 29.9017 | 0.0734684 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 601.115i | 1.46972i | 0.678219 | + | 0.734860i | \(0.262752\pi\) | ||||
−0.678219 | + | 0.734860i | \(0.737248\pi\) | |||||||
\(410\) | 127.892 | − | 41.2612i | 0.311933 | − | 0.100637i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 135.716 | + | 188.440i | 0.329409 | + | 0.457378i | ||||
\(413\) | −62.5444 | + | 62.5444i | −0.151439 | + | 0.151439i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.5073i | 0.0494153i | ||||||||
\(416\) | 3.23584 | − | 311.440i | 0.00777845 | − | 0.748654i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 136.225 | + | 69.7669i | 0.325897 | + | 0.166907i | ||||
\(419\) | 518.885 | + | 518.885i | 1.23839 | + | 1.23839i | 0.960659 | + | 0.277729i | \(0.0895819\pi\) |
0.277729 | + | 0.960659i | \(0.410418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −411.213 | − | 411.213i | −0.976754 | − | 0.976754i | 0.0229817 | − | 0.999736i | \(-0.492684\pi\) |
−0.999736 | + | 0.0229817i | \(0.992684\pi\) | |||||||
\(422\) | −122.599 | − | 380.005i | −0.290518 | − | 0.900485i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 168.613 | − | 229.060i | 0.397673 | − | 0.540236i | ||||
\(425\) | − | 514.049i | − | 1.20953i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 360.360 | − | 360.360i | 0.843936 | − | 0.843936i | ||||
\(428\) | −629.522 | − | 102.390i | −1.47084 | − | 0.239229i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 175.160 | + | 89.7072i | 0.407348 | + | 0.208622i | ||||
\(431\) | − | 41.1083i | − | 0.0953789i | −0.998862 | − | 0.0476895i | \(-0.984814\pi\) | ||
0.998862 | − | 0.0476895i | \(-0.0151858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −351.682 | −0.812199 | −0.406100 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406100 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(434\) | 378.107 | − | 738.281i | 0.871215 | − | 1.70111i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −453.035 | − | 73.6850i | −1.03907 | − | 0.169002i | ||||
\(437\) | 560.819 | + | 560.819i | 1.28334 | + | 1.28334i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −775.613 | −1.76677 | −0.883386 | − | 0.468646i | \(-0.844742\pi\) | ||||
−0.883386 | + | 0.468646i | \(0.844742\pi\) | |||||||
\(440\) | 5.48841 | + | 36.1079i | 0.0124737 | + | 0.0820633i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −414.609 | + | 133.763i | −0.938030 | + | 0.302631i | ||||
\(443\) | 241.372 | − | 241.372i | 0.544858 | − | 0.544858i | −0.380091 | − | 0.924949i | \(-0.624107\pi\) |
0.924949 | + | 0.380091i | \(0.124107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.1058 | − | 22.1058i | 0.0496759 | − | 0.0496759i | ||||
\(446\) | −111.778 | + | 218.255i | −0.250624 | + | 0.489361i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −612.534 | + | 190.615i | −1.36726 | + | 0.425480i | ||||
\(449\) | −266.360 | −0.593228 | −0.296614 | − | 0.954997i | \(-0.595858\pi\) | ||||
−0.296614 | + | 0.954997i | \(0.595858\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −106.798 | − | 106.798i | −0.236802 | − | 0.236802i | ||||
\(452\) | 401.714 | + | 557.772i | 0.888749 | + | 1.23401i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 256.923 | + | 796.355i | 0.565910 | + | 1.75409i | ||||
\(455\) | 139.035 | 0.305572 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 515.244i | − | 1.12745i | −0.825963 | − | 0.563725i | \(-0.809368\pi\) | ||
0.825963 | − | 0.563725i | \(-0.190632\pi\) | |||||||
\(458\) | 63.7277 | + | 197.529i | 0.139143 | + | 0.431287i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −30.3837 | + | 186.807i | −0.0660514 | + | 0.406102i | ||||
\(461\) | −5.67717 | + | 5.67717i | −0.0123149 | + | 0.0123149i | −0.713237 | − | 0.700923i | \(-0.752772\pi\) |
0.700923 | + | 0.713237i | \(0.252772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 464.510i | − | 1.00326i | −0.865082 | − | 0.501631i | \(-0.832733\pi\) | ||
0.865082 | − | 0.501631i | \(-0.167267\pi\) | |||||||
\(464\) | 248.992 | + | 498.882i | 0.536621 | + | 1.07518i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −142.431 | + | 278.106i | −0.305646 | + | 0.596794i | ||||
\(467\) | −495.985 | − | 495.985i | −1.06207 | − | 1.06207i | −0.997942 | − | 0.0641248i | \(-0.979574\pi\) |
−0.0641248 | − | 0.997942i | \(-0.520426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 102.286 | + | 102.286i | 0.218094 | + | 0.218094i | ||||
\(470\) | −123.707 | + | 39.9109i | −0.263207 | + | 0.0849167i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −56.8525 | − | 41.8497i | −0.120450 | − | 0.0886646i | ||||
\(473\) | − | 221.180i | − | 0.467610i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −387.987 | + | 387.987i | −0.816815 | + | 0.816815i | ||||
\(476\) | 524.407 | + | 728.129i | 1.10170 | + | 1.52968i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0083 | − | 23.4471i | 0.0251220 | − | 0.0490525i | ||||
\(479\) | 378.802i | 0.790818i | 0.918505 | + | 0.395409i | \(0.129397\pi\) | ||||
−0.918505 | + | 0.395409i | \(0.870603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 90.8504 | 0.188878 | ||||||||
\(482\) | −337.367 | − | 172.781i | −0.699932 | − | 0.358467i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −359.435 | + | 258.869i | −0.742633 | + | 0.534854i | ||||
\(485\) | −108.138 | − | 108.138i | −0.222964 | − | 0.222964i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 147.446 | 0.302764 | 0.151382 | − | 0.988475i | \(-0.451628\pi\) | ||||
0.151382 | + | 0.988475i | \(0.451628\pi\) | |||||||
\(488\) | 327.565 | + | 241.124i | 0.671240 | + | 0.494107i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −45.0453 | − | 139.622i | −0.0919292 | − | 0.284942i | ||||
\(491\) | −109.547 | + | 109.547i | −0.223110 | + | 0.223110i | −0.809807 | − | 0.586697i | \(-0.800428\pi\) |
0.586697 | + | 0.809807i | \(0.300428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 551.473 | − | 551.473i | 1.11861 | − | 1.11861i | ||||
\(494\) | 413.893 | + | 211.973i | 0.837840 | + | 0.429096i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 627.894 | + | 209.801i | 1.26592 | + | 0.422985i | ||||
\(497\) | −119.810 | −0.241067 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −360.523 | − | 360.523i | −0.722491 | − | 0.722491i | 0.246621 | − | 0.969112i | \(-0.420680\pi\) |
−0.969112 | + | 0.246621i | \(0.920680\pi\) | |||||||
\(500\) | −269.902 | − | 43.8989i | −0.539804 | − | 0.0877977i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 73.8722 | − | 23.8329i | 0.147156 | − | 0.0474760i | ||||
\(503\) | 927.420 | 1.84378 | 0.921889 | − | 0.387454i | \(-0.126645\pi\) | ||||
0.921889 | + | 0.387454i | \(0.126645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 203.117i | − | 0.402211i | ||||||
\(506\) | 202.438 | − | 65.3114i | 0.400075 | − | 0.129074i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 119.554 | − | 86.1042i | 0.235342 | − | 0.169496i | ||||
\(509\) | −677.931 | + | 677.931i | −1.33189 | + | 1.33189i | −0.428208 | + | 0.903680i | \(0.640855\pi\) |
−0.903680 | + | 0.428208i | \(0.859145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1115.95i | 2.18385i | ||||||||
\(512\) | −223.872 | − | 460.462i | −0.437249 | − | 0.899340i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −240.984 | − | 123.419i | −0.468841 | − | 0.240115i | ||||
\(515\) | −58.5045 | − | 58.5045i | −0.113601 | − | 0.113601i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 103.303 | + | 103.303i | 0.199812 | + | 0.199812i | ||||
\(518\) | −57.4548 | − | 178.086i | −0.110917 | − | 0.343795i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.6755 | + | 109.707i | 0.0320682 | + | 0.210974i | ||||
\(521\) | 143.173i | 0.274804i | 0.990515 | + | 0.137402i | \(0.0438753\pi\) | ||||
−0.990515 | + | 0.137402i | \(0.956125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 226.187 | − | 226.187i | 0.432481 | − | 0.432481i | −0.456991 | − | 0.889471i | \(-0.651073\pi\) |
0.889471 | + | 0.456991i | \(0.151073\pi\) | |||||||
\(524\) | −11.2324 | + | 69.0600i | −0.0214359 | + | 0.131794i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.2738 | − | 28.8204i | −0.106984 | − | 0.0547916i | ||||
\(527\) | − | 926.004i | − | 1.75712i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 573.288 | 1.08372 | ||||||||
\(530\) | −46.1934 | + | 90.1959i | −0.0871574 | + | 0.170181i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 153.762 | − | 945.371i | 0.289027 | − | 1.77701i | ||||
\(533\) | −324.484 | − | 324.484i | −0.608788 | − | 0.608788i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 227.235 | 0.424739 | ||||||||
\(536\) | −68.4415 | + | 92.9772i | −0.127689 | + | 0.173465i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 522.783 | − | 168.662i | 0.971716 | − | 0.313499i | ||||
\(539\) | −116.592 | + | 116.592i | −0.216312 | + | 0.216312i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −156.708 | + | 156.708i | −0.289663 | + | 0.289663i | −0.836947 | − | 0.547284i | \(-0.815662\pi\) |
0.547284 | + | 0.836947i | \(0.315662\pi\) | |||||||
\(542\) | −265.890 | + | 519.168i | −0.490571 | + | 0.957875i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −511.639 | + | 501.116i | −0.940512 | + | 0.921170i | ||||
\(545\) | 163.530 | 0.300055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 247.357 | + | 247.357i | 0.452207 | + | 0.452207i | 0.896086 | − | 0.443880i | \(-0.146398\pi\) |
−0.443880 | + | 0.896086i | \(0.646398\pi\) | |||||||
\(548\) | 472.845 | − | 340.549i | 0.862856 | − | 0.621440i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 45.1839 | + | 140.051i | 0.0821525 | + | 0.254638i | ||||
\(551\) | −832.466 | −1.51083 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.7082i | 0.0808466i | ||||||||
\(554\) | 265.019 | + | 821.447i | 0.478373 | + | 1.48276i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 461.033 | + | 74.9858i | 0.829196 | + | 0.134867i | ||||
\(557\) | 661.193 | − | 661.193i | 1.18706 | − | 1.18706i | 0.209184 | − | 0.977876i | \(-0.432919\pi\) |
0.977876 | − | 0.209184i | \(-0.0670808\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 672.011i | − | 1.20217i | ||||||
\(560\) | 204.503 | − | 102.067i | 0.365183 | − | 0.182263i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −193.150 | + | 377.139i | −0.343684 | + | 0.671066i | ||||
\(563\) | −246.685 | − | 246.685i | −0.438162 | − | 0.438162i | 0.453231 | − | 0.891393i | \(-0.350271\pi\) |
−0.891393 | + | 0.453231i | \(0.850271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −173.171 | − | 173.171i | −0.306497 | − | 0.306497i | ||||
\(566\) | 283.516 | − | 91.4689i | 0.500911 | − | 0.161606i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.3697 | − | 94.5372i | −0.0252988 | − | 0.166439i | ||||
\(569\) | 243.567i | 0.428061i | 0.976827 | + | 0.214030i | \(0.0686592\pi\) | ||||
−0.976827 | + | 0.214030i | \(0.931341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 59.9229 | − | 59.9229i | 0.104944 | − | 0.104944i | −0.652685 | − | 0.757629i | \(-0.726358\pi\) |
0.757629 | + | 0.652685i | \(0.226358\pi\) | |||||||
\(572\) | 101.202 | − | 72.8866i | 0.176926 | − | 0.127424i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −430.850 | + | 841.265i | −0.750610 | + | 1.46562i | ||||
\(575\) | 762.587i | 1.32624i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 136.609 | 0.236757 | 0.118378 | − | 0.992969i | \(-0.462230\pi\) | ||||
0.118378 | + | 0.992969i | \(0.462230\pi\) | |||||||
\(578\) | 377.156 | + | 193.159i | 0.652519 | + | 0.334185i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −116.096 | − | 161.196i | −0.200165 | − | 0.277925i | ||||
\(581\) | −101.991 | − | 101.991i | −0.175543 | − | 0.175543i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 113.893 | 0.195357 | ||||||||
\(584\) | −880.544 | + | 133.843i | −1.50778 | + | 0.229184i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 148.754 | + | 461.076i | 0.253846 | + | 0.786818i | ||||
\(587\) | 331.817 | − | 331.817i | 0.565276 | − | 0.565276i | −0.365525 | − | 0.930801i | \(-0.619111\pi\) |
0.930801 | + | 0.365525i | \(0.119111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −698.916 | + | 698.916i | −1.18661 | + | 1.18661i | ||||
\(590\) | 22.3865 | + | 11.4652i | 0.0379433 | + | 0.0194325i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 133.629 | − | 66.6942i | 0.225724 | − | 0.112659i | ||||
\(593\) | −131.285 | −0.221391 | −0.110695 | − | 0.993854i | \(-0.535308\pi\) | ||||
−0.110695 | + | 0.993854i | \(0.535308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −226.061 | − | 226.061i | −0.379934 | − | 0.379934i | ||||
\(596\) | 178.221 | − | 1095.75i | 0.299028 | − | 1.83850i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 615.069 | − | 198.436i | 1.02854 | − | 0.331833i | ||||
\(599\) | 136.119 | 0.227243 | 0.113621 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 498.566i | − | 0.829561i | −0.909922 | − | 0.414780i | \(-0.863858\pi\) | ||
0.909922 | − | 0.414780i | \(-0.136142\pi\) | |||||||
\(602\) | −1317.28 | + | 424.987i | −2.18818 | + | 0.705959i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 150.781 | + | 209.357i | 0.249638 | + | 0.346617i | ||||
\(605\) | 111.593 | − | 111.593i | 0.184451 | − | 0.184451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 568.740i | − | 0.936969i | −0.883472 | − | 0.468484i | \(-0.844800\pi\) | ||
0.883472 | − | 0.468484i | \(-0.155200\pi\) | |||||||
\(608\) | 764.393 | + | 7.94198i | 1.25723 | + | 0.0130625i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −128.984 | − | 66.0585i | −0.211449 | − | 0.108293i | ||||
\(611\) | 313.865 | + | 313.865i | 0.513691 | + | 0.513691i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −168.441 | − | 168.441i | −0.274782 | − | 0.274782i | 0.556240 | − | 0.831022i | \(-0.312244\pi\) |
−0.831022 | + | 0.556240i | \(0.812244\pi\) | |||||||
\(614\) | −23.5455 | − | 72.9813i | −0.0383478 | − | 0.118862i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −206.874 | − | 152.282i | −0.335834 | − | 0.247211i | ||||
\(617\) | − | 599.157i | − | 0.971081i | −0.874214 | − | 0.485541i | \(-0.838623\pi\) | ||
0.874214 | − | 0.485541i | \(-0.161377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 126.719 | − | 126.719i | 0.204715 | − | 0.204715i | −0.597301 | − | 0.802017i | \(-0.703760\pi\) |
0.802017 | + | 0.597301i | \(0.203760\pi\) | |||||||
\(620\) | −232.807 | − | 37.8654i | −0.375495 | − | 0.0610732i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −660.647 | − | 338.347i | −1.06213 | − | 0.543967i | ||||
\(623\) | 219.881i | 0.352939i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −476.800 | −0.762879 | ||||||||
\(626\) | 341.426 | − | 666.658i | 0.545409 | − | 1.06495i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 303.854 | + | 49.4210i | 0.483844 | + | 0.0786959i | ||||
\(629\) | −147.716 | − | 147.716i | −0.234842 | − | 0.234842i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 668.283 | 1.05909 | 0.529543 | − | 0.848283i | \(-0.322363\pi\) | ||||
0.529543 | + | 0.848283i | \(0.322363\pi\) | |||||||
\(632\) | −35.2773 | + | 5.36216i | −0.0558185 | + | 0.00848444i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 130.779 | − | 42.1923i | 0.206275 | − | 0.0665494i | ||||
\(635\) | −37.1177 | + | 37.1177i | −0.0584531 | + | 0.0584531i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −354.243 | + | 354.243i | −0.556112 | + | 0.556112i | ||||
\(638\) | −101.774 | + | 198.720i | −0.159520 | + | 0.311474i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 105.064 | + | 149.122i | 0.164163 | + | 0.233004i | ||||
\(641\) | −484.574 | −0.755966 | −0.377983 | − | 0.925813i | \(-0.623382\pi\) | ||||
−0.377983 | + | 0.925813i | \(0.623382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 75.2980 | + | 75.2980i | 0.117104 | + | 0.117104i | 0.763230 | − | 0.646126i | \(-0.223612\pi\) |
−0.646126 | + | 0.763230i | \(0.723612\pi\) | |||||||
\(644\) | −777.952 | − | 1080.17i | −1.20800 | − | 1.67728i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −328.306 | − | 1017.61i | −0.508213 | − | 1.57525i | ||||
\(647\) | 582.307 | 0.900011 | 0.450006 | − | 0.893026i | \(-0.351422\pi\) | ||||
0.450006 | + | 0.893026i | \(0.351422\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.2682i | − | 0.0435565i | ||||||
\(650\) | 137.282 | + | 425.518i | 0.211204 | + | 0.654644i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −95.1754 | + | 585.164i | −0.145974 | + | 0.897491i | ||||
\(653\) | −457.453 | + | 457.453i | −0.700541 | + | 0.700541i | −0.964527 | − | 0.263986i | \(-0.914963\pi\) |
0.263986 | + | 0.964527i | \(0.414963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 24.9283i | − | 0.0380584i | ||||||
\(656\) | −715.480 | − | 239.066i | −1.09067 | − | 0.364430i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 416.750 | − | 813.734i | 0.633359 | − | 1.23668i | ||||
\(659\) | 430.079 | + | 430.079i | 0.652623 | + | 0.652623i | 0.953624 | − | 0.301001i | \(-0.0973207\pi\) |
−0.301001 | + | 0.953624i | \(0.597321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −513.622 | − | 513.622i | −0.777038 | − | 0.777038i | 0.202288 | − | 0.979326i | \(-0.435162\pi\) |
−0.979326 | + | 0.202288i | \(0.935162\pi\) | |||||||
\(662\) | −5.08436 | + | 1.64034i | −0.00768031 | + | 0.00247785i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 68.2440 | − | 92.7089i | 0.102777 | − | 0.139622i | ||||
\(665\) | 341.246i | 0.513152i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −818.105 | + | 818.105i | −1.22654 | + | 1.22654i | ||||
\(668\) | −124.624 | − | 173.037i | −0.186562 | − | 0.259038i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.7503 | − | 36.6112i | 0.0279855 | − | 0.0546436i | ||||
\(671\) | 162.872i | 0.242730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1112.68 | −1.65332 | −0.826659 | − | 0.562703i | \(-0.809761\pi\) | ||||
−0.826659 | + | 0.562703i | \(0.809761\pi\) | |||||||
\(674\) | −688.871 | − | 352.802i | −1.02206 | − | 0.523446i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −241.061 | + | 173.615i | −0.356599 | + | 0.256827i | ||||
\(677\) | −633.271 | − | 633.271i | −0.935408 | − | 0.935408i | 0.0626291 | − | 0.998037i | \(-0.480051\pi\) |
−0.998037 | + | 0.0626291i | \(0.980051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1075.62 | 1.58412 | ||||||||
\(680\) | 151.262 | − | 205.488i | 0.222444 | − | 0.302188i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 81.3937 | + | 252.287i | 0.119346 | + | 0.369922i | ||||
\(683\) | 429.651 | − | 429.651i | 0.629065 | − | 0.629065i | −0.318768 | − | 0.947833i | \(-0.603269\pi\) |
0.947833 | + | 0.318768i | \(0.103269\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −146.803 | + | 146.803i | −0.214312 | + | 0.214312i | ||||
\(686\) | 44.1038 | + | 22.5876i | 0.0642913 | + | 0.0329265i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −493.330 | − | 988.439i | −0.717049 | − | 1.43668i | ||||
\(689\) | 346.042 | 0.502239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −151.617 | − | 151.617i | −0.219417 | − | 0.219417i | 0.588836 | − | 0.808253i | \(-0.299586\pi\) |
−0.808253 | + | 0.588836i | \(0.799586\pi\) | |||||||
\(692\) | 232.150 | + | 37.7586i | 0.335477 | + | 0.0545644i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1189.47 | + | 383.753i | −1.71394 | + | 0.552958i | ||||
\(695\) | −166.417 | −0.239449 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1055.17i | 1.51388i | ||||||||
\(698\) | 321.353 | − | 103.676i | 0.460391 | − | 0.148533i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 747.287 | − | 538.205i | 1.06755 | − | 0.768864i | ||||
\(701\) | 920.704 | − | 920.704i | 1.31341 | − | 1.31341i | 0.394533 | − | 0.918882i | \(-0.370906\pi\) |
0.918882 | − | 0.394533i | \(-0.129094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 222.982i | 0.317186i | ||||||||
\(704\) | 95.3473 | − | 181.500i | 0.135437 | − | 0.257812i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 917.906 | + | 470.102i | 1.30015 | + | 0.665866i | ||||
\(707\) | 1010.18 | + | 1010.18i | 1.42882 | + | 1.42882i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 405.348 | + | 405.348i | 0.571718 | + | 0.571718i | 0.932608 | − | 0.360890i | \(-0.117527\pi\) |
−0.360890 | + | 0.932608i | \(0.617527\pi\) | |||||||
\(710\) | 10.4605 | + | 32.4233i | 0.0147331 | + | 0.0456666i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −173.498 | + | 26.3718i | −0.243677 | + | 0.0370391i | ||||
\(713\) | 1373.72i | 1.92667i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.4199 | + | 31.4199i | −0.0439439 | + | 0.0439439i | ||||
\(716\) | 48.1958 | − | 296.321i | 0.0673125 | − | 0.413856i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −762.363 | − | 390.441i | −1.06179 | − | 0.543789i | ||||
\(719\) | − | 880.704i | − | 1.22490i | −0.790509 | − | 0.612450i | \(-0.790184\pi\) | ||
0.790509 | − | 0.612450i | \(-0.209816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 581.930 | 0.807115 | ||||||||
\(722\) | −191.147 | + | 373.227i | −0.264746 | + | 0.516935i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 60.4859 | − | 371.884i | 0.0835440 | − | 0.513651i | ||||
\(725\) | −565.983 | − | 565.983i | −0.780667 | − | 0.780667i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1000.46 | 1.37615 | 0.688077 | − | 0.725637i | \(-0.258455\pi\) | ||||
0.688077 | + | 0.725637i | \(0.258455\pi\) | |||||||
\(728\) | −628.547 | − | 462.680i | −0.863388 | − | 0.635549i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 301.999 | − | 97.4320i | 0.413697 | − | 0.133469i | ||||
\(731\) | −1092.64 | + | 1092.64i | −1.49472 | + | 1.49472i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 540.306 | − | 540.306i | 0.737116 | − | 0.737116i | −0.234903 | − | 0.972019i | \(-0.575477\pi\) |
0.972019 | + | 0.234903i | \(0.0754772\pi\) | |||||||
\(734\) | −200.097 | + | 390.704i | −0.272612 | + | 0.532295i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 759.011 | − | 743.401i | 1.03126 | − | 1.01006i | ||||
\(737\) | −46.2301 | −0.0627274 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 893.726 | + | 893.726i | 1.20937 | + | 1.20937i | 0.971230 | + | 0.238142i | \(0.0765384\pi\) |
0.238142 | + | 0.971230i | \(0.423462\pi\) | |||||||
\(740\) | −43.1775 | + | 31.0970i | −0.0583480 | + | 0.0420229i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −218.841 | − | 678.316i | −0.294934 | − | 0.914172i | ||||
\(743\) | −1295.75 | −1.74394 | −0.871969 | − | 0.489561i | \(-0.837157\pi\) | ||||
−0.871969 | + | 0.489561i | \(0.837157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 395.527i | 0.530909i | ||||||||
\(746\) | 369.092 | + | 1144.03i | 0.494761 | + | 1.53355i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −283.054 | − | 46.0380i | −0.378414 | − | 0.0615481i | ||||
\(749\) | −1130.13 | + | 1130.13i | −1.50885 | + | 1.50885i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 229.818i | − | 0.306016i | −0.988225 | − | 0.153008i | \(-0.951104\pi\) | ||
0.988225 | − | 0.153008i | \(-0.0488961\pi\) | |||||||
\(752\) | 692.066 | + | 231.243i | 0.920300 | + | 0.307504i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −309.220 | + | 603.774i | −0.410106 | + | 0.800761i | ||||
\(755\) | −64.9987 | − | 64.9987i | −0.0860910 | − | 0.0860910i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −373.678 | − | 373.678i | −0.493630 | − | 0.493630i | 0.415818 | − | 0.909448i | \(-0.363495\pi\) |
−0.909448 | + | 0.415818i | \(0.863495\pi\) | |||||||
\(758\) | 984.973 | − | 317.776i | 1.29944 | − | 0.419229i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −269.262 | + | 40.9280i | −0.354293 | + | 0.0538527i | ||||
\(761\) | − | 384.012i | − | 0.504615i | −0.967647 | − | 0.252307i | \(-0.918811\pi\) | ||
0.967647 | − | 0.252307i | \(-0.0811894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −813.296 | + | 813.296i | −1.06592 | + | 1.06592i | ||||
\(764\) | 369.222 | − | 265.918i | 0.483275 | − | 0.348060i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 194.440 | − | 379.658i | 0.253838 | − | 0.495637i | ||||
\(767\) | − | 85.8874i | − | 0.111978i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 865.026 | 1.12487 | 0.562436 | − | 0.826841i | \(-0.309864\pi\) | ||||
0.562436 | + | 0.826841i | \(0.309864\pi\) | |||||||
\(770\) | 81.4598 | + | 41.7193i | 0.105792 | + | 0.0541809i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −62.0876 | − | 86.2074i | −0.0804244 | − | 0.111668i | ||||
\(773\) | 1.78859 | + | 1.78859i | 0.00231383 | + | 0.00231383i | 0.708263 | − | 0.705949i | \(-0.249479\pi\) |
−0.705949 | + | 0.708263i | \(0.749479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −950.368 | −1.22628 | ||||||||
\(776\) | 129.007 | + | 848.725i | 0.166246 | + | 1.09372i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 183.066 | + | 567.428i | 0.235303 | + | 0.729341i | ||||
\(779\) | 796.409 | − | 796.409i | 1.02235 | − | 1.02235i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0753 | − | 27.0753i | 0.0346675 | − | 0.0346675i | ||||
\(782\) | −1322.70 | − | 677.413i | −1.69143 | − | 0.866257i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −260.991 | + | 781.098i | −0.332897 | + | 0.996299i | ||||
\(785\) | −109.681 | −0.139721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 143.702 | + | 143.702i | 0.182595 | + | 0.182595i | 0.792485 | − | 0.609891i | \(-0.208787\pi\) |
−0.609891 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(788\) | 47.1265 | − | 289.747i | 0.0598052 | − | 0.367699i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0990 | − | 3.90342i | 0.0153152 | − | 0.00494104i | ||||
\(791\) | 1722.49 | 2.17761 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 494.855i | 0.624029i | ||||||||
\(794\) | 1057.63 | − | 341.216i | 1.33203 | − | 0.429743i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −319.655 | − | 443.835i | −0.401577 | − | 0.557582i | ||||
\(797\) | 477.929 | − | 477.929i | 0.599660 | − | 0.599660i | −0.340562 | − | 0.940222i | \(-0.610617\pi\) |
0.940222 | + | 0.340562i | \(0.110617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1020.64i | − | 1.27740i | ||||||
\(800\) | 514.301 | + | 525.101i | 0.642877 | + | 0.656376i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −52.2091 | − | 26.7387i | −0.0650987 | − | 0.0333400i | ||||
\(803\) | −252.187 | − | 252.187i | −0.314056 | − | 0.314056i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 335.359 | + | 335.359i | 0.416595 | + | 0.416595i | ||||
\(806\) | 247.299 | + | 766.524i | 0.306823 | + | 0.951023i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −675.929 | + | 918.244i | −0.836545 | + | 1.13644i | ||||
\(809\) | 1524.96i | 1.88500i | 0.334212 | + | 0.942498i | \(0.391530\pi\) | ||||
−0.334212 | + | 0.942498i | \(0.608470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −576.427 | + | 576.427i | −0.710761 | + | 0.710761i | −0.966694 | − | 0.255933i | \(-0.917617\pi\) |
0.255933 | + | 0.966694i | \(0.417617\pi\) | |||||||
\(812\) | 1379.08 | + | 224.303i | 1.69837 | + | 0.276236i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 53.2286 | + | 27.2608i | 0.0653914 | + | 0.0334899i | ||||
\(815\) | − | 211.224i | − | 0.259170i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1649.37 | 2.01882 | ||||||||
\(818\) | −548.026 | + | 1070.06i | −0.669958 | + | 1.30814i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 265.281 | + | 43.1473i | 0.323514 | + | 0.0526186i | ||||
\(821\) | 386.324 | + | 386.324i | 0.470552 | + | 0.470552i | 0.902093 | − | 0.431541i | \(-0.142030\pi\) |
−0.431541 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 377.870 | 0.459138 | 0.229569 | − | 0.973292i | \(-0.426268\pi\) | ||||
0.229569 | + | 0.973292i | \(0.426268\pi\) | |||||||
\(824\) | 69.7950 | + | 459.176i | 0.0847026 | + | 0.557252i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −168.357 | + | 54.3161i | −0.203822 | + | 0.0657580i | ||||
\(827\) | −140.900 | + | 140.900i | −0.170375 | + | 0.170375i | −0.787144 | − | 0.616769i | \(-0.788441\pi\) |
0.616769 | + | 0.787144i | \(0.288441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −522.203 | + | 522.203i | −0.629919 | + | 0.629919i | −0.948048 | − | 0.318128i | \(-0.896946\pi\) |
0.318128 | + | 0.948048i | \(0.396946\pi\) | |||||||
\(830\) | −18.6962 | + | 36.5056i | −0.0225255 | + | 0.0439826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 289.694 | − | 551.451i | 0.348190 | − | 0.662802i | ||||
\(833\) | 1151.95 | 1.38289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53.7226 | + | 53.7226i | 0.0643385 | + | 0.0643385i | ||||
\(836\) | 178.892 | + | 248.387i | 0.213985 | + | 0.297114i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 450.621 | + | 1396.74i | 0.537734 | + | 1.66675i | ||||
\(839\) | 442.133 | 0.526976 | 0.263488 | − | 0.964663i | \(-0.415127\pi\) | ||||
0.263488 | + | 0.964663i | \(0.415127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 373.376i | − | 0.443967i | ||||||
\(842\) | −357.114 | − | 1106.91i | −0.424126 | − | 1.31462i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 128.203 | − | 788.226i | 0.151899 | − | 0.933917i | ||||
\(845\) | 74.8417 | − | 74.8417i | 0.0885701 | − | 0.0885701i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1109.99i | 1.31049i | ||||||||
\(848\) | 508.982 | − | 254.033i | 0.600215 | − | 0.299567i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 468.650 | − | 915.071i | 0.551352 | − | 1.07655i | ||||
\(851\) | 219.135 | + | 219.135i | 0.257503 | + | 0.257503i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −494.617 | − | 494.617i | −0.579856 | − | 0.579856i | 0.355007 | − | 0.934863i | \(-0.384478\pi\) |
−0.934863 | + | 0.355007i | \(0.884478\pi\) | |||||||
\(854\) | 970.020 | − | 312.952i | 1.13585 | − | 0.366454i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1027.28 | − | 756.190i | −1.20009 | − | 0.883400i | ||||
\(857\) | − | 1676.75i | − | 1.95654i | −0.207340 | − | 0.978269i | \(-0.566481\pi\) | ||
0.207340 | − | 0.978269i | \(-0.433519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 228.948 | − | 228.948i | 0.266529 | − | 0.266529i | −0.561171 | − | 0.827700i | \(-0.689649\pi\) |
0.827700 | + | 0.561171i | \(0.189649\pi\) | |||||||
\(860\) | 230.021 | + | 319.380i | 0.267466 | + | 0.371372i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.4777 | − | 73.1778i | 0.0434776 | − | 0.0848931i | ||||
\(863\) | 1603.23i | 1.85774i | 0.370401 | + | 0.928872i | \(0.379220\pi\) | ||||
−0.370401 | + | 0.928872i | \(0.620780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −83.7981 | −0.0968764 | ||||||||
\(866\) | −626.038 | − | 320.622i | −0.722907 | − | 0.370234i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1346.15 | − | 969.517i | 1.55087 | − | 1.11695i | ||||
\(869\) | −10.1034 | − | 10.1034i | −0.0116264 | − | 0.0116264i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −140.461 | −0.161264 | ||||||||
\(872\) | −739.281 | − | 544.192i | −0.847799 | − | 0.624074i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 487.038 | + | 1509.61i | 0.557252 | + | 1.72725i | ||||
\(875\) | −484.533 | + | 484.533i | −0.553752 | + | 0.553752i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 289.017 | − | 289.017i | 0.329552 | − | 0.329552i | −0.522864 | − | 0.852416i | \(-0.675136\pi\) |
0.852416 | + | 0.522864i | \(0.175136\pi\) | |||||||
\(878\) | −1380.69 | − | 707.113i | −1.57254 | − | 0.805367i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −23.1488 | + | 69.2801i | −0.0263055 | + | 0.0787274i | ||||
\(881\) | −937.450 | −1.06408 | −0.532038 | − | 0.846721i | \(-0.678574\pi\) | ||||
−0.532038 | + | 0.846721i | \(0.678574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −485.966 | − | 485.966i | −0.550357 | − | 0.550357i | 0.376187 | − | 0.926544i | \(-0.377235\pi\) |
−0.926544 | + | 0.376187i | \(0.877235\pi\) | |||||||
\(884\) | −860.005 | − | 139.877i | −0.972856 | − | 0.158232i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 649.726 | − | 209.617i | 0.733326 | − | 0.236588i | ||||
\(887\) | 534.193 | 0.602247 | 0.301123 | − | 0.953585i | \(-0.402638\pi\) | ||||
0.301123 | + | 0.953585i | \(0.402638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 369.201i | − | 0.415299i | ||||||
\(890\) | 59.5044 | − | 19.1976i | 0.0668589 | − | 0.0215703i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −397.958 | + | 286.614i | −0.446142 | + | 0.321316i | ||||
\(893\) | −770.346 | + | 770.346i | −0.862649 | + | 0.862649i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 106.961i | 0.119510i | ||||||||
\(896\) | −1264.17 | − | 219.118i | −1.41090 | − | 0.244552i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −474.153 | − | 242.835i | −0.528010 | − | 0.270418i | ||||
\(899\) | −1019.56 | − | 1019.56i | −1.13410 | − | 1.13410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −562.638 | − | 562.638i | −0.624460 | − | 0.624460i | ||||
\(902\) | −92.7475 | − | 287.479i | −0.102824 | − | 0.318712i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 206.590 | + | 1359.14i | 0.228529 | + | 1.50347i | ||||
\(905\) | 134.237i | 0.148328i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 368.669 | − | 368.669i | 0.406471 | − | 0.406471i | −0.474035 | − | 0.880506i | \(-0.657203\pi\) |
0.880506 | + | 0.474035i | \(0.157203\pi\) | |||||||
\(908\) | −268.668 | + | 1651.84i | −0.295890 | + | 1.81921i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 247.500 | + | 126.756i | 0.271978 | + | 0.139292i | ||||
\(911\) | − | 1592.43i | − | 1.74800i | −0.485927 | − | 0.873999i | \(-0.661518\pi\) | ||
0.485927 | − | 0.873999i | \(-0.338482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.0967 | 0.0504893 | ||||||||
\(914\) | 469.739 | − | 917.198i | 0.513938 | − | 1.00350i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −66.6408 | + | 409.726i | −0.0727519 | + | 0.447299i | ||||
\(917\) | 123.978 | + | 123.978i | 0.135199 | + | 0.135199i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −403.500 | −0.439064 | −0.219532 | − | 0.975605i | \(-0.570453\pi\) | ||||
−0.219532 | + | 0.975605i | \(0.570453\pi\) | |||||||
\(920\) | −224.395 | + | 304.839i | −0.243908 | + | 0.331347i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.2818 | + | 4.93029i | −0.0165747 | + | 0.00534738i | ||||
\(923\) | 82.2632 | − | 82.2632i | 0.0891258 | − | 0.0891258i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −151.602 | + | 151.602i | −0.163894 | + | 0.163894i | ||||
\(926\) | 423.486 | − | 826.886i | 0.457328 | − | 0.892965i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.5855 | + | 1115.07i | −0.0124844 | + | 1.20159i | ||||
\(929\) | −348.546 | −0.375184 | −0.187592 | − | 0.982247i | \(-0.560068\pi\) | ||||
−0.187592 | + | 0.982247i | \(0.560068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −869.449 | − | 869.449i | −0.933887 | − | 0.933887i | ||||
\(932\) | −507.089 | + | 365.211i | −0.544087 | + | 0.391858i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −430.734 | − | 1335.10i | −0.461171 | − | 1.42944i | ||||
\(935\) | 102.173 | 0.109276 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 248.875i | − | 0.265609i | −0.991142 | − | 0.132804i | \(-0.957602\pi\) | ||
0.991142 | − | 0.132804i | \(-0.0423982\pi\) | |||||||
\(938\) | 88.8292 | + | 275.334i | 0.0947007 | + | 0.293533i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −256.600 | − | 41.7353i | −0.272978 | − | 0.0443992i | ||||
\(941\) | −884.188 | + | 884.188i | −0.939626 | + | 0.939626i | −0.998278 | − | 0.0586528i | \(-0.981319\pi\) |
0.0586528 | + | 0.998278i | \(0.481319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1565.34i | − | 1.65996i | ||||||
\(944\) | −63.0508 | − | 126.329i | −0.0667911 | − | 0.133823i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 201.645 | − | 393.727i | 0.213156 | − | 0.416202i | ||||
\(947\) | −462.279 | − | 462.279i | −0.488151 | − | 0.488151i | 0.419571 | − | 0.907722i | \(-0.362180\pi\) |
−0.907722 | + | 0.419571i | \(0.862180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −766.221 | − | 766.221i | −0.807398 | − | 0.807398i | ||||
\(950\) | −1044.39 | + | 336.944i | −1.09935 | + | 0.354678i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 269.687 | + | 1774.25i | 0.283285 | + | 1.86371i | ||||
\(953\) | − | 707.656i | − | 0.742556i | −0.928522 | − | 0.371278i | \(-0.878920\pi\) | ||
0.928522 | − | 0.371278i | \(-0.121080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −114.632 | + | 114.632i | −0.120033 | + | 0.120033i | ||||
\(956\) | 42.7525 | − | 30.7909i | 0.0447202 | − | 0.0322081i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −345.347 | + | 674.314i | −0.360487 | + | 0.703877i | ||||
\(959\) | − | 1460.22i | − | 1.52265i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −750.983 | −0.781460 | ||||||||
\(962\) | 161.725 | + | 82.8267i | 0.168113 | + | 0.0860984i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −443.033 | − | 615.143i | −0.459578 | − | 0.638115i | ||||
\(965\) | 26.7647 | + | 26.7647i | 0.0277354 | + | 0.0277354i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −841.240 | −0.869949 | −0.434974 | − | 0.900443i | \(-0.643243\pi\) | ||||
−0.434974 | + | 0.900443i | \(0.643243\pi\) | |||||||
\(968\) | −875.844 | + | 133.129i | −0.904797 | + | 0.137530i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −93.9112 | − | 291.086i | −0.0968157 | − | 0.300088i | ||||
\(971\) | −308.415 | + | 308.415i | −0.317626 | + | 0.317626i | −0.847855 | − | 0.530229i | \(-0.822106\pi\) |
0.530229 | + | 0.847855i | \(0.322106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 827.654 | − | 827.654i | 0.850621 | − | 0.850621i | ||||
\(974\) | 262.472 | + | 134.424i | 0.269478 | + | 0.138012i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 363.278 | + | 727.866i | 0.372211 | + | 0.745764i | ||||
\(977\) | 1316.85 | 1.34786 | 0.673928 | − | 0.738797i | \(-0.264606\pi\) | ||||
0.673928 | + | 0.738797i | \(0.264606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.6897 | − | 49.6897i | −0.0507556 | − | 0.0507556i | ||||
\(980\) | 47.1044 | − | 289.611i | 0.0480657 | − | 0.295521i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −294.880 | + | 95.1352i | −0.300285 | + | 0.0968791i | ||||
\(983\) | −504.538 | −0.513263 | −0.256632 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256632 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 104.588i | 0.106181i | ||||||||
\(986\) | 1484.46 | − | 478.922i | 1.50554 | − | 0.485722i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 543.528 | + | 754.677i | 0.550129 | + | 0.763843i | ||||
\(989\) | 1620.92 | − | 1620.92i | 1.63895 | − | 1.63895i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 436.650i | − | 0.440616i | −0.975430 | − | 0.220308i | \(-0.929294\pi\) | ||
0.975430 | − | 0.220308i | \(-0.0707062\pi\) | |||||||
\(992\) | 926.457 | + | 945.911i | 0.933929 | + | 0.953539i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −213.277 | − | 109.229i | −0.214565 | − | 0.109888i | ||||
\(995\) | 137.797 | + | 137.797i | 0.138489 | + | 0.138489i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −383.801 | − | 383.801i | −0.384956 | − | 0.384956i | 0.487928 | − | 0.872884i | \(-0.337753\pi\) |
−0.872884 | + | 0.487928i | \(0.837753\pi\) | |||||||
\(998\) | −313.093 | − | 970.458i | −0.313720 | − | 0.972403i | ||||
\(999\) | 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 | 144.3.m.c.91.6 | 16 | ||
3.2 | odd | 2 | 48.3.l.a.43.3 | yes | 16 | ||
4.3 | odd | 2 | 576.3.m.c.271.4 | 16 | |||
8.3 | odd | 2 | 1152.3.m.c.415.5 | 16 | |||
8.5 | even | 2 | 1152.3.m.f.415.5 | 16 | |||
12.11 | even | 2 | 192.3.l.a.79.3 | 16 | |||
16.3 | odd | 4 | inner | 144.3.m.c.19.6 | 16 | ||
16.5 | even | 4 | 1152.3.m.c.991.5 | 16 | |||
16.11 | odd | 4 | 1152.3.m.f.991.5 | 16 | |||
16.13 | even | 4 | 576.3.m.c.559.4 | 16 | |||
24.5 | odd | 2 | 384.3.l.a.31.2 | 16 | |||
24.11 | even | 2 | 384.3.l.b.31.6 | 16 | |||
48.5 | odd | 4 | 384.3.l.b.223.6 | 16 | |||
48.11 | even | 4 | 384.3.l.a.223.2 | 16 | |||
48.29 | odd | 4 | 192.3.l.a.175.3 | 16 | |||
48.35 | even | 4 | 48.3.l.a.19.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.3 | ✓ | 16 | 48.35 | even | 4 | ||
48.3.l.a.43.3 | yes | 16 | 3.2 | odd | 2 | ||
144.3.m.c.19.6 | 16 | 16.3 | odd | 4 | inner | ||
144.3.m.c.91.6 | 16 | 1.1 | even | 1 | trivial | ||
192.3.l.a.79.3 | 16 | 12.11 | even | 2 | |||
192.3.l.a.175.3 | 16 | 48.29 | odd | 4 | |||
384.3.l.a.31.2 | 16 | 24.5 | odd | 2 | |||
384.3.l.a.223.2 | 16 | 48.11 | even | 4 | |||
384.3.l.b.31.6 | 16 | 24.11 | even | 2 | |||
384.3.l.b.223.6 | 16 | 48.5 | odd | 4 | |||
576.3.m.c.271.4 | 16 | 4.3 | odd | 2 | |||
576.3.m.c.559.4 | 16 | 16.13 | even | 4 | |||
1152.3.m.c.415.5 | 16 | 8.3 | odd | 2 | |||
1152.3.m.c.991.5 | 16 | 16.5 | even | 4 | |||
1152.3.m.f.415.5 | 16 | 8.5 | even | 2 | |||
1152.3.m.f.991.5 | 16 | 16.11 | odd | 4 |