Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4069419264.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.3 | ||
Root | \(-2.65095 + 1.53053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.n.451.4 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.534079 | − | 1.92737i | −0.267039 | − | 0.963686i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.42952 | + | 2.05874i | −0.857380 | + | 0.514684i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 11.9716i | − | 1.71023i | −0.518436 | − | 0.855117i | \(-0.673485\pi\) | ||
0.518436 | − | 0.855117i | \(-0.326515\pi\) | |||||||
\(8\) | 5.79958 | + | 5.51043i | 0.724948 | + | 0.688804i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.5382i | 1.32166i | 0.750537 | + | 0.660828i | \(0.229795\pi\) | ||||
−0.750537 | + | 0.660828i | \(0.770205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.4802 | −1.72925 | −0.864625 | − | 0.502418i | \(-0.832444\pi\) | ||||
−0.864625 | + | 0.502418i | \(0.832444\pi\) | |||||||
\(14\) | −23.0738 | + | 6.39379i | −1.64813 | + | 0.456699i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.52322 | − | 14.1209i | 0.470201 | − | 0.882559i | ||||
\(17\) | 12.6890 | 0.746414 | 0.373207 | − | 0.927748i | \(-0.378258\pi\) | ||||
0.373207 | + | 0.927748i | \(0.378258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.76336i | 0.461229i | 0.973045 | + | 0.230615i | \(0.0740737\pi\) | ||||
−0.973045 | + | 0.230615i | \(0.925926\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.0205 | − | 7.76455i | 1.27366 | − | 0.352934i | ||||
\(23\) | − | 4.99653i | − | 0.217241i | −0.994083 | − | 0.108620i | \(-0.965357\pi\) | ||
0.994083 | − | 0.108620i | \(-0.0346433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.0062 | + | 43.3278i | 0.461778 | + | 1.66645i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24.6464 | + | 41.0570i | 0.880229 | + | 1.46632i | ||||
\(29\) | −2.74712 | −0.0947282 | −0.0473641 | − | 0.998878i | \(-0.515082\pi\) | ||||
−0.0473641 | + | 0.998878i | \(0.515082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.3466i | 0.527310i | 0.964617 | + | 0.263655i | \(0.0849281\pi\) | ||||
−0.964617 | + | 0.263655i | \(0.915072\pi\) | |||||||
\(32\) | −31.2343 | − | 6.95833i | −0.976072 | − | 0.217448i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.77695 | − | 24.4565i | −0.199322 | − | 0.719309i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.4872 | −0.878032 | −0.439016 | − | 0.898479i | \(-0.644673\pi\) | ||||
−0.439016 | + | 0.898479i | \(0.644673\pi\) | |||||||
\(38\) | 16.8902 | − | 4.68032i | 0.444480 | − | 0.123166i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.7586 | −1.04289 | −0.521447 | − | 0.853284i | \(-0.674607\pi\) | ||||
−0.521447 | + | 0.853284i | \(0.674607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.5435i | 0.384733i | 0.981323 | + | 0.192367i | \(0.0616163\pi\) | ||||
−0.981323 | + | 0.192367i | \(0.938384\pi\) | |||||||
\(44\) | −29.9303 | − | 49.8591i | −0.680235 | − | 1.13316i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.63018 | + | 2.66854i | −0.209352 | + | 0.0580118i | ||||
\(47\) | 48.5912i | 1.03386i | 0.856029 | + | 0.516928i | \(0.172924\pi\) | ||||
−0.856029 | + | 0.516928i | \(0.827076\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −94.3200 | −1.92490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 77.0964 | − | 46.2809i | 1.48262 | − | 0.890017i | ||||
\(53\) | 94.1066 | 1.77560 | 0.887798 | − | 0.460233i | \(-0.152234\pi\) | ||||
0.887798 | + | 0.460233i | \(0.152234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 65.9689 | − | 69.4305i | 1.17802 | − | 1.23983i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.46718 | + | 5.29471i | 0.0252961 | + | 0.0912882i | ||||
\(59\) | 43.2650i | 0.733305i | 0.930358 | + | 0.366653i | \(0.119496\pi\) | ||||
−0.930358 | + | 0.366653i | \(0.880504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 56.7678 | 0.930620 | 0.465310 | − | 0.885148i | \(-0.345943\pi\) | ||||
0.465310 | + | 0.885148i | \(0.345943\pi\) | |||||||
\(62\) | 31.5060 | − | 8.73038i | 0.508161 | − | 0.140813i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.27028 | + | 63.9164i | 0.0510981 | + | 0.998694i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.1106i | 0.912098i | 0.889955 | + | 0.456049i | \(0.150736\pi\) | ||||
−0.889955 | + | 0.456049i | \(0.849264\pi\) | |||||||
\(68\) | −43.5173 | + | 26.1234i | −0.639961 | + | 0.384167i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.6643i | 0.558652i | 0.960196 | + | 0.279326i | \(0.0901110\pi\) | ||||
−0.960196 | + | 0.279326i | \(0.909889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 99.5452 | 1.36363 | 0.681817 | − | 0.731523i | \(-0.261190\pi\) | ||||
0.681817 | + | 0.731523i | \(0.261190\pi\) | |||||||
\(74\) | 17.3507 | + | 62.6149i | 0.234469 | + | 0.846147i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.0414 | − | 30.0541i | −0.237387 | − | 0.395449i | ||||
\(77\) | 174.046 | 2.26034 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7780i | 0.136430i | 0.997671 | + | 0.0682151i | \(0.0217304\pi\) | ||||
−0.997671 | + | 0.0682151i | \(0.978270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 22.8365 | + | 82.4118i | 0.278494 | + | 1.00502i | ||||
\(83\) | 140.263i | 1.68991i | 0.534837 | + | 0.844955i | \(0.320373\pi\) | ||||
−0.534837 | + | 0.844955i | \(0.679627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 31.8855 | − | 8.83554i | 0.370762 | − | 0.102739i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −80.1118 | + | 84.3156i | −0.910362 | + | 0.958131i | ||||
\(89\) | −54.8723 | −0.616543 | −0.308271 | − | 0.951298i | \(-0.599751\pi\) | ||||
−0.308271 | + | 0.951298i | \(0.599751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 269.125i | 2.95742i | ||||||||
\(92\) | 10.2865 | + | 17.1357i | 0.111810 | + | 0.186258i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 93.6533 | − | 25.9515i | 0.996312 | − | 0.276080i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.1601 | −0.145980 | −0.0729902 | − | 0.997333i | \(-0.523254\pi\) | ||||
−0.0729902 | + | 0.997333i | \(0.523254\pi\) | |||||||
\(98\) | 50.3743 | + | 181.790i | 0.514023 | + | 1.85500i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 163.410 | 1.61792 | 0.808962 | − | 0.587861i | \(-0.200030\pi\) | ||||
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 169.591i | − | 1.64651i | −0.567672 | − | 0.823255i | \(-0.692156\pi\) | ||
0.567672 | − | 0.823255i | \(-0.307844\pi\) | |||||||
\(104\) | −130.376 | − | 123.876i | −1.25362 | − | 1.19111i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −50.2603 | − | 181.378i | −0.474154 | − | 1.71112i | ||||
\(107\) | 8.14840i | 0.0761532i | 0.999275 | + | 0.0380766i | \(0.0121231\pi\) | ||||
−0.999275 | + | 0.0380766i | \(0.987877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −25.2322 | −0.231488 | −0.115744 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115744 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −169.051 | − | 90.0652i | −1.50938 | − | 0.804153i | ||||
\(113\) | 97.8142 | 0.865613 | 0.432806 | − | 0.901487i | \(-0.357523\pi\) | ||||
0.432806 | + | 0.901487i | \(0.357523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.42129 | − | 5.65559i | 0.0812180 | − | 0.0487551i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 83.3877 | − | 23.1069i | 0.706676 | − | 0.195821i | ||||
\(119\) | − | 151.909i | − | 1.27654i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −90.3597 | −0.746774 | ||||||||
\(122\) | −30.3185 | − | 109.413i | −0.248512 | − | 0.896825i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −33.6534 | − | 56.0611i | −0.271398 | − | 0.452105i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167.563i | 1.31939i | 0.751533 | + | 0.659695i | \(0.229315\pi\) | ||||
−0.751533 | + | 0.659695i | \(0.770685\pi\) | |||||||
\(128\) | 121.444 | − | 40.4394i | 0.948782 | − | 0.315933i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 82.0465i | 0.626309i | 0.949702 | + | 0.313155i | \(0.101386\pi\) | ||||
−0.949702 | + | 0.313155i | \(0.898614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.912 | 0.788810 | ||||||||
\(134\) | 117.783 | − | 32.6378i | 0.878976 | − | 0.243566i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.5911 | + | 69.9221i | 0.541111 | + | 0.514133i | ||||
\(137\) | −254.459 | −1.85737 | −0.928683 | − | 0.370874i | \(-0.879058\pi\) | ||||
−0.928683 | + | 0.370874i | \(0.879058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 78.9483i | 0.567974i | 0.958828 | + | 0.283987i | \(0.0916572\pi\) | ||||
−0.958828 | + | 0.283987i | \(0.908343\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 76.4478 | − | 21.1838i | 0.538365 | − | 0.149182i | ||||
\(143\) | − | 326.823i | − | 2.28547i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −53.1650 | − | 191.861i | −0.364144 | − | 1.31411i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 111.415 | − | 66.8825i | 0.752807 | − | 0.451909i | ||||
\(149\) | 32.3433 | 0.217069 | 0.108534 | − | 0.994093i | \(-0.465384\pi\) | ||||
0.108534 | + | 0.994093i | \(0.465384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 38.7953i | − | 0.256922i | −0.991715 | − | 0.128461i | \(-0.958996\pi\) | ||
0.991715 | − | 0.128461i | \(-0.0410038\pi\) | |||||||
\(152\) | −48.2899 | + | 50.8238i | −0.317697 | + | 0.334367i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −92.9543 | − | 335.452i | −0.603600 | − | 2.17826i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −44.2021 | −0.281542 | −0.140771 | − | 0.990042i | \(-0.544958\pi\) | ||||
−0.140771 | + | 0.990042i | \(0.544958\pi\) | |||||||
\(158\) | 20.7732 | − | 5.75629i | 0.131476 | − | 0.0364322i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −59.8167 | −0.371532 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 52.9366i | − | 0.324764i | −0.986728 | − | 0.162382i | \(-0.948082\pi\) | ||
0.986728 | − | 0.162382i | \(-0.0519177\pi\) | |||||||
\(164\) | 146.642 | − | 88.0287i | 0.894156 | − | 0.536760i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 270.338 | − | 74.9112i | 1.62854 | − | 0.451272i | ||||
\(167\) | 179.273i | 1.07349i | 0.843744 | + | 0.536745i | \(0.180346\pi\) | ||||
−0.843744 | + | 0.536745i | \(0.819654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 336.361 | 1.99030 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −34.0587 | − | 56.7364i | −0.198016 | − | 0.329863i | ||||
\(173\) | −177.276 | −1.02471 | −0.512357 | − | 0.858772i | \(-0.671228\pi\) | ||||
−0.512357 | + | 0.858772i | \(0.671228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 205.293 | + | 109.374i | 1.16644 | + | 0.621444i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29.3061 | + | 105.759i | 0.164641 | + | 0.594154i | ||||
\(179\) | 102.849i | 0.574573i | 0.957845 | + | 0.287286i | \(0.0927532\pi\) | ||||
−0.957845 | + | 0.287286i | \(0.907247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −115.413 | −0.637640 | −0.318820 | − | 0.947815i | \(-0.603286\pi\) | ||||
−0.318820 | + | 0.947815i | \(0.603286\pi\) | |||||||
\(182\) | 518.704 | − | 143.734i | 2.85002 | − | 0.789747i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 27.5331 | − | 28.9778i | 0.149636 | − | 0.157488i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 184.476i | 0.986503i | ||||||||
\(188\) | −100.036 | − | 166.645i | −0.532109 | − | 0.886407i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 191.305i | 1.00160i | 0.865563 | + | 0.500799i | \(0.166960\pi\) | ||||
−0.865563 | + | 0.500799i | \(0.833040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −160.332 | −0.830734 | −0.415367 | − | 0.909654i | \(-0.636347\pi\) | ||||
−0.415367 | + | 0.909654i | \(0.636347\pi\) | |||||||
\(194\) | 7.56261 | + | 27.2918i | 0.0389825 | + | 0.140679i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 323.472 | − | 194.180i | 1.65037 | − | 0.990714i | ||||
\(197\) | −355.081 | −1.80244 | −0.901220 | − | 0.433362i | \(-0.857327\pi\) | ||||
−0.901220 | + | 0.433362i | \(0.857327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 88.2032i | − | 0.443232i | −0.975134 | − | 0.221616i | \(-0.928867\pi\) | ||
0.975134 | − | 0.221616i | \(-0.0711332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −87.2740 | − | 314.952i | −0.432049 | − | 1.55917i | ||||
\(203\) | 32.8875i | 0.162007i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −326.864 | + | 90.5747i | −1.58672 | + | 0.439683i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −169.124 | + | 317.442i | −0.813095 | + | 1.52617i | ||||
\(209\) | −127.404 | −0.609586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 190.584i | 0.903243i | 0.892210 | + | 0.451622i | \(0.149154\pi\) | ||||
−0.892210 | + | 0.451622i | \(0.850846\pi\) | |||||||
\(212\) | −322.741 | + | 193.741i | −1.52236 | + | 0.913871i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7050 | − | 4.35188i | 0.0733878 | − | 0.0203359i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 195.696 | 0.901824 | ||||||||
\(218\) | 13.4760 | + | 48.6318i | 0.0618164 | + | 0.223082i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −285.253 | −1.29074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 79.2869i | − | 0.355547i | −0.984071 | − | 0.177773i | \(-0.943111\pi\) | ||
0.984071 | − | 0.177773i | \(-0.0568894\pi\) | |||||||
\(224\) | −83.3026 | + | 373.926i | −0.371887 | + | 1.66931i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −52.2405 | − | 188.524i | −0.231153 | − | 0.834178i | ||||
\(227\) | − | 353.645i | − | 1.55791i | −0.627082 | − | 0.778953i | \(-0.715751\pi\) | ||
0.627082 | − | 0.778953i | \(-0.284249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.7911 | −0.0995244 | −0.0497622 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497622 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.9321 | − | 15.1378i | −0.0686730 | − | 0.0652491i | ||||
\(233\) | −189.710 | −0.814205 | −0.407103 | − | 0.913382i | \(-0.633461\pi\) | ||||
−0.407103 | + | 0.913382i | \(0.633461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −89.0712 | − | 148.378i | −0.377420 | − | 0.628721i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −292.784 | + | 81.1311i | −1.23019 | + | 0.340887i | ||||
\(239\) | 267.778i | 1.12041i | 0.828355 | + | 0.560204i | \(0.189277\pi\) | ||||
−0.828355 | + | 0.560204i | \(0.810723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −301.663 | −1.25171 | −0.625857 | − | 0.779938i | \(-0.715251\pi\) | ||||
−0.625857 | + | 0.779938i | \(0.715251\pi\) | |||||||
\(242\) | 48.2592 | + | 174.157i | 0.199418 | + | 0.719656i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −194.686 | + | 116.870i | −0.797895 | + | 0.478975i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 197.002i | − | 0.797580i | ||||||
\(248\) | −90.0769 | + | 94.8035i | −0.363213 | + | 0.382272i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 63.1891i | 0.251749i | 0.992046 | + | 0.125875i | \(0.0401737\pi\) | ||||
−0.992046 | + | 0.125875i | \(0.959826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 72.6407 | 0.287117 | ||||||||
\(254\) | 322.955 | − | 89.4916i | 1.27148 | − | 0.352329i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −142.802 | − | 212.470i | −0.557822 | − | 0.829961i | ||||
\(257\) | 150.719 | 0.586456 | 0.293228 | − | 0.956043i | \(-0.405271\pi\) | ||||
0.293228 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 388.925i | 1.50164i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 158.134 | − | 43.8193i | 0.603565 | − | 0.167249i | ||||
\(263\) | − | 203.755i | − | 0.774735i | −0.921925 | − | 0.387368i | \(-0.873384\pi\) | ||
0.921925 | − | 0.387368i | \(-0.126616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −56.0311 | − | 202.204i | −0.210643 | − | 0.760165i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −125.810 | − | 209.580i | −0.469442 | − | 0.782014i | ||||
\(269\) | −76.3986 | −0.284010 | −0.142005 | − | 0.989866i | \(-0.545355\pi\) | ||||
−0.142005 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 169.216i | − | 0.624414i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||
0.950014 | − | 0.312207i | \(-0.101068\pi\) | |||||||
\(272\) | 95.4624 | − | 179.181i | 0.350965 | − | 0.658755i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 135.901 | + | 490.437i | 0.495990 | + | 1.78992i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 273.891 | 0.988774 | 0.494387 | − | 0.869242i | \(-0.335393\pi\) | ||||
0.494387 | + | 0.869242i | \(0.335393\pi\) | |||||||
\(278\) | 152.163 | − | 42.1646i | 0.547348 | − | 0.151671i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 311.672 | 1.10915 | 0.554577 | − | 0.832133i | \(-0.312880\pi\) | ||||
0.554577 | + | 0.832133i | \(0.312880\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 264.566i | − | 0.934861i | −0.884030 | − | 0.467431i | \(-0.845180\pi\) | ||
0.884030 | − | 0.467431i | \(-0.154820\pi\) | |||||||
\(284\) | −81.6583 | − | 136.029i | −0.287529 | − | 0.478977i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −629.909 | + | 174.549i | −2.20248 | + | 0.610311i | ||||
\(287\) | 511.891i | 1.78359i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −127.988 | −0.442866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −341.392 | + | 204.937i | −1.16915 | + | 0.701840i | ||||
\(293\) | 121.281 | 0.413927 | 0.206964 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206964 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −188.412 | − | 179.018i | −0.636527 | − | 0.604792i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.2739 | − | 62.3375i | −0.0579659 | − | 0.209186i | ||||
\(299\) | 112.323i | 0.375663i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 198.053 | 0.657984 | ||||||||
\(302\) | −74.7729 | + | 20.7197i | −0.247592 | + | 0.0686083i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 123.747 | + | 65.9286i | 0.407062 | + | 0.216870i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 161.768i | 0.526932i | 0.964669 | + | 0.263466i | \(0.0848656\pi\) | ||||
−0.964669 | + | 0.263466i | \(0.915134\pi\) | |||||||
\(308\) | −596.895 | + | 358.315i | −1.93797 | + | 1.16336i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.3813i | − | 0.0848273i | −0.999100 | − | 0.0424137i | \(-0.986495\pi\) | ||
0.999100 | − | 0.0424137i | \(-0.0135047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.39902 | −0.0172493 | −0.00862463 | − | 0.999963i | \(-0.502745\pi\) | ||||
−0.00862463 | + | 0.999963i | \(0.502745\pi\) | |||||||
\(314\) | 23.6074 | + | 85.1938i | 0.0751827 | + | 0.271318i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.1890 | − | 36.9633i | −0.0702184 | − | 0.116972i | ||||
\(317\) | 270.157 | 0.852231 | 0.426116 | − | 0.904669i | \(-0.359882\pi\) | ||||
0.426116 | + | 0.904669i | \(0.359882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 39.9382i | − | 0.125198i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 31.9468 | + | 115.289i | 0.0992137 | + | 0.358040i | ||||
\(323\) | 111.199i | 0.344268i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −102.028 | + | 28.2723i | −0.312971 | + | 0.0867248i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −247.982 | − | 235.619i | −0.756043 | − | 0.718349i | ||||
\(329\) | 581.716 | 1.76813 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 480.728i | 1.45235i | 0.687510 | + | 0.726174i | \(0.258704\pi\) | ||||
−0.687510 | + | 0.726174i | \(0.741296\pi\) | |||||||
\(332\) | −288.763 | − | 481.033i | −0.869770 | − | 1.44890i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 345.526 | − | 95.7459i | 1.03451 | − | 0.286664i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −568.382 | −1.68659 | −0.843297 | − | 0.537448i | \(-0.819388\pi\) | ||||
−0.843297 | + | 0.537448i | \(0.819388\pi\) | |||||||
\(338\) | −179.643 | − | 648.293i | −0.531489 | − | 1.91803i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −237.651 | −0.696923 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 542.554i | 1.58179i | ||||||||
\(344\) | −91.1620 | + | 95.9455i | −0.265006 | + | 0.278911i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 94.6791 | + | 341.676i | 0.273639 | + | 0.987503i | ||||
\(347\) | − | 370.184i | − | 1.06681i | −0.845859 | − | 0.533406i | \(-0.820912\pi\) | ||
0.845859 | − | 0.533406i | \(-0.179088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −488.570 | −1.39991 | −0.699957 | − | 0.714185i | \(-0.746797\pi\) | ||||
−0.699957 | + | 0.714185i | \(0.746797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 101.162 | − | 454.091i | 0.287391 | − | 1.29003i | ||||
\(353\) | −649.728 | −1.84059 | −0.920295 | − | 0.391226i | \(-0.872051\pi\) | ||||
−0.920295 | + | 0.391226i | \(0.872051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 188.186 | − | 112.968i | 0.528612 | − | 0.317325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 198.227 | − | 54.9292i | 0.553708 | − | 0.153434i | ||||
\(359\) | − | 405.910i | − | 1.13067i | −0.824862 | − | 0.565334i | \(-0.808747\pi\) | ||
0.824862 | − | 0.565334i | \(-0.191253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 284.204 | 0.787268 | ||||||||
\(362\) | 61.6395 | + | 222.443i | 0.170275 | + | 0.614484i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −554.058 | − | 922.970i | −1.52214 | − | 2.53563i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 46.2347i | 0.125980i | 0.998014 | + | 0.0629900i | \(0.0200636\pi\) | ||||
−0.998014 | + | 0.0629900i | \(0.979936\pi\) | |||||||
\(368\) | −70.5558 | − | 37.5900i | −0.191728 | − | 0.102147i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1126.61i | − | 3.03668i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −138.262 | −0.370676 | −0.185338 | − | 0.982675i | \(-0.559338\pi\) | ||||
−0.185338 | + | 0.982675i | \(0.559338\pi\) | |||||||
\(374\) | 355.554 | − | 98.5247i | 0.950679 | − | 0.263435i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −267.759 | + | 281.809i | −0.712124 | + | 0.749491i | ||||
\(377\) | 61.7559 | 0.163809 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 254.516i | 0.671546i | 0.941943 | + | 0.335773i | \(0.108998\pi\) | ||||
−0.941943 | + | 0.335773i | \(0.891002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 368.716 | − | 102.172i | 0.965226 | − | 0.267466i | ||||
\(383\) | 62.7205i | 0.163761i | 0.996642 | + | 0.0818805i | \(0.0260926\pi\) | ||||
−0.996642 | + | 0.0818805i | \(0.973907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 85.6298 | + | 309.019i | 0.221839 | + | 0.800567i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 48.5623 | − | 29.1519i | 0.125161 | − | 0.0751338i | ||||
\(389\) | −110.130 | −0.283112 | −0.141556 | − | 0.989930i | \(-0.545210\pi\) | ||||
−0.141556 | + | 0.989930i | \(0.545210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 63.4012i | − | 0.162152i | ||||||
\(392\) | −547.016 | − | 519.744i | −1.39545 | − | 1.32588i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 189.641 | + | 684.372i | 0.481322 | + | 1.73698i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −292.953 | −0.737916 | −0.368958 | − | 0.929446i | \(-0.620285\pi\) | ||||
−0.368958 | + | 0.929446i | \(0.620285\pi\) | |||||||
\(398\) | −170.000 | + | 47.1074i | −0.427136 | + | 0.118360i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −518.103 | −1.29203 | −0.646014 | − | 0.763325i | \(-0.723565\pi\) | ||||
−0.646014 | + | 0.763325i | \(0.723565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 367.476i | − | 0.911851i | ||||||
\(404\) | −560.419 | + | 336.419i | −1.38718 | + | 0.832720i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 63.3864 | − | 17.5645i | 0.156124 | − | 0.0432623i | ||||
\(407\) | − | 472.306i | − | 1.16046i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −181.984 | −0.444948 | −0.222474 | − | 0.974939i | \(-0.571413\pi\) | ||||
−0.222474 | + | 0.974939i | \(0.571413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 349.142 | + | 581.614i | 0.847432 | + | 1.41168i | ||||
\(413\) | 517.953 | 1.25412 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 702.155 | + | 156.425i | 1.68787 | + | 0.376022i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 68.0435 | + | 245.554i | 0.162784 | + | 0.587450i | ||||
\(419\) | 163.347i | 0.389849i | 0.980818 | + | 0.194925i | \(0.0624462\pi\) | ||||
−0.980818 | + | 0.194925i | \(0.937554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −467.206 | −1.10975 | −0.554876 | − | 0.831933i | \(-0.687234\pi\) | ||||
−0.554876 | + | 0.831933i | \(0.687234\pi\) | |||||||
\(422\) | 367.327 | − | 101.787i | 0.870442 | − | 0.241201i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 545.779 | + | 518.568i | 1.28721 | + | 1.22304i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 679.603i | − | 1.59158i | ||||||
\(428\) | −16.7754 | − | 27.9451i | −0.0391948 | − | 0.0652923i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 685.527i | 1.59055i | 0.606248 | + | 0.795275i | \(0.292674\pi\) | ||||
−0.606248 | + | 0.795275i | \(0.707326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −592.777 | −1.36900 | −0.684500 | − | 0.729013i | \(-0.739979\pi\) | ||||
−0.684500 | + | 0.729013i | \(0.739979\pi\) | |||||||
\(434\) | −104.517 | − | 377.178i | −0.240822 | − | 0.869074i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 86.5343 | − | 51.9464i | 0.198473 | − | 0.119143i | ||||
\(437\) | 43.7864 | 0.100198 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 464.439i | − | 1.05795i | −0.848638 | − | 0.528974i | \(-0.822577\pi\) | ||
0.848638 | − | 0.528974i | \(-0.177423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 152.347 | + | 549.788i | 0.344677 | + | 1.24386i | ||||
\(443\) | 54.2868i | 0.122544i | 0.998121 | + | 0.0612718i | \(0.0195156\pi\) | ||||
−0.998121 | + | 0.0612718i | \(0.980484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −152.815 | + | 42.3454i | −0.342635 | + | 0.0949449i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 765.184 | − | 39.1506i | 1.70800 | − | 0.0873897i | ||||
\(449\) | 428.051 | 0.953343 | 0.476671 | − | 0.879082i | \(-0.341843\pi\) | ||||
0.476671 | + | 0.879082i | \(0.341843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 621.634i | − | 1.37835i | ||||||
\(452\) | −335.456 | + | 201.374i | −0.742159 | + | 0.445517i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −681.605 | + | 188.874i | −1.50133 | + | 0.416022i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 66.5848 | 0.145700 | 0.0728498 | − | 0.997343i | \(-0.476791\pi\) | ||||
0.0728498 | + | 0.997343i | \(0.476791\pi\) | |||||||
\(458\) | 12.1722 | + | 43.9269i | 0.0265769 | + | 0.0959103i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 238.626 | 0.517627 | 0.258814 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258814 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 386.958i | 0.835762i | 0.908502 | + | 0.417881i | \(0.137227\pi\) | ||||
−0.908502 | + | 0.417881i | \(0.862773\pi\) | |||||||
\(464\) | −20.6672 | + | 38.7919i | −0.0445413 | + | 0.0836032i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 101.320 | + | 365.641i | 0.217425 | + | 0.784638i | ||||
\(467\) | 235.964i | 0.505276i | 0.967561 | + | 0.252638i | \(0.0812981\pi\) | ||||
−0.967561 | + | 0.252638i | \(0.918702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 731.593 | 1.55990 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −238.409 | + | 250.919i | −0.505104 | + | 0.531608i | ||||
\(473\) | −240.513 | −0.508485 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 312.740 | + | 520.974i | 0.657016 | + | 1.09448i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 516.107 | − | 143.014i | 1.07972 | − | 0.299193i | ||||
\(479\) | 529.496i | 1.10542i | 0.833374 | + | 0.552710i | \(0.186406\pi\) | ||||
−0.833374 | + | 0.552710i | \(0.813594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 730.320 | 1.51834 | ||||||||
\(482\) | 161.112 | + | 581.417i | 0.334257 | + | 1.20626i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 309.890 | − | 186.027i | 0.640270 | − | 0.384353i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 880.801i | − | 1.80863i | −0.426869 | − | 0.904314i | \(-0.640383\pi\) | ||
0.426869 | − | 0.904314i | \(-0.359617\pi\) | |||||||
\(488\) | 329.230 | + | 312.815i | 0.674651 | + | 0.641015i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 86.4466i | 0.176062i | 0.996118 | + | 0.0880312i | \(0.0280575\pi\) | ||||
−0.996118 | + | 0.0880312i | \(0.971942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.8583 | −0.0707065 | ||||||||
\(494\) | −379.697 | + | 105.215i | −0.768617 | + | 0.212985i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 230.830 | + | 122.979i | 0.465383 | + | 0.247942i | ||||
\(497\) | 474.846 | 0.955425 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 874.536i | − | 1.75258i | −0.481786 | − | 0.876289i | \(-0.660012\pi\) | ||
0.481786 | − | 0.876289i | \(-0.339988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 121.789 | − | 33.7479i | 0.242607 | − | 0.0672269i | ||||
\(503\) | − | 17.5479i | − | 0.0348865i | −0.999848 | − | 0.0174433i | \(-0.994447\pi\) | ||
0.999848 | − | 0.0174433i | \(-0.00555265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.7958 | − | 140.006i | −0.0766716 | − | 0.276691i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −344.967 | − | 574.659i | −0.679069 | − | 1.13122i | ||||
\(509\) | −609.132 | −1.19672 | −0.598362 | − | 0.801226i | \(-0.704181\pi\) | ||||
−0.598362 | + | 0.801226i | \(0.704181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1191.72i | − | 2.33213i | ||||||
\(512\) | −333.241 | + | 388.709i | −0.650861 | + | 0.759197i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −80.4959 | − | 290.492i | −0.156607 | − | 0.565159i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −706.430 | −1.36640 | ||||||||
\(518\) | 749.602 | − | 207.716i | 1.44711 | − | 0.400997i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −433.724 | −0.832484 | −0.416242 | − | 0.909254i | \(-0.636653\pi\) | ||||
−0.416242 | + | 0.909254i | \(0.636653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 473.223i | − | 0.904823i | −0.891809 | − | 0.452412i | \(-0.850564\pi\) | ||
0.891809 | − | 0.452412i | \(-0.149436\pi\) | |||||||
\(524\) | −168.912 | − | 281.380i | −0.322351 | − | 0.536985i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −392.712 | + | 108.821i | −0.746601 | + | 0.206885i | ||||
\(527\) | 207.423i | 0.393592i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 504.035 | 0.952807 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −359.797 | + | 215.985i | −0.676310 | + | 0.405988i | ||||
\(533\) | 961.224 | 1.80342 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −336.746 | + | 354.416i | −0.628257 | + | 0.661223i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.8029 | + | 147.249i | 0.0758418 | + | 0.273696i | ||||
\(539\) | − | 1371.24i | − | 2.54405i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 294.889 | 0.545081 | 0.272540 | − | 0.962144i | \(-0.412136\pi\) | ||||
0.272540 | + | 0.962144i | \(0.412136\pi\) | |||||||
\(542\) | −326.142 | + | 90.3747i | −0.601739 | + | 0.166743i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −396.333 | − | 88.2946i | −0.728554 | − | 0.162306i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 966.695i | 1.76727i | 0.468179 | + | 0.883634i | \(0.344910\pi\) | ||||
−0.468179 | + | 0.883634i | \(0.655090\pi\) | |||||||
\(548\) | 872.673 | − | 523.864i | 1.59247 | − | 0.955956i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.0740i | − | 0.0436914i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 129.030 | 0.233327 | ||||||||
\(554\) | −146.279 | − | 527.889i | −0.264042 | − | 0.952868i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −162.534 | − | 270.755i | −0.292327 | − | 0.486969i | ||||
\(557\) | 74.2603 | 0.133322 | 0.0666609 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666609 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 371.903i | − | 0.665300i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −166.457 | − | 600.708i | −0.296187 | − | 1.06887i | ||||
\(563\) | 663.688i | 1.17884i | 0.807826 | + | 0.589421i | \(0.200644\pi\) | ||||
−0.807826 | + | 0.589421i | \(0.799356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −509.916 | + | 141.299i | −0.900912 | + | 0.249645i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −218.567 | + | 230.036i | −0.384802 | + | 0.404993i | ||||
\(569\) | 667.450 | 1.17302 | 0.586511 | − | 0.809941i | \(-0.300501\pi\) | ||||
0.586511 | + | 0.809941i | \(0.300501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 185.898i | − | 0.325565i | −0.986662 | − | 0.162782i | \(-0.947953\pi\) | ||
0.986662 | − | 0.162782i | \(-0.0520469\pi\) | |||||||
\(572\) | 672.841 | + | 1120.84i | 1.17630 | + | 1.95952i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 986.603 | − | 273.390i | 1.71882 | − | 0.476289i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 664.331 | 1.15135 | 0.575676 | − | 0.817678i | \(-0.304739\pi\) | ||||
0.575676 | + | 0.817678i | \(0.304739\pi\) | |||||||
\(578\) | 68.3557 | + | 246.681i | 0.118263 | + | 0.426783i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1679.17 | 2.89014 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1368.14i | 2.34673i | ||||||||
\(584\) | 577.321 | + | 548.537i | 0.988563 | + | 0.939276i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −64.7734 | − | 233.753i | −0.110535 | − | 0.398896i | ||||
\(587\) | 763.083i | 1.29997i | 0.759946 | + | 0.649986i | \(0.225225\pi\) | ||||
−0.759946 | + | 0.649986i | \(0.774775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −143.251 | −0.243211 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −244.408 | + | 458.750i | −0.412852 | + | 0.774915i | ||||
\(593\) | 286.193 | 0.482618 | 0.241309 | − | 0.970448i | \(-0.422423\pi\) | ||||
0.241309 | + | 0.970448i | \(0.422423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −110.922 | + | 66.5862i | −0.186111 | + | 0.111722i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 216.489 | − | 59.9895i | 0.362021 | − | 0.100317i | ||||
\(599\) | 604.151i | 1.00860i | 0.863529 | + | 0.504300i | \(0.168249\pi\) | ||||
−0.863529 | + | 0.504300i | \(0.831751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 275.562 | 0.458505 | 0.229253 | − | 0.973367i | \(-0.426372\pi\) | ||||
0.229253 | + | 0.973367i | \(0.426372\pi\) | |||||||
\(602\) | −105.776 | − | 381.722i | −0.175707 | − | 0.634089i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 79.8692 | + | 133.049i | 0.132234 | + | 0.220280i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 52.1487i | − | 0.0859121i | −0.999077 | − | 0.0429561i | \(-0.986322\pi\) | ||
0.999077 | − | 0.0429561i | \(-0.0136775\pi\) | |||||||
\(608\) | 60.9784 | − | 273.717i | 0.100293 | − | 0.450193i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1092.34i | − | 1.78779i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 898.128 | 1.46513 | 0.732567 | − | 0.680695i | \(-0.238322\pi\) | ||||
0.732567 | + | 0.680695i | \(0.238322\pi\) | |||||||
\(614\) | 311.787 | − | 86.3968i | 0.507796 | − | 0.140711i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1009.39 | + | 959.070i | 1.63863 | + | 1.55693i | ||||
\(617\) | −636.868 | −1.03220 | −0.516101 | − | 0.856528i | \(-0.672617\pi\) | ||||
−0.516101 | + | 0.856528i | \(0.672617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 190.559i | 0.307849i | 0.988083 | + | 0.153925i | \(0.0491913\pi\) | ||||
−0.988083 | + | 0.153925i | \(0.950809\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −50.8466 | + | 14.0897i | −0.0817469 | + | 0.0226522i | ||||
\(623\) | 656.911i | 1.05443i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.88350 | + | 10.4059i | 0.00460623 | + | 0.0166229i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 151.592 | − | 91.0004i | 0.241388 | − | 0.144905i | ||||
\(629\) | −412.231 | −0.655376 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 578.160i | − | 0.916261i | −0.888885 | − | 0.458130i | \(-0.848519\pi\) | ||
0.888885 | − | 0.458130i | \(-0.151481\pi\) | |||||||
\(632\) | −59.3913 | + | 62.5078i | −0.0939736 | + | 0.0989047i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −144.285 | − | 520.693i | −0.227579 | − | 0.821283i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2120.34 | 3.32863 | ||||||||
\(638\) | −76.9757 | + | 21.3301i | −0.120652 | + | 0.0334328i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.3085 | 0.0550834 | 0.0275417 | − | 0.999621i | \(-0.491232\pi\) | ||||
0.0275417 | + | 0.999621i | \(0.491232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1045.67i | 1.62623i | 0.582100 | + | 0.813117i | \(0.302231\pi\) | ||||
−0.582100 | + | 0.813117i | \(0.697769\pi\) | |||||||
\(644\) | 205.143 | − | 123.147i | 0.318544 | − | 0.191222i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 214.321 | − | 59.3888i | 0.331766 | − | 0.0919331i | ||||
\(647\) | − | 2.71164i | − | 0.00419110i | −0.999998 | − | 0.00209555i | \(-0.999333\pi\) | ||
0.999998 | − | 0.00209555i | \(-0.000667035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −628.996 | −0.969177 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 108.982 | + | 181.547i | 0.167151 | + | 0.278446i | ||||
\(653\) | −206.765 | −0.316639 | −0.158319 | − | 0.987388i | \(-0.550608\pi\) | ||||
−0.158319 | + | 0.987388i | \(0.550608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −321.682 | + | 603.792i | −0.490370 | + | 0.920415i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −310.682 | − | 1121.18i | −0.472161 | − | 1.70393i | ||||
\(659\) | − | 708.330i | − | 1.07486i | −0.843309 | − | 0.537428i | \(-0.819396\pi\) | ||
0.843309 | − | 0.537428i | \(-0.180604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1229.66 | 1.86031 | 0.930155 | − | 0.367167i | \(-0.119672\pi\) | ||||
0.930155 | + | 0.367167i | \(0.119672\pi\) | |||||||
\(662\) | 926.540 | − | 256.746i | 1.39961 | − | 0.387834i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −772.907 | + | 813.464i | −1.16402 | + | 1.22510i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.7261i | 0.0205788i | ||||||||
\(668\) | −369.076 | − | 614.820i | −0.552508 | − | 0.920390i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 825.303i | 1.22996i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 753.492 | 1.11960 | 0.559801 | − | 0.828627i | \(-0.310878\pi\) | ||||
0.559801 | + | 0.828627i | \(0.310878\pi\) | |||||||
\(674\) | 303.561 | + | 1095.48i | 0.450387 | + | 1.62535i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1153.56 | + | 692.479i | −1.70645 | + | 1.02438i | ||||
\(677\) | 332.246 | 0.490762 | 0.245381 | − | 0.969427i | \(-0.421087\pi\) | ||||
0.245381 | + | 0.969427i | \(0.421087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 169.520i | 0.249661i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 126.924 | + | 458.041i | 0.186106 | + | 0.671615i | ||||
\(683\) | − | 1120.62i | − | 1.64074i | −0.571835 | − | 0.820368i | \(-0.693768\pi\) | ||
0.571835 | − | 0.820368i | \(-0.306232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1045.70 | − | 289.767i | 1.52435 | − | 0.422400i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 233.610 | + | 124.461i | 0.339550 | + | 0.180902i | ||||
\(689\) | −2115.54 | −3.07045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 331.115i | − | 0.479182i | −0.970874 | − | 0.239591i | \(-0.922987\pi\) | ||
0.970874 | − | 0.239591i | \(-0.0770134\pi\) | |||||||
\(692\) | 607.970 | − | 364.964i | 0.878570 | − | 0.527404i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −713.482 | + | 197.707i | −1.02807 | + | 0.284881i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −542.566 | −0.778431 | ||||||||
\(698\) | 260.935 | + | 941.655i | 0.373832 | + | 1.34908i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 564.971 | 0.805949 | 0.402975 | − | 0.915211i | \(-0.367976\pi\) | ||||
0.402975 | + | 0.915211i | \(0.367976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 284.697i | − | 0.404974i | ||||||
\(704\) | −929.230 | + | 47.5440i | −1.31993 | + | 0.0675341i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 347.006 | + | 1252.27i | 0.491510 | + | 1.77375i | ||||
\(707\) | − | 1956.29i | − | 2.76703i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.56083 | 0.00220146 | 0.00110073 | − | 0.999999i | \(-0.499650\pi\) | ||||
0.00110073 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −318.236 | − | 302.370i | −0.446961 | − | 0.424677i | ||||
\(713\) | 81.6765 | 0.114553 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −211.738 | − | 352.721i | −0.295723 | − | 0.492627i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −782.339 | + | 216.788i | −1.08961 | + | 0.301933i | ||||
\(719\) | 75.0325i | 0.104357i | 0.998638 | + | 0.0521784i | \(0.0166164\pi\) | ||||
−0.998638 | + | 0.0521784i | \(0.983384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2030.28 | −2.81592 | ||||||||
\(722\) | −151.787 | − | 547.766i | −0.210231 | − | 0.758678i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 395.810 | − | 237.604i | 0.546699 | − | 0.328183i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1229.26i | − | 1.69087i | −0.534082 | − | 0.845433i | \(-0.679343\pi\) | ||
0.534082 | − | 0.845433i | \(-0.320657\pi\) | |||||||
\(728\) | −1483.00 | + | 1560.81i | −2.03708 | + | 2.14397i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 209.922i | 0.287170i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 691.736 | 0.943705 | 0.471852 | − | 0.881678i | \(-0.343586\pi\) | ||||
0.471852 | + | 0.881678i | \(0.343586\pi\) | |||||||
\(734\) | 89.1114 | − | 24.6930i | 0.121405 | − | 0.0336416i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.7676 | + | 156.063i | −0.0472385 | + | 0.212042i | ||||
\(737\) | −888.438 | −1.20548 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 71.4311i | − | 0.0966591i | −0.998831 | − | 0.0483296i | \(-0.984610\pi\) | ||
0.998831 | − | 0.0483296i | \(-0.0153898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2171.40 | + | 601.698i | −2.92641 | + | 0.810914i | ||||
\(743\) | 1006.92i | 1.35521i | 0.735426 | + | 0.677605i | \(0.236982\pi\) | ||||
−0.735426 | + | 0.677605i | \(0.763018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 73.8428 | + | 266.482i | 0.0989850 | + | 0.357215i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −379.787 | − | 632.664i | −0.507737 | − | 0.845808i | ||||
\(749\) | 97.5496 | 0.130240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1110.14i | 1.47822i | 0.673587 | + | 0.739108i | \(0.264753\pi\) | ||||
−0.673587 | + | 0.739108i | \(0.735247\pi\) | |||||||
\(752\) | 686.154 | + | 365.562i | 0.912439 | + | 0.486120i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.9825 | − | 119.026i | −0.0437433 | − | 0.157860i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 326.752 | 0.431641 | 0.215821 | − | 0.976433i | \(-0.430757\pi\) | ||||
0.215821 | + | 0.976433i | \(0.430757\pi\) | |||||||
\(758\) | 490.547 | − | 135.932i | 0.647160 | − | 0.179329i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −162.162 | −0.213091 | −0.106546 | − | 0.994308i | \(-0.533979\pi\) | ||||
−0.106546 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 302.070i | 0.395898i | ||||||||
\(764\) | −393.847 | − | 656.085i | −0.515507 | − | 0.858750i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 120.886 | − | 33.4977i | 0.157814 | − | 0.0437306i | ||||
\(767\) | − | 972.608i | − | 1.26807i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −154.694 | −0.201162 | −0.100581 | − | 0.994929i | \(-0.532070\pi\) | ||||
−0.100581 | + | 0.994929i | \(0.532070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 549.861 | − | 330.081i | 0.712255 | − | 0.427566i | ||||
\(773\) | 208.302 | 0.269472 | 0.134736 | − | 0.990882i | \(-0.456981\pi\) | ||||
0.134736 | + | 0.990882i | \(0.456981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −82.1226 | − | 78.0283i | −0.105828 | − | 0.100552i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 58.8183 | + | 212.262i | 0.0756019 | + | 0.272831i | ||||
\(779\) | − | 374.709i | − | 0.481013i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −576.648 | −0.738346 | ||||||||
\(782\) | −122.198 | + | 33.8612i | −0.156263 | + | 0.0433008i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −709.590 | + | 1331.89i | −0.905089 | + | 1.69884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 377.158i | − | 0.479235i | −0.970867 | − | 0.239617i | \(-0.922978\pi\) | ||
0.970867 | − | 0.239617i | \(-0.0770220\pi\) | |||||||
\(788\) | 1217.76 | − | 731.017i | 1.54538 | − | 0.927687i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1171.00i | − | 1.48040i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1276.15 | −1.60927 | ||||||||
\(794\) | 156.460 | + | 564.629i | 0.197053 | + | 0.711119i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 181.587 | + | 302.495i | 0.228124 | + | 0.380018i | ||||
\(797\) | −321.141 | −0.402937 | −0.201468 | − | 0.979495i | \(-0.564571\pi\) | ||||
−0.201468 | + | 0.979495i | \(0.564571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 616.576i | 0.771685i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 276.708 | + | 998.577i | 0.345022 | + | 1.24511i | ||||
\(803\) | 1447.21i | 1.80225i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −708.263 | + | 196.261i | −0.878738 | + | 0.243500i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 947.712 | + | 900.462i | 1.17291 | + | 1.11443i | ||||
\(809\) | 861.938 | 1.06544 | 0.532718 | − | 0.846293i | \(-0.321171\pi\) | ||||
0.532718 | + | 0.846293i | \(0.321171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1011.44i | 1.24715i | 0.781765 | + | 0.623574i | \(0.214320\pi\) | ||||
−0.781765 | + | 0.623574i | \(0.785680\pi\) | |||||||
\(812\) | −67.7066 | − | 112.788i | −0.0833825 | − | 0.138902i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −910.308 | + | 252.248i | −1.11832 | + | 0.309887i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −144.977 | −0.177450 | ||||||||
\(818\) | 97.1935 | + | 350.750i | 0.118818 | + | 0.428790i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −68.0368 | −0.0828707 | −0.0414353 | − | 0.999141i | \(-0.513193\pi\) | ||||
−0.0414353 | + | 0.999141i | \(0.513193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 980.340i | − | 1.19118i | −0.803289 | − | 0.595589i | \(-0.796919\pi\) | ||
0.803289 | − | 0.595589i | \(-0.203081\pi\) | |||||||
\(824\) | 934.517 | − | 983.554i | 1.13412 | − | 1.19363i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −276.628 | − | 998.288i | −0.334900 | − | 1.20858i | ||||
\(827\) | 1183.88i | 1.43153i | 0.698341 | + | 0.715766i | \(0.253922\pi\) | ||||
−0.698341 | + | 0.715766i | \(0.746078\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 98.7892 | 0.119167 | 0.0595833 | − | 0.998223i | \(-0.481023\pi\) | ||||
0.0595833 | + | 0.998223i | \(0.481023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −73.5167 | − | 1436.86i | −0.0883614 | − | 1.72699i | ||||
\(833\) | −1196.83 | −1.43677 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 436.933 | − | 262.290i | 0.522647 | − | 0.313744i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 314.830 | − | 87.2401i | 0.375692 | − | 0.104105i | ||||
\(839\) | − | 407.965i | − | 0.486251i | −0.969995 | − | 0.243125i | \(-0.921827\pi\) | ||
0.969995 | − | 0.243125i | \(-0.0781727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −833.453 | −0.991027 | ||||||||
\(842\) | 249.525 | + | 900.479i | 0.296347 | + | 1.06945i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −392.363 | − | 653.613i | −0.464885 | − | 0.774423i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1081.75i | 1.27716i | ||||||||
\(848\) | 707.984 | − | 1328.87i | 0.834887 | − | 1.56707i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 162.323i | 0.190744i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −907.020 | −1.06333 | −0.531665 | − | 0.846955i | \(-0.678433\pi\) | ||||
−0.531665 | + | 0.846955i | \(0.678433\pi\) | |||||||
\(854\) | −1309.85 | + | 362.962i | −1.53378 | + | 0.425014i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44.9012 | + | 47.2573i | −0.0524546 | + | 0.0552071i | ||||
\(857\) | 693.549 | 0.809275 | 0.404638 | − | 0.914477i | \(-0.367398\pi\) | ||||
0.404638 | + | 0.914477i | \(0.367398\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 397.401i | − | 0.462632i | −0.972879 | − | 0.231316i | \(-0.925697\pi\) | ||
0.972879 | − | 0.231316i | \(-0.0743031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1321.27 | − | 366.126i | 1.53279 | − | 0.424740i | ||||
\(863\) | − | 1193.06i | − | 1.38246i | −0.722636 | − | 0.691229i | \(-0.757070\pi\) | ||
0.722636 | − | 0.691229i | \(-0.242930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 316.590 | + | 1142.50i | 0.365577 | + | 1.31929i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −671.142 | + | 402.886i | −0.773206 | + | 0.464154i | ||||
\(869\) | −156.693 | −0.180314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1373.78i | − | 1.57724i | ||||||
\(872\) | −146.336 | − | 139.040i | −0.167817 | − | 0.159450i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −23.3854 | − | 84.3927i | −0.0267567 | − | 0.0965591i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −136.545 | −0.155695 | −0.0778477 | − | 0.996965i | \(-0.524805\pi\) | ||||
−0.0778477 | + | 0.996965i | \(0.524805\pi\) | |||||||
\(878\) | −895.146 | + | 248.047i | −1.01953 | + | 0.282514i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 836.578 | 0.949578 | 0.474789 | − | 0.880100i | \(-0.342524\pi\) | ||||
0.474789 | + | 0.880100i | \(0.342524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 632.625i | − | 0.716450i | −0.933635 | − | 0.358225i | \(-0.883382\pi\) | ||
0.933635 | − | 0.358225i | \(-0.116618\pi\) | |||||||
\(884\) | 978.280 | − | 587.260i | 1.10665 | − | 0.664321i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 104.631 | − | 28.9934i | 0.118093 | − | 0.0327239i | ||||
\(887\) | − | 290.957i | − | 0.328024i | −0.986458 | − | 0.164012i | \(-0.947556\pi\) | ||
0.986458 | − | 0.164012i | \(-0.0524435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2006.00 | 2.25646 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 163.231 | + | 271.916i | 0.182994 | + | 0.304838i | ||||
\(893\) | −425.822 | −0.476844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −484.126 | − | 1453.88i | −0.540319 | − | 1.62264i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −228.613 | − | 825.013i | −0.254580 | − | 0.918723i | ||||
\(899\) | − | 44.9061i | − | 0.0499511i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1194.12 | 1.32533 | ||||||||
\(902\) | −1198.12 | + | 332.001i | −1.32829 | + | 0.368073i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 567.282 | + | 538.999i | 0.627524 | + | 0.596237i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 473.341i | 0.521875i | 0.965356 | + | 0.260938i | \(0.0840317\pi\) | ||||
−0.965356 | + | 0.260938i | \(0.915968\pi\) | |||||||
\(908\) | 728.061 | + | 1212.83i | 0.801830 | + | 1.33572i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1176.67i | 1.29163i | 0.763495 | + | 0.645813i | \(0.223482\pi\) | ||||
−0.763495 | + | 0.645813i | \(0.776518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2039.17 | −2.23348 | ||||||||
\(914\) | −35.5615 | − | 128.334i | −0.0389075 | − | 0.140409i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 78.1625 | − | 46.9208i | 0.0853303 | − | 0.0512236i | ||||
\(917\) | 982.230 | 1.07113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1491.24i | 1.62267i | 0.584580 | + | 0.811336i | \(0.301259\pi\) | ||||
−0.584580 | + | 0.811336i | \(0.698741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −127.445 | − | 459.921i | −0.138227 | − | 0.498830i | ||||
\(923\) | − | 891.663i | − | 0.966048i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 745.812 | − | 206.666i | 0.805412 | − | 0.223181i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 85.8043 | + | 19.1154i | 0.0924615 | + | 0.0205984i | ||||
\(929\) | 1217.24 | 1.31027 | 0.655134 | − | 0.755513i | \(-0.272612\pi\) | ||||
0.655134 | + | 0.755513i | \(0.272612\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 826.560i | − | 0.887819i | ||||||
\(932\) | 650.613 | − | 390.562i | 0.698083 | − | 0.419058i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 454.790 | − | 126.023i | 0.486927 | − | 0.134928i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −468.840 | −0.500363 | −0.250182 | − | 0.968199i | \(-0.580490\pi\) | ||||
−0.250182 | + | 0.968199i | \(0.580490\pi\) | |||||||
\(938\) | −390.728 | − | 1410.05i | −0.416555 | − | 1.50325i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −358.033 | −0.380481 | −0.190241 | − | 0.981737i | \(-0.560927\pi\) | ||||
−0.190241 | + | 0.981737i | \(0.560927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 213.645i | 0.226559i | ||||||||
\(944\) | 610.943 | + | 325.492i | 0.647185 | + | 0.344801i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 128.453 | + | 463.559i | 0.135785 | + | 0.490020i | ||||
\(947\) | 1148.77i | 1.21306i | 0.795059 | + | 0.606532i | \(0.207440\pi\) | ||||
−0.795059 | + | 0.606532i | \(0.792560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2237.80 | −2.35806 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 837.082 | − | 881.006i | 0.879288 | − | 0.925427i | ||||
\(953\) | −911.785 | −0.956753 | −0.478376 | − | 0.878155i | \(-0.658774\pi\) | ||||
−0.478376 | + | 0.878155i | \(0.658774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −551.283 | − | 918.348i | −0.576656 | − | 0.960615i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1020.54 | − | 282.792i | 1.06528 | − | 0.295190i | ||||
\(959\) | 3046.29i | 3.17653i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 693.788 | 0.721944 | ||||||||
\(962\) | −390.048 | − | 1407.60i | −0.405455 | − | 1.46320i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1034.56 | − | 621.045i | 1.07320 | − | 0.644237i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 311.565i | − | 0.322197i | −0.986938 | − | 0.161099i | \(-0.948496\pi\) | ||
0.986938 | − | 0.161099i | \(-0.0515037\pi\) | |||||||
\(968\) | −524.048 | − | 497.921i | −0.541372 | − | 0.514381i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 370.530i | − | 0.381596i | −0.981629 | − | 0.190798i | \(-0.938892\pi\) | ||
0.981629 | − | 0.190798i | \(-0.0611075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 945.141 | 0.971368 | ||||||||
\(974\) | −1697.63 | + | 470.417i | −1.74295 | + | 0.482974i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 427.077 | − | 801.615i | 0.437578 | − | 0.821327i | ||||
\(977\) | −1402.53 | −1.43555 | −0.717773 | − | 0.696278i | \(-0.754838\pi\) | ||||
−0.717773 | + | 0.696278i | \(0.754838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 797.746i | − | 0.814858i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 166.615 | − | 46.1693i | 0.169669 | − | 0.0470156i | ||||
\(983\) | − | 988.944i | − | 1.00605i | −0.864273 | − | 0.503023i | \(-0.832221\pi\) | ||
0.864273 | − | 0.503023i | \(-0.167779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.6171 | + | 67.1849i | 0.0188814 | + | 0.0681388i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 405.576 | + | 675.624i | 0.410502 | + | 0.683830i | ||||
\(989\) | 82.6603 | 0.0835797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 90.1483i | − | 0.0909670i | −0.998965 | − | 0.0454835i | \(-0.985517\pi\) | ||
0.998965 | − | 0.0454835i | \(-0.0144828\pi\) | |||||||
\(992\) | 113.745 | − | 510.575i | 0.114663 | − | 0.514693i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −253.605 | − | 915.205i | −0.255136 | − | 0.920729i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −655.605 | −0.657578 | −0.328789 | − | 0.944403i | \(-0.606640\pi\) | ||||
−0.328789 | + | 0.944403i | \(0.606640\pi\) | |||||||
\(998\) | −1685.56 | + | 467.071i | −1.68893 | + | 0.468007i | ||||
\(999\) | 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 | 900.3.c.n.451.3 | 8 | ||
3.2 | odd | 2 | 300.3.c.g.151.6 | yes | 8 | ||
4.3 | odd | 2 | inner | 900.3.c.n.451.4 | 8 | ||
5.2 | odd | 4 | 900.3.f.h.199.13 | 16 | |||
5.3 | odd | 4 | 900.3.f.h.199.4 | 16 | |||
5.4 | even | 2 | 900.3.c.t.451.6 | 8 | |||
12.11 | even | 2 | 300.3.c.g.151.5 | yes | 8 | ||
15.2 | even | 4 | 300.3.f.c.199.4 | 16 | |||
15.8 | even | 4 | 300.3.f.c.199.13 | 16 | |||
15.14 | odd | 2 | 300.3.c.e.151.3 | ✓ | 8 | ||
20.3 | even | 4 | 900.3.f.h.199.14 | 16 | |||
20.7 | even | 4 | 900.3.f.h.199.3 | 16 | |||
20.19 | odd | 2 | 900.3.c.t.451.5 | 8 | |||
60.23 | odd | 4 | 300.3.f.c.199.3 | 16 | |||
60.47 | odd | 4 | 300.3.f.c.199.14 | 16 | |||
60.59 | even | 2 | 300.3.c.e.151.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.c.e.151.3 | ✓ | 8 | 15.14 | odd | 2 | ||
300.3.c.e.151.4 | yes | 8 | 60.59 | even | 2 | ||
300.3.c.g.151.5 | yes | 8 | 12.11 | even | 2 | ||
300.3.c.g.151.6 | yes | 8 | 3.2 | odd | 2 | ||
300.3.f.c.199.3 | 16 | 60.23 | odd | 4 | |||
300.3.f.c.199.4 | 16 | 15.2 | even | 4 | |||
300.3.f.c.199.13 | 16 | 15.8 | even | 4 | |||
300.3.f.c.199.14 | 16 | 60.47 | odd | 4 | |||
900.3.c.n.451.3 | 8 | 1.1 | even | 1 | trivial | ||
900.3.c.n.451.4 | 8 | 4.3 | odd | 2 | inner | ||
900.3.c.t.451.5 | 8 | 20.19 | odd | 2 | |||
900.3.c.t.451.6 | 8 | 5.4 | even | 2 | |||
900.3.f.h.199.3 | 16 | 20.7 | even | 4 | |||
900.3.f.h.199.4 | 16 | 5.3 | odd | 4 | |||
900.3.f.h.199.13 | 16 | 5.2 | odd | 4 | |||
900.3.f.h.199.14 | 16 | 20.3 | even | 4 |