Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
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.f (of order \(2\), degree \(1\), not 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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 138x^{12} - 1000x^{10} + 5291x^{8} - 17800x^{6} + 39458x^{4} - 53588x^{2} + 32761 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-1.97048 + 0.960405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.i.199.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97048 | − | 0.342371i | −0.985239 | − | 0.171185i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.76556 | + | 1.34927i | 0.941391 | + | 0.337317i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.5108 | 1.64440 | 0.822199 | − | 0.569201i | \(-0.192747\pi\) | ||||
0.822199 | + | 0.569201i | \(0.192747\pi\) | |||||||
\(8\) | −6.95801 | − | 3.94792i | −0.869751 | − | 0.493490i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.97507i | − | 0.906824i | −0.891301 | − | 0.453412i | \(-0.850207\pi\) | ||
0.891301 | − | 0.453412i | \(-0.149793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.1245i | 1.08650i | 0.839571 | + | 0.543251i | \(0.182807\pi\) | ||||
−0.839571 | + | 0.543251i | \(0.817193\pi\) | |||||||
\(14\) | −22.6817 | − | 3.94096i | −1.62012 | − | 0.281497i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.3590 | + | 10.1615i | 0.772434 | + | 0.635095i | ||||
\(17\) | 30.5776i | 1.79868i | 0.437249 | + | 0.899341i | \(0.355953\pi\) | ||||
−0.437249 | + | 0.899341i | \(0.644047\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.2274i | 0.643548i | 0.946816 | + | 0.321774i | \(0.104279\pi\) | ||||
−0.946816 | + | 0.321774i | \(0.895721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.41517 | + | 19.6556i | −0.155235 | + | 0.893438i | ||||
\(23\) | 15.7638 | 0.685384 | 0.342692 | − | 0.939448i | \(-0.388661\pi\) | ||||
0.342692 | + | 0.939448i | \(0.388661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.83582 | − | 27.8320i | 0.185993 | − | 1.07046i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 43.3446 | + | 15.5311i | 1.54802 | + | 0.554683i | ||||
\(29\) | 18.8943 | 0.651529 | 0.325765 | − | 0.945451i | \(-0.394378\pi\) | ||||
0.325765 | + | 0.945451i | \(0.394378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 35.2490i | − | 1.13706i | −0.822661 | − | 0.568532i | \(-0.807512\pi\) | ||
0.822661 | − | 0.568532i | \(-0.192488\pi\) | |||||||
\(32\) | −20.8740 | − | 24.2544i | −0.652313 | − | 0.757949i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4689 | − | 60.2524i | 0.307908 | − | 1.77213i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 50.1245i | 1.35472i | 0.735653 | + | 0.677358i | \(0.236875\pi\) | ||||
−0.735653 | + | 0.677358i | \(0.763125\pi\) | |||||||
\(38\) | 4.18631 | − | 24.0938i | 0.110166 | − | 0.634049i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −28.8444 | −0.703522 | −0.351761 | − | 0.936090i | \(-0.614417\pi\) | ||||
−0.351761 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.4548 | −0.568717 | −0.284359 | − | 0.958718i | \(-0.591781\pi\) | ||||
−0.284359 | + | 0.958718i | \(0.591781\pi\) | |||||||
\(44\) | 13.4590 | − | 37.5618i | 0.305887 | − | 0.853676i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −31.0623 | − | 5.39707i | −0.675266 | − | 0.117328i | ||||
\(47\) | −55.6641 | −1.18434 | −0.592171 | − | 0.805812i | \(-0.701729\pi\) | ||||
−0.592171 | + | 0.805812i | \(0.701729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 83.4981 | 1.70404 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.0578 | + | 53.1868i | −0.366495 | + | 1.02282i | ||||
\(53\) | 2.46054i | 0.0464253i | 0.999731 | + | 0.0232127i | \(0.00738948\pi\) | ||||
−0.999731 | + | 0.0232127i | \(0.992611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −80.0921 | − | 45.4437i | −1.43022 | − | 0.811494i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −37.2309 | − | 6.46887i | −0.641912 | − | 0.111532i | ||||
\(59\) | 64.6577i | 1.09589i | 0.836513 | + | 0.547947i | \(0.184590\pi\) | ||||
−0.836513 | + | 0.547947i | \(0.815410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −30.2490 | −0.495886 | −0.247943 | − | 0.968775i | \(-0.579755\pi\) | ||||
−0.247943 | + | 0.968775i | \(0.579755\pi\) | |||||||
\(62\) | −12.0682 | + | 69.4573i | −0.194649 | + | 1.12028i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32.8278 | + | 54.9394i | 0.512935 | + | 0.858428i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.1981 | 0.988032 | 0.494016 | − | 0.869453i | \(-0.335528\pi\) | ||||
0.494016 | + | 0.869453i | \(0.335528\pi\) | |||||||
\(68\) | −41.2574 | + | 115.142i | −0.606726 | + | 1.69326i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5775i | 0.163064i | 0.996671 | + | 0.0815318i | \(0.0259812\pi\) | ||||
−0.996671 | + | 0.0815318i | \(0.974019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.24903i | − | 0.0308086i | −0.999881 | − | 0.0154043i | \(-0.995096\pi\) | ||
0.999881 | − | 0.0154043i | \(-0.00490354\pi\) | |||||||
\(74\) | 17.1612 | − | 98.7692i | 0.231908 | − | 1.33472i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.4981 | + | 46.0431i | −0.217080 | + | 0.605831i | ||||
\(77\) | − | 114.821i | − | 1.49118i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 78.4256i | − | 0.992729i | −0.868114 | − | 0.496364i | \(-0.834668\pi\) | ||
0.868114 | − | 0.496364i | \(-0.165332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 56.8373 | + | 9.87548i | 0.693137 | + | 0.120433i | ||||
\(83\) | 146.061 | 1.75977 | 0.879884 | − | 0.475189i | \(-0.157620\pi\) | ||||
0.879884 | + | 0.475189i | \(0.157620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 48.1877 | + | 8.37262i | 0.560322 | + | 0.0973561i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −39.3808 | + | 69.4066i | −0.447509 | + | 0.788712i | ||||
\(89\) | −87.4311 | −0.982372 | −0.491186 | − | 0.871055i | \(-0.663436\pi\) | ||||
−0.491186 | + | 0.871055i | \(0.663436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 162.584i | 1.78664i | ||||||||
\(92\) | 59.3597 | + | 21.2696i | 0.645214 | + | 0.231192i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 109.685 | + | 19.0578i | 1.16686 | + | 0.202742i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 126.747i | 1.30667i | 0.757068 | + | 0.653336i | \(0.226631\pi\) | ||||
−0.757068 | + | 0.653336i | \(0.773369\pi\) | |||||||
\(98\) | −164.531 | − | 28.5873i | −1.67889 | − | 0.291707i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66.1841 | 0.655289 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 105.030 | 1.01971 | 0.509856 | − | 0.860260i | \(-0.329699\pi\) | ||||
0.509856 | + | 0.860260i | \(0.329699\pi\) | |||||||
\(104\) | 55.7625 | − | 98.2785i | 0.536178 | − | 0.944986i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.842418 | − | 4.84844i | 0.00794734 | − | 0.0457400i | ||||
\(107\) | 68.2230 | 0.637598 | 0.318799 | − | 0.947822i | \(-0.396720\pi\) | ||||
0.318799 | + | 0.947822i | \(0.396720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 33.5019 | 0.307357 | 0.153679 | − | 0.988121i | \(-0.450888\pi\) | ||||
0.153679 | + | 0.988121i | \(0.450888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 142.261 | + | 116.967i | 1.27019 | + | 1.04435i | ||||
\(113\) | − | 143.944i | − | 1.27384i | −0.770931 | − | 0.636919i | \(-0.780209\pi\) | ||
0.770931 | − | 0.636919i | \(-0.219791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 71.1479 | + | 25.4935i | 0.613344 | + | 0.219772i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.1369 | − | 127.407i | 0.187601 | − | 1.07972i | ||||
\(119\) | 351.972i | 2.95775i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.4981 | 0.177670 | ||||||||
\(122\) | 59.6050 | + | 10.3564i | 0.488566 | + | 0.0848884i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 47.5603 | − | 132.732i | 0.383551 | − | 1.07042i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −199.983 | −1.57467 | −0.787335 | − | 0.616525i | \(-0.788540\pi\) | ||||
−0.787335 | + | 0.616525i | \(0.788540\pi\) | |||||||
\(128\) | −45.8769 | − | 119.496i | −0.358413 | − | 0.933563i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 247.414i | 1.88866i | 0.329007 | + | 0.944328i | \(0.393286\pi\) | ||||
−0.329007 | + | 0.944328i | \(0.606714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.747i | 1.05825i | ||||||||
\(134\) | −130.442 | − | 22.6643i | −0.973447 | − | 0.169137i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 120.718 | − | 212.759i | 0.887632 | − | 1.56441i | ||||
\(137\) | 141.375i | 1.03194i | 0.856608 | + | 0.515968i | \(0.172568\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 58.2705i | − | 0.419212i | −0.977786 | − | 0.209606i | \(-0.932782\pi\) | ||
0.977786 | − | 0.209606i | \(-0.0672182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.96380 | − | 22.8132i | 0.0279141 | − | 0.160657i | ||||
\(143\) | 140.893 | 0.985266 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.770003 | + | 4.43167i | −0.00527399 | + | 0.0303539i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −67.6314 | + | 188.747i | −0.456969 | + | 1.27532i | ||||
\(149\) | 265.527 | 1.78206 | 0.891029 | − | 0.453947i | \(-0.149984\pi\) | ||||
0.891029 | + | 0.453947i | \(0.149984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 217.988i | − | 1.44363i | −0.692086 | − | 0.721815i | \(-0.743308\pi\) | ||
0.692086 | − | 0.721815i | \(-0.256692\pi\) | |||||||
\(152\) | 48.2729 | − | 85.0785i | 0.317585 | − | 0.559727i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −39.3113 | + | 226.252i | −0.255268 | + | 1.46917i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 66.3735i | 0.422761i | 0.977404 | + | 0.211381i | \(0.0677960\pi\) | ||||
−0.977404 | + | 0.211381i | \(0.932204\pi\) | |||||||
\(158\) | −26.8506 | + | 154.536i | −0.169941 | + | 0.978075i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 181.454 | 1.12704 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 93.5195 | 0.573739 | 0.286870 | − | 0.957970i | \(-0.407385\pi\) | ||||
0.286870 | + | 0.957970i | \(0.407385\pi\) | |||||||
\(164\) | −108.615 | − | 38.9188i | −0.662290 | − | 0.237310i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −287.809 | − | 50.0069i | −1.73379 | − | 0.301247i | ||||
\(167\) | 47.2915 | 0.283182 | 0.141591 | − | 0.989925i | \(-0.454778\pi\) | ||||
0.141591 | + | 0.989925i | \(0.454778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.5019 | −0.180485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −92.0862 | − | 32.9961i | −0.535385 | − | 0.191838i | ||||
\(173\) | 229.534i | 1.32678i | 0.748272 | + | 0.663392i | \(0.230884\pi\) | ||||
−0.748272 | + | 0.663392i | \(0.769116\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 101.362 | − | 123.281i | 0.575919 | − | 0.700462i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 172.281 | + | 29.9339i | 0.967871 | + | 0.168168i | ||||
\(179\) | 150.868i | 0.842838i | 0.906866 | + | 0.421419i | \(0.138468\pi\) | ||||
−0.906866 | + | 0.421419i | \(0.861532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 54.4981 | 0.301094 | 0.150547 | − | 0.988603i | \(-0.451896\pi\) | ||||
0.150547 | + | 0.988603i | \(0.451896\pi\) | |||||||
\(182\) | 55.6641 | − | 320.369i | 0.305847 | − | 1.76027i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −109.685 | − | 62.2343i | −0.596113 | − | 0.338230i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 305.013 | 1.63109 | ||||||||
\(188\) | −209.607 | − | 75.1058i | −1.11493 | − | 0.399499i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 225.861i | 1.18252i | 0.806481 | + | 0.591260i | \(0.201369\pi\) | ||||
−0.806481 | + | 0.591260i | \(0.798631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 174.498i | − | 0.904135i | −0.891984 | − | 0.452068i | \(-0.850687\pi\) | ||
0.891984 | − | 0.452068i | \(-0.149313\pi\) | |||||||
\(194\) | 43.3945 | − | 249.752i | 0.223683 | − | 1.28738i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 314.417 | + | 112.661i | 1.60417 | + | 0.574802i | ||||
\(197\) | 15.9849i | 0.0811414i | 0.999177 | + | 0.0405707i | \(0.0129176\pi\) | ||||
−0.999177 | + | 0.0405707i | \(0.987082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 30.9492i | 0.155523i | 0.996972 | + | 0.0777617i | \(0.0247773\pi\) | ||||
−0.996972 | + | 0.0777617i | \(0.975223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −130.414 | − | 22.6595i | −0.645616 | − | 0.112176i | ||||
\(203\) | 217.489 | 1.07137 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −206.960 | − | 35.9593i | −1.00466 | − | 0.174560i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −143.526 | + | 174.564i | −0.690031 | + | 0.839251i | ||||
\(209\) | 121.969 | 0.583585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 190.667i | 0.903634i | 0.892111 | + | 0.451817i | \(0.149224\pi\) | ||||
−0.892111 | + | 0.451817i | \(0.850776\pi\) | |||||||
\(212\) | −3.31993 | + | 9.26533i | −0.0156600 | + | 0.0437044i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −134.432 | − | 23.3576i | −0.628187 | − | 0.109148i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 405.743i | − | 1.86978i | ||||||
\(218\) | −66.0148 | − | 11.4701i | −0.302820 | − | 0.0526151i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −431.893 | −1.95427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −317.957 | −1.42582 | −0.712909 | − | 0.701257i | \(-0.752623\pi\) | ||||
−0.712909 | + | 0.701257i | \(0.752623\pi\) | |||||||
\(224\) | −240.276 | − | 279.187i | −1.07266 | − | 1.24637i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −49.2821 | + | 283.638i | −0.218062 | + | 1.25503i | ||||
\(227\) | −39.9003 | −0.175772 | −0.0878860 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878860 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7510 | −0.0600479 | −0.0300239 | − | 0.999549i | \(-0.509558\pi\) | ||||
−0.0300239 | + | 0.999549i | \(0.509558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −131.467 | − | 74.5934i | −0.566668 | − | 0.321523i | ||||
\(233\) | − | 121.475i | − | 0.521352i | −0.965426 | − | 0.260676i | \(-0.916055\pi\) | ||
0.965426 | − | 0.260676i | \(-0.0839454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −87.2406 | + | 243.473i | −0.369664 | + | 1.03166i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 120.505 | − | 693.553i | 0.506323 | − | 2.91409i | ||||
\(239\) | 160.843i | 0.672984i | 0.941686 | + | 0.336492i | \(0.109240\pi\) | ||||
−0.941686 | + | 0.336492i | \(0.890760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.49419 | −0.0144987 | −0.00724935 | − | 0.999974i | \(-0.502308\pi\) | ||||
−0.00724935 | + | 0.999974i | \(0.502308\pi\) | |||||||
\(242\) | −42.3615 | − | 7.36031i | −0.175047 | − | 0.0304145i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −113.905 | − | 40.8141i | −0.466822 | − | 0.167271i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −172.706 | −0.699216 | ||||||||
\(248\) | −139.160 | + | 245.263i | −0.561130 | + | 0.988963i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 315.637i | − | 1.25752i | −0.777601 | − | 0.628759i | \(-0.783563\pi\) | ||
0.777601 | − | 0.628759i | \(-0.216437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 157.245i | − | 0.621522i | ||||||
\(254\) | 394.062 | + | 68.4684i | 1.55143 | + | 0.269561i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 49.4873 | + | 251.171i | 0.193310 | + | 0.981138i | ||||
\(257\) | − | 86.8117i | − | 0.337789i | −0.985634 | − | 0.168894i | \(-0.945980\pi\) | ||
0.985634 | − | 0.168894i | \(-0.0540196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 576.972i | 2.22769i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 84.7073 | − | 487.523i | 0.323310 | − | 1.86078i | ||||
\(263\) | 333.003 | 1.26617 | 0.633086 | − | 0.774082i | \(-0.281788\pi\) | ||||
0.633086 | + | 0.774082i | \(0.281788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 48.1877 | − | 277.339i | 0.181157 | − | 1.04263i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 249.273 | + | 89.3190i | 0.930124 | + | 0.333280i | ||||
\(269\) | −191.063 | −0.710271 | −0.355136 | − | 0.934815i | \(-0.615565\pi\) | ||||
−0.355136 | + | 0.934815i | \(0.615565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 261.165i | − | 0.963708i | −0.876252 | − | 0.481854i | \(-0.839964\pi\) | ||
0.876252 | − | 0.481854i | \(-0.160036\pi\) | |||||||
\(272\) | −310.714 | + | 377.907i | −1.14233 | + | 1.38936i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 48.4027 | − | 278.577i | 0.176652 | − | 1.01670i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 204.615i | − | 0.738682i | −0.929294 | − | 0.369341i | \(-0.879583\pi\) | ||
0.929294 | − | 0.369341i | \(-0.120417\pi\) | |||||||
\(278\) | −19.9501 | + | 114.821i | −0.0717631 | + | 0.413024i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 458.726 | 1.63248 | 0.816239 | − | 0.577714i | \(-0.196055\pi\) | ||||
0.816239 | + | 0.577714i | \(0.196055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −336.724 | −1.18984 | −0.594918 | − | 0.803786i | \(-0.702816\pi\) | ||||
−0.594918 | + | 0.803786i | \(0.702816\pi\) | |||||||
\(284\) | −15.6212 | + | 43.5959i | −0.0550041 | + | 0.153507i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −277.626 | − | 48.2376i | −0.970722 | − | 0.168663i | ||||
\(287\) | −332.022 | −1.15687 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −645.988 | −2.23525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.03455 | − | 8.46887i | 0.0103923 | − | 0.0290030i | ||||
\(293\) | − | 249.650i | − | 0.852046i | −0.904712 | − | 0.426023i | \(-0.859914\pi\) | ||
0.904712 | − | 0.426023i | \(-0.140086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 197.888 | − | 348.767i | 0.668539 | − | 1.17827i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −523.214 | − | 90.9086i | −1.75575 | − | 0.305062i | ||||
\(299\) | 222.656i | 0.744670i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −281.494 | −0.935197 | ||||||||
\(302\) | −74.6328 | + | 429.541i | −0.247128 | + | 1.42232i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −124.249 | + | 151.118i | −0.408714 | + | 0.497099i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −156.851 | −0.510916 | −0.255458 | − | 0.966820i | \(-0.582226\pi\) | ||||
−0.255458 | + | 0.966820i | \(0.582226\pi\) | |||||||
\(308\) | 154.924 | − | 432.365i | 0.503000 | − | 1.40378i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 164.769i | − | 0.529803i | −0.964275 | − | 0.264902i | \(-0.914661\pi\) | ||
0.964275 | − | 0.264902i | \(-0.0853395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 131.992i | 0.421700i | 0.977518 | + | 0.210850i | \(0.0676232\pi\) | ||||
−0.977518 | + | 0.210850i | \(0.932377\pi\) | |||||||
\(314\) | 22.7244 | − | 130.788i | 0.0723706 | − | 0.416521i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 105.817 | − | 295.316i | 0.334864 | − | 0.934546i | ||||
\(317\) | − | 169.833i | − | 0.535752i | −0.963453 | − | 0.267876i | \(-0.913678\pi\) | ||
0.963453 | − | 0.267876i | \(-0.0863217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 188.472i | − | 0.590822i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −357.551 | − | 62.1245i | −1.11041 | − | 0.192933i | ||||
\(323\) | −373.885 | −1.15754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −184.278 | − | 32.0184i | −0.565270 | − | 0.0982158i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 200.700 | + | 113.875i | 0.611889 | + | 0.347181i | ||||
\(329\) | −640.737 | −1.94753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 171.945i | − | 0.519472i | −0.965680 | − | 0.259736i | \(-0.916365\pi\) | ||
0.965680 | − | 0.259736i | \(-0.0836355\pi\) | |||||||
\(332\) | 550.001 | + | 197.075i | 1.65663 | + | 0.593600i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −93.1868 | − | 16.1912i | −0.279002 | − | 0.0484767i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 470.249i | − | 1.39540i | −0.716391 | − | 0.697699i | \(-0.754207\pi\) | ||
0.716391 | − | 0.697699i | \(-0.245793\pi\) | |||||||
\(338\) | 60.1034 | + | 10.4430i | 0.177821 | + | 0.0308964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −351.611 | −1.03112 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 397.100 | 1.15772 | ||||||||
\(344\) | 170.157 | + | 96.5458i | 0.494642 | + | 0.280656i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 78.5856 | − | 452.291i | 0.227126 | − | 1.30720i | ||||
\(347\) | −167.974 | −0.484074 | −0.242037 | − | 0.970267i | \(-0.577816\pi\) | ||||
−0.242037 | + | 0.970267i | \(0.577816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 158.747 | 0.454863 | 0.227431 | − | 0.973794i | \(-0.426967\pi\) | ||||
0.227431 | + | 0.973794i | \(0.426967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −241.939 | + | 208.220i | −0.687327 | + | 0.591534i | ||||
\(353\) | − | 201.076i | − | 0.569619i | −0.958584 | − | 0.284810i | \(-0.908070\pi\) | ||
0.958584 | − | 0.284810i | \(-0.0919304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −329.228 | − | 117.968i | −0.924796 | − | 0.331371i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 51.6528 | − | 297.282i | 0.144282 | − | 0.830397i | ||||
\(359\) | − | 689.161i | − | 1.91967i | −0.280567 | − | 0.959835i | \(-0.590522\pi\) | ||
0.280567 | − | 0.959835i | \(-0.409478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 211.490 | 0.585846 | ||||||||
\(362\) | −107.387 | − | 18.6585i | −0.296650 | − | 0.0515429i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −219.370 | + | 612.221i | −0.602664 | + | 1.68193i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5108 | 0.0313645 | 0.0156823 | − | 0.999877i | \(-0.495008\pi\) | ||||
0.0156823 | + | 0.999877i | \(0.495008\pi\) | |||||||
\(368\) | 194.824 | + | 160.184i | 0.529414 | + | 0.435283i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.3228i | 0.0763417i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 356.864i | − | 0.956740i | −0.878159 | − | 0.478370i | \(-0.841228\pi\) | ||
0.878159 | − | 0.478370i | \(-0.158772\pi\) | |||||||
\(374\) | −601.022 | − | 104.428i | −1.60701 | − | 0.279218i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 387.311 | + | 219.757i | 1.03008 | + | 0.584461i | ||||
\(377\) | 266.873i | 0.707887i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 554.623i | − | 1.46338i | −0.681635 | − | 0.731692i | \(-0.738731\pi\) | ||
0.681635 | − | 0.731692i | \(-0.261269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 77.3283 | − | 445.055i | 0.202430 | − | 1.16506i | ||||
\(383\) | −442.368 | −1.15501 | −0.577504 | − | 0.816388i | \(-0.695973\pi\) | ||||
−0.577504 | + | 0.816388i | \(0.695973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −59.7430 | + | 343.845i | −0.154775 | + | 0.890789i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −171.016 | + | 477.274i | −0.440762 | + | 1.23009i | ||||
\(389\) | 356.424 | 0.916257 | 0.458129 | − | 0.888886i | \(-0.348520\pi\) | ||||
0.458129 | + | 0.888886i | \(0.348520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 482.020i | 1.23279i | ||||||||
\(392\) | −580.980 | − | 329.644i | −1.48209 | − | 0.840928i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.47275 | − | 31.4978i | 0.0138902 | − | 0.0799436i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 512.864i | 1.29185i | 0.763402 | + | 0.645924i | \(0.223528\pi\) | ||||
−0.763402 | + | 0.645924i | \(0.776472\pi\) | |||||||
\(398\) | 10.5961 | − | 60.9846i | 0.0266233 | − | 0.153228i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3990 | −0.0259327 | −0.0129664 | − | 0.999916i | \(-0.504127\pi\) | ||||
−0.0129664 | + | 0.999916i | \(0.504127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 497.875 | 1.23542 | ||||||||
\(404\) | 249.221 | + | 89.3002i | 0.616883 | + | 0.221040i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −428.556 | − | 74.4618i | −1.05556 | − | 0.183403i | ||||
\(407\) | 499.995 | 1.22849 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −251.494 | −0.614900 | −0.307450 | − | 0.951564i | \(-0.599476\pi\) | ||||
−0.307450 | + | 0.951564i | \(0.599476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 395.498 | + | 141.714i | 0.959947 | + | 0.343966i | ||||
\(413\) | 744.261i | 1.80208i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 342.581 | − | 294.836i | 0.823513 | − | 0.708739i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −240.338 | − | 41.7587i | −0.574971 | − | 0.0999012i | ||||
\(419\) | − | 205.551i | − | 0.490574i | −0.969450 | − | 0.245287i | \(-0.921118\pi\) | ||
0.969450 | − | 0.245287i | \(-0.0788823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 811.230 | 1.92691 | 0.963456 | − | 0.267868i | \(-0.0863191\pi\) | ||||
0.963456 | + | 0.267868i | \(0.0863191\pi\) | |||||||
\(422\) | 65.2788 | − | 375.705i | 0.154689 | − | 0.890296i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.71403 | − | 17.1205i | 0.0229104 | − | 0.0403785i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −348.190 | −0.815433 | ||||||||
\(428\) | 256.898 | + | 92.0511i | 0.600229 | + | 0.215073i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 359.624i | − | 0.834394i | −0.908816 | − | 0.417197i | \(-0.863013\pi\) | ||
0.908816 | − | 0.417197i | \(-0.136987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 198.747i | 0.459000i | 0.973309 | + | 0.229500i | \(0.0737091\pi\) | ||||
−0.973309 | + | 0.229500i | \(0.926291\pi\) | |||||||
\(434\) | −138.915 | + | 799.508i | −0.320080 | + | 1.84218i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 126.154 | + | 45.2031i | 0.289343 | + | 0.103677i | ||||
\(437\) | 192.751i | 0.441077i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 353.251i | 0.804672i | 0.915492 | + | 0.402336i | \(0.131802\pi\) | ||||
−0.915492 | + | 0.402336i | \(0.868198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 851.036 | + | 147.868i | 1.92542 | + | 0.334542i | ||||
\(443\) | 209.837 | 0.473672 | 0.236836 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236836 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 626.528 | + | 108.859i | 1.40477 | + | 0.244079i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 377.874 | + | 632.395i | 0.843468 | + | 1.41160i | ||||
\(449\) | 617.155 | 1.37451 | 0.687255 | − | 0.726416i | \(-0.258816\pi\) | ||||
0.687255 | + | 0.726416i | \(0.258816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 287.725i | 0.637971i | ||||||||
\(452\) | 194.219 | − | 542.029i | 0.429687 | − | 1.19918i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 78.6226 | + | 13.6607i | 0.173177 | + | 0.0300896i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 129.253i | − | 0.282829i | −0.989950 | − | 0.141415i | \(-0.954835\pi\) | ||
0.989950 | − | 0.141415i | \(-0.0451650\pi\) | |||||||
\(458\) | 27.0960 | + | 4.70793i | 0.0591615 | + | 0.0102793i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6785 | −0.0405174 | −0.0202587 | − | 0.999795i | \(-0.506449\pi\) | ||||
−0.0202587 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −109.419 | −0.236327 | −0.118163 | − | 0.992994i | \(-0.537701\pi\) | ||||
−0.118163 | + | 0.992994i | \(0.537701\pi\) | |||||||
\(464\) | 233.514 | + | 191.995i | 0.503263 | + | 0.413782i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.5895 | + | 239.364i | −0.0892479 | + | 0.513656i | ||||
\(467\) | −250.979 | −0.537428 | −0.268714 | − | 0.963220i | \(-0.586599\pi\) | ||||
−0.268714 | + | 0.963220i | \(0.586599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 761.992 | 1.62472 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 255.264 | − | 449.889i | 0.540813 | − | 0.953155i | ||||
\(473\) | 243.939i | 0.515726i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −474.904 | + | 1325.37i | −0.997698 | + | 2.78440i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 55.0680 | − | 316.938i | 0.115205 | − | 0.663050i | ||||
\(479\) | − | 373.164i | − | 0.779048i | −0.921016 | − | 0.389524i | \(-0.872640\pi\) | ||
0.921016 | − | 0.389524i | \(-0.127360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −707.984 | −1.47190 | ||||||||
\(482\) | 6.88522 | + | 1.19631i | 0.0142847 | + | 0.00248197i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 80.9523 | + | 29.0066i | 0.167257 | + | 0.0599311i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 182.784 | 0.375326 | 0.187663 | − | 0.982233i | \(-0.439909\pi\) | ||||
0.187663 | + | 0.982233i | \(0.439909\pi\) | |||||||
\(488\) | 210.473 | + | 119.421i | 0.431297 | + | 0.244715i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 413.425i | 0.842005i | 0.907059 | + | 0.421003i | \(0.138322\pi\) | ||||
−0.907059 | + | 0.421003i | \(0.861678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 577.743i | 1.17189i | ||||||||
\(494\) | 340.314 | + | 59.1296i | 0.688895 | + | 0.119696i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 358.183 | − | 435.640i | 0.722143 | − | 0.878307i | ||||
\(497\) | 133.266i | 0.268141i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 92.8475i | − | 0.186067i | −0.995663 | − | 0.0930336i | \(-0.970344\pi\) | ||
0.995663 | − | 0.0930336i | \(-0.0296564\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −108.065 | + | 621.955i | −0.215269 | + | 1.23895i | ||||
\(503\) | −415.288 | −0.825622 | −0.412811 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412811 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −53.8362 | + | 309.848i | −0.106396 | + | 0.612348i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −753.049 | − | 269.831i | −1.48238 | − | 0.531163i | ||||
\(509\) | 396.009 | 0.778013 | 0.389006 | − | 0.921235i | \(-0.372818\pi\) | ||||
0.389006 | + | 0.921235i | \(0.372818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25.8881i | − | 0.0506616i | ||||||
\(512\) | −11.5200 | − | 511.870i | −0.0225000 | − | 0.999747i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.7218 | + | 171.060i | −0.0578245 | + | 0.332802i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 555.253i | 1.07399i | ||||||||
\(518\) | 197.538 | − | 1136.91i | 0.381348 | − | 2.19481i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −356.191 | −0.683668 | −0.341834 | − | 0.939760i | \(-0.611048\pi\) | ||||
−0.341834 | + | 0.939760i | \(0.611048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −261.837 | −0.500644 | −0.250322 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250322 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(524\) | −333.828 | + | 931.653i | −0.637075 | + | 1.77796i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −656.175 | − | 114.011i | −1.24748 | − | 0.216750i | ||||
\(527\) | 1077.83 | 2.04522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −280.502 | −0.530249 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −189.906 | + | 529.992i | −0.356965 | + | 0.996226i | ||||
\(533\) | − | 407.413i | − | 0.764378i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −460.607 | − | 261.345i | −0.859342 | − | 0.487584i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 376.485 | + | 65.4144i | 0.699787 | + | 0.121588i | ||||
\(539\) | − | 832.899i | − | 1.54527i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −581.984 | −1.07576 | −0.537878 | − | 0.843022i | \(-0.680774\pi\) | ||||
−0.537878 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(542\) | −89.4152 | + | 514.619i | −0.164973 | + | 0.949482i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 741.640 | − | 638.277i | 1.36331 | − | 1.17330i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −84.8307 | −0.155083 | −0.0775417 | − | 0.996989i | \(-0.524707\pi\) | ||||
−0.0775417 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(548\) | −190.753 | + | 532.357i | −0.348089 | + | 0.971455i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 231.029i | 0.419290i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 902.739i | − | 1.63244i | ||||||
\(554\) | −70.0541 | + | 403.189i | −0.126452 | + | 0.727778i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 78.6226 | − | 219.421i | 0.141408 | − | 0.394643i | ||||
\(557\) | − | 708.933i | − | 1.27277i | −0.771372 | − | 0.636385i | \(-0.780429\pi\) | ||
0.771372 | − | 0.636385i | \(-0.219571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 345.413i | − | 0.617912i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −903.910 | − | 157.055i | −1.60838 | − | 0.279456i | ||||
\(563\) | −1094.57 | −1.94418 | −0.972090 | − | 0.234607i | \(-0.924620\pi\) | ||||
−0.972090 | + | 0.234607i | \(0.924620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 663.507 | + | 115.284i | 1.17227 | + | 0.203683i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 45.7071 | − | 80.5564i | 0.0804703 | − | 0.141825i | ||||
\(569\) | −769.082 | −1.35164 | −0.675819 | − | 0.737068i | \(-0.736210\pi\) | ||||
−0.675819 | + | 0.737068i | \(0.736210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 871.192i | − | 1.52573i | −0.646558 | − | 0.762865i | \(-0.723792\pi\) | ||
0.646558 | − | 0.762865i | \(-0.276208\pi\) | |||||||
\(572\) | 530.542 | + | 190.102i | 0.927520 | + | 0.332347i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 654.241 | + | 113.675i | 1.13979 | + | 0.198039i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 216.739i | 0.375631i | 0.982204 | + | 0.187816i | \(0.0601408\pi\) | ||||
−0.982204 | + | 0.187816i | \(0.939859\pi\) | |||||||
\(578\) | 1272.91 | + | 221.168i | 2.20226 | + | 0.382643i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1681.27 | 2.89376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.5441 | 0.0420996 | ||||||||
\(584\) | −8.87900 | + | 15.6488i | −0.0152038 | + | 0.0267959i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −85.4727 | + | 491.929i | −0.145858 | + | 0.839469i | ||||
\(587\) | 148.024 | 0.252170 | 0.126085 | − | 0.992019i | \(-0.459759\pi\) | ||||
0.126085 | + | 0.992019i | \(0.459759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 431.004 | 0.731755 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −509.341 | + | 619.486i | −0.860373 | + | 1.04643i | ||||
\(593\) | 102.473i | 0.172804i | 0.996260 | + | 0.0864020i | \(0.0275370\pi\) | ||||
−0.996260 | + | 0.0864020i | \(0.972463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 999.857 | + | 358.267i | 1.67761 | + | 0.601118i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 76.2310 | − | 438.739i | 0.127477 | − | 0.733678i | ||||
\(599\) | − | 353.214i | − | 0.589673i | −0.955548 | − | 0.294836i | \(-0.904735\pi\) | ||
0.955548 | − | 0.294836i | \(-0.0952651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 422.498 | 0.702992 | 0.351496 | − | 0.936189i | \(-0.385673\pi\) | ||||
0.351496 | + | 0.936189i | \(0.385673\pi\) | |||||||
\(602\) | 554.678 | + | 96.3754i | 0.921392 | + | 0.160092i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 294.125 | − | 820.849i | 0.486961 | − | 1.35902i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 958.261 | 1.57868 | 0.789342 | − | 0.613954i | \(-0.210422\pi\) | ||||
0.789342 | + | 0.613954i | \(0.210422\pi\) | |||||||
\(608\) | 296.568 | − | 255.235i | 0.487777 | − | 0.419795i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 786.228i | − | 1.28679i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 885.611i | 1.44472i | 0.691519 | + | 0.722358i | \(0.256942\pi\) | ||||
−0.691519 | + | 0.722358i | \(0.743058\pi\) | |||||||
\(614\) | 309.072 | + | 53.7012i | 0.503374 | + | 0.0874613i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −453.304 | + | 798.924i | −0.735882 | + | 1.29695i | ||||
\(617\) | 37.8513i | 0.0613473i | 0.999529 | + | 0.0306737i | \(0.00976526\pi\) | ||||
−0.999529 | + | 0.0306737i | \(0.990235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 544.679i | − | 0.879934i | −0.898014 | − | 0.439967i | \(-0.854990\pi\) | ||
0.898014 | − | 0.439967i | \(-0.145010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −56.4120 | + | 324.673i | −0.0906946 | + | 0.521983i | ||||
\(623\) | −1006.40 | −1.61541 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 45.1903 | − | 260.088i | 0.0721890 | − | 0.415476i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −89.5557 | + | 249.934i | −0.142605 | + | 0.397984i | ||||
\(629\) | −1532.69 | −2.43670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 665.520i | 1.05471i | 0.849646 | + | 0.527353i | \(0.176816\pi\) | ||||
−0.849646 | + | 0.527353i | \(0.823184\pi\) | |||||||
\(632\) | −309.618 | + | 545.686i | −0.489902 | + | 0.863427i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −58.1460 | + | 334.653i | −0.0917129 | + | 0.527843i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1179.37i | 1.85144i | ||||||||
\(638\) | −64.5274 | + | 371.380i | −0.101140 | + | 0.582101i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1089.06 | −1.69901 | −0.849504 | − | 0.527582i | \(-0.823099\pi\) | ||||
−0.849504 | + | 0.527582i | \(0.823099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −277.692 | −0.431869 | −0.215935 | − | 0.976408i | \(-0.569280\pi\) | ||||
−0.215935 | + | 0.976408i | \(0.569280\pi\) | |||||||
\(644\) | 683.276 | + | 244.830i | 1.06099 | + | 0.380171i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 736.732 | + | 128.007i | 1.14045 | + | 0.198154i | ||||
\(647\) | −1049.77 | −1.62251 | −0.811257 | − | 0.584690i | \(-0.801216\pi\) | ||||
−0.811257 | + | 0.584690i | \(0.801216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 644.965 | 0.993783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 352.154 | + | 126.183i | 0.540113 | + | 0.193532i | ||||
\(653\) | 110.008i | 0.168465i | 0.996446 | + | 0.0842325i | \(0.0268438\pi\) | ||||
−0.996446 | + | 0.0842325i | \(0.973156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −356.487 | − | 293.103i | −0.543425 | − | 0.446803i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1262.56 | + | 219.370i | 1.91878 | + | 0.333389i | ||||
\(659\) | − | 363.189i | − | 0.551121i | −0.961284 | − | 0.275561i | \(-0.911137\pi\) | ||
0.961284 | − | 0.275561i | \(-0.0888635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −801.735 | −1.21291 | −0.606456 | − | 0.795117i | \(-0.707410\pi\) | ||||
−0.606456 | + | 0.795117i | \(0.707410\pi\) | |||||||
\(662\) | −58.8690 | + | 338.814i | −0.0889259 | + | 0.511803i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1016.29 | − | 576.636i | −1.53056 | − | 0.868428i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 297.847 | 0.446547 | ||||||||
\(668\) | 178.079 | + | 63.8089i | 0.266585 | + | 0.0955223i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 301.736i | 0.449681i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 447.743i | 0.665295i | 0.943051 | + | 0.332647i | \(0.107942\pi\) | ||||
−0.943051 | + | 0.332647i | \(0.892058\pi\) | |||||||
\(674\) | −161.000 | + | 926.615i | −0.238872 | + | 1.37480i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −114.857 | − | 41.1553i | −0.169907 | − | 0.0608806i | ||||
\(677\) | − | 299.167i | − | 0.441901i | −0.975285 | − | 0.220950i | \(-0.929084\pi\) | ||
0.975285 | − | 0.220950i | \(-0.0709159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1458.96i | 2.14869i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 692.841 | + | 120.381i | 1.01590 | + | 0.176512i | ||||
\(683\) | −339.673 | −0.497326 | −0.248663 | − | 0.968590i | \(-0.579991\pi\) | ||||
−0.248663 | + | 0.968590i | \(0.579991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −782.476 | − | 135.955i | −1.14064 | − | 0.198186i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −302.236 | − | 248.498i | −0.439297 | − | 0.361189i | ||||
\(689\) | −34.7540 | −0.0504412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 764.773i | − | 1.10676i | −0.832928 | − | 0.553381i | \(-0.813337\pi\) | ||
0.832928 | − | 0.553381i | \(-0.186663\pi\) | |||||||
\(692\) | −309.702 | + | 864.324i | −0.447547 | + | 1.24902i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 330.988 | + | 57.5093i | 0.476928 | + | 0.0828664i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 881.992i | − | 1.26541i | ||||||
\(698\) | −312.808 | − | 54.3504i | −0.448148 | − | 0.0778659i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −308.111 | −0.439531 | −0.219765 | − | 0.975553i | \(-0.570529\pi\) | ||||
−0.219765 | + | 0.975553i | \(0.570529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −612.893 | −0.871825 | ||||||||
\(704\) | 548.024 | − | 327.460i | 0.778443 | − | 0.465142i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −68.8424 | + | 396.215i | −0.0975105 | + | 0.561211i | ||||
\(707\) | 761.831 | 1.07755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 882.249 | 1.24436 | 0.622178 | − | 0.782875i | \(-0.286248\pi\) | ||||
0.622178 | + | 0.782875i | \(0.286248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 608.347 | + | 345.171i | 0.854420 | + | 0.484791i | ||||
\(713\) | − | 555.659i | − | 0.779325i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −203.561 | + | 568.103i | −0.284304 | + | 0.793440i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −235.949 | + | 1357.98i | −0.328619 | + | 1.89133i | ||||
\(719\) | − | 766.999i | − | 1.06676i | −0.845876 | − | 0.533379i | \(-0.820922\pi\) | ||
0.845876 | − | 0.533379i | \(-0.179078\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1208.98 | 1.67681 | ||||||||
\(722\) | −416.737 | − | 72.4081i | −0.577198 | − | 0.100288i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 205.216 | + | 73.5325i | 0.283447 | + | 0.101564i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 735.301 | 1.01142 | 0.505709 | − | 0.862704i | \(-0.331231\pi\) | ||||
0.505709 | + | 0.862704i | \(0.331231\pi\) | |||||||
\(728\) | 641.870 | − | 1131.26i | 0.881689 | − | 1.55393i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 747.770i | − | 1.02294i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 269.377i | − | 0.367500i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||
0.982973 | − | 0.183750i | \(-0.0588237\pi\) | |||||||
\(734\) | −22.6817 | − | 3.94096i | −0.0309015 | − | 0.00536915i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −329.055 | − | 382.342i | −0.447085 | − | 0.519486i | ||||
\(737\) | − | 660.331i | − | 0.895971i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 807.949i | 1.09330i | 0.837361 | + | 0.546650i | \(0.184097\pi\) | ||||
−0.837361 | + | 0.546650i | \(0.815903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.69688 | − | 55.8094i | 0.0130686 | − | 0.0752148i | ||||
\(743\) | 1017.72 | 1.36974 | 0.684870 | − | 0.728665i | \(-0.259859\pi\) | ||||
0.684870 | + | 0.728665i | \(0.259859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −122.180 | + | 703.192i | −0.163780 | + | 0.942617i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1148.55 | + | 411.545i | 1.53549 | + | 0.550194i | ||||
\(749\) | 785.300 | 1.04846 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 551.845i | 0.734814i | 0.930060 | + | 0.367407i | \(0.119754\pi\) | ||||
−0.930060 | + | 0.367407i | \(0.880246\pi\) | |||||||
\(752\) | −687.950 | − | 565.631i | −0.914827 | − | 0.752169i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 91.3697 | − | 525.868i | 0.121180 | − | 0.697438i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1168.86i | 1.54407i | 0.635578 | + | 0.772037i | \(0.280762\pi\) | ||||
−0.635578 | + | 0.772037i | \(0.719238\pi\) | |||||||
\(758\) | −189.887 | + | 1092.87i | −0.250510 | + | 1.44178i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 221.811 | 0.291473 | 0.145737 | − | 0.989323i | \(-0.453445\pi\) | ||||
0.145737 | + | 0.989323i | \(0.453445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 385.633 | 0.505417 | ||||||||
\(764\) | −304.747 | + | 850.495i | −0.398884 | + | 1.11321i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 871.677 | + | 151.454i | 1.13796 | + | 0.197721i | ||||
\(767\) | −913.259 | −1.19069 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5136 | −0.0448811 | −0.0224406 | − | 0.999748i | \(-0.507144\pi\) | ||||
−0.0224406 | + | 0.999748i | \(0.507144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 235.445 | − | 657.084i | 0.304980 | − | 0.851145i | ||||
\(773\) | − | 401.055i | − | 0.518829i | −0.965766 | − | 0.259415i | \(-0.916470\pi\) | ||
0.965766 | − | 0.259415i | \(-0.0835296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 500.388 | − | 881.908i | 0.644829 | − | 1.13648i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −702.326 | − | 122.029i | −0.902732 | − | 0.156850i | ||||
\(779\) | − | 352.693i | − | 0.452750i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 115.486 | 0.147870 | ||||||||
\(782\) | 165.029 | − | 949.809i | 0.211035 | − | 1.21459i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1031.95 | + | 848.467i | 1.31626 | + | 1.08223i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1030.24 | −1.30907 | −0.654534 | − | 0.756032i | \(-0.727135\pi\) | ||||
−0.654534 | + | 0.756032i | \(0.727135\pi\) | |||||||
\(788\) | −21.5679 | + | 60.1920i | −0.0273704 | + | 0.0763858i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1656.90i | − | 2.09469i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 427.253i | − | 0.538780i | ||||||
\(794\) | 175.590 | − | 1010.59i | 0.221146 | − | 1.27278i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −41.7587 | + | 116.541i | −0.0524607 | + | 0.146408i | ||||
\(797\) | 1070.94i | 1.34372i | 0.740679 | + | 0.671859i | \(0.234504\pi\) | ||||
−0.740679 | + | 0.671859i | \(0.765496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1702.07i | − | 2.13025i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.4910 | + | 3.56032i | 0.0255499 | + | 0.00443930i | ||||
\(803\) | −22.4342 | −0.0279380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −981.051 | − | 170.458i | −1.21718 | − | 0.211486i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −460.510 | − | 261.290i | −0.569938 | − | 0.323379i | ||||
\(809\) | 1265.04 | 1.56371 | 0.781854 | − | 0.623461i | \(-0.214274\pi\) | ||||
0.781854 | + | 0.623461i | \(0.214274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 966.144i | − | 1.19130i | −0.803244 | − | 0.595650i | \(-0.796895\pi\) | ||
0.803244 | − | 0.595650i | \(-0.203105\pi\) | |||||||
\(812\) | 818.967 | + | 293.450i | 1.00858 | + | 0.361392i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −985.230 | − | 171.184i | −1.21036 | − | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 299.019i | − | 0.365997i | ||||||
\(818\) | 495.564 | + | 86.1043i | 0.605824 | + | 0.105262i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −878.408 | −1.06992 | −0.534962 | − | 0.844876i | \(-0.679674\pi\) | ||||
−0.534962 | + | 0.844876i | \(0.679674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 887.674 | 1.07858 | 0.539292 | − | 0.842119i | \(-0.318692\pi\) | ||||
0.539292 | + | 0.842119i | \(0.318692\pi\) | |||||||
\(824\) | −730.802 | − | 414.651i | −0.886895 | − | 0.503218i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 254.813 | − | 1466.55i | 0.308491 | − | 1.77548i | ||||
\(827\) | −82.2846 | −0.0994977 | −0.0497489 | − | 0.998762i | \(-0.515842\pi\) | ||||
−0.0497489 | + | 0.998762i | \(0.515842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −348.475 | −0.420356 | −0.210178 | − | 0.977663i | \(-0.567404\pi\) | ||||
−0.210178 | + | 0.977663i | \(0.567404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −775.992 | + | 463.677i | −0.932683 | + | 0.557304i | ||||
\(833\) | 2553.17i | 3.06503i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 459.283 | + | 164.569i | 0.549382 | + | 0.196853i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −70.3746 | + | 405.033i | −0.0839792 | + | 0.483333i | ||||
\(839\) | 174.383i | 0.207847i | 0.994585 | + | 0.103923i | \(0.0331397\pi\) | ||||
−0.994585 | + | 0.103923i | \(0.966860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −484.004 | −0.575510 | ||||||||
\(842\) | −1598.51 | − | 277.741i | −1.89847 | − | 0.329859i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −257.261 | + | 717.968i | −0.304811 | + | 0.850673i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 247.459 | 0.292160 | ||||||||
\(848\) | −25.0028 | + | 30.4097i | −0.0294845 | + | 0.0358605i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 790.154i | 0.928500i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1549.11i | 1.81608i | 0.418888 | + | 0.908038i | \(0.362420\pi\) | ||||
−0.418888 | + | 0.908038i | \(0.637580\pi\) | |||||||
\(854\) | 686.101 | + | 119.210i | 0.803396 | + | 0.139590i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −474.696 | − | 269.339i | −0.554552 | − | 0.314649i | ||||
\(857\) | 376.279i | 0.439065i | 0.975605 | + | 0.219533i | \(0.0704532\pi\) | ||||
−0.975605 | + | 0.219533i | \(0.929547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1495.73i | − | 1.74124i | −0.491952 | − | 0.870622i | \(-0.663716\pi\) | ||
0.491952 | − | 0.870622i | \(-0.336284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −123.125 | + | 708.630i | −0.142836 | + | 0.822077i | ||||
\(863\) | 104.458 | 0.121041 | 0.0605204 | − | 0.998167i | \(-0.480724\pi\) | ||||
0.0605204 | + | 0.998167i | \(0.480724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 68.0452 | − | 391.627i | 0.0785741 | − | 0.452225i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 547.456 | − | 1527.85i | 0.630710 | − | 1.76020i | ||||
\(869\) | −782.300 | −0.900230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 935.017i | 1.07350i | ||||||||
\(872\) | −233.107 | − | 132.263i | −0.267324 | − | 0.151678i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 65.9922 | − | 379.811i | 0.0755060 | − | 0.434567i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 282.607i | − | 0.322243i | −0.986935 | − | 0.161121i | \(-0.948489\pi\) | ||
0.986935 | − | 0.161121i | \(-0.0515111\pi\) | |||||||
\(878\) | 120.943 | − | 696.073i | 0.137748 | − | 0.792794i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −578.468 | −0.656604 | −0.328302 | − | 0.944573i | \(-0.606476\pi\) | ||||
−0.328302 | + | 0.944573i | \(0.606476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1267.53 | 1.43548 | 0.717741 | − | 0.696311i | \(-0.245176\pi\) | ||||
0.717741 | + | 0.696311i | \(0.245176\pi\) | |||||||
\(884\) | −1626.32 | − | 582.740i | −1.83973 | − | 0.659208i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −413.479 | − | 71.8420i | −0.466680 | − | 0.0810858i | ||||
\(887\) | 49.7756 | 0.0561168 | 0.0280584 | − | 0.999606i | \(-0.491068\pi\) | ||||
0.0280584 | + | 0.999606i | \(0.491068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2301.96 | −2.58938 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1197.29 | − | 429.010i | −1.34225 | − | 0.480953i | ||||
\(893\) | − | 680.628i | − | 0.762181i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −528.078 | − | 1375.49i | −0.589373 | − | 1.53515i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1216.09 | − | 211.296i | −1.35422 | − | 0.235296i | ||||
\(899\) | − | 666.006i | − | 0.740830i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −75.2374 | −0.0835043 | ||||||||
\(902\) | 98.5086 | − | 566.955i | 0.109211 | − | 0.628554i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −568.278 | + | 1001.56i | −0.628626 | + | 1.10792i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1487.71 | −1.64026 | −0.820128 | − | 0.572180i | \(-0.806098\pi\) | ||||
−0.820128 | + | 0.572180i | \(0.806098\pi\) | |||||||
\(908\) | −150.247 | − | 53.8362i | −0.165470 | − | 0.0592909i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 678.826i | 0.745144i | 0.928003 | + | 0.372572i | \(0.121524\pi\) | ||||
−0.928003 | + | 0.372572i | \(0.878476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1456.97i | − | 1.59580i | ||||||
\(914\) | −44.2524 | + | 254.690i | −0.0484162 | + | 0.278654i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.7802 | − | 18.5537i | −0.0565286 | − | 0.0202552i | ||||
\(917\) | 2847.93i | 3.10570i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 820.849i | 0.893198i | 0.894734 | + | 0.446599i | \(0.147365\pi\) | ||||
−0.894734 | + | 0.446599i | \(0.852635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.8056 | + | 6.39499i | 0.0399193 | + | 0.00693599i | ||||
\(923\) | −163.527 | −0.177169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 215.608 | + | 37.4620i | 0.232838 | + | 0.0404557i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −394.401 | − | 458.270i | −0.425001 | − | 0.493826i | ||||
\(929\) | 455.044 | 0.489821 | 0.244911 | − | 0.969546i | \(-0.421241\pi\) | ||||
0.244911 | + | 0.969546i | \(0.421241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1020.97i | 1.09663i | ||||||||
\(932\) | 163.902 | − | 457.422i | 0.175861 | − | 0.490796i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 494.549 | + | 85.9279i | 0.529495 | + | 0.0919999i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1705.49i | − | 1.82016i | −0.414437 | − | 0.910078i | \(-0.636021\pi\) | ||
0.414437 | − | 0.910078i | \(-0.363979\pi\) | |||||||
\(938\) | −1501.49 | − | 260.884i | −1.60073 | − | 0.278128i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 77.3558 | 0.0822060 | 0.0411030 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411030 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −454.698 | −0.482183 | ||||||||
\(944\) | −657.020 | + | 799.102i | −0.695996 | + | 0.846506i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 83.5174 | − | 480.675i | 0.0882848 | − | 0.508114i | ||||
\(947\) | −382.779 | −0.404201 | −0.202101 | − | 0.979365i | \(-0.564777\pi\) | ||||
−0.202101 | + | 0.979365i | \(0.564777\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.7665 | 0.0334736 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1389.56 | − | 2449.02i | 1.45962 | − | 2.57250i | ||||
\(953\) | − | 1101.29i | − | 1.15560i | −0.816178 | − | 0.577800i | \(-0.803911\pi\) | ||
0.816178 | − | 0.577800i | \(-0.196089\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −217.020 | + | 605.665i | −0.227009 | + | 0.633541i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −127.760 | + | 735.311i | −0.133362 | + | 0.767548i | ||||
\(959\) | 1627.34i | 1.69691i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −281.490 | −0.292914 | ||||||||
\(962\) | 1395.07 | + | 242.393i | 1.45017 | + | 0.251968i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.1576 | − | 4.71459i | −0.0136489 | − | 0.00489066i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1339.59 | −1.38531 | −0.692655 | − | 0.721269i | \(-0.743559\pi\) | ||||
−0.692655 | + | 0.721269i | \(0.743559\pi\) | |||||||
\(968\) | −149.584 | − | 84.8727i | −0.154529 | − | 0.0876784i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 288.556i | − | 0.297174i | −0.988899 | − | 0.148587i | \(-0.952527\pi\) | ||
0.988899 | − | 0.148587i | \(-0.0474725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 670.739i | − | 0.689352i | ||||||
\(974\) | −360.171 | − | 62.5799i | −0.369786 | − | 0.0642504i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −373.846 | − | 307.376i | −0.383039 | − | 0.314934i | ||||
\(977\) | − | 1781.05i | − | 1.82298i | −0.411322 | − | 0.911490i | \(-0.634933\pi\) | ||
0.411322 | − | 0.911490i | \(-0.365067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 872.131i | 0.890839i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 141.545 | − | 814.644i | 0.144139 | − | 0.829576i | ||||
\(983\) | −1179.28 | −1.19968 | −0.599838 | − | 0.800122i | \(-0.704768\pi\) | ||||
−0.599838 | + | 0.800122i | \(0.704768\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 197.802 | − | 1138.43i | 0.200611 | − | 1.15459i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −650.337 | − | 233.027i | −0.658236 | − | 0.235857i | ||||
\(989\) | −385.502 | −0.389789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 363.373i | − | 0.366673i | −0.983050 | − | 0.183337i | \(-0.941310\pi\) | ||
0.983050 | − | 0.183337i | \(-0.0586898\pi\) | |||||||
\(992\) | −854.942 | + | 735.788i | −0.861837 | + | 0.741722i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 45.6265 | − | 262.598i | 0.0459019 | − | 0.264183i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 412.630i | 0.413872i | 0.978354 | + | 0.206936i | \(0.0663492\pi\) | ||||
−0.978354 | + | 0.206936i | \(0.933651\pi\) | |||||||
\(998\) | −31.7883 | + | 182.954i | −0.0318520 | + | 0.183321i | ||||
\(999\) | 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.f.i.199.2 | 16 | ||
3.2 | odd | 2 | inner | 900.3.f.i.199.16 | 16 | ||
4.3 | odd | 2 | inner | 900.3.f.i.199.13 | 16 | ||
5.2 | odd | 4 | 900.3.c.o.451.5 | 8 | |||
5.3 | odd | 4 | 180.3.c.c.91.4 | yes | 8 | ||
5.4 | even | 2 | inner | 900.3.f.i.199.15 | 16 | ||
12.11 | even | 2 | inner | 900.3.f.i.199.3 | 16 | ||
15.2 | even | 4 | 900.3.c.o.451.4 | 8 | |||
15.8 | even | 4 | 180.3.c.c.91.5 | yes | 8 | ||
15.14 | odd | 2 | inner | 900.3.f.i.199.1 | 16 | ||
20.3 | even | 4 | 180.3.c.c.91.3 | ✓ | 8 | ||
20.7 | even | 4 | 900.3.c.o.451.6 | 8 | |||
20.19 | odd | 2 | inner | 900.3.f.i.199.4 | 16 | ||
40.3 | even | 4 | 2880.3.e.i.2431.4 | 8 | |||
40.13 | odd | 4 | 2880.3.e.i.2431.1 | 8 | |||
60.23 | odd | 4 | 180.3.c.c.91.6 | yes | 8 | ||
60.47 | odd | 4 | 900.3.c.o.451.3 | 8 | |||
60.59 | even | 2 | inner | 900.3.f.i.199.14 | 16 | ||
120.53 | even | 4 | 2880.3.e.i.2431.5 | 8 | |||
120.83 | odd | 4 | 2880.3.e.i.2431.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.c.c.91.3 | ✓ | 8 | 20.3 | even | 4 | ||
180.3.c.c.91.4 | yes | 8 | 5.3 | odd | 4 | ||
180.3.c.c.91.5 | yes | 8 | 15.8 | even | 4 | ||
180.3.c.c.91.6 | yes | 8 | 60.23 | odd | 4 | ||
900.3.c.o.451.3 | 8 | 60.47 | odd | 4 | |||
900.3.c.o.451.4 | 8 | 15.2 | even | 4 | |||
900.3.c.o.451.5 | 8 | 5.2 | odd | 4 | |||
900.3.c.o.451.6 | 8 | 20.7 | even | 4 | |||
900.3.f.i.199.1 | 16 | 15.14 | odd | 2 | inner | ||
900.3.f.i.199.2 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.i.199.3 | 16 | 12.11 | even | 2 | inner | ||
900.3.f.i.199.4 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.i.199.13 | 16 | 4.3 | odd | 2 | inner | ||
900.3.f.i.199.14 | 16 | 60.59 | even | 2 | inner | ||
900.3.f.i.199.15 | 16 | 5.4 | even | 2 | inner | ||
900.3.f.i.199.16 | 16 | 3.2 | odd | 2 | inner | ||
2880.3.e.i.2431.1 | 8 | 40.13 | odd | 4 | |||
2880.3.e.i.2431.4 | 8 | 40.3 | even | 4 | |||
2880.3.e.i.2431.5 | 8 | 120.53 | even | 4 | |||
2880.3.e.i.2431.8 | 8 | 120.83 | odd | 4 |