Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 10.0.29471584693248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.3 | ||
Root | \(-1.31611 + 1.12599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1601 |
Dual form | 2100.2.bi.k.101.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.317079 | − | 1.70278i | 0.183066 | − | 0.983101i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73439 | − | 1.99797i | 0.655538 | − | 0.755162i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79892 | − | 1.07983i | −0.932974 | − | 0.359944i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38064 | + | 1.95181i | −1.01930 | + | 0.588494i | −0.913902 | − | 0.405936i | \(-0.866946\pi\) |
−0.105400 | + | 0.994430i | \(0.533612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.06329i | 1.68166i | 0.541303 | + | 0.840828i | \(0.317931\pi\) | ||||
−0.541303 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.53296 | − | 2.65516i | −0.371797 | − | 0.643971i | 0.618045 | − | 0.786143i | \(-0.287925\pi\) |
−0.989842 | + | 0.142171i | \(0.954592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94930 | − | 1.70278i | −0.676616 | − | 0.390645i | 0.121963 | − | 0.992535i | \(-0.461081\pi\) |
−0.798579 | + | 0.601890i | \(0.794415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.85217 | − | 3.58680i | −0.622394 | − | 0.782704i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.48871 | − | 1.43686i | −0.518933 | − | 0.299606i | 0.217565 | − | 0.976046i | \(-0.430189\pi\) |
−0.736498 | + | 0.676440i | \(0.763522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.72620 | + | 4.42356i | −0.524657 | + | 0.851314i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.97997i | 1.48184i | 0.671591 | + | 0.740922i | \(0.265611\pi\) | ||||
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.63161 | + | 3.25141i | −1.01147 | + | 0.583971i | −0.911621 | − | 0.411032i | \(-0.865168\pi\) |
−0.0998461 | + | 0.995003i | \(0.531835\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.25158 | + | 6.37537i | 0.391950 | + | 1.10981i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0654987 | − | 0.113447i | 0.0107679 | − | 0.0186506i | −0.860591 | − | 0.509296i | \(-0.829906\pi\) |
0.871359 | + | 0.490646i | \(0.163239\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.3245 | + | 1.92254i | 1.65324 | + | 0.307853i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.3654 | −1.93116 | −0.965579 | − | 0.260108i | \(-0.916242\pi\) | ||||
−0.965579 | + | 0.260108i | \(0.916242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.43247 | −0.675945 | −0.337972 | − | 0.941156i | \(-0.609741\pi\) | ||||
−0.337972 | + | 0.941156i | \(0.609741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.02960 | − | 8.71153i | 0.733643 | − | 1.27071i | −0.221674 | − | 0.975121i | \(-0.571152\pi\) |
0.955316 | − | 0.295586i | \(-0.0955148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.983778 | − | 6.93053i | −0.140540 | − | 0.990075i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00723 | + | 1.76839i | −0.701152 | + | 0.247625i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.64119 | + | 2.67959i | −0.637516 | + | 0.368070i | −0.783657 | − | 0.621194i | \(-0.786648\pi\) |
0.146141 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.83462 | + | 4.48210i | −0.507908 | + | 0.593668i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.28860 | + | 2.23193i | 0.167762 | + | 0.290572i | 0.937633 | − | 0.347628i | \(-0.113013\pi\) |
−0.769871 | + | 0.638200i | \(0.779679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44930 | + | 4.30086i | 0.953785 | + | 0.550668i | 0.894255 | − | 0.447558i | \(-0.147706\pi\) |
0.0595306 | + | 0.998226i | \(0.481040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.01190 | + | 3.71931i | −0.883416 | + | 0.468589i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.99884 | − | 13.8544i | −0.977213 | − | 1.69258i | −0.672429 | − | 0.740162i | \(-0.734749\pi\) |
−0.304785 | − | 0.952421i | \(-0.598585\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.23578 | + | 3.78214i | −0.389542 | + | 0.455316i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.63245i | 0.431093i | 0.976494 | + | 0.215547i | \(0.0691533\pi\) | ||||
−0.976494 | + | 0.215547i | \(0.930847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.72468 | − | 3.88250i | 0.787064 | − | 0.454412i | −0.0518638 | − | 0.998654i | \(-0.516516\pi\) |
0.838928 | + | 0.544242i | \(0.183183\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.96368 | + | 10.1396i | −0.223783 | + | 1.15552i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.22311 | + | 2.11848i | −0.137610 | + | 0.238348i | −0.926591 | − | 0.376069i | \(-0.877275\pi\) |
0.788981 | + | 0.614417i | \(0.210609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.66792 | + | 6.04473i | 0.740880 | + | 0.671637i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.63648 | −0.838213 | −0.419106 | − | 0.907937i | \(-0.637657\pi\) | ||||
−0.419106 | + | 0.907937i | \(0.637657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.5881 | + | 2.53028i | 1.45680 | + | 0.271275i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.11874 | − | 7.13387i | 0.436586 | − | 0.756189i | −0.560838 | − | 0.827926i | \(-0.689521\pi\) |
0.997424 | + | 0.0717367i | \(0.0228541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1143 | + | 10.5161i | 1.26992 | + | 1.10239i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.75077 | + | 10.6203i | 0.388937 | + | 1.10128i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74985i | 0.583809i | 0.956447 | + | 0.291904i | \(0.0942889\pi\) | ||||
−0.956447 | + | 0.291904i | \(0.905711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.5698 | − | 1.81245i | 1.16281 | − | 0.182158i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.54502 | + | 7.87220i | 0.452246 | + | 0.783313i | 0.998525 | − | 0.0542901i | \(-0.0172896\pi\) |
−0.546279 | + | 0.837603i | \(0.683956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.853234 | + | 0.492615i | 0.0840717 | + | 0.0485388i | 0.541446 | − | 0.840735i | \(-0.317877\pi\) |
−0.457375 | + | 0.889274i | \(0.651210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.11849 | − | 0.645758i | −0.108128 | − | 0.0624278i | 0.444961 | − | 0.895550i | \(-0.353218\pi\) |
−0.553089 | + | 0.833122i | \(0.686551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.68547 | + | 6.38342i | 0.353004 | + | 0.611421i | 0.986774 | − | 0.162101i | \(-0.0518269\pi\) |
−0.633770 | + | 0.773521i | \(0.718494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.172407 | − | 0.147502i | −0.0163642 | − | 0.0140002i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.52778i | 0.425938i | 0.977059 | + | 0.212969i | \(0.0683133\pi\) | ||||
−0.977059 | + | 0.212969i | \(0.931687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.54734 | − | 16.9707i | 0.605302 | − | 1.56894i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.96368 | − | 1.54228i | −0.730030 | − | 0.141381i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.11916 | − | 3.67050i | 0.192651 | − | 0.333681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.92083 | + | 21.0556i | −0.353529 | + | 1.89852i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.700855 | 0.0621908 | 0.0310954 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310954 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.40544 | + | 7.54752i | −0.123742 | + | 0.664522i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.66028 | − | 4.60774i | 0.232430 | − | 0.402580i | −0.726093 | − | 0.687597i | \(-0.758666\pi\) |
0.958523 | + | 0.285016i | \(0.0919991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.51735 | + | 2.93933i | −0.738548 | + | 0.254873i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.39919 | − | 1.96252i | 0.290412 | − | 0.167670i | −0.347715 | − | 0.937600i | \(-0.613042\pi\) |
0.638128 | + | 0.769930i | \(0.279709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.1726i | − | 1.37174i | −0.727724 | − | 0.685870i | \(-0.759422\pi\) | ||
0.727724 | − | 0.685870i | \(-0.240578\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.2390 | − | 11.3265i | −1.11493 | − | 0.953868i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.8344 | − | 20.4978i | −0.989645 | − | 1.71411i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1131 | − | 0.522368i | −0.999071 | − | 0.0430841i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.4366 | − | 10.0670i | −1.42846 | − | 0.824721i | −0.431459 | − | 0.902132i | \(-0.642001\pi\) |
−0.996999 | + | 0.0774116i | \(0.975334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.38980 | − | 4.13926i | −0.194479 | − | 0.336848i | 0.752250 | − | 0.658877i | \(-0.228968\pi\) |
−0.946730 | + | 0.322029i | \(0.895635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.42350 | + | 9.08693i | 0.115083 | + | 0.734635i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.62784 | + | 3.82658i | −0.528959 | + | 0.305395i | −0.740592 | − | 0.671955i | \(-0.765455\pi\) |
0.211633 | + | 0.977349i | \(0.432122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.09113 | + | 8.75257i | 0.245143 | + | 0.694124i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.18721 | + | 2.48030i | −0.566431 | + | 0.195475i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.23749 | + | 7.33954i | −0.331906 | + | 0.574877i | −0.982885 | − | 0.184218i | \(-0.941025\pi\) |
0.650980 | + | 0.759095i | \(0.274358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.5669 | 1.59152 | 0.795759 | − | 0.605614i | \(-0.207072\pi\) | ||||
0.795759 | + | 0.605614i | \(0.207072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.7635 | −1.82796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.41615 | + | 7.95070i | 0.490655 | + | 0.608005i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.30340 | + | 14.3819i | −0.631296 | + | 1.09344i | 0.355991 | + | 0.934489i | \(0.384143\pi\) |
−0.987287 | + | 0.158948i | \(0.949190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.20907 | − | 1.48651i | 0.316373 | − | 0.111733i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.336240 | + | 0.194128i | −0.0251318 | + | 0.0145098i | −0.512513 | − | 0.858679i | \(-0.671285\pi\) |
0.487381 | + | 0.873189i | \(0.337952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6789i | 1.53705i | 0.639820 | + | 0.768524i | \(0.279009\pi\) | ||||
−0.639820 | + | 0.768524i | \(0.720991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.68543 | − | 11.3208i | 0.715968 | − | 0.836859i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3648 | + | 5.98410i | 0.757947 | + | 0.437601i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.10985 | + | 13.1190i | 0.298947 | + | 0.954270i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2933 | + | 8.82961i | 1.10659 | + | 0.638888i | 0.937943 | − | 0.346789i | \(-0.112728\pi\) |
0.168644 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.6903 | − | 18.5161i | −0.769505 | − | 1.33282i | −0.937832 | − | 0.347090i | \(-0.887170\pi\) |
0.168327 | − | 0.985731i | \(-0.446163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.5070i | − | 1.60356i | −0.597619 | − | 0.801780i | \(-0.703886\pi\) | ||
0.597619 | − | 0.801780i | \(-0.296114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.48532 | + | 4.89900i | −0.601509 | + | 0.347281i | −0.769635 | − | 0.638484i | \(-0.779562\pi\) |
0.168126 | + | 0.985765i | \(0.446228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.1272 | + | 9.22732i | −1.84287 | + | 0.650845i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.9438 | + | 13.8404i | 1.11903 | + | 0.971405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.41415 | + | 6.70905i | 0.376309 | + | 0.466311i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2940 | 0.919568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.96291 | −0.135132 | −0.0675660 | − | 0.997715i | \(-0.521523\pi\) | ||||
−0.0675660 | + | 0.997715i | \(0.521523\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.18527 | + | 1.15178i | 0.423808 | + | 0.0789184i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.27118 | + | 16.8910i | −0.222062 | + | 1.14664i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.47878 | − | 12.6817i | −0.302648 | − | 0.856951i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0990 | − | 9.29478i | 1.08294 | − | 0.625234i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.78864i | − | 0.119776i | −0.998205 | − | 0.0598882i | \(-0.980926\pi\) | ||
0.998205 | − | 0.0598882i | \(-0.0190744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7981 | + | 23.8990i | 0.915813 | + | 1.58623i | 0.805707 | + | 0.592315i | \(0.201786\pi\) |
0.110106 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.37613 | − | 4.83596i | −0.553510 | − | 0.319569i | 0.197026 | − | 0.980398i | \(-0.436872\pi\) |
−0.750537 | + | 0.660829i | \(0.770205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.6429 | + | 6.55879i | 1.09502 | + | 0.431537i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.516767 | − | 0.298355i | −0.0338545 | − | 0.0195459i | 0.482977 | − | 0.875633i | \(-0.339555\pi\) |
−0.516832 | + | 0.856087i | \(0.672889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.21949 | + | 2.75441i | 0.209128 | + | 0.178918i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.90983i | 0.576329i | 0.957581 | + | 0.288165i | \(0.0930450\pi\) | ||||
−0.957581 | + | 0.288165i | \(0.906955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.82543 | − | 1.05391i | 0.117586 | − | 0.0678886i | −0.440053 | − | 0.897972i | \(-0.645040\pi\) |
0.557640 | + | 0.830083i | \(0.311707\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.4071 | − | 9.43735i | 0.795917 | − | 0.605406i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3245 | − | 17.8825i | 0.656930 | − | 1.13784i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.42137 | + | 13.0033i | −0.153448 | + | 0.824048i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.8229 | −1.88241 | −0.941204 | − | 0.337840i | \(-0.890304\pi\) | ||||
−0.941204 | + | 0.337840i | \(0.890304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.2179 | 0.705266 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.78489 | + | 11.7518i | −0.423230 | + | 0.733055i | −0.996253 | − | 0.0864836i | \(-0.972437\pi\) |
0.573024 | + | 0.819539i | \(0.305770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.113064 | − | 0.327626i | −0.00702543 | − | 0.0203577i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.61703 | − | 22.3353i | 0.533381 | − | 1.38252i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5291 | − | 6.07897i | 0.649252 | − | 0.374846i | −0.138918 | − | 0.990304i | \(-0.544362\pi\) |
0.788169 | + | 0.615458i | \(0.211029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.8415 | − | 9.27532i | −0.663486 | − | 0.567640i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2201 | + | 19.4338i | 0.684101 | + | 1.18490i | 0.973718 | + | 0.227756i | \(0.0731388\pi\) |
−0.289617 | + | 0.957143i | \(0.593528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.19179 | − | 4.15218i | −0.436870 | − | 0.252227i | 0.265399 | − | 0.964139i | \(-0.414496\pi\) |
−0.702269 | + | 0.711912i | \(0.747830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.7478 | − | 17.2935i | 1.31624 | − | 1.04665i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.02848 | + | 5.24547i | 0.181963 | + | 0.315170i | 0.942549 | − | 0.334068i | \(-0.108421\pi\) |
−0.760586 | + | 0.649238i | \(0.775088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.2734 | − | 3.01925i | 1.15387 | − | 0.180758i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.5771i | − | 1.04856i | −0.851545 | − | 0.524282i | \(-0.824334\pi\) | ||
0.851545 | − | 0.524282i | \(-0.175666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.10845 | + | 4.10407i | −0.422554 | + | 0.243961i | −0.696169 | − | 0.717878i | \(-0.745114\pi\) |
0.273616 | + | 0.961839i | \(0.411780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.4465 | + | 24.7058i | −1.26595 | + | 1.45834i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.80008 | − | 6.58193i | 0.223534 | − | 0.387172i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.79073 | + | 1.82316i | 0.573943 | + | 0.106875i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.88610 | 0.227028 | 0.113514 | − | 0.993536i | \(-0.463789\pi\) | ||||
0.113514 | + | 0.993536i | \(0.463789\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.582334 | − | 20.2755i | 0.0337905 | − | 1.17650i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.71210 | − | 15.0898i | 0.503834 | − | 0.872666i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.68763 | + | 8.85594i | −0.443108 | + | 0.510448i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.8458 | − | 5.24305i | 0.852866 | − | 0.301206i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.119756i | 0.00683482i | 0.999994 | + | 0.00341741i | \(0.00108780\pi\) | ||||
−0.999994 | + | 0.00341741i | \(0.998912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.10936 | − | 1.29667i | 0.0631092 | − | 0.0737651i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.57207 | − | 11.3832i | −0.372668 | − | 0.645480i | 0.617307 | − | 0.786722i | \(-0.288224\pi\) |
−0.989975 | + | 0.141243i | \(0.954890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1517 | − | 11.6346i | −1.13904 | − | 0.657625i | −0.192847 | − | 0.981229i | \(-0.561772\pi\) |
−0.946192 | + | 0.323604i | \(0.895105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.0933 | − | 17.3744i | −1.69021 | − | 0.975841i | −0.954344 | − | 0.298709i | \(-0.903444\pi\) |
−0.735861 | − | 0.677132i | \(-0.763223\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5754 | − | 26.9774i | −0.872056 | − | 1.51045i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.45423 | + | 1.69978i | −0.0811674 | + | 0.0948725i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4412i | 0.580962i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0381 | − | 4.25149i | 0.665711 | − | 0.235108i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.68208 | − | 25.1582i | −0.478659 | − | 1.38702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8024 | − | 22.1744i | 0.703684 | − | 1.21882i | −0.263481 | − | 0.964665i | \(-0.584871\pi\) |
0.967165 | − | 0.254151i | \(-0.0817961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.305829 | + | 0.246802i | −0.0167593 | + | 0.0135247i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5502 | −1.44628 | −0.723140 | − | 0.690702i | \(-0.757302\pi\) | ||||
−0.723140 | + | 0.690702i | \(0.757302\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.70982 | + | 1.43567i | 0.418740 | + | 0.0779747i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6923 | − | 21.9837i | 0.687327 | − | 1.19048i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5532 | − | 10.0547i | −0.839796 | − | 0.542902i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6519 | − | 9.61397i | 0.893920 | − | 0.516105i | 0.0186975 | − | 0.999825i | \(-0.494048\pi\) |
0.875223 | + | 0.483720i | \(0.160715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.40475i | − | 0.0751943i | −0.999293 | − | 0.0375972i | \(-0.988030\pi\) | ||
0.999293 | − | 0.0375972i | \(-0.0119704\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.8213 | − | 16.5297i | −1.43162 | − | 0.882292i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.43705 | + | 16.3454i | 0.502283 | + | 0.869980i | 0.999997 | + | 0.00263867i | \(0.000839917\pi\) |
−0.497713 | + | 0.867342i | \(0.665827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.15128 | + | 13.0714i | −0.272635 | + | 0.691811i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1592 | + | 11.0615i | 1.01118 | + | 0.583806i | 0.911537 | − | 0.411217i | \(-0.134896\pi\) |
0.0996440 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.70108 | − | 6.41046i | −0.194794 | − | 0.337392i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.57811 | − | 4.77230i | −0.292775 | − | 0.250481i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3631 | − | 6.56047i | 0.593147 | − | 0.342454i | −0.173194 | − | 0.984888i | \(-0.555409\pi\) |
0.766341 | + | 0.642434i | \(0.222075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34.6099 | + | 13.3526i | 1.80172 | + | 0.695109i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.69589 | + | 13.9204i | −0.139964 | + | 0.722712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.38003 | − | 12.7826i | 0.382123 | − | 0.661857i | −0.609242 | − | 0.792984i | \(-0.708526\pi\) |
0.991366 | + | 0.131127i | \(0.0418596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.3849 | −2.49195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9980 | 1.54089 | 0.770447 | − | 0.637505i | \(-0.220033\pi\) | ||||
0.770447 | + | 0.637505i | \(0.220033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.222226 | − | 1.19340i | 0.0113850 | − | 0.0611398i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.72052 | − | 13.3723i | 0.394500 | − | 0.683294i | −0.598537 | − | 0.801095i | \(-0.704251\pi\) |
0.993037 | + | 0.117801i | \(0.0375844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4061 | + | 4.78632i | 0.630639 | + | 0.243302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.53666 | + | 4.35129i | −0.382124 | + | 0.220619i | −0.678742 | − | 0.734377i | \(-0.737475\pi\) |
0.296618 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.81059i | 0.445570i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.00245 | − | 5.99089i | −0.353227 | − | 0.302201i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3904 | − | 13.5044i | −1.17393 | − | 0.677768i | −0.219327 | − | 0.975651i | \(-0.570386\pi\) |
−0.954602 | + | 0.297883i | \(0.903719\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.30437 | + | 15.4352i | 0.115363 | + | 0.772725i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.30215 | + | 2.48385i | 0.214839 | + | 0.124037i | 0.603558 | − | 0.797319i | \(-0.293749\pi\) |
−0.388719 | + | 0.921356i | \(0.627082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7143 | − | 34.1461i | −0.982037 | − | 1.70094i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.511365i | 0.0253474i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00387 | + | 4.04369i | −0.346319 | + | 0.199947i | −0.663063 | − | 0.748564i | \(-0.730744\pi\) |
0.316744 | + | 0.948511i | \(0.397410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.26393 | − | 6.41035i | −0.111672 | − | 0.316199i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.69427 | + | 1.29644i | 0.329403 | + | 0.0637937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.5383 | − | 5.12799i | −1.34856 | − | 0.251119i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.60294 | −0.371428 | −0.185714 | − | 0.982604i | \(-0.559460\pi\) | ||||
−0.185714 | + | 0.982604i | \(0.559460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.43892 | −0.216340 | −0.108170 | − | 0.994132i | \(-0.534499\pi\) | ||||
−0.108170 | + | 0.994132i | \(0.534499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.4844 | + | 18.9517i | −1.14185 | + | 0.921466i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5130 | − | 7.42413i | 1.04109 | − | 0.359279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.6558 | + | 13.6520i | −1.86632 | + | 0.659125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.24065 | − | 2.44834i | 0.204265 | − | 0.117932i | −0.394378 | − | 0.918948i | \(-0.629040\pi\) |
0.598643 | + | 0.801016i | \(0.295707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.6390i | − | 0.895732i | −0.894101 | − | 0.447866i | \(-0.852184\pi\) | ||
0.894101 | − | 0.447866i | \(-0.147816\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.89331 | + | 8.47547i | 0.234079 | + | 0.405437i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.87038 | − | 1.65722i | −0.136996 | − | 0.0790946i | 0.429936 | − | 0.902860i | \(-0.358536\pi\) |
−0.566932 | + | 0.823765i | \(0.691870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.73029 | + | 20.4603i | −0.225252 | + | 0.974301i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.707683 | + | 0.408581i | 0.0336231 | + | 0.0194123i | 0.516717 | − | 0.856156i | \(-0.327154\pi\) |
−0.483094 | + | 0.875568i | \(0.660487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.6707 | + | 26.4986i | −1.07229 | + | 1.25334i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.17892i | − | 0.244408i | −0.992505 | − | 0.122204i | \(-0.961004\pi\) | ||
0.992505 | − | 0.122204i | \(-0.0389962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.8032 | − | 24.1351i | 1.96843 | − | 1.13648i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.80601 | + | 2.75684i | −0.366758 | + | 0.129528i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.01889 | − | 10.4250i | 0.281552 | − | 0.487662i | −0.690215 | − | 0.723604i | \(-0.742484\pi\) |
0.971767 | + | 0.235942i | \(0.0758175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.9244 | + | 0.457366i | 0.743287 | + | 0.0213480i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.0451 | 1.07332 | 0.536658 | − | 0.843800i | \(-0.319686\pi\) | ||||
0.536658 | + | 0.843800i | \(0.319686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8549 | −1.29453 | −0.647263 | − | 0.762267i | \(-0.724086\pi\) | ||||
−0.647263 | + | 0.762267i | \(0.724086\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.10822 | − | 1.91950i | 0.0512825 | − | 0.0888240i | −0.839245 | − | 0.543754i | \(-0.817002\pi\) |
0.890527 | + | 0.454930i | \(0.150336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −41.5538 | − | 8.04748i | −1.91878 | − | 0.371598i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.41428 | + | 12.4991i | 0.203399 | + | 0.575927i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9846 | − | 8.65135i | 0.688992 | − | 0.397790i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.8838 | − | 2.48826i | 0.727271 | − | 0.113930i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.53276 | − | 6.11892i | −0.161416 | − | 0.279581i | 0.773961 | − | 0.633234i | \(-0.218273\pi\) |
−0.935377 | + | 0.353653i | \(0.884939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.687863 | + | 0.397138i | 0.0313638 | + | 0.0181079i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.94450 | + | 13.0247i | 0.0884777 | + | 0.592644i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.62036 | + | 8.00270i | 0.209368 | + | 0.362637i | 0.951516 | − | 0.307600i | \(-0.0995259\pi\) |
−0.742147 | + | 0.670237i | \(0.766193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.1540 | + | 9.54273i | 0.504402 | + | 0.431537i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.0713i | − | 0.635031i | −0.948253 | − | 0.317515i | \(-0.897152\pi\) | ||
0.948253 | − | 0.317515i | \(-0.102848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.1881 | − | 12.2330i | 0.954265 | − | 0.550945i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.25754 | + | 6.30010i | 0.325545 | + | 0.282598i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.50255 | + | 11.2627i | −0.291094 | + | 0.504190i | −0.974069 | − | 0.226252i | \(-0.927353\pi\) |
0.682975 | + | 0.730442i | \(0.260686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.52135 | − | 35.0210i | 0.291352 | − | 1.56462i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.580122 | 0.0258664 | 0.0129332 | − | 0.999916i | \(-0.495883\pi\) | ||||
0.0129332 | + | 0.999916i | \(0.495883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.53492 | + | 40.4641i | −0.334638 | + | 1.79707i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.86251 | − | 17.0824i | 0.437148 | − | 0.757163i | −0.560320 | − | 0.828276i | \(-0.689322\pi\) |
0.997468 | + | 0.0711133i | \(0.0226552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.90611 | − | 20.1695i | 0.172796 | − | 0.892245i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5727 | − | 8.40429i | 0.687553 | − | 0.371058i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.2674i | 1.72698i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.8564 | + | 18.6991i | 0.959390 | + | 0.820799i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0051 | + | 31.1857i | 0.788818 | + | 1.36627i | 0.926692 | + | 0.375822i | \(0.122640\pi\) |
−0.137874 | + | 0.990450i | \(0.544027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5387 | + | 10.7033i | 0.810640 | + | 0.468023i | 0.847178 | − | 0.531309i | \(-0.178300\pi\) |
−0.0365378 | + | 0.999332i | \(0.511633\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.2660 | + | 9.96855i | 0.752121 | + | 0.434237i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.37087 | − | 12.7667i | −0.320472 | − | 0.555075i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.19659 | − | 7.63846i | −0.0519277 | − | 0.331481i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 74.9754i | − | 3.24754i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.223943 | + | 0.634097i | 0.00966387 | + | 0.0273633i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8529 | + | 21.5095i | 0.725906 | + | 0.926479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.32759 | + | 4.03151i | −0.100071 | + | 0.173328i | −0.911714 | − | 0.410826i | \(-0.865240\pi\) |
0.811643 | + | 0.584154i | \(0.198574\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.2116 | + | 6.55684i | 1.51107 | + | 0.281381i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34057 | −0.313860 | −0.156930 | − | 0.987610i | \(-0.550160\pi\) | ||||
−0.156930 | + | 0.987610i | \(0.550160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.2058 | − | 20.0818i | −0.691647 | − | 0.857069i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5881 | − | 23.5353i | 0.578874 | − | 1.00264i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.11132 | + | 6.11800i | 0.0897825 | + | 0.260164i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.9154 | − | 16.1169i | 1.18281 | − | 0.682897i | 0.226149 | − | 0.974093i | \(-0.427386\pi\) |
0.956663 | + | 0.291196i | \(0.0940531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 26.8753i | − | 1.13671i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4761 | − | 15.7515i | 0.568960 | − | 0.665028i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4830 | + | 19.8892i | 0.483952 | + | 0.838230i | 0.999830 | − | 0.0184324i | \(-0.00586756\pi\) |
−0.515878 | + | 0.856662i | \(0.672534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.6420 | − | 2.83839i | 0.992870 | − | 0.119201i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.0347 | − | 9.25765i | −0.672211 | − | 0.388101i | 0.124703 | − | 0.992194i | \(-0.460202\pi\) |
−0.796914 | + | 0.604093i | \(0.793535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9408 | − | 38.0025i | −0.918193 | − | 1.59036i | −0.802158 | − | 0.597112i | \(-0.796315\pi\) |
−0.116035 | − | 0.993245i | \(-0.537019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.8841 | − | 23.2415i | 0.830670 | − | 0.970928i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6663 | + | 8.46761i | −0.610568 | + | 0.352511i | −0.773188 | − | 0.634177i | \(-0.781339\pi\) |
0.162620 | + | 0.986689i | \(0.448006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.9186 | + | 12.3321i | −1.45117 | + | 0.512507i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.2446 | + | 15.2575i | −0.549480 | + | 0.632987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4601 | − | 18.1175i | 0.433214 | − | 0.750349i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.3959 | −0.635456 | −0.317728 | − | 0.948182i | \(-0.602920\pi\) | ||||
−0.317728 | + | 0.948182i | \(0.602920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1458 | 0.912500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38.3246 | − | 7.13651i | −1.57646 | − | 0.293557i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.37500 | + | 4.11363i | −0.0975297 | + | 0.168926i | −0.910662 | − | 0.413153i | \(-0.864427\pi\) |
0.813132 | + | 0.582079i | \(0.197761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65141 | + | 16.0020i | 0.231297 | + | 0.654919i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.2300 | + | 11.1024i | −0.785716 | + | 0.453634i | −0.838452 | − | 0.544975i | \(-0.816539\pi\) |
0.0527360 | + | 0.998608i | \(0.483206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.5924i | 1.73738i | 0.495357 | + | 0.868689i | \(0.335037\pi\) | ||||
−0.495357 | + | 0.868689i | \(0.664963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.42770 | + | 47.4148i | 0.302479 | + | 1.93088i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.2862 | − | 9.40283i | −0.661035 | − | 0.381649i | 0.131636 | − | 0.991298i | \(-0.457977\pi\) |
−0.792671 | + | 0.609649i | \(0.791310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.6226 | − | 22.7602i | 1.15985 | − | 0.922290i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.8205 | + | 30.4960i | 2.13689 | + | 1.23373i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.74783 | + | 13.4196i | 0.312932 | + | 0.542014i | 0.978996 | − | 0.203881i | \(-0.0653555\pi\) |
−0.666064 | + | 0.745895i | \(0.732022\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.7219i | − | 0.713459i | −0.934208 | − | 0.356729i | \(-0.883892\pi\) | ||
0.934208 | − | 0.356729i | \(-0.116108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.96204 | − | 3.44219i | 0.239635 | − | 0.138353i | −0.375374 | − | 0.926873i | \(-0.622486\pi\) |
0.615009 | + | 0.788520i | \(0.289152\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.1408 | − | 7.09180i | 0.527320 | − | 0.284584i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.10976 | − | 20.6021i | −0.284847 | − | 0.825404i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.21527 | − | 22.6368i | 0.168341 | − | 0.904028i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.401627 | −0.0160139 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.6754 | −1.97755 | −0.988774 | − | 0.149421i | \(-0.952259\pi\) | ||||
−0.988774 | + | 0.149421i | \(0.952259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.622396 | + | 3.34240i | −0.0247380 | + | 0.132848i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.0218 | − | 5.96493i | 1.66496 | − | 0.236339i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.92244 | − | 10.1670i | 0.155169 | − | 0.402199i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3007 | + | 13.4527i | −0.920324 | + | 0.531349i | −0.883738 | − | 0.467981i | \(-0.844981\pi\) |
−0.0365856 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9638i | 0.550679i | 0.961347 | + | 0.275339i | \(0.0887902\pi\) | ||||
−0.961347 | + | 0.275339i | \(0.911210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.3377 | − | 26.5656i | −0.602985 | − | 1.04440i | −0.992366 | − | 0.123324i | \(-0.960644\pi\) |
0.389381 | − | 0.921077i | \(-0.372689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.71262 | − | 5.03023i | −0.342000 | − | 0.197454i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.7245 | + | 10.9259i | 1.08661 | + | 0.428220i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3602 | + | 6.55879i | 0.444557 | + | 0.256665i | 0.705529 | − | 0.708681i | \(-0.250710\pi\) |
−0.260971 | + | 0.965347i | \(0.584043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.0143 | + | 3.60527i | −0.897873 | + | 0.140655i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1306i | 1.44640i | 0.690638 | + | 0.723201i | \(0.257330\pi\) | ||||
−0.690638 | + | 0.723201i | \(0.742670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.41297 | − | 2.54783i | 0.171645 | − | 0.0990992i | −0.411716 | − | 0.911312i | \(-0.635071\pi\) |
0.583361 | + | 0.812213i | \(0.301737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.7223 | − | 30.3603i | −0.416420 | − | 1.17910i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4661 | − | 19.8599i | 0.443969 | − | 0.768977i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.04567 | − | 0.567142i | −0.117752 | − | 0.0219270i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.5779 | −1.29626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0339 | −1.11918 | −0.559588 | − | 0.828771i | \(-0.689040\pi\) | ||||
−0.559588 | + | 0.828771i | \(0.689040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4783 | − | 21.6131i | 0.479581 | − | 0.830658i | −0.520145 | − | 0.854078i | \(-0.674122\pi\) |
0.999726 | + | 0.0234197i | \(0.00745540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4880 | + | 9.97249i | 0.440870 | + | 0.382709i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.0699 | − | 15.9173i | 1.72708 | − | 0.609951i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.3107 | − | 16.9226i | 1.12154 | − | 0.647524i | 0.179749 | − | 0.983712i | \(-0.442471\pi\) |
0.941795 | + | 0.336189i | \(0.109138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.8905 | + | 12.7293i | −0.415498 | + | 0.485654i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.2472 | − | 28.1409i | −0.618967 | − | 1.07208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.82503 | + | 5.67249i | 0.373762 | + | 0.215792i | 0.675101 | − | 0.737726i | \(-0.264100\pi\) |
−0.301339 | + | 0.953517i | \(0.597434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.4453 | − | 26.2596i | 0.624706 | − | 0.997519i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9557 | + | 32.8323i | 0.717999 | + | 1.24361i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.671890 | + | 0.785338i | −0.0254132 | + | 0.0297042i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.1947i | − | 0.876052i | −0.898962 | − | 0.438026i | \(-0.855678\pi\) | ||
0.898962 | − | 0.438026i | \(-0.144322\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.386351 | + | 0.223060i | −0.0145715 | + | 0.00841285i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.6113 | + | 4.57266i | 0.887993 | + | 0.171972i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.29490 | − | 12.6351i | 0.273966 | − | 0.474522i | −0.695908 | − | 0.718131i | \(-0.744998\pi\) |
0.969874 | + | 0.243609i | \(0.0783312\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.71098 | − | 4.60871i | 0.214178 | − | 0.172840i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.6873 | 0.699844 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.1715 | + | 2.82512i | 0.566590 | + | 0.105506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.35171 | + | 16.1976i | −0.348760 | + | 0.604070i | −0.986029 | − | 0.166571i | \(-0.946730\pi\) |
0.637270 | + | 0.770641i | \(0.280064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.46407 | − | 0.850351i | 0.0917668 | − | 0.0316687i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.21578 | − | 3.44249i | −0.0452153 | − | 0.128027i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.0483i | − | 0.854815i | −0.904059 | − | 0.427407i | \(-0.859427\pi\) | ||
0.904059 | − | 0.427407i | \(-0.140573\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.1357 | − | 24.1190i | −0.449470 | − | 0.893295i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.79479 | + | 11.7689i | 0.251314 | + | 0.435289i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4109 | − | 8.89746i | −0.569213 | − | 0.328635i | 0.187622 | − | 0.982241i | \(-0.439922\pi\) |
−0.756835 | + | 0.653606i | \(0.773255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.0824 | + | 31.2245i | 1.99215 | + | 1.15017i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.97258 | + | 12.0769i | 0.256491 | + | 0.444255i | 0.965299 | − | 0.261146i | \(-0.0841004\pi\) |
−0.708809 | + | 0.705401i | \(0.750767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.1763 | − | 23.2504i | −0.998345 | − | 0.854127i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.8975i | 1.13352i | 0.823883 | + | 0.566760i | \(0.191803\pi\) | ||||
−0.823883 | + | 0.566760i | \(0.808197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.3739 | + | 8.24612i | 0.782031 | + | 0.301710i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.23010 | + | 1.11471i | −0.118025 | + | 0.0407305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.7085 | + | 20.2797i | −0.427249 | + | 0.740017i | −0.996628 | − | 0.0820583i | \(-0.973851\pi\) |
0.569378 | + | 0.822076i | \(0.307184\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.45623 | + | 50.7819i | −0.344604 | + | 1.85060i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.7901 | −0.937357 | −0.468679 | − | 0.883369i | \(-0.655270\pi\) | ||||
−0.468679 | + | 0.883369i | \(0.655270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.55697 | − | 19.1017i | 0.129110 | − | 0.693347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.03119 | + | 15.6425i | −0.327380 | + | 0.567039i | −0.981991 | − | 0.188927i | \(-0.939499\pi\) |
0.654611 | + | 0.755966i | \(0.272832\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.1459 | + | 3.70788i | 0.693129 | + | 0.134234i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.5328 | + | 7.81318i | −0.488642 | + | 0.282118i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.2208i | 1.66677i | 0.552696 | + | 0.833383i | \(0.313599\pi\) | ||||
−0.552696 | + | 0.833383i | \(0.686401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.8593 | + | 15.2794i | 0.643188 | + | 0.550275i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.03651 | − | 3.52734i | −0.0732482 | − | 0.126870i | 0.827075 | − | 0.562092i | \(-0.190003\pi\) |
−0.900323 | + | 0.435222i | \(0.856670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.593725 | + | 0.0886391i | −0.0212998 | + | 0.00317991i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.4694 | + | 21.0556i | 1.30665 | + | 0.754397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.08988 | − | 12.2800i | −0.253696 | − | 0.439414i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.2998 | − | 21.7550i | −1.26151 | − | 0.777459i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0876 | + | 5.82407i | −0.359584 | + | 0.207606i | −0.668898 | − | 0.743354i | \(-0.733234\pi\) |
0.309314 | + | 0.950960i | \(0.399900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.01260 | − | 19.8562i | −0.249655 | − | 0.706901i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.04638 | + | 7.85295i | 0.321652 | + | 0.279219i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.0774 | + | 45.1673i | −0.926034 | + | 1.60394i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.7250 | −1.30087 | −0.650433 | − | 0.759564i | \(-0.725412\pi\) | ||||
−0.650433 | + | 0.759564i | \(0.725412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8407 | −1.09106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.2314 | + | 15.5196i | −0.679509 | + | 0.548358i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1558 | + | 26.2507i | −0.534837 | + | 0.926366i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.6491 | − | 12.9433i | 1.29011 | − | 0.455626i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.1224 | + | 19.7006i | −1.19968 | + | 0.692635i | −0.960484 | − | 0.278336i | \(-0.910217\pi\) |
−0.239196 | + | 0.970971i | \(0.576884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.4733i | 1.77236i | 0.463345 | + | 0.886178i | \(0.346649\pi\) | ||||
−0.463345 | + | 0.886178i | \(0.653351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.35062 | + | 10.9295i | −0.327941 | + | 0.383313i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.0727 | + | 7.54752i | 0.457355 | + | 0.264054i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.5513 | − | 42.5152i | −0.788006 | − | 1.48560i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.6817 | + | 13.6726i | 0.826498 | + | 0.477179i | 0.852652 | − | 0.522479i | \(-0.174993\pi\) |
−0.0261543 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0437 | − | 20.8603i | −0.419817 | − | 0.727144i | 0.576104 | − | 0.817377i | \(-0.304572\pi\) |
−0.995921 | + | 0.0902322i | \(0.971239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 21.4026i | − | 0.744242i | −0.928184 | − | 0.372121i | \(-0.878631\pi\) | ||
0.928184 | − | 0.372121i | \(-0.121369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.3957 | − | 15.8169i | 0.951494 | − | 0.549345i | 0.0579490 | − | 0.998320i | \(-0.481544\pi\) |
0.893545 | + | 0.448974i | \(0.148211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.89216 | − | 3.49360i | 0.343155 | − | 0.121192i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.8936 | + | 13.2363i | −0.585328 | + | 0.458610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.970076 | − | 33.7757i | 0.0335307 | − | 1.16746i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.4562 | 1.39670 | 0.698351 | − | 0.715755i | \(-0.253917\pi\) | ||||
0.698351 | + | 0.715755i | \(0.253917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.6799 | −1.19586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.9300 | − | 5.57335i | −1.03084 | − | 0.191956i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.65809 | − | 10.6001i | −0.125693 | − | 0.364224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.73438 | + | 13.4054i | 0.162484 | + | 0.460074i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.326015 | + | 0.188225i | −0.0111756 | + | 0.00645226i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.7681i | 1.56707i | 0.621347 | + | 0.783536i | \(0.286586\pi\) | ||||
−0.621347 | + | 0.783536i | \(0.713414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.95930 | + | 5.12566i | 0.101088 | + | 0.175089i | 0.912133 | − | 0.409894i | \(-0.134434\pi\) |
−0.811045 | + | 0.584983i | \(0.801101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.8859 | + | 10.9038i | 0.644377 | + | 0.372031i | 0.786299 | − | 0.617847i | \(-0.211995\pi\) |
−0.141921 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.2683 | + | 44.3524i | 1.20194 | + | 1.51153i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.8100 | − | 18.9429i | −1.11687 | − | 0.644823i | −0.176267 | − | 0.984342i | \(-0.556402\pi\) |
−0.940599 | + | 0.339519i | \(0.889736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0027 | − | 8.55769i | −0.339708 | − | 0.290634i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.54910i | − | 0.323931i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 84.0032 | − | 48.4993i | 2.84634 | − | 1.64334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.20888 | − | 16.0934i | 0.210139 | − | 0.544678i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8427 | + | 46.4929i | −0.906412 | + | 1.56995i | −0.0874025 | + | 0.996173i | \(0.527857\pi\) |
−0.819010 | + | 0.573779i | \(0.805477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.23220 | − | 6.61717i | 0.0415611 | − | 0.223192i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.12570 | 0.0379259 | 0.0189630 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189630 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.0889 | 1.61832 | 0.809161 | − | 0.587587i | \(-0.199922\pi\) | ||||
0.809161 | + | 0.587587i | \(0.199922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.9434 | + | 44.9352i | −0.871093 | + | 1.50878i | −0.0102253 | + | 0.999948i | \(0.503255\pi\) |
−0.860867 | + | 0.508829i | \(0.830078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.21556 | − | 1.40029i | 0.0407684 | − | 0.0469641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.3401 | − | 7.42052i | −1.15044 | − | 0.248597i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.6676 | + | 17.1286i | −0.992789 | + | 0.573187i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.9322 | − | 19.6195i | −0.765684 | − | 0.655075i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.9462 | − | 44.9401i | −0.865353 | − | 1.49884i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2295 | + | 8.21540i | 0.474053 | + | 0.273695i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.6421 | + | 15.8984i | 0.420704 | + | 0.529065i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.57234 | − | 6.18747i | −0.118618 | − | 0.205452i | 0.800602 | − | 0.599196i | \(-0.204513\pi\) |
−0.919220 | + | 0.393744i | \(0.871180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.22049 | − | 26.9415i | −0.139985 | − | 0.893594i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 38.4884i | − | 1.27518i | −0.770377 | − | 0.637589i | \(-0.779932\pi\) | ||
0.770377 | − | 0.637589i | \(-0.220068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.8162 | − | 14.9050i | 0.854392 | − | 0.493283i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.59217 | − | 13.3068i | −0.151647 | − | 0.439429i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.0403 | + | 46.8351i | −0.891976 | + | 1.54495i | −0.0544730 | + | 0.998515i | \(0.517348\pi\) |
−0.837503 | + | 0.546433i | \(0.815985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.203918 | + | 0.0379721i | 0.00671932 | + | 0.00125122i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.0246 | −0.724950 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.85619 | − | 2.30014i | −0.0609654 | − | 0.0755465i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.8140 | + | 32.5869i | −0.617269 | + | 1.06914i | 0.372713 | + | 0.927947i | \(0.378427\pi\) |
−0.989982 | + | 0.141194i | \(0.954906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.89970 | + | 22.1154i | −0.291676 | + | 0.724802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.4669 | + | 7.58143i | −0.702794 | + | 0.248205i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.05652i | − | 0.0998522i | −0.998753 | − | 0.0499261i | \(-0.984101\pi\) | ||
0.998753 | − | 0.0499261i | \(-0.0158986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.2008 | + | 30.6248i | −0.855030 | + | 0.999402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.3577 | − | 47.3849i | −0.891835 | − | 1.54470i | −0.837674 | − | 0.546171i | \(-0.816085\pi\) |
−0.0541612 | − | 0.998532i | \(-0.517248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.7741 | + | 17.7674i | 1.00214 | + | 0.578587i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.20664 | − | 3.58341i | −0.201689 | − | 0.116445i | 0.395754 | − | 0.918356i | \(-0.370483\pi\) |
−0.597443 | + | 0.801911i | \(0.703817\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.5407 | + | 40.7737i | 0.764164 | + | 1.32357i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.1266 | + | 45.7332i | −1.26877 | + | 1.48300i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.140553i | − | 0.00455295i | −0.999997 | − | 0.00227648i | \(-0.999275\pi\) | ||
0.999997 | − | 0.00227648i | \(-0.000724625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −50.8753 | + | 17.9675i | −1.64456 | + | 0.580808i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.97446 | − | 10.1953i | 0.0637586 | − | 0.329222i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.64335 | − | 9.77457i | 0.182043 | − | 0.315309i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.43324 | + | 3.01520i | 0.0784102 | + | 0.0971636i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.4958 | −0.691258 | −0.345629 | − | 0.938371i | \(-0.612334\pi\) | ||||
−0.345629 | + | 0.938371i | \(0.612334\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.7790 | + | 3.31068i | 0.571144 | + | 0.106354i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.37642 | + | 12.7763i | −0.236721 | + | 0.410012i | −0.959771 | − | 0.280783i | \(-0.909406\pi\) |
0.723051 | + | 0.690795i | \(0.242739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.3123 | − | 28.0496i | −1.03589 | − | 0.899228i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.07585 | + | 0.621141i | −0.0344194 | + | 0.0198720i | −0.517111 | − | 0.855918i | \(-0.672993\pi\) |
0.482692 | + | 0.875790i | \(0.339659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.1561i | 1.02771i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.42232 | − | 21.8464i | −0.109266 | − | 0.697501i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.04373 | − | 10.4680i | −0.192765 | − | 0.333879i | 0.753401 | − | 0.657562i | \(-0.228412\pi\) |
−0.946166 | + | 0.323683i | \(0.895079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −45.5918 | + | 6.80654i | −1.45120 | + | 0.216655i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0311 | + | 6.36883i | 0.350770 | + | 0.202517i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.50767 | − | 7.80752i | −0.143191 | − | 0.248014i | 0.785506 | − | 0.618854i | \(-0.212403\pi\) |
−0.928697 | + | 0.370841i | \(0.879070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.6988 | − | 28.8307i | −1.06940 | − | 0.914915i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.2746 | − | 21.5205i | 1.18050 | − | 0.681562i | 0.224370 | − | 0.974504i | \(-0.427968\pi\) |
0.956130 | + | 0.292942i | \(0.0946344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.323277 | + | 0.599016i | 0.0102280 | + | 0.0189520i |
(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 | 2100.2.bi.k.1601.3 | 10 | ||
3.2 | odd | 2 | 2100.2.bi.j.1601.5 | 10 | |||
5.2 | odd | 4 | 2100.2.bo.h.1349.1 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.h.1349.10 | 20 | |||
5.4 | even | 2 | 420.2.bh.a.341.3 | yes | 10 | ||
7.3 | odd | 6 | 2100.2.bi.j.101.5 | 10 | |||
15.2 | even | 4 | 2100.2.bo.g.1349.7 | 20 | |||
15.8 | even | 4 | 2100.2.bo.g.1349.4 | 20 | |||
15.14 | odd | 2 | 420.2.bh.b.341.1 | yes | 10 | ||
21.17 | even | 6 | inner | 2100.2.bi.k.101.3 | 10 | ||
35.3 | even | 12 | 2100.2.bo.g.1949.7 | 20 | |||
35.9 | even | 6 | 2940.2.d.b.881.1 | 10 | |||
35.17 | even | 12 | 2100.2.bo.g.1949.4 | 20 | |||
35.19 | odd | 6 | 2940.2.d.a.881.10 | 10 | |||
35.24 | odd | 6 | 420.2.bh.b.101.1 | yes | 10 | ||
105.17 | odd | 12 | 2100.2.bo.h.1949.10 | 20 | |||
105.38 | odd | 12 | 2100.2.bo.h.1949.1 | 20 | |||
105.44 | odd | 6 | 2940.2.d.a.881.9 | 10 | |||
105.59 | even | 6 | 420.2.bh.a.101.3 | ✓ | 10 | ||
105.89 | even | 6 | 2940.2.d.b.881.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.3 | ✓ | 10 | 105.59 | even | 6 | ||
420.2.bh.a.341.3 | yes | 10 | 5.4 | even | 2 | ||
420.2.bh.b.101.1 | yes | 10 | 35.24 | odd | 6 | ||
420.2.bh.b.341.1 | yes | 10 | 15.14 | odd | 2 | ||
2100.2.bi.j.101.5 | 10 | 7.3 | odd | 6 | |||
2100.2.bi.j.1601.5 | 10 | 3.2 | odd | 2 | |||
2100.2.bi.k.101.3 | 10 | 21.17 | even | 6 | inner | ||
2100.2.bi.k.1601.3 | 10 | 1.1 | even | 1 | trivial | ||
2100.2.bo.g.1349.4 | 20 | 15.8 | even | 4 | |||
2100.2.bo.g.1349.7 | 20 | 15.2 | even | 4 | |||
2100.2.bo.g.1949.4 | 20 | 35.17 | even | 12 | |||
2100.2.bo.g.1949.7 | 20 | 35.3 | even | 12 | |||
2100.2.bo.h.1349.1 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.h.1349.10 | 20 | 5.3 | odd | 4 | |||
2100.2.bo.h.1949.1 | 20 | 105.38 | odd | 12 | |||
2100.2.bo.h.1949.10 | 20 | 105.17 | odd | 12 | |||
2940.2.d.a.881.9 | 10 | 105.44 | odd | 6 | |||
2940.2.d.a.881.10 | 10 | 35.19 | odd | 6 | |||
2940.2.d.b.881.1 | 10 | 35.9 | even | 6 | |||
2940.2.d.b.881.2 | 10 | 105.89 | even | 6 |