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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.5 | ||
Root | \(-1.31611 + 1.12599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.j.1601.5 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 1.63319 | − | 0.576792i | 0.942923 | − | 0.333011i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73439 | + | 1.99797i | 0.655538 | + | 0.755162i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.33462 | − | 1.88402i | 0.778208 | − | 0.628007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.38064 | + | 1.95181i | 1.01930 | + | 0.588494i | 0.913902 | − | 0.405936i | \(-0.133054\pi\) |
0.105400 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.06329i | − | 1.68166i | −0.541303 | − | 0.840828i | \(-0.682069\pi\) | ||
0.541303 | − | 0.840828i | \(-0.317931\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.53296 | − | 2.65516i | 0.371797 | − | 0.643971i | −0.618045 | − | 0.786143i | \(-0.712075\pi\) |
0.989842 | + | 0.142171i | \(0.0454084\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94930 | + | 1.70278i | −0.676616 | + | 0.390645i | −0.798579 | − | 0.601890i | \(-0.794415\pi\) |
0.121963 | + | 0.992535i | \(0.461081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.98500 | + | 2.26269i | 0.869599 | + | 0.493759i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.48871 | − | 1.43686i | 0.518933 | − | 0.299606i | −0.217565 | − | 0.976046i | \(-0.569811\pi\) |
0.736498 | + | 0.676440i | \(0.236478\pi\) | |||||||
\(24\) | 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 | −0.0998461 | − | 0.995003i | \(-0.531835\pi\) |
−0.911621 | + | 0.411032i | \(0.865168\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.64702 | + | 1.23776i | 1.15710 | + | 0.215466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0654987 | + | 0.113447i | 0.0107679 | + | 0.0186506i | 0.871359 | − | 0.490646i | \(-0.163239\pi\) |
−0.860591 | + | 0.509296i | \(0.829906\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.49726 | − | 9.90252i | −0.560009 | − | 1.58567i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3654 | 1.93116 | 0.965579 | − | 0.260108i | \(-0.0837583\pi\) | ||||
0.965579 | + | 0.260108i | \(0.0837583\pi\) | |||||||
\(42\) | 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 | −0.955316 | − | 0.295586i | \(-0.904485\pi\) |
0.221674 | − | 0.975121i | \(-0.428848\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.983778 | + | 6.93053i | −0.140540 | + | 0.990075i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.972138 | − | 5.22058i | 0.136127 | − | 0.731028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64119 | + | 2.67959i | 0.637516 | + | 0.368070i | 0.783657 | − | 0.621194i | \(-0.213352\pi\) |
−0.146141 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(54\) | 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 | \(-0.886987\pi\) |
0.769871 | + | 0.638200i | \(0.220321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44930 | − | 4.30086i | 0.953785 | − | 0.550668i | 0.0595306 | − | 0.998226i | \(-0.481040\pi\) |
0.894255 | + | 0.447558i | \(0.147706\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.81337 | + | 1.39688i | 0.984392 | + | 0.175990i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.99884 | + | 13.8544i | −0.977213 | + | 1.69258i | −0.304785 | + | 0.952421i | \(0.598585\pi\) |
−0.672429 | + | 0.740162i | \(0.734749\pi\) | |||||||
\(68\) | 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 | 0.838928 | − | 0.544242i | \(-0.183183\pi\) |
−0.0518638 | + | 0.998654i | \(0.516516\pi\) | |||||||
\(74\) | 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 | 0.788981 | − | 0.614417i | \(-0.210609\pi\) |
−0.926591 | + | 0.376069i | \(0.877275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.90093 | − | 8.79696i | 0.211214 | − | 0.977440i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.63648 | 0.838213 | 0.419106 | − | 0.907937i | \(-0.362343\pi\) | ||||
0.419106 | + | 0.907937i | \(0.362343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.60278 | + | 13.0328i | 0.493470 | + | 1.39726i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.11874 | − | 7.13387i | −0.436586 | − | 0.756189i | 0.560838 | − | 0.827926i | \(-0.310479\pi\) |
−0.997424 | + | 0.0717367i | \(0.977146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1143 | − | 10.5161i | 1.26992 | − | 1.10239i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0729 | − | 2.06191i | −1.14820 | − | 0.213810i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.74985i | − | 0.583809i | −0.956447 | − | 0.291904i | \(-0.905711\pi\) | ||
0.956447 | − | 0.291904i | \(-0.0942889\pi\) | |||||||
\(98\) | 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 | \(-0.982710\pi\) |
0.546279 | + | 0.837603i | \(0.316044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.853234 | − | 0.492615i | 0.0840717 | − | 0.0485388i | −0.457375 | − | 0.889274i | \(-0.651210\pi\) |
0.541446 | + | 0.840735i | \(0.317877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11849 | − | 0.645758i | 0.108128 | − | 0.0624278i | −0.444961 | − | 0.895550i | \(-0.646782\pi\) |
0.553089 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.68547 | − | 6.38342i | 0.353004 | − | 0.611421i | −0.633770 | − | 0.773521i | \(-0.718494\pi\) |
0.986774 | + | 0.162101i | \(0.0518269\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | −11.4234 | − | 14.1555i | −1.05609 | − | 1.30868i | ||||
\(118\) | 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 | ||||||||
\(123\) | 20.1951 | − | 7.13229i | 1.82093 | − | 0.643097i | ||||
\(124\) | 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 | ||||||||
\(129\) | −7.23906 | + | 2.55661i | −0.637364 | + | 0.225097i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.66028 | − | 4.60774i | −0.232430 | − | 0.402580i | 0.726093 | − | 0.687597i | \(-0.241334\pi\) |
−0.958523 | + | 0.285016i | \(0.908001\pi\) | |||||||
\(132\) | 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 | \(-0.386958\pi\) |
−0.638128 | + | 0.769930i | \(0.720291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1726i | 1.37174i | 0.727724 | + | 0.685870i | \(0.240578\pi\) | ||||
−0.727724 | + | 0.685870i | \(0.759422\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 2.39077 | + | 11.8863i | 0.197188 | + | 0.980366i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.4366 | − | 10.0670i | 1.42846 | − | 0.824721i | 0.431459 | − | 0.902132i | \(-0.357999\pi\) |
0.996999 | + | 0.0774116i | \(0.0246655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.38980 | + | 4.13926i | −0.194479 | + | 0.336848i | −0.946730 | − | 0.322029i | \(-0.895635\pi\) |
0.752250 | + | 0.658877i | \(0.228968\pi\) | |||||||
\(152\) | 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 | 0.211633 | − | 0.977349i | \(-0.432122\pi\) |
−0.740592 | + | 0.671955i | \(0.765455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.12551 | + | 1.69929i | 0.723700 | + | 0.134762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.18721 | + | 2.48030i | 0.566431 | + | 0.195475i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.23749 | − | 7.33954i | −0.331906 | − | 0.574877i | 0.650980 | − | 0.759095i | \(-0.274358\pi\) |
−0.982885 | + | 0.184218i | \(0.941025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.5669 | −1.59152 | −0.795759 | − | 0.605614i | \(-0.792928\pi\) | ||||
−0.795759 | + | 0.605614i | \(0.792928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.7635 | −1.82796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67743 | + | 9.53190i | −0.281220 | + | 0.728922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.30340 | + | 14.3819i | 0.631296 | + | 1.09344i | 0.987287 | + | 0.158948i | \(0.0508101\pi\) |
−0.355991 | + | 0.934489i | \(0.615857\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.817179 | + | 4.38842i | −0.0614229 | + | 0.329854i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.336240 | + | 0.194128i | 0.0251318 | + | 0.0145098i | 0.512513 | − | 0.858679i | \(-0.328715\pi\) |
−0.487381 | + | 0.873189i | \(0.662048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.6789i | − | 1.53705i | −0.639820 | − | 0.768524i | \(-0.720991\pi\) | ||
0.639820 | − | 0.768524i | \(-0.279009\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 13.5664 | − | 2.22531i | 0.986812 | − | 0.161868i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2933 | + | 8.82961i | −1.10659 | + | 0.638888i | −0.937943 | − | 0.346789i | \(-0.887272\pi\) |
−0.168644 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.6903 | + | 18.5161i | −0.769505 | + | 1.33282i | 0.168327 | + | 0.985731i | \(0.446163\pi\) |
−0.937832 | + | 0.347090i | \(0.887170\pi\) | |||||||
\(194\) | 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 | 0.168126 | − | 0.985765i | \(-0.446228\pi\) |
−0.769635 | + | 0.638484i | \(0.779562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.07253 | + | 27.2405i | −0.357789 | + | 1.92140i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.9438 | + | 13.8404i | −1.11903 | + | 0.971405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.10314 | − | 8.04332i | 0.215683 | − | 0.559049i | ||||
\(208\) | 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 | ||||||||
\(213\) | 2.09517 | + | 5.93249i | 0.143559 | + | 0.406488i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.27118 | − | 16.8910i | −0.222062 | − | 1.14664i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2221 | + | 2.46212i | 0.893465 | + | 0.166374i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0990 | − | 9.29478i | −1.08294 | − | 0.625234i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.78864i | 0.119776i | 0.998205 | + | 0.0598882i | \(0.0190744\pi\) | ||||
−0.998205 | + | 0.0598882i | \(0.980926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7981 | + | 23.8990i | −0.915813 | + | 1.58623i | −0.110106 | + | 0.993920i | \(0.535119\pi\) |
−0.805707 | + | 0.592315i | \(0.798214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.37613 | + | 4.83596i | −0.553510 | + | 0.319569i | −0.750537 | − | 0.660829i | \(-0.770205\pi\) |
0.197026 | + | 0.980398i | \(0.436872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.05553 | + | 15.4273i | 0.595810 | + | 1.01504i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.516767 | − | 0.298355i | 0.0338545 | − | 0.0195459i | −0.482977 | − | 0.875633i | \(-0.660445\pi\) |
0.516832 | + | 0.856087i | \(0.327111\pi\) | |||||||
\(234\) | 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 | 0.557640 | − | 0.830083i | \(-0.311707\pi\) |
−0.440053 | + | 0.897972i | \(0.645040\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.96943 | − | 15.4635i | −0.126339 | − | 0.991987i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3245 | + | 17.8825i | 0.656930 | + | 1.13784i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.4718 | − | 4.40466i | 0.790370 | − | 0.279134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8229 | 1.88241 | 0.941204 | − | 0.337840i | \(-0.109696\pi\) | ||||
0.941204 | + | 0.337840i | \(0.109696\pi\) | |||||||
\(252\) | 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 | \(-0.0275630\pi\) |
−0.573024 | + | 0.819539i | \(0.694230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.113064 | + | 0.327626i | −0.00702543 | + | 0.0203577i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0344 | + | 18.6302i | 0.930608 | + | 1.15318i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5291 | − | 6.07897i | −0.649252 | − | 0.374846i | 0.138918 | − | 0.990304i | \(-0.455638\pi\) |
−0.788169 | + | 0.615458i | \(0.788971\pi\) | |||||||
\(264\) | 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 | 0.289617 | + | 0.957143i | \(0.406472\pi\) |
−0.973718 | + | 0.227756i | \(0.926861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.19179 | + | 4.15218i | −0.436870 | + | 0.252227i | −0.702269 | − | 0.711912i | \(-0.747830\pi\) |
0.265399 | + | 0.964139i | \(0.414496\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.7193 | − | 24.1622i | 0.830332 | − | 1.46237i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.02848 | − | 5.24547i | 0.181963 | − | 0.315170i | −0.760586 | − | 0.649238i | \(-0.775088\pi\) |
0.942549 | + | 0.334068i | \(0.108421\pi\) | |||||||
\(278\) | 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 | 0.273616 | − | 0.961839i | \(-0.411780\pi\) |
−0.696169 | + | 0.717878i | \(0.745114\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −3.31647 | − | 9.39060i | −0.194415 | − | 0.550487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.88610 | −0.227028 | −0.113514 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113514 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.8503 | − | 9.63343i | 1.03578 | − | 0.558988i | ||||
\(298\) | 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 | ||||||||
\(303\) | −2.88226 | + | 15.4783i | −0.165581 | + | 0.889207i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.119756i | − | 0.00683482i | −0.999994 | − | 0.00341741i | \(-0.998912\pi\) | ||
0.999994 | − | 0.00341741i | \(-0.00108780\pi\) | |||||||
\(308\) | 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 | \(-0.711776\pi\) |
0.989975 | + | 0.141243i | \(0.0451097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1517 | + | 11.6346i | −1.13904 | + | 0.657625i | −0.946192 | − | 0.323604i | \(-0.895105\pi\) |
−0.192847 | + | 0.981229i | \(0.561772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0933 | − | 17.3744i | 1.69021 | − | 0.975841i | 0.735861 | − | 0.677132i | \(-0.236777\pi\) |
0.954344 | − | 0.298709i | \(-0.0965559\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 2.33717 | − | 12.5511i | 0.129246 | − | 0.694077i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.68208 | − | 25.1582i | 0.478659 | − | 1.38702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8024 | + | 22.1744i | 0.703684 | + | 1.21882i | 0.967165 | + | 0.254151i | \(0.0817961\pi\) |
−0.263481 | + | 0.964665i | \(0.584871\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.366651 | + | 0.141455i | 0.0200924 | + | 0.00775169i | ||||
\(334\) | 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 | ||||||||
\(339\) | 2.61159 | + | 7.39473i | 0.141842 | + | 0.401627i | ||||
\(340\) | 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 | \(-0.505952\pi\) |
−0.875223 | + | 0.483720i | \(0.839285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40475i | 0.0751943i | 0.999293 | + | 0.0375972i | \(0.0119704\pi\) | ||||
−0.999293 | + | 0.0375972i | \(0.988030\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.8213 | − | 16.5297i | −1.43162 | − | 0.882292i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.43705 | + | 16.3454i | −0.502283 | + | 0.869980i | 0.497713 | + | 0.867342i | \(0.334173\pi\) |
−0.999997 | + | 0.00263867i | \(0.999160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.1166 | − | 7.11222i | 0.641281 | − | 0.376419i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.1592 | + | 11.0615i | −1.01118 | + | 0.583806i | −0.911537 | − | 0.411217i | \(-0.865104\pi\) |
−0.0996440 | + | 0.995023i | \(0.531770\pi\) | |||||||
\(360\) | 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 | 0.766341 | − | 0.642434i | \(-0.222075\pi\) |
−0.173194 | + | 0.984888i | \(0.555409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.8687 | − | 23.2968i | 1.50284 | − | 1.21278i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.69589 | + | 13.9204i | 0.139964 | + | 0.722712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.38003 | + | 12.7826i | 0.382123 | + | 0.661857i | 0.991366 | − | 0.131127i | \(-0.0418596\pi\) |
−0.609242 | + | 0.792984i | \(0.708526\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | 1.14463 | − | 0.404247i | 0.0586411 | − | 0.0207102i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.72052 | − | 13.3723i | −0.394500 | − | 0.683294i | 0.598537 | − | 0.801095i | \(-0.295749\pi\) |
−0.993037 | + | 0.117801i | \(0.962416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.3481 | + | 8.35086i | −0.526025 | + | 0.424498i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.53666 | + | 4.35129i | 0.382124 | + | 0.220619i | 0.678742 | − | 0.734377i | \(-0.262525\pi\) |
−0.296618 | + | 0.954996i | \(0.595859\pi\) | |||||||
\(390\) | 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 | −0.954602 | − | 0.297883i | \(-0.903719\pi\) |
−0.219327 | + | 0.975651i | \(0.570386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.6058 | + | 0.112241i | −0.781269 | + | 0.00561909i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.30215 | + | 2.48385i | −0.214839 | + | 0.124037i | −0.603558 | − | 0.797319i | \(-0.706251\pi\) |
0.388719 | + | 0.921356i | \(0.372918\pi\) | |||||||
\(402\) | 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 | 0.316744 | − | 0.948511i | \(-0.397410\pi\) |
−0.663063 | + | 0.748564i | \(0.730744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.68349 | − | 1.24455i | −0.329672 | − | 0.0613891i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.69427 | + | 1.29644i | −0.329403 | + | 0.0637937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.32820 | + | 26.4129i | 0.456804 | + | 1.29345i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.60294 | 0.371428 | 0.185714 | − | 0.982604i | \(-0.440540\pi\) | ||||
0.185714 | + | 0.982604i | \(0.440540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.43892 | −0.216340 | −0.108170 | − | 0.994132i | \(-0.534499\pi\) | ||||
−0.108170 | + | 0.994132i | \(0.534499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.1549 | − | 10.8623i | −1.36894 | − | 0.528141i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5130 | + | 7.42413i | 1.04109 | + | 0.359279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.50490 | − | 40.3029i | 0.362340 | − | 1.94584i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.24065 | − | 2.44834i | −0.204265 | − | 0.117932i | 0.394378 | − | 0.918948i | \(-0.370960\pi\) |
−0.598643 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6390i | 0.895732i | 0.894101 | + | 0.447866i | \(0.147816\pi\) | ||||
−0.894101 | + | 0.447866i | \(0.852184\pi\) | |||||||
\(434\) | 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 | −0.566932 | − | 0.823765i | \(-0.691870\pi\) |
0.429936 | + | 0.902860i | \(0.358536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7605 | + | 18.0336i | 0.512405 | + | 0.858744i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.707683 | + | 0.408581i | −0.0336231 | + | 0.0194123i | −0.516717 | − | 0.856156i | \(-0.672846\pi\) |
0.483094 | + | 0.875568i | \(0.339513\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | −1.51551 | + | 8.13862i | −0.0712051 | + | 0.382386i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.01889 | + | 10.4250i | 0.281552 | + | 0.487662i | 0.971767 | − | 0.235942i | \(-0.0758175\pi\) |
−0.690215 | + | 0.723604i | \(0.742484\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.56611 | − | 14.0196i | −0.353156 | − | 0.654380i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0451 | −1.07332 | −0.536658 | − | 0.843800i | \(-0.680314\pi\) | ||||
−0.536658 | + | 0.843800i | \(0.680314\pi\) | |||||||
\(462\) | 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 | \(-0.182998\pi\) |
−0.890527 | + | 0.454930i | \(0.849664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −41.5538 | + | 8.04748i | −1.91878 | + | 0.371598i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0317 | − | 2.42666i | −0.600467 | − | 0.111815i | ||||
\(472\) | 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 | \(-0.781727\pi\) |
0.935377 | + | 0.353653i | \(0.115061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.687863 | − | 0.397138i | 0.0313638 | − | 0.0181079i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.1687 | − | 0.0947128i | 0.599197 | − | 0.00430958i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.62036 | − | 8.00270i | 0.209368 | − | 0.362637i | −0.742147 | − | 0.670237i | \(-0.766193\pi\) |
0.951516 | + | 0.307600i | \(0.0995259\pi\) | |||||||
\(488\) | 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 | 0.682975 | − | 0.730442i | \(-0.260686\pi\) |
−0.974069 | + | 0.226252i | \(0.927353\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.5897 | + | 11.8628i | −1.50068 | + | 0.529993i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.580122 | −0.0258664 | −0.0129332 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129332 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.8104 | + | 13.7066i | −1.72363 | + | 0.608732i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.86251 | − | 17.0824i | −0.437148 | − | 0.757163i | 0.560320 | − | 0.828276i | \(-0.310678\pi\) |
−0.997468 | + | 0.0711133i | \(0.977345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.90611 | + | 20.1695i | 0.172796 | + | 0.892245i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.508034 | + | 17.6885i | −0.0224302 | + | 0.780967i | ||||
\(514\) | 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 | 0.137874 | + | 0.990450i | \(0.455973\pi\) |
−0.926692 | + | 0.375822i | \(0.877360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5387 | − | 10.7033i | 0.810640 | − | 0.468023i | −0.0365378 | − | 0.999332i | \(-0.511633\pi\) |
0.847178 | + | 0.531309i | \(0.178300\pi\) | |||||||
\(524\) | 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 | ||||||||
\(537\) | 0.661116 | + | 0.123108i | 0.0285293 | + | 0.00531251i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.8529 | + | 21.5095i | −0.725906 | + | 0.926479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.32759 | − | 4.03151i | −0.100071 | − | 0.173328i | 0.811643 | − | 0.584154i | \(-0.198574\pi\) |
−0.911714 | + | 0.410826i | \(0.865240\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.9274 | − | 33.7725i | −0.511854 | − | 1.44932i | ||||
\(544\) | 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 | ||||||||
\(549\) | 9.28841 | − | 24.0755i | 0.396420 | − | 1.02752i | ||||
\(550\) | 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 | \(-0.572614\pi\) |
−0.956663 | + | 0.291196i | \(0.905947\pi\) | |||||||
\(558\) | 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 | \(-0.994132\pi\) |
0.515878 | + | 0.856662i | \(0.327466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.8730 | − | 11.4594i | 0.876585 | − | 0.481248i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0347 | − | 9.25765i | 0.672211 | − | 0.388101i | −0.124703 | − | 0.992194i | \(-0.539798\pi\) |
0.796914 | + | 0.604093i | \(0.206465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9408 | + | 38.0025i | −0.918193 | + | 1.59036i | −0.116035 | + | 0.993245i | \(0.537019\pi\) |
−0.802158 | + | 0.597112i | \(0.796315\pi\) | |||||||
\(572\) | 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 | 0.162620 | − | 0.986689i | \(-0.448006\pi\) |
−0.773188 | + | 0.634177i | \(0.781339\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.77934 | + | 36.4065i | −0.281740 | + | 1.51300i | ||||
\(580\) | 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 | \(-0.397080\pi\) | ||||
0.317728 | + | 0.948182i | \(0.397080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1458 | 0.912500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9819 | − | 36.7583i | −0.534003 | − | 1.51203i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.37500 | + | 4.11363i | 0.0975297 | + | 0.168926i | 0.910662 | − | 0.413153i | \(-0.135573\pi\) |
−0.813132 | + | 0.582079i | \(0.802239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.6839 | − | 3.10674i | −0.682825 | − | 0.127151i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.2300 | + | 11.1024i | 0.785716 | + | 0.453634i | 0.838452 | − | 0.544975i | \(-0.183461\pi\) |
−0.0527360 | + | 0.998608i | \(0.516794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.5924i | − | 1.73738i | −0.495357 | − | 0.868689i | \(-0.664963\pi\) | ||
0.495357 | − | 0.868689i | \(-0.335037\pi\) | |||||||
\(602\) | 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 | −0.792671 | − | 0.609649i | \(-0.791310\pi\) |
0.131636 | + | 0.991298i | \(0.457977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.0562 | + | 31.8002i | −0.731673 | + | 1.28861i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.8205 | + | 30.4960i | −2.13689 | + | 1.23373i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.74783 | − | 13.4196i | 0.312932 | − | 0.542014i | −0.666064 | − | 0.745895i | \(-0.732022\pi\) |
0.978996 | + | 0.203881i | \(0.0653555\pi\) | |||||||
\(614\) | 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 | 0.615009 | − | 0.788520i | \(-0.289152\pi\) |
−0.375374 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.428695 | − | 14.9261i | 0.0172029 | − | 0.598965i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.10976 | − | 20.6021i | 0.284847 | − | 0.825404i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.7117 | + | 7.66789i | −0.867082 | + | 0.306226i | ||||
\(628\) | 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 | ||||||||
\(633\) | −3.20580 | + | 1.13219i | −0.127419 | + | 0.0450004i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.0218 | + | 5.96493i | 1.66496 | + | 0.236339i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.84362 | + | 8.48041i | 0.270729 | + | 0.335480i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3007 | + | 13.4527i | 0.920324 | + | 0.531349i | 0.883738 | − | 0.467981i | \(-0.155019\pi\) |
0.0365856 | + | 0.999331i | \(0.488352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13.9638i | − | 0.550679i | −0.961347 | − | 0.275339i | \(-0.911210\pi\) | ||
0.961347 | − | 0.275339i | \(-0.0887902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3377 | − | 26.5656i | 0.602985 | − | 1.04440i | −0.389381 | − | 0.921077i | \(-0.627311\pi\) |
0.992366 | − | 0.123324i | \(-0.0393556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.71262 | + | 5.03023i | −0.342000 | + | 0.197454i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.0851 | − | 25.6994i | −0.591230 | − | 1.00724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3602 | + | 6.55879i | −0.444557 | + | 0.256665i | −0.705529 | − | 0.708681i | \(-0.749290\pi\) |
0.260971 | + | 0.965347i | \(0.415957\pi\) | |||||||
\(654\) | 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 | 0.583361 | − | 0.812213i | \(-0.301737\pi\) |
−0.411716 | + | 0.911312i | \(0.635071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.6539 | − | 5.89436i | −1.22934 | − | 0.228918i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4661 | + | 19.8599i | 0.443969 | + | 0.768977i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.03168 | + | 2.92120i | 0.0398869 | + | 0.112940i | ||||
\(670\) | 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 | \(-0.325878\pi\) |
−0.999726 | + | 0.0234197i | \(0.992545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4880 | − | 9.97249i | 0.440870 | − | 0.382709i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.75019 | + | 46.9903i | −0.335308 | + | 1.80067i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.3107 | − | 16.9226i | −1.12154 | − | 0.647524i | −0.179749 | − | 0.983712i | \(-0.557529\pi\) |
−0.941795 | + | 0.336189i | \(0.890862\pi\) | |||||||
\(684\) | 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 | −0.301339 | − | 0.953517i | \(-0.597434\pi\) |
0.675101 | + | 0.737726i | \(0.264100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.6878 | + | 19.9726i | 0.899823 | + | 0.758696i | ||||
\(694\) | 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 | 0.969874 | − | 0.243609i | \(-0.0783312\pi\) |
−0.695908 | + | 0.718131i | \(0.744998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.84675 | − | 2.64150i | −0.256773 | − | 0.0990639i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.6873 | −0.699844 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.13912 | + | 14.5515i | 0.191924 | + | 0.543434i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.35171 | + | 16.1976i | 0.348760 | + | 0.604070i | 0.986029 | − | 0.166571i | \(-0.0532696\pi\) |
−0.637270 | + | 0.770641i | \(0.719936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.46407 | + | 0.850351i | 0.0917668 | + | 0.0316687i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.58917 | + | 0.668348i | 0.133483 | + | 0.0248561i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0483i | 0.854815i | 0.904059 | + | 0.427407i | \(0.140573\pi\) | ||||
−0.904059 | + | 0.427407i | \(0.859427\pi\) | |||||||
\(728\) | 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 | −0.756835 | − | 0.653606i | \(-0.773255\pi\) |
0.187622 | + | 0.982241i | \(0.439922\pi\) | |||||||
\(734\) | 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 | −0.708809 | − | 0.705401i | \(-0.750767\pi\) |
0.965299 | + | 0.261146i | \(0.0841004\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | 17.8283 | − | 14.3873i | 0.652304 | − | 0.526404i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.23010 | + | 1.11471i | 0.118025 | + | 0.0407305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.7085 | − | 20.2797i | −0.427249 | − | 0.740017i | 0.569378 | − | 0.822076i | \(-0.307184\pi\) |
−0.996628 | + | 0.0820583i | \(0.973851\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.7065 | − | 17.2016i | 1.77497 | − | 0.626862i | ||||
\(754\) | 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 | ||||||||
\(759\) | 18.3210 | − | 6.47041i | 0.665011 | − | 0.234861i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.03119 | + | 15.6425i | 0.327380 | + | 0.567039i | 0.981991 | − | 0.188927i | \(-0.0605008\pi\) |
−0.654611 | + | 0.755966i | \(0.727168\pi\) | |||||||
\(762\) | 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 | \(-0.686401\pi\) | ||
0.552696 | − | 0.833383i | \(-0.313599\pi\) | |||||||
\(770\) | 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 | \(-0.809997\pi\) |
0.900323 | + | 0.435222i | \(0.143330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.00431744 | + | 0.600290i | 0.000154887 | + | 0.0215353i | ||||
\(778\) | 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 | 0.309314 | − | 0.950960i | \(-0.399900\pi\) |
−0.668898 | + | 0.743354i | \(0.733234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.7023 | − | 3.85503i | −0.737022 | − | 0.137243i | ||||
\(790\) | 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 | \(-0.274588\pi\) | ||||
0.650433 | + | 0.759564i | \(0.274588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8407 | −1.09106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.0561 | − | 8.89511i | −0.814647 | − | 0.314293i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1558 | + | 26.2507i | 0.534837 | + | 0.926366i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.11532 | + | 38.2107i | −0.250471 | + | 1.34508i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.1224 | + | 19.7006i | 1.19968 | + | 0.692635i | 0.960484 | − | 0.278336i | \(-0.0897829\pi\) |
0.239196 | + | 0.970971i | \(0.423116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 50.4733i | − | 1.77236i | −0.463345 | − | 0.886178i | \(-0.653351\pi\) | ||
0.463345 | − | 0.886178i | \(-0.346649\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 8.46970 | − | 47.3748i | 0.295955 | − | 1.65541i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.6817 | + | 13.6726i | −0.826498 | + | 0.477179i | −0.852652 | − | 0.522479i | \(-0.825007\pi\) |
0.0261543 | + | 0.999658i | \(0.491674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0437 | + | 20.8603i | −0.419817 | + | 0.727144i | −0.995921 | − | 0.0902322i | \(-0.971239\pi\) |
0.576104 | + | 0.817377i | \(0.304572\pi\) | |||||||
\(824\) | 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 | 0.893545 | − | 0.448974i | \(-0.148211\pi\) |
0.0579490 | + | 0.998320i | \(0.481544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.92053 | − | 10.3137i | 0.0666225 | − | 0.357777i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.8936 | + | 13.2363i | 0.585328 | + | 0.458610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.7357 | + | 16.0478i | −1.02782 | + | 0.554691i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4562 | −1.39670 | −0.698351 | − | 0.715755i | \(-0.746083\pi\) | ||||
−0.698351 | + | 0.715755i | \(0.746083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.6799 | −1.19586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.1383 | − | 28.7068i | −0.349183 | − | 0.988716i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.65809 | + | 10.6001i | −0.125693 | + | 0.364224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.9766 | − | 2.60263i | −0.479677 | − | 0.0893220i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.326015 | + | 0.188225i | 0.0111756 | + | 0.00645226i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 45.7681i | − | 1.56707i | −0.621347 | − | 0.783536i | \(-0.713414\pi\) | ||
0.621347 | − | 0.783536i | \(-0.286586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.95930 | + | 5.12566i | −0.101088 | + | 0.175089i | −0.912133 | − | 0.409894i | \(-0.865566\pi\) |
0.811045 | + | 0.584983i | \(0.198899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.8859 | − | 10.9038i | 0.644377 | − | 0.372031i | −0.141921 | − | 0.989878i | \(-0.545328\pi\) |
0.786299 | + | 0.617847i | \(0.211995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.2764 | + | 27.9791i | 1.67933 | + | 0.953526i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.8100 | − | 18.9429i | 1.11687 | − | 0.644823i | 0.176267 | − | 0.984342i | \(-0.443598\pi\) |
0.940599 | + | 0.339519i | \(0.110264\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −10.8328 | − | 13.4237i | −0.366636 | − | 0.454325i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8427 | − | 46.4929i | −0.906412 | − | 1.56995i | −0.819010 | − | 0.573779i | \(-0.805477\pi\) |
−0.0874025 | − | 0.996173i | \(-0.527857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.34674 | + | 2.24147i | −0.214070 | + | 0.0756029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.12570 | −0.0379259 | −0.0189630 | − | 0.999820i | \(-0.506036\pi\) | ||||
−0.0189630 | + | 0.999820i | \(0.506036\pi\) | |||||||
\(882\) | 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 | 0.860867 | + | 0.508829i | \(0.169922\pi\) |
0.0102253 | + | 0.999948i | \(0.496745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.21556 | + | 1.40029i | 0.0407684 | + | 0.0469641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.5964 | − | 26.0291i | 0.790509 | − | 0.872008i | ||||
\(892\) | 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 | ||||||||
\(903\) | −17.6634 | − | 10.0293i | −0.587801 | − | 0.333754i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.57234 | + | 6.18747i | −0.118618 | + | 0.205452i | −0.919220 | − | 0.393744i | \(-0.871180\pi\) |
0.800602 | + | 0.599196i | \(0.204513\pi\) | |||||||
\(908\) | 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 | −0.837503 | − | 0.546433i | \(-0.815985\pi\) |
−0.0544730 | − | 0.998515i | \(-0.517348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0690741 | − | 0.195584i | −0.00227607 | − | 0.00644471i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.0246 | 0.724950 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.06388 | − | 2.75758i | 0.0349425 | − | 0.0905709i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.8140 | + | 32.5869i | 0.617269 | + | 1.06914i | 0.989982 | + | 0.141194i | \(0.0450942\pi\) |
−0.372713 | + | 0.927947i | \(0.621573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.89970 | − | 22.1154i | −0.291676 | − | 0.724802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.16773 | − | 22.3816i | 0.136445 | − | 0.732740i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.05652i | 0.0998522i | 0.998753 | + | 0.0499261i | \(0.0158986\pi\) | ||||
−0.998753 | + | 0.0499261i | \(0.984101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.2008 | + | 30.6248i | −0.855030 | + | 0.999402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3577 | − | 47.3849i | 0.891835 | − | 1.54470i | 0.0541612 | − | 0.998532i | \(-0.482752\pi\) |
0.837674 | − | 0.546171i | \(-0.183915\pi\) | |||||||
\(942\) | 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 | \(-0.629517\pi\) |
0.597443 | + | 0.801911i | \(0.296183\pi\) | |||||||
\(948\) | 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 | ||||||||
\(957\) | −9.87729 | + | 53.0431i | −0.319287 | + | 1.71464i | ||||
\(958\) | 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 | ||||||||
\(963\) | 1.39462 | − | 3.61485i | 0.0449410 | − | 0.116487i | ||||
\(964\) | 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 | ||||||||
\(969\) | 6.02238 | + | 17.0524i | 0.193467 | + | 0.547802i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.37642 | + | 12.7763i | 0.236721 | + | 0.410012i | 0.959771 | − | 0.280783i | \(-0.0905940\pi\) |
−0.723051 | + | 0.690795i | \(0.757261\pi\) | |||||||
\(972\) | 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 | \(-0.327007\pi\) |
−0.482692 | + | 0.875790i | \(0.660341\pi\) | |||||||
\(978\) | 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 | \(-0.771588\pi\) |
0.946166 | + | 0.323683i | \(0.104921\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.331534 | − | 46.0959i | −0.0105528 | − | 1.46725i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.0311 | + | 6.36883i | −0.350770 | + | 0.202517i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.50767 | + | 7.80752i | −0.143191 | + | 0.248014i | −0.928697 | − | 0.370841i | \(-0.879070\pi\) |
0.785506 | + | 0.618854i | \(0.212403\pi\) | |||||||
\(992\) | 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 | 0.956130 | − | 0.292942i | \(-0.0946344\pi\) |
0.224370 | + | 0.974504i | \(0.427968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.680401 | + | 0.0195419i | 0.0215270 | + | 0.000618278i |
(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.j.101.5 | 10 | ||
3.2 | odd | 2 | 2100.2.bi.k.101.3 | 10 | |||
5.2 | odd | 4 | 2100.2.bo.g.1949.4 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.g.1949.7 | 20 | |||
5.4 | even | 2 | 420.2.bh.b.101.1 | yes | 10 | ||
7.5 | odd | 6 | 2100.2.bi.k.1601.3 | 10 | |||
15.2 | even | 4 | 2100.2.bo.h.1949.10 | 20 | |||
15.8 | even | 4 | 2100.2.bo.h.1949.1 | 20 | |||
15.14 | odd | 2 | 420.2.bh.a.101.3 | ✓ | 10 | ||
21.5 | even | 6 | inner | 2100.2.bi.j.1601.5 | 10 | ||
35.4 | even | 6 | 2940.2.d.a.881.10 | 10 | |||
35.12 | even | 12 | 2100.2.bo.h.1349.1 | 20 | |||
35.19 | odd | 6 | 420.2.bh.a.341.3 | yes | 10 | ||
35.24 | odd | 6 | 2940.2.d.b.881.1 | 10 | |||
35.33 | even | 12 | 2100.2.bo.h.1349.10 | 20 | |||
105.47 | odd | 12 | 2100.2.bo.g.1349.7 | 20 | |||
105.59 | even | 6 | 2940.2.d.a.881.9 | 10 | |||
105.68 | odd | 12 | 2100.2.bo.g.1349.4 | 20 | |||
105.74 | odd | 6 | 2940.2.d.b.881.2 | 10 | |||
105.89 | even | 6 | 420.2.bh.b.341.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.3 | ✓ | 10 | 15.14 | odd | 2 | ||
420.2.bh.a.341.3 | yes | 10 | 35.19 | odd | 6 | ||
420.2.bh.b.101.1 | yes | 10 | 5.4 | even | 2 | ||
420.2.bh.b.341.1 | yes | 10 | 105.89 | even | 6 | ||
2100.2.bi.j.101.5 | 10 | 1.1 | even | 1 | trivial | ||
2100.2.bi.j.1601.5 | 10 | 21.5 | even | 6 | inner | ||
2100.2.bi.k.101.3 | 10 | 3.2 | odd | 2 | |||
2100.2.bi.k.1601.3 | 10 | 7.5 | odd | 6 | |||
2100.2.bo.g.1349.4 | 20 | 105.68 | odd | 12 | |||
2100.2.bo.g.1349.7 | 20 | 105.47 | odd | 12 | |||
2100.2.bo.g.1949.4 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.g.1949.7 | 20 | 5.3 | odd | 4 | |||
2100.2.bo.h.1349.1 | 20 | 35.12 | even | 12 | |||
2100.2.bo.h.1349.10 | 20 | 35.33 | even | 12 | |||
2100.2.bo.h.1949.1 | 20 | 15.8 | even | 4 | |||
2100.2.bo.h.1949.10 | 20 | 15.2 | even | 4 | |||
2940.2.d.a.881.9 | 10 | 105.59 | even | 6 | |||
2940.2.d.a.881.10 | 10 | 35.4 | even | 6 | |||
2940.2.d.b.881.1 | 10 | 35.24 | odd | 6 | |||
2940.2.d.b.881.2 | 10 | 105.74 | odd | 6 |