Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(401,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.q (of order \(3\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.1201 |
Dual form | 1400.2.q.h.401.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.207107 | − | 0.358719i | 0.119573 | − | 0.207107i | −0.800025 | − | 0.599966i | \(-0.795181\pi\) |
0.919599 | + | 0.392859i | \(0.128514\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62132 | − | 2.09077i | −0.612801 | − | 0.790237i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.414214 | + | 0.717439i | −0.124890 | + | 0.216316i | −0.921690 | − | 0.387927i | \(-0.873191\pi\) |
0.796800 | + | 0.604243i | \(0.206524\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.82843 | + | 6.63103i | −0.928530 | + | 1.60826i | −0.142747 | + | 0.989759i | \(0.545593\pi\) |
−0.785783 | + | 0.618502i | \(0.787740\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | + | 4.89898i | 0.648886 | + | 1.12390i | 0.983389 | + | 0.181509i | \(0.0580980\pi\) |
−0.334504 | + | 0.942394i | \(0.608569\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.08579 | + | 0.148586i | −0.236938 | + | 0.0324242i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.79289 | − | 4.83743i | −0.582358 | − | 1.00867i | −0.995199 | − | 0.0978712i | \(-0.968797\pi\) |
0.412841 | − | 0.910803i | \(-0.364537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.82843 | −1.45370 | −0.726851 | − | 0.686795i | \(-0.759017\pi\) | ||||
−0.726851 | + | 0.686795i | \(0.759017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.414214 | + | 0.717439i | −0.0743950 | + | 0.128856i | −0.900823 | − | 0.434187i | \(-0.857036\pi\) |
0.826428 | + | 0.563042i | \(0.190369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.171573 | + | 0.297173i | 0.0298670 | + | 0.0517312i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | + | 4.89898i | 0.464991 | + | 0.805387i | 0.999201 | − | 0.0399642i | \(-0.0127244\pi\) |
−0.534211 | + | 0.845351i | \(0.679391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.414214 | + | 0.717439i | −0.0663273 | + | 0.114882i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.82843 | 0.910247 | 0.455124 | − | 0.890428i | \(-0.349595\pi\) | ||||
0.455124 | + | 0.890428i | \(0.349595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.89949 | 1.05216 | 0.526082 | − | 0.850434i | \(-0.323661\pi\) | ||||
0.526082 | + | 0.850434i | \(0.323661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.82843 | + | 10.0951i | 0.850163 | + | 1.47253i | 0.881060 | + | 0.473004i | \(0.156830\pi\) |
−0.0308969 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.58579 | + | 2.74666i | 0.222055 | + | 0.384610i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.82843 | + | 4.89898i | −0.388514 | + | 0.672927i | −0.992250 | − | 0.124258i | \(-0.960345\pi\) |
0.603736 | + | 0.797185i | \(0.293678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.34315 | 0.310357 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.32843 | − | 5.76500i | −0.426161 | − | 0.738133i | 0.570367 | − | 0.821390i | \(-0.306801\pi\) |
−0.996528 | + | 0.0832569i | \(0.973468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | − | 6.92820i | 0.356348 | − | 0.872872i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.44975 | + | 11.1713i | −0.787962 | + | 1.36479i | 0.139251 | + | 0.990257i | \(0.455530\pi\) |
−0.927213 | + | 0.374533i | \(0.877803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.31371 | −0.278538 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.82843 | − | 3.16693i | 0.214001 | − | 0.370661i | −0.738962 | − | 0.673747i | \(-0.764684\pi\) |
0.952963 | + | 0.303086i | \(0.0980170\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.17157 | − | 0.297173i | 0.247474 | − | 0.0338660i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.75736 | 0.522188 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.62132 | + | 2.80821i | −0.173824 | + | 0.301072i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.67157 | + | 4.62730i | 0.283186 | + | 0.490493i | 0.972168 | − | 0.234286i | \(-0.0752752\pi\) |
−0.688982 | + | 0.724779i | \(0.741942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.24264 | + | 4.18154i | 0.339921 | + | 0.438345i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.171573 | + | 0.297173i | 0.0177913 | + | 0.0308154i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34315 | −0.235495 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.74264 | − | 9.94655i | 0.571414 | − | 0.989718i | −0.425007 | − | 0.905190i | \(-0.639728\pi\) |
0.996421 | − | 0.0845282i | \(-0.0269383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.79289 | + | 6.56948i | 0.373725 | + | 0.647310i | 0.990135 | − | 0.140115i | \(-0.0447471\pi\) |
−0.616410 | + | 0.787425i | \(0.711414\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.79289 | − | 4.83743i | −0.269999 | − | 0.467652i | 0.698862 | − | 0.715256i | \(-0.253690\pi\) |
−0.968861 | + | 0.247604i | \(0.920357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.15685 | + | 15.8601i | −0.877068 | + | 1.51913i | −0.0225237 | + | 0.999746i | \(0.507170\pi\) |
−0.854544 | + | 0.519379i | \(0.826163\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.34315 | 0.222402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3137 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82843 | − | 4.89898i | −0.261488 | − | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.0711 | − | 2.74666i | 1.83991 | − | 0.251786i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.15685 | + | 8.93193i | 0.468805 | + | 0.811994i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.20711 | − | 2.09077i | 0.108841 | − | 0.188518i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315 | 0.385392 | 0.192696 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.42893 | − | 2.47498i | 0.125810 | − | 0.217910i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.82843 | − | 11.8272i | −0.596602 | − | 1.03335i | −0.993319 | − | 0.115404i | \(-0.963184\pi\) |
0.396716 | − | 0.917941i | \(-0.370150\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.65685 | − | 13.8564i | 0.490511 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | + | 3.46410i | −0.170872 | + | 0.295958i | −0.938725 | − | 0.344668i | \(-0.887992\pi\) |
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.48528 | 0.210799 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.828427 | − | 1.43488i | 0.0692766 | − | 0.119991i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.07107 | + | 2.02922i | 0.170819 | + | 0.167368i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.32843 | − | 4.03295i | −0.190752 | − | 0.330392i | 0.754748 | − | 0.656015i | \(-0.227759\pi\) |
−0.945500 | + | 0.325623i | \(0.894426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.58579 | − | 9.67487i | 0.454565 | − | 0.787329i | −0.544098 | − | 0.839022i | \(-0.683128\pi\) |
0.998663 | + | 0.0516921i | \(0.0164614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.6569 | −1.75085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.656854 | − | 1.13770i | 0.0524227 | − | 0.0907987i | −0.838623 | − | 0.544712i | \(-0.816639\pi\) |
0.891046 | + | 0.453913i | \(0.149972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.17157 | + | 2.02922i | 0.0929118 | + | 0.160928i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.58579 | + | 13.6823i | −0.440222 | + | 1.07832i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.82843 | − | 13.5592i | −0.613170 | − | 1.06204i | −0.990703 | − | 0.136045i | \(-0.956561\pi\) |
0.377533 | − | 0.925996i | \(-0.376773\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07107 | −0.160264 | −0.0801320 | − | 0.996784i | \(-0.525534\pi\) | ||||
−0.0801320 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.00000 | + | 13.8564i | −0.611775 | + | 1.05963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.17157 | + | 8.95743i | 0.393187 | + | 0.681021i | 0.992868 | − | 0.119219i | \(-0.0380390\pi\) |
−0.599681 | + | 0.800239i | \(0.704706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.828427 | − | 1.43488i | −0.0622684 | − | 0.107852i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.24264 | − | 5.61642i | 0.242366 | − | 0.419791i | −0.719022 | − | 0.694988i | \(-0.755410\pi\) |
0.961388 | + | 0.275197i | \(0.0887431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.17157 | −0.310071 | −0.155035 | − | 0.987909i | \(-0.549549\pi\) | ||||
−0.155035 | + | 0.987909i | \(0.549549\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.75736 | −0.203830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.17157 | − | 5.49333i | −0.231928 | − | 0.401712i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.91421 | − | 5.04757i | −0.284717 | − | 0.367156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.75736 | + | 4.77589i | 0.199516 | + | 0.345571i | 0.948371 | − | 0.317162i | \(-0.102730\pi\) |
−0.748856 | + | 0.662733i | \(0.769397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.65685 | + | 4.60181i | −0.191245 | + | 0.331245i | −0.945663 | − | 0.325149i | \(-0.894586\pi\) |
0.754418 | + | 0.656394i | \(0.227919\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.343146 | −0.0244481 | −0.0122241 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122241 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6569 | − | 20.1903i | 0.826332 | − | 1.43125i | −0.0745642 | − | 0.997216i | \(-0.523757\pi\) |
0.900897 | − | 0.434034i | \(-0.142910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.67157 | + | 4.62730i | 0.188438 | + | 0.326385i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6924 | + | 16.3674i | 0.890831 | + | 1.14877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.89949 | − | 13.6823i | 0.549053 | − | 0.950987i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.68629 | −0.324158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.6274 | 1.83311 | 0.916553 | − | 0.399912i | \(-0.130959\pi\) | ||||
0.916553 | + | 0.399912i | \(0.130959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.48528 | + | 4.30463i | −0.170289 | + | 0.294949i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.17157 | − | 0.297173i | 0.147416 | − | 0.0201734i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.757359 | − | 1.31178i | −0.0511776 | − | 0.0886422i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.65685 | − | 13.2621i | 0.515056 | − | 0.892103i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9706 | 1.00250 | 0.501252 | − | 0.865302i | \(-0.332873\pi\) | ||||
0.501252 | + | 0.865302i | \(0.332873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.00000 | − | 12.1244i | 0.464606 | − | 0.804722i | −0.534577 | − | 0.845120i | \(-0.679529\pi\) |
0.999184 | + | 0.0403978i | \(0.0128625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.343146 | − | 0.840532i | 0.0225773 | − | 0.0553029i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.82843 | + | 10.0951i | 0.381833 | + | 0.661354i | 0.991324 | − | 0.131439i | \(-0.0419596\pi\) |
−0.609491 | + | 0.792793i | \(0.708626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.65685 | 0.107624 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.4853 | −1.97193 | −0.985964 | − | 0.166955i | \(-0.946606\pi\) | ||||
−0.985964 | + | 0.166955i | \(0.946606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.17157 | + | 8.95743i | 0.331757 | + | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.65685 | − | 9.79796i | −0.359937 | − | 0.623429i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.985281 | − | 1.70656i | 0.0624397 | − | 0.108149i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4558 | −1.73300 | −0.866499 | − | 0.499179i | \(-0.833635\pi\) | ||||
−0.866499 | + | 0.499179i | \(0.833635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.62742 | 0.290923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.65685 | + | 13.2621i | 0.477621 | + | 0.827265i | 0.999671 | − | 0.0256506i | \(-0.00816572\pi\) |
−0.522050 | + | 0.852915i | \(0.674832\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.65685 | − | 13.8564i | 0.351500 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.0711 | − | 19.1757i | −0.685282 | − | 1.18694i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.86396 | + | 13.6208i | −0.484913 | + | 0.839893i | −0.999850 | − | 0.0173347i | \(-0.994482\pi\) |
0.514937 | + | 0.857228i | \(0.327815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.21320 | 0.135446 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.32843 | − | 5.76500i | 0.202938 | − | 0.351499i | −0.746536 | − | 0.665345i | \(-0.768284\pi\) |
0.949474 | + | 0.313847i | \(0.101618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65685 | + | 2.86976i | 0.100647 | + | 0.174325i | 0.911951 | − | 0.410298i | \(-0.134575\pi\) |
−0.811305 | + | 0.584624i | \(0.801242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.17157 | − | 0.297173i | 0.131430 | − | 0.0179857i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3137 | − | 24.7921i | 0.860027 | − | 1.48961i | −0.0118739 | − | 0.999930i | \(-0.503780\pi\) |
0.871901 | − | 0.489682i | \(-0.162887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34315 | −0.140280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.68629 | 0.160251 | 0.0801254 | − | 0.996785i | \(-0.474468\pi\) | ||||
0.0801254 | + | 0.996785i | \(0.474468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00000 | − | 15.5885i | 0.534994 | − | 0.926638i | −0.464169 | − | 0.885747i | \(-0.653647\pi\) |
0.999164 | − | 0.0408910i | \(-0.0130196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.44975 | − | 12.1859i | −0.557801 | − | 0.719311i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.8137 | − | 36.0504i | −1.22434 | − | 2.12061i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.24264 | + | 2.15232i | −0.0728449 | + | 0.126171i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9706 | −0.991431 | −0.495715 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495715 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.58579 | + | 9.67487i | 0.323034 | + | 0.559512i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.1863 | − | 14.4253i | −0.644767 | − | 0.831458i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.37868 | − | 4.11999i | −0.136652 | − | 0.236687i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.75736 | −0.271517 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.14214 | 0.178750 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8284 | + | 18.7554i | −0.614024 | + | 1.06352i | 0.376531 | + | 0.926404i | \(0.377117\pi\) |
−0.990555 | + | 0.137116i | \(0.956217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4853 | + | 18.1610i | 0.592663 | + | 1.02652i | 0.993872 | + | 0.110536i | \(0.0352568\pi\) |
−0.401209 | + | 0.915987i | \(0.631410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0000 | − | 19.0526i | −0.617822 | − | 1.07010i | −0.989882 | − | 0.141890i | \(-0.954682\pi\) |
0.372061 | − | 0.928208i | \(-0.378651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.24264 | − | 5.61642i | 0.181553 | − | 0.314459i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31371 | −0.129139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.3137 | −2.41004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.79289 | + | 6.56948i | 0.209747 | + | 0.363293i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6569 | − | 28.5533i | 0.642663 | − | 1.57420i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2426 | − | 22.9369i | −0.727881 | − | 1.26073i | −0.957777 | − | 0.287512i | \(-0.907172\pi\) |
0.229896 | − | 0.973215i | \(-0.426162\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | + | 13.8564i | −0.438397 | + | 0.759326i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.9706 | −1.36023 | −0.680117 | − | 0.733104i | \(-0.738071\pi\) | ||||
−0.680117 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.34315 | + | 4.05845i | −0.127262 | + | 0.220425i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.343146 | − | 0.594346i | −0.0185824 | − | 0.0321856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.69239 | − | 9.85951i | 0.305583 | − | 0.529286i | −0.671808 | − | 0.740726i | \(-0.734482\pi\) |
0.977391 | + | 0.211440i | \(0.0678152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.82843 | 0.526104 | 0.263052 | − | 0.964782i | \(-0.415271\pi\) | ||||
0.263052 | + | 0.964782i | \(0.415271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8284 | − | 29.1477i | 0.895687 | − | 1.55138i | 0.0627345 | − | 0.998030i | \(-0.480018\pi\) |
0.832952 | − | 0.553345i | \(-0.186649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.17157 | − | 7.76874i | 0.167857 | − | 0.411165i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.24264 | + | 5.61642i | 0.171140 | + | 0.296423i | 0.938819 | − | 0.344412i | \(-0.111922\pi\) |
−0.767679 | + | 0.640835i | \(0.778588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.50000 | + | 11.2583i | −0.342105 | + | 0.592544i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.27208 | 0.224226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7929 | − | 18.6938i | 0.563384 | − | 0.975810i | −0.433814 | − | 0.901003i | \(-0.642832\pi\) |
0.997198 | − | 0.0748078i | \(-0.0238343\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.24264 | + | 14.2767i | 0.429095 | + | 0.743214i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.8284 | − | 2.02922i | 0.769854 | − | 0.105352i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | + | 10.3923i | 0.310668 | + | 0.538093i | 0.978507 | − | 0.206213i | \(-0.0661139\pi\) |
−0.667839 | + | 0.744306i | \(0.732781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.6569 | 0.806369 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.68629 | 0.240719 | 0.120359 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120359 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.899495 | − | 1.55797i | 0.0460825 | − | 0.0798173i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.449747 | − | 0.778985i | −0.0229810 | − | 0.0398043i | 0.854306 | − | 0.519770i | \(-0.173982\pi\) |
−0.877287 | + | 0.479966i | \(0.840649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.75736 | + | 16.9002i | 0.495994 | + | 0.859088i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.65685 | + | 4.60181i | −0.134708 | + | 0.233321i | −0.925486 | − | 0.378782i | \(-0.876343\pi\) |
0.790778 | + | 0.612103i | \(0.209676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.7696 | 2.16295 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | −0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.3137 | − | 21.3280i | −0.618007 | − | 1.07042i | −0.989849 | − | 0.142124i | \(-0.954607\pi\) |
0.371842 | − | 0.928296i | \(-0.378726\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.79899 | − | 4.89898i | −0.190187 | − | 0.245256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.1569 | + | 27.9845i | 0.806835 | + | 1.39748i | 0.915045 | + | 0.403351i | \(0.132155\pi\) |
−0.108211 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.828427 | − | 1.43488i | 0.0412669 | − | 0.0714764i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.68629 | −0.232291 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5711 | − | 21.7737i | 0.621599 | − | 1.07664i | −0.367589 | − | 0.929988i | \(-0.619817\pi\) |
0.989188 | − | 0.146653i | \(-0.0468501\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.828427 | + | 1.43488i | 0.0408633 | + | 0.0707773i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4853 | + | 1.43488i | −0.515947 | + | 0.0706057i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.514719 | − | 0.891519i | 0.0252059 | − | 0.0436579i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3137 | −0.748124 | −0.374062 | − | 0.927404i | \(-0.622035\pi\) | ||||
−0.374062 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3431 | 1.33262 | 0.666312 | − | 0.745673i | \(-0.267872\pi\) | ||||
0.666312 | + | 0.745673i | \(0.267872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.4853 | + | 28.5533i | −0.801542 | + | 1.38831i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.65685 | + | 16.3059i | −0.322148 | + | 0.789098i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.343146 | − | 0.594346i | −0.0165672 | − | 0.0286953i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.414214 | − | 0.717439i | 0.0199520 | − | 0.0345578i | −0.855877 | − | 0.517179i | \(-0.826982\pi\) |
0.875829 | + | 0.482622i | \(0.160315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3137 | 0.928158 | 0.464079 | − | 0.885794i | \(-0.346385\pi\) | ||||
0.464079 | + | 0.885794i | \(0.346385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7990 | − | 27.3647i | 0.755768 | − | 1.30903i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.17157 | + | 15.8856i | 0.437735 | + | 0.758180i | 0.997514 | − | 0.0704621i | \(-0.0224474\pi\) |
−0.559779 | + | 0.828642i | \(0.689114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.0711 | + | 5.31925i | −0.908146 | + | 0.253297i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79289 | − | 13.4977i | −0.370252 | − | 0.641294i | 0.619353 | − | 0.785113i | \(-0.287395\pi\) |
−0.989604 | + | 0.143819i | \(0.954062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.92893 | −0.0912354 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.48528 | −0.353252 | −0.176626 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176626 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.41421 | + | 4.18154i | −0.113681 | + | 0.196901i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.31371 | − | 4.00746i | −0.108708 | − | 0.188287i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.4853 | + | 25.0892i | 0.677593 | + | 1.17363i | 0.975704 | + | 0.219094i | \(0.0703102\pi\) |
−0.298111 | + | 0.954531i | \(0.596357\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.24264 | + | 16.0087i | −0.431410 | + | 0.747223i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.31371 | 0.0611855 | 0.0305928 | − | 0.999532i | \(-0.490261\pi\) | ||||
0.0305928 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8995 | −0.692438 | −0.346219 | − | 0.938154i | \(-0.612535\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.9350 | − | 32.7964i | −0.876209 | − | 1.51764i | −0.855470 | − | 0.517853i | \(-0.826731\pi\) |
−0.0207390 | − | 0.999785i | \(-0.506602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.8137 | − | 4.62730i | 1.56137 | − | 0.213669i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.272078 | − | 0.471253i | −0.0125367 | − | 0.0217142i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.85786 | + | 4.94997i | −0.131405 | + | 0.227600i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0000 | −0.732590 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.757359 | − | 1.31178i | 0.0346046 | − | 0.0599370i | −0.848204 | − | 0.529669i | \(-0.822316\pi\) |
0.882809 | + | 0.469732i | \(0.155649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65685 | − | 9.79796i | −0.257930 | − | 0.446748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.75126 | + | 4.83743i | 0.170688 | + | 0.220111i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1421 | + | 33.1552i | −0.867413 | + | 1.50240i | −0.00278182 | + | 0.999996i | \(0.500885\pi\) |
−0.864631 | + | 0.502407i | \(0.832448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.48528 | −0.293275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51472 | 0.0683583 | 0.0341791 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341791 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.9706 | − | 51.9105i | 1.34981 | − | 2.33793i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.4558 | + | 25.0892i | 0.872714 | + | 1.12541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0711 | − | 38.2282i | −0.988037 | − | 1.71133i | −0.627576 | − | 0.778555i | \(-0.715953\pi\) |
−0.360461 | − | 0.932774i | \(-0.617381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.428932 | + | 0.742932i | −0.0191633 | + | 0.0331918i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.92893 | 0.175182 | 0.0875912 | − | 0.996157i | \(-0.472083\pi\) | ||||
0.0875912 | + | 0.996157i | \(0.472083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.86396 | + | 3.22848i | −0.0827814 | + | 0.143382i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7426 | + | 28.9991i | 0.742105 | + | 1.28536i | 0.951535 | + | 0.307539i | \(0.0995055\pi\) |
−0.209431 | + | 0.977823i | \(0.567161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.58579 | + | 1.31178i | −0.424050 | + | 0.0580299i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.82843 | + | 11.8272i | 0.301482 | + | 0.522183i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.65685 | −0.424708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.28427 | 0.188059 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.3137 | + | 31.7203i | −0.802338 | + | 1.38969i | 0.115735 | + | 0.993280i | \(0.463078\pi\) |
−0.918073 | + | 0.396410i | \(0.870256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9706 | + | 24.1977i | 0.610890 | + | 1.05809i | 0.991091 | + | 0.133189i | \(0.0425216\pi\) |
−0.380201 | + | 0.924904i | \(0.624145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.17157 | − | 5.49333i | −0.138156 | − | 0.239293i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.10051 | + | 7.10228i | −0.178283 | + | 0.308795i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | 0.490973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.6569 | −0.504914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.34315 | − | 2.32640i | −0.0579610 | − | 0.100391i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.14214 | − | 4.05845i | −0.178414 | − | 0.174810i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7426 | + | 20.3389i | 0.504856 | + | 0.874435i | 0.999984 | + | 0.00561582i | \(0.00178758\pi\) |
−0.495129 | + | 0.868820i | \(0.664879\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.863961 | + | 1.49642i | −0.0370761 | + | 0.0642177i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.27208 | 0.0971470 | 0.0485735 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485735 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.41421 | − | 16.3059i | 0.401789 | − | 0.695919i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.1421 | − | 38.3513i | −0.943287 | − | 1.63382i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 9.79796i | 0.170097 | − | 0.416652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.65685 | + | 14.9941i | −0.366803 | + | 0.635321i | −0.989064 | − | 0.147489i | \(-0.952881\pi\) |
0.622261 | + | 0.782810i | \(0.286214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7990 | −0.583635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.62742 | −0.110930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.03553 | + | 3.52565i | −0.0857875 | + | 0.148588i | −0.905727 | − | 0.423863i | \(-0.860674\pi\) |
0.819939 | + | 0.572451i | \(0.194007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.6213 | − | 2.68512i | 0.824018 | − | 0.112764i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.3137 | + | 31.7203i | 0.767751 | + | 1.32978i | 0.938780 | + | 0.344517i | \(0.111957\pi\) |
−0.171029 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.4853 | − | 18.1610i | 0.438795 | − | 0.760016i | −0.558801 | − | 0.829301i | \(-0.688739\pi\) |
0.997597 | + | 0.0692856i | \(0.0220720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.28427 | 0.0954268 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1421 | + | 19.2987i | −0.463853 | + | 0.803417i | −0.999149 | − | 0.0412474i | \(-0.986867\pi\) |
0.535296 | + | 0.844665i | \(0.320200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.10051 | + | 1.90613i | 0.0457354 | + | 0.0792161i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.71320 | − | 9.94655i | −0.319998 | − | 0.412652i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.34315 | − | 4.05845i | −0.0970432 | − | 0.168084i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6863 | 0.936363 | 0.468182 | − | 0.883632i | \(-0.344909\pi\) | ||||
0.468182 | + | 0.883632i | \(0.344909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.68629 | −0.193095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0710678 | + | 0.123093i | −0.00292334 | + | 0.00506337i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.9706 | + | 25.9298i | 0.614767 | + | 1.06481i | 0.990425 | + | 0.138050i | \(0.0440834\pi\) |
−0.375658 | + | 0.926758i | \(0.622583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.82843 | − | 8.36308i | −0.197614 | − | 0.342278i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3137 | + | 36.9164i | −0.870855 | + | 1.50836i | −0.00974040 | + | 0.999953i | \(0.503101\pi\) |
−0.861114 | + | 0.508412i | \(0.830233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.4853 | −1.48580 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6213 | + | 23.5928i | 0.552872 | + | 0.957603i | 0.998066 | + | 0.0621685i | \(0.0198016\pi\) |
−0.445193 | + | 0.895434i | \(0.646865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.50000 | − | 1.16320i | 0.344437 | − | 0.0471352i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.6569 | − | 20.1903i | −0.471586 | − | 0.816811i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4853 | − | 33.7495i | 0.787003 | − | 1.36313i | −0.140792 | − | 0.990039i | \(-0.544965\pi\) |
0.927795 | − | 0.373090i | \(-0.121702\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6863 | 0.510731 | 0.255365 | − | 0.966845i | \(-0.417804\pi\) | ||||
0.255365 | + | 0.966845i | \(0.417804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7279 | + | 34.1698i | −0.792932 | + | 1.37340i | 0.131212 | + | 0.991354i | \(0.458113\pi\) |
−0.924144 | + | 0.382044i | \(0.875220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.74264 | − | 11.6786i | −0.270573 | − | 0.468646i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.34315 | − | 13.0880i | 0.214069 | − | 0.524359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.970563 | + | 1.68106i | −0.0387605 | + | 0.0671352i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.3137 | −1.72703 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51472 | −0.0603000 | −0.0301500 | − | 0.999545i | \(-0.509598\pi\) | ||||
−0.0301500 | + | 0.999545i | \(0.509598\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.51472 | − | 9.55177i | 0.219190 | − | 0.379649i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.48528 | − | 13.5592i | 0.138092 | − | 0.537236i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.9706 | − | 29.3939i | −0.671345 | − | 1.16280i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.05635 | + | 12.2220i | −0.278709 | + | 0.482738i | −0.971064 | − | 0.238819i | \(-0.923240\pi\) |
0.692355 | + | 0.721557i | \(0.256573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3787 | + | 17.9764i | −0.408028 | + | 0.706725i | −0.994669 | − | 0.103122i | \(-0.967117\pi\) |
0.586641 | + | 0.809847i | \(0.300450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.65685 | + | 2.86976i | 0.0650372 | + | 0.112648i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.343146 | − | 0.840532i | 0.0134489 | − | 0.0329430i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.82843 | − | 13.5592i | −0.306350 | − | 0.530614i | 0.671211 | − | 0.741266i | \(-0.265774\pi\) |
−0.977561 | + | 0.210653i | \(0.932441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3431 | 0.403525 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.6863 | 0.494188 | 0.247094 | − | 0.968992i | \(-0.420524\pi\) | ||||
0.247094 | + | 0.968992i | \(0.420524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1569 | − | 43.5729i | 0.978488 | − | 1.69479i | 0.310581 | − | 0.950547i | \(-0.399476\pi\) |
0.667907 | − | 0.744244i | \(-0.267190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.17157 | − | 5.49333i | −0.123174 | − | 0.213343i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.8640 | + | 37.8695i | 0.846576 | + | 1.46631i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.10051 | − | 5.37023i | 0.119872 | − | 0.207625i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.51472 | 0.212893 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.65685 | 0.218056 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.4853 | + | 19.8931i | 0.441415 | + | 0.764554i | 0.997795 | − | 0.0663747i | \(-0.0211433\pi\) |
−0.556380 | + | 0.830928i | \(0.687810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.72792 | + | 12.5446i | 0.373323 | + | 0.481418i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.89949 | − | 5.02207i | −0.111109 | − | 0.192446i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.964466 | + | 1.67050i | −0.0369043 | + | 0.0639201i | −0.883888 | − | 0.467699i | \(-0.845083\pi\) |
0.846983 | + | 0.531619i | \(0.178416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.79899 | 0.221245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.65685 | − | 9.79796i | 0.215509 | − | 0.373273i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3848 | + | 37.0395i | 0.813515 | + | 1.40905i | 0.910389 | + | 0.413753i | \(0.135782\pi\) |
−0.0968739 | + | 0.995297i | \(0.530884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.79899 | + | 4.89898i | 0.144312 | + | 0.186097i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.3137 | + | 38.6485i | −0.845192 | + | 1.46392i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.82843 | 0.182628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0000 | −0.415464 | −0.207732 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207732 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0000 | + | 27.7128i | −0.603451 | + | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.1066 | + | 4.11999i | −1.13228 | + | 0.154948i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7132 | + | 30.6802i | 0.665233 | + | 1.15222i | 0.979222 | + | 0.202791i | \(0.0650013\pi\) |
−0.313989 | + | 0.949427i | \(0.601665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.65685 | + | 9.79796i | −0.212149 | + | 0.367452i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.62742 | 0.173298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.31371 | + | 10.9357i | −0.235790 | + | 0.408400i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8995 | + | 22.3426i | 0.481070 | + | 0.833238i | 0.999764 | − | 0.0217223i | \(-0.00691496\pi\) |
−0.518694 | + | 0.854960i | \(0.673582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.58579 | − | 18.5813i | 0.282509 | − | 0.692004i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.07107 | − | 3.58719i | −0.0770238 | − | 0.133409i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.0711 | −1.41198 | −0.705989 | − | 0.708223i | \(-0.749497\pi\) | ||||
−0.705989 | + | 0.708223i | \(0.749497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.4142 | + | 45.7508i | −0.976965 | + | 1.69215i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.82843 | + | 6.63103i | 0.141406 | + | 0.244923i | 0.928026 | − | 0.372514i | \(-0.121504\pi\) |
−0.786620 | + | 0.617437i | \(0.788171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.34315 | − | 9.25460i | −0.196817 | − | 0.340898i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.41421 | + | 14.5738i | −0.309522 | + | 0.536108i | −0.978258 | − | 0.207392i | \(-0.933502\pi\) |
0.668736 | + | 0.743500i | \(0.266836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.68629 | −0.172155 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7574 | 0.394649 | 0.197325 | − | 0.980338i | \(-0.436775\pi\) | ||||
0.197325 | + | 0.980338i | \(0.436775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.72792 | + | 11.6531i | 0.246162 | + | 0.426365i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.58579 | + | 13.6823i | −0.204100 | + | 0.499941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.00000 | + | 10.3923i | 0.218943 | + | 0.379221i | 0.954485 | − | 0.298259i | \(-0.0964058\pi\) |
−0.735542 | + | 0.677479i | \(0.763072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.68629 | + | 9.84895i | −0.207220 | + | 0.358916i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00000 | −0.218074 | −0.109037 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109037 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.958369 | − | 1.65994i | 0.0347866 | − | 0.0602522i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9706 | + | 38.0541i | 0.796432 | + | 1.37946i | 0.921926 | + | 0.387367i | \(0.126615\pi\) |
−0.125493 | + | 0.992094i | \(0.540051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.0061 | − | 6.56948i | 1.73794 | − | 0.237831i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | + | 6.92820i | −0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.2548 | 1.55981 | 0.779905 | − | 0.625898i | \(-0.215268\pi\) | ||||
0.779905 | + | 0.625898i | \(0.215268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.34315 | 0.228443 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1716 | − | 21.0818i | 0.437781 | − | 0.758259i | −0.559737 | − | 0.828670i | \(-0.689098\pi\) |
0.997518 | + | 0.0704113i | \(0.0224312\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.79899 | − | 4.89898i | −0.136288 | − | 0.175750i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.4853 | + | 28.5533i | 0.590647 | + | 1.02303i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97056 | − | 8.60927i | 0.177861 | − | 0.308064i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.8995 | −0.675413 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.792893 | + | 1.37333i | −0.0282636 | + | 0.0489540i | −0.879811 | − | 0.475323i | \(-0.842331\pi\) |
0.851548 | + | 0.524277i | \(0.175664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.25736 | + | 5.64191i | 0.115965 | + | 0.200857i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3431 | + | 23.6544i | 0.652207 | + | 0.841052i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.65685 | + | 11.5300i | 0.236392 | + | 0.409443i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3137 | 1.25088 | 0.625438 | − | 0.780274i | \(-0.284920\pi\) | ||||
0.625438 | + | 0.780274i | \(0.284920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −89.2548 | −3.15761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.55635 | + | 13.0880i | −0.266990 | + | 0.462441i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.51472 | + | 2.62357i | 0.0534533 | + | 0.0925838i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.37868 | − | 2.38794i | −0.0485318 | − | 0.0840596i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.9853 | − | 31.1514i | 0.632329 | − | 1.09523i | −0.354746 | − | 0.934963i | \(-0.615433\pi\) |
0.987074 | − | 0.160263i | \(-0.0512342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.1421 | 1.83096 | 0.915479 | − | 0.402366i | \(-0.131812\pi\) | ||||
0.915479 | + | 0.402366i | \(0.131812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37258 | 0.0481386 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.5147 | + | 33.8005i | 0.682734 | + | 1.18253i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.65685 | + | 13.8564i | −0.197666 | + | 0.484182i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3137 | + | 28.2562i | 0.569352 | + | 0.986147i | 0.996630 | + | 0.0820268i | \(0.0261393\pi\) |
−0.427278 | + | 0.904120i | \(0.640527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0061 | − | 25.9913i | 0.523080 | − | 0.906001i | −0.476560 | − | 0.879142i | \(-0.658116\pi\) |
0.999639 | − | 0.0268584i | \(-0.00855031\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.5269 | −0.470377 | −0.235188 | − | 0.971950i | \(-0.575571\pi\) | ||||
−0.235188 | + | 0.971950i | \(0.575571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.65685 | + | 4.60181i | −0.0922764 | + | 0.159827i | −0.908469 | − | 0.417953i | \(-0.862748\pi\) |
0.816192 | + | 0.577780i | \(0.196081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.92893 | − | 10.2692i | −0.205672 | − | 0.356235i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.2843 | − | 37.5108i | −1.32647 | − | 1.29967i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.1421 | 0.695384 | 0.347692 | − | 0.937609i | \(-0.386966\pi\) | ||||
0.347692 | + | 0.937609i | \(0.386966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.2843 | 1.11325 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.556349 | − | 0.963625i | 0.0191617 | − | 0.0331890i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3137 | − | 25.2633i | 0.354383 | − | 0.868058i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.72792 | − | 6.45695i | −0.127942 | − | 0.221602i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.7990 | − | 27.3647i | 0.541582 | − | 0.938048i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.6863 | −0.434370 | −0.217185 | − | 0.976130i | \(-0.569688\pi\) | ||||
−0.217185 | + | 0.976130i | \(0.569688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.48528 | + | 16.4290i | −0.324011 | + | 0.561204i | −0.981312 | − | 0.192425i | \(-0.938365\pi\) |
0.657301 | + | 0.753628i | \(0.271698\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3137 | + | 26.5241i | 0.522497 | + | 0.904991i | 0.999657 | + | 0.0261751i | \(0.00833275\pi\) |
−0.477160 | + | 0.878816i | \(0.658334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.32843 | + | 0.866025i | −0.215672 | + | 0.0295141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0061 | − | 48.5080i | −0.953339 | − | 1.65123i | −0.738125 | − | 0.674664i | \(-0.764289\pi\) |
−0.215214 | − | 0.976567i | \(-0.569045\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.2426 | −0.585591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.31371 | −0.112410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8995 | − | 22.3426i | 0.437083 | − | 0.757049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.48528 | − | 14.6969i | −0.287183 | − | 0.497416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1421 | − | 24.4949i | −0.477546 | − | 0.827134i | 0.522123 | − | 0.852870i | \(-0.325140\pi\) |
−0.999669 | + | 0.0257364i | \(0.991807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.51472 | + | 6.08767i | −0.118549 | + | 0.205332i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.4558 | −0.891320 | −0.445660 | − | 0.895202i | \(-0.647031\pi\) | ||||
−0.445660 | + | 0.895202i | \(0.647031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.68629 | −0.225012 | −0.112506 | − | 0.993651i | \(-0.535888\pi\) | ||||
−0.112506 | + | 0.993651i | \(0.535888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.79289 | + | 15.2297i | 0.295236 | + | 0.511365i | 0.975040 | − | 0.222030i | \(-0.0712682\pi\) |
−0.679803 | + | 0.733394i | \(0.737935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.04163 | − | 9.08052i | −0.236169 | − | 0.304551i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.10051 | − | 5.37023i | −0.103871 | − | 0.179910i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.9706 | + | 57.1067i | −1.10332 | + | 1.91100i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.62742 | 0.154505 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.24264 | − | 5.61642i | 0.108148 | − | 0.187318i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6569 | − | 37.5108i | −0.721494 | − | 1.24966i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.49138 | + | 1.02517i | −0.249297 | + | 0.0341156i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.1066 | − | 40.0218i | 0.767242 | − | 1.32890i | −0.171811 | − | 0.985130i | \(-0.554962\pi\) |
0.939053 | − | 0.343772i | \(-0.111705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4853 | 1.07747 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4853 | −0.612445 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.97056 | + | 3.41311i | −0.0652161 | + | 0.112958i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.6569 | + | 33.4523i | −0.450989 | + | 1.10469i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.6274 | + | 28.7995i | 0.548488 | + | 0.950009i | 0.998378 | + | 0.0569252i | \(0.0181296\pi\) |
−0.449891 | + | 0.893084i | \(0.648537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.985281 | + | 1.70656i | −0.0324661 | + | 0.0562330i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.7279 | + | 18.5813i | −0.352351 | + | 0.610290i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.60051 | − | 7.96831i | −0.150938 | − | 0.261432i | 0.780635 | − | 0.624988i | \(-0.214896\pi\) |
−0.931572 | + | 0.363556i | \(0.881563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.1421 | + | 10.6385i | −1.25006 | + | 0.348662i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.48528 | + | 7.76874i | 0.146842 | + | 0.254337i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.6274 | −0.608531 | −0.304266 | − | 0.952587i | \(-0.598411\pi\) | ||||
−0.304266 | + | 0.952587i | \(0.598411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.68629 | 0.283466 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.00000 | − | 8.66025i | 0.162995 | − | 0.282316i | −0.772946 | − | 0.634472i | \(-0.781218\pi\) |
0.935942 | + | 0.352155i | \(0.114551\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.2782 | − | 28.1946i | −0.530090 | − | 0.918143i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.55025 | + | 9.61332i | 0.180359 | + | 0.312391i | 0.942003 | − | 0.335605i | \(-0.108941\pi\) |
−0.761644 | + | 0.647996i | \(0.775607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.65685 | + | 6.33386i | −0.118707 | + | 0.205606i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.11270 | −0.295499 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.6274 | 1.76956 | 0.884778 | − | 0.466013i | \(-0.154310\pi\) | ||||
0.884778 | + | 0.466013i | \(0.154310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.34315 | − | 2.32640i | −0.0434177 | − | 0.0752017i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.4853 | − | 1.43488i | 0.338587 | − | 0.0463346i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1569 | + | 26.2524i | 0.488931 | + | 0.846853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.89949 | − | 13.6823i | 0.254558 | − | 0.440907i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7574 | 0.796143 | 0.398072 | − | 0.917354i | \(-0.369680\pi\) | ||||
0.398072 | + | 0.917354i | \(0.369680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.97056 | + | 15.5375i | −0.288176 | + | 0.499135i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00000 | − | 6.92820i | −0.128366 | − | 0.222337i | 0.794678 | − | 0.607032i | \(-0.207640\pi\) |
−0.923044 | + | 0.384695i | \(0.874307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.02944 | − | 5.19615i | −0.129178 | − | 0.166581i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1421 | − | 26.2269i | 0.484440 | − | 0.839074i | −0.515400 | − | 0.856949i | \(-0.672357\pi\) |
0.999840 | + | 0.0178751i | \(0.00569012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.42641 | −0.141469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.7990 | −1.65381 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.6924 | + | 35.8403i | −0.659985 | + | 1.14313i | 0.320634 | + | 0.947203i | \(0.396104\pi\) |
−0.980619 | + | 0.195924i | \(0.937229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.82843 | − | 10.0951i | −0.249182 | − | 0.321332i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.2696 | − | 33.3758i | −0.612736 | − | 1.06129i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.41421 | + | 4.18154i | −0.0766900 | + | 0.132831i | −0.901820 | − | 0.432112i | \(-0.857769\pi\) |
0.825130 | + | 0.564943i | \(0.191102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9706 | −0.348140 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.17157 | + | 12.4215i | −0.227126 | + | 0.393394i | −0.956955 | − | 0.290236i | \(-0.906266\pi\) |
0.729829 | + | 0.683630i | \(0.239600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.82843 | + | 11.8272i | 0.216042 | + | 0.374196i |
(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 | 1400.2.q.h.1201.2 | 4 | ||
5.2 | odd | 4 | 1400.2.bh.g.249.2 | 8 | |||
5.3 | odd | 4 | 1400.2.bh.g.249.3 | 8 | |||
5.4 | even | 2 | 280.2.q.d.81.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 1400.2.q.h.401.2 | 4 | ||
7.3 | odd | 6 | 9800.2.a.br.1.2 | 2 | |||
7.4 | even | 3 | 9800.2.a.bz.1.1 | 2 | |||
15.14 | odd | 2 | 2520.2.bi.k.361.2 | 4 | |||
20.19 | odd | 2 | 560.2.q.j.81.2 | 4 | |||
35.2 | odd | 12 | 1400.2.bh.g.849.3 | 8 | |||
35.4 | even | 6 | 1960.2.a.p.1.2 | 2 | |||
35.9 | even | 6 | 280.2.q.d.121.1 | yes | 4 | ||
35.19 | odd | 6 | 1960.2.q.q.961.2 | 4 | |||
35.23 | odd | 12 | 1400.2.bh.g.849.2 | 8 | |||
35.24 | odd | 6 | 1960.2.a.t.1.1 | 2 | |||
35.34 | odd | 2 | 1960.2.q.q.361.2 | 4 | |||
105.44 | odd | 6 | 2520.2.bi.k.1801.2 | 4 | |||
140.39 | odd | 6 | 3920.2.a.bz.1.1 | 2 | |||
140.59 | even | 6 | 3920.2.a.bp.1.2 | 2 | |||
140.79 | odd | 6 | 560.2.q.j.401.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.d.81.1 | ✓ | 4 | 5.4 | even | 2 | ||
280.2.q.d.121.1 | yes | 4 | 35.9 | even | 6 | ||
560.2.q.j.81.2 | 4 | 20.19 | odd | 2 | |||
560.2.q.j.401.2 | 4 | 140.79 | odd | 6 | |||
1400.2.q.h.401.2 | 4 | 7.2 | even | 3 | inner | ||
1400.2.q.h.1201.2 | 4 | 1.1 | even | 1 | trivial | ||
1400.2.bh.g.249.2 | 8 | 5.2 | odd | 4 | |||
1400.2.bh.g.249.3 | 8 | 5.3 | odd | 4 | |||
1400.2.bh.g.849.2 | 8 | 35.23 | odd | 12 | |||
1400.2.bh.g.849.3 | 8 | 35.2 | odd | 12 | |||
1960.2.a.p.1.2 | 2 | 35.4 | even | 6 | |||
1960.2.a.t.1.1 | 2 | 35.24 | odd | 6 | |||
1960.2.q.q.361.2 | 4 | 35.34 | odd | 2 | |||
1960.2.q.q.961.2 | 4 | 35.19 | odd | 6 | |||
2520.2.bi.k.361.2 | 4 | 15.14 | odd | 2 | |||
2520.2.bi.k.1801.2 | 4 | 105.44 | odd | 6 | |||
3920.2.a.bp.1.2 | 2 | 140.59 | even | 6 | |||
3920.2.a.bz.1.1 | 2 | 140.39 | odd | 6 | |||
9800.2.a.br.1.2 | 2 | 7.3 | odd | 6 | |||
9800.2.a.bz.1.1 | 2 | 7.4 | even | 3 |