Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
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.ce (of order \(12\), degree \(4\), 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: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.4 | ||
Character | \(\chi\) | \(=\) | 2100.493 |
Dual form | 2100.2.ce.e.1657.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.258819 | − | 0.965926i | −0.149429 | − | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64359 | + | 0.106918i | 0.999183 | + | 0.0404114i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.02114 | − | 5.23277i | 0.910909 | − | 1.57774i | 0.0981257 | − | 0.995174i | \(-0.468715\pi\) |
0.812783 | − | 0.582566i | \(-0.197951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18958 | + | 2.18958i | −0.607280 | + | 0.607280i | −0.942234 | − | 0.334954i | \(-0.891279\pi\) |
0.334954 | + | 0.942234i | \(0.391279\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.21931 | + | 1.66646i | −1.50840 | + | 0.404176i | −0.915905 | − | 0.401396i | \(-0.868525\pi\) |
−0.592499 | + | 0.805571i | \(0.701859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.37334 | − | 5.84280i | −0.773898 | − | 1.34043i | −0.935412 | − | 0.353560i | \(-0.884971\pi\) |
0.161514 | − | 0.986870i | \(-0.448362\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.580936 | − | 2.58118i | −0.126771 | − | 0.563261i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.01552 | − | 3.78997i | 0.211750 | − | 0.790262i | −0.775535 | − | 0.631304i | \(-0.782520\pi\) |
0.987285 | − | 0.158958i | \(-0.0508135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.45965i | 0.456746i | 0.973574 | + | 0.228373i | \(0.0733405\pi\) | ||||
−0.973574 | + | 0.228373i | \(0.926660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.81644 | − | 1.62607i | −0.505848 | − | 0.292051i | 0.225277 | − | 0.974295i | \(-0.427671\pi\) |
−0.731125 | + | 0.682243i | \(0.761004\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.83640 | − | 1.56386i | −1.01599 | − | 0.272233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.594521 | + | 0.159302i | 0.0977387 | + | 0.0261890i | 0.307357 | − | 0.951594i | \(-0.400555\pi\) |
−0.209618 | + | 0.977783i | \(0.567222\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.68168 | + | 1.54827i | 0.429412 | + | 0.247921i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.77442i | − | 1.05799i | −0.848626 | − | 0.528994i | \(-0.822570\pi\) | ||
0.848626 | − | 0.528994i | \(-0.177430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.33519 | + | 5.33519i | 0.813608 | + | 0.813608i | 0.985173 | − | 0.171565i | \(-0.0548822\pi\) |
−0.171565 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.72795 | − | 6.44881i | 0.252048 | − | 0.940656i | −0.717661 | − | 0.696393i | \(-0.754787\pi\) |
0.969709 | − | 0.244263i | \(-0.0785460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.97714 | + | 0.565297i | 0.996734 | + | 0.0807567i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21935 | + | 5.57608i | 0.450799 | + | 0.780807i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.38093 | + | 0.905917i | −0.464406 | + | 0.124437i | −0.483432 | − | 0.875382i | \(-0.660610\pi\) |
0.0190261 | + | 0.999819i | \(0.493943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.77063 | + | 4.77063i | −0.631885 | + | 0.631885i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.28621 | − | 3.95983i | 0.297639 | − | 0.515526i | −0.677956 | − | 0.735102i | \(-0.737134\pi\) |
0.975595 | + | 0.219576i | \(0.0704674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.38318 | + | 1.95328i | −0.433172 | + | 0.250092i | −0.700697 | − | 0.713459i | \(-0.747128\pi\) |
0.267525 | + | 0.963551i | \(0.413794\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.34288 | + | 1.22920i | −0.295175 | + | 0.154865i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.96837 | − | 11.0781i | −0.362644 | − | 1.35341i | −0.870586 | − | 0.492016i | \(-0.836260\pi\) |
0.507942 | − | 0.861391i | \(-0.330406\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.92366 | −0.472353 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.40725 | 0.641722 | 0.320861 | − | 0.947126i | \(-0.396028\pi\) | ||||
0.320861 | + | 0.947126i | \(0.396028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.87380 | + | 6.99311i | 0.219312 | + | 0.818482i | 0.984604 | + | 0.174799i | \(0.0559276\pi\) |
−0.765293 | + | 0.643683i | \(0.777406\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.54614 | − | 13.5103i | 0.973923 | − | 1.53964i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00023 | + | 4.61893i | −0.900096 | + | 0.519671i | −0.877231 | − | 0.480068i | \(-0.840612\pi\) |
−0.0228646 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.451016 | − | 0.451016i | 0.0495055 | − | 0.0495055i | −0.681921 | − | 0.731426i | \(-0.738855\pi\) |
0.731426 | + | 0.681921i | \(0.238855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.37584 | − | 0.636604i | 0.254717 | − | 0.0682511i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.04716 | − | 10.4740i | −0.640997 | − | 1.11024i | −0.985211 | − | 0.171348i | \(-0.945188\pi\) |
0.344213 | − | 0.938892i | \(-0.388146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.02246 | + | 5.55425i | −0.631325 | + | 0.582243i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.841717 | + | 3.14133i | −0.0872820 | + | 0.325741i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.62431 | − | 9.62431i | −0.977201 | − | 0.977201i | 0.0225452 | − | 0.999746i | \(-0.492823\pi\) |
−0.999746 | + | 0.0225452i | \(0.992823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.04229i | 0.607273i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.65132 | + | 4.99484i | 0.860838 | + | 0.497005i | 0.864293 | − | 0.502989i | \(-0.167766\pi\) |
−0.00345474 | + | 0.999994i | \(0.501100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.77343 | − | 2.61878i | −0.963005 | − | 0.258036i | −0.257133 | − | 0.966376i | \(-0.582778\pi\) |
−0.705872 | + | 0.708340i | \(0.749444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.2584 | − | 2.74873i | −0.991719 | − | 0.265730i | −0.273746 | − | 0.961802i | \(-0.588263\pi\) |
−0.717972 | + | 0.696072i | \(0.754930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3030 | + | 7.10312i | 1.17841 | + | 0.680355i | 0.955646 | − | 0.294517i | \(-0.0951588\pi\) |
0.222764 | + | 0.974872i | \(0.428492\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.615494i | − | 0.0584201i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.36172 | − | 2.36172i | −0.222172 | − | 0.222172i | 0.587241 | − | 0.809412i | \(-0.300214\pi\) |
−0.809412 | + | 0.587241i | \(0.800214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.801442 | − | 2.99102i | 0.0740933 | − | 0.276520i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.6195 | + | 3.74047i | −1.52350 | + | 0.342889i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.7546 | − | 22.0916i | −1.15951 | − | 2.00833i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.54359 | + | 1.75335i | −0.590016 | + | 0.158094i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.19418 | − | 9.19418i | 0.815851 | − | 0.815851i | −0.169653 | − | 0.985504i | \(-0.554265\pi\) |
0.985504 | + | 0.169653i | \(0.0542646\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.77255 | − | 6.53424i | 0.332154 | − | 0.575308i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0930 | − | 6.98191i | 1.05657 | − | 0.610013i | 0.132091 | − | 0.991238i | \(-0.457831\pi\) |
0.924482 | + | 0.381225i | \(0.124498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.29303 | − | 15.8066i | −0.719097 | − | 1.37061i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.39004 | − | 12.6518i | −0.289630 | − | 1.08092i | −0.945389 | − | 0.325945i | \(-0.894318\pi\) |
0.655758 | − | 0.754971i | \(-0.272349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.5083 | −1.90913 | −0.954563 | − | 0.298010i | \(-0.903677\pi\) | ||||
−0.954563 | + | 0.298010i | \(0.903677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.67630 | −0.562246 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.84254 | + | 18.0726i | 0.404954 | + | 1.51131i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.25978 | − | 6.88571i | −0.103905 | − | 0.567923i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1810 | − | 6.45533i | 0.915980 | − | 0.528841i | 0.0336298 | − | 0.999434i | \(-0.489293\pi\) |
0.882350 | + | 0.470593i | \(0.155960\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.64116 | + | 11.5028i | −0.540450 | + | 0.936086i | 0.458429 | + | 0.888731i | \(0.348413\pi\) |
−0.998878 | + | 0.0473549i | \(0.984921\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.55285 | − | 4.55285i | 0.368076 | − | 0.368076i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.21969 | + | 2.47041i | −0.735812 | + | 0.197160i | −0.607216 | − | 0.794537i | \(-0.707714\pi\) |
−0.128596 | + | 0.991697i | \(0.541047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.75010 | + | 3.03126i | 0.138792 | + | 0.240394i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.08983 | − | 9.91054i | 0.243513 | − | 0.781060i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.258041 | − | 0.963023i | 0.0202113 | − | 0.0754298i | −0.955084 | − | 0.296337i | \(-0.904235\pi\) |
0.975295 | + | 0.220907i | \(0.0709017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.32380 | + | 6.32380i | 0.489350 | + | 0.489350i | 0.908101 | − | 0.418751i | \(-0.137532\pi\) |
−0.418751 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.41148i | 0.262421i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.84280 | + | 3.37334i | 0.446810 | + | 0.257966i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1650 | + | 3.52754i | 1.00091 | + | 0.268194i | 0.721828 | − | 0.692072i | \(-0.243302\pi\) |
0.279086 | + | 0.960266i | \(0.409969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.41662 | − | 1.18343i | −0.331973 | − | 0.0889520i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.14649 | + | 1.81663i | 0.235180 | + | 0.135781i | 0.612959 | − | 0.790115i | \(-0.289979\pi\) |
−0.377780 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.31201i | 0.394838i | 0.980319 | + | 0.197419i | \(0.0632560\pi\) | ||||
−0.980319 | + | 0.197419i | \(0.936744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.76236 | + | 2.76236i | 0.204199 | + | 0.204199i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0692 | + | 37.5788i | −0.736334 | + | 2.74804i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.79370 | + | 1.94490i | 0.130472 | + | 0.141471i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.27281 | − | 7.40072i | −0.309170 | − | 0.535497i | 0.669011 | − | 0.743252i | \(-0.266718\pi\) |
−0.978181 | + | 0.207755i | \(0.933384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.12384 | + | 0.569081i | −0.152877 | + | 0.0409633i | −0.334446 | − | 0.942415i | \(-0.608549\pi\) |
0.181569 | + | 0.983378i | \(0.441883\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8683 | + | 12.8683i | −0.916829 | + | 0.916829i | −0.996797 | − | 0.0799682i | \(-0.974518\pi\) |
0.0799682 | + | 0.996797i | \(0.474518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.20848 | − | 7.28930i | 0.298331 | − | 0.516725i | −0.677423 | − | 0.735594i | \(-0.736903\pi\) |
0.975754 | + | 0.218869i | \(0.0702366\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.93237 | + | 5.73445i | −0.700575 | + | 0.404477i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.262982 | + | 6.50231i | −0.0184577 | + | 0.456372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.01552 | + | 3.78997i | 0.0705834 | + | 0.263421i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.7654 | −2.81980 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.8727 | 1.84999 | 0.924996 | − | 0.379976i | \(-0.124068\pi\) | ||||
0.924996 | + | 0.379976i | \(0.124068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.39950 | − | 5.22300i | −0.0958921 | − | 0.357874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.27166 | − | 4.59980i | −0.493632 | − | 0.312255i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.26985 | − | 3.61990i | 0.423677 | − | 0.244610i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.96883 | − | 17.2665i | 0.670576 | − | 1.16147i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1969 | + | 17.1969i | −1.15159 | + | 1.15159i | −0.165358 | + | 0.986234i | \(0.552878\pi\) |
−0.986234 | + | 0.165358i | \(0.947122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.90841 | − | 2.38700i | 0.591272 | − | 0.158431i | 0.0492376 | − | 0.998787i | \(-0.484321\pi\) |
0.542035 | + | 0.840356i | \(0.317654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.53248 | + | 6.11844i | 0.233433 | + | 0.404318i | 0.958816 | − | 0.284028i | \(-0.0916708\pi\) |
−0.725383 | + | 0.688345i | \(0.758337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.2618 | − | 4.75822i | −1.00416 | − | 0.313068i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.57364 | − | 13.3370i | 0.234117 | − | 0.873736i | −0.744428 | − | 0.667703i | \(-0.767278\pi\) |
0.978545 | − | 0.206033i | \(-0.0660556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.53216 | + | 6.53216i | 0.424309 | + | 0.424309i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.83543i | − | 0.442147i | −0.975257 | − | 0.221074i | \(-0.929044\pi\) | ||
0.975257 | − | 0.221074i | \(-0.0709561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.06234 | + | 2.92274i | 0.326094 | + | 0.188270i | 0.654106 | − | 0.756403i | \(-0.273045\pi\) |
−0.328012 | + | 0.944674i | \(0.606379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.965926 | − | 0.258819i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.1795 | + | 5.40708i | 1.28399 | + | 0.344044i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.552380 | − | 0.318917i | −0.0350056 | − | 0.0202105i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2887i | 0.901897i | 0.892550 | + | 0.450948i | \(0.148914\pi\) | ||||
−0.892550 | + | 0.450948i | \(0.851086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.7640 | − | 16.7640i | −1.05394 | − | 1.05394i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.25654 | − | 4.68946i | 0.0783807 | − | 0.292521i | −0.915598 | − | 0.402095i | \(-0.868282\pi\) |
0.993979 | + | 0.109574i | \(0.0349488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.55464 | + | 0.484693i | 0.0966005 | + | 0.0301174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22982 | − | 2.13012i | −0.0761243 | − | 0.131851i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.22980 | + | 1.93722i | −0.445809 | + | 0.119454i | −0.474738 | − | 0.880127i | \(-0.657457\pi\) |
0.0289290 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.55197 | + | 8.55197i | −0.523372 | + | 0.523372i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.78143 | − | 8.28169i | 0.291529 | − | 0.504943i | −0.682642 | − | 0.730753i | \(-0.739169\pi\) |
0.974172 | + | 0.225809i | \(0.0725026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0069 | − | 12.1283i | 1.27608 | − | 0.736743i | 0.299952 | − | 0.953954i | \(-0.403029\pi\) |
0.976125 | + | 0.217211i | \(0.0696961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.92372 | + | 4.37970i | 0.419042 | + | 0.265072i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.797887 | + | 2.97776i | 0.0479404 | + | 0.178916i | 0.985745 | − | 0.168249i | \(-0.0538111\pi\) |
−0.937804 | + | 0.347165i | \(0.887144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.25215 | 0.194701 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.45417 | 0.325369 | 0.162684 | − | 0.986678i | \(-0.447985\pi\) | ||||
0.162684 | + | 0.986678i | \(0.447985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.87133 | − | 6.98391i | −0.111239 | − | 0.415150i | 0.887739 | − | 0.460347i | \(-0.152275\pi\) |
−0.998978 | + | 0.0451971i | \(0.985608\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.724311 | − | 17.9088i | 0.0427547 | − | 1.05712i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.1803 | − | 12.2284i | 1.24590 | − | 0.719320i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.80541 | + | 11.7873i | −0.398940 | + | 0.690985i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0811 | − | 10.0811i | 0.588942 | − | 0.588942i | −0.348403 | − | 0.937345i | \(-0.613276\pi\) |
0.937345 | + | 0.348403i | \(0.113276\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.83640 | − | 1.56386i | 0.338662 | − | 0.0907443i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.07487 | + | 10.5220i | 0.351319 | + | 0.608503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5336 | + | 14.6745i | 0.780065 | + | 0.845823i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.58552 | − | 9.64929i | 0.148534 | − | 0.554337i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.65757 | − | 1.65757i | −0.0946023 | − | 0.0946023i | 0.658222 | − | 0.752824i | \(-0.271309\pi\) |
−0.752824 | + | 0.658222i | \(0.771309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1182i | 0.575604i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.6703 | − | 6.73786i | −0.661762 | − | 0.382069i | 0.131186 | − | 0.991358i | \(-0.458122\pi\) |
−0.792948 | + | 0.609289i | \(0.791455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.56627 | + | 2.02738i | 0.427671 | + | 0.114594i | 0.466233 | − | 0.884662i | \(-0.345611\pi\) |
−0.0385618 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.1191 | + | 6.73065i | 1.41083 | + | 0.378031i | 0.882221 | − | 0.470835i | \(-0.156047\pi\) |
0.528609 | + | 0.848866i | \(0.322714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8708 | + | 7.43095i | 0.720626 | + | 0.416054i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6203i | 0.592767i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.7166 | + | 30.7166i | 1.70912 | + | 1.70912i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.67684 | − | 13.7222i | 0.203330 | − | 0.758838i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.25750 | − | 16.8633i | 0.289855 | − | 0.929702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.62289 | − | 2.81093i | −0.0892020 | − | 0.154502i | 0.817972 | − | 0.575258i | \(-0.195098\pi\) |
−0.907174 | + | 0.420756i | \(0.861765\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.594521 | + | 0.159302i | −0.0325796 | + | 0.00872967i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.182629 | − | 0.182629i | 0.00994842 | − | 0.00994842i | −0.702115 | − | 0.712063i | \(-0.747761\pi\) |
0.712063 | + | 0.702115i | \(0.247761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.66999 | + | 2.89250i | −0.0907013 | + | 0.157099i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.0177 | + | 9.82520i | −0.921562 | + | 0.532064i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3842 | + | 2.24040i | 0.992656 | + | 0.120970i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.32084 | + | 12.3936i | 0.178272 | + | 0.665321i | 0.995971 | + | 0.0896748i | \(0.0285828\pi\) |
−0.817699 | + | 0.575646i | \(0.804751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6569 | 0.570453 | 0.285226 | − | 0.958460i | \(-0.407931\pi\) | ||||
0.285226 | + | 0.958460i | \(0.407931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.09653 | −0.165281 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.37072 | − | 12.5797i | −0.179405 | − | 0.669549i | −0.995759 | − | 0.0919975i | \(-0.970675\pi\) |
0.816354 | − | 0.577552i | \(-0.195992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.91446 | + | 15.0851i | 0.418877 | + | 0.798387i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1941 | − | 13.3911i | 1.22414 | − | 0.706757i | 0.258342 | − | 0.966054i | \(-0.416824\pi\) |
0.965798 | + | 0.259296i | \(0.0834906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2589 | + | 22.9651i | −0.697836 | + | 1.20869i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.0377 | + | 18.0377i | −0.946736 | + | 0.946736i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5660 | − | 5.77860i | 1.12574 | − | 0.301641i | 0.352535 | − | 0.935799i | \(-0.385320\pi\) |
0.773203 | + | 0.634158i | \(0.218653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.38721 | + | 5.86682i | 0.176331 | + | 0.305415i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.03465 | + | 2.03339i | −0.469056 | + | 0.105568i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.72854 | − | 10.1831i | 0.141279 | − | 0.527259i | −0.858614 | − | 0.512622i | \(-0.828674\pi\) |
0.999893 | − | 0.0146365i | \(-0.00465912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.38560 | − | 5.38560i | −0.277373 | − | 0.277373i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8216i | 1.63457i | 0.576235 | + | 0.817284i | \(0.304521\pi\) | ||||
−0.576235 | + | 0.817284i | \(0.695479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2605 | − | 6.50126i | −0.576894 | − | 0.333070i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.08362 | + | 2.16600i | 0.413054 | + | 0.110677i | 0.459361 | − | 0.888250i | \(-0.348079\pi\) |
−0.0463068 | + | 0.998927i | \(0.514745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.28800 | − | 1.95281i | −0.370470 | − | 0.0992671i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.9925 | − | 9.81065i | −0.861556 | − | 0.497420i | 0.00297686 | − | 0.999996i | \(-0.499052\pi\) |
−0.864533 | + | 0.502576i | \(0.832386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2633i | 1.27762i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.87392 | − | 9.87392i | −0.498073 | − | 0.498073i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.10212 | + | 26.5055i | −0.356445 | + | 1.33027i | 0.522210 | + | 0.852817i | \(0.325108\pi\) |
−0.878656 | + | 0.477456i | \(0.841559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.1217 | + | 12.1015i | −0.656904 | + | 0.605834i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.16991 | + | 8.95454i | 0.258173 | + | 0.447169i | 0.965752 | − | 0.259465i | \(-0.0835462\pi\) |
−0.707580 | + | 0.706634i | \(0.750213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.72724 | − | 2.60641i | 0.484548 | − | 0.129834i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.62972 | − | 2.62972i | 0.130351 | − | 0.130351i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.43985 | + | 9.42209i | −0.268983 | + | 0.465893i | −0.968600 | − | 0.248626i | \(-0.920021\pi\) |
0.699616 | + | 0.714519i | \(0.253354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3433 | + | 6.54905i | −0.559523 | + | 0.323041i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.46718 | − | 10.2237i | 0.318229 | − | 0.503077i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.82557 | + | 21.7413i | 0.285279 | + | 1.06468i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.9080 | 1.11913 | 0.559565 | − | 0.828787i | \(-0.310968\pi\) | ||||
0.559565 | + | 0.828787i | \(0.310968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.7174 | −1.74076 | −0.870379 | − | 0.492382i | \(-0.836126\pi\) | ||||
−0.870379 | + | 0.492382i | \(0.836126\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.72795 | + | 6.44881i | 0.0840160 | + | 0.313552i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.15259 | + | 4.80195i | −0.442925 | + | 0.232383i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.2035 | − | 9.35507i | 0.782310 | − | 0.451667i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7512 | − | 29.0139i | 0.806875 | − | 1.39755i | −0.108143 | − | 0.994135i | \(-0.534491\pi\) |
0.915018 | − | 0.403413i | \(-0.132176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.19361 | − | 3.19361i | 0.153475 | − | 0.153475i | −0.626193 | − | 0.779668i | \(-0.715388\pi\) |
0.779668 | + | 0.626193i | \(0.215388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.5697 | + | 6.85138i | −1.22316 | + | 0.327746i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.34916 | + | 7.53297i | 0.207574 | + | 0.359529i | 0.950950 | − | 0.309345i | \(-0.100110\pi\) |
−0.743376 | + | 0.668874i | \(0.766777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.32503 | + | 2.99901i | −0.301192 | + | 0.142810i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.98880 | − | 29.8146i | 0.379559 | − | 1.41653i | −0.467008 | − | 0.884253i | \(-0.654668\pi\) |
0.846568 | − | 0.532281i | \(-0.178665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.12922 | − | 9.12922i | −0.431797 | − | 0.431797i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8515i | 0.984044i | 0.870583 | + | 0.492022i | \(0.163742\pi\) | ||||
−0.870583 | + | 0.492022i | \(0.836258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.4490 | − | 20.4665i | −1.66923 | − | 0.963730i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.8297 | + | 3.43772i | 0.602793 | + | 0.161518i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.4789 | + | 7.09500i | 1.23863 | + | 0.331890i | 0.817935 | − | 0.575311i | \(-0.195119\pi\) |
0.420697 | + | 0.907201i | \(0.361786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.57608 | − | 3.21935i | −0.260269 | − | 0.150266i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7604i | 0.594309i | 0.954829 | + | 0.297155i | \(0.0960377\pi\) | ||||
−0.954829 | + | 0.297155i | \(0.903962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3005 | + | 11.3005i | 0.525179 | + | 0.525179i | 0.919131 | − | 0.393952i | \(-0.128892\pi\) |
−0.393952 | + | 0.919131i | \(0.628892\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.335282 | − | 1.25129i | 0.0155150 | − | 0.0579028i | −0.957734 | − | 0.287654i | \(-0.907125\pi\) |
0.973249 | + | 0.229751i | \(0.0737913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.66270 | − | 29.6034i | −0.307655 | − | 1.36696i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.77246 | + | 8.26615i | 0.219904 | + | 0.380884i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.0362 | − | 11.7995i | 2.02479 | − | 0.542540i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.47501 | − | 2.47501i | 0.113323 | − | 0.113323i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9924 | + | 32.8958i | −0.867785 | + | 1.50305i | −0.00353033 | + | 0.999994i | \(0.501124\pi\) |
−0.864255 | + | 0.503054i | \(0.832210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.65056 | + | 0.952949i | −0.0752589 | + | 0.0434507i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.3726 | − | 0.419512i | −0.471967 | − | 0.0190884i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.99476 | + | 26.1048i | 0.316963 | + | 1.18292i | 0.922148 | + | 0.386836i | \(0.126432\pi\) |
−0.605186 | + | 0.796084i | \(0.706901\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.996995 | −0.0450857 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1830 | 1.04623 | 0.523117 | − | 0.852261i | \(-0.324769\pi\) | ||||
0.523117 | + | 0.852261i | \(0.324769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.09890 | − | 15.2973i | −0.184605 | − | 0.688957i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.2945 | + | 0.578135i | 0.641198 | + | 0.0259329i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.565265 | − | 0.326356i | 0.0253047 | − | 0.0146097i | −0.487294 | − | 0.873238i | \(-0.662016\pi\) |
0.512599 | + | 0.858628i | \(0.328683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.47160 | − | 7.74504i | 0.199776 | − | 0.346023i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.465372 | − | 0.465372i | 0.0207499 | − | 0.0207499i | −0.696656 | − | 0.717406i | \(-0.745329\pi\) |
0.717406 | + | 0.696656i | \(0.245329\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.29523 | − | 0.882955i | 0.146346 | − | 0.0392134i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.93027 | + | 12.0036i | 0.307179 | + | 0.532050i | 0.977744 | − | 0.209801i | \(-0.0672816\pi\) |
−0.670565 | + | 0.741851i | \(0.733948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.20586 | + | 18.6873i | 0.186056 | + | 0.826676i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.74617 | − | 6.51680i | 0.0770953 | − | 0.287724i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.5248 | − | 28.5248i | −1.25452 | − | 1.25452i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.6294i | − | 0.598263i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.39370 | + | 4.26876i | 0.323924 | + | 0.187018i | 0.653140 | − | 0.757237i | \(-0.273451\pi\) |
−0.329216 | + | 0.944255i | \(0.606785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.5977 | − | 7.39479i | −1.20677 | − | 0.323352i | −0.401273 | − | 0.915958i | \(-0.631432\pi\) |
−0.805492 | + | 0.592607i | \(0.798099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.2261 | + | 5.41957i | 0.881063 | + | 0.236080i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.58602 | + | 3.80244i | 0.286349 | + | 0.165324i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.57242i | 0.198426i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8331 | + | 14.8331i | 0.642495 | + | 0.642495i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.940355 | − | 3.50945i | 0.0405793 | − | 0.151444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.0370 | − | 34.8019i | 1.03535 | − | 1.49903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.19049 | − | 14.1864i | −0.352137 | − | 0.609919i | 0.634487 | − | 0.772934i | \(-0.281212\pi\) |
−0.986624 | + | 0.163015i | \(0.947878\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.13101 | − | 1.37485i | 0.220193 | − | 0.0590004i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.1848 | + | 31.1848i | −1.33337 | + | 1.33337i | −0.431030 | + | 0.902338i | \(0.641850\pi\) |
−0.902338 | + | 0.431030i | \(0.858150\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.95328 | − | 3.38318i | 0.0833640 | − | 0.144391i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.3712 | − | 8.29724i | 0.612236 | − | 0.353474i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.6432 | + | 11.3552i | −0.920361 | + | 0.482872i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.28447 | − | 4.79369i | −0.0544245 | − | 0.203115i | 0.933360 | − | 0.358942i | \(-0.116862\pi\) |
−0.987784 | + | 0.155827i | \(0.950196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.3636 | −0.988177 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.9045 | 1.64255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.35434 | + | 5.05448i | 0.0570788 | + | 0.213021i | 0.988575 | − | 0.150730i | \(-0.0481625\pi\) |
−0.931496 | + | 0.363751i | \(0.881496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41439 | − | 2.23596i | 0.0593988 | − | 0.0939014i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.66634 | − | 5.00351i | 0.363312 | − | 0.209758i | −0.307221 | − | 0.951638i | \(-0.599399\pi\) |
0.670533 | + | 0.741880i | \(0.266066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1544 | + | 21.0521i | −0.508646 | + | 0.881001i | 0.491303 | + | 0.870988i | \(0.336521\pi\) |
−0.999950 | + | 0.0100130i | \(0.996813\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.04266 | + | 6.04266i | −0.252436 | + | 0.252436i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.4389 | − | 12.1753i | 1.89164 | − | 0.506865i | 0.893293 | − | 0.449475i | \(-0.148389\pi\) |
0.998352 | − | 0.0573900i | \(-0.0182778\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.09938 | + | 1.90418i | 0.0456887 | + | 0.0791351i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24052 | − | 1.14408i | 0.0514656 | − | 0.0474644i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.47381 | + | 20.4285i | −0.226702 | + | 0.846064i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.39281 | + | 9.39281i | 0.387683 | + | 0.387683i | 0.873860 | − | 0.486177i | \(-0.161609\pi\) |
−0.486177 | + | 0.873860i | \(0.661609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.9412i | 0.904072i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.7604 | + | 9.09927i | 0.648296 | + | 0.374294i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.3087 | − | 8.38913i | −1.28569 | − | 0.344500i | −0.449670 | − | 0.893195i | \(-0.648458\pi\) |
−0.836023 | + | 0.548694i | \(0.815125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.13016 | − | 2.17847i | −0.332745 | − | 0.0891588i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5175 | − | 6.64962i | −0.470591 | − | 0.271696i | 0.245896 | − | 0.969296i | \(-0.420918\pi\) |
−0.716487 | + | 0.697600i | \(0.754251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.90700i | − | 0.404115i | −0.979374 | − | 0.202058i | \(-0.935237\pi\) | ||
0.979374 | − | 0.202058i | \(-0.0647628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.10974 | + | 8.10974i | 0.330254 | + | 0.330254i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.78001 | − | 25.3033i | 0.275192 | − | 1.02703i | −0.680521 | − | 0.732729i | \(-0.738246\pi\) |
0.955713 | − | 0.294301i | \(-0.0950870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.34881 | − | 1.42890i | 0.257267 | − | 0.0579019i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3367 | + | 17.9037i | 0.418178 | + | 0.724305i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.1867 | − | 7.82055i | 1.17884 | − | 0.315869i | 0.384374 | − | 0.923178i | \(-0.374417\pi\) |
0.794466 | + | 0.607308i | \(0.207751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8767 | + | 17.8767i | −0.719689 | + | 0.719689i | −0.968541 | − | 0.248853i | \(-0.919946\pi\) |
0.248853 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.13720 | − | 10.6299i | 0.246675 | − | 0.427253i | −0.715926 | − | 0.698176i | \(-0.753995\pi\) |
0.962601 | + | 0.270922i | \(0.0873287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.39799 | − | 1.96183i | 0.136357 | − | 0.0787255i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.8663 | − | 28.3355i | −0.595607 | − | 1.13524i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5509 | + | 39.3764i | 0.421361 | + | 1.57254i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.96298 | −0.158014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.5840 | −1.25734 | −0.628670 | − | 0.777672i | \(-0.716400\pi\) | ||||
−0.628670 | + | 0.777672i | \(0.716400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.95516 | − | 25.9570i | −0.276443 | − | 1.03170i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.5148 | + | 14.0392i | −0.654339 | + | 0.556255i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.68281 | + | 2.70362i | −0.185249 | + | 0.106954i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.20316 | − | 10.7442i | 0.245010 | − | 0.424370i | −0.717124 | − | 0.696945i | \(-0.754542\pi\) |
0.962134 | + | 0.272575i | \(0.0878754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22763 | + | 1.22763i | −0.0484129 | + | 0.0484129i | −0.730899 | − | 0.682486i | \(-0.760899\pi\) |
0.682486 | + | 0.730899i | \(0.260899\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.5686 | − | 4.70749i | 0.690693 | − | 0.185070i | 0.103635 | − | 0.994615i | \(-0.466953\pi\) |
0.587058 | + | 0.809545i | \(0.300286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8139 | − | 23.9264i | −0.542244 | − | 0.939195i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.56102 | + | 8.21440i | −0.100374 | + | 0.321948i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.2461 | + | 38.2391i | −0.400962 | + | 1.49641i | 0.410421 | + | 0.911896i | \(0.365382\pi\) |
−0.811383 | + | 0.584514i | \(0.801285\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.11931 | − | 5.11931i | −0.199723 | − | 0.199723i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3001i | 0.596008i | 0.954565 | + | 0.298004i | \(0.0963209\pi\) | ||||
−0.954565 | + | 0.298004i | \(0.903679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.8540 | + | 21.2777i | 1.43346 | + | 0.827606i | 0.997383 | − | 0.0723057i | \(-0.0230357\pi\) |
0.436073 | + | 0.899911i | \(0.356369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.2583 | − | 5.16025i | −0.747930 | − | 0.200407i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.32199 | + | 2.49782i | 0.360949 | + | 0.0967159i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0619 | + | 12.1601i | 0.814298 | + | 0.470135i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.6046i | 0.911244i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1774 | + | 23.1774i | 0.893422 | + | 0.893422i | 0.994844 | − | 0.101421i | \(-0.0323390\pi\) |
−0.101421 | + | 0.994844i | \(0.532339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.02498 | + | 29.9496i | −0.308425 | + | 1.15106i | 0.621532 | + | 0.783389i | \(0.286511\pi\) |
−0.929957 | + | 0.367669i | \(0.880156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.4137 | − | 26.4717i | −0.936912 | − | 1.01589i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.61133 | − | 7.98706i | −0.176707 | − | 0.306065i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.1248 | + | 5.12448i | −0.731790 | + | 0.196083i | −0.605426 | − | 0.795901i | \(-0.706997\pi\) |
−0.126364 | + | 0.991984i | \(0.540331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.99568 | − | 4.99568i | 0.190597 | − | 0.190597i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.41924 | − | 9.38639i | 0.206456 | − | 0.357593i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.29096 | + | 1.32269i | −0.0871524 | + | 0.0503174i | −0.542943 | − | 0.839770i | \(-0.682690\pi\) |
0.455790 | + | 0.890087i | \(0.349357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.646032 | + | 15.9733i | −0.0245407 | + | 0.606776i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.2893 | + | 42.1322i | 0.427612 | + | 1.59587i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8075 | −0.522247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.3521 | 1.93954 | 0.969772 | − | 0.244015i | \(-0.0784645\pi\) | ||||
0.969772 | + | 0.244015i | \(0.0784645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.07476 | − | 4.01105i | −0.0405352 | − | 0.151280i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.3365 | + | 14.1293i | 0.840050 | + | 0.531387i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.96456 | + | 1.71159i | −0.111337 | + | 0.0642802i | −0.554634 | − | 0.832094i | \(-0.687142\pi\) |
0.443298 | + | 0.896374i | \(0.353808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.61893 | − | 8.00023i | 0.173224 | − | 0.300032i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.02291 | + | 9.02291i | −0.337911 | + | 0.337911i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.60252 | + | 1.76914i | −0.246576 | + | 0.0660697i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.8855 | − | 22.3183i | −0.480547 | − | 0.832333i | 0.519203 | − | 0.854651i | \(-0.326229\pi\) |
−0.999751 | + | 0.0223181i | \(0.992895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.5569 | − | 7.96795i | −0.951790 | − | 0.296742i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.51292 | − | 5.64630i | 0.0562662 | − | 0.209988i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.26918 | − | 8.26918i | −0.306687 | − | 0.306687i | 0.536936 | − | 0.843623i | \(-0.319582\pi\) |
−0.843623 | + | 0.536936i | \(0.819582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.0720 | − | 24.2903i | −1.55609 | − | 0.898409i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.6885 | + | 7.95500i | 1.09657 | + | 0.293825i | 0.761367 | − | 0.648322i | \(-0.224529\pi\) |
0.335202 | + | 0.942146i | \(0.391195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −66.9371 | − | 17.9358i | −2.46566 | − | 0.660672i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.72713 | + | 5.61596i | 0.357818 | + | 0.206586i | 0.668123 | − | 0.744051i | \(-0.267098\pi\) |
−0.310305 | + | 0.950637i | \(0.600431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 20.8913i | − | 0.767463i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1411 | − | 25.1411i | −0.922337 | − | 0.922337i | 0.0748575 | − | 0.997194i | \(-0.476150\pi\) |
−0.997194 | + | 0.0748575i | \(0.976150\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.165083 | + | 0.616100i | −0.00604008 | + | 0.0225419i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.8252 | − | 8.36334i | −0.980170 | − | 0.305590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0202455 | + | 0.0350663i | 0.000738769 | + | 0.00127959i | 0.866395 | − | 0.499360i | \(-0.166432\pi\) |
−0.865656 | + | 0.500640i | \(0.833098\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.8019 | − | 3.69819i | 0.502967 | − | 0.134770i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2352 | − | 10.2352i | 0.372005 | − | 0.372005i | −0.496202 | − | 0.868207i | \(-0.665272\pi\) |
0.868207 | + | 0.496202i | \(0.165272\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.8539 | + | 20.5316i | −0.430271 | + | 0.745251i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.7365 | + | 26.4060i | −1.65795 | + | 0.957216i | −0.684287 | + | 0.729213i | \(0.739886\pi\) |
−0.973660 | + | 0.228003i | \(0.926780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.7645 | + | 20.0931i | 1.14995 | + | 0.727421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.66453 | + | 13.6762i | 0.132318 | + | 0.493819i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0548 | 1.04774 | 0.523872 | − | 0.851797i | \(-0.324487\pi\) | ||||
0.523872 | + | 0.851797i | \(0.324487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.85489 | −0.174845 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.55647 | + | 17.0050i | 0.163885 | + | 0.611627i | 0.998180 | + | 0.0603084i | \(0.0192084\pi\) |
−0.834295 | + | 0.551319i | \(0.814125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0658076 | − | 1.62711i | 0.00236084 | − | 0.0583724i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.5816 | + | 22.8525i | −1.41816 | + | 0.818774i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3361 | − | 28.2949i | 0.584551 | − | 1.01247i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.73924 | + | 1.73924i | −0.0621552 | + | 0.0621552i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.26224 | − | 0.338216i | 0.0449939 | − | 0.0120561i | −0.236252 | − | 0.971692i | \(-0.575919\pi\) |
0.281246 | + | 0.959636i | \(0.409252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.74242 | + | 6.48206i | 0.133234 | + | 0.230767i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.99091 | − | 6.49593i | −0.213012 | − | 0.230969i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.13088 | − | 11.6846i | 0.111181 | − | 0.414933i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.7992 | − | 35.7992i | −1.26807 | − | 1.26807i | −0.947083 | − | 0.320988i | \(-0.895985\pi\) |
−0.320988 | − | 0.947083i | \(-0.604015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.9867i | 1.52076i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.4740 | + | 6.04716i | 0.370080 | + | 0.213666i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.2544 | + | 11.3220i | 1.49112 | + | 0.399546i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.23702 | − | 2.47505i | −0.325159 | − | 0.0871260i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.814233 | + | 0.470097i | 0.0286269 | + | 0.0165277i | 0.514245 | − | 0.857643i | \(-0.328072\pi\) |
−0.485618 | + | 0.874171i | \(0.661405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8145i | 0.695781i | 0.937535 | + | 0.347890i | \(0.113102\pi\) | ||||
−0.937535 | + | 0.347890i | \(0.886898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.1520 | − | 17.1520i | −0.601548 | − | 0.601548i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.1750 | − | 49.1699i | 0.460936 | − | 1.72024i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.43848 | − | 7.82135i | 0.0852074 | − | 0.273300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4231 | − | 23.2495i | −0.468469 | − | 0.811413i | 0.530881 | − | 0.847446i | \(-0.321861\pi\) |
−0.999351 | + | 0.0360334i | \(0.988528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.09611 | − | 0.293703i | 0.0382081 | − | 0.0102378i | −0.239664 | − | 0.970856i | \(-0.577037\pi\) |
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6331 | + | 10.6331i | −0.369749 | + | 0.369749i | −0.867386 | − | 0.497636i | \(-0.834201\pi\) |
0.497636 | + | 0.867386i | \(0.334201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.79297 | − | 4.83757i | 0.0970038 | − | 0.168016i | −0.813439 | − | 0.581650i | \(-0.802407\pi\) |
0.910443 | + | 0.413634i | \(0.135741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.66978 | − | 1.54140i | 0.0926138 | − | 0.0534706i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.3350 | + | 8.11135i | −1.53612 | + | 0.281042i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.841717 | − | 3.14133i | −0.0290940 | − | 0.108580i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.8150 | 0.615042 | 0.307521 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307521 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9501 | 0.791384 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.41164 | − | 5.26832i | −0.0486196 | − | 0.181451i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.3560 | − | 59.7649i | −1.07740 | − | 2.05355i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.26160 | + | 3.61514i | −0.214898 | + | 0.124071i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20749 | − | 2.09144i | 0.0413924 | − | 0.0716937i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9392 | − | 19.9392i | 0.682707 | − | 0.682707i | −0.277902 | − | 0.960609i | \(-0.589639\pi\) |
0.960609 | + | 0.277902i | \(0.0896392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.8413 | − | 3.97672i | 0.506970 | − | 0.135842i | 0.00373690 | − | 0.999993i | \(-0.498811\pi\) |
0.503233 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.75815 | + | 9.97341i | 0.196465 | + | 0.340288i | 0.947380 | − | 0.320111i | \(-0.103720\pi\) |
−0.750914 | + | 0.660399i | \(0.770387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.4860 | + | 3.93551i | −0.595922 | + | 0.134122i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.25094 | − | 4.66858i | 0.0425826 | − | 0.158920i | −0.941361 | − | 0.337402i | \(-0.890452\pi\) |
0.983943 | + | 0.178482i | \(0.0571185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.2936 | − | 17.2936i | −0.587322 | − | 0.587322i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.8178i | 1.89349i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.7559 | + | 17.7569i | 1.04212 | + | 0.601671i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.1471 | + | 3.52274i | 0.444960 | + | 0.119227i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.04462 | − | 0.815805i | −0.102810 | − | 0.0275478i | 0.207047 | − | 0.978331i | \(-0.433615\pi\) |
−0.309857 | + | 0.950783i | \(0.600281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.3467 | − | 7.12839i | −0.416445 | − | 0.240435i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4612i | 0.992573i | 0.868159 | + | 0.496287i | \(0.165303\pi\) | ||||
−0.868159 | + | 0.496287i | \(0.834697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.13917 | + | 3.13917i | 0.105641 | + | 0.105641i | 0.757952 | − | 0.652310i | \(-0.226200\pi\) |
−0.652310 | + | 0.757952i | \(0.726200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.68563 | − | 13.7550i | 0.123751 | − | 0.461846i | −0.876041 | − | 0.482237i | \(-0.839824\pi\) |
0.999792 | + | 0.0203909i | \(0.00649108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.2887 | − | 23.3226i | 0.848155 | − | 0.782215i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.02114 | − | 5.23277i | −0.101212 | − | 0.175304i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.5081 | + | 11.6580i | −1.45594 | + | 0.390119i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.59117 | − | 8.59117i | 0.286851 | − | 0.286851i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.99957 | − | 6.92746i | 0.133393 | − | 0.231044i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5174 | − | 11.2684i | 0.650218 | − | 0.375403i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.6717 | − | 16.8705i | 0.355132 | − | 0.561415i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4313 | − | 42.6623i | −0.379571 | − | 1.41658i | −0.846550 | − | 0.532309i | \(-0.821324\pi\) |
0.466979 | − | 0.884268i | \(-0.345342\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.98968 | −0.331337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5244 | −0.448084 | −0.224042 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224042 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.997481 | − | 3.72265i | −0.0330118 | − | 0.123202i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.7155 | − | 17.1643i | 1.08036 | − | 0.566817i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.9076 | − | 25.9274i | 1.48137 | − | 0.855267i | 0.481590 | − | 0.876397i | \(-0.340060\pi\) |
0.999777 | + | 0.0211294i | \(0.00672620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.17208 | + | 2.03010i | −0.0386212 | + | 0.0668939i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8396 | + | 11.8396i | −0.389705 | + | 0.389705i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.77343 | − | 2.61878i | 0.321002 | − | 0.0860121i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.9702 | + | 41.5177i | 0.786438 | + | 1.36215i | 0.928136 | + | 0.372241i | \(0.121410\pi\) |
−0.141698 | + | 0.989910i | \(0.545256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2334 | − | 42.6730i | −0.663122 | − | 1.39855i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.48777 | + | 13.0165i | −0.114184 | + | 0.426142i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.89255 | + | 3.89255i | 0.127164 | + | 0.127164i | 0.767824 | − | 0.640660i | \(-0.221339\pi\) |
−0.640660 | + | 0.767824i | \(0.721339\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 7.83318i | − | 0.255626i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.1107 | − | 24.3126i | −1.37277 | − | 0.792568i | −0.381493 | − | 0.924372i | \(-0.624590\pi\) |
−0.991276 | + | 0.131803i | \(0.957923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.6748 | − | 6.87955i | −0.836087 | − | 0.224029i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.2727 | + | 11.8628i | 1.43867 | + | 0.385490i | 0.892067 | − | 0.451903i | \(-0.149255\pi\) |
0.546601 | + | 0.837393i | \(0.315921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.4148 | − | 11.2091i | −0.630231 | − | 0.363864i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 26.0052i | − | 0.843277i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.2364 | − | 25.2364i | −0.817488 | − | 0.817488i | 0.168255 | − | 0.985743i | \(-0.446187\pi\) |
−0.985743 | + | 0.168255i | \(0.946187\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.84654 | − | 14.3555i | 0.124341 | − | 0.464047i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.60916 | − | 33.8086i | −0.245713 | − | 1.09174i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2118 | − | 17.6873i | −0.329412 | − | 0.570558i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2584 | − | 2.74873i | 0.330573 | − | 0.0885767i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.64834 | + | 9.64834i | −0.310270 | + | 0.310270i | −0.845014 | − | 0.534744i | \(-0.820408\pi\) |
0.534744 | + | 0.845014i | \(0.320408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.7199 | − | 37.6201i | 0.697745 | − | 1.20853i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.20795 | + | 3.58416i | −0.199223 | + | 0.115021i | −0.596293 | − | 0.802767i | \(-0.703360\pi\) |
0.397070 | + | 0.917788i | \(0.370027\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.5026 | − | 2.40655i | −1.90757 | − | 0.0771504i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.5776 | − | 39.4761i | −0.338407 | − | 1.26295i | −0.900128 | − | 0.435625i | \(-0.856528\pi\) |
0.561722 | − | 0.827326i | \(-0.310139\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.0773 | −2.33556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2062 | −0.453570 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.1457 | − | 37.8643i | −0.323598 | − | 1.20768i | −0.915714 | − | 0.401832i | \(-0.868374\pi\) |
0.592116 | − | 0.805853i | \(-0.298293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.6494 | − | 0.713820i | −0.561787 | − | 0.0227211i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.6382 | − | 14.8022i | 0.815246 | − | 0.470682i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3183 | − | 26.5321i | 0.486603 | − | 0.842821i | −0.513278 | − | 0.858222i | \(-0.671569\pi\) |
0.999881 | + | 0.0154009i | \(0.00490245\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.29511 | + | 2.29511i | −0.0728331 | + | 0.0728331i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.4853 | − | 7.09671i | 0.838797 | − | 0.224755i | 0.186249 | − | 0.982503i | \(-0.440367\pi\) |
0.652548 | + | 0.757748i | \(0.273700\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.307747 | + | 0.533033i | 0.00973668 | + | 0.0168644i |
(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.ce.e.493.4 | 32 | ||
5.2 | odd | 4 | inner | 2100.2.ce.e.157.1 | 32 | ||
5.3 | odd | 4 | 420.2.bo.a.157.8 | yes | 32 | ||
5.4 | even | 2 | 420.2.bo.a.73.6 | ✓ | 32 | ||
7.5 | odd | 6 | inner | 2100.2.ce.e.1993.1 | 32 | ||
15.8 | even | 4 | 1260.2.dq.c.577.2 | 32 | |||
15.14 | odd | 2 | 1260.2.dq.c.73.5 | 32 | |||
35.3 | even | 12 | 2940.2.x.c.97.12 | 32 | |||
35.4 | even | 6 | 2940.2.x.c.1273.12 | 32 | |||
35.12 | even | 12 | inner | 2100.2.ce.e.1657.4 | 32 | ||
35.18 | odd | 12 | 2940.2.x.c.97.8 | 32 | |||
35.19 | odd | 6 | 420.2.bo.a.313.8 | yes | 32 | ||
35.24 | odd | 6 | 2940.2.x.c.1273.8 | 32 | |||
35.33 | even | 12 | 420.2.bo.a.397.6 | yes | 32 | ||
105.68 | odd | 12 | 1260.2.dq.c.397.5 | 32 | |||
105.89 | even | 6 | 1260.2.dq.c.1153.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bo.a.73.6 | ✓ | 32 | 5.4 | even | 2 | ||
420.2.bo.a.157.8 | yes | 32 | 5.3 | odd | 4 | ||
420.2.bo.a.313.8 | yes | 32 | 35.19 | odd | 6 | ||
420.2.bo.a.397.6 | yes | 32 | 35.33 | even | 12 | ||
1260.2.dq.c.73.5 | 32 | 15.14 | odd | 2 | |||
1260.2.dq.c.397.5 | 32 | 105.68 | odd | 12 | |||
1260.2.dq.c.577.2 | 32 | 15.8 | even | 4 | |||
1260.2.dq.c.1153.2 | 32 | 105.89 | even | 6 | |||
2100.2.ce.e.157.1 | 32 | 5.2 | odd | 4 | inner | ||
2100.2.ce.e.493.4 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.ce.e.1657.4 | 32 | 35.12 | even | 12 | inner | ||
2100.2.ce.e.1993.1 | 32 | 7.5 | odd | 6 | inner | ||
2940.2.x.c.97.8 | 32 | 35.18 | odd | 12 | |||
2940.2.x.c.97.12 | 32 | 35.3 | even | 12 | |||
2940.2.x.c.1273.8 | 32 | 35.24 | odd | 6 | |||
2940.2.x.c.1273.12 | 32 | 35.4 | even | 6 |