Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.3 | ||
Root | \(2.03852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.1801 |
Dual form | 2520.2.bi.r.361.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.194868 | − | 2.63857i | 0.0736531 | − | 0.997284i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26541 | + | 2.19175i | 0.381535 | + | 0.660838i | 0.991282 | − | 0.131758i | \(-0.0420623\pi\) |
−0.609747 | + | 0.792596i | \(0.708729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45654 | 1.51337 | 0.756686 | − | 0.653779i | \(-0.226817\pi\) | ||||
0.756686 | + | 0.653779i | \(0.226817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.25817 | − | 5.64332i | −0.790223 | − | 1.36871i | −0.925829 | − | 0.377943i | \(-0.876632\pi\) |
0.135606 | − | 0.990763i | \(-0.456702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0406394 | + | 0.0703895i | −0.00932331 | + | 0.0161484i | −0.870649 | − | 0.491904i | \(-0.836301\pi\) |
0.861326 | + | 0.508052i | \(0.169634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.23551 | − | 2.13996i | 0.257621 | − | 0.446213i | −0.707983 | − | 0.706229i | \(-0.750395\pi\) |
0.965604 | + | 0.260017i | \(0.0837281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.37709 | −1.55559 | −0.777793 | − | 0.628520i | \(-0.783661\pi\) | ||||
−0.777793 | + | 0.628520i | \(0.783661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.852597 | − | 1.47674i | −0.153131 | − | 0.265231i | 0.779246 | − | 0.626718i | \(-0.215602\pi\) |
−0.932377 | + | 0.361488i | \(0.882269\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.18763 | + | 1.48804i | 0.369777 | + | 0.251525i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.18763 | − | 2.05704i | 0.195245 | − | 0.338175i | −0.751736 | − | 0.659465i | \(-0.770783\pi\) |
0.946981 | + | 0.321290i | \(0.104116\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.75135 | 0.585862 | 0.292931 | − | 0.956134i | \(-0.405369\pi\) | ||||
0.292931 | + | 0.956134i | \(0.405369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.44207 | 1.43990 | 0.719951 | − | 0.694025i | \(-0.244164\pi\) | ||||
0.719951 | + | 0.694025i | \(0.244164\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.962862 | + | 1.66773i | −0.140448 | + | 0.243263i | −0.927665 | − | 0.373413i | \(-0.878188\pi\) |
0.787218 | + | 0.616675i | \(0.211521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92405 | − | 1.02834i | −0.989150 | − | 0.146906i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.49368 | + | 4.31918i | 0.342533 | + | 0.593285i | 0.984902 | − | 0.173111i | \(-0.0553818\pi\) |
−0.642369 | + | 0.766395i | \(0.722048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.53082 | −0.341255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.65773 | + | 2.87127i | 0.215818 | + | 0.373808i | 0.953525 | − | 0.301313i | \(-0.0974249\pi\) |
−0.737707 | + | 0.675121i | \(0.764092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.150904 | + | 0.261373i | −0.0193213 | + | 0.0334654i | −0.875524 | − | 0.483174i | \(-0.839484\pi\) |
0.856203 | + | 0.516639i | \(0.172817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.72827 | + | 4.72550i | −0.338400 | + | 0.586126i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.58460 | − | 2.74461i | −0.193590 | − | 0.335308i | 0.752847 | − | 0.658195i | \(-0.228680\pi\) |
−0.946437 | + | 0.322887i | \(0.895347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.684541 | −0.0812401 | −0.0406200 | − | 0.999175i | \(-0.512933\pi\) | ||||
−0.0406200 | + | 0.999175i | \(0.512933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.64159 | − | 13.2356i | −0.894380 | − | 1.54911i | −0.834570 | − | 0.550902i | \(-0.814284\pi\) |
−0.0598097 | − | 0.998210i | \(-0.519049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.02967 | − | 2.91176i | 0.687144 | − | 0.331826i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.29931 | − | 12.6428i | 0.821237 | − | 1.42242i | −0.0835245 | − | 0.996506i | \(-0.526618\pi\) |
0.904762 | − | 0.425919i | \(-0.140049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0753 | 1.32543 | 0.662717 | − | 0.748870i | \(-0.269403\pi\) | ||||
0.662717 | + | 0.748870i | \(0.269403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.51634 | 0.706797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.79881 | − | 3.11563i | 0.190674 | − | 0.330256i | −0.754800 | − | 0.655955i | \(-0.772266\pi\) |
0.945474 | + | 0.325699i | \(0.105599\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06330 | − | 14.3974i | 0.111464 | − | 1.50926i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0406394 | − | 0.0703895i | −0.00416951 | − | 0.00722181i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.20088 | 0.934208 | 0.467104 | − | 0.884202i | \(-0.345297\pi\) | ||||
0.467104 | + | 0.884202i | \(0.345297\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.42273 | − | 11.1245i | −0.639085 | − | 1.10693i | −0.985634 | − | 0.168896i | \(-0.945980\pi\) |
0.346549 | − | 0.938032i | \(-0.387354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.63975 | − | 8.03629i | 0.457169 | − | 0.791839i | −0.541641 | − | 0.840610i | \(-0.682197\pi\) |
0.998810 | + | 0.0487704i | \(0.0155303\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.25817 | + | 3.91127i | −0.218306 | + | 0.378116i | −0.954290 | − | 0.298882i | \(-0.903386\pi\) |
0.735984 | + | 0.676998i | \(0.236720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.84277 | − | 6.65588i | −0.368071 | − | 0.637518i | 0.621193 | − | 0.783658i | \(-0.286648\pi\) |
−0.989264 | + | 0.146140i | \(0.953315\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.77947 | 0.261471 | 0.130735 | − | 0.991417i | \(-0.458266\pi\) | ||||
0.130735 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23551 | + | 2.13996i | 0.115212 | + | 0.199552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.5252 | + | 7.49720i | −1.42319 | + | 0.687267i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.29748 | − | 3.97936i | 0.208862 | − | 0.361760i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.76765 | −0.334325 | −0.167162 | − | 0.985929i | \(-0.553460\pi\) | ||||
−0.167162 | + | 0.985929i | \(0.553460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.92314 | − | 5.06302i | 0.255396 | − | 0.442358i | −0.709607 | − | 0.704597i | \(-0.751128\pi\) |
0.965003 | + | 0.262239i | \(0.0844609\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.177808 | + | 0.120946i | 0.0154179 | + | 0.0104874i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.57363 | − | 16.5820i | −0.817930 | − | 1.41670i | −0.907204 | − | 0.420690i | \(-0.861788\pi\) |
0.0892740 | − | 0.996007i | \(-0.471545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1266 | 1.02857 | 0.514283 | − | 0.857621i | \(-0.328058\pi\) | ||||
0.514283 | + | 0.857621i | \(0.328058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.90475 | + | 11.9594i | 0.577404 | + | 1.00009i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.18855 | − | 7.25477i | 0.347840 | − | 0.602476i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.90425 | − | 6.76235i | 0.319848 | − | 0.553994i | −0.660608 | − | 0.750731i | \(-0.729701\pi\) |
0.980456 | + | 0.196738i | \(0.0630347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.928544 | − | 1.60829i | −0.0755638 | − | 0.130880i | 0.825767 | − | 0.564011i | \(-0.190742\pi\) |
−0.901331 | + | 0.433130i | \(0.857409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.70519 | 0.136965 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.158141 | + | 0.273908i | 0.0126210 | + | 0.0218603i | 0.872267 | − | 0.489030i | \(-0.162649\pi\) |
−0.859646 | + | 0.510890i | \(0.829316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.40567 | − | 3.67698i | −0.426026 | − | 0.289786i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5976 | + | 20.0877i | −0.908396 | + | 1.57339i | −0.0921029 | + | 0.995749i | \(0.529359\pi\) |
−0.816293 | + | 0.577638i | \(0.803974\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.471014 | −0.0364482 | −0.0182241 | − | 0.999834i | \(-0.505801\pi\) | ||||
−0.0182241 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7738 | 1.29029 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.88341 | − | 4.99422i | 0.219222 | − | 0.379703i | −0.735348 | − | 0.677689i | \(-0.762981\pi\) |
0.954570 | + | 0.297986i | \(0.0963148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.38250 | + | 1.15052i | −0.180100 | + | 0.0869713i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.29840 | + | 12.6412i | 0.545508 | + | 0.944848i | 0.998575 | + | 0.0533709i | \(0.0169966\pi\) |
−0.453067 | + | 0.891477i | \(0.649670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5333 | 1.00592 | 0.502962 | − | 0.864308i | \(-0.332243\pi\) | ||||
0.502962 | + | 0.864308i | \(0.332243\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.18763 | + | 2.05704i | 0.0873163 | + | 0.151236i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.24583 | − | 14.2822i | 0.602995 | − | 1.04442i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.12661 | − | 8.87954i | 0.370948 | − | 0.642501i | −0.618763 | − | 0.785577i | \(-0.712366\pi\) |
0.989712 | + | 0.143076i | \(0.0456994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.02949 | − | 12.1754i | −0.505994 | − | 0.876407i | −0.999976 | − | 0.00693486i | \(-0.997793\pi\) |
0.493982 | − | 0.869472i | \(-0.335541\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.19423 | 0.655062 | 0.327531 | − | 0.944840i | \(-0.393783\pi\) | ||||
0.327531 | + | 0.944840i | \(0.393783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.05698 | + | 15.6872i | 0.642032 | + | 1.11203i | 0.984978 | + | 0.172678i | \(0.0552419\pi\) |
−0.342946 | + | 0.939355i | \(0.611425\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.63242 | + | 22.1035i | −0.114574 | + | 1.55136i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.87567 | + | 3.24876i | −0.131003 | + | 0.226903i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.205702 | −0.0142287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6566 | −1.00900 | −0.504501 | − | 0.863411i | \(-0.668324\pi\) | ||||
−0.504501 | + | 0.863411i | \(0.668324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.72103 | + | 8.17707i | −0.321972 | + | 0.557671i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.06262 | + | 1.96186i | −0.275789 | + | 0.133180i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.7783 | − | 30.7930i | −1.19590 | − | 2.07136i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.86639 | 0.124983 | 0.0624914 | − | 0.998046i | \(-0.480095\pi\) | ||||
0.0624914 | + | 0.998046i | \(0.480095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2455 | + | 22.9419i | 0.879137 | + | 1.52271i | 0.852290 | + | 0.523070i | \(0.175213\pi\) |
0.0268466 | + | 0.999640i | \(0.491453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.44839 | − | 9.43688i | 0.360040 | − | 0.623607i | −0.627927 | − | 0.778272i | \(-0.716097\pi\) |
0.987967 | + | 0.154665i | \(0.0494298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.29398 | + | 5.70535i | −0.215796 | + | 0.373770i | −0.953519 | − | 0.301334i | \(-0.902568\pi\) |
0.737723 | + | 0.675104i | \(0.235901\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.962862 | − | 1.66773i | −0.0628102 | − | 0.108790i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.12327 | 0.525450 | 0.262725 | − | 0.964871i | \(-0.415379\pi\) | ||||
0.262725 | + | 0.964871i | \(0.415379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3951 | + | 23.2010i | 0.862855 | + | 1.49451i | 0.869162 | + | 0.494528i | \(0.164659\pi\) |
−0.00630723 | + | 0.999980i | \(0.502008\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.35260 | − | 5.48223i | 0.278077 | − | 0.350247i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.221750 | + | 0.384083i | −0.0141096 | + | 0.0244386i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2561 | −0.962954 | −0.481477 | − | 0.876459i | \(-0.659899\pi\) | ||||
−0.481477 | + | 0.876459i | \(0.659899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.25368 | 0.393166 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.1063 | + | 26.1648i | −0.942304 | + | 1.63212i | −0.181242 | + | 0.983439i | \(0.558012\pi\) |
−0.761062 | + | 0.648679i | \(0.775322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.19619 | − | 3.53449i | −0.322876 | − | 0.219623i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4557 | + | 25.0380i | 0.891378 | + | 1.54391i | 0.838225 | + | 0.545325i | \(0.183594\pi\) |
0.0531531 | + | 0.998586i | \(0.483073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.98736 | −0.306371 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.08046 | − | 12.2637i | −0.431703 | − | 0.747732i | 0.565317 | − | 0.824874i | \(-0.308754\pi\) |
−0.997020 | + | 0.0771421i | \(0.975420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.76300 | − | 11.7139i | 0.410823 | − | 0.711566i | −0.584157 | − | 0.811641i | \(-0.698575\pi\) |
0.994980 | + | 0.100074i | \(0.0319081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.26541 | − | 2.19175i | 0.0763070 | − | 0.132168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0177 | − | 17.3511i | −0.601903 | − | 1.04253i | −0.992533 | − | 0.121979i | \(-0.961076\pi\) |
0.390629 | − | 0.920548i | \(-0.372257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.1557 | −1.08308 | −0.541540 | − | 0.840675i | \(-0.682159\pi\) | ||||
−0.541540 | + | 0.840675i | \(0.682159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.62711 | − | 11.4785i | −0.393941 | − | 0.682326i | 0.599025 | − | 0.800731i | \(-0.295555\pi\) |
−0.992965 | + | 0.118405i | \(0.962222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.731016 | − | 9.89817i | 0.0431505 | − | 0.584271i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7314 | + | 22.0514i | −0.748904 | + | 1.29714i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.46102 | −0.435878 | −0.217939 | − | 0.975962i | \(-0.569933\pi\) | ||||
−0.217939 | + | 0.975962i | \(0.569933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.31546 | −0.193033 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.74159 | − | 11.6768i | 0.389876 | − | 0.675286i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.83995 | − | 24.9135i | 0.106053 | − | 1.43599i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.150904 | − | 0.261373i | −0.00864073 | − | 0.0149662i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.9561 | 1.88090 | 0.940451 | − | 0.339928i | \(-0.110403\pi\) | ||||
0.940451 | + | 0.339928i | \(0.110403\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5638 | − | 26.9573i | −0.882543 | − | 1.52861i | −0.848505 | − | 0.529188i | \(-0.822497\pi\) |
−0.0340379 | − | 0.999421i | \(-0.510837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.87659 | − | 4.98240i | 0.162594 | − | 0.281622i | −0.773204 | − | 0.634157i | \(-0.781347\pi\) |
0.935798 | + | 0.352536i | \(0.114680\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.5395 | − | 28.6473i | 0.928951 | − | 1.60899i | 0.143872 | − | 0.989596i | \(-0.454045\pi\) |
0.785080 | − | 0.619395i | \(-0.212622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6004 | − | 18.3605i | −0.593511 | − | 1.02799i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.529640 | 0.0294700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.72827 | − | 4.72550i | −0.151337 | − | 0.262124i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.21277 | + | 2.86556i | 0.232258 | + | 0.157983i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6547 | + | 21.9186i | −0.695567 | + | 1.20476i | 0.274422 | + | 0.961609i | \(0.411513\pi\) |
−0.969989 | + | 0.243148i | \(0.921820\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.16921 | 0.173152 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.6450 | −1.56039 | −0.780195 | − | 0.625536i | \(-0.784880\pi\) | ||||
−0.780195 | + | 0.625536i | \(0.784880\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.15777 | − | 3.73736i | 0.116850 | − | 0.202390i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.06262 | + | 18.0692i | −0.219361 | + | 0.975644i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.9602 | − | 31.1080i | −0.964156 | − | 1.66997i | −0.711865 | − | 0.702316i | \(-0.752149\pi\) |
−0.252291 | − | 0.967651i | \(-0.581184\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8841 | −0.582614 | −0.291307 | − | 0.956630i | \(-0.594090\pi\) | ||||
−0.291307 | + | 0.956630i | \(0.594090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8026 | + | 23.9069i | 0.734640 | + | 1.27243i | 0.954881 | + | 0.296989i | \(0.0959824\pi\) |
−0.220241 | + | 0.975446i | \(0.570684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.342271 | − | 0.592830i | 0.0181658 | − | 0.0314641i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.45167 | − | 7.71053i | 0.234950 | − | 0.406946i | −0.724308 | − | 0.689477i | \(-0.757841\pi\) |
0.959258 | + | 0.282531i | \(0.0911739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49670 | + | 16.4488i | 0.499826 | + | 0.865724i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2832 | 0.799958 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4788 | + | 28.5421i | 0.860186 | + | 1.48989i | 0.871749 | + | 0.489953i | \(0.162986\pi\) |
−0.0115631 | + | 0.999933i | \(0.503681\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.8824 | − | 5.73806i | 0.616902 | − | 0.297905i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.17339 | + | 14.1567i | −0.423202 | + | 0.733008i | −0.996251 | − | 0.0865138i | \(-0.972427\pi\) |
0.573048 | + | 0.819521i | \(0.305761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.7099 | −2.35418 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1083 | −1.39246 | −0.696231 | − | 0.717818i | \(-0.745141\pi\) | ||||
−0.696231 | + | 0.717818i | \(0.745141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3853 | + | 21.4519i | −0.632858 | + | 1.09614i | 0.354106 | + | 0.935205i | \(0.384785\pi\) |
−0.986965 | + | 0.160938i | \(0.948548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.493174 | + | 6.67772i | −0.0251345 | + | 0.340328i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.04046 | − | 6.99829i | −0.204860 | − | 0.354827i | 0.745228 | − | 0.666809i | \(-0.232340\pi\) |
−0.950088 | + | 0.311982i | \(0.899007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1020 | −0.814312 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.29931 | + | 12.6428i | 0.367268 | + | 0.636127i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9374 | + | 24.1403i | −0.699498 | + | 1.21157i | 0.269143 | + | 0.963100i | \(0.413260\pi\) |
−0.968641 | + | 0.248466i | \(0.920074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.05722 | + | 13.9555i | −0.402358 | + | 0.696905i | −0.994010 | − | 0.109289i | \(-0.965143\pi\) |
0.591652 | + | 0.806194i | \(0.298476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.65223 | − | 8.05790i | −0.231744 | − | 0.401393i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.01135 | 0.297972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.06048 | − | 10.4971i | −0.299672 | − | 0.519046i | 0.676389 | − | 0.736544i | \(-0.263544\pi\) |
−0.976061 | + | 0.217498i | \(0.930210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.89908 | − | 3.81451i | 0.388688 | − | 0.187700i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.03764 | + | 10.4575i | −0.296376 | + | 0.513339i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.7920 | 1.45544 | 0.727718 | − | 0.685876i | \(-0.240581\pi\) | ||||
0.727718 | + | 0.685876i | \(0.240581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.96233 | 0.339323 | 0.169662 | − | 0.985502i | \(-0.445733\pi\) | ||||
0.169662 | + | 0.985502i | \(0.445733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.25817 | + | 5.64332i | −0.158045 | + | 0.273741i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.660244 | + | 0.449103i | 0.0319515 | + | 0.0217336i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8326 | + | 23.9588i | 0.666294 | + | 1.15406i | 0.978933 | + | 0.204183i | \(0.0654538\pi\) |
−0.312639 | + | 0.949872i | \(0.601213\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.80177 | 0.278815 | 0.139408 | − | 0.990235i | \(-0.455480\pi\) | ||||
0.139408 | + | 0.990235i | \(0.455480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.100420 | + | 0.173933i | 0.00480376 | + | 0.00832036i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.43224 | + | 14.6051i | −0.402449 | + | 0.697062i | −0.994021 | − | 0.109190i | \(-0.965174\pi\) |
0.591572 | + | 0.806252i | \(0.298508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.8173 | + | 29.1285i | −0.799015 | + | 1.38394i | 0.121243 | + | 0.992623i | \(0.461312\pi\) |
−0.920258 | + | 0.391312i | \(0.872021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.79881 | + | 3.11563i | 0.0852718 | + | 0.147695i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.87896 | −0.419024 | −0.209512 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209512 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.74698 | + | 8.22202i | 0.223527 | + | 0.387160i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.9369 | + | 8.11957i | 0.559610 | + | 0.380651i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.8641 | + | 27.4774i | −0.742092 | + | 1.28534i | 0.209449 | + | 0.977819i | \(0.432833\pi\) |
−0.951541 | + | 0.307521i | \(0.900500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0714 | 0.888242 | 0.444121 | − | 0.895967i | \(-0.353516\pi\) | ||||
0.444121 | + | 0.895967i | \(0.353516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5938 | 1.00355 | 0.501775 | − | 0.864998i | \(-0.332681\pi\) | ||||
0.501775 | + | 0.864998i | \(0.332681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4369 | − | 25.0054i | 0.668060 | − | 1.15711i | −0.310386 | − | 0.950611i | \(-0.600458\pi\) |
0.978446 | − | 0.206503i | \(-0.0662083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.55063 | + | 3.64624i | −0.348656 | + | 0.168368i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.9481 | + | 20.6947i | 0.549373 | + | 0.951542i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0812787 | 0.00372932 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.97105 | − | 12.0742i | −0.318515 | − | 0.551685i | 0.661663 | − | 0.749801i | \(-0.269851\pi\) |
−0.980179 | + | 0.198116i | \(0.936518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.48035 | − | 11.2243i | 0.295479 | − | 0.511784i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.60044 | + | 7.96820i | −0.208895 | + | 0.361817i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.55831 | − | 13.0914i | −0.342500 | − | 0.593227i | 0.642397 | − | 0.766372i | \(-0.277940\pi\) |
−0.984896 | + | 0.173146i | \(0.944607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.5713 | −1.42479 | −0.712396 | − | 0.701777i | \(-0.752390\pi\) | ||||
−0.712396 | + | 0.701777i | \(0.752390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.2940 | + | 47.2746i | 1.22926 | + | 2.12914i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.133395 | + | 1.80621i | −0.00598358 | + | 0.0810194i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.4432 | + | 26.7484i | −0.691333 | + | 1.19742i | 0.280068 | + | 0.959980i | \(0.409643\pi\) |
−0.971401 | + | 0.237444i | \(0.923690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.4451 | 1.71418 | 0.857091 | − | 0.515165i | \(-0.172269\pi\) | ||||
0.857091 | + | 0.515165i | \(0.172269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8455 | 0.571615 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1421 | − | 19.2987i | 0.493864 | − | 0.855398i | −0.506111 | − | 0.862469i | \(-0.668917\pi\) |
0.999975 | + | 0.00707034i | \(0.00225058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.4121 | + | 17.5836i | −1.61078 | + | 0.777854i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.63975 | + | 8.03629i | 0.204452 | + | 0.354121i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.87365 | −0.214343 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.98111 | − | 12.0916i | −0.305848 | − | 0.529744i | 0.671602 | − | 0.740912i | \(-0.265607\pi\) |
−0.977450 | + | 0.211168i | \(0.932273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.42987 | − | 4.20866i | 0.106251 | − | 0.184032i | −0.807998 | − | 0.589186i | \(-0.799449\pi\) |
0.914249 | + | 0.405154i | \(0.132782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.55582 | + | 9.62295i | −0.242015 | + | 0.419182i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.44704 | + | 14.6307i | 0.367263 | + | 0.636118i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.4694 | 0.886627 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.25817 | − | 3.91127i | −0.0976293 | − | 0.169099i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.50788 | − | 16.4771i | −0.280314 | − | 0.709718i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0587 | + | 19.1541i | −0.475449 | + | 0.823501i | −0.999605 | − | 0.0281212i | \(-0.991048\pi\) |
0.524156 | + | 0.851622i | \(0.324381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.68555 | 0.329213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0636 | 1.58473 | 0.792364 | − | 0.610049i | \(-0.208850\pi\) | ||||
0.792364 | + | 0.610049i | \(0.208850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.340440 | − | 0.589659i | 0.0145032 | − | 0.0251203i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.9364 | − | 21.7234i | −1.35807 | − | 0.923772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4331 | − | 28.4629i | −0.696291 | − | 1.20601i | −0.969744 | − | 0.244126i | \(-0.921499\pi\) |
0.273453 | − | 0.961885i | \(-0.411834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.5210 | 2.17911 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.83446 | − | 10.1056i | −0.245893 | − | 0.425899i | 0.716489 | − | 0.697598i | \(-0.245748\pi\) |
−0.962382 | + | 0.271699i | \(0.912415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.38974 | + | 2.40709i | −0.0584666 | + | 0.101267i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.88932 | + | 5.00446i | −0.121127 | + | 0.209798i | −0.920212 | − | 0.391420i | \(-0.871984\pi\) |
0.799086 | + | 0.601217i | \(0.205317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.7522 | − | 20.3554i | −0.491814 | − | 0.851847i | 0.508142 | − | 0.861274i | \(-0.330333\pi\) |
−0.999956 | + | 0.00942676i | \(0.996999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.47101 | −0.103048 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.48220 | − | 6.03135i | −0.144966 | − | 0.251088i | 0.784394 | − | 0.620263i | \(-0.212974\pi\) |
−0.929360 | + | 0.369174i | \(0.879641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.35308 | − | 31.8614i | 0.0976223 | − | 1.32183i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.31104 | + | 10.9310i | −0.261377 | + | 0.452718i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.95568 | −0.410915 | −0.205457 | − | 0.978666i | \(-0.565868\pi\) | ||||
−0.205457 | + | 0.978666i | \(0.565868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.138596 | 0.00571075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.8531 | + | 30.9225i | −0.733141 | + | 1.26984i | 0.222394 | + | 0.974957i | \(0.428613\pi\) |
−0.955534 | + | 0.294880i | \(0.904720\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.26982 | − | 17.1938i | 0.0520577 | − | 0.704877i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.76582 | + | 15.1828i | 0.358162 | + | 0.620354i | 0.987654 | − | 0.156653i | \(-0.0500703\pi\) |
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.9334 | 1.01705 | 0.508527 | − | 0.861046i | \(-0.330190\pi\) | ||||
0.508527 | + | 0.861046i | \(0.330190\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.29748 | + | 3.97936i | 0.0934060 | + | 0.161784i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7969 | + | 18.7008i | −0.438233 | + | 0.759042i | −0.997553 | − | 0.0699099i | \(-0.977729\pi\) |
0.559320 | + | 0.828952i | \(0.311062\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.25389 | + | 9.10001i | −0.212550 | + | 0.368147i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.54423 | + | 14.7990i | 0.345098 | + | 0.597728i | 0.985372 | − | 0.170419i | \(-0.0545122\pi\) |
−0.640273 | + | 0.768147i | \(0.721179\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.7252 | 1.19669 | 0.598345 | − | 0.801239i | \(-0.295825\pi\) | ||||
0.598345 | + | 0.801239i | \(0.295825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.12909 | + | 12.3479i | 0.286542 | + | 0.496306i | 0.972982 | − | 0.230881i | \(-0.0741608\pi\) |
−0.686440 | + | 0.727187i | \(0.740827\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.87027 | − | 5.35342i | −0.315316 | − | 0.214480i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4780 | −0.617149 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.15725 | −0.245116 | −0.122558 | − | 0.992461i | \(-0.539110\pi\) | ||||
−0.122558 | + | 0.992461i | \(0.539110\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.88383 | − | 3.26288i | 0.0747573 | − | 0.129483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.7814 | − | 5.61119i | −1.49695 | − | 0.222323i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.2435 | − | 24.6704i | −0.562583 | − | 0.974422i | −0.997270 | − | 0.0738407i | \(-0.976474\pi\) |
0.434687 | − | 0.900582i | \(-0.356859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.88877 | 0.153358 | 0.0766790 | − | 0.997056i | \(-0.475568\pi\) | ||||
0.0766790 | + | 0.997056i | \(0.475568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.7725 | − | 18.6585i | −0.423511 | − | 0.733542i | 0.572769 | − | 0.819717i | \(-0.305869\pi\) |
−0.996280 | + | 0.0861744i | \(0.972536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.19541 | + | 7.26666i | −0.164684 | + | 0.285241i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.20738 | + | 3.82330i | −0.0863815 | + | 0.149617i | −0.905979 | − | 0.423322i | \(-0.860864\pi\) |
0.819598 | + | 0.572940i | \(0.194197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.92314 | + | 5.06302i | 0.114216 | + | 0.197829i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7579 | −1.62666 | −0.813329 | − | 0.581804i | \(-0.802347\pi\) | ||||
−0.813329 | + | 0.581804i | \(0.802347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.13758 | + | 8.89855i | 0.199829 | + | 0.346113i | 0.948473 | − | 0.316859i | \(-0.102628\pi\) |
−0.748644 | + | 0.662972i | \(0.769295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.193646 | + | 0.0935130i | −0.00750929 | + | 0.00362628i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3500 | + | 17.9267i | −0.400752 | + | 0.694123i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.763820 | −0.0294870 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0484 | −0.888450 | −0.444225 | − | 0.895915i | \(-0.646521\pi\) | ||||
−0.444225 | + | 0.895915i | \(0.646521\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.64407 | − | 2.84760i | 0.0631866 | − | 0.109442i | −0.832702 | − | 0.553722i | \(-0.813207\pi\) |
0.895888 | + | 0.444280i | \(0.146540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.79296 | − | 24.2771i | 0.0688073 | − | 0.931671i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2241 | + | 35.0291i | 0.773852 | + | 1.34035i | 0.935438 | + | 0.353492i | \(0.115006\pi\) |
−0.161586 | + | 0.986859i | \(0.551661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1473 | 0.731579 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.6069 | + | 23.5678i | 0.518380 | + | 0.897860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2144 | + | 29.8162i | −0.654866 | + | 1.13426i | 0.327061 | + | 0.945003i | \(0.393942\pi\) |
−0.981927 | + | 0.189259i | \(0.939392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.06330 | + | 10.5019i | −0.229994 | + | 0.398362i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2225 | − | 21.1700i | −0.462961 | − | 0.801872i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1396 | 0.571815 | 0.285907 | − | 0.958257i | \(-0.407705\pi\) | ||||
0.285907 | + | 0.958257i | \(0.407705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0965291 | + | 0.167193i | 0.00364067 | + | 0.00630582i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.6043 | + | 14.7790i | −1.15099 | + | 0.555821i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0851 | + | 33.0564i | −0.716756 | + | 1.24146i | 0.245522 | + | 0.969391i | \(0.421041\pi\) |
−0.962278 | + | 0.272067i | \(0.912293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.21356 | −0.157799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.8095 | −0.516446 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.29398 | − | 12.6335i | 0.272020 | − | 0.471152i | −0.697359 | − | 0.716722i | \(-0.745642\pi\) |
0.969379 | + | 0.245570i | \(0.0789751\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3001 | − | 13.8083i | −0.756017 | − | 0.514248i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.18855 | + | 7.25477i | 0.155559 | + | 0.269436i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.76798 | 0.139747 | 0.0698734 | − | 0.997556i | \(-0.477740\pi\) | ||||
0.0698734 | + | 0.997556i | \(0.477740\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.7639 | − | 53.2846i | −1.13784 | − | 1.97080i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5404 | + | 21.7207i | −0.463191 | + | 0.802271i | −0.999118 | − | 0.0419938i | \(-0.986629\pi\) |
0.535927 | + | 0.844265i | \(0.319962\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.01034 | − | 6.94611i | 0.147723 | − | 0.255863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.32715 | + | 14.4230i | 0.306319 | + | 0.530560i | 0.977554 | − | 0.210684i | \(-0.0675692\pi\) |
−0.671235 | + | 0.741245i | \(0.734236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.8561 | 0.434959 | 0.217479 | − | 0.976065i | \(-0.430217\pi\) | ||||
0.217479 | + | 0.976065i | \(0.430217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.90425 | + | 6.76235i | 0.143041 | + | 0.247753i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.88009 | + | 6.72051i | 0.361011 | + | 0.245562i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0690 | + | 34.7605i | −0.732327 | + | 1.26843i | 0.223559 | + | 0.974690i | \(0.428232\pi\) |
−0.955886 | + | 0.293737i | \(0.905101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.85709 | 0.0675864 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.732857 | −0.0266361 | −0.0133181 | − | 0.999911i | \(-0.504239\pi\) | ||||
−0.0133181 | + | 0.999911i | \(0.504239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.02042 | − | 10.4277i | 0.218240 | − | 0.378003i | −0.736030 | − | 0.676949i | \(-0.763302\pi\) |
0.954270 | + | 0.298946i | \(0.0966351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3108 | + | 8.84239i | −0.662896 | + | 0.320116i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.04547 | + | 15.6672i | 0.326613 | + | 0.565710i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3382 | 0.733413 | 0.366706 | − | 0.930337i | \(-0.380485\pi\) | ||||
0.366706 | + | 0.930337i | \(0.380485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.4299 | + | 40.5818i | 0.842716 | + | 1.45963i | 0.887590 | + | 0.460634i | \(0.152378\pi\) |
−0.0448742 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.852597 | + | 1.47674i | −0.0306262 | + | 0.0530461i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.152452 | + | 0.264055i | −0.00546217 | + | 0.00946076i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.866224 | − | 1.50034i | −0.0309959 | − | 0.0536865i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.316282 | −0.0112886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.2234 | − | 17.7074i | −0.364424 | − | 0.631200i | 0.624260 | − | 0.781217i | \(-0.285401\pi\) |
−0.988684 | + | 0.150016i | \(0.952067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.541629 | − | 7.33382i | 0.0192581 | − | 0.260760i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.823413 | + | 1.42619i | −0.0292403 | + | 0.0506456i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.73313 | −0.309344 | −0.154672 | − | 0.987966i | \(-0.549432\pi\) | ||||
−0.154672 | + | 0.987966i | \(0.549432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5487 | 0.443940 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.3394 | − | 33.4969i | 0.682474 | − | 1.18208i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.88719 | − | 2.84296i | 0.207496 | − | 0.100201i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.922130 | − | 1.59718i | −0.0324204 | − | 0.0561537i | 0.849360 | − | 0.527814i | \(-0.176988\pi\) |
−0.881780 | + | 0.471660i | \(0.843655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.0744 | −1.23163 | −0.615814 | − | 0.787891i | \(-0.711173\pi\) | ||||
−0.615814 | + | 0.787891i | \(0.711173\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5976 | − | 20.0877i | −0.406247 | − | 0.703640i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.383720 | + | 0.664622i | −0.0134247 | + | 0.0232522i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.73800 | + | 3.01031i | −0.0606566 | + | 0.105060i | −0.894759 | − | 0.446549i | \(-0.852653\pi\) |
0.834102 | + | 0.551610i | \(0.185986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4674 | − | 44.1108i | −0.887737 | − | 1.53761i | −0.842544 | − | 0.538627i | \(-0.818943\pi\) |
−0.0451923 | − | 0.998978i | \(-0.514390\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1506 | −0.492063 | −0.246032 | − | 0.969262i | \(-0.579127\pi\) | ||||
−0.246032 | + | 0.969262i | \(0.579127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.9756 | − | 25.9384i | −0.520123 | − | 0.900879i | −0.999726 | − | 0.0233937i | \(-0.992553\pi\) |
0.479604 | − | 0.877485i | \(-0.340780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.7565 | + | 42.4252i | 0.580578 | + | 1.46994i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.235507 | − | 0.407910i | 0.00815006 | − | 0.0141163i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.6753 | −1.68046 | −0.840229 | − | 0.542232i | \(-0.817579\pi\) | ||||
−0.840229 | + | 0.542232i | \(0.817579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.1757 | 1.41985 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.38691 | + | 14.5266i | −0.288519 | + | 0.499729i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0521 | − | 6.83751i | −0.345394 | − | 0.234940i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.93465 | − | 5.08297i | −0.100599 | − | 0.174242i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.93054 | 0.271537 | 0.135768 | − | 0.990741i | \(-0.456650\pi\) | ||||
0.135768 | + | 0.990741i | \(0.456650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0956 | + | 27.8784i | 0.549816 | + | 0.952309i | 0.998287 | + | 0.0585114i | \(0.0186354\pi\) |
−0.448471 | + | 0.893797i | \(0.648031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.43224 | − | 14.6051i | 0.287704 | − | 0.498319i | −0.685557 | − | 0.728019i | \(-0.740441\pi\) |
0.973261 | + | 0.229700i | \(0.0737746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.4596 | − | 40.6331i | 0.798573 | − | 1.38317i | −0.121973 | − | 0.992533i | \(-0.538922\pi\) |
0.920546 | − | 0.390635i | \(-0.127745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.88341 | + | 4.99422i | 0.0980390 | + | 0.169809i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.9465 | 1.25332 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.64645 | − | 14.9761i | −0.292974 | − | 0.507446i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.194868 | − | 2.63857i | 0.00658773 | − | 0.0891998i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.48380 | − | 2.57002i | 0.0501044 | − | 0.0867834i | −0.839885 | − | 0.542764i | \(-0.817378\pi\) |
0.889990 | + | 0.455980i | \(0.150711\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.6911 | −0.899247 | −0.449623 | − | 0.893218i | \(-0.648442\pi\) | ||||
−0.449623 | + | 0.893218i | \(0.648442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.25049 | 0.0757349 | 0.0378674 | − | 0.999283i | \(-0.487944\pi\) | ||||
0.0378674 | + | 0.999283i | \(0.487944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9899 | − | 31.1594i | 0.604041 | − | 1.04623i | −0.388162 | − | 0.921591i | \(-0.626890\pi\) |
0.992202 | − | 0.124638i | \(-0.0397769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.734193 | + | 9.94119i | −0.0246241 | + | 0.333417i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0782602 | − | 0.135551i | −0.00261888 | − | 0.00453603i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.5968 | −0.487917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.14229 | + | 12.3708i | 0.238209 | + | 0.412589i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2497 | − | 28.1452i | 0.541355 | − | 0.937654i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.76667 | + | 11.7202i | −0.224932 | + | 0.389593i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.8575 | + | 51.7147i | 0.991401 | + | 1.71716i | 0.609025 | + | 0.793151i | \(0.291561\pi\) |
0.382376 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.5567 | −1.77441 | −0.887206 | − | 0.461373i | \(-0.847357\pi\) | ||||
−0.887206 | + | 0.461373i | \(0.847357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.2802 | + | 26.4660i | 0.505700 | + | 0.875897i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.7895 | − | 8.69951i | −0.422346 | − | 0.287283i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.381583 | − | 0.660921i | 0.0125873 | − | 0.0218018i | −0.859663 | − | 0.510861i | \(-0.829327\pi\) |
0.872250 | + | 0.489059i | \(0.162660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.73523 | −0.122946 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.37526 | −0.0780981 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8829 | + | 48.2945i | −0.914807 | + | 1.58449i | −0.107623 | + | 0.994192i | \(0.534324\pi\) |
−0.807184 | + | 0.590300i | \(0.799009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.353774 | − | 0.445589i | 0.0115945 | − | 0.0146036i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.24583 | + | 14.2822i | 0.269668 | + | 0.467078i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7785 | 0.842146 | 0.421073 | − | 0.907027i | \(-0.361654\pi\) | ||||
0.421073 | + | 0.907027i | \(0.361654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.52595 | − | 14.7674i | −0.277938 | − | 0.481403i | 0.692934 | − | 0.721001i | \(-0.256318\pi\) |
−0.970872 | + | 0.239598i | \(0.922984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.63481 | − | 8.02773i | 0.150930 | − | 0.261419i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6489 | − | 27.1047i | 0.508521 | − | 0.880785i | −0.491430 | − | 0.870917i | \(-0.663526\pi\) |
0.999951 | − | 0.00986776i | \(-0.00314106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.6966 | − | 72.2207i | −1.35353 | − | 2.34438i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3637 | 0.335713 | 0.167857 | − | 0.985811i | \(-0.446315\pi\) | ||||
0.167857 | + | 0.985811i | \(0.446315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.12661 | + | 8.87954i | 0.165893 | + | 0.287335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.6183 | + | 22.0293i | −1.47309 | + | 0.711365i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0462 | − | 24.3287i | 0.453102 | − | 0.784795i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0590 | 0.452575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1057 | 1.38618 | 0.693092 | − | 0.720849i | \(-0.256248\pi\) | ||||
0.693092 | + | 0.720849i | \(0.256248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.2096 | − | 31.5400i | 0.584375 | − | 1.01217i | −0.410578 | − | 0.911826i | \(-0.634673\pi\) |
0.994953 | − | 0.100342i | \(-0.0319938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.36308 | − | 31.9968i | 0.0757570 | − | 1.02577i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6092 | + | 42.6243i | 0.787317 | + | 1.36367i | 0.927605 | + | 0.373562i | \(0.121864\pi\) |
−0.140289 | + | 0.990111i | \(0.544803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.10492 | 0.290994 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.3368 | + | 33.4924i | 0.616749 | + | 1.06824i | 0.990075 | + | 0.140540i | \(0.0448840\pi\) |
−0.373326 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.59712 | + | 7.96244i | −0.146476 | + | 0.253704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6657 | − | 20.2057i | 0.370949 | − | 0.642502i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.33663 | − | 7.51127i | −0.137758 | − | 0.238603i | 0.788890 | − | 0.614535i | \(-0.210656\pi\) |
−0.926648 | + | 0.375931i | \(0.877323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.1140 | −0.574251 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.25185 | + | 10.8285i | 0.197998 | + | 0.342943i | 0.947879 | − | 0.318630i | \(-0.103223\pi\) |
−0.749881 | + | 0.661573i | \(0.769889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2520.2.bi.r.1801.3 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.s.1801.3 | yes | 10 | ||
7.4 | even | 3 | inner | 2520.2.bi.r.361.3 | ✓ | 10 | |
21.11 | odd | 6 | 2520.2.bi.s.361.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.3 | ✓ | 10 | 7.4 | even | 3 | inner | |
2520.2.bi.r.1801.3 | yes | 10 | 1.1 | even | 1 | trivial | |
2520.2.bi.s.361.3 | yes | 10 | 21.11 | odd | 6 | ||
2520.2.bi.s.1801.3 | yes | 10 | 3.2 | odd | 2 |