Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1343,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1343");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.n (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 800) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1407.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1407 |
Dual form | 1600.2.n.p.1343.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.22474 | − | 2.22474i | −1.28446 | − | 1.28446i | −0.938104 | − | 0.346353i | \(-0.887420\pi\) |
−0.346353 | − | 0.938104i | \(-0.612580\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 2.00000i | −0.755929 | + | 0.755929i | −0.975579 | − | 0.219650i | \(-0.929509\pi\) |
0.219650 | + | 0.975579i | \(0.429509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.89898i | 2.29966i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44949i | 1.04006i | 0.854148 | + | 0.520030i | \(0.174079\pi\) | ||||
−0.854148 | + | 0.520030i | \(0.825921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.44949 | − | 4.44949i | 1.23407 | − | 1.23407i | 0.271678 | − | 0.962388i | \(-0.412421\pi\) |
0.962388 | − | 0.271678i | \(-0.0875787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.775255 | + | 0.775255i | 0.188027 | + | 0.188027i | 0.794843 | − | 0.606816i | \(-0.207553\pi\) |
−0.606816 | + | 0.794843i | \(0.707553\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55051 | −0.585127 | −0.292564 | − | 0.956246i | \(-0.594508\pi\) | ||||
−0.292564 | + | 0.956246i | \(0.594508\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.89898 | 1.94192 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.449490 | − | 0.449490i | −0.0937251 | − | 0.0937251i | 0.658690 | − | 0.752415i | \(-0.271111\pi\) |
−0.752415 | + | 0.658690i | \(0.771111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.67423 | − | 8.67423i | 1.66936 | − | 1.66936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.89898i | − | 0.538327i | −0.963095 | − | 0.269163i | \(-0.913253\pi\) | ||
0.963095 | − | 0.269163i | \(-0.0867472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.89898i | − | 0.520672i | −0.965518 | − | 0.260336i | \(-0.916167\pi\) | ||
0.965518 | − | 0.260336i | \(-0.0838333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.67423 | − | 7.67423i | 1.33591 | − | 1.33591i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | − | 6.00000i | −0.986394 | − | 0.986394i | 0.0135147 | − | 0.999909i | \(-0.495698\pi\) |
−0.999909 | + | 0.0135147i | \(0.995698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.7980 | −3.17021 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.89898 | − | 2.89898i | −0.442090 | − | 0.442090i | 0.450624 | − | 0.892714i | \(-0.351202\pi\) |
−0.892714 | + | 0.450624i | \(0.851202\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.34847 | − | 7.34847i | 1.07188 | − | 1.07188i | 0.0746766 | − | 0.997208i | \(-0.476208\pi\) |
0.997208 | − | 0.0746766i | \(-0.0237924\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.44949i | − | 0.483025i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.44949 | + | 6.44949i | −0.885906 | + | 0.885906i | −0.994127 | − | 0.108221i | \(-0.965484\pi\) |
0.108221 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.67423 | + | 5.67423i | 0.751571 | + | 0.751571i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.79796 | 1.01521 | 0.507604 | − | 0.861591i | \(-0.330531\pi\) | ||||
0.507604 | + | 0.861591i | \(0.330531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.898979 | 0.115103 | 0.0575513 | − | 0.998343i | \(-0.481671\pi\) | ||||
0.0575513 | + | 0.998343i | \(0.481671\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.7980 | − | 13.7980i | −1.73838 | − | 1.73838i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.22474 | + | 4.22474i | −0.516135 | + | 0.516135i | −0.916400 | − | 0.400265i | \(-0.868918\pi\) |
0.400265 | + | 0.916400i | \(0.368918\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000i | 0.240772i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.00000i | − | 0.237356i | −0.992933 | − | 0.118678i | \(-0.962134\pi\) | ||
0.992933 | − | 0.118678i | \(-0.0378657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.67423 | + | 5.67423i | −0.664119 | + | 0.664119i | −0.956348 | − | 0.292229i | \(-0.905603\pi\) |
0.292229 | + | 0.956348i | \(0.405603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.89898 | − | 6.89898i | −0.786212 | − | 0.786212i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.898979 | 0.101143 | 0.0505715 | − | 0.998720i | \(-0.483896\pi\) | ||||
0.0505715 | + | 0.998720i | \(0.483896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −17.8990 | −1.98878 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.67423 | − | 4.67423i | −0.513064 | − | 0.513064i | 0.402400 | − | 0.915464i | \(-0.368176\pi\) |
−0.915464 | + | 0.402400i | \(0.868176\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.44949 | + | 6.44949i | −0.691458 | + | 0.691458i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.8990i | − | 1.26129i | −0.776072 | − | 0.630645i | \(-0.782791\pi\) | ||
0.776072 | − | 0.630645i | \(-0.217209\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.7980i | 1.86573i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.44949 | + | 6.44949i | −0.668781 | + | 0.668781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | − | 4.89898i | −0.497416 | − | 0.497416i | 0.413217 | − | 0.910633i | \(-0.364405\pi\) |
−0.910633 | + | 0.413217i | \(0.864405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.7980 | −2.39178 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6969 | −1.46240 | −0.731200 | − | 0.682163i | \(-0.761039\pi\) | ||||
−0.731200 | + | 0.682163i | \(0.761039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.44949 | − | 2.44949i | −0.241355 | − | 0.241355i | 0.576055 | − | 0.817411i | \(-0.304591\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.57321 | − | 5.57321i | 0.538783 | − | 0.538783i | −0.384388 | − | 0.923171i | \(-0.625588\pi\) |
0.923171 | + | 0.384388i | \(0.125588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.10102i | − | 0.297024i | −0.988911 | − | 0.148512i | \(-0.952552\pi\) | ||
0.988911 | − | 0.148512i | \(-0.0474483\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.6969i | 2.53396i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6742 | + | 11.6742i | −1.09822 | + | 1.09822i | −0.103601 | + | 0.994619i | \(0.533036\pi\) |
−0.994619 | + | 0.103601i | \(0.966964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.6969 | + | 30.6969i | 2.83793 | + | 2.83793i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.10102 | −0.284270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.898979 | −0.0817254 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1237 | − | 11.1237i | −1.00299 | − | 1.00299i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.44949 | − | 8.44949i | 0.749771 | − | 0.749771i | −0.224665 | − | 0.974436i | \(-0.572129\pi\) |
0.974436 | + | 0.224665i | \(0.0721288\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.8990i | 1.13569i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.7980i | − | 1.38027i | −0.723679 | − | 0.690137i | \(-0.757550\pi\) | ||
0.723679 | − | 0.690137i | \(-0.242450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.10102 | − | 5.10102i | 0.442315 | − | 0.442315i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.12372 | + | 2.12372i | 0.181442 | + | 0.181442i | 0.791984 | − | 0.610542i | \(-0.209048\pi\) |
−0.610542 | + | 0.791984i | \(0.709048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.24745 | −0.784358 | −0.392179 | − | 0.919889i | \(-0.628279\pi\) | ||||
−0.392179 | + | 0.919889i | \(0.628279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.6969 | −2.75358 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.3485 | + | 15.3485i | 1.28350 | + | 1.28350i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.22474 | + | 2.22474i | −0.183494 | + | 0.183494i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.8990i | − | 1.54826i | −0.633024 | − | 0.774132i | \(-0.718186\pi\) | ||
0.633024 | − | 0.774132i | \(-0.281814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22.6969i | − | 1.84705i | −0.383537 | − | 0.923525i | \(-0.625294\pi\) | ||
0.383537 | − | 0.923525i | \(-0.374706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.34847 | + | 5.34847i | −0.432398 | + | 0.432398i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24745 | − | 8.24745i | −0.658218 | − | 0.658218i | 0.296740 | − | 0.954958i | \(-0.404100\pi\) |
−0.954958 | + | 0.296740i | \(0.904100\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.6969 | 2.27582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.79796 | 0.141699 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.77526 | + | 7.77526i | 0.609005 | + | 0.609005i | 0.942686 | − | 0.333681i | \(-0.108291\pi\) |
−0.333681 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4495 | − | 10.4495i | 0.808606 | − | 0.808606i | −0.175817 | − | 0.984423i | \(-0.556257\pi\) |
0.984423 | + | 0.175817i | \(0.0562567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 26.5959i | − | 2.04584i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 17.5959i | − | 1.34559i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.79796 | − | 5.79796i | 0.440811 | − | 0.440811i | −0.451474 | − | 0.892284i | \(-0.649102\pi\) |
0.892284 | + | 0.451474i | \(0.149102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.3485 | − | 17.3485i | −1.30399 | − | 1.30399i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.2474 | −1.13965 | −0.569824 | − | 0.821767i | \(-0.692989\pi\) | ||||
−0.569824 | + | 0.821767i | \(0.692989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.7980 | 1.76889 | 0.884444 | − | 0.466646i | \(-0.154538\pi\) | ||||
0.884444 | + | 0.466646i | \(0.154538\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | − | 2.00000i | −0.147844 | − | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.67423 | + | 2.67423i | −0.195559 | + | 0.195559i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 34.6969i | 2.52383i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.1010i | − | 0.947957i | −0.880537 | − | 0.473978i | \(-0.842818\pi\) | ||
0.880537 | − | 0.473978i | \(-0.157182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.87628 | + | 3.87628i | −0.279020 | + | 0.279020i | −0.832718 | − | 0.553697i | \(-0.813216\pi\) |
0.553697 | + | 0.832718i | \(0.313216\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.55051 | − | 1.55051i | −0.110469 | − | 0.110469i | 0.649712 | − | 0.760181i | \(-0.274890\pi\) |
−0.760181 | + | 0.649712i | \(0.774890\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796 | 0.694559 | 0.347279 | − | 0.937762i | \(-0.387106\pi\) | ||||
0.347279 | + | 0.937762i | \(0.387106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.7980 | 1.32591 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.79796 | + | 5.79796i | 0.406937 | + | 0.406937i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.10102 | − | 3.10102i | 0.215536 | − | 0.215536i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.79796i | − | 0.608568i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2474i | 0.911992i | 0.889982 | + | 0.455996i | \(0.150717\pi\) | ||||
−0.889982 | + | 0.455996i | \(0.849283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.44949 | + | 4.44949i | −0.304874 | + | 0.304874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.79796 | + | 5.79796i | 0.393591 | + | 0.393591i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.2474 | 1.70606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.89898 | 0.464076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8990 | − | 16.8990i | −1.13164 | − | 1.13164i | −0.989905 | − | 0.141735i | \(-0.954732\pi\) |
−0.141735 | − | 0.989905i | \(-0.545268\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0000 | + | 10.0000i | −0.663723 | + | 0.663723i | −0.956256 | − | 0.292532i | \(-0.905502\pi\) |
0.292532 | + | 0.956256i | \(0.405502\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7980i | 0.911795i | 0.890032 | + | 0.455897i | \(0.150682\pi\) | ||||
−0.890032 | + | 0.455897i | \(0.849318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.6969i | 2.01971i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8990 | − | 16.8990i | 1.10709 | − | 1.10709i | 0.113558 | − | 0.993531i | \(-0.463775\pi\) |
0.993531 | − | 0.113558i | \(-0.0362246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | − | 2.00000i | −0.129914 | − | 0.129914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.5959 | −1.65566 | −0.827831 | − | 0.560977i | \(-0.810425\pi\) | ||||
−0.827831 | + | 0.560977i | \(0.810425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.89898 | 0.379987 | 0.189993 | − | 0.981785i | \(-0.439153\pi\) | ||||
0.189993 | + | 0.981785i | \(0.439153\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7980 | + | 13.7980i | 0.885139 | + | 0.885139i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3485 | + | 11.3485i | −0.722086 | + | 0.722086i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.7980i | 1.31802i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.4495i | − | 1.10140i | −0.834703 | − | 0.550701i | \(-0.814360\pi\) | ||
0.834703 | − | 0.550701i | \(-0.185640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.55051 | − | 1.55051i | 0.0974797 | − | 0.0974797i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.6969 | − | 18.6969i | −1.16628 | − | 1.16628i | −0.983074 | − | 0.183209i | \(-0.941351\pi\) |
−0.183209 | − | 0.983074i | \(-0.558649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0000 | 1.49129 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0000 | 1.23797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.24745 | + | 6.24745i | 0.385234 | + | 0.385234i | 0.872984 | − | 0.487749i | \(-0.162182\pi\) |
−0.487749 | + | 0.872984i | \(0.662182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.4722 | + | 26.4722i | −1.62007 | + | 1.62007i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8990i | 1.63400i | 0.576640 | + | 0.816998i | \(0.304364\pi\) | ||||
−0.576640 | + | 0.816998i | \(0.695636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.5959 | − | 39.5959i | 2.39645 | − | 2.39645i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.55051 | − | 7.55051i | −0.453666 | − | 0.453666i | 0.442903 | − | 0.896569i | \(-0.353949\pi\) |
−0.896569 | + | 0.442903i | \(0.853949\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000 | 1.19737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.7980 | 1.89691 | 0.948454 | − | 0.316916i | \(-0.102647\pi\) | ||||
0.948454 | + | 0.316916i | \(0.102647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5732 | + | 15.5732i | 0.925731 | + | 0.925731i | 0.997427 | − | 0.0716951i | \(-0.0228409\pi\) |
−0.0716951 | + | 0.997427i | \(0.522841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | + | 10.0000i | −0.590281 | + | 0.590281i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.7980i | − | 0.929292i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.7980i | 1.27782i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.89898 | + | 6.89898i | −0.403043 | + | 0.403043i | −0.879304 | − | 0.476261i | \(-0.841992\pi\) |
0.476261 | + | 0.879304i | \(0.341992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.9217 | + | 29.9217i | 1.73623 | + | 1.73623i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5959 | 0.668378 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.6969 | + | 32.6969i | 1.87839 | + | 1.87839i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.426786 | − | 0.426786i | 0.0243580 | − | 0.0243580i | −0.694823 | − | 0.719181i | \(-0.744517\pi\) |
0.719181 | + | 0.694823i | \(0.244517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8990i | 0.620021i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.1010i | − | 0.856300i | −0.903708 | − | 0.428150i | \(-0.859165\pi\) | ||
0.903708 | − | 0.428150i | \(-0.140835\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8990 | + | 16.8990i | −0.955187 | + | 0.955187i | −0.999038 | − | 0.0438513i | \(-0.986037\pi\) |
0.0438513 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.69694 | − | 6.69694i | −0.376138 | − | 0.376138i | 0.493569 | − | 0.869707i | \(-0.335692\pi\) |
−0.869707 | + | 0.493569i | \(0.835692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | 0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.7980 | −1.38409 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.97730 | − | 1.97730i | −0.110020 | − | 0.110020i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.89898 | + | 6.89898i | −0.381514 | + | 0.381514i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.3939i | 1.62054i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3485i | 0.568803i | 0.958705 | + | 0.284402i | \(0.0917949\pi\) | ||||
−0.958705 | + | 0.284402i | \(0.908205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 41.3939 | − | 41.3939i | 2.26837 | − | 2.26837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.42679 | + | 7.42679i | 0.404563 | + | 0.404563i | 0.879837 | − | 0.475275i | \(-0.157651\pi\) |
−0.475275 | + | 0.879837i | \(0.657651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51.9444 | 2.82123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0000 | 0.541530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.6742 | − | 20.6742i | 1.10985 | − | 1.10985i | 0.116682 | − | 0.993169i | \(-0.462774\pi\) |
0.993169 | − | 0.116682i | \(-0.0372257\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.6969i | − | 0.572594i | −0.958141 | − | 0.286297i | \(-0.907576\pi\) | ||
0.958141 | − | 0.286297i | \(-0.0924244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 77.1918i | − | 4.12020i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.10102 | − | 7.10102i | 0.377949 | − | 0.377949i | −0.492413 | − | 0.870362i | \(-0.663885\pi\) |
0.870362 | + | 0.492413i | \(0.163885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.89898 | + | 6.89898i | 0.365133 | + | 0.365133i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1010 | 1.00811 | 0.504057 | − | 0.863671i | \(-0.331840\pi\) | ||||
0.504057 | + | 0.863671i | \(0.331840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4949 | −0.657626 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | + | 2.00000i | 0.104973 | + | 0.104973i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6969 | + | 18.6969i | −0.975972 | + | 0.975972i | −0.999718 | − | 0.0237458i | \(-0.992441\pi\) |
0.0237458 | + | 0.999718i | \(0.492441\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34.4949i | 1.79573i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 25.7980i | − | 1.33936i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.44949 | − | 2.44949i | 0.126830 | − | 0.126830i | −0.640843 | − | 0.767672i | \(-0.721415\pi\) |
0.767672 | + | 0.640843i | \(0.221415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.8990 | − | 12.8990i | −0.664331 | − | 0.664331i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.0454 | −1.69743 | −0.848714 | − | 0.528852i | \(-0.822623\pi\) | ||||
−0.848714 | + | 0.528852i | \(0.822623\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.5959 | −1.92610 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7980 | + | 11.7980i | 0.602848 | + | 0.602848i | 0.941067 | − | 0.338220i | \(-0.109825\pi\) |
−0.338220 | + | 0.941067i | \(0.609825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.0000 | − | 20.0000i | 1.01666 | − | 1.01666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11.7980i | − | 0.598180i | −0.954225 | − | 0.299090i | \(-0.903317\pi\) | ||
0.954225 | − | 0.299090i | \(-0.0966831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.696938i | − | 0.0352457i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.1464 | + | 35.1464i | −1.77290 | + | 1.77290i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.79796 | + | 5.79796i | 0.290991 | + | 0.290991i | 0.837472 | − | 0.546481i | \(-0.184033\pi\) |
−0.546481 | + | 0.837472i | \(0.684033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.6969 | −1.13627 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.10102 | −0.204795 | −0.102398 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102398 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8990 | − | 12.8990i | −0.642544 | − | 0.642544i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.6969 | − | 20.6969i | 1.02591 | − | 1.02591i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7980i | 0.533925i | 0.963707 | + | 0.266962i | \(0.0860199\pi\) | ||||
−0.963707 | + | 0.266962i | \(0.913980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 9.44949i | − | 0.466109i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.5959 | + | 15.5959i | −0.767425 | + | 0.767425i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.5732 | + | 20.5732i | 1.00747 | + | 1.00747i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1464 | 1.08192 | 0.540962 | − | 0.841047i | \(-0.318060\pi\) | ||||
0.540962 | + | 0.841047i | \(0.318060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5959 | 1.34494 | 0.672471 | − | 0.740123i | \(-0.265233\pi\) | ||||
0.672471 | + | 0.740123i | \(0.265233\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 50.6969 | + | 50.6969i | 2.46497 | + | 2.46497i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.79796 | + | 1.79796i | −0.0870093 | + | 0.0870093i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 68.2929i | − | 3.29721i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8990i | 0.621322i | 0.950521 | + | 0.310661i | \(0.100550\pi\) | ||||
−0.950521 | + | 0.310661i | \(0.899450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.32577 | + | 6.32577i | −0.303997 | + | 0.303997i | −0.842575 | − | 0.538578i | \(-0.818962\pi\) |
0.538578 | + | 0.842575i | \(0.318962\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.14643 | + | 1.14643i | 0.0548411 | + | 0.0548411i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0000 | 1.24091 | 0.620456 | − | 0.784241i | \(-0.286947\pi\) | ||||
0.620456 | + | 0.784241i | \(0.286947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.89898 | 0.328523 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9217 | + | 16.9217i | 0.803973 | + | 0.803973i | 0.983714 | − | 0.179741i | \(-0.0575258\pi\) |
−0.179741 | + | 0.983714i | \(0.557526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.0454 | + | 42.0454i | −1.98868 | + | 1.98868i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.89898i | 0.278390i | 0.990265 | + | 0.139195i | \(0.0444515\pi\) | ||||
−0.990265 | + | 0.139195i | \(0.955549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.2474i | 0.812151i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −50.4949 | + | 50.4949i | −2.37246 | + | 2.37246i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0227 | − | 23.0227i | −1.07696 | − | 1.07696i | −0.996781 | − | 0.0801759i | \(-0.974452\pi\) |
−0.0801759 | − | 0.996781i | \(-0.525548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.4495 | 0.627768 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.20204 | −0.102559 | −0.0512796 | − | 0.998684i | \(-0.516330\pi\) | ||||
−0.0512796 | + | 0.998684i | \(0.516330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.69694 | + | 2.69694i | 0.125337 | + | 0.125337i | 0.766993 | − | 0.641656i | \(-0.221752\pi\) |
−0.641656 | + | 0.766993i | \(0.721752\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.4949 | − | 26.4949i | 1.22604 | − | 1.22604i | 0.260587 | − | 0.965450i | \(-0.416084\pi\) |
0.965450 | − | 0.260587i | \(-0.0839162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.8990i | − | 0.780322i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.6969i | 1.69091i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | − | 10.0000i | 0.459800 | − | 0.459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −44.4949 | − | 44.4949i | −2.03728 | − | 2.03728i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.89898 | −0.132458 | −0.0662289 | − | 0.997804i | \(-0.521097\pi\) | ||||
−0.0662289 | + | 0.997804i | \(0.521097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −53.3939 | −2.43455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | − | 4.00000i | −0.182006 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.4495 | + | 12.4495i | −0.564140 | + | 0.564140i | −0.930481 | − | 0.366341i | \(-0.880611\pi\) |
0.366341 | + | 0.930481i | \(0.380611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.5959i | − | 1.56448i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.59592i | 0.0720228i | 0.999351 | + | 0.0360114i | \(0.0114653\pi\) | ||||
−0.999351 | + | 0.0360114i | \(0.988535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.24745 | − | 2.24745i | 0.101220 | − | 0.101220i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 4.00000i | 0.179425 | + | 0.179425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.79796 | 0.349085 | 0.174542 | − | 0.984650i | \(-0.444155\pi\) | ||||
0.174542 | + | 0.984650i | \(0.444155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.4949 | −2.07724 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7980 | − | 13.7980i | −0.615221 | − | 0.615221i | 0.329081 | − | 0.944302i | \(-0.393261\pi\) |
−0.944302 | + | 0.329081i | \(0.893261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −59.1691 | + | 59.1691i | −2.62779 | + | 2.62779i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2020i | 0.895440i | 0.894174 | + | 0.447720i | \(0.147764\pi\) | ||||
−0.894174 | + | 0.447720i | \(0.852236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 22.6969i | − | 1.00405i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.1237 | + | 22.1237i | −0.976786 | + | 0.976786i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.3485 | + | 25.3485i | 1.11482 | + | 1.11482i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.7980 | −1.13240 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0000 | −0.832405 | −0.416203 | − | 0.909272i | \(-0.636639\pi\) | ||||
−0.416203 | + | 0.909272i | \(0.636639\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.22474 | + | 8.22474i | 0.359643 | + | 0.359643i | 0.863681 | − | 0.504038i | \(-0.168153\pi\) |
−0.504038 | + | 0.863681i | \(0.668153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.24745 | − | 2.24745i | 0.0979004 | − | 0.0979004i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.5959i | − | 0.982431i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.7980i | 2.33463i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2474 | − | 22.2474i | 0.963644 | − | 0.963644i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.9217 | + | 33.9217i | 1.46383 | + | 1.46383i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.44949 | 0.148580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.9444 | − | 52.9444i | −2.27206 | − | 2.27206i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.32577 | − | 1.32577i | 0.0566856 | − | 0.0566856i | −0.678196 | − | 0.734881i | \(-0.737238\pi\) |
0.734881 | + | 0.678196i | \(0.237238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.20204i | 0.264697i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.39388i | 0.314990i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.79796 | + | 1.79796i | −0.0764570 | + | 0.0764570i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.44949 | + | 8.44949i | 0.358016 | + | 0.358016i | 0.863081 | − | 0.505065i | \(-0.168531\pi\) |
−0.505065 | + | 0.863081i | \(0.668531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7980 | −1.09114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.8990 | 0.502375 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8990 | + | 10.8990i | 0.459337 | + | 0.459337i | 0.898438 | − | 0.439101i | \(-0.144703\pi\) |
−0.439101 | + | 0.898438i | \(0.644703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 35.7980 | − | 35.7980i | 1.50337 | − | 1.50337i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 44.5959i | − | 1.86956i | −0.355230 | − | 0.934779i | \(-0.615597\pi\) | ||
0.355230 | − | 0.934779i | \(-0.384403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0000i | 0.585882i | 0.956131 | + | 0.292941i | \(0.0946339\pi\) | ||||
−0.956131 | + | 0.292941i | \(0.905366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.1464 | + | 29.1464i | −1.21761 | + | 1.21761i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.22474 | − | 9.22474i | −0.384031 | − | 0.384031i | 0.488521 | − | 0.872552i | \(-0.337537\pi\) |
−0.872552 | + | 0.488521i | \(0.837537\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.2474 | 0.716780 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.6969 | 0.775680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.2474 | − | 22.2474i | −0.921395 | − | 0.921395i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.5732 | − | 15.5732i | 0.642775 | − | 0.642775i | −0.308461 | − | 0.951237i | \(-0.599814\pi\) |
0.951237 | + | 0.308461i | \(0.0998141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.39388i | 0.304659i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.89898i | 0.283786i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.22474 | − | 5.22474i | 0.214555 | − | 0.214555i | −0.591644 | − | 0.806199i | \(-0.701521\pi\) |
0.806199 | + | 0.591644i | \(0.201521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.7980 | − | 21.7980i | −0.892131 | − | 0.892131i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.30306 | −0.0532417 | −0.0266208 | − | 0.999646i | \(-0.508475\pi\) | ||||
−0.0266208 | + | 0.999646i | \(0.508475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6969 | −0.558710 | −0.279355 | − | 0.960188i | \(-0.590121\pi\) | ||||
−0.279355 | + | 0.960188i | \(0.590121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.1464 | − | 29.1464i | −1.18693 | − | 1.18693i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.79796 | + | 5.79796i | −0.235332 | + | 0.235332i | −0.814914 | − | 0.579582i | \(-0.803216\pi\) |
0.579582 | + | 0.814914i | \(0.303216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 25.7980i | − | 1.04539i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 65.3939i | − | 2.64555i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.14643 | + | 5.14643i | −0.207862 | + | 0.207862i | −0.803358 | − | 0.595496i | \(-0.796956\pi\) |
0.595496 | + | 0.803358i | \(0.296956\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5959 | + | 23.5959i | 0.949936 | + | 0.949936i | 0.998805 | − | 0.0488693i | \(-0.0155618\pi\) |
−0.0488693 | + | 0.998805i | \(0.515562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.0000 | −0.723481 | −0.361741 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361741 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.79796 | −0.312921 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.7980 | + | 23.7980i | 0.953445 | + | 0.953445i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.5732 | + | 19.5732i | −0.781679 | + | 0.781679i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.30306i | − | 0.370937i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.69694i | − | 0.186982i | −0.995620 | − | 0.0934911i | \(-0.970197\pi\) | ||
0.995620 | − | 0.0934911i | \(-0.0298027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.4722 | − | 29.4722i | 1.17141 | − | 1.17141i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.44949 | − | 4.44949i | −0.176295 | − | 0.176295i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7980 | 0.545839 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.7980 | 0.623982 | 0.311991 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311991 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.696938 | − | 0.696938i | −0.0274846 | − | 0.0274846i | 0.693231 | − | 0.720716i | \(-0.256187\pi\) |
−0.720716 | + | 0.693231i | \(0.756187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.5959 | − | 27.5959i | 1.08491 | − | 1.08491i | 0.0888637 | − | 0.996044i | \(-0.471676\pi\) |
0.996044 | − | 0.0888637i | \(-0.0283236\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.8990i | 1.05588i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 25.7980i | − | 1.01110i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.0000 | + | 26.0000i | −1.01746 | + | 1.01746i | −0.0176138 | + | 0.999845i | \(0.505607\pi\) |
−0.999845 | + | 0.0176138i | \(0.994393\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.1464 | − | 39.1464i | −1.52725 | − | 1.52725i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.14643 | −0.161522 | −0.0807610 | − | 0.996733i | \(-0.525735\pi\) | ||||
−0.0807610 | + | 0.996733i | \(0.525735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.2929 | −1.56721 | −0.783605 | − | 0.621259i | \(-0.786621\pi\) | ||||
−0.783605 | + | 0.621259i | \(0.786621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.3485 | − | 15.3485i | −0.596085 | − | 0.596085i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.30306 | + | 1.30306i | −0.0504547 | + | 0.0504547i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 75.1918i | 2.90708i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.10102i | 0.119714i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7980 | − | 13.7980i | 0.531872 | − | 0.531872i | −0.389257 | − | 0.921129i | \(-0.627268\pi\) |
0.921129 | + | 0.389257i | \(0.127268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.0000 | + | 28.0000i | 1.07613 | + | 1.07613i | 0.996853 | + | 0.0792746i | \(0.0252604\pi\) |
0.0792746 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.5959 | 0.752022 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44.4949 | 1.70505 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2247 | + | 12.2247i | 0.467767 | + | 0.467767i | 0.901190 | − | 0.433424i | \(-0.142695\pi\) |
−0.433424 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.6969 | − | 30.6969i | 1.17116 | − | 1.17116i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 57.3939i | 2.18653i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 39.9444i | − | 1.51956i | −0.650183 | − | 0.759778i | \(-0.725308\pi\) | ||
0.650183 | − | 0.759778i | \(-0.274692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 47.5959 | − | 47.5959i | 1.80802 | − | 1.80802i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.87628 | + | 3.87628i | 0.146824 | + | 0.146824i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −75.1918 | −2.84402 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1010 | 0.494819 | 0.247409 | − | 0.968911i | \(-0.420421\pi\) | ||||
0.247409 | + | 0.968911i | \(0.420421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3031 | + | 15.3031i | 0.577166 | + | 0.577166i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3939 | − | 29.3939i | 1.10547 | − | 1.10547i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0000i | 0.450669i | 0.974281 | + | 0.225335i | \(0.0723476\pi\) | ||||
−0.974281 | + | 0.225335i | \(0.927652\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.20204i | 0.232595i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.30306 | + | 1.30306i | −0.0488000 | + | 0.0488000i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 56.9444 | + | 56.9444i | 2.12663 | + | 2.12663i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.1010 | −1.15987 | −0.579936 | − | 0.814662i | \(-0.696923\pi\) | ||||
−0.579936 | + | 0.814662i | \(0.696923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.79796 | 0.364895 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.1237 | − | 13.1237i | −0.488077 | − | 0.488077i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1464 | + | 17.1464i | −0.635926 | + | 0.635926i | −0.949548 | − | 0.313622i | \(-0.898458\pi\) |
0.313622 | + | 0.949548i | \(0.398458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 7.69694i | − | 0.285072i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.49490i | − | 0.166250i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5505 | − | 15.5505i | 0.574371 | − | 0.574371i | −0.358976 | − | 0.933347i | \(-0.616874\pi\) |
0.933347 | + | 0.358976i | \(0.116874\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.5732 | − | 14.5732i | −0.536811 | − | 0.536811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.5959 | −1.23585 | −0.617923 | − | 0.786239i | \(-0.712026\pi\) | ||||
−0.617923 | + | 0.786239i | \(0.712026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.4949 | 1.85498 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.34847 | + | 5.34847i | 0.196216 | + | 0.196216i | 0.798376 | − | 0.602160i | \(-0.205693\pi\) |
−0.602160 | + | 0.798376i | \(0.705693\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.2474 | − | 32.2474i | 1.17987 | − | 1.17987i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.2929i | 0.814563i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.1918i | 1.50311i | 0.659670 | + | 0.751556i | \(0.270696\pi\) | ||||
−0.659670 | + | 0.751556i | \(0.729304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38.8207 | + | 38.8207i | −1.41470 | + | 1.41470i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6969 | − | 14.6969i | −0.534169 | − | 0.534169i | 0.387641 | − | 0.921810i | \(-0.373290\pi\) |
−0.921810 | + | 0.387641i | \(0.873290\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.89898 | −0.250417 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0000 | −0.616250 | −0.308125 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308125 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.20204 | + | 6.20204i | 0.224529 | + | 0.224529i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.6969 | − | 34.6969i | 1.25283 | − | 1.25283i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6969i | 0.926655i | 0.886187 | + | 0.463328i | \(0.153345\pi\) | ||||
−0.886187 | + | 0.463328i | \(0.846655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 83.1918i | 2.99608i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9444 | − | 28.9444i | 1.04106 | − | 1.04106i | 0.0419370 | − | 0.999120i | \(-0.486647\pi\) |
0.999120 | − | 0.0419370i | \(-0.0133529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −53.3939 | − | 53.3939i | −1.91549 | − | 1.91549i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.7526 | −0.456908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.89898 | 0.246865 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.1464 | − | 25.1464i | −0.898660 | − | 0.898660i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.89898 | + | 6.89898i | −0.245922 | + | 0.245922i | −0.819295 | − | 0.573373i | \(-0.805635\pi\) |
0.573373 | + | 0.819295i | \(0.305635\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 27.7980i | − | 0.989634i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 46.6969i | − | 1.66035i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | − | 4.00000i | 0.142044 | − | 0.142044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3485 | − | 11.3485i | −0.401983 | − | 0.401983i | 0.476948 | − | 0.878931i | \(-0.341743\pi\) |
−0.878931 | + | 0.476948i | \(0.841743\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3939 | 0.403086 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 82.0908 | 2.90054 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.5732 | − | 19.5732i | −0.690724 | − | 0.690724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.202041i | 0.00710338i | 0.999994 | + | 0.00355169i | \(0.00113054\pi\) | ||||
−0.999994 | + | 0.00355169i | \(0.998869\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.0000i | 0.912983i | 0.889728 | + | 0.456492i | \(0.150894\pi\) | ||||
−0.889728 | + | 0.456492i | \(0.849106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 59.8434 | − | 59.8434i | 2.09880 | − | 2.09880i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.39388 | + | 7.39388i | 0.258679 | + | 0.258679i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −122.788 | −4.29055 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7980 | −0.551353 | −0.275676 | − | 0.961251i | \(-0.588902\pi\) | ||||
−0.275676 | + | 0.961251i | \(0.588902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6969 | − | 10.6969i | −0.372872 | − | 0.372872i | 0.495650 | − | 0.868522i | \(-0.334930\pi\) |
−0.868522 | + | 0.495650i | \(0.834930\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.07832 | + | 3.07832i | −0.107044 | + | 0.107044i | −0.758600 | − | 0.651557i | \(-0.774116\pi\) |
0.651557 | + | 0.758600i | \(0.274116\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1010i | 1.28857i | 0.764785 | + | 0.644286i | \(0.222845\pi\) | ||||
−0.764785 | + | 0.644286i | \(0.777155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.5959i | 1.16543i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.775255 | − | 0.775255i | 0.0268610 | − | 0.0268610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.1464 | − | 25.1464i | −0.869188 | − | 0.869188i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.1918 | 1.35305 | 0.676526 | − | 0.736419i | \(-0.263485\pi\) | ||||
0.676526 | + | 0.736419i | \(0.263485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.5959 | 0.710204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −70.7423 | − | 70.7423i | −2.43650 | − | 2.43650i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.79796 | − | 1.79796i | 0.0617786 | − | 0.0617786i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 69.2929i | − | 2.37812i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.39388i | 0.184900i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.65153 | + | 4.65153i | −0.159265 | + | 0.159265i | −0.782241 | − | 0.622976i | \(-0.785924\pi\) |
0.622976 | + | 0.782241i | \(0.285924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.42679 | − | 7.42679i | −0.253694 | − | 0.253694i | 0.568789 | − | 0.822483i | \(-0.307412\pi\) |
−0.822483 | + | 0.568789i | \(0.807412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.3485 | 1.44491 | 0.722456 | − | 0.691417i | \(-0.243013\pi\) | ||||
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.4949 | 1.51638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.55051 | − | 5.55051i | −0.188942 | − | 0.188942i | 0.606297 | − | 0.795238i | \(-0.292654\pi\) |
−0.795238 | + | 0.606297i | \(0.792654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.1464 | + | 35.1464i | −1.19364 | + | 1.19364i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.10102i | 0.105195i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.5959i | 1.27389i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.7980 | − | 33.7980i | 1.14389 | − | 1.14389i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6969 | + | 10.6969i | 0.361210 | + | 0.361210i | 0.864258 | − | 0.503048i | \(-0.167788\pi\) |
−0.503048 | + | 0.864258i | \(0.667788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.6969 | 1.03538 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.2020 | 0.545861 | 0.272930 | − | 0.962034i | \(-0.412007\pi\) | ||||
0.272930 | + | 0.962034i | \(0.412007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8207 | − | 21.8207i | −0.734324 | − | 0.734324i | 0.237149 | − | 0.971473i | \(-0.423787\pi\) |
−0.971473 | + | 0.237149i | \(0.923787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.0000 | + | 40.0000i | −1.34307 | + | 1.34307i | −0.450081 | + | 0.892988i | \(0.648605\pi\) |
−0.892988 | + | 0.450081i | \(0.851395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.7980i | 1.13355i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 61.7423i | − | 2.06845i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.7423 | + | 18.7423i | −0.627189 | + | 0.627189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.89898 | + | 8.89898i | 0.297128 | + | 0.297128i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.40408 | −0.280292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0000 | −0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.7980 | − | 25.7980i | −0.858502 | − | 0.858502i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8990 | + | 10.8990i | −0.361895 | + | 0.361895i | −0.864510 | − | 0.502615i | \(-0.832371\pi\) |
0.502615 | + | 0.864510i | \(0.332371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 101.394i | − | 3.36302i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.7980i | − | 0.987250i | −0.869675 | − | 0.493625i | \(-0.835671\pi\) | ||
0.869675 | − | 0.493625i | \(-0.164329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.1237 | − | 16.1237i | 0.533617 | − | 0.533617i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.5959 | + | 31.5959i | 1.04339 | + | 1.04339i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.6969 | −1.87026 | −0.935130 | − | 0.354306i | \(-0.884717\pi\) | ||||
−0.935130 | + | 0.354306i | \(0.884717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.89898 | −0.0625735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.89898 | − | 8.89898i | −0.292913 | − | 0.292913i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.8990 | − | 16.8990i | 0.555035 | − | 0.555035i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.40408i | 0.210111i | 0.994466 | + | 0.105056i | \(0.0335020\pi\) | ||||
−0.994466 | + | 0.105056i | \(0.966498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.55051i | 0.0835896i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.5959 | + | 33.5959i | −1.09988 | + | 1.09988i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.3258 | + | 14.3258i | 0.468002 | + | 0.468002i | 0.901267 | − | 0.433264i | \(-0.142638\pi\) |
−0.433264 | + | 0.901267i | \(0.642638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 75.1918 | 2.45379 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.4949 | −0.994105 | −0.497053 | − | 0.867720i | \(-0.665584\pi\) | ||||
−0.497053 | + | 0.867720i | \(0.665584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.24745 | − | 2.24745i | −0.0731870 | − | 0.0731870i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.8990 | + | 26.8990i | −0.874099 | + | 0.874099i | −0.992916 | − | 0.118817i | \(-0.962090\pi\) |
0.118817 | + | 0.992916i | \(0.462090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.4949i | 1.63913i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7980i | 0.966265i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.8763 | + | 17.8763i | −0.579069 | + | 0.579069i | −0.934647 | − | 0.355577i | \(-0.884284\pi\) |
0.355577 | + | 0.934647i | \(0.384284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.2474 | − | 22.2474i | −0.719158 | − | 0.719158i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.49490 | −0.274315 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.5959 | 0.728901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.4495 | + | 38.4495i | 1.23902 | + | 1.23902i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8990 | − | 16.8990i | 0.543435 | − | 0.543435i | −0.381099 | − | 0.924534i | \(-0.624454\pi\) |
0.924534 | + | 0.381099i | \(0.124454\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.79796i | 0.282631i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.1464i | 1.03163i | 0.856701 | + | 0.515814i | \(0.172510\pi\) | ||||
−0.856701 | + | 0.515814i | \(0.827490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4949 | − | 18.4949i | 0.592919 | − | 0.592919i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.6742 | + | 33.6742i | 1.07733 | + | 1.07733i | 0.996748 | + | 0.0805866i | \(0.0256794\pi\) |
0.0805866 | + | 0.996748i | \(0.474321\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.0454 | 1.31182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.3939 | 0.683054 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.89898 | − | 2.89898i | −0.0924631 | − | 0.0924631i | 0.659362 | − | 0.751825i | \(-0.270826\pi\) |
−0.751825 | + | 0.659362i | \(0.770826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 65.3939 | − | 65.3939i | 2.08151 | − | 2.08151i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.60612i | 0.0828699i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.8990i | 1.04507i | 0.852618 | + | 0.522535i | \(0.175014\pi\) | ||||
−0.852618 | + | 0.522535i | \(0.824986\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.0227 | − | 23.0227i | 0.730603 | − | 0.730603i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7980 | − | 17.7980i | −0.563667 | − | 0.563667i | 0.366680 | − | 0.930347i | \(-0.380494\pi\) |
−0.930347 | + | 0.366680i | \(0.880494\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −104.091 | −3.29329 |
(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 | 1600.2.n.p.1407.1 | 4 | ||
4.3 | odd | 2 | 1600.2.n.t.1407.2 | 4 | |||
5.2 | odd | 4 | 1600.2.n.o.1343.1 | 4 | |||
5.3 | odd | 4 | 1600.2.n.t.1343.2 | 4 | |||
5.4 | even | 2 | 1600.2.n.s.1407.2 | 4 | |||
8.3 | odd | 2 | 800.2.n.k.607.1 | yes | 4 | ||
8.5 | even | 2 | 800.2.n.m.607.2 | yes | 4 | ||
20.3 | even | 4 | inner | 1600.2.n.p.1343.1 | 4 | ||
20.7 | even | 4 | 1600.2.n.s.1343.2 | 4 | |||
20.19 | odd | 2 | 1600.2.n.o.1407.1 | 4 | |||
40.3 | even | 4 | 800.2.n.m.543.2 | yes | 4 | ||
40.13 | odd | 4 | 800.2.n.k.543.1 | ✓ | 4 | ||
40.19 | odd | 2 | 800.2.n.n.607.2 | yes | 4 | ||
40.27 | even | 4 | 800.2.n.l.543.1 | yes | 4 | ||
40.29 | even | 2 | 800.2.n.l.607.1 | yes | 4 | ||
40.37 | odd | 4 | 800.2.n.n.543.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.2.n.k.543.1 | ✓ | 4 | 40.13 | odd | 4 | ||
800.2.n.k.607.1 | yes | 4 | 8.3 | odd | 2 | ||
800.2.n.l.543.1 | yes | 4 | 40.27 | even | 4 | ||
800.2.n.l.607.1 | yes | 4 | 40.29 | even | 2 | ||
800.2.n.m.543.2 | yes | 4 | 40.3 | even | 4 | ||
800.2.n.m.607.2 | yes | 4 | 8.5 | even | 2 | ||
800.2.n.n.543.2 | yes | 4 | 40.37 | odd | 4 | ||
800.2.n.n.607.2 | yes | 4 | 40.19 | odd | 2 | ||
1600.2.n.o.1343.1 | 4 | 5.2 | odd | 4 | |||
1600.2.n.o.1407.1 | 4 | 20.19 | odd | 2 | |||
1600.2.n.p.1343.1 | 4 | 20.3 | even | 4 | inner | ||
1600.2.n.p.1407.1 | 4 | 1.1 | even | 1 | trivial | ||
1600.2.n.s.1343.2 | 4 | 20.7 | even | 4 | |||
1600.2.n.s.1407.2 | 4 | 5.4 | even | 2 | |||
1600.2.n.t.1343.2 | 4 | 5.3 | odd | 4 | |||
1600.2.n.t.1407.2 | 4 | 4.3 | odd | 2 |