Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(65,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.65");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.e (of order \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 242x^{12} + 13297x^{8} + 201600x^{4} + 331776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Root | \(-1.53379 - 1.53379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.65 |
Dual form | 256.4.e.c.193.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.13572 | − | 1.13572i | −0.218570 | − | 0.218570i | 0.589326 | − | 0.807895i | \(-0.299393\pi\) |
−0.807895 | + | 0.589326i | \(0.799393\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.4583 | − | 10.4583i | 0.935422 | − | 0.935422i | −0.0626154 | − | 0.998038i | \(-0.519944\pi\) |
0.998038 | + | 0.0626154i | \(0.0199441\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.8978i | 0.588427i | 0.955740 | + | 0.294213i | \(0.0950577\pi\) | ||||
−0.955740 | + | 0.294213i | \(0.904942\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 24.4203i | − | 0.904455i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0933 | − | 12.0933i | 0.331480 | − | 0.331480i | −0.521669 | − | 0.853148i | \(-0.674690\pi\) |
0.853148 | + | 0.521669i | \(0.174690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.2588 | − | 16.2588i | −0.346875 | − | 0.346875i | 0.512069 | − | 0.858944i | \(-0.328879\pi\) |
−0.858944 | + | 0.512069i | \(0.828879\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −23.7555 | −0.408910 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.9788 | −0.441968 | −0.220984 | − | 0.975277i | \(-0.570927\pi\) | ||||
−0.220984 | + | 0.975277i | \(0.570927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 103.230 | + | 103.230i | 1.24646 | + | 1.24646i | 0.957274 | + | 0.289182i | \(0.0933834\pi\) |
0.289182 | + | 0.957274i | \(0.406617\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3769 | − | 12.3769i | 0.128612 | − | 0.128612i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 186.521i | − | 1.69097i | −0.534001 | − | 0.845484i | \(-0.679312\pi\) | ||
0.534001 | − | 0.845484i | \(-0.320688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 93.7538i | − | 0.750030i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −58.3991 | + | 58.3991i | −0.416256 | + | 0.416256i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −120.517 | − | 120.517i | −0.771706 | − | 0.771706i | 0.206699 | − | 0.978405i | \(-0.433728\pi\) |
−0.978405 | + | 0.206699i | \(0.933728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −263.876 | −1.52883 | −0.764413 | − | 0.644727i | \(-0.776971\pi\) | ||||
−0.764413 | + | 0.644727i | \(0.776971\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27.4693 | −0.144903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 113.973 | + | 113.973i | 0.550428 | + | 0.550428i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 169.573 | − | 169.573i | 0.753449 | − | 0.753449i | −0.221672 | − | 0.975121i | \(-0.571151\pi\) |
0.975121 | + | 0.221672i | \(0.0711515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.9309i | 0.151633i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 469.193i | − | 1.78721i | −0.448853 | − | 0.893606i | \(-0.648167\pi\) | ||
0.448853 | − | 0.893606i | \(-0.351833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 251.253 | − | 251.253i | 0.891064 | − | 0.891064i | −0.103560 | − | 0.994623i | \(-0.533023\pi\) |
0.994623 | + | 0.103560i | \(0.0330233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −255.396 | − | 255.396i | −0.846047 | − | 0.846047i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −202.196 | −0.627518 | −0.313759 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313759 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 224.238 | 0.653754 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 35.1833 | + | 35.1833i | 0.0966008 | + | 0.0966008i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 159.870 | − | 159.870i | 0.414335 | − | 0.414335i | −0.468910 | − | 0.883246i | \(-0.655353\pi\) |
0.883246 | + | 0.468910i | \(0.155353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 252.952i | − | 0.620147i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 234.482i | − | 0.544875i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −229.462 | + | 229.462i | −0.506328 | + | 0.506328i | −0.913397 | − | 0.407069i | \(-0.866551\pi\) |
0.407069 | + | 0.913397i | \(0.366551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 115.041 | + | 115.041i | 0.241467 | + | 0.241467i | 0.817457 | − | 0.575990i | \(-0.195383\pi\) |
−0.575990 | + | 0.817457i | \(0.695383\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 266.128 | 0.532205 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −340.080 | −0.648950 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 523.429 | + | 523.429i | 0.954433 | + | 0.954433i | 0.999006 | − | 0.0445736i | \(-0.0141929\pi\) |
−0.0445736 | + | 0.999006i | \(0.514193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −211.835 | + | 211.835i | −0.369594 | + | 0.369594i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 108.833i | − | 0.181917i | −0.995855 | − | 0.0909584i | \(-0.971007\pi\) | ||
0.995855 | − | 0.0909584i | \(-0.0289930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 771.343i | 1.23670i | 0.785904 | + | 0.618348i | \(0.212198\pi\) | ||||
−0.785904 | + | 0.618348i | \(0.787802\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −106.478 | + | 106.478i | −0.163934 | + | 0.163934i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 131.791 | + | 131.791i | 0.195052 | + | 0.195052i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −647.309 | −0.921873 | −0.460937 | − | 0.887433i | \(-0.652487\pi\) | ||||
−0.460937 | + | 0.887433i | \(0.652487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −526.697 | −0.722493 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −702.088 | − | 702.088i | −0.928485 | − | 0.928485i | 0.0691235 | − | 0.997608i | \(-0.477980\pi\) |
−0.997608 | + | 0.0691235i | \(0.977980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −323.987 | + | 323.987i | −0.413427 | + | 0.413427i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 273.748i | 0.337343i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 603.673i | 0.718980i | 0.933149 | + | 0.359490i | \(0.117049\pi\) | ||||
−0.933149 | + | 0.359490i | \(0.882951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 177.185 | − | 177.185i | 0.204111 | − | 0.204111i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 299.690 | + | 299.690i | 0.334155 | + | 0.334155i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2159.24 | 2.33193 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 741.131 | 0.775777 | 0.387889 | − | 0.921706i | \(-0.373204\pi\) | ||||
0.387889 | + | 0.921706i | \(0.373204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −295.323 | − | 295.323i | −0.299808 | − | 0.299808i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 159.461 | − | 159.461i | 0.157099 | − | 0.157099i | −0.624181 | − | 0.781280i | \(-0.714567\pi\) |
0.781280 | + | 0.624181i | \(0.214567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1654.11i | 1.58237i | 0.611577 | + | 0.791185i | \(0.290536\pi\) | ||||
−0.611577 | + | 0.791185i | \(0.709464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 258.883i | − | 0.240613i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 112.838 | − | 112.838i | 0.101949 | − | 0.101949i | −0.654293 | − | 0.756241i | \(-0.727034\pi\) |
0.756241 | + | 0.654293i | \(0.227034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 748.876 | + | 748.876i | 0.658067 | + | 0.658067i | 0.954922 | − | 0.296855i | \(-0.0959379\pi\) |
−0.296855 | + | 0.954922i | \(0.595938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −385.175 | −0.329362 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1476.61 | 1.22927 | 0.614635 | − | 0.788812i | \(-0.289303\pi\) | ||||
0.614635 | + | 0.788812i | \(0.289303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1950.70 | − | 1950.70i | −1.58177 | − | 1.58177i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −397.044 | + | 397.044i | −0.313733 | + | 0.313733i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 337.601i | − | 0.260066i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1038.50i | 0.780242i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −532.872 | + | 532.872i | −0.390630 | + | 0.390630i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 326.784 | + | 326.784i | 0.233828 | + | 0.233828i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1153.10 | 0.805679 | 0.402840 | − | 0.915271i | \(-0.368023\pi\) | ||||
0.402840 | + | 0.915271i | \(0.368023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −570.707 | −0.389519 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 281.478 | + | 281.478i | 0.187731 | + | 0.187731i | 0.794715 | − | 0.606983i | \(-0.207621\pi\) |
−0.606983 | + | 0.794715i | \(0.707621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1124.99 | + | 1124.99i | −0.733448 | + | 0.733448i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1221.51i | 0.778750i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2237.83i | 1.39556i | 0.716315 | + | 0.697778i | \(0.245828\pi\) | ||||
−0.716315 | + | 0.697778i | \(0.754172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 929.419 | − | 929.419i | 0.567139 | − | 0.567139i | −0.364187 | − | 0.931326i | \(-0.618653\pi\) |
0.931326 | + | 0.364187i | \(0.118653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 229.638 | + | 229.638i | 0.137156 | + | 0.137156i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −393.246 | −0.229964 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2520.82 | −1.44374 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −254.671 | − | 254.671i | −0.142891 | − | 0.142891i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −231.031 | + | 231.031i | −0.127025 | + | 0.127025i | −0.767761 | − | 0.640736i | \(-0.778629\pi\) |
0.640736 | + | 0.767761i | \(0.278629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2178.67i | − | 1.17416i | −0.809529 | − | 0.587079i | \(-0.800278\pi\) | ||
0.809529 | − | 0.587079i | \(-0.199722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 756.511i | 0.399740i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2759.71 | + | 2759.71i | −1.43010 | + | 1.43010i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −555.307 | − | 555.307i | −0.282282 | − | 0.282282i | 0.551736 | − | 0.834019i | \(-0.313965\pi\) |
−0.834019 | + | 0.551736i | \(0.813965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −363.134 | −0.181122 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2032.67 | 0.995011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1057.53 | + | 1057.53i | 0.508174 | + | 0.508174i | 0.913966 | − | 0.405791i | \(-0.133004\pi\) |
−0.405791 | + | 0.913966i | \(0.633004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −287.283 | + | 287.283i | −0.135545 | + | 0.135545i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 336.977i | 0.156144i | 0.996948 | + | 0.0780721i | \(0.0248764\pi\) | ||||
−0.996948 | + | 0.0780721i | \(0.975124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1668.30i | − | 0.759355i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2520.91 | − | 2520.91i | 1.12736 | − | 1.12736i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1291.91 | + | 1291.91i | 0.567760 | + | 0.567760i | 0.931500 | − | 0.363741i | \(-0.118501\pi\) |
−0.363741 | + | 0.931500i | \(0.618501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1021.71 | 0.441338 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 521.209 | 0.221336 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1037.43 | + | 1037.43i | 0.433190 | + | 0.433190i | 0.889712 | − | 0.456522i | \(-0.150905\pi\) |
−0.456522 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1650.79 | − | 1650.79i | 0.677914 | − | 0.677914i | −0.281614 | − | 0.959528i | \(-0.590870\pi\) |
0.959528 | + | 0.281614i | \(0.0908697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 261.309i | − | 0.105555i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3546.90i | − | 1.40959i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −374.637 | + | 374.637i | −0.146504 | + | 0.146504i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −636.422 | − | 636.422i | −0.244936 | − | 0.244936i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −102.447 | −0.0388106 | −0.0194053 | − | 0.999812i | \(-0.506177\pi\) | ||||
−0.0194053 | + | 0.999812i | \(0.506177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2158.90 | −0.805185 | −0.402593 | − | 0.915379i | \(-0.631891\pi\) | ||||
−0.402593 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 386.236 | + | 386.236i | 0.141841 | + | 0.141841i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3022.32 | − | 3022.32i | 1.09305 | − | 1.09305i | 0.0978506 | − | 0.995201i | \(-0.468803\pi\) |
0.995201 | − | 0.0978506i | \(-0.0311967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3300.90i | 1.17585i | 0.808914 | + | 0.587926i | \(0.200056\pi\) | ||||
−0.808914 | + | 0.587926i | \(0.799944\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1188.94i | − | 0.417220i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1313.37 | − | 1313.37i | 0.454093 | − | 0.454093i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4906.98 | − | 4906.98i | −1.67180 | − | 1.67180i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4554.89 | −1.52940 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2496.80 | 0.826350 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −77.0963 | − | 77.0963i | −0.0251541 | − | 0.0251541i | 0.694418 | − | 0.719572i | \(-0.255662\pi\) |
−0.719572 | + | 0.694418i | \(0.755662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −123.604 | + | 123.604i | −0.0397615 | + | 0.0397615i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5255.38i | − | 1.66704i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2875.68i | − | 0.899602i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 876.030 | − | 876.030i | 0.270304 | − | 0.270304i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 503.678 | + | 503.678i | 0.153308 | + | 0.153308i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1824.45 | −0.547865 | −0.273933 | − | 0.961749i | \(-0.588325\pi\) | ||||
−0.273933 | + | 0.961749i | \(0.588325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2289.49 | −0.678368 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2967.42 | + | 2967.42i | 0.867641 | + | 0.867641i | 0.992211 | − | 0.124569i | \(-0.0397550\pi\) |
−0.124569 | + | 0.992211i | \(0.539755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −792.161 | + | 792.161i | −0.228592 | + | 0.228592i | −0.812104 | − | 0.583513i | \(-0.801678\pi\) |
0.583513 | + | 0.812104i | \(0.301678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 299.355i | − | 0.0852646i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 892.148i | − | 0.250844i | −0.992104 | − | 0.125422i | \(-0.959972\pi\) | ||
0.992104 | − | 0.125422i | \(-0.0400284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2114.64 | + | 2114.64i | −0.586994 | + | 0.586994i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 735.163 | + | 735.163i | 0.201493 | + | 0.201493i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2647.81 | −0.716623 | −0.358311 | − | 0.933602i | \(-0.616647\pi\) | ||||
−0.358311 | + | 0.933602i | \(0.616647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2718.29 | −0.726559 | −0.363279 | − | 0.931680i | \(-0.618343\pi\) | ||||
−0.363279 | + | 0.931680i | \(0.618343\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2174.96 | + | 2174.96i | 0.574171 | + | 0.574171i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2345.15 | − | 2345.15i | 0.611536 | − | 0.611536i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3356.80i | − | 0.864730i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1594.75i | 0.405877i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2278.00 | + | 2278.00i | −0.572853 | + | 0.572853i | −0.932925 | − | 0.360071i | \(-0.882752\pi\) |
0.360071 | + | 0.932925i | \(0.382752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2255.66 | − | 2255.66i | −0.560521 | − | 0.560521i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 735.917 | 0.180725 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5058.41 | 1.22776 | 0.613881 | − | 0.789398i | \(-0.289607\pi\) | ||||
0.613881 | + | 0.789398i | \(0.289607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1847.97 | + | 1847.97i | 0.443350 | + | 0.443350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2943.06 | + | 2943.06i | −0.697973 | + | 0.697973i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7942.44i | − | 1.86217i | −0.364797 | − | 0.931087i | \(-0.618862\pi\) | ||
0.364797 | − | 0.931087i | \(-0.381138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3343.94i | − | 0.775157i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 685.604 | − | 685.604i | 0.157147 | − | 0.157147i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 67.1308 | + | 67.1308i | 0.0152158 | + | 0.0152158i | 0.714674 | − | 0.699458i | \(-0.246575\pi\) |
−0.699458 | + | 0.714674i | \(0.746575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2237.68 | −0.501585 | −0.250793 | − | 0.968041i | \(-0.580691\pi\) | ||||
−0.250793 | + | 0.968041i | \(0.580691\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −402.466 | −0.0892248 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1133.80 | − | 1133.80i | −0.248620 | − | 0.248620i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3646.89 | + | 3646.89i | −0.791048 | + | 0.791048i | −0.981665 | − | 0.190617i | \(-0.938951\pi\) |
0.190617 | + | 0.981665i | \(0.438951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6443.93i | 1.38275i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 367.919i | − | 0.0781075i | −0.999237 | − | 0.0390538i | \(-0.987566\pi\) | ||
0.999237 | − | 0.0390538i | \(-0.0124344\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4994.53 | − | 4994.53i | 1.04909 | − | 1.04909i | 0.0503634 | − | 0.998731i | \(-0.483962\pi\) |
0.998731 | − | 0.0503634i | \(-0.0160380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2452.29 | − | 2452.29i | −0.509688 | − | 0.509688i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5113.18 | 1.05164 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3953.31 | −0.804664 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −841.717 | − | 841.717i | −0.169561 | − | 0.169561i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6070.97 | − | 6070.97i | 1.21048 | − | 1.21048i | 0.239608 | − | 0.970870i | \(-0.422981\pi\) |
0.970870 | − | 0.239608i | \(-0.0770191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4799.58i | 0.947261i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1412.48i | 0.275961i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3032.60 | + | 3032.60i | −0.586555 | + | 0.586555i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2738.11 | + | 2738.11i | 0.524326 | + | 0.524326i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −362.207 | −0.0686741 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2406.27 | 0.451747 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4007.99 | − | 4007.99i | −0.745108 | − | 0.745108i | 0.228448 | − | 0.973556i | \(-0.426635\pi\) |
−0.973556 | + | 0.228448i | \(0.926635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1878.61 | − | 1878.61i | 0.345858 | − | 0.345858i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6413.20i | 1.16932i | 0.811278 | + | 0.584661i | \(0.198773\pi\) | ||||
−0.811278 | + | 0.584661i | \(0.801227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4044.09i | 0.730305i | 0.930948 | + | 0.365153i | \(0.118983\pi\) | ||||
−0.930948 | + | 0.365153i | \(0.881017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2783.25 | − | 2783.25i | 0.497837 | − | 0.497837i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6785.49 | + | 6785.49i | 1.20224 | + | 1.20224i | 0.973483 | + | 0.228760i | \(0.0734670\pi\) |
0.228760 | + | 0.973483i | \(0.426533\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2914.91 | −0.511610 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −256.306 | −0.0445657 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3197.95 | − | 3197.95i | −0.550894 | − | 0.550894i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1524.32 | + | 1524.32i | −0.260167 | + | 0.260167i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1701.03i | − | 0.287667i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2203.50i | − | 0.369248i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −490.326 | + | 490.326i | −0.0814222 | + | 0.0814222i | −0.746645 | − | 0.665223i | \(-0.768337\pi\) |
0.665223 | + | 0.746645i | \(0.268337\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4141.02 | − | 4141.02i | −0.681461 | − | 0.681461i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10948.4 | 1.78560 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4617.22 | 0.746338 | 0.373169 | − | 0.927763i | \(-0.378271\pi\) | ||||
0.373169 | + | 0.927763i | \(0.378271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1677.01 | − | 1677.01i | −0.268681 | − | 0.268681i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3191.14 | + | 3191.14i | −0.506775 | + | 0.506775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6181.65i | 0.973113i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4430.89i | 0.691453i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7690.50 | + | 7690.50i | −1.18976 | + | 1.18976i | −0.212629 | + | 0.977133i | \(0.568203\pi\) |
−0.977133 | + | 0.212629i | \(0.931797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3203.48 | + | 3203.48i | 0.491342 | + | 0.491342i | 0.908729 | − | 0.417387i | \(-0.137054\pi\) |
−0.417387 | + | 0.908729i | \(0.637054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1899.00 | 0.288778 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 914.110 | 0.137828 | 0.0689139 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689139 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1138.21 | − | 1138.21i | −0.170169 | − | 0.170169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −383.421 | + | 383.421i | −0.0568425 | + | 0.0568425i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6252.16i | − | 0.919155i | −0.888138 | − | 0.459577i | \(-0.848001\pi\) | ||
0.888138 | − | 0.459577i | \(-0.151999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14454.0i | 2.10731i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1179.45 | − | 1179.45i | 0.170537 | − | 0.170537i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8066.97 | + | 8066.97i | 1.15683 | + | 1.15683i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6025.24 | 0.856988 | 0.428494 | − | 0.903545i | \(-0.359044\pi\) | ||||
0.428494 | + | 0.903545i | \(0.359044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11457.8 | −1.61645 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1742.23 | + | 1742.23i | 0.243806 | + | 0.243806i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3971.27 | + | 3971.27i | −0.551273 | + | 0.551273i | −0.926808 | − | 0.375535i | \(-0.877459\pi\) |
0.375535 | + | 0.926808i | \(0.377459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 742.270i | − | 0.102215i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3918.93i | 0.535372i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7117.10 | − | 7117.10i | 0.964593 | − | 0.964593i | −0.0348013 | − | 0.999394i | \(-0.511080\pi\) |
0.999394 | + | 0.0348013i | \(0.0110798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1309.60 | − | 1309.60i | −0.176097 | − | 0.176097i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 779.648 | 0.104016 | 0.0520080 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520080 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2756.63 | 0.364911 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6135.67 | − | 6135.67i | −0.805927 | − | 0.805927i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10296.3 | + | 10296.3i | −1.34202 | + | 1.34202i | −0.447963 | + | 0.894052i | \(0.647850\pi\) |
−0.894052 | + | 0.447963i | \(0.852150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5778.19i | 0.747354i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 639.360i | − | 0.0820647i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6769.78 | + | 6769.78i | −0.862341 | + | 0.862341i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 795.225 | + | 795.225i | 0.100532 | + | 0.100532i | 0.755584 | − | 0.655052i | \(-0.227353\pi\) |
−0.655052 | + | 0.755584i | \(0.727353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2555.34 | 0.320619 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8140.19 | 1.01372 | 0.506860 | − | 0.862028i | \(-0.330806\pi\) | ||||
0.506860 | + | 0.862028i | \(0.330806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4290.31 | + | 4290.31i | 0.530312 | + | 0.530312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5508.38 | + | 5508.38i | −0.675836 | + | 0.675836i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4101.40i | − | 0.499506i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 243.511i | 0.0294397i | 0.999892 | + | 0.0147198i | \(0.00468564\pi\) | ||||
−0.999892 | + | 0.0147198i | \(0.995314\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2541.55 | − | 2541.55i | 0.305026 | − | 0.305026i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2500.63 | − | 2500.63i | −0.297937 | − | 0.297937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14685.4 | −1.73705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2111.12 | −0.247919 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10950.1 | − | 10950.1i | −1.27672 | − | 1.27672i | −0.942490 | − | 0.334233i | \(-0.891523\pi\) |
−0.334233 | − | 0.942490i | \(-0.608477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4623.28 | − | 4623.28i | 0.535214 | − | 0.535214i | −0.386906 | − | 0.922119i | \(-0.626456\pi\) |
0.922119 | + | 0.386906i | \(0.126456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4937.69i | 0.567562i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2904.38i | 0.331490i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1253.69 | + | 1253.69i | −0.142086 | + | 0.142086i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 446.618 | + | 446.618i | 0.0502632 | + | 0.0502632i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12116.9 | 1.35418 | 0.677090 | − | 0.735900i | \(-0.263241\pi\) | ||||
0.677090 | + | 0.735900i | \(0.263241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −939.963 | −0.104323 | −0.0521614 | − | 0.998639i | \(-0.516611\pi\) | ||||
−0.0521614 | + | 0.998639i | \(0.516611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2862.95 | + | 2862.95i | 0.315558 | + | 0.315558i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19254.6 | − | 19254.6i | 2.10772 | − | 2.10772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6773.26i | 0.736378i | 0.929751 | + | 0.368189i | \(0.120022\pi\) | ||||
−0.929751 | + | 0.368189i | \(0.879978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 5475.94i | − | 0.591291i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3342.04 | + | 3342.04i | −0.358431 | + | 0.358431i | −0.863234 | − | 0.504803i | \(-0.831565\pi\) |
0.504803 | + | 0.863234i | \(0.331565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6313.42 | + | 6313.42i | 0.672550 | + | 0.672550i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 524.773 | 0.0555278 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5035.15 | 0.529228 | 0.264614 | − | 0.964354i | \(-0.414755\pi\) | ||||
0.264614 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5674.11 | − | 5674.11i | −0.592424 | − | 0.592424i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2474.36 | + | 2474.36i | −0.256635 | + | 0.256635i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3706.13i | − | 0.381860i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7652.79i | − | 0.783331i | −0.920108 | − | 0.391666i | \(-0.871899\pi\) | ||
0.920108 | − | 0.391666i | \(-0.128101\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1809.13 | − | 1809.13i | 0.183972 | − | 0.183972i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10300.0 | − | 10300.0i | −1.04061 | − | 1.04061i | −0.999140 | − | 0.0414659i | \(-0.986797\pi\) |
−0.0414659 | − | 0.999140i | \(-0.513203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1213.28 | −0.121784 | −0.0608919 | − | 0.998144i | \(-0.519394\pi\) | ||||
−0.0608919 | + | 0.998144i | \(0.519394\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6268.51 | 0.625151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8124.34 | + | 8124.34i | 0.805031 | + | 0.805031i | 0.983877 | − | 0.178846i | \(-0.0572363\pi\) |
−0.178846 | + | 0.983877i | \(0.557236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5704.23 | + | 5704.23i | −0.561614 | + | 0.561614i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1261.35i | 0.123397i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6076.97i | − | 0.590739i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9678.23 | − | 9678.23i | 0.934880 | − | 0.934880i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3904.06 | − | 3904.06i | −0.374747 | − | 0.374747i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8755.05 | −0.835133 | −0.417566 | − | 0.908646i | \(-0.637117\pi\) | ||||
−0.417566 | + | 0.908646i | \(0.637117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5514.10 | −0.522706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2308.54 | − | 2308.54i | −0.217479 | − | 0.217479i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7751.00 | − | 7751.00i | 0.725680 | − | 0.725680i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14346.3i | − | 1.33489i | −0.744658 | − | 0.667446i | \(-0.767387\pi\) | ||
0.744658 | − | 0.667446i | \(-0.232613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2402.13i | − | 0.222143i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −933.557 | + | 933.557i | −0.0858062 | + | 0.0858062i | −0.748707 | − | 0.662901i | \(-0.769325\pi\) |
0.662901 | + | 0.748707i | \(0.269325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3733.48 | + | 3733.48i | 0.341070 | + | 0.341070i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6177.17 | −0.560895 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1186.04 | 0.107045 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11103.6 | + | 11103.6i | 0.996120 | + | 0.996120i | 0.999993 | − | 0.00387261i | \(-0.00123269\pi\) |
−0.00387261 | + | 0.999993i | \(0.501233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 382.712 | − | 382.712i | 0.0341284 | − | 0.0341284i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3340.94i | 0.296153i | 0.988976 | + | 0.148077i | \(0.0473082\pi\) | ||||
−0.988976 | + | 0.148077i | \(0.952692\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3335.40i | − | 0.293908i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1894.73 | + | 1894.73i | −0.165972 | + | 0.165972i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6399.94 | − | 6399.94i | −0.557313 | − | 0.557313i | 0.371229 | − | 0.928541i | \(-0.378937\pi\) |
−0.928541 | + | 0.371229i | \(0.878937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8405.95 | −0.727705 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12057.1 | −1.03769 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17299.2 | + | 17299.2i | 1.48018 | + | 1.48018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2445.23 | + | 2445.23i | −0.208009 | + | 0.208009i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2934.51i | − | 0.248190i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5430.32i | − | 0.456635i | −0.973587 | − | 0.228317i | \(-0.926678\pi\) | ||
0.973587 | − | 0.228317i | \(-0.0733224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4251.48 | + | 4251.48i | −0.355458 | + | 0.355458i | −0.862135 | − | 0.506678i | \(-0.830873\pi\) |
0.506678 | + | 0.862135i | \(0.330873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1160.38 | − | 1160.38i | −0.0964630 | − | 0.0964630i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8174.57 | 0.675693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22623.0 | −1.85937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5603.52 | + | 5603.52i | 0.457951 | + | 0.457951i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7628.52 | + | 7628.52i | −0.619940 | + | 0.619940i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2360.20i | − | 0.190730i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2356.46i | − | 0.189364i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2711.78 | − | 2711.78i | 0.216706 | − | 0.216706i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12763.5 | − | 12763.5i | −1.01432 | − | 1.01432i | −0.999896 | − | 0.0144213i | \(-0.995409\pi\) |
−0.0144213 | − | 0.999896i | \(-0.504591\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3749.68 | −0.296343 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15664.0 | 1.23114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5360.42 | + | 5360.42i | 0.419004 | + | 0.419004i | 0.884860 | − | 0.465857i | \(-0.154254\pi\) |
−0.465857 | + | 0.884860i | \(0.654254\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2809.33 | − | 2809.33i | 0.218396 | − | 0.218396i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24882.1i | − | 1.92380i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7054.26i | − | 0.542455i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4028.29 | + | 4028.29i | −0.308093 | + | 0.308093i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12284.0 | + | 12284.0i | 0.934456 | + | 0.934456i | 0.997980 | − | 0.0635245i | \(-0.0202341\pi\) |
−0.0635245 | + | 0.997980i | \(0.520234\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8170.15 | −0.618176 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 850.966 | 0.0640424 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5592.31 | − | 5592.31i | −0.418628 | − | 0.418628i | 0.466103 | − | 0.884731i | \(-0.345658\pi\) |
−0.884731 | + | 0.466103i | \(0.845658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15442.9 | − | 15442.9i | 1.14989 | − | 1.14989i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5739.85i | − | 0.425134i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5368.07i | − | 0.395503i | −0.980252 | − | 0.197751i | \(-0.936636\pi\) | ||
0.980252 | − | 0.197751i | \(-0.0633639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1135.50 | − | 1135.50i | 0.0832209 | − | 0.0832209i | −0.664271 | − | 0.747492i | \(-0.731258\pi\) |
0.747492 | + | 0.664271i | \(0.231258\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 116.351 | + | 116.351i | 0.00848281 | + | 0.00848281i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17487.0 | −1.26828 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11551.0 | 0.833407 | 0.416704 | − | 0.909042i | \(-0.363185\pi\) | ||||
0.416704 | + | 0.909042i | \(0.363185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2451.90 | + | 2451.90i | 0.175989 | + | 0.175989i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7651.23 | − | 7651.23i | 0.546345 | − | 0.546345i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3866.71i | − | 0.274687i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8304.85i | 0.586946i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7688.04 | + | 7688.04i | −0.540578 | + | 0.540578i | −0.923698 | − | 0.383120i | \(-0.874849\pi\) |
0.383120 | + | 0.923698i | \(0.374849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27240.1 | − | 27240.1i | −1.90561 | − | 1.90561i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6865.02 | −0.477816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6202.98 | −0.429554 | −0.214777 | − | 0.976663i | \(-0.568903\pi\) | ||||
−0.214777 | + | 0.976663i | \(0.568903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3530.75 | − | 3530.75i | −0.243272 | − | 0.243272i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3748.90 | − | 3748.90i | 0.257006 | − | 0.257006i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25399.0i | 1.73251i | 0.499601 | + | 0.866256i | \(0.333480\pi\) | ||||
−0.499601 | + | 0.866256i | \(0.666520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10592.6i | − | 0.718937i | −0.933157 | − | 0.359468i | \(-0.882958\pi\) | ||
0.933157 | − | 0.359468i | \(-0.117042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12782.3 | − | 12782.3i | 0.863241 | − | 0.863241i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10861.0 | + | 10861.0i | 0.729856 | + | 0.729856i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22149.9 | 1.48112 | 0.740559 | − | 0.671991i | \(-0.234561\pi\) | ||||
0.740559 | + | 0.671991i | \(0.234561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2983.25 | −0.198502 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3287.47 | + | 3287.47i | 0.217671 | + | 0.217671i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −706.775 | + | 706.775i | −0.0465683 | + | 0.0465683i | −0.730007 | − | 0.683439i | \(-0.760483\pi\) |
0.683439 | + | 0.730007i | \(0.260483\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11145.9i | 0.730808i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19532.2i | − | 1.27445i | −0.770676 | − | 0.637227i | \(-0.780081\pi\) | ||
0.770676 | − | 0.637227i | \(-0.219919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2955.47 | − | 2955.47i | 0.191907 | − | 0.191907i | −0.604613 | − | 0.796520i | \(-0.706672\pi\) |
0.796520 | + | 0.604613i | \(0.206672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10892.6 | + | 10892.6i | 0.703875 | + | 0.703875i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6578.72 | −0.423067 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18554.5 | 1.18748 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2835.66 | − | 2835.66i | −0.180615 | − | 0.180615i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5253.17 | + | 5253.17i | −0.333001 | + | 0.333001i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3807.03i | 0.240183i | 0.992763 | + | 0.120092i | \(0.0383188\pi\) | ||||
−0.992763 | + | 0.120092i | \(0.961681\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 175.120i | 0.0109959i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12059.5 | − | 12059.5i | 0.753650 | − | 0.753650i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3645.83 | − | 3645.83i | −0.226771 | − | 0.226771i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2657.73 | −0.164536 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13614.0 | −0.838876 | −0.419438 | − | 0.907784i | \(-0.637773\pi\) | ||||
−0.419438 | + | 0.907784i | \(0.637773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17427.0 | − | 17427.0i | −1.06882 | − | 1.06882i | −0.997450 | − | 0.0713737i | \(-0.977262\pi\) |
−0.0713737 | − | 0.997450i | \(-0.522738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5968.64 | + | 5968.64i | −0.364364 | + | 0.364364i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8973.38i | − | 0.545255i | −0.962120 | − | 0.272628i | \(-0.912107\pi\) | ||
0.962120 | − | 0.272628i | \(-0.0878927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5549.91i | 0.335675i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3265.96 | + | 3265.96i | −0.196626 | + | 0.196626i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12077.2 | − | 12077.2i | −0.723765 | − | 0.723765i | 0.245605 | − | 0.969370i | \(-0.421013\pi\) |
−0.969370 | + | 0.245605i | \(0.921013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5887.57 | 0.351216 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18836.4 | 1.11854 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7420.23 | − | 7420.23i | −0.438621 | − | 0.438621i | 0.452927 | − | 0.891548i | \(-0.350380\pi\) |
−0.891548 | + | 0.452927i | \(0.850380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14935.9 | + | 14935.9i | −0.878880 | + | 0.878880i | −0.993419 | − | 0.114539i | \(-0.963461\pi\) |
0.114539 | + | 0.993419i | \(0.463461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1144.08i | − | 0.0670169i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23531.0i | 1.37217i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22478.9 | + | 22478.9i | −1.30493 | + | 1.30493i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2072.06 | + | 2072.06i | 0.119747 | + | 0.119747i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2782.46 | 0.160083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10148.2 | −0.581257 | −0.290628 | − | 0.956836i | \(-0.593864\pi\) | ||||
−0.290628 | + | 0.956836i | \(0.593864\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5475.13 | + | 5475.13i | 0.312204 | + | 0.312204i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3810.25 | − | 3810.25i | 0.216307 | − | 0.216307i | −0.590633 | − | 0.806940i | \(-0.701122\pi\) |
0.806940 | + | 0.590633i | \(0.201122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8076.71i | 0.456488i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6740.32i | − | 0.379280i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9878.47 | − | 9878.47i | 0.553425 | − | 0.553425i | −0.374003 | − | 0.927428i | \(-0.622015\pi\) |
0.927428 | + | 0.374003i | \(0.122015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23404.0 | + | 23404.0i | 1.30543 | + | 1.30543i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1799.35 | 0.0999263 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5198.57 | −0.287445 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4045.86 | + | 4045.86i | 0.222737 | + | 0.222737i | 0.809650 | − | 0.586913i | \(-0.199657\pi\) |
−0.586913 | + | 0.809650i | \(0.699657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3218.37 | − | 3218.37i | 0.176415 | − | 0.176415i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19440.4i | − | 1.06103i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14535.0i | 0.789891i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1013.23 | + | 1013.23i | −0.0548267 | + | 0.0548267i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11492.0 | + | 11492.0i | 0.619181 | + | 0.619181i | 0.945321 | − | 0.326140i | \(-0.105748\pi\) |
−0.326140 | + | 0.945321i | \(0.605748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35010.1 | 1.87828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4803.27 | 0.256598 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1737.78 | + | 1737.78i | 0.0924413 | + | 0.0924413i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11844.5 | + | 11844.5i | −0.627402 | + | 0.627402i | −0.947414 | − | 0.320012i | \(-0.896313\pi\) |
0.320012 | + | 0.947414i | \(0.396313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15807.5i | 0.833793i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49218.4i | 2.58519i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4112.70 | + | 4112.70i | −0.215114 | + | 0.215114i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3007.18 | + | 3007.18i | 0.156632 | + | 0.156632i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4208.96 | 0.218314 | 0.109157 | − | 0.994025i | \(-0.465185\pi\) | ||||
0.109157 | + | 0.994025i | \(0.465185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18026.2 | −0.931109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3087.22 | + | 3087.22i | 0.158804 | + | 0.158804i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11298.9 | + | 11298.9i | −0.578803 | + | 0.578803i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17761.1i | − | 0.906083i | −0.891490 | − | 0.453041i | \(-0.850339\pi\) | ||
0.891490 | − | 0.453041i | \(-0.149661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9280.55i | 0.471501i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7783.52 | + | 7783.52i | −0.393822 | + | 0.393822i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3081.13 | + | 3081.13i | 0.155258 | + | 0.155258i | 0.780462 | − | 0.625204i | \(-0.214984\pi\) |
−0.625204 | + | 0.780462i | \(0.714984\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5326.88 | −0.267326 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12660.0 | 0.632750 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18416.2 | − | 18416.2i | −0.916714 | − | 0.916714i | 0.0800745 | − | 0.996789i | \(-0.474484\pi\) |
−0.996789 | + | 0.0800745i | \(0.974484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3812.39 | + | 3812.39i | −0.189004 | + | 0.189004i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29048.2i | 1.43429i | 0.696925 | + | 0.717144i | \(0.254551\pi\) | ||||
−0.696925 | + | 0.717144i | \(0.745449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4832.40i | 0.237645i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17145.2 | + | 17145.2i | −0.839772 | + | 0.839772i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1229.69 | + | 1229.69i | 0.0599893 | + | 0.0599893i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2569.49 | −0.124850 | −0.0624248 | − | 0.998050i | \(-0.519883\pi\) | ||||
−0.0624248 | + | 0.998050i | \(0.519883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5174.35 | 0.250417 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22785.3 | − | 22785.3i | −1.09833 | − | 1.09833i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16400.4 | − | 16400.4i | 0.787429 | − | 0.787429i | −0.193643 | − | 0.981072i | \(-0.562030\pi\) |
0.981072 | + | 0.193643i | \(0.0620305\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5123.59i | 0.245026i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4393.44i | − | 0.209280i | −0.994510 | − | 0.104640i | \(-0.966631\pi\) | ||
0.994510 | − | 0.104640i | \(-0.0333691\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8161.11 | + | 8161.11i | −0.387224 | + | 0.387224i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7911.85 | + | 7911.85i | 0.373926 | + | 0.373926i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7461.54 | 0.351266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22868.9 | −1.07240 | −0.536200 | − | 0.844091i | \(-0.680141\pi\) | ||||
−0.536200 | + | 0.844091i | \(0.680141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5744.94 | − | 5744.94i | −0.268352 | − | 0.268352i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17846.6 | + | 17846.6i | −0.830396 | + | 0.830396i | −0.987571 | − | 0.157175i | \(-0.949761\pi\) |
0.157175 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24739.4i | 1.14666i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4197.57i | − | 0.193805i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48435.0 | − | 48435.0i | 2.22768 | − | 2.22768i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1316.15 | − | 1316.15i | −0.0603017 | − | 0.0603017i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14076.2 | 0.642454 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11615.2 | −0.528106 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2229.13 | − | 2229.13i | −0.100966 | − | 0.100966i | 0.654820 | − | 0.755785i | \(-0.272745\pi\) |
−0.755785 | + | 0.654820i | \(0.772745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9020.39 | + | 9020.39i | −0.407014 | + | 0.407014i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16091.8i | 0.723336i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3740.85i | − | 0.167518i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3797.78 | + | 3797.78i | −0.169426 | + | 0.169426i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7260.72 | + | 7260.72i | 0.322695 | + | 0.322695i | 0.849800 | − | 0.527105i | \(-0.176723\pi\) |
−0.527105 | + | 0.849800i | \(0.676723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6263.80 | 0.277343 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14741.9 | 0.650285 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9328.10 | + | 9328.10i | 0.409940 | + | 0.409940i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21258.3 | − | 21258.3i | 0.930755 | − | 0.930755i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 152.484i | − | 0.00665140i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6066.32i | − | 0.263635i | −0.991274 | − | 0.131817i | \(-0.957919\pi\) | ||
0.991274 | − | 0.131817i | \(-0.0420813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16174.7 | − | 16174.7i | 0.700334 | − | 0.700334i | −0.264148 | − | 0.964482i | \(-0.585091\pi\) |
0.964482 | + | 0.264148i | \(0.0850907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2541.38 | + | 2541.38i | 0.109631 | + | 0.109631i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22120.1 | 0.950715 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51873.9 | 2.22134 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4326.92 | − | 4326.92i | −0.184609 | − | 0.184609i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1109.32 | − | 1109.32i | 0.0471566 | − | 0.0471566i | −0.683135 | − | 0.730292i | \(-0.739384\pi\) |
0.730292 | + | 0.683135i | \(0.239384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2875.65i | 0.121797i | 0.998144 | + | 0.0608985i | \(0.0193966\pi\) | ||||
−0.998144 | + | 0.0608985i | \(0.980603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2575.35i | 0.108681i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24943.8 | + | 24943.8i | −1.04883 | + | 1.04883i | −0.0500833 | + | 0.998745i | \(0.515949\pi\) |
−0.998745 | + | 0.0500833i | \(0.984051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4884.59 | + | 4884.59i | 0.204643 | + | 0.204643i | 0.801986 | − | 0.597343i | \(-0.203777\pi\) |
−0.597343 | + | 0.801986i | \(0.703777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8283.69 | 0.345798 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6946.61 | −0.288939 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3524.22 | + | 3524.22i | 0.146061 | + | 0.146061i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15410.1 | − | 15410.1i | 0.636382 | − | 0.636382i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24039.4i | 0.989193i | 0.869123 | + | 0.494596i | \(0.164684\pi\) | ||||
−0.869123 | + | 0.494596i | \(0.835316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4659.77i | 0.191060i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −417.853 | + | 417.853i | −0.0170719 | + | 0.0170719i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17447.7 | − | 17447.7i | −0.710318 | − | 0.710318i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11317.4 | −0.459116 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11344.8 | −0.458600 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31628.8 | − | 31628.8i | −1.27406 | − | 1.27406i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15724.1 | + | 15724.1i | −0.631163 | + | 0.631163i | −0.948360 | − | 0.317197i | \(-0.897258\pi\) |
0.317197 | + | 0.948360i | \(0.397258\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 52729.2i | − | 2.10912i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1796.16i | 0.0715935i | 0.999359 | + | 0.0357968i | \(0.0113969\pi\) | ||||
−0.999359 | + | 0.0357968i | \(0.988603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 863.555 | − | 863.555i | 0.0343005 | − | 0.0343005i | −0.689749 | − | 0.724049i | \(-0.742279\pi\) |
0.724049 | + | 0.689749i | \(0.242279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5807.15 | − | 5807.15i | −0.229857 | − | 0.229857i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39589.1 | −1.56156 | −0.780781 | − | 0.624805i | \(-0.785178\pi\) | ||||
−0.780781 | + | 0.624805i | \(0.785178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27022.6 | 1.06219 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4489.86 | + | 4489.86i | 0.175875 | + | 0.175875i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7828.13 | + | 7828.13i | −0.305582 | + | 0.305582i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 17020.6i | − | 0.662138i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 18098.6i | − | 0.701656i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3561.23 | + | 3561.23i | −0.137590 | + | 0.137590i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18503.2 | + | 18503.2i | 0.712438 | + | 0.712438i | 0.967045 | − | 0.254607i | \(-0.0819460\pi\) |
−0.254607 | + | 0.967045i | \(0.581946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13789.9 | −0.529147 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35346.0 | −1.35169 | −0.675844 | − | 0.737045i | \(-0.736221\pi\) | ||||
−0.675844 | + | 0.737045i | \(0.736221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24633.1 | + | 24633.1i | 0.938811 | + | 0.938811i | 0.998233 | − | 0.0594221i | \(-0.0189258\pi\) |
−0.0594221 | + | 0.998233i | \(0.518926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5450.98 | − | 5450.98i | 0.207042 | − | 0.207042i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7317.89i | − | 0.277013i | −0.990362 | − | 0.138507i | \(-0.955770\pi\) | ||
0.990362 | − | 0.138507i | \(-0.0442302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12566.3i | 0.474083i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6369.53 | + | 6369.53i | −0.239492 | + | 0.239492i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20872.8 | − | 20872.8i | −0.782174 | − | 0.782174i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21699.6 | 0.810431 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6888.38 | 0.256406 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31801.6 | + | 31801.6i | 1.17980 | + | 1.17980i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4952.57 | + | 4952.57i | −0.183123 | + | 0.183123i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6219.46i | − | 0.229203i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 34529.1i | − | 1.26827i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7815.82 | + | 7815.82i | −0.286130 | + | 0.286130i | −0.835548 | − | 0.549418i | \(-0.814850\pi\) |
0.549418 | + | 0.835548i | \(0.314850\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3894.09 | − | 3894.09i | −0.142089 | − | 0.142089i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39108.7 | −1.42232 | −0.711158 | − | 0.703032i | \(-0.751829\pi\) | ||||
−0.711158 | + | 0.703032i | \(0.751829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16981.2 | −0.615548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2732.85 | − | 2732.85i | −0.0987381 | − | 0.0987381i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3067.49 | + | 3067.49i | −0.110466 | + | 0.110466i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15863.3i | − | 0.569402i | −0.958616 | − | 0.284701i | \(-0.908106\pi\) | ||
0.958616 | − | 0.284701i | \(-0.0918944\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9103.92i | 0.325716i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1769.49 | + | 1769.49i | −0.0631025 | + | 0.0631025i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15898.1 | − | 15898.1i | −0.565109 | − | 0.565109i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40393.8 | 1.43118 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47226.0 | −1.66785 | −0.833927 | − | 0.551875i | \(-0.813912\pi\) | ||||
−0.833927 | + | 0.551875i | \(0.813912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23148.1 | + | 23148.1i | 0.814876 | + | 0.814876i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7283.60 | − | 7283.60i | 0.255578 | − | 0.255578i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7836.16i | 0.274085i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24564.3i | 0.856437i | 0.903675 | + | 0.428219i | \(0.140859\pi\) | ||||
−0.903675 | + | 0.428219i | \(0.859141\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4592.96 | − | 4592.96i | 0.159622 | − | 0.159622i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12767.7 | − | 12767.7i | −0.442310 | − | 0.442310i | 0.450478 | − | 0.892788i | \(-0.351254\pi\) |
−0.892788 | + | 0.450478i | \(0.851254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −87514.2 | −3.02212 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13311.8 | −0.458237 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −348.162 | − | 348.162i | −0.0119469 | − | 0.0119469i | 0.701108 | − | 0.713055i | \(-0.252689\pi\) |
−0.713055 | + | 0.701108i | \(0.752689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12541.1 | − | 12541.1i | 0.428980 | − | 0.428980i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 15412.8i | − | 0.525547i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 37577.4i | − | 1.27728i | −0.769504 | − | 0.638642i | \(-0.779496\pi\) | ||
0.769504 | − | 0.638642i | \(-0.220504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1071.43 | + | 1071.43i | −0.0363043 | + | 0.0363043i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3310.52 | + | 3310.52i | 0.111822 | + | 0.111822i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24387.5 | −0.821182 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39839.7 | 1.33731 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2755.55 | − | 2755.55i | −0.0922079 | − | 0.0922079i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22578.5 | + | 22578.5i | −0.753188 | + | 0.753188i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41535.5i | − | 1.38127i | −0.723202 | − | 0.690637i | \(-0.757330\pi\) | ||
0.723202 | − | 0.690637i | \(-0.242670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7263.96i | 0.240817i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26608.0 | − | 26608.0i | 0.879393 | − | 0.879393i | −0.114079 | − | 0.993472i | \(-0.536392\pi\) |
0.993472 | + | 0.114079i | \(0.0363917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10128.6 | + | 10128.6i | 0.333720 | + | 0.333720i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3462.41 | 0.113729 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41599.6 | 1.36222 | 0.681110 | − | 0.732181i | \(-0.261498\pi\) | ||||
0.681110 | + | 0.732181i | \(0.261498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7300.42 | + | 7300.42i | 0.238327 | + | 0.238327i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18287.8 | − | 18287.8i | 0.595192 | − | 0.595192i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28284.2i | 0.917726i | 0.888507 | + | 0.458863i | \(0.151743\pi\) | ||||
−0.888507 | + | 0.458863i | \(0.848257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 63216.8i | − | 2.04493i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2502.56 | + | 2502.56i | −0.0807065 | + | 0.0807065i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46863.9 | − | 46863.9i | −1.50676 | − | 1.50676i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40254.3 | 1.29033 | 0.645167 | − | 0.764042i | \(-0.276788\pi\) | ||||
0.645167 | + | 0.764042i | \(0.276788\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1113.75 | 0.0355928 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34522.0 | + | 34522.0i | 1.09992 | + | 1.09992i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34773.0 | − | 34773.0i | 1.10459 | − | 1.10459i | 0.110737 | − | 0.993850i | \(-0.464679\pi\) |
0.993850 | − | 0.110737i | \(-0.0353212\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19805.8i | 0.627255i |
(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 | 256.4.e.c.65.4 | ✓ | 16 | |
4.3 | odd | 2 | inner | 256.4.e.c.65.5 | yes | 16 | |
8.3 | odd | 2 | 256.4.e.d.65.4 | yes | 16 | ||
8.5 | even | 2 | 256.4.e.d.65.5 | yes | 16 | ||
16.3 | odd | 4 | 256.4.e.d.193.4 | yes | 16 | ||
16.5 | even | 4 | inner | 256.4.e.c.193.4 | yes | 16 | |
16.11 | odd | 4 | inner | 256.4.e.c.193.5 | yes | 16 | |
16.13 | even | 4 | 256.4.e.d.193.5 | yes | 16 | ||
32.3 | odd | 8 | 1024.4.b.l.513.10 | 16 | |||
32.5 | even | 8 | 1024.4.a.k.1.6 | 8 | |||
32.11 | odd | 8 | 1024.4.a.k.1.5 | 8 | |||
32.13 | even | 8 | 1024.4.b.l.513.9 | 16 | |||
32.19 | odd | 8 | 1024.4.b.l.513.7 | 16 | |||
32.21 | even | 8 | 1024.4.a.l.1.3 | 8 | |||
32.27 | odd | 8 | 1024.4.a.l.1.4 | 8 | |||
32.29 | even | 8 | 1024.4.b.l.513.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.4.e.c.65.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
256.4.e.c.65.5 | yes | 16 | 4.3 | odd | 2 | inner | |
256.4.e.c.193.4 | yes | 16 | 16.5 | even | 4 | inner | |
256.4.e.c.193.5 | yes | 16 | 16.11 | odd | 4 | inner | |
256.4.e.d.65.4 | yes | 16 | 8.3 | odd | 2 | ||
256.4.e.d.65.5 | yes | 16 | 8.5 | even | 2 | ||
256.4.e.d.193.4 | yes | 16 | 16.3 | odd | 4 | ||
256.4.e.d.193.5 | yes | 16 | 16.13 | even | 4 | ||
1024.4.a.k.1.5 | 8 | 32.11 | odd | 8 | |||
1024.4.a.k.1.6 | 8 | 32.5 | even | 8 | |||
1024.4.a.l.1.3 | 8 | 32.21 | even | 8 | |||
1024.4.a.l.1.4 | 8 | 32.27 | odd | 8 | |||
1024.4.b.l.513.7 | 16 | 32.19 | odd | 8 | |||
1024.4.b.l.513.8 | 16 | 32.29 | even | 8 | |||
1024.4.b.l.513.9 | 16 | 32.13 | even | 8 | |||
1024.4.b.l.513.10 | 16 | 32.3 | odd | 8 |