Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,4,Mod(289,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.7369626429\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(-8.67551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.289 |
Dual form | 504.4.s.j.361.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.47901 | − | 16.4181i | 0.847828 | − | 1.46848i | −0.0353138 | − | 0.999376i | \(-0.511243\pi\) |
0.883142 | − | 0.469106i | \(-0.155424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.8033 | − | 13.3819i | 0.691312 | − | 0.722556i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.3654 | + | 47.3983i | 0.750089 | + | 1.29919i | 0.947779 | + | 0.318928i | \(0.103323\pi\) |
−0.197690 | + | 0.980265i | \(0.563344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0173 | 1.32312 | 0.661558 | − | 0.749894i | \(-0.269896\pi\) | ||||
0.661558 | + | 0.749894i | \(0.269896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 61.2195 | + | 106.035i | 0.873407 | + | 1.51279i | 0.858450 | + | 0.512897i | \(0.171428\pi\) |
0.0149571 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.25288 | − | 10.8303i | 0.0755004 | − | 0.130771i | −0.825803 | − | 0.563958i | \(-0.809278\pi\) |
0.901304 | + | 0.433188i | \(0.142611\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −37.2195 | + | 64.4661i | −0.337427 | + | 0.584440i | −0.983948 | − | 0.178456i | \(-0.942890\pi\) |
0.646521 | + | 0.762896i | \(0.276223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.203 | − | 203.002i | −0.937626 | − | 1.62402i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 232.572 | 1.48923 | 0.744613 | − | 0.667496i | \(-0.232634\pi\) | ||||
0.744613 | + | 0.667496i | \(0.232634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.18387 | − | 8.97872i | −0.0300339 | − | 0.0520202i | 0.850618 | − | 0.525785i | \(-0.176228\pi\) |
−0.880652 | + | 0.473764i | \(0.842895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.3438 | − | 337.053i | −0.474947 | − | 1.62778i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 122.993 | − | 213.031i | 0.546486 | − | 0.946541i | −0.452026 | − | 0.892005i | \(-0.649299\pi\) |
0.998512 | − | 0.0545365i | \(-0.0173681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −238.653 | −0.909056 | −0.454528 | − | 0.890733i | \(-0.650192\pi\) | ||||
−0.454528 | + | 0.890733i | \(0.650192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −92.9718 | −0.329722 | −0.164861 | − | 0.986317i | \(-0.552718\pi\) | ||||
−0.164861 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −242.822 | + | 420.580i | −0.753601 | + | 1.30528i | 0.192465 | + | 0.981304i | \(0.438352\pi\) |
−0.946067 | + | 0.323972i | \(0.894982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.1521 | − | 342.665i | −0.0441751 | − | 0.999024i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −189.278 | − | 327.840i | −0.490555 | − | 0.849666i | 0.509386 | − | 0.860538i | \(-0.329872\pi\) |
−0.999941 | + | 0.0108725i | \(0.996539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1037.59 | 2.54379 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −91.3918 | − | 158.295i | −0.201664 | − | 0.349293i | 0.747400 | − | 0.664374i | \(-0.231302\pi\) |
−0.949065 | + | 0.315081i | \(0.897968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −198.235 | + | 343.353i | −0.416088 | + | 0.720686i | −0.995542 | − | 0.0943190i | \(-0.969933\pi\) |
0.579454 | + | 0.815005i | \(0.303266\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 587.863 | − | 1018.21i | 1.12178 | − | 1.94297i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 130.620 | + | 226.240i | 0.238175 | + | 0.412531i | 0.960191 | − | 0.279346i | \(-0.0901175\pi\) |
−0.722016 | + | 0.691877i | \(0.756784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 874.523 | 1.46179 | 0.730893 | − | 0.682492i | \(-0.239104\pi\) | ||||
0.730893 | + | 0.682492i | \(0.239104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.2032 | − | 131.988i | −0.122177 | − | 0.211617i | 0.798449 | − | 0.602062i | \(-0.205654\pi\) |
−0.920626 | + | 0.390446i | \(0.872321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 984.647 | + | 240.651i | 1.45729 | + | 0.356166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −286.679 | + | 496.542i | −0.408277 | + | 0.707156i | −0.994697 | − | 0.102851i | \(-0.967204\pi\) |
0.586420 | + | 0.810007i | \(0.300537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −317.754 | −0.420217 | −0.210108 | − | 0.977678i | \(-0.567382\pi\) | ||||
−0.210108 | + | 0.977678i | \(0.567382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2321.20 | 2.96200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −47.5080 | + | 82.2863i | −0.0565824 | + | 0.0980037i | −0.892929 | − | 0.450197i | \(-0.851354\pi\) |
0.836347 | + | 0.548201i | \(0.184687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 794.025 | − | 829.911i | 0.914686 | − | 0.956026i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −118.542 | − | 205.321i | −0.128023 | − | 0.221742i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1608.78 | −1.68398 | −0.841992 | − | 0.539490i | \(-0.818617\pi\) | ||||
−0.841992 | + | 0.539490i | \(0.818617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −391.521 | − | 678.135i | −0.385721 | − | 0.668089i | 0.606148 | − | 0.795352i | \(-0.292714\pi\) |
−0.991869 | + | 0.127263i | \(0.959381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 744.805 | − | 1290.04i | 0.712503 | − | 1.23409i | −0.251412 | − | 0.967880i | \(-0.580895\pi\) |
0.963915 | − | 0.266211i | \(-0.0857717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 356.385 | − | 617.276i | 0.321991 | − | 0.557704i | −0.658908 | − | 0.752223i | \(-0.728981\pi\) |
0.980899 | + | 0.194519i | \(0.0623147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −520.924 | − | 902.267i | −0.457757 | − | 0.792858i | 0.541085 | − | 0.840968i | \(-0.318014\pi\) |
−0.998842 | + | 0.0481100i | \(0.984680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −352.093 | −0.293116 | −0.146558 | − | 0.989202i | \(-0.546819\pi\) | ||||
−0.146558 | + | 0.989202i | \(0.546819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 705.609 | + | 1222.15i | 0.572160 | + | 0.991010i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2202.77 | + | 538.365i | 1.69687 | + | 0.414721i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −832.231 | + | 1441.47i | −0.625267 | + | 1.08299i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2074.13 | −1.48413 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1093.73 | −0.764194 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1083.19 | + | 1876.13i | −0.722430 | + | 1.25129i | 0.237593 | + | 0.971365i | \(0.423642\pi\) |
−0.960023 | + | 0.279921i | \(0.909692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −64.8730 | − | 222.339i | −0.0422947 | − | 0.144957i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −982.461 | − | 1701.67i | −0.612681 | − | 1.06119i | −0.990787 | − | 0.135432i | \(-0.956758\pi\) |
0.378105 | − | 0.925763i | \(-0.376576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −136.976 | −0.0835840 | −0.0417920 | − | 0.999126i | \(-0.513307\pi\) | ||||
−0.0417920 | + | 0.999126i | \(0.513307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1697.13 | + | 2939.51i | 0.992455 | + | 1.71898i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2204.55 | − | 3818.40i | 1.26261 | − | 2.18690i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −140.053 | + | 242.578i | −0.0770037 | + | 0.133374i | −0.901956 | − | 0.431828i | \(-0.857869\pi\) |
0.824952 | + | 0.565203i | \(0.191202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1097.07 | − | 1900.17i | −0.591245 | − | 1.02407i | −0.994065 | − | 0.108787i | \(-0.965303\pi\) |
0.402820 | − | 0.915279i | \(-0.368030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −196.552 | −0.101854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110.409 | + | 191.234i | 0.0561248 | + | 0.0972111i | 0.892723 | − | 0.450606i | \(-0.148792\pi\) |
−0.836598 | + | 0.547817i | \(0.815459\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 386.149 | + | 1323.45i | 0.189024 | + | 0.647840i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −738.431 | + | 1279.00i | −0.354837 | + | 0.614596i | −0.987090 | − | 0.160166i | \(-0.948797\pi\) |
0.632253 | + | 0.774762i | \(0.282130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2197.66 | −1.01832 | −0.509162 | − | 0.860671i | \(-0.670045\pi\) | ||||
−0.509162 | + | 0.860671i | \(0.670045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1649.15 | 0.750635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1045.80 | − | 1811.38i | 0.459601 | − | 0.796052i | −0.539339 | − | 0.842089i | \(-0.681326\pi\) |
0.998940 | + | 0.0460370i | \(0.0146592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4217.14 | − | 1030.69i | −1.82163 | − | 0.445214i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1167.27 | + | 2021.77i | 0.487406 | + | 0.844212i | 0.999895 | − | 0.0144814i | \(-0.00460974\pi\) |
−0.512489 | + | 0.858694i | \(0.671276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1758.40 | 0.722105 | 0.361053 | − | 0.932545i | \(-0.382417\pi\) | ||||
0.361053 | + | 0.932545i | \(0.382417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2331.71 | − | 4038.64i | −0.926652 | − | 1.60501i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3350.60 | + | 5803.40i | −1.31027 | + | 2.26945i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1850.34 | + | 3204.88i | −0.700973 | + | 1.21412i | 0.267152 | + | 0.963654i | \(0.413917\pi\) |
−0.968125 | + | 0.250467i | \(0.919416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1354.22 | − | 2345.58i | −0.505073 | − | 0.874812i | −0.999983 | − | 0.00586773i | \(-0.998132\pi\) |
0.494910 | − | 0.868944i | \(-0.335201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 160.686 | 0.0581138 | 0.0290569 | − | 0.999578i | \(-0.490750\pi\) | ||||
0.0290569 | + | 0.999578i | \(0.490750\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1033.00 | + | 1789.20i | 0.367976 | + | 0.637353i | 0.989249 | − | 0.146241i | \(-0.0467176\pi\) |
−0.621273 | + | 0.783594i | \(0.713384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2977.69 | − | 3112.27i | 1.02952 | − | 1.07605i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2262.19 | + | 3918.23i | −0.770723 | + | 1.33493i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 684.450 | 0.226528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1007.12 | −0.328592 | −0.164296 | − | 0.986411i | \(-0.552535\pi\) | ||||
−0.164296 | + | 0.986411i | \(0.552535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −881.280 | + | 1526.42i | −0.279548 | + | 0.484191i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −186.523 | − | 45.5869i | −0.0583503 | − | 0.0142610i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3796.67 | + | 6576.03i | 1.15562 | + | 2.00159i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1644.83 | 0.493929 | 0.246964 | − | 0.969025i | \(-0.420567\pi\) | ||||
0.246964 | + | 0.969025i | \(0.420567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 159.437 | + | 276.153i | 0.0466177 | + | 0.0807442i | 0.888393 | − | 0.459084i | \(-0.151822\pi\) |
−0.841775 | + | 0.539829i | \(0.818489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1268.05 | + | 2196.33i | −0.365918 | + | 0.633789i | −0.988923 | − | 0.148429i | \(-0.952578\pi\) |
0.623005 | + | 0.782218i | \(0.285912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1166.41 | − | 2020.28i | 0.327957 | − | 0.568038i | −0.654150 | − | 0.756365i | \(-0.726973\pi\) |
0.982106 | + | 0.188328i | \(0.0603067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4603.43 | + | 7973.37i | 1.27785 | + | 2.21330i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2713.85 | −0.734495 | −0.367248 | − | 0.930123i | \(-0.619700\pi\) | ||||
−0.367248 | + | 0.930123i | \(0.619700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2087.29 | + | 3615.30i | 0.557902 | + | 0.966315i | 0.997671 | + | 0.0682042i | \(0.0217269\pi\) |
−0.439769 | + | 0.898111i | \(0.644940\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5769.55 | − | 2999.36i | −1.50450 | − | 0.782130i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 387.786 | − | 671.666i | 0.0998958 | − | 0.173025i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6123.58 | −1.53991 | −0.769954 | − | 0.638099i | \(-0.779721\pi\) | ||||
−0.769954 | + | 0.638099i | \(0.779721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4074.11 | −1.01240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2316.96 | − | 4013.09i | 0.562365 | − | 0.974045i | −0.434925 | − | 0.900467i | \(-0.643225\pi\) |
0.997289 | − | 0.0735777i | \(-0.0234417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1276.04 | − | 4373.38i | −0.306137 | − | 1.04922i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1641.61 | + | 2843.36i | 0.384891 | + | 0.666650i | 0.991754 | − | 0.128156i | \(-0.0409058\pi\) |
−0.606863 | + | 0.794806i | \(0.707572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7176.69 | −1.66362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −399.493 | − | 691.942i | −0.0905483 | − | 0.156834i | 0.817194 | − | 0.576363i | \(-0.195529\pi\) |
−0.907742 | + | 0.419529i | \(0.862195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3353.04 | − | 5807.63i | 0.751596 | − | 1.30180i | −0.195453 | − | 0.980713i | \(-0.562618\pi\) |
0.947049 | − | 0.321089i | \(-0.104049\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6414.63 | − | 11110.5i | 1.40661 | − | 2.43631i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −581.135 | − | 1006.56i | −0.126054 | − | 0.218332i | 0.796090 | − | 0.605178i | \(-0.206898\pi\) |
−0.922145 | + | 0.386845i | \(0.873565\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2718.17 | −0.577055 | −0.288527 | − | 0.957472i | \(-0.593166\pi\) | ||||
−0.288527 | + | 0.957472i | \(0.593166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1504.74 | + | 2606.29i | 0.316069 | + | 0.547448i | 0.979664 | − | 0.200644i | \(-0.0643035\pi\) |
−0.663595 | + | 0.748092i | \(0.730970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3055.54 | + | 3193.63i | −0.628441 | + | 0.656844i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5039.17 | + | 8728.09i | −1.02568 | + | 1.77653i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4209.15 | −0.839252 | −0.419626 | − | 0.907697i | \(-0.637839\pi\) | ||||
−0.419626 | + | 0.907697i | \(0.637839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3465.21 | −0.683907 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2308.26 | + | 3998.02i | −0.446454 | + | 0.773282i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1190.34 | + | 1244.14i | −0.227941 | + | 0.238243i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3758.14 | + | 6509.29i | 0.705543 | + | 1.22204i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3114.82 | −0.579063 | −0.289531 | − | 0.957169i | \(-0.593499\pi\) | ||||
−0.289531 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4243.62 | − | 7350.16i | −0.773741 | − | 1.34016i | −0.935499 | − | 0.353329i | \(-0.885050\pi\) |
0.161758 | − | 0.986831i | \(-0.448284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2477.46 | − | 4291.08i | 0.447393 | − | 0.774908i | −0.550822 | − | 0.834623i | \(-0.685686\pi\) |
0.998215 | + | 0.0597148i | \(0.0190191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2804.40 | + | 4857.36i | −0.496879 | + | 0.860619i | −0.999994 | − | 0.00360042i | \(-0.998854\pi\) |
0.503115 | + | 0.864220i | \(0.332187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6364.43 | + | 11023.5i | 1.11705 | + | 1.93479i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1531.19 | 0.263770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7268.63 | − | 12589.6i | −1.24059 | − | 2.14876i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2519.26 | + | 8634.24i | 0.422162 | + | 1.44687i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3304.75 | − | 5723.99i | 0.548777 | − | 0.950510i | −0.449582 | − | 0.893239i | \(-0.648427\pi\) |
0.998359 | − | 0.0572706i | \(-0.0182398\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4952.57 | 0.807725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11455.5 | 1.85170 | 0.925850 | − | 0.377891i | \(-0.123350\pi\) | ||||
0.925850 | + | 0.377891i | \(0.123350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 283.717 | − | 491.413i | 0.0450562 | − | 0.0780395i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4779.52 | − | 4184.47i | −0.752390 | − | 0.658718i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3022.08 | − | 5234.39i | −0.467532 | − | 0.809789i | 0.531780 | − | 0.846883i | \(-0.321523\pi\) |
−0.999312 | + | 0.0370937i | \(0.988190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5487.93 | −0.841726 | −0.420863 | − | 0.907124i | \(-0.638273\pi\) | ||||
−0.420863 | + | 0.907124i | \(0.638273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3440.08 | + | 5958.39i | 0.518688 | + | 0.898394i | 0.999764 | + | 0.0217151i | \(0.00691268\pi\) |
−0.481076 | + | 0.876679i | \(0.659754\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8289.61 | − | 14358.0i | 1.23934 | − | 2.14660i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1969.17 | + | 3410.70i | −0.289495 | + | 0.501420i | −0.973689 | − | 0.227880i | \(-0.926821\pi\) |
0.684194 | + | 0.729300i | \(0.260154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3351.30 | + | 5804.63i | 0.488599 | + | 0.846279i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2889.32 | −0.414340 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −719.814 | − | 1246.75i | −0.102381 | − | 0.177330i | 0.810284 | − | 0.586038i | \(-0.199313\pi\) |
−0.912665 | + | 0.408708i | \(0.865980\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6810.52 | − | 1664.51i | −0.953058 | − | 0.232931i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1247.05 | − | 2159.96i | 0.173110 | − | 0.299835i | −0.766396 | − | 0.642369i | \(-0.777952\pi\) |
0.939506 | + | 0.342534i | \(0.111285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14423.5 | 1.97042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1309.25 | −0.177445 | −0.0887225 | − | 0.996056i | \(-0.528278\pi\) | ||||
−0.0887225 | + | 0.996056i | \(0.528278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3480.90 | − | 6029.10i | 0.464402 | − | 0.804367i | −0.534773 | − | 0.844996i | \(-0.679603\pi\) |
0.999174 | + | 0.0406289i | \(0.0129361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13284.5 | − | 13884.9i | 1.75855 | − | 1.83803i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3176.72 | + | 5502.25i | 0.414052 | + | 0.717159i | 0.995328 | − | 0.0965470i | \(-0.0307798\pi\) |
−0.581276 | + | 0.813706i | \(0.697446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9114.25 | −1.17884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5434.86 | + | 9413.45i | 0.692297 | + | 1.19909i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5752.70 | + | 9963.97i | −0.727254 | + | 1.25964i | 0.230785 | + | 0.973005i | \(0.425871\pi\) |
−0.958039 | + | 0.286637i | \(0.907463\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 826.664 | − | 1431.82i | 0.102947 | − | 0.178309i | −0.809951 | − | 0.586498i | \(-0.800506\pi\) |
0.912897 | + | 0.408189i | \(0.133840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −321.489 | − | 556.836i | −0.0397383 | − | 0.0688287i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13463.0 | 1.63965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2447.41 | + | 4239.04i | 0.295885 | + | 0.512487i | 0.975190 | − | 0.221368i | \(-0.0710523\pi\) |
−0.679306 | + | 0.733855i | \(0.737719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3288.41 | − | 803.699i | −0.391797 | − | 0.0957566i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3011.99 | + | 5216.92i | −0.356272 | + | 0.617081i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 265.504 | 0.0309563 | 0.0154782 | − | 0.999880i | \(-0.495073\pi\) | ||||
0.0154782 | + | 0.999880i | \(0.495073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11136.8 | 1.28925 | 0.644623 | − | 0.764500i | \(-0.277014\pi\) | ||||
0.644623 | + | 0.764500i | \(0.277014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14350.3 | − | 24855.4i | 1.63786 | − | 2.83685i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2056.67 | + | 7048.81i | 0.233089 | + | 0.798866i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2596.71 | + | 4497.63i | 0.290206 | + | 0.502652i | 0.973858 | − | 0.227156i | \(-0.0729427\pi\) |
−0.683652 | + | 0.729808i | \(0.739609\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6314.17 | 0.700785 | 0.350392 | − | 0.936603i | \(-0.386048\pi\) | ||||
0.350392 | + | 0.936603i | \(0.386048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 465.458 | + | 806.198i | 0.0509517 | + | 0.0882509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7711.66 | − | 13357.0i | 0.838399 | − | 1.45215i | −0.0528329 | − | 0.998603i | \(-0.516825\pi\) |
0.891232 | − | 0.453547i | \(-0.149842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4353.06 | + | 7539.72i | −0.466862 | + | 0.808629i | −0.999283 | − | 0.0378504i | \(-0.987949\pi\) |
0.532421 | + | 0.846480i | \(0.321282\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 900.657 | + | 1559.98i | 0.0959444 | + | 0.166181i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5495.91 | −0.577657 | −0.288829 | − | 0.957381i | \(-0.593266\pi\) | ||||
−0.288829 | + | 0.957381i | \(0.593266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6530.83 | − | 11311.7i | −0.681873 | − | 1.18104i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6099.02 | − | 20903.1i | −0.628409 | − | 2.15375i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5678.63 | − | 9835.67i | 0.581258 | − | 1.00677i | −0.414072 | − | 0.910244i | \(-0.635894\pi\) |
0.995331 | − | 0.0965247i | \(-0.0307727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14514.2 | −1.46637 | −0.733184 | − | 0.680030i | \(-0.761967\pi\) | ||||
−0.733184 | + | 0.680030i | \(0.761967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9971.00 | 1.00085 | 0.500423 | − | 0.865781i | \(-0.333178\pi\) | ||||
0.500423 | + | 0.865781i | \(0.333178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −198.739 | + | 344.226i | −0.0196928 | + | 0.0341089i | −0.875704 | − | 0.482849i | \(-0.839602\pi\) |
0.856011 | + | 0.516957i | \(0.172935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4699.88 | + | 1148.67i | 0.462730 | + | 0.113093i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2544.21 | − | 4406.70i | −0.247321 | − | 0.428373i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2931.43 | −0.283165 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7030.20 | − | 12176.7i | −0.670602 | − | 1.16152i | −0.977734 | − | 0.209849i | \(-0.932703\pi\) |
0.307132 | − | 0.951667i | \(-0.400631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7627.71 | − | 13211.6i | 0.723064 | − | 1.25238i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15249.6 | + | 26413.1i | −1.42773 | + | 2.47290i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6767.34 | + | 11721.4i | 0.629687 | + | 1.09065i | 0.987614 | + | 0.156900i | \(0.0501502\pi\) |
−0.357927 | + | 0.933749i | \(0.616516\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8693.29 | 0.799028 | 0.399514 | − | 0.916727i | \(-0.369179\pi\) | ||||
0.399514 | + | 0.916727i | \(0.369179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14238.0 | + | 24660.9i | 1.30070 | + | 2.25288i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11196.8 | − | 11702.8i | 1.01055 | − | 1.05622i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2008.97 | + | 3479.63i | −0.180228 | + | 0.312164i | −0.941958 | − | 0.335731i | \(-0.891017\pi\) |
0.761730 | + | 0.647894i | \(0.224350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −52.2455 | −0.00463124 | −0.00231562 | − | 0.999997i | \(-0.500737\pi\) | ||||
−0.00231562 | + | 0.999997i | \(0.500737\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14844.9 | −1.30810 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4619.55 | − | 8001.30i | 0.402275 | − | 0.696761i | −0.591725 | − | 0.806140i | \(-0.701553\pi\) |
0.994000 | + | 0.109379i | \(0.0348862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2741.90 | − | 670.131i | −0.237367 | − | 0.0580134i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14120.0 | − | 24456.6i | −1.20816 | − | 2.09259i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26579.7 | −2.26107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7486.70 | + | 12967.3i | 0.629555 | + | 1.09042i | 0.987641 | + | 0.156733i | \(0.0500961\pi\) |
−0.358086 | + | 0.933689i | \(0.616571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6801.76 | + | 11781.0i | −0.568681 | + | 0.984985i | 0.428015 | + | 0.903771i | \(0.359213\pi\) |
−0.996697 | + | 0.0812134i | \(0.974120\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 634.708 | − | 1099.35i | 0.0524636 | − | 0.0908696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3312.91 | + | 5738.13i | 0.272287 | + | 0.471614i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14800.6 | −1.20279 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6756.35 | − | 11702.3i | −0.545986 | − | 0.945675i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15827.1 | − | 10095.4i | 1.26479 | − | 0.806749i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8443.19 | − | 14624.0i | 0.670981 | − | 1.16217i | −0.306645 | − | 0.951824i | \(-0.599206\pi\) |
0.977626 | − | 0.210350i | \(-0.0674603\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19751.4 | −1.55240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5987.25 | −0.468001 | −0.234000 | − | 0.972237i | \(-0.575182\pi\) | ||||
−0.234000 | + | 0.972237i | \(0.575182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1454.25 | − | 2518.83i | 0.112437 | − | 0.194747i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2974.26 | + | 10193.7i | 0.228713 | + | 0.783869i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1119.35 | + | 1938.78i | 0.0851499 | + | 0.147484i | 0.905455 | − | 0.424442i | \(-0.139530\pi\) |
−0.820305 | + | 0.571926i | \(0.806196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5765.86 | −0.436261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4226.42 | + | 7320.38i | 0.316381 | + | 0.547988i | 0.979730 | − | 0.200322i | \(-0.0641989\pi\) |
−0.663349 | + | 0.748310i | \(0.730866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3337.49 | + | 5780.70i | −0.248512 | + | 0.430435i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7476.78 | − | 12950.2i | 0.550866 | − | 0.954128i | −0.447346 | − | 0.894361i | \(-0.647631\pi\) |
0.998212 | − | 0.0597671i | \(-0.0190358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8010.92 | − | 13875.3i | −0.587122 | − | 1.01693i | −0.994607 | − | 0.103713i | \(-0.966928\pi\) |
0.407485 | − | 0.913212i | \(-0.366406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17449.0 | 1.26552 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8056.54 | + | 13954.3i | 0.581279 | + | 1.00681i | 0.995328 | + | 0.0965505i | \(0.0307809\pi\) |
−0.414049 | + | 0.910255i | \(0.635886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4068.29 | + | 4252.16i | −0.290501 | + | 0.303630i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10359.4 | − | 17942.9i | 0.735919 | − | 1.27465i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9552.04 | 0.671644 | 0.335822 | − | 0.941925i | \(-0.390986\pi\) | ||||
0.335822 | + | 0.941925i | \(0.390986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −129.656 | −0.00907028 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12083.9 | + | 20929.9i | −0.836807 | + | 1.44939i | 0.0557443 | + | 0.998445i | \(0.482247\pi\) |
−0.892551 | + | 0.450947i | \(0.851087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29719.0 | − | 31062.2i | 2.04766 | − | 2.14021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 410.665 | + | 711.293i | 0.0280122 | + | 0.0485186i | 0.879692 | − | 0.475544i | \(-0.157749\pi\) |
−0.851679 | + | 0.524063i | \(0.824416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14674.7 | −0.995996 | −0.497998 | − | 0.867178i | \(-0.665931\pi\) | ||||
−0.497998 | + | 0.867178i | \(0.665931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15777.4 | + | 27327.3i | 1.06024 | + | 1.83639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2541.56 | + | 4402.11i | −0.169949 | + | 0.294359i | −0.938402 | − | 0.345547i | \(-0.887693\pi\) |
0.768453 | + | 0.639906i | \(0.221027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15059.2 | + | 26083.3i | −0.997102 | + | 1.72703i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11101.0 | + | 19227.5i | 0.731428 | + | 1.26687i | 0.956273 | + | 0.292476i | \(0.0944792\pi\) |
−0.224845 | + | 0.974395i | \(0.572187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14990.6 | 0.978121 | 0.489060 | − | 0.872250i | \(-0.337340\pi\) | ||||
0.489060 | + | 0.872250i | \(0.337340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1536.51 | − | 2661.32i | −0.0997700 | − | 0.172807i | 0.811819 | − | 0.583909i | \(-0.198477\pi\) |
−0.911589 | + | 0.411102i | \(0.865144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 492.891 | + | 1689.28i | 0.0316970 | + | 0.108635i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5010.29 | + | 8678.08i | −0.320659 | + | 0.555397i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30118.4 | 1.90922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26012.7 | 1.64113 | 0.820563 | − | 0.571556i | \(-0.193660\pi\) | ||||
0.820563 | + | 0.571556i | \(0.193660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10367.5 | + | 17957.0i | −0.647905 | + | 1.12220i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −939.691 | − | 21251.2i | −0.0584488 | − | 1.32182i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4016.12 | + | 6956.12i | 0.247468 | + | 0.428627i | 0.962823 | − | 0.270134i | \(-0.0870681\pi\) |
−0.715355 | + | 0.698762i | \(0.753735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24887.7 | −1.52640 | −0.763200 | − | 0.646162i | \(-0.776373\pi\) | ||||
−0.763200 | + | 0.646162i | \(0.776373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10542.2 | − | 18259.6i | −0.640580 | − | 1.10952i | −0.985303 | − | 0.170813i | \(-0.945360\pi\) |
0.344723 | − | 0.938704i | \(-0.387973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5001.95 | − | 8663.62i | 0.302532 | − | 0.524002i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6583.16 | − | 11402.4i | 0.394516 | − | 0.683322i | −0.598523 | − | 0.801106i | \(-0.704246\pi\) |
0.993039 | + | 0.117783i | \(0.0375788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20535.1 | + | 35567.8i | 1.22499 | + | 2.12175i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13903.4 | 0.821851 | 0.410926 | − | 0.911669i | \(-0.365206\pi\) | ||||
0.410926 | + | 0.911669i | \(0.365206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3153.30 | − | 5461.68i | −0.185551 | − | 0.321384i | 0.758211 | − | 0.652009i | \(-0.226074\pi\) |
−0.943762 | + | 0.330625i | \(0.892740\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4265.32 | − | 1042.46i | −0.248725 | − | 0.0607892i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8656.23 | + | 14993.0i | −0.502505 | + | 0.870364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21699.1 | −1.24841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24407.6 | −1.39798 | −0.698992 | − | 0.715129i | \(-0.746368\pi\) | ||||
−0.698992 | + | 0.715129i | \(0.746368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15540.1 | + | 26916.3i | −0.882209 | + | 1.52803i | −0.0333299 | + | 0.999444i | \(0.510611\pi\) |
−0.848879 | + | 0.528587i | \(0.822722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20597.6 | + | 21528.5i | −1.16416 | + | 1.21677i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14379.7 | + | 24906.4i | 0.805601 | + | 1.39534i | 0.915885 | + | 0.401442i | \(0.131491\pi\) |
−0.110283 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37251.0 | −2.07779 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11738.5 | − | 20331.7i | −0.649061 | − | 1.12421i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12447.7 | + | 21560.1i | −0.685287 | + | 1.18695i | 0.288059 | + | 0.957613i | \(0.406990\pi\) |
−0.973346 | + | 0.229340i | \(0.926343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1298.40 | + | 2248.89i | −0.0708649 | + | 0.122742i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14610.2 | − | 25305.6i | −0.793976 | − | 1.37521i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1702.74 | 0.0917427 | 0.0458714 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458714 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1538.12 | − | 2664.11i | −0.0825198 | − | 0.142929i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14087.5 | − | 3443.04i | −0.749385 | − | 0.183153i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3261.60 | + | 5649.26i | −0.172767 | + | 0.299242i | −0.939386 | − | 0.342860i | \(-0.888604\pi\) |
0.766619 | + | 0.642102i | \(0.221938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 771.765 | 0.0405369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 64348.4 | 3.36572 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12627.2 | + | 21871.0i | −0.654959 | + | 1.13442i | 0.326945 | + | 0.945044i | \(0.393981\pi\) |
−0.981904 | + | 0.189379i | \(0.939352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7727.27 | − | 26483.7i | −0.399138 | − | 1.36797i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27258.2 | − | 47212.6i | −1.39634 | − | 2.41853i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27964.9 | −1.42663 | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700843i | \(0.752808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5691.69 | − | 9858.29i | −0.287982 | − | 0.498799i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4647.19 | − | 8049.17i | 0.234172 | − | 0.405597i | −0.724860 | − | 0.688896i | \(-0.758096\pi\) |
0.959032 | + | 0.283299i | \(0.0914288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7148.91 | + | 12382.3i | −0.357305 | + | 0.618870i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9145.60 | − | 15840.6i | −0.455245 | − | 0.788508i | 0.543457 | − | 0.839437i | \(-0.317115\pi\) |
−0.998702 | + | 0.0509292i | \(0.983782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14742.4 | −0.727921 | −0.363960 | − | 0.931414i | \(-0.618576\pi\) | ||||
−0.363960 | + | 0.931414i | \(0.618576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2655.12 | + | 4598.80i | 0.130572 | + | 0.226157i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3697.46 | − | 12672.3i | −0.180377 | − | 0.618204i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14231.7 | + | 24650.0i | −0.691507 | + | 1.19773i | 0.279837 | + | 0.960048i | \(0.409720\pi\) |
−0.971344 | + | 0.237678i | \(0.923614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41596.4 | −2.00510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20336.7 | −0.976422 | −0.488211 | − | 0.872726i | \(-0.662350\pi\) | ||||
−0.488211 | + | 0.872726i | \(0.662350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19790.8 | − | 34278.7i | 0.942728 | − | 1.63285i | 0.182489 | − | 0.983208i | \(-0.441585\pi\) |
0.760238 | − | 0.649644i | \(-0.225082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18743.6 | − | 4581.01i | −0.889337 | − | 0.217357i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5667.87 | − | 9817.04i | −0.266825 | − | 0.462155i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10580.3 | 0.496146 | 0.248073 | − | 0.968741i | \(-0.420203\pi\) | ||||
0.248073 | + | 0.968741i | \(0.420203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12961.1 | + | 22449.3i | 0.603077 | + | 1.04456i | 0.992352 | + | 0.123439i | \(0.0393923\pi\) |
−0.389275 | + | 0.921122i | \(0.627274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1215.13 | + | 2104.67i | −0.0563211 | + | 0.0975509i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1492.27 | + | 2584.68i | −0.0686341 | + | 0.118878i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23931.7 | + | 41450.9i | 1.09647 | + | 1.89914i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4186.27 | 0.190337 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8610.00 | − | 14913.0i | −0.389979 | − | 0.675463i | 0.602467 | − | 0.798143i | \(-0.294184\pi\) |
−0.992446 | + | 0.122680i | \(0.960851\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4507.94 | + | 4711.68i | −0.202635 | + | 0.211793i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12294.0 | + | 21293.8i | −0.550533 | + | 0.953551i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6275.52 | 0.278909 | 0.139454 | − | 0.990228i | \(-0.455465\pi\) | ||||
0.139454 | + | 0.990228i | \(0.455465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59461.9 | −2.63280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4170.66 | − | 7223.80i | 0.183287 | − | 0.317463i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25388.8 | + | 6205.12i | 1.11160 | + | 0.271679i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2302.01 | − | 3987.20i | −0.100043 | − | 0.173279i | 0.811659 | − | 0.584131i | \(-0.198565\pi\) |
−0.911702 | + | 0.410852i | \(0.865231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5104.36 | 0.221009 | 0.110505 | − | 0.993876i | \(-0.464753\pi\) | ||||
0.110505 | + | 0.993876i | \(0.464753\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13999.2 | + | 24247.3i | 0.601682 | + | 1.04214i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −581.341 | + | 1006.91i | −0.0248942 | + | 0.0431180i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22817.7 | + | 39521.4i | −0.969967 | + | 1.68003i | −0.274334 | + | 0.961634i | \(0.588458\pi\) |
−0.695633 | + | 0.718398i | \(0.744876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19688.6 | + | 34101.6i | 0.833901 | + | 1.44436i | 0.894922 | + | 0.446222i | \(0.147231\pi\) |
−0.0610219 | + | 0.998136i | \(0.519436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30916.3 | 1.29996 | 0.649978 | − | 0.759953i | \(-0.274778\pi\) | ||||
0.649978 | + | 0.759953i | \(0.274778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1271.66 | + | 2202.59i | 0.0532771 | + | 0.0922786i | 0.891434 | − | 0.453151i | \(-0.149700\pi\) |
−0.838157 | + | 0.545429i | \(0.816367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35407.0 | − | 22584.5i | 1.47273 | − | 0.939382i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20831.6 | + | 36081.5i | −0.863364 | + | 1.49539i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7930.82 | 0.326343 | 0.163172 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163172 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29700.8 | 1.21780 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15632.3 | − | 27075.9i | 0.636410 | − | 1.10229i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8634.31 | + | 29592.3i | 0.350270 | + | 1.20048i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9155.51 | + | 15857.8i | 0.368798 | + | 0.638776i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41983.2 | 1.68520 | 0.842601 | − | 0.538538i | \(-0.181023\pi\) | ||||
0.842601 | + | 0.538538i | \(0.181023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5927.16 | − | 10266.1i | −0.236252 | − | 0.409200i | 0.723384 | − | 0.690446i | \(-0.242586\pi\) |
−0.959636 | + | 0.281246i | \(0.909252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4056.94 | − | 7026.83i | 0.161142 | − | 0.279106i | −0.774136 | − | 0.633019i | \(-0.781816\pi\) |
0.935279 | + | 0.353912i | \(0.115149\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22908.5 | − | 39678.7i | 0.903609 | − | 1.56510i | 0.0808353 | − | 0.996727i | \(-0.474241\pi\) |
0.822774 | − | 0.568369i | \(-0.192425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19826.3 | − | 34340.2i | −0.779325 | − | 1.34983i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31380.3 | −1.22498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8100.67 | + | 14030.8i | 0.315133 | + | 0.545826i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26555.7 | + | 27755.9i | −1.02599 | + | 1.07236i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15906.5 | + | 27550.9i | −0.612456 | + | 1.06081i | 0.378369 | + | 0.925655i | \(0.376485\pi\) |
−0.990825 | + | 0.135150i | \(0.956848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43551.6 | −1.66548 | −0.832742 | − | 0.553661i | \(-0.813230\pi\) | ||||
−0.832742 | + | 0.553661i | \(0.813230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40645.1 | 1.54906 | 0.774528 | − | 0.632540i | \(-0.217988\pi\) | ||||
0.774528 | + | 0.632540i | \(0.217988\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17014.1 | − | 29469.3i | 0.644056 | − | 1.11554i | −0.340462 | − | 0.940258i | \(-0.610584\pi\) |
0.984519 | − | 0.175280i | \(-0.0560831\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14003.3 | + | 14636.2i | −0.528297 | + | 0.552173i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3036.67 | + | 5259.68i | 0.113794 | + | 0.197098i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44258.2 | 1.65295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1205.62 | − | 2088.20i | −0.0447272 | − | 0.0774699i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23175.1 | − | 40140.4i | 0.856908 | − | 1.48421i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16667.9 | − | 28869.7i | 0.612221 | − | 1.06040i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25402.4 | − | 43998.2i | −0.929958 | − | 1.61073i | −0.783387 | − | 0.621534i | \(-0.786510\pi\) |
−0.146571 | − | 0.989200i | \(-0.546824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28738.3 | −1.04516 | −0.522582 | − | 0.852589i | \(-0.675031\pi\) | ||||
−0.522582 | + | 0.852589i | \(0.675031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8695.46 | − | 15061.0i | −0.315200 | − | 0.545943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11237.9 | + | 38515.8i | 0.404700 | + | 1.38703i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27371.1 | − | 47408.2i | 0.982470 | − | 1.70169i | 0.329790 | − | 0.944054i | \(-0.393022\pi\) |
0.652680 | − | 0.757634i | \(-0.273645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54235.5 | 1.93411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57660.9 | −2.04960 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21887.9 | − | 37911.0i | 0.773002 | − | 1.33888i | −0.162908 | − | 0.986641i | \(-0.552088\pi\) |
0.935911 | − | 0.352238i | \(-0.114579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3805.91 | − | 1978.54i | −0.133978 | − | 0.0696499i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63520.6 | + | 110021.i | 2.22176 | + | 3.84820i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35090.9 | 1.22345 | 0.611724 | − | 0.791071i | \(-0.290476\pi\) | ||||
0.611724 | + | 0.791071i | \(0.290476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15892.4 | − | 27526.4i | −0.550560 | − | 0.953599i | −0.998234 | − | 0.0594016i | \(-0.981081\pi\) |
0.447674 | − | 0.894197i | \(-0.352253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8882.54 | − | 15385.0i | 0.306740 | − | 0.531288i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28250.4 | − | 48931.2i | 0.969394 | − | 1.67904i | 0.272079 | − | 0.962275i | \(-0.412289\pi\) |
0.697315 | − | 0.716765i | \(-0.254378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4725.92 | − | 8185.53i | −0.161654 | − | 0.279993i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36669.1 | −1.24641 | −0.623204 | − | 0.782059i | \(-0.714169\pi\) | ||||
−0.623204 | + | 0.782059i | \(0.714169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35078.8 | + | 60758.2i | 1.18861 | + | 2.05873i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35350.4 | − | 8639.76i | −1.19033 | − | 0.290920i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14841.8 | − | 25706.7i | 0.498196 | − | 0.862901i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51346.8 | −1.71286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12012.4 | −0.399474 | −0.199737 | − | 0.979850i | \(-0.564009\pi\) | ||||
−0.199737 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18648.1 | + | 32299.5i | −0.616320 | + | 1.06750i | 0.373832 | + | 0.927497i | \(0.378044\pi\) |
−0.990151 | + | 0.140000i | \(0.955290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1753.75 | + | 1833.01i | −0.0577826 | + | 0.0603942i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4894.22 | + | 8477.04i | 0.160266 | + | 0.277589i | 0.934964 | − | 0.354742i | \(-0.115431\pi\) |
−0.774698 | + | 0.632331i | \(0.782098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5200.30 | −0.169767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2310.20 | − | 4001.39i | −0.0749583 | − | 0.129832i | 0.826110 | − | 0.563509i | \(-0.190549\pi\) |
−0.901068 | + | 0.433678i | \(0.857216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1523.15 | − | 2638.17i | 0.0492705 | − | 0.0853390i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3460.37 | − | 5993.53i | 0.111257 | − | 0.192703i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20182.7 | − | 34957.4i | −0.646946 | − | 1.12054i | −0.983848 | − | 0.179004i | \(-0.942713\pi\) |
0.336903 | − | 0.941540i | \(-0.390621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39167.1 | 1.24792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1497.18 | + | 2593.19i | 0.0475587 | + | 0.0823742i | 0.888825 | − | 0.458247i | \(-0.151523\pi\) |
−0.841266 | + | 0.540621i | \(0.818189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.4.s.j.289.4 | 8 | ||
3.2 | odd | 2 | 168.4.q.f.121.1 | yes | 8 | ||
7.4 | even | 3 | inner | 504.4.s.j.361.4 | 8 | ||
12.11 | even | 2 | 336.4.q.m.289.1 | 8 | |||
21.2 | odd | 6 | 1176.4.a.bd.1.4 | 4 | |||
21.5 | even | 6 | 1176.4.a.ba.1.1 | 4 | |||
21.11 | odd | 6 | 168.4.q.f.25.1 | ✓ | 8 | ||
84.11 | even | 6 | 336.4.q.m.193.1 | 8 | |||
84.23 | even | 6 | 2352.4.a.cm.1.4 | 4 | |||
84.47 | odd | 6 | 2352.4.a.cp.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.1 | ✓ | 8 | 21.11 | odd | 6 | ||
168.4.q.f.121.1 | yes | 8 | 3.2 | odd | 2 | ||
336.4.q.m.193.1 | 8 | 84.11 | even | 6 | |||
336.4.q.m.289.1 | 8 | 12.11 | even | 2 | |||
504.4.s.j.289.4 | 8 | 1.1 | even | 1 | trivial | ||
504.4.s.j.361.4 | 8 | 7.4 | even | 3 | inner | ||
1176.4.a.ba.1.1 | 4 | 21.5 | even | 6 | |||
1176.4.a.bd.1.4 | 4 | 21.2 | odd | 6 | |||
2352.4.a.cm.1.4 | 4 | 84.23 | even | 6 | |||
2352.4.a.cp.1.1 | 4 | 84.47 | odd | 6 |