Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(37,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bb (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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} + \cdots + 1370 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2773.3 | ||
Root | \(0.344446 - 1.84020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.2773 |
Dual form | 3420.2.bb.d.37.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.311108 | − | 2.21432i | −0.139132 | − | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.311108 | − | 0.311108i | 0.117588 | − | 0.117588i | −0.645864 | − | 0.763452i | \(-0.723503\pi\) |
0.763452 | + | 0.645864i | \(0.223503\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.90321 | −0.875351 | −0.437676 | − | 0.899133i | \(-0.644198\pi\) | ||||
−0.437676 | + | 0.899133i | \(0.644198\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.84674 | + | 2.84674i | −0.789544 | + | 0.789544i | −0.981419 | − | 0.191875i | \(-0.938543\pi\) |
0.191875 | + | 0.981419i | \(0.438543\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.52543 | − | 2.52543i | 0.612506 | − | 0.612506i | −0.331092 | − | 0.943598i | \(-0.607417\pi\) |
0.943598 | + | 0.331092i | \(0.107417\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34250 | − | 0.377784i | −0.996237 | − | 0.0866697i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.11753 | + | 4.11753i | 0.858565 | + | 0.858565i | 0.991169 | − | 0.132604i | \(-0.0423340\pi\) |
−0.132604 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | + | 1.37778i | −0.961285 | + | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.99151 | −0.555510 | −0.277755 | − | 0.960652i | \(-0.589590\pi\) | ||||
−0.277755 | + | 0.960652i | \(0.589590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.930683i | 0.167156i | 0.996501 | + | 0.0835778i | \(0.0266347\pi\) | ||||
−0.996501 | + | 0.0835778i | \(0.973365\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.785680 | − | 0.592104i | −0.132804 | − | 0.100084i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.11992 | + | 8.11992i | 1.33491 | + | 1.33491i | 0.900919 | + | 0.433988i | \(0.142894\pi\) |
0.433988 | + | 0.900919i | \(0.357106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.06083i | 0.321847i | 0.986967 | + | 0.160924i | \(0.0514473\pi\) | ||||
−0.986967 | + | 0.160924i | \(0.948553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.11753 | + | 2.11753i | 0.322921 | + | 0.322921i | 0.849886 | − | 0.526966i | \(-0.176670\pi\) |
−0.526966 | + | 0.849886i | \(0.676670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.73975 | − | 2.73975i | 0.399633 | − | 0.399633i | −0.478470 | − | 0.878104i | \(-0.658809\pi\) |
0.878104 | + | 0.478470i | \(0.158809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.80642i | 0.972346i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.565073 | − | 0.565073i | 0.0776188 | − | 0.0776188i | −0.667232 | − | 0.744850i | \(-0.732521\pi\) |
0.744850 | + | 0.667232i | \(0.232521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.903212 | + | 6.42864i | 0.121789 | + | 0.866838i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.32613 | −1.21416 | −0.607080 | − | 0.794641i | \(-0.707659\pi\) | ||||
−0.607080 | + | 0.794641i | \(0.707659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.52543 | 0.451385 | 0.225692 | − | 0.974199i | \(-0.427536\pi\) | ||||
0.225692 | + | 0.974199i | \(0.427536\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.18924 | + | 5.41795i | 0.891715 | + | 0.672014i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.144771 | − | 0.144771i | −0.0176866 | − | 0.0176866i | 0.698208 | − | 0.715895i | \(-0.253981\pi\) |
−0.715895 | + | 0.698208i | \(0.753981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.61568i | 1.14117i | 0.821238 | + | 0.570585i | \(0.193284\pi\) | ||||
−0.821238 | + | 0.570585i | \(0.806716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.09679 | − | 4.09679i | −0.479493 | − | 0.479493i | 0.425477 | − | 0.904969i | \(-0.360106\pi\) |
−0.904969 | + | 0.425477i | \(0.860106\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.903212 | + | 0.903212i | −0.102931 | + | 0.102931i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6072 | 1.41842 | 0.709210 | − | 0.704998i | \(-0.249052\pi\) | ||||
0.709210 | + | 0.704998i | \(0.249052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.21432 | − | 9.21432i | −1.01140 | − | 1.01140i | −0.999934 | − | 0.0114688i | \(-0.996349\pi\) |
−0.0114688 | − | 0.999934i | \(-0.503651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.37778 | − | 4.80642i | −0.691768 | − | 0.521330i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.55485 | 0.800812 | 0.400406 | − | 0.916338i | \(-0.368869\pi\) | ||||
0.400406 | + | 0.916338i | \(0.368869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.77129i | 0.185681i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.514449 | + | 9.73321i | 0.0527814 | + | 0.998606i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0421 | + | 12.0421i | 1.22269 | + | 1.22269i | 0.966671 | + | 0.256020i | \(0.0824113\pi\) |
0.256020 | + | 0.966671i | \(0.417589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.76986 | 0.872634 | 0.436317 | − | 0.899793i | \(-0.356283\pi\) | ||||
0.436317 | + | 0.899793i | \(0.356283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.54022 | + | 8.54022i | −0.841493 | + | 0.841493i | −0.989053 | − | 0.147560i | \(-0.952858\pi\) |
0.147560 | + | 0.989053i | \(0.452858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.77742 | − | 3.77742i | −0.365177 | − | 0.365177i | 0.500538 | − | 0.865715i | \(-0.333136\pi\) |
−0.865715 | + | 0.500538i | \(0.833136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7373 | 1.31580 | 0.657899 | − | 0.753106i | \(-0.271445\pi\) | ||||
0.657899 | + | 0.753106i | \(0.271445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.91606 | + | 1.91606i | −0.180248 | + | 0.180248i | −0.791464 | − | 0.611216i | \(-0.790681\pi\) |
0.611216 | + | 0.791464i | \(0.290681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.83654 | − | 10.3985i | 0.730761 | − | 0.969668i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.57136i | − | 0.144046i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57136 | −0.233760 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.54617 | + | 10.2143i | 0.406622 | + | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.12841 | − | 5.12841i | −0.455073 | − | 0.455073i | 0.441961 | − | 0.897034i | \(-0.354283\pi\) |
−0.897034 | + | 0.441961i | \(0.854283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3684 | 0.905893 | 0.452946 | − | 0.891538i | \(-0.350373\pi\) | ||||
0.452946 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.46852 | + | 1.23345i | −0.127337 | + | 0.106954i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.99063 | + | 7.99063i | −0.682686 | + | 0.682686i | −0.960605 | − | 0.277919i | \(-0.910355\pi\) |
0.277919 | + | 0.960605i | \(0.410355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1891i | 0.864231i | 0.901818 | + | 0.432115i | \(0.142233\pi\) | ||||
−0.901818 | + | 0.432115i | \(0.857767\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.26469 | − | 8.26469i | 0.691128 | − | 0.691128i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.930683 | + | 6.62416i | 0.0772890 | + | 0.550107i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.0874i | − | 1.48178i | −0.671627 | − | 0.740890i | \(-0.734404\pi\) | ||
0.671627 | − | 0.740890i | \(-0.265596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5379i | 1.10170i | 0.834605 | + | 0.550848i | \(0.185696\pi\) | ||||
−0.834605 | + | 0.550848i | \(0.814304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.06083 | − | 0.289543i | 0.165530 | − | 0.0232566i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1891 | − | 15.1891i | 1.21222 | − | 1.21222i | 0.241931 | − | 0.970293i | \(-0.422219\pi\) |
0.970293 | − | 0.241931i | \(-0.0777808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56199 | 0.201913 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.44938 | + | 5.44938i | 0.426829 | + | 0.426829i | 0.887547 | − | 0.460718i | \(-0.152408\pi\) |
−0.460718 | + | 0.887547i | \(0.652408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.42644 | + | 2.42644i | 0.187763 | + | 0.187763i | 0.794729 | − | 0.606965i | \(-0.207613\pi\) |
−0.606965 | + | 0.794729i | \(0.707613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.20787i | − | 0.246759i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.83825 | + | 5.83825i | −0.443874 | + | 0.443874i | −0.893312 | − | 0.449438i | \(-0.851624\pi\) |
0.449438 | + | 0.893312i | \(0.351624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.06668 | + | 1.92396i | −0.0806332 | + | 0.145437i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4516 | 1.52862 | 0.764311 | − | 0.644847i | \(-0.223079\pi\) | ||||
0.764311 | + | 0.644847i | \(0.223079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.9660i | − | 0.889429i | −0.895672 | − | 0.444715i | \(-0.853305\pi\) | ||
0.895672 | − | 0.444715i | \(-0.146695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.4539 | − | 20.5063i | 1.13620 | − | 1.50765i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.33185 | + | 7.33185i | −0.536158 | + | 0.536158i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0923 | −1.67090 | −0.835452 | − | 0.549564i | \(-0.814794\pi\) | ||||
−0.835452 | + | 0.549564i | \(0.814794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.42644 | + | 2.42644i | −0.174659 | + | 0.174659i | −0.789023 | − | 0.614364i | \(-0.789413\pi\) |
0.614364 | + | 0.789023i | \(0.289413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0874 | + | 13.0874i | −0.932440 | + | 0.932440i | −0.997858 | − | 0.0654179i | \(-0.979162\pi\) |
0.0654179 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.2953i | − | 0.729814i | −0.931044 | − | 0.364907i | \(-0.881101\pi\) | ||
0.931044 | − | 0.364907i | \(-0.118899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.930683 | + | 0.930683i | −0.0653211 | + | 0.0653211i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.56334 | − | 0.641140i | 0.318717 | − | 0.0447792i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6072 | + | 1.09679i | 0.872057 | + | 0.0758664i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9576i | 1.02972i | 0.857274 | + | 0.514860i | \(0.172156\pi\) | ||||
−0.857274 | + | 0.514860i | \(0.827844\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.03011 | − | 5.34767i | 0.274851 | − | 0.364708i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.289543 | + | 0.289543i | 0.0196554 | + | 0.0196554i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3785i | 0.967201i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.55659 | + | 3.55659i | −0.238167 | + | 0.238167i | −0.816091 | − | 0.577924i | \(-0.803863\pi\) |
0.577924 | + | 0.816091i | \(0.303863\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.83825 | − | 5.83825i | −0.387498 | − | 0.387498i | 0.486296 | − | 0.873794i | \(-0.338348\pi\) |
−0.873794 | + | 0.486296i | \(0.838348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5763i | 0.831064i | 0.909579 | + | 0.415532i | \(0.136405\pi\) | ||||
−0.909579 | + | 0.415532i | \(0.863595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.74620 | + | 8.74620i | 0.572983 | + | 0.572983i | 0.932961 | − | 0.359978i | \(-0.117216\pi\) |
−0.359978 | + | 0.932961i | \(0.617216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.91903 | − | 5.21432i | −0.451348 | − | 0.340145i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0923i | 1.10561i | 0.833310 | + | 0.552806i | \(0.186443\pi\) | ||||
−0.833310 | + | 0.552806i | \(0.813557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.8555i | 1.66550i | 0.553649 | + | 0.832750i | \(0.313235\pi\) | ||||
−0.553649 | + | 0.832750i | \(0.686765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0716 | − | 2.11753i | 0.962889 | − | 0.135284i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4374 | − | 11.2865i | 0.855002 | − | 0.718143i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.37778 | −0.339443 | −0.169721 | − | 0.985492i | \(-0.554287\pi\) | ||||
−0.169721 | + | 0.985492i | \(0.554287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9541 | − | 11.9541i | −0.751546 | − | 0.751546i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.48727 | + | 4.48727i | 0.279908 | + | 0.279908i | 0.833072 | − | 0.553164i | \(-0.186580\pi\) |
−0.553164 | + | 0.833072i | \(0.686580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.05234 | 0.313937 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.8365 | + | 11.8365i | 0.729872 | + | 0.729872i | 0.970594 | − | 0.240722i | \(-0.0773842\pi\) |
−0.240722 | + | 0.970594i | \(0.577384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.42705 | − | 1.07545i | −0.0876631 | − | 0.0660646i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.33462 | 0.386229 | 0.193114 | − | 0.981176i | \(-0.438141\pi\) | ||||
0.193114 | + | 0.981176i | \(0.438141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5669 | 0.824131 | 0.412066 | − | 0.911154i | \(-0.364807\pi\) | ||||
0.412066 | + | 0.911154i | \(0.364807\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.9541 | − | 4.00000i | 0.841462 | − | 0.241209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9032 | + | 11.9032i | −0.715195 | + | 0.715195i | −0.967617 | − | 0.252422i | \(-0.918773\pi\) |
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6961i | 1.59256i | 0.604930 | + | 0.796279i | \(0.293201\pi\) | ||||
−0.604930 | + | 0.796279i | \(0.706799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1684 | − | 13.1684i | −0.782779 | − | 0.782779i | 0.197520 | − | 0.980299i | \(-0.436711\pi\) |
−0.980299 | + | 0.197520i | \(0.936711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.641140 | + | 0.641140i | 0.0378453 | + | 0.0378453i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.24443i | 0.249672i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.7879 | + | 22.7879i | −1.33129 | + | 1.33129i | −0.427064 | + | 0.904221i | \(0.640452\pi\) |
−0.904221 | + | 0.427064i | \(0.859548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.90143 | + | 20.6510i | 0.168928 | + | 1.20235i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.4431 | −1.35575 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.31756 | 0.0759430 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.09679 | − | 7.80642i | −0.0628019 | − | 0.446995i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.5756 | − | 19.5756i | −1.11724 | − | 1.11724i | −0.992145 | − | 0.125093i | \(-0.960077\pi\) |
−0.125093 | − | 0.992145i | \(-0.539923\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.1289 | −1.70845 | −0.854227 | − | 0.519901i | \(-0.825969\pi\) | ||||
−0.854227 | + | 0.519901i | \(0.825969\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5620 | + | 11.5620i | 0.653522 | + | 0.653522i | 0.953839 | − | 0.300317i | \(-0.0970925\pi\) |
−0.300317 | + | 0.953839i | \(0.597092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6011 | − | 10.6011i | −0.595414 | − | 0.595414i | 0.343674 | − | 0.939089i | \(-0.388328\pi\) |
−0.939089 | + | 0.343674i | \(0.888328\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.68499 | 0.486266 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.9207 | + | 10.0126i | −0.663287 | + | 0.557116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.76045 | − | 17.6048i | 0.541412 | − | 0.976541i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.70471i | − | 0.0939839i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.7862i | 1.47230i | 0.676817 | + | 0.736151i | \(0.263359\pi\) | ||||
−0.676817 | + | 0.736151i | \(0.736641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.275531 | + | 0.365610i | −0.0150538 | + | 0.0199754i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0500 | − | 10.0500i | −0.547458 | − | 0.547458i | 0.378247 | − | 0.925705i | \(-0.376527\pi\) |
−0.925705 | + | 0.378247i | \(0.876527\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.70197i | − | 0.146320i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.29529 | + | 4.29529i | 0.231924 | + | 0.231924i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0573 | + | 18.0573i | −0.969367 | + | 0.969367i | −0.999545 | − | 0.0301774i | \(-0.990393\pi\) |
0.0301774 | + | 0.999545i | \(0.490393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.1941i | − | 1.56272i | −0.624079 | − | 0.781361i | \(-0.714526\pi\) | ||
0.624079 | − | 0.781361i | \(-0.285474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.89384 | + | 8.89384i | 0.473372 | + | 0.473372i | 0.903004 | − | 0.429632i | \(-0.141357\pi\) |
−0.429632 | + | 0.903004i | \(0.641357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.2922 | − | 2.99151i | 1.13007 | − | 0.158773i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.9037i | − | 1.47270i | −0.676601 | − | 0.736350i | \(-0.736548\pi\) | ||
0.676601 | − | 0.736350i | \(-0.263452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7146 | + | 3.28105i | 0.984977 | + | 0.172687i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.79706 | + | 10.3461i | −0.408117 | + | 0.541542i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.89676 | − | 1.89676i | 0.0990100 | − | 0.0990100i | −0.655867 | − | 0.754877i | \(-0.727697\pi\) |
0.754877 | + | 0.655867i | \(0.227697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.351597i | − | 0.0182540i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.05909 | − | 6.05909i | 0.313728 | − | 0.313728i | −0.532624 | − | 0.846352i | \(-0.678794\pi\) |
0.846352 | + | 0.532624i | \(0.178794\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.51606 | − | 8.51606i | 0.438599 | − | 0.438599i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.2144 | −1.29518 | −0.647588 | − | 0.761991i | \(-0.724222\pi\) | ||||
−0.647588 | + | 0.761991i | \(0.724222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3323 | + | 11.3323i | −0.579052 | + | 0.579052i | −0.934642 | − | 0.355590i | \(-0.884280\pi\) |
0.355590 | + | 0.934642i | \(0.384280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.28100 | + | 1.71900i | 0.116250 | + | 0.0876085i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 19.1338i | − | 0.970124i | −0.874480 | − | 0.485062i | \(-0.838797\pi\) | ||
0.874480 | − | 0.485062i | \(-0.161203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7971 | 1.05175 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.92219 | − | 27.9163i | −0.197347 | − | 1.40462i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.71900 | + | 6.71900i | −0.337217 | + | 0.337217i | −0.855319 | − | 0.518102i | \(-0.826639\pi\) |
0.518102 | + | 0.855319i | \(0.326639\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.56334i | 0.227882i | 0.993488 | + | 0.113941i | \(0.0363475\pi\) | ||||
−0.993488 | + | 0.113941i | \(0.963653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.64941 | − | 2.64941i | −0.131977 | − | 0.131977i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.5738 | − | 23.5738i | −1.16851 | − | 1.16851i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.5817 | 1.06715 | 0.533574 | − | 0.845754i | \(-0.320849\pi\) | ||||
0.533574 | + | 0.845754i | \(0.320849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.90143 | + | 2.90143i | −0.142770 | + | 0.142770i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.5368 | + | 23.2701i | −0.860848 | + | 1.14228i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.58120i | 0.370366i | 0.982704 | + | 0.185183i | \(0.0592878\pi\) | ||||
−0.982704 | + | 0.185183i | \(0.940712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.0149i | − | 1.21915i | −0.792728 | − | 0.609576i | \(-0.791340\pi\) | ||
0.792728 | − | 0.609576i | \(-0.208660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.65878 | + | 15.6178i | −0.420013 | + | 0.757573i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.09679 | − | 1.09679i | 0.0530773 | − | 0.0530773i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.2021i | 1.02127i | 0.859798 | + | 0.510635i | \(0.170590\pi\) | ||||
−0.859798 | + | 0.510635i | \(0.829410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0866 | − | 19.0866i | 0.917243 | − | 0.917243i | −0.0795855 | − | 0.996828i | \(-0.525360\pi\) |
0.996828 | + | 0.0795855i | \(0.0253597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.3248 | − | 19.4359i | −0.780922 | − | 0.929746i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.6622 | −1.84524 | −0.922622 | − | 0.385705i | \(-0.873958\pi\) | ||||
−0.922622 | + | 0.385705i | \(0.873958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.725457 | − | 0.725457i | −0.0344675 | − | 0.0344675i | 0.689663 | − | 0.724130i | \(-0.257759\pi\) |
−0.724130 | + | 0.689663i | \(0.757759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.35037 | − | 16.7288i | −0.111418 | − | 0.793023i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.0746 | 1.93843 | 0.969215 | − | 0.246216i | \(-0.0791872\pi\) | ||||
0.969215 | + | 0.246216i | \(0.0791872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.98302i | − | 0.281730i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.92219 | − | 0.551061i | 0.183875 | − | 0.0258341i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3684 | − | 15.3684i | 0.718904 | − | 0.718904i | −0.249477 | − | 0.968381i | \(-0.580259\pi\) |
0.968381 | + | 0.249477i | \(0.0802586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.9304 | 0.788528 | 0.394264 | − | 0.918997i | \(-0.371000\pi\) | ||||
0.394264 | + | 0.918997i | \(0.371000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.49532 | − | 1.49532i | −0.0694932 | − | 0.0694932i | 0.671506 | − | 0.740999i | \(-0.265648\pi\) |
−0.740999 | + | 0.671506i | \(0.765648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.2192 | − | 20.2192i | 0.935635 | − | 0.935635i | −0.0624153 | − | 0.998050i | \(-0.519880\pi\) |
0.998050 | + | 0.0624153i | \(0.0198803\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0900790 | −0.00415946 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.14764 | − | 6.14764i | −0.282669 | − | 0.282669i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.3924 | − | 4.16723i | 0.981550 | − | 0.191206i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.2587i | 0.514424i | 0.966355 | + | 0.257212i | \(0.0828039\pi\) | ||||
−0.966355 | + | 0.257212i | \(0.917196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.2306 | −2.10793 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.9187 | − | 30.4115i | 1.04068 | − | 1.38091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4539 | − | 15.4539i | −0.700284 | − | 0.700284i | 0.264187 | − | 0.964471i | \(-0.414896\pi\) |
−0.964471 | + | 0.264187i | \(0.914896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.9906 | 0.947294 | 0.473647 | − | 0.880715i | \(-0.342937\pi\) | ||||
0.473647 | + | 0.880715i | \(0.342937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.55485 | + | 7.55485i | −0.340253 | + | 0.340253i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.99151 | + | 2.99151i | 0.134188 | + | 0.134188i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.6780i | 1.10474i | 0.833599 | + | 0.552369i | \(0.186276\pi\) | ||||
−0.833599 | + | 0.552369i | \(0.813724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0065 | + | 15.0065i | 0.669105 | + | 0.669105i | 0.957509 | − | 0.288404i | \(-0.0931246\pi\) |
−0.288404 | + | 0.957509i | \(0.593125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.72837 | − | 19.4193i | −0.121411 | − | 0.864146i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.6306 | −1.53497 | −0.767487 | − | 0.641065i | \(-0.778493\pi\) | ||||
−0.767487 | + | 0.641065i | \(0.778493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.54909 | −0.112765 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.5677 | + | 16.2539i | 0.950387 | + | 0.716230i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.95407 | + | 7.95407i | −0.349819 | + | 0.349819i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 39.0418i | − | 1.71045i | −0.518255 | − | 0.855226i | \(-0.673418\pi\) | ||
0.518255 | − | 0.855226i | \(-0.326582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.2904 | + | 25.2904i | −1.10587 | + | 1.10587i | −0.112187 | + | 0.993687i | \(0.535785\pi\) |
−0.993687 | + | 0.112187i | \(0.964215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.35037 | + | 2.35037i | 0.102384 | + | 0.102384i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9081i | 0.474267i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.86665 | − | 5.86665i | −0.254113 | − | 0.254113i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.18924 | + | 9.53961i | −0.310818 | + | 0.412433i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 19.7605i | − | 0.851145i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.85283 | −0.380613 | −0.190307 | − | 0.981725i | \(-0.560948\pi\) | ||||
−0.190307 | + | 0.981725i | \(0.560948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.27379 | − | 30.4189i | −0.183069 | − | 1.30300i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9520 | − | 11.9520i | −0.511032 | − | 0.511032i | 0.403810 | − | 0.914843i | \(-0.367686\pi\) |
−0.914843 | + | 0.403810i | \(0.867686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9906 | + | 1.13015i | 0.553420 | + | 0.0481459i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.92219 | − | 3.92219i | 0.166789 | − | 0.166789i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8430 | + | 19.8430i | −0.840774 | + | 0.840774i | −0.988960 | − | 0.148185i | \(-0.952657\pi\) |
0.148185 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0561 | −0.509920 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4703 | + | 10.4703i | −0.441270 | + | 0.441270i | −0.892439 | − | 0.451169i | \(-0.851007\pi\) |
0.451169 | + | 0.892439i | \(0.351007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.83887 | + | 3.64666i | 0.203573 | + | 0.153416i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.6744 | 1.78901 | 0.894503 | − | 0.447062i | \(-0.147530\pi\) | ||||
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.2815 | −0.974299 | −0.487150 | − | 0.873319i | \(-0.661963\pi\) | ||||
−0.487150 | + | 0.873319i | \(0.661963\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.4637 | − | 14.1175i | −1.06191 | − | 0.588742i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5526 | + | 14.5526i | −0.605834 | + | 0.605834i | −0.941855 | − | 0.336021i | \(-0.890919\pi\) |
0.336021 | + | 0.941855i | \(0.390919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.73329 | −0.237857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.64053 | + | 1.64053i | −0.0679437 | + | 0.0679437i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.20495 | − | 6.20495i | 0.256106 | − | 0.256106i | −0.567362 | − | 0.823468i | \(-0.692036\pi\) |
0.823468 | + | 0.567362i | \(0.192036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.351597 | − | 4.04149i | 0.0144873 | − | 0.166527i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.5210 | − | 32.5210i | −1.33548 | − | 1.33548i | −0.900387 | − | 0.435089i | \(-0.856717\pi\) |
−0.435089 | − | 0.900387i | \(-0.643283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.47949 | + | 0.488863i | −0.142645 | + | 0.0200414i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8505 | −0.851929 | −0.425964 | − | 0.904740i | \(-0.640065\pi\) | ||||
−0.425964 | + | 0.904740i | \(0.640065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.64493i | − | 0.311843i | −0.987769 | − | 0.155922i | \(-0.950165\pi\) | ||
0.987769 | − | 0.155922i | \(-0.0498347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.799970 | + | 5.69381i | 0.0325234 | + | 0.231486i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0951 | − | 16.0951i | −0.653279 | − | 0.653279i | 0.300502 | − | 0.953781i | \(-0.402846\pi\) |
−0.953781 | + | 0.300502i | \(0.902846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.5987i | 0.631056i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.69535 | + | 9.69535i | 0.391591 | + | 0.391591i | 0.875254 | − | 0.483663i | \(-0.160694\pi\) |
−0.483663 | + | 0.875254i | \(0.660694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.3319 | − | 26.3319i | 1.06008 | − | 1.06008i | 0.0620046 | − | 0.998076i | \(-0.480251\pi\) |
0.998076 | − | 0.0620046i | \(-0.0197493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.0054i | 1.52757i | 0.645473 | + | 0.763783i | \(0.276660\pi\) | ||||
−0.645473 | + | 0.763783i | \(0.723340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.35037 | − | 2.35037i | 0.0941657 | − | 0.0941657i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.0125 | 1.63528 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0968 | 0.999087 | 0.499544 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499544 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.76045 | + | 12.9514i | −0.387332 | + | 0.513962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.3761 | − | 19.3761i | −0.767710 | − | 0.767710i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 10.1667i | − | 0.401562i | −0.979636 | − | 0.200781i | \(-0.935652\pi\) | ||
0.979636 | − | 0.200781i | \(-0.0643480\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1082 | + | 31.1082i | 1.22679 | + | 1.22679i | 0.965173 | + | 0.261614i | \(0.0842546\pi\) |
0.261614 | + | 0.965173i | \(0.415745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.6336 | + | 24.6336i | −0.968446 | + | 0.968446i | −0.999517 | − | 0.0310708i | \(-0.990108\pi\) |
0.0310708 | + | 0.999517i | \(0.490108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0757 | 1.06282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.09234 | − | 4.09234i | −0.160146 | − | 0.160146i | 0.622486 | − | 0.782631i | \(-0.286123\pi\) |
−0.782631 | + | 0.622486i | \(0.786123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.22570 | − | 22.9590i | −0.126038 | − | 0.897082i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.90522 | 0.385853 | 0.192926 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192926 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.1328i | − | 0.860866i | −0.902623 | − | 0.430433i | \(-0.858361\pi\) | ||
0.902623 | − | 0.430433i | \(-0.141639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.18813 | + | 2.86803i | 0.123630 | + | 0.111217i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3176 | − | 12.3176i | −0.476941 | − | 0.476941i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.2351 | −0.395120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1304 | − | 27.1304i | 1.04580 | − | 1.04580i | 0.0469019 | − | 0.998899i | \(-0.485065\pi\) |
0.998899 | − | 0.0469019i | \(-0.0149348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.5677 | − | 21.5677i | −0.828915 | − | 0.828915i | 0.158452 | − | 0.987367i | \(-0.449350\pi\) |
−0.987367 | + | 0.158452i | \(0.949350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.49279 | 0.287547 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0872 | − | 18.0872i | 0.692087 | − | 0.692087i | −0.270604 | − | 0.962691i | \(-0.587223\pi\) |
0.962691 | + | 0.270604i | \(0.0872233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1798 | + | 15.2079i | 0.771029 | + | 0.581063i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.21723i | 0.122567i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.09679 | 0.346058 | 0.173029 | − | 0.984917i | \(-0.444645\pi\) | ||||
0.173029 | + | 0.984917i | \(0.444645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.5620 | − | 3.16992i | 0.855825 | − | 0.120242i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.20448 | + | 5.20448i | 0.197134 | + | 0.197134i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0687 | 0.531367 | 0.265683 | − | 0.964060i | \(-0.414402\pi\) | ||||
0.265683 | + | 0.964060i | \(0.414402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.1932 | − | 38.3283i | −1.21419 | − | 1.44558i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.72837 | − | 2.72837i | 0.102611 | − | 0.102611i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.6035i | 1.52490i | 0.647050 | + | 0.762448i | \(0.276003\pi\) | ||||
−0.647050 | + | 0.762448i | \(0.723997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.83212 | + | 3.83212i | −0.143514 | + | 0.143514i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.8719 | − | 15.7295i | −0.780564 | − | 0.588248i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.5067i | 1.24959i | 0.780789 | + | 0.624794i | \(0.214817\pi\) | ||||
−0.780789 | + | 0.624794i | \(0.785183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.31386i | 0.197898i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.3785 | − | 4.12166i | 0.534003 | − | 0.153075i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.59210 | − | 2.59210i | 0.0961358 | − | 0.0961358i | −0.657403 | − | 0.753539i | \(-0.728345\pi\) |
0.753539 | + | 0.657403i | \(0.228345\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.6953 | 0.395582 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1334 | + | 15.1334i | 0.558963 | + | 0.558963i | 0.929012 | − | 0.370049i | \(-0.120659\pi\) |
−0.370049 | + | 0.929012i | \(0.620659\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.420302 | + | 0.420302i | 0.0154820 | + | 0.0154820i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13.4291i | − | 0.493998i | −0.969016 | − | 0.246999i | \(-0.920556\pi\) | ||
0.969016 | − | 0.246999i | \(-0.0794444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7186 | + | 23.7186i | −0.870152 | + | 0.870152i | −0.992489 | − | 0.122337i | \(-0.960961\pi\) |
0.122337 | + | 0.992489i | \(0.460961\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.0513 | + | 5.62714i | −1.46737 | + | 0.206162i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.35037 | −0.0858807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.3615i | − | 0.743002i | −0.928433 | − | 0.371501i | \(-0.878843\pi\) | ||
0.928433 | − | 0.371501i | \(-0.121157\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.9772 | − | 4.21174i | 1.09098 | − | 0.153281i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.67799 | + | 3.67799i | −0.133679 | + | 0.133679i | −0.770780 | − | 0.637101i | \(-0.780133\pi\) |
0.637101 | + | 0.770780i | \(0.280133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9126 | 0.576831 | 0.288415 | − | 0.957505i | \(-0.406872\pi\) | ||||
0.288415 | + | 0.957505i | \(0.406872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.27379 | − | 4.27379i | 0.154722 | − | 0.154722i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.5491 | − | 26.5491i | 0.958632 | − | 0.958632i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27.0277i | − | 0.974643i | −0.873223 | − | 0.487321i | \(-0.837974\pi\) | ||
0.873223 | − | 0.487321i | \(-0.162026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.89182 | − | 8.89182i | 0.319817 | − | 0.319817i | −0.528880 | − | 0.848697i | \(-0.677388\pi\) |
0.848697 | + | 0.528880i | \(0.177388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.28228 | − | 4.47326i | −0.0460609 | − | 0.160684i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.778549 | − | 8.94914i | 0.0278944 | − | 0.320636i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27.9163i | − | 0.998925i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.3590 | − | 28.9081i | −1.36909 | − | 1.03178i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9266 | + | 20.9266i | 0.745952 | + | 0.745952i | 0.973716 | − | 0.227764i | \(-0.0731416\pi\) |
−0.227764 | + | 0.973716i | \(0.573142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.19220i | 0.0423898i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0360 | + | 10.0360i | −0.356388 | + | 0.356388i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.3951 | − | 35.3951i | −1.25376 | − | 1.25376i | −0.954021 | − | 0.299738i | \(-0.903101\pi\) |
−0.299738 | − | 0.954021i | \(-0.596899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 13.8381i | − | 0.489556i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8938 | + | 11.8938i | 0.419725 | + | 0.419725i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.797056 | − | 5.67307i | −0.0280925 | − | 0.199949i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3555i | 0.645345i | 0.946511 | + | 0.322673i | \(0.104581\pi\) | ||||
−0.946511 | + | 0.322673i | \(0.895419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.77129i | 0.0621983i | 0.999516 | + | 0.0310991i | \(0.00990076\pi\) | ||||
−0.999516 | + | 0.0310991i | \(0.990099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3713 | − | 13.7620i | 0.363292 | − | 0.482063i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.39540 | − | 9.99534i | −0.293718 | − | 0.349693i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.7654 | −0.654917 | −0.327459 | − | 0.944865i | \(-0.606192\pi\) | ||||
−0.327459 | + | 0.944865i | \(0.606192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.6844 | − | 25.6844i | −0.895304 | − | 0.895304i | 0.0997127 | − | 0.995016i | \(-0.468208\pi\) |
−0.995016 | + | 0.0997127i | \(0.968208\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.7063 | − | 19.7063i | −0.685257 | − | 0.685257i | 0.275923 | − | 0.961180i | \(-0.411017\pi\) |
−0.961180 | + | 0.275923i | \(0.911017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1790 | 0.492457 | 0.246229 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246229 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.1891 | + | 17.1891i | 0.595568 | + | 0.595568i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.61803 | − | 6.12780i | 0.159813 | − | 0.212061i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.0319 | −0.657054 | −0.328527 | − | 0.944495i | \(-0.606552\pi\) | ||||
−0.328527 | + | 0.944495i | \(0.606552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0509 | −0.691409 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.10324 | + | 0.997992i | −0.244359 | + | 0.0343320i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.799970 | + | 0.799970i | −0.0274873 | + | 0.0274873i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66.8681i | 2.29221i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.9906 | − | 11.9906i | −0.410551 | − | 0.410551i | 0.471379 | − | 0.881931i | \(-0.343756\pi\) |
−0.881931 | + | 0.471379i | \(0.843756\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.5107 | − | 26.5107i | −0.905587 | − | 0.905587i | 0.0903251 | − | 0.995912i | \(-0.471209\pi\) |
−0.995912 | + | 0.0903251i | \(0.971209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.9719i | − | 1.53442i | −0.641395 | − | 0.767211i | \(-0.721644\pi\) | ||
0.641395 | − | 0.767211i | \(-0.278356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.4121 | − | 29.4121i | 1.00120 | − | 1.00120i | 0.00120035 | − | 0.999999i | \(-0.499618\pi\) |
0.999999 | − | 0.00120035i | \(-0.000382082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7441 | + | 11.1114i | 0.501314 | + | 0.377800i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.6013 | −1.24162 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.824253 | 0.0279287 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.59210 | + | 1.76341i | 0.155241 | + | 0.0596140i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.98977 | − | 6.98977i | −0.236028 | − | 0.236028i | 0.579175 | − | 0.815203i | \(-0.303375\pi\) |
−0.815203 | + | 0.579175i | \(0.803375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.5254 | −0.523065 | −0.261532 | − | 0.965195i | \(-0.584228\pi\) | ||||
−0.261532 | + | 0.965195i | \(0.584228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.40790 | + | 3.40790i | 0.114685 | + | 0.114685i | 0.762120 | − | 0.647435i | \(-0.224158\pi\) |
−0.647435 | + | 0.762120i | \(0.724158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.4077 | − | 23.4077i | −0.785954 | − | 0.785954i | 0.194874 | − | 0.980828i | \(-0.437570\pi\) |
−0.980828 | + | 0.194874i | \(0.937570\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.19098 | −0.107022 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.9324 | + | 10.8623i | −0.432766 | + | 0.363493i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.36265 | − | 45.2863i | −0.212680 | − | 1.51376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.78415i | − | 0.0928566i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.85410i | − | 0.0950840i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.4967 | + | 3.72273i | −0.880779 | + | 0.123748i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0781 | − | 22.0781i | −0.733091 | − | 0.733091i | 0.238140 | − | 0.971231i | \(-0.423462\pi\) |
−0.971231 | + | 0.238140i | \(0.923462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.67272i | 0.154814i | 0.997000 | + | 0.0774071i | \(0.0246641\pi\) | ||||
−0.997000 | + | 0.0774071i | \(0.975336\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.7511 | + | 26.7511i | 0.885333 | + | 0.885333i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.22570 | − | 3.22570i | 0.106522 | − | 0.106522i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.5303i | − | 0.545286i | −0.962115 | − | 0.272643i | \(-0.912102\pi\) | ||
0.962115 | − | 0.272643i | \(-0.0878978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.3733 | − | 27.3733i | −0.901004 | − | 0.901004i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.2153 | − | 27.8403i | −1.65107 | − | 0.915383i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.1655i | 1.08812i | 0.839045 | + | 0.544062i | \(0.183114\pi\) | ||||
−0.839045 | + | 0.544062i | \(0.816886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.57136 | − | 29.5569i | 0.0842729 | − | 0.968687i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.5161 | + | 13.9541i | 0.605540 | + | 0.456347i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6686 | − | 32.6686i | 1.06724 | − | 1.06724i | 0.0696672 | − | 0.997570i | \(-0.477806\pi\) |
0.997570 | − | 0.0696672i | \(-0.0221937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.86014i | 0.125837i | 0.998019 | + | 0.0629185i | \(0.0200408\pi\) | ||||
−0.998019 | + | 0.0629185i | \(0.979959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.48553 | + | 8.48553i | −0.276327 | + | 0.276327i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1733 | + | 36.1733i | −1.17547 | + | 1.17547i | −0.194590 | + | 0.980885i | \(0.562338\pi\) |
−0.980885 | + | 0.194590i | \(0.937662\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.3250 | 0.757161 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.5239 | + | 13.5239i | −0.438081 | + | 0.438081i | −0.891366 | − | 0.453285i | \(-0.850252\pi\) |
0.453285 | + | 0.891366i | \(0.350252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.18421 | + | 51.1338i | 0.232476 | + | 1.65465i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.97190i | 0.160551i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1338 | 0.972059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.12780 | + | 4.61803i | 0.197261 | + | 0.148660i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0163 | + | 21.0163i | −0.675839 | + | 0.675839i | −0.959056 | − | 0.283217i | \(-0.908598\pi\) |
0.283217 | + | 0.959056i | \(0.408598\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.4261i | − | 0.944329i | −0.881510 | − | 0.472164i | \(-0.843473\pi\) | ||
0.881510 | − | 0.472164i | \(-0.156527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.16992 | + | 3.16992i | 0.101623 | + | 0.101623i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.4917 | + | 10.4917i | 0.335658 | + | 0.335658i | 0.854730 | − | 0.519072i | \(-0.173722\pi\) |
−0.519072 | + | 0.854730i | \(0.673722\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.9333 | −0.700992 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.06697 | + | 4.06697i | −0.129716 | + | 0.129716i | −0.768984 | − | 0.639268i | \(-0.779237\pi\) |
0.639268 | + | 0.768984i | \(0.279237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.0513 | + | 24.9081i | 1.05310 | + | 0.793639i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.4380i | 0.554496i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8189i | 0.534271i | 0.963659 | + | 0.267135i | \(0.0860771\pi\) | ||||
−0.963659 | + | 0.267135i | \(0.913923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.7971 | + | 3.20294i | −0.722715 | + | 0.101540i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.1847 | − | 17.1847i | 0.544244 | − | 0.544244i | −0.380526 | − | 0.924770i | \(-0.624257\pi\) |
0.924770 | + | 0.380526i | \(0.124257\pi\) | |||||||
\(998\) | 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 | 3420.2.bb.d.2773.3 | 12 | ||
3.2 | odd | 2 | 380.2.l.b.113.3 | yes | 12 | ||
5.2 | odd | 4 | inner | 3420.2.bb.d.37.4 | 12 | ||
15.2 | even | 4 | 380.2.l.b.37.4 | yes | 12 | ||
15.8 | even | 4 | 1900.2.l.b.1557.3 | 12 | |||
15.14 | odd | 2 | 1900.2.l.b.493.4 | 12 | |||
19.18 | odd | 2 | inner | 3420.2.bb.d.2773.4 | 12 | ||
57.56 | even | 2 | 380.2.l.b.113.4 | yes | 12 | ||
95.37 | even | 4 | inner | 3420.2.bb.d.37.3 | 12 | ||
285.113 | odd | 4 | 1900.2.l.b.1557.4 | 12 | |||
285.227 | odd | 4 | 380.2.l.b.37.3 | ✓ | 12 | ||
285.284 | even | 2 | 1900.2.l.b.493.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.l.b.37.3 | ✓ | 12 | 285.227 | odd | 4 | ||
380.2.l.b.37.4 | yes | 12 | 15.2 | even | 4 | ||
380.2.l.b.113.3 | yes | 12 | 3.2 | odd | 2 | ||
380.2.l.b.113.4 | yes | 12 | 57.56 | even | 2 | ||
1900.2.l.b.493.3 | 12 | 285.284 | even | 2 | |||
1900.2.l.b.493.4 | 12 | 15.14 | odd | 2 | |||
1900.2.l.b.1557.3 | 12 | 15.8 | even | 4 | |||
1900.2.l.b.1557.4 | 12 | 285.113 | odd | 4 | |||
3420.2.bb.d.37.3 | 12 | 95.37 | even | 4 | inner | ||
3420.2.bb.d.37.4 | 12 | 5.2 | odd | 4 | inner | ||
3420.2.bb.d.2773.3 | 12 | 1.1 | even | 1 | trivial | ||
3420.2.bb.d.2773.4 | 12 | 19.18 | odd | 2 | inner |