Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(494,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.494");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.d (of order \(2\), degree \(1\), 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: | \(3.95259490005\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 494.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.494 |
Dual form | 495.2.d.b.494.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(397\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | 0.935414 | + | 0.353553i | \(0.115027\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.12132 | − | 0.707107i | −0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707107 | − | 2.12132i | 0.223607 | − | 0.670820i | ||||
\(11\) | 3.00000 | − | 1.41421i | 0.904534 | − | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 1.41421i | 0.377964i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264i | 0.973329i | 0.873589 | + | 0.486664i | \(0.161786\pi\) | ||||
−0.873589 | + | 0.486664i | \(0.838214\pi\) | |||||||
\(20\) | −2.12132 | − | 0.707107i | −0.474342 | − | 0.158114i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41421 | + | 3.00000i | 0.301511 | + | 0.639602i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 2.82843i | 0.554700i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41421 | 0.267261 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.00000i | 0.883883i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −3.00000 | − | 1.00000i | −0.507093 | − | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00000i | − | 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | −4.24264 | −0.688247 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | − | 6.36396i | 0.335410 | − | 1.00623i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41421 | −0.215666 | −0.107833 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107833 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(44\) | 3.00000 | − | 1.41421i | 0.452267 | − | 0.213201i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | 1.23771 | 0.618853 | − | 0.785507i | \(-0.287598\pi\) | ||||
0.618853 | + | 0.785507i | \(0.287598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −3.00000 | + | 4.00000i | −0.424264 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.82843 | 0.392232 | ||||||||
\(53\) | −4.24264 | −0.582772 | −0.291386 | − | 0.956606i | \(-0.594116\pi\) | ||||
−0.291386 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.36396 | + | 0.878680i | −0.992956 | + | 0.118481i | ||||
\(56\) | 4.24264i | 0.566947i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | 8.48528i | 1.10469i | 0.833616 | + | 0.552345i | \(0.186267\pi\) | ||||
−0.833616 | + | 0.552345i | \(0.813733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.48528i | − | 1.08643i | −0.839594 | − | 0.543214i | \(-0.817207\pi\) | ||
0.839594 | − | 0.543214i | \(-0.182793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | −6.00000 | − | 2.00000i | −0.744208 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | − | 3.00000i | 0.119523 | − | 0.358569i | ||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3137 | −1.32417 | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||||
−0.662085 | + | 0.749429i | \(0.730328\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.24264i | 0.486664i | ||||||||
\(77\) | 4.24264 | − | 2.00000i | 0.483494 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7279i | 1.43200i | 0.698099 | + | 0.716002i | \(0.254030\pi\) | ||||
−0.698099 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(80\) | 2.12132 | + | 0.707107i | 0.237171 | + | 0.0790569i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.00000i | − | 0.662589i | ||||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | − | 4.24264i | 0.153393 | − | 0.460179i | ||||
\(86\) | − | 1.41421i | − | 0.152499i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | + | 9.00000i | 0.452267 | + | 0.959403i | ||||
\(89\) | − | 7.07107i | − | 0.749532i | −0.927119 | − | 0.374766i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374766i | \(-0.122277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.48528i | 0.875190i | ||||||||
\(95\) | 3.00000 | − | 9.00000i | 0.307794 | − | 0.923381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.0000i | − | 1.21842i | −0.793011 | − | 0.609208i | \(-0.791488\pi\) | ||
0.793011 | − | 0.609208i | \(-0.208512\pi\) | |||||||
\(98\) | − | 5.00000i | − | 0.505076i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | + | 3.00000i | 0.400000 | + | 0.300000i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.0000i | − | 1.18240i | −0.806527 | − | 0.591198i | \(-0.798655\pi\) | ||
0.806527 | − | 0.591198i | \(-0.201345\pi\) | |||||||
\(104\) | 8.48528i | 0.832050i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.24264i | − | 0.412082i | ||||||
\(107\) | − | 14.0000i | − | 1.35343i | −0.736245 | − | 0.676716i | \(-0.763403\pi\) | ||
0.736245 | − | 0.676716i | \(-0.236597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.9706i | 1.62549i | 0.582623 | + | 0.812743i | \(0.302026\pi\) | ||||
−0.582623 | + | 0.812743i | \(0.697974\pi\) | |||||||
\(110\) | −0.878680 | − | 7.36396i | −0.0837788 | − | 0.702126i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.41421 | −0.133631 | ||||||||
\(113\) | 12.7279 | 1.19734 | 0.598671 | − | 0.800995i | \(-0.295696\pi\) | ||||
0.598671 | + | 0.800995i | \(0.295696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.48528 | −0.781133 | ||||||||
\(119\) | 2.82843i | 0.259281i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | − | 8.48528i | 0.636364 | − | 0.771389i | ||||
\(122\) | 8.48528 | 0.768221 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | − | 9.19239i | −0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.3848 | −1.63139 | −0.815693 | − | 0.578486i | \(-0.803644\pi\) | ||||
−0.815693 | + | 0.578486i | \(0.803644\pi\) | |||||||
\(128\) | 3.00000i | 0.265165i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 6.00000i | 0.175412 | − | 0.526235i | ||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000i | 0.520266i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −4.24264 | −0.362473 | −0.181237 | − | 0.983440i | \(-0.558010\pi\) | ||||
−0.181237 | + | 0.983440i | \(0.558010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24264i | 0.359856i | 0.983680 | + | 0.179928i | \(0.0575865\pi\) | ||||
−0.983680 | + | 0.179928i | \(0.942414\pi\) | |||||||
\(140\) | −3.00000 | − | 1.00000i | −0.253546 | − | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.48528 | 0.712069 | ||||||||
\(143\) | 8.48528 | − | 4.00000i | 0.709575 | − | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.7279 | − | 4.24264i | −1.05700 | − | 0.352332i | ||||
\(146\) | − | 11.3137i | − | 0.936329i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.24264i | − | 0.345261i | −0.984987 | − | 0.172631i | \(-0.944773\pi\) | ||
0.984987 | − | 0.172631i | \(-0.0552267\pi\) | |||||||
\(152\) | −12.7279 | −1.03237 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | + | 4.24264i | 0.161165 | + | 0.341882i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.0000i | 1.91541i | 0.287754 | + | 0.957704i | \(0.407091\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(158\) | −12.7279 | −1.01258 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.53553 | − | 10.6066i | 0.279508 | − | 0.838525i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 24.0000i | − | 1.87983i | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||
0.341415 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.0000 | 1.08661 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 4.24264 | + | 1.41421i | 0.325396 | + | 0.108465i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.41421 | −0.107833 | ||||||||
\(173\) | 14.0000i | 1.06440i | 0.846619 | + | 0.532200i | \(0.178635\pi\) | ||||
−0.846619 | + | 0.532200i | \(0.821365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.65685 | + | 4.24264i | 0.427618 | + | 0.320713i | ||||
\(176\) | −3.00000 | + | 1.41421i | −0.226134 | + | 0.106600i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.07107 | 0.529999 | ||||||||
\(179\) | − | 5.65685i | − | 0.422813i | −0.977398 | − | 0.211407i | \(-0.932196\pi\) | ||
0.977398 | − | 0.211407i | \(-0.0678044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.24264 | + | 12.7279i | −0.311925 | + | 0.935775i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82843 | + | 6.00000i | 0.206835 | + | 0.438763i | ||||
\(188\) | 8.48528 | 0.618853 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.00000 | + | 3.00000i | 0.652929 | + | 0.217643i | ||||
\(191\) | − | 2.82843i | − | 0.204658i | −0.994751 | − | 0.102329i | \(-0.967371\pi\) | ||
0.994751 | − | 0.102329i | \(-0.0326294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.7990 | 1.42516 | 0.712581 | − | 0.701590i | \(-0.247526\pi\) | ||||
0.712581 | + | 0.701590i | \(0.247526\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | 14.0000i | 0.997459i | 0.866758 | + | 0.498729i | \(0.166200\pi\) | ||||
−0.866758 | + | 0.498729i | \(0.833800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | −9.00000 | + | 12.0000i | −0.636396 | + | 0.848528i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | 8.48528 | 0.595550 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.7279 | + | 4.24264i | 0.888957 | + | 0.296319i | ||||
\(206\) | 12.0000 | 0.836080 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.82843 | −0.196116 | ||||||||
\(209\) | 6.00000 | + | 12.7279i | 0.415029 | + | 0.880409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.24264i | − | 0.292075i | −0.989279 | − | 0.146038i | \(-0.953348\pi\) | ||
0.989279 | − | 0.146038i | \(-0.0466521\pi\) | |||||||
\(212\) | −4.24264 | −0.291386 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.0000 | 0.957020 | ||||||||
\(215\) | 3.00000 | + | 1.00000i | 0.204598 | + | 0.0681994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.9706 | −1.14939 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.36396 | + | 0.878680i | −0.496478 | + | 0.0592406i | ||||
\(221\) | 5.65685i | 0.380521i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 7.07107i | 0.472456i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.7279i | 0.846649i | ||||||||
\(227\) | 2.00000i | 0.132745i | 0.997795 | + | 0.0663723i | \(0.0211425\pi\) | ||||
−0.997795 | + | 0.0663723i | \(0.978857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000i | 1.18176i | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | − | 6.00000i | −1.17419 | − | 0.391397i | ||||
\(236\) | 8.48528i | 0.552345i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.82843 | −0.183340 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | 8.48528 | + | 7.00000i | 0.545455 | + | 0.449977i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.48528i | − | 0.543214i | ||||||
\(245\) | 10.6066 | + | 3.53553i | 0.677631 | + | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000i | 0.763542i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.19239 | − | 6.36396i | 0.581378 | − | 0.402492i | ||||
\(251\) | 16.9706i | 1.07117i | 0.844481 | + | 0.535586i | \(0.179909\pi\) | ||||
−0.844481 | + | 0.535586i | \(0.820091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 18.3848i | − | 1.15356i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −29.6985 | −1.85254 | −0.926270 | − | 0.376860i | \(-0.877004\pi\) | ||||
−0.926270 | + | 0.376860i | \(0.877004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.48528i | − | 0.527250i | ||||||
\(260\) | −6.00000 | − | 2.00000i | −0.372104 | − | 0.124035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 18.0000i | − | 1.11204i | ||||||
\(263\) | 8.00000i | 0.493301i | 0.969104 | + | 0.246651i | \(0.0793300\pi\) | ||||
−0.969104 | + | 0.246651i | \(0.920670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | + | 3.00000i | 0.552866 | + | 0.184289i | ||||
\(266\) | −6.00000 | −0.367884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7279i | 0.776035i | 0.921652 | + | 0.388018i | \(0.126840\pi\) | ||||
−0.921652 | + | 0.388018i | \(0.873160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.7279i | − | 0.773166i | −0.922255 | − | 0.386583i | \(-0.873655\pi\) | ||
0.922255 | − | 0.386583i | \(-0.126345\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.24264i | − | 0.256307i | ||||||
\(275\) | 16.2426 | + | 3.34315i | 0.979468 | + | 0.201599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.1127 | 1.86938 | 0.934690 | − | 0.355463i | \(-0.115677\pi\) | ||||
0.934690 | + | 0.355463i | \(0.115677\pi\) | |||||||
\(278\) | −4.24264 | −0.254457 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | − | 9.00000i | 0.179284 | − | 0.537853i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.41421 | 0.0840663 | 0.0420331 | − | 0.999116i | \(-0.486616\pi\) | ||||
0.0420331 | + | 0.999116i | \(0.486616\pi\) | |||||||
\(284\) | − | 8.48528i | − | 0.503509i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | + | 8.48528i | 0.236525 | + | 0.501745i | ||||
\(287\) | −8.48528 | −0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 4.24264 | − | 12.7279i | 0.249136 | − | 0.747409i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.3137 | −0.662085 | ||||||||
\(293\) | 10.0000i | 0.584206i | 0.956387 | + | 0.292103i | \(0.0943550\pi\) | ||||
−0.956387 | + | 0.292103i | \(0.905645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 18.0000i | 0.349334 | − | 1.04800i | ||||
\(296\) | 18.0000 | 1.04623 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000i | 1.04271i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 4.24264 | 0.244137 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.24264i | − | 0.243332i | ||||||
\(305\) | −6.00000 | + | 18.0000i | −0.343559 | + | 1.03068i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0416 | −1.37213 | −0.686064 | − | 0.727541i | \(-0.740663\pi\) | ||||
−0.686064 | + | 0.727541i | \(0.740663\pi\) | |||||||
\(308\) | 4.24264 | − | 2.00000i | 0.241747 | − | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.9706i | − | 0.962312i | −0.876635 | − | 0.481156i | \(-0.840217\pi\) | ||
0.876635 | − | 0.481156i | \(-0.159783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −24.0000 | −1.35440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.7279i | 0.716002i | ||||||||
\(317\) | −21.2132 | −1.19145 | −0.595726 | − | 0.803188i | \(-0.703136\pi\) | ||||
−0.595726 | + | 0.803188i | \(0.703136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 8.48528i | 1.00781 | − | 0.475085i | ||||
\(320\) | 14.8492 | + | 4.94975i | 0.830098 | + | 0.276699i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.48528 | −0.472134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3137 | + | 8.48528i | 0.627572 | + | 0.470679i | ||||
\(326\) | 24.0000 | 1.32924 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 18.0000i | − | 0.993884i | ||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | − | 14.0000i | − | 0.768350i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3137 | 0.616297 | 0.308148 | − | 0.951338i | \(-0.400291\pi\) | ||||
0.308148 | + | 0.951338i | \(0.400291\pi\) | |||||||
\(338\) | − | 5.00000i | − | 0.271964i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.41421 | − | 4.24264i | 0.0766965 | − | 0.230089i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | − | 4.24264i | − | 0.228748i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0000 | −0.752645 | ||||||||
\(347\) | 14.0000i | 0.751559i | 0.926709 | + | 0.375780i | \(0.122625\pi\) | ||||
−0.926709 | + | 0.375780i | \(0.877375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.48528i | 0.454207i | 0.973871 | + | 0.227103i | \(0.0729255\pi\) | ||||
−0.973871 | + | 0.227103i | \(0.927074\pi\) | |||||||
\(350\) | −4.24264 | + | 5.65685i | −0.226779 | + | 0.302372i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.07107 | + | 15.0000i | 0.376889 | + | 0.799503i | ||||
\(353\) | 4.24264 | 0.225813 | 0.112906 | − | 0.993606i | \(-0.463984\pi\) | ||||
0.112906 | + | 0.993606i | \(0.463984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 18.0000i | −0.318447 | + | 0.955341i | ||||
\(356\) | − | 7.07107i | − | 0.374766i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.65685 | 0.298974 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 24.0000 | + | 8.00000i | 1.25622 | + | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.0000i | − | 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.7279 | − | 4.24264i | −0.661693 | − | 0.220564i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6274 | 1.17160 | 0.585802 | − | 0.810454i | \(-0.300780\pi\) | ||||
0.585802 | + | 0.810454i | \(0.300780\pi\) | |||||||
\(374\) | −6.00000 | + | 2.82843i | −0.310253 | + | 0.146254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.4558i | 1.31278i | ||||||||
\(377\) | 16.9706 | 0.874028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 3.00000 | − | 9.00000i | 0.153897 | − | 0.461690i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.82843 | 0.144715 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.4142 | + | 1.24264i | −0.530757 | + | 0.0633308i | ||||
\(386\) | 19.7990i | 1.00774i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 12.0000i | − | 0.609208i | ||||||
\(389\) | 21.2132i | 1.07555i | 0.843088 | + | 0.537776i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537776i | \(0.819265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 15.0000i | − | 0.757614i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0000 | −0.705310 | ||||||||
\(395\) | 9.00000 | − | 27.0000i | 0.452839 | − | 1.35852i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000i | 0.301131i | 0.988600 | + | 0.150566i | \(0.0481095\pi\) | ||||
−0.988600 | + | 0.150566i | \(0.951890\pi\) | |||||||
\(398\) | − | 20.0000i | − | 1.00251i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | − | 3.00000i | −0.200000 | − | 0.150000i | ||||
\(401\) | − | 26.8701i | − | 1.34183i | −0.741536 | − | 0.670913i | \(-0.765902\pi\) | ||
0.741536 | − | 0.670913i | \(-0.234098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.48528i | 0.421117i | ||||||||
\(407\) | −8.48528 | − | 18.0000i | −0.420600 | − | 0.892227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.48528i | − | 0.419570i | −0.977748 | − | 0.209785i | \(-0.932724\pi\) | ||
0.977748 | − | 0.209785i | \(-0.0672764\pi\) | |||||||
\(410\) | −4.24264 | + | 12.7279i | −0.209529 | + | 0.628587i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.0000i | − | 0.591198i | ||||||
\(413\) | 12.0000i | 0.590481i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.89949 | + | 29.6985i | −0.485947 | + | 1.45784i | ||||
\(416\) | 14.1421i | 0.693375i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.7279 | + | 6.00000i | −0.622543 | + | 0.293470i | ||||
\(419\) | − | 39.5980i | − | 1.93449i | −0.253849 | − | 0.967244i | \(-0.581697\pi\) | ||
0.253849 | − | 0.967244i | \(-0.418303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0000 | 1.16969 | 0.584844 | − | 0.811146i | \(-0.301156\pi\) | ||||
0.584844 | + | 0.811146i | \(0.301156\pi\) | |||||||
\(422\) | 4.24264 | 0.206529 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.7279i | − | 0.618123i | ||||||
\(425\) | −6.00000 | + | 8.00000i | −0.291043 | + | 0.388057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.0000i | − | 0.580721i | ||||||
\(428\) | − | 14.0000i | − | 0.676716i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.00000 | + | 3.00000i | −0.0482243 | + | 0.144673i | ||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9706i | 0.812743i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.1838i | − | 1.82241i | −0.411951 | − | 0.911206i | \(-0.635153\pi\) | ||
0.411951 | − | 0.911206i | \(-0.364847\pi\) | |||||||
\(440\) | −2.63604 | − | 22.0919i | −0.125668 | − | 1.05319i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.65685 | −0.269069 | ||||||||
\(443\) | 25.4558 | 1.20944 | 0.604722 | − | 0.796437i | \(-0.293284\pi\) | ||||
0.604722 | + | 0.796437i | \(0.293284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | + | 15.0000i | −0.237023 | + | 0.711068i | ||||
\(446\) | −24.0000 | −1.13643 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.89949 | −0.467707 | ||||||||
\(449\) | − | 32.5269i | − | 1.53504i | −0.641025 | − | 0.767520i | \(-0.721491\pi\) | ||
0.641025 | − | 0.767520i | \(-0.278509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | + | 8.48528i | −0.847587 | + | 0.399556i | ||||
\(452\) | 12.7279 | 0.598671 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | −8.48528 | − | 2.82843i | −0.397796 | − | 0.132599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2843 | −1.32308 | −0.661541 | − | 0.749909i | \(-0.730097\pi\) | ||||
−0.661541 | + | 0.749909i | \(0.730097\pi\) | |||||||
\(458\) | − | 14.0000i | − | 0.654177i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 8.48528 | 0.392652 | 0.196326 | − | 0.980539i | \(-0.437099\pi\) | ||||
0.196326 | + | 0.980539i | \(0.437099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.00000 | − | 18.0000i | 0.276759 | − | 0.830278i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.4558 | −1.17170 | ||||||||
\(473\) | −4.24264 | + | 2.00000i | −0.195077 | + | 0.0919601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7279 | + | 16.9706i | −0.583997 | + | 0.778663i | ||||
\(476\) | 2.82843i | 0.129641i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6.00000i | − | 0.274434i | ||||||
\(479\) | −6.00000 | −0.274147 | −0.137073 | − | 0.990561i | \(-0.543770\pi\) | ||||
−0.137073 | + | 0.990561i | \(0.543770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.9706i | − | 0.773791i | ||||||
\(482\) | 8.48528 | 0.386494 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | − | 8.48528i | 0.318182 | − | 0.385695i | ||||
\(485\) | −8.48528 | + | 25.4558i | −0.385297 | + | 1.15589i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | 25.4558 | 1.15233 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.53553 | + | 10.6066i | −0.159719 | + | 0.479157i | ||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000i | 0.540453i | ||||||||
\(494\) | −12.0000 | −0.539906 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 12.0000i | − | 0.538274i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | −6.36396 | − | 9.19239i | −0.284605 | − | 0.411096i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.9706 | −0.757433 | ||||||||
\(503\) | − | 16.0000i | − | 0.713405i | −0.934218 | − | 0.356702i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356702i | \(-0.116099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.7279 | + | 4.24264i | 0.566385 | + | 0.188795i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.3848 | −0.815693 | ||||||||
\(509\) | 4.24264i | 0.188052i | 0.995570 | + | 0.0940259i | \(0.0299736\pi\) | ||||
−0.995570 | + | 0.0940259i | \(0.970026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 29.6985i | − | 1.30994i | ||||||
\(515\) | −8.48528 | + | 25.4558i | −0.373906 | + | 1.12172i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558 | − | 12.0000i | 1.11955 | − | 0.527759i | ||||
\(518\) | 8.48528 | 0.372822 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | − | 18.0000i | 0.263117 | − | 0.789352i | ||||
\(521\) | 7.07107i | 0.309789i | 0.987931 | + | 0.154895i | \(0.0495038\pi\) | ||||
−0.987931 | + | 0.154895i | \(0.950496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.07107 | −0.309196 | −0.154598 | − | 0.987977i | \(-0.549408\pi\) | ||||
−0.154598 | + | 0.987977i | \(0.549408\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | −0.348817 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −3.00000 | + | 9.00000i | −0.130312 | + | 0.390935i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000i | 0.260133i | ||||||||
\(533\) | −16.9706 | −0.735077 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.89949 | + | 29.6985i | −0.427992 | + | 1.28398i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.7279 | −0.548740 | ||||||||
\(539\) | −15.0000 | + | 7.07107i | −0.646096 | + | 0.304572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 33.9411i | − | 1.45924i | −0.683851 | − | 0.729621i | \(-0.739696\pi\) | ||
0.683851 | − | 0.729621i | \(-0.260304\pi\) | |||||||
\(542\) | 12.7279 | 0.546711 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.0000 | −0.428746 | ||||||||
\(545\) | 12.0000 | − | 36.0000i | 0.514024 | − | 1.54207i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.89949 | 0.423272 | 0.211636 | − | 0.977349i | \(-0.432121\pi\) | ||||
0.211636 | + | 0.977349i | \(0.432121\pi\) | |||||||
\(548\) | −4.24264 | −0.181237 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.34315 | + | 16.2426i | −0.142552 | + | 0.692589i | ||||
\(551\) | 25.4558i | 1.08446i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000i | 0.765438i | ||||||||
\(554\) | 31.1127i | 1.32185i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.24264i | 0.179928i | ||||||||
\(557\) | 34.0000i | 1.44063i | 0.693649 | + | 0.720313i | \(0.256002\pi\) | ||||
−0.693649 | + | 0.720313i | \(0.743998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 3.00000 | + | 1.00000i | 0.126773 | + | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6.00000i | − | 0.253095i | ||||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | − | 9.00000i | −1.13590 | − | 0.378633i | ||||
\(566\) | 1.41421i | 0.0594438i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.4558 | 1.06810 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.24264i | − | 0.177549i | −0.996052 | − | 0.0887745i | \(-0.971705\pi\) | ||
0.996052 | − | 0.0887745i | \(-0.0282950\pi\) | |||||||
\(572\) | 8.48528 | − | 4.00000i | 0.354787 | − | 0.167248i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.48528i | − | 0.354169i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.7279 | − | 4.24264i | −0.528498 | − | 0.176166i | ||||
\(581\) | − | 19.7990i | − | 0.821401i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.7279 | + | 6.00000i | −0.527137 | + | 0.248495i | ||||
\(584\) | − | 33.9411i | − | 1.40449i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0000 | −0.413096 | ||||||||
\(587\) | 42.4264 | 1.75113 | 0.875563 | − | 0.483105i | \(-0.160491\pi\) | ||||
0.875563 | + | 0.483105i | \(0.160491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 18.0000 | + | 6.00000i | 0.741048 | + | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000i | 0.246598i | ||||||||
\(593\) | − | 2.00000i | − | 0.0821302i | −0.999156 | − | 0.0410651i | \(-0.986925\pi\) | ||
0.999156 | − | 0.0410651i | \(-0.0130751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | − | 6.00000i | 0.0819920 | − | 0.245976i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3137i | 0.462266i | 0.972922 | + | 0.231133i | \(0.0742432\pi\) | ||||
−0.972922 | + | 0.231133i | \(0.925757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.9411i | 1.38449i | 0.721664 | + | 0.692244i | \(0.243378\pi\) | ||||
−0.721664 | + | 0.692244i | \(0.756622\pi\) | |||||||
\(602\) | − | 2.00000i | − | 0.0815139i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.24264i | − | 0.172631i | ||||||
\(605\) | −20.8492 | + | 13.0503i | −0.847642 | + | 0.530568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.5269 | 1.32023 | 0.660113 | − | 0.751166i | \(-0.270508\pi\) | ||||
0.660113 | + | 0.751166i | \(0.270508\pi\) | |||||||
\(608\) | −21.2132 | −0.860309 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0000 | − | 6.00000i | −0.728799 | − | 0.242933i | ||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.2843 | 1.14239 | 0.571195 | − | 0.820814i | \(-0.306480\pi\) | ||||
0.571195 | + | 0.820814i | \(0.306480\pi\) | |||||||
\(614\) | − | 24.0416i | − | 0.970241i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | + | 12.7279i | 0.241747 | + | 0.512823i | ||||
\(617\) | 4.24264 | 0.170802 | 0.0854011 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854011 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.9706 | 0.680458 | ||||||||
\(623\) | − | 10.0000i | − | 0.400642i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.0000i | 0.957704i | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −38.1838 | −1.51887 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 21.2132i | − | 0.842484i | ||||||
\(635\) | 39.0000 | + | 13.0000i | 1.54767 | + | 0.515889i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1421 | −0.560332 | ||||||||
\(638\) | 8.48528 | + | 18.0000i | 0.335936 | + | 0.712627i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | − | 6.36396i | 0.0838525 | − | 0.251558i | ||||
\(641\) | 15.5563i | 0.614439i | 0.951639 | + | 0.307219i | \(0.0993986\pi\) | ||||
−0.951639 | + | 0.307219i | \(0.900601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 8.48528i | − | 0.333849i | ||||||
\(647\) | 16.9706 | 0.667182 | 0.333591 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333591 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | + | 25.4558i | 0.471041 | + | 0.999229i | ||||
\(650\) | −8.48528 | + | 11.3137i | −0.332820 | + | 0.443760i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 24.0000i | − | 0.939913i | ||||||
\(653\) | −29.6985 | −1.16219 | −0.581096 | − | 0.813835i | \(-0.697376\pi\) | ||||
−0.581096 | + | 0.813835i | \(0.697376\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.1838 | + | 12.7279i | 1.49196 | + | 0.497321i | ||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000i | 0.467809i | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 12.0000i | 0.466393i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.0000 | 1.62992 | ||||||||
\(665\) | 4.24264 | − | 12.7279i | 0.164523 | − | 0.493568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 8.00000i | − | 0.309529i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | − | 25.4558i | −0.463255 | − | 0.982712i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.7696 | −1.41736 | −0.708681 | − | 0.705529i | \(-0.750709\pi\) | ||||
−0.708681 | + | 0.705529i | \(0.750709\pi\) | |||||||
\(674\) | 11.3137i | 0.435788i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | 46.0000i | 1.76792i | 0.467559 | + | 0.883962i | \(0.345134\pi\) | ||||
−0.467559 | + | 0.883962i | \(0.654866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.9706i | − | 0.651270i | ||||||
\(680\) | 12.7279 | + | 4.24264i | 0.488094 | + | 0.162698i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | −1.29872 | −0.649361 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649361 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | + | 3.00000i | 0.343872 | + | 0.114624i | ||||
\(686\) | − | 16.9706i | − | 0.647939i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.41421 | 0.0539164 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 14.0000i | 0.532200i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.0000 | −0.531433 | ||||||||
\(695\) | 3.00000 | − | 9.00000i | 0.113796 | − | 0.341389i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | −8.48528 | −0.321173 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.65685 | + | 4.24264i | 0.213809 | + | 0.160357i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4558 | 0.960085 | ||||||||
\(704\) | −21.0000 | + | 9.89949i | −0.791467 | + | 0.373101i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.24264i | 0.159674i | ||||||||
\(707\) | −8.48528 | −0.319122 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | −18.0000 | − | 6.00000i | −0.675528 | − | 0.225176i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.2132 | 0.794998 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.8284 | + | 2.48528i | −0.778939 | + | 0.0929443i | ||||
\(716\) | − | 5.65685i | − | 0.211407i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 24.0000i | − | 0.895672i | ||||||
\(719\) | 31.1127i | 1.16031i | 0.814507 | + | 0.580154i | \(0.197008\pi\) | ||||
−0.814507 | + | 0.580154i | \(0.802992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.9706i | − | 0.632017i | ||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.0000 | + | 18.0000i | 0.891338 | + | 0.668503i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 48.0000i | − | 1.78022i | −0.455744 | − | 0.890111i | \(-0.650627\pi\) | ||
0.455744 | − | 0.890111i | \(-0.349373\pi\) | |||||||
\(728\) | 12.0000i | 0.444750i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | + | 24.0000i | −0.296093 | + | 0.888280i | ||||
\(731\) | − | 2.82843i | − | 0.104613i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.1127 | 1.14917 | 0.574587 | − | 0.818444i | \(-0.305163\pi\) | ||||
0.574587 | + | 0.818444i | \(0.305163\pi\) | |||||||
\(734\) | 12.0000 | 0.442928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 46.6690i | − | 1.71675i | −0.513024 | − | 0.858374i | \(-0.671475\pi\) | ||
0.513024 | − | 0.858374i | \(-0.328525\pi\) | |||||||
\(740\) | −4.24264 | + | 12.7279i | −0.155963 | + | 0.467888i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 6.00000i | − | 0.220267i | ||||||
\(743\) | − | 10.0000i | − | 0.366864i | −0.983032 | − | 0.183432i | \(-0.941279\pi\) | ||
0.983032 | − | 0.183432i | \(-0.0587208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.1838 | − | 12.7279i | −1.39894 | − | 0.466315i | ||||
\(746\) | 22.6274i | 0.828449i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.82843 | + | 6.00000i | 0.103418 | + | 0.219382i | ||||
\(749\) | − | 19.7990i | − | 0.723439i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | −8.48528 | −0.309426 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.9706i | 0.618031i | ||||||||
\(755\) | −3.00000 | + | 9.00000i | −0.109181 | + | 0.327544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(758\) | 16.0000i | 0.581146i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.0000 | + | 9.00000i | 0.979393 | + | 0.326464i | ||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0000i | 0.868858i | ||||||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | −1.24264 | − | 10.4142i | −0.0447817 | − | 0.375302i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.7990 | 0.712581 | ||||||||
\(773\) | −4.24264 | −0.152597 | −0.0762986 | − | 0.997085i | \(-0.524310\pi\) | ||||
−0.0762986 | + | 0.997085i | \(0.524310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.0000 | 1.29232 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.2132 | −0.760530 | ||||||||
\(779\) | − | 25.4558i | − | 0.912050i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | − | 25.4558i | −0.429394 | − | 0.910882i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000 | 0.178571 | ||||||||
\(785\) | 16.9706 | − | 50.9117i | 0.605705 | − | 1.81712i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.89949 | −0.352879 | −0.176439 | − | 0.984311i | \(-0.556458\pi\) | ||||
−0.176439 | + | 0.984311i | \(0.556458\pi\) | |||||||
\(788\) | 14.0000i | 0.498729i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.0000 | + | 9.00000i | 0.960617 | + | 0.320206i | ||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.0000i | − | 0.852265i | ||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 29.6985 | 1.05197 | 0.525987 | − | 0.850493i | \(-0.323696\pi\) | ||||
0.525987 | + | 0.850493i | \(0.323696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9706i | 0.600375i | ||||||||
\(800\) | −15.0000 | + | 20.0000i | −0.530330 | + | 0.707107i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.8701 | 0.948815 | ||||||||
\(803\) | −33.9411 | + | 16.0000i | −1.19776 | + | 0.564628i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 18.0000i | − | 0.633238i | ||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.6690i | 1.63877i | 0.573242 | + | 0.819386i | \(0.305685\pi\) | ||||
−0.573242 | + | 0.819386i | \(0.694315\pi\) | |||||||
\(812\) | 8.48528 | 0.297775 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.0000 | − | 8.48528i | 0.630900 | − | 0.297409i | ||||
\(815\) | −16.9706 | + | 50.9117i | −0.594453 | + | 1.78336i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.00000i | − | 0.209913i | ||||||
\(818\) | 8.48528 | 0.296681 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.7279 | + | 4.24264i | 0.444478 | + | 0.148159i | ||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 36.0000 | 1.25412 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | −0.417533 | ||||||||
\(827\) | − | 34.0000i | − | 1.18230i | −0.806563 | − | 0.591148i | \(-0.798675\pi\) | ||
0.806563 | − | 0.591148i | \(-0.201325\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.00000 | 0.208389 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(830\) | −29.6985 | − | 9.89949i | −1.03085 | − | 0.343616i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.7990 | −0.686406 | ||||||||
\(833\) | − | 10.0000i | − | 0.346479i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.65685 | + | 16.9706i | −0.195764 | + | 0.587291i | ||||
\(836\) | 6.00000 | + | 12.7279i | 0.207514 | + | 0.440204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.5980 | 1.36789 | ||||||||
\(839\) | − | 50.9117i | − | 1.75767i | −0.477129 | − | 0.878833i | \(-0.658323\pi\) | ||
0.477129 | − | 0.878833i | \(-0.341677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 24.0000i | 0.827095i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.24264i | − | 0.146038i | ||||||
\(845\) | 10.6066 | + | 3.53553i | 0.364878 | + | 0.121626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.89949 | − | 12.0000i | 0.340151 | − | 0.412325i | ||||
\(848\) | 4.24264 | 0.145693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.00000 | − | 6.00000i | −0.274398 | − | 0.205798i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2843 | −0.968435 | −0.484218 | − | 0.874948i | \(-0.660896\pi\) | ||||
−0.484218 | + | 0.874948i | \(0.660896\pi\) | |||||||
\(854\) | 12.0000 | 0.410632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.0000 | 1.43553 | ||||||||
\(857\) | − | 26.0000i | − | 0.888143i | −0.895991 | − | 0.444072i | \(-0.853534\pi\) | ||
0.895991 | − | 0.444072i | \(-0.146466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.0000 | −1.63774 | −0.818869 | − | 0.573980i | \(-0.805399\pi\) | ||||
−0.818869 | + | 0.573980i | \(0.805399\pi\) | |||||||
\(860\) | 3.00000 | + | 1.00000i | 0.102299 | + | 0.0340997i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000i | 0.613082i | ||||||||
\(863\) | 33.9411 | 1.15537 | 0.577685 | − | 0.816260i | \(-0.303956\pi\) | ||||
0.577685 | + | 0.816260i | \(0.303956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.89949 | − | 29.6985i | 0.336593 | − | 1.00978i | ||||
\(866\) | 18.0000 | 0.611665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000 | + | 38.1838i | 0.610608 | + | 1.29530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −50.9117 | −1.72409 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.00000 | − | 13.0000i | −0.304256 | − | 0.439480i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3137 | 0.382037 | 0.191018 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191018 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(878\) | 38.1838 | 1.28864 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.36396 | − | 0.878680i | 0.248239 | − | 0.0296203i | ||||
\(881\) | 21.2132i | 0.714691i | 0.933972 | + | 0.357345i | \(0.116318\pi\) | ||||
−0.933972 | + | 0.357345i | \(0.883682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 5.65685i | 0.190261i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.4558i | 0.855206i | ||||||||
\(887\) | 2.00000i | 0.0671534i | 0.999436 | + | 0.0335767i | \(0.0106898\pi\) | ||||
−0.999436 | + | 0.0335767i | \(0.989310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.0000 | −0.872012 | ||||||||
\(890\) | −15.0000 | − | 5.00000i | −0.502801 | − | 0.167600i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0000i | 0.803579i | ||||||||
\(893\) | 36.0000i | 1.20469i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | + | 12.0000i | −0.133705 | + | 0.401116i | ||||
\(896\) | 4.24264i | 0.141737i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.5269 | 1.08544 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.48528i | − | 0.282686i | ||||||
\(902\) | −8.48528 | − | 18.0000i | −0.282529 | − | 0.599334i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.1838i | 1.26997i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000i | 0.398453i | 0.979953 | + | 0.199227i | \(0.0638430\pi\) | ||||
−0.979953 | + | 0.199227i | \(0.936157\pi\) | |||||||
\(908\) | 2.00000i | 0.0663723i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.82843 | − | 8.48528i | 0.0937614 | − | 0.281284i | ||||
\(911\) | 2.82843i | 0.0937100i | 0.998902 | + | 0.0468550i | \(0.0149199\pi\) | ||||
−0.998902 | + | 0.0468550i | \(0.985080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.7990 | − | 42.0000i | −0.655251 | − | 1.39000i | ||||
\(914\) | − | 28.2843i | − | 0.935561i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | −25.4558 | −0.840626 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.7279i | − | 0.419855i | −0.977717 | − | 0.209928i | \(-0.932677\pi\) | ||
0.977717 | − | 0.209928i | \(-0.0673229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0000i | 0.592798i | ||||||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.0000 | − | 24.0000i | 0.591836 | − | 0.789115i | ||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30.0000i | 0.984798i | ||||||||
\(929\) | 55.1543i | 1.80955i | 0.425885 | + | 0.904777i | \(0.359963\pi\) | ||||
−0.425885 | + | 0.904777i | \(0.640037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 21.2132i | − | 0.695235i | ||||||
\(932\) | 10.0000i | 0.327561i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.48528i | 0.277647i | ||||||||
\(935\) | −1.75736 | − | 14.7279i | −0.0574718 | − | 0.481655i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82843 | 0.0924007 | 0.0462003 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462003 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0000 | − | 6.00000i | −0.587095 | − | 0.195698i | ||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 8.48528i | − | 0.276172i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00000 | − | 4.24264i | −0.0650256 | − | 0.137940i | ||||
\(947\) | −33.9411 | −1.10294 | −0.551469 | − | 0.834195i | \(-0.685933\pi\) | ||||
−0.551469 | + | 0.834195i | \(0.685933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.0000 | −1.03876 | ||||||||
\(950\) | −16.9706 | − | 12.7279i | −0.550598 | − | 0.412948i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.48528 | −0.275010 | ||||||||
\(953\) | − | 46.0000i | − | 1.49009i | −0.667016 | − | 0.745043i | \(-0.732429\pi\) | ||
0.667016 | − | 0.745043i | \(-0.267571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00000 | + | 6.00000i | −0.0647185 | + | 0.194155i | ||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.00000i | − | 0.193851i | ||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 16.9706 | 0.547153 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | −42.0000 | − | 14.0000i | −1.35203 | − | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3259 | −1.68269 | −0.841344 | − | 0.540500i | \(-0.818235\pi\) | ||||
−0.841344 | + | 0.540500i | \(0.818235\pi\) | |||||||
\(968\) | 25.4558 | + | 21.0000i | 0.818182 | + | 0.674966i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.4558 | − | 8.48528i | −0.817338 | − | 0.272446i | ||||
\(971\) | 19.7990i | 0.635380i | 0.948195 | + | 0.317690i | \(0.102907\pi\) | ||||
−0.948195 | + | 0.317690i | \(0.897093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000i | 0.192351i | ||||||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.48528i | 0.271607i | ||||||||
\(977\) | 38.1838 | 1.22161 | 0.610803 | − | 0.791782i | \(-0.290847\pi\) | ||||
0.610803 | + | 0.791782i | \(0.290847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.0000 | − | 21.2132i | −0.319601 | − | 0.677977i | ||||
\(980\) | 10.6066 | + | 3.53553i | 0.338815 | + | 0.112938i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 36.0000i | − | 1.14881i | ||||||
\(983\) | 50.9117 | 1.62383 | 0.811915 | − | 0.583775i | \(-0.198425\pi\) | ||||
0.811915 | + | 0.583775i | \(0.198425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.89949 | − | 29.6985i | 0.315424 | − | 0.946272i | ||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000i | 0.381771i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0000 | 0.380617 | ||||||||
\(995\) | 42.4264 | + | 14.1421i | 1.34501 | + | 0.448336i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.5980 | −1.25408 | −0.627040 | − | 0.778987i | \(-0.715734\pi\) | ||||
−0.627040 | + | 0.778987i | \(0.715734\pi\) | |||||||
\(998\) | 32.0000i | 1.01294i | ||||||||
\(999\) | 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 | 495.2.d.b.494.3 | yes | 4 | |
3.2 | odd | 2 | 495.2.d.a.494.2 | yes | 4 | ||
5.2 | odd | 4 | 2475.2.f.b.2276.2 | 2 | |||
5.3 | odd | 4 | 2475.2.f.d.2276.1 | 2 | |||
5.4 | even | 2 | inner | 495.2.d.b.494.2 | yes | 4 | |
11.10 | odd | 2 | 495.2.d.a.494.1 | ✓ | 4 | ||
15.2 | even | 4 | 2475.2.f.c.2276.2 | 2 | |||
15.8 | even | 4 | 2475.2.f.a.2276.1 | 2 | |||
15.14 | odd | 2 | 495.2.d.a.494.3 | yes | 4 | ||
33.32 | even | 2 | inner | 495.2.d.b.494.4 | yes | 4 | |
55.32 | even | 4 | 2475.2.f.c.2276.1 | 2 | |||
55.43 | even | 4 | 2475.2.f.a.2276.2 | 2 | |||
55.54 | odd | 2 | 495.2.d.a.494.4 | yes | 4 | ||
165.32 | odd | 4 | 2475.2.f.b.2276.1 | 2 | |||
165.98 | odd | 4 | 2475.2.f.d.2276.2 | 2 | |||
165.164 | even | 2 | inner | 495.2.d.b.494.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.d.a.494.1 | ✓ | 4 | 11.10 | odd | 2 | ||
495.2.d.a.494.2 | yes | 4 | 3.2 | odd | 2 | ||
495.2.d.a.494.3 | yes | 4 | 15.14 | odd | 2 | ||
495.2.d.a.494.4 | yes | 4 | 55.54 | odd | 2 | ||
495.2.d.b.494.1 | yes | 4 | 165.164 | even | 2 | inner | |
495.2.d.b.494.2 | yes | 4 | 5.4 | even | 2 | inner | |
495.2.d.b.494.3 | yes | 4 | 1.1 | even | 1 | trivial | |
495.2.d.b.494.4 | yes | 4 | 33.32 | even | 2 | inner | |
2475.2.f.a.2276.1 | 2 | 15.8 | even | 4 | |||
2475.2.f.a.2276.2 | 2 | 55.43 | even | 4 | |||
2475.2.f.b.2276.1 | 2 | 165.32 | odd | 4 | |||
2475.2.f.b.2276.2 | 2 | 5.2 | odd | 4 | |||
2475.2.f.c.2276.1 | 2 | 55.32 | even | 4 | |||
2475.2.f.c.2276.2 | 2 | 15.2 | even | 4 | |||
2475.2.f.d.2276.1 | 2 | 5.3 | odd | 4 | |||
2475.2.f.d.2276.2 | 2 | 165.98 | odd | 4 |