Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (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: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.143 |
Dual form | 450.6.f.c.107.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | − | 2.82843i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.0000 | − | 33.0000i | 0.254548 | − | 0.254548i | −0.568285 | − | 0.822832i | \(-0.692393\pi\) |
0.822832 | + | 0.568285i | \(0.192393\pi\) | |||||||
\(8\) | 45.2548 | − | 45.2548i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 258.801i | − | 0.644888i | −0.946589 | − | 0.322444i | \(-0.895496\pi\) | ||
0.946589 | − | 0.322444i | \(-0.104504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 213.000 | + | 213.000i | 0.349560 | + | 0.349560i | 0.859945 | − | 0.510386i | \(-0.170497\pi\) |
−0.510386 | + | 0.859945i | \(0.670497\pi\) | |||||||
\(14\) | −186.676 | −0.254548 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | −462.448 | − | 462.448i | −0.388097 | − | 0.388097i | 0.485911 | − | 0.874008i | \(-0.338488\pi\) |
−0.874008 | + | 0.485911i | \(0.838488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 722.000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −732.000 | + | 732.000i | −0.322444 | + | 0.322444i | ||||
\(23\) | −810.344 | + | 810.344i | −0.319411 | + | 0.319411i | −0.848541 | − | 0.529130i | \(-0.822518\pi\) |
0.529130 | + | 0.848541i | \(0.322518\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1204.91i | − | 0.349560i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 528.000 | + | 528.000i | 0.127274 | + | 0.127274i | ||||
\(29\) | 2537.10 | 0.560199 | 0.280100 | − | 0.959971i | \(-0.409633\pi\) | ||||
0.280100 | + | 0.959971i | \(0.409633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2764.00 | 0.516575 | 0.258288 | − | 0.966068i | \(-0.416842\pi\) | ||||
0.258288 | + | 0.966068i | \(0.416842\pi\) | |||||||
\(32\) | 724.077 | + | 724.077i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2616.00i | 0.388097i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4467.00 | + | 4467.00i | −0.536428 | + | 0.536428i | −0.922478 | − | 0.386050i | \(-0.873839\pi\) |
0.386050 | + | 0.922478i | \(0.373839\pi\) | |||||||
\(38\) | −2042.12 | + | 2042.12i | −0.229416 | + | 0.229416i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7632.51i | − | 0.709100i | −0.935037 | − | 0.354550i | \(-0.884634\pi\) | ||
0.935037 | − | 0.354550i | \(-0.115366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3240.00 | + | 3240.00i | 0.267223 | + | 0.267223i | 0.827980 | − | 0.560757i | \(-0.189490\pi\) |
−0.560757 | + | 0.827980i | \(0.689490\pi\) | |||||||
\(44\) | 4140.82 | 0.322444 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4584.00 | 0.319411 | ||||||||
\(47\) | −9927.78 | − | 9927.78i | −0.655552 | − | 0.655552i | 0.298772 | − | 0.954325i | \(-0.403423\pi\) |
−0.954325 | + | 0.298772i | \(0.903423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14629.0i | 0.870411i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3408.00 | + | 3408.00i | −0.174780 | + | 0.174780i | ||||
\(53\) | 7937.98 | − | 7937.98i | 0.388169 | − | 0.388169i | −0.485865 | − | 0.874034i | \(-0.661495\pi\) |
0.874034 | + | 0.485865i | \(0.161495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2986.82i | − | 0.127274i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7176.00 | − | 7176.00i | −0.280100 | − | 0.280100i | ||||
\(59\) | 11450.9 | 0.428262 | 0.214131 | − | 0.976805i | \(-0.431308\pi\) | ||||
0.214131 | + | 0.976805i | \(0.431308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29750.0 | 1.02368 | 0.511838 | − | 0.859082i | \(-0.328965\pi\) | ||||
0.511838 | + | 0.859082i | \(0.328965\pi\) | |||||||
\(62\) | −7817.77 | − | 7817.77i | −0.258288 | − | 0.258288i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 4096.00i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19866.0 | + | 19866.0i | −0.540659 | + | 0.540659i | −0.923722 | − | 0.383063i | \(-0.874869\pi\) |
0.383063 | + | 0.923722i | \(0.374869\pi\) | |||||||
\(68\) | 7399.17 | − | 7399.17i | 0.194049 | − | 0.194049i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 71284.8i | − | 1.67823i | −0.543954 | − | 0.839115i | \(-0.683074\pi\) | ||
0.543954 | − | 0.839115i | \(-0.316926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45066.0 | − | 45066.0i | −0.989787 | − | 0.989787i | 0.0101611 | − | 0.999948i | \(-0.496766\pi\) |
−0.999948 | + | 0.0101611i | \(0.996766\pi\) | |||||||
\(74\) | 25269.2 | 0.536428 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11552.0 | 0.229416 | ||||||||
\(77\) | −8540.44 | − | 8540.44i | −0.164155 | − | 0.164155i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2992.00i | − | 0.0539379i | −0.999636 | − | 0.0269689i | \(-0.991414\pi\) | ||
0.999636 | − | 0.0269689i | \(-0.00858552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21588.0 | + | 21588.0i | −0.354550 | + | 0.354550i | ||||
\(83\) | 28603.9 | − | 28603.9i | 0.455753 | − | 0.455753i | −0.441505 | − | 0.897259i | \(-0.645555\pi\) |
0.897259 | + | 0.441505i | \(0.145555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 18328.2i | − | 0.267223i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11712.0 | − | 11712.0i | −0.161222 | − | 0.161222i | ||||
\(89\) | 11705.4 | 0.156644 | 0.0783219 | − | 0.996928i | \(-0.475044\pi\) | ||||
0.0783219 | + | 0.996928i | \(0.475044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14058.0 | 0.177959 | ||||||||
\(92\) | −12965.5 | − | 12965.5i | −0.159706 | − | 0.159706i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 56160.0i | 0.655552i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −111372. | + | 111372.i | −1.20184 | + | 1.20184i | −0.228234 | + | 0.973606i | \(0.573295\pi\) |
−0.973606 | + | 0.228234i | \(0.926705\pi\) | |||||||
\(98\) | 41377.1 | − | 41377.1i | 0.435206 | − | 0.435206i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10173.9i | − | 0.0992389i | −0.998768 | − | 0.0496195i | \(-0.984199\pi\) | ||
0.998768 | − | 0.0496195i | \(-0.0158009\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −109833. | − | 109833.i | −1.02009 | − | 1.02009i | −0.999794 | − | 0.0202991i | \(-0.993538\pi\) |
−0.0202991 | − | 0.999794i | \(-0.506462\pi\) | |||||||
\(104\) | 19278.6 | 0.174780 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −44904.0 | −0.388169 | ||||||||
\(107\) | −131352. | − | 131352.i | −1.10912 | − | 1.10912i | −0.993267 | − | 0.115851i | \(-0.963040\pi\) |
−0.115851 | − | 0.993267i | \(-0.536960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 23758.0i | − | 0.191533i | −0.995404 | − | 0.0957665i | \(-0.969470\pi\) | ||
0.995404 | − | 0.0957665i | \(-0.0305302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8448.00 | + | 8448.00i | −0.0636369 | + | 0.0636369i | ||||
\(113\) | 82336.9 | − | 82336.9i | 0.606595 | − | 0.606595i | −0.335460 | − | 0.942054i | \(-0.608892\pi\) |
0.942054 | + | 0.335460i | \(0.108892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 40593.6i | 0.280100i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −32388.0 | − | 32388.0i | −0.214131 | − | 0.214131i | ||||
\(119\) | −30521.6 | −0.197578 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 94073.0 | 0.584119 | ||||||||
\(122\) | −84145.7 | − | 84145.7i | −0.511838 | − | 0.511838i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 44224.0i | 0.258288i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −227979. | + | 227979.i | −1.25425 | + | 1.25425i | −0.300460 | + | 0.953795i | \(0.597140\pi\) |
−0.953795 | + | 0.300460i | \(0.902860\pi\) | |||||||
\(128\) | −11585.2 | + | 11585.2i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 46563.0i | 0.237062i | 0.992950 | + | 0.118531i | \(0.0378186\pi\) | ||||
−0.992950 | + | 0.118531i | \(0.962181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23826.0 | − | 23826.0i | −0.116794 | − | 0.116794i | ||||
\(134\) | 112379. | 0.540659 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −41856.0 | −0.194049 | ||||||||
\(137\) | −150652. | − | 150652.i | −0.685762 | − | 0.685762i | 0.275531 | − | 0.961292i | \(-0.411146\pi\) |
−0.961292 | + | 0.275531i | \(0.911146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 152756.i | − | 0.670596i | −0.942112 | − | 0.335298i | \(-0.891163\pi\) | ||
0.942112 | − | 0.335298i | \(-0.108837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −201624. | + | 201624.i | −0.839115 | + | 0.839115i | ||||
\(143\) | 55124.6 | − | 55124.6i | 0.225427 | − | 0.225427i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 254932.i | 0.989787i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −71472.0 | − | 71472.0i | −0.268214 | − | 0.268214i | ||||
\(149\) | −462787. | −1.70772 | −0.853858 | − | 0.520506i | \(-0.825743\pi\) | ||||
−0.853858 | + | 0.520506i | \(0.825743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −179168. | −0.639467 | −0.319733 | − | 0.947508i | \(-0.603593\pi\) | ||||
−0.319733 | + | 0.947508i | \(0.603593\pi\) | |||||||
\(152\) | −32674.0 | − | 32674.0i | −0.114708 | − | 0.114708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 48312.0i | 0.164155i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −371961. | + | 371961.i | −1.20434 | + | 1.20434i | −0.231504 | + | 0.972834i | \(0.574365\pi\) |
−0.972834 | + | 0.231504i | \(0.925635\pi\) | |||||||
\(158\) | −8462.65 | + | 8462.65i | −0.0269689 | + | 0.0269689i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 53482.7i | 0.162611i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −189294. | − | 189294.i | −0.558043 | − | 0.558043i | 0.370707 | − | 0.928750i | \(-0.379115\pi\) |
−0.928750 | + | 0.370707i | \(0.879115\pi\) | |||||||
\(164\) | 122120. | 0.354550 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −161808. | −0.455753 | ||||||||
\(167\) | −258933. | − | 258933.i | −0.718448 | − | 0.718448i | 0.249839 | − | 0.968287i | \(-0.419622\pi\) |
−0.968287 | + | 0.249839i | \(0.919622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 280555.i | − | 0.755616i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −51840.0 | + | 51840.0i | −0.133612 | + | 0.133612i | ||||
\(173\) | 160164. | − | 160164.i | 0.406864 | − | 0.406864i | −0.473779 | − | 0.880644i | \(-0.657111\pi\) |
0.880644 | + | 0.473779i | \(0.157111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 66253.1i | 0.161222i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −33108.0 | − | 33108.0i | −0.0783219 | − | 0.0783219i | ||||
\(179\) | −484420. | −1.13003 | −0.565015 | − | 0.825081i | \(-0.691130\pi\) | ||||
−0.565015 | + | 0.825081i | \(0.691130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −266402. | −0.604423 | −0.302212 | − | 0.953241i | \(-0.597725\pi\) | ||||
−0.302212 | + | 0.953241i | \(0.597725\pi\) | |||||||
\(182\) | −39762.0 | − | 39762.0i | −0.0889795 | − | 0.0889795i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 73344.0i | 0.159706i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −119682. | + | 119682.i | −0.250279 | + | 0.250279i | ||||
\(188\) | 158844. | − | 158844.i | 0.327776 | − | 0.327776i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 43283.4i | 0.0858496i | 0.999078 | + | 0.0429248i | \(0.0136676\pi\) | ||||
−0.999078 | + | 0.0429248i | \(0.986332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −160494. | − | 160494.i | −0.310146 | − | 0.310146i | 0.534820 | − | 0.844966i | \(-0.320379\pi\) |
−0.844966 | + | 0.534820i | \(0.820379\pi\) | |||||||
\(194\) | 630015. | 1.20184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −234064. | −0.435206 | ||||||||
\(197\) | −387345. | − | 387345.i | −0.711102 | − | 0.711102i | 0.255664 | − | 0.966766i | \(-0.417706\pi\) |
−0.966766 | + | 0.255664i | \(0.917706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 414340.i | − | 0.741693i | −0.928694 | − | 0.370846i | \(-0.879068\pi\) | ||
0.928694 | − | 0.370846i | \(-0.120932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28776.0 | + | 28776.0i | −0.0496195 | + | 0.0496195i | ||||
\(203\) | 83724.3 | − | 83724.3i | 0.142597 | − | 0.142597i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 621309.i | 1.02009i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −54528.0 | − | 54528.0i | −0.0873899 | − | 0.0873899i | ||||
\(209\) | −186854. | −0.295895 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 589796. | 0.912002 | 0.456001 | − | 0.889979i | \(-0.349281\pi\) | ||||
0.456001 | + | 0.889979i | \(0.349281\pi\) | |||||||
\(212\) | 127008. | + | 127008.i | 0.194084 | + | 0.194084i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 743040.i | 1.10912i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 91212.0 | − | 91212.0i | 0.131493 | − | 0.131493i | ||||
\(218\) | −67197.8 | + | 67197.8i | −0.0957665 | + | 0.0957665i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 197003.i | − | 0.271326i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −330381. | − | 330381.i | −0.444890 | − | 0.444890i | 0.448761 | − | 0.893652i | \(-0.351865\pi\) |
−0.893652 | + | 0.448761i | \(0.851865\pi\) | |||||||
\(224\) | 47789.1 | 0.0636369 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −465768. | −0.606595 | ||||||||
\(227\) | 549430. | + | 549430.i | 0.707698 | + | 0.707698i | 0.966051 | − | 0.258353i | \(-0.0831796\pi\) |
−0.258353 | + | 0.966051i | \(0.583180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 630494.i | − | 0.794497i | −0.917711 | − | 0.397248i | \(-0.869965\pi\) | ||
0.917711 | − | 0.397248i | \(-0.130035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 114816. | − | 114816.i | 0.140050 | − | 0.140050i | ||||
\(233\) | 244516. | − | 244516.i | 0.295065 | − | 0.295065i | −0.544012 | − | 0.839077i | \(-0.683096\pi\) |
0.839077 | + | 0.544012i | \(0.183096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 183214.i | 0.214131i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 86328.0 | + | 86328.0i | 0.0987892 | + | 0.0987892i | ||||
\(239\) | −792670. | −0.897630 | −0.448815 | − | 0.893625i | \(-0.648154\pi\) | ||||
−0.448815 | + | 0.893625i | \(0.648154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 356612. | 0.395506 | 0.197753 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197753 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(242\) | −266079. | − | 266079.i | −0.292060 | − | 0.292060i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 476000.i | 0.511838i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 153786. | − | 153786.i | 0.160389 | − | 0.160389i | ||||
\(248\) | 125084. | − | 125084.i | 0.129144 | − | 0.129144i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.15393e6i | − | 1.15610i | −0.816003 | − | 0.578048i | \(-0.803815\pi\) | ||
0.816003 | − | 0.578048i | \(-0.196185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 209718. | + | 209718.i | 0.205984 | + | 0.205984i | ||||
\(254\) | 1.28964e6 | 1.25425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 859945. | + | 859945.i | 0.812153 | + | 0.812153i | 0.984956 | − | 0.172803i | \(-0.0552825\pi\) |
−0.172803 | + | 0.984956i | \(0.555282\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 294822.i | 0.273093i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 131700. | − | 131700.i | 0.118531 | − | 0.118531i | ||||
\(263\) | −679047. | + | 679047.i | −0.605356 | + | 0.605356i | −0.941729 | − | 0.336373i | \(-0.890800\pi\) |
0.336373 | + | 0.941729i | \(0.390800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 134780.i | 0.116794i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −317856. | − | 317856.i | −0.270329 | − | 0.270329i | ||||
\(269\) | −672535. | −0.566675 | −0.283338 | − | 0.959020i | \(-0.591442\pi\) | ||||
−0.283338 | + | 0.959020i | \(0.591442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.57142e6 | 1.29978 | 0.649889 | − | 0.760029i | \(-0.274815\pi\) | ||||
0.649889 | + | 0.760029i | \(0.274815\pi\) | |||||||
\(272\) | 118387. | + | 118387.i | 0.0970243 | + | 0.0970243i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 852216.i | 0.685762i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.04804e6 | − | 1.04804e6i | 0.820689 | − | 0.820689i | −0.165517 | − | 0.986207i | \(-0.552929\pi\) |
0.986207 | + | 0.165517i | \(0.0529294\pi\) | |||||||
\(278\) | −432059. | + | 432059.i | −0.335298 | + | 0.335298i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.74425e6i | − | 1.31778i | −0.752240 | − | 0.658889i | \(-0.771027\pi\) | ||
0.752240 | − | 0.658889i | \(-0.228973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.43080e6 | + | 1.43080e6i | 1.06197 | + | 1.06197i | 0.997948 | + | 0.0640246i | \(0.0203936\pi\) |
0.0640246 | + | 0.997948i | \(0.479606\pi\) | |||||||
\(284\) | 1.14056e6 | 0.839115 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −311832. | −0.225427 | ||||||||
\(287\) | −251873. | − | 251873.i | −0.180500 | − | 0.180500i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 992141.i | − | 0.698761i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 721056. | − | 721056.i | 0.494894 | − | 0.494894i | ||||
\(293\) | −666018. | + | 666018.i | −0.453228 | + | 0.453228i | −0.896425 | − | 0.443196i | \(-0.853844\pi\) |
0.443196 | + | 0.896425i | \(0.353844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 404307.i | 0.268214i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.30896e6 | + | 1.30896e6i | 0.853858 | + | 0.853858i | ||||
\(299\) | −345207. | −0.223306 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 213840. | 0.136042 | ||||||||
\(302\) | 506764. | + | 506764.i | 0.319733 | + | 0.319733i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 184832.i | 0.114708i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.08216e6 | − | 1.08216e6i | 0.655308 | − | 0.655308i | −0.298958 | − | 0.954266i | \(-0.596639\pi\) |
0.954266 | + | 0.298958i | \(0.0966391\pi\) | |||||||
\(308\) | 136647. | − | 136647.i | 0.0820773 | − | 0.0820773i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.79768e6i | − | 1.05393i | −0.849887 | − | 0.526966i | \(-0.823330\pi\) | ||
0.849887 | − | 0.526966i | \(-0.176670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 799266. | + | 799266.i | 0.461138 | + | 0.461138i | 0.899028 | − | 0.437891i | \(-0.144274\pi\) |
−0.437891 | + | 0.899028i | \(0.644274\pi\) | |||||||
\(314\) | 2.10413e6 | 1.20434 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 47872.0 | 0.0269689 | ||||||||
\(317\) | 906831. | + | 906831.i | 0.506848 | + | 0.506848i | 0.913558 | − | 0.406709i | \(-0.133324\pi\) |
−0.406709 | + | 0.913558i | \(0.633324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 656604.i | − | 0.361266i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 151272. | − | 151272.i | 0.0813053 | − | 0.0813053i | ||||
\(323\) | −333887. | + | 333887.i | −0.178071 | + | 0.178071i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.07081e6i | 0.558043i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −345408. | − | 345408.i | −0.177275 | − | 0.177275i | ||||
\(329\) | −655233. | −0.333738 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 107546. | 0.0539541 | 0.0269770 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269770 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(332\) | 457662. | + | 457662.i | 0.227877 | + | 0.227877i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.46474e6i | 0.718448i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.31587e6 | − | 1.31587e6i | 0.631156 | − | 0.631156i | −0.317202 | − | 0.948358i | \(-0.602743\pi\) |
0.948358 | + | 0.317202i | \(0.102743\pi\) | |||||||
\(338\) | −793529. | + | 793529.i | −0.377808 | + | 0.377808i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 715326.i | − | 0.333133i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.03739e6 | + | 1.03739e6i | 0.476108 | + | 0.476108i | ||||
\(344\) | 293251. | 0.133612 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −906024. | −0.406864 | ||||||||
\(347\) | 1.78519e6 | + | 1.78519e6i | 0.795905 | + | 0.795905i | 0.982447 | − | 0.186542i | \(-0.0597279\pi\) |
−0.186542 | + | 0.982447i | \(0.559728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.47933e6i | 0.650134i | 0.945691 | + | 0.325067i | \(0.105387\pi\) | ||||
−0.945691 | + | 0.325067i | \(0.894613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 187392. | − | 187392.i | 0.0806110 | − | 0.0806110i | ||||
\(353\) | −2.22216e6 | + | 2.22216e6i | −0.949156 | + | 0.949156i | −0.998769 | − | 0.0496125i | \(-0.984201\pi\) |
0.0496125 | + | 0.998769i | \(0.484201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 187287.i | 0.0783219i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.37015e6 | + | 1.37015e6i | 0.565015 | + | 0.565015i | ||||
\(359\) | −33075.6 | −0.0135448 | −0.00677239 | − | 0.999977i | \(-0.502156\pi\) | ||||
−0.00677239 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.95482e6 | 0.789474 | ||||||||
\(362\) | 753499. | + | 753499.i | 0.302212 | + | 0.302212i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 224928.i | 0.0889795i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24097e6 | − | 2.24097e6i | 0.868501 | − | 0.868501i | −0.123806 | − | 0.992306i | \(-0.539510\pi\) |
0.992306 | + | 0.123806i | \(0.0395099\pi\) | |||||||
\(368\) | 207448. | − | 207448.i | 0.0798528 | − | 0.0798528i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 523907.i | − | 0.197615i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.01738e6 | + | 1.01738e6i | 0.378625 | + | 0.378625i | 0.870606 | − | 0.491981i | \(-0.163727\pi\) |
−0.491981 | + | 0.870606i | \(0.663727\pi\) | |||||||
\(374\) | 677024. | 0.250279 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −898560. | −0.327776 | ||||||||
\(377\) | 540402. | + | 540402.i | 0.195823 | + | 0.195823i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.12654e6i | − | 0.760459i | −0.924892 | − | 0.380229i | \(-0.875845\pi\) | ||
0.924892 | − | 0.380229i | \(-0.124155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 122424. | − | 122424.i | 0.0429248 | − | 0.0429248i | ||||
\(383\) | 1.07621e6 | − | 1.07621e6i | 0.374885 | − | 0.374885i | −0.494368 | − | 0.869253i | \(-0.664600\pi\) |
0.869253 | + | 0.494368i | \(0.164600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 907891.i | 0.310146i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.78195e6 | − | 1.78195e6i | −0.600920 | − | 0.600920i | ||||
\(389\) | −4.19716e6 | −1.40631 | −0.703156 | − | 0.711036i | \(-0.748226\pi\) | ||||
−0.703156 | + | 0.711036i | \(0.748226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 749484. | 0.247925 | ||||||||
\(392\) | 662033. | + | 662033.i | 0.217603 | + | 0.217603i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.19115e6i | 0.711102i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.02632e6 | − | 2.02632e6i | 0.645257 | − | 0.645257i | −0.306586 | − | 0.951843i | \(-0.599187\pi\) |
0.951843 | + | 0.306586i | \(0.0991868\pi\) | |||||||
\(398\) | −1.17193e6 | + | 1.17193e6i | −0.370846 | + | 0.370846i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.02761e6i | 1.25080i | 0.780306 | + | 0.625398i | \(0.215063\pi\) | ||||
−0.780306 | + | 0.625398i | \(0.784937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 588732. | + | 588732.i | 0.180574 | + | 0.180574i | ||||
\(404\) | 162782. | 0.0496195 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −473616. | −0.142597 | ||||||||
\(407\) | 1.15606e6 | + | 1.15606e6i | 0.345936 | + | 0.345936i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.65537e6i | − | 1.67168i | −0.548973 | − | 0.835840i | \(-0.684981\pi\) | ||
0.548973 | − | 0.835840i | \(-0.315019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.75733e6 | − | 1.75733e6i | 0.510047 | − | 0.510047i | ||||
\(413\) | 377879. | − | 377879.i | 0.109013 | − | 0.109013i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 308457.i | 0.0873899i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 528504. | + | 528504.i | 0.147947 | + | 0.147947i | ||||
\(419\) | −43567.7 | −0.0121235 | −0.00606177 | − | 0.999982i | \(-0.501930\pi\) | ||||
−0.00606177 | + | 0.999982i | \(0.501930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.65783e6 | −1.00582 | −0.502908 | − | 0.864340i | \(-0.667736\pi\) | ||||
−0.502908 | + | 0.864340i | \(0.667736\pi\) | |||||||
\(422\) | −1.66820e6 | − | 1.66820e6i | −0.456001 | − | 0.456001i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 718464.i | − | 0.194084i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 981750. | − | 981750.i | 0.260574 | − | 0.260574i | ||||
\(428\) | 2.10163e6 | − | 2.10163e6i | 0.554559 | − | 0.554559i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 249959.i | − | 0.0648151i | −0.999475 | − | 0.0324076i | \(-0.989683\pi\) | ||
0.999475 | − | 0.0324076i | \(-0.0103175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.11368e6 | − | 1.11368e6i | −0.285456 | − | 0.285456i | 0.549824 | − | 0.835281i | \(-0.314695\pi\) |
−0.835281 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(434\) | −515973. | −0.131493 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 380128. | 0.0957665 | ||||||||
\(437\) | 585069. | + | 585069.i | 0.146556 | + | 0.146556i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.89281e6i | 0.716405i | 0.933644 | + | 0.358203i | \(0.116610\pi\) | ||||
−0.933644 | + | 0.358203i | \(0.883390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −557208. | + | 557208.i | −0.135663 | + | 0.135663i | ||||
\(443\) | 739934. | − | 739934.i | 0.179136 | − | 0.179136i | −0.611843 | − | 0.790979i | \(-0.709572\pi\) |
0.790979 | + | 0.611843i | \(0.209572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.86892e6i | 0.444890i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −135168. | − | 135168.i | −0.0318184 | − | 0.0318184i | ||||
\(449\) | −1.73408e6 | −0.405932 | −0.202966 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202966 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.97530e6 | −0.457290 | ||||||||
\(452\) | 1.31739e6 | + | 1.31739e6i | 0.303297 | + | 0.303297i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.10805e6i | − | 0.707698i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.99052e6 | + | 2.99052e6i | −0.669817 | + | 0.669817i | −0.957674 | − | 0.287856i | \(-0.907057\pi\) |
0.287856 | + | 0.957674i | \(0.407057\pi\) | |||||||
\(458\) | −1.78331e6 | + | 1.78331e6i | −0.397248 | + | 0.397248i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.77512e6i | 0.827329i | 0.910429 | + | 0.413665i | \(0.135751\pi\) | ||||
−0.910429 | + | 0.413665i | \(0.864249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.77997e6 | − | 1.77997e6i | −0.385887 | − | 0.385887i | 0.487331 | − | 0.873218i | \(-0.337971\pi\) |
−0.873218 | + | 0.487331i | \(0.837971\pi\) | |||||||
\(464\) | −649497. | −0.140050 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.38319e6 | −0.295065 | ||||||||
\(467\) | −1.10978e6 | − | 1.10978e6i | −0.235475 | − | 0.235475i | 0.579498 | − | 0.814973i | \(-0.303249\pi\) |
−0.814973 | + | 0.579498i | \(0.803249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.31116e6i | 0.275247i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 518208. | − | 518208.i | 0.107065 | − | 0.107065i | ||||
\(473\) | 838516. | − | 838516.i | 0.172329 | − | 0.172329i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 488345.i | − | 0.0987892i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.24201e6 | + | 2.24201e6i | 0.448815 | + | 0.448815i | ||||
\(479\) | 521344. | 0.103821 | 0.0519106 | − | 0.998652i | \(-0.483469\pi\) | ||||
0.0519106 | + | 0.998652i | \(0.483469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.90294e6 | −0.375027 | ||||||||
\(482\) | −1.00865e6 | − | 1.00865e6i | −0.197753 | − | 0.197753i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.50517e6i | 0.292060i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.98473e6 | + | 2.98473e6i | −0.570272 | + | 0.570272i | −0.932204 | − | 0.361932i | \(-0.882117\pi\) |
0.361932 | + | 0.932204i | \(0.382117\pi\) | |||||||
\(488\) | 1.34633e6 | − | 1.34633e6i | 0.255919 | − | 0.255919i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.65071e6i | − | 0.496202i | −0.968734 | − | 0.248101i | \(-0.920193\pi\) | ||
0.968734 | − | 0.248101i | \(-0.0798066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.17328e6 | − | 1.17328e6i | −0.217412 | − | 0.217412i | ||||
\(494\) | −869945. | −0.160389 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −707584. | −0.129144 | ||||||||
\(497\) | −2.35240e6 | − | 2.35240e6i | −0.427189 | − | 0.427189i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.33298e6i | − | 0.239648i | −0.992795 | − | 0.119824i | \(-0.961767\pi\) | ||
0.992795 | − | 0.119824i | \(-0.0382330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.26380e6 | + | 3.26380e6i | −0.578048 | + | 0.578048i | ||||
\(503\) | −3.60041e6 | + | 3.60041e6i | −0.634500 | + | 0.634500i | −0.949193 | − | 0.314693i | \(-0.898098\pi\) |
0.314693 | + | 0.949193i | \(0.398098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.18634e6i | − | 0.205984i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.64766e6 | − | 3.64766e6i | −0.627127 | − | 0.627127i | ||||
\(509\) | 1.32877e6 | 0.227329 | 0.113665 | − | 0.993519i | \(-0.463741\pi\) | ||||
0.113665 | + | 0.993519i | \(0.463741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.97436e6 | −0.503896 | ||||||||
\(512\) | −185364. | − | 185364.i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 4.86458e6i | − | 0.812153i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.56932e6 | + | 2.56932e6i | −0.422758 | + | 0.422758i | ||||
\(518\) | 833883. | − | 833883.i | 0.136546 | − | 0.136546i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.53594e6i | 1.21631i | 0.793820 | + | 0.608153i | \(0.208089\pi\) | ||||
−0.793820 | + | 0.608153i | \(0.791911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.14775e6 | − | 1.14775e6i | −0.183481 | − | 0.183481i | 0.609390 | − | 0.792871i | \(-0.291415\pi\) |
−0.792871 | + | 0.609390i | \(0.791415\pi\) | |||||||
\(524\) | −745008. | −0.118531 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.84127e6 | 0.605356 | ||||||||
\(527\) | −1.27821e6 | − | 1.27821e6i | −0.200481 | − | 0.200481i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.12303e6i | 0.795953i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 381216. | − | 381216.i | 0.0583972 | − | 0.0583972i | ||||
\(533\) | 1.62572e6 | − | 1.62572e6i | 0.247873 | − | 0.247873i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.79807e6i | 0.270329i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.90222e6 | + | 1.90222e6i | 0.283338 | + | 0.283338i | ||||
\(539\) | 3.78600e6 | 0.561318 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8642.00 | 0.00126947 | 0.000634733 | − | 1.00000i | \(-0.499798\pi\) | ||||
0.000634733 | 1.00000i | \(0.499798\pi\) | ||||||||
\(542\) | −4.44465e6 | − | 4.44465e6i | −0.649889 | − | 0.649889i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 669696.i | − | 0.0970243i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.56553e6 | + | 7.56553e6i | −1.08111 | + | 1.08111i | −0.0847073 | + | 0.996406i | \(0.526996\pi\) |
−0.996406 | + | 0.0847073i | \(0.973004\pi\) | |||||||
\(548\) | 2.41043e6 | − | 2.41043e6i | 0.342881 | − | 0.342881i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.83179e6i | − | 0.257037i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −98736.0 | − | 98736.0i | −0.0137298 | − | 0.0137298i | ||||
\(554\) | −5.92862e6 | −0.820689 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.44410e6 | 0.335298 | ||||||||
\(557\) | −7.92605e6 | − | 7.92605e6i | −1.08248 | − | 1.08248i | −0.996278 | − | 0.0861989i | \(-0.972528\pi\) |
−0.0861989 | − | 0.996278i | \(-0.527472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38024e6i | 0.186821i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.93348e6 | + | 4.93348e6i | −0.658889 | + | 0.658889i | ||||
\(563\) | 7.04595e6 | − | 7.04595e6i | 0.936847 | − | 0.936847i | −0.0612744 | − | 0.998121i | \(-0.519516\pi\) |
0.998121 | + | 0.0612744i | \(0.0195165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 8.09384e6i | − | 1.06197i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.22598e6 | − | 3.22598e6i | −0.419557 | − | 0.419557i | ||||
\(569\) | 4.20382e6 | 0.544332 | 0.272166 | − | 0.962250i | \(-0.412260\pi\) | ||||
0.272166 | + | 0.962250i | \(0.412260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26883e7 | 1.62860 | 0.814298 | − | 0.580448i | \(-0.197122\pi\) | ||||
0.814298 | + | 0.580448i | \(0.197122\pi\) | |||||||
\(572\) | 881994. | + | 881994.i | 0.112713 | + | 0.112713i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.42481e6i | 0.180500i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.48634e6 | + | 3.48634e6i | −0.435943 | + | 0.435943i | −0.890644 | − | 0.454701i | \(-0.849746\pi\) |
0.454701 | + | 0.890644i | \(0.349746\pi\) | |||||||
\(578\) | −2.80620e6 | + | 2.80620e6i | −0.349381 | + | 0.349381i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.88786e6i | − | 0.232022i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.05436e6 | − | 2.05436e6i | −0.250325 | − | 0.250325i | ||||
\(584\) | −4.07891e6 | −0.494894 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.76757e6 | 0.453228 | ||||||||
\(587\) | −7.17632e6 | − | 7.17632e6i | −0.859621 | − | 0.859621i | 0.131673 | − | 0.991293i | \(-0.457965\pi\) |
−0.991293 | + | 0.131673i | \(0.957965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.99561e6i | − | 0.237021i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.14355e6 | − | 1.14355e6i | 0.134107 | − | 0.134107i | ||||
\(593\) | 993240. | − | 993240.i | 0.115989 | − | 0.115989i | −0.646730 | − | 0.762719i | \(-0.723864\pi\) |
0.762719 | + | 0.646730i | \(0.223864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.40460e6i | − | 0.853858i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 976392. | + | 976392.i | 0.111653 | + | 0.111653i | ||||
\(599\) | 1.15789e7 | 1.31856 | 0.659278 | − | 0.751899i | \(-0.270862\pi\) | ||||
0.659278 | + | 0.751899i | \(0.270862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.10155e7 | −1.24399 | −0.621996 | − | 0.783020i | \(-0.713678\pi\) | ||||
−0.621996 | + | 0.783020i | \(0.713678\pi\) | |||||||
\(602\) | −604831. | − | 604831.i | −0.0680210 | − | 0.0680210i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 2.86669e6i | − | 0.319733i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.27601e6 | + | 6.27601e6i | −0.691372 | + | 0.691372i | −0.962534 | − | 0.271162i | \(-0.912592\pi\) |
0.271162 | + | 0.962534i | \(0.412592\pi\) | |||||||
\(608\) | 522784. | − | 522784.i | 0.0573539 | − | 0.0573539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.22923e6i | − | 0.458309i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.31846e6 | − | 5.31846e6i | −0.571656 | − | 0.571656i | 0.360935 | − | 0.932591i | \(-0.382458\pi\) |
−0.932591 | + | 0.360935i | \(0.882458\pi\) | |||||||
\(614\) | −6.12162e6 | −0.655308 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −772992. | −0.0820773 | ||||||||
\(617\) | 3.55725e6 | + | 3.55725e6i | 0.376185 | + | 0.376185i | 0.869724 | − | 0.493539i | \(-0.164297\pi\) |
−0.493539 | + | 0.869724i | \(0.664297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.89359e7i | 1.98636i | 0.116586 | + | 0.993181i | \(0.462805\pi\) | ||||
−0.116586 | + | 0.993181i | \(0.537195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.08462e6 | + | 5.08462e6i | −0.526966 | + | 0.526966i | ||||
\(623\) | 386280. | − | 386280.i | 0.0398733 | − | 0.0398733i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 4.52133e6i | − | 0.461138i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.95138e6 | − | 5.95138e6i | −0.602169 | − | 0.602169i | ||||
\(629\) | 4.13151e6 | 0.416373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.62094e6 | 0.861948 | 0.430974 | − | 0.902364i | \(-0.358170\pi\) | ||||
0.430974 | + | 0.902364i | \(0.358170\pi\) | |||||||
\(632\) | −135402. | − | 135402.i | −0.0134845 | − | 0.0134845i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 5.12981e6i | − | 0.506848i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.11598e6 | + | 3.11598e6i | −0.304261 | + | 0.304261i | ||||
\(638\) | −1.85716e6 | + | 1.85716e6i | −0.180633 | + | 0.180633i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.95492e6i | 0.284054i | 0.989863 | + | 0.142027i | \(0.0453619\pi\) | ||||
−0.989863 | + | 0.142027i | \(0.954638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.32876e6 | − | 8.32876e6i | −0.794425 | − | 0.794425i | 0.187785 | − | 0.982210i | \(-0.439869\pi\) |
−0.982210 | + | 0.187785i | \(0.939869\pi\) | |||||||
\(644\) | −855724. | −0.0813053 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.88875e6 | 0.178071 | ||||||||
\(647\) | −2.45184e6 | − | 2.45184e6i | −0.230267 | − | 0.230267i | 0.582537 | − | 0.812804i | \(-0.302060\pi\) |
−0.812804 | + | 0.582537i | \(0.802060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.96350e6i | − | 0.276181i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.02870e6 | − | 3.02870e6i | 0.279022 | − | 0.279022i | ||||
\(653\) | 1.32744e7 | − | 1.32744e7i | 1.21824 | − | 1.21824i | 0.249988 | − | 0.968249i | \(-0.419573\pi\) |
0.968249 | − | 0.249988i | \(-0.0804265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.95392e6i | 0.177275i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.85328e6 | + | 1.85328e6i | 0.166869 | + | 0.166869i | ||||
\(659\) | 1.75882e7 | 1.57764 | 0.788818 | − | 0.614626i | \(-0.210693\pi\) | ||||
0.788818 | + | 0.614626i | \(0.210693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.27670e6 | −0.558763 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(662\) | −304186. | − | 304186.i | −0.0269770 | − | 0.0269770i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.58893e6i | − | 0.227877i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.05592e6 | + | 2.05592e6i | −0.178934 | + | 0.178934i | ||||
\(668\) | 4.14292e6 | − | 4.14292e6i | 0.359224 | − | 0.359224i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.69933e6i | − | 0.660156i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.06163e6 | − | 5.06163e6i | −0.430777 | − | 0.430777i | 0.458115 | − | 0.888893i | \(-0.348525\pi\) |
−0.888893 | + | 0.458115i | \(0.848525\pi\) | |||||||
\(674\) | −7.44366e6 | −0.631156 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.48888e6 | 0.377808 | ||||||||
\(677\) | −4.86767e6 | − | 4.86767e6i | −0.408178 | − | 0.408178i | 0.472925 | − | 0.881103i | \(-0.343198\pi\) |
−0.881103 | + | 0.472925i | \(0.843198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.35055e6i | 0.611851i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.02325e6 | + | 2.02325e6i | −0.166567 | + | 0.166567i | ||||
\(683\) | −9.89201e6 | + | 9.89201e6i | −0.811395 | + | 0.811395i | −0.984843 | − | 0.173448i | \(-0.944509\pi\) |
0.173448 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 5.86835e6i | − | 0.476108i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −829440. | − | 829440.i | −0.0668058 | − | 0.0668058i | ||||
\(689\) | 3.38158e6 | 0.271376 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.09191e6 | −0.246338 | −0.123169 | − | 0.992386i | \(-0.539306\pi\) | ||||
−0.123169 | + | 0.992386i | \(0.539306\pi\) | |||||||
\(692\) | 2.56262e6 | + | 2.56262e6i | 0.203432 | + | 0.203432i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.00986e7i | − | 0.795905i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.52964e6 | + | 3.52964e6i | −0.275200 | + | 0.275200i | ||||
\(698\) | 4.18419e6 | − | 4.18419e6i | 0.325067 | − | 0.325067i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23298e7i | 0.947675i | 0.880612 | + | 0.473837i | \(0.157132\pi\) | ||||
−0.880612 | + | 0.473837i | \(0.842868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.22517e6 | + | 3.22517e6i | 0.246130 | + | 0.246130i | ||||
\(704\) | −1.06005e6 | −0.0806110 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.25704e7 | 0.949156 | ||||||||
\(707\) | −335737. | − | 335737.i | −0.0252610 | − | 0.0252610i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.51293e6i | 0.486587i | 0.969953 | + | 0.243294i | \(0.0782278\pi\) | ||||
−0.969953 | + | 0.243294i | \(0.921772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 529728. | − | 529728.i | 0.0391609 | − | 0.0391609i | ||||
\(713\) | −2.23979e6 | + | 2.23979e6i | −0.165000 | + | 0.165000i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 7.75073e6i | − | 0.565015i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 93552.0 | + | 93552.0i | 0.00677239 | + | 0.00677239i | ||||
\(719\) | 1.02328e7 | 0.738195 | 0.369098 | − | 0.929391i | \(-0.379667\pi\) | ||||
0.369098 | + | 0.929391i | \(0.379667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.24898e6 | −0.519324 | ||||||||
\(722\) | −5.52905e6 | − | 5.52905e6i | −0.394737 | − | 0.394737i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.26243e6i | − | 0.302212i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.39935e7 | − | 1.39935e7i | 0.981949 | − | 0.981949i | −0.0178905 | − | 0.999840i | \(-0.505695\pi\) |
0.999840 | + | 0.0178905i | \(0.00569504\pi\) | |||||||
\(728\) | 636192. | − | 636192.i | 0.0444898 | − | 0.0444898i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.99666e6i | − | 0.207417i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.89732e6 | + | 6.89732e6i | 0.474155 | + | 0.474155i | 0.903256 | − | 0.429101i | \(-0.141170\pi\) |
−0.429101 | + | 0.903256i | \(0.641170\pi\) | |||||||
\(734\) | −1.26768e7 | −0.868501 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.17350e6 | −0.0798528 | ||||||||
\(737\) | 5.14134e6 | + | 5.14134e6i | 0.348665 | + | 0.348665i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.89996e6i | 0.666841i | 0.942778 | + | 0.333421i | \(0.108203\pi\) | ||||
−0.942778 | + | 0.333421i | \(0.891797\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.48183e6 | + | 1.48183e6i | −0.0988073 | + | 0.0988073i | ||||
\(743\) | 1.42800e7 | − | 1.42800e7i | 0.948976 | − | 0.948976i | −0.0497843 | − | 0.998760i | \(-0.515853\pi\) |
0.998760 | + | 0.0497843i | \(0.0158534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 5.75514e6i | − | 0.378625i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.91491e6 | − | 1.91491e6i | −0.125140 | − | 0.125140i | ||||
\(749\) | −8.66924e6 | −0.564646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.78649e6 | 0.374382 | 0.187191 | − | 0.982324i | \(-0.440062\pi\) | ||||
0.187191 | + | 0.982324i | \(0.440062\pi\) | |||||||
\(752\) | 2.54151e6 | + | 2.54151e6i | 0.163888 | + | 0.163888i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 3.05698e6i | − | 0.195823i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −986385. | + | 986385.i | −0.0625614 | + | 0.0625614i | −0.737695 | − | 0.675134i | \(-0.764086\pi\) |
0.675134 | + | 0.737695i | \(0.264086\pi\) | |||||||
\(758\) | −6.01476e6 | + | 6.01476e6i | −0.380229 | + | 0.380229i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.59161e7i | 1.62221i | 0.584900 | + | 0.811105i | \(0.301134\pi\) | ||||
−0.584900 | + | 0.811105i | \(0.698866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −784014. | − | 784014.i | −0.0487542 | − | 0.0487542i | ||||
\(764\) | −692535. | −0.0429248 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.08794e6 | −0.374885 | ||||||||
\(767\) | 2.43904e6 | + | 2.43904e6i | 0.149703 | + | 0.149703i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.56460e6i | − | 0.461286i | −0.973038 | − | 0.230643i | \(-0.925917\pi\) | ||
0.973038 | − | 0.230643i | \(-0.0740829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.56790e6 | − | 2.56790e6i | 0.155073 | − | 0.155073i | ||||
\(773\) | −2.11501e7 | + | 2.11501e7i | −1.27311 | + | 1.27311i | −0.328657 | + | 0.944449i | \(0.606596\pi\) |
−0.944449 | + | 0.328657i | \(0.893404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.00802e7i | 0.600920i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.18714e7 | + | 1.18714e7i | 0.703156 | + | 0.703156i | ||||
\(779\) | −5.51067e6 | −0.325358 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.84486e7 | −1.08227 | ||||||||
\(782\) | −2.11986e6 | − | 2.11986e6i | −0.123963 | − | 0.123963i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 3.74502e6i | − | 0.217603i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.24337e6 | − | 5.24337e6i | 0.301768 | − | 0.301768i | −0.539937 | − | 0.841705i | \(-0.681552\pi\) |
0.841705 | + | 0.539937i | \(0.181552\pi\) | |||||||
\(788\) | 6.19751e6 | − | 6.19751e6i | 0.355551 | − | 0.355551i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.43424e6i | − | 0.308814i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.33675e6 | + | 6.33675e6i | 0.357836 | + | 0.357836i | ||||
\(794\) | −1.14626e7 | −0.645257 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.62944e6 | 0.370846 | ||||||||
\(797\) | 1.41641e7 | + | 1.41641e7i | 0.789848 | + | 0.789848i | 0.981469 | − | 0.191621i | \(-0.0613743\pi\) |
−0.191621 | + | 0.981469i | \(0.561374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.18216e6i | 0.508836i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.13918e7 | − | 1.13918e7i | 0.625398 | − | 0.625398i | ||||
\(803\) | −1.16631e7 | + | 1.16631e7i | −0.638302 | + | 0.638302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.33037e6i | − | 0.180574i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −460416. | − | 460416.i | −0.0248097 | − | 0.0248097i | ||||
\(809\) | −1.10071e7 | −0.591290 | −0.295645 | − | 0.955298i | \(-0.595535\pi\) | ||||
−0.295645 | + | 0.955298i | \(0.595535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.99290e6 | 0.319952 | 0.159976 | − | 0.987121i | \(-0.448858\pi\) | ||||
0.159976 | + | 0.987121i | \(0.448858\pi\) | |||||||
\(812\) | 1.33959e6 | + | 1.33959e6i | 0.0712986 | + | 0.0712986i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 6.53969e6i | − | 0.345936i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.33928e6 | − | 2.33928e6i | 0.122610 | − | 0.122610i | ||||
\(818\) | −1.59958e7 | + | 1.59958e7i | −0.835840 | + | 0.835840i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.27886e7i | 1.69772i | 0.528619 | + | 0.848859i | \(0.322710\pi\) | ||||
−0.528619 | + | 0.848859i | \(0.677290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.94173e6 | + | 9.94173e6i | 0.511637 | + | 0.511637i | 0.915028 | − | 0.403391i | \(-0.132168\pi\) |
−0.403391 | + | 0.915028i | \(0.632168\pi\) | |||||||
\(824\) | −9.94095e6 | −0.510047 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.13761e6 | −0.109013 | ||||||||
\(827\) | 7.37928e6 | + | 7.37928e6i | 0.375189 | + | 0.375189i | 0.869363 | − | 0.494174i | \(-0.164529\pi\) |
−0.494174 | + | 0.869363i | \(0.664529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.82419e7i | − | 0.921899i | −0.887426 | − | 0.460950i | \(-0.847509\pi\) | ||
0.887426 | − | 0.460950i | \(-0.152491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 872448. | − | 872448.i | 0.0436949 | − | 0.0436949i | ||||
\(833\) | 6.76515e6 | − | 6.76515e6i | 0.337804 | − | 0.337804i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2.98967e6i | − | 0.147947i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 123228. | + | 123228.i | 0.00606177 | + | 0.00606177i | ||||
\(839\) | 2.70804e7 | 1.32816 | 0.664080 | − | 0.747661i | \(-0.268823\pi\) | ||||
0.664080 | + | 0.747661i | \(0.268823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40743e7 | −0.686177 | ||||||||
\(842\) | 1.03459e7 | + | 1.03459e7i | 0.502908 | + | 0.502908i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.43674e6i | 0.456001i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.10441e6 | − | 3.10441e6i | 0.148686 | − | 0.148686i | ||||
\(848\) | −2.03212e6 | + | 2.03212e6i | −0.0970421 | + | 0.0970421i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 7.23962e6i | − | 0.342682i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.86524e7 | + | 1.86524e7i | 0.877731 | + | 0.877731i | 0.993300 | − | 0.115568i | \(-0.0368690\pi\) |
−0.115568 | + | 0.993300i | \(0.536869\pi\) | |||||||
\(854\) | −5.55362e6 | −0.260574 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.18886e7 | −0.554559 | ||||||||
\(857\) | −2.73159e6 | − | 2.73159e6i | −0.127047 | − | 0.127047i | 0.640724 | − | 0.767771i | \(-0.278634\pi\) |
−0.767771 | + | 0.640724i | \(0.778634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.85975e7i | − | 0.859946i | −0.902842 | − | 0.429973i | \(-0.858523\pi\) | ||
0.902842 | − | 0.429973i | \(-0.141477\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −706992. | + | 706992.i | −0.0324076 | + | 0.0324076i | ||||
\(863\) | −1.12074e7 | + | 1.12074e7i | −0.512245 | + | 0.512245i | −0.915214 | − | 0.402969i | \(-0.867978\pi\) |
0.402969 | + | 0.915214i | \(0.367978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.29991e6i | 0.285456i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.45939e6 | + | 1.45939e6i | 0.0657465 | + | 0.0657465i | ||||
\(869\) | −774333. | −0.0347839 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.46292e6 | −0.377985 | ||||||||
\(872\) | −1.07516e6 | − | 1.07516e6i | −0.0478833 | − | 0.0478833i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.30965e6i | − | 0.146556i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.76523e7 | − | 2.76523e7i | 1.21404 | − | 1.21404i | 0.244353 | − | 0.969686i | \(-0.421424\pi\) |
0.969686 | − | 0.244353i | \(-0.0785756\pi\) | |||||||
\(878\) | 8.18211e6 | − | 8.18211e6i | 0.358203 | − | 0.358203i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.14119e7i | 0.495357i | 0.968842 | + | 0.247678i | \(0.0796677\pi\) | ||||
−0.968842 | + | 0.247678i | \(0.920332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.53482e7 | + | 1.53482e7i | 0.662453 | + | 0.662453i | 0.955958 | − | 0.293505i | \(-0.0948217\pi\) |
−0.293505 | + | 0.955958i | \(0.594822\pi\) | |||||||
\(884\) | 3.15204e6 | 0.135663 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.18570e6 | −0.179136 | ||||||||
\(887\) | 1.86085e7 | + | 1.86085e7i | 0.794151 | + | 0.794151i | 0.982166 | − | 0.188015i | \(-0.0602055\pi\) |
−0.188015 | + | 0.982166i | \(0.560206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.50466e7i | 0.638535i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.28610e6 | − | 5.28610e6i | 0.222445 | − | 0.222445i | ||||
\(893\) | −7.16786e6 | + | 7.16786e6i | −0.300788 | + | 0.300788i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 764626.i | 0.0318184i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.90472e6 | + | 4.90472e6i | 0.202966 | + | 0.202966i | ||||
\(899\) | 7.01254e6 | 0.289385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.34180e6 | −0.301294 | ||||||||
\(902\) | 5.58700e6 | + | 5.58700e6i | 0.228645 | + | 0.228645i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.45229e6i | − | 0.303297i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.18773e7 | − | 2.18773e7i | 0.883030 | − | 0.883030i | −0.110812 | − | 0.993841i | \(-0.535345\pi\) |
0.993841 | + | 0.110812i | \(0.0353450\pi\) | |||||||
\(908\) | −8.79089e6 | + | 8.79089e6i | −0.353849 | + | 0.353849i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.41972e7i | − | 0.566771i | −0.959006 | − | 0.283385i | \(-0.908542\pi\) | ||
0.959006 | − | 0.283385i | \(-0.0914575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.40272e6 | − | 7.40272e6i | −0.293910 | − | 0.293910i | ||||
\(914\) | 1.69169e7 | 0.669817 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.00879e7 | 0.397248 | ||||||||
\(917\) | 1.53658e6 | + | 1.53658e6i | 0.0603436 | + | 0.0603436i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.37905e7i | 0.538631i | 0.963052 | + | 0.269315i | \(0.0867974\pi\) | ||||
−0.963052 | + | 0.269315i | \(0.913203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.06776e7 | − | 1.06776e7i | 0.413665 | − | 0.413665i | ||||
\(923\) | 1.51837e7 | − | 1.51837e7i | 0.586641 | − | 0.586641i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.00690e7i | 0.385887i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.83706e6 | + | 1.83706e6i | 0.0700249 | + | 0.0700249i | ||||
\(929\) | −4.48053e7 | −1.70330 | −0.851649 | − | 0.524113i | \(-0.824397\pi\) | ||||
−0.851649 | + | 0.524113i | \(0.824397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.05621e7 | 0.399372 | ||||||||
\(932\) | 3.91226e6 | + | 3.91226e6i | 0.147532 | + | 0.147532i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.27787e6i | 0.235475i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.64785e7 | − | 2.64785e7i | 0.985244 | − | 0.985244i | −0.0146490 | − | 0.999893i | \(-0.504663\pi\) |
0.999893 | + | 0.0146490i | \(0.00466308\pi\) | |||||||
\(938\) | 3.70851e6 | − | 3.70851e6i | 0.137623 | − | 0.137623i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.46220e7i | 1.27461i | 0.770610 | + | 0.637307i | \(0.219952\pi\) | ||||
−0.770610 | + | 0.637307i | \(0.780048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.18496e6 | + | 6.18496e6i | 0.226495 | + | 0.226495i | ||||
\(944\) | −2.93143e6 | −0.107065 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.74336e6 | −0.172329 | ||||||||
\(947\) | 505689. | + | 505689.i | 0.0183235 | + | 0.0183235i | 0.716209 | − | 0.697886i | \(-0.245876\pi\) |
−0.697886 | + | 0.716209i | \(0.745876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.91981e7i | − | 0.691979i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.38125e6 | + | 1.38125e6i | −0.0493946 | + | 0.0493946i | ||||
\(953\) | −2.13467e7 | + | 2.13467e7i | −0.761374 | + | 0.761374i | −0.976571 | − | 0.215197i | \(-0.930961\pi\) |
0.215197 | + | 0.976571i | \(0.430961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.26827e7i | − | 0.448815i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.47458e6 | − | 1.47458e6i | −0.0519106 | − | 0.0519106i | ||||
\(959\) | −9.94303e6 | −0.349118 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09895e7 | −0.733150 | ||||||||
\(962\) | 5.38233e6 | + | 5.38233e6i | 0.187514 | + | 0.187514i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.70579e6i | 0.197753i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.35296e6 | − | 4.35296e6i | 0.149699 | − | 0.149699i | −0.628285 | − | 0.777983i | \(-0.716243\pi\) |
0.777983 | + | 0.628285i | \(0.216243\pi\) | |||||||
\(968\) | 4.25726e6 | − | 4.25726e6i | 0.146030 | − | 0.146030i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 5.77443e7i | − | 1.96545i | −0.185081 | − | 0.982723i | \(-0.559255\pi\) | ||
0.185081 | − | 0.982723i | \(-0.440745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.04095e6 | − | 5.04095e6i | −0.170699 | − | 0.170699i | ||||
\(974\) | 1.68842e7 | 0.570272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.61600e6 | −0.255919 | ||||||||
\(977\) | 3.22881e7 | + | 3.22881e7i | 1.08219 | + | 1.08219i | 0.996305 | + | 0.0858902i | \(0.0273734\pi\) |
0.0858902 | + | 0.996305i | \(0.472627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.02938e6i | − | 0.101018i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.49735e6 | + | 7.49735e6i | −0.248101 | + | 0.248101i | ||||
\(983\) | −1.46650e7 | + | 1.46650e7i | −0.484059 | + | 0.484059i | −0.906425 | − | 0.422366i | \(-0.861200\pi\) |
0.422366 | + | 0.906425i | \(0.361200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.63705e6i | 0.217412i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.46058e6 | + | 2.46058e6i | 0.0801945 | + | 0.0801945i | ||||
\(989\) | −5.25103e6 | −0.170708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.45331e7 | 1.76391 | 0.881954 | − | 0.471335i | \(-0.156228\pi\) | ||||
0.881954 | + | 0.471335i | \(0.156228\pi\) | |||||||
\(992\) | 2.00135e6 | + | 2.00135e6i | 0.0645719 | + | 0.0645719i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.33072e7i | 0.427189i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −289683. | + | 289683.i | −0.00922965 | + | 0.00922965i | −0.711707 | − | 0.702477i | \(-0.752077\pi\) |
0.702477 | + | 0.711707i | \(0.252077\pi\) | |||||||
\(998\) | −3.77024e6 | + | 3.77024e6i | −0.119824 | + | 0.119824i | ||||
\(999\) | 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 | 450.6.f.c.143.1 | yes | 4 | |
3.2 | odd | 2 | inner | 450.6.f.c.143.2 | yes | 4 | |
5.2 | odd | 4 | inner | 450.6.f.c.107.2 | yes | 4 | |
5.3 | odd | 4 | 450.6.f.a.107.1 | ✓ | 4 | ||
5.4 | even | 2 | 450.6.f.a.143.2 | yes | 4 | ||
15.2 | even | 4 | inner | 450.6.f.c.107.1 | yes | 4 | |
15.8 | even | 4 | 450.6.f.a.107.2 | yes | 4 | ||
15.14 | odd | 2 | 450.6.f.a.143.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.f.a.107.1 | ✓ | 4 | 5.3 | odd | 4 | ||
450.6.f.a.107.2 | yes | 4 | 15.8 | even | 4 | ||
450.6.f.a.143.1 | yes | 4 | 15.14 | odd | 2 | ||
450.6.f.a.143.2 | yes | 4 | 5.4 | even | 2 | ||
450.6.f.c.107.1 | yes | 4 | 15.2 | even | 4 | inner | |
450.6.f.c.107.2 | yes | 4 | 5.2 | odd | 4 | inner | |
450.6.f.c.143.1 | yes | 4 | 1.1 | even | 1 | trivial | |
450.6.f.c.143.2 | yes | 4 | 3.2 | odd | 2 | inner |