Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(689,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1380.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.n (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.22 | ||
Character | \(\chi\) | \(=\) | 1380.689 |
Dual form | 1380.2.n.a.689.24 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.403788 | − | 1.68433i | −0.233127 | − | 0.972446i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.20116 | + | 0.393570i | 0.984388 | + | 0.176010i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.85443 | −1.45684 | −0.728418 | − | 0.685133i | \(-0.759744\pi\) | ||||
−0.728418 | + | 0.685133i | \(0.759744\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67391 | + | 1.36022i | −0.891304 | + | 0.453407i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.62241 | −1.09220 | −0.546099 | − | 0.837721i | \(-0.683888\pi\) | ||||
−0.546099 | + | 0.837721i | \(0.683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57565i | 0.437007i | 0.975836 | + | 0.218504i | \(0.0701175\pi\) | ||||
−0.975836 | + | 0.218504i | \(0.929882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.225902 | − | 3.86639i | −0.0583276 | − | 0.998297i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.19481i | − | 1.25993i | −0.776625 | − | 0.629964i | \(-0.783070\pi\) | ||
0.776625 | − | 0.629964i | \(-0.216930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.52090i | 1.49600i | 0.663700 | + | 0.747999i | \(0.268985\pi\) | ||||
−0.663700 | + | 0.747999i | \(0.731015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55637 | + | 6.49211i | 0.339628 | + | 1.41669i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.03526 | + | 2.59166i | 0.841409 | + | 0.540398i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.69021 | + | 1.73262i | 0.938041 | + | 0.346524i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.37075 | + | 3.95450i | 0.648701 | + | 0.761043i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.95654i | 1.84888i | 0.381325 | + | 0.924441i | \(0.375468\pi\) | ||||
−0.381325 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.99350 | 1.61528 | 0.807641 | − | 0.589675i | \(-0.200744\pi\) | ||||
0.807641 | + | 0.589675i | \(0.200744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.46269 | + | 6.10132i | 0.254621 | + | 1.06210i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.48420 | − | 1.51699i | −1.43409 | − | 0.256417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.60205 | 0.920972 | 0.460486 | − | 0.887667i | \(-0.347675\pi\) | ||||
0.460486 | + | 0.887667i | \(0.347675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.65391 | − | 0.636229i | 0.424966 | − | 0.101878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.15604i | − | 0.336716i | −0.985726 | − | 0.168358i | \(-0.946153\pi\) | ||
0.985726 | − | 0.168358i | \(-0.0538465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.84370 | −1.34865 | −0.674326 | − | 0.738434i | \(-0.735566\pi\) | ||||
−0.674326 | + | 0.738434i | \(0.735566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.42105 | + | 1.94169i | −0.957193 | + | 0.289451i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.35089 | −1.36397 | −0.681984 | − | 0.731367i | \(-0.738883\pi\) | ||||
−0.681984 | + | 0.731367i | \(0.738883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.85659 | 1.12237 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.74976 | + | 2.09760i | −1.22521 | + | 0.293723i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.55833i | 0.900856i | 0.892813 | + | 0.450428i | \(0.148729\pi\) | ||||
−0.892813 | + | 0.450428i | \(0.851271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.97351 | − | 1.42567i | −1.07515 | − | 0.192238i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.9833 | − | 2.63306i | 1.45478 | − | 0.348758i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.15719i | − | 0.671408i | −0.941967 | − | 0.335704i | \(-0.891026\pi\) | ||
0.941967 | − | 0.335704i | \(-0.108974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7339i | 1.37434i | 0.726498 | + | 0.687168i | \(0.241146\pi\) | ||||
−0.726498 | + | 0.687168i | \(0.758854\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.3064 | − | 5.24287i | 1.29848 | − | 0.660540i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.620129 | + | 3.46826i | −0.0769175 | + | 0.430185i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.14099 | −0.261563 | −0.130782 | − | 0.991411i | \(-0.541749\pi\) | ||||
−0.130782 | + | 0.991411i | \(0.541749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.73581 | − | 7.84317i | 0.329353 | − | 0.944207i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.71690i | − | 1.03451i | −0.855833 | − | 0.517253i | \(-0.826955\pi\) | ||
0.855833 | − | 0.517253i | \(-0.173045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6914i | 1.25134i | 0.780090 | + | 0.625668i | \(0.215173\pi\) | ||||
−0.780090 | + | 0.625668i | \(0.784827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.02445 | − | 8.59945i | 0.118293 | − | 0.992979i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.9623 | 1.59115 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40689i | 1.05836i | 0.848510 | + | 0.529179i | \(0.177500\pi\) | ||||
−0.848510 | + | 0.529179i | \(0.822500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.29959 | − | 7.27422i | 0.588844 | − | 0.808247i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.23889i | 0.575043i | 0.957774 | + | 0.287521i | \(0.0928312\pi\) | ||||
−0.957774 | + | 0.287521i | \(0.907169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.04452 | − | 11.4346i | 0.221760 | − | 1.24026i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.7701 | − | 4.02033i | 1.79794 | − | 0.431025i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.33287 | −0.777282 | −0.388641 | − | 0.921389i | \(-0.627055\pi\) | ||||
−0.388641 | + | 0.921389i | \(0.627055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.07323i | − | 0.636648i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.63147 | − | 15.1480i | −0.376566 | − | 1.57077i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.56643 | + | 14.3536i | −0.263310 | + | 1.47264i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.45455 | 0.249221 | 0.124611 | − | 0.992206i | \(-0.460232\pi\) | ||||
0.124611 | + | 0.992206i | \(0.460232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.68600 | − | 4.92728i | 0.973480 | − | 0.495210i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.883578i | − | 0.0879193i | −0.999033 | − | 0.0439597i | \(-0.986003\pi\) | ||
0.999033 | − | 0.0439597i | \(-0.0139973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7691 | −1.15964 | −0.579821 | − | 0.814744i | \(-0.696877\pi\) | ||||
−0.579821 | + | 0.814744i | \(0.696877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.870721 | + | 14.9027i | 0.0849737 | + | 1.45436i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.24813i | − | 0.120662i | −0.998178 | − | 0.0603308i | \(-0.980784\pi\) | ||
0.998178 | − | 0.0603308i | \(-0.0192156\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.90303i | 0.565407i | 0.959207 | + | 0.282704i | \(0.0912313\pi\) | ||||
−0.959207 | + | 0.282704i | \(0.908769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.26204 | − | 9.43569i | −0.214703 | − | 0.895596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.00542i | − | 0.282726i | −0.989958 | − | 0.141363i | \(-0.954851\pi\) | ||
0.989958 | − | 0.141363i | \(-0.0451485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.86225 | + | 7.29281i | 0.733158 | + | 0.680058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.14324 | − | 4.21315i | −0.198142 | − | 0.389506i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.0230i | 1.83551i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12187 | 0.192897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.63147 | + | 0.870582i | −0.327439 | + | 0.0784977i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.64198 | + | 5.65970i | 0.862405 | + | 0.506219i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1502i | 1.43310i | 0.697534 | + | 0.716551i | \(0.254280\pi\) | ||||
−0.697534 | + | 0.716551i | \(0.745720\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.57098 | + | 14.8957i | 0.314407 | + | 1.31149i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 17.5863i | − | 1.53652i | −0.640138 | − | 0.768260i | \(-0.721123\pi\) | ||
0.640138 | − | 0.768260i | \(-0.278877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 25.1343i | − | 2.17942i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.86319 | + | 10.0311i | 0.504623 | + | 0.863340i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.9660i | − | 0.936889i | −0.883493 | − | 0.468445i | \(-0.844815\pi\) | ||
0.883493 | − | 0.468445i | \(-0.155185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.07537 | −0.684944 | −0.342472 | − | 0.939528i | \(-0.611264\pi\) | ||||
−0.342472 | + | 0.939528i | \(0.611264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.77578 | + | 15.7500i | 0.317978 | + | 1.32639i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.70766i | − | 0.477298i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.91859 | + | 21.9159i | −0.325421 | + | 1.82002i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.17240 | − | 13.2331i | −0.261655 | − | 1.09145i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5875 | −1.03121 | −0.515606 | − | 0.856826i | \(-0.672433\pi\) | ||||
−0.515606 | + | 0.856826i | \(0.672433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8991 | −1.45661 | −0.728306 | − | 0.685252i | \(-0.759692\pi\) | ||||
−0.728306 | + | 0.685252i | \(0.759692\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.06610 | + | 13.8905i | 0.571260 | + | 1.12298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.7961 | + | 3.53957i | 1.59006 | + | 0.284305i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.44382 | 0.594082 | 0.297041 | − | 0.954865i | \(-0.404000\pi\) | ||||
0.297041 | + | 0.954865i | \(0.404000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.0464 | − | 2.64818i | 0.876034 | − | 0.210014i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.5536 | − | 9.98936i | −1.22580 | − | 0.787272i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5357i | 1.53015i | 0.643941 | + | 0.765075i | \(0.277298\pi\) | ||||
−0.643941 | + | 0.765075i | \(0.722702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.818309 | + | 14.0057i | 0.0637053 | + | 1.09034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7702 | 1.45248 | 0.726242 | − | 0.687439i | \(-0.241265\pi\) | ||||
0.726242 | + | 0.687439i | \(0.241265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5173 | 0.809025 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.86987 | − | 17.4363i | −0.678296 | − | 1.33339i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.89789 | −0.676494 | −0.338247 | − | 0.941057i | \(-0.609834\pi\) | ||||
−0.338247 | + | 0.941057i | \(0.609834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.0780 | − | 6.67825i | −1.36657 | − | 0.504829i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.68638 | + | 2.08241i | −0.652909 | + | 0.156523i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.51478i | 0.337450i | 0.985663 | + | 0.168725i | \(0.0539650\pi\) | ||||
−0.985663 | + | 0.168725i | \(0.946035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.64364i | 0.122171i | 0.998133 | + | 0.0610853i | \(0.0194562\pi\) | ||||
−0.998133 | + | 0.0610853i | \(0.980544\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0794 | − | 4.33422i | 1.33647 | − | 0.320395i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.3310 | + | 2.20480i | 0.906594 | + | 0.162100i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8178i | 1.37609i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.9923 | − | 15.2423i | −0.945051 | − | 1.10872i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.548393 | 0.0396803 | 0.0198402 | − | 0.999803i | \(-0.493684\pi\) | ||||
0.0198402 | + | 0.999803i | \(0.493684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7429i | 1.06122i | 0.847617 | + | 0.530608i | \(0.178036\pi\) | ||||
−0.847617 | + | 0.530608i | \(0.821964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.09208 | − | 0.355942i | 0.436263 | − | 0.0254896i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4470 | 1.17180 | 0.585899 | − | 0.810384i | \(-0.300742\pi\) | ||||
0.585899 | + | 0.810384i | \(0.300742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.7568i | − | 1.47141i | −0.677304 | − | 0.735704i | \(-0.736852\pi\) | ||
0.677304 | − | 0.735704i | \(-0.263148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.864506 | + | 3.60612i | 0.0609775 | + | 0.254356i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 38.3767i | − | 2.69352i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.848551 | − | 4.74578i | 0.0592654 | − | 0.331460i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.3151 | − | 1.44102i | −0.994972 | − | 0.100158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 23.6214i | − | 1.63393i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.80755 | 0.330965 | 0.165483 | − | 0.986213i | \(-0.447082\pi\) | ||||
0.165483 | + | 0.986213i | \(0.447082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.6821 | + | 3.51978i | −1.00600 | + | 0.241171i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.4664 | − | 3.48061i | −1.32760 | − | 0.237376i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.6648 | −2.35320 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.0078 | − | 4.31706i | 1.21686 | − | 0.291720i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.18522 | 0.550597 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.47165i | − | 0.0985488i | −0.998785 | − | 0.0492744i | \(-0.984309\pi\) | ||
0.998785 | − | 0.0492744i | \(-0.0156909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.8979 | + | 1.74685i | −0.993196 | + | 0.116457i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.0587i | 1.72958i | 0.502137 | + | 0.864788i | \(0.332547\pi\) | ||||
−0.502137 | + | 0.864788i | \(0.667453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.78901i | − | 0.580794i | −0.956906 | − | 0.290397i | \(-0.906213\pi\) | ||
0.956906 | − | 0.290397i | \(-0.0937874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.63781 | − | 23.5171i | −0.370941 | − | 1.54731i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.58544 | 0.562451 | 0.281225 | − | 0.959642i | \(-0.409259\pi\) | ||||
0.281225 | + | 0.959642i | \(0.409259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.5828 | − | 3.68023i | −1.34267 | − | 0.240072i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8443 | − | 3.79839i | 1.02920 | − | 0.246732i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5449i | 1.32894i | 0.747315 | + | 0.664470i | \(0.231342\pi\) | ||||
−0.747315 | + | 0.664470i | \(0.768658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.8622i | − | 0.957361i | −0.877989 | − | 0.478681i | \(-0.841115\pi\) | ||
0.877989 | − | 0.478681i | \(-0.158885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3921 | − | 5.98900i | −0.923252 | − | 0.384195i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2936 | + | 3.09212i | 1.10485 | + | 0.197548i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.2747 | −0.653762 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.82400 | − | 2.11540i | 0.559198 | − | 0.134058i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.39169 | 0.214081 | 0.107041 | − | 0.994255i | \(-0.465862\pi\) | ||||
0.107041 | + | 0.994255i | \(0.465862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.6174 | − | 9.38806i | −0.918986 | − | 0.590222i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.0852 | + | 1.17352i | −1.25778 | + | 0.0734885i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.2553 | −1.13873 | −0.569367 | − | 0.822083i | \(-0.692812\pi\) | ||||
−0.569367 | + | 0.822083i | \(0.692812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.5927 | −1.34170 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.5431 | − | 26.6229i | −0.838297 | − | 1.64792i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.42459i | 0.457820i | 0.973448 | + | 0.228910i | \(0.0735162\pi\) | ||||
−0.973448 | + | 0.228910i | \(0.926484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.58116 | + | 14.4359i | −0.158560 | + | 0.886793i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96092 | + | 12.3509i | 0.181206 | + | 0.755865i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.96364i | − | 0.363609i | −0.983335 | − | 0.181805i | \(-0.941806\pi\) | ||
0.983335 | − | 0.181805i | \(-0.0581938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79000 | 0.108735 | 0.0543674 | − | 0.998521i | \(-0.482686\pi\) | ||||
0.0543674 | + | 0.998521i | \(0.482686\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.2293 | + | 2.45230i | −0.619106 | + | 0.148420i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.9899 | − | 6.27626i | −1.02453 | − | 0.378473i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.30335i | − | 0.0783110i | −0.999233 | − | 0.0391555i | \(-0.987533\pi\) | ||
0.999233 | − | 0.0391555i | \(-0.0124668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.0478 | + | 12.2332i | −1.43971 | + | 0.732380i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.1310 | −1.08160 | −0.540801 | − | 0.841150i | \(-0.681879\pi\) | ||||
−0.540801 | + | 0.841150i | \(0.681879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.07042 | 0.182518 | 0.0912588 | − | 0.995827i | \(-0.470911\pi\) | ||||
0.0912588 | + | 0.995827i | \(0.470911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.2124 | − | 1.47308i | 1.49345 | − | 0.0872579i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.31028i | 0.490540i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.98610 | −0.587417 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.991117 | − | 4.13426i | −0.0581003 | − | 0.242355i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 32.8876i | − | 1.92131i | −0.277737 | − | 0.960657i | \(-0.589584\pi\) | ||
0.277737 | − | 0.960657i | \(-0.410416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.02971 | − | 11.3518i | 0.118174 | − | 0.660927i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.2102 | − | 14.3248i | −0.708510 | − | 0.831210i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.08355 | + | 6.35816i | −0.236158 | + | 0.367702i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.0874 | 1.96476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.48823 | + | 0.356778i | −0.0854968 | + | 0.0204964i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.22454 | + | 23.6270i | −0.241897 | + | 1.35288i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.1903i | − | 0.981100i | −0.871413 | − | 0.490550i | \(-0.836796\pi\) | ||
0.871413 | − | 0.490550i | \(-0.163204\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.75221 | + | 19.8230i | 0.270344 | + | 1.12769i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.1149i | − | 1.87778i | −0.344224 | − | 0.938888i | \(-0.611858\pi\) | ||
0.344224 | − | 0.938888i | \(-0.388142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.09052 | −0.231210 | −0.115605 | − | 0.993295i | \(-0.536881\pi\) | ||||
−0.115605 | + | 0.993295i | \(0.536881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.7494 | − | 7.48411i | 1.39447 | − | 0.421682i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.0968 | −1.69041 | −0.845203 | − | 0.534445i | \(-0.820521\pi\) | ||||
−0.845203 | + | 0.534445i | \(0.820521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.0667i | − | 2.01935i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.10226 | + | 0.503981i | −0.117337 | + | 0.0281295i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.8749 | 1.88485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.73001 | + | 7.39013i | −0.151433 | + | 0.409931i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.94262 | − | 2.38357i | 0.549828 | − | 0.131812i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.0423 | 1.98708 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.88833 | 0.158757 | 0.0793784 | − | 0.996845i | \(-0.474706\pi\) | ||||
0.0793784 | + | 0.996845i | \(0.474706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.9794 | + | 7.62003i | −0.820865 | + | 0.417575i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.71266 | − | 0.842629i | −0.257480 | − | 0.0460377i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.48092 | 0.189618 | 0.0948088 | − | 0.995496i | \(-0.469776\pi\) | ||||
0.0948088 | + | 0.995496i | \(0.469776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.06211 | + | 1.21355i | −0.274936 | + | 0.0659112i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.5782 | −1.76421 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.30168 | −0.178274 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.10879 | − | 16.1873i | 0.490401 | − | 0.871497i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.93765 | 0.157701 | 0.0788507 | − | 0.996886i | \(-0.474875\pi\) | ||||
0.0788507 | + | 0.996886i | \(0.474875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.531226 | −0.0284359 | −0.0142179 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142179 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.23091 | + | 5.31113i | −0.332581 | + | 0.283487i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.40672 | −0.340996 | −0.170498 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170498 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.43071 | − | 19.1873i | 0.182083 | − | 1.01836i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.7253 | − | 8.08506i | 1.78493 | − | 0.427907i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4878 | 1.76742 | 0.883708 | − | 0.468038i | \(-0.155039\pi\) | ||||
0.883708 | + | 0.468038i | \(0.155039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.5222 | −1.23801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.856784 | − | 3.57391i | −0.0449695 | − | 0.187582i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.20782 | + | 23.5335i | −0.220247 | + | 1.23180i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7030 | −0.558691 | −0.279346 | − | 0.960191i | \(-0.590118\pi\) | ||||
−0.279346 | + | 0.960191i | \(0.590118\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.93269 | + | 5.76505i | 0.152670 | + | 0.300116i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 25.2786i | − | 1.31240i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.1273 | 1.19748 | 0.598742 | − | 0.800942i | \(-0.295667\pi\) | ||||
0.598742 | + | 0.800942i | \(0.295667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.63946 | − | 18.5256i | 0.291220 | − | 0.956656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.6880 | −0.807975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1959i | 0.934661i | 0.884083 | + | 0.467330i | \(0.154784\pi\) | ||||
−0.884083 | + | 0.467330i | \(0.845216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.2023 | − | 6.52127i | 1.39362 | − | 0.334095i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.6826i | 1.26122i | 0.776099 | + | 0.630611i | \(0.217196\pi\) | ||||
−0.776099 | + | 0.630611i | \(0.782804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.7333 | + | 5.49515i | 1.56631 | + | 0.280059i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.6473 | − | 12.0294i | 1.20206 | − | 0.611488i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.549183 | 0.0278447 | 0.0139224 | − | 0.999903i | \(-0.495568\pi\) | ||||
0.0139224 | + | 0.999903i | \(0.495568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.4632 | − | 20.9624i | 0.680863 | − | 1.06011i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.6210 | + | 7.10113i | −1.49418 | + | 0.358205i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.70227 | + | 20.7061i | −0.186281 | + | 1.04184i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8586i | 1.19743i | 0.800962 | + | 0.598716i | \(0.204322\pi\) | ||||
−0.800962 | + | 0.598716i | \(0.795678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −42.3344 | + | 10.1489i | −2.11937 | + | 0.508083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.40232 | −0.219841 | −0.109921 | − | 0.993940i | \(-0.535060\pi\) | ||||
−0.109921 | + | 0.993940i | \(0.535060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.1706i | 0.705889i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.5282 | − | 13.9260i | 0.721910 | − | 0.691987i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.2929 | −1.00588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2444 | −0.506554 | −0.253277 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253277 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.4703 | + | 4.42794i | −0.911075 | + | 0.218414i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.8780i | 0.978132i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.06187 | + | 11.5316i | −0.101213 | + | 0.566065i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.26074 | + | 13.6016i | 0.159679 | + | 0.666071i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0221 | −1.17355 | −0.586777 | − | 0.809748i | \(-0.699604\pi\) | ||||
−0.586777 | + | 0.809748i | \(0.699604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.37345i | − | 0.164412i | −0.996615 | − | 0.0822060i | \(-0.973803\pi\) | ||
0.996615 | − | 0.0822060i | \(-0.0261965\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.0034 | − | 12.7193i | 1.21571 | − | 0.618433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.00064 | − | 24.3647i | 0.436595 | − | 1.18186i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 41.3730i | − | 2.00218i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.61356 | + | 2.30468i | −0.464147 | + | 0.111271i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.0488 | 1.64008 | 0.820038 | − | 0.572310i | \(-0.193952\pi\) | ||||
0.820038 | + | 0.572310i | \(0.193952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0954 | −0.725441 | −0.362720 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362720 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 38.4958 | − | 2.24920i | 1.84573 | − | 0.107841i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.9000 | + | 26.3135i | −0.808435 | + | 1.25875i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7435 | −0.608214 | −0.304107 | − | 0.952638i | \(-0.598358\pi\) | ||||
−0.304107 | + | 0.952638i | \(0.598358\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0078 | + | 10.6867i | −1.00037 | + | 0.508891i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.6598 | 1.21914 | 0.609568 | − | 0.792734i | \(-0.291343\pi\) | ||||
0.609568 | + | 0.792734i | \(0.291343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.1408 | − | 2.88599i | −0.765148 | − | 0.136809i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.08270 | + | 21.2015i | 0.240403 | + | 1.00280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.1929i | 0.952962i | 0.879185 | + | 0.476481i | \(0.158088\pi\) | ||||
−0.879185 | + | 0.476481i | \(0.841912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.81005i | 0.367761i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.22746 | + | 30.1480i | 0.339576 | + | 1.41648i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.39024 | − | 13.3681i | 0.112056 | − | 0.626709i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0704 | −0.471071 | −0.235536 | − | 0.971866i | \(-0.575684\pi\) | ||||
−0.235536 | + | 0.971866i | \(0.575684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.5429 | − | 17.5104i | 0.958859 | − | 0.817316i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.98459i | 0.465029i | 0.972593 | + | 0.232514i | \(0.0746952\pi\) | ||||
−0.972593 | + | 0.232514i | \(0.925305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3677i | 0.528301i | 0.964482 | + | 0.264150i | \(0.0850915\pi\) | ||||
−0.964482 | + | 0.264150i | \(0.914909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.03165 | − | 34.7724i | −0.0942154 | − | 1.61253i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.31931i | 0.384972i | 0.981300 | + | 0.192486i | \(0.0616550\pi\) | ||||
−0.981300 | + | 0.192486i | \(0.938345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.25228 | 0.381055 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00573 | − | 12.5378i | −0.138497 | − | 0.577713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.0355 | 1.47300 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2982 | + | 30.5844i | −0.518399 | + | 1.40331i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.92079 | − | 17.5364i | −0.408455 | − | 0.802936i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.6309 | 1.53664 | 0.768318 | − | 0.640068i | \(-0.221094\pi\) | ||||
0.768318 | + | 0.640068i | \(0.221094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.82688i | 0.402471i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.5450 | + | 30.2309i | −0.479813 | + | 1.37555i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.40285 | + | 0.966036i | 0.245331 | + | 0.0438654i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.7679i | − | 1.30360i | −0.758392 | − | 0.651798i | \(-0.774015\pi\) | ||
0.758392 | − | 0.651798i | \(-0.225985\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.9044 | − | 7.88826i | 1.48799 | − | 0.356720i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.1190i | 0.953088i | 0.879151 | + | 0.476544i | \(0.158111\pi\) | ||||
−0.879151 | + | 0.476544i | \(0.841889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.7224 | 2.32946 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.2597 | − | 7.03361i | 1.04544 | − | 0.316137i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.5986i | 1.50710i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4630 | 0.736983 | 0.368492 | − | 0.929631i | \(-0.379874\pi\) | ||||
0.368492 | + | 0.929631i | \(0.379874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.57919 | − | 31.6152i | −0.338613 | − | 1.41246i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 26.1029i | − | 1.16387i | −0.813235 | − | 0.581936i | \(-0.802295\pi\) | ||
0.813235 | − | 0.581936i | \(-0.197705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.347750 | − | 1.94490i | 0.0154747 | − | 0.0865468i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.24677 | − | 17.7146i | −0.188606 | − | 0.786733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3194i | 0.590371i | 0.955440 | + | 0.295186i | \(0.0953815\pi\) | ||||
−0.955440 | + | 0.295186i | \(0.904618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 41.2093i | − | 1.82299i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.7869 | + | 21.9803i | −1.13852 | + | 0.970456i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.9056 | − | 4.63195i | −1.14154 | − | 0.204108i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.8728 | 1.48972 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.59286 | + | 14.9870i | 0.157709 | + | 0.657854i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4699 | 0.896802 | 0.448401 | − | 0.893832i | \(-0.351994\pi\) | ||||
0.448401 | + | 0.893832i | \(0.351994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.93791 | −0.0847388 | −0.0423694 | − | 0.999102i | \(-0.513491\pi\) | ||||
−0.0423694 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.94866 | + | 33.1459i | −0.172334 | + | 1.44661i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 46.7196i | − | 2.03514i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.56660 | + | 20.9160i | 0.415939 | + | 0.909392i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.01491 | + | 13.7899i | 0.304421 | + | 0.598429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.39716 | 0.147147 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.491228 | − | 2.74734i | 0.0212376 | − | 0.118778i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.60436 | − | 1.82301i | 0.328152 | − | 0.0786688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.4598 | −1.22585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2890 | −1.73216 | −0.866080 | − | 0.499905i | \(-0.833368\pi\) | ||||
−0.866080 | + | 0.499905i | \(0.833368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.76842 | − | 0.663681i | 0.118804 | − | 0.0284813i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.32325 | + | 12.9935i | −0.0995172 | + | 0.556580i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7493i | 0.545120i | 0.962139 | + | 0.272560i | \(0.0878704\pi\) | ||||
−0.962139 | + | 0.272560i | \(0.912130\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.6005 | − | 28.7015i | −0.623134 | − | 1.22495i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −64.9256 | −2.76592 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 36.2582i | − | 1.54185i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.26551 | − | 21.6597i | −0.0537181 | − | 0.919404i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 40.4426i | − | 1.71361i | −0.515642 | − | 0.856804i | \(-0.672447\pi\) | ||
0.515642 | − | 0.856804i | \(-0.327553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.9346i | − | 0.589370i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.6952 | − | 7.59838i | 1.33817 | − | 0.320804i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.66702i | 0.323126i | 0.986862 | + | 0.161563i | \(0.0516535\pi\) | ||||
−0.986862 | + | 0.161563i | \(0.948346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.18284 | − | 6.61542i | 0.0497626 | − | 0.278313i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.4269 | + | 28.0379i | −0.857849 | + | 1.17748i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.76808 | −0.283733 | −0.141866 | − | 0.989886i | \(-0.545310\pi\) | ||||
−0.141866 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.2756i | 1.30884i | 0.756130 | + | 0.654421i | \(0.227088\pi\) | ||||
−0.756130 | + | 0.654421i | \(0.772912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.221434 | − | 0.923672i | −0.00925056 | − | 0.0385870i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4358 | + | 19.1470i | 0.602015 | + | 0.798484i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 10.6638i | − | 0.443938i | −0.975054 | − | 0.221969i | \(-0.928752\pi\) | ||
0.975054 | − | 0.221969i | \(-0.0712483\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.8318 | − | 5.95300i | 1.03198 | − | 0.247398i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.1929i | − | 0.837743i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 23.7570i | − | 0.983914i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.05943 | − | 10.1173i | −0.126492 | − | 0.418300i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.2614 | −0.877552 | −0.438776 | − | 0.898597i | \(-0.644588\pi\) | ||||
−0.438776 | + | 0.898597i | \(0.644588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.6458i | 2.41646i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.64109 | − | 27.7021i | −0.273178 | − | 1.13951i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.2613 | 0.749901 | 0.374950 | − | 0.927045i | \(-0.377660\pi\) | ||||
0.374950 | + | 0.927045i | \(0.377660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.88046 | + | 44.0739i | −0.323067 | + | 1.80685i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.9612 | + | 8.38133i | −1.43086 | + | 0.343025i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9.66719i | − | 0.394991i | −0.980304 | − | 0.197495i | \(-0.936719\pi\) | ||
0.980304 | − | 0.197495i | \(-0.0632807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2939 | 0.583061 | 0.291531 | − | 0.956562i | \(-0.405835\pi\) | ||||
0.291531 | + | 0.956562i | \(0.405835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.72481 | − | 2.91222i | 0.233132 | − | 0.118595i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.67056 | + | 0.835102i | 0.189885 | + | 0.0339517i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.83706i | 0.236919i | 0.992959 | + | 0.118459i | \(0.0377956\pi\) | ||||
−0.992959 | + | 0.118459i | \(0.962204\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −64.6389 | + | 15.4961i | −2.61930 | + | 0.627932i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.7337i | − | 0.596064i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0410 | −0.890226 | −0.445113 | − | 0.895474i | \(-0.646836\pi\) | ||||
−0.445113 | + | 0.895474i | \(0.646836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.33608 | + | 0.487052i | −0.336143 | + | 0.0196398i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8081i | 0.475378i | 0.971341 | + | 0.237689i | \(0.0763898\pi\) | ||||
−0.971341 | + | 0.237689i | \(0.923610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.3240i | 1.09825i | 0.835742 | + | 0.549123i | \(0.185038\pi\) | ||||
−0.835742 | + | 0.549123i | \(0.814962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.35313 | + | 24.6932i | 0.134557 | + | 0.990906i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.2640 | 1.13237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9961 | + | 16.2527i | 0.759842 | + | 0.650107i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.7861 | + | 9.53804i | −1.58891 | + | 0.380913i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 29.1016i | − | 1.16036i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.72151i | 0.148151i | 0.997253 | + | 0.0740755i | \(0.0236006\pi\) | ||||
−0.997253 | + | 0.0740755i | \(0.976399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.94123 | − | 8.09748i | −0.0771570 | − | 0.321846i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.35625 | + | 35.5493i | −0.252240 | + | 1.41073i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3793i | 0.490484i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8569 | + | 23.3082i | 0.469052 | + | 0.922059i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4449 | −0.886521 | −0.443261 | − | 0.896393i | \(-0.646178\pi\) | ||||
−0.443261 | + | 0.896393i | \(0.646178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5307 | 0.533597 | 0.266799 | − | 0.963752i | \(-0.414034\pi\) | ||||
0.266799 | + | 0.963752i | \(0.414034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.99781 | + | 34.1932i | 0.0786636 | + | 1.34636i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5478 | −0.886444 | −0.443222 | − | 0.896412i | \(-0.646165\pi\) | ||||
−0.443222 | + | 0.896412i | \(0.646165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6814i | 0.733311i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.9972 | + | 58.3868i | 0.548595 | + | 2.28836i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.1467 | −1.06233 | −0.531166 | − | 0.847268i | \(-0.678246\pi\) | ||||
−0.531166 | + | 0.847268i | \(0.678246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.92143 | − | 38.7102i | 0.270443 | − | 1.51253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.5427 | − | 28.5879i | −0.567364 | − | 1.11532i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0104 | 1.01322 | 0.506611 | − | 0.862175i | \(-0.330898\pi\) | ||||
0.506611 | + | 0.862175i | \(0.330898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 11.1835i | − | 0.434988i | −0.976062 | − | 0.217494i | \(-0.930212\pi\) | ||
0.976062 | − | 0.217494i | \(-0.0697882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.30509 | − | 13.7866i | −0.128359 | − | 0.535426i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.89212 | − | 55.3247i | 0.383600 | − | 2.14540i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.8040 | + | 40.1772i | −0.999133 | + | 1.55567i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.47873 | + | 0.594234i | −0.0958334 | + | 0.0229744i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 38.8826i | − | 1.50105i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.70314i | − | 0.219840i | −0.993940 | − | 0.109920i | \(-0.964941\pi\) | ||
0.993940 | − | 0.109920i | \(-0.0350594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.95787 | + | 24.3876i | 0.344789 | + | 0.938680i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.49317i | − | 0.249553i | −0.992185 | − | 0.124776i | \(-0.960179\pi\) | ||
0.992185 | − | 0.124776i | \(-0.0398214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.46087 | −0.363075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.8913 | − | 10.5222i | 1.68192 | − | 0.403211i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0744250 | 0.00284779 | 0.00142390 | − | 0.999999i | \(-0.499547\pi\) | ||||
0.00142390 | + | 0.999999i | \(0.499547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.31589 | − | 24.1379i | 0.164902 | − | 0.922263i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8036 | + | 3.54890i | −0.564791 | + | 0.135399i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3336 | −0.393681 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.10705 | 0.346449 | 0.173224 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173224 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −37.3340 | + | 18.9918i | −1.41820 | + | 0.721440i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.7752 | − | 3.17822i | −0.674251 | − | 0.120557i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.2002 | −0.424238 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.46670 | − | 14.4607i | −0.131123 | − | 0.546953i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.3600 | 0.542368 | 0.271184 | − | 0.962527i | \(-0.412585\pi\) | ||||
0.271184 | + | 0.962527i | \(0.412585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.5305i | 1.37777i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.11238 | + | 36.1542i | 0.0795569 | + | 1.36165i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.40569i | 0.128084i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 47.8766i | − | 1.79804i | −0.437905 | − | 0.899021i | \(-0.644279\pi\) | ||
0.437905 | − | 0.899021i | \(-0.355721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.7955 | − | 25.1532i | −0.479867 | − | 0.943318i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.2911 | + | 23.3081i | 1.35911 | + | 0.872895i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.24636 | − | 12.5635i | 0.0840092 | − | 0.469847i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.6043 | − | 8.29578i | 1.29232 | − | 0.309812i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 34.0023i | − | 1.26807i | −0.773304 | − | 0.634036i | \(-0.781397\pi\) | ||
0.773304 | − | 0.634036i | \(-0.218603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.3630 | 1.68941 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.0329 | + | 6.00120i | −0.930982 | + | 0.223187i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.2509 | + | 46.6982i | −0.640682 | + | 1.73433i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.4234 | 1.49922 | 0.749610 | − | 0.661880i | \(-0.230241\pi\) | ||||
0.749610 | + | 0.661880i | \(0.230241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.27609 | + | 26.6592i | −0.158374 | + | 0.987379i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9414i | 1.69920i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0958 | 1.00081 | 0.500403 | − | 0.865793i | \(-0.333185\pi\) | ||||
0.500403 | + | 0.865793i | \(0.333185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.77482 | − | 30.3767i | −0.0654651 | − | 1.12046i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.75554 | 0.285679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.8420 | 1.42882 | 0.714412 | − | 0.699725i | \(-0.246694\pi\) | ||||
0.714412 | + | 0.699725i | \(0.246694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.14879 | + | 17.3059i | 0.152410 | + | 0.635748i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.63643i | − | 0.316840i | −0.987372 | − | 0.158420i | \(-0.949360\pi\) | ||
0.987372 | − | 0.158420i | \(-0.0506400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.7072 | − | 4.95407i | −1.01511 | − | 0.181503i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.12605 | − | 14.0083i | −0.260729 | − | 0.512538i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.81084i | 0.175784i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1656i | 1.10076i | 0.834915 | + | 0.550379i | \(0.185517\pi\) | ||||
−0.834915 | + | 0.550379i | \(0.814483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.36952 | − | 5.71271i | −0.0499082 | − | 0.208183i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.3989 | − | 7.04456i | −1.43387 | − | 0.256378i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.5310 | 1.72754 | 0.863772 | − | 0.503883i | \(-0.168096\pi\) | ||||
0.863772 | + | 0.503883i | \(0.168096\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.91024 | + | 28.4112i | −0.359719 | + | 1.03126i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.3590i | 0.375514i | 0.982215 | + | 0.187757i | \(0.0601218\pi\) | ||||
−0.982215 | + | 0.187757i | \(0.939878\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 22.7528i | − | 0.823706i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.0867 | + | 33.3561i | 0.364687 | + | 1.20599i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.12593 | 0.293410 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.78917i | 0.172702i | 0.996265 | + | 0.0863509i | \(0.0275206\pi\) | ||||
−0.996265 | + | 0.0863509i | \(0.972479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.37127 | + | 30.7479i | 0.265470 | + | 1.10736i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.772116i | − | 0.0277711i | −0.999904 | − | 0.0138855i | \(-0.995580\pi\) | ||
0.999904 | − | 0.0138855i | \(-0.00442005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.1814 | + | 15.5823i | 1.51520 | + | 0.559734i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.71887 | + | 36.3691i | 0.312788 | + | 1.30474i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.0593 | 0.503727 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.5762i | 1.12989i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.3731 | + | 33.5610i | −1.40708 | + | 1.19937i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.3850 | + | 2.92966i | 0.584807 | + | 0.104564i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0859 | 0.609045 | 0.304523 | − | 0.952505i | \(-0.401503\pi\) | ||||
0.304523 | + | 0.952505i | \(0.401503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.5054 | − | 2.99796i | 0.445205 | − | 0.106730i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5842i | 0.411886i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.9129 | −0.600595 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.3571 | − | 1.48154i | 0.899323 | − | 0.0525448i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.2162i | 1.67248i | 0.548361 | + | 0.836241i | \(0.315252\pi\) | ||||
−0.548361 | + | 0.836241i | \(0.684748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.5761i | 1.71850i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.6074 | − | 9.97432i | 0.692794 | − | 0.352425i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 38.7287i | − | 1.36671i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.3044 | − | 28.1096i | −1.06809 | − | 0.990733i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.0447 | + | 2.40804i | −0.353590 | + | 0.0847672i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.7441i | − | 1.11606i | −0.829820 | − | 0.558031i | \(-0.811557\pi\) | ||
0.829820 | − | 0.558031i | \(-0.188443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17600 | 0.0412948 | 0.0206474 | − | 0.999787i | \(-0.493427\pi\) | ||||
0.0206474 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.722781 | − | 3.01495i | −0.0253491 | − | 0.105739i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.68864 | + | 43.0011i | −0.269321 | + | 1.50626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 57.6689i | − | 2.01758i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.26094 | + | 16.2393i | 0.288661 | + | 0.567446i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.4926i | 1.06420i | 0.846682 | + | 0.532100i | \(0.178597\pi\) | ||||
−0.846682 | + | 0.532100i | \(0.821403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.7241i | 1.90756i | 0.300501 | + | 0.953781i | \(0.402846\pi\) | ||||
−0.300501 | + | 0.953781i | \(0.597154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.71097 | + | 31.1507i | −0.129200 | + | 1.08453i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 30.5522i | − | 1.06240i | −0.847245 | − | 0.531202i | \(-0.821741\pi\) | ||
0.847245 | − | 0.531202i | \(-0.178259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.9785 | 0.485492 | 0.242746 | − | 0.970090i | \(-0.421952\pi\) | ||||
0.242746 | + | 0.970090i | \(0.421952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.19527 | + | 0.526279i | −0.0761532 | + | 0.0182564i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 40.8135i | − | 1.41411i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.3163 | + | 7.38739i | 1.42981 | + | 0.255651i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.3149 | + | 35.5648i | 1.04783 | + | 1.22930i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.6423 | 1.29956 | 0.649779 | − | 0.760123i | \(-0.274861\pi\) | ||||
0.649779 | + | 0.760123i | \(0.274861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70.1326 | −2.41837 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.32106 | + | 30.5385i | 0.252151 | + | 1.05180i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1503 | + | 4.13930i | 0.796395 | + | 0.142396i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.17857 | −0.281019 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.23980 | − | 5.17159i | −0.0425498 | − | 0.177489i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.6057 | + | 14.5186i | 0.774914 | + | 0.497692i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.1904i | − | 0.725544i | −0.931878 | − | 0.362772i | \(-0.881830\pi\) | ||
0.931878 | − | 0.362772i | \(-0.118170\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6616 | − | 41.8710i | −0.433018 | − | 1.43196i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.5880 | −1.11318 | −0.556592 | − | 0.830786i | \(-0.687891\pi\) | ||||
−0.556592 | + | 0.830786i | \(0.687891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.8008 | 1.56270 | 0.781351 | − | 0.624092i | \(-0.214531\pi\) | ||||
0.781351 | + | 0.624092i | \(0.214531\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.9972 | − | 3.35559i | 0.477024 | − | 0.114358i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.66726 | −0.0567541 | −0.0283771 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283771 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5857 | − | 3.50194i | −0.665933 | − | 0.119070i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.03227 | + | 16.8198i | 0.136943 | + | 0.571232i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34.0756i | − | 1.15594i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.37345i | − | 0.114305i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.56324 | + | 3.33873i | −0.222132 | + | 0.112999i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.1643 | − | 21.8149i | −1.25638 | − | 0.737477i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 45.6739i | − | 1.54230i | −0.636655 | − | 0.771149i | \(-0.719683\pi\) | ||
0.636655 | − | 0.771149i | \(-0.280317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.3935 | + | 13.2796i | −1.86837 | + | 0.447910i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.64912 | −0.122942 | −0.0614710 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614710 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.5125i | − | 0.892216i | −0.894979 | − | 0.446108i | \(-0.852810\pi\) | ||
0.894979 | − | 0.446108i | \(-0.147190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.9397 | + | 1.16502i | −0.670265 | + | 0.0391616i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.8506 | 1.20375 | 0.601873 | − | 0.798592i | \(-0.294421\pi\) | ||||
0.601873 | + | 0.798592i | \(0.294421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 62.2499i | − | 2.08779i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.1973 | + | 26.3502i | −0.643134 | + | 0.882766i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 60.9763i | − | 2.04049i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.77688 | + | 9.93775i | −0.0593946 | + | 0.332182i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.3581 | + | 4.31069i | 0.412625 | + | 0.143930i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 89.5442i | 2.98646i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.0693 | 1.13501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.7641 | − | 57.4143i | −0.458040 | − | 1.91063i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.646886 | + | 3.61791i | −0.0215032 | + | 0.120263i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5499 | −0.416714 | −0.208357 | − | 0.978053i | \(-0.566812\pi\) | ||||
−0.208357 | + | 0.978053i | \(0.566812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.20186 | + | 2.36261i | 0.0398632 | + | 0.0783628i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2713 | −1.20172 | −0.600861 | − | 0.799354i | \(-0.705175\pi\) | ||||
−0.600861 | + | 0.799354i | \(0.705175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.9774i | − | 0.628061i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.5015 | − | 2.42481i | 1.37200 | − | 0.0801617i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 67.7850i | 2.23846i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.8092i | − | 0.983313i | −0.870789 | − | 0.491657i | \(-0.836392\pi\) | ||
0.870789 | − | 0.491657i | \(-0.163608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.9540 | + | 6.94122i | −0.954067 | + | 0.228721i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7348 | 0.452086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.2748 | + | 9.70623i | 0.863909 | + | 0.319139i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.4695 | − | 16.0085i | 1.03359 | − | 0.525790i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 44.6592i | − | 1.46522i | −0.680648 | − | 0.732611i | \(-0.738302\pi\) | ||
0.680648 | − | 0.732611i | \(-0.261698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.2321i | 1.67906i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −55.7763 | + | 13.3714i | −1.82604 | + | 0.437760i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.40610 | + | 41.4209i | −0.242205 | + | 1.35461i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.56496 | 0.312474 | 0.156237 | − | 0.987720i | \(-0.450064\pi\) | ||||
0.156237 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.65170 | + | 6.88977i | 0.0539013 | + | 0.224839i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.391211 | −0.0127531 | −0.00637656 | − | 0.999980i | \(-0.502030\pi\) | ||||
−0.00637656 | + | 0.999980i | \(0.502030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.58771 | − | 8.70016i | 0.181961 | − | 0.283316i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.5992 | − | 38.6641i | −0.735153 | − | 1.25774i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.3716 | 1.44188 | 0.720942 | − | 0.692996i | \(-0.243710\pi\) | ||||
0.720942 | + | 0.692996i | \(0.243710\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8459 | −0.546842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.1527 | + | 50.6929i | 0.394080 | + | 1.64383i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.3734i | − | 0.530386i | −0.964195 | − | 0.265193i | \(-0.914564\pi\) | ||
0.964195 | − | 0.265193i | \(-0.0854357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.20710 | + | 0.215831i | 0.0390608 | + | 0.00698412i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −60.7480 | + | 14.5633i | −1.96371 | + | 0.470764i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.2677i | 1.36489i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.8831 | 1.60913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.69774 | + | 3.33740i | 0.0547088 | + | 0.107546i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.80235 | + | 32.4514i | −0.186784 | + | 1.04465i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.53370i | − | 0.145794i | −0.997339 | − | 0.0728970i | \(-0.976776\pi\) | ||
0.997339 | − | 0.0728970i | \(-0.0232244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.6783 | − | 57.0564i | −0.439409 | − | 1.83291i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.46255 | −0.111119 | −0.0555593 | − | 0.998455i | \(-0.517694\pi\) | ||||
−0.0555593 | + | 0.998455i | \(0.517694\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.1259 | 0.997851 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5497 | + | 1.61417i | 0.433939 | + | 0.0516949i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 6.08953i | − | 0.194821i | −0.995244 | − | 0.0974107i | \(-0.968944\pi\) | ||
0.995244 | − | 0.0974107i | \(-0.0310560\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.5627 | 0.848946 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.02942 | − | 15.7842i | −0.256360 | − | 0.503950i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 34.3403i | − | 1.09529i | −0.836712 | − | 0.547643i | \(-0.815525\pi\) | ||
0.836712 | − | 0.547643i | \(-0.184475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.2024 | + | 6.47303i | 1.15350 | + | 0.206248i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.5535 | − | 60.7070i | −0.463241 | − | 1.93233i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.6866 | − | 22.9199i | −1.13477 | − | 0.728809i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.6161 | 0.496062 | 0.248031 | − | 0.968752i | \(-0.420217\pi\) | ||||
0.248031 | + | 0.968752i | \(0.420217\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.16627 | − | 4.86488i | −0.0370105 | − | 0.154382i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.16923 | − | 45.6889i | 0.258982 | − | 1.44844i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.4949i | − | 0.427386i | −0.976901 | − | 0.213693i | \(-0.931451\pi\) | ||
0.976901 | − | 0.213693i | \(-0.0685493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.8831 | + | 22.1533i | 0.597435 | + | 0.700899i |
(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 | 1380.2.n.a.689.22 | yes | 48 | |
3.2 | odd | 2 | inner | 1380.2.n.a.689.25 | yes | 48 | |
5.4 | even | 2 | inner | 1380.2.n.a.689.28 | yes | 48 | |
15.14 | odd | 2 | inner | 1380.2.n.a.689.23 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.n.a.689.21 | ✓ | 48 | |
69.68 | even | 2 | inner | 1380.2.n.a.689.26 | yes | 48 | |
115.114 | odd | 2 | inner | 1380.2.n.a.689.27 | yes | 48 | |
345.344 | even | 2 | inner | 1380.2.n.a.689.24 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.n.a.689.21 | ✓ | 48 | 23.22 | odd | 2 | inner | |
1380.2.n.a.689.22 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.n.a.689.23 | yes | 48 | 15.14 | odd | 2 | inner | |
1380.2.n.a.689.24 | yes | 48 | 345.344 | even | 2 | inner | |
1380.2.n.a.689.25 | yes | 48 | 3.2 | odd | 2 | inner | |
1380.2.n.a.689.26 | yes | 48 | 69.68 | even | 2 | inner | |
1380.2.n.a.689.27 | yes | 48 | 115.114 | odd | 2 | inner | |
1380.2.n.a.689.28 | yes | 48 | 5.4 | even | 2 | inner |