Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.2 | ||
Root | \(-0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.a.1077.7 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.08239i | − | 0.624919i | −0.949931 | − | 0.312460i | \(-0.898847\pi\) | ||
0.949931 | − | 0.312460i | \(-0.101153\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.08239i | 0.484061i | 0.970269 | + | 0.242030i | \(0.0778133\pi\) | ||||
−0.970269 | + | 0.242030i | \(0.922187\pi\) | |||||||
\(6\) | −1.08239 | −0.441885 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.82843 | 0.609476 | ||||||||
\(10\) | 1.08239 | 0.342282 | ||||||||
\(11\) | −1.41421 | + | 3.00000i | −0.426401 | + | 0.904534i | ||||
\(12\) | 1.08239i | 0.312460i | ||||||||
\(13\) | −2.29610 | −0.636824 | −0.318412 | − | 0.947952i | \(-0.603149\pi\) | ||||
−0.318412 | + | 0.947952i | \(0.603149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17157 | 0.302499 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | − | 1.82843i | − | 0.430964i | ||||||
\(19\) | 5.54328 | 1.27172 | 0.635858 | − | 0.771806i | \(-0.280647\pi\) | ||||
0.635858 | + | 0.771806i | \(0.280647\pi\) | |||||||
\(20\) | − | 1.08239i | − | 0.242030i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 1.41421i | 0.639602 | + | 0.301511i | ||||
\(23\) | 6.24264 | 1.30168 | 0.650840 | − | 0.759215i | \(-0.274417\pi\) | ||||
0.650840 | + | 0.759215i | \(0.274417\pi\) | |||||||
\(24\) | 1.08239 | 0.220942 | ||||||||
\(25\) | 3.82843 | 0.765685 | ||||||||
\(26\) | 2.29610i | 0.450302i | ||||||||
\(27\) | − | 5.22625i | − | 1.00579i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75736i | 0.326333i | 0.986599 | + | 0.163167i | \(0.0521708\pi\) | ||||
−0.986599 | + | 0.163167i | \(0.947829\pi\) | |||||||
\(30\) | − | 1.17157i | − | 0.213899i | ||||||
\(31\) | − | 1.39942i | − | 0.251343i | −0.992072 | − | 0.125671i | \(-0.959891\pi\) | ||
0.992072 | − | 0.125671i | \(-0.0401085\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 3.24718 | + | 1.53073i | 0.565261 | + | 0.266467i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | − | 5.54328i | − | 0.899238i | ||||||
\(39\) | 2.48528i | 0.397964i | ||||||||
\(40\) | −1.08239 | −0.171141 | ||||||||
\(41\) | −4.59220 | −0.717181 | −0.358591 | − | 0.933495i | \(-0.616743\pi\) | ||||
−0.358591 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 1.41421 | − | 3.00000i | 0.213201 | − | 0.452267i | ||||
\(45\) | 1.97908i | 0.295023i | ||||||||
\(46\) | − | 6.24264i | − | 0.920427i | ||||||
\(47\) | 4.90923i | 0.716084i | 0.933705 | + | 0.358042i | \(0.116556\pi\) | ||||
−0.933705 | + | 0.358042i | \(0.883444\pi\) | |||||||
\(48\) | − | 1.08239i | − | 0.156230i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 3.82843i | − | 0.541421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.29610 | 0.318412 | ||||||||
\(53\) | 4.48528 | 0.616101 | 0.308050 | − | 0.951370i | \(-0.400323\pi\) | ||||
0.308050 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(54\) | −5.22625 | −0.711203 | ||||||||
\(55\) | −3.24718 | − | 1.53073i | −0.437849 | − | 0.206404i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 1.75736 | 0.230753 | ||||||||
\(59\) | − | 7.20533i | − | 0.938054i | −0.883184 | − | 0.469027i | \(-0.844605\pi\) | ||
0.883184 | − | 0.469027i | \(-0.155395\pi\) | |||||||
\(60\) | −1.17157 | −0.151249 | ||||||||
\(61\) | 5.54328 | 0.709744 | 0.354872 | − | 0.934915i | \(-0.384524\pi\) | ||||
0.354872 | + | 0.934915i | \(0.384524\pi\) | |||||||
\(62\) | −1.39942 | −0.177726 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 2.48528i | − | 0.308261i | ||||||
\(66\) | 1.53073 | − | 3.24718i | 0.188420 | − | 0.399700i | ||||
\(67\) | 11.6569 | 1.42411 | 0.712056 | − | 0.702123i | \(-0.247764\pi\) | ||||
0.712056 | + | 0.702123i | \(0.247764\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.75699i | − | 0.813445i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 1.82843i | 0.215482i | ||||||||
\(73\) | −15.6788 | −1.83506 | −0.917530 | − | 0.397667i | \(-0.869820\pi\) | ||||
−0.917530 | + | 0.397667i | \(0.869820\pi\) | |||||||
\(74\) | − | 6.00000i | − | 0.697486i | ||||||
\(75\) | − | 4.14386i | − | 0.478492i | ||||||
\(76\) | −5.54328 | −0.635858 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.48528 | 0.281403 | ||||||||
\(79\) | − | 8.48528i | − | 0.954669i | −0.878722 | − | 0.477334i | \(-0.841603\pi\) | ||
0.878722 | − | 0.477334i | \(-0.158397\pi\) | |||||||
\(80\) | 1.08239i | 0.121015i | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 4.59220i | 0.507124i | ||||||||
\(83\) | 13.3827 | 1.46894 | 0.734469 | − | 0.678643i | \(-0.237431\pi\) | ||||
0.734469 | + | 0.678643i | \(0.237431\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.24264 | 0.457496 | ||||||||
\(87\) | 1.90215 | 0.203932 | ||||||||
\(88\) | −3.00000 | − | 1.41421i | −0.319801 | − | 0.150756i | ||||
\(89\) | − | 3.56420i | − | 0.377805i | −0.981996 | − | 0.188902i | \(-0.939507\pi\) | ||
0.981996 | − | 0.188902i | \(-0.0604930\pi\) | |||||||
\(90\) | 1.97908 | 0.208613 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.24264 | −0.650840 | ||||||||
\(93\) | −1.51472 | −0.157069 | ||||||||
\(94\) | 4.90923 | 0.506348 | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | −1.08239 | −0.110471 | ||||||||
\(97\) | − | 8.60474i | − | 0.873679i | −0.899539 | − | 0.436840i | \(-0.856098\pi\) | ||
0.899539 | − | 0.436840i | \(-0.143902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.58579 | + | 5.48528i | −0.259881 | + | 0.551292i | ||||
\(100\) | −3.82843 | −0.382843 | ||||||||
\(101\) | −16.6298 | −1.65473 | −0.827365 | − | 0.561665i | \(-0.810161\pi\) | ||||
−0.827365 | + | 0.561665i | \(0.810161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.43996i | 0.634548i | 0.948334 | + | 0.317274i | \(0.102768\pi\) | ||||
−0.948334 | + | 0.317274i | \(0.897232\pi\) | |||||||
\(104\) | − | 2.29610i | − | 0.225151i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.48528i | − | 0.435649i | ||||||
\(107\) | 12.7279i | 1.23045i | 0.788350 | + | 0.615227i | \(0.210936\pi\) | ||||
−0.788350 | + | 0.615227i | \(0.789064\pi\) | |||||||
\(108\) | 5.22625i | 0.502896i | ||||||||
\(109\) | 3.51472i | 0.336649i | 0.985732 | + | 0.168324i | \(0.0538356\pi\) | ||||
−0.985732 | + | 0.168324i | \(0.946164\pi\) | |||||||
\(110\) | −1.53073 | + | 3.24718i | −0.145950 | + | 0.309606i | ||||
\(111\) | − | 6.49435i | − | 0.616417i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.41421 | −0.133038 | −0.0665190 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665190 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 6.75699i | 0.630092i | ||||||||
\(116\) | − | 1.75736i | − | 0.163167i | ||||||
\(117\) | −4.19825 | −0.388129 | ||||||||
\(118\) | −7.20533 | −0.663304 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.17157i | 0.106949i | ||||||||
\(121\) | −7.00000 | − | 8.48528i | −0.636364 | − | 0.771389i | ||||
\(122\) | − | 5.54328i | − | 0.501865i | ||||||
\(123\) | 4.97056i | 0.448181i | ||||||||
\(124\) | 1.39942i | 0.125671i | ||||||||
\(125\) | 9.55582i | 0.854699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 4.59220 | 0.404321 | ||||||||
\(130\) | −2.48528 | −0.217974 | ||||||||
\(131\) | −6.88830 | −0.601834 | −0.300917 | − | 0.953650i | \(-0.597293\pi\) | ||||
−0.300917 | + | 0.953650i | \(0.597293\pi\) | |||||||
\(132\) | −3.24718 | − | 1.53073i | −0.282630 | − | 0.133233i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 11.6569i | − | 1.00700i | ||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9706 | −1.44989 | −0.724947 | − | 0.688805i | \(-0.758136\pi\) | ||||
−0.724947 | + | 0.688805i | \(0.758136\pi\) | |||||||
\(138\) | −6.75699 | −0.575193 | ||||||||
\(139\) | 13.3827 | 1.13510 | 0.567551 | − | 0.823338i | \(-0.307891\pi\) | ||||
0.567551 | + | 0.823338i | \(0.307891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.31371 | 0.447495 | ||||||||
\(142\) | − | 2.00000i | − | 0.167836i | ||||||
\(143\) | 3.24718 | − | 6.88830i | 0.271543 | − | 0.576029i | ||||
\(144\) | 1.82843 | 0.152369 | ||||||||
\(145\) | −1.90215 | −0.157965 | ||||||||
\(146\) | 15.6788i | 1.29758i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 6.72792i | 0.551173i | 0.961276 | + | 0.275586i | \(0.0888720\pi\) | ||||
−0.961276 | + | 0.275586i | \(0.911128\pi\) | |||||||
\(150\) | −4.14386 | −0.338345 | ||||||||
\(151\) | − | 6.00000i | − | 0.488273i | −0.969741 | − | 0.244137i | \(-0.921495\pi\) | ||
0.969741 | − | 0.244137i | \(-0.0785045\pi\) | |||||||
\(152\) | 5.54328i | 0.449619i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.51472 | 0.121665 | ||||||||
\(156\) | − | 2.48528i | − | 0.198982i | ||||||
\(157\) | 11.5349i | 0.920585i | 0.887767 | + | 0.460292i | \(0.152255\pi\) | ||||
−0.887767 | + | 0.460292i | \(0.847745\pi\) | |||||||
\(158\) | −8.48528 | −0.675053 | ||||||||
\(159\) | − | 4.85483i | − | 0.385013i | ||||||
\(160\) | 1.08239 | 0.0855706 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.171573i | 0.0134800i | ||||||||
\(163\) | −8.14214 | −0.637741 | −0.318871 | − | 0.947798i | \(-0.603304\pi\) | ||||
−0.318871 | + | 0.947798i | \(0.603304\pi\) | |||||||
\(164\) | 4.59220 | 0.358591 | ||||||||
\(165\) | −1.65685 | + | 3.51472i | −0.128986 | + | 0.273620i | ||||
\(166\) | − | 13.3827i | − | 1.03870i | ||||||
\(167\) | 20.2710 | 1.56861 | 0.784307 | − | 0.620373i | \(-0.213019\pi\) | ||||
0.784307 | + | 0.620373i | \(0.213019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.72792 | −0.594456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.1355 | 0.775079 | ||||||||
\(172\) | − | 4.24264i | − | 0.323498i | ||||||
\(173\) | 25.8142 | 1.96262 | 0.981310 | − | 0.192434i | \(-0.0616381\pi\) | ||||
0.981310 | + | 0.192434i | \(0.0616381\pi\) | |||||||
\(174\) | − | 1.90215i | − | 0.144202i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.41421 | + | 3.00000i | −0.106600 | + | 0.226134i | ||||
\(177\) | −7.79899 | −0.586208 | ||||||||
\(178\) | −3.56420 | −0.267148 | ||||||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | − | 1.97908i | − | 0.147512i | ||||||
\(181\) | 20.4567i | 1.52053i | 0.649612 | + | 0.760266i | \(0.274931\pi\) | ||||
−0.649612 | + | 0.760266i | \(0.725069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.00000i | − | 0.443533i | ||||||
\(184\) | 6.24264i | 0.460214i | ||||||||
\(185\) | 6.49435i | 0.477474i | ||||||||
\(186\) | 1.51472i | 0.111065i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 4.90923i | − | 0.358042i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −1.75736 | −0.127158 | −0.0635790 | − | 0.997977i | \(-0.520251\pi\) | ||||
−0.0635790 | + | 0.997977i | \(0.520251\pi\) | |||||||
\(192\) | 1.08239i | 0.0781149i | ||||||||
\(193\) | 2.48528i | 0.178894i | 0.995992 | + | 0.0894472i | \(0.0285100\pi\) | ||||
−0.995992 | + | 0.0894472i | \(0.971490\pi\) | |||||||
\(194\) | −8.60474 | −0.617785 | ||||||||
\(195\) | −2.69005 | −0.192638 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4853i | 1.45952i | 0.683706 | + | 0.729758i | \(0.260367\pi\) | ||||
−0.683706 | + | 0.729758i | \(0.739633\pi\) | |||||||
\(198\) | 5.48528 | + | 2.58579i | 0.389822 | + | 0.183764i | ||||
\(199\) | 24.6549i | 1.74774i | 0.486159 | + | 0.873870i | \(0.338398\pi\) | ||||
−0.486159 | + | 0.873870i | \(0.661602\pi\) | |||||||
\(200\) | 3.82843i | 0.270711i | ||||||||
\(201\) | − | 12.6173i | − | 0.889955i | ||||||
\(202\) | 16.6298i | 1.17007i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.97056i | − | 0.347159i | ||||||
\(206\) | 6.43996 | 0.448693 | ||||||||
\(207\) | 11.4142 | 0.793343 | ||||||||
\(208\) | −2.29610 | −0.159206 | ||||||||
\(209\) | −7.83938 | + | 16.6298i | −0.542261 | + | 1.15031i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.7279i | − | 1.70234i | −0.524890 | − | 0.851170i | \(-0.675893\pi\) | ||
0.524890 | − | 0.851170i | \(-0.324107\pi\) | |||||||
\(212\) | −4.48528 | −0.308050 | ||||||||
\(213\) | − | 2.16478i | − | 0.148329i | ||||||
\(214\) | 12.7279 | 0.870063 | ||||||||
\(215\) | −4.59220 | −0.313186 | ||||||||
\(216\) | 5.22625 | 0.355601 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.51472 | 0.238047 | ||||||||
\(219\) | 16.9706i | 1.14676i | ||||||||
\(220\) | 3.24718 | + | 1.53073i | 0.218925 | + | 0.103202i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.49435 | −0.435872 | ||||||||
\(223\) | − | 7.89377i | − | 0.528606i | −0.964440 | − | 0.264303i | \(-0.914858\pi\) | ||
0.964440 | − | 0.264303i | \(-0.0851419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 1.41421i | 0.0940721i | ||||||||
\(227\) | 0.951076 | 0.0631251 | 0.0315626 | − | 0.999502i | \(-0.489952\pi\) | ||||
0.0315626 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(228\) | 6.00000i | 0.397360i | ||||||||
\(229\) | − | 28.4818i | − | 1.88213i | −0.338230 | − | 0.941064i | \(-0.609828\pi\) | ||
0.338230 | − | 0.941064i | \(-0.390172\pi\) | |||||||
\(230\) | 6.75699 | 0.445542 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.75736 | −0.115376 | ||||||||
\(233\) | − | 8.48528i | − | 0.555889i | −0.960597 | − | 0.277945i | \(-0.910347\pi\) | ||
0.960597 | − | 0.277945i | \(-0.0896532\pi\) | |||||||
\(234\) | 4.19825i | 0.274448i | ||||||||
\(235\) | −5.31371 | −0.346628 | ||||||||
\(236\) | 7.20533i | 0.469027i | ||||||||
\(237\) | −9.18440 | −0.596591 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.4853i | 1.71319i | 0.515989 | + | 0.856595i | \(0.327425\pi\) | ||||
−0.515989 | + | 0.856595i | \(0.672575\pi\) | |||||||
\(240\) | 1.17157 | 0.0756247 | ||||||||
\(241\) | 4.59220 | 0.295810 | 0.147905 | − | 0.989002i | \(-0.452747\pi\) | ||||
0.147905 | + | 0.989002i | \(0.452747\pi\) | |||||||
\(242\) | −8.48528 | + | 7.00000i | −0.545455 | + | 0.449977i | ||||
\(243\) | − | 15.4930i | − | 0.993879i | ||||||
\(244\) | −5.54328 | −0.354872 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.97056 | 0.316912 | ||||||||
\(247\) | −12.7279 | −0.809858 | ||||||||
\(248\) | 1.39942 | 0.0888631 | ||||||||
\(249\) | − | 14.4853i | − | 0.917967i | ||||||
\(250\) | 9.55582 | 0.604363 | ||||||||
\(251\) | 12.1689i | 0.768097i | 0.923313 | + | 0.384049i | \(0.125470\pi\) | ||||
−0.923313 | + | 0.384049i | \(0.874530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.82843 | + | 18.7279i | −0.555038 | + | 1.17741i | ||||
\(254\) | −6.00000 | −0.376473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0418i | 1.37493i | 0.726218 | + | 0.687465i | \(0.241276\pi\) | ||||
−0.726218 | + | 0.687465i | \(0.758724\pi\) | |||||||
\(258\) | − | 4.59220i | − | 0.285898i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.48528i | 0.154131i | ||||||||
\(261\) | 3.21320i | 0.198892i | ||||||||
\(262\) | 6.88830i | 0.425561i | ||||||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | −1.53073 | + | 3.24718i | −0.0942101 | + | 0.199850i | ||||
\(265\) | 4.85483i | 0.298230i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.85786 | −0.236097 | ||||||||
\(268\) | −11.6569 | −0.712056 | ||||||||
\(269\) | − | 3.50981i | − | 0.213997i | −0.994259 | − | 0.106998i | \(-0.965876\pi\) | ||
0.994259 | − | 0.106998i | \(-0.0341240\pi\) | |||||||
\(270\) | − | 5.65685i | − | 0.344265i | ||||||
\(271\) | −26.7653 | −1.62588 | −0.812938 | − | 0.582350i | \(-0.802133\pi\) | ||||
−0.812938 | + | 0.582350i | \(0.802133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9706i | 1.02523i | ||||||||
\(275\) | −5.41421 | + | 11.4853i | −0.326489 | + | 0.692589i | ||||
\(276\) | 6.75699i | 0.406723i | ||||||||
\(277\) | − | 18.7279i | − | 1.12525i | −0.826712 | − | 0.562626i | \(-0.809791\pi\) | ||
0.826712 | − | 0.562626i | \(-0.190209\pi\) | |||||||
\(278\) | − | 13.3827i | − | 0.802638i | ||||||
\(279\) | − | 2.55873i | − | 0.153187i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0000i | − | 0.715860i | −0.933748 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | − | 5.31371i | − | 0.316427i | ||||||
\(283\) | 22.5671 | 1.34147 | 0.670736 | − | 0.741696i | \(-0.265978\pi\) | ||||
0.670736 | + | 0.741696i | \(0.265978\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | 6.49435 | 0.384692 | ||||||||
\(286\) | −6.88830 | − | 3.24718i | −0.407314 | − | 0.192010i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.82843i | − | 0.107741i | ||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 1.90215i | 0.111698i | ||||||||
\(291\) | −9.31371 | −0.545979 | ||||||||
\(292\) | 15.6788 | 0.917530 | ||||||||
\(293\) | −0.951076 | −0.0555625 | −0.0277812 | − | 0.999614i | \(-0.508844\pi\) | ||||
−0.0277812 | + | 0.999614i | \(0.508844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.79899 | 0.454075 | ||||||||
\(296\) | 6.00000i | 0.348743i | ||||||||
\(297\) | 15.6788 | + | 7.39104i | 0.909774 | + | 0.428871i | ||||
\(298\) | 6.72792 | 0.389738 | ||||||||
\(299\) | −14.3337 | −0.828941 | ||||||||
\(300\) | 4.14386i | 0.239246i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 18.0000i | 1.03407i | ||||||||
\(304\) | 5.54328 | 0.317929 | ||||||||
\(305\) | 6.00000i | 0.343559i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.44543 | −0.424933 | −0.212467 | − | 0.977168i | \(-0.568150\pi\) | ||||
−0.212467 | + | 0.977168i | \(0.568150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.97056 | 0.396541 | ||||||||
\(310\) | − | 1.51472i | − | 0.0860302i | ||||||
\(311\) | − | 33.3910i | − | 1.89343i | −0.322074 | − | 0.946714i | \(-0.604380\pi\) | ||
0.322074 | − | 0.946714i | \(-0.395620\pi\) | |||||||
\(312\) | −2.48528 | −0.140701 | ||||||||
\(313\) | − | 10.3212i | − | 0.583388i | −0.956512 | − | 0.291694i | \(-0.905781\pi\) | ||
0.956512 | − | 0.291694i | \(-0.0942189\pi\) | |||||||
\(314\) | 11.5349 | 0.650952 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −22.9706 | −1.29016 | −0.645078 | − | 0.764117i | \(-0.723175\pi\) | ||||
−0.645078 | + | 0.764117i | \(0.723175\pi\) | |||||||
\(318\) | −4.85483 | −0.272246 | ||||||||
\(319\) | −5.27208 | − | 2.48528i | −0.295180 | − | 0.139149i | ||||
\(320\) | − | 1.08239i | − | 0.0605076i | ||||||
\(321\) | 13.7766 | 0.768935 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.171573 | 0.00953183 | ||||||||
\(325\) | −8.79045 | −0.487607 | ||||||||
\(326\) | 8.14214i | 0.450951i | ||||||||
\(327\) | 3.80430 | 0.210378 | ||||||||
\(328\) | − | 4.59220i | − | 0.253562i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.51472 | + | 1.65685i | 0.193479 | + | 0.0912068i | ||||
\(331\) | 20.4853 | 1.12597 | 0.562986 | − | 0.826466i | \(-0.309652\pi\) | ||||
0.562986 | + | 0.826466i | \(0.309652\pi\) | |||||||
\(332\) | −13.3827 | −0.734469 | ||||||||
\(333\) | 10.9706 | 0.601183 | ||||||||
\(334\) | − | 20.2710i | − | 1.10918i | ||||||
\(335\) | 12.6173i | 0.689356i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.4853i | − | 1.44275i | −0.692547 | − | 0.721373i | \(-0.743512\pi\) | ||
0.692547 | − | 0.721373i | \(-0.256488\pi\) | |||||||
\(338\) | 7.72792i | 0.420344i | ||||||||
\(339\) | 1.53073i | 0.0831380i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.19825 | + | 1.97908i | 0.227348 | + | 0.107173i | ||||
\(342\) | − | 10.1355i | − | 0.548064i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.24264 | −0.228748 | ||||||||
\(345\) | 7.31371 | 0.393757 | ||||||||
\(346\) | − | 25.8142i | − | 1.38778i | ||||||
\(347\) | − | 7.75736i | − | 0.416437i | −0.978082 | − | 0.208218i | \(-0.933234\pi\) | ||
0.978082 | − | 0.208218i | \(-0.0667665\pi\) | |||||||
\(348\) | −1.90215 | −0.101966 | ||||||||
\(349\) | −29.0614 | −1.55562 | −0.777811 | − | 0.628498i | \(-0.783670\pi\) | ||||
−0.777811 | + | 0.628498i | \(0.783670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.0000i | 0.640513i | ||||||||
\(352\) | 3.00000 | + | 1.41421i | 0.159901 | + | 0.0753778i | ||||
\(353\) | 1.21371i | 0.0645992i | 0.999478 | + | 0.0322996i | \(0.0102831\pi\) | ||||
−0.999478 | + | 0.0322996i | \(0.989717\pi\) | |||||||
\(354\) | 7.79899i | 0.414512i | ||||||||
\(355\) | 2.16478i | 0.114895i | ||||||||
\(356\) | 3.56420i | 0.188902i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.65685i | 0.298974i | ||||||||
\(359\) | − | 2.48528i | − | 0.131168i | −0.997847 | − | 0.0655841i | \(-0.979109\pi\) | ||
0.997847 | − | 0.0655841i | \(-0.0208911\pi\) | |||||||
\(360\) | −1.97908 | −0.104306 | ||||||||
\(361\) | 11.7279 | 0.617259 | ||||||||
\(362\) | 20.4567 | 1.07518 | ||||||||
\(363\) | −9.18440 | + | 7.57675i | −0.482056 | + | 0.397676i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 16.9706i | − | 0.888280i | ||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | − | 11.1409i | − | 0.581553i | −0.956791 | − | 0.290776i | \(-0.906086\pi\) | ||
0.956791 | − | 0.290776i | \(-0.0939136\pi\) | |||||||
\(368\) | 6.24264 | 0.325420 | ||||||||
\(369\) | −8.39651 | −0.437105 | ||||||||
\(370\) | 6.49435 | 0.337625 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.51472 | 0.0785345 | ||||||||
\(373\) | − | 20.4853i | − | 1.06069i | −0.847783 | − | 0.530344i | \(-0.822063\pi\) | ||
0.847783 | − | 0.530344i | \(-0.177937\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3431 | 0.534118 | ||||||||
\(376\) | −4.90923 | −0.253174 | ||||||||
\(377\) | − | 4.03507i | − | 0.207817i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6569 | −0.598772 | −0.299386 | − | 0.954132i | \(-0.596782\pi\) | ||||
−0.299386 | + | 0.954132i | \(0.596782\pi\) | |||||||
\(380\) | − | 6.00000i | − | 0.307794i | ||||||
\(381\) | −6.49435 | −0.332716 | ||||||||
\(382\) | 1.75736i | 0.0899143i | ||||||||
\(383\) | 14.4650i | 0.739129i | 0.929205 | + | 0.369565i | \(0.120493\pi\) | ||||
−0.929205 | + | 0.369565i | \(0.879507\pi\) | |||||||
\(384\) | 1.08239 | 0.0552356 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.48528 | 0.126497 | ||||||||
\(387\) | 7.75736i | 0.394329i | ||||||||
\(388\) | 8.60474i | 0.436840i | ||||||||
\(389\) | −32.0000 | −1.62246 | −0.811232 | − | 0.584724i | \(-0.801203\pi\) | ||||
−0.811232 | + | 0.584724i | \(0.801203\pi\) | |||||||
\(390\) | 2.69005i | 0.136216i | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.45584i | 0.376098i | ||||||||
\(394\) | 20.4853 | 1.03203 | ||||||||
\(395\) | 9.18440 | 0.462117 | ||||||||
\(396\) | 2.58579 | − | 5.48528i | 0.129941 | − | 0.275646i | ||||
\(397\) | 1.71644i | 0.0861458i | 0.999072 | + | 0.0430729i | \(0.0137148\pi\) | ||||
−0.999072 | + | 0.0430729i | \(0.986285\pi\) | |||||||
\(398\) | 24.6549 | 1.23584 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.82843 | 0.191421 | ||||||||
\(401\) | 0.485281 | 0.0242338 | 0.0121169 | − | 0.999927i | \(-0.496143\pi\) | ||||
0.0121169 | + | 0.999927i | \(0.496143\pi\) | |||||||
\(402\) | −12.6173 | −0.629293 | ||||||||
\(403\) | 3.21320i | 0.160061i | ||||||||
\(404\) | 16.6298 | 0.827365 | ||||||||
\(405\) | − | 0.185709i | − | 0.00922796i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.48528 | + | 18.0000i | −0.420600 | + | 0.892227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.8519 | −1.87165 | −0.935827 | − | 0.352459i | \(-0.885345\pi\) | ||||
−0.935827 | + | 0.352459i | \(0.885345\pi\) | |||||||
\(410\) | −4.97056 | −0.245479 | ||||||||
\(411\) | 18.3688i | 0.906066i | ||||||||
\(412\) | − | 6.43996i | − | 0.317274i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 11.4142i | − | 0.560978i | ||||||
\(415\) | 14.4853i | 0.711054i | ||||||||
\(416\) | 2.29610i | 0.112576i | ||||||||
\(417\) | − | 14.4853i | − | 0.709347i | ||||||
\(418\) | 16.6298 | + | 7.83938i | 0.813392 | + | 0.383437i | ||||
\(419\) | − | 8.47343i | − | 0.413954i | −0.978346 | − | 0.206977i | \(-0.933637\pi\) | ||
0.978346 | − | 0.206977i | \(-0.0663625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6569 | 0.860542 | 0.430271 | − | 0.902700i | \(-0.358418\pi\) | ||||
0.430271 | + | 0.902700i | \(0.358418\pi\) | |||||||
\(422\) | −24.7279 | −1.20374 | ||||||||
\(423\) | 8.97616i | 0.436436i | ||||||||
\(424\) | 4.48528i | 0.217825i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.16478 | −0.104884 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.7279i | − | 0.615227i | ||||||
\(429\) | −7.45584 | − | 3.51472i | −0.359972 | − | 0.169692i | ||||
\(430\) | 4.59220i | 0.221456i | ||||||||
\(431\) | − | 2.48528i | − | 0.119712i | −0.998207 | − | 0.0598559i | \(-0.980936\pi\) | ||
0.998207 | − | 0.0598559i | \(-0.0190641\pi\) | |||||||
\(432\) | − | 5.22625i | − | 0.251448i | ||||||
\(433\) | − | 22.6758i | − | 1.08973i | −0.838523 | − | 0.544866i | \(-0.816581\pi\) | ||
0.838523 | − | 0.544866i | \(-0.183419\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05887i | 0.0987155i | ||||||||
\(436\) | − | 3.51472i | − | 0.168324i | ||||||
\(437\) | 34.6047 | 1.65537 | ||||||||
\(438\) | 16.9706 | 0.810885 | ||||||||
\(439\) | −6.49435 | −0.309959 | −0.154979 | − | 0.987918i | \(-0.549531\pi\) | ||||
−0.154979 | + | 0.987918i | \(0.549531\pi\) | |||||||
\(440\) | 1.53073 | − | 3.24718i | 0.0729749 | − | 0.154803i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.6274 | 1.07506 | 0.537531 | − | 0.843244i | \(-0.319357\pi\) | ||||
0.537531 | + | 0.843244i | \(0.319357\pi\) | |||||||
\(444\) | 6.49435i | 0.308208i | ||||||||
\(445\) | 3.85786 | 0.182880 | ||||||||
\(446\) | −7.89377 | −0.373781 | ||||||||
\(447\) | 7.28225 | 0.344439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.7279 | −1.92207 | −0.961035 | − | 0.276428i | \(-0.910849\pi\) | ||||
−0.961035 | + | 0.276428i | \(0.910849\pi\) | |||||||
\(450\) | − | 7.00000i | − | 0.329983i | ||||||
\(451\) | 6.49435 | − | 13.7766i | 0.305807 | − | 0.648715i | ||||
\(452\) | 1.41421 | 0.0665190 | ||||||||
\(453\) | −6.49435 | −0.305131 | ||||||||
\(454\) | − | 0.951076i | − | 0.0446362i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | − | 31.4558i | − | 1.47144i | −0.677285 | − | 0.735721i | \(-0.736843\pi\) | ||
0.677285 | − | 0.735721i | \(-0.263157\pi\) | |||||||
\(458\) | −28.4818 | −1.33086 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 6.75699i | − | 0.315046i | ||||||
\(461\) | −29.0614 | −1.35352 | −0.676762 | − | 0.736201i | \(-0.736618\pi\) | ||||
−0.676762 | + | 0.736201i | \(0.736618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.31371 | −0.246949 | −0.123474 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123474 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(464\) | 1.75736i | 0.0815834i | ||||||||
\(465\) | − | 1.63952i | − | 0.0760309i | ||||||
\(466\) | −8.48528 | −0.393073 | ||||||||
\(467\) | 32.1773i | 1.48899i | 0.667630 | + | 0.744493i | \(0.267309\pi\) | ||||
−0.667630 | + | 0.744493i | \(0.732691\pi\) | |||||||
\(468\) | 4.19825 | 0.194064 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.31371i | 0.245103i | ||||||||
\(471\) | 12.4853 | 0.575291 | ||||||||
\(472\) | 7.20533 | 0.331652 | ||||||||
\(473\) | −12.7279 | − | 6.00000i | −0.585230 | − | 0.275880i | ||||
\(474\) | 9.18440i | 0.421854i | ||||||||
\(475\) | 21.2220 | 0.973734 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.20101 | 0.375498 | ||||||||
\(478\) | 26.4853 | 1.21141 | ||||||||
\(479\) | −9.18440 | −0.419646 | −0.209823 | − | 0.977739i | \(-0.567289\pi\) | ||||
−0.209823 | + | 0.977739i | \(0.567289\pi\) | |||||||
\(480\) | − | 1.17157i | − | 0.0534747i | ||||||
\(481\) | −13.7766 | −0.628159 | ||||||||
\(482\) | − | 4.59220i | − | 0.209169i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | + | 8.48528i | 0.318182 | + | 0.385695i | ||||
\(485\) | 9.31371 | 0.422914 | ||||||||
\(486\) | −15.4930 | −0.702779 | ||||||||
\(487\) | −2.44365 | −0.110732 | −0.0553662 | − | 0.998466i | \(-0.517633\pi\) | ||||
−0.0553662 | + | 0.998466i | \(0.517633\pi\) | |||||||
\(488\) | 5.54328i | 0.250932i | ||||||||
\(489\) | 8.81298i | 0.398537i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 39.9411i | − | 1.80252i | −0.433281 | − | 0.901259i | \(-0.642644\pi\) | ||
0.433281 | − | 0.901259i | \(-0.357356\pi\) | |||||||
\(492\) | − | 4.97056i | − | 0.224090i | ||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.7279i | 0.572656i | ||||||||
\(495\) | −5.93723 | − | 2.79884i | −0.266858 | − | 0.125798i | ||||
\(496\) | − | 1.39942i | − | 0.0628357i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.4853 | −0.649101 | ||||||||
\(499\) | 28.6274 | 1.28154 | 0.640770 | − | 0.767733i | \(-0.278615\pi\) | ||||
0.640770 | + | 0.767733i | \(0.278615\pi\) | |||||||
\(500\) | − | 9.55582i | − | 0.427349i | ||||||
\(501\) | − | 21.9411i | − | 0.980257i | ||||||
\(502\) | 12.1689 | 0.543127 | ||||||||
\(503\) | −6.49435 | −0.289569 | −0.144784 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144784 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.0000i | − | 0.800989i | ||||||
\(506\) | 18.7279 | + | 8.82843i | 0.832558 | + | 0.392471i | ||||
\(507\) | 8.36464i | 0.371487i | ||||||||
\(508\) | 6.00000i | 0.266207i | ||||||||
\(509\) | 32.4399i | 1.43787i | 0.695076 | + | 0.718937i | \(0.255371\pi\) | ||||
−0.695076 | + | 0.718937i | \(0.744629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 28.9706i | − | 1.27908i | ||||||
\(514\) | 22.0418 | 0.972222 | ||||||||
\(515\) | −6.97056 | −0.307160 | ||||||||
\(516\) | −4.59220 | −0.202160 | ||||||||
\(517\) | −14.7277 | − | 6.94269i | −0.647723 | − | 0.305339i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.9411i | − | 1.22648i | ||||||
\(520\) | 2.48528 | 0.108987 | ||||||||
\(521\) | − | 28.3504i | − | 1.24206i | −0.783789 | − | 0.621028i | \(-0.786715\pi\) | ||
0.783789 | − | 0.621028i | \(-0.213285\pi\) | |||||||
\(522\) | 3.21320 | 0.140638 | ||||||||
\(523\) | −0.951076 | −0.0415877 | −0.0207938 | − | 0.999784i | \(-0.506619\pi\) | ||||
−0.0207938 | + | 0.999784i | \(0.506619\pi\) | |||||||
\(524\) | 6.88830 | 0.300917 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.24718 | + | 1.53073i | 0.141315 | + | 0.0666166i | ||||
\(529\) | 15.9706 | 0.694372 | ||||||||
\(530\) | 4.85483 | 0.210880 | ||||||||
\(531\) | − | 13.1744i | − | 0.571721i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5442 | 0.456718 | ||||||||
\(534\) | 3.85786i | 0.166946i | ||||||||
\(535\) | −13.7766 | −0.595615 | ||||||||
\(536\) | 11.6569i | 0.503499i | ||||||||
\(537\) | 6.12293i | 0.264224i | ||||||||
\(538\) | −3.50981 | −0.151319 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.65685 | −0.243432 | ||||||||
\(541\) | − | 10.9706i | − | 0.471661i | −0.971794 | − | 0.235831i | \(-0.924219\pi\) | ||
0.971794 | − | 0.235831i | \(-0.0757811\pi\) | |||||||
\(542\) | 26.7653i | 1.14967i | ||||||||
\(543\) | 22.1421 | 0.950210 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.80430 | −0.162958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.0000i | 1.02617i | 0.858339 | + | 0.513083i | \(0.171497\pi\) | ||||
−0.858339 | + | 0.513083i | \(0.828503\pi\) | |||||||
\(548\) | 16.9706 | 0.724947 | ||||||||
\(549\) | 10.1355 | 0.432572 | ||||||||
\(550\) | 11.4853 | + | 5.41421i | 0.489734 | + | 0.230863i | ||||
\(551\) | 9.74153i | 0.415003i | ||||||||
\(552\) | 6.75699 | 0.287596 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.7279 | −0.795673 | ||||||||
\(555\) | 7.02944 | 0.298383 | ||||||||
\(556\) | −13.3827 | −0.567551 | ||||||||
\(557\) | − | 6.00000i | − | 0.254228i | −0.991888 | − | 0.127114i | \(-0.959429\pi\) | ||
0.991888 | − | 0.127114i | \(-0.0405714\pi\) | |||||||
\(558\) | −2.55873 | −0.108320 | ||||||||
\(559\) | − | 9.74153i | − | 0.412023i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | −27.1593 | −1.14463 | −0.572313 | − | 0.820035i | \(-0.693954\pi\) | ||||
−0.572313 | + | 0.820035i | \(0.693954\pi\) | |||||||
\(564\) | −5.31371 | −0.223747 | ||||||||
\(565\) | − | 1.53073i | − | 0.0643985i | ||||||
\(566\) | − | 22.5671i | − | 0.948564i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.00000i | 0.0839181i | ||||||||
\(569\) | − | 30.0000i | − | 1.25767i | −0.777541 | − | 0.628833i | \(-0.783533\pi\) | ||
0.777541 | − | 0.628833i | \(-0.216467\pi\) | |||||||
\(570\) | − | 6.49435i | − | 0.272019i | ||||||
\(571\) | − | 36.0000i | − | 1.50655i | −0.657704 | − | 0.753277i | \(-0.728472\pi\) | ||
0.657704 | − | 0.753277i | \(-0.271528\pi\) | |||||||
\(572\) | −3.24718 | + | 6.88830i | −0.135771 | + | 0.288014i | ||||
\(573\) | 1.90215i | 0.0794635i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.8995 | 0.996678 | ||||||||
\(576\) | −1.82843 | −0.0761845 | ||||||||
\(577\) | 33.2053i | 1.38235i | 0.722686 | + | 0.691177i | \(0.242907\pi\) | ||||
−0.722686 | + | 0.691177i | \(0.757093\pi\) | |||||||
\(578\) | 17.0000i | 0.707107i | ||||||||
\(579\) | 2.69005 | 0.111795 | ||||||||
\(580\) | 1.90215 | 0.0789826 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.31371i | 0.386066i | ||||||||
\(583\) | −6.34315 | + | 13.4558i | −0.262706 | + | 0.557284i | ||||
\(584\) | − | 15.6788i | − | 0.648792i | ||||||
\(585\) | − | 4.54416i | − | 0.187878i | ||||||
\(586\) | 0.951076i | 0.0392886i | ||||||||
\(587\) | − | 37.0321i | − | 1.52848i | −0.644933 | − | 0.764239i | \(-0.723115\pi\) | ||
0.644933 | − | 0.764239i | \(-0.276885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.75736i | − | 0.319636i | ||||||
\(590\) | − | 7.79899i | − | 0.321079i | ||||||
\(591\) | 22.1731 | 0.912080 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | 28.6675 | 1.17723 | 0.588616 | − | 0.808413i | \(-0.299673\pi\) | ||||
0.588616 | + | 0.808413i | \(0.299673\pi\) | |||||||
\(594\) | 7.39104 | − | 15.6788i | 0.303258 | − | 0.643307i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.72792i | − | 0.275586i | ||||||
\(597\) | 26.6863 | 1.09220 | ||||||||
\(598\) | 14.3337i | 0.586150i | ||||||||
\(599\) | −26.0000 | −1.06233 | −0.531166 | − | 0.847268i | \(-0.678246\pi\) | ||||
−0.531166 | + | 0.847268i | \(0.678246\pi\) | |||||||
\(600\) | 4.14386 | 0.169172 | ||||||||
\(601\) | 35.9497 | 1.46642 | 0.733210 | − | 0.680003i | \(-0.238021\pi\) | ||||
0.733210 | + | 0.680003i | \(0.238021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3137 | 0.867961 | ||||||||
\(604\) | 6.00000i | 0.244137i | ||||||||
\(605\) | 9.18440 | − | 7.57675i | 0.373399 | − | 0.308039i | ||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | −46.2484 | −1.87716 | −0.938582 | − | 0.345057i | \(-0.887860\pi\) | ||||
−0.938582 | + | 0.345057i | \(0.887860\pi\) | |||||||
\(608\) | − | 5.54328i | − | 0.224810i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | − | 11.2721i | − | 0.456019i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7574i | 0.555655i | 0.960631 | + | 0.277827i | \(0.0896143\pi\) | ||||
−0.960631 | + | 0.277827i | \(0.910386\pi\) | |||||||
\(614\) | 7.44543i | 0.300473i | ||||||||
\(615\) | −5.38010 | −0.216947 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.41421 | 0.0569341 | 0.0284670 | − | 0.999595i | \(-0.490937\pi\) | ||||
0.0284670 | + | 0.999595i | \(0.490937\pi\) | |||||||
\(618\) | − | 6.97056i | − | 0.280397i | ||||||
\(619\) | − | 1.71644i | − | 0.0689897i | −0.999405 | − | 0.0344948i | \(-0.989018\pi\) | ||
0.999405 | − | 0.0344948i | \(-0.0109822\pi\) | |||||||
\(620\) | −1.51472 | −0.0608326 | ||||||||
\(621\) | − | 32.6256i | − | 1.30922i | ||||||
\(622\) | −33.3910 | −1.33886 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.48528i | 0.0994909i | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | −10.3212 | −0.412518 | ||||||||
\(627\) | 18.0000 | + | 8.48528i | 0.718851 | + | 0.338869i | ||||
\(628\) | − | 11.5349i | − | 0.460292i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2132 | 0.605628 | 0.302814 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302814 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(632\) | 8.48528 | 0.337526 | ||||||||
\(633\) | −26.7653 | −1.06383 | ||||||||
\(634\) | 22.9706i | 0.912278i | ||||||||
\(635\) | 6.49435 | 0.257721 | ||||||||
\(636\) | 4.85483i | 0.192507i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.48528 | + | 5.27208i | −0.0983932 | + | 0.208724i | ||||
\(639\) | 3.65685 | 0.144663 | ||||||||
\(640\) | −1.08239 | −0.0427853 | ||||||||
\(641\) | 2.78680 | 0.110072 | 0.0550359 | − | 0.998484i | \(-0.482473\pi\) | ||||
0.0550359 | + | 0.998484i | \(0.482473\pi\) | |||||||
\(642\) | − | 13.7766i | − | 0.543719i | ||||||
\(643\) | − | 5.04054i | − | 0.198780i | −0.995049 | − | 0.0993898i | \(-0.968311\pi\) | ||
0.995049 | − | 0.0993898i | \(-0.0316891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.97056i | 0.195716i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.56420i | 0.140123i | 0.997543 | + | 0.0700616i | \(0.0223196\pi\) | ||||
−0.997543 | + | 0.0700616i | \(0.977680\pi\) | |||||||
\(648\) | − | 0.171573i | − | 0.00674002i | ||||||
\(649\) | 21.6160 | + | 10.1899i | 0.848501 | + | 0.399987i | ||||
\(650\) | 8.79045i | 0.344790i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.14214 | 0.318871 | ||||||||
\(653\) | 21.4558 | 0.839632 | 0.419816 | − | 0.907609i | \(-0.362095\pi\) | ||||
0.419816 | + | 0.907609i | \(0.362095\pi\) | |||||||
\(654\) | − | 3.80430i | − | 0.148760i | ||||||
\(655\) | − | 7.45584i | − | 0.291324i | ||||||
\(656\) | −4.59220 | −0.179295 | ||||||||
\(657\) | −28.6675 | −1.11842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.21320i | 0.358895i | 0.983768 | + | 0.179448i | \(0.0574311\pi\) | ||||
−0.983768 | + | 0.179448i | \(0.942569\pi\) | |||||||
\(660\) | 1.65685 | − | 3.51472i | 0.0644930 | − | 0.136810i | ||||
\(661\) | − | 33.4454i | − | 1.30087i | −0.759560 | − | 0.650437i | \(-0.774586\pi\) | ||
0.759560 | − | 0.650437i | \(-0.225414\pi\) | |||||||
\(662\) | − | 20.4853i | − | 0.796183i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.3827i | 0.519348i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 10.9706i | − | 0.425101i | ||||||
\(667\) | 10.9706i | 0.424782i | ||||||||
\(668\) | −20.2710 | −0.784307 | ||||||||
\(669\) | −8.54416 | −0.330336 | ||||||||
\(670\) | 12.6173 | 0.487448 | ||||||||
\(671\) | −7.83938 | + | 16.6298i | −0.302636 | + | 0.641988i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 45.9411i | − | 1.77090i | −0.464734 | − | 0.885450i | \(-0.653850\pi\) | ||
0.464734 | − | 0.885450i | \(-0.346150\pi\) | |||||||
\(674\) | −26.4853 | −1.02017 | ||||||||
\(675\) | − | 20.0083i | − | 0.770121i | ||||||
\(676\) | 7.72792 | 0.297228 | ||||||||
\(677\) | 19.8770 | 0.763935 | 0.381968 | − | 0.924176i | \(-0.375247\pi\) | ||||
0.381968 | + | 0.924176i | \(0.375247\pi\) | |||||||
\(678\) | 1.53073 | 0.0587875 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.02944i | − | 0.0394481i | ||||||
\(682\) | 1.97908 | − | 4.19825i | 0.0757827 | − | 0.160759i | ||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | −10.1355 | −0.387540 | ||||||||
\(685\) | − | 18.3688i | − | 0.701836i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.8284 | −1.17618 | ||||||||
\(688\) | 4.24264i | 0.161749i | ||||||||
\(689\) | −10.2987 | −0.392348 | ||||||||
\(690\) | − | 7.31371i | − | 0.278428i | ||||||
\(691\) | − | 4.25265i | − | 0.161778i | −0.996723 | − | 0.0808891i | \(-0.974224\pi\) | ||
0.996723 | − | 0.0808891i | \(-0.0257760\pi\) | |||||||
\(692\) | −25.8142 | −0.981310 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.75736 | −0.294465 | ||||||||
\(695\) | 14.4853i | 0.549458i | ||||||||
\(696\) | 1.90215i | 0.0721009i | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 29.0614i | 1.09999i | ||||||||
\(699\) | −9.18440 | −0.347386 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.9411i | 1.50856i | 0.656555 | + | 0.754278i | \(0.272013\pi\) | ||||
−0.656555 | + | 0.754278i | \(0.727987\pi\) | |||||||
\(702\) | 12.0000 | 0.452911 | ||||||||
\(703\) | 33.2597 | 1.25441 | ||||||||
\(704\) | 1.41421 | − | 3.00000i | 0.0533002 | − | 0.113067i | ||||
\(705\) | 5.75152i | 0.216615i | ||||||||
\(706\) | 1.21371 | 0.0456785 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.79899 | 0.293104 | ||||||||
\(709\) | −23.3137 | −0.875565 | −0.437782 | − | 0.899081i | \(-0.644236\pi\) | ||||
−0.437782 | + | 0.899081i | \(0.644236\pi\) | |||||||
\(710\) | 2.16478 | 0.0812429 | ||||||||
\(711\) | − | 15.5147i | − | 0.581847i | ||||||
\(712\) | 3.56420 | 0.133574 | ||||||||
\(713\) | − | 8.73606i | − | 0.327168i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.45584 | + | 3.51472i | 0.278833 | + | 0.131443i | ||||
\(716\) | 5.65685 | 0.211407 | ||||||||
\(717\) | 28.6675 | 1.07061 | ||||||||
\(718\) | −2.48528 | −0.0927499 | ||||||||
\(719\) | 23.2011i | 0.865255i | 0.901573 | + | 0.432628i | \(0.142414\pi\) | ||||
−0.901573 | + | 0.432628i | \(0.857586\pi\) | |||||||
\(720\) | 1.97908i | 0.0737558i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 11.7279i | − | 0.436468i | ||||||
\(723\) | − | 4.97056i | − | 0.184857i | ||||||
\(724\) | − | 20.4567i | − | 0.760266i | ||||||
\(725\) | 6.72792i | 0.249869i | ||||||||
\(726\) | 7.57675 | + | 9.18440i | 0.281199 | + | 0.340865i | ||||
\(727\) | − | 25.9999i | − | 0.964285i | −0.876093 | − | 0.482142i | \(-0.839859\pi\) | ||
0.876093 | − | 0.482142i | \(-0.160141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2843 | −0.640158 | ||||||||
\(730\) | −16.9706 | −0.628109 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | 0.951076 | 0.0351288 | 0.0175644 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175644 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(734\) | −11.1409 | −0.411220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.24264i | − | 0.230107i | ||||||
\(737\) | −16.4853 | + | 34.9706i | −0.607243 | + | 1.28816i | ||||
\(738\) | 8.39651i | 0.309080i | ||||||||
\(739\) | − | 24.0000i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(740\) | − | 6.49435i | − | 0.238737i | ||||||
\(741\) | 13.7766i | 0.506096i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.4264i | 1.33636i | 0.744002 | + | 0.668178i | \(0.232925\pi\) | ||||
−0.744002 | + | 0.668178i | \(0.767075\pi\) | |||||||
\(744\) | − | 1.51472i | − | 0.0555323i | ||||||
\(745\) | −7.28225 | −0.266801 | ||||||||
\(746\) | −20.4853 | −0.750019 | ||||||||
\(747\) | 24.4692 | 0.895282 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 10.3431i | − | 0.377678i | ||||||
\(751\) | 19.4142 | 0.708435 | 0.354217 | − | 0.935163i | \(-0.384747\pi\) | ||||
0.354217 | + | 0.935163i | \(0.384747\pi\) | |||||||
\(752\) | 4.90923i | 0.179021i | ||||||||
\(753\) | 13.1716 | 0.479999 | ||||||||
\(754\) | −4.03507 | −0.146949 | ||||||||
\(755\) | 6.49435 | 0.236354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1421 | −1.38630 | −0.693150 | − | 0.720794i | \(-0.743778\pi\) | ||||
−0.693150 | + | 0.720794i | \(0.743778\pi\) | |||||||
\(758\) | 11.6569i | 0.423396i | ||||||||
\(759\) | 20.2710 | + | 9.55582i | 0.735789 | + | 0.346854i | ||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | −28.6675 | −1.03919 | −0.519597 | − | 0.854411i | \(-0.673918\pi\) | ||||
−0.519597 | + | 0.854411i | \(0.673918\pi\) | |||||||
\(762\) | 6.49435i | 0.235266i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.75736 | 0.0635790 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.4650 | 0.522643 | ||||||||
\(767\) | 16.5442i | 0.597375i | ||||||||
\(768\) | − | 1.08239i | − | 0.0390575i | ||||||
\(769\) | 6.49435 | 0.234192 | 0.117096 | − | 0.993121i | \(-0.462641\pi\) | ||||
0.117096 | + | 0.993121i | \(0.462641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8579 | 0.859220 | ||||||||
\(772\) | − | 2.48528i | − | 0.0894472i | ||||||
\(773\) | − | 25.6829i | − | 0.923750i | −0.886945 | − | 0.461875i | \(-0.847177\pi\) | ||
0.886945 | − | 0.461875i | \(-0.152823\pi\) | |||||||
\(774\) | 7.75736 | 0.278833 | ||||||||
\(775\) | − | 5.35757i | − | 0.192450i | ||||||
\(776\) | 8.60474 | 0.308892 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.0000i | 1.14726i | ||||||||
\(779\) | −25.4558 | −0.912050 | ||||||||
\(780\) | 2.69005 | 0.0963192 | ||||||||
\(781\) | −2.82843 | + | 6.00000i | −0.101209 | + | 0.214697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.18440 | 0.328224 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4853 | −0.445619 | ||||||||
\(786\) | 7.45584 | 0.265941 | ||||||||
\(787\) | −8.79045 | −0.313346 | −0.156673 | − | 0.987651i | \(-0.550077\pi\) | ||||
−0.156673 | + | 0.987651i | \(0.550077\pi\) | |||||||
\(788\) | − | 20.4853i | − | 0.729758i | ||||||
\(789\) | 25.9774 | 0.924820 | ||||||||
\(790\) | − | 9.18440i | − | 0.326766i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.48528 | − | 2.58579i | −0.194911 | − | 0.0918819i | ||||
\(793\) | −12.7279 | −0.451982 | ||||||||
\(794\) | 1.71644 | 0.0609143 | ||||||||
\(795\) | 5.25483 | 0.186370 | ||||||||
\(796\) | − | 24.6549i | − | 0.873870i | ||||||
\(797\) | 26.0543i | 0.922892i | 0.887168 | + | 0.461446i | \(0.152669\pi\) | ||||
−0.887168 | + | 0.461446i | \(0.847331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 3.82843i | − | 0.135355i | ||||||
\(801\) | − | 6.51688i | − | 0.230263i | ||||||
\(802\) | − | 0.485281i | − | 0.0171359i | ||||||
\(803\) | 22.1731 | − | 47.0363i | 0.782472 | − | 1.65987i | ||||
\(804\) | 12.6173i | 0.444977i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.21320 | 0.113180 | ||||||||
\(807\) | −3.79899 | −0.133731 | ||||||||
\(808\) | − | 16.6298i | − | 0.585035i | ||||||
\(809\) | 14.4853i | 0.509275i | 0.967037 | + | 0.254638i | \(0.0819562\pi\) | ||||
−0.967037 | + | 0.254638i | \(0.918044\pi\) | |||||||
\(810\) | −0.185709 | −0.00652515 | ||||||||
\(811\) | 6.88830 | 0.241881 | 0.120940 | − | 0.992660i | \(-0.461409\pi\) | ||||
0.120940 | + | 0.992660i | \(0.461409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.9706i | 1.01604i | ||||||||
\(814\) | 18.0000 | + | 8.48528i | 0.630900 | + | 0.297409i | ||||
\(815\) | − | 8.81298i | − | 0.308705i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.5181i | 0.822795i | ||||||||
\(818\) | 37.8519i | 1.32346i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.97056i | 0.173580i | ||||||||
\(821\) | − | 13.7574i | − | 0.480135i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) | ||
0.970756 | − | 0.240068i | \(-0.0771696\pi\) | |||||||
\(822\) | 18.3688 | 0.640686 | ||||||||
\(823\) | 8.78680 | 0.306288 | 0.153144 | − | 0.988204i | \(-0.451060\pi\) | ||||
0.153144 | + | 0.988204i | \(0.451060\pi\) | |||||||
\(824\) | −6.43996 | −0.224347 | ||||||||
\(825\) | 12.4316 | + | 5.86030i | 0.432812 | + | 0.204030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9706i | 0.590124i | 0.955478 | + | 0.295062i | \(0.0953404\pi\) | ||||
−0.955478 | + | 0.295062i | \(0.904660\pi\) | |||||||
\(828\) | −11.4142 | −0.396671 | ||||||||
\(829\) | 21.9874i | 0.763654i | 0.924234 | + | 0.381827i | \(0.124705\pi\) | ||||
−0.924234 | + | 0.381827i | \(0.875295\pi\) | |||||||
\(830\) | 14.4853 | 0.502791 | ||||||||
\(831\) | −20.2710 | −0.703192 | ||||||||
\(832\) | 2.29610 | 0.0796030 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.4853 | −0.501584 | ||||||||
\(835\) | 21.9411i | 0.759304i | ||||||||
\(836\) | 7.83938 | − | 16.6298i | 0.271131 | − | 0.575155i | ||||
\(837\) | −7.31371 | −0.252799 | ||||||||
\(838\) | −8.47343 | −0.292710 | ||||||||
\(839\) | 27.0823i | 0.934986i | 0.883997 | + | 0.467493i | \(0.154843\pi\) | ||||
−0.883997 | + | 0.467493i | \(0.845157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9117 | 0.893506 | ||||||||
\(842\) | − | 17.6569i | − | 0.608495i | ||||||
\(843\) | −12.9887 | −0.447355 | ||||||||
\(844\) | 24.7279i | 0.851170i | ||||||||
\(845\) | − | 8.36464i | − | 0.287752i | ||||||
\(846\) | 8.97616 | 0.308607 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.48528 | 0.154025 | ||||||||
\(849\) | − | 24.4264i | − | 0.838312i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.4558 | 1.28397 | ||||||||
\(852\) | 2.16478i | 0.0741643i | ||||||||
\(853\) | −5.54328 | −0.189798 | −0.0948991 | − | 0.995487i | \(-0.530253\pi\) | ||||
−0.0948991 | + | 0.995487i | \(0.530253\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9706i | 0.375185i | ||||||||
\(856\) | −12.7279 | −0.435031 | ||||||||
\(857\) | −1.90215 | −0.0649763 | −0.0324881 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324881 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(858\) | −3.51472 | + | 7.45584i | −0.119991 | + | 0.254538i | ||||
\(859\) | 11.5349i | 0.393566i | 0.980447 | + | 0.196783i | \(0.0630494\pi\) | ||||
−0.980447 | + | 0.196783i | \(0.936951\pi\) | |||||||
\(860\) | 4.59220 | 0.156593 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.48528 | −0.0846490 | ||||||||
\(863\) | −30.7279 | −1.04599 | −0.522995 | − | 0.852336i | \(-0.675185\pi\) | ||||
−0.522995 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(864\) | −5.22625 | −0.177801 | ||||||||
\(865\) | 27.9411i | 0.950027i | ||||||||
\(866\) | −22.6758 | −0.770557 | ||||||||
\(867\) | 18.4007i | 0.624919i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.4558 | + | 12.0000i | 0.863530 | + | 0.407072i | ||||
\(870\) | 2.05887 | 0.0698024 | ||||||||
\(871\) | −26.7653 | −0.906908 | ||||||||
\(872\) | −3.51472 | −0.119023 | ||||||||
\(873\) | − | 15.7331i | − | 0.532486i | ||||||
\(874\) | − | 34.6047i | − | 1.17052i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 16.9706i | − | 0.573382i | ||||||
\(877\) | 54.0000i | 1.82345i | 0.410801 | + | 0.911725i | \(0.365249\pi\) | ||||
−0.410801 | + | 0.911725i | \(0.634751\pi\) | |||||||
\(878\) | 6.49435i | 0.219174i | ||||||||
\(879\) | 1.02944i | 0.0347221i | ||||||||
\(880\) | −3.24718 | − | 1.53073i | −0.109462 | − | 0.0516010i | ||||
\(881\) | 31.4888i | 1.06089i | 0.847721 | + | 0.530443i | \(0.177974\pi\) | ||||
−0.847721 | + | 0.530443i | \(0.822026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.4264 | −1.42776 | −0.713881 | − | 0.700267i | \(-0.753064\pi\) | ||||
−0.713881 | + | 0.700267i | \(0.753064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 8.44157i | − | 0.283760i | ||||||
\(886\) | − | 22.6274i | − | 0.760183i | ||||||
\(887\) | 9.18440 | 0.308382 | 0.154191 | − | 0.988041i | \(-0.450723\pi\) | ||||
0.154191 | + | 0.988041i | \(0.450723\pi\) | |||||||
\(888\) | 6.49435 | 0.217936 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 3.85786i | − | 0.129316i | ||||||
\(891\) | 0.242641 | − | 0.514719i | 0.00812877 | − | 0.0172437i | ||||
\(892\) | 7.89377i | 0.264303i | ||||||||
\(893\) | 27.2132i | 0.910655i | ||||||||
\(894\) | − | 7.28225i | − | 0.243555i | ||||||
\(895\) | − | 6.12293i | − | 0.204667i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.5147i | 0.518021i | ||||||||
\(898\) | 40.7279i | 1.35911i | ||||||||
\(899\) | 2.45928 | 0.0820216 | ||||||||
\(900\) | −7.00000 | −0.233333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −13.7766 | − | 6.49435i | −0.458711 | − | 0.216238i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.41421i | − | 0.0470360i | ||||||
\(905\) | −22.1421 | −0.736029 | ||||||||
\(906\) | 6.49435i | 0.215760i | ||||||||
\(907\) | −1.79899 | −0.0597345 | −0.0298672 | − | 0.999554i | \(-0.509508\pi\) | ||||
−0.0298672 | + | 0.999554i | \(0.509508\pi\) | |||||||
\(908\) | −0.951076 | −0.0315626 | ||||||||
\(909\) | −30.4064 | −1.00852 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.2426 | 1.26704 | 0.633518 | − | 0.773728i | \(-0.281610\pi\) | ||||
0.633518 | + | 0.773728i | \(0.281610\pi\) | |||||||
\(912\) | − | 6.00000i | − | 0.198680i | ||||||
\(913\) | −18.9259 | + | 40.1480i | −0.626357 | + | 1.32870i | ||||
\(914\) | −31.4558 | −1.04047 | ||||||||
\(915\) | 6.49435 | 0.214697 | ||||||||
\(916\) | 28.4818i | 0.941064i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.4264i | − | 1.00367i | −0.864962 | − | 0.501837i | \(-0.832658\pi\) | ||
0.864962 | − | 0.501837i | \(-0.167342\pi\) | |||||||
\(920\) | −6.75699 | −0.222771 | ||||||||
\(921\) | 8.05887i | 0.265549i | ||||||||
\(922\) | 29.0614i | 0.957087i | ||||||||
\(923\) | −4.59220 | −0.151154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.9706 | 0.755267 | ||||||||
\(926\) | 5.31371i | 0.174619i | ||||||||
\(927\) | 11.7750i | 0.386742i | ||||||||
\(928\) | 1.75736 | 0.0576881 | ||||||||
\(929\) | − | 42.2040i | − | 1.38467i | −0.721578 | − | 0.692334i | \(-0.756583\pi\) | ||
0.721578 | − | 0.692334i | \(-0.243417\pi\) | |||||||
\(930\) | −1.63952 | −0.0537620 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.48528i | 0.277945i | ||||||||
\(933\) | −36.1421 | −1.18324 | ||||||||
\(934\) | 32.1773 | 1.05287 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 4.19825i | − | 0.137224i | ||||||
\(937\) | 35.9497 | 1.17443 | 0.587213 | − | 0.809432i | \(-0.300225\pi\) | ||||
0.587213 | + | 0.809432i | \(0.300225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1716 | −0.364571 | ||||||||
\(940\) | 5.31371 | 0.173314 | ||||||||
\(941\) | 40.1480 | 1.30879 | 0.654393 | − | 0.756155i | \(-0.272924\pi\) | ||||
0.654393 | + | 0.756155i | \(0.272924\pi\) | |||||||
\(942\) | − | 12.4853i | − | 0.406792i | ||||||
\(943\) | −28.6675 | −0.933541 | ||||||||
\(944\) | − | 7.20533i | − | 0.234513i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | + | 12.7279i | −0.195077 | + | 0.413820i | ||||
\(947\) | −3.51472 | −0.114213 | −0.0571065 | − | 0.998368i | \(-0.518187\pi\) | ||||
−0.0571065 | + | 0.998368i | \(0.518187\pi\) | |||||||
\(948\) | 9.18440 | 0.298296 | ||||||||
\(949\) | 36.0000 | 1.16861 | ||||||||
\(950\) | − | 21.2220i | − | 0.688534i | ||||||
\(951\) | 24.8632i | 0.806243i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.9411i | − | 1.48818i | −0.668080 | − | 0.744090i | \(-0.732884\pi\) | ||
0.668080 | − | 0.744090i | \(-0.267116\pi\) | |||||||
\(954\) | − | 8.20101i | − | 0.265518i | ||||||
\(955\) | − | 1.90215i | − | 0.0615522i | ||||||
\(956\) | − | 26.4853i | − | 0.856595i | ||||||
\(957\) | −2.69005 | + | 5.70646i | −0.0869569 | + | 0.184464i | ||||
\(958\) | 9.18440i | 0.296735i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.17157 | −0.0378124 | ||||||||
\(961\) | 29.0416 | 0.936827 | ||||||||
\(962\) | 13.7766i | 0.444176i | ||||||||
\(963\) | 23.2721i | 0.749932i | ||||||||
\(964\) | −4.59220 | −0.147905 | ||||||||
\(965\) | −2.69005 | −0.0865957 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19.4558i | − | 0.625658i | −0.949810 | − | 0.312829i | \(-0.898723\pi\) | ||
0.949810 | − | 0.312829i | \(-0.101277\pi\) | |||||||
\(968\) | 8.48528 | − | 7.00000i | 0.272727 | − | 0.224989i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 9.31371i | − | 0.299045i | ||||||
\(971\) | − | 36.2442i | − | 1.16313i | −0.813499 | − | 0.581566i | \(-0.802440\pi\) | ||
0.813499 | − | 0.581566i | \(-0.197560\pi\) | |||||||
\(972\) | 15.4930i | 0.496940i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.44365i | 0.0782996i | ||||||||
\(975\) | 9.51472i | 0.304715i | ||||||||
\(976\) | 5.54328 | 0.177436 | ||||||||
\(977\) | −44.2426 | −1.41545 | −0.707724 | − | 0.706489i | \(-0.750278\pi\) | ||||
−0.707724 | + | 0.706489i | \(0.750278\pi\) | |||||||
\(978\) | 8.81298 | 0.281808 | ||||||||
\(979\) | 10.6926 | + | 5.04054i | 0.341737 | + | 0.161096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.42641i | 0.205179i | ||||||||
\(982\) | −39.9411 | −1.27457 | ||||||||
\(983\) | 45.0028i | 1.43537i | 0.696370 | + | 0.717683i | \(0.254797\pi\) | ||||
−0.696370 | + | 0.717683i | \(0.745203\pi\) | |||||||
\(984\) | −4.97056 | −0.158456 | ||||||||
\(985\) | −22.1731 | −0.706494 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.7279 | 0.404929 | ||||||||
\(989\) | 26.4853i | 0.842183i | ||||||||
\(990\) | −2.79884 | + | 5.93723i | −0.0889528 | + | 0.188697i | ||||
\(991\) | −57.5980 | −1.82966 | −0.914830 | − | 0.403839i | \(-0.867676\pi\) | ||||
−0.914830 | + | 0.403839i | \(0.867676\pi\) | |||||||
\(992\) | −1.39942 | −0.0444316 | ||||||||
\(993\) | − | 22.1731i | − | 0.703642i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.6863 | −0.846012 | ||||||||
\(996\) | 14.4853i | 0.458984i | ||||||||
\(997\) | 6.10040 | 0.193202 | 0.0966009 | − | 0.995323i | \(-0.469203\pi\) | ||||
0.0966009 | + | 0.995323i | \(0.469203\pi\) | |||||||
\(998\) | − | 28.6274i | − | 0.906185i | ||||||
\(999\) | − | 31.3575i | − | 0.992108i |
(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 | 1078.2.c.a.1077.2 | ✓ | 8 | |
7.2 | even | 3 | 1078.2.i.a.1011.3 | 16 | |||
7.3 | odd | 6 | 1078.2.i.a.901.7 | 16 | |||
7.4 | even | 3 | 1078.2.i.a.901.6 | 16 | |||
7.5 | odd | 6 | 1078.2.i.a.1011.2 | 16 | |||
7.6 | odd | 2 | inner | 1078.2.c.a.1077.3 | yes | 8 | |
11.10 | odd | 2 | inner | 1078.2.c.a.1077.6 | yes | 8 | |
77.10 | even | 6 | 1078.2.i.a.901.3 | 16 | |||
77.32 | odd | 6 | 1078.2.i.a.901.2 | 16 | |||
77.54 | even | 6 | 1078.2.i.a.1011.6 | 16 | |||
77.65 | odd | 6 | 1078.2.i.a.1011.7 | 16 | |||
77.76 | even | 2 | inner | 1078.2.c.a.1077.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.a.1077.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1078.2.c.a.1077.3 | yes | 8 | 7.6 | odd | 2 | inner | |
1078.2.c.a.1077.6 | yes | 8 | 11.10 | odd | 2 | inner | |
1078.2.c.a.1077.7 | yes | 8 | 77.76 | even | 2 | inner | |
1078.2.i.a.901.2 | 16 | 77.32 | odd | 6 | |||
1078.2.i.a.901.3 | 16 | 77.10 | even | 6 | |||
1078.2.i.a.901.6 | 16 | 7.4 | even | 3 | |||
1078.2.i.a.901.7 | 16 | 7.3 | odd | 6 | |||
1078.2.i.a.1011.2 | 16 | 7.5 | odd | 6 | |||
1078.2.i.a.1011.3 | 16 | 7.2 | even | 3 | |||
1078.2.i.a.1011.6 | 16 | 77.54 | even | 6 | |||
1078.2.i.a.1011.7 | 16 | 77.65 | odd | 6 |