Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.2 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.l.865.2 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.119562 | − | 0.207087i | 0.0534696 | − | 0.0926120i | −0.838052 | − | 0.545591i | \(-0.816305\pi\) |
0.891521 | + | 0.452979i | \(0.149639\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.710533 | + | 2.54856i | 0.268556 | + | 0.963264i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.21053 | + | 2.09671i | 0.364990 | + | 0.632180i | 0.988774 | − | 0.149416i | \(-0.0477392\pi\) |
−0.623785 | + | 0.781596i | \(0.714406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.760877 | 0.211029 | 0.105515 | − | 0.994418i | \(-0.466351\pi\) | ||||
0.105515 | + | 0.994418i | \(0.466351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.71053 | − | 2.96273i | −0.414865 | − | 0.718568i | 0.580549 | − | 0.814225i | \(-0.302838\pi\) |
−0.995414 | + | 0.0956576i | \(0.969505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.590972 | + | 1.02359i | −0.135578 | + | 0.234828i | −0.925818 | − | 0.377969i | \(-0.876623\pi\) |
0.790240 | + | 0.612797i | \(0.209956\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.09097 | + | 1.88962i | −0.227483 | + | 0.394013i | −0.957062 | − | 0.289885i | \(-0.906383\pi\) |
0.729578 | + | 0.683897i | \(0.239716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.47141 | + | 4.28061i | 0.494282 | + | 0.856122i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.89931 | 0.538389 | 0.269194 | − | 0.963086i | \(-0.413243\pi\) | ||||
0.269194 | + | 0.963086i | \(0.413243\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32326 | + | 4.02400i | 0.417270 | + | 0.722732i | 0.995664 | − | 0.0930254i | \(-0.0296538\pi\) |
−0.578394 | + | 0.815757i | \(0.696320\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.612725 | + | 0.157568i | 0.103569 | + | 0.0266338i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.89248 | + | 5.00992i | −0.475520 | + | 0.823625i | −0.999607 | − | 0.0280398i | \(-0.991073\pi\) |
0.524087 | + | 0.851665i | \(0.324407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.54583 | −1.33463 | −0.667317 | − | 0.744774i | \(-0.732557\pi\) | ||||
−0.667317 | + | 0.744774i | \(0.732557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.37756 | −0.515073 | −0.257537 | − | 0.966269i | \(-0.582911\pi\) | ||||
−0.257537 | + | 0.966269i | \(0.582911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.58414 | − | 4.47585i | 0.376935 | − | 0.652870i | −0.613680 | − | 0.789555i | \(-0.710311\pi\) |
0.990615 | + | 0.136685i | \(0.0436447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.99028 | + | 3.62167i | −0.855755 | + | 0.517381i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.56238 | − | 2.70612i | −0.214610 | − | 0.371715i | 0.738542 | − | 0.674207i | \(-0.235515\pi\) |
−0.953152 | + | 0.302493i | \(0.902181\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.578933 | 0.0780634 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.11273 | + | 5.39140i | 0.405242 | + | 0.701900i | 0.994350 | − | 0.106155i | \(-0.0338538\pi\) |
−0.589107 | + | 0.808055i | \(0.700520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.681943 | + | 1.18116i | −0.0873139 | + | 0.151232i | −0.906375 | − | 0.422474i | \(-0.861162\pi\) |
0.819061 | + | 0.573706i | \(0.194495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0909717 | − | 0.157568i | 0.0112836 | − | 0.0195438i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.03379 | + | 12.1829i | 0.859314 | + | 1.48838i | 0.872584 | + | 0.488464i | \(0.162443\pi\) |
−0.0132695 | + | 0.999912i | \(0.504224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.02408 | 0.952283 | 0.476141 | − | 0.879369i | \(-0.342035\pi\) | ||||
0.476141 | + | 0.879369i | \(0.342035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.91423 | + | 6.77965i | 0.458126 | + | 0.793497i | 0.998862 | − | 0.0476949i | \(-0.0151875\pi\) |
−0.540736 | + | 0.841192i | \(0.681854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.48345 | + | 4.57489i | −0.510936 | + | 0.521357i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.27292 | + | 3.93680i | −0.255723 | + | 0.442925i | −0.965092 | − | 0.261913i | \(-0.915647\pi\) |
0.709369 | + | 0.704838i | \(0.248980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0104 | 1.31831 | 0.659157 | − | 0.752006i | \(-0.270913\pi\) | ||||
0.659157 | + | 0.752006i | \(0.270913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.818057 | −0.0887307 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.73912 | + | 4.74430i | −0.290346 | + | 0.502895i | −0.973892 | − | 0.227013i | \(-0.927104\pi\) |
0.683545 | + | 0.729908i | \(0.260437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.540628 | + | 1.93914i | 0.0566732 | + | 0.203277i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.141315 | + | 0.244765i | 0.0144986 | + | 0.0251123i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3639 | 1.05229 | 0.526147 | − | 0.850394i | \(-0.323636\pi\) | ||||
0.526147 | + | 0.850394i | \(0.323636\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.06238 | − | 8.76830i | −0.503726 | − | 0.872479i | −0.999991 | − | 0.00430755i | \(-0.998629\pi\) |
0.496265 | − | 0.868171i | \(-0.334704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.31806 | − | 2.28294i | 0.129872 | − | 0.224945i | −0.793755 | − | 0.608238i | \(-0.791877\pi\) |
0.923627 | + | 0.383293i | \(0.125210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.16991 | − | 3.75839i | 0.209773 | − | 0.363337i | −0.741870 | − | 0.670544i | \(-0.766061\pi\) |
0.951643 | + | 0.307207i | \(0.0993943\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.46457 | + | 11.1970i | 0.619194 | + | 1.07248i | 0.989633 | + | 0.143619i | \(0.0458738\pi\) |
−0.370439 | + | 0.928857i | \(0.620793\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1352 | −1.23565 | −0.617826 | − | 0.786315i | \(-0.711987\pi\) | ||||
−0.617826 | + | 0.786315i | \(0.711987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.260877 | + | 0.451852i | 0.0243269 | + | 0.0421354i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.33530 | − | 6.46451i | 0.580756 | − | 0.592601i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.56922 | − | 4.45002i | 0.233565 | − | 0.404547i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.37756 | 0.212655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.86156 | −0.342658 | −0.171329 | − | 0.985214i | \(-0.554806\pi\) | ||||
−0.171329 | + | 0.985214i | \(0.554806\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.25636 | + | 12.5684i | −0.633991 | + | 1.09811i | 0.352736 | + | 0.935723i | \(0.385251\pi\) |
−0.986728 | + | 0.162383i | \(0.948082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.02859 | − | 0.778828i | −0.262612 | − | 0.0675330i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.70370 | − | 9.87909i | −0.487300 | − | 0.844028i | 0.512594 | − | 0.858631i | \(-0.328685\pi\) |
−0.999893 | + | 0.0146035i | \(0.995351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.91874 | 0.162746 | 0.0813728 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813728 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.921067 | + | 1.59533i | 0.0770235 | + | 0.133409i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.346647 | − | 0.600410i | 0.0287874 | − | 0.0498613i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.57730 | + | 13.1243i | −0.620756 | + | 1.07518i | 0.368589 | + | 0.929593i | \(0.379841\pi\) |
−0.989345 | + | 0.145589i | \(0.953492\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.94966 | + | 10.3051i | 0.484176 | + | 0.838618i | 0.999835 | − | 0.0181764i | \(-0.00578604\pi\) |
−0.515659 | + | 0.856794i | \(0.672453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.11109 | 0.0892449 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.92395 | − | 3.33237i | −0.153548 | − | 0.265952i | 0.778982 | − | 0.627047i | \(-0.215736\pi\) |
−0.932529 | + | 0.361095i | \(0.882403\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.59097 | − | 1.43777i | −0.440630 | − | 0.113312i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.47661 | − | 7.75372i | 0.350635 | − | 0.607318i | −0.635726 | − | 0.771915i | \(-0.719299\pi\) |
0.986361 | + | 0.164597i | \(0.0526323\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19562 | 0.169902 | 0.0849509 | − | 0.996385i | \(-0.472927\pi\) | ||||
0.0849509 | + | 0.996385i | \(0.472927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4211 | −0.955467 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.15335 | − | 12.3900i | 0.543859 | − | 0.941992i | −0.454818 | − | 0.890584i | \(-0.650296\pi\) |
0.998678 | − | 0.0514079i | \(-0.0163708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.15335 | + | 9.34004i | −0.691928 | + | 0.706041i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.66539 | + | 16.7409i | 0.722425 | + | 1.25128i | 0.960025 | + | 0.279914i | \(0.0903060\pi\) |
−0.237600 | + | 0.971363i | \(0.576361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32614 | 0.0985710 | 0.0492855 | − | 0.998785i | \(-0.484306\pi\) | ||||
0.0492855 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.691658 | + | 1.19799i | 0.0508517 | + | 0.0880778i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.14132 | − | 7.17297i | 0.302843 | − | 0.524539i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5172 | − | 21.6805i | 0.905716 | − | 1.56875i | 0.0857621 | − | 0.996316i | \(-0.472668\pi\) |
0.819954 | − | 0.572430i | \(-0.193999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.97661 | − | 3.42359i | −0.142280 | − | 0.246436i | 0.786075 | − | 0.618131i | \(-0.212110\pi\) |
−0.928355 | + | 0.371695i | \(0.878777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.51135 | 0.107679 | 0.0538396 | − | 0.998550i | \(-0.482854\pi\) | ||||
0.0538396 | + | 0.998550i | \(0.482854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5241 | − | 23.4244i | −0.958696 | − | 1.66051i | −0.725673 | − | 0.688040i | \(-0.758471\pi\) |
−0.233023 | − | 0.972471i | \(-0.574862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.06006 | + | 7.38906i | 0.144588 | + | 0.518611i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.02175 | + | 1.76973i | −0.0713624 | + | 0.123603i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.86156 | −0.197938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.42107 | −0.648573 | −0.324286 | − | 0.945959i | \(-0.605124\pi\) | ||||
−0.324286 | + | 0.945959i | \(0.605124\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.403827 | + | 0.699448i | −0.0275407 | + | 0.0477020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.60464 | + | 8.78014i | −0.584121 | + | 0.596035i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.30150 | − | 2.25427i | −0.0875487 | − | 0.151639i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.03775 | 0.471283 | 0.235641 | − | 0.971840i | \(-0.424281\pi\) | ||||
0.235641 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.3759 | + | 21.4357i | 0.821419 | + | 1.42274i | 0.904626 | + | 0.426207i | \(0.140151\pi\) |
−0.0832066 | + | 0.996532i | \(0.526516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8542 | − | 23.9961i | 0.915509 | − | 1.58571i | 0.109356 | − | 0.994003i | \(-0.465121\pi\) |
0.806154 | − | 0.591706i | \(-0.201545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.86389 | − | 6.69245i | 0.253132 | − | 0.438437i | −0.711255 | − | 0.702934i | \(-0.751873\pi\) |
0.964386 | + | 0.264497i | \(0.0852061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.617927 | − | 1.07028i | −0.0403091 | − | 0.0698174i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.3880 | −1.77158 | −0.885790 | − | 0.464086i | \(-0.846383\pi\) | ||||
−0.885790 | + | 0.464086i | \(0.846383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6683 | − | 18.4780i | −0.687204 | − | 1.19027i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) |
0.285535 | − | 0.958368i | \(-0.407829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0337917 | + | 1.67352i | 0.00215887 | + | 0.106917i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.449657 | + | 0.778828i | −0.0286110 | + | 0.0495556i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.66595 | 0.294512 | 0.147256 | − | 0.989098i | \(-0.452956\pi\) | ||||
0.147256 | + | 0.989098i | \(0.452956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.28263 | −0.332116 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.14652 | + | 1.98583i | −0.0715178 | + | 0.123872i | −0.899567 | − | 0.436783i | \(-0.856118\pi\) |
0.828049 | + | 0.560656i | \(0.189451\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8233 | − | 3.81193i | −0.921072 | − | 0.236862i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.39536 | − | 4.14888i | −0.147704 | − | 0.255831i | 0.782675 | − | 0.622431i | \(-0.213855\pi\) |
−0.930378 | + | 0.366600i | \(0.880522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.747204 | −0.0459004 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.49316 | − | 16.4426i | −0.578808 | − | 1.00253i | −0.995616 | − | 0.0935310i | \(-0.970185\pi\) |
0.416808 | − | 0.908995i | \(-0.363149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0579 | − | 24.3489i | 0.853955 | − | 1.47909i | −0.0236567 | − | 0.999720i | \(-0.507531\pi\) |
0.877611 | − | 0.479373i | \(-0.159136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.98345 | + | 10.3636i | −0.360816 | + | 0.624951i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.08577 | + | 7.07676i | 0.245490 | + | 0.425201i | 0.962269 | − | 0.272099i | \(-0.0877178\pi\) |
−0.716779 | + | 0.697300i | \(0.754384\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.4315 | 1.39780 | 0.698902 | − | 0.715217i | \(-0.253672\pi\) | ||||
0.698902 | + | 0.715217i | \(0.253672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.10752 | − | 1.91829i | −0.0658354 | − | 0.114030i | 0.831229 | − | 0.555930i | \(-0.187638\pi\) |
−0.897064 | + | 0.441900i | \(0.854305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.07210 | − | 21.7795i | −0.358425 | − | 1.28561i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.64815 | − | 4.58673i | 0.155774 | − | 0.269808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.1866 | −1.29615 | −0.648077 | − | 0.761575i | \(-0.724427\pi\) | ||||
−0.648077 | + | 0.761575i | \(0.724427\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.48865 | 0.0866726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.830095 | + | 1.43777i | −0.0480056 | + | 0.0831482i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.39987 | − | 8.60790i | −0.138326 | − | 0.496151i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.163069 | + | 0.282443i | 0.00933728 | + | 0.0161726i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0183 | 0.914214 | 0.457107 | − | 0.889412i | \(-0.348886\pi\) | ||||
0.457107 | + | 0.889412i | \(0.348886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.35348 | + | 5.80840i | 0.190159 | + | 0.329364i | 0.945303 | − | 0.326195i | \(-0.105766\pi\) |
−0.755144 | + | 0.655559i | \(0.772433\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0322 | − | 24.3044i | 0.793144 | − | 1.37377i | −0.130866 | − | 0.991400i | \(-0.541776\pi\) |
0.924011 | − | 0.382366i | \(-0.124891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.63323 | + | 2.82885i | −0.0917316 | + | 0.158884i | −0.908240 | − | 0.418450i | \(-0.862574\pi\) |
0.816508 | + | 0.577334i | \(0.195907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.50972 | + | 6.07900i | 0.196506 | + | 0.340359i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.04351 | 0.224987 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.88044 | + | 3.25701i | 0.104308 | + | 0.180667i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2431 | + | 3.40557i | 0.730115 | + | 0.187755i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9617 | − | 18.9862i | 0.602509 | − | 1.04358i | −0.389931 | − | 0.920844i | \(-0.627501\pi\) |
0.992440 | − | 0.122732i | \(-0.0391657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.36389 | 0.183789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0733 | −0.766624 | −0.383312 | − | 0.923619i | \(-0.625217\pi\) | ||||
−0.383312 | + | 0.923619i | \(0.625217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.62476 | + | 9.74238i | −0.304598 | + | 0.527579i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4863 | − | 12.6933i | −0.728193 | − | 0.685372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.50808 | + | 4.34412i | 0.134641 | + | 0.233205i | 0.925460 | − | 0.378845i | \(-0.123679\pi\) |
−0.790819 | + | 0.612050i | \(0.790345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7382 | −0.574801 | −0.287401 | − | 0.957810i | \(-0.592791\pi\) | ||||
−0.287401 | + | 0.957810i | \(0.592791\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.16307 | − | 2.01449i | −0.0619039 | − | 0.107221i | 0.833413 | − | 0.552651i | \(-0.186384\pi\) |
−0.895316 | + | 0.445431i | \(0.853051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.959372 | − | 1.66168i | 0.0509182 | − | 0.0881928i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.97141 | − | 8.61073i | 0.262381 | − | 0.454457i | −0.704493 | − | 0.709711i | \(-0.748826\pi\) |
0.966874 | + | 0.255254i | \(0.0821590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.80150 | + | 15.2447i | 0.463237 | + | 0.802350i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.87197 | 0.0979832 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.464574 | − | 0.804665i | −0.0242505 | − | 0.0420032i | 0.853645 | − | 0.520855i | \(-0.174387\pi\) |
−0.877896 | + | 0.478851i | \(0.841053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.78659 | − | 5.90461i | 0.300425 | − | 0.306552i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.1352 | − | 26.2149i | 0.783669 | − | 1.35735i | −0.146122 | − | 0.989267i | \(-0.546679\pi\) |
0.929791 | − | 0.368088i | \(-0.119988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.20602 | 0.113616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.5757 | −1.46783 | −0.733917 | − | 0.679240i | \(-0.762310\pi\) | ||||
−0.733917 | + | 0.679240i | \(0.762310\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.8107 | − | 20.4567i | 0.603497 | − | 1.04529i | −0.388790 | − | 0.921326i | \(-0.627107\pi\) |
0.992287 | − | 0.123961i | \(-0.0395597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.411351 | + | 1.47544i | 0.0209644 | + | 0.0751956i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.23749 | + | 14.2677i | 0.417657 | + | 0.723404i | 0.995703 | − | 0.0926005i | \(-0.0295180\pi\) |
−0.578046 | + | 0.816004i | \(0.696185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.46457 | 0.377500 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.543507 | + | 0.941382i | 0.0273468 | + | 0.0473660i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.41586 | − | 11.1126i | 0.322003 | − | 0.557726i | −0.658898 | − | 0.752232i | \(-0.728977\pi\) |
0.980901 | + | 0.194507i | \(0.0623105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8187 | + | 27.3989i | −0.789950 | + | 1.36823i | 0.136046 | + | 0.990702i | \(0.456560\pi\) |
−0.925997 | + | 0.377532i | \(0.876773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.76771 | + | 3.06177i | 0.0880561 | + | 0.152518i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0058 | −0.694240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0144 | − | 20.8095i | −0.594072 | − | 1.02896i | −0.993677 | − | 0.112275i | \(-0.964186\pi\) |
0.399605 | − | 0.916687i | \(-0.369147\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5286 | + | 11.7637i | −0.567285 | + | 0.578855i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.43598 | − | 2.48720i | 0.0704897 | − | 0.122092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.72777 | −0.0844073 | −0.0422036 | − | 0.999109i | \(-0.513438\pi\) | ||||
−0.0422036 | + | 0.999109i | \(0.513438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0949 | −0.979367 | −0.489683 | − | 0.871900i | \(-0.662888\pi\) | ||||
−0.489683 | + | 0.871900i | \(0.662888\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.45486 | − | 14.6442i | 0.410121 | − | 0.710350i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.49480 | − | 0.898718i | −0.169125 | − | 0.0434920i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4246 | − | 18.0560i | −0.502137 | − | 0.869727i | −0.999997 | − | 0.00246928i | \(-0.999214\pi\) |
0.497860 | − | 0.867257i | \(-0.334119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2255 | 0.491404 | 0.245702 | − | 0.969345i | \(-0.420982\pi\) | ||||
0.245702 | + | 0.969345i | \(0.420982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.28947 | − | 2.23342i | −0.0616836 | − | 0.106839i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.55718 | − | 6.16122i | 0.169775 | − | 0.294059i | −0.768566 | − | 0.639771i | \(-0.779029\pi\) |
0.938341 | + | 0.345712i | \(0.112363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.22094 | + | 9.04293i | −0.248054 | + | 0.429642i | −0.962986 | − | 0.269552i | \(-0.913124\pi\) |
0.714932 | + | 0.699194i | \(0.246458\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.654988 | + | 1.13447i | 0.0310494 | + | 0.0537792i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.3502 | 1.95144 | 0.975719 | − | 0.219028i | \(-0.0702885\pi\) | ||||
0.975719 | + | 0.219028i | \(0.0702885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.3450 | − | 17.9181i | −0.487128 | − | 0.843730i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.466208 | + | 0.119889i | 0.0218562 | + | 0.00562051i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.87592 | − | 11.9095i | 0.321642 | − | 0.557101i | −0.659185 | − | 0.751981i | \(-0.729099\pi\) |
0.980827 | + | 0.194880i | \(0.0624318\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.54583 | 0.304870 | 0.152435 | − | 0.988314i | \(-0.451289\pi\) | ||||
0.152435 | + | 0.988314i | \(0.451289\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.228720 | −0.0106295 | −0.00531475 | − | 0.999986i | \(-0.501692\pi\) | ||||
−0.00531475 | + | 0.999986i | \(0.501692\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.3788 | + | 30.1010i | −0.804195 | + | 1.39291i | 0.112638 | + | 0.993636i | \(0.464070\pi\) |
−0.916833 | + | 0.399271i | \(0.869263\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.0510 | + | 26.5824i | −1.20292 | + | 1.22746i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.08865 | − | 7.08175i | −0.187996 | − | 0.325619i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.84213 | −0.268055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4721 | − | 21.6023i | −0.569865 | − | 0.987035i | −0.996579 | − | 0.0826481i | \(-0.973662\pi\) |
0.426714 | − | 0.904387i | \(-0.359671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.20082 | + | 3.81193i | −0.100349 | + | 0.173809i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.23912 | − | 2.14622i | 0.0562657 | − | 0.0974550i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.88207 | + | 6.72395i | 0.175914 | + | 0.304691i | 0.940477 | − | 0.339857i | \(-0.110379\pi\) |
−0.764564 | + | 0.644548i | \(0.777045\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.6224 | −1.11120 | −0.555598 | − | 0.831451i | \(-0.687510\pi\) | ||||
−0.555598 | + | 0.831451i | \(0.687510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.95937 | − | 8.58988i | −0.223359 | − | 0.386869i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.70137 | + | 20.4498i | 0.255742 | + | 0.917300i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3811 | + | 21.4447i | −0.554255 | + | 0.959998i | 0.443706 | + | 0.896173i | \(0.353664\pi\) |
−0.997961 | + | 0.0638259i | \(0.979670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.01367 | 0.134373 | 0.0671865 | − | 0.997740i | \(-0.478598\pi\) | ||||
0.0671865 | + | 0.997740i | \(0.478598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.42107 | −0.107736 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7323 | − | 30.7132i | 0.785970 | − | 1.36134i | −0.142448 | − | 0.989802i | \(-0.545497\pi\) |
0.928418 | − | 0.371537i | \(-0.121169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4971 | + | 14.7928i | −0.641315 | + | 0.654395i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.315178 | − | 0.545904i | −0.0138884 | − | 0.0240554i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.5127 | 0.550309 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.48276 | − | 6.03232i | −0.152582 | − | 0.264281i | 0.779594 | − | 0.626286i | \(-0.215426\pi\) |
−0.932176 | + | 0.362005i | \(0.882092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.6940 | − | 28.9148i | 0.729977 | − | 1.26436i | −0.226916 | − | 0.973914i | \(-0.572864\pi\) |
0.956892 | − | 0.290443i | \(-0.0938025\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.94802 | − | 13.7664i | 0.346221 | − | 0.599673i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.11956 | + | 15.7955i | 0.396503 | + | 0.686763i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.50232 | −0.281647 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.518875 | − | 0.898718i | −0.0224329 | − | 0.0388549i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.8450 | − | 8.17571i | −0.639420 | − | 0.352153i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.10752 | − | 7.11444i | 0.176596 | − | 0.305874i | −0.764116 | − | 0.645079i | \(-0.776825\pi\) |
0.940713 | + | 0.339205i | \(0.110158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.09166 | 0.132432 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.50232 | −0.363533 | −0.181767 | − | 0.983342i | \(-0.558182\pi\) | ||||
−0.181767 | + | 0.983342i | \(0.558182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.71341 | + | 2.96772i | −0.0729938 | + | 0.126429i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.6482 | − | 2.99542i | −0.495330 | − | 0.127378i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.83009 | + | 13.5621i | 0.331772 | + | 0.574646i | 0.982859 | − | 0.184357i | \(-0.0590203\pi\) |
−0.651088 | + | 0.759003i | \(0.725687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.56991 | −0.108695 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.2443 | + | 36.7963i | 0.895342 | + | 1.55078i | 0.833381 | + | 0.552698i | \(0.186402\pi\) |
0.0619602 | + | 0.998079i | \(0.480265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.57046 | + | 2.72012i | −0.0660698 | + | 0.114436i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.422701 | + | 0.732140i | −0.0177206 | + | 0.0306929i | −0.874750 | − | 0.484575i | \(-0.838974\pi\) |
0.857029 | + | 0.515268i | \(0.172308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8353 | + | 25.6955i | 0.620838 | + | 1.07532i | 0.989330 | + | 0.145692i | \(0.0465408\pi\) |
−0.368492 | + | 0.929631i | \(0.620126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.7850 | −0.449764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.04871 | + | 10.4767i | 0.251811 | + | 0.436150i | 0.964024 | − | 0.265813i | \(-0.0856405\pi\) |
−0.712213 | + | 0.701963i | \(0.752307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.53379 | + | 30.6092i | 0.354041 | + | 1.26988i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.78263 | − | 6.55171i | 0.156661 | − | 0.271344i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.9338 | −0.575109 | −0.287555 | − | 0.957764i | \(-0.592842\pi\) | ||||
−0.287555 | + | 0.957764i | \(0.592842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.49192 | −0.226291 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.77743 | + | 11.7389i | −0.278316 | + | 0.482057i | −0.970966 | − | 0.239216i | \(-0.923109\pi\) |
0.692651 | + | 0.721273i | \(0.256443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.581257 | − | 2.08486i | −0.0238292 | − | 0.0854711i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.3960 | − | 35.3270i | −0.833360 | − | 1.44342i | −0.895359 | − | 0.445345i | \(-0.853081\pi\) |
0.0619992 | − | 0.998076i | \(-0.480252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2164 | 1.23255 | 0.616277 | − | 0.787530i | \(-0.288640\pi\) | ||||
0.616277 | + | 0.787530i | \(0.288640\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.614360 | − | 1.06410i | −0.0249773 | − | 0.0432619i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.10752 | − | 7.11444i | 0.166719 | − | 0.288766i | −0.770545 | − | 0.637385i | \(-0.780016\pi\) |
0.937264 | + | 0.348619i | \(0.113349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.96621 | − | 3.40557i | 0.0795443 | − | 0.137775i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0224 | + | 29.4837i | 0.687530 | + | 1.19084i | 0.972635 | + | 0.232340i | \(0.0746383\pi\) |
−0.285105 | + | 0.958496i | \(0.592028\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.9064 | 1.52606 | 0.763028 | − | 0.646365i | \(-0.223712\pi\) | ||||
0.763028 | + | 0.646365i | \(0.223712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0293 | + | 34.6917i | 0.805045 | + | 1.39438i | 0.916261 | + | 0.400582i | \(0.131192\pi\) |
−0.111216 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.0374 | − | 3.60983i | −0.562395 | − | 0.144625i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0728 | + | 20.9107i | −0.482911 | + | 0.836427i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.7907 | 0.789107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.44514 | 0.137149 | 0.0685745 | − | 0.997646i | \(-0.478155\pi\) | ||||
0.0685745 | + | 0.997646i | \(0.478155\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.461695 | + | 0.799679i | −0.0183218 | + | 0.0317343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.55787 | + | 2.75564i | −0.180589 | + | 0.109183i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.47537 | − | 14.6798i | −0.334757 | − | 0.579816i | 0.648681 | − | 0.761060i | \(-0.275321\pi\) |
−0.983438 | + | 0.181244i | \(0.941988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8090 | 1.29386 | 0.646931 | − | 0.762549i | \(-0.276052\pi\) | ||||
0.646931 | + | 0.762549i | \(0.276052\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.5374 | − | 23.4474i | −0.532208 | − | 0.921812i | −0.999293 | − | 0.0375994i | \(-0.988029\pi\) |
0.467084 | − | 0.884213i | \(-0.345304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.53611 | + | 13.0529i | −0.295818 | + | 0.512372i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9487 | − | 27.6240i | 0.624121 | − | 1.08101i | −0.364589 | − | 0.931169i | \(-0.618790\pi\) |
0.988710 | − | 0.149841i | \(-0.0478762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.73517 | + | 3.00539i | 0.0677985 | + | 0.117430i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9852 | −1.32388 | −0.661938 | − | 0.749559i | \(-0.730266\pi\) | ||||
−0.661938 | + | 0.749559i | \(0.730266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.58414 | − | 13.1361i | −0.294989 | − | 0.510935i | 0.679994 | − | 0.733218i | \(-0.261983\pi\) |
−0.974982 | + | 0.222283i | \(0.928649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.523388 | + | 0.534063i | −0.0202961 | + | 0.0207101i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.16307 | + | 5.47860i | −0.122475 | + | 0.212132i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.30206 | −0.127475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7324 | 0.683535 | 0.341767 | − | 0.939785i | \(-0.388975\pi\) | ||||
0.341767 | + | 0.939785i | \(0.388975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.67154 | − | 2.89519i | 0.0642425 | − | 0.111271i | −0.832115 | − | 0.554603i | \(-0.812870\pi\) |
0.896358 | + | 0.443332i | \(0.146204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.36389 | + | 26.4130i | 0.282600 | + | 1.01364i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7427 | + | 41.1235i | 0.908489 | + | 1.57355i | 0.816164 | + | 0.577820i | \(0.196096\pi\) |
0.0923244 | + | 0.995729i | \(0.470570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72777 | −0.104223 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.18878 | − | 2.05903i | −0.0452889 | − | 0.0784427i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.67674 | − | 6.36830i | 0.139870 | − | 0.242262i | −0.787577 | − | 0.616216i | \(-0.788665\pi\) |
0.927447 | + | 0.373954i | \(0.121998\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.229408 | − | 0.397347i | 0.00870195 | − | 0.0150722i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6179 | + | 25.3190i | 0.553693 | + | 0.959025i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1729 | 1.70616 | 0.853079 | − | 0.521782i | \(-0.174733\pi\) | ||||
0.853079 | + | 0.521782i | \(0.174733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.41874 | − | 5.92144i | −0.128940 | − | 0.223331i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7495 | − | 19.1319i | 0.705149 | − | 0.719531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.9246 | + | 34.5105i | −0.748285 | + | 1.29607i | 0.200359 | + | 0.979723i | \(0.435789\pi\) |
−0.948644 | + | 0.316346i | \(0.897544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.1384 | −0.379687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.440497 | 0.0164737 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.4211 | + | 35.3703i | −0.761577 | + | 1.31909i | 0.180460 | + | 0.983582i | \(0.442241\pi\) |
−0.942037 | + | 0.335508i | \(0.891092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.75473 | + | 1.73704i | 0.251559 | + | 0.0646906i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.16539 | + | 12.4108i | 0.266116 | + | 0.460926i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.42898 | −0.238438 | −0.119219 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119219 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.77743 | + | 10.0068i | 0.213686 | + | 0.370115i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0773 | − | 19.1864i | 0.409149 | − | 0.708667i | −0.585645 | − | 0.810567i | \(-0.699159\pi\) |
0.994795 | + | 0.101900i | \(0.0324922\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.0293 | + | 29.4956i | −0.627282 | + | 1.08648i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.62081 | + | 16.6637i | 0.353907 | + | 0.612985i | 0.986930 | − | 0.161148i | \(-0.0515196\pi\) |
−0.633023 | + | 0.774133i | \(0.718186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.8616 | −1.13220 | −0.566100 | − | 0.824336i | \(-0.691549\pi\) | ||||
−0.566100 | + | 0.824336i | \(0.691549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.81191 | + | 3.13832i | 0.0663832 | + | 0.114979i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1202 | + | 2.85967i | 0.406325 | + | 0.104490i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.12476 | + | 3.68020i | −0.0775337 | + | 0.134292i | −0.902185 | − | 0.431349i | \(-0.858038\pi\) |
0.824652 | + | 0.565641i | \(0.191371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.84540 | 0.103555 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.69578 | 0.0979798 | 0.0489899 | − | 0.998799i | \(-0.484400\pi\) | ||||
0.0489899 | + | 0.998799i | \(0.484400\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5064 | − | 33.7862i | 0.707108 | − | 1.22475i | −0.258817 | − | 0.965926i | \(-0.583333\pi\) |
0.965925 | − | 0.258821i | \(-0.0833339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.9428 | + | 24.4312i | −0.866788 | + | 0.884467i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.36840 | + | 4.10219i | 0.0855180 | + | 0.148121i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0930 | −1.15730 | −0.578652 | − | 0.815574i | \(-0.696421\pi\) | ||||
−0.578652 | + | 0.815574i | \(0.696421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3873 | − | 21.4554i | −0.445539 | − | 0.771697i | 0.552550 | − | 0.833480i | \(-0.313655\pi\) |
−0.998090 | + | 0.0617828i | \(0.980321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.4834 | + | 19.8899i | −0.412498 | + | 0.714467i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.05034 | − | 8.74745i | 0.180947 | − | 0.313410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.71341 | + | 16.8241i | 0.347573 | + | 0.602014i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.920120 | −0.0328405 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.03543 | − | 6.98956i | −0.143847 | − | 0.249151i | 0.785095 | − | 0.619375i | \(-0.212614\pi\) |
−0.928942 | + | 0.370224i | \(0.879281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.33297 | − | 33.4757i | −0.331842 | − | 1.19026i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.518875 | + | 0.898718i | −0.0184258 | + | 0.0319144i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.6342 | 1.15596 | 0.577982 | − | 0.816050i | \(-0.303840\pi\) | ||||
0.577982 | + | 0.816050i | \(0.303840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.6810 | −0.625509 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.47661 | + | 16.4140i | −0.334422 | + | 0.579237i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.966208 | + | 0.985915i | −0.0340544 | + | 0.0347489i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.74200 | − | 8.21339i | −0.166720 | − | 0.288767i | 0.770545 | − | 0.637386i | \(-0.219984\pi\) |
−0.937265 | + | 0.348618i | \(0.886651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.95074 | −0.244073 | −0.122037 | − | 0.992526i | \(-0.538943\pi\) | ||||
−0.122037 | + | 0.992526i | \(0.538943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.07046 | − | 1.85409i | −0.0374967 | − | 0.0649461i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.99604 | − | 3.45725i | 0.0698327 | − | 0.120954i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7096 | + | 41.0662i | −0.827470 | + | 1.43322i | 0.0725464 | + | 0.997365i | \(0.476887\pi\) |
−0.900017 | + | 0.435856i | \(0.856446\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6895 | + | 25.4429i | 0.512043 | + | 0.886884i | 0.999903 | + | 0.0139620i | \(0.00444437\pi\) |
−0.487860 | + | 0.872922i | \(0.662222\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.6238 | −0.717160 | −0.358580 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358580 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.4698 | + | 33.7226i | 0.676213 | + | 1.17124i | 0.976113 | + | 0.217265i | \(0.0697135\pi\) |
−0.299899 | + | 0.953971i | \(0.596953\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.9766 | + | 11.5526i | 0.726797 | + | 0.400274i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.262511 | − | 0.454683i | 0.00908458 | − | 0.0157350i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.3743 | −0.634351 | −0.317175 | − | 0.948367i | \(-0.602734\pi\) | ||||
−0.317175 | + | 0.948367i | \(0.602734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5940 | −0.710137 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.48508 | + | 2.57224i | −0.0510884 | + | 0.0884877i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1666 | + | 3.38591i | 0.452411 | + | 0.116341i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.31122 | − | 10.9314i | −0.216346 | − | 0.374722i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.1819 | 0.964931 | 0.482466 | − | 0.875915i | \(-0.339741\pi\) | ||||
0.482466 | + | 0.875915i | \(0.339741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.83762 | + | 15.3072i | 0.301887 | + | 0.522884i | 0.976563 | − | 0.215230i | \(-0.0690500\pi\) |
−0.674676 | + | 0.738114i | \(0.735717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.1449 | + | 24.4997i | −0.482617 | + | 0.835917i | −0.999801 | − | 0.0199570i | \(-0.993647\pi\) |
0.517184 | + | 0.855874i | \(0.326980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.7821 | − | 42.9238i | 0.843592 | − | 1.46114i | −0.0432471 | − | 0.999064i | \(-0.513770\pi\) |
0.886839 | − | 0.462079i | \(-0.152896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.71053 | − | 2.96273i | −0.0581599 | − | 0.100736i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0058 | −0.373345 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.35185 | + | 9.26967i | 0.181340 | + | 0.314091i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.68934 | + | 6.05935i | 0.0571100 | + | 0.204843i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.08701 | − | 8.81097i | 0.171776 | − | 0.297525i | −0.767265 | − | 0.641331i | \(-0.778383\pi\) |
0.939041 | + | 0.343805i | \(0.111716\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.2919 | −1.22271 | −0.611353 | − | 0.791358i | \(-0.709374\pi\) | ||||
−0.611353 | + | 0.791358i | \(0.709374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00327 | −0.235679 | −0.117839 | − | 0.993033i | \(-0.537597\pi\) | ||||
−0.117839 | + | 0.993033i | \(0.537597\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.2930 | − | 40.3447i | 0.782104 | − | 1.35464i | −0.148611 | − | 0.988896i | \(-0.547480\pi\) |
0.930714 | − | 0.365747i | \(-0.119187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.74377 | − | 9.84141i | −0.0920231 | − | 0.330070i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.05430 | + | 5.29021i | 0.102208 | + | 0.177030i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.62244 | 0.154511 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.73585 | + | 11.6668i | 0.224653 | + | 0.389111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.34501 | + | 9.25783i | −0.178068 | + | 0.308423i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.158555 | − | 0.274626i | 0.00527055 | − | 0.00912886i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.54583 | + | 14.8018i | 0.283760 | + | 0.491486i | 0.972308 | − | 0.233705i | \(-0.0750849\pi\) |
−0.688548 | + | 0.725191i | \(0.741752\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7634 | −0.886710 | −0.443355 | − | 0.896346i | \(-0.646212\pi\) | ||||
−0.443355 | + | 0.896346i | \(0.646212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5390 | + | 25.1823i | 0.481170 | + | 0.833412i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.1871 | − | 9.56300i | −1.22803 | − | 0.315798i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.99441 | + | 17.3108i | −0.329685 | + | 0.571031i | −0.982449 | − | 0.186530i | \(-0.940276\pi\) |
0.652764 | + | 0.757561i | \(0.273609\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.10533 | 0.200959 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5940 | −0.940164 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.8126 | + | 46.4408i | −0.879693 | + | 1.52367i | −0.0280145 | + | 0.999608i | \(0.508918\pi\) |
−0.851678 | + | 0.524065i | \(0.824415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.167026 | − | 8.27192i | −0.00547407 | − | 0.271101i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.990285 | − | 1.71522i | −0.0323858 | − | 0.0560938i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.87524 | −0.257273 | −0.128636 | − | 0.991692i | \(-0.541060\pi\) | ||||
−0.128636 | + | 0.991692i | \(0.541060\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.4406 | + | 30.2081i | 0.568548 | + | 0.984755i | 0.996710 | + | 0.0810523i | \(0.0258281\pi\) |
−0.428162 | + | 0.903702i | \(0.640839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.32326 | − | 16.1484i | 0.303607 | − | 0.525863i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.59905 | + | 2.76964i | −0.0519622 | + | 0.0900012i | −0.890837 | − | 0.454324i | \(-0.849881\pi\) |
0.838874 | + | 0.544325i | \(0.183214\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.97825 | + | 5.15847i | 0.0966780 | + | 0.167451i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6465 | 1.67299 | 0.836497 | − | 0.547971i | \(-0.184600\pi\) | ||||
0.836497 | + | 0.547971i | \(0.184600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.99316 | − | 5.18431i | −0.0968565 | − | 0.167760i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.1248 | − | 21.5556i | 0.682154 | − | 0.696067i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.70494 | − | 8.14920i | 0.151772 | − | 0.262877i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.945308 | −0.0304305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.1021 | −1.19312 | −0.596561 | − | 0.802568i | \(-0.703467\pi\) | ||||
−0.596561 | + | 0.802568i | \(0.703467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.86320 | + | 15.3515i | −0.284434 | + | 0.492653i | −0.972472 | − | 0.233021i | \(-0.925139\pi\) |
0.688038 | + | 0.725675i | \(0.258472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.36333 | + | 4.89003i | 0.0437064 | + | 0.156767i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.4577 | − | 33.7018i | −0.622508 | − | 1.07822i | −0.989017 | − | 0.147801i | \(-0.952780\pi\) |
0.366509 | − | 0.930415i | \(-0.380553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.2632 | −0.423894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.6478 | + | 35.7630i | 0.658561 | + | 1.14066i | 0.980988 | + | 0.194067i | \(0.0621680\pi\) |
−0.322427 | + | 0.946594i | \(0.604499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.180699 | − | 0.312981i | 0.00575756 | − | 0.00997239i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.68482 | − | 6.38230i | 0.117171 | − | 0.202945i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.72257 | + | 16.8400i | 0.308848 | + | 0.534940i | 0.978111 | − | 0.208086i | \(-0.0667233\pi\) |
−0.669263 | + | 0.743026i | \(0.733390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.46784 | −0.205044 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.1693 | − | 29.7382i | −0.543759 | − | 0.941818i | −0.998684 | − | 0.0512881i | \(-0.983667\pi\) |
0.454925 | − | 0.890530i | \(-0.349666\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.s.l.1297.2 | yes | 6 | |
3.2 | odd | 2 | 1512.2.s.k.1297.2 | yes | 6 | ||
7.4 | even | 3 | inner | 1512.2.s.l.865.2 | yes | 6 | |
21.11 | odd | 6 | 1512.2.s.k.865.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.k.865.2 | ✓ | 6 | 21.11 | odd | 6 | ||
1512.2.s.k.1297.2 | yes | 6 | 3.2 | odd | 2 | ||
1512.2.s.l.865.2 | yes | 6 | 7.4 | even | 3 | inner | |
1512.2.s.l.1297.2 | yes | 6 | 1.1 | even | 1 | trivial |