Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.5 | ||
Root | \(-0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.v.1351.2 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | 2.55496i | 0.965683i | 0.875708 | + | 0.482842i | \(0.160395\pi\) | ||||
−0.875708 | + | 0.482842i | \(0.839605\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.85086i | 1.16108i | 0.814233 | + | 0.580538i | \(0.197158\pi\) | ||||
−0.814233 | + | 0.580538i | \(0.802842\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.55496 | −0.682841 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.40581 | 1.79617 | 0.898087 | − | 0.439818i | \(-0.144957\pi\) | ||||
0.898087 | + | 0.439818i | \(0.144957\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.93900i | 0.674253i | 0.941459 | + | 0.337127i | \(0.109455\pi\) | ||||
−0.941459 | + | 0.337127i | \(0.890545\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 2.55496i | − 0.557538i | ||||||||
\(22\) | −3.85086 | −0.821005 | ||||||||
\(23\) | 1.80194 | 0.375730 | 0.187865 | − | 0.982195i | \(-0.439843\pi\) | ||||
0.187865 | + | 0.982195i | \(0.439843\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − 2.55496i | − 0.482842i | ||||||||
\(29\) | 8.03684 | 1.49240 | 0.746201 | − | 0.665720i | \(-0.231876\pi\) | ||||
0.746201 | + | 0.665720i | \(0.231876\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 1.13706i | − 0.204223i | −0.994773 | − | 0.102111i | \(-0.967440\pi\) | ||||
0.994773 | − | 0.102111i | \(-0.0325598\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 3.85086i | − 0.670348i | ||||||||
\(34\) | 7.40581i | 1.27009i | ||||||||
\(35\) | 2.55496 | 0.431867 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 3.44504i | − 0.566361i | −0.959067 | − | 0.283181i | \(-0.908610\pi\) | ||||
0.959067 | − | 0.283181i | \(-0.0913896\pi\) | |||||||
\(38\) | −2.93900 | −0.476769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 1.55496i | 0.242844i | 0.992601 | + | 0.121422i | \(0.0387454\pi\) | ||||
−0.992601 | + | 0.121422i | \(0.961255\pi\) | |||||||
\(42\) | 2.55496 | 0.394239 | ||||||||
\(43\) | 10.4547 | 1.59433 | 0.797166 | − | 0.603761i | \(-0.206332\pi\) | ||||
0.797166 | + | 0.603761i | \(0.206332\pi\) | |||||||
\(44\) | − 3.85086i | − 0.580538i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 1.80194i | 0.265681i | ||||||||
\(47\) | − 9.71379i | − 1.41690i | −0.705760 | − | 0.708451i | \(-0.749394\pi\) | ||||
0.705760 | − | 0.708451i | \(-0.250606\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.472189 | 0.0674556 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | −7.40581 | −1.03702 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.93900 | −1.22787 | −0.613933 | − | 0.789358i | \(-0.710414\pi\) | ||||
−0.613933 | + | 0.789358i | \(0.710414\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 3.85086 | 0.519249 | ||||||||
\(56\) | 2.55496 | 0.341421 | ||||||||
\(57\) | − 2.93900i | − 0.389280i | ||||||||
\(58\) | 8.03684i | 1.05529i | ||||||||
\(59\) | − 11.7845i | − 1.53421i | −0.641522 | − | 0.767104i | \(-0.721697\pi\) | ||||
0.641522 | − | 0.767104i | \(-0.278303\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | −10.0586 | −1.28787 | −0.643936 | − | 0.765079i | \(-0.722700\pi\) | ||||
−0.643936 | + | 0.765079i | \(0.722700\pi\) | |||||||
\(62\) | 1.13706 | 0.144407 | ||||||||
\(63\) | 2.55496i | 0.321894i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.85086 | 0.474007 | ||||||||
\(67\) | − 1.36227i | − 0.166428i | −0.996532 | − | 0.0832140i | \(-0.973481\pi\) | ||||
0.996532 | − | 0.0832140i | \(-0.0265185\pi\) | |||||||
\(68\) | −7.40581 | −0.898087 | ||||||||
\(69\) | −1.80194 | −0.216928 | ||||||||
\(70\) | 2.55496i | 0.305376i | ||||||||
\(71\) | 12.0761i | 1.43317i | 0.697502 | + | 0.716583i | \(0.254295\pi\) | ||||
−0.697502 | + | 0.716583i | \(0.745705\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 2.29590i | 0.268714i | 0.990933 | + | 0.134357i | \(0.0428970\pi\) | ||||
−0.990933 | + | 0.134357i | \(0.957103\pi\) | |||||||
\(74\) | 3.44504 | 0.400478 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 2.93900i | − 0.337127i | ||||||||
\(77\) | −9.83877 | −1.12123 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.81700 | 0.991990 | 0.495995 | − | 0.868325i | \(-0.334803\pi\) | ||||
0.495995 | + | 0.868325i | \(0.334803\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.55496 | −0.171716 | ||||||||
\(83\) | 15.9051i | 1.74582i | 0.487884 | + | 0.872908i | \(0.337769\pi\) | ||||
−0.487884 | + | 0.872908i | \(0.662231\pi\) | |||||||
\(84\) | 2.55496i | 0.278769i | ||||||||
\(85\) | − 7.40581i | − 0.803273i | ||||||||
\(86\) | 10.4547i | 1.12736i | ||||||||
\(87\) | −8.03684 | −0.861639 | ||||||||
\(88\) | 3.85086 | 0.410503 | ||||||||
\(89\) | − 15.6799i | − 1.66207i | −0.556220 | − | 0.831035i | \(-0.687749\pi\) | ||||
0.556220 | − | 0.831035i | \(-0.312251\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.80194 | −0.187865 | ||||||||
\(93\) | 1.13706i | 0.117908i | ||||||||
\(94\) | 9.71379 | 1.00190 | ||||||||
\(95\) | 2.93900 | 0.301535 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | − 1.98254i | − 0.201297i | −0.994922 | − | 0.100648i | \(-0.967908\pi\) | ||||
0.994922 | − | 0.100648i | \(-0.0320917\pi\) | |||||||
\(98\) | 0.472189i | 0.0476983i | ||||||||
\(99\) | 3.85086i | 0.387025i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.48188 | 0.346460 | 0.173230 | − | 0.984881i | \(-0.444580\pi\) | ||||
0.173230 | + | 0.984881i | \(0.444580\pi\) | |||||||
\(102\) | − 7.40581i | − 0.733285i | ||||||||
\(103\) | −8.65817 | −0.853115 | −0.426557 | − | 0.904460i | \(-0.640274\pi\) | ||||
−0.426557 | + | 0.904460i | \(0.640274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.55496 | −0.249338 | ||||||||
\(106\) | − 8.93900i | − 0.868233i | ||||||||
\(107\) | 13.9366 | 1.34730 | 0.673651 | − | 0.739049i | \(-0.264725\pi\) | ||||
0.673651 | + | 0.739049i | \(0.264725\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 5.39373i | − 0.516626i | −0.966061 | − | 0.258313i | \(-0.916833\pi\) | ||||
0.966061 | − | 0.258313i | \(-0.0831665\pi\) | |||||||
\(110\) | 3.85086i | 0.367165i | ||||||||
\(111\) | 3.44504i | 0.326989i | ||||||||
\(112\) | 2.55496i | 0.241421i | ||||||||
\(113\) | 9.44265 | 0.888290 | 0.444145 | − | 0.895955i | \(-0.353508\pi\) | ||||
0.444145 | + | 0.895955i | \(0.353508\pi\) | |||||||
\(114\) | 2.93900 | 0.275263 | ||||||||
\(115\) | − 1.80194i | − 0.168032i | ||||||||
\(116\) | −8.03684 | −0.746201 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7845 | 1.08485 | ||||||||
\(119\) | 18.9215i | 1.73453i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −3.82908 | −0.348099 | ||||||||
\(122\) | − 10.0586i | − 0.910663i | ||||||||
\(123\) | − 1.55496i | − 0.140206i | ||||||||
\(124\) | 1.13706i | 0.102111i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.55496 | −0.227614 | ||||||||
\(127\) | 0.499336 | 0.0443089 | 0.0221545 | − | 0.999755i | \(-0.492947\pi\) | ||||
0.0221545 | + | 0.999755i | \(0.492947\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −10.4547 | −0.920488 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.12498 | −0.0982901 | −0.0491451 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491451 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(132\) | 3.85086i | 0.335174i | ||||||||
\(133\) | −7.50902 | −0.651115 | ||||||||
\(134\) | 1.36227 | 0.117682 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 7.40581i | − 0.635043i | ||||||||
\(137\) | 14.1468i | 1.20864i | 0.796742 | + | 0.604319i | \(0.206555\pi\) | ||||
−0.796742 | + | 0.604319i | \(0.793445\pi\) | |||||||
\(138\) | − 1.80194i | − 0.153391i | ||||||||
\(139\) | 7.17629 | 0.608685 | 0.304343 | − | 0.952563i | \(-0.401563\pi\) | ||||
0.304343 | + | 0.952563i | \(0.401563\pi\) | |||||||
\(140\) | −2.55496 | −0.215933 | ||||||||
\(141\) | 9.71379i | 0.818049i | ||||||||
\(142\) | −12.0761 | −1.01340 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 8.03684i | − 0.667423i | ||||||||
\(146\) | −2.29590 | −0.190010 | ||||||||
\(147\) | −0.472189 | −0.0389455 | ||||||||
\(148\) | 3.44504i | 0.283181i | ||||||||
\(149\) | − 3.25667i | − 0.266797i | −0.991063 | − | 0.133398i | \(-0.957411\pi\) | ||||
0.991063 | − | 0.133398i | \(-0.0425890\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 0.137063i | 0.0111541i | 0.999984 | + | 0.00557703i | \(0.00177523\pi\) | ||||
−0.999984 | + | 0.00557703i | \(0.998225\pi\) | |||||||
\(152\) | 2.93900 | 0.238384 | ||||||||
\(153\) | 7.40581 | 0.598725 | ||||||||
\(154\) | − 9.83877i | − 0.792831i | ||||||||
\(155\) | −1.13706 | −0.0913311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.35152 | 0.347289 | 0.173645 | − | 0.984808i | \(-0.444446\pi\) | ||||
0.173645 | + | 0.984808i | \(0.444446\pi\) | |||||||
\(158\) | 8.81700i | 0.701443i | ||||||||
\(159\) | 8.93900 | 0.708909 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.60388i | 0.362836i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 11.6189i | 0.910066i | 0.890475 | + | 0.455033i | \(0.150372\pi\) | ||||
−0.890475 | + | 0.455033i | \(0.849628\pi\) | |||||||
\(164\) | − 1.55496i | − 0.121422i | ||||||||
\(165\) | −3.85086 | −0.299789 | ||||||||
\(166\) | −15.9051 | −1.23448 | ||||||||
\(167\) | 20.8146i | 1.61068i | 0.592811 | + | 0.805341i | \(0.298018\pi\) | ||||
−0.592811 | + | 0.805341i | \(0.701982\pi\) | |||||||
\(168\) | −2.55496 | −0.197119 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.40581 | 0.568000 | ||||||||
\(171\) | 2.93900i | 0.224751i | ||||||||
\(172\) | −10.4547 | −0.797166 | ||||||||
\(173\) | 8.89440 | 0.676228 | 0.338114 | − | 0.941105i | \(-0.390211\pi\) | ||||
0.338114 | + | 0.941105i | \(0.390211\pi\) | |||||||
\(174\) | − 8.03684i | − 0.609271i | ||||||||
\(175\) | − 2.55496i | − 0.193137i | ||||||||
\(176\) | 3.85086i | 0.290269i | ||||||||
\(177\) | 11.7845i | 0.885776i | ||||||||
\(178\) | 15.6799 | 1.17526 | ||||||||
\(179\) | −0.188374 | −0.0140797 | −0.00703985 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00703985 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −18.1588 | −1.34974 | −0.674868 | − | 0.737939i | \(-0.735799\pi\) | ||||
−0.674868 | + | 0.737939i | \(0.735799\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0586 | 0.743554 | ||||||||
\(184\) | − 1.80194i | − 0.132841i | ||||||||
\(185\) | −3.44504 | −0.253285 | ||||||||
\(186\) | −1.13706 | −0.0833735 | ||||||||
\(187\) | 28.5187i | 2.08549i | ||||||||
\(188\) | 9.71379i | 0.708451i | ||||||||
\(189\) | − 2.55496i | − 0.185846i | ||||||||
\(190\) | 2.93900i | 0.213218i | ||||||||
\(191\) | 0.469205 | 0.0339505 | 0.0169752 | − | 0.999856i | \(-0.494596\pi\) | ||||
0.0169752 | + | 0.999856i | \(0.494596\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 17.9312i | − 1.29072i | −0.763879 | − | 0.645359i | \(-0.776708\pi\) | ||||
0.763879 | − | 0.645359i | \(-0.223292\pi\) | |||||||
\(194\) | 1.98254 | 0.142338 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.472189 | −0.0337278 | ||||||||
\(197\) | 8.17390i | 0.582366i | 0.956667 | + | 0.291183i | \(0.0940489\pi\) | ||||
−0.956667 | + | 0.291183i | \(0.905951\pi\) | |||||||
\(198\) | −3.85086 | −0.273668 | ||||||||
\(199\) | 23.7536 | 1.68385 | 0.841924 | − | 0.539595i | \(-0.181423\pi\) | ||||
0.841924 | + | 0.539595i | \(0.181423\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 1.36227i | 0.0960873i | ||||||||
\(202\) | 3.48188i | 0.244984i | ||||||||
\(203\) | 20.5338i | 1.44119i | ||||||||
\(204\) | 7.40581 | 0.518511 | ||||||||
\(205\) | 1.55496 | 0.108603 | ||||||||
\(206\) | − 8.65817i | − 0.603243i | ||||||||
\(207\) | 1.80194 | 0.125243 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3177 | −0.782859 | ||||||||
\(210\) | − 2.55496i | − 0.176309i | ||||||||
\(211\) | 24.2392 | 1.66870 | 0.834348 | − | 0.551238i | \(-0.185844\pi\) | ||||
0.834348 | + | 0.551238i | \(0.185844\pi\) | |||||||
\(212\) | 8.93900 | 0.613933 | ||||||||
\(213\) | − 12.0761i | − 0.827438i | ||||||||
\(214\) | 13.9366i | 0.952687i | ||||||||
\(215\) | − 10.4547i | − 0.713007i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 2.90515 | 0.197214 | ||||||||
\(218\) | 5.39373 | 0.365310 | ||||||||
\(219\) | − 2.29590i | − 0.155142i | ||||||||
\(220\) | −3.85086 | −0.259625 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.44504 | −0.231216 | ||||||||
\(223\) | 22.5579i | 1.51059i | 0.655384 | + | 0.755296i | \(0.272507\pi\) | ||||
−0.655384 | + | 0.755296i | \(0.727493\pi\) | |||||||
\(224\) | −2.55496 | −0.170710 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 9.44265i | 0.628116i | ||||||||
\(227\) | 23.7439i | 1.57594i | 0.615714 | + | 0.787970i | \(0.288868\pi\) | ||||
−0.615714 | + | 0.787970i | \(0.711132\pi\) | |||||||
\(228\) | 2.93900i | 0.194640i | ||||||||
\(229\) | − 3.11529i | − 0.205864i | −0.994688 | − | 0.102932i | \(-0.967178\pi\) | ||||
0.994688 | − | 0.102932i | \(-0.0328225\pi\) | |||||||
\(230\) | 1.80194 | 0.118816 | ||||||||
\(231\) | 9.83877 | 0.647344 | ||||||||
\(232\) | − 8.03684i | − 0.527644i | ||||||||
\(233\) | 12.5603 | 0.822855 | 0.411427 | − | 0.911443i | \(-0.365030\pi\) | ||||
0.411427 | + | 0.911443i | \(0.365030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.71379 | −0.633658 | ||||||||
\(236\) | 11.7845i | 0.767104i | ||||||||
\(237\) | −8.81700 | −0.572726 | ||||||||
\(238\) | −18.9215 | −1.22650 | ||||||||
\(239\) | 8.52111i | 0.551185i | 0.961275 | + | 0.275592i | \(0.0888740\pi\) | ||||
−0.961275 | + | 0.275592i | \(0.911126\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 11.6136i | 0.748095i | 0.927409 | + | 0.374048i | \(0.122030\pi\) | ||||
−0.927409 | + | 0.374048i | \(0.877970\pi\) | |||||||
\(242\) | − 3.82908i | − 0.246143i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.0586 | 0.643936 | ||||||||
\(245\) | − 0.472189i | − 0.0301670i | ||||||||
\(246\) | 1.55496 | 0.0991405 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.13706 | −0.0722036 | ||||||||
\(249\) | − 15.9051i | − 1.00795i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.7463 | −1.43573 | −0.717867 | − | 0.696180i | \(-0.754882\pi\) | ||||
−0.717867 | + | 0.696180i | \(0.754882\pi\) | |||||||
\(252\) | − 2.55496i | − 0.160947i | ||||||||
\(253\) | 6.93900i | 0.436251i | ||||||||
\(254\) | 0.499336i | 0.0313311i | ||||||||
\(255\) | 7.40581i | 0.463770i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.39373 | −0.461208 | −0.230604 | − | 0.973048i | \(-0.574070\pi\) | ||||
−0.230604 | + | 0.973048i | \(0.574070\pi\) | |||||||
\(258\) | − 10.4547i | − 0.650883i | ||||||||
\(259\) | 8.80194 | 0.546926 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.03684 | 0.497468 | ||||||||
\(262\) | − 1.12498i | − 0.0695016i | ||||||||
\(263\) | −11.7735 | −0.725983 | −0.362991 | − | 0.931792i | \(-0.618245\pi\) | ||||
−0.362991 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(264\) | −3.85086 | −0.237004 | ||||||||
\(265\) | 8.93900i | 0.549118i | ||||||||
\(266\) | − 7.50902i | − 0.460408i | ||||||||
\(267\) | 15.6799i | 0.959597i | ||||||||
\(268\) | 1.36227i | 0.0832140i | ||||||||
\(269\) | −22.8810 | −1.39508 | −0.697539 | − | 0.716547i | \(-0.745722\pi\) | ||||
−0.697539 | + | 0.716547i | \(0.745722\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 2.13036i | 0.129410i | 0.997904 | + | 0.0647050i | \(0.0206107\pi\) | ||||
−0.997904 | + | 0.0647050i | \(0.979389\pi\) | |||||||
\(272\) | 7.40581 | 0.449043 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.1468 | −0.854637 | ||||||||
\(275\) | − 3.85086i | − 0.232215i | ||||||||
\(276\) | 1.80194 | 0.108464 | ||||||||
\(277\) | 14.7084 | 0.883743 | 0.441872 | − | 0.897078i | \(-0.354315\pi\) | ||||
0.441872 | + | 0.897078i | \(0.354315\pi\) | |||||||
\(278\) | 7.17629i | 0.430405i | ||||||||
\(279\) | − 1.13706i | − 0.0680742i | ||||||||
\(280\) | − 2.55496i | − 0.152688i | ||||||||
\(281\) | − 12.5942i | − 0.751306i | −0.926760 | − | 0.375653i | \(-0.877418\pi\) | ||||
0.926760 | − | 0.375653i | \(-0.122582\pi\) | |||||||
\(282\) | −9.71379 | −0.578448 | ||||||||
\(283\) | 1.62565 | 0.0966346 | 0.0483173 | − | 0.998832i | \(-0.484614\pi\) | ||||
0.0483173 | + | 0.998832i | \(0.484614\pi\) | |||||||
\(284\) | − 12.0761i | − 0.716583i | ||||||||
\(285\) | −2.93900 | −0.174091 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.97285 | −0.234510 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 37.8461 | 2.22624 | ||||||||
\(290\) | 8.03684 | 0.471939 | ||||||||
\(291\) | 1.98254i | 0.116219i | ||||||||
\(292\) | − 2.29590i | − 0.134357i | ||||||||
\(293\) | − 13.0664i | − 0.763346i | −0.924297 | − | 0.381673i | \(-0.875348\pi\) | ||||
0.924297 | − | 0.381673i | \(-0.124652\pi\) | |||||||
\(294\) | − 0.472189i | − 0.0275386i | ||||||||
\(295\) | −11.7845 | −0.686119 | ||||||||
\(296\) | −3.44504 | −0.200239 | ||||||||
\(297\) | − 3.85086i | − 0.223449i | ||||||||
\(298\) | 3.25667 | 0.188654 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 26.7114i | 1.53962i | ||||||||
\(302\) | −0.137063 | −0.00788711 | ||||||||
\(303\) | −3.48188 | −0.200029 | ||||||||
\(304\) | 2.93900i | 0.168563i | ||||||||
\(305\) | 10.0586i | 0.575954i | ||||||||
\(306\) | 7.40581i | 0.423362i | ||||||||
\(307\) | − 26.2489i | − 1.49810i | −0.662511 | − | 0.749052i | \(-0.730509\pi\) | ||||
0.662511 | − | 0.749052i | \(-0.269491\pi\) | |||||||
\(308\) | 9.83877 | 0.560616 | ||||||||
\(309\) | 8.65817 | 0.492546 | ||||||||
\(310\) | − 1.13706i | − 0.0645809i | ||||||||
\(311\) | −27.1250 | −1.53812 | −0.769058 | − | 0.639179i | \(-0.779274\pi\) | ||||
−0.769058 | + | 0.639179i | \(0.779274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1323 | 1.08142 | 0.540710 | − | 0.841209i | \(-0.318156\pi\) | ||||
0.540710 | + | 0.841209i | \(0.318156\pi\) | |||||||
\(314\) | 4.35152i | 0.245570i | ||||||||
\(315\) | 2.55496 | 0.143956 | ||||||||
\(316\) | −8.81700 | −0.495995 | ||||||||
\(317\) | 6.67456i | 0.374881i | 0.982276 | + | 0.187440i | \(0.0600191\pi\) | ||||
−0.982276 | + | 0.187440i | \(0.939981\pi\) | |||||||
\(318\) | 8.93900i | 0.501274i | ||||||||
\(319\) | 30.9487i | 1.73279i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −13.9366 | −0.777866 | ||||||||
\(322\) | −4.60388 | −0.256564 | ||||||||
\(323\) | 21.7657i | 1.21108i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.6189 | −0.643514 | ||||||||
\(327\) | 5.39373i | 0.298274i | ||||||||
\(328\) | 1.55496 | 0.0858582 | ||||||||
\(329\) | 24.8183 | 1.36828 | ||||||||
\(330\) | − 3.85086i | − 0.211983i | ||||||||
\(331\) | − 18.1360i | − 0.996845i | −0.866934 | − | 0.498422i | \(-0.833913\pi\) | ||||
0.866934 | − | 0.498422i | \(-0.166087\pi\) | |||||||
\(332\) | − 15.9051i | − 0.872908i | ||||||||
\(333\) | − 3.44504i | − 0.188787i | ||||||||
\(334\) | −20.8146 | −1.13892 | ||||||||
\(335\) | −1.36227 | −0.0744289 | ||||||||
\(336\) | − 2.55496i | − 0.139384i | ||||||||
\(337\) | −10.8780 | −0.592563 | −0.296281 | − | 0.955101i | \(-0.595747\pi\) | ||||
−0.296281 | + | 0.955101i | \(0.595747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.44265 | −0.512854 | ||||||||
\(340\) | 7.40581i | 0.401637i | ||||||||
\(341\) | 4.37867 | 0.237118 | ||||||||
\(342\) | −2.93900 | −0.158923 | ||||||||
\(343\) | 19.0911i | 1.03082i | ||||||||
\(344\) | − 10.4547i | − 0.563681i | ||||||||
\(345\) | 1.80194i | 0.0970131i | ||||||||
\(346\) | 8.89440i | 0.478166i | ||||||||
\(347\) | −7.42865 | −0.398791 | −0.199395 | − | 0.979919i | \(-0.563898\pi\) | ||||
−0.199395 | + | 0.979919i | \(0.563898\pi\) | |||||||
\(348\) | 8.03684 | 0.430820 | ||||||||
\(349\) | 28.7275i | 1.53775i | 0.639399 | + | 0.768875i | \(0.279183\pi\) | ||||
−0.639399 | + | 0.768875i | \(0.720817\pi\) | |||||||
\(350\) | 2.55496 | 0.136568 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.85086 | −0.205251 | ||||||||
\(353\) | 31.2131i | 1.66131i | 0.556790 | + | 0.830654i | \(0.312033\pi\) | ||||
−0.556790 | + | 0.830654i | \(0.687967\pi\) | |||||||
\(354\) | −11.7845 | −0.626338 | ||||||||
\(355\) | 12.0761 | 0.640931 | ||||||||
\(356\) | 15.6799i | 0.831035i | ||||||||
\(357\) | − 18.9215i | − 1.00143i | ||||||||
\(358\) | − 0.188374i | − 0.00995585i | ||||||||
\(359\) | 0.0247542i | 0.00130648i | 1.00000 | 0.000653238i | \(0.000207932\pi\) | |||||
−1.00000 | 0.000653238i | \(0.999792\pi\) | ||||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 10.3623 | 0.545383 | ||||||||
\(362\) | − 18.1588i | − 0.954407i | ||||||||
\(363\) | 3.82908 | 0.200975 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.29590 | 0.120173 | ||||||||
\(366\) | 10.0586i | 0.525772i | ||||||||
\(367\) | 17.5284 | 0.914975 | 0.457488 | − | 0.889216i | \(-0.348749\pi\) | ||||
0.457488 | + | 0.889216i | \(0.348749\pi\) | |||||||
\(368\) | 1.80194 | 0.0939325 | ||||||||
\(369\) | 1.55496i | 0.0809479i | ||||||||
\(370\) | − 3.44504i | − 0.179099i | ||||||||
\(371\) | − 22.8388i | − 1.18573i | ||||||||
\(372\) | − 1.13706i | − 0.0589540i | ||||||||
\(373\) | −35.3056 | −1.82805 | −0.914027 | − | 0.405653i | \(-0.867044\pi\) | ||||
−0.914027 | + | 0.405653i | \(0.867044\pi\) | |||||||
\(374\) | −28.5187 | −1.47467 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −9.71379 | −0.500951 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.55496 | 0.131413 | ||||||||
\(379\) | − 18.2567i | − 0.937782i | −0.883256 | − | 0.468891i | \(-0.844654\pi\) | ||||
0.883256 | − | 0.468891i | \(-0.155346\pi\) | |||||||
\(380\) | −2.93900 | −0.150768 | ||||||||
\(381\) | −0.499336 | −0.0255818 | ||||||||
\(382\) | 0.469205i | 0.0240066i | ||||||||
\(383\) | 2.83148i | 0.144682i | 0.997380 | + | 0.0723409i | \(0.0230469\pi\) | ||||
−0.997380 | + | 0.0723409i | \(0.976953\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 9.83877i | 0.501430i | ||||||||
\(386\) | 17.9312 | 0.912676 | ||||||||
\(387\) | 10.4547 | 0.531444 | ||||||||
\(388\) | 1.98254i | 0.100648i | ||||||||
\(389\) | −28.8025 | −1.46035 | −0.730173 | − | 0.683262i | \(-0.760561\pi\) | ||||
−0.730173 | + | 0.683262i | \(0.760561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.3448 | 0.674876 | ||||||||
\(392\) | − 0.472189i | − 0.0238491i | ||||||||
\(393\) | 1.12498 | 0.0567478 | ||||||||
\(394\) | −8.17390 | −0.411795 | ||||||||
\(395\) | − 8.81700i | − 0.443632i | ||||||||
\(396\) | − 3.85086i | − 0.193513i | ||||||||
\(397\) | 21.4306i | 1.07557i | 0.843082 | + | 0.537785i | \(0.180739\pi\) | ||||
−0.843082 | + | 0.537785i | \(0.819261\pi\) | |||||||
\(398\) | 23.7536i | 1.19066i | ||||||||
\(399\) | 7.50902 | 0.375921 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 19.5284i | 0.975202i | 0.873067 | + | 0.487601i | \(0.162128\pi\) | ||||
−0.873067 | + | 0.487601i | \(0.837872\pi\) | |||||||
\(402\) | −1.36227 | −0.0679440 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.48188 | −0.173230 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | −20.5338 | −1.01907 | ||||||||
\(407\) | 13.2664 | 0.657589 | ||||||||
\(408\) | 7.40581i | 0.366642i | ||||||||
\(409\) | − 30.2707i | − 1.49679i | −0.663254 | − | 0.748394i | \(-0.730825\pi\) | ||||
0.663254 | − | 0.748394i | \(-0.269175\pi\) | |||||||
\(410\) | 1.55496i | 0.0767939i | ||||||||
\(411\) | − 14.1468i | − 0.697808i | ||||||||
\(412\) | 8.65817 | 0.426557 | ||||||||
\(413\) | 30.1089 | 1.48156 | ||||||||
\(414\) | 1.80194i | 0.0885604i | ||||||||
\(415\) | 15.9051 | 0.780753 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.17629 | −0.351425 | ||||||||
\(418\) | − 11.3177i | − 0.553565i | ||||||||
\(419\) | −24.4873 | −1.19628 | −0.598140 | − | 0.801391i | \(-0.704093\pi\) | ||||
−0.598140 | + | 0.801391i | \(0.704093\pi\) | |||||||
\(420\) | 2.55496 | 0.124669 | ||||||||
\(421\) | 8.90408i | 0.433959i | 0.976176 | + | 0.216979i | \(0.0696204\pi\) | ||||
−0.976176 | + | 0.216979i | \(0.930380\pi\) | |||||||
\(422\) | 24.2392i | 1.17995i | ||||||||
\(423\) | − 9.71379i | − 0.472301i | ||||||||
\(424\) | 8.93900i | 0.434116i | ||||||||
\(425\) | −7.40581 | −0.359235 | ||||||||
\(426\) | 12.0761 | 0.585087 | ||||||||
\(427\) | − 25.6993i | − 1.24368i | ||||||||
\(428\) | −13.9366 | −0.673651 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.4547 | 0.504172 | ||||||||
\(431\) | − 1.48619i | − 0.0715872i | −0.999359 | − | 0.0357936i | \(-0.988604\pi\) | ||||
0.999359 | − | 0.0357936i | \(-0.0113959\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.5719 | −0.892511 | −0.446255 | − | 0.894906i | \(-0.647243\pi\) | ||||
−0.446255 | + | 0.894906i | \(0.647243\pi\) | |||||||
\(434\) | 2.90515i | 0.139452i | ||||||||
\(435\) | 8.03684i | 0.385337i | ||||||||
\(436\) | 5.39373i | 0.258313i | ||||||||
\(437\) | 5.29590i | 0.253337i | ||||||||
\(438\) | 2.29590 | 0.109702 | ||||||||
\(439\) | −0.532123 | −0.0253968 | −0.0126984 | − | 0.999919i | \(-0.504042\pi\) | ||||
−0.0126984 | + | 0.999919i | \(0.504042\pi\) | |||||||
\(440\) | − 3.85086i | − 0.183582i | ||||||||
\(441\) | 0.472189 | 0.0224852 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.5230 | 1.21264 | 0.606318 | − | 0.795222i | \(-0.292646\pi\) | ||||
0.606318 | + | 0.795222i | \(0.292646\pi\) | |||||||
\(444\) | − 3.44504i | − 0.163494i | ||||||||
\(445\) | −15.6799 | −0.743300 | ||||||||
\(446\) | −22.5579 | −1.06815 | ||||||||
\(447\) | 3.25667i | 0.154035i | ||||||||
\(448\) | − 2.55496i | − 0.120710i | ||||||||
\(449\) | − 40.7730i | − 1.92420i | −0.272703 | − | 0.962098i | \(-0.587918\pi\) | ||||
0.272703 | − | 0.962098i | \(-0.412082\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | −5.98792 | −0.281960 | ||||||||
\(452\) | −9.44265 | −0.444145 | ||||||||
\(453\) | − 0.137063i | − 0.00643980i | ||||||||
\(454\) | −23.7439 | −1.11436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.93900 | −0.137631 | ||||||||
\(457\) | 15.1511i | 0.708737i | 0.935106 | + | 0.354368i | \(0.115304\pi\) | ||||
−0.935106 | + | 0.354368i | \(0.884696\pi\) | |||||||
\(458\) | 3.11529 | 0.145568 | ||||||||
\(459\) | −7.40581 | −0.345674 | ||||||||
\(460\) | 1.80194i | 0.0840158i | ||||||||
\(461\) | 19.5743i | 0.911668i | 0.890065 | + | 0.455834i | \(0.150659\pi\) | ||||
−0.890065 | + | 0.455834i | \(0.849341\pi\) | |||||||
\(462\) | 9.83877i | 0.457741i | ||||||||
\(463\) | 31.2905i | 1.45419i | 0.686535 | + | 0.727097i | \(0.259131\pi\) | ||||
−0.686535 | + | 0.727097i | \(0.740869\pi\) | |||||||
\(464\) | 8.03684 | 0.373101 | ||||||||
\(465\) | 1.13706 | 0.0527300 | ||||||||
\(466\) | 12.5603i | 0.581846i | ||||||||
\(467\) | 32.3032 | 1.49481 | 0.747407 | − | 0.664367i | \(-0.231299\pi\) | ||||
0.747407 | + | 0.664367i | \(0.231299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48055 | 0.160717 | ||||||||
\(470\) | − 9.71379i | − 0.448064i | ||||||||
\(471\) | −4.35152 | −0.200507 | ||||||||
\(472\) | −11.7845 | −0.542425 | ||||||||
\(473\) | 40.2597i | 1.85114i | ||||||||
\(474\) | − 8.81700i | − 0.404978i | ||||||||
\(475\) | − 2.93900i | − 0.134851i | ||||||||
\(476\) | − 18.9215i | − 0.867267i | ||||||||
\(477\) | −8.93900 | −0.409289 | ||||||||
\(478\) | −8.52111 | −0.389746 | ||||||||
\(479\) | − 9.32842i | − 0.426226i | −0.977028 | − | 0.213113i | \(-0.931640\pi\) | ||||
0.977028 | − | 0.213113i | \(-0.0683603\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.6136 | −0.528983 | ||||||||
\(483\) | − 4.60388i | − 0.209484i | ||||||||
\(484\) | 3.82908 | 0.174049 | ||||||||
\(485\) | −1.98254 | −0.0900226 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | − 10.6571i | − 0.482920i | −0.970411 | − | 0.241460i | \(-0.922374\pi\) | ||||
0.970411 | − | 0.241460i | \(-0.0776262\pi\) | |||||||
\(488\) | 10.0586i | 0.455332i | ||||||||
\(489\) | − 11.6189i | − 0.525427i | ||||||||
\(490\) | 0.472189 | 0.0213313 | ||||||||
\(491\) | −40.8611 | −1.84404 | −0.922019 | − | 0.387146i | \(-0.873461\pi\) | ||||
−0.922019 | + | 0.387146i | \(0.873461\pi\) | |||||||
\(492\) | 1.55496i | 0.0701029i | ||||||||
\(493\) | 59.5193 | 2.68061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.85086 | 0.173083 | ||||||||
\(496\) | − 1.13706i | − 0.0510557i | ||||||||
\(497\) | −30.8538 | −1.38398 | ||||||||
\(498\) | 15.9051 | 0.712727 | ||||||||
\(499\) | − 19.0556i | − 0.853047i | −0.904477 | − | 0.426523i | \(-0.859738\pi\) | ||||
0.904477 | − | 0.426523i | \(-0.140262\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 20.8146i | − 0.929928i | ||||||||
\(502\) | − 22.7463i | − 1.01522i | ||||||||
\(503\) | −16.9825 | −0.757214 | −0.378607 | − | 0.925558i | \(-0.623597\pi\) | ||||
−0.378607 | + | 0.925558i | \(0.623597\pi\) | |||||||
\(504\) | 2.55496 | 0.113807 | ||||||||
\(505\) | − 3.48188i | − 0.154942i | ||||||||
\(506\) | −6.93900 | −0.308476 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.499336 | −0.0221545 | ||||||||
\(509\) | 43.0116i | 1.90646i | 0.302252 | + | 0.953228i | \(0.402262\pi\) | ||||
−0.302252 | + | 0.953228i | \(0.597738\pi\) | |||||||
\(510\) | −7.40581 | −0.327935 | ||||||||
\(511\) | −5.86592 | −0.259493 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 2.93900i | − 0.129760i | ||||||||
\(514\) | − 7.39373i | − 0.326124i | ||||||||
\(515\) | 8.65817i | 0.381525i | ||||||||
\(516\) | 10.4547 | 0.460244 | ||||||||
\(517\) | 37.4064 | 1.64513 | ||||||||
\(518\) | 8.80194i | 0.386735i | ||||||||
\(519\) | −8.89440 | −0.390421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.1021 | −1.09975 | −0.549873 | − | 0.835249i | \(-0.685324\pi\) | ||||
−0.549873 | + | 0.835249i | \(0.685324\pi\) | |||||||
\(522\) | 8.03684i | 0.351763i | ||||||||
\(523\) | −3.86725 | −0.169103 | −0.0845515 | − | 0.996419i | \(-0.526946\pi\) | ||||
−0.0845515 | + | 0.996419i | \(0.526946\pi\) | |||||||
\(524\) | 1.12498 | 0.0491451 | ||||||||
\(525\) | 2.55496i | 0.111508i | ||||||||
\(526\) | − 11.7735i | − 0.513347i | ||||||||
\(527\) | − 8.42088i | − 0.366819i | ||||||||
\(528\) | − 3.85086i | − 0.167587i | ||||||||
\(529\) | −19.7530 | −0.858827 | ||||||||
\(530\) | −8.93900 | −0.388285 | ||||||||
\(531\) | − 11.7845i | − 0.511403i | ||||||||
\(532\) | 7.50902 | 0.325558 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −15.6799 | −0.678537 | ||||||||
\(535\) | − 13.9366i | − 0.602532i | ||||||||
\(536\) | −1.36227 | −0.0588412 | ||||||||
\(537\) | 0.188374 | 0.00812892 | ||||||||
\(538\) | − 22.8810i | − 0.986469i | ||||||||
\(539\) | 1.81833i | 0.0783211i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 42.6152i | − 1.83217i | −0.400983 | − | 0.916086i | \(-0.631331\pi\) | ||||
0.400983 | − | 0.916086i | \(-0.368669\pi\) | |||||||
\(542\) | −2.13036 | −0.0915067 | ||||||||
\(543\) | 18.1588 | 0.779270 | ||||||||
\(544\) | 7.40581i | 0.317522i | ||||||||
\(545\) | −5.39373 | −0.231042 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.7928 | −1.27385 | −0.636925 | − | 0.770926i | \(-0.719794\pi\) | ||||
−0.636925 | + | 0.770926i | \(0.719794\pi\) | |||||||
\(548\) | − 14.1468i | − 0.604319i | ||||||||
\(549\) | −10.0586 | −0.429291 | ||||||||
\(550\) | 3.85086 | 0.164201 | ||||||||
\(551\) | 23.6203i | 1.00626i | ||||||||
\(552\) | 1.80194i | 0.0766956i | ||||||||
\(553\) | 22.5271i | 0.957949i | ||||||||
\(554\) | 14.7084i | 0.624901i | ||||||||
\(555\) | 3.44504 | 0.146234 | ||||||||
\(556\) | −7.17629 | −0.304343 | ||||||||
\(557\) | 37.7700i | 1.60037i | 0.599756 | + | 0.800183i | \(0.295264\pi\) | ||||
−0.599756 | + | 0.800183i | \(0.704736\pi\) | |||||||
\(558\) | 1.13706 | 0.0481357 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.55496 | 0.107967 | ||||||||
\(561\) | − 28.5187i | − 1.20406i | ||||||||
\(562\) | 12.5942 | 0.531254 | ||||||||
\(563\) | −25.0237 | −1.05462 | −0.527311 | − | 0.849672i | \(-0.676800\pi\) | ||||
−0.527311 | + | 0.849672i | \(0.676800\pi\) | |||||||
\(564\) | − 9.71379i | − 0.409024i | ||||||||
\(565\) | − 9.44265i | − 0.397255i | ||||||||
\(566\) | 1.62565i | 0.0683310i | ||||||||
\(567\) | 2.55496i | 0.107298i | ||||||||
\(568\) | 12.0761 | 0.506700 | ||||||||
\(569\) | −3.81402 | −0.159892 | −0.0799460 | − | 0.996799i | \(-0.525475\pi\) | ||||
−0.0799460 | + | 0.996799i | \(0.525475\pi\) | |||||||
\(570\) | − 2.93900i | − 0.123101i | ||||||||
\(571\) | 4.76702 | 0.199494 | 0.0997468 | − | 0.995013i | \(-0.468197\pi\) | ||||
0.0997468 | + | 0.995013i | \(0.468197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.469205 | −0.0196013 | ||||||||
\(574\) | − 3.97285i | − 0.165824i | ||||||||
\(575\) | −1.80194 | −0.0751460 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 20.9879i | − 0.873738i | −0.899525 | − | 0.436869i | \(-0.856087\pi\) | ||||
0.899525 | − | 0.436869i | \(-0.143913\pi\) | |||||||
\(578\) | 37.8461i | 1.57419i | ||||||||
\(579\) | 17.9312i | 0.745197i | ||||||||
\(580\) | 8.03684i | 0.333711i | ||||||||
\(581\) | −40.6370 | −1.68591 | ||||||||
\(582\) | −1.98254 | −0.0821790 | ||||||||
\(583\) | − 34.4228i | − 1.42565i | ||||||||
\(584\) | 2.29590 | 0.0950049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0664 | 0.539767 | ||||||||
\(587\) | − 13.9312i | − 0.575003i | −0.957780 | − | 0.287502i | \(-0.907175\pi\) | ||||
0.957780 | − | 0.287502i | \(-0.0928247\pi\) | |||||||
\(588\) | 0.472189 | 0.0194727 | ||||||||
\(589\) | 3.34183 | 0.137698 | ||||||||
\(590\) | − 11.7845i | − 0.485159i | ||||||||
\(591\) | − 8.17390i | − 0.336229i | ||||||||
\(592\) | − 3.44504i | − 0.141590i | ||||||||
\(593\) | 9.75600i | 0.400631i | 0.979731 | + | 0.200316i | \(0.0641967\pi\) | ||||
−0.979731 | + | 0.200316i | \(0.935803\pi\) | |||||||
\(594\) | 3.85086 | 0.158002 | ||||||||
\(595\) | 18.9215 | 0.775708 | ||||||||
\(596\) | 3.25667i | 0.133398i | ||||||||
\(597\) | −23.7536 | −0.972171 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.88769 | −0.404000 | −0.202000 | − | 0.979386i | \(-0.564744\pi\) | ||||
−0.202000 | + | 0.979386i | \(0.564744\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | 4.32304 | 0.176341 | 0.0881703 | − | 0.996105i | \(-0.471898\pi\) | ||||
0.0881703 | + | 0.996105i | \(0.471898\pi\) | |||||||
\(602\) | −26.7114 | −1.08868 | ||||||||
\(603\) | − 1.36227i | − 0.0554760i | ||||||||
\(604\) | − 0.137063i | − 0.00557703i | ||||||||
\(605\) | 3.82908i | 0.155674i | ||||||||
\(606\) | − 3.48188i | − 0.141442i | ||||||||
\(607\) | 37.5948 | 1.52592 | 0.762962 | − | 0.646443i | \(-0.223744\pi\) | ||||
0.762962 | + | 0.646443i | \(0.223744\pi\) | |||||||
\(608\) | −2.93900 | −0.119192 | ||||||||
\(609\) | − 20.5338i | − 0.832071i | ||||||||
\(610\) | −10.0586 | −0.407261 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.40581 | −0.299362 | ||||||||
\(613\) | − 33.8595i | − 1.36757i | −0.729683 | − | 0.683786i | \(-0.760332\pi\) | ||||
0.729683 | − | 0.683786i | \(-0.239668\pi\) | |||||||
\(614\) | 26.2489 | 1.05932 | ||||||||
\(615\) | −1.55496 | −0.0627020 | ||||||||
\(616\) | 9.83877i | 0.396415i | ||||||||
\(617\) | − 43.1333i | − 1.73648i | −0.496142 | − | 0.868241i | \(-0.665250\pi\) | ||||
0.496142 | − | 0.868241i | \(-0.334750\pi\) | |||||||
\(618\) | 8.65817i | 0.348283i | ||||||||
\(619\) | 14.6606i | 0.589258i | 0.955612 | + | 0.294629i | \(0.0951960\pi\) | ||||
−0.955612 | + | 0.294629i | \(0.904804\pi\) | |||||||
\(620\) | 1.13706 | 0.0456656 | ||||||||
\(621\) | −1.80194 | −0.0723093 | ||||||||
\(622\) | − 27.1250i | − 1.08761i | ||||||||
\(623\) | 40.0616 | 1.60503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.1323i | 0.764680i | ||||||||
\(627\) | 11.3177 | 0.451984 | ||||||||
\(628\) | −4.35152 | −0.173645 | ||||||||
\(629\) | − 25.5133i | − 1.01728i | ||||||||
\(630\) | 2.55496i | 0.101792i | ||||||||
\(631\) | − 10.5265i | − 0.419053i | −0.977803 | − | 0.209526i | \(-0.932808\pi\) | ||||
0.977803 | − | 0.209526i | \(-0.0671922\pi\) | |||||||
\(632\) | − 8.81700i | − 0.350722i | ||||||||
\(633\) | −24.2392 | −0.963422 | ||||||||
\(634\) | −6.67456 | −0.265081 | ||||||||
\(635\) | − 0.499336i | − 0.0198155i | ||||||||
\(636\) | −8.93900 | −0.354454 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −30.9487 | −1.22527 | ||||||||
\(639\) | 12.0761i | 0.477722i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 16.5435 | 0.653428 | 0.326714 | − | 0.945123i | \(-0.394059\pi\) | ||||
0.326714 | + | 0.945123i | \(0.394059\pi\) | |||||||
\(642\) | − 13.9366i | − 0.550034i | ||||||||
\(643\) | 43.4282i | 1.71264i | 0.516446 | + | 0.856320i | \(0.327255\pi\) | ||||
−0.516446 | + | 0.856320i | \(0.672745\pi\) | |||||||
\(644\) | − 4.60388i | − 0.181418i | ||||||||
\(645\) | 10.4547i | 0.411655i | ||||||||
\(646\) | −21.7657 | −0.856360 | ||||||||
\(647\) | −28.7687 | −1.13101 | −0.565507 | − | 0.824744i | \(-0.691319\pi\) | ||||
−0.565507 | + | 0.824744i | \(0.691319\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 45.3803 | 1.78133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.90515 | −0.113862 | ||||||||
\(652\) | − 11.6189i | − 0.455033i | ||||||||
\(653\) | −30.0978 | −1.17782 | −0.588910 | − | 0.808199i | \(-0.700443\pi\) | ||||
−0.588910 | + | 0.808199i | \(0.700443\pi\) | |||||||
\(654\) | −5.39373 | −0.210912 | ||||||||
\(655\) | 1.12498i | 0.0439567i | ||||||||
\(656\) | 1.55496i | 0.0607109i | ||||||||
\(657\) | 2.29590i | 0.0895715i | ||||||||
\(658\) | 24.8183i | 0.967519i | ||||||||
\(659\) | 46.6015 | 1.81534 | 0.907668 | − | 0.419689i | \(-0.137861\pi\) | ||||
0.907668 | + | 0.419689i | \(0.137861\pi\) | |||||||
\(660\) | 3.85086 | 0.149894 | ||||||||
\(661\) | − 40.9788i | − 1.59389i | −0.604051 | − | 0.796946i | \(-0.706448\pi\) | ||||
0.604051 | − | 0.796946i | \(-0.293552\pi\) | |||||||
\(662\) | 18.1360 | 0.704876 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.9051 | 0.617239 | ||||||||
\(665\) | 7.50902i | 0.291187i | ||||||||
\(666\) | 3.44504 | 0.133493 | ||||||||
\(667\) | 14.4819 | 0.560741 | ||||||||
\(668\) | − 20.8146i | − 0.805341i | ||||||||
\(669\) | − 22.5579i | − 0.872140i | ||||||||
\(670\) | − 1.36227i | − 0.0526292i | ||||||||
\(671\) | − 38.7342i | − 1.49532i | ||||||||
\(672\) | 2.55496 | 0.0985596 | ||||||||
\(673\) | 49.2586 | 1.89878 | 0.949389 | − | 0.314101i | \(-0.101703\pi\) | ||||
0.949389 | + | 0.314101i | \(0.101703\pi\) | |||||||
\(674\) | − 10.8780i | − 0.419005i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.1909 | −1.19876 | −0.599382 | − | 0.800463i | \(-0.704587\pi\) | ||||
−0.599382 | + | 0.800463i | \(0.704587\pi\) | |||||||
\(678\) | − 9.44265i | − 0.362643i | ||||||||
\(679\) | 5.06531 | 0.194389 | ||||||||
\(680\) | −7.40581 | −0.284000 | ||||||||
\(681\) | − 23.7439i | − 0.909869i | ||||||||
\(682\) | 4.37867i | 0.167668i | ||||||||
\(683\) | − 27.0164i | − 1.03375i | −0.856060 | − | 0.516877i | \(-0.827095\pi\) | ||||
0.856060 | − | 0.516877i | \(-0.172905\pi\) | |||||||
\(684\) | − 2.93900i | − 0.112376i | ||||||||
\(685\) | 14.1468 | 0.540520 | ||||||||
\(686\) | −19.0911 | −0.728903 | ||||||||
\(687\) | 3.11529i | 0.118856i | ||||||||
\(688\) | 10.4547 | 0.398583 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.80194 | −0.0685986 | ||||||||
\(691\) | − 9.03551i | − 0.343727i | −0.985121 | − | 0.171863i | \(-0.945021\pi\) | ||||
0.985121 | − | 0.171863i | \(-0.0549788\pi\) | |||||||
\(692\) | −8.89440 | −0.338114 | ||||||||
\(693\) | −9.83877 | −0.373744 | ||||||||
\(694\) | − 7.42865i | − 0.281988i | ||||||||
\(695\) | − 7.17629i | − 0.272212i | ||||||||
\(696\) | 8.03684i | 0.304635i | ||||||||
\(697\) | 11.5157i | 0.436189i | ||||||||
\(698\) | −28.7275 | −1.08735 | ||||||||
\(699\) | −12.5603 | −0.475075 | ||||||||
\(700\) | 2.55496i | 0.0965683i | ||||||||
\(701\) | 16.5332 | 0.624450 | 0.312225 | − | 0.950008i | \(-0.398926\pi\) | ||||
0.312225 | + | 0.950008i | \(0.398926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1250 | 0.381871 | ||||||||
\(704\) | − 3.85086i | − 0.145135i | ||||||||
\(705\) | 9.71379 | 0.365843 | ||||||||
\(706\) | −31.2131 | −1.17472 | ||||||||
\(707\) | 8.89605i | 0.334570i | ||||||||
\(708\) | − 11.7845i | − 0.442888i | ||||||||
\(709\) | − 28.4868i | − 1.06984i | −0.844902 | − | 0.534922i | \(-0.820341\pi\) | ||||
0.844902 | − | 0.534922i | \(-0.179659\pi\) | |||||||
\(710\) | 12.0761i | 0.453207i | ||||||||
\(711\) | 8.81700 | 0.330663 | ||||||||
\(712\) | −15.6799 | −0.587631 | ||||||||
\(713\) | − 2.04892i | − 0.0767326i | ||||||||
\(714\) | 18.9215 | 0.708121 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.188374 | 0.00703985 | ||||||||
\(717\) | − 8.52111i | − 0.318227i | ||||||||
\(718\) | −0.0247542 | −0.000923817 0 | ||||||||
\(719\) | 36.4064 | 1.35773 | 0.678865 | − | 0.734263i | \(-0.262472\pi\) | ||||
0.678865 | + | 0.734263i | \(0.262472\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | − 22.1213i | − 0.823839i | ||||||||
\(722\) | 10.3623i | 0.385644i | ||||||||
\(723\) | − 11.6136i | − 0.431913i | ||||||||
\(724\) | 18.1588 | 0.674868 | ||||||||
\(725\) | −8.03684 | −0.298481 | ||||||||
\(726\) | 3.82908i | 0.142111i | ||||||||
\(727\) | −36.1196 | −1.33960 | −0.669801 | − | 0.742541i | \(-0.733621\pi\) | ||||
−0.669801 | + | 0.742541i | \(0.733621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.29590i | 0.0849750i | ||||||||
\(731\) | 77.4258 | 2.86370 | ||||||||
\(732\) | −10.0586 | −0.371777 | ||||||||
\(733\) | − 17.1648i | − 0.633996i | −0.948426 | − | 0.316998i | \(-0.897325\pi\) | ||||
0.948426 | − | 0.316998i | \(-0.102675\pi\) | |||||||
\(734\) | 17.5284i | 0.646985i | ||||||||
\(735\) | 0.472189i | 0.0174170i | ||||||||
\(736\) | 1.80194i | 0.0664203i | ||||||||
\(737\) | 5.24591 | 0.193236 | ||||||||
\(738\) | −1.55496 | −0.0572388 | ||||||||
\(739\) | 21.5821i | 0.793911i | 0.917838 | + | 0.396955i | \(0.129933\pi\) | ||||
−0.917838 | + | 0.396955i | \(0.870067\pi\) | |||||||
\(740\) | 3.44504 | 0.126642 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.8388 | 0.838438 | ||||||||
\(743\) | − 16.6698i | − 0.611555i | −0.952103 | − | 0.305777i | \(-0.901084\pi\) | ||||
0.952103 | − | 0.305777i | \(-0.0989163\pi\) | |||||||
\(744\) | 1.13706 | 0.0416868 | ||||||||
\(745\) | −3.25667 | −0.119315 | ||||||||
\(746\) | − 35.3056i | − 1.29263i | ||||||||
\(747\) | 15.9051i | 0.581939i | ||||||||
\(748\) | − 28.5187i | − 1.04275i | ||||||||
\(749\) | 35.6075i | 1.30107i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −11.8009 | −0.430620 | −0.215310 | − | 0.976546i | \(-0.569076\pi\) | ||||
−0.215310 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(752\) | − 9.71379i | − 0.354226i | ||||||||
\(753\) | 22.7463 | 0.828922 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.137063 | 0.00498825 | ||||||||
\(756\) | 2.55496i | 0.0929229i | ||||||||
\(757\) | 5.44371 | 0.197855 | 0.0989276 | − | 0.995095i | \(-0.468459\pi\) | ||||
0.0989276 | + | 0.995095i | \(0.468459\pi\) | |||||||
\(758\) | 18.2567 | 0.663112 | ||||||||
\(759\) | − 6.93900i | − 0.251870i | ||||||||
\(760\) | − 2.93900i | − 0.106609i | ||||||||
\(761\) | − 20.4064i | − 0.739732i | −0.929085 | − | 0.369866i | \(-0.879404\pi\) | ||||
0.929085 | − | 0.369866i | \(-0.120596\pi\) | |||||||
\(762\) | − 0.499336i | − 0.0180890i | ||||||||
\(763\) | 13.7808 | 0.498897 | ||||||||
\(764\) | −0.469205 | −0.0169752 | ||||||||
\(765\) | − 7.40581i | − 0.267758i | ||||||||
\(766\) | −2.83148 | −0.102305 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 28.4282i | 1.02515i | 0.858644 | + | 0.512573i | \(0.171308\pi\) | ||||
−0.858644 | + | 0.512573i | \(0.828692\pi\) | |||||||
\(770\) | −9.83877 | −0.354565 | ||||||||
\(771\) | 7.39373 | 0.266279 | ||||||||
\(772\) | 17.9312i | 0.645359i | ||||||||
\(773\) | 41.9874i | 1.51018i | 0.655619 | + | 0.755092i | \(0.272408\pi\) | ||||
−0.655619 | + | 0.755092i | \(0.727592\pi\) | |||||||
\(774\) | 10.4547i | 0.375788i | ||||||||
\(775\) | 1.13706i | 0.0408445i | ||||||||
\(776\) | −1.98254 | −0.0711691 | ||||||||
\(777\) | −8.80194 | −0.315768 | ||||||||
\(778\) | − 28.8025i | − 1.03262i | ||||||||
\(779\) | −4.57002 | −0.163738 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.5032 | −1.66401 | ||||||||
\(782\) | 13.3448i | 0.477210i | ||||||||
\(783\) | −8.03684 | −0.287213 | ||||||||
\(784\) | 0.472189 | 0.0168639 | ||||||||
\(785\) | − 4.35152i | − 0.155312i | ||||||||
\(786\) | 1.12498i | 0.0401268i | ||||||||
\(787\) | 11.6950i | 0.416882i | 0.978035 | + | 0.208441i | \(0.0668389\pi\) | ||||
−0.978035 | + | 0.208441i | \(0.933161\pi\) | |||||||
\(788\) | − 8.17390i | − 0.291183i | ||||||||
\(789\) | 11.7735 | 0.419146 | ||||||||
\(790\) | 8.81700 | 0.313695 | ||||||||
\(791\) | 24.1256i | 0.857807i | ||||||||
\(792\) | 3.85086 | 0.136834 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.4306 | −0.760542 | ||||||||
\(795\) | − 8.93900i | − 0.317034i | ||||||||
\(796\) | −23.7536 | −0.841924 | ||||||||
\(797\) | −50.5502 | −1.79058 | −0.895289 | − | 0.445485i | \(-0.853031\pi\) | ||||
−0.895289 | + | 0.445485i | \(0.853031\pi\) | |||||||
\(798\) | 7.50902i | 0.265817i | ||||||||
\(799\) | − 71.9385i | − 2.54500i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | − 15.6799i | − 0.554023i | ||||||||
\(802\) | −19.5284 | −0.689572 | ||||||||
\(803\) | −8.84117 | −0.311998 | ||||||||
\(804\) | − 1.36227i | − 0.0480437i | ||||||||
\(805\) | 4.60388 | 0.162265 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.8810 | 0.805449 | ||||||||
\(808\) | − 3.48188i | − 0.122492i | ||||||||
\(809\) | −19.3134 | −0.679021 | −0.339511 | − | 0.940602i | \(-0.610261\pi\) | ||||
−0.339511 | + | 0.940602i | \(0.610261\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 1.06638i | − 0.0374455i | −0.999825 | − | 0.0187228i | \(-0.994040\pi\) | ||||
0.999825 | − | 0.0187228i | \(-0.00595999\pi\) | |||||||
\(812\) | − 20.5338i | − 0.720594i | ||||||||
\(813\) | − 2.13036i | − 0.0747149i | ||||||||
\(814\) | 13.2664i | 0.464986i | ||||||||
\(815\) | 11.6189 | 0.406994 | ||||||||
\(816\) | −7.40581 | −0.259255 | ||||||||
\(817\) | 30.7265i | 1.07498i | ||||||||
\(818\) | 30.2707 | 1.05839 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.55496 | −0.0543015 | ||||||||
\(821\) | 3.22760i | 0.112644i | 0.998413 | + | 0.0563220i | \(0.0179374\pi\) | ||||
−0.998413 | + | 0.0563220i | \(0.982063\pi\) | |||||||
\(822\) | 14.1468 | 0.493425 | ||||||||
\(823\) | 29.0017 | 1.01093 | 0.505467 | − | 0.862846i | \(-0.331320\pi\) | ||||
0.505467 | + | 0.862846i | \(0.331320\pi\) | |||||||
\(824\) | 8.65817i | 0.301622i | ||||||||
\(825\) | 3.85086i | 0.134070i | ||||||||
\(826\) | 30.1089i | 1.04762i | ||||||||
\(827\) | 17.9414i | 0.623883i | 0.950101 | + | 0.311942i | \(0.100979\pi\) | ||||
−0.950101 | + | 0.311942i | \(0.899021\pi\) | |||||||
\(828\) | −1.80194 | −0.0626217 | ||||||||
\(829\) | 18.9903 | 0.659561 | 0.329780 | − | 0.944058i | \(-0.393025\pi\) | ||||
0.329780 | + | 0.944058i | \(0.393025\pi\) | |||||||
\(830\) | 15.9051i | 0.552076i | ||||||||
\(831\) | −14.7084 | −0.510229 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.49694 | 0.121162 | ||||||||
\(834\) | − 7.17629i | − 0.248495i | ||||||||
\(835\) | 20.8146 | 0.720319 | ||||||||
\(836\) | 11.3177 | 0.391430 | ||||||||
\(837\) | 1.13706i | 0.0393027i | ||||||||
\(838\) | − 24.4873i | − 0.845898i | ||||||||
\(839\) | 36.8189i | 1.27113i | 0.772047 | + | 0.635565i | \(0.219233\pi\) | ||||
−0.772047 | + | 0.635565i | \(0.780767\pi\) | |||||||
\(840\) | 2.55496i | 0.0881544i | ||||||||
\(841\) | 35.5907 | 1.22727 | ||||||||
\(842\) | −8.90408 | −0.306855 | ||||||||
\(843\) | 12.5942i | 0.433767i | ||||||||
\(844\) | −24.2392 | −0.834348 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.71379 | 0.333967 | ||||||||
\(847\) | − 9.78315i | − 0.336153i | ||||||||
\(848\) | −8.93900 | −0.306967 | ||||||||
\(849\) | −1.62565 | −0.0557920 | ||||||||
\(850\) | − 7.40581i | − 0.254017i | ||||||||
\(851\) | − 6.20775i | − 0.212799i | ||||||||
\(852\) | 12.0761i | 0.413719i | ||||||||
\(853\) | − 14.6746i | − 0.502447i | −0.967929 | − | 0.251224i | \(-0.919167\pi\) | ||||
0.967929 | − | 0.251224i | \(-0.0808330\pi\) | |||||||
\(854\) | 25.6993 | 0.879413 | ||||||||
\(855\) | 2.93900 | 0.100512 | ||||||||
\(856\) | − 13.9366i | − 0.476343i | ||||||||
\(857\) | 14.2784 | 0.487742 | 0.243871 | − | 0.969808i | \(-0.421583\pi\) | ||||
0.243871 | + | 0.969808i | \(0.421583\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3593 | 0.387574 | 0.193787 | − | 0.981044i | \(-0.437923\pi\) | ||||
0.193787 | + | 0.981044i | \(0.437923\pi\) | |||||||
\(860\) | 10.4547i | 0.356503i | ||||||||
\(861\) | 3.97285 | 0.135394 | ||||||||
\(862\) | 1.48619 | 0.0506198 | ||||||||
\(863\) | 26.7041i | 0.909018i | 0.890742 | + | 0.454509i | \(0.150185\pi\) | ||||
−0.890742 | + | 0.454509i | \(0.849815\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 8.89440i | − 0.302419i | ||||||||
\(866\) | − 18.5719i | − 0.631100i | ||||||||
\(867\) | −37.8461 | −1.28532 | ||||||||
\(868\) | −2.90515 | −0.0986072 | ||||||||
\(869\) | 33.9530i | 1.15178i | ||||||||
\(870\) | −8.03684 | −0.272474 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.39373 | −0.182655 | ||||||||
\(873\) | − 1.98254i | − 0.0670989i | ||||||||
\(874\) | −5.29590 | −0.179136 | ||||||||
\(875\) | −2.55496 | −0.0863733 | ||||||||
\(876\) | 2.29590i | 0.0775712i | ||||||||
\(877\) | 12.7041i | 0.428987i | 0.976725 | + | 0.214494i | \(0.0688101\pi\) | ||||
−0.976725 | + | 0.214494i | \(0.931190\pi\) | |||||||
\(878\) | − 0.532123i | − 0.0179583i | ||||||||
\(879\) | 13.0664i | 0.440718i | ||||||||
\(880\) | 3.85086 | 0.129812 | ||||||||
\(881\) | −52.1342 | −1.75645 | −0.878223 | − | 0.478252i | \(-0.841271\pi\) | ||||
−0.878223 | + | 0.478252i | \(0.841271\pi\) | |||||||
\(882\) | 0.472189i | 0.0158994i | ||||||||
\(883\) | −6.17390 | −0.207768 | −0.103884 | − | 0.994589i | \(-0.533127\pi\) | ||||
−0.103884 | + | 0.994589i | \(0.533127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.7845 | 0.396131 | ||||||||
\(886\) | 25.5230i | 0.857463i | ||||||||
\(887\) | 0.0978347 | 0.00328497 | 0.00164248 | − | 0.999999i | \(-0.499477\pi\) | ||||
0.00164248 | + | 0.999999i | \(0.499477\pi\) | |||||||
\(888\) | 3.44504 | 0.115608 | ||||||||
\(889\) | 1.27578i | 0.0427884i | ||||||||
\(890\) | − 15.6799i | − 0.525593i | ||||||||
\(891\) | 3.85086i | 0.129008i | ||||||||
\(892\) | − 22.5579i | − 0.755296i | ||||||||
\(893\) | 28.5488 | 0.955351 | ||||||||
\(894\) | −3.25667 | −0.108919 | ||||||||
\(895\) | 0.188374i | 0.00629663i | ||||||||
\(896\) | 2.55496 | 0.0853552 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.7730 | 1.36061 | ||||||||
\(899\) | − 9.13839i | − 0.304782i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −66.2006 | −2.20546 | ||||||||
\(902\) | − 5.98792i | − 0.199376i | ||||||||
\(903\) | − 26.7114i | − 0.888900i | ||||||||
\(904\) | − 9.44265i | − 0.314058i | ||||||||
\(905\) | 18.1588i | 0.603620i | ||||||||
\(906\) | 0.137063 | 0.00455362 | ||||||||
\(907\) | 6.44265 | 0.213925 | 0.106962 | − | 0.994263i | \(-0.465888\pi\) | ||||
0.106962 | + | 0.994263i | \(0.465888\pi\) | |||||||
\(908\) | − 23.7439i | − 0.787970i | ||||||||
\(909\) | 3.48188 | 0.115487 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0965 | 1.06340 | 0.531702 | − | 0.846931i | \(-0.321553\pi\) | ||||
0.531702 | + | 0.846931i | \(0.321553\pi\) | |||||||
\(912\) | − 2.93900i | − 0.0973201i | ||||||||
\(913\) | −61.2484 | −2.02703 | ||||||||
\(914\) | −15.1511 | −0.501153 | ||||||||
\(915\) | − 10.0586i | − 0.332527i | ||||||||
\(916\) | 3.11529i | 0.102932i | ||||||||
\(917\) | − 2.87428i | − 0.0949171i | ||||||||
\(918\) | − 7.40581i | − 0.244428i | ||||||||
\(919\) | 14.1062 | 0.465320 | 0.232660 | − | 0.972558i | \(-0.425257\pi\) | ||||
0.232660 | + | 0.972558i | \(0.425257\pi\) | |||||||
\(920\) | −1.80194 | −0.0594081 | ||||||||
\(921\) | 26.2489i | 0.864931i | ||||||||
\(922\) | −19.5743 | −0.644646 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −9.83877 | −0.323672 | ||||||||
\(925\) | 3.44504i | 0.113272i | ||||||||
\(926\) | −31.2905 | −1.02827 | ||||||||
\(927\) | −8.65817 | −0.284372 | ||||||||
\(928\) | 8.03684i | 0.263822i | ||||||||
\(929\) | 31.4959i | 1.03335i | 0.856183 | + | 0.516673i | \(0.172830\pi\) | ||||
−0.856183 | + | 0.516673i | \(0.827170\pi\) | |||||||
\(930\) | 1.13706i | 0.0372858i | ||||||||
\(931\) | 1.38776i | 0.0454821i | ||||||||
\(932\) | −12.5603 | −0.411427 | ||||||||
\(933\) | 27.1250 | 0.888032 | ||||||||
\(934\) | 32.3032i | 1.05699i | ||||||||
\(935\) | 28.5187 | 0.932662 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.0592 | −0.328620 | −0.164310 | − | 0.986409i | \(-0.552540\pi\) | ||||
−0.164310 | + | 0.986409i | \(0.552540\pi\) | |||||||
\(938\) | 3.48055i | 0.113644i | ||||||||
\(939\) | −19.1323 | −0.624358 | ||||||||
\(940\) | 9.71379 | 0.316829 | ||||||||
\(941\) | − 20.7802i | − 0.677414i | −0.940892 | − | 0.338707i | \(-0.890010\pi\) | ||||
0.940892 | − | 0.338707i | \(-0.109990\pi\) | |||||||
\(942\) | − 4.35152i | − 0.141780i | ||||||||
\(943\) | 2.80194i | 0.0912436i | ||||||||
\(944\) | − 11.7845i | − 0.383552i | ||||||||
\(945\) | −2.55496 | −0.0831128 | ||||||||
\(946\) | −40.2597 | −1.30895 | ||||||||
\(947\) | 41.0307i | 1.33332i | 0.745362 | + | 0.666660i | \(0.232277\pi\) | ||||
−0.745362 | + | 0.666660i | \(0.767723\pi\) | |||||||
\(948\) | 8.81700 | 0.286363 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.93900 | 0.0953538 | ||||||||
\(951\) | − 6.67456i | − 0.216438i | ||||||||
\(952\) | 18.9215 | 0.613251 | ||||||||
\(953\) | 56.3484 | 1.82530 | 0.912652 | − | 0.408738i | \(-0.134031\pi\) | ||||
0.912652 | + | 0.408738i | \(0.134031\pi\) | |||||||
\(954\) | − 8.93900i | − 0.289411i | ||||||||
\(955\) | − 0.469205i | − 0.0151831i | ||||||||
\(956\) | − 8.52111i | − 0.275592i | ||||||||
\(957\) | − 30.9487i | − 1.00043i | ||||||||
\(958\) | 9.32842 | 0.301388 | ||||||||
\(959\) | −36.1444 | −1.16716 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 29.7071 | 0.958293 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.9366 | 0.449101 | ||||||||
\(964\) | − 11.6136i | − 0.374048i | ||||||||
\(965\) | −17.9312 | −0.577227 | ||||||||
\(966\) | 4.60388 | 0.148127 | ||||||||
\(967\) | − 9.63102i | − 0.309713i | −0.987937 | − | 0.154856i | \(-0.950509\pi\) | ||||
0.987937 | − | 0.154856i | \(-0.0494915\pi\) | |||||||
\(968\) | 3.82908i | 0.123071i | ||||||||
\(969\) | − 21.7657i | − 0.699215i | ||||||||
\(970\) | − 1.98254i | − 0.0636556i | ||||||||
\(971\) | 4.72050 | 0.151488 | 0.0757440 | − | 0.997127i | \(-0.475867\pi\) | ||||
0.0757440 | + | 0.997127i | \(0.475867\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 18.3351i | 0.587797i | ||||||||
\(974\) | 10.6571 | 0.341476 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0586 | −0.321968 | ||||||||
\(977\) | 2.75063i | 0.0880004i | 0.999032 | + | 0.0440002i | \(0.0140102\pi\) | ||||
−0.999032 | + | 0.0440002i | \(0.985990\pi\) | |||||||
\(978\) | 11.6189 | 0.371533 | ||||||||
\(979\) | 60.3812 | 1.92979 | ||||||||
\(980\) | 0.472189i | 0.0150835i | ||||||||
\(981\) | − 5.39373i | − 0.172209i | ||||||||
\(982\) | − 40.8611i | − 1.30393i | ||||||||
\(983\) | 7.87907i | 0.251303i | 0.992074 | + | 0.125652i | \(0.0401021\pi\) | ||||
−0.992074 | + | 0.125652i | \(0.959898\pi\) | |||||||
\(984\) | −1.55496 | −0.0495703 | ||||||||
\(985\) | 8.17390 | 0.260442 | ||||||||
\(986\) | 59.5193i | 1.89548i | ||||||||
\(987\) | −24.8183 | −0.789976 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.8388 | 0.599038 | ||||||||
\(990\) | 3.85086i | 0.122388i | ||||||||
\(991\) | 13.3609 | 0.424424 | 0.212212 | − | 0.977224i | \(-0.431933\pi\) | ||||
0.212212 | + | 0.977224i | \(0.431933\pi\) | |||||||
\(992\) | 1.13706 | 0.0361018 | ||||||||
\(993\) | 18.1360i | 0.575529i | ||||||||
\(994\) | − 30.8538i | − 0.978624i | ||||||||
\(995\) | − 23.7536i | − 0.753040i | ||||||||
\(996\) | 15.9051i | 0.503974i | ||||||||
\(997\) | 47.1554 | 1.49343 | 0.746713 | − | 0.665147i | \(-0.231631\pi\) | ||||
0.746713 | + | 0.665147i | \(0.231631\pi\) | |||||||
\(998\) | 19.0556 | 0.603195 | ||||||||
\(999\) | 3.44504i | 0.108996i |
(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 | 5070.2.b.v.1351.5 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bs.1.2 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bl.1.2 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.v.1351.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bl.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bs.1.2 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.v.1351.2 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.v.1351.5 | 6 | 1.1 | even | 1 | trivial |