Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(289,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bo (of order \(9\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(-0.766044 + 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.769 |
Dual form | 912.2.bo.f.625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.766044 | − | 0.642788i | 0.442276 | − | 0.371114i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.20574 | + | 1.16679i | 1.43365 | + | 0.521806i | 0.937975 | − | 0.346703i | \(-0.112699\pi\) |
0.495674 | + | 0.868509i | \(0.334921\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.43969 | + | 2.49362i | −0.544153 | + | 0.942500i | 0.454507 | + | 0.890743i | \(0.349815\pi\) |
−0.998660 | + | 0.0517569i | \(0.983518\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.173648 | − | 0.984808i | 0.0578827 | − | 0.328269i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.173648 | − | 0.300767i | −0.0523569 | − | 0.0906848i | 0.838659 | − | 0.544657i | \(-0.183340\pi\) |
−0.891016 | + | 0.453972i | \(0.850007\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26604 | − | 1.06234i | −0.351138 | − | 0.294639i | 0.450109 | − | 0.892974i | \(-0.351385\pi\) |
−0.801247 | + | 0.598334i | \(0.795830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.20574 | − | 1.16679i | 0.827718 | − | 0.301265i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.20574 | + | 6.83807i | 0.292434 | + | 1.65848i | 0.677452 | + | 0.735567i | \(0.263084\pi\) |
−0.385017 | + | 0.922909i | \(0.625805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82635 | + | 3.31839i | 0.648410 | + | 0.761292i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.83564i | 0.109109 | + | 0.618788i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.39053 | − | 2.32596i | 1.33252 | − | 0.484997i | 0.425069 | − | 0.905161i | \(-0.360250\pi\) |
0.907448 | + | 0.420164i | \(0.138027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.08512 | + | 4.26692i | 1.01702 | + | 0.853385i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | − | 0.866025i | −0.0962250 | − | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.10354 | − | 6.25849i | 0.204922 | − | 1.16217i | −0.692640 | − | 0.721284i | \(-0.743552\pi\) |
0.897562 | − | 0.440888i | \(-0.145337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.798133 | − | 1.38241i | 0.143349 | − | 0.248288i | −0.785407 | − | 0.618980i | \(-0.787546\pi\) |
0.928756 | + | 0.370692i | \(0.120880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.326352 | − | 0.118782i | −0.0568106 | − | 0.0206774i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.52481 | + | 6.31407i | −1.27193 | + | 1.06727i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.2121 | −1.84326 | −0.921632 | − | 0.388066i | \(-0.873143\pi\) | ||||
−0.921632 | + | 0.388066i | \(0.873143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.65270 | −0.264644 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.67365 | + | 2.24346i | −0.417554 | + | 0.350369i | −0.827232 | − | 0.561861i | \(-0.810086\pi\) |
0.409678 | + | 0.912230i | \(0.365641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.14543 | + | 0.780873i | 0.327175 | + | 0.119082i | 0.500385 | − | 0.865803i | \(-0.333192\pi\) |
−0.173210 | + | 0.984885i | \(0.555414\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.70574 | − | 2.95442i | 0.254276 | − | 0.440419i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.971782 | + | 5.51125i | −0.141749 | + | 0.803898i | 0.828171 | + | 0.560475i | \(0.189381\pi\) |
−0.969920 | + | 0.243423i | \(0.921730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.645430 | − | 1.11792i | −0.0922042 | − | 0.159702i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.31908 | + | 4.46324i | 0.744820 | + | 0.624978i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.86097 | + | 0.677337i | −0.255623 | + | 0.0930393i | −0.466653 | − | 0.884440i | \(-0.654540\pi\) |
0.211030 | + | 0.977480i | \(0.432318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.205737 | − | 1.16679i | −0.0277416 | − | 0.157330i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.29813 | + | 0.725293i | 0.569302 | + | 0.0960674i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0773815 | − | 0.438852i | −0.0100742 | − | 0.0571337i | 0.979356 | − | 0.202142i | \(-0.0647902\pi\) |
−0.989430 | + | 0.145008i | \(0.953679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7763 | − | 4.28623i | 1.50780 | − | 0.548795i | 0.549735 | − | 0.835339i | \(-0.314729\pi\) |
0.958067 | + | 0.286544i | \(0.0925064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.20574 | + | 1.85083i | 0.277897 | + | 0.233183i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.81908 | − | 4.88279i | −0.349664 | − | 0.605635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.187319 | − | 1.06234i | 0.0228846 | − | 0.129785i | −0.971225 | − | 0.238163i | \(-0.923455\pi\) |
0.994110 | + | 0.108378i | \(0.0345657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.40033 | − | 5.88954i | 0.409352 | − | 0.709018i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.6211 | − | 5.68561i | −1.85388 | − | 0.674758i | −0.983095 | − | 0.183096i | \(-0.941388\pi\) |
−0.870786 | − | 0.491662i | \(-0.836390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.51367 | − | 7.98292i | 1.11349 | − | 0.934330i | 0.115233 | − | 0.993338i | \(-0.463238\pi\) |
0.998257 | + | 0.0590086i | \(0.0187939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.63816 | 0.766508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.36824 | − | 7.02179i | 0.941501 | − | 0.790013i | −0.0363452 | − | 0.999339i | \(-0.511572\pi\) |
0.977846 | + | 0.209326i | \(0.0671271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.939693 | − | 0.342020i | −0.104410 | − | 0.0380022i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.85844 | − | 10.1471i | 0.643047 | − | 1.11379i | −0.341701 | − | 0.939809i | \(-0.611003\pi\) |
0.984749 | − | 0.173982i | \(-0.0556635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.11334 | + | 23.3279i | −0.446154 | + | 2.53027i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.17752 | − | 5.50362i | −0.340666 | − | 0.590050i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.37346 | + | 1.15247i | 0.145586 | + | 0.122161i | 0.712672 | − | 0.701497i | \(-0.247485\pi\) |
−0.567086 | + | 0.823659i | \(0.691929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47178 | − | 1.62760i | 0.468770 | − | 0.170618i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.277189 | − | 1.57202i | −0.0287431 | − | 0.163010i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.18866 | + | 13.9357i | 0.532346 | + | 1.42977i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.634285 | + | 3.59721i | 0.0644019 | + | 0.365241i | 0.999928 | + | 0.0119843i | \(0.00381481\pi\) |
−0.935526 | + | 0.353257i | \(0.885074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.326352 | + | 0.118782i | −0.0327996 | + | 0.0119381i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.58899 | − | 6.36792i | −0.755133 | − | 0.633632i | 0.181722 | − | 0.983350i | \(-0.441833\pi\) |
−0.936855 | + | 0.349718i | \(0.886277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.92262 | + | 6.79417i | 0.386507 | + | 0.669450i | 0.991977 | − | 0.126418i | \(-0.0403481\pi\) |
−0.605470 | + | 0.795868i | \(0.707015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.70574 | + | 9.67372i | −0.166463 | + | 0.944058i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0136706 | + | 0.0236781i | −0.00132158 | + | 0.00228905i | −0.866685 | − | 0.498855i | \(-0.833754\pi\) |
0.865364 | + | 0.501144i | \(0.167087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1236 | + | 3.68469i | 0.969666 | + | 0.352929i | 0.777814 | − | 0.628494i | \(-0.216329\pi\) |
0.191852 | + | 0.981424i | \(0.438551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.58899 | + | 7.20702i | −0.815231 | + | 0.684060i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6604 | −1.09692 | −0.548461 | − | 0.836176i | \(-0.684786\pi\) | ||||
−0.548461 | + | 0.836176i | \(0.684786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.2003 | 2.16344 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.26604 | + | 1.06234i | −0.117046 | + | 0.0982131i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.7875 | − | 6.83807i | −1.72224 | − | 0.626845i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.43969 | − | 9.42182i | 0.494518 | − | 0.856529i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.606067 | + | 3.43718i | −0.0546472 | + | 0.309920i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.79426 | + | 4.83981i | 0.249926 | + | 0.432885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4192 | − | 10.4210i | −1.10203 | − | 0.924711i | −0.104467 | − | 0.994528i | \(-0.533314\pi\) |
−0.997560 | + | 0.0698178i | \(0.977758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.14543 | − | 0.780873i | 0.188895 | − | 0.0687520i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.486329 | + | 2.75811i | 0.0424908 | + | 0.240977i | 0.998655 | − | 0.0518550i | \(-0.0165134\pi\) |
−0.956164 | + | 0.292832i | \(0.905402\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.3439 | + | 2.27038i | −1.07035 | + | 0.196867i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.592396 | − | 3.35965i | −0.0509854 | − | 0.289152i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0680 | + | 5.48432i | −1.28735 | + | 0.468557i | −0.892856 | − | 0.450341i | \(-0.851302\pi\) |
−0.394494 | + | 0.918899i | \(0.629080\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.59240 | + | 1.33618i | 0.135065 | + | 0.113333i | 0.707818 | − | 0.706395i | \(-0.249680\pi\) |
−0.572752 | + | 0.819728i | \(0.694124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.79813 | + | 4.84651i | 0.235645 | + | 0.408150i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0996702 | + | 0.565258i | −0.00833484 | + | 0.0472692i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8400 | − | 18.7755i | 0.900215 | − | 1.55922i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.21301 | − | 0.441500i | −0.100047 | − | 0.0364143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.27719 | + | 1.07169i | −0.104631 | + | 0.0877962i | −0.693603 | − | 0.720358i | \(-0.743978\pi\) |
0.588971 | + | 0.808154i | \(0.299533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0523 | −1.63183 | −0.815917 | − | 0.578169i | \(-0.803768\pi\) | ||||
−0.815917 | + | 0.578169i | \(0.803768\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.94356 | 0.561354 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.17159 | − | 3.50038i | 0.335070 | − | 0.281157i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85117 | + | 1.40171i | 0.307357 | + | 0.111869i | 0.491094 | − | 0.871107i | \(-0.336597\pi\) |
−0.183737 | + | 0.982975i | \(0.558820\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.990200 | + | 1.71508i | −0.0785280 | + | 0.136014i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.40033 | + | 19.2842i | −0.267984 | + | 1.51981i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.06758 | − | 7.04526i | −0.318598 | − | 0.551827i | 0.661598 | − | 0.749859i | \(-0.269879\pi\) |
−0.980196 | + | 0.198031i | \(0.936545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.907604 | − | 0.761570i | −0.0706569 | − | 0.0592881i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5890 | + | 4.58202i | −0.974166 | + | 0.354567i | −0.779569 | − | 0.626316i | \(-0.784562\pi\) |
−0.194596 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.78312 | − | 10.1126i | −0.137163 | − | 0.777890i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.75877 | − | 2.20718i | 0.287440 | − | 0.168787i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.177519 | − | 1.00676i | −0.0134965 | − | 0.0765424i | 0.977316 | − | 0.211788i | \(-0.0679287\pi\) |
−0.990812 | + | 0.135246i | \(0.956818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.9611 | + | 6.53731i | −1.35773 | + | 0.494174i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.341367 | − | 0.286441i | −0.0256587 | − | 0.0215302i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.01754 | + | 1.76243i | 0.0760546 | + | 0.131730i | 0.901544 | − | 0.432687i | \(-0.142434\pi\) |
−0.825490 | + | 0.564417i | \(0.809101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.87299 | − | 21.9648i | 0.287877 | − | 1.63263i | −0.406947 | − | 0.913452i | \(-0.633407\pi\) |
0.694824 | − | 0.719180i | \(-0.255482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.26604 | − | 10.8531i | 0.463199 | − | 0.802285i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35.9432 | − | 13.0822i | −2.64259 | − | 0.961825i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.84730 | − | 1.55007i | 0.135088 | − | 0.113352i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.87939 | 0.209444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.7861 | −0.780456 | −0.390228 | − | 0.920718i | \(-0.627604\pi\) | ||||
−0.390228 | + | 0.920718i | \(0.627604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.19459 | + | 1.84148i | −0.157970 | + | 0.132553i | −0.718347 | − | 0.695685i | \(-0.755101\pi\) |
0.560377 | + | 0.828238i | \(0.310656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.29813 | − | 1.92836i | −0.379407 | − | 0.138093i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.16772 | − | 7.21870i | 0.296938 | − | 0.514311i | −0.678496 | − | 0.734604i | \(-0.737368\pi\) |
0.975434 | + | 0.220293i | \(0.0707013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.526874 | − | 2.98805i | 0.0373491 | − | 0.211817i | −0.960422 | − | 0.278550i | \(-0.910146\pi\) |
0.997771 | + | 0.0667324i | \(0.0212574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.539363 | − | 0.934204i | −0.0380437 | − | 0.0658937i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0175 | + | 11.7621i | 0.983839 | + | 0.825539i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1887 | + | 4.07234i | −0.781450 | + | 0.284425i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.18092 | − | 6.69734i | −0.0820798 | − | 0.465497i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.507274 | − | 1.42631i | 0.0350889 | − | 0.0986598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.88919 | + | 16.3854i | 0.198900 | + | 1.12802i | 0.906755 | + | 0.421659i | \(0.138552\pi\) |
−0.707855 | + | 0.706358i | \(0.750337\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.6211 | + | 5.68561i | −1.07034 | + | 0.389571i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.96657 | + | 5.00654i | 0.406916 | + | 0.341443i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.29813 | + | 3.98048i | 0.156007 | + | 0.270213i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.15657 | − | 12.2305i | 0.145728 | − | 0.826463i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.73783 | − | 9.93821i | 0.385968 | − | 0.668516i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.67752 | − | 2.79439i | −0.514125 | − | 0.187126i | 0.0719114 | − | 0.997411i | \(-0.477090\pi\) |
−0.586036 | + | 0.810285i | \(0.699312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.08512 | − | 4.26692i | 0.339008 | − | 0.284462i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.80066 | −0.119514 | −0.0597570 | − | 0.998213i | \(-0.519033\pi\) | ||||
−0.0597570 | + | 0.998213i | \(0.519033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7392 | −1.23832 | −0.619160 | − | 0.785265i | \(-0.712527\pi\) | ||||
−0.619160 | + | 0.785265i | \(0.712527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.766044 | − | 0.642788i | 0.0504020 | − | 0.0422923i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.85117 | + | 1.40171i | 0.252298 | + | 0.0918291i | 0.465073 | − | 0.885272i | \(-0.346028\pi\) |
−0.212775 | + | 0.977101i | \(0.568250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.54576 | + | 16.5337i | −0.622697 | + | 1.07854i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.89693 | − | 10.7580i | 0.123219 | − | 0.698807i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1138 | − | 24.4458i | −0.912946 | − | 1.58127i | −0.809881 | − | 0.586595i | \(-0.800468\pi\) |
−0.103066 | − | 0.994675i | \(-0.532865\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.02687 | + | 4.21805i | 0.323809 | + | 0.271708i | 0.790172 | − | 0.612885i | \(-0.209991\pi\) |
−0.466362 | + | 0.884594i | \(0.654436\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.939693 | + | 0.342020i | −0.0602813 | + | 0.0219406i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.764700 | − | 4.33683i | −0.0488549 | − | 0.277070i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0530334 | − | 7.20377i | −0.00337444 | − | 0.458365i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.03462 | − | 11.5389i | −0.128938 | − | 0.731247i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.35756 | − | 3.04190i | 0.527525 | − | 0.192003i | −0.0645080 | − | 0.997917i | \(-0.520548\pi\) |
0.592033 | + | 0.805914i | \(0.298326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80928 | − | 1.51816i | −0.113748 | − | 0.0954462i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.8439 | + | 20.5142i | 0.741693 | + | 1.28465i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.33837 | + | 13.2616i | −0.145864 | + | 0.827234i | 0.820806 | + | 0.571207i | \(0.193525\pi\) |
−0.966670 | + | 0.256027i | \(0.917586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.1420 | − | 27.9588i | 1.00302 | − | 1.73728i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.97178 | − | 2.17355i | −0.369644 | − | 0.134539i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8327 | − | 10.7680i | 0.791301 | − | 0.663981i | −0.154766 | − | 0.987951i | \(-0.549462\pi\) |
0.946067 | + | 0.323971i | \(0.105018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.75608 | −0.415023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.79292 | 0.109725 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.74969 | − | 2.30726i | 0.167651 | − | 0.140676i | −0.555102 | − | 0.831782i | \(-0.687321\pi\) |
0.722753 | + | 0.691106i | \(0.242876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5141 | + | 8.19448i | 1.36764 | + | 0.497779i | 0.918407 | − | 0.395637i | \(-0.129476\pi\) |
0.449230 | + | 0.893416i | \(0.351699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.37939 | − | 4.12122i | 0.144007 | − | 0.249427i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.400330 | − | 2.27038i | 0.0241408 | − | 0.136909i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.36097 | + | 16.2137i | 0.562446 | + | 0.974185i | 0.997282 | + | 0.0736755i | \(0.0234729\pi\) |
−0.434836 | + | 0.900510i | \(0.643194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.22281 | − | 1.02606i | −0.0732078 | − | 0.0614286i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.99660 | − | 3.63846i | 0.596347 | − | 0.217053i | −0.0261718 | − | 0.999657i | \(-0.508332\pi\) |
0.622519 | + | 0.782605i | \(0.286109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.43330 | + | 13.7999i | 0.144644 | + | 0.820319i | 0.967652 | + | 0.252289i | \(0.0811833\pi\) |
−0.823008 | + | 0.568030i | \(0.807706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.9324 | + | 7.34013i | 0.766050 | + | 0.434792i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.74510 | − | 9.89695i | −0.103010 | − | 0.584199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.3307 | + | 10.6755i | −1.72533 | + | 0.627970i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.79813 | + | 2.34791i | 0.164029 | + | 0.137637i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.76011 | + | 9.97681i | 0.336509 | + | 0.582852i | 0.983774 | − | 0.179414i | \(-0.0574202\pi\) |
−0.647264 | + | 0.762266i | \(0.724087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.263985 | − | 1.49713i | 0.0153698 | − | 0.0871665i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.173648 | + | 0.300767i | −0.0100761 | + | 0.0174523i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5617 | − | 3.84413i | −0.610796 | − | 0.222312i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.03596 | + | 4.22567i | −0.290268 | + | 0.243564i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.90673 | −0.569127 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.7529 | 2.44802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.29220 | + | 2.76249i | −0.187896 | + | 0.157663i | −0.731883 | − | 0.681430i | \(-0.761358\pi\) |
0.543987 | + | 0.839093i | \(0.316914\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.37211 | + | 2.68323i | 0.419385 | + | 0.152644i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4966 | + | 19.9127i | −0.651912 | + | 1.12915i | 0.330746 | + | 0.943720i | \(0.392700\pi\) |
−0.982658 | + | 0.185425i | \(0.940634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.59926 | + | 9.06985i | −0.0903955 | + | 0.512658i | 0.905666 | + | 0.423992i | \(0.139372\pi\) |
−0.996061 | + | 0.0886663i | \(0.971740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.91147 | + | 8.50692i | 0.276730 | + | 0.479311i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.57011 | + | 2.15658i | 0.144352 | + | 0.121125i | 0.712104 | − | 0.702074i | \(-0.247742\pi\) |
−0.567752 | + | 0.823199i | \(0.692187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.07398 | + | 0.754866i | −0.116120 | + | 0.0422644i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.00474774 | + | 0.0269258i | 0.000264993 | + | 0.00150285i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.2836 | + | 23.3279i | −1.07297 | + | 1.29800i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.90508 | − | 10.8042i | −0.105675 | − | 0.599311i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.1236 | − | 3.68469i | 0.559837 | − | 0.203764i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3439 | − | 10.3578i | −0.680541 | − | 0.571042i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0371 | − | 19.1169i | −0.606656 | − | 1.05076i | −0.991787 | − | 0.127897i | \(-0.959177\pi\) |
0.385131 | − | 0.922862i | \(-0.374156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.94697 | + | 11.0418i | −0.106693 | + | 0.605087i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.84002 | − | 3.18701i | 0.100531 | − | 0.174125i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3255 | + | 4.48611i | 0.671411 | + | 0.244374i | 0.655155 | − | 0.755494i | \(-0.272603\pi\) |
0.0162559 | + | 0.999868i | \(0.494825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.93242 | + | 7.49519i | −0.485142 | + | 0.407083i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.554378 | −0.0300212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4388 | −0.887613 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.7724 | − | 14.9128i | 0.956836 | − | 0.802881i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.23055 | + | 2.99568i | 0.441839 | + | 0.160816i | 0.553354 | − | 0.832947i | \(-0.313348\pi\) |
−0.111514 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.63176 | + | 2.82629i | −0.0873461 | + | 0.151288i | −0.906389 | − | 0.422445i | \(-0.861172\pi\) |
0.819042 | + | 0.573733i | \(0.194505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.286989 | + | 1.62760i | −0.0153183 | + | 0.0868746i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.5419 | − | 25.1873i | −0.773987 | − | 1.34058i | −0.935362 | − | 0.353691i | \(-0.884926\pi\) |
0.161376 | − | 0.986893i | \(-0.448407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.4432 | − | 36.4531i | −2.30572 | − | 1.93473i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.7875 | + | 6.83807i | −0.994338 | + | 0.361909i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.14796 | − | 6.51038i | −0.0605868 | − | 0.343605i | −1.00000 | 0.000817017i | \(-0.999740\pi\) | |
0.939413 | − | 0.342788i | \(-0.111371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.02347 | + | 18.7579i | −0.159130 | + | 0.987258i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.88919 | − | 10.7141i | −0.0991565 | − | 0.562345i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.8127 | − | 14.4907i | 2.08389 | − | 0.758475i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.43969 | + | 3.72534i | 0.231750 | + | 0.194461i | 0.751266 | − | 0.659999i | \(-0.229443\pi\) |
−0.519516 | + | 0.854461i | \(0.673888\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.74510 | + | 3.02260i | 0.0908463 | + | 0.157350i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.990200 | − | 5.61570i | 0.0514086 | − | 0.291553i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9449 | − | 22.4212i | 0.670262 | − | 1.16093i | −0.307568 | − | 0.951526i | \(-0.599515\pi\) |
0.977830 | − | 0.209401i | \(-0.0671516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.25150 | + | 1.91139i | 0.271186 | + | 0.0987037i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.04576 | + | 6.75119i | −0.414378 | + | 0.347704i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1557 | 0.983962 | 0.491981 | − | 0.870606i | \(-0.336273\pi\) | ||||
0.491981 | + | 0.870606i | \(0.336273\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.2121 | −0.830573 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.42649 | − | 6.23156i | 0.379476 | − | 0.318418i | −0.433021 | − | 0.901384i | \(-0.642552\pi\) |
0.812497 | + | 0.582966i | \(0.198108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.20574 | + | 1.16679i | 0.163379 | + | 0.0594653i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.14156 | − | 1.97724i | 0.0580287 | − | 0.100509i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.142026 | + | 0.805470i | −0.00720101 | + | 0.0408390i | −0.988197 | − | 0.153191i | \(-0.951045\pi\) |
0.980996 | + | 0.194030i | \(0.0621560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6104 | + | 40.8944i | 1.19403 | + | 2.06812i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.14543 | + | 1.80023i | 0.108223 | + | 0.0908096i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.0194 | − | 12.7460i | 1.76201 | − | 0.641321i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.642026 | − | 3.64111i | −0.0322224 | − | 0.182742i | 0.964449 | − | 0.264270i | \(-0.0851311\pi\) |
−0.996671 | + | 0.0815281i | \(0.974020\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.99660 | + | 9.67372i | −0.400331 | + | 0.484292i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.77513 | − | 21.4098i | −0.188521 | − | 1.06916i | −0.921347 | − | 0.388740i | \(-0.872910\pi\) |
0.732827 | − | 0.680416i | \(-0.238201\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.47906 | + | 0.902302i | −0.123491 | + | 0.0449469i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.61334 | − | 2.19285i | −0.129858 | − | 0.108964i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.94697 | + | 3.37225i | 0.0965076 | + | 0.167156i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.704088 | + | 3.99308i | −0.0348149 | + | 0.197445i | −0.997254 | − | 0.0740509i | \(-0.976407\pi\) |
0.962440 | + | 0.271496i | \(0.0875184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.01754 | + | 13.8868i | −0.395476 | + | 0.684985i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.20574 | + | 0.438852i | 0.0593304 | + | 0.0215945i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.6202 | − | 25.6934i | 1.50309 | − | 1.26124i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.07873 | 0.101796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4989 | −1.14800 | −0.573998 | − | 0.818857i | \(-0.694608\pi\) | ||||
−0.573998 | + | 0.818857i | \(0.694608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6748 | + | 14.8309i | −0.861419 | + | 0.722816i | −0.962273 | − | 0.272085i | \(-0.912287\pi\) |
0.100855 | + | 0.994901i | \(0.467842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.25877 | + | 1.91404i | 0.255690 | + | 0.0930636i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.0462 | + | 39.9172i | −1.11791 | + | 1.93627i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.26604 | + | 35.5365i | −0.303235 | + | 1.71973i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.286989 | + | 0.497079i | 0.0138560 | + | 0.0239992i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.69253 | + | 2.25930i | 0.129695 | + | 0.108827i | 0.705328 | − | 0.708881i | \(-0.250800\pi\) |
−0.575633 | + | 0.817708i | \(0.695244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0574 | − | 11.6679i | 1.54058 | − | 0.560725i | 0.574395 | − | 0.818578i | \(-0.305237\pi\) |
0.966184 | + | 0.257853i | \(0.0830152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.76470 | − | 21.3507i | −0.180504 | − | 1.02369i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.7803 | + | 14.6323i | 1.23324 | + | 0.699958i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.68463 | − | 9.55401i | −0.0804030 | − | 0.455988i | −0.998254 | − | 0.0590636i | \(-0.981189\pi\) |
0.917851 | − | 0.396925i | \(-0.129923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.21301 | + | 0.441500i | −0.0577624 | + | 0.0210238i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.6302 | − | 9.75887i | −0.552566 | − | 0.463658i | 0.323243 | − | 0.946316i | \(-0.395227\pi\) |
−0.875809 | + | 0.482658i | \(0.839671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.05825 | + | 5.29704i | 0.144975 | + | 0.251104i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.289515 | + | 1.64192i | −0.0136936 | + | 0.0776603i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.4192 | + | 30.1710i | −0.822064 | + | 1.42386i | 0.0820794 | + | 0.996626i | \(0.473844\pi\) |
−0.904143 | + | 0.427230i | \(0.859489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.13903 | + | 0.414574i | 0.0536350 | + | 0.0195215i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.3610 | + | 12.8894i | −0.721721 | + | 0.605596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.2344 | 0.761081 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.8749 | −1.49105 | −0.745523 | − | 0.666479i | \(-0.767800\pi\) | ||||
−0.745523 | + | 0.666479i | \(0.767800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.31908 | − | 4.46324i | 0.248273 | − | 0.208326i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0449 | + | 3.65604i | 0.467837 | + | 0.170279i | 0.565172 | − | 0.824973i | \(-0.308810\pi\) |
−0.0973354 | + | 0.995252i | \(0.531032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.65910 | − | 13.2660i | 0.355949 | − | 0.616521i | −0.631331 | − | 0.775513i | \(-0.717491\pi\) |
0.987280 | + | 0.158992i | \(0.0508245\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.945622 | − | 5.36289i | 0.0438522 | − | 0.248698i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.2562 | + | 24.6925i | 0.659700 | + | 1.14263i | 0.980693 | + | 0.195553i | \(0.0626501\pi\) |
−0.320993 | + | 0.947082i | \(0.604017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.37939 | + | 1.99654i | 0.109870 | + | 0.0921917i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.85117 | − | 1.40171i | 0.177452 | − | 0.0645874i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.137689 | − | 0.780873i | −0.00633094 | − | 0.0359046i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.213011 | + | 28.9343i | 0.00977362 | + | 1.32760i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.343893 | + | 1.95031i | 0.0157458 | + | 0.0892987i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.56583 | − | 2.75374i | 0.345691 | − | 0.125821i | −0.163339 | − | 0.986570i | \(-0.552226\pi\) |
0.509030 | + | 0.860749i | \(0.330004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1951 | + | 11.9111i | 0.647239 | + | 0.543098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.79086 | + | 16.9583i | 0.445500 | + | 0.771628i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.16385 | + | 12.2718i | −0.0982553 | + | 0.557233i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.05778 | − | 5.29623i | 0.138561 | − | 0.239995i | −0.788391 | − | 0.615175i | \(-0.789086\pi\) |
0.926952 | + | 0.375179i | \(0.122419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.64455 | − | 2.78239i | −0.345699 | − | 0.125824i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3778 | − | 14.5817i | 0.784249 | − | 0.658063i | −0.160066 | − | 0.987106i | \(-0.551171\pi\) |
0.944315 | + | 0.329043i | \(0.106726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.1266 | 1.98736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.18479 | −0.0532525 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.6673 | − | 30.7675i | 1.64475 | − | 1.38011i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.3567 | + | 8.50114i | 1.04559 | + | 0.380563i | 0.806996 | − | 0.590557i | \(-0.201092\pi\) |
0.238593 | + | 0.971120i | \(0.423314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.69846 | + | 11.6021i | −0.299265 | + | 0.518343i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.34524 | + | 24.6431i | −0.193745 | + | 1.09878i | 0.720451 | + | 0.693506i | \(0.243935\pi\) |
−0.914195 | + | 0.405274i | \(0.867176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8983 | − | 29.2687i | −0.751963 | − | 1.30244i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.86618 | − | 6.60051i | −0.349349 | − | 0.293139i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.845075 | + | 0.307582i | −0.0374573 | + | 0.0136333i | −0.360681 | − | 0.932689i | \(-0.617456\pi\) |
0.323224 | + | 0.946323i | \(0.395233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.20961 | + | 35.2164i | 0.274697 | + | 1.55788i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.46064 | − | 4.10689i | 0.0644887 | − | 0.181324i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.64749 | + | 26.3572i | 0.204793 | + | 1.16144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.82635 | − | 0.664738i | 0.0803229 | − | 0.0292351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.783119 | − | 0.657115i | −0.0343751 | − | 0.0288441i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.31773 | + | 5.74648i | 0.145353 | + | 0.251758i | 0.929504 | − | 0.368811i | \(-0.120235\pi\) |
−0.784152 | + | 0.620569i | \(0.786902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.59034 | + | 37.3757i | −0.288175 | + | 1.63432i | 0.405542 | + | 0.914076i | \(0.367083\pi\) |
−0.693718 | + | 0.720247i | \(0.744028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.55690 | + | 16.5530i | −0.417097 | + | 0.722434i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4153 | + | 3.79088i | 0.453700 | + | 0.165133i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8097 | − | 14.9442i | 0.774337 | − | 0.649746i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.445622 | −0.0193384 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.76827 | 0.249851 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0714517 | + | 0.0599551i | −0.00308913 | + | 0.00259209i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.91235 | + | 0.696039i | 0.0825241 | + | 0.0300363i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.224155 | + | 0.388249i | −0.00965506 | + | 0.0167230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.62742 | − | 14.9009i | 0.112962 | − | 0.640638i | −0.874778 | − | 0.484525i | \(-0.838993\pi\) |
0.987739 | − | 0.156113i | \(-0.0498963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.1518 | − | 19.3155i | −0.478571 | − | 0.828909i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.1544 | + | 23.6243i | 1.20600 | + | 1.01195i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.6215 | − | 11.1453i | 1.30928 | − | 0.476540i | 0.409274 | − | 0.912412i | \(-0.365782\pi\) |
0.900009 | + | 0.435872i | \(0.143560\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.17617 | − | 12.3417i | −0.0928769 | − | 0.526731i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.8871 | − | 14.0267i | 1.01763 | − | 0.597558i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.46198 | + | 30.9764i | 0.232267 | + | 1.31725i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.9432 | + | 13.0822i | −1.52570 | + | 0.555310i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.2777 | − | 12.8195i | −0.647335 | − | 0.543179i | 0.258926 | − | 0.965897i | \(-0.416631\pi\) |
−0.906261 | + | 0.422719i | \(0.861076\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.88666 | − | 3.26779i | −0.0797972 | − | 0.138213i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.418748 | − | 2.37484i | 0.0176796 | − | 0.100266i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.98411 | − | 3.43658i | 0.0836202 | − | 0.144834i | −0.821182 | − | 0.570666i | \(-0.806685\pi\) |
0.904802 | + | 0.425832i | \(0.140018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.3803 | − | 13.6053i | −1.57260 | − | 0.572380i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.20574 | − | 1.85083i | 0.0926322 | − | 0.0777277i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.8135 | 0.621012 | 0.310506 | − | 0.950571i | \(-0.399501\pi\) | ||||
0.310506 | + | 0.950571i | \(0.399501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0615 | −0.881396 | −0.440698 | − | 0.897655i | \(-0.645269\pi\) | ||||
−0.440698 | + | 0.897655i | \(0.645269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.26264 | + | 6.93318i | −0.345177 | + | 0.289638i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.4213 | + | 15.4401i | 1.76909 | + | 0.643897i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.1211 | − | 38.3148i | 0.920913 | − | 1.59507i | 0.122907 | − | 0.992418i | \(-0.460778\pi\) |
0.798006 | − | 0.602649i | \(-0.205888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.497474 | + | 2.82131i | −0.0206743 | + | 0.117250i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8687 | + | 29.2175i | 0.699832 | + | 1.21214i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.526874 | + | 0.442100i | 0.0218209 | + | 0.0183099i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.29813 | + | 1.92836i | −0.219051 | + | 0.0797280i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.73689 | − | 9.85041i | −0.0716892 | − | 0.406570i | −0.999443 | − | 0.0333765i | \(-0.989374\pi\) |
0.927754 | − | 0.373193i | \(-0.121737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.84318 | − | 1.25865i | 0.281968 | − | 0.0518617i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44743 | − | 8.20880i | −0.0595395 | − | 0.337665i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.7981 | − | 3.93020i | 0.443426 | − | 0.161394i | −0.110651 | − | 0.993859i | \(-0.535294\pi\) |
0.554077 | + | 0.832465i | \(0.313071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −52.2490 | − | 43.8421i | −2.14200 | − | 1.79735i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.51707 | − | 2.62765i | −0.0620897 | − | 0.107543i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.11422 | + | 6.31905i | −0.0455257 | + | 0.258189i | −0.999073 | − | 0.0430552i | \(-0.986291\pi\) |
0.953547 | + | 0.301244i | \(0.0974020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7579 | + | 27.2935i | −0.642778 | + | 1.11332i | 0.342032 | + | 0.939688i | \(0.388885\pi\) |
−0.984810 | + | 0.173636i | \(0.944448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.01367 | − | 0.368946i | −0.0412799 | − | 0.0150246i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.4315 | − | 23.8569i | 1.15591 | − | 0.969921i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.748341 | −0.0303742 | −0.0151871 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151871 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.2986 | 0.741497 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.08512 | − | 5.94512i | 0.286633 | − | 0.240514i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.8371 | + | 10.4958i | 1.16472 | + | 0.423923i | 0.850781 | − | 0.525520i | \(-0.176129\pi\) |
0.313938 | + | 0.949443i | \(0.398352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.95336 | + | 10.3115i | −0.240063 | + | 0.415801i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.73917 | + | 26.8772i | −0.190792 | + | 1.08203i | 0.727493 | + | 0.686115i | \(0.240685\pi\) |
−0.918285 | + | 0.395919i | \(0.870426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.61856 | − | 11.4637i | −0.266022 | − | 0.460764i | 0.701809 | − | 0.712365i | \(-0.252376\pi\) |
−0.967831 | + | 0.251601i | \(0.919043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.20961 | − | 4.37138i | −0.209054 | − | 0.175417i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.85117 | + | 1.76568i | −0.194358 | + | 0.0707405i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.45290 | − | 13.9111i | −0.0981159 | − | 0.556443i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.528218 | − | 1.41868i | −0.0210950 | − | 0.0566568i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.5189 | − | 76.6694i | −0.539033 | − | 3.05701i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5013 | + | 4.18615i | −0.457861 | + | 0.166648i | −0.560646 | − | 0.828056i | \(-0.689447\pi\) |
0.102784 | + | 0.994704i | \(0.467225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.7456 | + | 10.6948i | 0.506591 | + | 0.425080i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.6536 | − | 47.8975i | −1.09740 | − | 1.90075i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.370462 | + | 2.10100i | −0.0146783 | + | 0.0832445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.31180 | + | 14.3965i | −0.328810 | + | 0.569515i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.41370 | − | 3.06233i | −0.332321 | − | 0.120955i | 0.170470 | − | 0.985363i | \(-0.445471\pi\) |
−0.502791 | + | 0.864408i | \(0.667694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0305 | − | 20.1640i | 0.947670 | − | 0.795190i | −0.0312334 | − | 0.999512i | \(-0.509944\pi\) |
0.978904 | + | 0.204322i | \(0.0654991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.78880 | 0.306684 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.54933 | 0.218166 | 0.109083 | − | 0.994033i | \(-0.465208\pi\) | ||||
0.109083 | + | 0.994033i | \(0.465208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.118555 | + | 0.0994798i | −0.00465371 | + | 0.00390492i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.31908 | + | 1.57202i | 0.169278 | + | 0.0616122i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4552 | + | 33.6974i | −0.761340 | + | 1.31868i | 0.180820 | + | 0.983516i | \(0.442125\pi\) |
−0.942160 | + | 0.335163i | \(0.891209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.65910 | + | 9.40923i | −0.0648264 | + | 0.367649i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.20961 | − | 10.7554i | −0.242260 | − | 0.419606i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.2708 | + | 25.4003i | 1.17918 | + | 0.989454i | 0.999984 | + | 0.00564104i | \(0.00179561\pi\) |
0.179201 | + | 0.983813i | \(0.442649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.0859997 | − | 0.0313013i | 0.00334500 | − | 0.00121748i | −0.340347 | − | 0.940300i | \(-0.610545\pi\) |
0.343692 | + | 0.939082i | \(0.388322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.99273 | − | 11.3013i | −0.0773911 | − | 0.438907i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.2203 | − | 7.12452i | −1.63723 | − | 0.276277i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.50480 | − | 42.5619i | −0.290587 | − | 1.64800i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.67752 | + | 2.79439i | −0.296830 | + | 0.108037i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.33409 | − | 2.79764i | −0.128711 | − | 0.108002i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.9281 | + | 34.5165i | 0.768173 | + | 1.33052i | 0.938552 | + | 0.345137i | \(0.112167\pi\) |
−0.170379 | + | 0.985379i | \(0.554499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.15270 | − | 6.53731i | 0.0443676 | − | 0.251621i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6912 | + | 25.4459i | −0.564628 | + | 0.977965i | 0.432456 | + | 0.901655i | \(0.357647\pi\) |
−0.997084 | + | 0.0763098i | \(0.975686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.88326 | − | 3.59721i | −0.379285 | − | 0.138048i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.37939 | + | 1.15744i | −0.0528582 | + | 0.0443533i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.0933 | 0.807112 | 0.403556 | − | 0.914955i | \(-0.367774\pi\) | ||||
0.403556 | + | 0.914955i | \(0.367774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.7033 | −2.09010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.3550 | + | 12.0453i | −0.547679 | + | 0.459557i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.07563 | + | 1.11944i | 0.117172 | + | 0.0426471i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.08172 | + | 13.9979i | −0.307443 | + | 0.532507i | −0.977802 | − | 0.209530i | \(-0.932807\pi\) |
0.670359 | + | 0.742037i | \(0.266140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.173648 | − | 0.984808i | 0.00659635 | − | 0.0374098i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.54576 | + | 6.14144i | 0.134498 | + | 0.232958i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5646 | − | 15.5776i | −0.703186 | − | 0.590043i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.85117 | − | 1.40171i | 0.145665 | − | 0.0530175i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.48561 | − | 19.7679i | −0.131650 | − | 0.746623i | −0.977134 | − | 0.212623i | \(-0.931799\pi\) |
0.845484 | − | 0.534000i | \(-0.179312\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.6894 | − | 37.2063i | −1.19519 | − | 1.40326i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.31521 | + | 18.8015i | 0.124858 | + | 0.708105i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.8050 | − | 9.75622i | 1.00811 | − | 0.366920i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7998 | − | 25.0050i | −1.11915 | − | 0.939082i | −0.120593 | − | 0.992702i | \(-0.538480\pi\) |
−0.998561 | + | 0.0536201i | \(0.982924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.46198 | − | 9.46043i | −0.204840 | − | 0.354794i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.88507 | − | 10.6907i | 0.0705963 | − | 0.400372i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.979055 | + | 1.69577i | −0.0366146 | + | 0.0634183i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.5253 | − | 9.65441i | −0.990605 | − | 0.360551i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.34549 | + | 1.96810i | −0.0874718 | + | 0.0733976i | −0.685475 | − | 0.728096i | \(-0.740405\pi\) |
0.598003 | + | 0.801494i | \(0.295961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5895 | −0.841275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.56212 | 0.244048 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.3161 | − | 27.1165i | 1.20019 | − | 1.00708i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4226 | − | 5.97734i | −0.609081 | − | 0.221687i | 0.0190200 | − | 0.999819i | \(-0.493945\pi\) |
−0.628101 | + | 0.778132i | \(0.716168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | + | 0.866025i | −0.0185185 | + | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.75284 | + | 15.6121i | −0.101817 | + | 0.577436i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7087 | + | 35.8686i | 0.764894 | + | 1.32484i | 0.940302 | + | 0.340340i | \(0.110542\pi\) |
−0.175408 | + | 0.984496i | \(0.556124\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.37346 | − | 2.83067i | −0.124432 | − | 0.104411i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.352044 | + | 0.128134i | −0.0129677 | + | 0.00471986i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.59358 | − | 26.0515i | −0.168978 | − | 0.958319i | −0.944868 | − | 0.327451i | \(-0.893810\pi\) |
0.775890 | − | 0.630868i | \(-0.217301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.67112 | − | 5.48432i | −0.171598 | − | 0.201472i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.61793 | + | 14.8470i | 0.0960424 | + | 0.544684i | 0.994423 | + | 0.105466i | \(0.0336333\pi\) |
−0.898381 | + | 0.439218i | \(0.855256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.34477 | + | 1.94534i | −0.195817 | + | 0.0712716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.97565 | − | 7.53147i | −0.328402 | − | 0.275562i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0393628 | − | 0.0681784i | −0.00143829 | − | 0.00249119i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.921274 | − | 5.22481i | 0.0336178 | − | 0.190656i | −0.963374 | − | 0.268161i | \(-0.913584\pi\) |
0.996992 | + | 0.0775048i | \(0.0246953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.44697 | − | 7.70237i | 0.162056 | − | 0.280690i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64.2825 | − | 23.3969i | −2.33948 | − | 0.851500i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.23442 | − | 5.23130i | 0.226594 | − | 0.190135i | −0.522422 | − | 0.852687i | \(-0.674971\pi\) |
0.749016 | + | 0.662552i | \(0.230527\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.36184 | −0.0857295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.2113 | −1.67516 | −0.837579 | − | 0.546316i | \(-0.816030\pi\) | ||||
−0.837579 | + | 0.546316i | \(0.816030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.7631 | + | 19.9396i | −0.860282 | + | 0.721863i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.2592 | + | 8.10170i | 0.804784 | + | 0.292918i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.368241 | + | 0.637812i | −0.0132964 | + | 0.0230301i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.66132 | + | 26.4357i | −0.168092 | + | 0.953295i | 0.777728 | + | 0.628601i | \(0.216372\pi\) |
−0.945819 | + | 0.324693i | \(0.894739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.73308 | + | 11.6620i | 0.242486 | + | 0.419998i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.1065 | − | 13.5150i | −0.579312 | − | 0.486100i | 0.305409 | − | 0.952221i | \(-0.401207\pi\) |
−0.884721 | + | 0.466121i | \(0.845651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.95723 | − | 3.62414i | 0.357674 | − | 0.130183i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.60607 | − | 31.7936i | −0.201117 | − | 1.14059i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0013 | − | 2.53142i | −0.537479 | − | 0.0906974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.00253 | + | 5.68561i | 0.0358732 | + | 0.203447i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.97178 | + | 2.17355i | −0.213414 | + | 0.0776764i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7103 | + | 8.98703i | 0.382268 | + | 0.320761i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.7656 | + | 39.4312i | 0.811507 | + | 1.40557i | 0.911809 | + | 0.410615i | \(0.134686\pi\) |
−0.100302 | + | 0.994957i | \(0.531981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.90895 | − | 16.4975i | 0.103561 | − | 0.587325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7875 | − | 29.0767i | 0.596893 | − | 1.03385i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.4628 | − | 7.08386i | −0.691143 | − | 0.251555i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.17546 | + | 4.34273i | −0.183555 | + | 0.154021i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.1780 | 1.28149 | 0.640745 | − | 0.767754i | \(-0.278626\pi\) | ||||
0.640745 | + | 0.767754i | \(0.278626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.8580 | −1.37470 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.37346 | − | 1.15247i | 0.0485287 | − | 0.0407204i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.05303 | − | 1.47518i | −0.143028 | − | 0.0520581i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.4013 | + | 57.8527i | −1.17724 | + | 2.03904i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.623303 | − | 3.53493i | 0.0219413 | − | 0.124435i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.18938 | − | 2.06006i | −0.0418163 | − | 0.0724280i | 0.844360 | − | 0.535777i | \(-0.179981\pi\) |
−0.886176 | + | 0.463349i | \(0.846648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3904 | + | 23.8223i | 0.996921 | + | 0.836516i | 0.986555 | − | 0.163431i | \(-0.0522560\pi\) |
0.0103658 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.5141 | − | 8.19448i | 0.789605 | − | 0.287393i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.81924 | − | 27.3313i | −0.168811 | − | 0.957373i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.47250 | + | 9.32640i | 0.121487 | + | 0.326289i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.826352 | − | 4.68647i | −0.0288751 | − | 0.163759i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3949 | − | 8.87901i | 0.851387 | − | 0.309879i | 0.120781 | − | 0.992679i | \(-0.461460\pi\) |
0.730606 | + | 0.682800i | \(0.239238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.4805 | + | 28.9325i | 1.20191 | + | 1.00852i | 0.999573 | + | 0.0292095i | \(0.00929900\pi\) |
0.202340 | + | 0.979315i | \(0.435145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.15270 | − | 1.99654i | −0.0401320 | − | 0.0695106i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.92473 | − | 16.5870i | 0.101703 | − | 0.576786i | −0.890783 | − | 0.454429i | \(-0.849843\pi\) |
0.992486 | − | 0.122358i | \(-0.0390455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.50000 | − | 11.2583i | 0.225754 | − | 0.391018i | −0.730791 | − | 0.682601i | \(-0.760849\pi\) |
0.956545 | + | 0.291583i | \(0.0941820\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.5929 | + | 6.40328i | 0.610290 | + | 0.222127i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.86618 | − | 5.76141i | 0.237899 | − | 0.199621i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.7033 | −1.58163 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.59627 | −0.0551750 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.02687 | + | 0.861650i | −0.0354516 | + | 0.0297475i | −0.660341 | − | 0.750966i | \(-0.729588\pi\) |
0.624890 | + | 0.780713i | \(0.285144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6998 | − | 3.89441i | −0.368959 | − | 0.134290i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.31908 | − | 9.21291i | 0.183199 | − | 0.317310i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.08306 | − | 34.4988i | 0.209264 | − | 1.18679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.6630 | + | 27.1291i | 0.538186 | + | 0.932166i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7344 | + | 9.00725i | 0.368404 | + | 0.309128i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −71.6515 | + | 26.0790i | −2.45618 | + | 0.893977i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.37969 | − | 7.82461i | −0.0472397 | − | 0.267910i | 0.952035 | − | 0.305989i | \(-0.0989871\pi\) |
−0.999275 | + | 0.0380795i | \(0.987876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.6250 | − | 2.68993i | 0.500163 | − | 0.0919938i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.31356 | + | 47.1485i | 0.283986 | + | 1.61056i | 0.708886 | + | 0.705323i | \(0.249198\pi\) |
−0.424900 | + | 0.905240i | \(0.639691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.53849 | − | 0.559963i | 0.0524924 | − | 0.0191057i | −0.315640 | − | 0.948879i | \(-0.602219\pi\) |
0.368133 | + | 0.929773i | \(0.379997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.69846 | − | 6.45978i | −0.262363 | − | 0.220149i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4616 | + | 30.2443i | 0.594399 | + | 1.02953i | 0.993631 | + | 0.112679i | \(0.0359432\pi\) |
−0.399233 | + | 0.916850i | \(0.630723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.605600 | − | 3.43453i | 0.0205910 | − | 0.116777i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6065 | + | 27.0313i | −0.530026 | + | 0.918031i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.56506 | − | 1.29757i | −0.120936 | − | 0.0440172i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.36571 | + | 1.14597i | −0.0462755 | + | 0.0388297i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.65270 | 0.123625 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.0915 | −0.543993 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.88120 | + | 4.09581i | −0.164826 | + | 0.138306i | −0.721470 | − | 0.692446i | \(-0.756533\pi\) |
0.556644 | + | 0.830751i | \(0.312089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8255 | + | 3.94015i | 0.365134 | + | 0.132898i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.63697 | + | 4.56737i | −0.0888419 | + | 0.153879i | −0.907022 | − | 0.421084i | \(-0.861650\pi\) |
0.818180 | + | 0.574962i | \(0.194983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.564588 | − | 3.20194i | 0.0189999 | − | 0.107754i | −0.973833 | − | 0.227265i | \(-0.927022\pi\) |
0.992833 | + | 0.119511i | \(0.0381327\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.760115 | − | 1.31656i | −0.0255510 | − | 0.0442556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.1368 | + | 14.3795i | 0.575398 | + | 0.482816i | 0.883432 | − | 0.468559i | \(-0.155227\pi\) |
−0.308034 | + | 0.951375i | \(0.599671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.8658 | − | 15.9658i | 1.47121 | − | 0.535477i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0603074 | + | 0.342020i | 0.00202037 | + | 0.0114581i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0351 | + | 12.3520i | −0.703912 | + | 0.413343i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.20557 | + | 6.83716i | 0.0402979 | + | 0.228541i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.5617 | + | 3.84413i | −0.352643 | + | 0.128352i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.77101 | − | 6.52065i | −0.259178 | − | 0.217476i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.87551 | − | 11.9087i | −0.229057 | − | 0.396738i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14156 | + | 6.47410i | −0.0379887 | + | 0.215445i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.0442 | − | 65.8944i | 1.26463 | − | 2.19040i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.96703 | + | 1.07991i | 0.0985187 | + | 0.0358579i | 0.390809 | − | 0.920472i | \(-0.372195\pi\) |
−0.292291 | + | 0.956330i | \(0.594417\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.58899 | + | 6.36792i | −0.251711 | + | 0.211211i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.3387 | 1.46901 | 0.734504 | − | 0.678604i | \(-0.237415\pi\) | ||||
0.734504 | + | 0.678604i | \(0.237415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.06923 | −0.134672 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.7506 | − | 27.4810i | 1.08270 | − | 0.908495i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.57785 | − | 2.75811i | −0.250243 | − | 0.0910809i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.10220 | − | 12.3014i | 0.234280 | − | 0.405785i | −0.724783 | − | 0.688977i | \(-0.758060\pi\) |
0.959063 | + | 0.283192i | \(0.0913935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.746282 | + | 4.23238i | −0.0245908 | + | 0.139462i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7369 | + | 23.7931i | 0.452157 | + | 0.783159i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.0151 | − | 47.8413i | −1.87464 | − | 1.57301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.37211 | − | 2.68323i | 0.242132 | − | 0.0881288i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.67881 | − | 15.1923i | −0.0878888 | − | 0.498442i | −0.996696 | − | 0.0812253i | \(-0.974117\pi\) |
0.908807 | − | 0.417217i | \(-0.136994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.88548 | − | 5.30142i | 0.0617940 | − | 0.173747i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.99273 | + | 22.6439i | 0.130716 | + | 0.741327i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.73055 | − | 2.81369i | 0.252816 | − | 0.0920175i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.42830 | − | 6.23308i | −0.242672 | − | 0.203626i | 0.513337 | − | 0.858187i | \(-0.328409\pi\) |
−0.756009 | + | 0.654561i | \(0.772853\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.60488 | + | 7.97589i | 0.150275 | + | 0.260283i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.12314 | + | 17.7122i | −0.101811 | + | 0.577402i | 0.890635 | + | 0.454720i | \(0.150261\pi\) |
−0.992446 | + | 0.122682i | \(0.960851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8678 | + | 20.5557i | −0.386470 | + | 0.669385i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.23055 | + | 3.35965i | 0.300270 | + | 0.109289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.68067 | + | 1.41025i | −0.0546146 | + | 0.0458271i | −0.669686 | − | 0.742644i | \(-0.733571\pi\) |
0.615072 | + | 0.788471i | \(0.289127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.5253 | −0.666279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.35504 | 0.108795 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.66456 | + | 7.27043i | −0.280673 | + | 0.235512i | −0.772246 | − | 0.635324i | \(-0.780867\pi\) |
0.491573 | + | 0.870836i | \(0.336422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.5774 | − | 12.5852i | −1.11890 | − | 0.407246i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.10354 | + | 1.91139i | −0.0356724 | + | 0.0617864i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.01754 | − | 45.4697i | 0.258900 | − | 1.46829i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2260 | + | 24.6401i | 0.458902 | + | 0.794842i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0209445 | + | 0.0175745i | 0.000674928 | + | 0.000566332i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.18392 | + | 3.34267i | −0.295641 | + | 0.107604i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.12402 | − | 46.0736i | −0.261251 | − | 1.48163i | −0.779503 | − | 0.626399i | \(-0.784528\pi\) |
0.518252 | − | 0.855228i | \(-0.326583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.222811 | + | 30.2655i | 0.00715773 | + | 0.972267i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4834 | − | 59.4543i | −0.336428 | − | 1.90798i | −0.412654 | − | 0.910888i | \(-0.635398\pi\) |
0.0762258 | − | 0.997091i | \(-0.475713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.62449 | + | 2.04715i | −0.180313 | + | 0.0656285i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.40420 | − | 7.05196i | −0.269150 | − | 0.225844i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.3978 | − | 19.7416i | −0.364648 | − | 0.631589i | 0.624072 | − | 0.781367i | \(-0.285477\pi\) |
−0.988720 | + | 0.149778i | \(0.952144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.108126 | − | 0.613214i | 0.00345573 | − | 0.0195984i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.38666 | − | 9.32997i | 0.171983 | − | 0.297883i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.9359 | − | 10.5318i | −0.922911 | − | 0.335912i | −0.163515 | − | 0.986541i | \(-0.552283\pi\) |
−0.759396 | + | 0.650629i | \(0.774505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.7833 | − | 18.2784i | 0.694075 | − | 0.582398i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.1138 | −0.512908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.5267 | 0.493721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.2467 | − | 24.5409i | 0.929054 | − | 0.779569i | −0.0465937 | − | 0.998914i | \(-0.514837\pi\) |
0.975647 | + | 0.219345i | \(0.0703922\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.7430 | − | 7.54985i | −0.658260 | − | 0.239587i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.17546 | − | 8.96416i | 0.164073 | − | 0.284183i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.37423 | − | 30.4788i | 0.170203 | − | 0.965272i | −0.773332 | − | 0.634001i | \(-0.781411\pi\) |
0.943536 | − | 0.331271i | \(-0.107477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.60607 | + | 9.70999i | 0.177368 | + | 0.307211i |
(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 | 912.2.bo.f.769.1 | 6 | ||
4.3 | odd | 2 | 114.2.i.d.85.1 | yes | 6 | ||
12.11 | even | 2 | 342.2.u.a.199.1 | 6 | |||
19.17 | even | 9 | inner | 912.2.bo.f.625.1 | 6 | ||
76.51 | even | 18 | 2166.2.a.u.1.1 | 3 | |||
76.55 | odd | 18 | 114.2.i.d.55.1 | ✓ | 6 | ||
76.63 | odd | 18 | 2166.2.a.o.1.1 | 3 | |||
228.131 | even | 18 | 342.2.u.a.55.1 | 6 | |||
228.203 | odd | 18 | 6498.2.a.bn.1.3 | 3 | |||
228.215 | even | 18 | 6498.2.a.bs.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.d.55.1 | ✓ | 6 | 76.55 | odd | 18 | ||
114.2.i.d.85.1 | yes | 6 | 4.3 | odd | 2 | ||
342.2.u.a.55.1 | 6 | 228.131 | even | 18 | |||
342.2.u.a.199.1 | 6 | 12.11 | even | 2 | |||
912.2.bo.f.625.1 | 6 | 19.17 | even | 9 | inner | ||
912.2.bo.f.769.1 | 6 | 1.1 | even | 1 | trivial | ||
2166.2.a.o.1.1 | 3 | 76.63 | odd | 18 | |||
2166.2.a.u.1.1 | 3 | 76.51 | even | 18 | |||
6498.2.a.bn.1.3 | 3 | 228.203 | odd | 18 | |||
6498.2.a.bs.1.3 | 3 | 228.215 | even | 18 |