Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 191.3 | ||
Character | \(\chi\) | \(=\) | 432.191 |
Dual form | 432.2.be.b.95.3 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) |
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 | ||||||||
\(3\) | 0.249148 | − | 1.71404i | 0.143846 | − | 0.989600i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.47612 | − | 1.75917i | −0.660141 | − | 0.786726i | 0.327265 | − | 0.944933i | \(-0.393873\pi\) |
−0.987406 | + | 0.158207i | \(0.949429\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.590654 | + | 1.62281i | 0.223246 | + | 0.613364i | 0.999862 | − | 0.0166105i | \(-0.00528752\pi\) |
−0.776616 | + | 0.629975i | \(0.783065\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87585 | − | 0.854099i | −0.958617 | − | 0.284700i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.867802 | − | 0.728172i | −0.261652 | − | 0.219552i | 0.502518 | − | 0.864567i | \(-0.332407\pi\) |
−0.764170 | + | 0.645014i | \(0.776851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22373 | − | 6.94010i | −0.339401 | − | 1.92484i | −0.378501 | − | 0.925601i | \(-0.623560\pi\) |
0.0391000 | − | 0.999235i | \(-0.487551\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.38306 | + | 2.09183i | −0.873502 | + | 0.540109i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.48526 | + | 0.857517i | −0.360229 | + | 0.207979i | −0.669181 | − | 0.743099i | \(-0.733355\pi\) |
0.308952 | + | 0.951078i | \(0.400022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.94280 | + | 2.27638i | 0.904541 | + | 0.522237i | 0.878671 | − | 0.477428i | \(-0.158431\pi\) |
0.0258702 | + | 0.999665i | \(0.491764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.92872 | − | 0.608084i | 0.639098 | − | 0.132695i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.51976 | − | 2.37300i | −1.35946 | − | 0.494804i | −0.443575 | − | 0.896237i | \(-0.646290\pi\) |
−0.915889 | + | 0.401433i | \(0.868512\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0475130 | + | 0.269460i | −0.00950260 | + | 0.0538919i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.18047 | + | 4.71652i | −0.419632 | + | 0.907694i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.35318 | − | 1.12024i | −1.17976 | − | 0.208023i | −0.450827 | − | 0.892612i | \(-0.648871\pi\) |
−0.728930 | + | 0.684589i | \(0.759982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.56666 | + | 4.30438i | −0.281381 | + | 0.773089i | 0.715817 | + | 0.698288i | \(0.246054\pi\) |
−0.997198 | + | 0.0748009i | \(0.976168\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46433 | + | 1.30602i | −0.254906 | + | 0.227349i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.98292 | − | 3.43452i | 0.335175 | − | 0.580540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47273 | + | 2.55085i | 0.242116 | + | 0.419357i | 0.961317 | − | 0.275445i | \(-0.0888253\pi\) |
−0.719201 | + | 0.694802i | \(0.755492\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.2005 | + | 0.368401i | −1.95364 | + | 0.0589913i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.14576 | − | 1.25999i | 1.11598 | − | 0.196778i | 0.414905 | − | 0.909865i | \(-0.363815\pi\) |
0.701076 | + | 0.713087i | \(0.252704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.337693 | − | 0.402447i | 0.0514978 | − | 0.0613727i | −0.739681 | − | 0.672958i | \(-0.765023\pi\) |
0.791178 | + | 0.611585i | \(0.209468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.74260 | + | 6.31987i | 0.408842 | + | 0.942110i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.97326 | − | 3.26600i | 1.30888 | − | 0.476395i | 0.409004 | − | 0.912533i | \(-0.365876\pi\) |
0.899880 | + | 0.436138i | \(0.143654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.07767 | − | 2.58248i | 0.439668 | − | 0.368925i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.09977 | + | 2.75945i | 0.153998 | + | 0.386400i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.57289i | − | 1.17758i | −0.808287 | − | 0.588788i | \(-0.799605\pi\) | ||
0.808287 | − | 0.588788i | \(-0.200395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.60148i | 0.350784i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.88414 | − | 6.19096i | 0.646920 | − | 0.820012i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0297 | − | 9.25501i | 1.43594 | − | 1.20490i | 0.493850 | − | 0.869547i | \(-0.335589\pi\) |
0.942093 | − | 0.335352i | \(-0.108855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.269170 | + | 0.0979697i | −0.0344636 | + | 0.0125437i | −0.359194 | − | 0.933263i | \(-0.616949\pi\) |
0.324731 | + | 0.945806i | \(0.394726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.312594 | − | 5.17143i | −0.0393832 | − | 0.651539i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4025 | + | 12.3972i | −1.29027 | + | 1.53768i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.85364 | − | 1.03215i | 0.715135 | − | 0.126098i | 0.195770 | − | 0.980650i | \(-0.437279\pi\) |
0.519365 | + | 0.854552i | \(0.326168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.69179 | + | 10.5839i | −0.685212 | + | 1.27415i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.36269 | − | 2.36024i | −0.161721 | − | 0.280109i | 0.773765 | − | 0.633473i | \(-0.218371\pi\) |
−0.935486 | + | 0.353364i | \(0.885038\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.58277 | + | 2.74144i | −0.185249 | + | 0.320861i | −0.943660 | − | 0.330915i | \(-0.892643\pi\) |
0.758411 | + | 0.651776i | \(0.225976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.450026 | + | 0.148574i | 0.0519645 | + | 0.0171559i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.669113 | − | 1.83837i | 0.0762525 | − | 0.209502i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.41150 | + | 1.65950i | 1.05888 | + | 0.186709i | 0.675858 | − | 0.737032i | \(-0.263773\pi\) |
0.383019 | + | 0.923741i | \(0.374884\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.54103 | + | 4.91252i | 0.837892 | + | 0.545836i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.731691 | + | 4.14963i | −0.0803135 | + | 0.455481i | 0.917956 | + | 0.396681i | \(0.129838\pi\) |
−0.998270 | + | 0.0587991i | \(0.981273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.70095 | + | 1.34704i | 0.401424 | + | 0.146106i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.50301 | + | 10.6105i | −0.375562 | + | 1.13756i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.83560 | − | 3.36919i | −0.618573 | − | 0.357133i | 0.157740 | − | 0.987481i | \(-0.449579\pi\) |
−0.776313 | + | 0.630348i | \(0.782912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5397 | − | 6.08507i | 1.10486 | − | 0.637889i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.98753 | + | 3.75775i | 0.724573 | + | 0.389660i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.81551 | − | 10.2963i | −0.186267 | − | 1.05638i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21229 | − | 2.69543i | −0.326159 | − | 0.273680i | 0.464974 | − | 0.885324i | \(-0.346064\pi\) |
−0.791133 | + | 0.611645i | \(0.790508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.87374 | + | 2.83530i | 0.188318 | + | 0.284959i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01338 | + | 2.78424i | 0.100835 | + | 0.277042i | 0.979844 | − | 0.199763i | \(-0.0640171\pi\) |
−0.879009 | + | 0.476805i | \(0.841795\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.21708 | − | 9.79274i | −0.809653 | − | 0.964907i | 0.190205 | − | 0.981744i | \(-0.439085\pi\) |
−0.999858 | + | 0.0168372i | \(0.994640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.39286 | − | 4.25451i | −0.526289 | − | 0.415198i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.4207 | −1.10408 | −0.552038 | − | 0.833819i | \(-0.686150\pi\) | ||||
−0.552038 | + | 0.833819i | \(0.686150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0047 | 1.72454 | 0.862269 | − | 0.506451i | \(-0.169043\pi\) | ||||
0.862269 | + | 0.506451i | \(0.169043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.73918 | − | 1.88878i | 0.449823 | − | 0.179275i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.65099 | + | 9.11809i | 0.719745 | + | 0.857758i | 0.994606 | − | 0.103726i | \(-0.0330764\pi\) |
−0.274861 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.44944 | + | 14.9722i | 0.508163 | + | 1.39617i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.40827 | + | 21.0039i | −0.222645 | + | 1.94181i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.26886 | − | 1.90380i | −0.207986 | − | 0.174521i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.68728 | − | 9.56907i | −0.153390 | − | 0.869915i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.379318 | − | 12.5620i | −0.0342020 | − | 1.13268i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.39970 | + | 5.42692i | −0.840734 | + | 0.485398i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.853895 | + | 0.492997i | 0.0757710 | + | 0.0437464i | 0.537407 | − | 0.843323i | \(-0.319404\pi\) |
−0.461636 | + | 0.887070i | \(0.652737\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.605674 | − | 0.679088i | −0.0533267 | − | 0.0597904i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.93676 | + | 3.25271i | 0.780808 | + | 0.284191i | 0.701510 | − | 0.712660i | \(-0.252510\pi\) |
0.0792985 | + | 0.996851i | \(0.474732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.36529 | + | 7.74297i | −0.118386 | + | 0.671400i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.5158 | − | 3.12633i | 0.991122 | − | 0.269072i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.5074 | + | 3.79234i | 1.83750 | + | 0.324001i | 0.981277 | − | 0.192601i | \(-0.0616924\pi\) |
0.856225 | + | 0.516603i | \(0.172804\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.57836 | + | 18.0739i | −0.557969 | + | 1.53301i | 0.264609 | + | 0.964356i | \(0.414757\pi\) |
−0.822578 | + | 0.568652i | \(0.807465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.36237 | − | 16.1942i | −0.283163 | − | 1.36380i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.99163 | + | 6.91371i | −0.333797 | + | 0.578153i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.40737 | + | 12.8299i | 0.615149 | + | 1.06547i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.65966 | − | 5.91867i | −0.301844 | − | 0.488164i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.02217 | − | 0.356564i | 0.165663 | − | 0.0292108i | −0.0902014 | − | 0.995924i | \(-0.528751\pi\) |
0.255864 | + | 0.966713i | \(0.417640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.39929 | + | 7.62638i | −0.520767 | + | 0.620626i | −0.960762 | − | 0.277374i | \(-0.910536\pi\) |
0.439995 | + | 0.898000i | \(0.354980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00380 | − | 1.19753i | 0.404533 | − | 0.0968146i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.88472 | − | 3.59774i | 0.793960 | − | 0.288978i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.86613 | − | 6.60047i | 0.627785 | − | 0.526775i | −0.272455 | − | 0.962169i | \(-0.587835\pi\) |
0.900240 | + | 0.435394i | \(0.143391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6943 | − | 2.13592i | −1.16533 | − | 0.169389i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.9819i | − | 0.944310i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.6034i | − | 1.77044i | −0.465176 | − | 0.885218i | \(-0.654009\pi\) | ||
0.465176 | − | 0.885218i | \(-0.345991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.45904 | + | 0.648154i | 0.347136 | + | 0.0504587i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.1820 | + | 12.7392i | −1.17482 | + | 0.985787i | −0.174816 | + | 0.984601i | \(0.555933\pi\) |
−0.999999 | + | 0.00118593i | \(0.999623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −34.4514 | + | 12.5393i | −2.65011 | + | 0.964561i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.39466 | − | 9.91406i | −0.718427 | − | 0.758147i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.13700 | + | 7.31379i | −0.466587 | + | 0.556057i | −0.947103 | − | 0.320929i | \(-0.896005\pi\) |
0.480516 | + | 0.876986i | \(0.340449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.465345 | + | 0.0820529i | −0.0351768 | + | 0.00620262i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.1154 | − | 21.2112i | −0.985814 | − | 1.59433i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.34317 | + | 4.05850i | 0.175137 | + | 0.303346i | 0.940209 | − | 0.340599i | \(-0.110630\pi\) |
−0.765072 | + | 0.643945i | \(0.777296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.90627 | − | 10.2300i | 0.439009 | − | 0.760387i | −0.558604 | − | 0.829435i | \(-0.688663\pi\) |
0.997613 | + | 0.0690479i | \(0.0219961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.100861 | + | 0.485776i | 0.00745584 | + | 0.0359096i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.31345 | − | 6.35615i | 0.170088 | − | 0.467313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.91333 | + | 0.337372i | 0.139917 | + | 0.0246711i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.94191 | − | 0.752655i | −0.650428 | − | 0.0547476i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.84710 | + | 16.1467i | −0.206009 | + | 1.16833i | 0.689835 | + | 0.723966i | \(0.257683\pi\) |
−0.895844 | + | 0.444368i | \(0.853428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.21489 | − | 0.442183i | −0.0874495 | − | 0.0318290i | 0.297925 | − | 0.954589i | \(-0.403705\pi\) |
−0.385374 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.6575 | + | 20.9189i | 1.33609 | + | 1.49804i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.7961 | − | 10.2746i | −1.26792 | − | 0.732035i | −0.293327 | − | 0.956012i | \(-0.594763\pi\) |
−0.974594 | + | 0.223977i | \(0.928096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12484 | + | 3.53618i | −0.434179 | + | 0.250673i | −0.701125 | − | 0.713038i | \(-0.747319\pi\) |
0.266947 | + | 0.963711i | \(0.413985\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.310728 | − | 10.2905i | −0.0219171 | − | 0.725837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.93460 | − | 10.9717i | −0.135782 | − | 0.770060i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7645 | − | 10.7107i | −0.891515 | − | 0.748070i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.7231 | + | 12.3929i | 1.16233 | + | 0.861367i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.76398 | − | 4.84648i | −0.122017 | − | 0.335238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.31514 | − | 9.90960i | −0.572438 | − | 0.682205i | 0.399692 | − | 0.916650i | \(-0.369117\pi\) |
−0.972129 | + | 0.234445i | \(0.924673\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.38506 | + | 1.74765i | −0.300459 | + | 0.119747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.20645 | −0.0822792 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.91054 | −0.537002 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.30458 | + | 3.39595i | 0.290877 | + | 0.229477i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.76881 | + | 9.25851i | 0.522587 | + | 0.622795i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.39317 | − | 9.32266i | −0.227224 | − | 0.624292i | 0.772722 | − | 0.634745i | \(-0.218895\pi\) |
−0.999945 | + | 0.0104532i | \(0.996673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.366785 | − | 0.734345i | 0.0244523 | − | 0.0489563i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.37742 | − | 5.35129i | −0.423284 | − | 0.355178i | 0.406127 | − | 0.913817i | \(-0.366879\pi\) |
−0.829411 | + | 0.558639i | \(0.811324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.18404 | − | 12.3863i | −0.144325 | − | 0.818508i | −0.967907 | − | 0.251310i | \(-0.919139\pi\) |
0.823581 | − | 0.567198i | \(-0.191973\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.98433 | − | 1.60491i | −0.196355 | − | 0.105596i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.7507 | − | 10.2484i | 1.16289 | − | 0.671393i | 0.210893 | − | 0.977509i | \(-0.432363\pi\) |
0.951994 | + | 0.306116i | \(0.0990296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.9911 | − | 10.9645i | −1.23884 | − | 0.715245i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.18931 | − | 15.7182i | 0.337082 | − | 1.02101i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.90855 | + | 3.60642i | 0.640931 | + | 0.233280i | 0.641982 | − | 0.766720i | \(-0.278112\pi\) |
−0.00105129 | + | 0.999999i | \(0.500335\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.569580 | + | 3.23025i | −0.0366898 | + | 0.208078i | −0.997642 | − | 0.0686372i | \(-0.978135\pi\) |
0.960952 | + | 0.276716i | \(0.0892460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2991 | − | 11.7017i | 0.660686 | − | 0.750662i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.08604 | − | 1.60211i | −0.580486 | − | 0.102355i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9734 | − | 30.1491i | 0.698219 | − | 1.91834i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.93031 | + | 2.28802i | 0.439191 | + | 0.144997i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5827 | + | 23.5259i | −0.857333 | + | 1.48494i | 0.0171305 | + | 0.999853i | \(0.494547\pi\) |
−0.874464 | + | 0.485091i | \(0.838786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.92991 | + | 6.80680i | 0.247071 | + | 0.427940i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.23095 | − | 6.00795i | 0.202330 | − | 0.376233i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.8463 | − | 3.14678i | 1.11322 | − | 0.196291i | 0.413358 | − | 0.910569i | \(-0.364356\pi\) |
0.699862 | + | 0.714278i | \(0.253245\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.26966 | + | 3.89663i | −0.203167 | + | 0.242125i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.3140 | + | 8.64788i | 1.07171 | + | 0.535290i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.9414 | − | 8.34997i | 1.41463 | − | 0.514881i | 0.482141 | − | 0.876093i | \(-0.339859\pi\) |
0.932484 | + | 0.361212i | \(0.117637\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0812 | + | 12.6546i | −0.926430 | + | 0.777367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.22884 | + | 9.16302i | −0.442398 | + | 0.560767i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.9539i | − | 1.09467i | −0.836913 | − | 0.547336i | \(-0.815642\pi\) | ||
0.836913 | − | 0.547336i | \(-0.184358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9608i | 0.787315i | 0.919257 | + | 0.393658i | \(0.128790\pi\) | ||||
−0.919257 | + | 0.393658i | \(0.871210\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.80411 | − | 19.5814i | −0.472326 | − | 1.18512i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.237445 | − | 0.199240i | 0.0143185 | − | 0.0120146i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5757 | − | 4.57718i | 0.755600 | − | 0.275016i | 0.0646398 | − | 0.997909i | \(-0.479410\pi\) |
0.690960 | + | 0.722893i | \(0.257188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.18185 | − | 11.0407i | 0.489835 | − | 0.660987i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6425 | + | 15.0667i | −0.754188 | + | 0.898806i | −0.997466 | − | 0.0711505i | \(-0.977333\pi\) |
0.243278 | + | 0.969957i | \(0.421777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.5889 | + | 5.74630i | −1.93721 | + | 0.341582i | −0.999975 | − | 0.00711797i | \(-0.997734\pi\) |
−0.937234 | + | 0.348700i | \(0.886623\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.1005 | + | 0.546557i | −1.07218 | + | 0.0323752i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.26540 | + | 10.8520i | 0.369835 | + | 0.640573i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.02933 | + | 12.1752i | −0.413490 | + | 0.716185i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.42041 | + | 4.83443i | −0.317750 | + | 0.283399i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.70081 | − | 7.42041i | 0.157783 | − | 0.433505i | −0.835461 | − | 0.549550i | \(-0.814799\pi\) |
0.993244 | + | 0.116045i | \(0.0370216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.5623 | − | 5.74161i | −1.89585 | − | 0.334289i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.32665 | − | 2.50525i | 0.309084 | − | 0.145369i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.49044 | + | 48.1517i | −0.491015 | + | 2.78468i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.852555 | + | 0.310305i | 0.0491405 | + | 0.0178857i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.02477 | − | 1.04328i | 0.288665 | − | 0.0599351i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.569672 | + | 0.328901i | 0.0326193 | + | 0.0188328i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.34321 | − | 2.50755i | 0.247880 | − | 0.143114i | −0.370913 | − | 0.928668i | \(-0.620955\pi\) |
0.618793 | + | 0.785554i | \(0.287622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.8324 | + | 11.6445i | −1.07134 | + | 0.662435i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.21509 | + | 6.89111i | 0.0689014 | + | 0.390759i | 0.999683 | + | 0.0251831i | \(0.00801689\pi\) |
−0.930781 | + | 0.365576i | \(0.880872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.39378 | + | 6.20412i | 0.417921 | + | 0.350678i | 0.827372 | − | 0.561655i | \(-0.189835\pi\) |
−0.409450 | + | 0.912332i | \(0.634280\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.63601 | + | 8.18356i | −0.486584 | + | 0.461092i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.807269 | + | 2.21795i | 0.0453408 | + | 0.124573i | 0.960296 | − | 0.278982i | \(-0.0899969\pi\) |
−0.914956 | + | 0.403554i | \(0.867775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.69758 | + | 5.59835i | 0.263014 | + | 0.313448i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.84544 | + | 19.5754i | −0.158817 | + | 1.09259i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.80813 | −0.434456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.92822 | 0.106958 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.48584 | − | 30.8607i | 0.248067 | − | 1.70660i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6002 | + | 12.6328i | 0.584407 | + | 0.696469i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.95113 | − | 8.10818i | −0.162209 | − | 0.445666i | 0.831785 | − | 0.555098i | \(-0.187319\pi\) |
−0.993994 | + | 0.109432i | \(0.965097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.05668 | − | 8.59371i | −0.112706 | − | 0.470933i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.4564 | − | 8.77397i | −0.571294 | − | 0.479373i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.218162 | + | 1.23726i | 0.0118840 | + | 0.0673977i | 0.990173 | − | 0.139848i | \(-0.0446613\pi\) |
−0.978289 | + | 0.207245i | \(0.933550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.5350 | − | 10.8423i | 0.952370 | − | 0.588874i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.49388 | − | 2.59454i | 0.243357 | − | 0.140502i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4778 | + | 9.51348i | 0.889719 | + | 0.513680i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27.0206 | − | 5.61024i | 1.45474 | − | 0.302045i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5931 | − | 7.13131i | −1.05181 | − | 0.382829i | −0.242466 | − | 0.970160i | \(-0.577956\pi\) |
−0.809347 | + | 0.587331i | \(0.800179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21404 | + | 18.2277i | −0.172043 | + | 0.975707i | 0.769458 | + | 0.638698i | \(0.220526\pi\) |
−0.941501 | + | 0.337009i | \(0.890585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.4014 | + | 9.36094i | 1.88959 | + | 0.499650i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6452 | + | 1.87704i | 0.566588 | + | 0.0999048i | 0.449602 | − | 0.893229i | \(-0.351566\pi\) |
0.116986 | + | 0.993134i | \(0.462677\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.14058 | + | 5.88120i | −0.113610 | + | 0.312142i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.82847 | + | 3.41459i | −0.202624 | + | 0.180719i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.479687 | − | 0.830842i | 0.0253169 | − | 0.0438502i | −0.853089 | − | 0.521765i | \(-0.825274\pi\) |
0.878406 | + | 0.477915i | \(0.158607\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.863791 | + | 1.49613i | 0.0454627 | + | 0.0787437i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.8221 | + | 0.507954i | −0.882933 | + | 0.0266607i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.15902 | − | 1.26233i | 0.374720 | − | 0.0660733i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8294 | − | 15.2895i | 0.669688 | − | 0.798103i | −0.319054 | − | 0.947737i | \(-0.603365\pi\) |
0.988741 | + | 0.149634i | \(0.0478095\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.6263 | − | 2.47964i | −1.12582 | − | 0.129085i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.9122 | − | 5.06361i | 0.722283 | − | 0.262890i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8836 | − | 15.8452i | 0.977754 | − | 0.820433i | −0.00599498 | − | 0.999982i | \(-0.501908\pi\) |
0.983749 | + | 0.179549i | \(0.0574638\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.96002 | + | 17.4635i | 0.359414 | + | 0.901813i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.4626i | 2.34144i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.36788i | − | 0.429829i | −0.976633 | − | 0.214915i | \(-0.931053\pi\) | ||
0.976633 | − | 0.214915i | \(-0.0689473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.05776 | − | 1.34078i | 0.0541908 | − | 0.0686902i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.716215 | − | 0.600976i | 0.0365969 | − | 0.0307084i | −0.624306 | − | 0.781180i | \(-0.714618\pi\) |
0.660903 | + | 0.750472i | \(0.270174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.22171 | + | 1.53658i | −0.215158 | + | 0.0783112i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.31489 | + | 0.868955i | −0.0668394 | + | 0.0441715i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.06355 | + | 9.60976i | −0.408838 | + | 0.487234i | −0.930694 | − | 0.365800i | \(-0.880796\pi\) |
0.521855 | + | 0.853034i | \(0.325240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7185 | − | 2.06628i | 0.592627 | − | 0.104496i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.80185 | − | 14.5075i | 0.393551 | − | 0.731808i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.9732 | − | 19.0061i | −0.552120 | − | 0.956299i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5305 | + | 18.2393i | −0.528509 | + | 0.915404i | 0.470939 | + | 0.882166i | \(0.343915\pi\) |
−0.999447 | + | 0.0332380i | \(0.989418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.9316 | + | 4.26931i | 0.647388 | + | 0.213733i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.15588 | + | 3.17576i | −0.0577220 | + | 0.158590i | −0.965202 | − | 0.261505i | \(-0.915781\pi\) |
0.907480 | + | 0.420095i | \(0.138003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.7899 | + | 5.60543i | 1.58357 | + | 0.279226i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.48950 | − | 20.5174i | −0.123704 | − | 1.01952i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.579416 | − | 3.28603i | 0.0287206 | − | 0.162883i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3709 | − | 8.87029i | −1.20506 | − | 0.438607i | −0.340075 | − | 0.940398i | \(-0.610452\pi\) |
−0.864989 | + | 0.501791i | \(0.832675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8587 | − | 35.9197i | 0.584949 | − | 1.77179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.5338 | + | 12.4326i | 1.05961 | + | 0.611767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.37997 | − | 4.83818i | 0.411356 | − | 0.237497i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.3404 | + | 15.7786i | 1.43680 | + | 0.772683i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.30706 | + | 30.0979i | 0.259267 | + | 1.47038i | 0.784877 | + | 0.619651i | \(0.212726\pi\) |
−0.525610 | + | 0.850725i | \(0.676163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.65610 | + | 3.06783i | 0.178187 | + | 0.149517i | 0.727519 | − | 0.686087i | \(-0.240673\pi\) |
−0.549332 | + | 0.835604i | \(0.685118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.5952 | + | 1.72848i | −1.39035 | + | 0.0840414i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.160497 | − | 0.440962i | −0.00778524 | − | 0.0213898i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.317972 | − | 0.378945i | −0.0153878 | − | 0.0183384i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.8559 | + | 8.56435i | 0.524125 | + | 0.413491i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.3238 | 1.55698 | 0.778491 | − | 0.627656i | \(-0.215985\pi\) | ||||
0.778491 | + | 0.627656i | \(0.215985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6596 | 0.704497 | 0.352249 | − | 0.935907i | \(-0.385417\pi\) | ||||
0.352249 | + | 0.935907i | \(0.385417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.8365 | − | 9.49996i | 1.14287 | − | 0.455488i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.3043 | − | 24.1977i | −0.971285 | − | 1.15753i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.75846 | + | 7.57882i | 0.131654 | + | 0.361717i | 0.987951 | − | 0.154767i | \(-0.0494627\pi\) |
−0.856297 | + | 0.516484i | \(0.827240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0566 | + | 4.79818i | −0.526506 | + | 0.228485i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.3346 | − | 14.5455i | −0.823593 | − | 0.691076i | 0.130218 | − | 0.991485i | \(-0.458432\pi\) |
−0.953810 | + | 0.300409i | \(0.902877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.68707 | + | 15.2392i | 0.127380 | + | 0.722405i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.107343 | − | 3.55492i | −0.00507715 | − | 0.168142i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.54560 | − | 3.20175i | 0.261713 | − | 0.151100i | −0.363403 | − | 0.931632i | \(-0.618385\pi\) |
0.625116 | + | 0.780532i | \(0.285052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.11860 | − | 4.10992i | −0.335202 | − | 0.193529i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.4775 | + | 12.8687i | 0.539261 | + | 0.604625i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −26.2625 | − | 9.55876i | −1.23120 | − | 0.448122i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41804 | − | 8.04210i | 0.0663331 | − | 0.376194i | −0.933511 | − | 0.358548i | \(-0.883272\pi\) |
0.999844 | − | 0.0176455i | \(-0.00561702\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.805924 | − | 8.87507i | −0.0376173 | − | 0.414253i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.5599 | + | 3.80159i | 1.00414 | + | 0.177058i | 0.651459 | − | 0.758684i | \(-0.274157\pi\) |
0.352686 | + | 0.935742i | \(0.385269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.20720 | + | 6.06423i | −0.102577 | + | 0.281829i | −0.980356 | − | 0.197238i | \(-0.936803\pi\) |
0.877778 | + | 0.479067i | \(0.159025\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.70391 | − | 17.8392i | −0.171765 | − | 0.827271i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0625 | − | 20.8929i | 0.558188 | − | 0.966810i | −0.439460 | − | 0.898262i | \(-0.644830\pi\) |
0.997648 | − | 0.0685478i | \(-0.0218366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.13246 | + | 8.88969i | 0.236995 | + | 0.410488i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.35362 | − | 15.1273i | −0.430992 | − | 0.697031i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.586102 | + | 0.103346i | −0.0269490 | + | 0.00475183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.800726 | + | 0.954268i | −0.0367398 | + | 0.0437848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.32209 | + | 24.6543i | −0.335256 | + | 1.12884i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6931 | − | 7.53168i | 0.945493 | − | 0.344131i | 0.177160 | − | 0.984182i | \(-0.443309\pi\) |
0.768333 | + | 0.640051i | \(0.221087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9009 | − | 13.3424i | 0.725019 | − | 0.608363i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.5375 | − | 2.98528i | −0.934489 | − | 0.135835i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.62976i | 0.437265i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.57215i | 0.116555i | 0.998300 | + | 0.0582777i | \(0.0185609\pi\) | ||||
−0.998300 | + | 0.0582777i | \(0.981439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −38.7431 | − | 5.63160i | −1.75202 | − | 0.254670i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4783 | − | 20.5398i | 1.10469 | − | 0.926946i | 0.106960 | − | 0.994263i | \(-0.465888\pi\) |
0.997732 | + | 0.0673168i | \(0.0214438\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3968 | − | 3.78412i | 0.468247 | − | 0.170428i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.22192 | − | 7.48147i | 0.0998680 | − | 0.336267i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.02535 | − | 3.60547i | 0.135705 | − | 0.161727i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8045 | + | 4.55003i | −1.15517 | + | 0.203687i | −0.718231 | − | 0.695805i | \(-0.755048\pi\) |
−0.436937 | + | 0.899492i | \(0.643937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0529 | + | 29.1964i | 0.806543 | + | 1.30440i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.4076 | + | 23.2226i | 0.597814 | + | 1.03544i | 0.993143 | + | 0.116905i | \(0.0372972\pi\) |
−0.395329 | + | 0.918540i | \(0.629369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.40208 | − | 5.89258i | 0.151391 | − | 0.262216i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9093 | + | 62.1752i | 0.573323 | + | 2.76130i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.39845 | + | 9.33715i | −0.150633 | + | 0.413862i | −0.991942 | − | 0.126693i | \(-0.959564\pi\) |
0.841308 | + | 0.540555i | \(0.181786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.38370 | − | 0.949292i | −0.238161 | − | 0.0419942i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3337 | + | 13.6327i | −0.853605 | + | 0.601900i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.09771 | + | 28.9105i | −0.224632 | + | 1.27395i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1652 | − | 3.69984i | −0.447066 | − | 0.162719i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0071 | + | 12.3413i | 0.483158 | + | 0.541721i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.45901 | − | 5.46116i | −0.414407 | − | 0.239258i | 0.278275 | − | 0.960502i | \(-0.410237\pi\) |
−0.692681 | + | 0.721244i | \(0.743571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.09476 | + | 2.94146i | −0.222778 | + | 0.128621i | −0.607236 | − | 0.794521i | \(-0.707722\pi\) |
0.384458 | + | 0.923143i | \(0.374388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0247019 | + | 0.818062i | 0.00107808 | + | 0.0357032i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.36417 | − | 7.73657i | −0.0594240 | − | 0.337010i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2571 | + | 16.1586i | 0.837266 | + | 0.702550i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.6244 | + | 17.1956i | −1.71955 | + | 0.746224i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.4889 | − | 48.0504i | −0.757529 | − | 2.08129i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8583 | + | 20.0909i | 0.728846 | + | 0.868605i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.54021 | − | 3.00512i | 0.325384 | − | 0.129681i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.55130 | −0.196038 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.3090 | −1.34608 | −0.673039 | − | 0.739607i | \(-0.735011\pi\) | ||||
−0.673039 | + | 0.739607i | \(0.735011\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0630 | − | 12.6723i | −0.689329 | − | 0.543822i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5771 | − | 31.6734i | −1.13844 | − | 1.35674i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.77952 | + | 4.88920i | 0.0760870 | + | 0.209047i | 0.971905 | − | 0.235374i | \(-0.0756315\pi\) |
−0.895818 | + | 0.444421i | \(0.853409\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.857767 | − | 0.0518489i | 0.0366086 | − | 0.00221286i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.4993 | − | 18.8791i | −0.958500 | − | 0.804277i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.86589 | + | 16.2533i | 0.121870 | + | 0.691159i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3183 | − | 5.54896i | −0.437987 | − | 0.235540i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.3579 | + | 14.0631i | −1.03208 | + | 0.595871i | −0.917580 | − | 0.397552i | \(-0.869860\pi\) |
−0.114499 | + | 0.993423i | \(0.536526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.20627 | − | 1.85114i | −0.135611 | − | 0.0782949i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05497 | − | 3.19547i | 0.0445410 | − | 0.134913i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1504 | + | 9.15398i | 1.05996 | + | 0.385794i | 0.812414 | − | 0.583081i | \(-0.198153\pi\) |
0.247547 | + | 0.968876i | \(0.420375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.74651 | − | 26.9188i | 0.199687 | − | 1.13248i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.51794 | + | 15.1393i | −0.147740 | + | 0.635789i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.77648 | + | 0.489568i | 0.116396 | + | 0.0205238i | 0.231543 | − | 0.972825i | \(-0.425623\pi\) |
−0.115147 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.98909 | − | 27.4448i | 0.418031 | − | 1.14853i | −0.534787 | − | 0.844987i | \(-0.679608\pi\) |
0.952818 | − | 0.303543i | \(-0.0981695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.9667 | + | 8.90296i | 1.12655 | + | 0.371926i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.949200 | − | 1.64406i | 0.0395844 | − | 0.0685622i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3591 | − | 33.5310i | −0.805930 | − | 1.39591i | −0.915661 | − | 0.401951i | \(-0.868332\pi\) |
0.109731 | − | 0.993961i | \(-0.465001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.06060 | + | 1.97219i | −0.0440772 | + | 0.0819616i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.16622 | + | 1.26360i | −0.297305 | + | 0.0524229i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.24254 | + | 7.43957i | −0.258539 | + | 0.308115i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.5043 | − | 26.7677i | 1.67465 | − | 1.10671i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2093 | + | 3.71586i | −0.421381 | + | 0.153370i | −0.544003 | − | 0.839083i | \(-0.683092\pi\) |
0.122622 | + | 0.992453i | \(0.460870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9754 | + | 13.4050i | −0.658256 | + | 0.552343i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.0449 | + | 27.9433i | −0.906807 | + | 1.14944i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.1060i | − | 0.415003i | −0.978235 | − | 0.207501i | \(-0.933467\pi\) | ||
0.978235 | − | 0.207501i | \(-0.0665332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.80156i | 0.278837i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.53515 | + | 11.3792i | 0.185611 | + | 0.465722i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.142727 | + | 0.119762i | −0.00583168 | + | 0.00489336i | −0.645699 | − | 0.763592i | \(-0.723434\pi\) |
0.639867 | + | 0.768486i | \(0.278989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.1284 | − | 10.2379i | 1.14738 | − | 0.417612i | 0.302806 | − | 0.953052i | \(-0.402076\pi\) |
0.844573 | + | 0.535440i | \(0.179854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.7157 | − | 2.03126i | −0.721441 | − | 0.0827194i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.3430 | + | 17.0933i | −0.583126 | + | 0.694942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7567 | − | 2.95465i | 0.680132 | − | 0.119926i | 0.177099 | − | 0.984193i | \(-0.443329\pi\) |
0.503033 | + | 0.864267i | \(0.332217\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.2879 | + | 0.582409i | −0.781584 | + | 0.0236004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.6472 | − | 58.2786i | −1.36122 | − | 2.35770i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6554 | − | 25.3840i | 0.591928 | − | 1.02525i | −0.402045 | − | 0.915620i | \(-0.631700\pi\) |
0.993973 | − | 0.109629i | \(-0.0349662\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.5389 | + | 19.2104i | −0.868530 | + | 0.774636i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.62643 | + | 18.2060i | −0.266770 | + | 0.732945i | 0.731901 | + | 0.681411i | \(0.238633\pi\) |
−0.998671 | + | 0.0515338i | \(0.983589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.171532 | − | 0.0302457i | −0.00689445 | − | 0.00121568i | 0.170200 | − | 0.985410i | \(-0.445559\pi\) |
−0.177094 | + | 0.984194i | \(0.556670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.4084 | − | 25.5763i | 1.01961 | − | 1.02634i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.02072 | − | 11.4601i | 0.0809586 | − | 0.459139i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7075 | + | 8.99281i | 0.988302 | + | 0.359712i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.74654 | + | 1.81603i | −0.349303 | + | 0.0725252i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.37479 | − | 2.52579i | −0.174434 | − | 0.100710i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9875 | + | 11.5398i | −0.795691 | + | 0.459392i | −0.841962 | − | 0.539537i | \(-0.818599\pi\) |
0.0462714 | + | 0.998929i | \(0.485266\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0571 | + | 11.7835i | −0.757453 | + | 0.468352i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.393186 | − | 2.22987i | −0.0156031 | − | 0.0884897i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.6889 | − | 18.1991i | −0.859344 | − | 0.721075i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.90300 | + | 7.95157i | 0.0752816 | + | 0.314559i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1866 | − | 27.9876i | −0.402348 | − | 1.10544i | −0.961123 | − | 0.276122i | \(-0.910951\pi\) |
0.558775 | − | 0.829320i | \(-0.311272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1310 | + | 32.3334i | 1.06994 | + | 1.27511i | 0.959647 | + | 0.281207i | \(0.0907348\pi\) |
0.110294 | + | 0.993899i | \(0.464821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.300585 | + | 2.06790i | −0.0118355 | + | 0.0814235i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.3033 | −0.876834 | −0.438417 | − | 0.898772i | \(-0.644461\pi\) | ||||
−0.438417 | + | 0.898772i | \(0.644461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.3108 | −0.640256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.97090 | + | 13.5590i | −0.0772455 | + | 0.531417i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.2527 | + | 14.6022i | 0.479487 | + | 0.571430i | 0.950511 | − | 0.310690i | \(-0.100560\pi\) |
−0.471025 | + | 0.882120i | \(0.656116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.46965 | − | 20.5227i | −0.291863 | − | 0.801888i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.89327 | − | 6.53212i | 0.268932 | − | 0.254842i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.06327 | + | 0.892192i | 0.0414193 | + | 0.0347549i | 0.663262 | − | 0.748387i | \(-0.269171\pi\) |
−0.621843 | + | 0.783142i | \(0.713616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.42078 | + | 36.4141i | 0.249739 | + | 1.41634i | 0.809223 | + | 0.587502i | \(0.199888\pi\) |
−0.559484 | + | 0.828841i | \(0.689000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.8050 | − | 11.0093i | 0.691489 | − | 0.427565i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.6365 | − | 9.02776i | 0.606359 | − | 0.350082i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.7629 | + | 22.3798i | 1.50091 | + | 0.866548i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.8248 | + | 3.49330i | −0.650484 | + | 0.135059i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.304925 | + | 0.110984i | 0.0117715 | + | 0.00428447i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.93462 | − | 27.9856i | 0.190215 | − | 1.07877i | −0.728854 | − | 0.684669i | \(-0.759947\pi\) |
0.919069 | − | 0.394096i | \(-0.128942\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.16731 | − | 0.811644i | −0.0449298 | − | 0.0312402i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8917 | + | 6.15234i | 1.34100 | + | 0.236454i | 0.797683 | − | 0.603077i | \(-0.206059\pi\) |
0.543313 | + | 0.839530i | \(0.317170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.47682 | − | 6.80500i | 0.0950516 | − | 0.261152i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.7612 | + | 9.59787i | −0.412371 | + | 0.367791i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.7063 | − | 30.6681i | 0.677511 | − | 1.17348i | −0.298217 | − | 0.954498i | \(-0.596392\pi\) |
0.975728 | − | 0.218986i | \(-0.0702749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.0762 | − | 43.4332i | −0.958111 | − | 1.65950i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.7747 | + | 0.657500i | −0.830756 | + | 0.0250852i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59.4967 | + | 10.4909i | −2.26664 | + | 0.399670i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47685 | − | 4.14355i | 0.132266 | − | 0.157628i | −0.695847 | − | 0.718191i | \(-0.744971\pi\) |
0.828112 | + | 0.560563i | \(0.189415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.49442 | + | 4.71540i | −0.132742 | + | 0.179123i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.5056 | − | 15.1068i | 1.57440 | − | 0.573033i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.53288 | + | 7.99904i | −0.361084 | + | 0.302985i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.1435 | − | 32.9787i | −0.497134 | − | 1.24737i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.4485i | − | 1.33887i | −0.742870 | − | 0.669436i | \(-0.766536\pi\) | ||
0.742870 | − | 0.669436i | \(-0.233464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4100i | 0.505767i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.5251 | + | 29.8196i | −0.886008 | + | 1.12307i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.91973 | + | 3.28904i | −0.147417 | + | 0.123697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.5781 | − | 6.39792i | 0.660161 | − | 0.240279i | 0.00985524 | − | 0.999951i | \(-0.496863\pi\) |
0.650306 | + | 0.759672i | \(0.274641\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.6487 | − | 12.8108i | −0.961901 | − | 0.480444i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.4286 | − | 24.3458i | 0.765055 | − | 0.911757i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0545 | − | 3.18350i | 0.675201 | − | 0.119056i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.65023 | − | 16.0851i | 0.323049 | − | 0.600709i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9949 | + | 31.1681i | 0.671097 | + | 1.16237i | 0.977593 | + | 0.210503i | \(0.0675101\pi\) |
−0.306496 | + | 0.951872i | \(0.599157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0383 | − | 19.1189i | 0.411087 | − | 0.712024i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.39485 | + | 1.78109i | 0.200637 | + | 0.0662395i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.603717 | − | 1.65870i | 0.0224215 | − | 0.0616026i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.82609 | − | 1.37995i | −0.290254 | − | 0.0511796i | 0.0266254 | − | 0.999645i | \(-0.491524\pi\) |
−0.316879 | + | 0.948466i | \(0.602635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.4911 | − | 20.5685i | −0.647819 | − | 0.761795i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.156458 | + | 0.887319i | −0.00578682 | + | 0.0328187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.97374 | + | 3.26618i | 0.331453 | + | 0.120639i | 0.502385 | − | 0.864644i | \(-0.332456\pi\) |
−0.170933 | + | 0.985283i | \(0.554678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.00985 | + | 15.1746i | −0.184791 | + | 0.559725i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.83138 | − | 3.36675i | −0.214802 | − | 0.124016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.3163 | + | 13.4617i | −0.857704 | + | 0.495195i | −0.863243 | − | 0.504789i | \(-0.831570\pi\) |
0.00553893 | + | 0.999985i | \(0.498237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −48.9427 | − | 26.3204i | −1.79795 | − | 0.966903i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.09650 | − | 11.8899i | −0.0769132 | − | 0.436196i | −0.998810 | − | 0.0487619i | \(-0.984472\pi\) |
0.921897 | − | 0.387434i | \(-0.126639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.61223 | − | 3.03102i | −0.132342 | − | 0.111048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.64842 | − | 11.3088i | 0.206665 | − | 0.413766i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.74566 | − | 18.5335i | −0.246481 | − | 0.677201i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0832 | + | 29.8929i | 0.915297 | + | 1.09081i | 0.995569 | + | 0.0940360i | \(0.0299769\pi\) |
−0.0802713 | + | 0.996773i | \(0.525579\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.9402 | + | 29.1427i | 1.34618 | + | 1.06202i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.8622 | 0.832042 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8793 | 0.540797 | 0.270398 | − | 0.962749i | \(-0.412845\pi\) | ||||
0.270398 | + | 0.962749i | \(0.412845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.6462 | − | 5.04011i | 0.459029 | − | 0.182944i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.15327 | + | 10.9084i | 0.331806 | + | 0.395431i | 0.905993 | − | 0.423294i | \(-0.139126\pi\) |
−0.574187 | + | 0.818724i | \(0.694682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6346 | + | 29.2182i | 0.384997 | + | 1.05777i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.49287 | − | 7.03485i | −0.343216 | − | 0.254345i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −77.7280 | − | 65.2215i | −2.80659 | − | 2.35501i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.349200 | − | 1.98041i | −0.0125925 | − | 0.0714154i | 0.977864 | − | 0.209242i | \(-0.0670995\pi\) |
−0.990456 | + | 0.137826i | \(0.955988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.947333 | − | 31.3732i | −0.0341174 | − | 1.12988i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2389 | + | 12.2623i | −0.763910 | + | 0.441044i | −0.830698 | − | 0.556724i | \(-0.812058\pi\) |
0.0667878 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08542 | − | 0.626666i | −0.0389894 | − | 0.0225105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.86434 | + | 6.57516i | 0.210382 | + | 0.235883i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.0425 | + | 11.2986i | 1.11221 | + | 0.404813i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.536121 | + | 3.04049i | −0.0191839 | + | 0.108797i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.1365 | − | 27.5223i | 0.683884 | − | 0.983565i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.2227 | − | 4.09479i | −0.828854 | − | 0.146149i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.81446 | + | 10.4801i | −0.135971 | + | 0.373577i | −0.988926 | − | 0.148407i | \(-0.952586\pi\) |
0.852956 | + | 0.521984i | \(0.174808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.59637 | − | 41.4027i | −0.306039 | − | 1.47398i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2778 | + | 17.8017i | −0.365438 | + | 0.632957i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00931 | + | 1.74818i | 0.0358416 | + | 0.0620795i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.9330 | + | 29.0026i | 0.636019 | + | 1.02862i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.9401 | + | 5.63191i | −1.13138 | + | 0.199492i | −0.707831 | − | 0.706382i | \(-0.750326\pi\) |
−0.423547 | + | 0.905874i | \(0.639215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5270 | + | 12.5456i | −0.372419 | + | 0.443831i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9047 | + | 14.6735i | 0.491298 | + | 0.518461i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.36977 | − | 1.22650i | 0.118917 | − | 0.0432821i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.0783 | + | 17.6868i | −0.742912 | + | 0.623378i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.7737 | − | 4.47319i | −1.08329 | − | 0.157464i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.2942i | 1.76825i | 0.467250 | + | 0.884125i | \(0.345245\pi\) | ||||
−0.467250 | + | 0.884125i | \(0.654755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.1337i | 1.02302i | 0.859276 | + | 0.511512i | \(0.170914\pi\) | ||||
−0.859276 | + | 0.511512i | \(0.829086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.2154 | + | 3.22917i | 0.779127 | + | 0.113252i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.7633 | + | 33.3654i | −1.39285 | + | 1.16874i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.24758 | − | 0.818053i | 0.0786329 | − | 0.0286200i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.5077 | + | 8.49785i | −1.24074 | + | 0.296939i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.24195 | − | 8.63062i | 0.252746 | − | 0.301211i | −0.624721 | − | 0.780848i | \(-0.714787\pi\) |
0.877467 | + | 0.479637i | \(0.159232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.2233 | − | 6.38715i | 1.26267 | − | 0.222642i | 0.498062 | − | 0.867142i | \(-0.334045\pi\) |
0.764605 | + | 0.644499i | \(0.222934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.282346 | − | 0.456629i | −0.00983001 | − | 0.0158978i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8729 | + | 20.5645i | 0.412862 | + | 0.715097i | 0.995201 | − | 0.0978483i | \(-0.0311960\pi\) |
−0.582340 | + | 0.812946i | \(0.697863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.19006 | + | 10.7215i | −0.214990 | + | 0.372373i | −0.953269 | − | 0.302122i | \(-0.902305\pi\) |
0.738280 | + | 0.674495i | \(0.235638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.71224 | − | 22.6956i | −0.163466 | − | 0.787302i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.35664 | + | 6.47482i | −0.0816528 | + | 0.224339i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.8208 | + | 7.90312i | 1.55109 | + | 0.273499i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.8856 | − | 16.7748i | −0.583652 | − | 0.579821i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.34934 | − | 24.6663i | 0.150156 | − | 0.851576i | −0.812926 | − | 0.582367i | \(-0.802127\pi\) |
0.963082 | − | 0.269209i | \(-0.0867622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8569 | + | 4.31556i | 0.408859 | + | 0.148812i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.6751 | + | 25.4236i | 0.780972 | + | 0.875634i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.9132 | + | 42.0965i | 2.50829 | + | 1.44816i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5322 | − | 8.39015i | 0.499331 | − | 0.288289i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.72992 | + | 57.2903i | 0.0593705 | + | 1.96620i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.54870 | − | 20.1257i | −0.121648 | − | 0.689900i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5488 | + | 20.5989i | 0.840534 | + | 0.705292i | 0.957684 | − | 0.287823i | \(-0.0929314\pi\) |
−0.117150 | + | 0.993114i | \(0.537376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.57290 | + | 31.1612i | −0.122190 | + | 1.06569i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.97196 | + | 8.16540i | 0.101520 | + | 0.278925i | 0.980046 | − | 0.198770i | \(-0.0636947\pi\) |
−0.878526 | + | 0.477695i | \(0.841472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.4663 | − | 26.7742i | −0.766539 | − | 0.913525i | 0.231704 | − | 0.972786i | \(-0.425570\pi\) |
−0.998243 | + | 0.0592610i | \(0.981126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.1617 | − | 8.03538i | 0.687110 | − | 0.273845i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.7973 | 0.571787 | 0.285894 | − | 0.958261i | \(-0.407710\pi\) | ||||
0.285894 | + | 0.958261i | \(0.407710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.9252 | 0.745478 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.1173 | + | 15.0819i | 0.649258 | + | 0.512210i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.95891 | − | 8.29331i | −0.236065 | − | 0.281331i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3265 | − | 39.3617i | −0.485435 | − | 1.33372i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.93591 | + | 10.4953i | 0.234745 | + | 0.355211i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.3588 | − | 12.0485i | −0.485417 | − | 0.407313i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.16969 | − | 17.9762i | −0.107033 | − | 0.607014i | −0.990389 | − | 0.138311i | \(-0.955833\pi\) |
0.883356 | − | 0.468703i | \(-0.155278\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.0460 | − | 6.47807i | −0.406300 | − | 0.218500i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0580 | + | 7.53906i | −0.439937 | + | 0.253997i | −0.703571 | − | 0.710625i | \(-0.748412\pi\) |
0.263634 | + | 0.964623i | \(0.415079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.9799 | − | 29.4332i | −1.71561 | − | 0.990508i | −0.926534 | − | 0.376212i | \(-0.877226\pi\) |
−0.789076 | − | 0.614295i | \(-0.789440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.9542 | + | 54.3825i | −0.603523 | + | 1.82805i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.26584 | + | 1.55264i | 0.143233 | + | 0.0521325i | 0.412642 | − | 0.910893i | \(-0.364606\pi\) |
−0.269409 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.295683 | + | 1.67690i | −0.00991688 | + | 0.0562414i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.96696 | − | 9.75426i | −0.0993969 | − | 0.326780i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.8144 | + | 7.54934i | 1.43273 | + | 0.252629i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.68079 | − | 10.1129i | 0.123035 | − | 0.338036i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 80.4184 | + | 26.5498i | 2.68509 | + | 0.886473i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.7752 | − | 25.5914i | 0.492781 | − | 0.853522i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.35140 | + | 12.7330i | 0.244911 | + | 0.424198i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.744287 | − | 1.38400i | 0.0247683 | − | 0.0460566i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.7146 | + | 4.71051i | −0.888024 | + | 0.156583i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.1038 | − | 33.4928i | 0.933170 | − | 1.11211i | −0.0603187 | − | 0.998179i | \(-0.519212\pi\) |
0.993489 | − | 0.113930i | \(-0.0363439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.536315 | − | 8.87258i | −0.0177884 | − | 0.294285i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.4906 | + | 7.09401i | −0.645753 | + | 0.235035i | −0.644074 | − | 0.764964i | \(-0.722757\pi\) |
−0.00167985 | + | 0.999999i | \(0.500535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.65660 | − | 3.06825i | 0.121016 | − | 0.101544i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.705681 | − | 0.894495i | 0.0233291 | − | 0.0295711i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4239i | 0.542364i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.4910i | 1.23671i | 0.785897 | + | 0.618357i | \(0.212202\pi\) | ||||
−0.785897 | + | 0.618357i | \(0.787798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.21594 | − | 8.06918i | −0.105969 | − | 0.265888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.7128 | + | 12.3455i | −0.484276 | + | 0.406356i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.757324 | + | 0.275643i | −0.0249007 | + | 0.00906310i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2671 | + | 35.1807i | 0.501439 | + | 1.15548i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.3763 | − | 35.0093i | 0.963805 | − | 1.14862i | −0.0250429 | − | 0.999686i | \(-0.507972\pi\) |
0.988848 | − | 0.148931i | \(-0.0475833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0134 | − | 3.17624i | 0.590364 | − | 0.104097i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1144 | − | 0.365801i | 0.396607 | − | 0.0119758i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.23082 | − | 3.86389i | −0.0729555 | − | 0.126363i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.33351 | − | 14.4341i | 0.272244 | − | 0.471540i | −0.697192 | − | 0.716884i | \(-0.745568\pi\) |
0.969436 | + | 0.245344i | \(0.0789009\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.4762 | − | 11.1275i | 0.407147 | − | 0.363132i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.201193 | + | 0.552774i | −0.00655871 | + | 0.0180199i | −0.942929 | − | 0.332994i | \(-0.891941\pi\) |
0.936370 | + | 0.351014i | \(0.114163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.5786 | − | 8.74205i | −1.61450 | − | 0.284680i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.8753 | + | 16.8414i | 0.386303 | + | 0.547850i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.71530 | + | 26.7418i | −0.153227 | + | 0.868991i | 0.807163 | + | 0.590329i | \(0.201002\pi\) |
−0.960389 | + | 0.278662i | \(0.910109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9627 | + | 7.62981i | 0.680479 | + | 0.247674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00279 | − | 0.831091i | 0.129799 | − | 0.0269500i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.9811 | − | 6.33992i | −0.355711 | − | 0.205370i | 0.311486 | − | 0.950251i | \(-0.399173\pi\) |
−0.667198 | + | 0.744880i | \(0.732506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.6075 | − | 18.8259i | 1.05515 | − | 0.609193i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7662 | − | 6.65700i | 0.348021 | − | 0.215190i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.54920 | + | 37.1424i | 0.211485 | + | 1.19939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.67417 | + | 6.43939i | 0.247554 | + | 0.207722i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.8441 | + | 9.75437i | 1.05839 | + | 0.314330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.01544 | + | 2.78991i | 0.0326883 | + | 0.0898104i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6644 | − | 18.6681i | −0.503733 | − | 0.600326i | 0.452921 | − | 0.891550i | \(-0.350382\pi\) |
−0.956655 | + | 0.291224i | \(0.905937\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.94538 | + | 13.3834i | −0.0624947 | + | 0.429938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.678594 | 0.0217771 | 0.0108886 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108886 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.2160 | −1.06486 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.480412 | − | 3.30504i | 0.0153855 | − | 0.105846i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2188 | − | 15.7535i | −0.422907 | − | 0.504000i | 0.511955 | − | 0.859012i | \(-0.328921\pi\) |
−0.934862 | + | 0.355012i | \(0.884477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.61080 | + | 7.17311i | 0.0834415 | + | 0.229254i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.7788 | − | 15.3778i | −1.65317 | − | 0.490975i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4879 | + | 28.9388i | 1.09999 | + | 0.923005i | 0.997425 | − | 0.0717208i | \(-0.0228491\pi\) |
0.102570 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.19444 | + | 46.4730i | 0.261097 | + | 1.48075i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.2941 | − | 15.0217i | 0.773290 | − | 0.478145i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.15669 | + | 1.82251i | −0.100377 | + | 0.0579526i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.54334 | + | 5.50985i | 0.303154 | + | 0.175026i | 0.643859 | − | 0.765144i | \(-0.277332\pi\) |
−0.340705 | + | 0.940170i | \(0.610666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.6330 | + | 3.03822i | −0.464364 | + | 0.0964150i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2618 | + | 5.55483i | 0.483830 | + | 0.176100i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.69470 | + | 26.6250i | −0.148683 | + | 0.843222i | 0.815653 | + | 0.578541i | \(0.196378\pi\) |
−0.964336 | + | 0.264681i | \(0.914733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.2424 | + | 1.38412i | −0.482247 | + | 0.0437918i |
(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 | 432.2.be.b.191.3 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.c.191.4 | yes | 36 | ||
27.14 | odd | 18 | 432.2.be.c.95.4 | yes | 36 | ||
108.95 | even | 18 | inner | 432.2.be.b.95.3 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.95.3 | ✓ | 36 | 108.95 | even | 18 | inner | |
432.2.be.b.191.3 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.c.95.4 | yes | 36 | 27.14 | odd | 18 | ||
432.2.be.c.191.4 | yes | 36 | 4.3 | odd | 2 |