Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(55,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.u (of order \(9\), 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: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{10} + 237x^{8} + 1312x^{6} + 5283x^{4} + 11049x^{2} + 16129 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(0.925476 + 1.60297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.73 |
Dual form | 342.2.u.f.253.1 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.766044 | + | 0.642788i | 0.541675 | + | 0.454519i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.173648 | + | 0.984808i | 0.0868241 | + | 0.492404i | ||||
\(5\) | −0.318787 | + | 1.80793i | −0.142566 | + | 0.808532i | 0.826723 | + | 0.562609i | \(0.190202\pi\) |
−0.969289 | + | 0.245923i | \(0.920909\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.425476 | + | 0.736946i | 0.160815 | + | 0.278539i | 0.935161 | − | 0.354223i | \(-0.115254\pi\) |
−0.774346 | + | 0.632762i | \(0.781921\pi\) | |||||||
\(8\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.40632 | + | 1.18004i | −0.444718 | + | 0.373163i | ||||
\(11\) | −1.64693 | + | 2.85257i | −0.496568 | + | 0.860081i | −0.999992 | − | 0.00395854i | \(-0.998740\pi\) |
0.503424 | + | 0.864039i | \(0.332073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.464002 | + | 0.168883i | 0.128691 | + | 0.0468397i | 0.405563 | − | 0.914067i | \(-0.367076\pi\) |
−0.276872 | + | 0.960907i | \(0.589298\pi\) | |||||||
\(14\) | −0.147766 | + | 0.838024i | −0.0394922 | + | 0.223971i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.234923 | + | 0.0855050i | ||||
\(17\) | 1.06143 | + | 0.890650i | 0.257436 | + | 0.216014i | 0.762366 | − | 0.647146i | \(-0.224037\pi\) |
−0.504931 | + | 0.863160i | \(0.668482\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.39726 | − | 3.64049i | 0.549969 | − | 0.835185i | ||||
\(20\) | −1.83582 | −0.410502 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.09521 | + | 1.12657i | −0.659902 | + | 0.240185i | ||||
\(23\) | 0.631658 | + | 3.58231i | 0.131710 | + | 0.746964i | 0.977095 | + | 0.212806i | \(0.0682601\pi\) |
−0.845385 | + | 0.534158i | \(0.820629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.53147 | + | 0.557409i | 0.306294 | + | 0.111482i | ||||
\(26\) | 0.246890 | + | 0.427626i | 0.0484192 | + | 0.0838644i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.651867 | + | 0.546981i | −0.123191 | + | 0.103370i | ||||
\(29\) | −1.72511 | + | 1.44754i | −0.320345 | + | 0.268801i | −0.788752 | − | 0.614712i | \(-0.789272\pi\) |
0.468407 | + | 0.883513i | \(0.344828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.40906 | − | 5.90467i | −0.612286 | − | 1.06051i | −0.990854 | − | 0.134937i | \(-0.956917\pi\) |
0.378568 | − | 0.925573i | \(-0.376417\pi\) | |||||||
\(32\) | −0.939693 | − | 0.342020i | −0.166116 | − | 0.0604612i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.240608 | + | 1.36455i | 0.0412639 | + | 0.234019i | ||||
\(35\) | −1.46798 | + | 0.534303i | −0.248135 | + | 0.0903136i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.72214 | 0.776314 | 0.388157 | − | 0.921593i | \(-0.373112\pi\) | ||||
0.388157 | + | 0.921593i | \(0.373112\pi\) | |||||||
\(38\) | 4.17647 | − | 1.24785i | 0.677512 | − | 0.202428i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.40632 | − | 1.18004i | −0.222359 | − | 0.186581i | ||||
\(41\) | 5.89726 | − | 2.14643i | 0.920997 | − | 0.335215i | 0.162362 | − | 0.986731i | \(-0.448089\pi\) |
0.758635 | + | 0.651516i | \(0.225867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.414432 | − | 2.35036i | 0.0632004 | − | 0.358427i | −0.936764 | − | 0.349962i | \(-0.886194\pi\) |
0.999964 | − | 0.00846480i | \(-0.00269446\pi\) | |||||||
\(44\) | −3.09521 | − | 1.12657i | −0.466621 | − | 0.169836i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.81879 | + | 3.15023i | −0.268166 | + | 0.464476i | ||||
\(47\) | 1.19510 | − | 1.00281i | 0.174323 | − | 0.146275i | −0.551452 | − | 0.834207i | \(-0.685926\pi\) |
0.725775 | + | 0.687932i | \(0.241481\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.13794 | − | 5.43507i | 0.448277 | − | 0.776439i | ||||
\(50\) | 0.814878 | + | 1.41141i | 0.115241 | + | 0.199604i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0857441 | + | 0.486279i | −0.0118906 | + | 0.0674347i | ||||
\(53\) | −2.31071 | − | 13.1047i | −0.317401 | − | 1.80007i | −0.558432 | − | 0.829551i | \(-0.688597\pi\) |
0.241031 | − | 0.970517i | \(-0.422514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.63222 | − | 3.88690i | −0.624609 | − | 0.524109i | ||||
\(56\) | −0.850952 | −0.113713 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.25197 | −0.295698 | ||||||||
\(59\) | 2.03001 | + | 1.70338i | 0.264285 | + | 0.221761i | 0.765294 | − | 0.643681i | \(-0.222593\pi\) |
−0.501010 | + | 0.865442i | \(0.667038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.55932 | + | 8.84332i | 0.199650 | + | 1.13227i | 0.905639 | + | 0.424049i | \(0.139391\pi\) |
−0.705989 | + | 0.708222i | \(0.749497\pi\) | |||||||
\(62\) | 1.18396 | − | 6.71455i | 0.150363 | − | 0.852748i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | −0.453247 | + | 0.785046i | −0.0562183 | + | 0.0973730i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.56239 | + | 5.50650i | −0.801723 | + | 0.672726i | −0.948617 | − | 0.316427i | \(-0.897517\pi\) |
0.146894 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(68\) | −0.692802 | + | 1.19997i | −0.0840146 | + | 0.145518i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.46798 | − | 0.534303i | −0.175458 | − | 0.0638614i | ||||
\(71\) | 1.87624 | − | 10.6407i | 0.222668 | − | 1.26282i | −0.644424 | − | 0.764668i | \(-0.722903\pi\) |
0.867092 | − | 0.498147i | \(-0.165986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.85055 | − | 1.40148i | 0.450672 | − | 0.164031i | −0.106705 | − | 0.994291i | \(-0.534030\pi\) |
0.557377 | + | 0.830259i | \(0.311808\pi\) | |||||||
\(74\) | 3.61737 | + | 3.03533i | 0.420510 | + | 0.352850i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00146 | + | 1.72867i | 0.458999 | + | 0.198292i | ||||
\(77\) | −2.80291 | −0.319422 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.480486 | − | 0.174883i | 0.0540589 | − | 0.0196758i | −0.314849 | − | 0.949142i | \(-0.601954\pi\) |
0.368908 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(80\) | −0.318787 | − | 1.80793i | −0.0356415 | − | 0.202133i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.89726 | + | 2.14643i | 0.651243 | + | 0.237033i | ||||
\(83\) | −6.62628 | − | 11.4770i | −0.727328 | − | 1.25977i | −0.958008 | − | 0.286740i | \(-0.907428\pi\) |
0.230680 | − | 0.973030i | \(-0.425905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.94861 | + | 1.63507i | −0.211356 | + | 0.177349i | ||||
\(86\) | 1.82826 | − | 1.53409i | 0.197146 | − | 0.165425i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.64693 | − | 2.85257i | −0.175563 | − | 0.304084i | ||||
\(89\) | −7.29938 | − | 2.65676i | −0.773733 | − | 0.281616i | −0.0751759 | − | 0.997170i | \(-0.523952\pi\) |
−0.698557 | + | 0.715555i | \(0.746174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0729641 | + | 0.413800i | 0.00764871 | + | 0.0433780i | ||||
\(92\) | −3.41820 | + | 1.24412i | −0.356372 | + | 0.129709i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.56009 | 0.160911 | ||||||||
\(95\) | 5.81754 | + | 5.49462i | 0.596867 | + | 0.563736i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3209 | + | 11.1776i | 1.35254 | + | 1.13491i | 0.978210 | + | 0.207616i | \(0.0665706\pi\) |
0.374327 | + | 0.927297i | \(0.377874\pi\) | |||||||
\(98\) | 5.89740 | − | 2.14648i | 0.595727 | − | 0.216827i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.283004 | + | 1.60500i | −0.0283004 | + | 0.160500i | ||||
\(101\) | 5.65216 | + | 2.05722i | 0.562411 | + | 0.204701i | 0.607552 | − | 0.794280i | \(-0.292152\pi\) |
−0.0451411 | + | 0.998981i | \(0.514374\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0827516 | − | 0.143330i | 0.00815376 | − | 0.0141227i | −0.861920 | − | 0.507045i | \(-0.830738\pi\) |
0.870073 | + | 0.492922i | \(0.164071\pi\) | |||||||
\(104\) | −0.378258 | + | 0.317396i | −0.0370912 | + | 0.0311232i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.65343 | − | 11.5241i | 0.646238 | − | 1.11932i | ||||
\(107\) | −6.42161 | − | 11.1226i | −0.620800 | − | 1.07526i | −0.989337 | − | 0.145644i | \(-0.953474\pi\) |
0.368537 | − | 0.929613i | \(-0.379859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.54061 | + | 8.73721i | −0.147563 | + | 0.836873i | 0.817710 | + | 0.575631i | \(0.195243\pi\) |
−0.965273 | + | 0.261243i | \(0.915868\pi\) | |||||||
\(110\) | −1.05004 | − | 5.95507i | −0.100117 | − | 0.567794i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.651867 | − | 0.546981i | −0.0615956 | − | 0.0516849i | ||||
\(113\) | 12.3830 | 1.16489 | 0.582446 | − | 0.812870i | \(-0.302096\pi\) | ||||
0.582446 | + | 0.812870i | \(0.302096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.67794 | −0.622721 | ||||||||
\(116\) | −1.72511 | − | 1.44754i | −0.160172 | − | 0.134401i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.460166 | + | 2.60973i | 0.0423617 | + | 0.240245i | ||||
\(119\) | −0.204746 | + | 1.16117i | −0.0187690 | + | 0.106444i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0752474 | + | 0.130332i | 0.00684068 | + | 0.0118484i | ||||
\(122\) | −4.48987 | + | 7.77668i | −0.406494 | + | 0.704068i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.22299 | − | 4.38261i | 0.469038 | − | 0.393570i | ||||
\(125\) | −6.08553 | + | 10.5404i | −0.544306 | + | 0.942766i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0698 | − | 4.02908i | −0.982287 | − | 0.357523i | −0.199558 | − | 0.979886i | \(-0.563951\pi\) |
−0.782729 | + | 0.622363i | \(0.786173\pi\) | |||||||
\(128\) | 0.173648 | − | 0.984808i | 0.0153485 | − | 0.0870455i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.851825 | + | 0.310039i | −0.0747100 | + | 0.0271922i | ||||
\(131\) | 14.4010 | + | 12.0838i | 1.25822 | + | 1.05577i | 0.995870 | + | 0.0907961i | \(0.0289412\pi\) |
0.262348 | + | 0.964973i | \(0.415503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.70282 | + | 0.217709i | 0.321075 | + | 0.0188777i | ||||
\(134\) | −8.56659 | −0.740041 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.30204 | + | 0.473905i | −0.111649 | + | 0.0406370i | ||||
\(137\) | 2.34967 | + | 13.3256i | 0.200746 | + | 1.13849i | 0.903995 | + | 0.427542i | \(0.140621\pi\) |
−0.703250 | + | 0.710943i | \(0.748268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.8020 | − | 6.47941i | −1.50995 | − | 0.549576i | −0.551334 | − | 0.834284i | \(-0.685881\pi\) |
−0.958614 | + | 0.284708i | \(0.908103\pi\) | |||||||
\(140\) | −0.781098 | − | 1.35290i | −0.0660148 | − | 0.114341i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.27698 | − | 6.94521i | 0.694588 | − | 0.582829i | ||||
\(143\) | −1.24593 | + | 1.04546i | −0.104190 | + | 0.0874255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.06711 | − | 3.58034i | −0.171664 | − | 0.297331i | ||||
\(146\) | 3.85055 | + | 1.40148i | 0.318674 | + | 0.115988i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.819990 | + | 4.65040i | 0.0674028 | + | 0.382260i | ||||
\(149\) | −14.2772 | + | 5.19648i | −1.16964 | + | 0.425713i | −0.852530 | − | 0.522678i | \(-0.824933\pi\) |
−0.317105 | + | 0.948390i | \(0.602711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.70848 | −0.301792 | −0.150896 | − | 0.988550i | \(-0.548216\pi\) | ||||
−0.150896 | + | 0.988550i | \(0.548216\pi\) | |||||||
\(152\) | 1.95413 | + | 3.89633i | 0.158501 | + | 0.316034i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.14716 | − | 1.80168i | −0.173023 | − | 0.145183i | ||||
\(155\) | 11.7620 | − | 4.28102i | 0.944748 | − | 0.343860i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.73648 | + | 15.5193i | −0.218395 | + | 1.23858i | 0.656523 | + | 0.754306i | \(0.272026\pi\) |
−0.874918 | + | 0.484272i | \(0.839085\pi\) | |||||||
\(158\) | 0.480486 | + | 0.174883i | 0.0382254 | + | 0.0139129i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.917911 | − | 1.58987i | 0.0725673 | − | 0.125690i | ||||
\(161\) | −2.37121 | + | 1.98968i | −0.186878 | + | 0.156809i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.19734 | − | 7.27000i | 0.328761 | − | 0.569430i | −0.653506 | − | 0.756922i | \(-0.726702\pi\) |
0.982266 | + | 0.187492i | \(0.0600357\pi\) | |||||||
\(164\) | 3.13787 | + | 5.43494i | 0.245026 | + | 0.424398i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.30128 | − | 13.0512i | 0.178614 | − | 1.01297i | ||||
\(167\) | −0.666871 | − | 3.78201i | −0.0516040 | − | 0.292661i | 0.948074 | − | 0.318051i | \(-0.103028\pi\) |
−0.999678 | + | 0.0253900i | \(0.991917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.77180 | − | 8.19952i | −0.751677 | − | 0.630732i | ||||
\(170\) | −2.54372 | −0.195095 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.38662 | 0.181978 | ||||||||
\(173\) | 3.70984 | + | 3.11292i | 0.282054 | + | 0.236671i | 0.772828 | − | 0.634616i | \(-0.218842\pi\) |
−0.490774 | + | 0.871287i | \(0.663286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.240823 | + | 1.36577i | 0.0182045 | + | 0.103243i | ||||
\(176\) | 0.571973 | − | 3.24382i | 0.0431141 | − | 0.244512i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.88392 | − | 6.72714i | −0.291112 | − | 0.504221i | ||||
\(179\) | −12.2886 | + | 21.2844i | −0.918491 | + | 1.59087i | −0.116782 | + | 0.993158i | \(0.537258\pi\) |
−0.801709 | + | 0.597715i | \(0.796076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.28442 | + | 7.79056i | −0.690106 | + | 0.579067i | −0.918940 | − | 0.394398i | \(-0.870953\pi\) |
0.228834 | + | 0.973465i | \(0.426509\pi\) | |||||||
\(182\) | −0.210092 | + | 0.363889i | −0.0155730 | + | 0.0269733i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.41820 | − | 1.24412i | −0.251993 | − | 0.0917180i | ||||
\(185\) | −1.50536 | + | 8.53730i | −0.110676 | + | 0.627675i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.28874 | + | 1.56098i | −0.313624 | + | 0.114150i | ||||
\(188\) | 1.19510 | + | 1.00281i | 0.0871616 | + | 0.0731373i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.924622 | + | 7.94857i | 0.0670791 | + | 0.576650i | ||||
\(191\) | −20.2083 | −1.46222 | −0.731112 | − | 0.682258i | \(-0.760998\pi\) | ||||
−0.731112 | + | 0.682258i | \(0.760998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7482 | − | 5.00392i | 0.989614 | − | 0.360190i | 0.204043 | − | 0.978962i | \(-0.434592\pi\) |
0.785571 | + | 0.618772i | \(0.212369\pi\) | |||||||
\(194\) | 3.01961 | + | 17.1251i | 0.216796 | + | 1.22951i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.89740 | + | 2.14648i | 0.421243 | + | 0.153320i | ||||
\(197\) | −9.47773 | − | 16.4159i | −0.675261 | − | 1.16959i | −0.976393 | − | 0.216003i | \(-0.930698\pi\) |
0.301132 | − | 0.953582i | \(-0.402636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.03692 | − | 5.06557i | 0.427946 | − | 0.359089i | −0.403230 | − | 0.915099i | \(-0.632113\pi\) |
0.831176 | + | 0.556010i | \(0.187668\pi\) | |||||||
\(200\) | −1.24847 | + | 1.04759i | −0.0882798 | + | 0.0740756i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00745 | + | 5.20906i | 0.211604 | + | 0.366508i | ||||
\(203\) | −1.80075 | − | 0.655419i | −0.126388 | − | 0.0460014i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00062 | + | 11.3461i | 0.139730 | + | 0.792446i | ||||
\(206\) | 0.155522 | − | 0.0566054i | 0.0108357 | − | 0.00394389i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.493780 | −0.0342375 | ||||||||
\(209\) | 6.43662 | + | 12.8340i | 0.445230 | + | 0.887744i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.535882 | + | 0.449659i | 0.0368917 | + | 0.0309558i | 0.661047 | − | 0.750344i | \(-0.270112\pi\) |
−0.624155 | + | 0.781300i | \(0.714557\pi\) | |||||||
\(212\) | 12.5044 | − | 4.55121i | 0.858802 | − | 0.312579i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.23020 | − | 12.6481i | 0.152453 | − | 0.864606i | ||||
\(215\) | 4.11718 | + | 1.49853i | 0.280789 | + | 0.102199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.90095 | − | 5.02459i | 0.196929 | − | 0.341091i | ||||
\(218\) | −6.79634 | + | 5.70281i | −0.460306 | + | 0.386243i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.02347 | − | 5.23680i | 0.203842 | − | 0.353065i | ||||
\(221\) | 0.342092 | + | 0.592521i | 0.0230116 | + | 0.0398573i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.62922 | + | 14.9110i | −0.176066 | + | 0.998517i | 0.760841 | + | 0.648938i | \(0.224787\pi\) |
−0.936907 | + | 0.349579i | \(0.886325\pi\) | |||||||
\(224\) | −0.147766 | − | 0.838024i | −0.00987304 | − | 0.0559928i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.48590 | + | 7.95962i | 0.630993 | + | 0.529466i | ||||
\(227\) | 17.0328 | 1.13051 | 0.565253 | − | 0.824917i | \(-0.308778\pi\) | ||||
0.565253 | + | 0.824917i | \(0.308778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9202 | 0.853790 | 0.426895 | − | 0.904301i | \(-0.359607\pi\) | ||||
0.426895 | + | 0.904301i | \(0.359607\pi\) | |||||||
\(230\) | −5.11560 | − | 4.29250i | −0.337313 | − | 0.283039i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.391050 | − | 2.21776i | −0.0256737 | − | 0.145603i | ||||
\(233\) | 4.52454 | − | 25.6599i | 0.296412 | − | 1.68104i | −0.364994 | − | 0.931010i | \(-0.618929\pi\) |
0.661406 | − | 0.750028i | \(-0.269960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.43203 | + | 2.48034i | 0.0934151 | + | 0.161800i | ||||
\(236\) | −1.32499 | + | 2.29496i | −0.0862498 | + | 0.149389i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.903230 | + | 0.757900i | −0.0585477 | + | 0.0491273i | ||||
\(239\) | −13.0578 | + | 22.6168i | −0.844641 | + | 1.46296i | 0.0412918 | + | 0.999147i | \(0.486853\pi\) |
−0.885933 | + | 0.463814i | \(0.846481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.62593 | − | 1.68370i | −0.297983 | − | 0.108457i | 0.188702 | − | 0.982034i | \(-0.439572\pi\) |
−0.486685 | + | 0.873578i | \(0.661794\pi\) | |||||||
\(242\) | −0.0261332 | + | 0.148208i | −0.00167990 | + | 0.00952720i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.43820 | + | 3.07125i | −0.540200 | + | 0.196617i | ||||
\(245\) | 8.82591 | + | 7.40582i | 0.563867 | + | 0.473140i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.72715 | − | 1.28434i | 0.109896 | − | 0.0817205i | ||||
\(248\) | 6.81813 | 0.432952 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.4371 | + | 4.16275i | −0.723343 | + | 0.263275i | ||||
\(251\) | −1.19432 | − | 6.77335i | −0.0753851 | − | 0.427530i | −0.999020 | − | 0.0442569i | \(-0.985908\pi\) |
0.923635 | − | 0.383273i | \(-0.125203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.2591 | − | 4.09797i | −0.707852 | − | 0.257637i | ||||
\(254\) | −5.89013 | − | 10.2020i | −0.369579 | − | 0.640130i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | −1.41720 | + | 1.18917i | −0.0884024 | + | 0.0741784i | −0.685918 | − | 0.727679i | \(-0.740599\pi\) |
0.597515 | + | 0.801857i | \(0.296155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00915 | + | 3.47996i | 0.124843 | + | 0.216234i | ||||
\(260\) | −0.851825 | − | 0.310039i | −0.0528279 | − | 0.0192278i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.26443 | + | 18.5135i | 0.201677 | + | 1.14377i | ||||
\(263\) | 8.72514 | − | 3.17569i | 0.538015 | − | 0.195821i | −0.0586985 | − | 0.998276i | \(-0.518695\pi\) |
0.596714 | + | 0.802454i | \(0.296473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.4290 | 1.50066 | ||||||||
\(266\) | 2.69658 | + | 2.54690i | 0.165338 | + | 0.156160i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.56239 | − | 5.50650i | −0.400862 | − | 0.336363i | ||||
\(269\) | 20.5799 | − | 7.49047i | 1.25478 | − | 0.456702i | 0.372764 | − | 0.927926i | \(-0.378410\pi\) |
0.882013 | + | 0.471224i | \(0.156188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.958450 | − | 5.43564i | 0.0582217 | − | 0.330192i | −0.941760 | − | 0.336286i | \(-0.890829\pi\) |
0.999981 | + | 0.00609486i | \(0.00194007\pi\) | |||||||
\(272\) | −1.30204 | − | 0.473905i | −0.0789479 | − | 0.0287347i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.76560 | + | 11.7184i | −0.408725 | + | 0.707932i | ||||
\(275\) | −4.11227 | + | 3.45060i | −0.247979 | + | 0.208079i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2448 | + | 28.1368i | −0.976056 | + | 1.69058i | −0.299651 | + | 0.954049i | \(0.596870\pi\) |
−0.676405 | + | 0.736530i | \(0.736463\pi\) | |||||||
\(278\) | −9.47226 | − | 16.4064i | −0.568109 | − | 0.983993i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.271273 | − | 1.53846i | 0.0162116 | − | 0.0919407i | ||||
\(281\) | −4.79977 | − | 27.2209i | −0.286331 | − | 1.62386i | −0.700494 | − | 0.713659i | \(-0.747037\pi\) |
0.414163 | − | 0.910203i | \(-0.364074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.57314 | − | 7.19372i | −0.509620 | − | 0.427622i | 0.351375 | − | 0.936235i | \(-0.385714\pi\) |
−0.860995 | + | 0.508613i | \(0.830159\pi\) | |||||||
\(284\) | 10.8048 | 0.641148 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.62644 | −0.0961736 | ||||||||
\(287\) | 4.09094 | + | 3.43271i | 0.241481 | + | 0.202626i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.61863 | − | 14.8510i | −0.154037 | − | 0.873588i | ||||
\(290\) | 0.717899 | − | 4.07141i | 0.0421565 | − | 0.239081i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.04883 | + | 3.54868i | 0.119899 | + | 0.207671i | ||||
\(293\) | 6.30300 | − | 10.9171i | 0.368225 | − | 0.637785i | −0.621063 | − | 0.783761i | \(-0.713299\pi\) |
0.989288 | + | 0.145976i | \(0.0466322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.72674 | + | 3.12710i | −0.216979 | + | 0.182067i | ||||
\(296\) | −2.36107 | + | 4.08949i | −0.137234 | + | 0.237697i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.2772 | − | 5.19648i | −0.827057 | − | 0.301024i | ||||
\(299\) | −0.311900 | + | 1.76888i | −0.0180377 | + | 0.102297i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.90842 | − | 0.694608i | 0.110000 | − | 0.0400366i | ||||
\(302\) | −2.84086 | − | 2.38377i | −0.163473 | − | 0.137170i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00756 | + | 4.24085i | −0.0577878 | + | 0.243229i | ||||
\(305\) | −16.4852 | −0.943941 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.9464 | − | 10.1716i | 1.59498 | − | 0.580527i | 0.616591 | − | 0.787283i | \(-0.288513\pi\) |
0.978392 | + | 0.206757i | \(0.0662908\pi\) | |||||||
\(308\) | −0.486721 | − | 2.76033i | −0.0277335 | − | 0.157285i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.7620 | + | 4.28102i | 0.668038 | + | 0.243146i | ||||
\(311\) | −11.7886 | − | 20.4185i | −0.668470 | − | 1.15782i | −0.978332 | − | 0.207043i | \(-0.933616\pi\) |
0.309862 | − | 0.950782i | \(-0.399717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4587 | − | 14.6496i | 0.986824 | − | 0.828044i | 0.00171930 | − | 0.999999i | \(-0.499453\pi\) |
0.985105 | + | 0.171955i | \(0.0550083\pi\) | |||||||
\(314\) | −12.0719 | + | 10.1295i | −0.681257 | + | 0.571642i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.255661 | + | 0.442819i | 0.0143821 | + | 0.0249105i | ||||
\(317\) | −11.9824 | − | 4.36122i | −0.672996 | − | 0.244951i | −0.0171588 | − | 0.999853i | \(-0.505462\pi\) |
−0.655837 | + | 0.754902i | \(0.727684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28806 | − | 7.30498i | −0.0721178 | − | 0.409000i | ||||
\(320\) | 1.72511 | − | 0.627888i | 0.0964365 | − | 0.0351000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.09540 | −0.172500 | ||||||||
\(323\) | 5.78693 | − | 1.72903i | 0.321994 | − | 0.0962055i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.616468 | + | 0.517278i | 0.0341955 | + | 0.0286934i | ||||
\(326\) | 7.88841 | − | 2.87115i | 0.436899 | − | 0.159018i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.08977 | + | 6.18039i | −0.0601724 | + | 0.341255i | ||||
\(329\) | 1.24750 | + | 0.454053i | 0.0687770 | + | 0.0250328i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58384 | − | 2.74329i | 0.0870558 | − | 0.150785i | −0.819210 | − | 0.573494i | \(-0.805587\pi\) |
0.906265 | + | 0.422709i | \(0.138921\pi\) | |||||||
\(332\) | 10.1520 | − | 8.51858i | 0.557166 | − | 0.467518i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.92018 | − | 3.32585i | 0.105068 | − | 0.181982i | ||||
\(335\) | −7.86337 | − | 13.6198i | −0.429622 | − | 0.744127i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.71555 | − | 9.72937i | 0.0934520 | − | 0.529992i | −0.901759 | − | 0.432240i | \(-0.857723\pi\) |
0.995211 | − | 0.0977528i | \(-0.0311654\pi\) | |||||||
\(338\) | −2.21509 | − | 12.5624i | −0.120485 | − | 0.683304i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.94861 | − | 1.63507i | −0.105678 | − | 0.0886744i | ||||
\(341\) | 22.4580 | 1.21617 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2971 | 0.609988 | ||||||||
\(344\) | 1.82826 | + | 1.53409i | 0.0985731 | + | 0.0827126i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.840952 | + | 4.76928i | 0.0452099 | + | 0.256398i | ||||
\(347\) | 2.51433 | − | 14.2595i | 0.134976 | − | 0.765488i | −0.839900 | − | 0.542741i | \(-0.817387\pi\) |
0.974876 | − | 0.222747i | \(-0.0715023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.80380 | − | 3.12427i | −0.0965552 | − | 0.167239i | 0.813701 | − | 0.581283i | \(-0.197449\pi\) |
−0.910257 | + | 0.414045i | \(0.864116\pi\) | |||||||
\(350\) | −0.693422 | + | 1.20104i | −0.0370650 | + | 0.0641984i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.52324 | − | 2.11725i | 0.134489 | − | 0.112850i | ||||
\(353\) | −2.01297 | + | 3.48657i | −0.107140 | + | 0.185572i | −0.914610 | − | 0.404336i | \(-0.867503\pi\) |
0.807471 | + | 0.589908i | \(0.200836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.6395 | + | 6.78422i | 0.989282 | + | 0.360069i | ||||
\(356\) | 1.34887 | − | 7.64983i | 0.0714900 | − | 0.405440i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.0949 | + | 8.40587i | −1.22061 | + | 0.444264i | ||||
\(359\) | −3.79911 | − | 3.18783i | −0.200509 | − | 0.168247i | 0.537004 | − | 0.843579i | \(-0.319556\pi\) |
−0.737514 | + | 0.675332i | \(0.764000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.50631 | − | 17.4544i | −0.395069 | − | 0.918651i | ||||
\(362\) | −12.1200 | −0.637011 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.394843 | + | 0.143711i | −0.0206954 | + | 0.00753251i | ||||
\(365\) | 1.30628 | + | 7.40830i | 0.0683740 | + | 0.387768i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3202 | − | 8.48786i | −1.21730 | − | 0.443063i | −0.348073 | − | 0.937468i | \(-0.613164\pi\) |
−0.869232 | + | 0.494405i | \(0.835386\pi\) | |||||||
\(368\) | −1.81879 | − | 3.15023i | −0.0948108 | − | 0.164217i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.64084 | + | 5.57233i | −0.345241 | + | 0.289692i | ||||
\(371\) | 8.67430 | − | 7.27860i | 0.450347 | − | 0.377886i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.271862 | + | 0.470879i | 0.0140765 | + | 0.0243812i | 0.872978 | − | 0.487760i | \(-0.162186\pi\) |
−0.858901 | + | 0.512141i | \(0.828852\pi\) | |||||||
\(374\) | −4.28874 | − | 1.56098i | −0.221766 | − | 0.0807161i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.270907 | + | 1.53639i | 0.0139710 | + | 0.0792333i | ||||
\(377\) | −1.04492 | + | 0.380319i | −0.0538160 | + | 0.0195874i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.73521 | −0.140498 | −0.0702492 | − | 0.997529i | \(-0.522379\pi\) | ||||
−0.0702492 | + | 0.997529i | \(0.522379\pi\) | |||||||
\(380\) | −4.40094 | + | 6.68329i | −0.225763 | + | 0.342846i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4805 | − | 12.9897i | −0.792050 | − | 0.664609i | ||||
\(383\) | 32.1559 | − | 11.7038i | 1.64309 | − | 0.598036i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
0.987575 | + | 0.157146i | \(0.0502294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.893533 | − | 5.06748i | 0.0455387 | − | 0.258263i | ||||
\(386\) | 13.7482 | + | 5.00392i | 0.699763 | + | 0.254693i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.69463 | + | 15.0595i | −0.441403 | + | 0.764532i | ||||
\(389\) | −15.8300 | + | 13.2829i | −0.802610 | + | 0.673470i | −0.948832 | − | 0.315782i | \(-0.897733\pi\) |
0.146221 | + | 0.989252i | \(0.453289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.52012 | + | 4.36498i | −0.127448 | + | 0.220746i | ||||
\(392\) | 3.13794 | + | 5.43507i | 0.158490 | + | 0.274513i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.29158 | − | 18.6675i | 0.165828 | − | 0.940455i | ||||
\(395\) | 0.163003 | + | 0.924437i | 0.00820158 | + | 0.0465135i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.02469 | − | 2.53802i | −0.151805 | − | 0.127379i | 0.563722 | − | 0.825965i | \(-0.309369\pi\) |
−0.715527 | + | 0.698585i | \(0.753813\pi\) | |||||||
\(398\) | 7.88063 | 0.395020 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.62976 | −0.0814878 | ||||||||
\(401\) | −14.7172 | − | 12.3492i | −0.734944 | − | 0.616692i | 0.196530 | − | 0.980498i | \(-0.437033\pi\) |
−0.931475 | + | 0.363806i | \(0.881477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.584614 | − | 3.31551i | −0.0291217 | − | 0.165157i | ||||
\(404\) | −1.04448 | + | 5.92353i | −0.0519647 | + | 0.294706i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.958159 | − | 1.65958i | −0.0475526 | − | 0.0823635i | ||||
\(407\) | −7.77702 | + | 13.4702i | −0.385493 | + | 0.667693i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.83816 | + | 1.54240i | −0.0908909 | + | 0.0762665i | −0.687101 | − | 0.726562i | \(-0.741117\pi\) |
0.596210 | + | 0.802829i | \(0.296673\pi\) | |||||||
\(410\) | −5.76056 | + | 9.97759i | −0.284494 | + | 0.492758i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.155522 | + | 0.0566054i | 0.00766202 | + | 0.00278875i | ||||
\(413\) | −0.391579 | + | 2.22075i | −0.0192683 | + | 0.109276i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8621 | − | 8.32112i | 1.12226 | − | 0.408468i | ||||
\(416\) | −0.378258 | − | 0.317396i | −0.0185456 | − | 0.0155616i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.31878 | + | 13.9688i | −0.162327 | + | 0.683235i | ||||
\(419\) | −29.0694 | −1.42013 | −0.710066 | − | 0.704135i | \(-0.751335\pi\) | ||||
−0.710066 | + | 0.704135i | \(0.751335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0777 | + | 7.30770i | −0.978529 | + | 0.356156i | −0.781268 | − | 0.624195i | \(-0.785427\pi\) |
−0.197261 | + | 0.980351i | \(0.563205\pi\) | |||||||
\(422\) | 0.121475 | + | 0.688917i | 0.00591330 | + | 0.0335360i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.5044 | + | 4.55121i | 0.607265 | + | 0.221026i | ||||
\(425\) | 1.12910 | + | 1.95566i | 0.0547693 | + | 0.0948633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.85360 | + | 4.91175i | −0.283275 | + | 0.237696i | ||||
\(428\) | 9.83847 | − | 8.25546i | 0.475561 | − | 0.399043i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.19071 | + | 3.79441i | 0.105645 | + | 0.182983i | ||||
\(431\) | 19.1193 | + | 6.95886i | 0.920944 | + | 0.335196i | 0.758614 | − | 0.651540i | \(-0.225877\pi\) |
0.162330 | + | 0.986737i | \(0.448099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.03917 | − | 34.2499i | −0.290224 | − | 1.64594i | −0.686004 | − | 0.727598i | \(-0.740637\pi\) |
0.395780 | − | 0.918345i | \(-0.370474\pi\) | |||||||
\(434\) | 5.45200 | − | 1.98437i | 0.261704 | − | 0.0952526i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.87200 | −0.424892 | ||||||||
\(437\) | 14.5556 | + | 6.28818i | 0.696289 | + | 0.300804i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4994 | + | 13.8446i | 0.787473 | + | 0.660769i | 0.945119 | − | 0.326727i | \(-0.105946\pi\) |
−0.157645 | + | 0.987496i | \(0.550390\pi\) | |||||||
\(440\) | 5.68226 | − | 2.06818i | 0.270891 | − | 0.0985964i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.118807 | + | 0.673790i | −0.00565109 | + | 0.0320489i | ||||
\(443\) | −14.2595 | − | 5.19003i | −0.677489 | − | 0.246586i | −0.0197202 | − | 0.999806i | \(-0.506278\pi\) |
−0.657769 | + | 0.753220i | \(0.728500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.13018 | − | 12.3498i | 0.338003 | − | 0.585439i | ||||
\(446\) | −11.5987 | + | 9.73249i | −0.549216 | + | 0.460847i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.425476 | − | 0.736946i | 0.0201018 | − | 0.0348174i | ||||
\(449\) | 8.26581 | + | 14.3168i | 0.390088 | + | 0.675652i | 0.992461 | − | 0.122563i | \(-0.0391114\pi\) |
−0.602373 | + | 0.798215i | \(0.705778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.58955 | + | 20.3573i | −0.169025 | + | 0.958589i | ||||
\(452\) | 2.15028 | + | 12.1948i | 0.101141 | + | 0.573597i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.0479 | + | 10.9485i | 0.612367 | + | 0.513837i | ||||
\(455\) | −0.771382 | −0.0361629 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.605508 | 0.0283245 | 0.0141622 | − | 0.999900i | \(-0.495492\pi\) | ||||
0.0141622 | + | 0.999900i | \(0.495492\pi\) | |||||||
\(458\) | 9.89744 | + | 8.30493i | 0.462477 | + | 0.388064i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.15961 | − | 6.57649i | −0.0540672 | − | 0.306630i | ||||
\(461\) | 2.48270 | − | 14.0801i | 0.115631 | − | 0.655775i | −0.870805 | − | 0.491628i | \(-0.836402\pi\) |
0.986436 | − | 0.164147i | \(-0.0524871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.36374 | + | 9.29026i | 0.249274 | + | 0.431755i | 0.963325 | − | 0.268339i | \(-0.0864747\pi\) |
−0.714051 | + | 0.700094i | \(0.753141\pi\) | |||||||
\(464\) | 1.12598 | − | 1.95026i | 0.0522725 | − | 0.0905387i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.9599 | − | 16.7483i | 0.924623 | − | 0.775851i | ||||
\(467\) | −9.33085 | + | 16.1615i | −0.431780 | + | 0.747865i | −0.997027 | − | 0.0770567i | \(-0.975448\pi\) |
0.565246 | + | 0.824922i | \(0.308781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.85013 | − | 2.49324i | −0.316310 | − | 0.115127i | ||||
\(470\) | −0.497337 | + | 2.82054i | −0.0229405 | + | 0.130102i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.49017 | + | 0.906349i | −0.114620 | + | 0.0417181i | ||||
\(473\) | 6.02202 | + | 5.05308i | 0.276893 | + | 0.232341i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.70057 | − | 4.23904i | 0.261560 | − | 0.194501i | ||||
\(476\) | −1.17908 | −0.0540432 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.5407 | + | 8.93208i | −1.12247 | + | 0.408544i | ||||
\(479\) | 5.76837 | + | 32.7140i | 0.263563 | + | 1.49474i | 0.773095 | + | 0.634290i | \(0.218708\pi\) |
−0.509532 | + | 0.860452i | \(0.670181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.19108 | + | 0.797488i | 0.0999046 | + | 0.0363623i | ||||
\(482\) | −2.46141 | − | 4.26328i | −0.112114 | − | 0.194187i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.115286 | + | 0.0967362i | −0.00524026 | + | 0.00439710i | ||||
\(485\) | −24.4549 | + | 20.5201i | −1.11044 | + | 0.931769i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3045 | + | 26.5081i | 0.693511 | + | 1.20120i | 0.970680 | + | 0.240375i | \(0.0772704\pi\) |
−0.277169 | + | 0.960821i | \(0.589396\pi\) | |||||||
\(488\) | −8.43820 | − | 3.07125i | −0.381979 | − | 0.139029i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00067 | + | 11.3464i | 0.0903811 | + | 0.512577i | ||||
\(491\) | −3.92851 | + | 1.42986i | −0.177291 | + | 0.0645287i | −0.429141 | − | 0.903238i | \(-0.641183\pi\) |
0.251849 | + | 0.967766i | \(0.418961\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.12034 | −0.140533 | ||||||||
\(494\) | 2.14863 | + | 0.126330i | 0.0966714 | + | 0.00568383i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.22299 | + | 4.38261i | 0.234519 | + | 0.196785i | ||||
\(497\) | 8.63989 | − | 3.14466i | 0.387552 | − | 0.141057i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.25750 | + | 12.8029i | −0.101060 | + | 0.573138i | 0.891661 | + | 0.452703i | \(0.149540\pi\) |
−0.992721 | + | 0.120435i | \(0.961571\pi\) | |||||||
\(500\) | −11.4371 | − | 4.16275i | −0.511480 | − | 0.186164i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.43892 | − | 5.95638i | 0.153486 | − | 0.265846i | ||||
\(503\) | 8.29245 | − | 6.95819i | 0.369742 | − | 0.310250i | −0.438917 | − | 0.898527i | \(-0.644638\pi\) |
0.808660 | + | 0.588277i | \(0.200193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.52115 | + | 9.56291i | −0.245688 | + | 0.425544i | ||||
\(506\) | −5.99083 | − | 10.3764i | −0.266325 | − | 0.461288i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.04562 | − | 11.6013i | 0.0907597 | − | 0.514724i | ||||
\(509\) | 2.08167 | + | 11.8057i | 0.0922684 | + | 0.523280i | 0.995550 | + | 0.0942324i | \(0.0300397\pi\) |
−0.903282 | + | 0.429048i | \(0.858849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.67113 | + | 2.24135i | 0.118164 | + | 0.0991513i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.85002 | −0.0816009 | ||||||||
\(515\) | 0.232751 | + | 0.195301i | 0.0102562 | + | 0.00860599i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.892330 | + | 5.06065i | 0.0392446 | + | 0.222567i | ||||
\(518\) | −0.697772 | + | 3.95726i | −0.0306583 | + | 0.173872i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.453247 | − | 0.785046i | −0.0198762 | − | 0.0344266i | ||||
\(521\) | −19.7922 | + | 34.2811i | −0.867112 | + | 1.50188i | −0.00217681 | + | 0.999998i | \(0.500693\pi\) |
−0.864935 | + | 0.501884i | \(0.832640\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.4462 | − | 8.76542i | 0.456781 | − | 0.383285i | −0.385164 | − | 0.922848i | \(-0.625855\pi\) |
0.841945 | + | 0.539563i | \(0.181411\pi\) | |||||||
\(524\) | −9.39955 | + | 16.2805i | −0.410621 | + | 0.711217i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.72514 | + | 3.17569i | 0.380434 | + | 0.138467i | ||||
\(527\) | 1.64049 | − | 9.30371i | 0.0714611 | − | 0.405276i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.17897 | − | 3.34087i | 0.399085 | − | 0.145255i | ||||
\(530\) | 18.7137 | + | 15.7027i | 0.812872 | + | 0.682080i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.428586 | + | 3.68437i | 0.0185816 | + | 0.159738i | ||||
\(533\) | 3.09883 | 0.134225 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.1559 | − | 8.06410i | 0.957885 | − | 0.348642i | ||||
\(536\) | −1.48757 | − | 8.43644i | −0.0642534 | − | 0.364399i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.5799 | + | 7.49047i | 0.887262 | + | 0.322937i | ||||
\(539\) | 10.3359 | + | 17.9024i | 0.445200 | + | 0.771109i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.6562 | + | 28.2409i | −1.44699 | + | 1.21417i | −0.512257 | + | 0.858832i | \(0.671190\pi\) |
−0.934737 | + | 0.355340i | \(0.884365\pi\) | |||||||
\(542\) | 4.22818 | − | 3.54786i | 0.181616 | − | 0.152394i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.692802 | − | 1.19997i | −0.0297037 | − | 0.0514482i | ||||
\(545\) | −15.3052 | − | 5.57062i | −0.655601 | − | 0.238619i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.972903 | − | 5.51761i | −0.0415983 | − | 0.235916i | 0.956919 | − | 0.290356i | \(-0.0937737\pi\) |
−0.998517 | + | 0.0544401i | \(0.982663\pi\) | |||||||
\(548\) | −12.7152 | + | 4.62794i | −0.543165 | + | 0.197696i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.36819 | −0.228900 | ||||||||
\(551\) | 1.13422 | + | 9.75036i | 0.0483192 | + | 0.415379i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.333314 | + | 0.279684i | 0.0141740 | + | 0.0118934i | ||||
\(554\) | −30.5303 | + | 11.1121i | −1.29711 | + | 0.472108i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.28968 | − | 18.6567i | 0.139514 | − | 0.791221i | ||||
\(557\) | 35.2279 | + | 12.8219i | 1.49266 | + | 0.543282i | 0.954147 | − | 0.299338i | \(-0.0967659\pi\) |
0.538508 | + | 0.842620i | \(0.318988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.589233 | − | 1.02058i | 0.0249219 | − | 0.0431660i | ||||
\(560\) | 1.19671 | − | 1.00416i | 0.0505703 | − | 0.0424335i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.8204 | − | 23.9376i | 0.582978 | − | 1.00975i | ||||
\(563\) | −0.786588 | − | 1.36241i | −0.0331507 | − | 0.0574188i | 0.848974 | − | 0.528435i | \(-0.177221\pi\) |
−0.882125 | + | 0.471016i | \(0.843887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.94753 | + | 22.3876i | −0.166074 | + | 0.941852i | ||||
\(566\) | −1.94337 | − | 11.0214i | −0.0816860 | − | 0.463265i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.27698 | + | 6.94521i | 0.347294 | + | 0.291414i | ||||
\(569\) | −23.7454 | −0.995457 | −0.497729 | − | 0.867333i | \(-0.665832\pi\) | ||||
−0.497729 | + | 0.867333i | \(0.665832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0880 | −0.715110 | −0.357555 | − | 0.933892i | \(-0.616389\pi\) | ||||
−0.357555 | + | 0.933892i | \(0.616389\pi\) | |||||||
\(572\) | −1.24593 | − | 1.04546i | −0.0520948 | − | 0.0437128i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.927341 | + | 5.25921i | 0.0387065 | + | 0.219515i | ||||
\(575\) | −1.02945 | + | 5.83829i | −0.0429310 | + | 0.243474i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.02192 | − | 15.6264i | −0.375587 | − | 0.650537i | 0.614827 | − | 0.788662i | \(-0.289226\pi\) |
−0.990415 | + | 0.138125i | \(0.955892\pi\) | |||||||
\(578\) | 7.54005 | − | 13.0597i | 0.313625 | − | 0.543214i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.16699 | − | 2.65742i | 0.131502 | − | 0.110343i | ||||
\(581\) | 5.63864 | − | 9.76641i | 0.233930 | − | 0.405179i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.1876 | + | 14.9910i | 1.70581 | + | 0.620866i | ||||
\(584\) | −0.711552 | + | 4.03541i | −0.0294442 | + | 0.166987i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8458 | − | 4.31151i | 0.489344 | − | 0.178107i | ||||
\(587\) | 1.20843 | + | 1.01399i | 0.0498771 | + | 0.0418519i | 0.667385 | − | 0.744712i | \(-0.267413\pi\) |
−0.617508 | + | 0.786564i | \(0.711858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.6683 | − | 1.74436i | −1.22246 | − | 0.0718751i | ||||
\(590\) | −4.86491 | −0.200285 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.43736 | + | 1.61507i | −0.182374 | + | 0.0663788i | ||||
\(593\) | −0.401996 | − | 2.27983i | −0.0165080 | − | 0.0936215i | 0.975441 | − | 0.220263i | \(-0.0706914\pi\) |
−0.991949 | + | 0.126641i | \(0.959580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.03405 | − | 0.740332i | −0.0833878 | − | 0.0303507i | ||||
\(596\) | −7.59675 | − | 13.1580i | −0.311175 | − | 0.538971i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.37594 | + | 1.15455i | −0.0562664 | + | 0.0472131i | ||||
\(599\) | 3.53882 | − | 2.96942i | 0.144592 | − | 0.121327i | −0.567623 | − | 0.823289i | \(-0.692137\pi\) |
0.712215 | + | 0.701962i | \(0.247692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6076 | − | 32.2293i | −0.759019 | − | 1.31466i | −0.943351 | − | 0.331795i | \(-0.892346\pi\) |
0.184333 | − | 0.982864i | \(-0.440988\pi\) | |||||||
\(602\) | 1.90842 | + | 0.694608i | 0.0777814 | + | 0.0283101i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.643971 | − | 3.65214i | −0.0262028 | − | 0.148604i | ||||
\(605\) | −0.259620 | + | 0.0944940i | −0.0105551 | + | 0.00384173i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.7882 | −1.57437 | −0.787183 | − | 0.616720i | \(-0.788461\pi\) | ||||
−0.787183 | + | 0.616720i | \(0.788461\pi\) | |||||||
\(608\) | −3.49781 | + | 2.60103i | −0.141855 | + | 0.105486i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6284 | − | 10.5965i | −0.511309 | − | 0.429039i | ||||
\(611\) | 0.723886 | − | 0.263473i | 0.0292853 | − | 0.0106590i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.74411 | + | 32.5765i | −0.232002 | + | 1.31575i | 0.616833 | + | 0.787094i | \(0.288415\pi\) |
−0.848835 | + | 0.528657i | \(0.822696\pi\) | |||||||
\(614\) | 27.9464 | + | 10.1716i | 1.12782 | + | 0.410494i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.40146 | − | 2.42740i | 0.0564663 | − | 0.0978025i | ||||
\(617\) | −1.31244 | + | 1.10127i | −0.0528370 | + | 0.0443355i | −0.668824 | − | 0.743421i | \(-0.733202\pi\) |
0.615987 | + | 0.787756i | \(0.288757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0194 | + | 24.2823i | −0.563486 | + | 0.975987i | 0.433703 | + | 0.901056i | \(0.357207\pi\) |
−0.997189 | + | 0.0749305i | \(0.976126\pi\) | |||||||
\(620\) | 6.25844 | + | 10.8399i | 0.251345 | + | 0.435342i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.09414 | − | 23.2190i | 0.164160 | − | 0.930997i | ||||
\(623\) | −1.14782 | − | 6.50963i | −0.0459866 | − | 0.260803i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8741 | − | 9.12444i | −0.434964 | − | 0.364978i | ||||
\(626\) | 22.7907 | 0.910900 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.7587 | −0.628842 | ||||||||
\(629\) | 5.01224 | + | 4.20577i | 0.199851 | + | 0.167695i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.14023 | + | 6.46656i | 0.0453918 | + | 0.257430i | 0.999056 | − | 0.0434438i | \(-0.0138330\pi\) |
−0.953664 | + | 0.300873i | \(0.902722\pi\) | |||||||
\(632\) | −0.0887903 | + | 0.503555i | −0.00353189 | + | 0.0200303i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.37568 | − | 11.0430i | −0.253211 | − | 0.438574i | ||||
\(635\) | 10.8132 | − | 18.7291i | 0.429110 | − | 0.743240i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.37390 | − | 1.99194i | 0.0940574 | − | 0.0789235i | ||||
\(638\) | 3.70883 | − | 6.42389i | 0.146834 | − | 0.254324i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.72511 | + | 0.627888i | 0.0681909 | + | 0.0248195i | ||||
\(641\) | 2.08964 | − | 11.8509i | 0.0825357 | − | 0.468083i | −0.915326 | − | 0.402715i | \(-0.868067\pi\) |
0.997861 | − | 0.0653683i | \(-0.0208222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.4445 | − | 9.98899i | 1.08231 | − | 0.393927i | 0.261541 | − | 0.965192i | \(-0.415769\pi\) |
0.820766 | + | 0.571265i | \(0.193547\pi\) | |||||||
\(644\) | −2.37121 | − | 1.98968i | −0.0934389 | − | 0.0784046i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.54444 | + | 2.39526i | 0.218143 | + | 0.0942402i | ||||
\(647\) | 8.90424 | 0.350062 | 0.175031 | − | 0.984563i | \(-0.443997\pi\) | ||||
0.175031 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.20228 | + | 2.98539i | −0.321968 | + | 0.117187i | ||||
\(650\) | 0.139742 | + | 0.792516i | 0.00548113 | + | 0.0310850i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.88841 | + | 2.87115i | 0.308934 | + | 0.112443i | ||||
\(653\) | −15.4522 | − | 26.7639i | −0.604690 | − | 1.04735i | −0.992100 | − | 0.125446i | \(-0.959964\pi\) |
0.387410 | − | 0.921907i | \(-0.373370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.4376 | + | 22.1838i | −1.03300 | + | 0.866792i | ||||
\(656\) | −4.80749 | + | 4.03396i | −0.187701 | + | 0.157500i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.663782 | + | 1.14970i | 0.0258769 | + | 0.0448201i | ||||
\(659\) | −6.91436 | − | 2.51662i | −0.269345 | − | 0.0980336i | 0.203817 | − | 0.979009i | \(-0.434665\pi\) |
−0.473162 | + | 0.880975i | \(0.656888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.96137 | − | 39.4799i | −0.270766 | − | 1.53559i | −0.752098 | − | 0.659051i | \(-0.770958\pi\) |
0.481332 | − | 0.876538i | \(-0.340153\pi\) | |||||||
\(662\) | 2.97665 | − | 1.08341i | 0.115691 | − | 0.0421080i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2526 | 0.514299 | ||||||||
\(665\) | −1.57401 | + | 6.62504i | −0.0610376 | + | 0.256908i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.27521 | − | 5.26553i | −0.242977 | − | 0.203882i | ||||
\(668\) | 3.60876 | − | 1.31348i | 0.139627 | − | 0.0508201i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.73092 | − | 15.4878i | 0.105505 | − | 0.598346i | ||||
\(671\) | −27.7942 | − | 10.1163i | −1.07298 | − | 0.390534i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.2630 | − | 29.9003i | 0.665438 | − | 1.15257i | −0.313728 | − | 0.949513i | \(-0.601578\pi\) |
0.979166 | − | 0.203060i | \(-0.0650886\pi\) | |||||||
\(674\) | 7.56810 | − | 6.35039i | 0.291512 | − | 0.244608i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.37809 | − | 11.0472i | 0.245311 | − | 0.424891i | ||||
\(677\) | 2.29275 | + | 3.97116i | 0.0881176 | + | 0.152624i | 0.906715 | − | 0.421743i | \(-0.138582\pi\) |
−0.818598 | + | 0.574367i | \(0.805248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.56954 | + | 14.5726i | −0.0986101 | + | 0.559246i | ||||
\(680\) | −0.441713 | − | 2.50508i | −0.0169389 | − | 0.0960654i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.2038 | + | 14.4357i | 0.658767 | + | 0.552771i | ||||
\(683\) | 1.71380 | 0.0655766 | 0.0327883 | − | 0.999462i | \(-0.489561\pi\) | ||||
0.0327883 | + | 0.999462i | \(0.489561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.8409 | −0.949121 | ||||||||
\(686\) | 8.65411 | + | 7.26166i | 0.330415 | + | 0.277251i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.414432 | + | 2.35036i | 0.0158001 | + | 0.0896067i | ||||
\(689\) | 1.14098 | − | 6.47084i | 0.0434680 | − | 0.246519i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.7082 | + | 34.1355i | 0.749734 | + | 1.29858i | 0.947950 | + | 0.318419i | \(0.103152\pi\) |
−0.198217 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(692\) | −2.42142 | + | 4.19403i | −0.0920487 | + | 0.159433i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0919 | − | 9.30720i | 0.421042 | − | 0.353296i | ||||
\(695\) | 17.3894 | − | 30.1193i | 0.659617 | − | 1.14249i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.17127 | + | 2.97410i | 0.309509 | + | 0.112652i | ||||
\(698\) | 0.626453 | − | 3.55279i | 0.0237116 | − | 0.134475i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.30321 | + | 0.474328i | −0.0492566 | + | 0.0179279i | ||||
\(701\) | −9.88950 | − | 8.29828i | −0.373521 | − | 0.313422i | 0.436631 | − | 0.899641i | \(-0.356171\pi\) |
−0.810153 | + | 0.586219i | \(0.800616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3202 | − | 17.1909i | 0.426948 | − | 0.648366i | ||||
\(704\) | 3.29386 | 0.124142 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.78315 | + | 1.37696i | −0.142381 | + | 0.0518224i | ||||
\(707\) | 0.888800 | + | 5.04063i | 0.0334268 | + | 0.189573i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.95651 | − | 1.80402i | −0.186146 | − | 0.0677515i | 0.247265 | − | 0.968948i | \(-0.420468\pi\) |
−0.433411 | + | 0.901196i | \(0.642690\pi\) | |||||||
\(710\) | 9.91787 | + | 17.1783i | 0.372211 | + | 0.644688i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.95051 | − | 4.99307i | 0.223005 | − | 0.187123i | ||||
\(713\) | 18.9990 | − | 15.9421i | 0.711519 | − | 0.597035i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.49293 | − | 2.58583i | −0.0558324 | − | 0.0967046i | ||||
\(716\) | −23.0949 | − | 8.40587i | −0.863099 | − | 0.314142i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.861188 | − | 4.88404i | −0.0321393 | − | 0.182271i | ||||
\(719\) | −5.98107 | + | 2.17693i | −0.223056 | + | 0.0811858i | −0.451131 | − | 0.892458i | \(-0.648979\pi\) |
0.228075 | + | 0.973644i | \(0.426757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.140835 | 0.00524498 | ||||||||
\(722\) | 5.46929 | − | 18.1958i | 0.203546 | − | 0.677177i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.28442 | − | 7.79056i | −0.345053 | − | 0.289534i | ||||
\(725\) | −3.44882 | + | 1.25527i | −0.128086 | + | 0.0466195i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.47318 | − | 42.3825i | 0.277165 | − | 1.57188i | −0.454835 | − | 0.890576i | \(-0.650302\pi\) |
0.732000 | − | 0.681304i | \(-0.238587\pi\) | |||||||
\(728\) | −0.394843 | − | 0.143711i | −0.0146339 | − | 0.00532629i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.76129 | + | 6.51475i | −0.139212 | + | 0.241122i | ||||
\(731\) | 2.53324 | − | 2.12564i | 0.0936954 | − | 0.0786198i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2604 | + | 31.6280i | −0.674464 | + | 1.16821i | 0.302161 | + | 0.953257i | \(0.402292\pi\) |
−0.976625 | + | 0.214950i | \(0.931041\pi\) | |||||||
\(734\) | −12.4084 | − | 21.4920i | −0.458003 | − | 0.793285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.631658 | − | 3.58231i | 0.0232832 | − | 0.132046i | ||||
\(737\) | −4.89985 | − | 27.7885i | −0.180488 | − | 1.02360i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.1129 | + | 21.0722i | 0.923794 | + | 0.775155i | 0.974693 | − | 0.223549i | \(-0.0717642\pi\) |
−0.0508988 | + | 0.998704i | \(0.516209\pi\) | |||||||
\(740\) | −8.66900 | −0.318679 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.3235 | 0.415698 | ||||||||
\(743\) | −29.9769 | − | 25.1536i | −1.09974 | − | 0.922795i | −0.102337 | − | 0.994750i | \(-0.532632\pi\) |
−0.997408 | + | 0.0719543i | \(0.977076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.84349 | − | 27.4688i | −0.177452 | − | 1.00638i | ||||
\(746\) | −0.0944168 | + | 0.535464i | −0.00345684 | + | 0.0196047i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.28199 | − | 3.95253i | −0.0834379 | − | 0.144519i | ||||
\(749\) | 5.46448 | − | 9.46475i | 0.199668 | − | 0.345835i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8836 | + | 16.6843i | −0.725563 | + | 0.608819i | −0.928918 | − | 0.370286i | \(-0.879260\pi\) |
0.203355 | + | 0.979105i | \(0.434815\pi\) | |||||||
\(752\) | −0.780046 | + | 1.35108i | −0.0284454 | + | 0.0492688i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.04492 | − | 0.380319i | −0.0380537 | − | 0.0138504i | ||||
\(755\) | 1.18222 | − | 6.70469i | 0.0430253 | − | 0.244009i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.4791 | + | 3.81407i | −0.380869 | + | 0.138625i | −0.525358 | − | 0.850882i | \(-0.676068\pi\) |
0.144489 | + | 0.989506i | \(0.453846\pi\) | |||||||
\(758\) | −2.09529 | − | 1.75816i | −0.0761045 | − | 0.0638593i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.66725 | + | 2.29083i | −0.278120 | + | 0.0830971i | ||||
\(761\) | 42.5374 | 1.54198 | 0.770991 | − | 0.636846i | \(-0.219761\pi\) | ||||
0.770991 | + | 0.636846i | \(0.219761\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.09434 | + | 2.58213i | −0.256832 | + | 0.0934793i | ||||
\(764\) | −3.50914 | − | 19.9013i | −0.126956 | − | 0.720004i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.1559 | + | 11.7038i | 1.16184 | + | 0.422875i | ||||
\(767\) | 0.654256 | + | 1.13320i | 0.0236238 | + | 0.0409177i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.42581 | − | 2.03550i | 0.0874771 | − | 0.0734020i | −0.598000 | − | 0.801496i | \(-0.704038\pi\) |
0.685478 | + | 0.728094i | \(0.259593\pi\) | |||||||
\(770\) | 3.94180 | − | 3.30756i | 0.142053 | − | 0.119196i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.31524 | + | 12.6704i | 0.263281 | + | 0.456017i | ||||
\(773\) | 31.8571 | + | 11.5950i | 1.14582 | + | 0.417045i | 0.844012 | − | 0.536324i | \(-0.180187\pi\) |
0.301808 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.92956 | − | 10.9431i | −0.0693118 | − | 0.393087i | ||||
\(776\) | −16.3406 | + | 5.94748i | −0.586592 | + | 0.213502i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.6645 | −0.740859 | ||||||||
\(779\) | 6.32320 | − | 26.6144i | 0.226552 | − | 0.953561i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.2632 | + | 22.8765i | 0.975554 | + | 0.818587i | ||||
\(782\) | −4.73628 | + | 1.72386i | −0.169369 | + | 0.0616452i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.08980 | + | 6.18054i | −0.0389213 | + | 0.220733i | ||||
\(785\) | −27.1856 | − | 9.89473i | −0.970294 | − | 0.353158i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.26214 | + | 14.3104i | −0.294513 | + | 0.510112i | −0.974872 | − | 0.222768i | \(-0.928491\pi\) |
0.680358 | + | 0.732880i | \(0.261824\pi\) | |||||||
\(788\) | 14.5207 | − | 12.1843i | 0.517280 | − | 0.434049i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.469349 | + | 0.812936i | −0.0166987 | + | 0.0289230i | ||||
\(791\) | 5.26865 | + | 9.12557i | 0.187332 | + | 0.324468i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.769960 | + | 4.36666i | −0.0273421 | + | 0.155065i | ||||
\(794\) | −0.685642 | − | 3.88847i | −0.0243325 | − | 0.137997i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.03692 | + | 5.06557i | 0.213973 | + | 0.179544i | ||||
\(797\) | −44.2751 | −1.56830 | −0.784152 | − | 0.620569i | \(-0.786902\pi\) | ||||
−0.784152 | + | 0.620569i | \(0.786902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.16167 | 0.0764744 | ||||||||
\(800\) | −1.24847 | − | 1.04759i | −0.0441399 | − | 0.0370378i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.33613 | − | 18.9201i | −0.117803 | − | 0.668093i | ||||
\(803\) | −2.34375 | + | 13.2921i | −0.0827093 | + | 0.469067i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.84130 | − | 4.92128i | −0.100143 | − | 0.173452i | ||||
\(806\) | 1.68333 | − | 2.91561i | 0.0592927 | − | 0.102698i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.60768 | + | 3.86631i | −0.162098 | + | 0.136016i | ||||
\(809\) | −0.439437 | + | 0.761127i | −0.0154498 | + | 0.0267598i | −0.873647 | − | 0.486560i | \(-0.838251\pi\) |
0.858197 | + | 0.513320i | \(0.171585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.2662 | + | 7.74026i | 0.746756 | + | 0.271797i | 0.687240 | − | 0.726430i | \(-0.258822\pi\) |
0.0595162 | + | 0.998227i | \(0.481044\pi\) | |||||||
\(812\) | 0.332765 | − | 1.88720i | 0.0116778 | − | 0.0662279i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.6160 | + | 5.31980i | −0.512291 | + | 0.186459i | ||||
\(815\) | 11.8056 | + | 9.90608i | 0.413532 | + | 0.346995i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.56297 | − | 7.14316i | −0.264595 | − | 0.249908i | ||||
\(818\) | −2.39954 | −0.0838980 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8263 | + | 3.94046i | −0.378071 | + | 0.137607i | ||||
\(821\) | −6.03179 | − | 34.2080i | −0.210511 | − | 1.19387i | −0.888528 | − | 0.458822i | \(-0.848272\pi\) |
0.678017 | − | 0.735046i | \(-0.262839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.83830 | + | 0.669088i | 0.0640792 | + | 0.0233229i | 0.373861 | − | 0.927485i | \(-0.378034\pi\) |
−0.309782 | + | 0.950808i | \(0.600256\pi\) | |||||||
\(824\) | 0.0827516 | + | 0.143330i | 0.00288279 | + | 0.00499313i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.72744 | + | 1.44949i | −0.0601053 | + | 0.0504343i | ||||
\(827\) | 5.29969 | − | 4.44697i | 0.184288 | − | 0.154636i | −0.545976 | − | 0.837801i | \(-0.683841\pi\) |
0.730265 | + | 0.683164i | \(0.239397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.14317 | − | 10.6403i | −0.213361 | − | 0.369552i | 0.739403 | − | 0.673263i | \(-0.235108\pi\) |
−0.952764 | + | 0.303711i | \(0.901774\pi\) | |||||||
\(830\) | 22.8621 | + | 8.32112i | 0.793555 | + | 0.288830i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0857441 | − | 0.486279i | −0.00297264 | − | 0.0168587i | ||||
\(833\) | 8.17146 | − | 2.97417i | 0.283124 | − | 0.103049i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.05022 | 0.243983 | ||||||||
\(836\) | −11.5213 | + | 8.56743i | −0.398472 | + | 0.296311i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.2684 | − | 18.6854i | −0.769251 | − | 0.645478i | ||||
\(839\) | −14.5631 | + | 5.30052i | −0.502772 | + | 0.182994i | −0.580941 | − | 0.813946i | \(-0.697315\pi\) |
0.0781681 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.15516 | + | 23.5651i | −0.143281 | + | 0.812590i | ||||
\(842\) | −20.0777 | − | 7.30770i | −0.691925 | − | 0.251840i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.349772 | + | 0.605824i | −0.0120397 | + | 0.0208533i | ||||
\(845\) | 17.9393 | − | 15.0529i | 0.617130 | − | 0.517834i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0640319 | + | 0.110907i | −0.00220016 | + | 0.00381079i | ||||
\(848\) | 6.65343 | + | 11.5241i | 0.228480 | + | 0.395738i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.392132 | + | 2.22389i | −0.0134500 | + | 0.0762788i | ||||
\(851\) | 2.98278 | + | 16.9162i | 0.102248 | + | 0.579879i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9049 | + | 14.1849i | 0.578813 | + | 0.485682i | 0.884557 | − | 0.466432i | \(-0.154461\pi\) |
−0.305744 | + | 0.952114i | \(0.598905\pi\) | |||||||
\(854\) | −7.64133 | −0.261481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8432 | 0.438972 | ||||||||
\(857\) | 20.8911 | + | 17.5297i | 0.713627 | + | 0.598804i | 0.925614 | − | 0.378468i | \(-0.123549\pi\) |
−0.211987 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.37678 | + | 24.8219i | 0.149334 | + | 0.846914i | 0.963785 | + | 0.266682i | \(0.0859272\pi\) |
−0.814451 | + | 0.580232i | \(0.802962\pi\) | |||||||
\(860\) | −0.760824 | + | 4.31485i | −0.0259439 | + | 0.147135i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.1732 | + | 17.6204i | 0.346499 | + | 0.600155i | ||||
\(863\) | −13.8776 | + | 24.0368i | −0.472400 | + | 0.818221i | −0.999501 | − | 0.0315818i | \(-0.989946\pi\) |
0.527101 | + | 0.849803i | \(0.323279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.81060 | + | 5.71477i | −0.231567 | + | 0.194308i | ||||
\(866\) | 17.3891 | − | 30.1188i | 0.590906 | − | 1.02348i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.45200 | + | 1.98437i | 0.185053 | + | 0.0673538i | ||||
\(869\) | −0.292463 | + | 1.65864i | −0.00992111 | + | 0.0562654i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.97491 | + | 1.44675i | −0.134685 | + | 0.0490213i | ||||
\(872\) | −6.79634 | − | 5.70281i | −0.230153 | − | 0.193122i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.10828 | + | 14.1732i | 0.240441 | + | 0.479415i | ||||
\(875\) | −10.3570 | −0.350130 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7800 | − | 4.28756i | 0.397782 | − | 0.144781i | −0.135381 | − | 0.990794i | \(-0.543226\pi\) |
0.533162 | + | 0.846013i | \(0.321003\pi\) | |||||||
\(878\) | 3.74011 | + | 21.2112i | 0.126223 | + | 0.715844i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.68226 | + | 2.06818i | 0.191549 | + | 0.0697182i | ||||
\(881\) | 28.2494 | + | 48.9295i | 0.951748 | + | 1.64848i | 0.741641 | + | 0.670797i | \(0.234048\pi\) |
0.210107 | + | 0.977678i | \(0.432619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1279 | − | 11.8547i | 0.475442 | − | 0.398943i | −0.373333 | − | 0.927697i | \(-0.621785\pi\) |
0.848775 | + | 0.528754i | \(0.177341\pi\) | |||||||
\(884\) | −0.524116 | + | 0.439785i | −0.0176279 | + | 0.0147916i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.58732 | − | 13.1416i | −0.254901 | − | 0.441502i | ||||
\(887\) | 11.6097 | + | 4.22560i | 0.389817 | + | 0.141882i | 0.529490 | − | 0.848316i | \(-0.322383\pi\) |
−0.139674 | + | 0.990198i | \(0.544605\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.74072 | − | 9.87213i | −0.0583820 | − | 0.331101i | ||||
\(890\) | 13.4004 | − | 4.87733i | 0.449181 | − | 0.163489i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.1411 | −0.506960 | ||||||||
\(893\) | −0.785749 | − | 6.75474i | −0.0262941 | − | 0.226039i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.5634 | − | 29.0021i | −1.15533 | − | 0.969433i | ||||
\(896\) | 0.799633 | − | 0.291043i | 0.0267139 | − | 0.00972305i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.87068 | + | 16.2805i | −0.0957960 | + | 0.543286i | ||||
\(899\) | 14.4282 | + | 5.25145i | 0.481209 | + | 0.175146i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.21902 | − | 15.9678i | 0.307130 | − | 0.531965i | ||||
\(902\) | −15.8352 | + | 13.2873i | −0.527254 | + | 0.442419i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.19148 | + | 10.7240i | −0.205926 | + | 0.356674i | ||||
\(905\) | −11.1250 | − | 19.2691i | −0.369809 | − | 0.640528i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.57989 | − | 8.96001i | 0.0524594 | − | 0.297512i | −0.947278 | − | 0.320412i | \(-0.896179\pi\) |
0.999738 | + | 0.0228997i | \(0.00728984\pi\) | |||||||
\(908\) | 2.95771 | + | 16.7740i | 0.0981552 | + | 0.556666i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.590913 | − | 0.495835i | −0.0195886 | − | 0.0164368i | ||||
\(911\) | 5.50145 | 0.182271 | 0.0911355 | − | 0.995839i | \(-0.470950\pi\) | ||||
0.0911355 | + | 0.995839i | \(0.470950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.6520 | 1.44467 | ||||||||
\(914\) | 0.463846 | + | 0.389213i | 0.0153427 | + | 0.0128740i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24357 | + | 12.7239i | 0.0741295 | + | 0.420409i | ||||
\(917\) | −2.77787 | + | 15.7541i | −0.0917335 | + | 0.520246i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2195 | + | 40.2174i | 0.765941 | + | 1.32665i | 0.939748 | + | 0.341869i | \(0.111060\pi\) |
−0.173807 | + | 0.984780i | \(0.555607\pi\) | |||||||
\(920\) | 3.33897 | − | 5.78327i | 0.110083 | − | 0.190669i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.9524 | − | 9.19013i | 0.360697 | − | 0.302661i | ||||
\(923\) | 2.66761 | − | 4.62043i | 0.0878053 | − | 0.152083i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.23181 | + | 2.63216i | 0.237780 | + | 0.0865450i | ||||
\(926\) | −1.86281 | + | 10.5645i | −0.0612156 | + | 0.347171i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.11616 | − | 0.770219i | 0.0694663 | − | 0.0252837i | ||||
\(929\) | −6.57462 | − | 5.51676i | −0.215706 | − | 0.180999i | 0.528532 | − | 0.848914i | \(-0.322743\pi\) |
−0.744238 | + | 0.667914i | \(0.767187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.2639 | − | 24.4529i | −0.401932 | − | 0.801412i | ||||
\(932\) | 26.0558 | 0.853485 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.5363 | + | 6.38268i | −0.573804 | + | 0.208848i | ||||
\(935\) | −1.45494 | − | 8.25138i | −0.0475816 | − | 0.269849i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.45128 | − | 0.528223i | −0.0474113 | − | 0.0172563i | 0.318206 | − | 0.948022i | \(-0.396920\pi\) |
−0.365617 | + | 0.930765i | \(0.619142\pi\) | |||||||
\(938\) | −3.64488 | − | 6.31311i | −0.119009 | − | 0.206130i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.19399 | + | 1.84098i | −0.0715601 | + | 0.0600461i | ||||
\(941\) | −14.9610 | + | 12.5538i | −0.487715 | + | 0.409242i | −0.853207 | − | 0.521573i | \(-0.825345\pi\) |
0.365491 | + | 0.930815i | \(0.380901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4142 | + | 19.7700i | 0.371698 | + | 0.643800i | ||||
\(944\) | −2.49017 | − | 0.906349i | −0.0810483 | − | 0.0294992i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.36508 | + | 7.74176i | 0.0443826 | + | 0.251706i | ||||
\(947\) | −5.74365 | + | 2.09052i | −0.186644 | + | 0.0679328i | −0.433651 | − | 0.901081i | \(-0.642775\pi\) |
0.247007 | + | 0.969014i | \(0.420553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.02335 | 0.0656806 | ||||||||
\(950\) | 7.09169 | + | 0.416959i | 0.230085 | + | 0.0135279i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.903230 | − | 0.757900i | −0.0292738 | − | 0.0245637i | ||||
\(953\) | −37.7175 | + | 13.7280i | −1.22179 | + | 0.444695i | −0.870778 | − | 0.491676i | \(-0.836384\pi\) |
−0.351011 | + | 0.936371i | \(0.614162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.44216 | − | 36.5353i | 0.208463 | − | 1.18225i | ||||
\(956\) | −24.5407 | − | 8.93208i | −0.793703 | − | 0.288884i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.6093 | + | 28.7682i | −0.536624 | + | 0.929459i | ||||
\(959\) | −8.82054 | + | 7.40131i | −0.284830 | + | 0.239001i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.74344 | + | 13.4120i | −0.249788 | + | 0.432646i | ||||
\(962\) | 1.16585 | + | 2.01931i | 0.0375885 | + | 0.0651052i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.854838 | − | 4.84803i | 0.0275325 | − | 0.156144i | ||||
\(965\) | 4.66401 | + | 26.4509i | 0.150140 | + | 0.851486i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.9495 | − | 15.9006i | −0.609376 | − | 0.511327i | 0.285068 | − | 0.958507i | \(-0.407984\pi\) |
−0.894444 | + | 0.447180i | \(0.852428\pi\) | |||||||
\(968\) | −0.150495 | −0.00483709 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.9236 | −1.02500 | ||||||||
\(971\) | 31.9088 | + | 26.7747i | 1.02400 | + | 0.859240i | 0.990125 | − | 0.140186i | \(-0.0447700\pi\) |
0.0338773 | + | 0.999426i | \(0.489214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.79936 | − | 15.8760i | −0.0897434 | − | 0.508960i | ||||
\(974\) | −5.31518 | + | 30.1439i | −0.170309 | + | 0.965872i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.48987 | − | 7.77668i | −0.143717 | − | 0.248926i | ||||
\(977\) | 18.5791 | − | 32.1799i | 0.594398 | − | 1.02953i | −0.399234 | − | 0.916849i | \(-0.630724\pi\) |
0.993632 | − | 0.112678i | \(-0.0359428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.6001 | − | 16.4465i | 0.626423 | − | 0.525631i | ||||
\(980\) | −5.76070 | + | 9.97783i | −0.184019 | + | 0.318730i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.92851 | − | 1.42986i | −0.125364 | − | 0.0456287i | ||||
\(983\) | −5.76922 | + | 32.7189i | −0.184010 | + | 1.04357i | 0.743212 | + | 0.669056i | \(0.233301\pi\) |
−0.927221 | + | 0.374514i | \(0.877810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.7002 | − | 11.9019i | 1.04192 | − | 0.379227i | ||||
\(986\) | −2.39032 | − | 2.00572i | −0.0761233 | − | 0.0638750i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.56474 | + | 1.47789i | 0.0497811 | + | 0.0470178i | ||||
\(989\) | 8.68151 | 0.276056 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3334 | − | 10.6765i | 0.931807 | − | 0.339150i | 0.168882 | − | 0.985636i | \(-0.445984\pi\) |
0.762926 | + | 0.646486i | \(0.223762\pi\) | |||||||
\(992\) | 1.18396 | + | 6.71455i | 0.0375906 | + | 0.213187i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.63989 | + | 3.14466i | 0.274041 | + | 0.0997427i | ||||
\(995\) | 7.23372 | + | 12.5292i | 0.229324 | + | 0.397201i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48758 | − | 7.12193i | 0.268804 | − | 0.225554i | −0.498415 | − | 0.866939i | \(-0.666084\pi\) |
0.767219 | + | 0.641385i | \(0.221640\pi\) | |||||||
\(998\) | −9.95891 | + | 8.35652i | −0.315244 | + | 0.264521i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 342.2.u.f.73.1 | ✓ | 12 | |
3.2 | odd | 2 | 342.2.u.g.73.2 | yes | 12 | ||
19.5 | even | 9 | 6498.2.a.ce.1.2 | 6 | |||
19.6 | even | 9 | inner | 342.2.u.f.253.1 | yes | 12 | |
19.14 | odd | 18 | 6498.2.a.cc.1.2 | 6 | |||
57.5 | odd | 18 | 6498.2.a.cb.1.5 | 6 | |||
57.14 | even | 18 | 6498.2.a.cd.1.5 | 6 | |||
57.44 | odd | 18 | 342.2.u.g.253.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.u.f.73.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
342.2.u.f.253.1 | yes | 12 | 19.6 | even | 9 | inner | |
342.2.u.g.73.2 | yes | 12 | 3.2 | odd | 2 | ||
342.2.u.g.253.2 | yes | 12 | 57.44 | odd | 18 | ||
6498.2.a.cb.1.5 | 6 | 57.5 | odd | 18 | |||
6498.2.a.cc.1.2 | 6 | 19.14 | odd | 18 | |||
6498.2.a.cd.1.5 | 6 | 57.14 | even | 18 | |||
6498.2.a.ce.1.2 | 6 | 19.5 | even | 9 |