Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(749,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.n (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 749.16 | ||
Character | \(\chi\) | \(=\) | 975.749 |
Dual form | 975.2.n.q.824.16 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35176 | + | 1.35176i | 0.955840 | + | 0.955840i | 0.999065 | − | 0.0432252i | \(-0.0137633\pi\) |
−0.0432252 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(3\) | 0.875587 | + | 1.49444i | 0.505520 | + | 0.862815i | ||||
\(4\) | 1.65452i | 0.827261i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.836541 | + | 3.20371i | −0.341516 | + | 1.30791i | ||||
\(7\) | 3.04341 | + | 3.04341i | 1.15030 | + | 1.15030i | 0.986492 | + | 0.163808i | \(0.0523778\pi\) |
0.163808 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(8\) | 0.467005 | − | 0.467005i | 0.165111 | − | 0.165111i | ||||
\(9\) | −1.46670 | + | 2.61702i | −0.488898 | + | 0.872341i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.65064 | − | 1.65064i | −0.497686 | − | 0.497686i | 0.413031 | − | 0.910717i | \(-0.364470\pi\) |
−0.910717 | + | 0.413031i | \(0.864470\pi\) | |||||||
\(12\) | −2.47258 | + | 1.44868i | −0.713773 | + | 0.418197i | ||||
\(13\) | 2.93636 | + | 2.09231i | 0.814400 | + | 0.580303i | ||||
\(14\) | 8.22793i | 2.19901i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.57160 | 1.14290 | ||||||||
\(17\) | − | 4.34228i | − | 1.05316i | −0.850126 | − | 0.526579i | \(-0.823475\pi\) | ||
0.850126 | − | 0.526579i | \(-0.176525\pi\) | |||||||
\(18\) | −5.52021 | + | 1.55497i | −1.30113 | + | 0.366509i | ||||
\(19\) | −3.93929 | − | 3.93929i | −0.903736 | − | 0.903736i | 0.0920208 | − | 0.995757i | \(-0.470667\pi\) |
−0.995757 | + | 0.0920208i | \(0.970667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.88342 | + | 7.21296i | −0.410996 | + | 1.57400i | ||||
\(22\) | − | 4.46254i | − | 0.951417i | ||||||
\(23\) | 3.46204i | 0.721884i | 0.932588 | + | 0.360942i | \(0.117545\pi\) | ||||
−0.932588 | + | 0.360942i | \(0.882455\pi\) | |||||||
\(24\) | 1.10681 | + | 0.289007i | 0.225927 | + | 0.0589933i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.14095 | + | 6.79757i | 0.223759 | + | 1.33311i | ||||
\(27\) | −5.19520 | + | 0.0995434i | −0.999816 | + | 0.0191571i | ||||
\(28\) | −5.03538 | + | 5.03538i | −0.951598 | + | 0.951598i | ||||
\(29\) | − | 5.82342i | − | 1.08138i | −0.841221 | − | 0.540691i | \(-0.818163\pi\) | ||
0.841221 | − | 0.540691i | \(-0.181837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77766 | + | 1.77766i | 0.319277 | + | 0.319277i | 0.848489 | − | 0.529212i | \(-0.177513\pi\) |
−0.529212 | + | 0.848489i | \(0.677513\pi\) | |||||||
\(32\) | 5.24571 | + | 5.24571i | 0.927319 | + | 0.927319i | ||||
\(33\) | 1.02150 | − | 3.91206i | 0.177821 | − | 0.681002i | ||||
\(34\) | 5.86973 | − | 5.86973i | 1.00665 | − | 1.00665i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.32992 | − | 2.42668i | −0.721653 | − | 0.404447i | ||||
\(37\) | −4.39024 | − | 4.39024i | −0.721750 | − | 0.721750i | 0.247211 | − | 0.968962i | \(-0.420486\pi\) |
−0.968962 | + | 0.247211i | \(0.920486\pi\) | |||||||
\(38\) | − | 10.6500i | − | 1.72765i | ||||||
\(39\) | −0.555794 | + | 6.22022i | −0.0889983 | + | 0.996032i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.91144 | + | 5.91144i | −0.923212 | + | 0.923212i | −0.997255 | − | 0.0740434i | \(-0.976410\pi\) |
0.0740434 | + | 0.997255i | \(0.476410\pi\) | |||||||
\(42\) | −12.2961 | + | 7.20427i | −1.89733 | + | 1.11164i | ||||
\(43\) | −8.59781 | −1.31115 | −0.655576 | − | 0.755129i | \(-0.727574\pi\) | ||||
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(44\) | 2.73102 | − | 2.73102i | 0.411716 | − | 0.411716i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.67985 | + | 4.67985i | −0.690006 | + | 0.690006i | ||||
\(47\) | 6.54241 | − | 6.54241i | 0.954309 | − | 0.954309i | −0.0446917 | − | 0.999001i | \(-0.514231\pi\) |
0.999001 | + | 0.0446917i | \(0.0142305\pi\) | |||||||
\(48\) | 4.00283 | + | 6.83198i | 0.577759 | + | 0.986111i | ||||
\(49\) | 11.5247i | 1.64638i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.48927 | − | 3.80204i | 0.908680 | − | 0.532393i | ||||
\(52\) | −3.46178 | + | 4.85827i | −0.480062 | + | 0.673722i | ||||
\(53\) | −1.40983 | −0.193655 | −0.0968277 | − | 0.995301i | \(-0.530870\pi\) | ||||
−0.0968277 | + | 0.995301i | \(0.530870\pi\) | |||||||
\(54\) | −7.15723 | − | 6.88811i | −0.973976 | − | 0.937354i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.84257 | 0.379855 | ||||||||
\(57\) | 2.43784 | − | 9.33623i | 0.322900 | − | 1.23661i | ||||
\(58\) | 7.87188 | − | 7.87188i | 1.03363 | − | 1.03363i | ||||
\(59\) | −4.52860 | − | 4.52860i | −0.589573 | − | 0.589573i | 0.347943 | − | 0.937516i | \(-0.386880\pi\) |
−0.937516 | + | 0.347943i | \(0.886880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47788 | 0.573334 | 0.286667 | − | 0.958030i | \(-0.407453\pi\) | ||||
0.286667 | + | 0.958030i | \(0.407453\pi\) | |||||||
\(62\) | 4.80594i | 0.610355i | ||||||||
\(63\) | −12.4284 | + | 3.50091i | −1.56583 | + | 0.441074i | ||||
\(64\) | 5.03870i | 0.629837i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.66900 | − | 3.90734i | 0.820897 | − | 0.480961i | ||||
\(67\) | −4.35368 | + | 4.35368i | −0.531886 | + | 0.531886i | −0.921133 | − | 0.389247i | \(-0.872735\pi\) |
0.389247 | + | 0.921133i | \(0.372735\pi\) | |||||||
\(68\) | 7.18440 | 0.871236 | ||||||||
\(69\) | −5.17380 | + | 3.03131i | −0.622852 | + | 0.364927i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.80223 | − | 6.80223i | 0.807276 | − | 0.807276i | −0.176945 | − | 0.984221i | \(-0.556622\pi\) |
0.984221 | + | 0.176945i | \(0.0566215\pi\) | |||||||
\(72\) | 0.537208 | + | 1.90712i | 0.0633106 | + | 0.224756i | ||||
\(73\) | 7.30145 | + | 7.30145i | 0.854571 | + | 0.854571i | 0.990692 | − | 0.136121i | \(-0.0434637\pi\) |
−0.136121 | + | 0.990692i | \(0.543464\pi\) | |||||||
\(74\) | − | 11.8691i | − | 1.37976i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.51765 | − | 6.51765i | 0.747626 | − | 0.747626i | ||||
\(77\) | − | 10.0471i | − | 1.14498i | ||||||
\(78\) | −9.15955 | + | 7.65695i | −1.03712 | + | 0.866979i | ||||
\(79\) | 2.67693 | 0.301178 | 0.150589 | − | 0.988596i | \(-0.451883\pi\) | ||||
0.150589 | + | 0.988596i | \(0.451883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.69761 | − | 7.67675i | −0.521957 | − | 0.852972i | ||||
\(82\) | −15.9817 | −1.76489 | ||||||||
\(83\) | −4.42241 | − | 4.42241i | −0.485423 | − | 0.485423i | 0.421436 | − | 0.906858i | \(-0.361526\pi\) |
−0.906858 | + | 0.421436i | \(0.861526\pi\) | |||||||
\(84\) | −11.9340 | − | 3.11616i | −1.30211 | − | 0.340001i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.6222 | − | 11.6222i | −1.25325 | − | 1.25325i | ||||
\(87\) | 8.70275 | − | 5.09891i | 0.933033 | − | 0.546661i | ||||
\(88\) | −1.54171 | −0.164347 | ||||||||
\(89\) | −2.02174 | − | 2.02174i | −0.214304 | − | 0.214304i | 0.591789 | − | 0.806093i | \(-0.298422\pi\) |
−0.806093 | + | 0.591789i | \(0.798422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56879 | + | 15.3043i | 0.269282 | + | 1.60433i | ||||
\(92\) | −5.72801 | −0.597187 | ||||||||
\(93\) | −1.10011 | + | 4.21310i | −0.114076 | + | 0.436878i | ||||
\(94\) | 17.6876 | 1.82433 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.24632 | + | 12.4325i | −0.331326 | + | 1.26888i | ||||
\(97\) | −1.21361 | + | 1.21361i | −0.123224 | + | 0.123224i | −0.766029 | − | 0.642806i | \(-0.777770\pi\) |
0.642806 | + | 0.766029i | \(0.277770\pi\) | |||||||
\(98\) | −15.5786 | + | 15.5786i | −1.57368 | + | 1.57368i | ||||
\(99\) | 6.74074 | − | 1.89877i | 0.677470 | − | 0.190834i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.82645 | 0.579754 | 0.289877 | − | 0.957064i | \(-0.406386\pi\) | ||||
0.289877 | + | 0.957064i | \(0.406386\pi\) | |||||||
\(102\) | 13.9114 | + | 3.63249i | 1.37743 | + | 0.359671i | ||||
\(103\) | 0.655146 | 0.0645535 | 0.0322767 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322767 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(104\) | 2.34842 | − | 0.394175i | 0.230281 | − | 0.0386520i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.90576 | − | 1.90576i | −0.185104 | − | 0.185104i | ||||
\(107\) | 0.228933 | 0.0221318 | 0.0110659 | − | 0.999939i | \(-0.496478\pi\) | ||||
0.0110659 | + | 0.999939i | \(0.496478\pi\) | |||||||
\(108\) | −0.164697 | − | 8.59557i | −0.0158480 | − | 0.827109i | ||||
\(109\) | 9.83957 | + | 9.83957i | 0.942459 | + | 0.942459i | 0.998432 | − | 0.0559728i | \(-0.0178260\pi\) |
−0.0559728 | + | 0.998432i | \(0.517826\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.71691 | − | 10.4050i | 0.257877 | − | 0.987596i | ||||
\(112\) | 13.9133 | + | 13.9133i | 1.31468 | + | 1.31468i | ||||
\(113\) | 6.58296 | 0.619273 | 0.309636 | − | 0.950855i | \(-0.399793\pi\) | ||||
0.309636 | + | 0.950855i | \(0.399793\pi\) | |||||||
\(114\) | 15.9157 | − | 9.32498i | 1.49065 | − | 0.873365i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.63498 | 0.894585 | ||||||||
\(117\) | −9.78238 | + | 4.61574i | −0.904381 | + | 0.426725i | ||||
\(118\) | − | 12.2432i | − | 1.12708i | ||||||
\(119\) | 13.2153 | − | 13.2153i | 1.21145 | − | 1.21145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.55078i | − | 0.504616i | ||||||
\(122\) | 6.05303 | + | 6.05303i | 0.548016 | + | 0.548016i | ||||
\(123\) | −14.0103 | − | 3.65831i | −1.26326 | − | 0.329858i | ||||
\(124\) | −2.94117 | + | 2.94117i | −0.264125 | + | 0.264125i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −21.5327 | − | 12.0679i | −1.91828 | − | 1.07509i | ||||
\(127\) | 8.21272 | 0.728761 | 0.364381 | − | 0.931250i | \(-0.381281\pi\) | ||||
0.364381 | + | 0.931250i | \(0.381281\pi\) | |||||||
\(128\) | 3.68030 | − | 3.68030i | 0.325296 | − | 0.325296i | ||||
\(129\) | −7.52812 | − | 12.8489i | −0.662814 | − | 1.13128i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.36853i | − | 0.643791i | −0.946775 | − | 0.321896i | \(-0.895680\pi\) | ||
0.946775 | − | 0.321896i | \(-0.104320\pi\) | |||||||
\(132\) | 6.47258 | + | 1.69010i | 0.563366 | + | 0.147104i | ||||
\(133\) | − | 23.9778i | − | 2.07914i | ||||||
\(134\) | −11.7703 | −1.01680 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.02787 | − | 2.02787i | −0.173888 | − | 0.173888i | ||||
\(137\) | −1.95599 | + | 1.95599i | −0.167112 | + | 0.167112i | −0.785709 | − | 0.618597i | \(-0.787701\pi\) |
0.618597 | + | 0.785709i | \(0.287701\pi\) | |||||||
\(138\) | −11.0914 | − | 2.89613i | −0.944159 | − | 0.246535i | ||||
\(139\) | −14.3848 | −1.22010 | −0.610052 | − | 0.792361i | \(-0.708852\pi\) | ||||
−0.610052 | + | 0.792361i | \(0.708852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5057 | + | 4.04879i | 1.30581 | + | 0.340969i | ||||
\(142\) | 18.3900 | 1.54325 | ||||||||
\(143\) | −1.39322 | − | 8.30053i | −0.116507 | − | 0.694125i | ||||
\(144\) | −6.70515 | + | 11.9640i | −0.558762 | + | 0.996999i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 19.7397i | 1.63367i | ||||||||
\(147\) | −17.2229 | + | 10.0908i | −1.42052 | + | 0.832279i | ||||
\(148\) | 7.26374 | − | 7.26374i | 0.597076 | − | 0.597076i | ||||
\(149\) | −4.35495 | + | 4.35495i | −0.356772 | + | 0.356772i | −0.862622 | − | 0.505850i | \(-0.831179\pi\) |
0.505850 | + | 0.862622i | \(0.331179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31495 | − | 4.31495i | 0.351145 | − | 0.351145i | −0.509390 | − | 0.860536i | \(-0.670129\pi\) |
0.860536 | + | 0.509390i | \(0.170129\pi\) | |||||||
\(152\) | −3.67934 | −0.298434 | ||||||||
\(153\) | 11.3638 | + | 6.36880i | 0.918712 | + | 0.514887i | ||||
\(154\) | 13.5813 | − | 13.5813i | 1.09442 | − | 1.09442i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.2915 | − | 0.919573i | −0.823978 | − | 0.0736248i | ||||
\(157\) | − | 17.4089i | − | 1.38938i | −0.719308 | − | 0.694691i | \(-0.755541\pi\) | ||
0.719308 | − | 0.694691i | \(-0.244459\pi\) | |||||||
\(158\) | 3.61858 | + | 3.61858i | 0.287878 | + | 0.287878i | ||||
\(159\) | −1.23443 | − | 2.10691i | −0.0978967 | − | 0.167089i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5364 | + | 10.5364i | −0.830384 | + | 0.830384i | ||||
\(162\) | 4.02709 | − | 16.7272i | 0.316398 | − | 1.31421i | ||||
\(163\) | −2.05453 | − | 2.05453i | −0.160923 | − | 0.160923i | 0.622052 | − | 0.782976i | \(-0.286299\pi\) |
−0.782976 | + | 0.622052i | \(0.786299\pi\) | |||||||
\(164\) | −9.78060 | − | 9.78060i | −0.763737 | − | 0.763737i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 11.9561i | − | 0.927973i | ||||||
\(167\) | 13.6508 | − | 13.6508i | 1.05633 | − | 1.05633i | 0.0580142 | − | 0.998316i | \(-0.481523\pi\) |
0.998316 | − | 0.0580142i | \(-0.0184769\pi\) | |||||||
\(168\) | 2.48892 | + | 4.24805i | 0.192024 | + | 0.327744i | ||||
\(169\) | 4.24445 | + | 12.2876i | 0.326496 | + | 0.945199i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.0870 | − | 4.53148i | 1.23020 | − | 0.346531i | ||||
\(172\) | − | 14.2253i | − | 1.08467i | ||||||
\(173\) | 7.23751i | 0.550257i | 0.961407 | + | 0.275129i | \(0.0887205\pi\) | ||||
−0.961407 | + | 0.275129i | \(0.911280\pi\) | |||||||
\(174\) | 18.6566 | + | 4.87153i | 1.41435 | + | 0.369310i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.54606 | − | 7.54606i | −0.568806 | − | 0.568806i | ||||
\(177\) | 2.80253 | − | 10.7329i | 0.210651 | − | 0.806734i | ||||
\(178\) | − | 5.46583i | − | 0.409681i | ||||||
\(179\) | 10.1878 | 0.761474 | 0.380737 | − | 0.924683i | \(-0.375670\pi\) | ||||
0.380737 | + | 0.924683i | \(0.375670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8159i | 1.54723i | 0.633655 | + | 0.773616i | \(0.281554\pi\) | ||||
−0.633655 | + | 0.773616i | \(0.718446\pi\) | |||||||
\(182\) | −17.2154 | + | 24.1602i | −1.27609 | + | 1.79087i | ||||
\(183\) | 3.92077 | + | 6.69192i | 0.289832 | + | 0.494681i | ||||
\(184\) | 1.61679 | + | 1.61679i | 0.119191 | + | 0.119191i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.18219 | + | 4.20802i | −0.526624 | + | 0.308547i | ||||
\(187\) | −7.16754 | + | 7.16754i | −0.524142 | + | 0.524142i | ||||
\(188\) | 10.8246 | + | 10.8246i | 0.789462 | + | 0.789462i | ||||
\(189\) | −16.1141 | − | 15.5082i | −1.17213 | − | 1.12805i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.6575i | 1.49472i | 0.664417 | + | 0.747362i | \(0.268680\pi\) | ||||
−0.664417 | + | 0.747362i | \(0.731320\pi\) | |||||||
\(192\) | −7.53002 | + | 4.41182i | −0.543433 | + | 0.318395i | ||||
\(193\) | 2.66617 | + | 2.66617i | 0.191915 | + | 0.191915i | 0.796523 | − | 0.604608i | \(-0.206670\pi\) |
−0.604608 | + | 0.796523i | \(0.706670\pi\) | |||||||
\(194\) | −3.28104 | −0.235565 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.0678 | −1.36199 | ||||||||
\(197\) | 16.8317 | + | 16.8317i | 1.19921 | + | 1.19921i | 0.974404 | + | 0.224804i | \(0.0721741\pi\) |
0.224804 | + | 0.974404i | \(0.427826\pi\) | |||||||
\(198\) | 11.6786 | + | 6.54519i | 0.829960 | + | 0.465146i | ||||
\(199\) | 6.70679i | 0.475432i | 0.971335 | + | 0.237716i | \(0.0763987\pi\) | ||||
−0.971335 | + | 0.237716i | \(0.923601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.3183 | − | 2.69428i | −0.727799 | − | 0.190040i | ||||
\(202\) | 7.87598 | + | 7.87598i | 0.554152 | + | 0.554152i | ||||
\(203\) | 17.7231 | − | 17.7231i | 1.24391 | − | 1.24391i | ||||
\(204\) | 6.29056 | + | 10.7366i | 0.440427 | + | 0.751715i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.885602 | + | 0.885602i | 0.0617028 | + | 0.0617028i | ||||
\(207\) | −9.06022 | − | 5.07775i | −0.629729 | − | 0.352928i | ||||
\(208\) | 13.4239 | + | 9.56522i | 0.930779 | + | 0.663229i | ||||
\(209\) | 13.0047i | 0.899555i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.4362 | −1.75110 | −0.875549 | − | 0.483129i | \(-0.839500\pi\) | ||||
−0.875549 | + | 0.483129i | \(0.839500\pi\) | |||||||
\(212\) | − | 2.33260i | − | 0.160203i | ||||||
\(213\) | 16.1214 | + | 4.20957i | 1.10462 | + | 0.288435i | ||||
\(214\) | 0.309463 | + | 0.309463i | 0.0211544 | + | 0.0211544i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.37970 | + | 2.47267i | −0.161918 | + | 0.168244i | ||||
\(217\) | 10.8203i | 0.734529i | ||||||||
\(218\) | 26.6015i | 1.80168i | ||||||||
\(219\) | −4.51852 | + | 17.3046i | −0.305333 | + | 1.16934i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.08541 | − | 12.7505i | 0.611151 | − | 0.857692i | ||||
\(222\) | 17.7377 | − | 10.3924i | 1.19047 | − | 0.697495i | ||||
\(223\) | −5.17991 | + | 5.17991i | −0.346872 | + | 0.346872i | −0.858943 | − | 0.512071i | \(-0.828878\pi\) |
0.512071 | + | 0.858943i | \(0.328878\pi\) | |||||||
\(224\) | 31.9297i | 2.13339i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.89859 | + | 8.89859i | 0.591926 | + | 0.591926i | ||||
\(227\) | −20.0123 | − | 20.0123i | −1.32827 | − | 1.32827i | −0.906883 | − | 0.421383i | \(-0.861545\pi\) |
−0.421383 | − | 0.906883i | \(-0.638455\pi\) | |||||||
\(228\) | 15.4470 | + | 4.03346i | 1.02300 | + | 0.267122i | ||||
\(229\) | −11.2696 | + | 11.2696i | −0.744713 | + | 0.744713i | −0.973481 | − | 0.228768i | \(-0.926530\pi\) |
0.228768 | + | 0.973481i | \(0.426530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.0148 | − | 8.79714i | 0.987904 | − | 0.578809i | ||||
\(232\) | −2.71957 | − | 2.71957i | −0.178548 | − | 0.178548i | ||||
\(233\) | − | 10.0133i | − | 0.655994i | −0.944679 | − | 0.327997i | \(-0.893626\pi\) | ||
0.944679 | − | 0.327997i | \(-0.106374\pi\) | |||||||
\(234\) | −19.4628 | − | 6.98407i | −1.27233 | − | 0.456563i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.49266 | − | 7.49266i | 0.487731 | − | 0.487731i | ||||
\(237\) | 2.34389 | + | 4.00051i | 0.152252 | + | 0.259861i | ||||
\(238\) | 35.7280 | 2.31590 | ||||||||
\(239\) | −12.6708 | + | 12.6708i | −0.819603 | + | 0.819603i | −0.986050 | − | 0.166448i | \(-0.946770\pi\) |
0.166448 | + | 0.986050i | \(0.446770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.25390 | + | 6.25390i | −0.402849 | + | 0.402849i | −0.879236 | − | 0.476387i | \(-0.841946\pi\) |
0.476387 | + | 0.879236i | \(0.341946\pi\) | |||||||
\(242\) | 7.50333 | − | 7.50333i | 0.482333 | − | 0.482333i | ||||
\(243\) | 7.35927 | − | 13.7420i | 0.472097 | − | 0.881547i | ||||
\(244\) | 7.40875i | 0.474297i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.9934 | − | 23.8837i | −0.892185 | − | 1.52277i | ||||
\(247\) | −3.32496 | − | 19.8094i | −0.211562 | − | 1.26044i | ||||
\(248\) | 1.66035 | 0.105432 | ||||||||
\(249\) | 2.73682 | − | 10.4812i | 0.173439 | − | 0.664221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2440 | −0.899071 | −0.449535 | − | 0.893263i | \(-0.648410\pi\) | ||||
−0.449535 | + | 0.893263i | \(0.648410\pi\) | |||||||
\(252\) | −5.79234 | − | 20.5631i | −0.364883 | − | 1.29535i | ||||
\(253\) | 5.71457 | − | 5.71457i | 0.359272 | − | 0.359272i | ||||
\(254\) | 11.1016 | + | 11.1016i | 0.696579 | + | 0.696579i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.0272 | 1.25170 | ||||||||
\(257\) | 24.9676i | 1.55743i | 0.627376 | + | 0.778717i | \(0.284129\pi\) | ||||
−0.627376 | + | 0.778717i | \(0.715871\pi\) | |||||||
\(258\) | 7.19241 | − | 27.5449i | 0.447780 | − | 1.71487i | ||||
\(259\) | − | 26.7226i | − | 1.66046i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.2400 | + | 8.54119i | 0.943334 | + | 0.528686i | ||||
\(262\) | 9.96050 | − | 9.96050i | 0.615361 | − | 0.615361i | ||||
\(263\) | 4.70892 | 0.290364 | 0.145182 | − | 0.989405i | \(-0.453623\pi\) | ||||
0.145182 | + | 0.989405i | \(0.453623\pi\) | |||||||
\(264\) | −1.34990 | − | 2.30400i | −0.0830808 | − | 0.141801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 32.4122 | − | 32.4122i | 1.98732 | − | 1.98732i | ||||
\(267\) | 1.25116 | − | 4.79158i | 0.0765697 | − | 0.293240i | ||||
\(268\) | −7.20325 | − | 7.20325i | −0.440009 | − | 0.440009i | ||||
\(269\) | 18.3605i | 1.11946i | 0.828675 | + | 0.559730i | \(0.189095\pi\) | ||||
−0.828675 | + | 0.559730i | \(0.810905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.79066 | − | 7.79066i | 0.473249 | − | 0.473249i | −0.429715 | − | 0.902964i | \(-0.641386\pi\) |
0.902964 | + | 0.429715i | \(0.141386\pi\) | |||||||
\(272\) | − | 19.8512i | − | 1.20365i | ||||||
\(273\) | −20.6222 | + | 17.2392i | −1.24811 | + | 1.04336i | ||||
\(274\) | −5.28807 | −0.319464 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.01537 | − | 8.56016i | −0.301890 | − | 0.515261i | ||||
\(277\) | 5.90222 | 0.354630 | 0.177315 | − | 0.984154i | \(-0.443259\pi\) | ||||
0.177315 | + | 0.984154i | \(0.443259\pi\) | |||||||
\(278\) | −19.4448 | − | 19.4448i | −1.16622 | − | 1.16622i | ||||
\(279\) | −7.25945 | + | 2.04489i | −0.434612 | + | 0.122424i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.71699 | − | 3.71699i | −0.221737 | − | 0.221737i | 0.587492 | − | 0.809230i | \(-0.300115\pi\) |
−0.809230 | + | 0.587492i | \(0.800115\pi\) | |||||||
\(282\) | 15.4870 | + | 26.4330i | 0.922238 | + | 1.57406i | ||||
\(283\) | −2.46580 | −0.146577 | −0.0732884 | − | 0.997311i | \(-0.523349\pi\) | ||||
−0.0732884 | + | 0.997311i | \(0.523349\pi\) | |||||||
\(284\) | 11.2544 | + | 11.2544i | 0.667827 | + | 0.667827i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.33704 | − | 13.1036i | 0.552111 | − | 0.774835i | ||||
\(287\) | −35.9818 | −2.12394 | ||||||||
\(288\) | −21.4220 | + | 6.03428i | −1.26230 | + | 0.355573i | ||||
\(289\) | −1.85540 | −0.109141 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.87630 | − | 0.751048i | −0.168612 | − | 0.0440272i | ||||
\(292\) | −12.0804 | + | 12.0804i | −0.706953 | + | 0.706953i | ||||
\(293\) | 2.46556 | − | 2.46556i | 0.144039 | − | 0.144039i | −0.631410 | − | 0.775449i | \(-0.717523\pi\) |
0.775449 | + | 0.631410i | \(0.217523\pi\) | |||||||
\(294\) | −36.9217 | − | 9.64086i | −2.15332 | − | 0.562266i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.10052 | −0.238338 | ||||||||
\(297\) | 8.73971 | + | 8.41109i | 0.507129 | + | 0.488061i | ||||
\(298\) | −11.7737 | −0.682033 | ||||||||
\(299\) | −7.24366 | + | 10.1658i | −0.418912 | + | 0.587903i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.1666 | − | 26.1666i | −1.50822 | − | 1.50822i | ||||
\(302\) | 11.6656 | 0.671278 | ||||||||
\(303\) | 5.10156 | + | 8.70728i | 0.293077 | + | 0.500220i | ||||
\(304\) | −18.0089 | − | 18.0089i | −1.03288 | − | 1.03288i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.75211 | + | 23.9703i | 0.385992 | + | 1.37029i | ||||
\(307\) | 7.33272 | + | 7.33272i | 0.418500 | + | 0.418500i | 0.884687 | − | 0.466186i | \(-0.154372\pi\) |
−0.466186 | + | 0.884687i | \(0.654372\pi\) | |||||||
\(308\) | 16.6232 | 0.947195 | ||||||||
\(309\) | 0.573637 | + | 0.979076i | 0.0326331 | + | 0.0556977i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.15959 | 0.235869 | 0.117934 | − | 0.993021i | \(-0.462373\pi\) | ||||
0.117934 | + | 0.993021i | \(0.462373\pi\) | |||||||
\(312\) | 2.64531 | + | 3.16443i | 0.149761 | + | 0.179151i | ||||
\(313\) | − | 15.3278i | − | 0.866380i | −0.901303 | − | 0.433190i | \(-0.857388\pi\) | ||
0.901303 | − | 0.433190i | \(-0.142612\pi\) | |||||||
\(314\) | 23.5327 | − | 23.5327i | 1.32803 | − | 1.32803i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.42904i | 0.249153i | ||||||||
\(317\) | −6.41472 | − | 6.41472i | −0.360287 | − | 0.360287i | 0.503632 | − | 0.863918i | \(-0.331997\pi\) |
−0.863918 | + | 0.503632i | \(0.831997\pi\) | |||||||
\(318\) | 1.17938 | − | 4.51669i | 0.0661365 | − | 0.253284i | ||||
\(319\) | −9.61237 | + | 9.61237i | −0.538189 | + | 0.538189i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.200451 | + | 0.342126i | 0.0111881 | + | 0.0190956i | ||||
\(322\) | −28.4854 | −1.58743 | ||||||||
\(323\) | −17.1055 | + | 17.1055i | −0.951777 | + | 0.951777i | ||||
\(324\) | 12.7013 | − | 7.77230i | 0.705630 | − | 0.431794i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 5.55447i | − | 0.307634i | ||||||
\(327\) | −6.08924 | + | 23.3200i | −0.336736 | + | 1.28960i | ||||
\(328\) | 5.52134i | 0.304865i | ||||||||
\(329\) | 39.8225 | 2.19548 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.7642 | − | 11.7642i | −0.646616 | − | 0.646616i | 0.305557 | − | 0.952174i | \(-0.401157\pi\) |
−0.952174 | + | 0.305557i | \(0.901157\pi\) | |||||||
\(332\) | 7.31697 | − | 7.31697i | 0.401571 | − | 0.401571i | ||||
\(333\) | 17.9285 | − | 5.05021i | 0.982475 | − | 0.276750i | ||||
\(334\) | 36.9052 | 2.01937 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.61024 | + | 32.9748i | −0.469727 | + | 1.79892i | ||||
\(337\) | 10.8474 | 0.590894 | 0.295447 | − | 0.955359i | \(-0.404532\pi\) | ||||
0.295447 | + | 0.955359i | \(0.404532\pi\) | |||||||
\(338\) | −10.8724 | + | 22.3474i | −0.591381 | + | 1.21554i | ||||
\(339\) | 5.76395 | + | 9.83783i | 0.313055 | + | 0.534318i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.86855i | − | 0.317800i | ||||||
\(342\) | 27.8712 | + | 15.6203i | 1.50710 | + | 0.844648i | ||||
\(343\) | −13.7704 | + | 13.7704i | −0.743533 | + | 0.743533i | ||||
\(344\) | −4.01522 | + | 4.01522i | −0.216486 | + | 0.216486i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.78339 | + | 9.78339i | −0.525958 | + | 0.525958i | ||||
\(347\) | −8.70464 | −0.467289 | −0.233645 | − | 0.972322i | \(-0.575065\pi\) | ||||
−0.233645 | + | 0.972322i | \(0.575065\pi\) | |||||||
\(348\) | 8.43626 | + | 14.3989i | 0.452231 | + | 0.771861i | ||||
\(349\) | 23.6983 | − | 23.6983i | 1.26854 | − | 1.26854i | 0.321700 | − | 0.946842i | \(-0.395746\pi\) |
0.946842 | − | 0.321700i | \(-0.104254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4633 | − | 10.5777i | −0.825368 | − | 0.564595i | ||||
\(352\) | − | 17.3175i | − | 0.923028i | ||||||
\(353\) | −10.1103 | − | 10.1103i | −0.538119 | − | 0.538119i | 0.384857 | − | 0.922976i | \(-0.374251\pi\) |
−0.922976 | + | 0.384857i | \(0.874251\pi\) | |||||||
\(354\) | 18.2967 | − | 10.7200i | 0.972457 | − | 0.569759i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.34501 | − | 3.34501i | 0.177285 | − | 0.177285i | ||||
\(357\) | 31.3207 | + | 8.17834i | 1.65767 | + | 0.432843i | ||||
\(358\) | 13.7715 | + | 13.7715i | 0.727847 | + | 0.727847i | ||||
\(359\) | −14.1823 | − | 14.1823i | −0.748515 | − | 0.748515i | 0.225686 | − | 0.974200i | \(-0.427538\pi\) |
−0.974200 | + | 0.225686i | \(0.927538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0361i | 0.633478i | ||||||||
\(362\) | −28.1381 | + | 28.1381i | −1.47891 | + | 1.47891i | ||||
\(363\) | 8.29530 | − | 4.86019i | 0.435390 | − | 0.255094i | ||||
\(364\) | −25.3213 | + | 4.25011i | −1.32720 | + | 0.222766i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.74593 | + | 14.3458i | −0.195803 | + | 0.749869i | ||||
\(367\) | − | 3.99669i | − | 0.208625i | −0.994545 | − | 0.104313i | \(-0.966736\pi\) | ||
0.994545 | − | 0.104313i | \(-0.0332643\pi\) | |||||||
\(368\) | 15.8270i | 0.825042i | ||||||||
\(369\) | −6.80009 | − | 24.1406i | −0.353998 | − | 1.25671i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.29069 | − | 4.29069i | −0.222762 | − | 0.222762i | ||||
\(372\) | −6.97066 | − | 1.82015i | −0.361412 | − | 0.0943705i | ||||
\(373\) | − | 13.2904i | − | 0.688150i | −0.938942 | − | 0.344075i | \(-0.888193\pi\) | ||
0.938942 | − | 0.344075i | \(-0.111807\pi\) | |||||||
\(374\) | −19.3776 | −1.00199 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 6.11068i | − | 0.315134i | ||||||
\(377\) | 12.1844 | − | 17.0997i | 0.627530 | − | 0.880678i | ||||
\(378\) | −0.819036 | − | 42.7457i | −0.0421267 | − | 2.19860i | ||||
\(379\) | −3.56862 | − | 3.56862i | −0.183308 | − | 0.183308i | 0.609488 | − | 0.792795i | \(-0.291375\pi\) |
−0.792795 | + | 0.609488i | \(0.791375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.19095 | + | 12.2734i | 0.368404 | + | 0.628786i | ||||
\(382\) | −27.9240 | + | 27.9240i | −1.42872 | + | 1.42872i | ||||
\(383\) | −22.1631 | − | 22.1631i | −1.13248 | − | 1.13248i | −0.989763 | − | 0.142718i | \(-0.954416\pi\) |
−0.142718 | − | 0.989763i | \(-0.545584\pi\) | |||||||
\(384\) | 8.72240 | + | 2.27756i | 0.445113 | + | 0.116226i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.20806i | 0.366881i | ||||||||
\(387\) | 12.6104 | − | 22.5006i | 0.641021 | − | 1.14377i | ||||
\(388\) | −2.00795 | − | 2.00795i | −0.101938 | − | 0.101938i | ||||
\(389\) | −20.9424 | −1.06182 | −0.530910 | − | 0.847428i | \(-0.678150\pi\) | ||||
−0.530910 | + | 0.847428i | \(0.678150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0331 | 0.760258 | ||||||||
\(392\) | 5.38208 | + | 5.38208i | 0.271836 | + | 0.271836i | ||||
\(393\) | 11.0118 | − | 6.45179i | 0.555473 | − | 0.325450i | ||||
\(394\) | 45.5049i | 2.29250i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.14156 | + | 11.1527i | 0.157869 | + | 0.560445i | ||||
\(397\) | −13.9072 | − | 13.9072i | −0.697984 | − | 0.697984i | 0.265991 | − | 0.963975i | \(-0.414301\pi\) |
−0.963975 | + | 0.265991i | \(0.914301\pi\) | |||||||
\(398\) | −9.06598 | + | 9.06598i | −0.454437 | + | 0.454437i | ||||
\(399\) | 35.8333 | − | 20.9946i | 1.79391 | − | 1.05105i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0696 | − | 15.0696i | −0.752542 | − | 0.752542i | 0.222411 | − | 0.974953i | \(-0.428607\pi\) |
−0.974953 | + | 0.222411i | \(0.928607\pi\) | |||||||
\(402\) | −10.3059 | − | 17.5900i | −0.514011 | − | 0.877307i | ||||
\(403\) | 1.50043 | + | 8.93927i | 0.0747418 | + | 0.445297i | ||||
\(404\) | 9.63999i | 0.479607i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 47.9147 | 2.37797 | ||||||||
\(407\) | 14.4934i | 0.718411i | ||||||||
\(408\) | 1.25495 | − | 4.80609i | 0.0621292 | − | 0.237937i | ||||
\(409\) | 11.5380 | + | 11.5380i | 0.570517 | + | 0.570517i | 0.932273 | − | 0.361756i | \(-0.117823\pi\) |
−0.361756 | + | 0.932273i | \(0.617823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.63575 | − | 1.21047i | −0.228665 | − | 0.0597081i | ||||
\(412\) | 1.08395i | 0.0534026i | ||||||||
\(413\) | − | 27.5647i | − | 1.35637i | ||||||
\(414\) | −5.38335 | − | 19.1112i | −0.264577 | − | 0.939263i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.42764 | + | 26.3790i | 0.217083 | + | 1.29334i | ||||
\(417\) | −12.5952 | − | 21.4972i | −0.616787 | − | 1.05272i | ||||
\(418\) | −17.5793 | + | 17.5793i | −0.859830 | + | 0.859830i | ||||
\(419\) | 15.8168i | 0.772702i | 0.922352 | + | 0.386351i | \(0.126265\pi\) | ||||
−0.922352 | + | 0.386351i | \(0.873735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.66657 | − | 4.66657i | −0.227435 | − | 0.227435i | 0.584186 | − | 0.811620i | \(-0.301414\pi\) |
−0.811620 | + | 0.584186i | \(0.801414\pi\) | |||||||
\(422\) | −34.3836 | − | 34.3836i | −1.67377 | − | 1.67377i | ||||
\(423\) | 7.52591 | + | 26.7174i | 0.365922 | + | 1.29904i | ||||
\(424\) | −0.658398 | + | 0.658398i | −0.0319746 | + | 0.0319746i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.1020 | + | 27.4827i | 0.780146 | + | 1.33154i | ||||
\(427\) | 13.6280 | + | 13.6280i | 0.659506 | + | 0.659506i | ||||
\(428\) | 0.378774i | 0.0183087i | ||||||||
\(429\) | 11.1847 | − | 9.34992i | 0.540005 | − | 0.451418i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0478 | + | 18.0478i | −0.869333 | + | 0.869333i | −0.992398 | − | 0.123066i | \(-0.960727\pi\) |
0.123066 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(432\) | −23.7504 | + | 0.455073i | −1.14269 | + | 0.0218947i | ||||
\(433\) | −16.9581 | −0.814953 | −0.407477 | − | 0.913216i | \(-0.633591\pi\) | ||||
−0.407477 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(434\) | −14.6264 | + | 14.6264i | −0.702092 | + | 0.702092i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.2798 | + | 16.2798i | −0.779660 | + | 0.779660i | ||||
\(437\) | 13.6380 | − | 13.6380i | 0.652393 | − | 0.652393i | ||||
\(438\) | −29.4997 | + | 17.2838i | −1.40955 | + | 0.825851i | ||||
\(439\) | 1.91889i | 0.0915836i | 0.998951 | + | 0.0457918i | \(0.0145811\pi\) | ||||
−0.998951 | + | 0.0457918i | \(0.985419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.1603 | − | 16.9032i | −1.43621 | − | 0.804913i | ||||
\(442\) | 29.5170 | − | 4.95434i | 1.40398 | − | 0.235654i | ||||
\(443\) | 14.7100 | 0.698891 | 0.349446 | − | 0.936957i | \(-0.386370\pi\) | ||||
0.349446 | + | 0.936957i | \(0.386370\pi\) | |||||||
\(444\) | 17.2152 | + | 4.49518i | 0.817000 | + | 0.213332i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0040 | −0.663109 | ||||||||
\(447\) | −10.3214 | − | 2.69507i | −0.488183 | − | 0.127473i | ||||
\(448\) | −15.3348 | + | 15.3348i | −0.724502 | + | 0.724502i | ||||
\(449\) | −17.4536 | − | 17.4536i | −0.823684 | − | 0.823684i | 0.162950 | − | 0.986634i | \(-0.447899\pi\) |
−0.986634 | + | 0.162950i | \(0.947899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5153 | 0.918940 | ||||||||
\(452\) | 10.8916i | 0.512300i | ||||||||
\(453\) | 10.2265 | + | 2.67031i | 0.480485 | + | 0.125462i | ||||
\(454\) | − | 54.1039i | − | 2.53922i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.22158 | − | 5.49855i | −0.150864 | − | 0.257493i | ||||
\(457\) | −11.4157 | + | 11.4157i | −0.534003 | + | 0.534003i | −0.921761 | − | 0.387758i | \(-0.873250\pi\) |
0.387758 | + | 0.921761i | \(0.373250\pi\) | |||||||
\(458\) | −30.4675 | −1.42365 | ||||||||
\(459\) | 0.432245 | + | 22.5590i | 0.0201755 | + | 1.05296i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3346 | + | 21.3346i | −0.993652 | + | 0.993652i | −0.999980 | − | 0.00632789i | \(-0.997986\pi\) |
0.00632789 | + | 0.999980i | \(0.497986\pi\) | |||||||
\(462\) | 32.1881 | + | 8.40484i | 1.49753 | + | 0.391029i | ||||
\(463\) | 16.3113 | + | 16.3113i | 0.758050 | + | 0.758050i | 0.975967 | − | 0.217917i | \(-0.0699263\pi\) |
−0.217917 | + | 0.975967i | \(0.569926\pi\) | |||||||
\(464\) | − | 26.6224i | − | 1.23591i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.5356 | − | 13.5356i | 0.627026 | − | 0.627026i | ||||
\(467\) | 36.2978i | 1.67966i | 0.542850 | + | 0.839830i | \(0.317345\pi\) | ||||
−0.542850 | + | 0.839830i | \(0.682655\pi\) | |||||||
\(468\) | −7.63684 | − | 16.1852i | −0.353013 | − | 0.748159i | ||||
\(469\) | −26.5000 | −1.22366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.0166 | − | 15.2430i | 1.19878 | − | 0.702361i | ||||
\(472\) | −4.22975 | −0.194690 | ||||||||
\(473\) | 14.1919 | + | 14.1919i | 0.652543 | + | 0.652543i | ||||
\(474\) | −2.23936 | + | 8.57612i | −0.102857 | + | 0.393914i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.8650 | + | 21.8650i | 1.00218 | + | 1.00218i | ||||
\(477\) | 2.06779 | − | 3.68956i | 0.0946778 | − | 0.168933i | ||||
\(478\) | −34.2557 | −1.56682 | ||||||||
\(479\) | −18.5322 | − | 18.5322i | −0.846756 | − | 0.846756i | 0.142971 | − | 0.989727i | \(-0.454334\pi\) |
−0.989727 | + | 0.142971i | \(0.954334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.70557 | − | 22.0771i | −0.168960 | − | 1.00663i | ||||
\(482\) | −16.9076 | −0.770119 | ||||||||
\(483\) | −24.9715 | − | 6.52047i | −1.13624 | − | 0.296691i | ||||
\(484\) | 9.18389 | 0.417449 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.5238 | − | 8.62787i | 1.29387 | − | 0.391368i | ||||
\(487\) | −5.87880 | + | 5.87880i | −0.266394 | + | 0.266394i | −0.827645 | − | 0.561252i | \(-0.810320\pi\) |
0.561252 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(488\) | 2.09119 | − | 2.09119i | 0.0946638 | − | 0.0946638i | ||||
\(489\) | 1.27145 | − | 4.86929i | 0.0574970 | − | 0.220197i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1861 | −0.459693 | −0.229847 | − | 0.973227i | \(-0.573822\pi\) | ||||
−0.229847 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(492\) | 6.05275 | − | 23.1803i | 0.272879 | − | 1.04505i | ||||
\(493\) | −25.2869 | −1.13887 | ||||||||
\(494\) | 22.2831 | − | 31.2722i | 1.00256 | − | 1.40700i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.12675 | + | 8.12675i | 0.364902 | + | 0.364902i | ||||
\(497\) | 41.4039 | 1.85722 | ||||||||
\(498\) | 17.8676 | − | 10.4686i | 0.800669 | − | 0.469109i | ||||
\(499\) | 14.5185 | + | 14.5185i | 0.649937 | + | 0.649937i | 0.952978 | − | 0.303041i | \(-0.0980019\pi\) |
−0.303041 | + | 0.952978i | \(0.598002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.3527 | + | 8.44782i | 1.44541 | + | 0.377421i | ||||
\(502\) | −19.2544 | − | 19.2544i | −0.859368 | − | 0.859368i | ||||
\(503\) | −17.4820 | −0.779483 | −0.389742 | − | 0.920924i | \(-0.627436\pi\) | ||||
−0.389742 | + | 0.920924i | \(0.627436\pi\) | |||||||
\(504\) | −4.16919 | + | 7.43907i | −0.185710 | + | 0.331363i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.4495 | 0.686813 | ||||||||
\(507\) | −14.6467 | + | 17.1019i | −0.650481 | + | 0.759523i | ||||
\(508\) | 13.5881i | 0.602876i | ||||||||
\(509\) | 7.35152 | − | 7.35152i | 0.325850 | − | 0.325850i | −0.525156 | − | 0.851006i | \(-0.675993\pi\) |
0.851006 | + | 0.525156i | \(0.175993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.4426i | 1.96603i | ||||||||
\(512\) | 19.7114 | + | 19.7114i | 0.871128 | + | 0.871128i | ||||
\(513\) | 20.8576 | + | 20.0733i | 0.920883 | + | 0.886257i | ||||
\(514\) | −33.7502 | + | 33.7502i | −1.48866 | + | 1.48866i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.2588 | − | 12.4554i | 0.935865 | − | 0.548320i | ||||
\(517\) | −21.5983 | −0.949893 | ||||||||
\(518\) | 36.1225 | − | 36.1225i | 1.58713 | − | 1.58713i | ||||
\(519\) | −10.8160 | + | 6.33706i | −0.474770 | + | 0.278166i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.94874i | − | 0.392052i | −0.980599 | − | 0.196026i | \(-0.937196\pi\) | ||
0.980599 | − | 0.196026i | \(-0.0628036\pi\) | |||||||
\(522\) | 9.05524 | + | 32.1465i | 0.396337 | + | 1.40702i | ||||
\(523\) | − | 29.1992i | − | 1.27679i | −0.769708 | − | 0.638396i | \(-0.779598\pi\) | ||
0.769708 | − | 0.638396i | \(-0.220402\pi\) | |||||||
\(524\) | 12.1914 | 0.532583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.36534 | + | 6.36534i | 0.277542 | + | 0.277542i | ||||
\(527\) | 7.71909 | − | 7.71909i | 0.336249 | − | 0.336249i | ||||
\(528\) | 4.66990 | − | 17.8844i | 0.203231 | − | 0.778317i | ||||
\(529\) | 11.0143 | 0.478883 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.4935 | − | 5.20937i | 0.802550 | − | 0.226067i | ||||
\(532\) | 39.6717 | 1.71999 | ||||||||
\(533\) | −29.7267 | + | 4.98955i | −1.28761 | + | 0.216121i | ||||
\(534\) | 8.16834 | − | 4.78581i | 0.353479 | − | 0.207102i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.06638i | 0.175641i | ||||||||
\(537\) | 8.92033 | + | 15.2251i | 0.384941 | + | 0.657011i | ||||
\(538\) | −24.8191 | + | 24.8191i | −1.07003 | + | 1.07003i | ||||
\(539\) | 19.0231 | − | 19.0231i | 0.819382 | − | 0.819382i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.91853 | − | 7.91853i | 0.340444 | − | 0.340444i | −0.516090 | − | 0.856534i | \(-0.672613\pi\) |
0.856534 | + | 0.516090i | \(0.172613\pi\) | |||||||
\(542\) | 21.0622 | 0.904701 | ||||||||
\(543\) | −31.1080 | + | 18.2261i | −1.33497 | + | 0.782157i | ||||
\(544\) | 22.7783 | − | 22.7783i | 0.976613 | − | 0.976613i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −51.1795 | − | 4.57303i | −2.19028 | − | 0.195708i | ||||
\(547\) | 39.7240i | 1.69848i | 0.528010 | + | 0.849238i | \(0.322938\pi\) | ||||
−0.528010 | + | 0.849238i | \(0.677062\pi\) | |||||||
\(548\) | −3.23623 | − | 3.23623i | −0.138245 | − | 0.138245i | ||||
\(549\) | −6.56769 | + | 11.7187i | −0.280302 | + | 0.500143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.9402 | + | 22.9402i | −0.977284 | + | 0.977284i | ||||
\(552\) | −1.00055 | + | 3.83183i | −0.0425863 | + | 0.163093i | ||||
\(553\) | 8.14700 | + | 8.14700i | 0.346446 | + | 0.346446i | ||||
\(554\) | 7.97840 | + | 7.97840i | 0.338970 | + | 0.338970i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 23.8000i | − | 1.00934i | ||||||
\(557\) | −31.1861 | + | 31.1861i | −1.32140 | + | 1.32140i | −0.408752 | + | 0.912645i | \(0.634036\pi\) |
−0.912645 | + | 0.408752i | \(0.865964\pi\) | |||||||
\(558\) | −12.5773 | − | 7.04885i | −0.532438 | − | 0.298402i | ||||
\(559\) | −25.2463 | − | 17.9893i | −1.06780 | − | 0.760866i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.9872 | − | 4.43565i | −0.717202 | − | 0.187273i | ||||
\(562\) | − | 10.0490i | − | 0.423891i | ||||||
\(563\) | 28.5302i | 1.20240i | 0.799097 | + | 0.601202i | \(0.205311\pi\) | ||||
−0.799097 | + | 0.601202i | \(0.794689\pi\) | |||||||
\(564\) | −6.69880 | + | 25.6545i | −0.282071 | + | 1.08025i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.33318 | − | 3.33318i | −0.140104 | − | 0.140104i | ||||
\(567\) | 9.06674 | − | 37.6602i | 0.380767 | − | 1.58158i | ||||
\(568\) | − | 6.35334i | − | 0.266580i | ||||||
\(569\) | 7.59495 | 0.318397 | 0.159198 | − | 0.987247i | \(-0.449109\pi\) | ||||
0.159198 | + | 0.987247i | \(0.449109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.7934i | 1.62345i | 0.584039 | + | 0.811726i | \(0.301472\pi\) | ||||
−0.584039 | + | 0.811726i | \(0.698528\pi\) | |||||||
\(572\) | 13.7334 | − | 2.30511i | 0.574222 | − | 0.0963816i | ||||
\(573\) | −30.8714 | + | 18.0874i | −1.28967 | + | 0.755614i | ||||
\(574\) | −48.6389 | − | 48.6389i | −2.03015 | − | 2.03015i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.1864 | − | 7.39023i | −0.549432 | − | 0.307926i | ||||
\(577\) | 31.8022 | − | 31.8022i | 1.32394 | − | 1.32394i | 0.413387 | − | 0.910555i | \(-0.364346\pi\) |
0.910555 | − | 0.413387i | \(-0.135654\pi\) | |||||||
\(578\) | −2.50805 | − | 2.50805i | −0.104321 | − | 0.104321i | ||||
\(579\) | −1.64997 | + | 6.31890i | −0.0685703 | + | 0.262604i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 26.9184i | − | 1.11676i | ||||||
\(582\) | −2.87283 | − | 4.90331i | −0.119083 | − | 0.203249i | ||||
\(583\) | 2.32712 | + | 2.32712i | 0.0963796 | + | 0.0963796i | ||||
\(584\) | 6.81963 | 0.282198 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.66570 | 0.275357 | ||||||||
\(587\) | −30.0859 | − | 30.0859i | −1.24178 | − | 1.24178i | −0.959263 | − | 0.282514i | \(-0.908832\pi\) |
−0.282514 | − | 0.959263i | \(-0.591168\pi\) | |||||||
\(588\) | −16.6955 | − | 28.4957i | −0.688512 | − | 1.17514i | ||||
\(589\) | − | 14.0054i | − | 0.577084i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.4163 | + | 39.8915i | −0.428470 | + | 1.64092i | ||||
\(592\) | −20.0704 | − | 20.0704i | −0.824889 | − | 0.824889i | ||||
\(593\) | −15.4861 | + | 15.4861i | −0.635939 | + | 0.635939i | −0.949551 | − | 0.313612i | \(-0.898461\pi\) |
0.313612 | + | 0.949551i | \(0.398461\pi\) | |||||||
\(594\) | 0.444217 | + | 23.1838i | 0.0182264 | + | 0.951243i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.20536 | − | 7.20536i | −0.295143 | − | 0.295143i | ||||
\(597\) | −10.0229 | + | 5.87238i | −0.410209 | + | 0.240340i | ||||
\(598\) | −23.5334 | + | 3.95002i | −0.962354 | + | 0.161528i | ||||
\(599\) | 4.96005i | 0.202662i | 0.994853 | + | 0.101331i | \(0.0323101\pi\) | ||||
−0.994853 | + | 0.101331i | \(0.967690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.48773 | 0.142267 | 0.0711336 | − | 0.997467i | \(-0.477338\pi\) | ||||
0.0711336 | + | 0.997467i | \(0.477338\pi\) | |||||||
\(602\) | − | 70.7421i | − | 2.88323i | ||||||
\(603\) | −5.00815 | − | 17.7792i | −0.203948 | − | 0.724025i | ||||
\(604\) | 7.13917 | + | 7.13917i | 0.290489 | + | 0.290489i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.87406 | + | 18.6663i | −0.197995 | + | 0.758265i | ||||
\(607\) | − | 14.2336i | − | 0.577725i | −0.957371 | − | 0.288862i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288862i | \(-0.0932770\pi\) | |||||||
\(608\) | − | 41.3288i | − | 1.67610i | ||||||
\(609\) | 42.0041 | + | 10.9679i | 1.70209 | + | 0.444444i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.8997 | − | 5.52212i | 1.33098 | − | 0.223401i | ||||
\(612\) | −10.5373 | + | 18.8017i | −0.425946 | + | 0.760015i | ||||
\(613\) | 14.0265 | − | 14.0265i | 0.566525 | − | 0.566525i | −0.364628 | − | 0.931153i | \(-0.618804\pi\) |
0.931153 | + | 0.364628i | \(0.118804\pi\) | |||||||
\(614\) | 19.8242i | 0.800039i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.69206 | − | 4.69206i | −0.189049 | − | 0.189049i | ||||
\(617\) | −10.8617 | − | 10.8617i | −0.437277 | − | 0.437277i | 0.453817 | − | 0.891095i | \(-0.350062\pi\) |
−0.891095 | + | 0.453817i | \(0.850062\pi\) | |||||||
\(618\) | −0.548057 | + | 2.09890i | −0.0220461 | + | 0.0844301i | ||||
\(619\) | 8.83108 | − | 8.83108i | 0.354951 | − | 0.354951i | −0.506997 | − | 0.861948i | \(-0.669244\pi\) |
0.861948 | + | 0.506997i | \(0.169244\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.344623 | − | 17.9860i | −0.0138292 | − | 0.721752i | ||||
\(622\) | 5.62278 | + | 5.62278i | 0.225453 | + | 0.225453i | ||||
\(623\) | − | 12.3060i | − | 0.493028i | ||||||
\(624\) | −2.54087 | + | 28.4364i | −0.101716 | + | 1.13837i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.7196 | − | 20.7196i | 0.828121 | − | 0.828121i | ||||
\(627\) | −19.4347 | + | 11.3868i | −0.776149 | + | 0.454743i | ||||
\(628\) | 28.8034 | 1.14938 | ||||||||
\(629\) | −19.0636 | + | 19.0636i | −0.760117 | + | 0.760117i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.70247 | − | 7.70247i | 0.306630 | − | 0.306630i | −0.536971 | − | 0.843601i | \(-0.680431\pi\) |
0.843601 | + | 0.536971i | \(0.180431\pi\) | |||||||
\(632\) | 1.25014 | − | 1.25014i | 0.0497279 | − | 0.0497279i | ||||
\(633\) | −22.2716 | − | 38.0128i | −0.885216 | − | 1.51087i | ||||
\(634\) | − | 17.3424i | − | 0.688753i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.48592 | − | 2.04239i | 0.138226 | − | 0.0809861i | ||||
\(637\) | −24.1132 | + | 33.8406i | −0.955400 | + | 1.34081i | ||||
\(638\) | −25.9873 | −1.02885 | ||||||||
\(639\) | 7.82478 | + | 27.7784i | 0.309544 | + | 1.09890i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.3950 | 1.79299 | 0.896497 | − | 0.443050i | \(-0.146103\pi\) | ||||
0.896497 | + | 0.443050i | \(0.146103\pi\) | |||||||
\(642\) | −0.191512 | + | 0.733434i | −0.00755836 | + | 0.0289463i | ||||
\(643\) | −27.0118 | + | 27.0118i | −1.06524 | + | 1.06524i | −0.0675241 | + | 0.997718i | \(0.521510\pi\) |
−0.997718 | + | 0.0675241i | \(0.978490\pi\) | |||||||
\(644\) | −17.4327 | − | 17.4327i | −0.686944 | − | 0.686944i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.2452 | −1.81949 | ||||||||
\(647\) | 45.8906i | 1.80414i | 0.431585 | + | 0.902072i | \(0.357954\pi\) | ||||
−0.431585 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(648\) | −5.77888 | − | 1.39127i | −0.227016 | − | 0.0546543i | ||||
\(649\) | 14.9502i | 0.586845i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.1702 | + | 9.47410i | −0.633762 | + | 0.371319i | ||||
\(652\) | 3.39926 | − | 3.39926i | 0.133125 | − | 0.133125i | ||||
\(653\) | 39.0950 | 1.52991 | 0.764953 | − | 0.644086i | \(-0.222762\pi\) | ||||
0.764953 | + | 0.644086i | \(0.222762\pi\) | |||||||
\(654\) | −39.7543 | + | 23.2919i | −1.55452 | + | 0.910786i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.0247 | + | 27.0247i | −1.05514 | + | 1.05514i | ||||
\(657\) | −29.8171 | + | 8.39906i | −1.16328 | + | 0.327678i | ||||
\(658\) | 53.8305 | + | 53.8305i | 2.09853 | + | 2.09853i | ||||
\(659\) | − | 19.2439i | − | 0.749637i | −0.927098 | − | 0.374818i | \(-0.877705\pi\) | ||
0.927098 | − | 0.374818i | \(-0.122295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9974 | + | 26.9974i | −1.05008 | + | 1.05008i | −0.0513985 | + | 0.998678i | \(0.516368\pi\) |
−0.998678 | + | 0.0513985i | \(0.983632\pi\) | |||||||
\(662\) | − | 31.8047i | − | 1.23612i | ||||||
\(663\) | 27.0099 | + | 2.41341i | 1.04898 | + | 0.0937292i | ||||
\(664\) | −4.13057 | −0.160297 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 31.0617 | + | 17.4084i | 1.20362 | + | 0.674560i | ||||
\(667\) | 20.1609 | 0.780633 | ||||||||
\(668\) | 22.5855 | + | 22.5855i | 0.873860 | + | 0.873860i | ||||
\(669\) | −12.2765 | − | 3.20560i | −0.474637 | − | 0.123936i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.39137 | − | 7.39137i | −0.285341 | − | 0.285341i | ||||
\(672\) | −47.7169 | + | 27.9572i | −1.84072 | + | 1.07847i | ||||
\(673\) | 34.1891 | 1.31789 | 0.658946 | − | 0.752190i | \(-0.271002\pi\) | ||||
0.658946 | + | 0.752190i | \(0.271002\pi\) | |||||||
\(674\) | 14.6631 | + | 14.6631i | 0.564800 | + | 0.564800i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.3301 | + | 7.02253i | −0.781926 | + | 0.270097i | ||||
\(677\) | 14.1540 | 0.543984 | 0.271992 | − | 0.962300i | \(-0.412318\pi\) | ||||
0.271992 | + | 0.962300i | \(0.412318\pi\) | |||||||
\(678\) | −5.50691 | + | 21.0899i | −0.211492 | + | 0.809953i | ||||
\(679\) | −7.38705 | −0.283489 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3847 | − | 47.4298i | 0.474582 | − | 1.81751i | ||||
\(682\) | 7.93288 | − | 7.93288i | 0.303766 | − | 0.303766i | ||||
\(683\) | 21.9481 | − | 21.9481i | 0.839819 | − | 0.839819i | −0.149016 | − | 0.988835i | \(-0.547610\pi\) |
0.988835 | + | 0.149016i | \(0.0476105\pi\) | |||||||
\(684\) | 7.49742 | + | 26.6162i | 0.286671 | + | 1.01770i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.2286 | −1.42140 | ||||||||
\(687\) | −26.7091 | − | 6.97419i | −1.01902 | − | 0.266082i | ||||
\(688\) | −39.3057 | −1.49852 | ||||||||
\(689\) | −4.13978 | − | 2.94981i | −0.157713 | − | 0.112379i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1129 | − | 19.1129i | −0.727090 | − | 0.727090i | 0.242949 | − | 0.970039i | \(-0.421885\pi\) |
−0.970039 | + | 0.242949i | \(0.921885\pi\) | |||||||
\(692\) | −11.9746 | −0.455206 | ||||||||
\(693\) | 26.2936 | + | 14.7361i | 0.998811 | + | 0.559778i | ||||
\(694\) | −11.7666 | − | 11.7666i | −0.446654 | − | 0.446654i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.68301 | − | 6.44544i | 0.0637943 | − | 0.244314i | ||||
\(697\) | 25.6691 | + | 25.6691i | 0.972287 | + | 0.972287i | ||||
\(698\) | 64.0690 | 2.42505 | ||||||||
\(699\) | 14.9643 | − | 8.76753i | 0.566002 | − | 0.331618i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.2762 | 0.916900 | 0.458450 | − | 0.888720i | \(-0.348405\pi\) | ||||
0.458450 | + | 0.888720i | \(0.348405\pi\) | |||||||
\(702\) | −6.60414 | − | 35.2012i | −0.249257 | − | 1.32858i | ||||
\(703\) | 34.5889i | 1.30454i | ||||||||
\(704\) | 8.31707 | − | 8.31707i | 0.313461 | − | 0.313461i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 27.3335i | − | 1.02871i | ||||||
\(707\) | 17.7323 | + | 17.7323i | 0.666891 | + | 0.666891i | ||||
\(708\) | 17.7578 | + | 4.63685i | 0.667379 | + | 0.174263i | ||||
\(709\) | −11.9543 | + | 11.9543i | −0.448954 | + | 0.448954i | −0.895007 | − | 0.446053i | \(-0.852829\pi\) |
0.446053 | + | 0.895007i | \(0.352829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.92624 | + | 7.00559i | −0.147246 | + | 0.262730i | ||||
\(712\) | −1.88833 | −0.0707680 | ||||||||
\(713\) | −6.15432 | + | 6.15432i | −0.230481 | + | 0.230481i | ||||
\(714\) | 31.2829 | + | 53.3933i | 1.17073 | + | 1.99819i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.8560i | 0.629937i | ||||||||
\(717\) | −30.0300 | − | 7.84132i | −1.12149 | − | 0.292839i | ||||
\(718\) | − | 38.3423i | − | 1.43092i | ||||||
\(719\) | −41.3666 | −1.54271 | −0.771357 | − | 0.636403i | \(-0.780422\pi\) | ||||
−0.771357 | + | 0.636403i | \(0.780422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.99388 | + | 1.99388i | 0.0742559 | + | 0.0742559i | ||||
\(722\) | −16.2699 | + | 16.2699i | −0.605504 | + | 0.605504i | ||||
\(723\) | −14.8219 | − | 3.87024i | −0.551232 | − | 0.143936i | ||||
\(724\) | −34.4403 | −1.27996 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.7831 | + | 4.64345i | 0.659993 | + | 0.172335i | ||||
\(727\) | 22.9941 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(728\) | 8.34682 | + | 5.94755i | 0.309354 | + | 0.220431i | ||||
\(729\) | 26.9802 | − | 1.03430i | 0.999266 | − | 0.0383073i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.3341i | 1.38085i | ||||||||
\(732\) | −11.0719 | + | 6.48701i | −0.409230 | + | 0.239767i | ||||
\(733\) | 27.5771 | − | 27.5771i | 1.01858 | − | 1.01858i | 0.0187592 | − | 0.999824i | \(-0.494028\pi\) |
0.999824 | − | 0.0187592i | \(-0.00597159\pi\) | |||||||
\(734\) | 5.40257 | − | 5.40257i | 0.199413 | − | 0.199413i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.1608 | + | 18.1608i | −0.669417 | + | 0.669417i | ||||
\(737\) | 14.3727 | 0.529425 | ||||||||
\(738\) | 23.4403 | − | 41.8245i | 0.862850 | − | 1.53958i | ||||
\(739\) | −7.93961 | + | 7.93961i | −0.292063 | + | 0.292063i | −0.837895 | − | 0.545832i | \(-0.816214\pi\) |
0.545832 | + | 0.837895i | \(0.316214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.6927 | − | 22.3138i | 0.980581 | − | 0.819719i | ||||
\(742\) | − | 11.6000i | − | 0.425849i | ||||||
\(743\) | 23.9349 | + | 23.9349i | 0.878087 | + | 0.878087i | 0.993337 | − | 0.115249i | \(-0.0367667\pi\) |
−0.115249 | + | 0.993337i | \(0.536767\pi\) | |||||||
\(744\) | 1.45378 | + | 2.48129i | 0.0532982 | + | 0.0909686i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.9654 | − | 17.9654i | 0.657761 | − | 0.657761i | ||||
\(747\) | 18.0599 | − | 5.08722i | 0.660776 | − | 0.186132i | ||||
\(748\) | −11.8588 | − | 11.8588i | −0.433602 | − | 0.433602i | ||||
\(749\) | 0.696736 | + | 0.696736i | 0.0254582 | + | 0.0254582i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.7833i | 1.56119i | 0.625039 | + | 0.780593i | \(0.285083\pi\) | ||||
−0.625039 | + | 0.780593i | \(0.714917\pi\) | |||||||
\(752\) | 29.9093 | − | 29.9093i | 1.09068 | − | 1.09068i | ||||
\(753\) | −12.4718 | − | 21.2867i | −0.454498 | − | 0.775731i | ||||
\(754\) | 39.5851 | − | 6.64426i | 1.44161 | − | 0.241970i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 25.6586 | − | 26.6611i | 0.933194 | − | 0.969653i | ||||
\(757\) | 42.2733i | 1.53645i | 0.640180 | + | 0.768225i | \(0.278860\pi\) | ||||
−0.640180 | + | 0.768225i | \(0.721140\pi\) | |||||||
\(758\) | − | 9.64784i | − | 0.350425i | ||||||
\(759\) | 13.5437 | + | 3.53647i | 0.491605 | + | 0.128366i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.2564 | − | 18.2564i | −0.661795 | − | 0.661795i | 0.294008 | − | 0.955803i | \(-0.405011\pi\) |
−0.955803 | + | 0.294008i | \(0.905011\pi\) | |||||||
\(762\) | −6.87028 | + | 26.3112i | −0.248884 | + | 0.953154i | ||||
\(763\) | 59.8916i | 2.16822i | ||||||||
\(764\) | −34.1783 | −1.23653 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 59.9185i | − | 2.16494i | ||||||
\(767\) | −3.82236 | − | 22.7728i | −0.138017 | − | 0.822280i | ||||
\(768\) | 17.5355 | + | 29.9294i | 0.632759 | + | 1.07998i | ||||
\(769\) | −30.7881 | − | 30.7881i | −1.11025 | − | 1.11025i | −0.993116 | − | 0.117131i | \(-0.962630\pi\) |
−0.117131 | − | 0.993116i | \(-0.537370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.3125 | + | 21.8613i | −1.34378 | + | 0.787314i | ||||
\(772\) | −4.41124 | + | 4.41124i | −0.158764 | + | 0.158764i | ||||
\(773\) | 3.19753 | + | 3.19753i | 0.115007 | + | 0.115007i | 0.762268 | − | 0.647261i | \(-0.224086\pi\) |
−0.647261 | + | 0.762268i | \(0.724086\pi\) | |||||||
\(774\) | 47.4617 | − | 13.3693i | 1.70598 | − | 0.480550i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.13353i | 0.0406913i | ||||||||
\(777\) | 39.9352 | − | 23.3979i | 1.43267 | − | 0.839396i | ||||
\(778\) | −28.3091 | − | 28.3091i | −1.01493 | − | 1.01493i | ||||
\(779\) | 46.5738 | 1.66868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.4560 | −0.803540 | ||||||||
\(782\) | 20.3212 | + | 20.3212i | 0.726685 | + | 0.726685i | ||||
\(783\) | 0.579683 | + | 30.2538i | 0.0207162 | + | 1.08118i | ||||
\(784\) | 52.6862i | 1.88165i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.6066 | + | 6.16407i | 0.842021 | + | 0.219865i | ||||
\(787\) | −25.0983 | − | 25.0983i | −0.894657 | − | 0.894657i | 0.100301 | − | 0.994957i | \(-0.468020\pi\) |
−0.994957 | + | 0.100301i | \(0.968020\pi\) | |||||||
\(788\) | −27.8484 | + | 27.8484i | −0.992058 | + | 0.992058i | ||||
\(789\) | 4.12307 | + | 7.03719i | 0.146785 | + | 0.250531i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0346 | + | 20.0346i | 0.712350 | + | 0.712350i | ||||
\(792\) | 2.26122 | − | 4.03470i | 0.0803491 | − | 0.143367i | ||||
\(793\) | 13.1487 | + | 9.36913i | 0.466924 | + | 0.332708i | ||||
\(794\) | − | 37.5986i | − | 1.33432i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0965 | −0.393306 | ||||||||
\(797\) | 39.5305i | 1.40024i | 0.714025 | + | 0.700120i | \(0.246870\pi\) | ||||
−0.714025 | + | 0.700120i | \(0.753130\pi\) | |||||||
\(798\) | 76.8178 | + | 20.0584i | 2.71932 | + | 0.710059i | ||||
\(799\) | −28.4090 | − | 28.4090i | −1.00504 | − | 1.00504i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.25622 | − | 2.32566i | 0.291719 | − | 0.0821733i | ||||
\(802\) | − | 40.7411i | − | 1.43862i | ||||||
\(803\) | − | 24.1041i | − | 0.850616i | ||||||
\(804\) | 4.45775 | − | 17.0719i | 0.157213 | − | 0.602079i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.0555 | + | 14.1120i | −0.354191 | + | 0.497074i | ||||
\(807\) | −27.4387 | + | 16.0762i | −0.965887 | + | 0.565910i | ||||
\(808\) | 2.72098 | − | 2.72098i | 0.0957238 | − | 0.0957238i | ||||
\(809\) | 37.4805i | 1.31774i | 0.752255 | + | 0.658872i | \(0.228966\pi\) | ||||
−0.752255 | + | 0.658872i | \(0.771034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.40079 | − | 5.40079i | −0.189647 | − | 0.189647i | 0.605896 | − | 0.795544i | \(-0.292815\pi\) |
−0.795544 | + | 0.605896i | \(0.792815\pi\) | |||||||
\(812\) | 29.3232 | + | 29.3232i | 1.02904 | + | 1.02904i | ||||
\(813\) | 18.4641 | + | 4.82127i | 0.647563 | + | 0.169089i | ||||
\(814\) | −19.5916 | + | 19.5916i | −0.686686 | + | 0.686686i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 29.6664 | − | 17.3814i | 1.03853 | − | 0.608472i | ||||
\(817\) | 33.8693 | + | 33.8693i | 1.18494 | + | 1.18494i | ||||
\(818\) | 31.1933i | 1.09065i | ||||||||
\(819\) | −43.8194 | − | 15.7242i | −1.53117 | − | 0.549448i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.9025 | − | 26.9025i | 0.938905 | − | 0.938905i | −0.0593332 | − | 0.998238i | \(-0.518897\pi\) |
0.998238 | + | 0.0593332i | \(0.0188974\pi\) | |||||||
\(822\) | −4.63017 | − | 7.90270i | −0.161496 | − | 0.275638i | ||||
\(823\) | −22.4341 | −0.782003 | −0.391002 | − | 0.920390i | \(-0.627871\pi\) | ||||
−0.391002 | + | 0.920390i | \(0.627871\pi\) | |||||||
\(824\) | 0.305956 | − | 0.305956i | 0.0106585 | − | 0.0106585i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.2610 | − | 37.2610i | 1.29648 | − | 1.29648i | ||||
\(827\) | −19.5590 | + | 19.5590i | −0.680134 | + | 0.680134i | −0.960030 | − | 0.279896i | \(-0.909700\pi\) |
0.279896 | + | 0.960030i | \(0.409700\pi\) | |||||||
\(828\) | 8.40125 | − | 14.9903i | 0.291964 | − | 0.520950i | ||||
\(829\) | − | 3.42144i | − | 0.118832i | −0.998233 | − | 0.0594158i | \(-0.981076\pi\) | ||
0.998233 | − | 0.0594158i | \(-0.0189238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.16791 | + | 8.82051i | 0.179273 | + | 0.305980i | ||||
\(832\) | −10.5425 | + | 14.7954i | −0.365496 | + | 0.512940i | ||||
\(833\) | 50.0433 | 1.73390 | ||||||||
\(834\) | 12.0335 | − | 46.0848i | 0.416686 | − | 1.59579i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −21.5166 | −0.744166 | ||||||||
\(837\) | −9.41224 | − | 9.05833i | −0.325335 | − | 0.313102i | ||||
\(838\) | −21.3806 | + | 21.3806i | −0.738579 | + | 0.738579i | ||||
\(839\) | 26.6448 | + | 26.6448i | 0.919880 | + | 0.919880i | 0.997020 | − | 0.0771405i | \(-0.0245790\pi\) |
−0.0771405 | + | 0.997020i | \(0.524579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.91224 | −0.169388 | ||||||||
\(842\) | − | 12.6162i | − | 0.434782i | ||||||
\(843\) | 2.30027 | − | 8.80937i | 0.0792255 | − | 0.303411i | ||||
\(844\) | − | 42.0847i | − | 1.44861i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.9423 | + | 46.2888i | −0.891914 | + | 1.59144i | ||||
\(847\) | 16.8933 | − | 16.8933i | 0.580460 | − | 0.580460i | ||||
\(848\) | −6.44519 | −0.221329 | ||||||||
\(849\) | −2.15902 | − | 3.68499i | −0.0740975 | − | 0.126469i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1992 | − | 15.1992i | 0.521020 | − | 0.521020i | ||||
\(852\) | −6.96483 | + | 26.6733i | −0.238611 | + | 0.913812i | ||||
\(853\) | −1.95181 | − | 1.95181i | −0.0668287 | − | 0.0668287i | 0.672902 | − | 0.739731i | \(-0.265047\pi\) |
−0.739731 | + | 0.672902i | \(0.765047\pi\) | |||||||
\(854\) | 36.8437i | 1.26077i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.106913 | − | 0.106913i | 0.00365420 | − | 0.00365420i | ||||
\(857\) | − | 25.9594i | − | 0.886756i | −0.896335 | − | 0.443378i | \(-0.853780\pi\) | ||
0.896335 | − | 0.443378i | \(-0.146220\pi\) | |||||||
\(858\) | 27.7580 | + | 2.48025i | 0.947642 | + | 0.0846745i | ||||
\(859\) | 7.56942 | 0.258265 | 0.129133 | − | 0.991627i | \(-0.458781\pi\) | ||||
0.129133 | + | 0.991627i | \(0.458781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.5052 | − | 53.7727i | −1.07370 | − | 1.83257i | ||||
\(862\) | −48.7927 | −1.66189 | ||||||||
\(863\) | −22.0019 | − | 22.0019i | −0.748953 | − | 0.748953i | 0.225330 | − | 0.974283i | \(-0.427654\pi\) |
−0.974283 | + | 0.225330i | \(0.927654\pi\) | |||||||
\(864\) | −27.7747 | − | 26.7303i | −0.944914 | − | 0.909384i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.9233 | − | 22.9233i | −0.778965 | − | 0.778965i | ||||
\(867\) | −1.62456 | − | 2.77278i | −0.0551730 | − | 0.0941684i | ||||
\(868\) | −17.9024 | −0.607647 | ||||||||
\(869\) | −4.41865 | − | 4.41865i | −0.149892 | − | 0.149892i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.8932 | + | 3.67472i | −0.741824 | + | 0.124513i | ||||
\(872\) | 9.19025 | 0.311221 | ||||||||
\(873\) | −1.39605 | − | 4.95606i | −0.0472492 | − | 0.167737i | ||||
\(874\) | 36.8706 | 1.24717 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28.6309 | − | 7.47599i | −0.967348 | − | 0.252590i | ||||
\(877\) | 19.8856 | − | 19.8856i | 0.671491 | − | 0.671491i | −0.286569 | − | 0.958060i | \(-0.592515\pi\) |
0.958060 | + | 0.286569i | \(0.0925148\pi\) | |||||||
\(878\) | −2.59388 | + | 2.59388i | −0.0875393 | + | 0.0875393i | ||||
\(879\) | 5.84344 | + | 1.52582i | 0.197094 | + | 0.0514645i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.1817 | −1.21899 | −0.609497 | − | 0.792788i | \(-0.708629\pi\) | ||||
−0.609497 | + | 0.792788i | \(0.708629\pi\) | |||||||
\(882\) | −17.9205 | − | 63.6186i | −0.603414 | − | 2.14215i | ||||
\(883\) | 29.6055 | 0.996305 | 0.498153 | − | 0.867089i | \(-0.334012\pi\) | ||||
0.498153 | + | 0.867089i | \(0.334012\pi\) | |||||||
\(884\) | 21.0960 | + | 15.0320i | 0.709535 | + | 0.505581i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.8844 | + | 19.8844i | 0.668028 | + | 0.668028i | ||||
\(887\) | 35.4670 | 1.19087 | 0.595433 | − | 0.803405i | \(-0.296980\pi\) | ||||
0.595433 | + | 0.803405i | \(0.296980\pi\) | |||||||
\(888\) | −3.59036 | − | 6.12798i | −0.120485 | − | 0.205642i | ||||
\(889\) | 24.9947 | + | 24.9947i | 0.838294 | + | 0.838294i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.91748 | + | 20.4256i | −0.164742 | + | 0.684283i | ||||
\(892\) | −8.57027 | − | 8.57027i | −0.286954 | − | 0.286954i | ||||
\(893\) | −51.5450 | −1.72489 | ||||||||
\(894\) | −10.3089 | − | 17.5951i | −0.344782 | − | 0.588468i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.4013 | 0.748375 | ||||||||
\(897\) | −21.5346 | − | 1.92418i | −0.719020 | − | 0.0642465i | ||||
\(898\) | − | 47.1861i | − | 1.57462i | ||||||
\(899\) | 10.3521 | − | 10.3521i | 0.345260 | − | 0.345260i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.12188i | 0.203950i | ||||||||
\(902\) | 26.3800 | + | 26.3800i | 0.878360 | + | 0.878360i | ||||
\(903\) | 16.1933 | − | 62.0156i | 0.538878 | − | 2.06375i | ||||
\(904\) | 3.07427 | − | 3.07427i | 0.102249 | − | 0.102249i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.2142 | + | 17.4335i | 0.339345 | + | 0.579188i | ||||
\(907\) | 27.3235 | 0.907261 | 0.453630 | − | 0.891190i | \(-0.350129\pi\) | ||||
0.453630 | + | 0.891190i | \(0.350129\pi\) | |||||||
\(908\) | 33.1109 | − | 33.1109i | 1.09882 | − | 1.09882i | ||||
\(909\) | −8.54563 | + | 15.2480i | −0.283441 | + | 0.505743i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.2417i | − | 1.10135i | −0.834721 | − | 0.550674i | \(-0.814371\pi\) | ||
0.834721 | − | 0.550674i | \(-0.185629\pi\) | |||||||
\(912\) | 11.1448 | − | 42.6815i | 0.369042 | − | 1.41333i | ||||
\(913\) | 14.5996i | 0.483176i | ||||||||
\(914\) | −30.8626 | −1.02084 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.6457 | − | 18.6457i | −0.616072 | − | 0.616072i | ||||
\(917\) | 22.4254 | − | 22.4254i | 0.740553 | − | 0.740553i | ||||
\(918\) | −29.9101 | + | 31.0787i | −0.987181 | + | 1.02575i | ||||
\(919\) | 1.10008 | 0.0362882 | 0.0181441 | − | 0.999835i | \(-0.494224\pi\) | ||||
0.0181441 | + | 0.999835i | \(0.494224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.53787 | + | 17.3787i | −0.149528 | + | 0.572649i | ||||
\(922\) | −57.6786 | −1.89955 | ||||||||
\(923\) | 34.2062 | − | 5.74141i | 1.12591 | − | 0.188981i | ||||
\(924\) | 14.5551 | + | 24.8424i | 0.478826 | + | 0.817254i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44.0980i | 1.44915i | ||||||||
\(927\) | −0.960900 | + | 1.71453i | −0.0315601 | + | 0.0563126i | ||||
\(928\) | 30.5480 | − | 30.5480i | 1.00279 | − | 1.00279i | ||||
\(929\) | 13.5362 | − | 13.5362i | 0.444110 | − | 0.444110i | −0.449281 | − | 0.893391i | \(-0.648320\pi\) |
0.893391 | + | 0.449281i | \(0.148320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.3991 | − | 45.3991i | 1.48789 | − | 1.48789i | ||||
\(932\) | 16.5673 | 0.542678 | ||||||||
\(933\) | 3.64209 | + | 6.21626i | 0.119237 | + | 0.203511i | ||||
\(934\) | −49.0659 | + | 49.0659i | −1.60549 | + | 1.60549i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.41285 | + | 6.72399i | −0.0788663 | + | 0.219780i | ||||
\(937\) | − | 5.70697i | − | 0.186439i | −0.995646 | − | 0.0932194i | \(-0.970284\pi\) | ||
0.995646 | − | 0.0932194i | \(-0.0297158\pi\) | |||||||
\(938\) | −35.8217 | − | 35.8217i | −1.16962 | − | 1.16962i | ||||
\(939\) | 22.9065 | − | 13.4208i | 0.747526 | − | 0.437973i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.18292 | − | 4.18292i | 0.136359 | − | 0.136359i | −0.635632 | − | 0.771992i | \(-0.719261\pi\) |
0.771992 | + | 0.635632i | \(0.219261\pi\) | |||||||
\(942\) | 55.7731 | + | 14.5633i | 1.81719 | + | 0.474497i | ||||
\(943\) | −20.4656 | − | 20.4656i | −0.666452 | − | 0.666452i | ||||
\(944\) | −20.7029 | − | 20.7029i | −0.673823 | − | 0.673823i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.3681i | 1.24745i | ||||||||
\(947\) | 27.3594 | − | 27.3594i | 0.889060 | − | 0.889060i | −0.105372 | − | 0.994433i | \(-0.533603\pi\) |
0.994433 | + | 0.105372i | \(0.0336035\pi\) | |||||||
\(948\) | −6.61893 | + | 3.87801i | −0.214973 | + | 0.125952i | ||||
\(949\) | 6.16279 | + | 36.7167i | 0.200053 | + | 1.19187i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.96976 | − | 15.2031i | 0.128728 | − | 0.492993i | ||||
\(952\) | − | 12.3432i | − | 0.400047i | ||||||
\(953\) | 58.2895i | 1.88818i | 0.329686 | + | 0.944091i | \(0.393057\pi\) | ||||
−0.329686 | + | 0.944091i | \(0.606943\pi\) | |||||||
\(954\) | 7.78257 | − | 2.19224i | 0.251970 | − | 0.0709765i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.9640 | − | 20.9640i | −0.678025 | − | 0.678025i | ||||
\(957\) | −22.7816 | − | 5.94863i | −0.736423 | − | 0.192292i | ||||
\(958\) | − | 50.1021i | − | 1.61873i | ||||||
\(959\) | −11.9058 | −0.384457 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 24.6799i | − | 0.796125i | ||||||
\(962\) | 24.8339 | − | 34.8520i | 0.800677 | − | 1.12367i | ||||
\(963\) | −0.335775 | + | 0.599122i | −0.0108202 | + | 0.0193064i | ||||
\(964\) | −10.3472 | − | 10.3472i | −0.333261 | − | 0.333261i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24.9414 | − | 42.5697i | −0.802477 | − | 1.36966i | ||||
\(967\) | −18.1367 | + | 18.1367i | −0.583238 | + | 0.583238i | −0.935792 | − | 0.352553i | \(-0.885313\pi\) |
0.352553 | + | 0.935792i | \(0.385313\pi\) | |||||||
\(968\) | −2.59224 | − | 2.59224i | −0.0833178 | − | 0.0833178i | ||||
\(969\) | −40.5405 | − | 10.5858i | −1.30235 | − | 0.340064i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0923i | 0.965708i | 0.875701 | + | 0.482854i | \(0.160400\pi\) | ||||
−0.875701 | + | 0.482854i | \(0.839600\pi\) | |||||||
\(972\) | 22.7364 | + | 12.1761i | 0.729269 | + | 0.390547i | ||||
\(973\) | −43.7789 | − | 43.7789i | −1.40349 | − | 1.40349i | ||||
\(974\) | −15.8935 | −0.509260 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.4711 | 0.655264 | ||||||||
\(977\) | −20.4292 | − | 20.4292i | −0.653589 | − | 0.653589i | 0.300266 | − | 0.953855i | \(-0.402924\pi\) |
−0.953855 | + | 0.300266i | \(0.902924\pi\) | |||||||
\(978\) | 8.30082 | − | 4.86342i | 0.265431 | − | 0.155515i | ||||
\(979\) | 6.67433i | 0.213313i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.1820 | + | 11.3187i | −1.28291 | + | 0.361379i | ||||
\(982\) | −13.7692 | − | 13.7692i | −0.439393 | − | 0.439393i | ||||
\(983\) | −16.7861 | + | 16.7861i | −0.535394 | + | 0.535394i | −0.922173 | − | 0.386778i | \(-0.873588\pi\) |
0.386778 | + | 0.922173i | \(0.373588\pi\) | |||||||
\(984\) | −8.25131 | + | 4.83441i | −0.263042 | + | 0.154115i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −34.1819 | − | 34.1819i | −1.08857 | − | 1.08857i | ||||
\(987\) | 34.8680 | + | 59.5123i | 1.10986 | + | 1.89430i | ||||
\(988\) | 32.7751 | − | 5.50122i | 1.04272 | − | 0.175017i | ||||
\(989\) | − | 29.7659i | − | 0.946501i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34181 | 0.0743900 | 0.0371950 | − | 0.999308i | \(-0.488158\pi\) | ||||
0.0371950 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(992\) | 18.6502i | 0.592143i | ||||||||
\(993\) | 7.28027 | − | 27.8813i | 0.231032 | − | 0.884788i | ||||
\(994\) | 55.9682 | + | 55.9682i | 1.77520 | + | 1.77520i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.3414 | + | 4.52812i | 0.549484 | + | 0.143479i | ||||
\(997\) | − | 39.0215i | − | 1.23582i | −0.786248 | − | 0.617911i | \(-0.787979\pi\) | ||
0.786248 | − | 0.617911i | \(-0.212021\pi\) | |||||||
\(998\) | 39.2511i | 1.24247i | ||||||||
\(999\) | 23.2452 | + | 22.3711i | 0.735444 | + | 0.707791i |
(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 | 975.2.n.q.749.16 | 40 | ||
3.2 | odd | 2 | inner | 975.2.n.q.749.5 | 40 | ||
5.2 | odd | 4 | 975.2.o.p.476.5 | 40 | |||
5.3 | odd | 4 | 195.2.o.a.86.16 | yes | 40 | ||
5.4 | even | 2 | 975.2.n.r.749.5 | 40 | |||
13.5 | odd | 4 | 975.2.n.r.824.16 | 40 | |||
15.2 | even | 4 | 975.2.o.p.476.16 | 40 | |||
15.8 | even | 4 | 195.2.o.a.86.5 | ✓ | 40 | ||
15.14 | odd | 2 | 975.2.n.r.749.16 | 40 | |||
39.5 | even | 4 | 975.2.n.r.824.5 | 40 | |||
65.18 | even | 4 | 195.2.o.a.161.5 | yes | 40 | ||
65.44 | odd | 4 | inner | 975.2.n.q.824.5 | 40 | ||
65.57 | even | 4 | 975.2.o.p.551.16 | 40 | |||
195.44 | even | 4 | inner | 975.2.n.q.824.16 | 40 | ||
195.83 | odd | 4 | 195.2.o.a.161.16 | yes | 40 | ||
195.122 | odd | 4 | 975.2.o.p.551.5 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.o.a.86.5 | ✓ | 40 | 15.8 | even | 4 | ||
195.2.o.a.86.16 | yes | 40 | 5.3 | odd | 4 | ||
195.2.o.a.161.5 | yes | 40 | 65.18 | even | 4 | ||
195.2.o.a.161.16 | yes | 40 | 195.83 | odd | 4 | ||
975.2.n.q.749.5 | 40 | 3.2 | odd | 2 | inner | ||
975.2.n.q.749.16 | 40 | 1.1 | even | 1 | trivial | ||
975.2.n.q.824.5 | 40 | 65.44 | odd | 4 | inner | ||
975.2.n.q.824.16 | 40 | 195.44 | even | 4 | inner | ||
975.2.n.r.749.5 | 40 | 5.4 | even | 2 | |||
975.2.n.r.749.16 | 40 | 15.14 | odd | 2 | |||
975.2.n.r.824.5 | 40 | 39.5 | even | 4 | |||
975.2.n.r.824.16 | 40 | 13.5 | odd | 4 | |||
975.2.o.p.476.5 | 40 | 5.2 | odd | 4 | |||
975.2.o.p.476.16 | 40 | 15.2 | even | 4 | |||
975.2.o.p.551.5 | 40 | 195.122 | odd | 4 | |||
975.2.o.p.551.16 | 40 | 65.57 | even | 4 |