Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(59,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.t (of order \(6\), degree \(2\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.2 | ||
Root | \(-1.72286 - 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.89 |
Dual form | 210.2.t.e.59.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.01575 | + | 1.40294i | −0.586445 | + | 0.809989i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.792893 | + | 2.09077i | 0.354593 | + | 0.935021i | ||||
\(6\) | −0.707107 | − | 1.58114i | −0.288675 | − | 0.645497i | ||||
\(7\) | 1.41421 | + | 2.23607i | 0.534522 | + | 0.845154i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.936492 | − | 2.85008i | −0.312164 | − | 0.950028i | ||||
\(10\) | −2.20711 | − | 0.358719i | −0.697948 | − | 0.113437i | ||||
\(11\) | −0.184829 | + | 0.106711i | −0.0557279 | + | 0.0321745i | −0.527605 | − | 0.849490i | \(-0.676910\pi\) |
0.471877 | + | 0.881664i | \(0.343577\pi\) | |||||||
\(12\) | 1.72286 | + | 0.178197i | 0.497347 | + | 0.0514410i | ||||
\(13\) | −6.70141 | −1.85864 | −0.929318 | − | 0.369279i | \(-0.879605\pi\) | ||||
−0.929318 | + | 0.369279i | \(0.879605\pi\) | |||||||
\(14\) | −2.64360 | + | 0.106711i | −0.706531 | + | 0.0285197i | ||||
\(15\) | −3.73861 | − | 1.01132i | −0.965306 | − | 0.261123i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.73861 | + | 1.58114i | −0.664211 | + | 0.383482i | −0.793880 | − | 0.608075i | \(-0.791942\pi\) |
0.129668 | + | 0.991557i | \(0.458609\pi\) | |||||||
\(18\) | 2.93649 | + | 0.614017i | 0.692138 | + | 0.144725i | ||||
\(19\) | 4.23861 | + | 2.44716i | 0.972404 | + | 0.561418i | 0.899968 | − | 0.435955i | \(-0.143589\pi\) |
0.0724360 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(20\) | 1.41421 | − | 1.73205i | 0.316228 | − | 0.387298i | ||||
\(21\) | −4.57357 | − | 0.287233i | −0.998034 | − | 0.0626795i | ||||
\(22\) | − | 0.213422i | − | 0.0455017i | ||||||
\(23\) | 3.23861 | − | 5.60944i | 0.675297 | − | 1.16965i | −0.301084 | − | 0.953597i | \(-0.597349\pi\) |
0.976382 | − | 0.216052i | \(-0.0693181\pi\) | |||||||
\(24\) | −1.01575 | + | 1.40294i | −0.207340 | + | 0.286374i | ||||
\(25\) | −3.74264 | + | 3.31552i | −0.748528 | + | 0.663103i | ||||
\(26\) | 3.35071 | − | 5.80359i | 0.657127 | − | 1.13818i | ||||
\(27\) | 4.94975 | + | 1.58114i | 0.952579 | + | 0.304290i | ||||
\(28\) | 1.22938 | − | 2.34278i | 0.232332 | − | 0.442744i | ||||
\(29\) | 2.02265i | 0.375596i | 0.982208 | + | 0.187798i | \(0.0601350\pi\) | ||||
−0.982208 | + | 0.187798i | \(0.939865\pi\) | |||||||
\(30\) | 2.74514 | − | 2.73207i | 0.501191 | − | 0.498806i | ||||
\(31\) | −0.261387 | + | 0.150912i | −0.0469465 | + | 0.0271046i | −0.523290 | − | 0.852155i | \(-0.675295\pi\) |
0.476343 | + | 0.879260i | \(0.341962\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.0380311 | − | 0.367696i | 0.00662037 | − | 0.0640076i | ||||
\(34\) | − | 3.16228i | − | 0.542326i | ||||||
\(35\) | −3.55378 | + | 4.72976i | −0.600699 | + | 0.799475i | ||||
\(36\) | −2.00000 | + | 2.23607i | −0.333333 | + | 0.372678i | ||||
\(37\) | 6.17913 | + | 3.56752i | 1.01584 | + | 0.586497i | 0.912897 | − | 0.408190i | \(-0.133840\pi\) |
0.102946 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(38\) | −4.23861 | + | 2.44716i | −0.687594 | + | 0.396982i | ||||
\(39\) | 6.80698 | − | 9.40169i | 1.08999 | − | 1.50548i | ||||
\(40\) | 0.792893 | + | 2.09077i | 0.125367 | + | 0.330580i | ||||
\(41\) | 6.70141 | 1.04658 | 0.523292 | − | 0.852153i | \(-0.324704\pi\) | ||||
0.523292 | + | 0.852153i | \(0.324704\pi\) | |||||||
\(42\) | 2.53553 | − | 3.81721i | 0.391241 | − | 0.589008i | ||||
\(43\) | 2.02265i | 0.308451i | 0.988036 | + | 0.154225i | \(0.0492882\pi\) | ||||
−0.988036 | + | 0.154225i | \(0.950712\pi\) | |||||||
\(44\) | 0.184829 | + | 0.106711i | 0.0278640 | + | 0.0160873i | ||||
\(45\) | 5.21633 | − | 4.21780i | 0.777605 | − | 0.628753i | ||||
\(46\) | 3.23861 | + | 5.60944i | 0.477507 | + | 0.827067i | ||||
\(47\) | 6.71584 | + | 3.87739i | 0.979606 | + | 0.565576i | 0.902151 | − | 0.431420i | \(-0.141987\pi\) |
0.0774546 | + | 0.996996i | \(0.475321\pi\) | |||||||
\(48\) | −0.707107 | − | 1.58114i | −0.102062 | − | 0.228218i | ||||
\(49\) | −3.00000 | + | 6.32456i | −0.428571 | + | 0.903508i | ||||
\(50\) | −1.00000 | − | 4.89898i | −0.141421 | − | 0.692820i | ||||
\(51\) | 0.563508 | − | 5.44816i | 0.0789069 | − | 0.762895i | ||||
\(52\) | 3.35071 | + | 5.80359i | 0.464659 | + | 0.804813i | ||||
\(53\) | −2.50000 | − | 4.33013i | −0.343401 | − | 0.594789i | 0.641661 | − | 0.766989i | \(-0.278246\pi\) |
−0.985062 | + | 0.172200i | \(0.944912\pi\) | |||||||
\(54\) | −3.84418 | + | 3.49604i | −0.523127 | + | 0.475750i | ||||
\(55\) | −0.369657 | − | 0.301824i | −0.0498446 | − | 0.0406979i | ||||
\(56\) | 1.41421 | + | 2.23607i | 0.188982 | + | 0.298807i | ||||
\(57\) | −7.73861 | + | 3.46081i | −1.02500 | + | 0.458396i | ||||
\(58\) | −1.75166 | − | 1.01132i | −0.230005 | − | 0.132793i | ||||
\(59\) | 2.45877 | + | 4.25871i | 0.320105 | + | 0.554437i | 0.980509 | − | 0.196472i | \(-0.0629486\pi\) |
−0.660405 | + | 0.750910i | \(0.729615\pi\) | |||||||
\(60\) | 0.993475 | + | 3.74340i | 0.128257 | + | 0.483270i | ||||
\(61\) | 3.00000 | + | 1.73205i | 0.384111 | + | 0.221766i | 0.679605 | − | 0.733578i | \(-0.262151\pi\) |
−0.295495 | + | 0.955344i | \(0.595484\pi\) | |||||||
\(62\) | − | 0.301824i | − | 0.0383317i | ||||||
\(63\) | 5.04858 | − | 6.12469i | 0.636062 | − | 0.771638i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.31350 | − | 14.0111i | −0.659059 | − | 1.73786i | ||||
\(66\) | 0.299418 | + | 0.216784i | 0.0368558 | + | 0.0266842i | ||||
\(67\) | 4.61230 | − | 2.66291i | 0.563482 | − | 0.325326i | −0.191060 | − | 0.981578i | \(-0.561192\pi\) |
0.754542 | + | 0.656252i | \(0.227859\pi\) | |||||||
\(68\) | 2.73861 | + | 1.58114i | 0.332106 | + | 0.191741i | ||||
\(69\) | 4.58009 | + | 10.2414i | 0.551378 | + | 1.23292i | ||||
\(70\) | −2.31920 | − | 5.44255i | −0.277197 | − | 0.650509i | ||||
\(71\) | − | 2.02265i | − | 0.240044i | −0.992771 | − | 0.120022i | \(-0.961703\pi\) | ||
0.992771 | − | 0.120022i | \(-0.0382965\pi\) | |||||||
\(72\) | −0.936492 | − | 2.85008i | −0.110367 | − | 0.335886i | ||||
\(73\) | −5.99430 | − | 10.3824i | −0.701580 | − | 1.21517i | −0.967912 | − | 0.251291i | \(-0.919145\pi\) |
0.266331 | − | 0.963882i | \(-0.414188\pi\) | |||||||
\(74\) | −6.17913 | + | 3.56752i | −0.718310 | + | 0.414716i | ||||
\(75\) | −0.849876 | − | 8.61845i | −0.0981353 | − | 0.995173i | ||||
\(76\) | − | 4.89433i | − | 0.561418i | ||||||
\(77\) | −0.500000 | − | 0.262377i | −0.0569803 | − | 0.0299007i | ||||
\(78\) | 4.73861 | + | 10.5959i | 0.536542 | + | 1.19974i | ||||
\(79\) | −0.261387 | + | 0.452736i | −0.0294084 | + | 0.0509368i | −0.880355 | − | 0.474315i | \(-0.842696\pi\) |
0.850947 | + | 0.525252i | \(0.176029\pi\) | |||||||
\(80\) | −2.20711 | − | 0.358719i | −0.246762 | − | 0.0401061i | ||||
\(81\) | −7.24597 | + | 5.33816i | −0.805107 | + | 0.593129i | ||||
\(82\) | −3.35071 | + | 5.80359i | −0.370023 | + | 0.640899i | ||||
\(83\) | 16.7169i | 1.83491i | 0.397835 | + | 0.917457i | \(0.369762\pi\) | ||||
−0.397835 | + | 0.917457i | \(0.630238\pi\) | |||||||
\(84\) | 2.03803 | + | 4.10444i | 0.222367 | + | 0.447831i | ||||
\(85\) | −5.47723 | − | 4.47214i | −0.594089 | − | 0.485071i | ||||
\(86\) | −1.75166 | − | 1.01132i | −0.188887 | − | 0.109054i | ||||
\(87\) | −2.83766 | − | 2.05451i | −0.304229 | − | 0.220266i | ||||
\(88\) | −0.184829 | + | 0.106711i | −0.0197028 | + | 0.0113754i | ||||
\(89\) | 5.28720 | − | 9.15769i | 0.560442 | − | 0.970714i | −0.437016 | − | 0.899454i | \(-0.643965\pi\) |
0.997458 | − | 0.0712599i | \(-0.0227020\pi\) | |||||||
\(90\) | 1.04456 | + | 6.62638i | 0.110106 | + | 0.698482i | ||||
\(91\) | −9.47723 | − | 14.9848i | −0.993483 | − | 1.57083i | ||||
\(92\) | −6.47723 | −0.675297 | ||||||||
\(93\) | 0.0537841 | − | 0.520000i | 0.00557715 | − | 0.0539215i | ||||
\(94\) | −6.71584 | + | 3.87739i | −0.692686 | + | 0.399922i | ||||
\(95\) | −1.75569 | + | 10.8023i | −0.180130 | + | 1.10829i | ||||
\(96\) | 1.72286 | + | 0.178197i | 0.175839 | + | 0.0181872i | ||||
\(97\) | 3.50333 | 0.355709 | 0.177854 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177854 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(98\) | −3.97723 | − | 5.76035i | −0.401760 | − | 0.581884i | ||||
\(99\) | 0.477226 | + | 0.426844i | 0.0479630 | + | 0.0428994i | ||||
\(100\) | 4.74264 | + | 1.58346i | 0.474264 | + | 0.158346i | ||||
\(101\) | 5.65685 | + | 9.79796i | 0.562878 | + | 0.974933i | 0.997244 | + | 0.0741967i | \(0.0236393\pi\) |
−0.434366 | + | 0.900737i | \(0.643027\pi\) | |||||||
\(102\) | 4.43649 | + | 3.21209i | 0.439278 | + | 0.318045i | ||||
\(103\) | 5.28720 | − | 9.15769i | 0.520963 | − | 0.902334i | −0.478740 | − | 0.877957i | \(-0.658906\pi\) |
0.999703 | − | 0.0243776i | \(-0.00776038\pi\) | |||||||
\(104\) | −6.70141 | −0.657127 | ||||||||
\(105\) | −3.02581 | − | 9.79002i | −0.295289 | − | 0.955408i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | −2.73861 | + | 4.74342i | −0.264752 | + | 0.458563i | −0.967499 | − | 0.252877i | \(-0.918623\pi\) |
0.702747 | + | 0.711440i | \(0.251957\pi\) | |||||||
\(108\) | −1.10557 | − | 5.07718i | −0.106383 | − | 0.488552i | ||||
\(109\) | −6.21584 | − | 10.7661i | −0.595369 | − | 1.03121i | −0.993495 | − | 0.113879i | \(-0.963672\pi\) |
0.398125 | − | 0.917331i | \(-0.369661\pi\) | |||||||
\(110\) | 0.446216 | − | 0.169221i | 0.0425450 | − | 0.0161346i | ||||
\(111\) | −11.2815 | + | 5.04524i | −1.07079 | + | 0.478873i | ||||
\(112\) | −2.64360 | + | 0.106711i | −0.249797 | + | 0.0100832i | ||||
\(113\) | 6.52277 | 0.613611 | 0.306806 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306806 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(114\) | 0.872155 | − | 8.43224i | 0.0816848 | − | 0.789752i | ||||
\(115\) | 14.2959 | + | 2.32351i | 1.33310 | + | 0.216668i | ||||
\(116\) | 1.75166 | − | 1.01132i | 0.162638 | − | 0.0938990i | ||||
\(117\) | 6.27582 | + | 19.0996i | 0.580199 | + | 1.76576i | ||||
\(118\) | −4.91754 | −0.452696 | ||||||||
\(119\) | −7.40852 | − | 3.88766i | −0.679138 | − | 0.356381i | ||||
\(120\) | −3.73861 | − | 1.01132i | −0.341287 | − | 0.0923207i | ||||
\(121\) | −5.47723 | + | 9.48683i | −0.497930 | + | 0.862439i | ||||
\(122\) | −3.00000 | + | 1.73205i | −0.271607 | + | 0.156813i | ||||
\(123\) | −6.80698 | + | 9.40169i | −0.613765 | + | 0.847722i | ||||
\(124\) | 0.261387 | + | 0.150912i | 0.0234733 | + | 0.0135523i | ||||
\(125\) | −9.89949 | − | 5.19615i | −0.885438 | − | 0.464758i | ||||
\(126\) | 2.77984 | + | 7.43455i | 0.247648 | + | 0.662322i | ||||
\(127\) | − | 13.6298i | − | 1.20945i | −0.796434 | − | 0.604726i | \(-0.793283\pi\) | ||
0.796434 | − | 0.604726i | \(-0.206717\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.83766 | − | 2.05451i | −0.249842 | − | 0.180889i | ||||
\(130\) | 14.7907 | + | 2.40393i | 1.29723 | + | 0.210838i | ||||
\(131\) | −3.01326 | + | 5.21911i | −0.263269 | + | 0.455996i | −0.967109 | − | 0.254363i | \(-0.918134\pi\) |
0.703839 | + | 0.710359i | \(0.251467\pi\) | |||||||
\(132\) | −0.337449 | + | 0.150912i | −0.0293712 | + | 0.0131352i | ||||
\(133\) | 0.522278 | + | 12.9386i | 0.0452873 | + | 1.12192i | ||||
\(134\) | 5.32582i | 0.460081i | ||||||||
\(135\) | 0.618823 | + | 11.6025i | 0.0532598 | + | 0.998581i | ||||
\(136\) | −2.73861 | + | 1.58114i | −0.234834 | + | 0.135582i | ||||
\(137\) | −3.73861 | − | 6.47547i | −0.319411 | − | 0.553237i | 0.660954 | − | 0.750426i | \(-0.270152\pi\) |
−0.980365 | + | 0.197190i | \(0.936818\pi\) | |||||||
\(138\) | −11.1594 | − | 1.15422i | −0.949947 | − | 0.0982539i | ||||
\(139\) | − | 7.53185i | − | 0.638843i | −0.947613 | − | 0.319422i | \(-0.896511\pi\) | ||
0.947613 | − | 0.319422i | \(-0.103489\pi\) | |||||||
\(140\) | 5.87298 | + | 0.712788i | 0.496358 | + | 0.0602416i | ||||
\(141\) | −12.2614 | + | 5.48346i | −1.03260 | + | 0.461791i | ||||
\(142\) | 1.75166 | + | 1.01132i | 0.146996 | + | 0.0848683i | ||||
\(143\) | 1.23861 | − | 0.715113i | 0.103578 | − | 0.0598008i | ||||
\(144\) | 2.93649 | + | 0.614017i | 0.244708 | + | 0.0511681i | ||||
\(145\) | −4.22889 | + | 1.60374i | −0.351190 | + | 0.133184i | ||||
\(146\) | 11.9886 | 0.992184 | ||||||||
\(147\) | −5.82572 | − | 10.6330i | −0.480498 | − | 0.876996i | ||||
\(148\) | − | 7.13505i | − | 0.586497i | ||||||
\(149\) | −2.12132 | − | 1.22474i | −0.173785 | − | 0.100335i | 0.410584 | − | 0.911823i | \(-0.365325\pi\) |
−0.584370 | + | 0.811488i | \(0.698658\pi\) | |||||||
\(150\) | 7.88874 | + | 3.57321i | 0.644113 | + | 0.291751i | ||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 4.23861 | + | 2.44716i | 0.343797 | + | 0.198491i | ||||
\(153\) | 7.07107 | + | 6.32456i | 0.571662 | + | 0.511310i | ||||
\(154\) | 0.477226 | − | 0.301824i | 0.0384559 | − | 0.0243217i | ||||
\(155\) | −0.522774 | − | 0.426844i | −0.0419903 | − | 0.0342849i | ||||
\(156\) | −11.5456 | − | 1.19417i | −0.924387 | − | 0.0956102i | ||||
\(157\) | −4.39526 | − | 7.61282i | −0.350780 | − | 0.607569i | 0.635606 | − | 0.772013i | \(-0.280750\pi\) |
−0.986386 | + | 0.164445i | \(0.947417\pi\) | |||||||
\(158\) | −0.261387 | − | 0.452736i | −0.0207949 | − | 0.0360177i | ||||
\(159\) | 8.61430 | + | 0.890985i | 0.683158 | + | 0.0706597i | ||||
\(160\) | 1.41421 | − | 1.73205i | 0.111803 | − | 0.136931i | ||||
\(161\) | 17.1232 | − | 0.691190i | 1.34950 | − | 0.0544734i | ||||
\(162\) | −1.00000 | − | 8.94427i | −0.0785674 | − | 0.702728i | ||||
\(163\) | 12.7279 | + | 7.34847i | 0.996928 | + | 0.575577i | 0.907338 | − | 0.420402i | \(-0.138111\pi\) |
0.0895899 | + | 0.995979i | \(0.471444\pi\) | |||||||
\(164\) | −3.35071 | − | 5.80359i | −0.261646 | − | 0.453184i | ||||
\(165\) | 0.798922 | − | 0.212029i | 0.0621960 | − | 0.0165064i | ||||
\(166\) | −14.4772 | − | 8.35843i | −1.12365 | − | 0.648740i | ||||
\(167\) | − | 14.6830i | − | 1.13620i | −0.822958 | − | 0.568102i | \(-0.807678\pi\) | ||
0.822958 | − | 0.568102i | \(-0.192322\pi\) | |||||||
\(168\) | −4.57357 | − | 0.287233i | −0.352858 | − | 0.0221605i | ||||
\(169\) | 31.9089 | 2.45453 | ||||||||
\(170\) | 6.61160 | − | 2.50735i | 0.507086 | − | 0.192305i | ||||
\(171\) | 3.00520 | − | 14.3722i | 0.229813 | − | 1.09907i | ||||
\(172\) | 1.75166 | − | 1.01132i | 0.133563 | − | 0.0771127i | ||||
\(173\) | −9.97723 | − | 5.76035i | −0.758554 | − | 0.437952i | 0.0702221 | − | 0.997531i | \(-0.477629\pi\) |
−0.828776 | + | 0.559580i | \(0.810963\pi\) | |||||||
\(174\) | 3.19808 | − | 1.43023i | 0.242446 | − | 0.108425i | ||||
\(175\) | −12.7066 | − | 3.67995i | −0.960529 | − | 0.278178i | ||||
\(176\) | − | 0.213422i | − | 0.0160873i | ||||||
\(177\) | −8.47223 | − | 0.876291i | −0.636812 | − | 0.0658660i | ||||
\(178\) | 5.28720 | + | 9.15769i | 0.396292 | + | 0.686398i | ||||
\(179\) | 12.9128 | − | 7.45518i | 0.965144 | − | 0.557226i | 0.0673918 | − | 0.997727i | \(-0.478532\pi\) |
0.897752 | + | 0.440500i | \(0.145199\pi\) | |||||||
\(180\) | −6.26089 | − | 2.40858i | −0.466659 | − | 0.179525i | ||||
\(181\) | 3.16228i | 0.235050i | 0.993070 | + | 0.117525i | \(0.0374961\pi\) | ||||
−0.993070 | + | 0.117525i | \(0.962504\pi\) | |||||||
\(182\) | 17.7158 | − | 0.715113i | 1.31319 | − | 0.0530077i | ||||
\(183\) | −5.47723 | + | 2.44949i | −0.404888 | + | 0.181071i | ||||
\(184\) | 3.23861 | − | 5.60944i | 0.238754 | − | 0.413534i | ||||
\(185\) | −2.55948 | + | 15.7478i | −0.188177 | + | 1.15780i | ||||
\(186\) | 0.423441 | + | 0.306579i | 0.0310482 | + | 0.0224794i | ||||
\(187\) | 0.337449 | − | 0.584480i | 0.0246767 | − | 0.0427414i | ||||
\(188\) | − | 7.75478i | − | 0.565576i | ||||||
\(189\) | 3.46447 | + | 13.3040i | 0.252003 | + | 0.967726i | ||||
\(190\) | −8.47723 | − | 6.92163i | −0.615003 | − | 0.502148i | ||||
\(191\) | 1.38201 | + | 0.797901i | 0.0999984 | + | 0.0577341i | 0.549165 | − | 0.835714i | \(-0.314946\pi\) |
−0.449167 | + | 0.893448i | \(0.648279\pi\) | |||||||
\(192\) | −1.01575 | + | 1.40294i | −0.0733057 | + | 0.101249i | ||||
\(193\) | 6.36396 | − | 3.67423i | 0.458088 | − | 0.264477i | −0.253152 | − | 0.967427i | \(-0.581467\pi\) |
0.711240 | + | 0.702949i | \(0.248134\pi\) | |||||||
\(194\) | −1.75166 | + | 3.03397i | −0.125762 | + | 0.217826i | ||||
\(195\) | 25.0540 | + | 6.77729i | 1.79415 | + | 0.485332i | ||||
\(196\) | 6.97723 | − | 0.564201i | 0.498373 | − | 0.0403001i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | −0.608270 | + | 0.199868i | −0.0432279 | + | 0.0142040i | ||||
\(199\) | −19.4317 | + | 11.2189i | −1.37748 | + | 0.795286i | −0.991855 | − | 0.127372i | \(-0.959346\pi\) |
−0.385620 | + | 0.922658i | \(0.626012\pi\) | |||||||
\(200\) | −3.74264 | + | 3.31552i | −0.264645 | + | 0.234442i | ||||
\(201\) | −0.949046 | + | 9.17565i | −0.0669405 | + | 0.647200i | ||||
\(202\) | −11.3137 | −0.796030 | ||||||||
\(203\) | −4.52277 | + | 2.86045i | −0.317437 | + | 0.200764i | ||||
\(204\) | −5.00000 | + | 2.23607i | −0.350070 | + | 0.156556i | ||||
\(205\) | 5.31350 | + | 14.0111i | 0.371111 | + | 0.978578i | ||||
\(206\) | 5.28720 | + | 9.15769i | 0.368376 | + | 0.638047i | ||||
\(207\) | −19.0203 | − | 3.97713i | −1.32200 | − | 0.276429i | ||||
\(208\) | 3.35071 | − | 5.80359i | 0.232330 | − | 0.402407i | ||||
\(209\) | −1.04456 | −0.0722535 | ||||||||
\(210\) | 9.99131 | + | 2.27458i | 0.689466 | + | 0.156961i | ||||
\(211\) | 13.5228 | 0.930946 | 0.465473 | − | 0.885062i | \(-0.345884\pi\) | ||||
0.465473 | + | 0.885062i | \(0.345884\pi\) | |||||||
\(212\) | −2.50000 | + | 4.33013i | −0.171701 | + | 0.297394i | ||||
\(213\) | 2.83766 | + | 2.05451i | 0.194433 | + | 0.140773i | ||||
\(214\) | −2.73861 | − | 4.74342i | −0.187208 | − | 0.324253i | ||||
\(215\) | −4.22889 | + | 1.60374i | −0.288408 | + | 0.109374i | ||||
\(216\) | 4.94975 | + | 1.58114i | 0.336788 | + | 0.107583i | ||||
\(217\) | −0.707107 | − | 0.371058i | −0.0480015 | − | 0.0251890i | ||||
\(218\) | 12.4317 | 0.841979 | ||||||||
\(219\) | 20.6547 | + | 2.13633i | 1.39571 | + | 0.144360i | ||||
\(220\) | −0.0765585 | + | 0.471045i | −0.00516158 | + | 0.0317578i | ||||
\(221\) | 18.3526 | − | 10.5959i | 1.23453 | − | 0.712755i | ||||
\(222\) | 1.27144 | − | 12.2927i | 0.0853337 | − | 0.825031i | ||||
\(223\) | −6.39617 | −0.428319 | −0.214160 | − | 0.976799i | \(-0.568701\pi\) | ||||
−0.214160 | + | 0.976799i | \(0.568701\pi\) | |||||||
\(224\) | 1.22938 | − | 2.34278i | 0.0821417 | − | 0.156533i | ||||
\(225\) | 12.9545 | + | 7.56189i | 0.863630 | + | 0.504126i | ||||
\(226\) | −3.26139 | + | 5.64889i | −0.216944 | + | 0.375758i | ||||
\(227\) | 9.00000 | − | 5.19615i | 0.597351 | − | 0.344881i | −0.170648 | − | 0.985332i | \(-0.554586\pi\) |
0.767999 | + | 0.640451i | \(0.221253\pi\) | |||||||
\(228\) | 6.86646 | + | 4.97143i | 0.454742 | + | 0.329241i | ||||
\(229\) | −6.26139 | − | 3.61501i | −0.413764 | − | 0.238887i | 0.278642 | − | 0.960395i | \(-0.410116\pi\) |
−0.692406 | + | 0.721508i | \(0.743449\pi\) | |||||||
\(230\) | −9.16018 | + | 11.2189i | −0.604004 | + | 0.739751i | ||||
\(231\) | 0.875977 | − | 0.434960i | 0.0576350 | − | 0.0286183i | ||||
\(232\) | 2.02265i | 0.132793i | ||||||||
\(233\) | 2.00000 | − | 3.46410i | 0.131024 | − | 0.226941i | −0.793047 | − | 0.609160i | \(-0.791507\pi\) |
0.924072 | + | 0.382219i | \(0.124840\pi\) | |||||||
\(234\) | −19.6786 | − | 4.11478i | −1.28643 | − | 0.268992i | ||||
\(235\) | −2.78179 | + | 17.1156i | −0.181464 | + | 1.11650i | ||||
\(236\) | 2.45877 | − | 4.25871i | 0.160052 | − | 0.277219i | ||||
\(237\) | −0.369657 | − | 0.826579i | −0.0240118 | − | 0.0536921i | ||||
\(238\) | 7.07107 | − | 4.47214i | 0.458349 | − | 0.289886i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 2.74514 | − | 2.73207i | 0.177198 | − | 0.176354i | ||||
\(241\) | 3.45445 | − | 1.99443i | 0.222521 | − | 0.128472i | −0.384596 | − | 0.923085i | \(-0.625659\pi\) |
0.607117 | + | 0.794613i | \(0.292326\pi\) | |||||||
\(242\) | −5.47723 | − | 9.48683i | −0.352089 | − | 0.609837i | ||||
\(243\) | −0.129018 | − | 15.5879i | −0.00827648 | − | 0.999966i | ||||
\(244\) | − | 3.46410i | − | 0.221766i | ||||||
\(245\) | −15.6019 | − | 1.25761i | −0.996767 | − | 0.0803460i | ||||
\(246\) | −4.73861 | − | 10.5959i | −0.302123 | − | 0.675567i | ||||
\(247\) | −28.4047 | − | 16.3995i | −1.80735 | − | 1.04347i | ||||
\(248\) | −0.261387 | + | 0.150912i | −0.0165981 | + | 0.00958292i | ||||
\(249\) | −23.4528 | − | 16.9802i | −1.48626 | − | 1.07608i | ||||
\(250\) | 9.44975 | − | 5.97514i | 0.597655 | − | 0.377901i | ||||
\(251\) | −16.6009 | −1.04784 | −0.523920 | − | 0.851768i | \(-0.675531\pi\) | ||||
−0.523920 | + | 0.851768i | \(0.675531\pi\) | |||||||
\(252\) | −7.82843 | − | 1.30986i | −0.493145 | − | 0.0825133i | ||||
\(253\) | 1.38238i | 0.0869095i | ||||||||
\(254\) | 11.8038 | + | 6.81491i | 0.740635 | + | 0.427606i | ||||
\(255\) | 11.8377 | − | 3.14164i | 0.741303 | − | 0.196737i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −20.4772 | − | 11.8225i | −1.27733 | − | 0.737469i | −0.300977 | − | 0.953631i | \(-0.597313\pi\) |
−0.976357 | + | 0.216162i | \(0.930646\pi\) | |||||||
\(258\) | 3.19808 | − | 1.43023i | 0.199104 | − | 0.0890420i | ||||
\(259\) | 0.761387 | + | 18.8622i | 0.0473103 | + | 1.17204i | ||||
\(260\) | −9.47723 | + | 11.6072i | −0.587753 | + | 0.719847i | ||||
\(261\) | 5.76471 | − | 1.89419i | 0.356827 | − | 0.117248i | ||||
\(262\) | −3.01326 | − | 5.21911i | −0.186160 | − | 0.322438i | ||||
\(263\) | 1.00000 | + | 1.73205i | 0.0616626 | + | 0.106803i | 0.895209 | − | 0.445647i | \(-0.147026\pi\) |
−0.833546 | + | 0.552450i | \(0.813693\pi\) | |||||||
\(264\) | 0.0380311 | − | 0.367696i | 0.00234065 | − | 0.0226301i | ||||
\(265\) | 7.07107 | − | 8.66025i | 0.434372 | − | 0.531995i | ||||
\(266\) | −11.4663 | − | 6.01701i | −0.703046 | − | 0.368927i | ||||
\(267\) | 7.47723 | + | 16.7196i | 0.457599 | + | 1.02322i | ||||
\(268\) | −4.61230 | − | 2.66291i | −0.281741 | − | 0.162663i | ||||
\(269\) | −14.4474 | − | 25.0236i | −0.880872 | − | 1.52572i | −0.850373 | − | 0.526180i | \(-0.823624\pi\) |
−0.0304992 | − | 0.999535i | \(-0.509710\pi\) | |||||||
\(270\) | −10.3574 | − | 5.26531i | −0.630333 | − | 0.320437i | ||||
\(271\) | 5.47723 | + | 3.16228i | 0.332718 | + | 0.192095i | 0.657047 | − | 0.753850i | \(-0.271805\pi\) |
−0.324329 | + | 0.945944i | \(0.605139\pi\) | |||||||
\(272\) | − | 3.16228i | − | 0.191741i | ||||||
\(273\) | 30.6493 | + | 1.92487i | 1.85498 | + | 0.116498i | ||||
\(274\) | 7.47723 | 0.451716 | ||||||||
\(275\) | 0.337946 | − | 1.01218i | 0.0203789 | − | 0.0610369i | ||||
\(276\) | 6.57926 | − | 9.08717i | 0.396025 | − | 0.546983i | ||||
\(277\) | −8.48528 | + | 4.89898i | −0.509831 | + | 0.294351i | −0.732764 | − | 0.680483i | \(-0.761770\pi\) |
0.222933 | + | 0.974834i | \(0.428437\pi\) | |||||||
\(278\) | 6.52277 | + | 3.76593i | 0.391210 | + | 0.225865i | ||||
\(279\) | 0.674899 | + | 0.603648i | 0.0404051 | + | 0.0361395i | ||||
\(280\) | −3.55378 | + | 4.72976i | −0.212379 | + | 0.282657i | ||||
\(281\) | − | 11.6072i | − | 0.692427i | −0.938156 | − | 0.346213i | \(-0.887467\pi\) | ||
0.938156 | − | 0.346213i | \(-0.112533\pi\) | |||||||
\(282\) | 1.38188 | − | 13.3604i | 0.0822897 | − | 0.795600i | ||||
\(283\) | 12.3583 | + | 21.4051i | 0.734623 | + | 1.27240i | 0.954889 | + | 0.296964i | \(0.0959741\pi\) |
−0.220266 | + | 0.975440i | \(0.570693\pi\) | |||||||
\(284\) | −1.75166 | + | 1.01132i | −0.103942 | + | 0.0600110i | ||||
\(285\) | −13.3717 | − | 13.4356i | −0.792069 | − | 0.795857i | ||||
\(286\) | 1.43023i | 0.0845711i | ||||||||
\(287\) | 9.47723 | + | 14.9848i | 0.559423 | + | 0.884525i | ||||
\(288\) | −2.00000 | + | 2.23607i | −0.117851 | + | 0.131762i | ||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | 0.725563 | − | 4.46420i | 0.0426065 | − | 0.262147i | ||||
\(291\) | −3.55851 | + | 4.91496i | −0.208604 | + | 0.288120i | ||||
\(292\) | −5.99430 | + | 10.3824i | −0.350790 | + | 0.607586i | ||||
\(293\) | 4.59250i | 0.268297i | 0.990961 | + | 0.134148i | \(0.0428299\pi\) | ||||
−0.990961 | + | 0.134148i | \(0.957170\pi\) | |||||||
\(294\) | 12.1213 | + | 0.271281i | 0.706930 | + | 0.0158214i | ||||
\(295\) | −6.95445 | + | 8.51743i | −0.404904 | + | 0.495904i | ||||
\(296\) | 6.17913 | + | 3.56752i | 0.359155 | + | 0.207358i | ||||
\(297\) | −1.08358 | + | 0.235952i | −0.0628757 | + | 0.0136913i | ||||
\(298\) | 2.12132 | − | 1.22474i | 0.122885 | − | 0.0709476i | ||||
\(299\) | −21.7033 | + | 37.5912i | −1.25513 | + | 2.17395i | ||||
\(300\) | −7.03886 | + | 5.04524i | −0.406389 | + | 0.291287i | ||||
\(301\) | −4.52277 | + | 2.86045i | −0.260688 | + | 0.164874i | ||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | −19.4919 | − | 2.01607i | −1.11978 | − | 0.115820i | ||||
\(304\) | −4.23861 | + | 2.44716i | −0.243101 | + | 0.140354i | ||||
\(305\) | −1.24264 | + | 7.64564i | −0.0711534 | + | 0.437788i | ||||
\(306\) | −9.01276 | + | 2.96145i | −0.515225 | + | 0.169295i | ||||
\(307\) | −3.50333 | −0.199945 | −0.0999727 | − | 0.994990i | \(-0.531876\pi\) | ||||
−0.0999727 | + | 0.994990i | \(0.531876\pi\) | |||||||
\(308\) | 0.0227744 | + | 0.564201i | 0.00129769 | + | 0.0321484i | ||||
\(309\) | 7.47723 | + | 16.7196i | 0.425365 | + | 0.951144i | ||||
\(310\) | 0.631045 | − | 0.239314i | 0.0358409 | − | 0.0135921i | ||||
\(311\) | −14.4474 | − | 25.0236i | −0.819236 | − | 1.41896i | −0.906246 | − | 0.422750i | \(-0.861065\pi\) |
0.0870106 | − | 0.996207i | \(-0.472269\pi\) | |||||||
\(312\) | 6.80698 | − | 9.40169i | 0.385369 | − | 0.532266i | ||||
\(313\) | −11.6190 | + | 20.1246i | −0.656742 | + | 1.13751i | 0.324712 | + | 0.945813i | \(0.394733\pi\) |
−0.981454 | + | 0.191697i | \(0.938601\pi\) | |||||||
\(314\) | 8.79052 | 0.496078 | ||||||||
\(315\) | 16.8083 | + | 5.69921i | 0.947041 | + | 0.321114i | ||||
\(316\) | 0.522774 | 0.0294084 | ||||||||
\(317\) | −16.9545 | + | 29.3660i | −0.952257 | + | 1.64936i | −0.211733 | + | 0.977328i | \(0.567911\pi\) |
−0.740524 | + | 0.672030i | \(0.765423\pi\) | |||||||
\(318\) | −5.07877 | + | 7.01471i | −0.284803 | + | 0.393365i | ||||
\(319\) | −0.215838 | − | 0.373843i | −0.0120846 | − | 0.0209312i | ||||
\(320\) | 0.792893 | + | 2.09077i | 0.0443241 | + | 0.116878i | ||||
\(321\) | −3.87298 | − | 8.66025i | −0.216169 | − | 0.483368i | ||||
\(322\) | −7.96300 | + | 15.1747i | −0.443761 | + | 0.845653i | ||||
\(323\) | −15.4772 | −0.861176 | ||||||||
\(324\) | 8.24597 | + | 3.60611i | 0.458109 | + | 0.200339i | ||||
\(325\) | 25.0810 | − | 22.2186i | 1.39124 | − | 1.23247i | ||||
\(326\) | −12.7279 | + | 7.34847i | −0.704934 | + | 0.406994i | ||||
\(327\) | 21.4180 | + | 2.21529i | 1.18442 | + | 0.122506i | ||||
\(328\) | 6.70141 | 0.370023 | ||||||||
\(329\) | 0.827520 | + | 20.5005i | 0.0456226 | + | 1.13023i | ||||
\(330\) | −0.215838 | + | 0.797901i | −0.0118815 | + | 0.0439230i | ||||
\(331\) | 5.71584 | − | 9.90012i | 0.314171 | − | 0.544160i | −0.665090 | − | 0.746763i | \(-0.731607\pi\) |
0.979261 | + | 0.202603i | \(0.0649402\pi\) | |||||||
\(332\) | 14.4772 | − | 8.35843i | 0.794541 | − | 0.458728i | ||||
\(333\) | 4.38104 | − | 20.9520i | 0.240079 | − | 1.14816i | ||||
\(334\) | 12.7158 | + | 7.34149i | 0.695780 | + | 0.401709i | ||||
\(335\) | 9.22460 | + | 7.53185i | 0.503994 | + | 0.411509i | ||||
\(336\) | 2.53553 | − | 3.81721i | 0.138325 | − | 0.208246i | ||||
\(337\) | − | 17.1464i | − | 0.934025i | −0.884251 | − | 0.467013i | \(-0.845330\pi\) | ||
0.884251 | − | 0.467013i | \(-0.154670\pi\) | |||||||
\(338\) | −15.9545 | + | 27.6339i | −0.867808 | + | 1.50309i | ||||
\(339\) | −6.62553 | + | 9.15107i | −0.359849 | + | 0.497018i | ||||
\(340\) | −1.13437 | + | 6.97948i | −0.0615199 | + | 0.378516i | ||||
\(341\) | 0.0322079 | − | 0.0557857i | 0.00174416 | − | 0.00302097i | ||||
\(342\) | 10.9441 | + | 9.78866i | 0.591787 | + | 0.529310i | ||||
\(343\) | −18.3848 | + | 2.23607i | −0.992685 | + | 0.120736i | ||||
\(344\) | 2.02265i | 0.109054i | ||||||||
\(345\) | −17.7809 | + | 17.6962i | −0.957290 | + | 0.952734i | ||||
\(346\) | 9.97723 | − | 5.76035i | 0.536379 | − | 0.309679i | ||||
\(347\) | 3.26139 | + | 5.64889i | 0.175080 | + | 0.303248i | 0.940189 | − | 0.340653i | \(-0.110648\pi\) |
−0.765109 | + | 0.643901i | \(0.777315\pi\) | |||||||
\(348\) | −0.360429 | + | 3.48474i | −0.0193210 | + | 0.186801i | ||||
\(349\) | − | 32.5282i | − | 1.74120i | −0.491994 | − | 0.870599i | \(-0.663732\pi\) | ||
0.491994 | − | 0.870599i | \(-0.336268\pi\) | |||||||
\(350\) | 9.54024 | − | 9.16427i | 0.509947 | − | 0.489851i | ||||
\(351\) | −33.1703 | − | 10.5959i | −1.77050 | − | 0.565565i | ||||
\(352\) | 0.184829 | + | 0.106711i | 0.00985140 | + | 0.00568771i | ||||
\(353\) | 11.4772 | − | 6.62638i | 0.610871 | − | 0.352687i | −0.162435 | − | 0.986719i | \(-0.551935\pi\) |
0.773306 | + | 0.634033i | \(0.218602\pi\) | |||||||
\(354\) | 4.99501 | − | 6.89902i | 0.265482 | − | 0.366679i | ||||
\(355\) | 4.22889 | − | 1.60374i | 0.224446 | − | 0.0851178i | ||||
\(356\) | −10.5744 | −0.560442 | ||||||||
\(357\) | 12.9794 | − | 6.44482i | 0.686942 | − | 0.341096i | ||||
\(358\) | 14.9104i | 0.788037i | ||||||||
\(359\) | −5.62465 | − | 3.24739i | −0.296857 | − | 0.171391i | 0.344173 | − | 0.938906i | \(-0.388159\pi\) |
−0.641030 | + | 0.767516i | \(0.721493\pi\) | |||||||
\(360\) | 5.21633 | − | 4.21780i | 0.274925 | − | 0.222298i | ||||
\(361\) | 2.47723 | + | 4.29068i | 0.130380 | + | 0.225825i | ||||
\(362\) | −2.73861 | − | 1.58114i | −0.143938 | − | 0.0831028i | ||||
\(363\) | −7.74597 | − | 17.3205i | −0.406558 | − | 0.909091i | ||||
\(364\) | −8.23861 | + | 15.6999i | −0.431821 | + | 0.822900i | ||||
\(365\) | 16.9545 | − | 20.7649i | 0.887437 | − | 1.08688i | ||||
\(366\) | 0.617292 | − | 5.96816i | 0.0322664 | − | 0.311961i | ||||
\(367\) | 4.05781 | + | 7.02834i | 0.211816 | + | 0.366876i | 0.952283 | − | 0.305217i | \(-0.0987289\pi\) |
−0.740467 | + | 0.672093i | \(0.765396\pi\) | |||||||
\(368\) | 3.23861 | + | 5.60944i | 0.168824 | + | 0.292412i | ||||
\(369\) | −6.27582 | − | 19.0996i | −0.326706 | − | 0.994285i | ||||
\(370\) | −12.3583 | − | 10.0905i | −0.642476 | − | 0.524579i | ||||
\(371\) | 6.14692 | − | 11.7139i | 0.319132 | − | 0.608155i | ||||
\(372\) | −0.477226 | + | 0.213422i | −0.0247430 | + | 0.0110654i | ||||
\(373\) | 3.13367 | + | 1.80922i | 0.162255 | + | 0.0936781i | 0.578929 | − | 0.815378i | \(-0.303471\pi\) |
−0.416674 | + | 0.909056i | \(0.636804\pi\) | |||||||
\(374\) | 0.337449 | + | 0.584480i | 0.0174491 | + | 0.0302227i | ||||
\(375\) | 17.3453 | − | 8.61041i | 0.895710 | − | 0.444640i | ||||
\(376\) | 6.71584 | + | 3.87739i | 0.346343 | + | 0.199961i | ||||
\(377\) | − | 13.5546i | − | 0.698097i | ||||||
\(378\) | −13.2539 | − | 3.65170i | −0.681705 | − | 0.187823i | ||||
\(379\) | −9.52277 | −0.489152 | −0.244576 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244576 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(380\) | 10.2329 | − | 3.88068i | 0.524938 | − | 0.199075i | ||||
\(381\) | 19.1219 | + | 13.8445i | 0.979642 | + | 0.709277i | ||||
\(382\) | −1.38201 | + | 0.797901i | −0.0707096 | + | 0.0408242i | ||||
\(383\) | −0.715838 | − | 0.413289i | −0.0365776 | − | 0.0211181i | 0.481600 | − | 0.876391i | \(-0.340056\pi\) |
−0.518177 | + | 0.855273i | \(0.673389\pi\) | |||||||
\(384\) | −0.707107 | − | 1.58114i | −0.0360844 | − | 0.0806872i | ||||
\(385\) | 0.152124 | − | 1.25342i | 0.00775298 | − | 0.0638803i | ||||
\(386\) | 7.34847i | 0.374027i | ||||||||
\(387\) | 5.76471 | − | 1.89419i | 0.293037 | − | 0.0962872i | ||||
\(388\) | −1.75166 | − | 3.03397i | −0.0889272 | − | 0.154026i | ||||
\(389\) | 6.36396 | − | 3.67423i | 0.322666 | − | 0.186291i | −0.329914 | − | 0.944011i | \(-0.607020\pi\) |
0.652580 | + | 0.757720i | \(0.273687\pi\) | |||||||
\(390\) | −18.3963 | + | 18.3087i | −0.931533 | + | 0.927099i | ||||
\(391\) | 20.4828i | 1.03586i | ||||||||
\(392\) | −3.00000 | + | 6.32456i | −0.151523 | + | 0.319438i | ||||
\(393\) | −4.26139 | − | 9.52875i | −0.214959 | − | 0.480662i | ||||
\(394\) | −4.50000 | + | 7.79423i | −0.226707 | + | 0.392668i | ||||
\(395\) | −1.15382 | − | 0.187529i | −0.0580549 | − | 0.00943563i | ||||
\(396\) | 0.131045 | − | 0.626711i | 0.00658524 | − | 0.0314934i | ||||
\(397\) | 15.1867 | − | 26.3041i | 0.762198 | − | 1.32017i | −0.179517 | − | 0.983755i | \(-0.557453\pi\) |
0.941715 | − | 0.336411i | \(-0.109213\pi\) | |||||||
\(398\) | − | 22.4378i | − | 1.12470i | ||||||
\(399\) | −18.6827 | − | 12.4097i | −0.935303 | − | 0.621264i | ||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | 26.2834 | + | 15.1747i | 1.31253 | + | 0.757789i | 0.982514 | − | 0.186187i | \(-0.0596131\pi\) |
0.330014 | + | 0.943976i | \(0.392946\pi\) | |||||||
\(402\) | −7.47182 | − | 5.40972i | −0.372661 | − | 0.269812i | ||||
\(403\) | 1.75166 | − | 1.01132i | 0.0872565 | − | 0.0503776i | ||||
\(404\) | 5.65685 | − | 9.79796i | 0.281439 | − | 0.487467i | ||||
\(405\) | −16.9061 | − | 10.9171i | −0.840073 | − | 0.542473i | ||||
\(406\) | −0.215838 | − | 5.34706i | −0.0107119 | − | 0.265370i | ||||
\(407\) | −1.52277 | −0.0754811 | ||||||||
\(408\) | 0.563508 | − | 5.44816i | 0.0278978 | − | 0.269724i | ||||
\(409\) | −19.4317 | + | 11.2189i | −0.960835 | + | 0.554738i | −0.896430 | − | 0.443186i | \(-0.853848\pi\) |
−0.0644048 | + | 0.997924i | \(0.520515\pi\) | |||||||
\(410\) | −14.7907 | − | 2.40393i | −0.730462 | − | 0.118721i | ||||
\(411\) | 12.8822 | + | 1.33242i | 0.635433 | + | 0.0657234i | ||||
\(412\) | −10.5744 | −0.520963 | ||||||||
\(413\) | −6.04555 | + | 11.5207i | −0.297482 | + | 0.566897i | ||||
\(414\) | 12.9545 | − | 14.4835i | 0.636677 | − | 0.711826i | ||||
\(415\) | −34.9511 | + | 13.2547i | −1.71568 | + | 0.650647i | ||||
\(416\) | 3.35071 | + | 5.80359i | 0.164282 | + | 0.284544i | ||||
\(417\) | 10.5667 | + | 7.65050i | 0.517456 | + | 0.374647i | ||||
\(418\) | 0.522278 | − | 0.904612i | 0.0255455 | − | 0.0442460i | ||||
\(419\) | 16.6009 | 0.811007 | 0.405504 | − | 0.914093i | \(-0.367096\pi\) | ||||
0.405504 | + | 0.914093i | \(0.367096\pi\) | |||||||
\(420\) | −6.96550 | + | 7.51544i | −0.339882 | + | 0.366716i | ||||
\(421\) | −2.95445 | −0.143991 | −0.0719956 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719956 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(422\) | −6.76139 | + | 11.7111i | −0.329139 | + | 0.570086i | ||||
\(423\) | 4.76157 | − | 22.7719i | 0.231515 | − | 1.10721i | ||||
\(424\) | −2.50000 | − | 4.33013i | −0.121411 | − | 0.210290i | ||||
\(425\) | 5.00735 | − | 14.9975i | 0.242892 | − | 0.727488i | ||||
\(426\) | −3.19808 | + | 1.43023i | −0.154948 | + | 0.0692947i | ||||
\(427\) | 0.369657 | + | 9.15769i | 0.0178890 | + | 0.443172i | ||||
\(428\) | 5.47723 | 0.264752 | ||||||||
\(429\) | −0.254862 | + | 2.46408i | −0.0123049 | + | 0.118967i | ||||
\(430\) | 0.725563 | − | 4.46420i | 0.0349897 | − | 0.215283i | ||||
\(431\) | −32.0928 | + | 18.5288i | −1.54586 | + | 0.892501i | −0.547406 | + | 0.836867i | \(0.684385\pi\) |
−0.998451 | + | 0.0556344i | \(0.982282\pi\) | |||||||
\(432\) | −3.84418 | + | 3.49604i | −0.184953 | + | 0.168203i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0.674899 | − | 0.426844i | 0.0323962 | − | 0.0204891i | ||||
\(435\) | 2.04555 | − | 7.56189i | 0.0980766 | − | 0.362565i | ||||
\(436\) | −6.21584 | + | 10.7661i | −0.297685 | + | 0.515605i | ||||
\(437\) | 27.4545 | − | 15.8508i | 1.31332 | − | 0.758248i | ||||
\(438\) | −12.1775 | + | 16.8193i | −0.581862 | + | 0.803658i | ||||
\(439\) | 19.6931 | + | 11.3698i | 0.939899 | + | 0.542651i | 0.889929 | − | 0.456100i | \(-0.150754\pi\) |
0.0499701 | + | 0.998751i | \(0.484087\pi\) | |||||||
\(440\) | −0.369657 | − | 0.301824i | −0.0176227 | − | 0.0143889i | ||||
\(441\) | 20.8350 | + | 2.62736i | 0.992143 | + | 0.125112i | ||||
\(442\) | 21.1917i | 1.00799i | ||||||||
\(443\) | 18.4772 | − | 32.0035i | 0.877879 | − | 1.52053i | 0.0242161 | − | 0.999707i | \(-0.492291\pi\) |
0.853663 | − | 0.520825i | \(-0.174376\pi\) | |||||||
\(444\) | 10.0101 | + | 7.24745i | 0.475056 | + | 0.343949i | ||||
\(445\) | 23.3388 | + | 3.79324i | 1.10637 | + | 0.179817i | ||||
\(446\) | 3.19808 | − | 5.53924i | 0.151434 | − | 0.262291i | ||||
\(447\) | 3.87298 | − | 1.73205i | 0.183186 | − | 0.0819232i | ||||
\(448\) | 1.41421 | + | 2.23607i | 0.0668153 | + | 0.105644i | ||||
\(449\) | 3.51660i | 0.165959i | 0.996551 | + | 0.0829793i | \(0.0264435\pi\) | ||||
−0.996551 | + | 0.0829793i | \(0.973556\pi\) | |||||||
\(450\) | −13.0260 | + | 7.43794i | −0.614052 | + | 0.350628i | ||||
\(451\) | −1.23861 | + | 0.715113i | −0.0583240 | + | 0.0336734i | ||||
\(452\) | −3.26139 | − | 5.64889i | −0.153403 | − | 0.265701i | ||||
\(453\) | −3.44572 | − | 0.356394i | −0.161894 | − | 0.0167448i | ||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 23.8154 | − | 31.6961i | 1.11648 | − | 1.48593i | ||||
\(456\) | −7.73861 | + | 3.46081i | −0.362394 | + | 0.162067i | ||||
\(457\) | 32.8322 | + | 18.9557i | 1.53582 | + | 0.886708i | 0.999077 | + | 0.0429646i | \(0.0136803\pi\) |
0.536747 | + | 0.843743i | \(0.319653\pi\) | |||||||
\(458\) | 6.26139 | − | 3.61501i | 0.292575 | − | 0.168918i | ||||
\(459\) | −16.0554 | + | 3.49611i | −0.749404 | + | 0.163184i | ||||
\(460\) | −5.13575 | − | 13.5424i | −0.239455 | − | 0.631417i | ||||
\(461\) | 16.2957 | 0.758965 | 0.379482 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379482 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(462\) | −0.0613019 | + | 0.976098i | −0.00285202 | + | 0.0454122i | ||||
\(463\) | − | 17.6751i | − | 0.821433i | −0.911763 | − | 0.410716i | \(-0.865279\pi\) | ||
0.911763 | − | 0.410716i | \(-0.134721\pi\) | |||||||
\(464\) | −1.75166 | − | 1.01132i | −0.0813189 | − | 0.0469495i | ||||
\(465\) | 1.12985 | − | 0.299855i | 0.0523954 | − | 0.0139054i | ||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | −29.7386 | − | 17.1696i | −1.37614 | − | 0.794514i | −0.384447 | − | 0.923147i | \(-0.625608\pi\) |
−0.991692 | + | 0.128633i | \(0.958941\pi\) | |||||||
\(468\) | 13.4028 | − | 14.9848i | 0.619546 | − | 0.692673i | ||||
\(469\) | 12.4772 | + | 6.54749i | 0.576145 | + | 0.302335i | ||||
\(470\) | −13.4317 | − | 10.9669i | −0.619557 | − | 0.505866i | ||||
\(471\) | 15.1448 | + | 1.56644i | 0.697837 | + | 0.0721780i | ||||
\(472\) | 2.45877 | + | 4.25871i | 0.113174 | + | 0.196023i | ||||
\(473\) | −0.215838 | − | 0.373843i | −0.00992426 | − | 0.0171893i | ||||
\(474\) | 0.900667 | + | 0.0931568i | 0.0413690 | + | 0.00427883i | ||||
\(475\) | −23.9772 | + | 4.89433i | −1.10015 | + | 0.224567i | ||||
\(476\) | 0.337449 | + | 8.35979i | 0.0154670 | + | 0.383170i | ||||
\(477\) | −10.0000 | + | 11.1803i | −0.457869 | + | 0.511913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.68906 | − | 9.85374i | −0.259940 | − | 0.450229i | 0.706286 | − | 0.707927i | \(-0.250369\pi\) |
−0.966226 | + | 0.257698i | \(0.917036\pi\) | |||||||
\(480\) | 0.993475 | + | 3.74340i | 0.0453457 | + | 0.170862i | ||||
\(481\) | −41.4089 | − | 23.9074i | −1.88808 | − | 1.09009i | ||||
\(482\) | 3.98886i | 0.181687i | ||||||||
\(483\) | −16.4232 | + | 24.7249i | −0.747283 | + | 1.12502i | ||||
\(484\) | 10.9545 | 0.497930 | ||||||||
\(485\) | 2.77776 | + | 7.32465i | 0.126132 | + | 0.332595i | ||||
\(486\) | 13.5640 | + | 7.68223i | 0.615278 | + | 0.348473i | ||||
\(487\) | 31.7232 | − | 18.3154i | 1.43751 | − | 0.829949i | 0.439838 | − | 0.898077i | \(-0.355036\pi\) |
0.997677 | + | 0.0681277i | \(0.0217025\pi\) | |||||||
\(488\) | 3.00000 | + | 1.73205i | 0.135804 | + | 0.0784063i | ||||
\(489\) | −23.2379 | + | 10.3923i | −1.05085 | + | 0.469956i | ||||
\(490\) | 8.89006 | − | 12.8828i | 0.401612 | − | 0.581986i | ||||
\(491\) | 4.04529i | 0.182561i | 0.995825 | + | 0.0912807i | \(0.0290961\pi\) | ||||
−0.995825 | + | 0.0912807i | \(0.970904\pi\) | |||||||
\(492\) | 11.5456 | + | 1.19417i | 0.520515 | + | 0.0538374i | ||||
\(493\) | −3.19808 | − | 5.53924i | −0.144034 | − | 0.249475i | ||||
\(494\) | 28.4047 | − | 16.3995i | 1.27799 | − | 0.737846i | ||||
\(495\) | −0.514043 | + | 1.33621i | −0.0231045 | + | 0.0600582i | ||||
\(496\) | − | 0.301824i | − | 0.0135523i | ||||||
\(497\) | 4.52277 | − | 2.86045i | 0.202874 | − | 0.128309i | ||||
\(498\) | 26.4317 | − | 11.8206i | 1.18443 | − | 0.529694i | ||||
\(499\) | 20.9545 | − | 36.2942i | 0.938050 | − | 1.62475i | 0.168947 | − | 0.985625i | \(-0.445963\pi\) |
0.769103 | − | 0.639125i | \(-0.220703\pi\) | |||||||
\(500\) | 0.449747 | + | 11.1713i | 0.0201133 | + | 0.499595i | ||||
\(501\) | 20.5994 | + | 14.9143i | 0.920312 | + | 0.666321i | ||||
\(502\) | 8.30045 | − | 14.3768i | 0.370467 | − | 0.641668i | ||||
\(503\) | 22.4378i | 1.00045i | 0.865895 | + | 0.500225i | \(0.166749\pi\) | ||||
−0.865895 | + | 0.500225i | \(0.833251\pi\) | |||||||
\(504\) | 5.04858 | − | 6.12469i | 0.224882 | − | 0.272815i | ||||
\(505\) | −16.0000 | + | 19.5959i | −0.711991 | + | 0.872007i | ||||
\(506\) | −1.19718 | − | 0.691190i | −0.0532210 | − | 0.0307272i | ||||
\(507\) | −32.4116 | + | 44.7663i | −1.43945 | + | 1.98814i | ||||
\(508\) | −11.8038 | + | 6.81491i | −0.523708 | + | 0.302363i | ||||
\(509\) | −4.61230 | + | 7.98873i | −0.204437 | + | 0.354094i | −0.949953 | − | 0.312393i | \(-0.898870\pi\) |
0.745517 | + | 0.666487i | \(0.232203\pi\) | |||||||
\(510\) | −3.19808 | + | 11.8225i | −0.141614 | + | 0.523511i | ||||
\(511\) | 14.7386 | − | 28.0867i | 0.651998 | − | 1.24248i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.1108 | + | 18.8147i | 0.755458 | + | 0.830688i | ||||
\(514\) | 20.4772 | − | 11.8225i | 0.903212 | − | 0.521470i | ||||
\(515\) | 23.3388 | + | 3.79324i | 1.02843 | + | 0.167150i | ||||
\(516\) | −0.360429 | + | 3.48474i | −0.0158670 | + | 0.153407i | ||||
\(517\) | −1.65504 | −0.0727885 | ||||||||
\(518\) | −16.7158 | − | 8.77172i | −0.734452 | − | 0.385407i | ||||
\(519\) | 18.2158 | − | 8.14637i | 0.799587 | − | 0.357586i | ||||
\(520\) | −5.31350 | − | 14.0111i | −0.233013 | − | 0.614428i | ||||
\(521\) | 9.31280 | + | 16.1302i | 0.408001 | + | 0.706679i | 0.994666 | − | 0.103151i | \(-0.0328926\pi\) |
−0.586664 | + | 0.809830i | \(0.699559\pi\) | |||||||
\(522\) | −1.24194 | + | 5.93948i | −0.0543582 | + | 0.259964i | ||||
\(523\) | 7.03886 | − | 12.1917i | 0.307788 | − | 0.533104i | −0.670090 | − | 0.742280i | \(-0.733745\pi\) |
0.977878 | + | 0.209175i | \(0.0670780\pi\) | |||||||
\(524\) | 6.02651 | 0.263269 | ||||||||
\(525\) | 18.0695 | − | 14.0887i | 0.788619 | − | 0.614882i | ||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | 0.477226 | − | 0.826579i | 0.0207883 | − | 0.0360063i | ||||
\(528\) | 0.299418 | + | 0.216784i | 0.0130305 | + | 0.00943430i | ||||
\(529\) | −9.47723 | − | 16.4150i | −0.412053 | − | 0.713697i | ||||
\(530\) | 3.96447 | + | 10.4539i | 0.172205 | + | 0.454086i | ||||
\(531\) | 9.83508 | − | 10.9960i | 0.426806 | − | 0.477184i | ||||
\(532\) | 10.9441 | − | 6.92163i | 0.474485 | − | 0.300091i | ||||
\(533\) | −44.9089 | −1.94522 | ||||||||
\(534\) | −18.2182 | − | 1.88433i | −0.788379 | − | 0.0815427i | ||||
\(535\) | −12.0888 | − | 1.96479i | −0.522645 | − | 0.0849452i | ||||
\(536\) | 4.61230 | − | 2.66291i | 0.199221 | − | 0.115020i | ||||
\(537\) | −2.65698 | + | 25.6885i | −0.114657 | + | 1.10854i | ||||
\(538\) | 28.8948 | 1.24574 | ||||||||
\(539\) | −0.120413 | − | 1.48909i | −0.00518655 | − | 0.0641397i | ||||
\(540\) | 9.73861 | − | 6.33715i | 0.419083 | − | 0.272707i | ||||
\(541\) | −9.73861 | + | 16.8678i | −0.418696 | + | 0.725202i | −0.995809 | − | 0.0914622i | \(-0.970846\pi\) |
0.577113 | + | 0.816664i | \(0.304179\pi\) | |||||||
\(542\) | −5.47723 | + | 3.16228i | −0.235267 | + | 0.135831i | ||||
\(543\) | −4.43649 | − | 3.21209i | −0.190388 | − | 0.137844i | ||||
\(544\) | 2.73861 | + | 1.58114i | 0.117417 | + | 0.0677908i | ||||
\(545\) | 17.5810 | − | 21.5323i | 0.753089 | − | 0.922342i | ||||
\(546\) | −16.9917 | + | 25.5807i | −0.727176 | + | 1.09475i | ||||
\(547\) | 23.2144i | 0.992575i | 0.868158 | + | 0.496287i | \(0.165304\pi\) | ||||
−0.868158 | + | 0.496287i | \(0.834696\pi\) | |||||||
\(548\) | −3.73861 | + | 6.47547i | −0.159706 | + | 0.276618i | ||||
\(549\) | 2.12702 | − | 10.1723i | 0.0907789 | − | 0.434143i | ||||
\(550\) | 0.707603 | + | 0.798761i | 0.0301723 | + | 0.0340593i | ||||
\(551\) | −4.94975 | + | 8.57321i | −0.210866 | + | 0.365231i | ||||
\(552\) | 4.58009 | + | 10.2414i | 0.194942 | + | 0.435903i | ||||
\(553\) | −1.38201 | + | 0.0557857i | −0.0587689 | + | 0.00237225i | ||||
\(554\) | − | 9.79796i | − | 0.416275i | ||||||
\(555\) | −19.4935 | − | 19.5867i | −0.827451 | − | 0.831409i | ||||
\(556\) | −6.52277 | + | 3.76593i | −0.276627 | + | 0.159711i | ||||
\(557\) | 18.9317 | + | 32.7906i | 0.802161 | + | 1.38938i | 0.918191 | + | 0.396138i | \(0.129650\pi\) |
−0.116030 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(558\) | −0.860224 | + | 0.282656i | −0.0364162 | + | 0.0119658i | ||||
\(559\) | − | 13.5546i | − | 0.573298i | ||||||
\(560\) | −2.31920 | − | 5.44255i | −0.0980041 | − | 0.229990i | ||||
\(561\) | 0.477226 | + | 1.06711i | 0.0201485 | + | 0.0450534i | ||||
\(562\) | 10.0521 | + | 5.80359i | 0.424023 | + | 0.244810i | ||||
\(563\) | 9.00000 | − | 5.19615i | 0.379305 | − | 0.218992i | −0.298211 | − | 0.954500i | \(-0.596390\pi\) |
0.677516 | + | 0.735508i | \(0.263057\pi\) | |||||||
\(564\) | 10.8795 | + | 7.87694i | 0.458110 | + | 0.331679i | ||||
\(565\) | 5.17186 | + | 13.6376i | 0.217582 | + | 0.573739i | ||||
\(566\) | −24.7165 | −1.03891 | ||||||||
\(567\) | −22.1838 | − | 8.65317i | −0.931634 | − | 0.363399i | ||||
\(568\) | − | 2.02265i | − | 0.0848683i | ||||||
\(569\) | −10.4218 | − | 6.01701i | −0.436903 | − | 0.252246i | 0.265380 | − | 0.964144i | \(-0.414503\pi\) |
−0.702283 | + | 0.711898i | \(0.747836\pi\) | |||||||
\(570\) | 18.3214 | − | 4.86239i | 0.767399 | − | 0.203663i | ||||
\(571\) | 3.47723 | + | 6.02273i | 0.145517 | + | 0.252043i | 0.929566 | − | 0.368656i | \(-0.120182\pi\) |
−0.784048 | + | 0.620700i | \(0.786849\pi\) | |||||||
\(572\) | −1.23861 | − | 0.715113i | −0.0517890 | − | 0.0299004i | ||||
\(573\) | −2.52319 | + | 1.12840i | −0.105408 | + | 0.0471397i | ||||
\(574\) | −17.7158 | + | 0.715113i | −0.739445 | + | 0.0298483i | ||||
\(575\) | 6.47723 | + | 31.7318i | 0.270119 | + | 1.32331i | ||||
\(576\) | −0.936492 | − | 2.85008i | −0.0390205 | − | 0.118754i | ||||
\(577\) | 7.40852 | + | 12.8319i | 0.308421 | + | 0.534200i | 0.978017 | − | 0.208525i | \(-0.0668663\pi\) |
−0.669596 | + | 0.742725i | \(0.733533\pi\) | |||||||
\(578\) | −3.50000 | − | 6.06218i | −0.145581 | − | 0.252153i | ||||
\(579\) | −1.30948 | + | 12.6604i | −0.0544199 | + | 0.526148i | ||||
\(580\) | 3.50333 | + | 2.86045i | 0.145468 | + | 0.118774i | ||||
\(581\) | −37.3800 | + | 23.6412i | −1.55079 | + | 0.980803i | ||||
\(582\) | −2.47723 | − | 5.53924i | −0.102684 | − | 0.229609i | ||||
\(583\) | 0.924143 | + | 0.533554i | 0.0382741 | + | 0.0220976i | ||||
\(584\) | −5.99430 | − | 10.3824i | −0.248046 | − | 0.429628i | ||||
\(585\) | −34.9568 | + | 28.2652i | −1.44529 | + | 1.16862i | ||||
\(586\) | −3.97723 | − | 2.29625i | −0.164298 | − | 0.0948573i | ||||
\(587\) | 27.4110i | 1.13137i | 0.824621 | + | 0.565686i | \(0.191389\pi\) | ||||
−0.824621 | + | 0.565686i | \(0.808611\pi\) | |||||||
\(588\) | −6.29560 | + | 10.3617i | −0.259626 | + | 0.427311i | ||||
\(589\) | −1.47723 | −0.0608680 | ||||||||
\(590\) | −3.89908 | − | 10.2814i | −0.160523 | − | 0.423280i | ||||
\(591\) | −9.14178 | + | 12.6265i | −0.376042 | + | 0.519384i | ||||
\(592\) | −6.17913 | + | 3.56752i | −0.253961 | + | 0.146624i | ||||
\(593\) | 31.4317 | + | 18.1471i | 1.29074 | + | 0.745212i | 0.978786 | − | 0.204884i | \(-0.0656818\pi\) |
0.311958 | + | 0.950096i | \(0.399015\pi\) | |||||||
\(594\) | 0.337449 | − | 1.05638i | 0.0138457 | − | 0.0433440i | ||||
\(595\) | 2.25403 | − | 18.5720i | 0.0924064 | − | 0.761378i | ||||
\(596\) | 2.44949i | 0.100335i | ||||||||
\(597\) | 3.99834 | − | 38.6571i | 0.163641 | − | 1.58213i | ||||
\(598\) | −21.7033 | − | 37.5912i | −0.887513 | − | 1.53722i | ||||
\(599\) | −4.98196 | + | 2.87633i | −0.203557 | + | 0.117524i | −0.598314 | − | 0.801262i | \(-0.704162\pi\) |
0.394756 | + | 0.918786i | \(0.370829\pi\) | |||||||
\(600\) | −0.849876 | − | 8.61845i | −0.0346961 | − | 0.351847i | ||||
\(601\) | 16.7169i | 0.681895i | 0.940082 | + | 0.340947i | \(0.110748\pi\) | ||||
−0.940082 | + | 0.340947i | \(0.889252\pi\) | |||||||
\(602\) | −0.215838 | − | 5.34706i | −0.00879691 | − | 0.217930i | ||||
\(603\) | −11.9089 | − | 10.6516i | −0.484968 | − | 0.433769i | ||||
\(604\) | 1.00000 | − | 1.73205i | 0.0406894 | − | 0.0704761i | ||||
\(605\) | −24.1776 | − | 3.92957i | −0.982961 | − | 0.159760i | ||||
\(606\) | 11.4919 | − | 15.8725i | 0.466828 | − | 0.644775i | ||||
\(607\) | −13.2180 | + | 22.8942i | −0.536502 | + | 0.929248i | 0.462587 | + | 0.886574i | \(0.346921\pi\) |
−0.999089 | + | 0.0426745i | \(0.986412\pi\) | |||||||
\(608\) | − | 4.89433i | − | 0.198491i | ||||||
\(609\) | 0.580971 | − | 9.25070i | 0.0235422 | − | 0.374857i | ||||
\(610\) | −6.00000 | − | 4.89898i | −0.242933 | − | 0.198354i | ||||
\(611\) | −45.0056 | − | 25.9840i | −1.82073 | − | 1.05120i | ||||
\(612\) | 1.94169 | − | 9.28600i | 0.0784882 | − | 0.375364i | ||||
\(613\) | −22.0407 | + | 12.7252i | −0.890216 | + | 0.513967i | −0.874013 | − | 0.485902i | \(-0.838491\pi\) |
−0.0162031 | + | 0.999869i | \(0.505158\pi\) | |||||||
\(614\) | 1.75166 | − | 3.03397i | 0.0706914 | − | 0.122441i | ||||
\(615\) | −25.0540 | − | 6.77729i | −1.01027 | − | 0.273287i | ||||
\(616\) | −0.500000 | − | 0.262377i | −0.0201456 | − | 0.0105715i | ||||
\(617\) | 25.4772 | 1.02567 | 0.512837 | − | 0.858486i | \(-0.328594\pi\) | ||||
0.512837 | + | 0.858486i | \(0.328594\pi\) | |||||||
\(618\) | −18.2182 | − | 1.88433i | −0.732843 | − | 0.0757987i | ||||
\(619\) | −23.1475 | + | 13.3642i | −0.930377 | + | 0.537154i | −0.886931 | − | 0.461902i | \(-0.847167\pi\) |
−0.0434463 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(620\) | −0.108270 | + | 0.666158i | −0.00434823 | + | 0.0267535i | ||||
\(621\) | 24.8996 | − | 22.6446i | 0.999187 | − | 0.908697i | ||||
\(622\) | 28.8948 | 1.15857 | ||||||||
\(623\) | 27.9545 | − | 1.12840i | 1.11997 | − | 0.0452085i | ||||
\(624\) | 4.73861 | + | 10.5959i | 0.189696 | + | 0.424174i | ||||
\(625\) | 3.01472 | − | 24.8176i | 0.120589 | − | 0.992703i | ||||
\(626\) | −11.6190 | − | 20.1246i | −0.464387 | − | 0.804341i | ||||
\(627\) | 1.06101 | − | 1.46545i | 0.0423727 | − | 0.0585245i | ||||
\(628\) | −4.39526 | + | 7.61282i | −0.175390 | + | 0.303784i | ||||
\(629\) | −22.5630 | −0.899646 | ||||||||
\(630\) | −13.3398 | + | 11.7068i | −0.531471 | + | 0.466411i | ||||
\(631\) | −7.47723 | −0.297664 | −0.148832 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148832 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(632\) | −0.261387 | + | 0.452736i | −0.0103974 | + | 0.0180089i | ||||
\(633\) | −13.7358 | + | 18.9717i | −0.545949 | + | 0.754056i | ||||
\(634\) | −16.9545 | − | 29.3660i | −0.673347 | − | 1.16627i | ||||
\(635\) | 28.4968 | − | 10.8070i | 1.13086 | − | 0.428863i | ||||
\(636\) | −3.53553 | − | 7.90569i | −0.140193 | − | 0.313481i | ||||
\(637\) | 20.1042 | − | 42.3834i | 0.796559 | − | 1.67929i | ||||
\(638\) | 0.431677 | 0.0170902 | ||||||||
\(639\) | −5.76471 | + | 1.89419i | −0.228049 | + | 0.0749331i | ||||
\(640\) | −2.20711 | − | 0.358719i | −0.0872436 | − | 0.0141796i | ||||
\(641\) | −5.43982 | + | 3.14068i | −0.214860 | + | 0.124049i | −0.603568 | − | 0.797312i | \(-0.706255\pi\) |
0.388708 | + | 0.921361i | \(0.372921\pi\) | |||||||
\(642\) | 9.43649 | + | 0.976025i | 0.372429 | + | 0.0385206i | ||||
\(643\) | 20.4095 | 0.804871 | 0.402436 | − | 0.915448i | \(-0.368164\pi\) | ||||
0.402436 | + | 0.915448i | \(0.368164\pi\) | |||||||
\(644\) | −9.16018 | − | 14.4835i | −0.360962 | − | 0.570731i | ||||
\(645\) | 2.04555 | − | 7.56189i | 0.0805434 | − | 0.297749i | ||||
\(646\) | 7.73861 | − | 13.4037i | 0.304472 | − | 0.527360i | ||||
\(647\) | −20.6703 | + | 11.9340i | −0.812633 | + | 0.469174i | −0.847869 | − | 0.530205i | \(-0.822115\pi\) |
0.0352364 | + | 0.999379i | \(0.488782\pi\) | |||||||
\(648\) | −7.24597 | + | 5.33816i | −0.284648 | + | 0.209703i | ||||
\(649\) | −0.908902 | − | 0.524755i | −0.0356775 | − | 0.0205984i | ||||
\(650\) | 6.70141 | + | 32.8301i | 0.262851 | + | 1.28770i | ||||
\(651\) | 1.23882 | − | 0.615127i | 0.0485531 | − | 0.0241087i | ||||
\(652\) | − | 14.6969i | − | 0.575577i | ||||||
\(653\) | 12.9317 | − | 22.3983i | 0.506056 | − | 0.876514i | −0.493920 | − | 0.869507i | \(-0.664436\pi\) |
0.999975 | − | 0.00700659i | \(-0.00223029\pi\) | |||||||
\(654\) | −12.6275 | + | 17.4409i | −0.493775 | + | 0.681994i | ||||
\(655\) | −13.3012 | − | 2.16183i | −0.519719 | − | 0.0844696i | ||||
\(656\) | −3.35071 | + | 5.80359i | −0.130823 | + | 0.226592i | ||||
\(657\) | −23.9772 | + | 26.8073i | −0.935440 | + | 1.04585i | ||||
\(658\) | −18.1677 | − | 9.53361i | −0.708252 | − | 0.371659i | ||||
\(659\) | 34.2929i | 1.33586i | 0.744224 | + | 0.667930i | \(0.232819\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(660\) | −0.583084 | − | 0.585872i | −0.0226965 | − | 0.0228050i | ||||
\(661\) | 11.4772 | − | 6.62638i | 0.446412 | − | 0.257736i | −0.259901 | − | 0.965635i | \(-0.583690\pi\) |
0.706314 | + | 0.707899i | \(0.250357\pi\) | |||||||
\(662\) | 5.71584 | + | 9.90012i | 0.222152 | + | 0.384779i | ||||
\(663\) | −3.77630 | + | 36.5104i | −0.146659 | + | 1.41795i | ||||
\(664\) | 16.7169i | 0.648740i | ||||||||
\(665\) | −26.6376 | + | 11.3509i | −1.03296 | + | 0.440170i | ||||
\(666\) | 15.9545 | + | 14.2701i | 0.618222 | + | 0.552955i | ||||
\(667\) | 11.3459 | + | 6.55057i | 0.439316 | + | 0.253639i | ||||
\(668\) | −12.7158 | + | 7.34149i | −0.491991 | + | 0.284051i | ||||
\(669\) | 6.49693 | − | 8.97345i | 0.251186 | − | 0.346934i | ||||
\(670\) | −11.1351 | + | 4.22281i | −0.430185 | + | 0.163141i | ||||
\(671\) | −0.739315 | −0.0285409 | ||||||||
\(672\) | 2.03803 | + | 4.10444i | 0.0786188 | + | 0.158332i | ||||
\(673\) | − | 48.4514i | − | 1.86766i | −0.357713 | − | 0.933832i | \(-0.616443\pi\) | ||
0.357713 | − | 0.933832i | \(-0.383557\pi\) | |||||||
\(674\) | 14.8492 | + | 8.57321i | 0.571971 | + | 0.330228i | ||||
\(675\) | −23.7674 | + | 10.4933i | −0.914808 | + | 0.403888i | ||||
\(676\) | −15.9545 | − | 27.6339i | −0.613633 | − | 1.06284i | ||||
\(677\) | −28.5000 | − | 16.4545i | −1.09534 | − | 0.632397i | −0.160350 | − | 0.987060i | \(-0.551262\pi\) |
−0.934994 | + | 0.354663i | \(0.884596\pi\) | |||||||
\(678\) | −4.61230 | − | 10.3134i | −0.177134 | − | 0.396084i | ||||
\(679\) | 4.95445 | + | 7.83368i | 0.190134 | + | 0.300629i | ||||
\(680\) | −5.47723 | − | 4.47214i | −0.210042 | − | 0.171499i | ||||
\(681\) | −1.85188 | + | 17.9045i | −0.0709641 | + | 0.686101i | ||||
\(682\) | 0.0322079 | + | 0.0557857i | 0.00123330 | + | 0.00213615i | ||||
\(683\) | −1.47723 | − | 2.55863i | −0.0565245 | − | 0.0979032i | 0.836379 | − | 0.548152i | \(-0.184669\pi\) |
−0.892903 | + | 0.450249i | \(0.851335\pi\) | |||||||
\(684\) | −13.9493 | + | 4.58350i | −0.533363 | + | 0.175254i | ||||
\(685\) | 10.5744 | − | 12.9509i | 0.404027 | − | 0.494830i | ||||
\(686\) | 7.25590 | − | 17.0397i | 0.277031 | − | 0.650579i | ||||
\(687\) | 11.4317 | − | 5.11240i | 0.436146 | − | 0.195050i | ||||
\(688\) | −1.75166 | − | 1.01132i | −0.0667815 | − | 0.0385563i | ||||
\(689\) | 16.7535 | + | 29.0180i | 0.638259 | + | 1.10550i | ||||
\(690\) | −6.43496 | − | 24.2468i | −0.244975 | − | 0.923060i | ||||
\(691\) | 3.00000 | + | 1.73205i | 0.114125 | + | 0.0658903i | 0.555976 | − | 0.831198i | \(-0.312345\pi\) |
−0.441851 | + | 0.897089i | \(0.645678\pi\) | |||||||
\(692\) | 11.5207i | 0.437952i | ||||||||
\(693\) | −0.279552 | + | 1.67076i | −0.0106193 | + | 0.0634668i | ||||
\(694\) | −6.52277 | −0.247601 | ||||||||
\(695\) | 15.7474 | − | 5.97195i | 0.597332 | − | 0.226529i | ||||
\(696\) | −2.83766 | − | 2.05451i | −0.107561 | − | 0.0778760i | ||||
\(697\) | −18.3526 | + | 10.5959i | −0.695153 | + | 0.401347i | ||||
\(698\) | 28.1703 | + | 16.2641i | 1.06626 | + | 0.615606i | ||||
\(699\) | 2.82843 | + | 6.32456i | 0.106981 | + | 0.239217i | ||||
\(700\) | 3.16637 | + | 12.8442i | 0.119678 | + | 0.485466i | ||||
\(701\) | − | 7.03320i | − | 0.265640i | −0.991140 | − | 0.132820i | \(-0.957597\pi\) | ||
0.991140 | − | 0.132820i | \(-0.0424033\pi\) | |||||||
\(702\) | 25.7614 | − | 23.4284i | 0.972302 | − | 0.884247i | ||||
\(703\) | 17.4606 | + | 30.2427i | 0.658540 | + | 1.14063i | ||||
\(704\) | −0.184829 | + | 0.106711i | −0.00696599 | + | 0.00402182i | ||||
\(705\) | −21.1866 | − | 21.2879i | −0.797934 | − | 0.801750i | ||||
\(706\) | 13.2528i | 0.498774i | ||||||||
\(707\) | −13.9089 | + | 26.5055i | −0.523098 | + | 0.996843i | ||||
\(708\) | 3.47723 | + | 7.77531i | 0.130682 | + | 0.292214i | ||||
\(709\) | −5.21584 | + | 9.03410i | −0.195885 | + | 0.339283i | −0.947190 | − | 0.320672i | \(-0.896091\pi\) |
0.751305 | + | 0.659955i | \(0.229425\pi\) | |||||||
\(710\) | −0.725563 | + | 4.46420i | −0.0272299 | + | 0.167538i | ||||
\(711\) | 1.53512 | + | 0.320992i | 0.0575716 | + | 0.0120382i | ||||
\(712\) | 5.28720 | − | 9.15769i | 0.198146 | − | 0.343199i | ||||
\(713\) | 1.95498i | 0.0732146i | ||||||||
\(714\) | −0.908312 | + | 14.4629i | −0.0339927 | + | 0.541260i | ||||
\(715\) | 2.47723 | + | 2.02265i | 0.0926430 | + | 0.0756427i | ||||
\(716\) | −12.9128 | − | 7.45518i | −0.482572 | − | 0.278613i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.62465 | − | 3.24739i | 0.209910 | − | 0.121192i | ||||
\(719\) | 23.6398 | − | 40.9453i | 0.881614 | − | 1.52700i | 0.0320690 | − | 0.999486i | \(-0.489790\pi\) |
0.849545 | − | 0.527515i | \(-0.176876\pi\) | |||||||
\(720\) | 1.04456 | + | 6.62638i | 0.0389283 | + | 0.246951i | ||||
\(721\) | 27.9545 | − | 1.12840i | 1.04108 | − | 0.0420239i | ||||
\(722\) | −4.95445 | −0.184386 | ||||||||
\(723\) | −0.710802 | + | 6.87224i | −0.0264350 | + | 0.255581i | ||||
\(724\) | 2.73861 | − | 1.58114i | 0.101780 | − | 0.0587626i | ||||
\(725\) | −6.70611 | − | 7.57004i | −0.249059 | − | 0.281144i | ||||
\(726\) | 18.8730 | + | 1.95205i | 0.700442 | + | 0.0724474i | ||||
\(727\) | 23.6076 | 0.875556 | 0.437778 | − | 0.899083i | \(-0.355766\pi\) | ||||
0.437778 | + | 0.899083i | \(0.355766\pi\) | |||||||
\(728\) | −9.47723 | − | 14.9848i | −0.351249 | − | 0.555374i | ||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 9.50569 | + | 25.0654i | 0.351821 | + | 0.927713i | ||||
\(731\) | −3.19808 | − | 5.53924i | −0.118285 | − | 0.204876i | ||||
\(732\) | 4.85993 | + | 3.51867i | 0.179628 | + | 0.130054i | ||||
\(733\) | −18.1677 | + | 31.4674i | −0.671041 | + | 1.16228i | 0.306569 | + | 0.951849i | \(0.400819\pi\) |
−0.977609 | + | 0.210428i | \(0.932514\pi\) | |||||||
\(734\) | −8.11562 | −0.299553 | ||||||||
\(735\) | 17.6120 | − | 20.6111i | 0.649629 | − | 0.760252i | ||||
\(736\) | −6.47723 | −0.238754 | ||||||||
\(737\) | −0.568323 | + | 0.984365i | −0.0209345 | + | 0.0362595i | ||||
\(738\) | 19.6786 | + | 4.11478i | 0.724381 | + | 0.151467i | ||||
\(739\) | 2.23861 | + | 3.87739i | 0.0823487 | + | 0.142632i | 0.904258 | − | 0.426986i | \(-0.140425\pi\) |
−0.821910 | + | 0.569618i | \(0.807091\pi\) | |||||||
\(740\) | 14.9177 | − | 5.65733i | 0.548387 | − | 0.207968i | ||||
\(741\) | 51.8596 | − | 23.1923i | 1.90511 | − | 0.851991i | ||||
\(742\) | 7.07107 | + | 11.1803i | 0.259587 | + | 0.410443i | ||||
\(743\) | −19.4317 | −0.712879 | −0.356440 | − | 0.934318i | \(-0.616009\pi\) | ||||
−0.356440 | + | 0.934318i | \(0.616009\pi\) | |||||||
\(744\) | 0.0537841 | − | 0.520000i | 0.00197182 | − | 0.0190641i | ||||
\(745\) | 0.878680 | − | 5.40629i | 0.0321923 | − | 0.198071i | ||||
\(746\) | −3.13367 | + | 1.80922i | −0.114732 | + | 0.0662404i | ||||
\(747\) | 47.6445 | − | 15.6552i | 1.74322 | − | 0.572794i | ||||
\(748\) | −0.674899 | −0.0246767 | ||||||||
\(749\) | −14.4796 | + | 0.584480i | −0.529073 | + | 0.0213564i | ||||
\(750\) | −1.21584 | + | 19.3267i | −0.0443961 | + | 0.705712i | ||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | −6.71584 | + | 3.87739i | −0.244901 | + | 0.141394i | ||||
\(753\) | 16.8624 | − | 23.2901i | 0.614501 | − | 0.848739i | ||||
\(754\) | 11.7386 | + | 6.77729i | 0.427495 | + | 0.246814i | ||||
\(755\) | −2.82843 | + | 3.46410i | −0.102937 | + | 0.126072i | ||||
\(756\) | 9.78940 | − | 9.65234i | 0.356037 | − | 0.351052i | ||||
\(757\) | 30.2476i | 1.09937i | 0.835373 | + | 0.549683i | \(0.185252\pi\) | ||||
−0.835373 | + | 0.549683i | \(0.814748\pi\) | |||||||
\(758\) | 4.76139 | − | 8.24696i | 0.172941 | − | 0.299543i | ||||
\(759\) | −1.93940 | − | 1.40416i | −0.0703958 | − | 0.0509677i | ||||
\(760\) | −1.75569 | + | 10.8023i | −0.0636856 | + | 0.391841i | ||||
\(761\) | −4.76492 | + | 8.25308i | −0.172728 | + | 0.299174i | −0.939373 | − | 0.342898i | \(-0.888592\pi\) |
0.766645 | + | 0.642072i | \(0.221925\pi\) | |||||||
\(762\) | −21.5507 | + | 9.63774i | −0.780698 | + | 0.349139i | ||||
\(763\) | 15.2833 | − | 29.1247i | 0.553293 | − | 1.05438i | ||||
\(764\) | − | 1.59580i | − | 0.0577341i | ||||||
\(765\) | −7.61659 | + | 19.7987i | −0.275378 | + | 0.715823i | ||||
\(766\) | 0.715838 | − | 0.413289i | 0.0258643 | − | 0.0149328i | ||||
\(767\) | −16.4772 | − | 28.5394i | −0.594958 | − | 1.03050i | ||||
\(768\) | 1.72286 | + | 0.178197i | 0.0621683 | + | 0.00643013i | ||||
\(769\) | 28.8412i | 1.04004i | 0.854154 | + | 0.520020i | \(0.174076\pi\) | ||||
−0.854154 | + | 0.520020i | \(0.825924\pi\) | |||||||
\(770\) | 1.00943 | + | 0.758455i | 0.0363775 | + | 0.0273328i | ||||
\(771\) | 37.3861 | − | 16.7196i | 1.34643 | − | 0.602141i | ||||
\(772\) | −6.36396 | − | 3.67423i | −0.229044 | − | 0.132239i | ||||
\(773\) | −24.9772 | + | 14.4206i | −0.898368 | + | 0.518673i | −0.876670 | − | 0.481091i | \(-0.840241\pi\) |
−0.0216979 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(774\) | −1.24194 | + | 5.93948i | −0.0446406 | + | 0.213490i | ||||
\(775\) | 0.477927 | − | 1.43144i | 0.0171677 | − | 0.0514189i | ||||
\(776\) | 3.50333 | 0.125762 | ||||||||
\(777\) | −27.2360 | − | 18.0912i | −0.977084 | − | 0.649017i | ||||
\(778\) | 7.34847i | 0.263455i | ||||||||
\(779\) | 28.4047 | + | 16.3995i | 1.01770 | + | 0.587571i | ||||
\(780\) | −6.65768 | − | 25.0860i | −0.238383 | − | 0.898224i | ||||
\(781\) | 0.215838 | + | 0.373843i | 0.00772330 | + | 0.0133772i | ||||
\(782\) | −17.7386 | − | 10.2414i | −0.634331 | − | 0.366231i | ||||
\(783\) | −3.19808 | + | 10.0116i | −0.114290 | + | 0.357785i | ||||
\(784\) | −3.97723 | − | 5.76035i | −0.142044 | − | 0.205727i | ||||
\(785\) | 12.4317 | − | 15.2256i | 0.443706 | − | 0.543426i | ||||
\(786\) | 10.3828 | + | 1.07391i | 0.370343 | + | 0.0383050i | ||||
\(787\) | −17.3402 | − | 30.0341i | −0.618112 | − | 1.07060i | −0.989830 | − | 0.142256i | \(-0.954564\pi\) |
0.371718 | − | 0.928346i | \(-0.378769\pi\) | |||||||
\(788\) | −4.50000 | − | 7.79423i | −0.160306 | − | 0.277658i | ||||
\(789\) | −3.44572 | − | 0.356394i | −0.122671 | − | 0.0126880i | ||||
\(790\) | 0.739315 | − | 0.905472i | 0.0263036 | − | 0.0322152i | ||||
\(791\) | 9.22460 | + | 14.5854i | 0.327989 | + | 0.518596i | ||||
\(792\) | 0.477226 | + | 0.426844i | 0.0169575 | + | 0.0151672i | ||||
\(793\) | −20.1042 | − | 11.6072i | −0.713922 | − | 0.412183i | ||||
\(794\) | 15.1867 | + | 26.3041i | 0.538956 | + | 0.933498i | ||||
\(795\) | 4.96737 | + | 18.7170i | 0.176175 | + | 0.663823i | ||||
\(796\) | 19.4317 | + | 11.2189i | 0.688738 | + | 0.397643i | ||||
\(797\) | − | 28.9201i | − | 1.02440i | −0.858865 | − | 0.512201i | \(-0.828830\pi\) | ||
0.858865 | − | 0.512201i | \(-0.171170\pi\) | |||||||
\(798\) | 20.0885 | − | 9.97479i | 0.711124 | − | 0.353104i | ||||
\(799\) | −24.5228 | −0.867553 | ||||||||
\(800\) | 4.74264 | + | 1.58346i | 0.167678 | + | 0.0559839i | ||||
\(801\) | −31.0516 | − | 6.49286i | −1.09716 | − | 0.229414i | ||||
\(802\) | −26.2834 | + | 15.1747i | −0.928098 | + | 0.535838i | ||||
\(803\) | 2.21584 | + | 1.27931i | 0.0781952 | + | 0.0451460i | ||||
\(804\) | 8.42087 | − | 3.76593i | 0.296981 | − | 0.132814i | ||||
\(805\) | 15.0220 | + | 35.2526i | 0.529455 | + | 1.24249i | ||||
\(806\) | 2.02265i | 0.0712447i | ||||||||
\(807\) | 49.7816 | + | 5.14896i | 1.75240 | + | 0.181252i | ||||
\(808\) | 5.65685 | + | 9.79796i | 0.199007 | + | 0.344691i | ||||
\(809\) | 34.7686 | − | 20.0737i | 1.22240 | − | 0.705753i | 0.256971 | − | 0.966419i | \(-0.417275\pi\) |
0.965429 | + | 0.260666i | \(0.0839421\pi\) | |||||||
\(810\) | 17.9075 | − | 9.18262i | 0.629206 | − | 0.322644i | ||||
\(811\) | 6.70527i | 0.235454i | 0.993046 | + | 0.117727i | \(0.0375608\pi\) | ||||
−0.993046 | + | 0.117727i | \(0.962439\pi\) | |||||||
\(812\) | 4.73861 | + | 2.48661i | 0.166293 | + | 0.0872629i | ||||
\(813\) | −10.0000 | + | 4.47214i | −0.350715 | + | 0.156845i | ||||
\(814\) | 0.761387 | − | 1.31876i | 0.0266866 | − | 0.0462226i | ||||
\(815\) | −5.27208 | + | 32.4377i | −0.184673 | + | 1.13624i | ||||
\(816\) | 4.43649 | + | 3.21209i | 0.155308 | + | 0.112446i | ||||
\(817\) | −4.94975 | + | 8.57321i | −0.173170 | + | 0.299939i | ||||
\(818\) | − | 22.4378i | − | 0.784518i | ||||||
\(819\) | −33.8326 | + | 41.0440i | −1.18221 | + | 1.43420i | ||||
\(820\) | 9.47723 | − | 11.6072i | 0.330959 | − | 0.405340i | ||||
\(821\) | −44.0814 | − | 25.4504i | −1.53845 | − | 0.888226i | −0.998930 | − | 0.0462557i | \(-0.985271\pi\) |
−0.539523 | − | 0.841971i | \(-0.681396\pi\) | |||||||
\(822\) | −7.59501 | + | 10.4901i | −0.264907 | + | 0.365885i | ||||
\(823\) | 28.2199 | − | 16.2927i | 0.983682 | − | 0.567929i | 0.0803025 | − | 0.996771i | \(-0.474411\pi\) |
0.903380 | + | 0.428841i | \(0.141078\pi\) | |||||||
\(824\) | 5.28720 | − | 9.15769i | 0.184188 | − | 0.319023i | ||||
\(825\) | 1.07676 | + | 1.50225i | 0.0374881 | + | 0.0523015i | ||||
\(826\) | −6.95445 | − | 10.9960i | −0.241976 | − | 0.382598i | ||||
\(827\) | 39.9089 | 1.38777 | 0.693884 | − | 0.720087i | \(-0.255898\pi\) | ||||
0.693884 | + | 0.720087i | \(0.255898\pi\) | |||||||
\(828\) | 6.06587 | + | 18.4606i | 0.210803 | + | 0.641552i | ||||
\(829\) | −16.3069 | + | 9.41481i | −0.566363 | + | 0.326990i | −0.755696 | − | 0.654923i | \(-0.772701\pi\) |
0.189332 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(830\) | 5.99666 | − | 36.8959i | 0.208147 | − | 1.28068i | ||||
\(831\) | 1.74597 | − | 16.8805i | 0.0605669 | − | 0.585578i | ||||
\(832\) | −6.70141 | −0.232330 | ||||||||
\(833\) | −1.78416 | − | 22.0639i | −0.0618175 | − | 0.764470i | ||||
\(834\) | −11.9089 | + | 5.32582i | −0.412372 | + | 0.184418i | ||||
\(835\) | 30.6987 | − | 11.6420i | 1.06237 | − | 0.402889i | ||||
\(836\) | 0.522278 | + | 0.904612i | 0.0180634 | + | 0.0312867i | ||||
\(837\) | −1.53241 | + | 0.333687i | −0.0529680 | + | 0.0115339i | ||||
\(838\) | −8.30045 | + | 14.3768i | −0.286734 | + | 0.496639i | ||||
\(839\) | 37.3156 | 1.28828 | 0.644139 | − | 0.764908i | \(-0.277216\pi\) | ||||
0.644139 | + | 0.764908i | \(0.277216\pi\) | |||||||
\(840\) | −3.02581 | − | 9.79002i | −0.104400 | − | 0.337788i | ||||
\(841\) | 24.9089 | 0.858928 | ||||||||
\(842\) | 1.47723 | − | 2.55863i | 0.0509086 | − | 0.0881762i | ||||
\(843\) | 16.2842 | + | 11.7900i | 0.560858 | + | 0.406070i | ||||
\(844\) | −6.76139 | − | 11.7111i | −0.232737 | − | 0.403112i | ||||
\(845\) | 25.3004 | + | 66.7142i | 0.870359 | + | 2.29504i | ||||
\(846\) | 17.3402 | + | 15.5096i | 0.596169 | + | 0.533230i | ||||
\(847\) | −28.9592 | + | 1.16896i | −0.995049 | + | 0.0401659i | ||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | −42.5831 | − | 4.40441i | −1.46145 | − | 0.151159i | ||||
\(850\) | 10.4846 | + | 11.8353i | 0.359618 | + | 0.405946i | ||||
\(851\) | 40.0236 | − | 23.1077i | 1.37199 | − | 0.792120i | ||||
\(852\) | 0.360429 | − | 3.48474i | 0.0123481 | − | 0.119385i | ||||
\(853\) | −53.9165 | −1.84607 | −0.923033 | − | 0.384720i | \(-0.874298\pi\) | ||||
−0.923033 | + | 0.384720i | \(0.874298\pi\) | |||||||
\(854\) | −8.11562 | − | 4.25871i | −0.277711 | − | 0.145730i | ||||
\(855\) | 32.4317 | − | 5.11240i | 1.10914 | − | 0.174840i | ||||
\(856\) | −2.73861 | + | 4.74342i | −0.0936039 | + | 0.162127i | ||||
\(857\) | 34.9545 | − | 20.1810i | 1.19402 | − | 0.689369i | 0.234805 | − | 0.972042i | \(-0.424555\pi\) |
0.959216 | + | 0.282674i | \(0.0912214\pi\) | |||||||
\(858\) | −2.00653 | − | 1.45276i | −0.0685016 | − | 0.0495963i | ||||
\(859\) | −15.5228 | − | 8.96208i | −0.529630 | − | 0.305782i | 0.211236 | − | 0.977435i | \(-0.432251\pi\) |
−0.740866 | + | 0.671653i | \(0.765585\pi\) | |||||||
\(860\) | 3.50333 | + | 2.86045i | 0.119462 | + | 0.0975407i | ||||
\(861\) | −30.6493 | − | 1.92487i | −1.04453 | − | 0.0655994i | ||||
\(862\) | − | 37.0576i | − | 1.26219i | ||||||
\(863\) | 7.76139 | − | 13.4431i | 0.264201 | − | 0.457609i | −0.703153 | − | 0.711038i | \(-0.748225\pi\) |
0.967354 | + | 0.253429i | \(0.0815585\pi\) | |||||||
\(864\) | −1.10557 | − | 5.07718i | −0.0376122 | − | 0.172729i | ||||
\(865\) | 4.13270 | − | 25.4274i | 0.140516 | − | 0.864559i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.94975 | − | 11.0680i | −0.168102 | − | 0.375888i | ||||
\(868\) | 0.0322079 | + | 0.797901i | 0.00109321 | + | 0.0270825i | ||||
\(869\) | − | 0.111571i | − | 0.00378480i | ||||||
\(870\) | 5.52602 | + | 5.55244i | 0.187349 | + | 0.188245i | ||||
\(871\) | −30.9089 | + | 17.8453i | −1.04731 | + | 0.604664i | ||||
\(872\) | −6.21584 | − | 10.7661i | −0.210495 | − | 0.364588i | ||||
\(873\) | −3.28084 | − | 9.98478i | −0.111039 | − | 0.337933i | ||||
\(874\) | 31.7017i | 1.07232i | ||||||||
\(875\) | −2.38105 | − | 29.4844i | −0.0804942 | − | 0.996755i | ||||
\(876\) | −8.47723 | − | 18.9557i | −0.286419 | − | 0.640452i | ||||
\(877\) | −36.6169 | − | 21.1408i | −1.23647 | − | 0.713874i | −0.268096 | − | 0.963392i | \(-0.586394\pi\) |
−0.968370 | + | 0.249518i | \(0.919728\pi\) | |||||||
\(878\) | −19.6931 | + | 11.3698i | −0.664609 | + | 0.383712i | ||||
\(879\) | −6.44302 | − | 4.66485i | −0.217318 | − | 0.157341i | ||||
\(880\) | 0.446216 | − | 0.169221i | 0.0150419 | − | 0.00570443i | ||||
\(881\) | −26.5004 | −0.892821 | −0.446411 | − | 0.894828i | \(-0.647298\pi\) | ||||
−0.446411 | + | 0.894828i | \(0.647298\pi\) | |||||||
\(882\) | −12.6929 | + | 16.7300i | −0.427391 | + | 0.563327i | ||||
\(883\) | 29.2823i | 0.985428i | 0.870191 | + | 0.492714i | \(0.163995\pi\) | ||||
−0.870191 | + | 0.492714i | \(0.836005\pi\) | |||||||
\(884\) | −18.3526 | − | 10.5959i | −0.617264 | − | 0.356377i | ||||
\(885\) | −4.88545 | − | 18.4083i | −0.164223 | − | 0.618788i | ||||
\(886\) | 18.4772 | + | 32.0035i | 0.620755 | + | 1.07518i | ||||
\(887\) | 3.00000 | + | 1.73205i | 0.100730 | + | 0.0581566i | 0.549519 | − | 0.835481i | \(-0.314811\pi\) |
−0.448789 | + | 0.893638i | \(0.648144\pi\) | |||||||
\(888\) | −11.2815 | + | 5.04524i | −0.378582 | + | 0.169307i | ||||
\(889\) | 30.4772 | − | 19.2755i | 1.02217 | − | 0.646479i | ||||
\(890\) | −14.9545 | + | 18.3154i | −0.501274 | + | 0.613933i | ||||
\(891\) | 0.769622 | − | 1.75987i | 0.0257833 | − | 0.0589578i | ||||
\(892\) | 3.19808 | + | 5.53924i | 0.107080 | + | 0.185468i | ||||
\(893\) | 18.9772 | + | 32.8695i | 0.635049 | + | 1.09994i | ||||
\(894\) | −0.436492 | + | 4.22013i | −0.0145985 | + | 0.141142i | ||||
\(895\) | 25.8255 | + | 21.0864i | 0.863251 | + | 0.704842i | ||||
\(896\) | −2.64360 | + | 0.106711i | −0.0883164 | + | 0.00356496i | ||||
\(897\) | −30.6931 | − | 68.6318i | −1.02481 | − | 2.29155i | ||||
\(898\) | −3.04546 | − | 1.75830i | −0.101628 | − | 0.0586752i | ||||
\(899\) | −0.305242 | − | 0.528694i | −0.0101804 | − | 0.0176329i | ||||
\(900\) | 0.0715641 | − | 14.9998i | 0.00238547 | − | 0.499994i | ||||
\(901\) | 13.6931 | + | 7.90569i | 0.456182 | + | 0.263377i | ||||
\(902\) | − | 1.43023i | − | 0.0476213i | ||||||
\(903\) | 0.580971 | − | 9.25070i | 0.0193335 | − | 0.307844i | ||||
\(904\) | 6.52277 | 0.216944 | ||||||||
\(905\) | −6.61160 | + | 2.50735i | −0.219777 | + | 0.0833471i | ||||
\(906\) | 2.03151 | − | 2.80588i | 0.0674923 | − | 0.0932192i | ||||
\(907\) | −8.48528 | + | 4.89898i | −0.281749 | + | 0.162668i | −0.634215 | − | 0.773157i | \(-0.718677\pi\) |
0.352466 | + | 0.935825i | \(0.385343\pi\) | |||||||
\(908\) | −9.00000 | − | 5.19615i | −0.298675 | − | 0.172440i | ||||
\(909\) | 22.6274 | − | 25.2982i | 0.750504 | − | 0.839089i | ||||
\(910\) | 15.5419 | + | 36.4727i | 0.515209 | + | 1.20906i | ||||
\(911\) | 15.1238i | 0.501073i | 0.968107 | + | 0.250537i | \(0.0806071\pi\) | ||||
−0.968107 | + | 0.250537i | \(0.919393\pi\) | |||||||
\(912\) | 0.872155 | − | 8.43224i | 0.0288799 | − | 0.279219i | ||||
\(913\) | −1.78387 | − | 3.08976i | −0.0590375 | − | 0.102256i | ||||
\(914\) | −32.8322 | + | 18.9557i | −1.08599 | + | 0.626997i | ||||
\(915\) | −9.46418 | − | 9.50944i | −0.312876 | − | 0.314372i | ||||
\(916\) | 7.23003i | 0.238887i | ||||||||
\(917\) | −15.9317 | + | 0.643094i | −0.526110 | + | 0.0212368i | ||||
\(918\) | 5.00000 | − | 15.6525i | 0.165025 | − | 0.516609i | ||||
\(919\) | 16.2158 | − | 28.0867i | 0.534911 | − | 0.926493i | −0.464256 | − | 0.885701i | \(-0.653678\pi\) |
0.999168 | − | 0.0407925i | \(-0.0129883\pi\) | |||||||
\(920\) | 14.2959 | + | 2.32351i | 0.471323 | + | 0.0766038i | ||||
\(921\) | 3.55851 | − | 4.91496i | 0.117257 | − | 0.161954i | ||||
\(922\) | −8.14783 | + | 14.1125i | −0.268335 | + | 0.464769i | ||||
\(923\) | 13.5546i | 0.446155i | ||||||||
\(924\) | −0.814675 | − | 0.541138i | −0.0268008 | − | 0.0178021i | ||||
\(925\) | −34.9545 | + | 7.13505i | −1.14930 | + | 0.234599i | ||||
\(926\) | 15.3071 | + | 8.83756i | 0.503023 | + | 0.290420i | ||||
\(927\) | −31.0516 | − | 6.49286i | −1.01987 | − | 0.213253i | ||||
\(928\) | 1.75166 | − | 1.01132i | 0.0575012 | − | 0.0331983i | ||||
\(929\) | 11.8360 | − | 20.5005i | 0.388326 | − | 0.672601i | −0.603898 | − | 0.797061i | \(-0.706387\pi\) |
0.992225 | + | 0.124461i | \(0.0397201\pi\) | |||||||
\(930\) | −0.305242 | + | 1.12840i | −0.0100093 | + | 0.0370018i | ||||
\(931\) | −28.1931 | + | 19.4658i | −0.923990 | + | 0.637967i | ||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | 49.7816 | + | 5.14896i | 1.62978 | + | 0.168569i | ||||
\(934\) | 29.7386 | − | 17.1696i | 0.973077 | − | 0.561806i | ||||
\(935\) | 1.48957 | + | 0.242099i | 0.0487143 | + | 0.00791750i | ||||
\(936\) | 6.27582 | + | 19.0996i | 0.205131 | + | 0.624290i | ||||
\(937\) | −22.6918 | −0.741310 | −0.370655 | − | 0.928771i | \(-0.620867\pi\) | ||||
−0.370655 | + | 0.928771i | \(0.620867\pi\) | |||||||
\(938\) | −11.9089 | + | 7.53185i | −0.388839 | + | 0.245924i | ||||
\(939\) | −16.4317 | − | 36.7423i | −0.536228 | − | 1.19904i | ||||
\(940\) | 16.2135 | − | 6.14871i | 0.528825 | − | 0.200549i | ||||
\(941\) | −2.49098 | − | 4.31450i | −0.0812036 | − | 0.140649i | 0.822564 | − | 0.568673i | \(-0.192543\pi\) |
−0.903767 | + | 0.428024i | \(0.859210\pi\) | |||||||
\(942\) | −8.92900 | + | 12.3326i | −0.290923 | + | 0.401818i | ||||
\(943\) | 21.7033 | − | 37.5912i | 0.706756 | − | 1.22414i | ||||
\(944\) | −4.91754 | −0.160052 | ||||||||
\(945\) | −25.0687 | + | 17.7921i | −0.815486 | + | 0.578777i | ||||
\(946\) | 0.431677 | 0.0140350 | ||||||||
\(947\) | 16.4317 | − | 28.4605i | 0.533958 | − | 0.924842i | −0.465255 | − | 0.885177i | \(-0.654037\pi\) |
0.999213 | − | 0.0396654i | \(-0.0126292\pi\) | |||||||
\(948\) | −0.531010 | + | 0.733422i | −0.0172464 | + | 0.0238204i | ||||
\(949\) | 40.1703 | + | 69.5770i | 1.30398 | + | 2.25856i | ||||
\(950\) | 7.74999 | − | 23.2120i | 0.251443 | − | 0.753098i | ||||
\(951\) | −23.9772 | − | 53.6147i | −0.777514 | − | 1.73858i | ||||
\(952\) | −7.40852 | − | 3.88766i | −0.240111 | − | 0.126000i | ||||
\(953\) | 25.0455 | 0.811305 | 0.405652 | − | 0.914027i | \(-0.367044\pi\) | ||||
0.405652 | + | 0.914027i | \(0.367044\pi\) | |||||||
\(954\) | −4.68246 | − | 14.2504i | −0.151600 | − | 0.461375i | ||||
\(955\) | −0.572445 | + | 3.52211i | −0.0185239 | + | 0.113973i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.743718 | + | 0.0769235i | 0.0240410 | + | 0.00248658i | ||||
\(958\) | 11.3781 | 0.367611 | ||||||||
\(959\) | 9.19239 | − | 17.5175i | 0.296838 | − | 0.565669i | ||||
\(960\) | −3.73861 | − | 1.01132i | −0.120663 | − | 0.0326403i | ||||
\(961\) | −15.4545 | + | 26.7679i | −0.498531 | + | 0.863480i | ||||
\(962\) | 41.4089 | − | 23.9074i | 1.33508 | − | 0.770807i | ||||
\(963\) | 16.0838 | + | 3.36311i | 0.518294 | + | 0.108375i | ||||
\(964\) | −3.45445 | − | 1.99443i | −0.111260 | − | 0.0642362i | ||||
\(965\) | 12.7279 | + | 10.3923i | 0.409726 | + | 0.334540i | ||||
\(966\) | −13.2008 | − | 26.5854i | −0.424728 | − | 0.855371i | ||||
\(967\) | 46.4287i | 1.49305i | 0.665359 | + | 0.746524i | \(0.268279\pi\) | ||||
−0.665359 | + | 0.746524i | \(0.731721\pi\) | |||||||
\(968\) | −5.47723 | + | 9.48683i | −0.176045 | + | 0.304918i | ||||
\(969\) | 15.7210 | − | 21.7136i | 0.505033 | − | 0.697543i | ||||
\(970\) | −7.73221 | − | 1.25671i | −0.248266 | − | 0.0403506i | ||||
\(971\) | 0.490070 | − | 0.848827i | 0.0157271 | − | 0.0272401i | −0.858055 | − | 0.513558i | \(-0.828327\pi\) |
0.873782 | + | 0.486318i | \(0.161660\pi\) | |||||||
\(972\) | −13.4350 | + | 7.90569i | −0.430929 | + | 0.253575i | ||||
\(973\) | 16.8417 | − | 10.6516i | 0.539921 | − | 0.341476i | ||||
\(974\) | 36.6308i | 1.17373i | ||||||||
\(975\) | 5.69537 | + | 57.7558i | 0.182398 | + | 1.84967i | ||||
\(976\) | −3.00000 | + | 1.73205i | −0.0960277 | + | 0.0554416i | ||||
\(977\) | 19.9545 | + | 34.5621i | 0.638399 | + | 1.10574i | 0.985784 | + | 0.168018i | \(0.0537365\pi\) |
−0.347385 | + | 0.937723i | \(0.612930\pi\) | |||||||
\(978\) | 2.61895 | − | 25.3208i | 0.0837448 | − | 0.809669i | ||||
\(979\) | 2.25681i | 0.0721278i | ||||||||
\(980\) | 6.71181 | + | 14.1404i | 0.214401 | + | 0.451699i | ||||
\(981\) | −24.8634 | + | 27.7981i | −0.793826 | + | 0.887524i | ||||
\(982\) | −3.50333 | − | 2.02265i | −0.111796 | − | 0.0645452i | ||||
\(983\) | −29.2842 | + | 16.9072i | −0.934020 | + | 0.539257i | −0.888081 | − | 0.459688i | \(-0.847961\pi\) |
−0.0459391 | + | 0.998944i | \(0.514628\pi\) | |||||||
\(984\) | −6.80698 | + | 9.40169i | −0.216999 | + | 0.299715i | ||||
\(985\) | 7.13604 | + | 18.8169i | 0.227373 | + | 0.599557i | ||||
\(986\) | 6.39617 | 0.203696 | ||||||||
\(987\) | −29.6016 | − | 19.6625i | −0.942230 | − | 0.625865i | ||||
\(988\) | 32.7989i | 1.04347i | ||||||||
\(989\) | 11.3459 | + | 6.55057i | 0.360779 | + | 0.208296i | ||||
\(990\) | −0.900171 | − | 1.11328i | −0.0286093 | − | 0.0353823i | ||||
\(991\) | −10.7386 | − | 18.5998i | −0.341123 | − | 0.590843i | 0.643518 | − | 0.765431i | \(-0.277474\pi\) |
−0.984642 | + | 0.174588i | \(0.944141\pi\) | |||||||
\(992\) | 0.261387 | + | 0.150912i | 0.00829905 | + | 0.00479146i | ||||
\(993\) | 8.08342 | + | 18.0751i | 0.256519 | + | 0.573595i | ||||
\(994\) | 0.215838 | + | 5.34706i | 0.00684598 | + | 0.169599i | ||||
\(995\) | −38.8634 | − | 31.7318i | −1.23205 | − | 1.00597i | ||||
\(996\) | −2.97889 | + | 28.8008i | −0.0943899 | + | 0.912588i | ||||
\(997\) | −7.74597 | − | 13.4164i | −0.245317 | − | 0.424902i | 0.716904 | − | 0.697172i | \(-0.245559\pi\) |
−0.962221 | + | 0.272270i | \(0.912225\pi\) | |||||||
\(998\) | 20.9545 | + | 36.2942i | 0.663302 | + | 1.14887i | ||||
\(999\) | 24.9444 | + | 27.4284i | 0.789206 | + | 0.867796i |
(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 | 210.2.t.e.89.2 | yes | 8 | |
3.2 | odd | 2 | 210.2.t.f.89.4 | yes | 8 | ||
5.2 | odd | 4 | 1050.2.s.i.551.4 | 16 | |||
5.3 | odd | 4 | 1050.2.s.i.551.5 | 16 | |||
5.4 | even | 2 | 210.2.t.f.89.3 | yes | 8 | ||
7.2 | even | 3 | 1470.2.d.f.1469.1 | 8 | |||
7.3 | odd | 6 | inner | 210.2.t.e.59.1 | ✓ | 8 | |
7.5 | odd | 6 | 1470.2.d.f.1469.8 | 8 | |||
15.2 | even | 4 | 1050.2.s.i.551.6 | 16 | |||
15.8 | even | 4 | 1050.2.s.i.551.3 | 16 | |||
15.14 | odd | 2 | inner | 210.2.t.e.89.1 | yes | 8 | |
21.2 | odd | 6 | 1470.2.d.e.1469.4 | 8 | |||
21.5 | even | 6 | 1470.2.d.e.1469.5 | 8 | |||
21.17 | even | 6 | 210.2.t.f.59.3 | yes | 8 | ||
35.3 | even | 12 | 1050.2.s.i.101.3 | 16 | |||
35.9 | even | 6 | 1470.2.d.e.1469.8 | 8 | |||
35.17 | even | 12 | 1050.2.s.i.101.6 | 16 | |||
35.19 | odd | 6 | 1470.2.d.e.1469.1 | 8 | |||
35.24 | odd | 6 | 210.2.t.f.59.4 | yes | 8 | ||
105.17 | odd | 12 | 1050.2.s.i.101.4 | 16 | |||
105.38 | odd | 12 | 1050.2.s.i.101.5 | 16 | |||
105.44 | odd | 6 | 1470.2.d.f.1469.5 | 8 | |||
105.59 | even | 6 | inner | 210.2.t.e.59.2 | yes | 8 | |
105.89 | even | 6 | 1470.2.d.f.1469.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.1 | ✓ | 8 | 7.3 | odd | 6 | inner | |
210.2.t.e.59.2 | yes | 8 | 105.59 | even | 6 | inner | |
210.2.t.e.89.1 | yes | 8 | 15.14 | odd | 2 | inner | |
210.2.t.e.89.2 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.t.f.59.3 | yes | 8 | 21.17 | even | 6 | ||
210.2.t.f.59.4 | yes | 8 | 35.24 | odd | 6 | ||
210.2.t.f.89.3 | yes | 8 | 5.4 | even | 2 | ||
210.2.t.f.89.4 | yes | 8 | 3.2 | odd | 2 | ||
1050.2.s.i.101.3 | 16 | 35.3 | even | 12 | |||
1050.2.s.i.101.4 | 16 | 105.17 | odd | 12 | |||
1050.2.s.i.101.5 | 16 | 105.38 | odd | 12 | |||
1050.2.s.i.101.6 | 16 | 35.17 | even | 12 | |||
1050.2.s.i.551.3 | 16 | 15.8 | even | 4 | |||
1050.2.s.i.551.4 | 16 | 5.2 | odd | 4 | |||
1050.2.s.i.551.5 | 16 | 5.3 | odd | 4 | |||
1050.2.s.i.551.6 | 16 | 15.2 | even | 4 | |||
1470.2.d.e.1469.1 | 8 | 35.19 | odd | 6 | |||
1470.2.d.e.1469.4 | 8 | 21.2 | odd | 6 | |||
1470.2.d.e.1469.5 | 8 | 21.5 | even | 6 | |||
1470.2.d.e.1469.8 | 8 | 35.9 | even | 6 | |||
1470.2.d.f.1469.1 | 8 | 7.2 | even | 3 | |||
1470.2.d.f.1469.4 | 8 | 105.89 | even | 6 | |||
1470.2.d.f.1469.5 | 8 | 105.44 | odd | 6 | |||
1470.2.d.f.1469.8 | 8 | 7.5 | odd | 6 |