Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(239,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.g (of order \(4\), 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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.58498535041007616.52 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(-0.779723 + 1.54662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.239 |
Dual form | 1014.2.g.b.437.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.64497 | + | 0.542278i | −0.949725 | + | 0.313084i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.32634 | − | 2.32634i | −1.04037 | − | 1.04037i | −0.999150 | − | 0.0412220i | \(-0.986875\pi\) |
−0.0412220 | − | 0.999150i | \(-0.513125\pi\) | |||||||
\(6\) | 1.54662 | + | 0.779723i | 0.631405 | + | 0.318321i | ||||
\(7\) | 1.76690 | + | 1.76690i | 0.667824 | + | 0.667824i | 0.957212 | − | 0.289388i | \(-0.0934517\pi\) |
−0.289388 | + | 0.957212i | \(0.593452\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.41187 | − | 1.78406i | 0.803956 | − | 0.594688i | ||||
\(10\) | 3.28995i | 1.04037i | ||||||||
\(11\) | −1.08456 | + | 1.08456i | −0.327006 | + | 0.327006i | −0.851447 | − | 0.524441i | \(-0.824274\pi\) |
0.524441 | + | 0.851447i | \(0.324274\pi\) | |||||||
\(12\) | −0.542278 | − | 1.64497i | −0.156542 | − | 0.474863i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 2.49877i | − | 0.667824i | ||||||
\(15\) | 5.08829 | + | 2.56525i | 1.31379 | + | 0.662344i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.73724 | −1.39149 | −0.695743 | − | 0.718291i | \(-0.744925\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(18\) | −2.96697 | − | 0.443925i | −0.699322 | − | 0.104634i | ||||
\(19\) | −2.28995 | + | 2.28995i | −0.525349 | + | 0.525349i | −0.919182 | − | 0.393833i | \(-0.871149\pi\) |
0.393833 | + | 0.919182i | \(0.371149\pi\) | |||||||
\(20\) | 2.32634 | − | 2.32634i | 0.520186 | − | 0.520186i | ||||
\(21\) | −3.86465 | − | 1.94835i | −0.843335 | − | 0.425164i | ||||
\(22\) | 1.53379 | 0.327006 | ||||||||
\(23\) | 4.65268 | 0.970152 | 0.485076 | − | 0.874472i | \(-0.338792\pi\) | ||||
0.485076 | + | 0.874472i | \(0.338792\pi\) | |||||||
\(24\) | −0.779723 | + | 1.54662i | −0.159160 | + | 0.315702i | ||||
\(25\) | 5.82374i | 1.16475i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.00000 | + | 4.24264i | −0.577350 | + | 0.816497i | ||||
\(28\) | −1.76690 | + | 1.76690i | −0.333912 | + | 0.333912i | ||||
\(29\) | 4.65268i | 0.863982i | 0.901878 | + | 0.431991i | \(0.142189\pi\) | ||||
−0.901878 | + | 0.431991i | \(0.857811\pi\) | |||||||
\(30\) | −1.78406 | − | 5.41187i | −0.325724 | − | 0.988068i | ||||
\(31\) | 3.82374 | − | 3.82374i | 0.686764 | − | 0.686764i | −0.274752 | − | 0.961515i | \(-0.588596\pi\) |
0.961515 | + | 0.274752i | \(0.0885956\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 1.19593 | − | 2.37220i | 0.208185 | − | 0.412946i | ||||
\(34\) | 4.05684 | + | 4.05684i | 0.695743 | + | 0.695743i | ||||
\(35\) | − | 8.22081i | − | 1.38957i | ||||||
\(36\) | 1.78406 | + | 2.41187i | 0.297344 | + | 0.401978i | ||||
\(37\) | 3.05684 | + | 3.05684i | 0.502542 | + | 0.502542i | 0.912227 | − | 0.409685i | \(-0.134361\pi\) |
−0.409685 | + | 0.912227i | \(0.634361\pi\) | |||||||
\(38\) | 3.23847 | 0.525349 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.28995 | −0.520186 | ||||||||
\(41\) | 0.410044 | + | 0.410044i | 0.0640382 | + | 0.0640382i | 0.738401 | − | 0.674362i | \(-0.235581\pi\) |
−0.674362 | + | 0.738401i | \(0.735581\pi\) | |||||||
\(42\) | 1.35503 | + | 4.11041i | 0.209085 | + | 0.634250i | ||||
\(43\) | 0.222358i | 0.0339093i | 0.999856 | + | 0.0169546i | \(0.00539709\pi\) | ||||
−0.999856 | + | 0.0169546i | \(0.994603\pi\) | |||||||
\(44\) | −1.08456 | − | 1.08456i | −0.163503 | − | 0.163503i | ||||
\(45\) | −9.76118 | − | 1.46049i | −1.45511 | − | 0.217717i | ||||
\(46\) | −3.28995 | − | 3.28995i | −0.485076 | − | 0.485076i | ||||
\(47\) | 7.65354 | − | 7.65354i | 1.11638 | − | 1.11638i | 0.124116 | − | 0.992268i | \(-0.460391\pi\) |
0.992268 | − | 0.124116i | \(-0.0396094\pi\) | |||||||
\(48\) | 1.64497 | − | 0.542278i | 0.237431 | − | 0.0782711i | ||||
\(49\) | − | 0.756152i | − | 0.108022i | ||||||
\(50\) | 4.11801 | − | 4.11801i | 0.582374 | − | 0.582374i | ||||
\(51\) | 9.43760 | − | 3.11118i | 1.32153 | − | 0.435652i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.9689i | − | 1.50669i | −0.657627 | − | 0.753344i | \(-0.728440\pi\) | ||
0.657627 | − | 0.753344i | \(-0.271560\pi\) | |||||||
\(54\) | 5.12132 | − | 0.878680i | 0.696923 | − | 0.119573i | ||||
\(55\) | 5.04610 | 0.680416 | ||||||||
\(56\) | 2.49877 | 0.333912 | ||||||||
\(57\) | 2.52511 | − | 5.00868i | 0.334459 | − | 0.663416i | ||||
\(58\) | 3.28995 | − | 3.28995i | 0.431991 | − | 0.431991i | ||||
\(59\) | 4.65268 | − | 4.65268i | 0.605728 | − | 0.605728i | −0.336099 | − | 0.941827i | \(-0.609108\pi\) |
0.941827 | + | 0.336099i | \(0.109108\pi\) | |||||||
\(60\) | −2.56525 | + | 5.08829i | −0.331172 | + | 0.656896i | ||||
\(61\) | 3.06759 | 0.392764 | 0.196382 | − | 0.980527i | \(-0.437081\pi\) | ||||
0.196382 | + | 0.980527i | \(0.437081\pi\) | |||||||
\(62\) | −5.40758 | −0.686764 | ||||||||
\(63\) | 7.41378 | + | 1.10927i | 0.934049 | + | 0.139754i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.52305 | + | 0.831742i | −0.310566 | + | 0.102380i | ||||
\(67\) | −0.533794 | + | 0.533794i | −0.0652133 | + | 0.0652133i | −0.738961 | − | 0.673748i | \(-0.764683\pi\) |
0.673748 | + | 0.738961i | \(0.264683\pi\) | |||||||
\(68\) | − | 5.73724i | − | 0.695743i | ||||||
\(69\) | −7.65354 | + | 2.52305i | −0.921378 | + | 0.303739i | ||||
\(70\) | −5.81299 | + | 5.81299i | −0.694786 | + | 0.694786i | ||||
\(71\) | 5.48443 | + | 5.48443i | 0.650882 | + | 0.650882i | 0.953205 | − | 0.302324i | \(-0.0977623\pi\) |
−0.302324 | + | 0.953205i | \(0.597762\pi\) | |||||||
\(72\) | 0.443925 | − | 2.96697i | 0.0523171 | − | 0.349661i | ||||
\(73\) | −2.28995 | − | 2.28995i | −0.268018 | − | 0.268018i | 0.560283 | − | 0.828301i | \(-0.310692\pi\) |
−0.828301 | + | 0.560283i | \(0.810692\pi\) | |||||||
\(74\) | − | 4.32303i | − | 0.502542i | ||||||
\(75\) | −3.15808 | − | 9.57989i | −0.364664 | − | 1.10619i | ||||
\(76\) | −2.28995 | − | 2.28995i | −0.262675 | − | 0.262675i | ||||
\(77\) | −3.83260 | −0.436765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1137 | 1.58791 | 0.793957 | − | 0.607974i | \(-0.208018\pi\) | ||||
0.793957 | + | 0.607974i | \(0.208018\pi\) | |||||||
\(80\) | 2.32634 | + | 2.32634i | 0.260093 | + | 0.260093i | ||||
\(81\) | 2.63423 | − | 8.60586i | 0.292692 | − | 0.956207i | ||||
\(82\) | − | 0.579890i | − | 0.0640382i | ||||||
\(83\) | −1.39902 | − | 1.39902i | −0.153562 | − | 0.153562i | 0.626145 | − | 0.779707i | \(-0.284632\pi\) |
−0.779707 | + | 0.626145i | \(0.784632\pi\) | |||||||
\(84\) | 1.94835 | − | 3.86465i | 0.212582 | − | 0.421667i | ||||
\(85\) | 13.3468 | + | 13.3468i | 1.44766 | + | 1.44766i | ||||
\(86\) | 0.157231 | − | 0.157231i | 0.0169546 | − | 0.0169546i | ||||
\(87\) | −2.52305 | − | 7.65354i | −0.270499 | − | 0.820546i | ||||
\(88\) | 1.53379i | 0.163503i | ||||||||
\(89\) | 6.41175 | − | 6.41175i | 0.679644 | − | 0.679644i | −0.280275 | − | 0.959920i | \(-0.590426\pi\) |
0.959920 | + | 0.280275i | \(0.0904257\pi\) | |||||||
\(90\) | 5.86947 | + | 7.93492i | 0.618697 | + | 0.836414i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.65268i | 0.485076i | ||||||||
\(93\) | −4.21642 | + | 8.36347i | −0.437222 | + | 0.867252i | ||||
\(94\) | −10.8237 | −1.11638 | ||||||||
\(95\) | 10.6544 | 1.09312 | ||||||||
\(96\) | −1.54662 | − | 0.779723i | −0.157851 | − | 0.0795801i | ||||
\(97\) | 11.5799 | − | 11.5799i | 1.17576 | − | 1.17576i | 0.194946 | − | 0.980814i | \(-0.437547\pi\) |
0.980814 | − | 0.194946i | \(-0.0624531\pi\) | |||||||
\(98\) | −0.534680 | + | 0.534680i | −0.0540108 | + | 0.0540108i | ||||
\(99\) | −0.680889 | + | 4.55072i | −0.0684320 | + | 0.457365i | ||||
\(100\) | −5.82374 | −0.582374 | ||||||||
\(101\) | 12.8235 | 1.27599 | 0.637993 | − | 0.770042i | \(-0.279765\pi\) | ||||
0.637993 | + | 0.770042i | \(0.279765\pi\) | |||||||
\(102\) | −8.87333 | − | 4.47346i | −0.878591 | − | 0.442938i | ||||
\(103\) | − | 2.11368i | − | 0.208267i | −0.994563 | − | 0.104134i | \(-0.966793\pi\) | ||
0.994563 | − | 0.104134i | \(-0.0332070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.45797 | + | 13.5230i | 0.435053 | + | 1.31971i | ||||
\(106\) | −7.75615 | + | 7.75615i | −0.753344 | + | 0.753344i | ||||
\(107\) | 2.16911i | 0.209696i | 0.994488 | + | 0.104848i | \(0.0334356\pi\) | ||||
−0.994488 | + | 0.104848i | \(0.966564\pi\) | |||||||
\(108\) | −4.24264 | − | 3.00000i | −0.408248 | − | 0.288675i | ||||
\(109\) | −2.47695 | + | 2.47695i | −0.237249 | + | 0.237249i | −0.815710 | − | 0.578461i | \(-0.803653\pi\) |
0.578461 | + | 0.815710i | \(0.303653\pi\) | |||||||
\(110\) | −3.56813 | − | 3.56813i | −0.340208 | − | 0.340208i | ||||
\(111\) | −6.68608 | − | 3.37076i | −0.634615 | − | 0.319939i | ||||
\(112\) | −1.76690 | − | 1.76690i | −0.166956 | − | 0.166956i | ||||
\(113\) | 15.6215i | 1.46955i | 0.678310 | + | 0.734775i | \(0.262712\pi\) | ||||
−0.678310 | + | 0.734775i | \(0.737288\pi\) | |||||||
\(114\) | −5.32720 | + | 1.75615i | −0.498938 | + | 0.164479i | ||||
\(115\) | −10.8237 | − | 10.8237i | −1.00932 | − | 1.00932i | ||||
\(116\) | −4.65268 | −0.431991 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.57989 | −0.605728 | ||||||||
\(119\) | −10.1371 | − | 10.1371i | −0.929268 | − | 0.929268i | ||||
\(120\) | 5.41187 | − | 1.78406i | 0.494034 | − | 0.162862i | ||||
\(121\) | 8.64748i | 0.786134i | ||||||||
\(122\) | −2.16911 | − | 2.16911i | −0.196382 | − | 0.196382i | ||||
\(123\) | −0.896870 | − | 0.452154i | −0.0808680 | − | 0.0407693i | ||||
\(124\) | 3.82374 | + | 3.82374i | 0.343382 | + | 0.343382i | ||||
\(125\) | 1.91630 | − | 1.91630i | 0.171399 | − | 0.171399i | ||||
\(126\) | −4.45797 | − | 6.02671i | −0.397147 | − | 0.536902i | ||||
\(127\) | − | 10.6936i | − | 0.948901i | −0.880282 | − | 0.474451i | \(-0.842647\pi\) | ||
0.880282 | − | 0.474451i | \(-0.157353\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.120580 | − | 0.365773i | −0.0106165 | − | 0.0322045i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.264467i | − | 0.0231066i | −0.999933 | − | 0.0115533i | \(-0.996322\pi\) | ||
0.999933 | − | 0.0115533i | \(-0.00367761\pi\) | |||||||
\(132\) | 2.37220 | + | 1.19593i | 0.206473 | + | 0.104093i | ||||
\(133\) | −8.09219 | −0.701682 | ||||||||
\(134\) | 0.754898 | 0.0652133 | ||||||||
\(135\) | 16.8489 | − | 2.89081i | 1.45012 | − | 0.248801i | ||||
\(136\) | −4.05684 | + | 4.05684i | −0.347871 | + | 0.347871i | ||||
\(137\) | −3.66371 | + | 3.66371i | −0.313012 | + | 0.313012i | −0.846075 | − | 0.533063i | \(-0.821041\pi\) |
0.533063 | + | 0.846075i | \(0.321041\pi\) | |||||||
\(138\) | 7.19593 | + | 3.62780i | 0.612559 | + | 0.308819i | ||||
\(139\) | 2.22236 | 0.188498 | 0.0942490 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942490 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(140\) | 8.22081 | 0.694786 | ||||||||
\(141\) | −8.43952 | + | 16.7402i | −0.710735 | + | 1.40978i | ||||
\(142\) | − | 7.75615i | − | 0.650882i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.41187 | + | 1.78406i | −0.200989 | + | 0.148672i | ||||
\(145\) | 10.8237 | − | 10.8237i | 0.898863 | − | 0.898863i | ||||
\(146\) | 3.23847i | 0.268018i | ||||||||
\(147\) | 0.410044 | + | 1.24385i | 0.0338199 | + | 0.102591i | ||||
\(148\) | −3.05684 | + | 3.05684i | −0.251271 | + | 0.251271i | ||||
\(149\) | 6.41175 | + | 6.41175i | 0.525271 | + | 0.525271i | 0.919159 | − | 0.393887i | \(-0.128870\pi\) |
−0.393887 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(150\) | −4.54090 | + | 9.00711i | −0.370763 | + | 0.735427i | ||||
\(151\) | −0.812993 | − | 0.812993i | −0.0661605 | − | 0.0661605i | 0.673252 | − | 0.739413i | \(-0.264897\pi\) |
−0.739413 | + | 0.673252i | \(0.764897\pi\) | |||||||
\(152\) | 3.23847i | 0.262675i | ||||||||
\(153\) | −13.8375 | + | 10.2356i | −1.11869 | + | 0.827500i | ||||
\(154\) | 2.71005 | + | 2.71005i | 0.218382 | + | 0.218382i | ||||
\(155\) | −17.7907 | −1.42898 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.09219 | 0.645827 | 0.322914 | − | 0.946428i | \(-0.395338\pi\) | ||||
0.322914 | + | 0.946428i | \(0.395338\pi\) | |||||||
\(158\) | −9.97988 | − | 9.97988i | −0.793957 | − | 0.793957i | ||||
\(159\) | 5.94817 | + | 18.0435i | 0.471720 | + | 1.43094i | ||||
\(160\) | − | 3.28995i | − | 0.260093i | ||||||
\(161\) | 8.22081 | + | 8.22081i | 0.647891 | + | 0.647891i | ||||
\(162\) | −7.94794 | + | 4.22258i | −0.624449 | + | 0.331757i | ||||
\(163\) | −17.2274 | − | 17.2274i | −1.34935 | − | 1.34935i | −0.886366 | − | 0.462986i | \(-0.846778\pi\) |
−0.462986 | − | 0.886366i | \(-0.653222\pi\) | |||||||
\(164\) | −0.410044 | + | 0.410044i | −0.0320191 | + | 0.0320191i | ||||
\(165\) | −8.30069 | + | 2.73639i | −0.646208 | + | 0.213027i | ||||
\(166\) | 1.97851i | 0.153562i | ||||||||
\(167\) | −6.82180 | + | 6.82180i | −0.527886 | + | 0.527886i | −0.919942 | − | 0.392055i | \(-0.871764\pi\) |
0.392055 | + | 0.919942i | \(0.371764\pi\) | |||||||
\(168\) | −4.11041 | + | 1.35503i | −0.317125 | + | 0.104543i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | − | 18.8752i | − | 1.44766i | ||||||
\(171\) | −1.43764 | + | 9.60846i | −0.109939 | + | 0.734777i | ||||
\(172\) | −0.222358 | −0.0169546 | ||||||||
\(173\) | −1.85465 | −0.141006 | −0.0705032 | − | 0.997512i | \(-0.522461\pi\) | ||||
−0.0705032 | + | 0.997512i | \(0.522461\pi\) | |||||||
\(174\) | −3.62780 | + | 7.19593i | −0.275023 | + | 0.545522i | ||||
\(175\) | −10.2899 | + | 10.2899i | −0.777847 | + | 0.777847i | ||||
\(176\) | 1.08456 | − | 1.08456i | 0.0817515 | − | 0.0817515i | ||||
\(177\) | −5.13049 | + | 10.1766i | −0.385631 | + | 0.764919i | ||||
\(178\) | −9.06759 | −0.679644 | ||||||||
\(179\) | 0.264467 | 0.0197672 | 0.00988361 | − | 0.999951i | \(-0.496854\pi\) | ||||
0.00988361 | + | 0.999951i | \(0.496854\pi\) | |||||||
\(180\) | 1.46049 | − | 9.76118i | 0.108858 | − | 0.727555i | ||||
\(181\) | − | 8.11368i | − | 0.603085i | −0.953453 | − | 0.301543i | \(-0.902498\pi\) | ||
0.953453 | − | 0.301543i | \(-0.0975016\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.04610 | + | 1.66348i | −0.373018 | + | 0.122968i | ||||
\(184\) | 3.28995 | − | 3.28995i | 0.242538 | − | 0.242538i | ||||
\(185\) | − | 14.2225i | − | 1.04566i | ||||||
\(186\) | 8.89533 | − | 2.93241i | 0.652237 | − | 0.215015i | ||||
\(187\) | 6.22236 | − | 6.22236i | 0.455024 | − | 0.455024i | ||||
\(188\) | 7.65354 | + | 7.65354i | 0.558192 | + | 0.558192i | ||||
\(189\) | −12.7970 | + | 2.19562i | −0.930845 | + | 0.159708i | ||||
\(190\) | −7.53379 | − | 7.53379i | −0.546559 | − | 0.546559i | ||||
\(191\) | 16.1272i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198302\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801698\pi\) | |||||||
\(192\) | 0.542278 | + | 1.64497i | 0.0391355 | + | 0.118716i | ||||
\(193\) | 2.53379 | + | 2.53379i | 0.182386 | + | 0.182386i | 0.792395 | − | 0.610008i | \(-0.208834\pi\) |
−0.610008 | + | 0.792395i | \(0.708834\pi\) | |||||||
\(194\) | −16.3764 | −1.17576 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.756152 | 0.0540108 | ||||||||
\(197\) | −4.49545 | − | 4.49545i | −0.320288 | − | 0.320288i | 0.528590 | − | 0.848877i | \(-0.322721\pi\) |
−0.848877 | + | 0.528590i | \(0.822721\pi\) | |||||||
\(198\) | 3.69931 | − | 2.73639i | 0.262898 | − | 0.194467i | ||||
\(199\) | − | 23.1383i | − | 1.64023i | −0.572199 | − | 0.820115i | \(-0.693909\pi\) | ||
0.572199 | − | 0.820115i | \(-0.306091\pi\) | |||||||
\(200\) | 4.11801 | + | 4.11801i | 0.291187 | + | 0.291187i | ||||
\(201\) | 0.588611 | − | 1.16754i | 0.0415174 | − | 0.0823519i | ||||
\(202\) | −9.06759 | − | 9.06759i | −0.637993 | − | 0.637993i | ||||
\(203\) | −8.22081 | + | 8.22081i | −0.576988 | + | 0.576988i | ||||
\(204\) | 3.11118 | + | 9.43760i | 0.217826 | + | 0.660764i | ||||
\(205\) | − | 1.90781i | − | 0.133247i | ||||||
\(206\) | −1.49460 | + | 1.49460i | −0.104134 | + | 0.104134i | ||||
\(207\) | 11.2217 | − | 8.30069i | 0.779960 | − | 0.576938i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.96715i | − | 0.343585i | ||||||
\(210\) | 6.40996 | − | 12.7145i | 0.442329 | − | 0.877382i | ||||
\(211\) | 15.2899 | 1.05260 | 0.526302 | − | 0.850298i | \(-0.323578\pi\) | ||||
0.526302 | + | 0.850298i | \(0.323578\pi\) | |||||||
\(212\) | 10.9689 | 0.753344 | ||||||||
\(213\) | −11.9958 | − | 6.04765i | −0.821940 | − | 0.414378i | ||||
\(214\) | 1.53379 | − | 1.53379i | 0.104848 | − | 0.104848i | ||||
\(215\) | 0.517281 | − | 0.517281i | 0.0352783 | − | 0.0352783i | ||||
\(216\) | 0.878680 | + | 5.12132i | 0.0597866 | + | 0.348462i | ||||
\(217\) | 13.5123 | 0.917275 | ||||||||
\(218\) | 3.50294 | 0.237249 | ||||||||
\(219\) | 5.00868 | + | 2.52511i | 0.338455 | + | 0.170631i | ||||
\(220\) | 5.04610i | 0.340208i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.34428 | + | 7.11126i | 0.157338 | + | 0.477277i | ||||
\(223\) | 3.30069 | − | 3.30069i | 0.221031 | − | 0.221031i | −0.587902 | − | 0.808932i | \(-0.700046\pi\) |
0.808932 | + | 0.587902i | \(0.200046\pi\) | |||||||
\(224\) | 2.49877i | 0.166956i | ||||||||
\(225\) | 10.3899 | + | 14.0461i | 0.692662 | + | 0.936406i | ||||
\(226\) | 11.0461 | − | 11.0461i | 0.734775 | − | 0.734775i | ||||
\(227\) | −4.33822 | − | 4.33822i | −0.287938 | − | 0.287938i | 0.548326 | − | 0.836264i | \(-0.315265\pi\) |
−0.836264 | + | 0.548326i | \(0.815265\pi\) | |||||||
\(228\) | 5.00868 | + | 2.52511i | 0.331708 | + | 0.167230i | ||||
\(229\) | −2.47695 | − | 2.47695i | −0.163682 | − | 0.163682i | 0.620514 | − | 0.784195i | \(-0.286924\pi\) |
−0.784195 | + | 0.620514i | \(0.786924\pi\) | |||||||
\(230\) | 15.3071i | 1.00932i | ||||||||
\(231\) | 6.30452 | − | 2.07833i | 0.414807 | − | 0.136744i | ||||
\(232\) | 3.28995 | + | 3.28995i | 0.215995 | + | 0.215995i | ||||
\(233\) | 12.0534 | 0.789645 | 0.394823 | − | 0.918757i | \(-0.370806\pi\) | ||||
0.394823 | + | 0.918757i | \(0.370806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.6095 | −2.32291 | ||||||||
\(236\) | 4.65268 | + | 4.65268i | 0.302864 | + | 0.302864i | ||||
\(237\) | −23.2166 | + | 7.65354i | −1.50808 | + | 0.497151i | ||||
\(238\) | 14.3360i | 0.929268i | ||||||||
\(239\) | 14.7898 | + | 14.7898i | 0.956672 | + | 0.956672i | 0.999100 | − | 0.0424271i | \(-0.0135090\pi\) |
−0.0424271 | + | 0.999100i | \(0.513509\pi\) | |||||||
\(240\) | −5.08829 | − | 2.56525i | −0.328448 | − | 0.165586i | ||||
\(241\) | 12.3821 | + | 12.3821i | 0.797604 | + | 0.797604i | 0.982717 | − | 0.185114i | \(-0.0592653\pi\) |
−0.185114 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(242\) | 6.11469 | − | 6.11469i | 0.393067 | − | 0.393067i | ||||
\(243\) | 0.333537 | + | 15.5849i | 0.0213964 | + | 0.999771i | ||||
\(244\) | 3.06759i | 0.196382i | ||||||||
\(245\) | −1.75907 | + | 1.75907i | −0.112383 | + | 0.112383i | ||||
\(246\) | 0.314462 | + | 0.953903i | 0.0200493 | + | 0.0608187i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 5.40758i | − | 0.343382i | ||||||
\(249\) | 3.06000 | + | 1.54269i | 0.193920 | + | 0.0977639i | ||||
\(250\) | −2.71005 | −0.171399 | ||||||||
\(251\) | 12.2946 | 0.776026 | 0.388013 | − | 0.921654i | \(-0.373161\pi\) | ||||
0.388013 | + | 0.921654i | \(0.373161\pi\) | |||||||
\(252\) | −1.10927 | + | 7.41378i | −0.0698772 | + | 0.467024i | ||||
\(253\) | −5.04610 | + | 5.04610i | −0.317245 | + | 0.317245i | ||||
\(254\) | −7.56150 | + | 7.56150i | −0.474451 | + | 0.474451i | ||||
\(255\) | −29.1928 | − | 14.7174i | −1.82812 | − | 0.921641i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.0352 | −1.87355 | −0.936773 | − | 0.349938i | \(-0.886203\pi\) | ||||
−0.936773 | + | 0.349938i | \(0.886203\pi\) | |||||||
\(258\) | −0.173378 | + | 0.343903i | −0.0107940 | + | 0.0214105i | ||||
\(259\) | 10.8022i | 0.671219i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.30069 | + | 11.2217i | 0.513800 | + | 0.694604i | ||||
\(262\) | −0.187007 | + | 0.187007i | −0.0115533 | + | 0.0115533i | ||||
\(263\) | − | 18.6107i | − | 1.14759i | −0.819000 | − | 0.573794i | \(-0.805471\pi\) | ||
0.819000 | − | 0.573794i | \(-0.194529\pi\) | |||||||
\(264\) | −0.831742 | − | 2.52305i | −0.0511902 | − | 0.155283i | ||||
\(265\) | −25.5173 | + | 25.5173i | −1.56752 | + | 1.56752i | ||||
\(266\) | 5.72204 | + | 5.72204i | 0.350841 | + | 0.350841i | ||||
\(267\) | −7.07020 | + | 14.0241i | −0.432690 | + | 0.858261i | ||||
\(268\) | −0.533794 | − | 0.533794i | −0.0326066 | − | 0.0326066i | ||||
\(269\) | 0.820089i | 0.0500017i | 0.999687 | + | 0.0250008i | \(0.00795884\pi\) | ||||
−0.999687 | + | 0.0250008i | \(0.992041\pi\) | |||||||
\(270\) | −13.9581 | − | 9.86984i | −0.849460 | − | 0.600659i | ||||
\(271\) | 9.85909 | + | 9.85909i | 0.598897 | + | 0.598897i | 0.940019 | − | 0.341122i | \(-0.110807\pi\) |
−0.341122 | + | 0.940019i | \(0.610807\pi\) | |||||||
\(272\) | 5.73724 | 0.347871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.18127 | 0.313012 | ||||||||
\(275\) | −6.31617 | − | 6.31617i | −0.380879 | − | 0.380879i | ||||
\(276\) | −2.52305 | − | 7.65354i | −0.151870 | − | 0.460689i | ||||
\(277\) | 17.3871i | 1.04469i | 0.852733 | + | 0.522346i | \(0.174943\pi\) | ||||
−0.852733 | + | 0.522346i | \(0.825057\pi\) | |||||||
\(278\) | −1.57144 | − | 1.57144i | −0.0942490 | − | 0.0942490i | ||||
\(279\) | 2.40056 | − | 16.0442i | 0.143718 | − | 0.960538i | ||||
\(280\) | −5.81299 | − | 5.81299i | −0.347393 | − | 0.347393i | ||||
\(281\) | 13.5480 | − | 13.5480i | 0.808207 | − | 0.808207i | −0.176156 | − | 0.984362i | \(-0.556366\pi\) |
0.984362 | + | 0.176156i | \(0.0563662\pi\) | |||||||
\(282\) | 17.8048 | − | 5.86947i | 1.06026 | − | 0.349522i | ||||
\(283\) | 17.6475i | 1.04903i | 0.851400 | + | 0.524517i | \(0.175754\pi\) | ||||
−0.851400 | + | 0.524517i | \(0.824246\pi\) | |||||||
\(284\) | −5.48443 | + | 5.48443i | −0.325441 | + | 0.325441i | ||||
\(285\) | −17.5262 | + | 5.77764i | −1.03816 | + | 0.342238i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.44901i | 0.0855325i | ||||||||
\(288\) | 2.96697 | + | 0.443925i | 0.174831 | + | 0.0261585i | ||||
\(289\) | 15.9159 | 0.936231 | ||||||||
\(290\) | −15.3071 | −0.898863 | ||||||||
\(291\) | −12.7691 | + | 25.3281i | −0.748537 | + | 1.48476i | ||||
\(292\) | 2.28995 | − | 2.28995i | 0.134009 | − | 0.134009i | ||||
\(293\) | −15.4643 | + | 15.4643i | −0.903435 | + | 0.903435i | −0.995732 | − | 0.0922970i | \(-0.970579\pi\) |
0.0922970 | + | 0.995732i | \(0.470579\pi\) | |||||||
\(294\) | 0.589589 | − | 1.16948i | 0.0343855 | − | 0.0682054i | ||||
\(295\) | −21.6475 | −1.26036 | ||||||||
\(296\) | 4.32303 | 0.251271 | ||||||||
\(297\) | −1.34771 | − | 7.85505i | −0.0782023 | − | 0.455796i | ||||
\(298\) | − | 9.06759i | − | 0.525271i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9.57989 | − | 3.15808i | 0.553095 | − | 0.182332i | ||||
\(301\) | −0.392884 | + | 0.392884i | −0.0226454 | + | 0.0226454i | ||||
\(302\) | 1.14975i | 0.0661605i | ||||||||
\(303\) | −21.0943 | + | 6.95390i | −1.21184 | + | 0.399491i | ||||
\(304\) | 2.28995 | − | 2.28995i | 0.131337 | − | 0.131337i | ||||
\(305\) | −7.13626 | − | 7.13626i | −0.408621 | − | 0.408621i | ||||
\(306\) | 17.0222 | + | 2.54690i | 0.973097 | + | 0.145597i | ||||
\(307\) | 20.8698 | + | 20.8698i | 1.19110 | + | 1.19110i | 0.976758 | + | 0.214347i | \(0.0687623\pi\) |
0.214347 | + | 0.976758i | \(0.431238\pi\) | |||||||
\(308\) | − | 3.83260i | − | 0.218382i | ||||||
\(309\) | 1.14620 | + | 3.47695i | 0.0652053 | + | 0.197797i | ||||
\(310\) | 12.5799 | + | 12.5799i | 0.714490 | + | 0.714490i | ||||
\(311\) | −15.6215 | −0.885816 | −0.442908 | − | 0.896567i | \(-0.646053\pi\) | ||||
−0.442908 | + | 0.896567i | \(0.646053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4036 | 0.983711 | 0.491856 | − | 0.870677i | \(-0.336319\pi\) | ||||
0.491856 | + | 0.870677i | \(0.336319\pi\) | |||||||
\(314\) | −5.72204 | − | 5.72204i | −0.322914 | − | 0.322914i | ||||
\(315\) | −14.6665 | − | 19.8275i | −0.826362 | − | 1.11715i | ||||
\(316\) | 14.1137i | 0.793957i | ||||||||
\(317\) | 2.89362 | + | 2.89362i | 0.162522 | + | 0.162522i | 0.783683 | − | 0.621161i | \(-0.213339\pi\) |
−0.621161 | + | 0.783683i | \(0.713339\pi\) | |||||||
\(318\) | 8.55267 | − | 16.9646i | 0.479610 | − | 0.951330i | ||||
\(319\) | −5.04610 | − | 5.04610i | −0.282527 | − | 0.282527i | ||||
\(320\) | −2.32634 | + | 2.32634i | −0.130046 | + | 0.130046i | ||||
\(321\) | −1.17626 | − | 3.56813i | −0.0656525 | − | 0.199154i | ||||
\(322\) | − | 11.6260i | − | 0.647891i | ||||||
\(323\) | 13.1380 | − | 13.1380i | 0.731016 | − | 0.731016i | ||||
\(324\) | 8.60586 | + | 2.63423i | 0.478103 | + | 0.146346i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.3632i | 1.34935i | ||||||||
\(327\) | 2.73132 | − | 5.41771i | 0.151042 | − | 0.299600i | ||||
\(328\) | 0.579890 | 0.0320191 | ||||||||
\(329\) | 27.0460 | 1.49110 | ||||||||
\(330\) | 7.80439 | + | 3.93456i | 0.429618 | + | 0.216590i | ||||
\(331\) | −2.06759 | + | 2.06759i | −0.113645 | + | 0.113645i | −0.761642 | − | 0.647998i | \(-0.775607\pi\) |
0.647998 | + | 0.761642i | \(0.275607\pi\) | |||||||
\(332\) | 1.39902 | − | 1.39902i | 0.0767811 | − | 0.0767811i | ||||
\(333\) | 12.8263 | + | 1.91910i | 0.702877 | + | 0.105166i | ||||
\(334\) | 9.64748 | 0.527886 | ||||||||
\(335\) | 2.48357 | 0.135692 | ||||||||
\(336\) | 3.86465 | + | 1.94835i | 0.210834 | + | 0.106291i | ||||
\(337\) | 20.5634i | 1.12016i | 0.828438 | + | 0.560080i | \(0.189230\pi\) | ||||
−0.828438 | + | 0.560080i | \(0.810770\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.47122 | − | 25.6970i | −0.460093 | − | 1.39567i | ||||
\(340\) | −13.3468 | + | 13.3468i | −0.723831 | + | 0.723831i | ||||
\(341\) | 8.29412i | 0.449152i | ||||||||
\(342\) | 7.81077 | − | 5.77764i | 0.422358 | − | 0.312419i | ||||
\(343\) | 13.7043 | − | 13.7043i | 0.739964 | − | 0.739964i | ||||
\(344\) | 0.157231 | + | 0.157231i | 0.00847732 | + | 0.00847732i | ||||
\(345\) | 23.6742 | + | 11.9353i | 1.27458 | + | 0.642574i | ||||
\(346\) | 1.31144 | + | 1.31144i | 0.0705032 | + | 0.0705032i | ||||
\(347\) | − | 2.72473i | − | 0.146271i | −0.997322 | − | 0.0731357i | \(-0.976699\pi\) | ||
0.997322 | − | 0.0731357i | \(-0.0233006\pi\) | |||||||
\(348\) | 7.65354 | − | 2.52305i | 0.410273 | − | 0.135250i | ||||
\(349\) | −21.6367 | − | 21.6367i | −1.15819 | − | 1.15819i | −0.984865 | − | 0.173323i | \(-0.944550\pi\) |
−0.173323 | − | 0.984865i | \(-0.555450\pi\) | |||||||
\(350\) | 14.5522 | 0.777847 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.53379 | −0.0817515 | ||||||||
\(353\) | −1.49460 | − | 1.49460i | −0.0795495 | − | 0.0795495i | 0.666212 | − | 0.745762i | \(-0.267914\pi\) |
−0.745762 | + | 0.666212i | \(0.767914\pi\) | |||||||
\(354\) | 10.8237 | − | 3.56813i | 0.575275 | − | 0.189644i | ||||
\(355\) | − | 25.5173i | − | 1.35432i | ||||||
\(356\) | 6.41175 | + | 6.41175i | 0.339822 | + | 0.339822i | ||||
\(357\) | 22.1724 | + | 11.1781i | 1.17349 | + | 0.591610i | ||||
\(358\) | −0.187007 | − | 0.187007i | −0.00988361 | − | 0.00988361i | ||||
\(359\) | 0.314462 | − | 0.314462i | 0.0165967 | − | 0.0165967i | −0.698760 | − | 0.715356i | \(-0.746264\pi\) |
0.715356 | + | 0.698760i | \(0.246264\pi\) | |||||||
\(360\) | −7.93492 | + | 5.86947i | −0.418207 | + | 0.309348i | ||||
\(361\) | 8.51230i | 0.448016i | ||||||||
\(362\) | −5.73724 | + | 5.73724i | −0.301543 | + | 0.301543i | ||||
\(363\) | −4.68934 | − | 14.2249i | −0.246126 | − | 0.746612i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.6544i | 0.557676i | ||||||||
\(366\) | 4.74439 | + | 2.39187i | 0.247993 | + | 0.125025i | ||||
\(367\) | 21.0461 | 1.09860 | 0.549299 | − | 0.835626i | \(-0.314895\pi\) | ||||
0.549299 | + | 0.835626i | \(0.314895\pi\) | |||||||
\(368\) | −4.65268 | −0.242538 | ||||||||
\(369\) | 1.72052 | + | 0.257428i | 0.0895666 | + | 0.0134012i | ||||
\(370\) | −10.0568 | + | 10.0568i | −0.522830 | + | 0.522830i | ||||
\(371\) | 19.3808 | − | 19.3808i | 1.00620 | − | 1.00620i | ||||
\(372\) | −8.36347 | − | 4.21642i | −0.433626 | − | 0.218611i | ||||
\(373\) | −4.22737 | −0.218885 | −0.109442 | − | 0.993993i | \(-0.534907\pi\) | ||||
−0.109442 | + | 0.993993i | \(0.534907\pi\) | |||||||
\(374\) | −8.79974 | −0.455024 | ||||||||
\(375\) | −2.11309 | + | 4.19142i | −0.109120 | + | 0.216444i | ||||
\(376\) | − | 10.8237i | − | 0.558192i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 10.6014 | + | 7.49631i | 0.545276 | + | 0.385568i | ||||
\(379\) | 18.1598 | − | 18.1598i | 0.932805 | − | 0.932805i | −0.0650751 | − | 0.997880i | \(-0.520729\pi\) |
0.997880 | + | 0.0650751i | \(0.0207287\pi\) | |||||||
\(380\) | 10.6544i | 0.546559i | ||||||||
\(381\) | 5.79889 | + | 17.5906i | 0.297086 | + | 0.901196i | ||||
\(382\) | 11.4036 | − | 11.4036i | 0.583460 | − | 0.583460i | ||||
\(383\) | −19.4425 | − | 19.4425i | −0.993464 | − | 0.993464i | 0.00651435 | − | 0.999979i | \(-0.497926\pi\) |
−0.999979 | + | 0.00651435i | \(0.997926\pi\) | |||||||
\(384\) | 0.779723 | − | 1.54662i | 0.0397901 | − | 0.0789256i | ||||
\(385\) | 8.91593 | + | 8.91593i | 0.454398 | + | 0.454398i | ||||
\(386\) | − | 3.58333i | − | 0.182386i | ||||||
\(387\) | 0.396701 | + | 0.536298i | 0.0201654 | + | 0.0272616i | ||||
\(388\) | 11.5799 | + | 11.5799i | 0.587880 | + | 0.587880i | ||||
\(389\) | −2.16911 | −0.109978 | −0.0549892 | − | 0.998487i | \(-0.517512\pi\) | ||||
−0.0549892 | + | 0.998487i | \(0.517512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6936 | −1.34995 | ||||||||
\(392\) | −0.534680 | − | 0.534680i | −0.0270054 | − | 0.0270054i | ||||
\(393\) | 0.143415 | + | 0.435041i | 0.00723432 | + | 0.0219449i | ||||
\(394\) | 6.35753i | 0.320288i | ||||||||
\(395\) | −32.8333 | − | 32.8333i | −1.65202 | − | 1.65202i | ||||
\(396\) | −4.55072 | − | 0.680889i | −0.228683 | − | 0.0342160i | ||||
\(397\) | −10.2685 | − | 10.2685i | −0.515359 | − | 0.515359i | 0.400805 | − | 0.916164i | \(-0.368731\pi\) |
−0.916164 | + | 0.400805i | \(0.868731\pi\) | |||||||
\(398\) | −16.3612 | + | 16.3612i | −0.820115 | + | 0.820115i | ||||
\(399\) | 13.3114 | − | 4.38822i | 0.666405 | − | 0.219686i | ||||
\(400\) | − | 5.82374i | − | 0.291187i | ||||||
\(401\) | 5.83282 | − | 5.83282i | 0.291277 | − | 0.291277i | −0.546307 | − | 0.837585i | \(-0.683967\pi\) |
0.837585 | + | 0.546307i | \(0.183967\pi\) | |||||||
\(402\) | −1.24179 | + | 0.409365i | −0.0619347 | + | 0.0204172i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.8235i | 0.637993i | ||||||||
\(405\) | −26.1483 | + | 13.8921i | −1.29932 | + | 0.690302i | ||||
\(406\) | 11.6260 | 0.576988 | ||||||||
\(407\) | −6.63063 | −0.328668 | ||||||||
\(408\) | 4.47346 | − | 8.87333i | 0.221469 | − | 0.439295i | ||||
\(409\) | 6.62599 | − | 6.62599i | 0.327634 | − | 0.327634i | −0.524052 | − | 0.851686i | \(-0.675580\pi\) |
0.851686 | + | 0.524052i | \(0.175580\pi\) | |||||||
\(410\) | −1.34902 | + | 1.34902i | −0.0666235 | + | 0.0666235i | ||||
\(411\) | 4.03996 | − | 8.01346i | 0.199276 | − | 0.395275i | ||||
\(412\) | 2.11368 | 0.104134 | ||||||||
\(413\) | 16.4416 | 0.809040 | ||||||||
\(414\) | −13.8044 | − | 2.06544i | −0.678449 | − | 0.101511i | ||||
\(415\) | 6.50919i | 0.319523i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.65572 | + | 1.20514i | −0.179021 | + | 0.0590157i | ||||
\(418\) | −3.51230 | + | 3.51230i | −0.171792 | + | 0.171792i | ||||
\(419\) | 8.41198i | 0.410952i | 0.978662 | + | 0.205476i | \(0.0658743\pi\) | ||||
−0.978662 | + | 0.205476i | \(0.934126\pi\) | |||||||
\(420\) | −13.5230 | + | 4.45797i | −0.659855 | + | 0.217526i | ||||
\(421\) | 0.964649 | − | 0.964649i | 0.0470141 | − | 0.0470141i | −0.683209 | − | 0.730223i | \(-0.739416\pi\) |
0.730223 | + | 0.683209i | \(0.239416\pi\) | |||||||
\(422\) | −10.8116 | − | 10.8116i | −0.526302 | − | 0.526302i | ||||
\(423\) | 4.80493 | − | 32.1137i | 0.233624 | − | 1.56142i | ||||
\(424\) | −7.75615 | − | 7.75615i | −0.376672 | − | 0.376672i | ||||
\(425\) | − | 33.4122i | − | 1.62073i | ||||||
\(426\) | 4.20599 | + | 12.7587i | 0.203781 | + | 0.618159i | ||||
\(427\) | 5.42011 | + | 5.42011i | 0.262297 | + | 0.262297i | ||||
\(428\) | −2.16911 | −0.104848 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.731545 | −0.0352783 | ||||||||
\(431\) | 25.4442 | + | 25.4442i | 1.22560 | + | 1.22560i | 0.965610 | + | 0.259993i | \(0.0837203\pi\) |
0.259993 | + | 0.965610i | \(0.416280\pi\) | |||||||
\(432\) | 3.00000 | − | 4.24264i | 0.144338 | − | 0.204124i | ||||
\(433\) | − | 39.6740i | − | 1.90661i | −0.302010 | − | 0.953305i | \(-0.597658\pi\) | ||
0.302010 | − | 0.953305i | \(-0.402342\pi\) | |||||||
\(434\) | −9.55464 | − | 9.55464i | −0.458637 | − | 0.458637i | ||||
\(435\) | −11.9353 | + | 23.6742i | −0.572253 | + | 1.13509i | ||||
\(436\) | −2.47695 | − | 2.47695i | −0.118624 | − | 0.118624i | ||||
\(437\) | −10.6544 | + | 10.6544i | −0.509669 | + | 0.509669i | ||||
\(438\) | −1.75615 | − | 5.32720i | −0.0839122 | − | 0.254543i | ||||
\(439\) | − | 18.0000i | − | 0.859093i | −0.903045 | − | 0.429547i | \(-0.858673\pi\) | ||
0.903045 | − | 0.429547i | \(-0.141327\pi\) | |||||||
\(440\) | 3.56813 | − | 3.56813i | 0.170104 | − | 0.170104i | ||||
\(441\) | −1.34902 | − | 1.82374i | −0.0642392 | − | 0.0868447i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 31.9899i | − | 1.51988i | −0.649991 | − | 0.759942i | \(-0.725227\pi\) | ||
0.649991 | − | 0.759942i | \(-0.274773\pi\) | |||||||
\(444\) | 3.37076 | − | 6.68608i | 0.159969 | − | 0.317307i | ||||
\(445\) | −29.8319 | −1.41417 | ||||||||
\(446\) | −4.66788 | −0.221031 | ||||||||
\(447\) | −14.0241 | − | 7.07020i | −0.663318 | − | 0.334409i | ||||
\(448\) | 1.76690 | − | 1.76690i | 0.0834780 | − | 0.0834780i | ||||
\(449\) | 5.95612 | − | 5.95612i | 0.281087 | − | 0.281087i | −0.552456 | − | 0.833542i | \(-0.686309\pi\) |
0.833542 | + | 0.552456i | \(0.186309\pi\) | |||||||
\(450\) | 2.58530 | − | 17.2789i | 0.121872 | − | 0.814534i | ||||
\(451\) | −0.889432 | −0.0418817 | ||||||||
\(452\) | −15.6215 | −0.734775 | ||||||||
\(453\) | 1.77822 | + | 0.896483i | 0.0835481 | + | 0.0421205i | ||||
\(454\) | 6.13517i | 0.287938i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.75615 | − | 5.32720i | −0.0822393 | − | 0.249469i | ||||
\(457\) | −10.4251 | + | 10.4251i | −0.487667 | + | 0.487667i | −0.907569 | − | 0.419903i | \(-0.862064\pi\) |
0.419903 | + | 0.907569i | \(0.362064\pi\) | |||||||
\(458\) | 3.50294i | 0.163682i | ||||||||
\(459\) | 17.2117 | − | 24.3411i | 0.803374 | − | 1.13614i | ||||
\(460\) | 10.8237 | − | 10.8237i | 0.504659 | − | 0.504659i | ||||
\(461\) | 27.4444 | + | 27.4444i | 1.27821 | + | 1.27821i | 0.941667 | + | 0.336547i | \(0.109259\pi\) |
0.336547 | + | 0.941667i | \(0.390741\pi\) | |||||||
\(462\) | −5.92757 | − | 2.98836i | −0.275775 | − | 0.139031i | ||||
\(463\) | −8.89133 | − | 8.89133i | −0.413215 | − | 0.413215i | 0.469642 | − | 0.882857i | \(-0.344383\pi\) |
−0.882857 | + | 0.469642i | \(0.844383\pi\) | |||||||
\(464\) | − | 4.65268i | − | 0.215995i | ||||||
\(465\) | 29.2651 | − | 9.64748i | 1.35714 | − | 0.447391i | ||||
\(466\) | −8.52305 | − | 8.52305i | −0.394823 | − | 0.394823i | ||||
\(467\) | 36.9303 | 1.70893 | 0.854466 | − | 0.519508i | \(-0.173885\pi\) | ||||
0.854466 | + | 0.519508i | \(0.173885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.88632 | −0.0871020 | ||||||||
\(470\) | 25.1797 | + | 25.1797i | 1.16145 | + | 1.16145i | ||||
\(471\) | −13.3114 | + | 4.38822i | −0.613359 | + | 0.202198i | ||||
\(472\) | − | 6.57989i | − | 0.302864i | ||||||
\(473\) | −0.241160 | − | 0.241160i | −0.0110885 | − | 0.0110885i | ||||
\(474\) | 21.8285 | + | 11.0048i | 1.00262 | + | 0.505465i | ||||
\(475\) | −13.3360 | − | 13.3360i | −0.611900 | − | 0.611900i | ||||
\(476\) | 10.1371 | − | 10.1371i | 0.464634 | − | 0.464634i | ||||
\(477\) | −19.5691 | − | 26.4554i | −0.896010 | − | 1.21131i | ||||
\(478\) | − | 20.9159i | − | 0.956672i | ||||||
\(479\) | −3.62978 | + | 3.62978i | −0.165849 | + | 0.165849i | −0.785152 | − | 0.619303i | \(-0.787415\pi\) |
0.619303 | + | 0.785152i | \(0.287415\pi\) | |||||||
\(480\) | 1.78406 | + | 5.41187i | 0.0814310 | + | 0.247017i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 17.5110i | − | 0.797604i | ||||||
\(483\) | −17.9810 | − | 9.06505i | −0.818163 | − | 0.412474i | ||||
\(484\) | −8.64748 | −0.393067 | ||||||||
\(485\) | −53.8776 | −2.44645 | ||||||||
\(486\) | 10.7843 | − | 11.2560i | 0.489187 | − | 0.510584i | ||||
\(487\) | −9.33604 | + | 9.33604i | −0.423056 | + | 0.423056i | −0.886255 | − | 0.463198i | \(-0.846702\pi\) |
0.463198 | + | 0.886255i | \(0.346702\pi\) | |||||||
\(488\) | 2.16911 | − | 2.16911i | 0.0981911 | − | 0.0981911i | ||||
\(489\) | 37.6806 | + | 18.9965i | 1.70397 | + | 0.859053i | ||||
\(490\) | 2.48770 | 0.112383 | ||||||||
\(491\) | −9.37867 | −0.423254 | −0.211627 | − | 0.977351i | \(-0.567876\pi\) | ||||
−0.211627 | + | 0.977351i | \(0.567876\pi\) | |||||||
\(492\) | 0.452154 | − | 0.896870i | 0.0203847 | − | 0.0404340i | ||||
\(493\) | − | 26.6936i | − | 1.20222i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.1705 | − | 9.00256i | 0.547024 | − | 0.404635i | ||||
\(496\) | −3.82374 | + | 3.82374i | −0.171691 | + | 0.171691i | ||||
\(497\) | 19.3808i | 0.869349i | ||||||||
\(498\) | −1.07290 | − | 3.25459i | −0.0480779 | − | 0.145842i | ||||
\(499\) | 0.176261 | − | 0.176261i | 0.00789054 | − | 0.00789054i | −0.703151 | − | 0.711041i | \(-0.748224\pi\) |
0.711041 | + | 0.703151i | \(0.248224\pi\) | |||||||
\(500\) | 1.91630 | + | 1.91630i | 0.0856995 | + | 0.0856995i | ||||
\(501\) | 7.52236 | − | 14.9210i | 0.336074 | − | 0.666620i | ||||
\(502\) | −8.69357 | − | 8.69357i | −0.388013 | − | 0.388013i | ||||
\(503\) | − | 14.1725i | − | 0.631922i | −0.948772 | − | 0.315961i | \(-0.897673\pi\) | ||
0.948772 | − | 0.315961i | \(-0.102327\pi\) | |||||||
\(504\) | 6.02671 | − | 4.45797i | 0.268451 | − | 0.198574i | ||||
\(505\) | −29.8319 | − | 29.8319i | −1.32750 | − | 1.32750i | ||||
\(506\) | 7.13626 | 0.317245 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.6936 | 0.474451 | ||||||||
\(509\) | 0.724506 | + | 0.724506i | 0.0321132 | + | 0.0321132i | 0.722981 | − | 0.690868i | \(-0.242771\pi\) |
−0.690868 | + | 0.722981i | \(0.742771\pi\) | |||||||
\(510\) | 10.2356 | + | 31.0492i | 0.453240 | + | 1.37488i | ||||
\(511\) | − | 8.09219i | − | 0.357978i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.84558 | − | 16.5852i | −0.125635 | − | 0.732257i | ||||
\(514\) | 21.2381 | + | 21.2381i | 0.936773 | + | 0.936773i | ||||
\(515\) | −4.91715 | + | 4.91715i | −0.216676 | + | 0.216676i | ||||
\(516\) | 0.365773 | − | 0.120580i | 0.0161022 | − | 0.00530823i | ||||
\(517\) | 16.6014i | 0.730128i | ||||||||
\(518\) | 7.63834 | − | 7.63834i | 0.335610 | − | 0.335610i | ||||
\(519\) | 3.05085 | − | 1.00574i | 0.133917 | − | 0.0441469i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.5279i | 1.03078i | 0.856957 | + | 0.515388i | \(0.172352\pi\) | ||||
−0.856957 | + | 0.515388i | \(0.827648\pi\) | |||||||
\(522\) | 2.06544 | − | 13.8044i | 0.0904020 | − | 0.604202i | ||||
\(523\) | −6.09219 | −0.266393 | −0.133197 | − | 0.991090i | \(-0.542524\pi\) | ||||
−0.133197 | + | 0.991090i | \(0.542524\pi\) | |||||||
\(524\) | 0.264467 | 0.0115533 | ||||||||
\(525\) | 11.3467 | − | 22.5067i | 0.495209 | − | 0.982272i | ||||
\(526\) | −13.1598 | + | 13.1598i | −0.573794 | + | 0.573794i | ||||
\(527\) | −21.9377 | + | 21.9377i | −0.955622 | + | 0.955622i | ||||
\(528\) | −1.19593 | + | 2.37220i | −0.0520463 | + | 0.103237i | ||||
\(529\) | −1.35252 | −0.0588053 | ||||||||
\(530\) | 36.0869 | 1.56752 | ||||||||
\(531\) | 2.92098 | − | 19.5224i | 0.126760 | − | 0.847198i | ||||
\(532\) | − | 8.09219i | − | 0.350841i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.9159 | − | 4.91715i | 0.645475 | − | 0.212786i | ||||
\(535\) | 5.04610 | − | 5.04610i | 0.218162 | − | 0.218162i | ||||
\(536\) | 0.754898i | 0.0326066i | ||||||||
\(537\) | −0.435041 | + | 0.143415i | −0.0187734 | + | 0.00618880i | ||||
\(538\) | 0.579890 | − | 0.579890i | 0.0250008 | − | 0.0250008i | ||||
\(539\) | 0.820089 | + | 0.820089i | 0.0353237 | + | 0.0353237i | ||||
\(540\) | 2.89081 | + | 16.8489i | 0.124401 | + | 0.725060i | ||||
\(541\) | −14.5477 | − | 14.5477i | −0.625453 | − | 0.625453i | 0.321468 | − | 0.946920i | \(-0.395824\pi\) |
−0.946920 | + | 0.321468i | \(0.895824\pi\) | |||||||
\(542\) | − | 13.9429i | − | 0.598897i | ||||||
\(543\) | 4.39987 | + | 13.3468i | 0.188817 | + | 0.572765i | ||||
\(544\) | −4.05684 | − | 4.05684i | −0.173936 | − | 0.173936i | ||||
\(545\) | 11.5245 | 0.493654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1302 | 0.689676 | 0.344838 | − | 0.938662i | \(-0.387934\pi\) | ||||
0.344838 | + | 0.938662i | \(0.387934\pi\) | |||||||
\(548\) | −3.66371 | − | 3.66371i | −0.156506 | − | 0.156506i | ||||
\(549\) | 7.39862 | − | 5.47277i | 0.315765 | − | 0.233572i | ||||
\(550\) | 8.93241i | 0.380879i | ||||||||
\(551\) | −10.6544 | − | 10.6544i | −0.453892 | − | 0.453892i | ||||
\(552\) | −3.62780 | + | 7.19593i | −0.154410 | + | 0.306279i | ||||
\(553\) | 24.9374 | + | 24.9374i | 1.06045 | + | 1.06045i | ||||
\(554\) | 12.2946 | − | 12.2946i | 0.522346 | − | 0.522346i | ||||
\(555\) | 7.71256 | + | 23.3957i | 0.327380 | + | 0.993090i | ||||
\(556\) | 2.22236i | 0.0942490i | ||||||||
\(557\) | −6.66457 | + | 6.66457i | −0.282387 | + | 0.282387i | −0.834060 | − | 0.551673i | \(-0.813989\pi\) |
0.551673 | + | 0.834060i | \(0.313989\pi\) | |||||||
\(558\) | −13.0424 | + | 9.64748i | −0.552128 | + | 0.408410i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.22081i | 0.347393i | ||||||||
\(561\) | −6.86136 | + | 13.6099i | −0.289687 | + | 0.574609i | ||||
\(562\) | −19.1598 | −0.808207 | ||||||||
\(563\) | −41.2952 | −1.74039 | −0.870193 | − | 0.492710i | \(-0.836006\pi\) | ||||
−0.870193 | + | 0.492710i | \(0.836006\pi\) | |||||||
\(564\) | −16.7402 | − | 8.43952i | −0.704890 | − | 0.355368i | ||||
\(565\) | 36.3411 | − | 36.3411i | 1.52888 | − | 1.52888i | ||||
\(566\) | 12.4787 | − | 12.4787i | 0.524517 | − | 0.524517i | ||||
\(567\) | 19.8601 | − | 10.5513i | 0.834045 | − | 0.443111i | ||||
\(568\) | 7.75615 | 0.325441 | ||||||||
\(569\) | 9.35536 | 0.392197 | 0.196099 | − | 0.980584i | \(-0.437173\pi\) | ||||
0.196099 | + | 0.980584i | \(0.437173\pi\) | |||||||
\(570\) | 16.4783 | + | 8.30747i | 0.690200 | + | 0.347962i | ||||
\(571\) | − | 9.96203i | − | 0.416898i | −0.978033 | − | 0.208449i | \(-0.933158\pi\) | ||
0.978033 | − | 0.208449i | \(-0.0668415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.74541 | − | 26.5287i | −0.365345 | − | 1.10825i | ||||
\(574\) | 1.02461 | − | 1.02461i | 0.0427662 | − | 0.0427662i | ||||
\(575\) | 27.0960i | 1.12998i | ||||||||
\(576\) | −1.78406 | − | 2.41187i | −0.0743360 | − | 0.100495i | ||||
\(577\) | −25.8022 | + | 25.8022i | −1.07416 | + | 1.07416i | −0.0771415 | + | 0.997020i | \(0.524579\pi\) |
−0.997020 | + | 0.0771415i | \(0.975421\pi\) | |||||||
\(578\) | −11.2543 | − | 11.2543i | −0.468116 | − | 0.468116i | ||||
\(579\) | −5.54204 | − | 2.79400i | −0.230319 | − | 0.116115i | ||||
\(580\) | 10.8237 | + | 10.8237i | 0.449431 | + | 0.449431i | ||||
\(581\) | − | 4.94384i | − | 0.205105i | ||||||
\(582\) | 26.9388 | − | 8.88058i | 1.11665 | − | 0.368112i | ||||
\(583\) | 11.8963 | + | 11.8963i | 0.492696 | + | 0.492696i | ||||
\(584\) | −3.23847 | −0.134009 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.8698 | 0.903435 | ||||||||
\(587\) | 20.5387 | + | 20.5387i | 0.847723 | + | 0.847723i | 0.989849 | − | 0.142126i | \(-0.0453938\pi\) |
−0.142126 | + | 0.989849i | \(0.545394\pi\) | |||||||
\(588\) | −1.24385 | + | 0.410044i | −0.0512954 | + | 0.0169099i | ||||
\(589\) | 17.5123i | 0.721582i | ||||||||
\(590\) | 15.3071 | + | 15.3071i | 0.630182 | + | 0.630182i | ||||
\(591\) | 9.83268 | + | 4.95711i | 0.404463 | + | 0.203908i | ||||
\(592\) | −3.05684 | − | 3.05684i | −0.125635 | − | 0.125635i | ||||
\(593\) | −23.9379 | + | 23.9379i | −0.983013 | + | 0.983013i | −0.999858 | − | 0.0168449i | \(-0.994638\pi\) |
0.0168449 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(594\) | −4.60138 | + | 6.50733i | −0.188797 | + | 0.266999i | ||||
\(595\) | 47.1648i | 1.93357i | ||||||||
\(596\) | −6.41175 | + | 6.41175i | −0.262636 | + | 0.262636i | ||||
\(597\) | 12.5474 | + | 38.0619i | 0.513530 | + | 1.55777i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.0774i | 1.67838i | 0.543841 | + | 0.839188i | \(0.316969\pi\) | ||||
−0.543841 | + | 0.839188i | \(0.683031\pi\) | |||||||
\(600\) | −9.00711 | − | 4.54090i | −0.367714 | − | 0.185382i | ||||
\(601\) | −32.0265 | −1.30639 | −0.653194 | − | 0.757191i | \(-0.726571\pi\) | ||||
−0.653194 | + | 0.757191i | \(0.726571\pi\) | |||||||
\(602\) | 0.555621 | 0.0226454 | ||||||||
\(603\) | −0.335118 | + | 2.23976i | −0.0136471 | + | 0.0912102i | ||||
\(604\) | 0.812993 | − | 0.812993i | 0.0330802 | − | 0.0330802i | ||||
\(605\) | 20.1170 | − | 20.1170i | 0.817872 | − | 0.817872i | ||||
\(606\) | 19.8331 | + | 9.99878i | 0.805664 | + | 0.406173i | ||||
\(607\) | 32.9424 | 1.33709 | 0.668546 | − | 0.743671i | \(-0.266917\pi\) | ||||
0.668546 | + | 0.743671i | \(0.266917\pi\) | |||||||
\(608\) | −3.23847 | −0.131337 | ||||||||
\(609\) | 9.06505 | − | 17.9810i | 0.367334 | − | 0.728626i | ||||
\(610\) | 10.0922i | 0.408621i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −10.2356 | − | 13.8375i | −0.413750 | − | 0.559347i | ||||
\(613\) | −18.0296 | + | 18.0296i | −0.728209 | + | 0.728209i | −0.970263 | − | 0.242054i | \(-0.922179\pi\) |
0.242054 | + | 0.970263i | \(0.422179\pi\) | |||||||
\(614\) | − | 29.5144i | − | 1.19110i | ||||||
\(615\) | 1.03456 | + | 3.13829i | 0.0417175 | + | 0.126548i | ||||
\(616\) | −2.71005 | + | 2.71005i | −0.109191 | + | 0.109191i | ||||
\(617\) | −3.10809 | − | 3.10809i | −0.125127 | − | 0.125127i | 0.641770 | − | 0.766897i | \(-0.278200\pi\) |
−0.766897 | + | 0.641770i | \(0.778200\pi\) | |||||||
\(618\) | 1.64809 | − | 3.26906i | 0.0662958 | − | 0.131501i | ||||
\(619\) | 14.3114 | + | 14.3114i | 0.575225 | + | 0.575225i | 0.933584 | − | 0.358359i | \(-0.116664\pi\) |
−0.358359 | + | 0.933584i | \(0.616664\pi\) | |||||||
\(620\) | − | 17.7907i | − | 0.714490i | ||||||
\(621\) | −13.9581 | + | 19.7397i | −0.560117 | + | 0.792126i | ||||
\(622\) | 11.0461 | + | 11.0461i | 0.442908 | + | 0.442908i | ||||
\(623\) | 22.6578 | 0.907766 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.2028 | 0.808110 | ||||||||
\(626\) | −12.3062 | − | 12.3062i | −0.491856 | − | 0.491856i | ||||
\(627\) | 2.69357 | + | 8.17082i | 0.107571 | + | 0.326311i | ||||
\(628\) | 8.09219i | 0.322914i | ||||||||
\(629\) | −17.5378 | − | 17.5378i | −0.699279 | − | 0.699279i | ||||
\(630\) | −3.64942 | + | 24.3909i | −0.145397 | + | 0.971758i | ||||
\(631\) | 12.8130 | + | 12.8130i | 0.510077 | + | 0.510077i | 0.914550 | − | 0.404473i | \(-0.132545\pi\) |
−0.404473 | + | 0.914550i | \(0.632545\pi\) | |||||||
\(632\) | 9.97988 | − | 9.97988i | 0.396978 | − | 0.396978i | ||||
\(633\) | −25.1515 | + | 8.29140i | −0.999684 | + | 0.329554i | ||||
\(634\) | − | 4.09219i | − | 0.162522i | ||||||
\(635\) | −24.8769 | + | 24.8769i | −0.987210 | + | 0.987210i | ||||
\(636\) | −18.0435 | + | 5.94817i | −0.715470 | + | 0.235860i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.13626i | 0.282527i | ||||||||
\(639\) | 23.0123 | + | 3.44315i | 0.910352 | + | 0.136209i | ||||
\(640\) | 3.28995 | 0.130046 | ||||||||
\(641\) | 13.1147 | 0.517998 | 0.258999 | − | 0.965878i | \(-0.416607\pi\) | ||||
0.258999 | + | 0.965878i | \(0.416607\pi\) | |||||||
\(642\) | −1.69131 | + | 3.35479i | −0.0667505 | + | 0.132403i | ||||
\(643\) | 5.60138 | − | 5.60138i | 0.220897 | − | 0.220897i | −0.587979 | − | 0.808876i | \(-0.700076\pi\) |
0.808876 | + | 0.587979i | \(0.200076\pi\) | |||||||
\(644\) | −8.22081 | + | 8.22081i | −0.323945 | + | 0.323945i | ||||
\(645\) | −0.570403 | + | 1.13142i | −0.0224596 | + | 0.0445497i | ||||
\(646\) | −18.5799 | −0.731016 | ||||||||
\(647\) | −11.4745 | −0.451108 | −0.225554 | − | 0.974231i | \(-0.572419\pi\) | ||||
−0.225554 | + | 0.974231i | \(0.572419\pi\) | |||||||
\(648\) | −4.22258 | − | 7.94794i | −0.165879 | − | 0.312225i | ||||
\(649\) | 10.0922i | 0.396153i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.2274 | + | 7.32742i | −0.871159 | + | 0.287184i | ||||
\(652\) | 17.2274 | − | 17.2274i | 0.674676 | − | 0.674676i | ||||
\(653\) | − | 12.1946i | − | 0.477211i | −0.971117 | − | 0.238605i | \(-0.923310\pi\) | ||
0.971117 | − | 0.238605i | \(-0.0766903\pi\) | |||||||
\(654\) | −5.76224 | + | 1.89957i | −0.225321 | + | 0.0742789i | ||||
\(655\) | −0.615242 | + | 0.615242i | −0.0240395 | + | 0.0240395i | ||||
\(656\) | −0.410044 | − | 0.410044i | −0.0160095 | − | 0.0160095i | ||||
\(657\) | −9.60846 | − | 1.43764i | −0.374862 | − | 0.0560876i | ||||
\(658\) | −19.1244 | − | 19.1244i | −0.745548 | − | 0.745548i | ||||
\(659\) | − | 31.9632i | − | 1.24511i | −0.782577 | − | 0.622554i | \(-0.786095\pi\) | ||
0.782577 | − | 0.622554i | \(-0.213905\pi\) | |||||||
\(660\) | −2.73639 | − | 8.30069i | −0.106514 | − | 0.323104i | ||||
\(661\) | 12.2470 | + | 12.2470i | 0.476352 | + | 0.476352i | 0.903963 | − | 0.427611i | \(-0.140645\pi\) |
−0.427611 | + | 0.903963i | \(0.640645\pi\) | |||||||
\(662\) | 2.92401 | 0.113645 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.97851 | −0.0767811 | ||||||||
\(665\) | 18.8252 | + | 18.8252i | 0.730010 | + | 0.730010i | ||||
\(666\) | −7.71256 | − | 10.4266i | −0.298856 | − | 0.404022i | ||||
\(667\) | 21.6475i | 0.838194i | ||||||||
\(668\) | −6.82180 | − | 6.82180i | −0.263943 | − | 0.263943i | ||||
\(669\) | −3.63965 | + | 7.21944i | −0.140717 | + | 0.279120i | ||||
\(670\) | −1.75615 | − | 1.75615i | −0.0678461 | − | 0.0678461i | ||||
\(671\) | −3.32697 | + | 3.32697i | −0.128436 | + | 0.128436i | ||||
\(672\) | −1.35503 | − | 4.11041i | −0.0522713 | − | 0.158562i | ||||
\(673\) | − | 41.8483i | − | 1.61314i | −0.591142 | − | 0.806568i | \(-0.701323\pi\) | ||
0.591142 | − | 0.806568i | \(-0.298677\pi\) | |||||||
\(674\) | 14.5405 | − | 14.5405i | 0.560080 | − | 0.560080i | ||||
\(675\) | −24.7080 | − | 17.4712i | −0.951013 | − | 0.672467i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.9360i | 0.612470i | 0.951956 | + | 0.306235i | \(0.0990694\pi\) | ||||
−0.951956 | + | 0.306235i | \(0.900931\pi\) | |||||||
\(678\) | −12.1805 | + | 24.1606i | −0.467788 | + | 0.927881i | ||||
\(679\) | 40.9209 | 1.57040 | ||||||||
\(680\) | 18.8752 | 0.723831 | ||||||||
\(681\) | 9.48878 | + | 4.78374i | 0.363611 | + | 0.183313i | ||||
\(682\) | 5.86483 | − | 5.86483i | 0.224576 | − | 0.224576i | ||||
\(683\) | 23.5279 | − | 23.5279i | 0.900270 | − | 0.900270i | −0.0951894 | − | 0.995459i | \(-0.530346\pi\) |
0.995459 | + | 0.0951894i | \(0.0303457\pi\) | |||||||
\(684\) | −9.60846 | − | 1.43764i | −0.367389 | − | 0.0549695i | ||||
\(685\) | 17.0461 | 0.651298 | ||||||||
\(686\) | −19.3808 | −0.739964 | ||||||||
\(687\) | 5.41771 | + | 2.73132i | 0.206699 | + | 0.104206i | ||||
\(688\) | − | 0.222358i | − | 0.00847732i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.30069 | − | 25.1797i | −0.316002 | − | 0.958576i | ||||
\(691\) | −14.1763 | + | 14.1763i | −0.539290 | + | 0.539290i | −0.923321 | − | 0.384030i | \(-0.874536\pi\) |
0.384030 | + | 0.923321i | \(0.374536\pi\) | |||||||
\(692\) | − | 1.85465i | − | 0.0705032i | ||||||
\(693\) | −9.24372 | + | 6.83760i | −0.351140 | + | 0.259739i | ||||
\(694\) | −1.92668 | + | 1.92668i | −0.0731357 | + | 0.0731357i | ||||
\(695\) | −5.16997 | − | 5.16997i | −0.196108 | − | 0.196108i | ||||
\(696\) | −7.19593 | − | 3.62780i | −0.272761 | − | 0.137512i | ||||
\(697\) | −2.35252 | − | 2.35252i | −0.0891082 | − | 0.0891082i | ||||
\(698\) | 30.5990i | 1.15819i | ||||||||
\(699\) | −19.8275 | + | 6.53630i | −0.749946 | + | 0.247226i | ||||
\(700\) | −10.2899 | − | 10.2899i | −0.388923 | − | 0.388923i | ||||
\(701\) | 22.9723 | 0.867651 | 0.433825 | − | 0.900997i | \(-0.357163\pi\) | ||||
0.433825 | + | 0.900997i | \(0.357163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 1.08456 | + | 1.08456i | 0.0408757 | + | 0.0408757i | ||||
\(705\) | 58.5767 | − | 19.3102i | 2.20612 | − | 0.727266i | ||||
\(706\) | 2.11368i | 0.0795495i | ||||||||
\(707\) | 22.6578 | + | 22.6578i | 0.852135 | + | 0.852135i | ||||
\(708\) | −10.1766 | − | 5.13049i | −0.382460 | − | 0.192816i | ||||
\(709\) | 3.10867 | + | 3.10867i | 0.116749 | + | 0.116749i | 0.763068 | − | 0.646319i | \(-0.223692\pi\) |
−0.646319 | + | 0.763068i | \(0.723692\pi\) | |||||||
\(710\) | −18.0435 | + | 18.0435i | −0.677159 | + | 0.677159i | ||||
\(711\) | 34.0404 | − | 25.1797i | 1.27661 | − | 0.944313i | ||||
\(712\) | − | 9.06759i | − | 0.339822i | ||||||
\(713\) | 17.7907 | − | 17.7907i | 0.666265 | − | 0.666265i | ||||
\(714\) | −7.77412 | − | 23.5824i | −0.290939 | − | 0.882549i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.264467i | 0.00988361i | ||||||||
\(717\) | −32.3490 | − | 16.3086i | −1.20810 | − | 0.609057i | ||||
\(718\) | −0.444716 | −0.0165967 | ||||||||
\(719\) | 8.46197 | 0.315578 | 0.157789 | − | 0.987473i | \(-0.449563\pi\) | ||||
0.157789 | + | 0.987473i | \(0.449563\pi\) | |||||||
\(720\) | 9.76118 | + | 1.46049i | 0.363778 | + | 0.0544292i | ||||
\(721\) | 3.73466 | − | 3.73466i | 0.139086 | − | 0.139086i | ||||
\(722\) | 6.01911 | − | 6.01911i | 0.224008 | − | 0.224008i | ||||
\(723\) | −27.0828 | − | 13.6537i | −1.00722 | − | 0.507787i | ||||
\(724\) | 8.11368 | 0.301543 | ||||||||
\(725\) | −27.0960 | −1.00632 | ||||||||
\(726\) | −6.74264 | + | 13.3744i | −0.250243 | + | 0.496369i | ||||
\(727\) | 13.0461i | 0.483853i | 0.970295 | + | 0.241926i | \(0.0777793\pi\) | ||||
−0.970295 | + | 0.241926i | \(0.922221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.00000 | − | 25.4558i | −0.333333 | − | 0.942809i | ||||
\(730\) | 7.53379 | − | 7.53379i | 0.278838 | − | 0.278838i | ||||
\(731\) | − | 1.27572i | − | 0.0471842i | ||||||
\(732\) | −1.66348 | − | 5.04610i | −0.0614842 | − | 0.186509i | ||||
\(733\) | 14.8180 | − | 14.8180i | 0.547315 | − | 0.547315i | −0.378348 | − | 0.925663i | \(-0.623508\pi\) |
0.925663 | + | 0.378348i | \(0.123508\pi\) | |||||||
\(734\) | −14.8818 | − | 14.8818i | −0.549299 | − | 0.549299i | ||||
\(735\) | 1.93971 | − | 3.84752i | 0.0715474 | − | 0.141918i | ||||
\(736\) | 3.28995 | + | 3.28995i | 0.121269 | + | 0.121269i | ||||
\(737\) | − | 1.15786i | − | 0.0426502i | ||||||
\(738\) | −1.03456 | − | 1.39862i | −0.0380827 | − | 0.0514839i | ||||
\(739\) | 15.9159 | + | 15.9159i | 0.585477 | + | 0.585477i | 0.936403 | − | 0.350926i | \(-0.114133\pi\) |
−0.350926 | + | 0.936403i | \(0.614133\pi\) | |||||||
\(740\) | 14.2225 | 0.522830 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.4086 | −1.00620 | ||||||||
\(743\) | −12.3062 | − | 12.3062i | −0.451472 | − | 0.451472i | 0.444371 | − | 0.895843i | \(-0.353427\pi\) |
−0.895843 | + | 0.444371i | \(0.853427\pi\) | |||||||
\(744\) | 2.93241 | + | 8.89533i | 0.107507 | + | 0.326118i | ||||
\(745\) | − | 29.8319i | − | 1.09295i | ||||||
\(746\) | 2.98920 | + | 2.98920i | 0.109442 | + | 0.109442i | ||||
\(747\) | −5.87018 | − | 0.878310i | −0.214779 | − | 0.0321357i | ||||
\(748\) | 6.22236 | + | 6.22236i | 0.227512 | + | 0.227512i | ||||
\(749\) | −3.83260 | + | 3.83260i | −0.140040 | + | 0.140040i | ||||
\(750\) | 4.45797 | − | 1.46960i | 0.162782 | − | 0.0536623i | ||||
\(751\) | − | 6.71506i | − | 0.245036i | −0.992466 | − | 0.122518i | \(-0.960903\pi\) | ||
0.992466 | − | 0.122518i | \(-0.0390970\pi\) | |||||||
\(752\) | −7.65354 | + | 7.65354i | −0.279096 | + | 0.279096i | ||||
\(753\) | −20.2242 | + | 6.66707i | −0.737012 | + | 0.242962i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.78260i | 0.137663i | ||||||||
\(756\) | −2.19562 | − | 12.7970i | −0.0798538 | − | 0.465422i | ||||
\(757\) | −35.1813 | −1.27869 | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(758\) | −25.6818 | −0.932805 | ||||||||
\(759\) | 5.56430 | − | 11.0371i | 0.201971 | − | 0.400621i | ||||
\(760\) | 7.53379 | − | 7.53379i | 0.273279 | − | 0.273279i | ||||
\(761\) | −25.5514 | + | 25.5514i | −0.926238 | + | 0.926238i | −0.997460 | − | 0.0712220i | \(-0.977310\pi\) |
0.0712220 | + | 0.997460i | \(0.477310\pi\) | |||||||
\(762\) | 8.33802 | − | 16.5389i | 0.302055 | − | 0.599141i | ||||
\(763\) | −8.75304 | −0.316881 | ||||||||
\(764\) | −16.1272 | −0.583460 | ||||||||
\(765\) | 56.0022 | + | 8.37918i | 2.02477 | + | 0.302950i | ||||
\(766\) | 27.4958i | 0.993464i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.64497 | + | 0.542278i | −0.0593578 | + | 0.0195678i | ||||
\(769\) | 36.1433 | − | 36.1433i | 1.30336 | − | 1.30336i | 0.377249 | − | 0.926112i | \(-0.376870\pi\) |
0.926112 | − | 0.377249i | \(-0.123130\pi\) | |||||||
\(770\) | − | 12.6090i | − | 0.454398i | ||||||
\(771\) | 49.4071 | − | 16.2874i | 1.77935 | − | 0.586578i | ||||
\(772\) | −2.53379 | + | 2.53379i | −0.0911932 | + | 0.0911932i | ||||
\(773\) | −32.0971 | − | 32.0971i | −1.15445 | − | 1.15445i | −0.985650 | − | 0.168803i | \(-0.946010\pi\) |
−0.168803 | − | 0.985650i | \(-0.553990\pi\) | |||||||
\(774\) | 0.0987103 | − | 0.659730i | 0.00354807 | − | 0.0237135i | ||||
\(775\) | 22.2685 | + | 22.2685i | 0.799907 | + | 0.799907i | ||||
\(776\) | − | 16.3764i | − | 0.587880i | ||||||
\(777\) | −5.85782 | − | 17.7694i | −0.210148 | − | 0.637474i | ||||
\(778\) | 1.53379 | + | 1.53379i | 0.0549892 | + | 0.0549892i | ||||
\(779\) | −1.87796 | −0.0672848 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.8963 | −0.425684 | ||||||||
\(782\) | 18.8752 | + | 18.8752i | 0.674976 | + | 0.674976i | ||||
\(783\) | −19.7397 | − | 13.9581i | −0.705438 | − | 0.498820i | ||||
\(784\) | 0.756152i | 0.0270054i | ||||||||
\(785\) | −18.8252 | − | 18.8252i | −0.671901 | − | 0.671901i | ||||
\(786\) | 0.206211 | − | 0.409030i | 0.00735531 | − | 0.0145896i | ||||
\(787\) | −14.7562 | − | 14.7562i | −0.526000 | − | 0.526000i | 0.393377 | − | 0.919377i | \(-0.371307\pi\) |
−0.919377 | + | 0.393377i | \(0.871307\pi\) | |||||||
\(788\) | 4.49545 | − | 4.49545i | 0.160144 | − | 0.160144i | ||||
\(789\) | 10.0922 | + | 30.6142i | 0.359292 | + | 1.08989i | ||||
\(790\) | 46.4332i | 1.65202i | ||||||||
\(791\) | −27.6016 | + | 27.6016i | −0.981402 | + | 0.981402i | ||||
\(792\) | 2.73639 | + | 3.69931i | 0.0972333 | + | 0.131449i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 14.5218i | 0.515359i | ||||||||
\(795\) | 28.1378 | − | 55.8128i | 0.997945 | − | 1.97947i | ||||
\(796\) | 23.1383 | 0.820115 | ||||||||
\(797\) | 34.0411 | 1.20580 | 0.602899 | − | 0.797817i | \(-0.294012\pi\) | ||||
0.602899 | + | 0.797817i | \(0.294012\pi\) | |||||||
\(798\) | −12.5155 | − | 6.30967i | −0.443045 | − | 0.223360i | ||||
\(799\) | −43.9102 | + | 43.9102i | −1.55343 | + | 1.55343i | ||||
\(800\) | −4.11801 | + | 4.11801i | −0.145593 | + | 0.145593i | ||||
\(801\) | 4.02533 | − | 26.9033i | 0.142228 | − | 0.950581i | ||||
\(802\) | −8.24886 | −0.291277 | ||||||||
\(803\) | 4.96715 | 0.175287 | ||||||||
\(804\) | 1.16754 | + | 0.588611i | 0.0411760 | + | 0.0207587i | ||||
\(805\) | − | 38.2489i | − | 1.34810i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.444716 | − | 1.34902i | −0.0156547 | − | 0.0474879i | ||||
\(808\) | 9.06759 | − | 9.06759i | 0.318997 | − | 0.318997i | ||||
\(809\) | − | 19.8186i | − | 0.696785i | −0.937349 | − | 0.348392i | \(-0.886728\pi\) | ||
0.937349 | − | 0.348392i | \(-0.113272\pi\) | |||||||
\(810\) | 28.3128 | + | 8.66646i | 0.994811 | + | 0.304508i | ||||
\(811\) | −25.0265 | + | 25.0265i | −0.878799 | + | 0.878799i | −0.993410 | − | 0.114611i | \(-0.963438\pi\) |
0.114611 | + | 0.993410i | \(0.463438\pi\) | |||||||
\(812\) | −8.22081 | − | 8.22081i | −0.288494 | − | 0.288494i | ||||
\(813\) | −21.5643 | − | 10.8716i | −0.756293 | − | 0.381282i | ||||
\(814\) | 4.68856 | + | 4.68856i | 0.164334 | + | 0.164334i | ||||
\(815\) | 80.1535i | 2.80766i | ||||||||
\(816\) | −9.43760 | + | 3.11118i | −0.330382 | + | 0.108913i | ||||
\(817\) | −0.509187 | − | 0.509187i | −0.0178142 | − | 0.0178142i | ||||
\(818\) | −9.37056 | −0.327634 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.90781 | 0.0666235 | ||||||||
\(821\) | −5.31554 | − | 5.31554i | −0.185514 | − | 0.185514i | 0.608240 | − | 0.793753i | \(-0.291876\pi\) |
−0.793753 | + | 0.608240i | \(0.791876\pi\) | |||||||
\(822\) | −8.52305 | + | 2.80969i | −0.297275 | + | 0.0979991i | ||||
\(823\) | 54.4118i | 1.89667i | 0.317264 | + | 0.948337i | \(0.397236\pi\) | ||||
−0.317264 | + | 0.948337i | \(0.602764\pi\) | |||||||
\(824\) | −1.49460 | − | 1.49460i | −0.0520669 | − | 0.0520669i | ||||
\(825\) | 13.8150 | + | 6.96481i | 0.480978 | + | 0.242483i | ||||
\(826\) | −11.6260 | − | 11.6260i | −0.404520 | − | 0.404520i | ||||
\(827\) | 19.6453 | − | 19.6453i | 0.683134 | − | 0.683134i | −0.277571 | − | 0.960705i | \(-0.589529\pi\) |
0.960705 | + | 0.277571i | \(0.0895294\pi\) | |||||||
\(828\) | 8.30069 | + | 11.2217i | 0.288469 | + | 0.389980i | ||||
\(829\) | − | 0.248858i | − | 0.00864320i | −0.999991 | − | 0.00432160i | \(-0.998624\pi\) | ||
0.999991 | − | 0.00432160i | \(-0.00137561\pi\) | |||||||
\(830\) | 4.60269 | − | 4.60269i | 0.159762 | − | 0.159762i | ||||
\(831\) | −9.42867 | − | 28.6014i | −0.327077 | − | 0.992171i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.33822i | 0.150311i | ||||||||
\(834\) | 3.43714 | + | 1.73282i | 0.119019 | + | 0.0600028i | ||||
\(835\) | 31.7397 | 1.09840 | ||||||||
\(836\) | 4.96715 | 0.171792 | ||||||||
\(837\) | 4.75153 | + | 27.6940i | 0.164237 | + | 0.957243i | ||||
\(838\) | 5.94817 | − | 5.94817i | 0.205476 | − | 0.205476i | ||||
\(839\) | −6.29286 | + | 6.29286i | −0.217254 | + | 0.217254i | −0.807340 | − | 0.590086i | \(-0.799094\pi\) |
0.590086 | + | 0.807340i | \(0.299094\pi\) | |||||||
\(840\) | 12.7145 | + | 6.40996i | 0.438691 | + | 0.221165i | ||||
\(841\) | 7.35252 | 0.253535 | ||||||||
\(842\) | −1.36422 | −0.0470141 | ||||||||
\(843\) | −14.9393 | + | 29.6329i | −0.514537 | + | 1.02061i | ||||
\(844\) | 15.2899i | 0.526302i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.1054 | + | 19.3102i | −0.897524 | + | 0.663900i | ||||
\(847\) | −15.2792 | + | 15.2792i | −0.525000 | + | 0.525000i | ||||
\(848\) | 10.9689i | 0.376672i | ||||||||
\(849\) | −9.56984 | − | 29.0296i | −0.328436 | − | 0.996294i | ||||
\(850\) | −23.6260 | + | 23.6260i | −0.810365 | + | 0.810365i | ||||
\(851\) | 14.2225 | + | 14.2225i | 0.487542 | + | 0.487542i | ||||
\(852\) | 6.04765 | − | 11.9958i | 0.207189 | − | 0.410970i | ||||
\(853\) | −26.2596 | − | 26.2596i | −0.899112 | − | 0.899112i | 0.0962459 | − | 0.995358i | \(-0.469316\pi\) |
−0.995358 | + | 0.0962459i | \(0.969316\pi\) | |||||||
\(854\) | − | 7.66519i | − | 0.262297i | ||||||
\(855\) | 25.6970 | − | 19.0081i | 0.878819 | − | 0.650064i | ||||
\(856\) | 1.53379 | + | 1.53379i | 0.0524240 | + | 0.0524240i | ||||
\(857\) | −48.8871 | −1.66995 | −0.834976 | − | 0.550286i | \(-0.814519\pi\) | ||||
−0.834976 | + | 0.550286i | \(0.814519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6905 | −0.398873 | −0.199437 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199437 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(860\) | 0.517281 | + | 0.517281i | 0.0176391 | + | 0.0176391i | ||||
\(861\) | −0.785767 | − | 2.38358i | −0.0267789 | − | 0.0812323i | ||||
\(862\) | − | 35.9835i | − | 1.22560i | ||||||
\(863\) | 41.0424 | + | 41.0424i | 1.39710 | + | 1.39710i | 0.808221 | + | 0.588879i | \(0.200431\pi\) |
0.588879 | + | 0.808221i | \(0.299569\pi\) | |||||||
\(864\) | −5.12132 | + | 0.878680i | −0.174231 | + | 0.0298933i | ||||
\(865\) | 4.31455 | + | 4.31455i | 0.146699 | + | 0.146699i | ||||
\(866\) | −28.0537 | + | 28.0537i | −0.953305 | + | 0.953305i | ||||
\(867\) | −26.1813 | + | 8.63086i | −0.889163 | + | 0.293119i | ||||
\(868\) | 13.5123i | 0.458637i | ||||||||
\(869\) | −15.3071 | + | 15.3071i | −0.519257 | + | 0.519257i | ||||
\(870\) | 25.1797 | − | 8.30069i | 0.853673 | − | 0.281420i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.50294i | 0.118624i | ||||||||
\(873\) | 7.26991 | − | 48.5885i | 0.246049 | − | 1.64447i | ||||
\(874\) | 15.0676 | 0.509669 | ||||||||
\(875\) | 6.77180 | 0.228929 | ||||||||
\(876\) | −2.52511 | + | 5.00868i | −0.0853156 | + | 0.169228i | ||||
\(877\) | −12.3518 | + | 12.3518i | −0.417091 | + | 0.417091i | −0.884200 | − | 0.467109i | \(-0.845296\pi\) |
0.467109 | + | 0.884200i | \(0.345296\pi\) | |||||||
\(878\) | −12.7279 | + | 12.7279i | −0.429547 | + | 0.429547i | ||||
\(879\) | 17.0524 | − | 33.8243i | 0.575164 | − | 1.14087i | ||||
\(880\) | −5.04610 | −0.170104 | ||||||||
\(881\) | 26.2259 | 0.883574 | 0.441787 | − | 0.897120i | \(-0.354345\pi\) | ||||
0.441787 | + | 0.897120i | \(0.354345\pi\) | |||||||
\(882\) | −0.335675 | + | 2.24348i | −0.0113028 | + | 0.0755419i | ||||
\(883\) | 39.6095i | 1.33297i | 0.745520 | + | 0.666483i | \(0.232201\pi\) | ||||
−0.745520 | + | 0.666483i | \(0.767799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 35.6095 | − | 11.7389i | 1.19700 | − | 0.394600i | ||||
\(886\) | −22.6203 | + | 22.6203i | −0.759942 | + | 0.759942i | ||||
\(887\) | − | 9.11420i | − | 0.306025i | −0.988224 | − | 0.153013i | \(-0.951103\pi\) | ||
0.988224 | − | 0.153013i | \(-0.0488975\pi\) | |||||||
\(888\) | −7.11126 | + | 2.34428i | −0.238638 | + | 0.0786690i | ||||
\(889\) | 18.8944 | − | 18.8944i | 0.633699 | − | 0.633699i | ||||
\(890\) | 21.0943 | + | 21.0943i | 0.707083 | + | 0.707083i | ||||
\(891\) | 6.47657 | + | 12.1905i | 0.216973 | + | 0.408397i | ||||
\(892\) | 3.30069 | + | 3.30069i | 0.110515 | + | 0.110515i | ||||
\(893\) | 35.0524i | 1.17298i | ||||||||
\(894\) | 4.91715 | + | 14.9159i | 0.164454 | + | 0.498863i | ||||
\(895\) | −0.615242 | − | 0.615242i | −0.0205653 | − | 0.0205653i | ||||
\(896\) | −2.49877 | −0.0834780 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.42323 | −0.281087 | ||||||||
\(899\) | 17.7907 | + | 17.7907i | 0.593351 | + | 0.593351i | ||||
\(900\) | −14.0461 | + | 10.3899i | −0.468203 | + | 0.346331i | ||||
\(901\) | 62.9310i | 2.09653i | ||||||||
\(902\) | 0.628923 | + | 0.628923i | 0.0209409 | + | 0.0209409i | ||||
\(903\) | 0.433231 | − | 0.859335i | 0.0144170 | − | 0.0285969i | ||||
\(904\) | 11.0461 | + | 11.0461i | 0.367388 | + | 0.367388i | ||||
\(905\) | −18.8752 | + | 18.8752i | −0.627433 | + | 0.627433i | ||||
\(906\) | −0.623482 | − | 1.89130i | −0.0207138 | − | 0.0628343i | ||||
\(907\) | − | 11.4251i | − | 0.379365i | −0.981845 | − | 0.189682i | \(-0.939254\pi\) | ||
0.981845 | − | 0.189682i | \(-0.0607458\pi\) | |||||||
\(908\) | 4.33822 | − | 4.33822i | 0.143969 | − | 0.143969i | ||||
\(909\) | 30.9286 | − | 22.8780i | 1.02584 | − | 0.758814i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.4541i | − | 0.644544i | −0.946647 | − | 0.322272i | \(-0.895553\pi\) | ||
0.946647 | − | 0.322272i | \(-0.104447\pi\) | |||||||
\(912\) | −2.52511 | + | 5.00868i | −0.0836148 | + | 0.165854i | ||||
\(913\) | 3.03463 | 0.100431 | ||||||||
\(914\) | 14.7433 | 0.487667 | ||||||||
\(915\) | 15.6088 | + | 7.86911i | 0.516010 | + | 0.260145i | ||||
\(916\) | 2.47695 | − | 2.47695i | 0.0818408 | − | 0.0818408i | ||||
\(917\) | 0.467286 | − | 0.467286i | 0.0154312 | − | 0.0154312i | ||||
\(918\) | −29.3822 | + | 5.04120i | −0.969759 | + | 0.166384i | ||||
\(919\) | −48.8502 | −1.61142 | −0.805710 | − | 0.592310i | \(-0.798216\pi\) | ||||
−0.805710 | + | 0.592310i | \(0.798216\pi\) | |||||||
\(920\) | −15.3071 | −0.504659 | ||||||||
\(921\) | −45.6476 | − | 23.0131i | −1.50414 | − | 0.758306i | ||||
\(922\) | − | 38.8123i | − | 1.27821i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.07833 | + | 6.30452i | 0.0683721 | + | 0.207403i | ||||
\(925\) | −17.8022 | + | 17.8022i | −0.585334 | + | 0.585334i | ||||
\(926\) | 12.5742i | 0.413215i | ||||||||
\(927\) | −3.77095 | − | 5.09793i | −0.123854 | − | 0.167438i | ||||
\(928\) | −3.28995 | + | 3.28995i | −0.107998 | + | 0.107998i | ||||
\(929\) | −2.38799 | − | 2.38799i | −0.0783474 | − | 0.0783474i | 0.666847 | − | 0.745195i | \(-0.267643\pi\) |
−0.745195 | + | 0.666847i | \(0.767643\pi\) | |||||||
\(930\) | −27.5154 | − | 13.8718i | −0.902265 | − | 0.454873i | ||||
\(931\) | 1.73155 | + | 1.73155i | 0.0567491 | + | 0.0567491i | ||||
\(932\) | 12.0534i | 0.394823i | ||||||||
\(933\) | 25.6970 | − | 8.47122i | 0.841282 | − | 0.277335i | ||||
\(934\) | −26.1137 | − | 26.1137i | −0.854466 | − | 0.854466i | ||||
\(935\) | −28.9507 | −0.946788 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7067 | 1.42784 | 0.713918 | − | 0.700229i | \(-0.246919\pi\) | ||||
0.713918 | + | 0.700229i | \(0.246919\pi\) | |||||||
\(938\) | 1.33383 | + | 1.33383i | 0.0435510 | + | 0.0435510i | ||||
\(939\) | −28.6285 | + | 9.43760i | −0.934256 | + | 0.307985i | ||||
\(940\) | − | 35.6095i | − | 1.16145i | ||||||
\(941\) | 36.7731 | + | 36.7731i | 1.19877 | + | 1.19877i | 0.974536 | + | 0.224233i | \(0.0719877\pi\) |
0.224233 | + | 0.974536i | \(0.428012\pi\) | |||||||
\(942\) | 12.5155 | + | 6.30967i | 0.407778 | + | 0.205580i | ||||
\(943\) | 1.90781 | + | 1.90781i | 0.0621267 | + | 0.0621267i | ||||
\(944\) | −4.65268 | + | 4.65268i | −0.151432 | + | 0.151432i | ||||
\(945\) | 34.8780 | + | 24.6624i | 1.13458 | + | 0.802269i | ||||
\(946\) | 0.341051i | 0.0110885i | ||||||||
\(947\) | 35.3168 | − | 35.3168i | 1.14764 | − | 1.14764i | 0.160628 | − | 0.987015i | \(-0.448648\pi\) |
0.987015 | − | 0.160628i | \(-0.0513519\pi\) | |||||||
\(948\) | −7.65354 | − | 23.2166i | −0.248575 | − | 0.754041i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.8600i | 0.611900i | ||||||||
\(951\) | −6.32907 | − | 3.19078i | −0.205234 | − | 0.103468i | ||||
\(952\) | −14.3360 | −0.464634 | ||||||||
\(953\) | −52.6019 | −1.70394 | −0.851971 | − | 0.523589i | \(-0.824593\pi\) | ||||
−0.851971 | + | 0.523589i | \(0.824593\pi\) | |||||||
\(954\) | −4.86935 | + | 32.5443i | −0.157651 | + | 1.05366i | ||||
\(955\) | 37.5173 | − | 37.5173i | 1.21403 | − | 1.21403i | ||||
\(956\) | −14.7898 | + | 14.7898i | −0.478336 | + | 0.478336i | ||||
\(957\) | 11.0371 | + | 5.56430i | 0.356778 | + | 0.179868i | ||||
\(958\) | 5.13328 | 0.165849 | ||||||||
\(959\) | −12.9468 | −0.418074 | ||||||||
\(960\) | 2.56525 | − | 5.08829i | 0.0827929 | − | 0.164224i | ||||
\(961\) | 1.75805i | 0.0567111i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.86984 | + | 5.23161i | 0.124704 | + | 0.168586i | ||||
\(964\) | −12.3821 | + | 12.3821i | −0.398802 | + | 0.398802i | ||||
\(965\) | − | 11.7889i | − | 0.379500i | ||||||
\(966\) | 6.30452 | + | 19.1244i | 0.202844 | + | 0.615318i | ||||
\(967\) | 37.4636 | − | 37.4636i | 1.20475 | − | 1.20475i | 0.232042 | − | 0.972706i | \(-0.425459\pi\) |
0.972706 | − | 0.232042i | \(-0.0745407\pi\) | |||||||
\(968\) | 6.11469 | + | 6.11469i | 0.196534 | + | 0.196534i | ||||
\(969\) | −14.4872 | + | 28.7360i | −0.465395 | + | 0.923134i | ||||
\(970\) | 38.0972 | + | 38.0972i | 1.22323 | + | 1.22323i | ||||
\(971\) | − | 52.0962i | − | 1.67185i | −0.548845 | − | 0.835924i | \(-0.684932\pi\) | ||
0.548845 | − | 0.835924i | \(-0.315068\pi\) | |||||||
\(972\) | −15.5849 | + | 0.333537i | −0.499886 | + | 0.0106982i | ||||
\(973\) | 3.92668 | + | 3.92668i | 0.125883 | + | 0.125883i | ||||
\(974\) | 13.2032 | 0.423056 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.06759 | −0.0981911 | ||||||||
\(977\) | −14.4414 | − | 14.4414i | −0.462021 | − | 0.462021i | 0.437296 | − | 0.899318i | \(-0.355936\pi\) |
−0.899318 | + | 0.437296i | \(0.855936\pi\) | |||||||
\(978\) | −13.2116 | − | 40.0768i | −0.422461 | − | 1.28151i | ||||
\(979\) | 13.9078i | 0.444495i | ||||||||
\(980\) | −1.75907 | − | 1.75907i | −0.0561913 | − | 0.0561913i | ||||
\(981\) | −1.55504 | + | 10.3931i | −0.0496487 | + | 0.331827i | ||||
\(982\) | 6.63172 | + | 6.63172i | 0.211627 | + | 0.211627i | ||||
\(983\) | −26.7699 | + | 26.7699i | −0.853827 | + | 0.853827i | −0.990602 | − | 0.136775i | \(-0.956326\pi\) |
0.136775 | + | 0.990602i | \(0.456326\pi\) | |||||||
\(984\) | −0.953903 | + | 0.314462i | −0.0304093 | + | 0.0100247i | ||||
\(985\) | 20.9159i | 0.666437i | ||||||||
\(986\) | −18.8752 | + | 18.8752i | −0.601109 | + | 0.601109i | ||||
\(987\) | −44.4900 | + | 14.6665i | −1.41613 | + | 0.466839i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.03456i | 0.0328971i | ||||||||
\(990\) | −14.9716 | − | 2.24009i | −0.475830 | − | 0.0711947i | ||||
\(991\) | −43.9241 | −1.39529 | −0.697647 | − | 0.716442i | \(-0.745770\pi\) | ||||
−0.697647 | + | 0.716442i | \(0.745770\pi\) | |||||||
\(992\) | 5.40758 | 0.171691 | ||||||||
\(993\) | 2.27992 | − | 4.52233i | 0.0723510 | − | 0.143512i | ||||
\(994\) | 13.7043 | − | 13.7043i | 0.434675 | − | 0.434675i | ||||
\(995\) | −53.8276 | + | 53.8276i | −1.70645 | + | 1.70645i | ||||
\(996\) | −1.54269 | + | 3.06000i | −0.0488820 | + | 0.0969599i | ||||
\(997\) | −34.5254 | −1.09343 | −0.546716 | − | 0.837318i | \(-0.684122\pi\) | ||||
−0.546716 | + | 0.837318i | \(0.684122\pi\) | |||||||
\(998\) | −0.249271 | −0.00789054 | ||||||||
\(999\) | −22.1396 | + | 3.79856i | −0.700466 | + | 0.120181i |
(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 | 1014.2.g.b.239.1 | 12 | ||
3.2 | odd | 2 | inner | 1014.2.g.b.239.4 | 12 | ||
13.5 | odd | 4 | 78.2.g.a.47.1 | yes | 12 | ||
13.8 | odd | 4 | inner | 1014.2.g.b.437.4 | 12 | ||
13.12 | even | 2 | 78.2.g.a.5.4 | yes | 12 | ||
39.5 | even | 4 | 78.2.g.a.47.4 | yes | 12 | ||
39.8 | even | 4 | inner | 1014.2.g.b.437.1 | 12 | ||
39.38 | odd | 2 | 78.2.g.a.5.1 | ✓ | 12 | ||
52.31 | even | 4 | 624.2.bf.f.593.5 | 12 | |||
52.51 | odd | 2 | 624.2.bf.f.161.5 | 12 | |||
156.83 | odd | 4 | 624.2.bf.f.593.6 | 12 | |||
156.155 | even | 2 | 624.2.bf.f.161.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.g.a.5.1 | ✓ | 12 | 39.38 | odd | 2 | ||
78.2.g.a.5.4 | yes | 12 | 13.12 | even | 2 | ||
78.2.g.a.47.1 | yes | 12 | 13.5 | odd | 4 | ||
78.2.g.a.47.4 | yes | 12 | 39.5 | even | 4 | ||
624.2.bf.f.161.5 | 12 | 52.51 | odd | 2 | |||
624.2.bf.f.161.6 | 12 | 156.155 | even | 2 | |||
624.2.bf.f.593.5 | 12 | 52.31 | even | 4 | |||
624.2.bf.f.593.6 | 12 | 156.83 | odd | 4 | |||
1014.2.g.b.239.1 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.g.b.239.4 | 12 | 3.2 | odd | 2 | inner | ||
1014.2.g.b.437.1 | 12 | 39.8 | even | 4 | inner | ||
1014.2.g.b.437.4 | 12 | 13.8 | odd | 4 | inner |