Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(0.655911 - 1.25291i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.g.30.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.156598 | − | 0.0904119i | −0.110731 | − | 0.0639308i | 0.443611 | − | 0.896219i | \(-0.353697\pi\) |
−0.554343 | + | 0.832288i | \(0.687030\pi\) | |||||||
\(3\) | 1.82601 | 1.05425 | 0.527125 | − | 0.849788i | \(-0.323270\pi\) | ||||
0.527125 | + | 0.849788i | \(0.323270\pi\) | |||||||
\(4\) | −0.983651 | − | 1.70373i | −0.491826 | − | 0.851867i | ||||
\(5\) | −2.32670 | + | 1.34332i | −1.04053 | + | 0.600751i | −0.919984 | − | 0.391956i | \(-0.871799\pi\) |
−0.120548 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(6\) | −0.285950 | − | 0.165093i | −0.116739 | − | 0.0673990i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.717383i | 0.253633i | ||||||||
\(9\) | 0.334323 | 0.111441 | ||||||||
\(10\) | 0.485809 | 0.153626 | ||||||||
\(11\) | − | 2.69424i | − | 0.812345i | −0.913796 | − | 0.406172i | \(-0.866863\pi\) | ||
0.913796 | − | 0.406172i | \(-0.133137\pi\) | |||||||
\(12\) | −1.79616 | − | 3.11104i | −0.518507 | − | 0.898080i | ||||
\(13\) | −1.92153 | − | 3.05086i | −0.532937 | − | 0.846155i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.24858 | + | 2.45292i | −1.09698 | + | 0.633342i | ||||
\(16\) | −1.90244 | + | 3.29513i | −0.475611 | + | 0.823782i | ||||
\(17\) | −2.38247 | − | 4.12655i | −0.577833 | − | 1.00084i | −0.995727 | − | 0.0923405i | \(-0.970565\pi\) |
0.417894 | − | 0.908496i | \(-0.362768\pi\) | |||||||
\(18\) | −0.0523543 | − | 0.0302268i | −0.0123400 | − | 0.00712452i | ||||
\(19\) | − | 0.188424i | − | 0.0432275i | −0.999766 | − | 0.0216138i | \(-0.993120\pi\) | ||
0.999766 | − | 0.0216138i | \(-0.00688041\pi\) | |||||||
\(20\) | 4.57732 | + | 2.64272i | 1.02352 | + | 0.590930i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.243592 | + | 0.421913i | −0.0519339 | + | 0.0899521i | ||||
\(23\) | 2.19964 | − | 3.80989i | 0.458657 | − | 0.794418i | −0.540233 | − | 0.841516i | \(-0.681664\pi\) |
0.998890 | + | 0.0470977i | \(0.0149972\pi\) | |||||||
\(24\) | 1.30995i | 0.267392i | ||||||||
\(25\) | 1.10902 | − | 1.92088i | 0.221804 | − | 0.384177i | ||||
\(26\) | 0.0250743 | + | 0.651487i | 0.00491747 | + | 0.127767i | ||||
\(27\) | −4.86756 | −0.936762 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54280 | − | 6.13631i | −0.657882 | − | 1.13948i | −0.981163 | − | 0.193182i | \(-0.938119\pi\) |
0.323281 | − | 0.946303i | \(-0.395214\pi\) | |||||||
\(30\) | 0.887093 | 0.161960 | ||||||||
\(31\) | −3.20369 | − | 1.84965i | −0.575400 | − | 0.332207i | 0.183903 | − | 0.982944i | \(-0.441127\pi\) |
−0.759303 | + | 0.650737i | \(0.774460\pi\) | |||||||
\(32\) | 1.83838 | − | 1.06139i | 0.324983 | − | 0.187629i | ||||
\(33\) | − | 4.91972i | − | 0.856414i | ||||||
\(34\) | 0.861613i | 0.147765i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.328857 | − | 0.569598i | −0.0548096 | − | 0.0949329i | ||||
\(37\) | 6.88848 | + | 3.97707i | 1.13246 | + | 0.653826i | 0.944552 | − | 0.328361i | \(-0.106496\pi\) |
0.187907 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(38\) | −0.0170358 | + | 0.0295069i | −0.00276357 | + | 0.00478665i | ||||
\(39\) | −3.50874 | − | 5.57090i | −0.561848 | − | 0.892058i | ||||
\(40\) | −0.963675 | − | 1.66913i | −0.152370 | − | 0.263913i | ||||
\(41\) | −4.70215 | + | 2.71479i | −0.734353 | + | 0.423979i | −0.820013 | − | 0.572345i | \(-0.806034\pi\) |
0.0856594 | + | 0.996324i | \(0.472700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00533 | + | 6.93743i | −0.610807 | + | 1.05795i | 0.380298 | + | 0.924864i | \(0.375821\pi\) |
−0.991105 | + | 0.133084i | \(0.957512\pi\) | |||||||
\(44\) | −4.59027 | + | 2.65020i | −0.692010 | + | 0.399532i | ||||
\(45\) | −0.777869 | + | 0.449103i | −0.115958 | + | 0.0669483i | ||||
\(46\) | −0.688919 | + | 0.397748i | −0.101576 | + | 0.0586447i | ||||
\(47\) | −1.60118 | + | 0.924445i | −0.233557 | + | 0.134844i | −0.612212 | − | 0.790694i | \(-0.709720\pi\) |
0.378655 | + | 0.925538i | \(0.376387\pi\) | |||||||
\(48\) | −3.47389 | + | 6.01695i | −0.501412 | + | 0.868471i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.347341 | + | 0.200538i | −0.0491215 | + | 0.0283603i | ||||
\(51\) | −4.35041 | − | 7.53514i | −0.609180 | − | 1.05513i | ||||
\(52\) | −3.30773 | + | 6.27476i | −0.458700 | + | 0.870152i | ||||
\(53\) | 3.53622 | − | 6.12491i | 0.485737 | − | 0.841321i | −0.514128 | − | 0.857713i | \(-0.671885\pi\) |
0.999866 | + | 0.0163917i | \(0.00521788\pi\) | |||||||
\(54\) | 0.762250 | + | 0.440085i | 0.103729 | + | 0.0598880i | ||||
\(55\) | 3.61923 | + | 6.26869i | 0.488017 | + | 0.845271i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.344066i | − | 0.0455726i | ||||||
\(58\) | 1.28125i | 0.168236i | ||||||||
\(59\) | 6.57216 | − | 3.79444i | 0.855623 | − | 0.493994i | −0.00692130 | − | 0.999976i | \(-0.502203\pi\) |
0.862544 | + | 0.505982i | \(0.168870\pi\) | |||||||
\(60\) | 8.35825 | + | 4.82564i | 1.07905 | + | 0.622987i | ||||
\(61\) | 0.411564 | 0.0526954 | 0.0263477 | − | 0.999653i | \(-0.491612\pi\) | ||||
0.0263477 | + | 0.999653i | \(0.491612\pi\) | |||||||
\(62\) | 0.334461 | + | 0.579304i | 0.0424766 | + | 0.0735716i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.22592 | 0.903240 | ||||||||
\(65\) | 8.56910 | + | 4.51719i | 1.06287 | + | 0.560289i | ||||
\(66\) | −0.444801 | + | 0.770418i | −0.0547512 | + | 0.0948319i | ||||
\(67\) | 11.4010i | 1.39286i | 0.717626 | + | 0.696429i | \(0.245229\pi\) | ||||
−0.717626 | + | 0.696429i | \(0.754771\pi\) | |||||||
\(68\) | −4.68703 | + | 8.11818i | −0.568386 | + | 0.984474i | ||||
\(69\) | 4.01658 | − | 6.95692i | 0.483539 | − | 0.837514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.89675 | + | 1.67244i | 0.343781 | + | 0.198482i | 0.661943 | − | 0.749554i | \(-0.269732\pi\) |
−0.318162 | + | 0.948037i | \(0.603065\pi\) | |||||||
\(72\) | 0.239838i | 0.0282651i | ||||||||
\(73\) | 12.3112 | + | 7.10790i | 1.44092 | + | 0.831917i | 0.997911 | − | 0.0645994i | \(-0.0205769\pi\) |
0.443011 | + | 0.896516i | \(0.353910\pi\) | |||||||
\(74\) | −0.719148 | − | 1.24560i | −0.0835993 | − | 0.144798i | ||||
\(75\) | 2.02509 | − | 3.50756i | 0.233837 | − | 0.405018i | ||||
\(76\) | −0.321025 | + | 0.185344i | −0.0368241 | + | 0.0212604i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0457859 | + | 1.18962i | 0.00518423 | + | 0.134698i | ||||
\(79\) | −4.55529 | − | 7.89000i | −0.512511 | − | 0.887695i | −0.999895 | − | 0.0145069i | \(-0.995382\pi\) |
0.487384 | − | 0.873188i | \(-0.337951\pi\) | |||||||
\(80\) | − | 10.2224i | − | 1.14290i | ||||||
\(81\) | −9.89120 | −1.09902 | ||||||||
\(82\) | 0.981797 | 0.108421 | ||||||||
\(83\) | − | 16.5866i | − | 1.82061i | −0.413934 | − | 0.910307i | \(-0.635845\pi\) | ||
0.413934 | − | 0.910307i | \(-0.364155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0866 | + | 6.40083i | 1.20251 | + | 0.694268i | ||||
\(86\) | 1.25445 | − | 0.724258i | 0.135271 | − | 0.0780988i | ||||
\(87\) | −6.46920 | − | 11.2050i | −0.693571 | − | 1.20130i | ||||
\(88\) | 1.93280 | 0.206037 | ||||||||
\(89\) | 5.10232 | + | 2.94582i | 0.540844 | + | 0.312257i | 0.745421 | − | 0.666594i | \(-0.232248\pi\) |
−0.204577 | + | 0.978851i | \(0.565582\pi\) | |||||||
\(90\) | 0.162417 | 0.0171203 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.65473 | −0.902318 | ||||||||
\(93\) | −5.84998 | − | 3.37749i | −0.606615 | − | 0.350229i | ||||
\(94\) | 0.334323 | 0.0344828 | ||||||||
\(95\) | 0.253115 | + | 0.438407i | 0.0259690 | + | 0.0449796i | ||||
\(96\) | 3.35691 | − | 1.93811i | 0.342613 | − | 0.197808i | ||||
\(97\) | −0.390659 | − | 0.225547i | −0.0396654 | − | 0.0229008i | 0.480036 | − | 0.877249i | \(-0.340624\pi\) |
−0.519702 | + | 0.854348i | \(0.673957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.900747i | − | 0.0905285i | ||||||
\(100\) | −4.36356 | −0.436356 | ||||||||
\(101\) | −7.65680 | −0.761880 | −0.380940 | − | 0.924600i | \(-0.624400\pi\) | ||||
−0.380940 | + | 0.924600i | \(0.624400\pi\) | |||||||
\(102\) | 1.57332i | 0.155782i | ||||||||
\(103\) | −2.57870 | − | 4.46644i | −0.254087 | − | 0.440091i | 0.710560 | − | 0.703636i | \(-0.248442\pi\) |
−0.964647 | + | 0.263545i | \(0.915108\pi\) | |||||||
\(104\) | 2.18863 | − | 1.37847i | 0.214613 | − | 0.135170i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.10753 | + | 0.639433i | −0.107573 | + | 0.0621072i | ||||
\(107\) | −4.01644 | + | 6.95669i | −0.388284 | + | 0.672528i | −0.992219 | − | 0.124506i | \(-0.960265\pi\) |
0.603935 | + | 0.797034i | \(0.293599\pi\) | |||||||
\(108\) | 4.78798 | + | 8.29303i | 0.460724 | + | 0.797997i | ||||
\(109\) | −1.15490 | − | 0.666781i | −0.110619 | − | 0.0638660i | 0.443670 | − | 0.896190i | \(-0.353676\pi\) |
−0.554289 | + | 0.832324i | \(0.687010\pi\) | |||||||
\(110\) | − | 1.30889i | − | 0.124797i | ||||||
\(111\) | 12.5785 | + | 7.26217i | 1.19389 | + | 0.689295i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.96917 | − | 17.2671i | 0.937821 | − | 1.62435i | 0.168296 | − | 0.985736i | \(-0.446173\pi\) |
0.769525 | − | 0.638617i | \(-0.220493\pi\) | |||||||
\(114\) | −0.0311076 | + | 0.0538800i | −0.00291349 | + | 0.00504632i | ||||
\(115\) | 11.8193i | 1.10216i | ||||||||
\(116\) | −6.96976 | + | 12.0720i | −0.647126 | + | 1.12086i | ||||
\(117\) | −0.642412 | − | 1.01997i | −0.0593910 | − | 0.0942964i | ||||
\(118\) | −1.37225 | −0.126326 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.75968 | − | 3.04786i | −0.160636 | − | 0.278230i | ||||
\(121\) | 3.74106 | 0.340096 | ||||||||
\(122\) | −0.0644501 | − | 0.0372103i | −0.00583503 | − | 0.00336886i | ||||
\(123\) | −8.58619 | + | 4.95724i | −0.774191 | + | 0.446979i | ||||
\(124\) | 7.27765i | 0.653553i | ||||||||
\(125\) | − | 7.47412i | − | 0.668505i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.98361 | − | 6.89981i | −0.353488 | − | 0.612259i | 0.633370 | − | 0.773849i | \(-0.281671\pi\) |
−0.986858 | + | 0.161590i | \(0.948338\pi\) | |||||||
\(128\) | −4.80833 | − | 2.77609i | −0.425000 | − | 0.245374i | ||||
\(129\) | −7.31378 | + | 12.6678i | −0.643942 | + | 1.11534i | ||||
\(130\) | −0.933496 | − | 1.48213i | −0.0818730 | − | 0.129992i | ||||
\(131\) | 5.00897 | + | 8.67579i | 0.437636 | + | 0.758007i | 0.997507 | − | 0.0705727i | \(-0.0224827\pi\) |
−0.559871 | + | 0.828580i | \(0.689149\pi\) | |||||||
\(132\) | −8.38190 | + | 4.83929i | −0.729551 | + | 0.421206i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.03079 | − | 1.78538i | 0.0890465 | − | 0.154233i | ||||
\(135\) | 11.3254 | − | 6.53870i | 0.974731 | − | 0.562761i | ||||
\(136\) | 2.96032 | − | 1.70914i | 0.253845 | − | 0.146558i | ||||
\(137\) | 4.38811 | − | 2.53348i | 0.374902 | − | 0.216450i | −0.300696 | − | 0.953720i | \(-0.597219\pi\) |
0.675598 | + | 0.737270i | \(0.263886\pi\) | |||||||
\(138\) | −1.25798 | + | 0.726293i | −0.107086 | + | 0.0618261i | ||||
\(139\) | 3.86289 | − | 6.69073i | 0.327646 | − | 0.567500i | −0.654398 | − | 0.756150i | \(-0.727078\pi\) |
0.982044 | + | 0.188650i | \(0.0604113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.92378 | + | 1.68805i | −0.246227 | + | 0.142159i | ||||
\(142\) | −0.302417 | − | 0.523802i | −0.0253783 | − | 0.0439565i | ||||
\(143\) | −8.21974 | + | 5.17707i | −0.687370 | + | 0.432928i | ||||
\(144\) | −0.636031 | + | 1.10164i | −0.0530025 | + | 0.0918031i | ||||
\(145\) | 16.4861 | + | 9.51824i | 1.36909 | + | 0.790447i | ||||
\(146\) | −1.28528 | − | 2.22617i | −0.106370 | − | 0.184239i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 15.6482i | − | 1.28627i | ||||||
\(149\) | 14.3185i | 1.17301i | 0.809944 | + | 0.586507i | \(0.199498\pi\) | ||||
−0.809944 | + | 0.586507i | \(0.800502\pi\) | |||||||
\(150\) | −0.634250 | + | 0.366184i | −0.0517863 | + | 0.0298988i | ||||
\(151\) | −5.60534 | − | 3.23624i | −0.456156 | − | 0.263362i | 0.254271 | − | 0.967133i | \(-0.418165\pi\) |
−0.710427 | + | 0.703771i | \(0.751498\pi\) | |||||||
\(152\) | 0.135172 | 0.0109639 | ||||||||
\(153\) | −0.796513 | − | 1.37960i | −0.0643943 | − | 0.111534i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.93871 | 0.798296 | ||||||||
\(156\) | −6.03996 | + | 11.4578i | −0.483584 | + | 0.917357i | ||||
\(157\) | 7.95937 | − | 13.7860i | 0.635227 | − | 1.10025i | −0.351240 | − | 0.936285i | \(-0.614240\pi\) |
0.986467 | − | 0.163960i | \(-0.0524267\pi\) | |||||||
\(158\) | 1.64741i | 0.131061i | ||||||||
\(159\) | 6.45718 | − | 11.1842i | 0.512088 | − | 0.886962i | ||||
\(160\) | −2.85157 | + | 4.93907i | −0.225437 | + | 0.390468i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.54894 | + | 0.894282i | 0.121696 | + | 0.0702614i | ||||
\(163\) | − | 4.78162i | − | 0.374525i | −0.982310 | − | 0.187263i | \(-0.940038\pi\) | ||
0.982310 | − | 0.187263i | \(-0.0599616\pi\) | |||||||
\(164\) | 9.25056 | + | 5.34081i | 0.722348 | + | 0.417048i | ||||
\(165\) | 6.60876 | + | 11.4467i | 0.514492 | + | 0.891126i | ||||
\(166\) | −1.49962 | + | 2.59743i | −0.116393 | + | 0.201599i | ||||
\(167\) | 2.34729 | − | 1.35521i | 0.181639 | − | 0.104869i | −0.406424 | − | 0.913685i | \(-0.633224\pi\) |
0.588062 | + | 0.808816i | \(0.299891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.61544 | + | 11.7246i | −0.431957 | + | 0.901894i | ||||
\(170\) | −1.15742 | − | 2.00472i | −0.0887703 | − | 0.153755i | ||||
\(171\) | − | 0.0629946i | − | 0.00481732i | ||||||
\(172\) | 15.7594 | 1.20164 | ||||||||
\(173\) | −0.899816 | −0.0684118 | −0.0342059 | − | 0.999415i | \(-0.510890\pi\) | ||||
−0.0342059 | + | 0.999415i | \(0.510890\pi\) | |||||||
\(174\) | 2.33957i | 0.177362i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.87787 | + | 5.12564i | 0.669195 | + | 0.386360i | ||||
\(177\) | 12.0009 | − | 6.92870i | 0.902039 | − | 0.520793i | ||||
\(178\) | −0.532675 | − | 0.922620i | −0.0399257 | − | 0.0691533i | ||||
\(179\) | 11.0558 | 0.826351 | 0.413175 | − | 0.910651i | \(-0.364420\pi\) | ||||
0.413175 | + | 0.910651i | \(0.364420\pi\) | |||||||
\(180\) | 1.53030 | + | 0.883522i | 0.114062 | + | 0.0658538i | ||||
\(181\) | 3.52898 | 0.262307 | 0.131153 | − | 0.991362i | \(-0.458132\pi\) | ||||
0.131153 | + | 0.991362i | \(0.458132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.751521 | 0.0555540 | ||||||||
\(184\) | 2.73315 | + | 1.57799i | 0.201491 | + | 0.116331i | ||||
\(185\) | −21.3699 | −1.57115 | ||||||||
\(186\) | 0.610730 | + | 1.05782i | 0.0447809 | + | 0.0775628i | ||||
\(187\) | −11.1179 | + | 6.41894i | −0.813024 | + | 0.469400i | ||||
\(188\) | 3.15002 | + | 1.81866i | 0.229738 | + | 0.132640i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 0.0915382i | − | 0.00664088i | ||||||
\(191\) | −20.4004 | −1.47612 | −0.738059 | − | 0.674736i | \(-0.764258\pi\) | ||||
−0.738059 | + | 0.674736i | \(0.764258\pi\) | |||||||
\(192\) | 13.1946 | 0.952240 | ||||||||
\(193\) | 17.2646i | 1.24273i | 0.783521 | + | 0.621365i | \(0.213422\pi\) | ||||
−0.783521 | + | 0.621365i | \(0.786578\pi\) | |||||||
\(194\) | 0.0407842 | + | 0.0706403i | 0.00292814 | + | 0.00507168i | ||||
\(195\) | 15.6473 | + | 8.24845i | 1.12053 | + | 0.590684i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.29264 | + | 2.47836i | −0.305838 | + | 0.176576i | −0.645063 | − | 0.764130i | \(-0.723169\pi\) |
0.339224 | + | 0.940705i | \(0.389835\pi\) | |||||||
\(198\) | −0.0814383 | + | 0.141055i | −0.00578757 | + | 0.0100244i | ||||
\(199\) | −3.59097 | − | 6.21975i | −0.254557 | − | 0.440906i | 0.710218 | − | 0.703982i | \(-0.248596\pi\) |
−0.964775 | + | 0.263076i | \(0.915263\pi\) | |||||||
\(200\) | 1.37801 | + | 0.795593i | 0.0974399 | + | 0.0562569i | ||||
\(201\) | 20.8184i | 1.46842i | ||||||||
\(202\) | 1.19904 | + | 0.692265i | 0.0843641 | + | 0.0487076i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.55858 | + | 14.8239i | −0.599221 | + | 1.03788i | ||||
\(205\) | 7.29367 | − | 12.6330i | 0.509412 | − | 0.882327i | ||||
\(206\) | 0.932580i | 0.0649759i | ||||||||
\(207\) | 0.735392 | − | 1.27374i | 0.0511132 | − | 0.0885307i | ||||
\(208\) | 13.7086 | − | 0.527611i | 0.950518 | − | 0.0365833i | ||||
\(209\) | −0.507661 | −0.0351157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.79636 | + | 15.2357i | 0.605566 | + | 1.04887i | 0.991962 | + | 0.126539i | \(0.0403868\pi\) |
−0.386395 | + | 0.922333i | \(0.626280\pi\) | |||||||
\(212\) | −13.9136 | −0.955592 | ||||||||
\(213\) | 5.28951 | + | 3.05390i | 0.362431 | + | 0.209250i | ||||
\(214\) | 1.25793 | − | 0.726269i | 0.0859906 | − | 0.0496467i | ||||
\(215\) | − | 21.5218i | − | 1.46777i | ||||||
\(216\) | − | 3.49190i | − | 0.237594i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.120570 | + | 0.208833i | 0.00816602 | + | 0.0141440i | ||||
\(219\) | 22.4805 | + | 12.9791i | 1.51909 | + | 0.877048i | ||||
\(220\) | 7.12013 | − | 12.3324i | 0.480039 | − | 0.831452i | ||||
\(221\) | −8.01153 | + | 15.1979i | −0.538914 | + | 1.02232i | ||||
\(222\) | −1.31317 | − | 2.27448i | −0.0881344 | − | 0.152653i | ||||
\(223\) | −12.2157 | + | 7.05271i | −0.818020 | + | 0.472284i | −0.849733 | − | 0.527213i | \(-0.823237\pi\) |
0.0317129 | + | 0.999497i | \(0.489904\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.370772 | − | 0.642195i | 0.0247181 | − | 0.0428130i | ||||
\(226\) | −3.12230 | + | 1.80266i | −0.207693 | + | 0.119911i | ||||
\(227\) | −2.48443 | + | 1.43439i | −0.164897 | + | 0.0952035i | −0.580178 | − | 0.814490i | \(-0.697017\pi\) |
0.415280 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(228\) | −0.586196 | + | 0.338441i | −0.0388218 | + | 0.0224138i | ||||
\(229\) | 7.59860 | − | 4.38706i | 0.502130 | − | 0.289905i | −0.227463 | − | 0.973787i | \(-0.573043\pi\) |
0.729593 | + | 0.683882i | \(0.239710\pi\) | |||||||
\(230\) | 1.06861 | − | 1.85088i | 0.0704618 | − | 0.122043i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.40208 | − | 2.54154i | 0.289011 | − | 0.166861i | ||||
\(233\) | 2.55371 | + | 4.42316i | 0.167299 | + | 0.289771i | 0.937469 | − | 0.348068i | \(-0.113162\pi\) |
−0.770170 | + | 0.637839i | \(0.779829\pi\) | |||||||
\(234\) | 0.00838290 | + | 0.217807i | 0.000548007 | + | 0.0142385i | ||||
\(235\) | 2.48365 | − | 4.30181i | 0.162016 | − | 0.280619i | ||||
\(236\) | −12.9294 | − | 7.46481i | −0.841634 | − | 0.485918i | ||||
\(237\) | −8.31803 | − | 14.4072i | −0.540314 | − | 0.935851i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.49797i | 0.161580i | 0.996731 | + | 0.0807901i | \(0.0257443\pi\) | ||||
−0.996731 | + | 0.0807901i | \(0.974256\pi\) | |||||||
\(240\) | − | 18.6662i | − | 1.20490i | ||||||
\(241\) | −6.91532 | + | 3.99256i | −0.445455 | + | 0.257183i | −0.705909 | − | 0.708303i | \(-0.749461\pi\) |
0.260454 | + | 0.965486i | \(0.416128\pi\) | |||||||
\(242\) | −0.585842 | − | 0.338236i | −0.0376593 | − | 0.0217426i | ||||
\(243\) | −3.45877 | −0.221880 | ||||||||
\(244\) | −0.404835 | − | 0.701195i | −0.0259169 | − | 0.0448894i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.79277 | 0.114303 | ||||||||
\(247\) | −0.574856 | + | 0.362063i | −0.0365772 | + | 0.0230375i | ||||
\(248\) | 1.32691 | − | 2.29827i | 0.0842588 | − | 0.145941i | ||||
\(249\) | − | 30.2873i | − | 1.91938i | ||||||
\(250\) | −0.675749 | + | 1.17043i | −0.0427381 | + | 0.0740246i | ||||
\(251\) | −12.6285 | + | 21.8732i | −0.797105 | + | 1.38063i | 0.124389 | + | 0.992234i | \(0.460303\pi\) |
−0.921494 | + | 0.388393i | \(0.873030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2648 | − | 5.92637i | −0.645341 | − | 0.372588i | ||||
\(254\) | 1.44066i | 0.0903952i | ||||||||
\(255\) | 20.2442 | + | 11.6880i | 1.26774 | + | 0.731931i | ||||
\(256\) | −6.72394 | − | 11.6462i | −0.420246 | − | 0.727888i | ||||
\(257\) | 1.68682 | − | 2.92165i | 0.105221 | − | 0.182248i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) |
0.913828 | + | 0.406101i | \(0.133112\pi\) | |||||||
\(258\) | 2.29065 | − | 1.32250i | 0.142609 | − | 0.0823355i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.732915 | − | 19.0428i | −0.0454535 | − | 1.18099i | ||||
\(261\) | −1.18444 | − | 2.05151i | −0.0733150 | − | 0.126985i | ||||
\(262\) | − | 1.81148i | − | 0.111914i | ||||||
\(263\) | −0.158935 | −0.00980037 | −0.00490019 | − | 0.999988i | \(-0.501560\pi\) | ||||
−0.00490019 | + | 0.999988i | \(0.501560\pi\) | |||||||
\(264\) | 3.52932 | 0.217215 | ||||||||
\(265\) | 19.0011i | 1.16723i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.31689 | + | 5.37911i | 0.570185 | + | 0.329196i | ||||
\(268\) | 19.4243 | − | 11.2146i | 1.18653 | − | 0.685043i | ||||
\(269\) | −11.6633 | − | 20.2014i | −0.711124 | − | 1.23170i | −0.964435 | − | 0.264318i | \(-0.914853\pi\) |
0.253311 | − | 0.967385i | \(-0.418480\pi\) | |||||||
\(270\) | −2.36470 | −0.143911 | ||||||||
\(271\) | −10.2373 | − | 5.91049i | −0.621870 | − | 0.359037i | 0.155727 | − | 0.987800i | \(-0.450228\pi\) |
−0.777597 | + | 0.628763i | \(0.783561\pi\) | |||||||
\(272\) | 18.1300 | 1.09929 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.916226 | −0.0553513 | ||||||||
\(275\) | −5.17532 | − | 2.98797i | −0.312084 | − | 0.180182i | ||||
\(276\) | −15.8036 | −0.951268 | ||||||||
\(277\) | −13.6827 | − | 23.6991i | −0.822111 | − | 1.42394i | −0.904107 | − | 0.427306i | \(-0.859463\pi\) |
0.0819961 | − | 0.996633i | \(-0.473870\pi\) | |||||||
\(278\) | −1.20984 | + | 0.698503i | −0.0725615 | + | 0.0418934i | ||||
\(279\) | −1.07107 | − | 0.618382i | −0.0641232 | − | 0.0370215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.5383i | − | 1.70245i | −0.524801 | − | 0.851225i | \(-0.675860\pi\) | ||
0.524801 | − | 0.851225i | \(-0.324140\pi\) | |||||||
\(282\) | 0.610478 | 0.0363534 | ||||||||
\(283\) | 17.9721 | 1.06833 | 0.534165 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(284\) | − | 6.58040i | − | 0.390475i | ||||||
\(285\) | 0.462190 | + | 0.800537i | 0.0273778 | + | 0.0474197i | ||||
\(286\) | 1.75526 | − | 0.0675561i | 0.103791 | − | 0.00399468i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.614613 | − | 0.354847i | 0.0362164 | − | 0.0209096i | ||||
\(289\) | −2.85229 | + | 4.94032i | −0.167782 | + | 0.290607i | ||||
\(290\) | −1.72112 | − | 2.98107i | −0.101068 | − | 0.175055i | ||||
\(291\) | −0.713347 | − | 0.411851i | −0.0418172 | − | 0.0241432i | ||||
\(292\) | − | 27.9668i | − | 1.63663i | ||||||
\(293\) | −12.8943 | − | 7.44453i | −0.753293 | − | 0.434914i | 0.0735896 | − | 0.997289i | \(-0.476554\pi\) |
−0.826882 | + | 0.562375i | \(0.809888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1943 | + | 17.6570i | −0.593535 | + | 1.02803i | ||||
\(296\) | −2.85308 | + | 4.94168i | −0.165832 | + | 0.287229i | ||||
\(297\) | 13.1144i | 0.760974i | ||||||||
\(298\) | 1.29456 | − | 2.24224i | 0.0749918 | − | 0.129890i | ||||
\(299\) | −15.8501 | + | 0.610035i | −0.916636 | + | 0.0352792i | ||||
\(300\) | −7.96793 | −0.460028 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.585190 | + | 1.01358i | 0.0336739 | + | 0.0583249i | ||||
\(303\) | −13.9814 | −0.803211 | ||||||||
\(304\) | 0.620883 | + | 0.358467i | 0.0356101 | + | 0.0205595i | ||||
\(305\) | −0.957586 | + | 0.552862i | −0.0548312 | + | 0.0316568i | ||||
\(306\) | 0.288057i | 0.0164671i | ||||||||
\(307\) | − | 23.5161i | − | 1.34214i | −0.741396 | − | 0.671068i | \(-0.765836\pi\) | ||
0.741396 | − | 0.671068i | \(-0.234164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.70874 | − | 8.15577i | −0.267871 | − | 0.463966i | ||||
\(310\) | −1.55638 | − | 0.898577i | −0.0883965 | − | 0.0510358i | ||||
\(311\) | −0.815450 | + | 1.41240i | −0.0462399 | + | 0.0800899i | −0.888219 | − | 0.459420i | \(-0.848057\pi\) |
0.841979 | + | 0.539510i | \(0.181391\pi\) | |||||||
\(312\) | 3.99647 | − | 2.51711i | 0.226255 | − | 0.142503i | ||||
\(313\) | −0.348367 | − | 0.603389i | −0.0196909 | − | 0.0341056i | 0.856012 | − | 0.516956i | \(-0.172935\pi\) |
−0.875703 | + | 0.482850i | \(0.839602\pi\) | |||||||
\(314\) | −2.49284 | + | 1.43924i | −0.140679 | + | 0.0812212i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.96164 | + | 15.5220i | −0.504132 | + | 0.873182i | ||||
\(317\) | −18.5579 | + | 10.7144i | −1.04231 | + | 0.601780i | −0.920488 | − | 0.390771i | \(-0.872208\pi\) |
−0.121826 | + | 0.992551i | \(0.538875\pi\) | |||||||
\(318\) | −2.02236 | + | 1.16761i | −0.113409 | + | 0.0654764i | ||||
\(319\) | −16.5327 | + | 9.54517i | −0.925654 | + | 0.534427i | ||||
\(320\) | −16.8126 | + | 9.70673i | −0.939850 | + | 0.542623i | ||||
\(321\) | −7.33408 | + | 12.7030i | −0.409348 | + | 0.709012i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.777544 | + | 0.448915i | −0.0432637 | + | 0.0249783i | ||||
\(324\) | 9.72949 | + | 16.8520i | 0.540527 | + | 0.936221i | ||||
\(325\) | −7.99136 | + | 0.307569i | −0.443281 | + | 0.0170609i | ||||
\(326\) | −0.432315 | + | 0.748792i | −0.0239437 | + | 0.0414717i | ||||
\(327\) | −2.10886 | − | 1.21755i | −0.116620 | − | 0.0673307i | ||||
\(328\) | −1.94754 | − | 3.37324i | −0.107535 | − | 0.186256i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 2.39004i | − | 0.131568i | ||||||
\(331\) | − | 1.52046i | − | 0.0835722i | −0.999127 | − | 0.0417861i | \(-0.986695\pi\) | ||
0.999127 | − | 0.0417861i | \(-0.0133048\pi\) | |||||||
\(332\) | −28.2591 | + | 16.3154i | −1.55092 | + | 0.895425i | ||||
\(333\) | 2.30298 | + | 1.32962i | 0.126202 | + | 0.0728630i | ||||
\(334\) | −0.490108 | −0.0268175 | ||||||||
\(335\) | −15.3152 | − | 26.5268i | −0.836761 | − | 1.44931i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.2304 | −1.75570 | −0.877850 | − | 0.478936i | \(-0.841023\pi\) | ||||
−0.877850 | + | 0.478936i | \(0.841023\pi\) | |||||||
\(338\) | 1.93941 | − | 1.32835i | 0.105490 | − | 0.0722527i | ||||
\(339\) | 18.2038 | − | 31.5300i | 0.988697 | − | 1.71247i | ||||
\(340\) | − | 25.1848i | − | 1.36584i | ||||||
\(341\) | −4.98341 | + | 8.63153i | −0.269867 | + | 0.467423i | ||||
\(342\) | −0.00569546 | + | 0.00986483i | −0.000307975 | + | 0.000533429i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.97679 | − | 2.87335i | −0.268331 | − | 0.154921i | ||||
\(345\) | 21.5822i | 1.16195i | ||||||||
\(346\) | 0.140909 | + | 0.0813541i | 0.00757534 | + | 0.00437362i | ||||
\(347\) | −4.09215 | − | 7.08782i | −0.219678 | − | 0.380494i | 0.735031 | − | 0.678033i | \(-0.237167\pi\) |
−0.954710 | + | 0.297539i | \(0.903834\pi\) | |||||||
\(348\) | −12.7269 | + | 22.0436i | −0.682232 | + | 1.18166i | ||||
\(349\) | 18.9220 | − | 10.9246i | 1.01287 | − | 0.584782i | 0.100841 | − | 0.994903i | \(-0.467847\pi\) |
0.912031 | + | 0.410120i | \(0.134513\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.35317 | + | 14.8502i | 0.499235 | + | 0.792646i | ||||
\(352\) | −2.85964 | − | 4.95304i | −0.152419 | − | 0.263998i | ||||
\(353\) | − | 0.567179i | − | 0.0301879i | −0.999886 | − | 0.0150940i | \(-0.995195\pi\) | ||
0.999886 | − | 0.0150940i | \(-0.00480474\pi\) | |||||||
\(354\) | −2.50575 | −0.133179 | ||||||||
\(355\) | −8.98650 | −0.476954 | ||||||||
\(356\) | − | 11.5907i | − | 0.614303i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.73132 | − | 0.999577i | −0.0915030 | − | 0.0528293i | ||||
\(359\) | 28.0630 | − | 16.2022i | 1.48111 | − | 0.855118i | 0.481336 | − | 0.876536i | \(-0.340152\pi\) |
0.999771 | + | 0.0214184i | \(0.00681822\pi\) | |||||||
\(360\) | −0.322179 | − | 0.558030i | −0.0169803 | − | 0.0294108i | ||||
\(361\) | 18.9645 | 0.998131 | ||||||||
\(362\) | −0.552631 | − | 0.319061i | −0.0290456 | − | 0.0167695i | ||||
\(363\) | 6.83122 | 0.358546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.1928 | −1.99910 | ||||||||
\(366\) | −0.117687 | − | 0.0679464i | −0.00615158 | − | 0.00355162i | ||||
\(367\) | 7.86888 | 0.410752 | 0.205376 | − | 0.978683i | \(-0.434158\pi\) | ||||
0.205376 | + | 0.978683i | \(0.434158\pi\) | |||||||
\(368\) | 8.36939 | + | 14.4962i | 0.436285 | + | 0.755667i | ||||
\(369\) | −1.57204 | + | 0.907617i | −0.0818371 | + | 0.0472487i | ||||
\(370\) | 3.34648 | + | 1.93209i | 0.173975 | + | 0.100445i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.2891i | 0.689007i | ||||||||
\(373\) | −2.09163 | −0.108300 | −0.0541502 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541502 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(374\) | 2.32139 | 0.120036 | ||||||||
\(375\) | − | 13.6478i | − | 0.704771i | ||||||
\(376\) | −0.663180 | − | 1.14866i | −0.0342009 | − | 0.0592377i | ||||
\(377\) | −11.9134 | + | 22.5997i | −0.613571 | + | 1.16394i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.3983 | − | 7.15817i | 0.636859 | − | 0.367691i | −0.146545 | − | 0.989204i | \(-0.546815\pi\) |
0.783404 | + | 0.621513i | \(0.213482\pi\) | |||||||
\(380\) | 0.497953 | − | 0.862480i | 0.0255444 | − | 0.0442443i | ||||
\(381\) | −7.27412 | − | 12.5991i | −0.372665 | − | 0.645474i | ||||
\(382\) | 3.19466 | + | 1.84444i | 0.163453 | + | 0.0943695i | ||||
\(383\) | − | 25.1873i | − | 1.28701i | −0.765441 | − | 0.643507i | \(-0.777479\pi\) | ||
0.765441 | − | 0.643507i | \(-0.222521\pi\) | |||||||
\(384\) | −8.78006 | − | 5.06917i | −0.448056 | − | 0.258685i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.56092 | − | 2.70359i | 0.0794488 | − | 0.137609i | ||||
\(387\) | −1.33907 | + | 2.31934i | −0.0680689 | + | 0.117899i | ||||
\(388\) | 0.887438i | 0.0450528i | ||||||||
\(389\) | 14.0512 | − | 24.3373i | 0.712422 | − | 1.23395i | −0.251524 | − | 0.967851i | \(-0.580932\pi\) |
0.963946 | − | 0.266099i | \(-0.0857350\pi\) | |||||||
\(390\) | −1.70458 | − | 2.70639i | −0.0863146 | − | 0.137043i | ||||
\(391\) | −20.9623 | −1.06011 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.14644 | + | 15.8421i | 0.461377 | + | 0.799128i | ||||
\(394\) | 0.896292 | 0.0451546 | ||||||||
\(395\) | 21.1976 | + | 12.2384i | 1.06657 | + | 0.615783i | ||||
\(396\) | −1.53463 | + | 0.886021i | −0.0771183 | + | 0.0445243i | ||||
\(397\) | 21.7765i | 1.09293i | 0.837482 | + | 0.546465i | \(0.184027\pi\) | ||||
−0.837482 | + | 0.546465i | \(0.815973\pi\) | |||||||
\(398\) | 1.29867i | 0.0650963i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.21970 | + | 7.30874i | 0.210985 | + | 0.365437i | ||||
\(401\) | −17.7786 | − | 10.2645i | −0.887821 | − | 0.512584i | −0.0145918 | − | 0.999894i | \(-0.504645\pi\) |
−0.873229 | + | 0.487310i | \(0.837978\pi\) | |||||||
\(402\) | 1.88223 | − | 3.26012i | 0.0938772 | − | 0.162600i | ||||
\(403\) | 0.512971 | + | 13.3282i | 0.0255529 | + | 0.663923i | ||||
\(404\) | 7.53162 | + | 13.0451i | 0.374712 | + | 0.649020i | ||||
\(405\) | 23.0138 | − | 13.2871i | 1.14357 | − | 0.660239i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7152 | − | 18.5592i | 0.531132 | − | 0.919947i | ||||
\(408\) | 5.40558 | − | 3.12091i | 0.267616 | − | 0.154508i | ||||
\(409\) | −5.42879 | + | 3.13431i | −0.268436 | + | 0.154982i | −0.628177 | − | 0.778071i | \(-0.716199\pi\) |
0.359741 | + | 0.933052i | \(0.382865\pi\) | |||||||
\(410\) | −2.28435 | + | 1.31887i | −0.112816 | + | 0.0651343i | ||||
\(411\) | 8.01275 | − | 4.62616i | 0.395240 | − | 0.228192i | ||||
\(412\) | −5.07308 | + | 8.78683i | −0.249933 | + | 0.432896i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.230322 | + | 0.132976i | −0.0113197 | + | 0.00653543i | ||||
\(415\) | 22.2811 | + | 38.5920i | 1.09374 | + | 1.89441i | ||||
\(416\) | −6.77065 | − | 3.56914i | −0.331958 | − | 0.174991i | ||||
\(417\) | 7.05369 | − | 12.2174i | 0.345421 | − | 0.598286i | ||||
\(418\) | 0.0794987 | + | 0.0458986i | 0.00388841 | + | 0.00224497i | ||||
\(419\) | 17.0817 | + | 29.5864i | 0.834497 | + | 1.44539i | 0.894439 | + | 0.447189i | \(0.147575\pi\) |
−0.0599424 | + | 0.998202i | \(0.519092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5233i | 0.561613i | 0.959764 | + | 0.280806i | \(0.0906019\pi\) | ||||
−0.959764 | + | 0.280806i | \(0.909398\pi\) | |||||||
\(422\) | − | 3.18118i | − | 0.154858i | ||||||
\(423\) | −0.535313 | + | 0.309063i | −0.0260278 | + | 0.0150272i | ||||
\(424\) | 4.39391 | + | 2.53682i | 0.213387 | + | 0.123199i | ||||
\(425\) | −10.5688 | −0.512664 | ||||||||
\(426\) | −0.552218 | − | 0.956469i | −0.0267550 | − | 0.0463411i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.8031 | 0.763873 | ||||||||
\(429\) | −15.0094 | + | 9.45340i | −0.724659 | + | 0.456414i | ||||
\(430\) | −1.94582 | + | 3.37026i | −0.0938359 | + | 0.162529i | ||||
\(431\) | 8.77001i | 0.422436i | 0.977439 | + | 0.211218i | \(0.0677431\pi\) | ||||
−0.977439 | + | 0.211218i | \(0.932257\pi\) | |||||||
\(432\) | 9.26026 | − | 16.0392i | 0.445534 | − | 0.771688i | ||||
\(433\) | −11.0535 | + | 19.1452i | −0.531196 | + | 0.920058i | 0.468141 | + | 0.883654i | \(0.344924\pi\) |
−0.999337 | + | 0.0364046i | \(0.988409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.1038 | + | 17.3804i | 1.44337 | + | 0.833328i | ||||
\(436\) | 2.62352i | 0.125644i | ||||||||
\(437\) | −0.717877 | − | 0.414467i | −0.0343407 | − | 0.0198266i | ||||
\(438\) | −2.34693 | − | 4.06501i | −0.112141 | − | 0.194234i | ||||
\(439\) | 5.18547 | − | 8.98150i | 0.247489 | − | 0.428664i | −0.715339 | − | 0.698777i | \(-0.753728\pi\) |
0.962828 | + | 0.270114i | \(0.0870612\pi\) | |||||||
\(440\) | −4.49705 | + | 2.59637i | −0.214389 | + | 0.123777i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.62866 | − | 1.65562i | 0.125032 | − | 0.0787496i | ||||
\(443\) | −17.9068 | − | 31.0156i | −0.850780 | − | 1.47359i | −0.880506 | − | 0.474036i | \(-0.842797\pi\) |
0.0297257 | − | 0.999558i | \(-0.490537\pi\) | |||||||
\(444\) | − | 28.5738i | − | 1.35605i | ||||||
\(445\) | −15.8287 | −0.750354 | ||||||||
\(446\) | 2.55059 | 0.120774 | ||||||||
\(447\) | 26.1457i | 1.23665i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7023 | − | 11.3751i | −0.929809 | − | 0.536825i | −0.0430575 | − | 0.999073i | \(-0.513710\pi\) |
−0.886751 | + | 0.462247i | \(0.847043\pi\) | |||||||
\(450\) | −0.116124 | + | 0.0670443i | −0.00547415 | + | 0.00316050i | ||||
\(451\) | 7.31430 | + | 12.6687i | 0.344417 | + | 0.596548i | ||||
\(452\) | −39.2248 | −1.84498 | ||||||||
\(453\) | −10.2354 | − | 5.90942i | −0.480902 | − | 0.277649i | ||||
\(454\) | 0.518742 | 0.0243458 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.246827 | 0.0115587 | ||||||||
\(457\) | −27.1215 | − | 15.6586i | −1.26869 | − | 0.732478i | −0.293949 | − | 0.955821i | \(-0.594969\pi\) |
−0.974740 | + | 0.223344i | \(0.928303\pi\) | |||||||
\(458\) | −1.58657 | −0.0741354 | ||||||||
\(459\) | 11.5968 | + | 20.0862i | 0.541292 | + | 0.937546i | ||||
\(460\) | 20.1370 | − | 11.6261i | 0.938891 | − | 0.542069i | ||||
\(461\) | 7.28113 | + | 4.20376i | 0.339116 | + | 0.195789i | 0.659881 | − | 0.751370i | \(-0.270607\pi\) |
−0.320765 | + | 0.947159i | \(0.603940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.0392i | − | 0.466563i | −0.972409 | − | 0.233281i | \(-0.925054\pi\) | ||
0.972409 | − | 0.233281i | \(-0.0749463\pi\) | |||||||
\(464\) | 26.9599 | 1.25158 | ||||||||
\(465\) | 18.1482 | 0.841603 | ||||||||
\(466\) | − | 0.923545i | − | 0.0427824i | ||||||
\(467\) | 13.1756 | + | 22.8209i | 0.609696 | + | 1.05602i | 0.991290 | + | 0.131695i | \(0.0420418\pi\) |
−0.381594 | + | 0.924330i | \(0.624625\pi\) | |||||||
\(468\) | −1.10585 | + | 2.09780i | −0.0511180 | + | 0.0969706i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.777869 | + | 0.449103i | −0.0358804 | + | 0.0207156i | ||||
\(471\) | 14.5339 | − | 25.1735i | 0.669687 | − | 1.15993i | ||||
\(472\) | 2.72206 | + | 4.71475i | 0.125293 | + | 0.217014i | ||||
\(473\) | 18.6911 | + | 10.7913i | 0.859418 | + | 0.496185i | ||||
\(474\) | 3.00819i | 0.138171i | ||||||||
\(475\) | −0.361941 | − | 0.208967i | −0.0166070 | − | 0.00958806i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.18224 | − | 2.04770i | 0.0541310 | − | 0.0937577i | ||||
\(478\) | 0.225846 | − | 0.391177i | 0.0103300 | − | 0.0178920i | ||||
\(479\) | − | 8.58414i | − | 0.392220i | −0.980582 | − | 0.196110i | \(-0.937169\pi\) | ||
0.980582 | − | 0.196110i | \(-0.0628309\pi\) | |||||||
\(480\) | −5.20701 | + | 9.01880i | −0.237666 | + | 0.411650i | ||||
\(481\) | −1.10297 | − | 28.6578i | −0.0502913 | − | 1.30668i | ||||
\(482\) | 1.44390 | 0.0657678 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.67990 | − | 6.37377i | −0.167268 | − | 0.289717i | ||||
\(485\) | 1.21193 | 0.0550308 | ||||||||
\(486\) | 0.541637 | + | 0.312714i | 0.0245691 | + | 0.0141850i | ||||
\(487\) | 18.4084 | − | 10.6281i | 0.834166 | − | 0.481606i | −0.0211110 | − | 0.999777i | \(-0.506720\pi\) |
0.855277 | + | 0.518171i | \(0.173387\pi\) | |||||||
\(488\) | 0.295249i | 0.0133653i | ||||||||
\(489\) | − | 8.73130i | − | 0.394843i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2268 | − | 19.4453i | −0.506657 | − | 0.877556i | −0.999970 | − | 0.00770409i | \(-0.997548\pi\) |
0.493313 | − | 0.869852i | \(-0.335786\pi\) | |||||||
\(492\) | 16.8916 | + | 9.75240i | 0.761534 | + | 0.439672i | ||||
\(493\) | −16.8812 | + | 29.2391i | −0.760292 | + | 1.31686i | ||||
\(494\) | 0.122756 | − | 0.00472460i | 0.00552306 | − | 0.000212570i | ||||
\(495\) | 1.20999 | + | 2.09577i | 0.0543851 | + | 0.0941978i | ||||
\(496\) | 12.1897 | − | 7.03772i | 0.547333 | − | 0.316003i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.73833 | + | 4.74293i | −0.122708 | + | 0.212536i | ||||
\(499\) | 33.6694 | − | 19.4390i | 1.50725 | − | 0.870210i | 0.507284 | − | 0.861779i | \(-0.330650\pi\) |
0.999964 | − | 0.00843082i | \(-0.00268365\pi\) | |||||||
\(500\) | −12.7339 | + | 7.35193i | −0.569478 | + | 0.328788i | ||||
\(501\) | 4.28619 | − | 2.47463i | 0.191493 | − | 0.110558i | ||||
\(502\) | 3.95520 | − | 2.28354i | 0.176529 | − | 0.101919i | ||||
\(503\) | 2.72850 | − | 4.72591i | 0.121658 | − | 0.210718i | −0.798764 | − | 0.601645i | \(-0.794512\pi\) |
0.920422 | + | 0.390927i | \(0.127846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.8151 | − | 10.2855i | 0.792760 | − | 0.457700i | ||||
\(506\) | 1.07163 | + | 1.85612i | 0.0476397 | + | 0.0825144i | ||||
\(507\) | −10.2539 | + | 21.4093i | −0.455390 | + | 0.950821i | ||||
\(508\) | −7.83697 | + | 13.5740i | −0.347709 | + | 0.602250i | ||||
\(509\) | −9.43315 | − | 5.44623i | −0.418117 | − | 0.241400i | 0.276154 | − | 0.961113i | \(-0.410940\pi\) |
−0.694271 | + | 0.719713i | \(0.744273\pi\) | |||||||
\(510\) | −2.11347 | − | 3.66064i | −0.0935860 | − | 0.162096i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.5360i | 0.598214i | ||||||||
\(513\) | 0.917168i | 0.0404939i | ||||||||
\(514\) | −0.528304 | + | 0.305017i | −0.0233025 | + | 0.0134537i | ||||
\(515\) | 11.9997 | + | 6.92804i | 0.528771 | + | 0.305286i | ||||
\(516\) | 28.7768 | 1.26683 | ||||||||
\(517\) | 2.49068 | + | 4.31398i | 0.109540 | + | 0.189729i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.64308 | −0.0721230 | ||||||||
\(520\) | −3.24056 | + | 6.14733i | −0.142108 | + | 0.269578i | ||||
\(521\) | 13.9480 | − | 24.1587i | 0.611074 | − | 1.05841i | −0.379985 | − | 0.924993i | \(-0.624071\pi\) |
0.991060 | − | 0.133419i | \(-0.0425957\pi\) | |||||||
\(522\) | 0.428350i | 0.0187484i | ||||||||
\(523\) | 8.36180 | − | 14.4831i | 0.365636 | − | 0.633300i | −0.623242 | − | 0.782029i | \(-0.714185\pi\) |
0.988878 | + | 0.148729i | \(0.0475182\pi\) | |||||||
\(524\) | 9.85416 | − | 17.0679i | 0.430481 | − | 0.745615i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0248890 | + | 0.0143696i | 0.00108521 | + | 0.000626546i | ||||
\(527\) | 17.6269i | 0.767842i | ||||||||
\(528\) | 16.2111 | + | 9.35949i | 0.705498 | + | 0.407319i | ||||
\(529\) | 1.82314 | + | 3.15777i | 0.0792668 | + | 0.137294i | ||||
\(530\) | 1.71793 | − | 2.97554i | 0.0746219 | − | 0.129249i | ||||
\(531\) | 2.19723 | − | 1.26857i | 0.0953515 | − | 0.0550512i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.3178 | + | 9.12904i | 0.750116 | + | 0.395423i | ||||
\(534\) | −0.972671 | − | 1.68472i | −0.0420916 | − | 0.0729048i | ||||
\(535\) | − | 21.5815i | − | 0.933049i | ||||||
\(536\) | −8.17890 | −0.353275 | ||||||||
\(537\) | 20.1881 | 0.871179 | ||||||||
\(538\) | 4.21800i | 0.181851i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −22.2804 | − | 12.8636i | −0.958796 | − | 0.553561i | ||||
\(541\) | −9.66528 | + | 5.58025i | −0.415543 | + | 0.239914i | −0.693169 | − | 0.720776i | \(-0.743786\pi\) |
0.277626 | + | 0.960689i | \(0.410453\pi\) | |||||||
\(542\) | 1.06876 | + | 1.85114i | 0.0459070 | + | 0.0795133i | ||||
\(543\) | 6.44396 | 0.276537 | ||||||||
\(544\) | −8.75976 | − | 5.05745i | −0.375572 | − | 0.216836i | ||||
\(545\) | 3.58280 | 0.153470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.6556 | 1.56728 | 0.783640 | − | 0.621215i | \(-0.213361\pi\) | ||||
0.783640 | + | 0.621215i | \(0.213361\pi\) | |||||||
\(548\) | −8.63275 | − | 4.98412i | −0.368773 | − | 0.212911i | ||||
\(549\) | 0.137595 | 0.00587242 | ||||||||
\(550\) | 0.540297 | + | 0.935821i | 0.0230383 | + | 0.0399036i | ||||
\(551\) | −1.15623 | + | 0.667551i | −0.0492571 | + | 0.0284386i | ||||
\(552\) | 4.99077 | + | 2.88142i | 0.212421 | + | 0.122641i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.94830i | 0.210233i | ||||||||
\(555\) | −39.0217 | −1.65638 | ||||||||
\(556\) | −15.1990 | −0.644579 | ||||||||
\(557\) | 33.0776i | 1.40154i | 0.713386 | + | 0.700772i | \(0.247161\pi\) | ||||
−0.713386 | + | 0.700772i | \(0.752839\pi\) | |||||||
\(558\) | 0.111818 | + | 0.193675i | 0.00473364 | + | 0.00819890i | ||||
\(559\) | 28.8615 | − | 1.11081i | 1.22071 | − | 0.0469823i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.3015 | + | 11.7211i | −0.857130 | + | 0.494864i | ||||
\(562\) | −2.58020 | + | 4.46903i | −0.108839 | + | 0.188515i | ||||
\(563\) | −8.89836 | − | 15.4124i | −0.375021 | − | 0.649556i | 0.615309 | − | 0.788286i | \(-0.289031\pi\) |
−0.990330 | + | 0.138730i | \(0.955698\pi\) | |||||||
\(564\) | 5.75197 | + | 3.32090i | 0.242202 | + | 0.139835i | ||||
\(565\) | 53.5672i | 2.25359i | ||||||||
\(566\) | −2.81439 | − | 1.62489i | −0.118298 | − | 0.0682992i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.19978 | + | 2.07808i | −0.0503417 | + | 0.0871943i | ||||
\(569\) | −4.11047 | + | 7.11954i | −0.172320 | + | 0.298467i | −0.939231 | − | 0.343287i | \(-0.888460\pi\) |
0.766911 | + | 0.641754i | \(0.221793\pi\) | |||||||
\(570\) | − | 0.167150i | − | 0.00700114i | ||||||
\(571\) | −12.8776 | + | 22.3047i | −0.538912 | + | 0.933424i | 0.460051 | + | 0.887893i | \(0.347831\pi\) |
−0.998963 | + | 0.0455309i | \(0.985502\pi\) | |||||||
\(572\) | 16.9057 | + | 8.91183i | 0.706863 | + | 0.372622i | ||||
\(573\) | −37.2513 | −1.55620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.87891 | − | 8.45051i | −0.203464 | − | 0.352411i | ||||
\(576\) | 2.41579 | 0.100658 | ||||||||
\(577\) | −0.666314 | − | 0.384697i | −0.0277390 | − | 0.0160151i | 0.486066 | − | 0.873922i | \(-0.338431\pi\) |
−0.513805 | + | 0.857907i | \(0.671765\pi\) | |||||||
\(578\) | 0.893326 | − | 0.515762i | 0.0371575 | − | 0.0214529i | ||||
\(579\) | 31.5253i | 1.31015i | ||||||||
\(580\) | − | 37.4505i | − | 1.55505i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.0744725 | + | 0.128990i | 0.00308698 | + | 0.00534681i | ||||
\(583\) | −16.5020 | − | 9.52743i | −0.683443 | − | 0.394586i | ||||
\(584\) | −5.09908 | + | 8.83187i | −0.211002 | + | 0.365465i | ||||
\(585\) | 2.86485 | + | 1.51020i | 0.118447 | + | 0.0624392i | ||||
\(586\) | 1.34615 | + | 2.33159i | 0.0556088 | + | 0.0963173i | ||||
\(587\) | 10.4727 | − | 6.04644i | 0.432256 | − | 0.249563i | −0.268051 | − | 0.963405i | \(-0.586380\pi\) |
0.700307 | + | 0.713841i | \(0.253046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.348520 | + | 0.603654i | −0.0143605 | + | 0.0248731i | ||||
\(590\) | 3.19281 | − | 1.84337i | 0.131446 | − | 0.0758904i | ||||
\(591\) | −7.83842 | + | 4.52552i | −0.322430 | + | 0.186155i | ||||
\(592\) | −26.2099 | + | 15.1323i | −1.07722 | + | 0.621933i | ||||
\(593\) | −13.8115 | + | 7.97406i | −0.567170 | + | 0.327456i | −0.756018 | − | 0.654551i | \(-0.772858\pi\) |
0.188848 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(594\) | 1.18570 | − | 2.05369i | 0.0486497 | − | 0.0842638i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.3949 | − | 14.0844i | 0.999253 | − | 0.576919i | ||||
\(597\) | −6.55717 | − | 11.3573i | −0.268367 | − | 0.464825i | ||||
\(598\) | 2.53725 | + | 1.33751i | 0.103756 | + | 0.0546948i | ||||
\(599\) | 3.55511 | − | 6.15763i | 0.145258 | − | 0.251594i | −0.784211 | − | 0.620494i | \(-0.786932\pi\) |
0.929469 | + | 0.368900i | \(0.120266\pi\) | |||||||
\(600\) | 2.51626 | + | 1.45276i | 0.102726 | + | 0.0593088i | ||||
\(601\) | 10.3953 | + | 18.0051i | 0.424032 | + | 0.734445i | 0.996329 | − | 0.0856011i | \(-0.0272811\pi\) |
−0.572297 | + | 0.820046i | \(0.693948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.81163i | 0.155221i | ||||||||
\(604\) | 12.7333i | 0.518112i | ||||||||
\(605\) | −8.70432 | + | 5.02544i | −0.353881 | + | 0.204313i | ||||
\(606\) | 2.18946 | + | 1.26409i | 0.0889408 | + | 0.0513500i | ||||
\(607\) | 7.71405 | 0.313104 | 0.156552 | − | 0.987670i | \(-0.449962\pi\) | ||||
0.156552 | + | 0.987670i | \(0.449962\pi\) | |||||||
\(608\) | −0.199992 | − | 0.346396i | −0.00811074 | − | 0.0140482i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.199941 | 0.00809539 | ||||||||
\(611\) | 5.89707 | + | 3.10864i | 0.238570 | + | 0.125762i | ||||
\(612\) | −1.56698 | + | 2.71409i | −0.0633415 | + | 0.109711i | ||||
\(613\) | 20.4378i | 0.825476i | 0.910850 | + | 0.412738i | \(0.135428\pi\) | ||||
−0.910850 | + | 0.412738i | \(0.864572\pi\) | |||||||
\(614\) | −2.12614 | + | 3.68257i | −0.0858038 | + | 0.148617i | ||||
\(615\) | 13.3183 | − | 23.0680i | 0.537047 | − | 0.930193i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.98209 | − | 2.29906i | −0.160313 | − | 0.0925567i | 0.417697 | − | 0.908586i | \(-0.362837\pi\) |
−0.578010 | + | 0.816030i | \(0.696171\pi\) | |||||||
\(618\) | 1.70290i | 0.0685008i | ||||||||
\(619\) | −8.70599 | − | 5.02641i | −0.349923 | − | 0.202028i | 0.314728 | − | 0.949182i | \(-0.398087\pi\) |
−0.664651 | + | 0.747154i | \(0.731420\pi\) | |||||||
\(620\) | −9.77623 | − | 16.9329i | −0.392623 | − | 0.680042i | ||||
\(621\) | −10.7069 | + | 18.5449i | −0.429653 | + | 0.744181i | ||||
\(622\) | 0.255396 | − | 0.147453i | 0.0102404 | − | 0.00591232i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 25.0320 | − | 0.963425i | 1.00208 | − | 0.0385679i | ||||
\(625\) | 15.5853 | + | 26.9944i | 0.623410 | + | 1.07978i | ||||
\(626\) | 0.125986i | 0.00503541i | ||||||||
\(627\) | −0.926996 | −0.0370207 | ||||||||
\(628\) | −31.3170 | −1.24968 | ||||||||
\(629\) | − | 37.9009i | − | 1.51121i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.29923 | − | 3.63686i | −0.250768 | − | 0.144781i | 0.369348 | − | 0.929291i | \(-0.379581\pi\) |
−0.620116 | + | 0.784510i | \(0.712914\pi\) | |||||||
\(632\) | 5.66015 | − | 3.26789i | 0.225149 | − | 0.129990i | ||||
\(633\) | 16.0623 | + | 27.8207i | 0.638418 | + | 1.10577i | ||||
\(634\) | 3.87483 | 0.153889 | ||||||||
\(635\) | 18.5373 | + | 10.7025i | 0.735631 | + | 0.424717i | ||||
\(636\) | −25.4065 | −1.00743 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.45199 | 0.136665 | ||||||||
\(639\) | 0.968451 | + | 0.559136i | 0.0383113 | + | 0.0221191i | ||||
\(640\) | 14.9167 | 0.589635 | ||||||||
\(641\) | 1.92516 | + | 3.33448i | 0.0760394 | + | 0.131704i | 0.901538 | − | 0.432700i | \(-0.142439\pi\) |
−0.825498 | + | 0.564404i | \(0.809106\pi\) | |||||||
\(642\) | 2.29700 | − | 1.32618i | 0.0906555 | − | 0.0523400i | ||||
\(643\) | −2.49163 | − | 1.43855i | −0.0982605 | − | 0.0567307i | 0.450065 | − | 0.892996i | \(-0.351401\pi\) |
−0.548325 | + | 0.836265i | \(0.684734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 39.2990i | − | 1.54740i | ||||||
\(646\) | 0.162349 | 0.00638754 | ||||||||
\(647\) | 37.1001 | 1.45856 | 0.729278 | − | 0.684218i | \(-0.239856\pi\) | ||||
0.729278 | + | 0.684218i | \(0.239856\pi\) | |||||||
\(648\) | − | 7.09577i | − | 0.278748i | ||||||
\(649\) | −10.2231 | − | 17.7070i | −0.401293 | − | 0.695061i | ||||
\(650\) | 1.27924 | + | 0.674349i | 0.0501758 | + | 0.0264501i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.14661 | + | 4.70345i | −0.319046 | + | 0.184201i | ||||
\(653\) | −10.0475 | + | 17.4028i | −0.393189 | + | 0.681023i | −0.992868 | − | 0.119218i | \(-0.961961\pi\) |
0.599679 | + | 0.800240i | \(0.295295\pi\) | |||||||
\(654\) | 0.220162 | + | 0.381332i | 0.00860902 | + | 0.0149113i | ||||
\(655\) | −23.3087 | − | 13.4573i | −0.910748 | − | 0.525820i | ||||
\(656\) | − | 20.6589i | − | 0.806596i | ||||||
\(657\) | 4.11593 | + | 2.37634i | 0.160578 | + | 0.0927097i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.95529 | + | 8.58281i | −0.193031 | + | 0.334339i | −0.946253 | − | 0.323427i | \(-0.895165\pi\) |
0.753223 | + | 0.657766i | \(0.228498\pi\) | |||||||
\(660\) | 13.0014 | − | 22.5192i | 0.506080 | − | 0.876557i | ||||
\(661\) | 47.2266i | 1.83690i | 0.395537 | + | 0.918450i | \(0.370558\pi\) | ||||
−0.395537 | + | 0.918450i | \(0.629442\pi\) | |||||||
\(662\) | −0.137468 | + | 0.238102i | −0.00534284 | + | 0.00925408i | ||||
\(663\) | −14.6292 | + | 27.7515i | −0.568150 | + | 1.07778i | ||||
\(664\) | 11.8989 | 0.461768 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.240428 | − | 0.416433i | −0.00931639 | − | 0.0161365i | ||||
\(667\) | −31.1716 | −1.20697 | ||||||||
\(668\) | −4.61783 | − | 2.66611i | −0.178669 | − | 0.103155i | ||||
\(669\) | −22.3059 | + | 12.8783i | −0.862397 | + | 0.497905i | ||||
\(670\) | 5.53872i | 0.213979i | ||||||||
\(671\) | − | 1.10885i | − | 0.0428068i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.45845 | + | 5.99020i | 0.133313 | + | 0.230905i | 0.924952 | − | 0.380084i | \(-0.124105\pi\) |
−0.791639 | + | 0.610990i | \(0.790772\pi\) | |||||||
\(674\) | 5.04721 | + | 2.91401i | 0.194411 | + | 0.112243i | ||||
\(675\) | −5.39823 | + | 9.35001i | −0.207778 | + | 0.359882i | ||||
\(676\) | 25.4993 | − | 1.96573i | 0.980742 | − | 0.0756050i | ||||
\(677\) | −6.16453 | − | 10.6773i | −0.236922 | − | 0.410361i | 0.722908 | − | 0.690945i | \(-0.242805\pi\) |
−0.959830 | + | 0.280584i | \(0.909472\pi\) | |||||||
\(678\) | −5.70137 | + | 3.29169i | −0.218960 | + | 0.126416i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.59185 | + | 7.95331i | −0.176089 | + | 0.304996i | ||||
\(681\) | −4.53660 | + | 2.61921i | −0.173843 | + | 0.100368i | ||||
\(682\) | 1.56078 | − | 0.901120i | 0.0597655 | − | 0.0345057i | ||||
\(683\) | 21.2491 | − | 12.2682i | 0.813076 | − | 0.469430i | −0.0349470 | − | 0.999389i | \(-0.511126\pi\) |
0.848023 | + | 0.529960i | \(0.177793\pi\) | |||||||
\(684\) | −0.107326 | + | 0.0619648i | −0.00410372 | + | 0.00236928i | ||||
\(685\) | −6.80655 | + | 11.7893i | −0.260065 | + | 0.450446i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8751 | − | 8.01082i | 0.529370 | − | 0.305632i | ||||
\(688\) | −15.2398 | − | 26.3961i | −0.581012 | − | 1.00634i | ||||
\(689\) | −25.4812 | + | 0.980713i | −0.970756 | + | 0.0373622i | ||||
\(690\) | 1.95129 | − | 3.37973i | 0.0742843 | − | 0.128664i | ||||
\(691\) | 7.88703 | + | 4.55358i | 0.300037 | + | 0.173226i | 0.642459 | − | 0.766320i | \(-0.277914\pi\) |
−0.342423 | + | 0.939546i | \(0.611247\pi\) | |||||||
\(692\) | 0.885106 | + | 1.53305i | 0.0336467 | + | 0.0582777i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.47992i | 0.0561769i | ||||||||
\(695\) | 20.7564i | 0.787336i | ||||||||
\(696\) | 8.03826 | − | 4.64089i | 0.304690 | − | 0.175913i | ||||
\(697\) | 22.4055 | + | 12.9358i | 0.848667 | + | 0.489978i | ||||
\(698\) | −3.95087 | −0.149542 | ||||||||
\(699\) | 4.66312 | + | 8.07675i | 0.176375 | + | 0.305491i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.286950 | 0.0108380 | 0.00541898 | − | 0.999985i | \(-0.498275\pi\) | ||||
0.00541898 | + | 0.999985i | \(0.498275\pi\) | |||||||
\(702\) | −0.122050 | − | 3.17115i | −0.00460650 | − | 0.119687i | ||||
\(703\) | 0.749377 | − | 1.29796i | 0.0282633 | − | 0.0489534i | ||||
\(704\) | − | 19.4684i | − | 0.733742i | ||||||
\(705\) | 4.53518 | − | 7.85516i | 0.170805 | − | 0.295842i | ||||
\(706\) | −0.0512797 | + | 0.0888191i | −0.00192994 | + | 0.00334275i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −23.6093 | − | 13.6308i | −0.887292 | − | 0.512278i | ||||
\(709\) | 18.5848i | 0.697967i | 0.937129 | + | 0.348984i | \(0.113473\pi\) | ||||
−0.937129 | + | 0.348984i | \(0.886527\pi\) | |||||||
\(710\) | 1.40727 | + | 0.812486i | 0.0528138 | + | 0.0304921i | ||||
\(711\) | −1.52294 | − | 2.63781i | −0.0571147 | − | 0.0989256i | ||||
\(712\) | −2.11328 | + | 3.66031i | −0.0791986 | + | 0.137176i | ||||
\(713\) | −14.0940 | + | 8.13715i | −0.527823 | + | 0.304739i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1704 | − | 23.0872i | 0.455148 | − | 0.863414i | ||||
\(716\) | −10.8751 | − | 18.8362i | −0.406421 | − | 0.703941i | ||||
\(717\) | 4.56132i | 0.170346i | ||||||||
\(718\) | −5.85947 | −0.218674 | ||||||||
\(719\) | 41.6949 | 1.55496 | 0.777479 | − | 0.628909i | \(-0.216498\pi\) | ||||
0.777479 | + | 0.628909i | \(0.216498\pi\) | |||||||
\(720\) | − | 3.41757i | − | 0.127365i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.96980 | − | 1.71462i | −0.110525 | − | 0.0638114i | ||||
\(723\) | −12.6275 | + | 7.29046i | −0.469620 | + | 0.271135i | ||||
\(724\) | −3.47128 | − | 6.01244i | −0.129009 | − | 0.223451i | ||||
\(725\) | −15.7162 | −0.583684 | ||||||||
\(726\) | −1.06975 | − | 0.617623i | −0.0397023 | − | 0.0229221i | ||||
\(727\) | −32.7039 | −1.21292 | −0.606461 | − | 0.795113i | \(-0.707411\pi\) | ||||
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.3578 | 0.865105 | ||||||||
\(730\) | 5.98091 | + | 3.45308i | 0.221363 | + | 0.127804i | ||||
\(731\) | 38.1702 | 1.41178 | ||||||||
\(732\) | −0.739235 | − | 1.28039i | −0.0273229 | − | 0.0473246i | ||||
\(733\) | 8.60423 | − | 4.96765i | 0.317804 | − | 0.183484i | −0.332609 | − | 0.943065i | \(-0.607929\pi\) |
0.650413 | + | 0.759580i | \(0.274596\pi\) | |||||||
\(734\) | −1.23225 | − | 0.711440i | −0.0454832 | − | 0.0262597i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 9.33871i | − | 0.344230i | ||||||
\(737\) | 30.7171 | 1.13148 | ||||||||
\(738\) | 0.328237 | 0.0120826 | ||||||||
\(739\) | 10.4022i | 0.382649i | 0.981527 | + | 0.191325i | \(0.0612784\pi\) | ||||
−0.981527 | + | 0.191325i | \(0.938722\pi\) | |||||||
\(740\) | 21.0205 | + | 36.4086i | 0.772730 | + | 1.33841i | ||||
\(741\) | −1.04969 | + | 0.661133i | −0.0385615 | + | 0.0242873i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.47972 | + | 0.854317i | −0.0542857 | + | 0.0313419i | −0.526897 | − | 0.849929i | \(-0.676645\pi\) |
0.472612 | + | 0.881271i | \(0.343311\pi\) | |||||||
\(744\) | 2.42295 | − | 4.19668i | 0.0888297 | − | 0.153858i | ||||
\(745\) | −19.2343 | − | 33.3148i | −0.704690 | − | 1.22056i | ||||
\(746\) | 0.327545 | + | 0.189108i | 0.0119923 | + | 0.00692374i | ||||
\(747\) | − | 5.54528i | − | 0.202891i | ||||||
\(748\) | 21.8723 | + | 12.6280i | 0.799732 | + | 0.461726i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.23393 | + | 2.13722i | −0.0450566 | + | 0.0780404i | ||||
\(751\) | 14.9906 | − | 25.9645i | 0.547015 | − | 0.947458i | −0.451462 | − | 0.892290i | \(-0.649097\pi\) |
0.998477 | − | 0.0551673i | \(-0.0175692\pi\) | |||||||
\(752\) | − | 7.03481i | − | 0.256533i | ||||||
\(753\) | −23.0598 | + | 39.9408i | −0.840347 | + | 1.45552i | ||||
\(754\) | 3.90890 | − | 2.46195i | 0.142354 | − | 0.0896590i | ||||
\(755\) | 17.3893 | 0.632860 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.20229 | − | 7.27858i | −0.152735 | − | 0.264545i | 0.779497 | − | 0.626406i | \(-0.215475\pi\) |
−0.932232 | + | 0.361861i | \(0.882141\pi\) | |||||||
\(758\) | −2.58874 | −0.0940271 | ||||||||
\(759\) | −18.7436 | − | 10.8216i | −0.680350 | − | 0.392800i | ||||
\(760\) | −0.314506 | + | 0.181580i | −0.0114083 | + | 0.00658660i | ||||
\(761\) | − | 51.0590i | − | 1.85089i | −0.378885 | − | 0.925444i | \(-0.623692\pi\) | ||
0.378885 | − | 0.925444i | \(-0.376308\pi\) | |||||||
\(762\) | 2.63067i | 0.0952990i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.0668 | + | 34.7568i | 0.725993 | + | 1.25746i | ||||
\(765\) | 3.70650 | + | 2.13995i | 0.134009 | + | 0.0773699i | ||||
\(766\) | −2.27723 | + | 3.94429i | −0.0822798 | + | 0.142513i | ||||
\(767\) | −24.2049 | − | 12.7596i | −0.873988 | − | 0.460722i | ||||
\(768\) | −12.2780 | − | 21.2661i | −0.443044 | − | 0.767375i | ||||
\(769\) | 0.610062 | − | 0.352220i | 0.0219994 | − | 0.0127014i | −0.488960 | − | 0.872306i | \(-0.662624\pi\) |
0.510959 | + | 0.859605i | \(0.329290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.08015 | − | 5.33498i | 0.110929 | − | 0.192134i | ||||
\(772\) | 29.4142 | − | 16.9823i | 1.05864 | − | 0.611206i | ||||
\(773\) | 1.09571 | − | 0.632607i | 0.0394099 | − | 0.0227533i | −0.480166 | − | 0.877178i | \(-0.659423\pi\) |
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(774\) | 0.419392 | − | 0.242136i | 0.0150747 | − | 0.00870341i | ||||
\(775\) | −7.10593 | + | 4.10261i | −0.255253 | + | 0.147370i | ||||
\(776\) | 0.161803 | − | 0.280252i | 0.00580840 | − | 0.0100604i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.40076 | + | 2.54078i | −0.157775 | + | 0.0910914i | ||||
\(779\) | 0.511533 | + | 0.886001i | 0.0183276 | + | 0.0317443i | ||||
\(780\) | −1.33831 | − | 34.7724i | −0.0479193 | − | 1.24505i | ||||
\(781\) | 4.50596 | − | 7.80456i | 0.161236 | − | 0.279269i | ||||
\(782\) | 3.28265 | + | 1.89524i | 0.117387 | + | 0.0677737i | ||||
\(783\) | 17.2448 | + | 29.8689i | 0.616279 | + | 1.06743i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.7679i | 1.52645i | ||||||||
\(786\) | − | 3.30779i | − | 0.117985i | ||||||
\(787\) | −37.9292 | + | 21.8984i | −1.35203 | + | 0.780595i | −0.988534 | − | 0.151000i | \(-0.951751\pi\) |
−0.363497 | + | 0.931595i | \(0.618417\pi\) | |||||||
\(788\) | 8.44493 | + | 4.87568i | 0.300838 | + | 0.173689i | ||||
\(789\) | −0.290218 | −0.0103320 | ||||||||
\(790\) | −2.21300 | − | 3.83303i | −0.0787351 | − | 0.136373i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.646180 | 0.0229610 | ||||||||
\(793\) | −0.790833 | − | 1.25562i | −0.0280833 | − | 0.0445884i | ||||
\(794\) | 1.96885 | − | 3.41015i | 0.0698719 | − | 0.121022i | ||||
\(795\) | 34.6963i | 1.23055i | ||||||||
\(796\) | −7.06453 | + | 12.2361i | −0.250396 | + | 0.433698i | ||||
\(797\) | −6.84183 | + | 11.8504i | −0.242350 | + | 0.419763i | −0.961383 | − | 0.275213i | \(-0.911252\pi\) |
0.719033 | + | 0.694976i | \(0.244585\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.62954 | + | 4.40492i | 0.269914 | + | 0.155835i | ||||
\(800\) | − | 4.70842i | − | 0.166468i | ||||||
\(801\) | 1.70582 | + | 0.984857i | 0.0602722 | + | 0.0347982i | ||||
\(802\) | 1.85606 | + | 3.21479i | 0.0655398 | + | 0.113518i | ||||
\(803\) | 19.1504 | − | 33.1695i | 0.675803 | − | 1.17053i | ||||
\(804\) | 35.4691 | − | 20.4781i | 1.25090 | − | 0.722206i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.12469 | − | 2.13354i | 0.0396157 | − | 0.0751508i | ||||
\(807\) | −21.2973 | − | 36.8881i | −0.749702 | − | 1.29852i | ||||
\(808\) | − | 5.49285i | − | 0.193238i | ||||||
\(809\) | 9.11375 | 0.320422 | 0.160211 | − | 0.987083i | \(-0.448782\pi\) | ||||
0.160211 | + | 0.987083i | \(0.448782\pi\) | |||||||
\(810\) | −4.80523 | −0.168839 | ||||||||
\(811\) | 2.31899i | 0.0814309i | 0.999171 | + | 0.0407154i | \(0.0129637\pi\) | ||||
−0.999171 | + | 0.0407154i | \(0.987036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.6934 | − | 10.7926i | −0.655606 | − | 0.378514i | ||||
\(814\) | −3.35595 | + | 1.93756i | −0.117626 | + | 0.0679114i | ||||
\(815\) | 6.42325 | + | 11.1254i | 0.224997 | + | 0.389706i | ||||
\(816\) | 33.1057 | 1.15893 | ||||||||
\(817\) | 1.30718 | + | 0.754702i | 0.0457325 | + | 0.0264037i | ||||
\(818\) | 1.13352 | 0.0396325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.6977 | −1.00217 | ||||||||
\(821\) | 8.78557 | + | 5.07235i | 0.306619 | + | 0.177026i | 0.645412 | − | 0.763834i | \(-0.276686\pi\) |
−0.338794 | + | 0.940861i | \(0.610019\pi\) | |||||||
\(822\) | −1.67304 | −0.0583540 | ||||||||
\(823\) | −13.4089 | − | 23.2249i | −0.467405 | − | 0.809570i | 0.531901 | − | 0.846806i | \(-0.321478\pi\) |
−0.999306 | + | 0.0372366i | \(0.988144\pi\) | |||||||
\(824\) | 3.20414 | − | 1.84991i | 0.111622 | − | 0.0644448i | ||||
\(825\) | −9.45021 | − | 5.45608i | −0.329014 | − | 0.189956i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6015i | 1.16844i | 0.811596 | + | 0.584219i | \(0.198599\pi\) | ||||
−0.811596 | + | 0.584219i | \(0.801401\pi\) | |||||||
\(828\) | −2.89348 | −0.100555 | ||||||||
\(829\) | 11.8666 | 0.412142 | 0.206071 | − | 0.978537i | \(-0.433932\pi\) | ||||
0.206071 | + | 0.978537i | \(0.433932\pi\) | |||||||
\(830\) | − | 8.05791i | − | 0.279694i | ||||||
\(831\) | −24.9847 | − | 43.2748i | −0.866710 | − | 1.50119i | ||||
\(832\) | −13.8848 | − | 22.0452i | −0.481370 | − | 0.764281i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.20919 | + | 1.27547i | −0.0764979 | + | 0.0441661i | ||||
\(835\) | −3.64096 | + | 6.30633i | −0.126001 | + | 0.218240i | ||||
\(836\) | 0.499362 | + | 0.864920i | 0.0172708 | + | 0.0299139i | ||||
\(837\) | 15.5942 | + | 9.00330i | 0.539013 | + | 0.311199i | ||||
\(838\) | − | 6.17756i | − | 0.213400i | ||||||
\(839\) | 29.9798 | + | 17.3088i | 1.03502 | + | 0.597568i | 0.918418 | − | 0.395611i | \(-0.129467\pi\) |
0.116600 | + | 0.993179i | \(0.462801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6029 | + | 18.3648i | −0.365617 | + | 0.633267i | ||||
\(842\) | 1.04185 | − | 1.80453i | 0.0359044 | − | 0.0621882i | ||||
\(843\) | − | 52.1112i | − | 1.79481i | ||||||
\(844\) | 17.3051 | − | 29.9733i | 0.595666 | − | 1.03172i | ||||
\(845\) | −2.68450 | − | 34.8230i | −0.0923494 | − | 1.19795i | ||||
\(846\) | 0.111772 | 0.00384280 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13.4549 | + | 23.3046i | 0.462044 | + | 0.800283i | ||||
\(849\) | 32.8173 | 1.12629 | ||||||||
\(850\) | 1.65506 | + | 0.955548i | 0.0567680 | + | 0.0327750i | ||||
\(851\) | 30.3044 | − | 17.4963i | 1.03882 | − | 0.599764i | ||||
\(852\) | − | 12.0159i | − | 0.411658i | ||||||
\(853\) | 29.1897i | 0.999436i | 0.866188 | + | 0.499718i | \(0.166563\pi\) | ||||
−0.866188 | + | 0.499718i | \(0.833437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0846220 | + | 0.146570i | 0.00289401 | + | 0.00501258i | ||||
\(856\) | −4.99061 | − | 2.88133i | −0.170575 | − | 0.0984817i | ||||
\(857\) | 12.6599 | − | 21.9276i | 0.432455 | − | 0.749033i | −0.564629 | − | 0.825345i | \(-0.690981\pi\) |
0.997084 | + | 0.0763112i | \(0.0243142\pi\) | |||||||
\(858\) | 3.20513 | − | 0.123358i | 0.109421 | − | 0.00421139i | ||||
\(859\) | 13.0424 | + | 22.5902i | 0.445002 | + | 0.770766i | 0.998052 | − | 0.0623818i | \(-0.0198696\pi\) |
−0.553050 | + | 0.833148i | \(0.686536\pi\) | |||||||
\(860\) | −36.6674 | + | 21.1699i | −1.25035 | + | 0.721888i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.792913 | − | 1.37337i | 0.0270067 | − | 0.0467770i | ||||
\(863\) | −31.2061 | + | 18.0169i | −1.06227 | + | 0.613302i | −0.926059 | − | 0.377378i | \(-0.876826\pi\) |
−0.136210 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(864\) | −8.94843 | + | 5.16638i | −0.304432 | + | 0.175764i | ||||
\(865\) | 2.09360 | − | 1.20874i | 0.0711846 | − | 0.0410985i | ||||
\(866\) | 3.46190 | − | 1.99873i | 0.117640 | − | 0.0679196i | ||||
\(867\) | −5.20832 | + | 9.02108i | −0.176884 | + | 0.306372i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.2576 | + | 12.2731i | −0.721114 | + | 0.416335i | ||||
\(870\) | −3.14279 | − | 5.44348i | −0.106551 | − | 0.184551i | ||||
\(871\) | 34.7829 | − | 21.9074i | 1.17857 | − | 0.742305i | ||||
\(872\) | 0.478337 | − | 0.828504i | 0.0161985 | − | 0.0280567i | ||||
\(873\) | −0.130606 | − | 0.0754055i | −0.00442035 | − | 0.00255209i | ||||
\(874\) | 0.0749454 | + | 0.129809i | 0.00253507 | + | 0.00439086i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 51.0677i | − | 1.72542i | ||||||
\(877\) | 9.12168i | 0.308017i | 0.988070 | + | 0.154009i | \(0.0492184\pi\) | ||||
−0.988070 | + | 0.154009i | \(0.950782\pi\) | |||||||
\(878\) | −1.62407 | + | 0.937657i | −0.0548097 | + | 0.0316444i | ||||
\(879\) | −23.5452 | − | 13.5938i | −0.794158 | − | 0.458507i | ||||
\(880\) | −27.5415 | −0.928425 | ||||||||
\(881\) | −6.51653 | − | 11.2870i | −0.219548 | − | 0.380268i | 0.735122 | − | 0.677935i | \(-0.237125\pi\) |
−0.954670 | + | 0.297667i | \(0.903791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.13222 | −0.0717548 | −0.0358774 | − | 0.999356i | \(-0.511423\pi\) | ||||
−0.0358774 | + | 0.999356i | \(0.511423\pi\) | |||||||
\(884\) | 33.7737 | − | 1.29987i | 1.13593 | − | 0.0437194i | ||||
\(885\) | −18.6149 | + | 32.2420i | −0.625734 | + | 1.08380i | ||||
\(886\) | 6.47597i | 0.217564i | ||||||||
\(887\) | −23.5857 | + | 40.8517i | −0.791932 | + | 1.37167i | 0.132838 | + | 0.991138i | \(0.457591\pi\) |
−0.924769 | + | 0.380528i | \(0.875742\pi\) | |||||||
\(888\) | −5.20976 | + | 9.02356i | −0.174828 | + | 0.302811i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.47875 | + | 1.43111i | 0.0830878 | + | 0.0479708i | ||||
\(891\) | 26.6493i | 0.892785i | ||||||||
\(892\) | 24.0319 | + | 13.8748i | 0.804647 | + | 0.464563i | ||||
\(893\) | 0.174188 | + | 0.301702i | 0.00582898 | + | 0.0100961i | ||||
\(894\) | 2.36388 | − | 4.09437i | 0.0790601 | − | 0.136936i | ||||
\(895\) | −25.7236 | + | 14.8515i | −0.859844 | + | 0.496431i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.9425 | + | 1.11393i | −0.966363 | + | 0.0371931i | ||||
\(898\) | 2.05689 | + | 3.56264i | 0.0686394 | + | 0.118887i | ||||
\(899\) | 26.2118i | 0.874213i | ||||||||
\(900\) | −1.45884 | −0.0486280 | ||||||||
\(901\) | −33.6997 | −1.12270 | ||||||||
\(902\) | − | 2.64520i | − | 0.0880755i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.3871 | + | 7.15171i | 0.411990 | + | 0.237862i | ||||
\(905\) | −8.21087 | + | 4.74055i | −0.272939 | + | 0.157581i | ||||
\(906\) | 1.06856 | + | 1.85081i | 0.0355007 | + | 0.0614889i | ||||
\(907\) | −16.0431 | −0.532702 | −0.266351 | − | 0.963876i | \(-0.585818\pi\) | ||||
−0.266351 | + | 0.963876i | \(0.585818\pi\) | |||||||
\(908\) | 4.88763 | + | 2.82187i | 0.162202 | + | 0.0936471i | ||||
\(909\) | −2.55984 | −0.0849047 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4319 | −0.809466 | −0.404733 | − | 0.914435i | \(-0.632636\pi\) | ||||
−0.404733 | + | 0.914435i | \(0.632636\pi\) | |||||||
\(912\) | 1.13374 | + | 0.654565i | 0.0375419 | + | 0.0216748i | ||||
\(913\) | −44.6883 | −1.47897 | ||||||||
\(914\) | 2.83144 | + | 4.90420i | 0.0936558 | + | 0.162217i | ||||
\(915\) | −1.74856 | + | 1.00953i | −0.0578057 | + | 0.0333742i | ||||
\(916\) | −14.9488 | − | 8.63067i | −0.493921 | − | 0.285165i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 4.19395i | − | 0.138421i | ||||||
\(919\) | 15.9160 | 0.525020 | 0.262510 | − | 0.964929i | \(-0.415450\pi\) | ||||
0.262510 | + | 0.964929i | \(0.415450\pi\) | |||||||
\(920\) | −8.47897 | −0.279543 | ||||||||
\(921\) | − | 42.9407i | − | 1.41494i | ||||||
\(922\) | −0.760140 | − | 1.31660i | −0.0250339 | − | 0.0433600i | ||||
\(923\) | −0.463824 | − | 12.0512i | −0.0152670 | − | 0.396671i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2790 | − | 8.82131i | 0.502369 | − | 0.290043i | ||||
\(926\) | −0.907665 | + | 1.57212i | −0.0298277 | + | 0.0516632i | ||||
\(927\) | −0.862118 | − | 1.49323i | −0.0283157 | − | 0.0490442i | ||||
\(928\) | −13.0260 | − | 7.52059i | −0.427601 | − | 0.246875i | ||||
\(929\) | 47.3235i | 1.55263i | 0.630342 | + | 0.776317i | \(0.282914\pi\) | ||||
−0.630342 | + | 0.776317i | \(0.717086\pi\) | |||||||
\(930\) | −2.84197 | − | 1.64081i | −0.0931920 | − | 0.0538044i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.02393 | − | 8.70170i | 0.164564 | − | 0.285034i | ||||
\(933\) | −1.48902 | + | 2.57906i | −0.0487484 | + | 0.0844347i | ||||
\(934\) | − | 4.76494i | − | 0.155914i | ||||||
\(935\) | 17.2454 | − | 29.8699i | 0.563985 | − | 0.976850i | ||||
\(936\) | 0.731710 | − | 0.460855i | 0.0239167 | − | 0.0150635i | ||||
\(937\) | 29.7044 | 0.970401 | 0.485200 | − | 0.874403i | \(-0.338747\pi\) | ||||
0.485200 | + | 0.874403i | \(0.338747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.636122 | − | 1.10180i | −0.0207591 | − | 0.0359558i | ||||
\(940\) | −9.77219 | −0.318734 | ||||||||
\(941\) | 35.0068 | + | 20.2112i | 1.14119 | + | 0.658866i | 0.946725 | − | 0.322043i | \(-0.104370\pi\) |
0.194465 | + | 0.980909i | \(0.437703\pi\) | |||||||
\(942\) | −4.55196 | + | 2.62808i | −0.148311 | + | 0.0856273i | ||||
\(943\) | 23.8863i | 0.777844i | ||||||||
\(944\) | 28.8748i | 0.939795i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.95133 | − | 3.37980i | −0.0634431 | − | 0.109887i | ||||
\(947\) | 39.7703 | + | 22.9614i | 1.29236 | + | 0.746146i | 0.979072 | − | 0.203512i | \(-0.0652356\pi\) |
0.313290 | + | 0.949658i | \(0.398569\pi\) | |||||||
\(948\) | −16.3641 | + | 28.3434i | −0.531481 | + | 0.920551i | ||||
\(949\) | −1.97126 | − | 51.2179i | −0.0639898 | − | 1.66260i | ||||
\(950\) | 0.0377862 | + | 0.0654476i | 0.00122595 | + | 0.00212340i | ||||
\(951\) | −33.8869 | + | 19.5646i | −1.09886 | + | 0.634426i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.19465 | − | 10.7294i | 0.200664 | − | 0.347561i | −0.748078 | − | 0.663610i | \(-0.769023\pi\) |
0.948743 | + | 0.316050i | \(0.102357\pi\) | |||||||
\(954\) | −0.370273 | + | 0.213777i | −0.0119880 | + | 0.00692129i | ||||
\(955\) | 47.4655 | − | 27.4042i | 1.53595 | − | 0.886780i | ||||
\(956\) | 4.25587 | − | 2.45713i | 0.137645 | − | 0.0794693i | ||||
\(957\) | −30.1890 | + | 17.4296i | −0.975870 | + | 0.563419i | ||||
\(958\) | −0.776108 | + | 1.34426i | −0.0250749 | + | 0.0434310i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.6999 | + | 17.7246i | −0.990836 | + | 0.572060i | ||||
\(961\) | −8.65757 | − | 14.9953i | −0.279276 | − | 0.483721i | ||||
\(962\) | −2.41828 | + | 4.58748i | −0.0779686 | + | 0.147906i | ||||
\(963\) | −1.34279 | + | 2.32578i | −0.0432708 | + | 0.0749472i | ||||
\(964\) | 13.6045 | + | 7.85457i | 0.438172 | + | 0.252979i | ||||
\(965\) | −23.1918 | − | 40.1694i | −0.746572 | − | 1.29310i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.44932i | 0.303870i | 0.988391 | + | 0.151935i | \(0.0485504\pi\) | ||||
−0.988391 | + | 0.151935i | \(0.951450\pi\) | |||||||
\(968\) | 2.68377i | 0.0862596i | ||||||||
\(969\) | −1.41980 | + | 0.819725i | −0.0456107 | + | 0.0263333i | ||||
\(970\) | −0.189785 | − | 0.109573i | −0.00609364 | − | 0.00351816i | ||||
\(971\) | 20.9763 | 0.673163 | 0.336581 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336581 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(972\) | 3.40223 | + | 5.89283i | 0.109126 | + | 0.189013i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.84363 | −0.123158 | ||||||||
\(975\) | −14.5923 | + | 0.561625i | −0.467328 | + | 0.0179864i | ||||
\(976\) | −0.782977 | + | 1.35616i | −0.0250625 | + | 0.0434095i | ||||
\(977\) | 13.1843i | 0.421802i | 0.977507 | + | 0.210901i | \(0.0676398\pi\) | ||||
−0.977507 | + | 0.210901i | \(0.932360\pi\) | |||||||
\(978\) | −0.789413 | + | 1.36730i | −0.0252426 | + | 0.0437215i | ||||
\(979\) | 7.93676 | − | 13.7469i | 0.253660 | − | 0.439352i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.386109 | − | 0.222920i | −0.0123275 | − | 0.00711729i | ||||
\(982\) | 4.06013i | 0.129564i | ||||||||
\(983\) | −20.2294 | − | 11.6794i | −0.645216 | − | 0.372516i | 0.141405 | − | 0.989952i | \(-0.454838\pi\) |
−0.786621 | + | 0.617436i | \(0.788171\pi\) | |||||||
\(984\) | −3.55624 | − | 6.15959i | −0.113369 | − | 0.196360i | ||||
\(985\) | 6.65846 | − | 11.5328i | 0.212156 | − | 0.367465i | ||||
\(986\) | 5.28713 | − | 3.05252i | 0.168376 | − | 0.0972122i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.18232 | + | 0.623257i | 0.0376145 | + | 0.0198285i | ||||
\(989\) | 17.6206 | + | 30.5197i | 0.560302 | + | 0.970471i | ||||
\(990\) | − | 0.437591i | − | 0.0139076i | ||||||
\(991\) | 39.4929 | 1.25453 | 0.627267 | − | 0.778804i | \(-0.284173\pi\) | ||||
0.627267 | + | 0.778804i | \(0.284173\pi\) | |||||||
\(992\) | −7.85281 | −0.249327 | ||||||||
\(993\) | − | 2.77639i | − | 0.0881060i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.7102 | + | 9.64766i | 0.529750 | + | 0.305851i | ||||
\(996\) | −51.6015 | + | 29.7922i | −1.63506 | + | 0.944001i | ||||
\(997\) | −25.7396 | − | 44.5822i | −0.815180 | − | 1.41193i | −0.909199 | − | 0.416363i | \(-0.863305\pi\) |
0.0940184 | − | 0.995570i | \(-0.470029\pi\) | |||||||
\(998\) | −7.03007 | −0.222533 | ||||||||
\(999\) | −33.5301 | − | 19.3586i | −1.06085 | − | 0.612479i |
(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 | 637.2.u.g.361.3 | 12 | ||
7.2 | even | 3 | 637.2.k.i.569.4 | 12 | |||
7.3 | odd | 6 | 637.2.q.g.491.4 | 12 | |||
7.4 | even | 3 | 637.2.q.i.491.4 | 12 | |||
7.5 | odd | 6 | 91.2.k.b.23.4 | yes | 12 | ||
7.6 | odd | 2 | 91.2.u.b.88.3 | yes | 12 | ||
13.4 | even | 6 | 637.2.k.i.459.3 | 12 | |||
21.5 | even | 6 | 819.2.bm.f.478.3 | 12 | |||
21.20 | even | 2 | 819.2.do.e.361.4 | 12 | |||
91.4 | even | 6 | 637.2.q.i.589.4 | 12 | |||
91.11 | odd | 12 | 8281.2.a.co.1.6 | 12 | |||
91.17 | odd | 6 | 637.2.q.g.589.4 | 12 | |||
91.24 | even | 12 | 8281.2.a.cp.1.6 | 12 | |||
91.30 | even | 6 | inner | 637.2.u.g.30.3 | 12 | ||
91.41 | even | 12 | 1183.2.e.j.508.6 | 24 | |||
91.54 | even | 12 | 1183.2.e.j.170.6 | 24 | |||
91.67 | odd | 12 | 8281.2.a.co.1.7 | 12 | |||
91.69 | odd | 6 | 91.2.k.b.4.3 | ✓ | 12 | ||
91.76 | even | 12 | 1183.2.e.j.508.7 | 24 | |||
91.80 | even | 12 | 8281.2.a.cp.1.7 | 12 | |||
91.82 | odd | 6 | 91.2.u.b.30.3 | yes | 12 | ||
91.89 | even | 12 | 1183.2.e.j.170.7 | 24 | |||
273.173 | even | 6 | 819.2.do.e.667.4 | 12 | |||
273.251 | even | 6 | 819.2.bm.f.550.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.3 | ✓ | 12 | 91.69 | odd | 6 | ||
91.2.k.b.23.4 | yes | 12 | 7.5 | odd | 6 | ||
91.2.u.b.30.3 | yes | 12 | 91.82 | odd | 6 | ||
91.2.u.b.88.3 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.i.459.3 | 12 | 13.4 | even | 6 | |||
637.2.k.i.569.4 | 12 | 7.2 | even | 3 | |||
637.2.q.g.491.4 | 12 | 7.3 | odd | 6 | |||
637.2.q.g.589.4 | 12 | 91.17 | odd | 6 | |||
637.2.q.i.491.4 | 12 | 7.4 | even | 3 | |||
637.2.q.i.589.4 | 12 | 91.4 | even | 6 | |||
637.2.u.g.30.3 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.g.361.3 | 12 | 1.1 | even | 1 | trivial | ||
819.2.bm.f.478.3 | 12 | 21.5 | even | 6 | |||
819.2.bm.f.550.4 | 12 | 273.251 | even | 6 | |||
819.2.do.e.361.4 | 12 | 21.20 | even | 2 | |||
819.2.do.e.667.4 | 12 | 273.173 | even | 6 | |||
1183.2.e.j.170.6 | 24 | 91.54 | even | 12 | |||
1183.2.e.j.170.7 | 24 | 91.89 | even | 12 | |||
1183.2.e.j.508.6 | 24 | 91.41 | even | 12 | |||
1183.2.e.j.508.7 | 24 | 91.76 | even | 12 | |||
8281.2.a.co.1.6 | 12 | 91.11 | odd | 12 | |||
8281.2.a.co.1.7 | 12 | 91.67 | odd | 12 | |||
8281.2.a.cp.1.6 | 12 | 91.24 | even | 12 | |||
8281.2.a.cp.1.7 | 12 | 91.80 | even | 12 |