Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(324,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.b (of order \(2\), degree \(1\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2058981376.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 324.6 | ||
Root | \(0.148421 - 0.148421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.324 |
Dual form | 475.2.b.e.324.3 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.95594i | 1.38306i | 0.722348 | + | 0.691530i | \(0.243063\pi\) | ||||
−0.722348 | + | 0.691530i | \(0.756937\pi\) | |||||||
\(3\) | − 0.296842i | − 0.171382i | −0.996322 | − | 0.0856908i | \(-0.972690\pi\) | ||||
0.996322 | − | 0.0856908i | \(-0.0273097\pi\) | |||||||
\(4\) | −1.82571 | −0.912855 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.580605 | 0.237031 | ||||||||
\(7\) | − 3.56331i | − 1.34680i | −0.739277 | − | 0.673402i | \(-0.764832\pi\) | ||||
0.739277 | − | 0.673402i | \(-0.235168\pi\) | |||||||
\(8\) | 0.340899i | 0.120526i | ||||||||
\(9\) | 2.91188 | 0.970628 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.56331 | 1.67740 | 0.838700 | − | 0.544594i | \(-0.183316\pi\) | ||||
0.838700 | + | 0.544594i | \(0.183316\pi\) | |||||||
\(12\) | 0.541947i | 0.156447i | ||||||||
\(13\) | − 5.26647i | − 1.46065i | −0.683097 | − | 0.730327i | \(-0.739368\pi\) | ||||
0.683097 | − | 0.730327i | \(-0.260632\pi\) | |||||||
\(14\) | 6.96962 | 1.86271 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.31820 | −1.07955 | ||||||||
\(17\) | 1.40632i | 0.341082i | 0.985351 | + | 0.170541i | \(0.0545515\pi\) | ||||
−0.985351 | + | 0.170541i | \(0.945448\pi\) | |||||||
\(18\) | 5.69548i | 1.34244i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05774 | −0.230817 | ||||||||
\(22\) | 10.8815i | 2.31995i | ||||||||
\(23\) | 6.96962i | 1.45327i | 0.687025 | + | 0.726633i | \(0.258916\pi\) | ||||
−0.687025 | + | 0.726633i | \(0.741084\pi\) | |||||||
\(24\) | 0.101193 | 0.0206560 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.3009 | 2.02017 | ||||||||
\(27\) | − 1.75489i | − 0.337730i | ||||||||
\(28\) | 6.50557i | 1.22944i | ||||||||
\(29\) | −1.40632 | −0.261146 | −0.130573 | − | 0.991439i | \(-0.541682\pi\) | ||||
−0.130573 | + | 0.991439i | \(0.541682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.75489 | 0.315188 | 0.157594 | − | 0.987504i | \(-0.449626\pi\) | ||||
0.157594 | + | 0.987504i | \(0.449626\pi\) | |||||||
\(32\) | − 7.76435i | − 1.37256i | ||||||||
\(33\) | − 1.65142i | − 0.287476i | ||||||||
\(34\) | −2.75067 | −0.471737 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.31626 | −0.886043 | ||||||||
\(37\) | 3.61504i | 0.594309i | 0.954829 | + | 0.297155i | \(0.0960377\pi\) | ||||
−0.954829 | + | 0.297155i | \(0.903962\pi\) | |||||||
\(38\) | − 1.95594i | − 0.317296i | ||||||||
\(39\) | −1.56331 | −0.250329 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.34858 | 0.679134 | 0.339567 | − | 0.940582i | \(-0.389720\pi\) | ||||
0.339567 | + | 0.940582i | \(0.389720\pi\) | |||||||
\(42\) | − 2.06888i | − 0.319234i | ||||||||
\(43\) | 3.56331i | 0.543399i | 0.962382 | + | 0.271700i | \(0.0875857\pi\) | ||||
−0.962382 | + | 0.271700i | \(0.912414\pi\) | |||||||
\(44\) | −10.1570 | −1.53122 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.6322 | −2.00996 | ||||||||
\(47\) | − 8.26046i | − 1.20491i | −0.798152 | − | 0.602456i | \(-0.794189\pi\) | ||||
0.798152 | − | 0.602456i | \(-0.205811\pi\) | |||||||
\(48\) | 1.28182i | 0.185015i | ||||||||
\(49\) | −5.69716 | −0.813879 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.417453 | 0.0584552 | ||||||||
\(52\) | 9.61504i | 1.33337i | ||||||||
\(53\) | 7.61504i | 1.04601i | 0.852331 | + | 0.523003i | \(0.175188\pi\) | ||||
−0.852331 | + | 0.523003i | \(0.824812\pi\) | |||||||
\(54\) | 3.43247 | 0.467100 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.21473 | 0.162325 | ||||||||
\(57\) | 0.296842i | 0.0393177i | ||||||||
\(58\) | − 2.75067i | − 0.361181i | ||||||||
\(59\) | −9.47519 | −1.23356 | −0.616782 | − | 0.787134i | \(-0.711564\pi\) | ||||
−0.616782 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.21473 | 1.17983 | 0.589913 | − | 0.807467i | \(-0.299162\pi\) | ||||
0.589913 | + | 0.807467i | \(0.299162\pi\) | |||||||
\(62\) | 3.43247i | 0.435924i | ||||||||
\(63\) | − 10.3759i | − 1.30725i | ||||||||
\(64\) | 6.55023 | 0.818779 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.23009 | 0.397596 | ||||||||
\(67\) | − 4.76090i | − 0.581636i | −0.956778 | − | 0.290818i | \(-0.906073\pi\) | ||||
0.956778 | − | 0.290818i | \(-0.0939274\pi\) | |||||||
\(68\) | − 2.56753i | − 0.311358i | ||||||||
\(69\) | 2.06888 | 0.249063 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0689 | −1.66967 | −0.834834 | − | 0.550502i | \(-0.814437\pi\) | ||||
−0.834834 | + | 0.550502i | \(0.814437\pi\) | |||||||
\(72\) | 0.992660i | 0.116986i | ||||||||
\(73\) | − 6.59368i | − 0.771732i | −0.922555 | − | 0.385866i | \(-0.873903\pi\) | ||||
0.922555 | − | 0.385866i | \(-0.126097\pi\) | |||||||
\(74\) | −7.07082 | −0.821966 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.82571 | 0.209423 | ||||||||
\(77\) | − 19.8238i | − 2.25913i | ||||||||
\(78\) | − 3.05774i | − 0.346221i | ||||||||
\(79\) | −5.47519 | −0.616007 | −0.308004 | − | 0.951385i | \(-0.599661\pi\) | ||||
−0.308004 | + | 0.951385i | \(0.599661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.21473 | 0.912748 | ||||||||
\(82\) | 8.50557i | 0.939283i | ||||||||
\(83\) | 4.15699i | 0.456289i | 0.973627 | + | 0.228144i | \(0.0732659\pi\) | ||||
−0.973627 | + | 0.228144i | \(0.926734\pi\) | |||||||
\(84\) | 1.93112 | 0.210703 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.96962 | −0.751554 | ||||||||
\(87\) | 0.417453i | 0.0447557i | ||||||||
\(88\) | 1.89653i | 0.202171i | ||||||||
\(89\) | 9.23009 | 0.978387 | 0.489194 | − | 0.872175i | \(-0.337291\pi\) | ||||
0.489194 | + | 0.872175i | \(0.337291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.7660 | −1.96721 | ||||||||
\(92\) | − 12.7245i | − 1.32662i | ||||||||
\(93\) | − 0.520926i | − 0.0540175i | ||||||||
\(94\) | 16.1570 | 1.66647 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.30478 | −0.235231 | ||||||||
\(97\) | 11.5116i | 1.16882i | 0.811457 | + | 0.584411i | \(0.198675\pi\) | ||||
−0.811457 | + | 0.584411i | \(0.801325\pi\) | |||||||
\(98\) | − 11.1433i | − 1.12564i | ||||||||
\(99\) | 16.1997 | 1.62813 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8511 | −1.17923 | −0.589616 | − | 0.807684i | \(-0.700721\pi\) | ||||
−0.589616 | + | 0.807684i | \(0.700721\pi\) | |||||||
\(102\) | 0.816515i | 0.0808470i | ||||||||
\(103\) | − 1.35458i | − 0.133471i | −0.997771 | − | 0.0667354i | \(-0.978742\pi\) | ||||
0.997771 | − | 0.0667354i | \(-0.0212583\pi\) | |||||||
\(104\) | 1.79533 | 0.176047 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.8946 | −1.44669 | ||||||||
\(107\) | − 7.06287i | − 0.682794i | −0.939919 | − | 0.341397i | \(-0.889100\pi\) | ||||
0.939919 | − | 0.341397i | \(-0.110900\pi\) | |||||||
\(108\) | 3.20393i | 0.308298i | ||||||||
\(109\) | −10.1844 | −0.975484 | −0.487742 | − | 0.872988i | \(-0.662179\pi\) | ||||
−0.487742 | + | 0.872988i | \(0.662179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.07310 | 0.101854 | ||||||||
\(112\) | 15.3871i | 1.45394i | ||||||||
\(113\) | − 1.86015i | − 0.174988i | −0.996165 | − | 0.0874940i | \(-0.972114\pi\) | ||||
0.996165 | − | 0.0874940i | \(-0.0278859\pi\) | |||||||
\(114\) | −0.580605 | −0.0543787 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.56753 | 0.238389 | ||||||||
\(117\) | − 15.3353i | − 1.41775i | ||||||||
\(118\) | − 18.5329i | − 1.70609i | ||||||||
\(119\) | 5.01114 | 0.459370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9504 | 1.81367 | ||||||||
\(122\) | 18.0235i | 1.63177i | ||||||||
\(123\) | − 1.29084i | − 0.116391i | ||||||||
\(124\) | −3.20393 | −0.287721 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20.2947 | 1.80800 | ||||||||
\(127\) | − 4.89053i | − 0.433964i | −0.976176 | − | 0.216982i | \(-0.930379\pi\) | ||||
0.976176 | − | 0.216982i | \(-0.0696213\pi\) | |||||||
\(128\) | − 2.71684i | − 0.240137i | ||||||||
\(129\) | 1.05774 | 0.0931287 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.81263 | 0.245741 | 0.122870 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122870 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(132\) | 3.01502i | 0.262424i | ||||||||
\(133\) | 3.56331i | 0.308978i | ||||||||
\(134\) | 9.31204 | 0.804438 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.479412 | −0.0411093 | ||||||||
\(137\) | 9.23009i | 0.788579i | 0.918986 | + | 0.394290i | \(0.129009\pi\) | ||||
−0.918986 | + | 0.394290i | \(0.870991\pi\) | |||||||
\(138\) | 4.04660i | 0.344470i | ||||||||
\(139\) | 3.67878 | 0.312030 | 0.156015 | − | 0.987755i | \(-0.450135\pi\) | ||||
0.156015 | + | 0.987755i | \(0.450135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.45205 | −0.206500 | ||||||||
\(142\) | − 27.5179i | − 2.30925i | ||||||||
\(143\) | − 29.2990i | − 2.45010i | ||||||||
\(144\) | −12.5741 | −1.04784 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.8969 | 1.06735 | ||||||||
\(147\) | 1.69115i | 0.139484i | ||||||||
\(148\) | − 6.60002i | − 0.542519i | ||||||||
\(149\) | −7.09925 | −0.581593 | −0.290797 | − | 0.956785i | \(-0.593920\pi\) | ||||
−0.290797 | + | 0.956785i | \(0.593920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3567 | −1.49385 | −0.746924 | − | 0.664910i | \(-0.768470\pi\) | ||||
−0.746924 | + | 0.664910i | \(0.768470\pi\) | |||||||
\(152\) | − 0.340899i | − 0.0276506i | ||||||||
\(153\) | 4.09503i | 0.331064i | ||||||||
\(154\) | 38.7742 | 3.12451 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.85415 | 0.228515 | ||||||||
\(157\) | 17.2301i | 1.37511i | 0.726132 | + | 0.687555i | \(0.241316\pi\) | ||||
−0.726132 | + | 0.687555i | \(0.758684\pi\) | |||||||
\(158\) | − 10.7092i | − 0.851975i | ||||||||
\(159\) | 2.26046 | 0.179266 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.8349 | 1.95726 | ||||||||
\(162\) | 16.0675i | 1.26238i | ||||||||
\(163\) | − 10.8662i | − 0.851103i | −0.904934 | − | 0.425551i | \(-0.860080\pi\) | ||||
0.904934 | − | 0.425551i | \(-0.139920\pi\) | |||||||
\(164\) | −7.93925 | −0.619951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.13083 | −0.631075 | ||||||||
\(167\) | 2.82977i | 0.218974i | 0.993988 | + | 0.109487i | \(0.0349209\pi\) | ||||
−0.993988 | + | 0.109487i | \(0.965079\pi\) | |||||||
\(168\) | − 0.360582i | − 0.0278195i | ||||||||
\(169\) | −14.7357 | −1.13351 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.91188 | −0.222677 | ||||||||
\(172\) | − 6.50557i | − 0.496045i | ||||||||
\(173\) | 9.26647i | 0.704516i | 0.935903 | + | 0.352258i | \(0.114586\pi\) | ||||
−0.935903 | + | 0.352258i | \(0.885414\pi\) | |||||||
\(174\) | −0.816515 | −0.0618998 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.0235 | −1.81084 | ||||||||
\(177\) | 2.81263i | 0.211410i | ||||||||
\(178\) | 18.0535i | 1.35317i | ||||||||
\(179\) | 3.59067 | 0.268379 | 0.134190 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134190 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7630 | −1.46897 | −0.734487 | − | 0.678623i | \(-0.762577\pi\) | ||||
−0.734487 | + | 0.678623i | \(0.762577\pi\) | |||||||
\(182\) | − 36.7053i | − 2.72078i | ||||||||
\(183\) | − 2.73532i | − 0.202200i | ||||||||
\(184\) | −2.37594 | −0.175157 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.01890 | 0.0747095 | ||||||||
\(187\) | 7.82377i | 0.572131i | ||||||||
\(188\) | 15.0812i | 1.09991i | ||||||||
\(189\) | −6.25323 | −0.454855 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.31398 | 0.601579 | 0.300789 | − | 0.953691i | \(-0.402750\pi\) | ||||
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(192\) | − 1.94438i | − 0.140324i | ||||||||
\(193\) | 22.2514i | 1.60169i | 0.598869 | + | 0.800847i | \(0.295617\pi\) | ||||
−0.598869 | + | 0.800847i | \(0.704383\pi\) | |||||||
\(194\) | −22.5160 | −1.61655 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4014 | 0.742954 | ||||||||
\(197\) | − 8.81263i | − 0.627874i | −0.949444 | − | 0.313937i | \(-0.898352\pi\) | ||||
0.949444 | − | 0.313937i | \(-0.101648\pi\) | |||||||
\(198\) | 31.6857i | 2.25180i | ||||||||
\(199\) | −21.0659 | −1.49332 | −0.746660 | − | 0.665206i | \(-0.768344\pi\) | ||||
−0.746660 | + | 0.665206i | \(0.768344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.41323 | −0.0996818 | ||||||||
\(202\) | − 23.1801i | − 1.63095i | ||||||||
\(203\) | 5.01114i | 0.351713i | ||||||||
\(204\) | −0.762149 | −0.0533611 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.64948 | 0.184598 | ||||||||
\(207\) | 20.2947i | 1.41058i | ||||||||
\(208\) | 22.7417i | 1.57685i | ||||||||
\(209\) | −5.56331 | −0.384822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.34556 | 0.368004 | 0.184002 | − | 0.982926i | \(-0.441095\pi\) | ||||
0.184002 | + | 0.982926i | \(0.441095\pi\) | |||||||
\(212\) | − 13.9029i | − 0.954853i | ||||||||
\(213\) | 4.17623i | 0.286151i | ||||||||
\(214\) | 13.8146 | 0.944345 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.598242 | 0.0407052 | ||||||||
\(217\) | − 6.25323i | − 0.424497i | ||||||||
\(218\) | − 19.9200i | − 1.34915i | ||||||||
\(219\) | −1.95728 | −0.132261 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.40632 | 0.498203 | ||||||||
\(222\) | 2.09891i | 0.140870i | ||||||||
\(223\) | 3.10947i | 0.208226i | 0.994565 | + | 0.104113i | \(0.0332003\pi\) | ||||
−0.994565 | + | 0.104113i | \(0.966800\pi\) | |||||||
\(224\) | −27.6668 | −1.84856 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.63834 | 0.242019 | ||||||||
\(227\) | 14.4692i | 0.960354i | 0.877172 | + | 0.480177i | \(0.159428\pi\) | ||||
−0.877172 | + | 0.480177i | \(0.840572\pi\) | |||||||
\(228\) | − 0.541947i | − 0.0358913i | ||||||||
\(229\) | 5.21473 | 0.344599 | 0.172299 | − | 0.985045i | \(-0.444880\pi\) | ||||
0.172299 | + | 0.985045i | \(0.444880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.88452 | −0.387173 | ||||||||
\(232\) | − 0.479412i | − 0.0314750i | ||||||||
\(233\) | 3.18737i | 0.208811i | 0.994535 | + | 0.104406i | \(0.0332940\pi\) | ||||
−0.994535 | + | 0.104406i | \(0.966706\pi\) | |||||||
\(234\) | 29.9950 | 1.96084 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 17.2990 | 1.12607 | ||||||||
\(237\) | 1.62527i | 0.105572i | ||||||||
\(238\) | 9.80150i | 0.635337i | ||||||||
\(239\) | −16.5209 | −1.06865 | −0.534325 | − | 0.845279i | \(-0.679434\pi\) | ||||
−0.534325 | + | 0.845279i | \(0.679434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2271 | −0.787615 | −0.393807 | − | 0.919193i | \(-0.628842\pi\) | ||||
−0.393807 | + | 0.919193i | \(0.628842\pi\) | |||||||
\(242\) | 39.0218i | 2.50842i | ||||||||
\(243\) | − 7.70316i | − 0.494158i | ||||||||
\(244\) | −16.8234 | −1.07701 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.52481 | 0.160976 | ||||||||
\(247\) | 5.26647i | 0.335097i | ||||||||
\(248\) | 0.598242i | 0.0379884i | ||||||||
\(249\) | 1.23397 | 0.0781996 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.52093 | 0.285358 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(252\) | 18.9435i | 1.19333i | ||||||||
\(253\) | 38.7742i | 2.43771i | ||||||||
\(254\) | 9.56559 | 0.600198 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.4144 | 1.15090 | ||||||||
\(257\) | 15.9290i | 0.993625i | 0.867858 | + | 0.496813i | \(0.165496\pi\) | ||||
−0.867858 | + | 0.496813i | \(0.834504\pi\) | |||||||
\(258\) | 2.06888i | 0.128803i | ||||||||
\(259\) | 12.8815 | 0.800418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.09503 | −0.253476 | ||||||||
\(262\) | 5.50135i | 0.339874i | ||||||||
\(263\) | − 0.854147i | − 0.0526689i | −0.999653 | − | 0.0263345i | \(-0.991617\pi\) | ||||
0.999653 | − | 0.0263345i | \(-0.00838349\pi\) | |||||||
\(264\) | 0.562969 | 0.0346483 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.96962 | −0.427335 | ||||||||
\(267\) | − 2.73988i | − 0.167678i | ||||||||
\(268\) | 8.69202i | 0.530950i | ||||||||
\(269\) | −10.3913 | −0.633569 | −0.316784 | − | 0.948498i | \(-0.602603\pi\) | ||||
−0.316784 | + | 0.948498i | \(0.602603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.19971 | −0.498097 | −0.249048 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249048 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(272\) | − 6.07276i | − 0.368215i | ||||||||
\(273\) | 5.57054i | 0.337145i | ||||||||
\(274\) | −18.0535 | −1.09065 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.77717 | −0.227359 | ||||||||
\(277\) | 14.6484i | 0.880137i | 0.897964 | + | 0.440069i | \(0.145046\pi\) | ||||
−0.897964 | + | 0.440069i | \(0.854954\pi\) | |||||||
\(278\) | 7.19549i | 0.431557i | ||||||||
\(279\) | 5.11005 | 0.305931 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.6129 | −1.88587 | −0.942935 | − | 0.332977i | \(-0.891947\pi\) | ||||
−0.942935 | + | 0.332977i | \(0.891947\pi\) | |||||||
\(282\) | − 4.79607i | − 0.285602i | ||||||||
\(283\) | − 24.7326i | − 1.47020i | −0.677957 | − | 0.735101i | \(-0.737135\pi\) | ||||
0.677957 | − | 0.735101i | \(-0.262865\pi\) | |||||||
\(284\) | 25.6857 | 1.52417 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 57.3071 | 3.38864 | ||||||||
\(287\) | − 15.4953i | − 0.914660i | ||||||||
\(288\) | − 22.6089i | − 1.33224i | ||||||||
\(289\) | 15.0223 | 0.883663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.41712 | 0.200315 | ||||||||
\(292\) | 12.0382i | 0.704480i | ||||||||
\(293\) | − 30.2857i | − 1.76931i | −0.466245 | − | 0.884655i | \(-0.654394\pi\) | ||||
0.466245 | − | 0.884655i | \(-0.345606\pi\) | |||||||
\(294\) | −3.30780 | −0.192915 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.23237 | −0.0716298 | ||||||||
\(297\) | − 9.76302i | − 0.566508i | ||||||||
\(298\) | − 13.8857i | − 0.804379i | ||||||||
\(299\) | 36.7053 | 2.12272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6972 | 0.731852 | ||||||||
\(302\) | − 35.9046i | − 2.06608i | ||||||||
\(303\) | 3.51791i | 0.202099i | ||||||||
\(304\) | 4.31820 | 0.247666 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.00965 | −0.457881 | ||||||||
\(307\) | − 23.0629i | − 1.31627i | −0.752901 | − | 0.658134i | \(-0.771346\pi\) | ||||
0.752901 | − | 0.658134i | \(-0.228654\pi\) | |||||||
\(308\) | 36.1925i | 2.06226i | ||||||||
\(309\) | −0.402096 | −0.0228744 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3152 | −0.584921 | −0.292460 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292460 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(312\) | − 0.532930i | − 0.0301712i | ||||||||
\(313\) | 4.95038i | 0.279812i | 0.990165 | + | 0.139906i | \(0.0446801\pi\) | ||||
−0.990165 | + | 0.139906i | \(0.955320\pi\) | |||||||
\(314\) | −33.7011 | −1.90186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.99612 | 0.562326 | ||||||||
\(317\) | − 14.2433i | − 0.799985i | −0.916518 | − | 0.399992i | \(-0.869013\pi\) | ||||
0.916518 | − | 0.399992i | \(-0.130987\pi\) | |||||||
\(318\) | 4.42134i | 0.247936i | ||||||||
\(319\) | −7.82377 | −0.438047 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.09656 | −0.117018 | ||||||||
\(322\) | 48.5756i | 2.70702i | ||||||||
\(323\) | − 1.40632i | − 0.0782495i | ||||||||
\(324\) | −14.9977 | −0.833207 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.2536 | 1.17713 | ||||||||
\(327\) | 3.02314i | 0.167180i | ||||||||
\(328\) | 1.48243i | 0.0818534i | ||||||||
\(329\) | −29.4346 | −1.62278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.04272 | 0.112278 | 0.0561390 | − | 0.998423i | \(-0.482121\pi\) | ||||
0.0561390 | + | 0.998423i | \(0.482121\pi\) | |||||||
\(332\) | − 7.58946i | − 0.416526i | ||||||||
\(333\) | 10.5266i | 0.576854i | ||||||||
\(334\) | −5.53487 | −0.302855 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.56753 | 0.249179 | ||||||||
\(337\) | 34.6951i | 1.88996i | 0.327128 | + | 0.944980i | \(0.393919\pi\) | ||||
−0.327128 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(338\) | − 28.8221i | − 1.56772i | ||||||||
\(339\) | −0.552170 | −0.0299898 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.76302 | 0.528697 | ||||||||
\(342\) | − 5.69548i | − 0.307976i | ||||||||
\(343\) | − 4.64243i | − 0.250668i | ||||||||
\(344\) | −1.21473 | −0.0654938 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.1247 | −0.974388 | ||||||||
\(347\) | 7.35280i | 0.394719i | 0.980331 | + | 0.197359i | \(0.0632366\pi\) | ||||
−0.980331 | + | 0.197359i | \(0.936763\pi\) | |||||||
\(348\) | − 0.762149i | − 0.0408555i | ||||||||
\(349\) | 31.7630 | 1.70024 | 0.850118 | − | 0.526593i | \(-0.176531\pi\) | ||||
0.850118 | + | 0.526593i | \(0.176531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.24209 | −0.493306 | ||||||||
\(352\) | − 43.1955i | − 2.30233i | ||||||||
\(353\) | 7.52179i | 0.400345i | 0.979761 | + | 0.200172i | \(0.0641502\pi\) | ||||
−0.979761 | + | 0.200172i | \(0.935850\pi\) | |||||||
\(354\) | −5.50135 | −0.292393 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.8515 | −0.893126 | ||||||||
\(357\) | − 1.48751i | − 0.0787276i | ||||||||
\(358\) | 7.02314i | 0.371185i | ||||||||
\(359\) | 30.3982 | 1.60436 | 0.802178 | − | 0.597085i | \(-0.203674\pi\) | ||||
0.802178 | + | 0.597085i | \(0.203674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 38.6553i | − 2.03168i | ||||||||
\(363\) | − 5.92211i | − 0.310830i | ||||||||
\(364\) | 34.2613 | 1.79578 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.35012 | 0.279655 | ||||||||
\(367\) | 3.91577i | 0.204401i | 0.994764 | + | 0.102201i | \(0.0325884\pi\) | ||||
−0.994764 | + | 0.102201i | \(0.967412\pi\) | |||||||
\(368\) | − 30.0962i | − 1.56887i | ||||||||
\(369\) | 12.6626 | 0.659186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1347 | 1.40877 | ||||||||
\(372\) | 0.951060i | 0.0493102i | ||||||||
\(373\) | − 26.7759i | − 1.38641i | −0.720743 | − | 0.693203i | \(-0.756199\pi\) | ||||
0.720743 | − | 0.693203i | \(-0.243801\pi\) | |||||||
\(374\) | −15.3028 | −0.791291 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.81599 | 0.145223 | ||||||||
\(377\) | 7.40632i | 0.381445i | ||||||||
\(378\) | − 12.2310i | − 0.629092i | ||||||||
\(379\) | −14.9504 | −0.767950 | −0.383975 | − | 0.923344i | \(-0.625445\pi\) | ||||
−0.383975 | + | 0.923344i | \(0.625445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45171 | −0.0743735 | ||||||||
\(382\) | 16.2617i | 0.832019i | ||||||||
\(383\) | 27.9910i | 1.43027i | 0.698985 | + | 0.715136i | \(0.253635\pi\) | ||||
−0.698985 | + | 0.715136i | \(0.746365\pi\) | |||||||
\(384\) | −0.806471 | −0.0411551 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −43.5225 | −2.21524 | ||||||||
\(387\) | 10.3759i | 0.527439i | ||||||||
\(388\) | − 21.0168i | − 1.06697i | ||||||||
\(389\) | 35.2036 | 1.78489 | 0.892447 | − | 0.451152i | \(-0.148987\pi\) | ||||
0.892447 | + | 0.451152i | \(0.148987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.80150 | −0.495683 | ||||||||
\(392\) | − 1.94216i | − 0.0980937i | ||||||||
\(393\) | − 0.834907i | − 0.0421155i | ||||||||
\(394\) | 17.2370 | 0.868388 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −29.5760 | −1.48625 | ||||||||
\(397\) | − 35.9735i | − 1.80546i | −0.430208 | − | 0.902730i | \(-0.641560\pi\) | ||||
0.430208 | − | 0.902730i | \(-0.358440\pi\) | |||||||
\(398\) | − 41.2036i | − 2.06535i | ||||||||
\(399\) | 1.05774 | 0.0529532 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2421 | 1.16065 | 0.580327 | − | 0.814383i | \(-0.302925\pi\) | ||||
0.580327 | + | 0.814383i | \(0.302925\pi\) | |||||||
\(402\) | − 2.76420i | − 0.137866i | ||||||||
\(403\) | − 9.24209i | − 0.460381i | ||||||||
\(404\) | 21.6367 | 1.07647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.80150 | −0.486440 | ||||||||
\(407\) | 20.1116i | 0.996895i | ||||||||
\(408\) | 0.142310i | 0.00704538i | ||||||||
\(409\) | 31.8926 | 1.57699 | 0.788495 | − | 0.615041i | \(-0.210861\pi\) | ||||
0.788495 | + | 0.615041i | \(0.210861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.73988 | 0.135148 | ||||||||
\(412\) | 2.47307i | 0.121840i | ||||||||
\(413\) | 33.7630i | 1.66137i | ||||||||
\(414\) | −39.6953 | −1.95092 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −40.8907 | −2.00483 | ||||||||
\(417\) | − 1.09202i | − 0.0534763i | ||||||||
\(418\) | − 10.8815i | − 0.532232i | ||||||||
\(419\) | −31.8238 | −1.55469 | −0.777346 | − | 0.629073i | \(-0.783435\pi\) | ||||
−0.777346 | + | 0.629073i | \(0.783435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.348578 | 0.0169887 | 0.00849433 | − | 0.999964i | \(-0.497296\pi\) | ||||
0.00849433 | + | 0.999964i | \(0.497296\pi\) | |||||||
\(422\) | 10.4556i | 0.508971i | ||||||||
\(423\) | − 24.0535i | − 1.16952i | ||||||||
\(424\) | −2.59596 | −0.126071 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.16847 | −0.395763 | ||||||||
\(427\) | − 32.8349i | − 1.58899i | ||||||||
\(428\) | 12.8948i | 0.623292i | ||||||||
\(429\) | −8.69716 | −0.419903 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.2764 | 1.41019 | 0.705097 | − | 0.709111i | \(-0.250904\pi\) | ||||
0.705097 | + | 0.709111i | \(0.250904\pi\) | |||||||
\(432\) | 7.57799i | 0.364596i | ||||||||
\(433\) | 0.883290i | 0.0424482i | 0.999775 | + | 0.0212241i | \(0.00675635\pi\) | ||||
−0.999775 | + | 0.0212241i | \(0.993244\pi\) | |||||||
\(434\) | 12.2310 | 0.587105 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.5937 | 0.890476 | ||||||||
\(437\) | − 6.96962i | − 0.333402i | ||||||||
\(438\) | − 3.82833i | − 0.182925i | ||||||||
\(439\) | 13.8584 | 0.661424 | 0.330712 | − | 0.943732i | \(-0.392711\pi\) | ||||
0.330712 | + | 0.943732i | \(0.392711\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.5895 | −0.789974 | ||||||||
\(442\) | 14.4863i | 0.689044i | ||||||||
\(443\) | 13.5753i | 0.644982i | 0.946572 | + | 0.322491i | \(0.104520\pi\) | ||||
−0.946572 | + | 0.322491i | \(0.895480\pi\) | |||||||
\(444\) | −1.95916 | −0.0929778 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.08195 | −0.287989 | ||||||||
\(447\) | 2.10735i | 0.0996745i | ||||||||
\(448\) | − 23.3405i | − 1.10273i | ||||||||
\(449\) | 15.6334 | 0.737785 | 0.368893 | − | 0.929472i | \(-0.379737\pi\) | ||||
0.368893 | + | 0.929472i | \(0.379737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.1925 | 1.13918 | ||||||||
\(452\) | 3.39609i | 0.159739i | ||||||||
\(453\) | 5.44904i | 0.256018i | ||||||||
\(454\) | −28.3009 | −1.32823 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.101193 | −0.00473880 | ||||||||
\(457\) | 5.30284i | 0.248057i | 0.992279 | + | 0.124028i | \(0.0395814\pi\) | ||||
−0.992279 | + | 0.124028i | \(0.960419\pi\) | |||||||
\(458\) | 10.1997i | 0.476601i | ||||||||
\(459\) | 2.46794 | 0.115193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.374734 | 0.0174531 | 0.00872656 | − | 0.999962i | \(-0.497222\pi\) | ||||
0.00872656 | + | 0.999962i | \(0.497222\pi\) | |||||||
\(462\) | − 11.5098i | − 0.535484i | ||||||||
\(463\) | − 6.65564i | − 0.309314i | −0.987968 | − | 0.154657i | \(-0.950573\pi\) | ||||
0.987968 | − | 0.154657i | \(-0.0494272\pi\) | |||||||
\(464\) | 6.07276 | 0.281921 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.23431 | −0.288799 | ||||||||
\(467\) | − 0.854147i | − 0.0395252i | −0.999805 | − | 0.0197626i | \(-0.993709\pi\) | ||||
0.999805 | − | 0.0197626i | \(-0.00629104\pi\) | |||||||
\(468\) | 27.9979i | 1.29420i | ||||||||
\(469\) | −16.9645 | −0.783349 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.11461 | 0.235669 | ||||||||
\(472\) | − 3.23009i | − 0.148677i | ||||||||
\(473\) | 19.8238i | 0.911498i | ||||||||
\(474\) | −3.17893 | −0.146013 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.14889 | −0.419339 | ||||||||
\(477\) | 22.1741i | 1.01528i | ||||||||
\(478\) | − 32.3140i | − 1.47801i | ||||||||
\(479\) | 17.0731 | 0.780090 | 0.390045 | − | 0.920796i | \(-0.372460\pi\) | ||||
0.390045 | + | 0.920796i | \(0.372460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0385 | 0.868081 | ||||||||
\(482\) | − 23.9154i | − 1.08932i | ||||||||
\(483\) | − 7.37204i | − 0.335439i | ||||||||
\(484\) | −36.4236 | −1.65562 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.0669 | 0.683450 | ||||||||
\(487\) | 12.8259i | 0.581197i | 0.956845 | + | 0.290598i | \(0.0938543\pi\) | ||||
−0.956845 | + | 0.290598i | \(0.906146\pi\) | |||||||
\(488\) | 3.14129i | 0.142200i | ||||||||
\(489\) | −3.22553 | −0.145863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4054 | −0.469591 | −0.234796 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234796 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(492\) | 2.35670i | 0.106248i | ||||||||
\(493\) | − 1.97773i | − 0.0890723i | ||||||||
\(494\) | −10.3009 | −0.463460 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.57799 | −0.340262 | ||||||||
\(497\) | 50.1317i | 2.24872i | ||||||||
\(498\) | 2.41357i | 0.108155i | ||||||||
\(499\) | −36.1612 | −1.61880 | −0.809399 | − | 0.587258i | \(-0.800207\pi\) | ||||
−0.809399 | + | 0.587258i | \(0.800207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.839995 | 0.0375282 | ||||||||
\(502\) | 8.84267i | 0.394668i | ||||||||
\(503\) | − 33.2536i | − 1.48270i | −0.671117 | − | 0.741352i | \(-0.734185\pi\) | ||||
0.671117 | − | 0.741352i | \(-0.265815\pi\) | |||||||
\(504\) | 3.53715 | 0.157557 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −75.8400 | −3.37150 | ||||||||
\(507\) | 4.37416i | 0.194263i | ||||||||
\(508\) | 8.92869i | 0.396146i | ||||||||
\(509\) | −7.29084 | −0.323161 | −0.161580 | − | 0.986860i | \(-0.551659\pi\) | ||||
−0.161580 | + | 0.986860i | \(0.551659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4953 | −1.03937 | ||||||||
\(512\) | 30.5839i | 1.35163i | ||||||||
\(513\) | 1.75489i | 0.0774805i | ||||||||
\(514\) | −31.1563 | −1.37424 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.93112 | −0.0850130 | ||||||||
\(517\) | − 45.9555i | − 2.02112i | ||||||||
\(518\) | 25.1955i | 1.10703i | ||||||||
\(519\) | 2.75067 | 0.120741 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.87849 | −0.432785 | −0.216392 | − | 0.976306i | \(-0.569429\pi\) | ||||
−0.216392 | + | 0.976306i | \(0.569429\pi\) | |||||||
\(522\) | − 8.00965i | − 0.350573i | ||||||||
\(523\) | 11.1925i | 0.489414i | 0.969597 | + | 0.244707i | \(0.0786918\pi\) | ||||
−0.969597 | + | 0.244707i | \(0.921308\pi\) | |||||||
\(524\) | −5.13505 | −0.224326 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.67066 | 0.0728443 | ||||||||
\(527\) | 2.46794i | 0.107505i | ||||||||
\(528\) | 7.13117i | 0.310344i | ||||||||
\(529\) | −25.5756 | −1.11198 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.5907 | −1.19733 | ||||||||
\(532\) | − 6.50557i | − 0.282052i | ||||||||
\(533\) | − 22.9016i | − 0.991980i | ||||||||
\(534\) | 5.35904 | 0.231908 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.62299 | 0.0701023 | ||||||||
\(537\) | − 1.06586i | − 0.0459953i | ||||||||
\(538\) | − 20.3248i | − 0.876263i | ||||||||
\(539\) | −31.6950 | −1.36520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.22587 | 0.0956974 | 0.0478487 | − | 0.998855i | \(-0.484763\pi\) | ||||
0.0478487 | + | 0.998855i | \(0.484763\pi\) | |||||||
\(542\) | − 16.0382i | − 0.688898i | ||||||||
\(543\) | 5.86649i | 0.251755i | ||||||||
\(544\) | 10.9191 | 0.468154 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.8957 | −0.466291 | ||||||||
\(547\) | − 34.9675i | − 1.49510i | −0.664204 | − | 0.747552i | \(-0.731229\pi\) | ||||
0.664204 | − | 0.747552i | \(-0.268771\pi\) | |||||||
\(548\) | − 16.8515i | − 0.719859i | ||||||||
\(549\) | 26.8322 | 1.14517 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40632 | 0.0599111 | ||||||||
\(552\) | 0.705278i | 0.0300186i | ||||||||
\(553\) | 19.5098i | 0.829641i | ||||||||
\(554\) | −28.6514 | −1.21728 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.71640 | −0.284839 | ||||||||
\(557\) | − 8.88539i | − 0.376486i | −0.982122 | − | 0.188243i | \(-0.939721\pi\) | ||||
0.982122 | − | 0.188243i | \(-0.0602793\pi\) | |||||||
\(558\) | 9.99497i | 0.423121i | ||||||||
\(559\) | 18.7660 | 0.793719 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.32242 | 0.0980527 | ||||||||
\(562\) | − 61.8331i | − 2.60827i | ||||||||
\(563\) | 29.6767i | 1.25072i | 0.780335 | + | 0.625362i | \(0.215048\pi\) | ||||
−0.780335 | + | 0.625362i | \(0.784952\pi\) | |||||||
\(564\) | 4.47674 | 0.188505 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 48.3756 | 2.03338 | ||||||||
\(567\) | − 29.2716i | − 1.22929i | ||||||||
\(568\) | − 4.79607i | − 0.201239i | ||||||||
\(569\) | 22.1152 | 0.927116 | 0.463558 | − | 0.886067i | \(-0.346573\pi\) | ||||
0.463558 | + | 0.886067i | \(0.346573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2656 | −1.39212 | −0.696060 | − | 0.717983i | \(-0.745065\pi\) | ||||
−0.696060 | + | 0.717983i | \(0.745065\pi\) | |||||||
\(572\) | 53.4914i | 2.23659i | ||||||||
\(573\) | − 2.46794i | − 0.103100i | ||||||||
\(574\) | 30.3080 | 1.26503 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.0735 | 0.794730 | ||||||||
\(577\) | 0.934140i | 0.0388887i | 0.999811 | + | 0.0194444i | \(0.00618972\pi\) | ||||
−0.999811 | + | 0.0194444i | \(0.993810\pi\) | |||||||
\(578\) | 29.3827i | 1.22216i | ||||||||
\(579\) | 6.60516 | 0.274501 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8126 | 0.614532 | ||||||||
\(582\) | 6.68368i | 0.277047i | ||||||||
\(583\) | 42.3648i | 1.75457i | ||||||||
\(584\) | 2.24778 | 0.0930139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 59.2371 | 2.44706 | ||||||||
\(587\) | 1.57531i | 0.0650200i | 0.999471 | + | 0.0325100i | \(0.0103501\pi\) | ||||
−0.999471 | + | 0.0325100i | \(0.989650\pi\) | |||||||
\(588\) | − 3.08756i | − 0.127329i | ||||||||
\(589\) | −1.75489 | −0.0723092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.61596 | −0.107606 | ||||||||
\(592\) | − 15.6105i | − 0.641587i | ||||||||
\(593\) | − 26.0162i | − 1.06836i | −0.845371 | − | 0.534180i | \(-0.820621\pi\) | ||||
0.845371 | − | 0.534180i | \(-0.179379\pi\) | |||||||
\(594\) | 19.0959 | 0.783514 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9612 | 0.530911 | ||||||||
\(597\) | 6.25323i | 0.255928i | ||||||||
\(598\) | 71.7934i | 2.93585i | ||||||||
\(599\) | −19.5359 | −0.798217 | −0.399109 | − | 0.916904i | \(-0.630680\pi\) | ||||
−0.399109 | + | 0.916904i | \(0.630680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.5299 | 1.77562 | 0.887811 | − | 0.460208i | \(-0.152225\pi\) | ||||
0.887811 | + | 0.460208i | \(0.152225\pi\) | |||||||
\(602\) | 24.8349i | 1.01220i | ||||||||
\(603\) | − 13.8632i | − 0.564552i | ||||||||
\(604\) | 33.5140 | 1.36367 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.88083 | −0.279515 | ||||||||
\(607\) | − 12.5847i | − 0.510796i | −0.966836 | − | 0.255398i | \(-0.917794\pi\) | ||||
0.966836 | − | 0.255398i | \(-0.0822065\pi\) | |||||||
\(608\) | 7.76435i | 0.314886i | ||||||||
\(609\) | 1.48751 | 0.0602771 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.5034 | −1.75996 | ||||||||
\(612\) | − 7.47634i | − 0.302213i | ||||||||
\(613\) | 18.2412i | 0.736756i | 0.929676 | + | 0.368378i | \(0.120087\pi\) | ||||
−0.929676 | + | 0.368378i | \(0.879913\pi\) | |||||||
\(614\) | 45.1097 | 1.82048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.75791 | 0.272284 | ||||||||
\(617\) | 26.7314i | 1.07617i | 0.842892 | + | 0.538084i | \(0.180852\pi\) | ||||
−0.842892 | + | 0.538084i | \(0.819148\pi\) | |||||||
\(618\) | − 0.786477i | − 0.0316367i | ||||||||
\(619\) | −2.92690 | −0.117642 | −0.0588211 | − | 0.998269i | \(-0.518734\pi\) | ||||
−0.0588211 | + | 0.998269i | \(0.518734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.2310 | 0.490811 | ||||||||
\(622\) | − 20.1759i | − 0.808980i | ||||||||
\(623\) | − 32.8896i | − 1.31770i | ||||||||
\(624\) | 6.75067 | 0.270243 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.68267 | −0.386997 | ||||||||
\(627\) | 1.65142i | 0.0659514i | ||||||||
\(628\) | − 31.4572i | − 1.25528i | ||||||||
\(629\) | −5.08389 | −0.202708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2493 | −0.527447 | −0.263724 | − | 0.964598i | \(-0.584951\pi\) | ||||
−0.263724 | + | 0.964598i | \(0.584951\pi\) | |||||||
\(632\) | − 1.86649i | − 0.0742450i | ||||||||
\(633\) | − 1.58679i | − 0.0630691i | ||||||||
\(634\) | 27.8591 | 1.10643 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.12695 | −0.163644 | ||||||||
\(637\) | 30.0039i | 1.18880i | ||||||||
\(638\) | − 15.3028i | − 0.605845i | ||||||||
\(639\) | −40.9669 | −1.62063 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.93026 | 0.273729 | 0.136864 | − | 0.990590i | \(-0.456298\pi\) | ||||
0.136864 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(642\) | − 4.10074i | − 0.161843i | ||||||||
\(643\) | − 14.4794i | − 0.571012i | −0.958377 | − | 0.285506i | \(-0.907838\pi\) | ||||
0.958377 | − | 0.285506i | \(-0.0921617\pi\) | |||||||
\(644\) | −45.3414 | −1.78670 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.75067 | 0.108224 | ||||||||
\(647\) | 6.35549i | 0.249860i | 0.992166 | + | 0.124930i | \(0.0398707\pi\) | ||||
−0.992166 | + | 0.124930i | \(0.960129\pi\) | |||||||
\(648\) | 2.80040i | 0.110010i | ||||||||
\(649\) | −52.7134 | −2.06918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.85622 | −0.0727510 | ||||||||
\(652\) | 19.8385i | 0.776934i | ||||||||
\(653\) | 34.4030i | 1.34629i | 0.739509 | + | 0.673146i | \(0.235058\pi\) | ||||
−0.739509 | + | 0.673146i | \(0.764942\pi\) | |||||||
\(654\) | −5.91309 | −0.231220 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.7780 | −0.733159 | ||||||||
\(657\) | − 19.2000i | − 0.749065i | ||||||||
\(658\) | − 57.5723i | − 2.24440i | ||||||||
\(659\) | 19.6214 | 0.764341 | 0.382170 | − | 0.924092i | \(-0.375177\pi\) | ||||
0.382170 | + | 0.924092i | \(0.375177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.8054 | 1.54825 | 0.774126 | − | 0.633032i | \(-0.218190\pi\) | ||||
0.774126 | + | 0.633032i | \(0.218190\pi\) | |||||||
\(662\) | 3.99544i | 0.155287i | ||||||||
\(663\) | − 2.19850i | − 0.0853828i | ||||||||
\(664\) | −1.41712 | −0.0549947 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.5894 | −0.797823 | ||||||||
\(667\) | − 9.80150i | − 0.379515i | ||||||||
\(668\) | − 5.16635i | − 0.199892i | ||||||||
\(669\) | 0.923022 | 0.0356861 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.2644 | 1.97904 | ||||||||
\(672\) | 8.21266i | 0.316810i | ||||||||
\(673\) | 8.90374i | 0.343214i | 0.985166 | + | 0.171607i | \(0.0548959\pi\) | ||||
−0.985166 | + | 0.171607i | \(0.945104\pi\) | |||||||
\(674\) | −67.8615 | −2.61393 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.9030 | 1.03473 | ||||||||
\(677\) | 22.2695i | 0.855886i | 0.903806 | + | 0.427943i | \(0.140762\pi\) | ||||
−0.903806 | + | 0.427943i | \(0.859238\pi\) | |||||||
\(678\) | − 1.08001i | − 0.0414776i | ||||||||
\(679\) | 41.0193 | 1.57417 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.29506 | 0.164587 | ||||||||
\(682\) | 19.0959i | 0.731220i | ||||||||
\(683\) | − 15.4054i | − 0.589472i | −0.955579 | − | 0.294736i | \(-0.904768\pi\) | ||||
0.955579 | − | 0.294736i | \(-0.0952317\pi\) | |||||||
\(684\) | 5.31626 | 0.203272 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.08033 | 0.346689 | ||||||||
\(687\) | − 1.54795i | − 0.0590580i | ||||||||
\(688\) | − 15.3871i | − 0.586627i | ||||||||
\(689\) | 40.1044 | 1.52785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8773 | −0.680084 | −0.340042 | − | 0.940410i | \(-0.610441\pi\) | ||||
−0.340042 | + | 0.940410i | \(0.610441\pi\) | |||||||
\(692\) | − 16.9179i | − 0.643122i | ||||||||
\(693\) | − 57.7245i | − 2.19277i | ||||||||
\(694\) | −14.3817 | −0.545920 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.142310 | −0.00539423 | ||||||||
\(697\) | 6.11548i | 0.231640i | ||||||||
\(698\) | 62.1266i | 2.35153i | ||||||||
\(699\) | 0.946144 | 0.0357864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3609 | 1.33556 | 0.667782 | − | 0.744357i | \(-0.267244\pi\) | ||||
0.667782 | + | 0.744357i | \(0.267244\pi\) | |||||||
\(702\) | − 18.0770i | − 0.682272i | ||||||||
\(703\) | − 3.61504i | − 0.136344i | ||||||||
\(704\) | 36.4409 | 1.37342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.7122 | −0.553701 | ||||||||
\(707\) | 42.2292i | 1.58819i | ||||||||
\(708\) | − 5.13505i | − 0.192987i | ||||||||
\(709\) | −6.90410 | −0.259289 | −0.129644 | − | 0.991561i | \(-0.541384\pi\) | ||||
−0.129644 | + | 0.991561i | \(0.541384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.9431 | −0.597914 | ||||||||
\(712\) | 3.14653i | 0.117921i | ||||||||
\(713\) | 12.2310i | 0.458053i | ||||||||
\(714\) | 2.90949 | 0.108885 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.55552 | −0.244991 | ||||||||
\(717\) | 4.90410i | 0.183147i | ||||||||
\(718\) | 59.4572i | 2.21892i | ||||||||
\(719\) | 38.9431 | 1.45233 | 0.726167 | − | 0.687518i | \(-0.241300\pi\) | ||||
0.726167 | + | 0.687518i | \(0.241300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82678 | −0.179759 | ||||||||
\(722\) | 1.95594i | 0.0727926i | ||||||||
\(723\) | 3.62951i | 0.134983i | ||||||||
\(724\) | 36.0816 | 1.34096 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.5833 | 0.429897 | ||||||||
\(727\) | − 6.18347i | − 0.229332i | −0.993404 | − | 0.114666i | \(-0.963420\pi\) | ||||
0.993404 | − | 0.114666i | \(-0.0365798\pi\) | |||||||
\(728\) | − 6.39733i | − 0.237101i | ||||||||
\(729\) | 22.3576 | 0.828058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.01114 | −0.185344 | ||||||||
\(732\) | 4.99390i | 0.184580i | ||||||||
\(733\) | 0.688715i | 0.0254383i | 0.999919 | + | 0.0127191i | \(0.00404874\pi\) | ||||
−0.999919 | + | 0.0127191i | \(0.995951\pi\) | |||||||
\(734\) | −7.65902 | −0.282699 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 54.1146 | 1.99469 | ||||||||
\(737\) | − 26.4863i | − 0.975636i | ||||||||
\(738\) | 24.7672i | 0.911695i | ||||||||
\(739\) | 26.2532 | 0.965741 | 0.482870 | − | 0.875692i | \(-0.339594\pi\) | ||||
0.482870 | + | 0.875692i | \(0.339594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.56331 | 0.0574295 | ||||||||
\(742\) | 53.0740i | 1.94841i | ||||||||
\(743\) | 32.5688i | 1.19483i | 0.801931 | + | 0.597416i | \(0.203806\pi\) | ||||
−0.801931 | + | 0.597416i | \(0.796194\pi\) | |||||||
\(744\) | 0.177583 | 0.00651052 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 52.3722 | 1.91748 | ||||||||
\(747\) | 12.1047i | 0.442887i | ||||||||
\(748\) | − 14.2839i | − 0.522273i | ||||||||
\(749\) | −25.1672 | −0.919589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4833 | 1.65971 | 0.829855 | − | 0.557979i | \(-0.188423\pi\) | ||||
0.829855 | + | 0.557979i | \(0.188423\pi\) | |||||||
\(752\) | 35.6703i | 1.30076i | ||||||||
\(753\) | − 1.34200i | − 0.0489052i | ||||||||
\(754\) | −14.4863 | −0.527561 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.4166 | 0.415217 | ||||||||
\(757\) | 2.74947i | 0.0999311i | 0.998751 | + | 0.0499656i | \(0.0159112\pi\) | ||||
−0.998751 | + | 0.0499656i | \(0.984089\pi\) | |||||||
\(758\) | − 29.2421i | − 1.06212i | ||||||||
\(759\) | 11.5098 | 0.417779 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.2978 | −1.20704 | −0.603521 | − | 0.797347i | \(-0.706236\pi\) | ||||
−0.603521 | + | 0.797347i | \(0.706236\pi\) | |||||||
\(762\) | − 2.83947i | − 0.102863i | ||||||||
\(763\) | 36.2900i | 1.31379i | ||||||||
\(764\) | −15.1789 | −0.549154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.7488 | −1.97815 | ||||||||
\(767\) | 49.9008i | 1.80181i | ||||||||
\(768\) | − 5.46617i | − 0.197244i | ||||||||
\(769\) | 19.1540 | 0.690710 | 0.345355 | − | 0.938472i | \(-0.387759\pi\) | ||||
0.345355 | + | 0.938472i | \(0.387759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.72840 | 0.170289 | ||||||||
\(772\) | − 40.6247i | − 1.46212i | ||||||||
\(773\) | − 0.569309i | − 0.0204766i | −0.999948 | − | 0.0102383i | \(-0.996741\pi\) | ||||
0.999948 | − | 0.0102383i | \(-0.00325901\pi\) | |||||||
\(774\) | −20.2947 | −0.729479 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.92429 | −0.140874 | ||||||||
\(777\) | − 3.82377i | − 0.137177i | ||||||||
\(778\) | 68.8562i | 2.46862i | ||||||||
\(779\) | −4.34858 | −0.155804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −78.2695 | −2.80070 | ||||||||
\(782\) | − 19.1712i | − 0.685559i | ||||||||
\(783\) | 2.46794i | 0.0881969i | ||||||||
\(784\) | 24.6015 | 0.878624 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.63303 | 0.0582483 | ||||||||
\(787\) | 15.9991i | 0.570307i | 0.958482 | + | 0.285153i | \(0.0920445\pi\) | ||||
−0.958482 | + | 0.285153i | \(0.907956\pi\) | |||||||
\(788\) | 16.0893i | 0.573158i | ||||||||
\(789\) | −0.253546 | −0.00902649 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.62828 | −0.235675 | ||||||||
\(792\) | 5.52247i | 0.196232i | ||||||||
\(793\) | − 48.5290i | − 1.72332i | ||||||||
\(794\) | 70.3621 | 2.49706 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.4602 | 1.36318 | ||||||||
\(797\) | − 35.7528i | − 1.26643i | −0.773976 | − | 0.633214i | \(-0.781735\pi\) | ||||
0.773976 | − | 0.633214i | \(-0.218265\pi\) | |||||||
\(798\) | 2.06888i | 0.0732374i | ||||||||
\(799\) | 11.6168 | 0.410974 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.8769 | 0.949650 | ||||||||
\(802\) | 45.4602i | 1.60526i | ||||||||
\(803\) | − 36.6827i | − 1.29450i | ||||||||
\(804\) | 2.58016 | 0.0909951 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.0770 | 0.636735 | ||||||||
\(807\) | 3.08457i | 0.108582i | ||||||||
\(808\) | − 4.04004i | − 0.142128i | ||||||||
\(809\) | −23.2036 | −0.815796 | −0.407898 | − | 0.913028i | \(-0.633738\pi\) | ||||
−0.407898 | + | 0.913028i | \(0.633738\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7549 | −0.763918 | −0.381959 | − | 0.924179i | \(-0.624750\pi\) | ||||
−0.381959 | + | 0.924179i | \(0.624750\pi\) | |||||||
\(812\) | − 9.14889i | − 0.321063i | ||||||||
\(813\) | 2.43402i | 0.0853647i | ||||||||
\(814\) | −39.3371 | −1.37877 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.80265 | −0.0631053 | ||||||||
\(817\) | − 3.56331i | − 0.124664i | ||||||||
\(818\) | 62.3802i | 2.18107i | ||||||||
\(819\) | −54.6445 | −1.90943 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.2532 | 1.82365 | 0.911825 | − | 0.410579i | \(-0.134673\pi\) | ||||
0.911825 | + | 0.410579i | \(0.134673\pi\) | |||||||
\(822\) | 5.35904i | 0.186918i | ||||||||
\(823\) | 9.44783i | 0.329331i | 0.986349 | + | 0.164665i | \(0.0526544\pi\) | ||||
−0.986349 | + | 0.164665i | \(0.947346\pi\) | |||||||
\(824\) | 0.461775 | 0.0160867 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −66.0385 | −2.29777 | ||||||||
\(827\) | − 50.2216i | − 1.74638i | −0.487383 | − | 0.873188i | \(-0.662048\pi\) | ||||
0.487383 | − | 0.873188i | \(-0.337952\pi\) | |||||||
\(828\) | − 37.0523i | − 1.28766i | ||||||||
\(829\) | −44.2066 | −1.53536 | −0.767680 | − | 0.640834i | \(-0.778589\pi\) | ||||
−0.767680 | + | 0.640834i | \(0.778589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.34826 | 0.150839 | ||||||||
\(832\) | − 34.4966i | − 1.19595i | ||||||||
\(833\) | − 8.01200i | − 0.277599i | ||||||||
\(834\) | 2.13592 | 0.0739609 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.1570 | 0.351287 | ||||||||
\(837\) | − 3.07965i | − 0.106448i | ||||||||
\(838\) | − 62.2455i | − 2.15023i | ||||||||
\(839\) | 30.4033 | 1.04964 | 0.524819 | − | 0.851214i | \(-0.324133\pi\) | ||||
0.524819 | + | 0.851214i | \(0.324133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0223 | −0.931803 | ||||||||
\(842\) | 0.681799i | 0.0234963i | ||||||||
\(843\) | 9.38404i | 0.323204i | ||||||||
\(844\) | −9.75945 | −0.335934 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 47.0473 | 1.61752 | ||||||||
\(847\) | − 71.0893i | − 2.44266i | ||||||||
\(848\) | − 32.8833i | − 1.12922i | ||||||||
\(849\) | −7.34168 | −0.251966 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.1955 | −0.863690 | ||||||||
\(852\) | − 7.62459i | − 0.261214i | ||||||||
\(853\) | − 3.93925i | − 0.134877i | −0.997723 | − | 0.0674386i | \(-0.978517\pi\) | ||||
0.997723 | − | 0.0674386i | \(-0.0214827\pi\) | |||||||
\(854\) | 64.2232 | 2.19767 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.40773 | 0.0822945 | ||||||||
\(857\) | 27.4388i | 0.937292i | 0.883386 | + | 0.468646i | \(0.155258\pi\) | ||||
−0.883386 | + | 0.468646i | \(0.844742\pi\) | |||||||
\(858\) | − 17.0111i | − 0.580751i | ||||||||
\(859\) | −32.4517 | −1.10724 | −0.553619 | − | 0.832770i | \(-0.686754\pi\) | ||||
−0.553619 | + | 0.832770i | \(0.686754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.59966 | −0.156756 | ||||||||
\(862\) | 57.2629i | 1.95038i | ||||||||
\(863\) | 2.10861i | 0.0717778i | 0.999356 | + | 0.0358889i | \(0.0114263\pi\) | ||||
−0.999356 | + | 0.0358889i | \(0.988574\pi\) | |||||||
\(864\) | −13.6256 | −0.463553 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.72766 | −0.0587084 | ||||||||
\(867\) | − 4.45924i | − 0.151444i | ||||||||
\(868\) | 11.4166i | 0.387504i | ||||||||
\(869\) | −30.4602 | −1.03329 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0731 | −0.849569 | ||||||||
\(872\) | − 3.47184i | − 0.117571i | ||||||||
\(873\) | 33.5204i | 1.13449i | ||||||||
\(874\) | 13.6322 | 0.461115 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.57343 | 0.120735 | ||||||||
\(877\) | − 37.6613i | − 1.27173i | −0.771799 | − | 0.635866i | \(-0.780643\pi\) | ||||
0.771799 | − | 0.635866i | \(-0.219357\pi\) | |||||||
\(878\) | 27.1062i | 0.914789i | ||||||||
\(879\) | −8.99007 | −0.303227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.8818 | −1.34365 | −0.671827 | − | 0.740708i | \(-0.734490\pi\) | ||||
−0.671827 | + | 0.740708i | \(0.734490\pi\) | |||||||
\(882\) | − 32.4480i | − 1.09258i | ||||||||
\(883\) | − 36.0458i | − 1.21304i | −0.795070 | − | 0.606518i | \(-0.792566\pi\) | ||||
0.795070 | − | 0.606518i | \(-0.207434\pi\) | |||||||
\(884\) | −13.5218 | −0.454787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.5525 | −0.892050 | ||||||||
\(887\) | − 26.2057i | − 0.879902i | −0.898022 | − | 0.439951i | \(-0.854996\pi\) | ||||
0.898022 | − | 0.439951i | \(-0.145004\pi\) | |||||||
\(888\) | 0.365818i | 0.0122760i | ||||||||
\(889\) | −17.4264 | −0.584464 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.7011 | 1.53104 | ||||||||
\(892\) | − 5.67700i | − 0.190080i | ||||||||
\(893\) | 8.26046i | 0.276426i | ||||||||
\(894\) | −4.12186 | −0.137856 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.68093 | −0.323417 | ||||||||
\(897\) | − 10.8957i | − 0.363796i | ||||||||
\(898\) | 30.5780i | 1.02040i | ||||||||
\(899\) | −2.46794 | −0.0823103 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7092 | −0.356774 | ||||||||
\(902\) | 47.3191i | 1.57555i | ||||||||
\(903\) | − 3.76905i | − 0.125426i | ||||||||
\(904\) | 0.634123 | 0.0210906 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.6580 | −0.354088 | ||||||||
\(907\) | − 22.8036i | − 0.757182i | −0.925564 | − | 0.378591i | \(-0.876409\pi\) | ||||
0.925564 | − | 0.378591i | \(-0.123591\pi\) | |||||||
\(908\) | − 26.4166i | − 0.876664i | ||||||||
\(909\) | −34.5091 | −1.14460 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.44146 | 0.147152 | 0.0735761 | − | 0.997290i | \(-0.476559\pi\) | ||||
0.0735761 | + | 0.997290i | \(0.476559\pi\) | |||||||
\(912\) | − 1.28182i | − 0.0424454i | ||||||||
\(913\) | 23.1266i | 0.765379i | ||||||||
\(914\) | −10.3721 | −0.343077 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.52059 | −0.314569 | ||||||||
\(917\) | − 10.0223i | − 0.330965i | ||||||||
\(918\) | 4.82714i | 0.159319i | ||||||||
\(919\) | −37.0111 | −1.22088 | −0.610442 | − | 0.792061i | \(-0.709008\pi\) | ||||
−0.610442 | + | 0.792061i | \(0.709008\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.84602 | −0.225584 | ||||||||
\(922\) | 0.732959i | 0.0241387i | ||||||||
\(923\) | 74.0932i | 2.43881i | ||||||||
\(924\) | 10.7434 | 0.353433 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.0181 | 0.427800 | ||||||||
\(927\) | − 3.94438i | − 0.129550i | ||||||||
\(928\) | 10.9191i | 0.358438i | ||||||||
\(929\) | 3.04185 | 0.0997999 | 0.0499000 | − | 0.998754i | \(-0.484110\pi\) | ||||
0.0499000 | + | 0.998754i | \(0.484110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.69716 | 0.186717 | ||||||||
\(932\) | − 5.81921i | − 0.190615i | ||||||||
\(933\) | 3.06198i | 0.100245i | ||||||||
\(934\) | 1.67066 | 0.0546657 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.22781 | 0.170876 | ||||||||
\(937\) | 38.6099i | 1.26133i | 0.776055 | + | 0.630666i | \(0.217218\pi\) | ||||
−0.776055 | + | 0.630666i | \(0.782782\pi\) | |||||||
\(938\) | − 33.1817i | − 1.08342i | ||||||||
\(939\) | 1.46948 | 0.0479547 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.69716 | 0.0879248 | 0.0439624 | − | 0.999033i | \(-0.486002\pi\) | ||||
0.0439624 | + | 0.999033i | \(0.486002\pi\) | |||||||
\(942\) | 10.0039i | 0.325944i | ||||||||
\(943\) | 30.3080i | 0.986963i | ||||||||
\(944\) | 40.9158 | 1.33170 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.7742 | −1.26066 | ||||||||
\(947\) | − 20.1877i | − 0.656012i | −0.944676 | − | 0.328006i | \(-0.893623\pi\) | ||||
0.944676 | − | 0.328006i | \(-0.106377\pi\) | |||||||
\(948\) | − 2.96727i | − 0.0963723i | ||||||||
\(949\) | −34.7254 | −1.12723 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.22801 | −0.137103 | ||||||||
\(952\) | 1.70829i | 0.0553661i | ||||||||
\(953\) | − 5.18559i | − 0.167978i | −0.996467 | − | 0.0839888i | \(-0.973234\pi\) | ||||
0.996467 | − | 0.0839888i | \(-0.0267660\pi\) | |||||||
\(954\) | −43.3713 | −1.40420 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30.1624 | 0.975523 | ||||||||
\(957\) | 2.32242i | 0.0750732i | ||||||||
\(958\) | 33.3940i | 1.07891i | ||||||||
\(959\) | 32.8896 | 1.06206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9203 | −0.900656 | ||||||||
\(962\) | 37.2382i | 1.20061i | ||||||||
\(963\) | − 20.5663i | − 0.662739i | ||||||||
\(964\) | 22.3231 | 0.718979 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.4193 | 0.463933 | ||||||||
\(967\) | 58.0054i | 1.86533i | 0.360744 | + | 0.932665i | \(0.382523\pi\) | ||||
−0.360744 | + | 0.932665i | \(0.617477\pi\) | |||||||
\(968\) | 6.80107i | 0.218595i | ||||||||
\(969\) | −0.417453 | −0.0134105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.3221 | −0.780533 | −0.390267 | − | 0.920702i | \(-0.627617\pi\) | ||||
−0.390267 | + | 0.920702i | \(0.627617\pi\) | |||||||
\(972\) | 14.0637i | 0.451095i | ||||||||
\(973\) | − 13.1086i | − 0.420244i | ||||||||
\(974\) | −25.0867 | −0.803830 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.7911 | −1.27368 | ||||||||
\(977\) | − 36.1134i | − 1.15537i | −0.816260 | − | 0.577685i | \(-0.803956\pi\) | ||||
0.816260 | − | 0.577685i | \(-0.196044\pi\) | |||||||
\(978\) | − 6.30895i | − 0.201738i | ||||||||
\(979\) | 51.3498 | 1.64115 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.6557 | −0.946832 | ||||||||
\(982\) | − 20.3525i | − 0.649473i | ||||||||
\(983\) | − 21.1603i | − 0.674909i | −0.941342 | − | 0.337455i | \(-0.890434\pi\) | ||||
0.941342 | − | 0.337455i | \(-0.109566\pi\) | |||||||
\(984\) | 0.440046 | 0.0140282 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.86832 | 0.123192 | ||||||||
\(987\) | 8.73741i | 0.278115i | ||||||||
\(988\) | − 9.61504i | − 0.305895i | ||||||||
\(989\) | −24.8349 | −0.789704 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2652 | 0.643746 | 0.321873 | − | 0.946783i | \(-0.395688\pi\) | ||||
0.321873 | + | 0.946783i | \(0.395688\pi\) | |||||||
\(992\) | − 13.6256i | − 0.432614i | ||||||||
\(993\) | − 0.606364i | − 0.0192424i | ||||||||
\(994\) | −98.0548 | −3.11011 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.25287 | −0.0713849 | ||||||||
\(997\) | 24.2875i | 0.769193i | 0.923085 | + | 0.384597i | \(0.125659\pi\) | ||||
−0.923085 | + | 0.384597i | \(0.874341\pi\) | |||||||
\(998\) | − 70.7293i | − 2.23890i | ||||||||
\(999\) | 6.34402 | 0.200716 |
(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 | 475.2.b.e.324.6 | 8 | ||
5.2 | odd | 4 | 475.2.a.i.1.1 | 4 | |||
5.3 | odd | 4 | 95.2.a.b.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 475.2.b.e.324.3 | 8 | ||
15.2 | even | 4 | 4275.2.a.bo.1.4 | 4 | |||
15.8 | even | 4 | 855.2.a.m.1.1 | 4 | |||
20.3 | even | 4 | 1520.2.a.t.1.3 | 4 | |||
20.7 | even | 4 | 7600.2.a.cf.1.2 | 4 | |||
35.13 | even | 4 | 4655.2.a.y.1.4 | 4 | |||
40.3 | even | 4 | 6080.2.a.ch.1.2 | 4 | |||
40.13 | odd | 4 | 6080.2.a.cc.1.3 | 4 | |||
95.18 | even | 4 | 1805.2.a.p.1.1 | 4 | |||
95.37 | even | 4 | 9025.2.a.bf.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
475.2.a.i.1.1 | 4 | 5.2 | odd | 4 | |||
475.2.b.e.324.3 | 8 | 5.4 | even | 2 | inner | ||
475.2.b.e.324.6 | 8 | 1.1 | even | 1 | trivial | ||
855.2.a.m.1.1 | 4 | 15.8 | even | 4 | |||
1520.2.a.t.1.3 | 4 | 20.3 | even | 4 | |||
1805.2.a.p.1.1 | 4 | 95.18 | even | 4 | |||
4275.2.a.bo.1.4 | 4 | 15.2 | even | 4 | |||
4655.2.a.y.1.4 | 4 | 35.13 | even | 4 | |||
6080.2.a.cc.1.3 | 4 | 40.13 | odd | 4 | |||
6080.2.a.ch.1.2 | 4 | 40.3 | even | 4 | |||
7600.2.a.cf.1.2 | 4 | 20.7 | even | 4 | |||
9025.2.a.bf.1.4 | 4 | 95.37 | even | 4 |